diff --git a/changelog b/changelog
index f766cd4..315c425 100644
--- a/changelog
+++ b/changelog
@@ -1,99 +1,120 @@
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20130727 tpd src/axiom-website/patches.html 20130727.01.tpd.patch
20130727 tpd src/axiom-website/CATS/index.html add rich3c
20130727 tpd src/axiom-website/CATS/rich3c.input added
diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html
index cc3cf50..379e70d 100644
--- a/src/axiom-website/CATS/index.html
+++ b/src/axiom-website/CATS/index.html
@@ -389,6 +389,24 @@ They have been rewritten using Axiom syntax.
x^m (a+b x^n)^p (part 10)
source
pdf
+ (a+b x^n)^m (c+d x^n)^p
+ source
+ pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 1)
+ source
+ pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 2)
+ source
+ pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 3)
+ source
+ pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 4)
+ source
+ pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 5)
+ source
+ pdf
Rich
diff --git a/src/axiom-website/CATS/rich5.input.pamphlet b/src/axiom-website/CATS/rich5.input.pamphlet
new file mode 100644
index 0000000..55e1b1d
--- /dev/null
+++ b/src/axiom-website/CATS/rich5.input.pamphlet
@@ -0,0 +1,22971 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich5.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b*x^n)^m*(c+d*x^n)^p|
+There are:
+\begin{itemize}
+\item 173 integrals in this file.
+\item 172 supplied "optimal results".
+\item 172 matching answers.
+\item 2 cases where Axiom answer differs from Rubi
+\item 63 cases where Axiom supplied 2 results.
+\item 5 cases that Axiom failed to integrate.
+\item 56 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich5.output
+)spool rich5.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 994
+t0:=(a+b*x^2)*(c+d*x^2)^4
+--R
+--R
+--R (1)
+--R 4 10 4 3 8 3 2 2 6 2 2 3 4
+--R b d x + (a d + 4b c d )x + (4a c d + 6b c d )x + (6a c d + 4b c d)x
+--R +
+--R 3 4 2 4
+--R (4a c d + b c )x + a c
+--R Type: Polynomial(Integer)
+--E 1
+
+--S 2 of 994
+r0:=a*c^4*x+1/3*c^3*(b*c+4*a*d)*x^3+2/5*c^2*d*(2*b*c+3*a*d)*x^5+_
+ 2/7*c*d^2*(3*b*c+2*a*d)*x^7+1/9*d^3*(4*b*c+a*d)*x^9+1/11*b*d^4*x^11
+--R
+--R
+--R (2)
+--R 1 4 11 1 4 4 3 9 4 3 6 2 2 7
+--R -- b d x + (- a d + - b c d )x + (- a c d + - b c d )x
+--R 11 9 9 7 7
+--R +
+--R 6 2 2 4 3 5 4 3 1 4 3 4
+--R (- a c d + - b c d)x + (- a c d + - b c )x + a c x
+--R 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 2
+
+--S 3 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 4 11 1 4 4 3 9 4 3 6 2 2 7
+--R -- b d x + (- a d + - b c d )x + (- a c d + - b c d )x
+--R 11 9 9 7 7
+--R +
+--R 6 2 2 4 3 5 4 3 1 4 3 4
+--R (- a c d + - b c d)x + (- a c d + - b c )x + a c x
+--R 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 3
+
+--S 4 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 4
+
+--S 5 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 5
+
+)clear all
+
+--S 6 of 994
+t0:=(a+b*x^2)*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c
+--R Type: Polynomial(Integer)
+--E 6
+
+--S 7 of 994
+r0:=a*c^3*x+1/3*c^2*(b*c+3*a*d)*x^3+3/5*c*d*(b*c+a*d)*x^5+_
+ 1/7*d^2*(3*b*c+a*d)*x^7+1/9*b*d^3*x^9
+--R
+--R
+--R (2)
+--R 1 3 9 1 3 3 2 7 3 2 3 2 5
+--R - b d x + (- a d + - b c d )x + (- a c d + - b c d)x
+--R 9 7 7 5 5
+--R +
+--R 2 1 3 3 3
+--R (a c d + - b c )x + a c x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 7
+
+--S 8 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 3 9 1 3 3 2 7 3 2 3 2 5
+--R - b d x + (- a d + - b c d )x + (- a c d + - b c d)x
+--R 9 7 7 5 5
+--R +
+--R 2 1 3 3 3
+--R (a c d + - b c )x + a c x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 8
+
+--S 9 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 9
+
+--S 10 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 10
+
+)clear all
+
+--S 11 of 994
+t0:=(a+b*x^2)*(c+d*x^2)^2
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R (1) b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Polynomial(Integer)
+--E 11
+
+--S 12 of 994
+r0:=a*c^2*x+1/3*c*(b*c+2*a*d)*x^3+1/5*d*(2*b*c+a*d)*x^5+1/7*b*d^2*x^7
+--R
+--R
+--R 1 2 7 1 2 2 5 2 1 2 3 2
+--R (2) - b d x + (- a d + - b c d)x + (- a c d + - b c )x + a c x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 12
+
+--S 13 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 7 1 2 2 5 2 1 2 3 2
+--R (3) - b d x + (- a d + - b c d)x + (- a c d + - b c )x + a c x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 13
+
+--S 14 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 14
+
+--S 15 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 15
+
+)clear all
+
+--S 16 of 994
+t0:=(a+b*x^2)*(c+d*x^2)
+--R
+--R
+--R 4 2
+--R (1) b d x + (a d + b c)x + a c
+--R Type: Polynomial(Integer)
+--E 16
+
+--S 17 of 994
+r0:=a*c*x+1/3*(b*c+a*d)*x^3+1/5*b*d*x^5
+--R
+--R
+--R 1 5 1 1 3
+--R (2) - b d x + (- a d + - b c)x + a c x
+--R 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 17
+
+--S 18 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 1 1 3
+--R (3) - b d x + (- a d + - b c)x + a c x
+--R 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 18
+
+--S 19 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 19
+
+--S 20 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 20
+
+)clear all
+
+--S 21 of 994
+t0:=(a+b*x^2)/(c+d*x^2)
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 21
+
+--S 22 of 994
+r0:=b*x/d-(b*c-a*d)*atan(x*sqrt(d)/sqrt(c))/(d^(3/2)*sqrt(c))
+--R
+--R
+--R +-+
+--R x\|d +-+ +-+
+--R (a d - b c)atan(-----) + b x\|c \|d
+--R +-+
+--R \|c
+--R (2) ------------------------------------
+--R +-+ +-+
+--R d\|c \|d
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x +-----+
+--R (a d - b c)log(---------------------------) + 2b x\|- c d
+--R 2
+--R d x + c
+--R [----------------------------------------------------------,
+--R +-----+
+--R 2d\|- c d
+--R +---+
+--R x\|c d +---+
+--R (a d - b c)atan(-------) + b x\|c d
+--R c
+--R ------------------------------------]
+--R +---+
+--R d\|c d
+--R Type: Union(List(Expression(Integer)),...)
+--E 23
+
+--S 24 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d - b c)\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R +-----+ x\|d
+--R (- 2a d + 2b c)\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R +-----+ +-+ +-+
+--R 2d\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+--S 26 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|c d +---+ x\|d
+--R (a d - b c)\|c \|d atan(-------) + (- a d + b c)\|c d atan(-----)
+--R c +-+
+--R \|c
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R d\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 27
+
+)clear all
+
+--S 28 of 994
+t0:=(a+b*x^2)/(c+d*x^2)^2
+--R
+--R
+--R 2
+--R b x + a
+--R (1) -------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 28
+
+--S 29 of 994
+r0:=-1/2*(b*c-a*d)*x/(c*d*(c+d*x^2))+1/2*(b*c+a*d)*_
+ atan(x*sqrt(d)/sqrt(c))/(c^(3/2)*d^(3/2))
+--R
+--R
+--R +-+
+--R 2 2 2 x\|d +-+ +-+
+--R ((a d + b c d)x + a c d + b c )atan(-----) + (a d - b c)x\|c \|d
+--R +-+
+--R \|c
+--R (2) -------------------------------------------------------------------
+--R 2 2 2 +-+ +-+
+--R (2c d x + 2c d)\|c \|d
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 (d x - c)\|- c d + 2c d x
+--R ((a d + b c d)x + a c d + b c )log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-----+
+--R (2a d - 2b c)x\|- c d
+--R /
+--R 2 2 2 +-----+
+--R (4c d x + 4c d)\|- c d
+--R ,
+--R +---+
+--R 2 2 2 x\|c d +---+
+--R ((a d + b c d)x + a c d + b c )atan(-------) + (a d - b c)x\|c d
+--R c
+--R -------------------------------------------------------------------]
+--R 2 2 2 +---+
+--R (2c d x + 2c d)\|c d
+--R Type: Union(List(Expression(Integer)),...)
+--E 30
+
+--S 31 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d + b c)\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R +-----+ x\|d
+--R (- 2a d - 2b c)\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R +-----+ +-+ +-+
+--R 4c d\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|c d +---+ x\|d
+--R (a d + b c)\|c \|d atan(-------) + (- a d - b c)\|c d atan(-----)
+--R c +-+
+--R \|c
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R 2c d\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 33
+
+--S 34 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 34
+
+)clear all
+
+--S 35 of 994
+t0:=(a+b*x^2)/(c+d*x^2)^3
+--R
+--R
+--R 2
+--R b x + a
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 35
+
+--S 36 of 994
+r0:=-1/4*(b*c-a*d)*x/(c*d*(c+d*x^2)^2)+1/8*(b*c+3*a*d)*x/(c^2*_
+ d*(c+d*x^2))+1/8*(b*c+3*a*d)*atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*d^(3/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 4 2 2 2 2 3 x\|d
+--R ((3a d + b c d )x + (6a c d + 2b c d)x + 3a c d + b c )atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 +-+ +-+
+--R ((3a d + b c d)x + (5a c d - b c )x)\|c \|d
+--R /
+--R 2 3 4 3 2 2 4 +-+ +-+
+--R (8c d x + 16c d x + 8c d)\|c \|d
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 4 2 2 2 2 3
+--R ((3a d + b c d )x + (6a c d + 2b c d)x + 3a c d + b c )
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 +-----+
+--R ((6a d + 2b c d)x + (10a c d - 2b c )x)\|- c d
+--R /
+--R 2 3 4 3 2 2 4 +-----+
+--R (16c d x + 32c d x + 16c d)\|- c d
+--R ,
+--R
+--R 3 2 4 2 2 2 2 3
+--R ((3a d + b c d )x + (6a c d + 2b c d)x + 3a c d + b c )
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 2 +---+
+--R ((3a d + b c d)x + (5a c d - b c )x)\|c d
+--R /
+--R 2 3 4 3 2 2 4 +---+
+--R (8c d x + 16c d x + 8c d)\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 37
+
+--S 38 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (3a d + b c)\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R +-----+ x\|d
+--R (- 6a d - 2b c)\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-----+ +-+ +-+
+--R 16c d\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 38
+
+--S 39 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|c d +---+ x\|d
+--R (3a d + b c)\|c \|d atan(-------) + (- 3a d - b c)\|c d atan(-----)
+--R c +-+
+--R \|c
+--R (6) -------------------------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 8c d\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 40
+
+--S 41 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 41
+
+)clear all
+
+--S 42 of 994
+t0:=(a+b*x^2)^2*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 42
+
+--S 43 of 994
+r0:=a^2*c^3*x+1/3*a*c^2*(2*b*c+3*a*d)*x^3+1/5*c*(b^2*c^2+6*a*b*c*d+_
+ 3*a^2*d^2)*x^5+1/7*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^7+_
+ 1/9*b*d^2*(3*b*c+2*a*d)*x^9+1/11*b^2*d^3*x^11
+--R
+--R
+--R (2)
+--R 1 2 3 11 2 3 1 2 2 9 1 2 3 6 2 3 2 2 7
+--R -- b d x + (- a b d + - b c d )x + (- a d + - a b c d + - b c d)x
+--R 11 9 3 7 7 7
+--R +
+--R 3 2 2 6 2 1 2 3 5 2 2 2 3 3 2 3
+--R (- a c d + - a b c d + - b c )x + (a c d + - a b c )x + a c x
+--R 5 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 43
+
+--S 44 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 3 11 2 3 1 2 2 9 1 2 3 6 2 3 2 2 7
+--R -- b d x + (- a b d + - b c d )x + (- a d + - a b c d + - b c d)x
+--R 11 9 3 7 7 7
+--R +
+--R 3 2 2 6 2 1 2 3 5 2 2 2 3 3 2 3
+--R (- a c d + - a b c d + - b c )x + (a c d + - a b c )x + a c x
+--R 5 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 44
+
+--S 45 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 45
+
+--S 46 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 46
+
+)clear all
+
+--S 47 of 994
+t0:=(a+b*x^2)^2*(c+d*x^2)^2
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 47
+
+--S 48 of 994
+r0:=a^2*c^2*x+2/3*a*c*(b*c+a*d)*x^3+1/5*(b^2*c^2+4*a*b*c*d+a^2*d^2)*x^5+_
+ 2/7*b*d*(b*c+a*d)*x^7+1/9*b^2*d^2*x^9
+--R
+--R
+--R (2)
+--R 1 2 2 9 2 2 2 2 7 1 2 2 4 1 2 2 5
+--R - b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 9 7 7 5 5 5
+--R +
+--R 2 2 2 2 3 2 2
+--R (- a c d + - a b c )x + a c x
+--R 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 48
+
+--S 49 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 2 9 2 2 2 2 7 1 2 2 4 1 2 2 5
+--R - b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 9 7 7 5 5 5
+--R +
+--R 2 2 2 2 3 2 2
+--R (- a c d + - a b c )x + a c x
+--R 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 49
+
+--S 50 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 50
+
+--S 51 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 51
+
+)clear all
+
+--S 52 of 994
+t0:=(a+b*x^2)^2*(c+d*x^2)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R (1) b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Polynomial(Integer)
+--E 52
+
+--S 53 of 994
+r0:=a^2*c*x+1/3*a*(2*b*c+a*d)*x^3+1/5*b*(b*c+2*a*d)*x^5+1/7*b^2*d*x^7
+--R
+--R
+--R 1 2 7 2 1 2 5 1 2 2 3 2
+--R (2) - b d x + (- a b d + - b c)x + (- a d + - a b c)x + a c x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 53
+
+--S 54 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 7 2 1 2 5 1 2 2 3 2
+--R (3) - b d x + (- a b d + - b c)x + (- a d + - a b c)x + a c x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 54
+
+--S 55 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 55
+
+--S 56 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 56
+
+)clear all
+
+--S 57 of 994
+t0:=(a+b*x^2)^2/(c+d*x^2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 57
+
+--S 58 of 994
+r0:=-b*(b*c-2*a*d)*x/d^2+1/3*b^2*x^3/d+(b*c-a*d)^2*atan(x*sqrt(d)/_
+ sqrt(c))/(d^(5/2)*sqrt(c))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 x\|d 2 3 2 +-+ +-+
+--R (3a d - 6a b c d + 3b c )atan(-----) + (b d x + (6a b d - 3b c)x)\|c \|d
+--R +-+
+--R \|c
+--R ---------------------------------------------------------------------------
+--R 2 +-+ +-+
+--R 3d \|c \|d
+--R Type: Expression(Integer)
+--E 58
+
+--S 59 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 2 (d x - c)\|- c d + 2c d x
+--R (3a d - 6a b c d + 3b c )log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 +-----+
+--R (2b d x + (12a b d - 6b c)x)\|- c d
+--R /
+--R 2 +-----+
+--R 6d \|- c d
+--R ,
+--R +---+
+--R 2 2 2 2 x\|c d 2 3 2 +---+
+--R (3a d - 6a b c d + 3b c )atan(-------) + (b d x + (6a b d - 3b c)x)\|c d
+--R c
+--R ---------------------------------------------------------------------------]
+--R 2 +---+
+--R 3d \|c d
+--R Type: Union(List(Expression(Integer)),...)
+--E 59
+
+--S 60 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d - 2a b c d + b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 2a d + 4a b c d - 2b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-----+ +-+ +-+
+--R 2d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 60
+
+--S 61 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (a d - 2a b c d + b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- a d + 2a b c d - b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-+ +-+ +---+
+--R d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 63
+
+)clear all
+
+--S 64 of 994
+t0:=(a+b*x^2)^2/(c+d*x^2)^2
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 64
+
+--S 65 of 994
+r0:=b^2*x/d^2+1/2*(b*c-a*d)^2*x/(c*d^2*(c+d*x^2))-1/2*(b*c-a*d)*_
+ (3*b*c+a*d)*atan(x*sqrt(d)/sqrt(c))/(c^(3/2)*d^(5/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 2 2 2 2 2 2 2 2 3 x\|d
+--R ((a d + 2a b c d - 3b c d)x + a c d + 2a b c d - 3b c )atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 +-+ +-+
+--R (2b c d x + (a d - 2a b c d + 3b c )x)\|c \|d
+--R /
+--R 3 2 2 2 +-+ +-+
+--R (2c d x + 2c d )\|c \|d
+--R Type: Expression(Integer)
+--E 65
+
+--S 66 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((a d + 2a b c d - 3b c d)x + a c d + 2a b c d - 3b c )
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 2 2 2 +-----+
+--R (4b c d x + (2a d - 4a b c d + 6b c )x)\|- c d
+--R /
+--R 3 2 2 2 +-----+
+--R (4c d x + 4c d )\|- c d
+--R ,
+--R
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((a d + 2a b c d - 3b c d)x + a c d + 2a b c d - 3b c )
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 2 2 2 2 +---+
+--R (2b c d x + (a d - 2a b c d + 3b c )x)\|c d
+--R /
+--R 3 2 2 2 +---+
+--R (2c d x + 2c d )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 66
+
+--S 67 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d + 2a b c d - 3b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 2a d - 4a b c d + 6b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4c d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 68
+
+--S 69 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (a d + 2a b c d - 3b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- a d - 2a b c d + 3b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-+ +-+ +---+
+--R 2c d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 994
+t0:=(a+b*x^2)^2/(c+d*x^2)^3
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 71
+
+--S 72 of 994
+r0:=-1/4*(b*c-a*d)*x*(a+b*x^2)/(c*d*(c+d*x^2)^2)+3/8*(a^2/c^2-b^2/d^2)*x/_
+ (c+d*x^2)+1/8*(3*b^2*c^2+2*a*b*c*d+3*a^2*d^2)*atan(x*sqrt(d)/_
+ sqrt(c))/(c^(5/2)*d^(5/2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 2a b c d + 3b c d )x + (6a c d + 4a b c d + 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 2a b c d + 3b c
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+ +-+
+--R ((3a d + 2a b c d - 5b c d)x + (5a c d - 2a b c d - 3b c )x)\|c \|d
+--R /
+--R 2 4 4 3 3 2 4 2 +-+ +-+
+--R (8c d x + 16c d x + 8c d )\|c \|d
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 2a b c d + 3b c d )x + (6a c d + 4a b c d + 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 2a b c d + 3b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((6a d + 4a b c d - 10b c d)x + (10a c d - 4a b c d - 6b c )x)
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 2 4 4 3 3 2 4 2 +-----+
+--R (16c d x + 32c d x + 16c d )\|- c d
+--R ,
+--R
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 2a b c d + 3b c d )x + (6a c d + 4a b c d + 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 2a b c d + 3b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +---+
+--R ((3a d + 2a b c d - 5b c d)x + (5a c d - 2a b c d - 3b c )x)\|c d
+--R /
+--R 2 4 4 3 3 2 4 2 +---+
+--R (8c d x + 16c d x + 8c d )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 73
+
+--S 74 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (3a d + 2a b c d + 3b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 6a d - 4a b c d - 6b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 2 +-----+ +-+ +-+
+--R 16c d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 75
+
+--S 76 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (3a d + 2a b c d + 3b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 3a d - 2a b c d - 3b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 2 +-+ +-+ +---+
+--R 8c d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 77
+
+)clear all
+
+--S 78 of 994
+t0:=(a+b*x^2)^3*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 3 3 12 2 3 3 2 10 2 3 2 2 3 2 8
+--R b d x + (3a b d + 3b c d )x + (3a b d + 9a b c d + 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 6 3 2 2 2 2 3 4
+--R (a d + 9a b c d + 9a b c d + b c )x + (3a c d + 9a b c d + 3a b c )x
+--R +
+--R 3 2 2 3 2 3 3
+--R (3a c d + 3a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 78
+
+--S 79 of 994
+r0:=a^3*c^3*x+a^2*c^2*(b*c+a*d)*x^3+3/5*a*c*(b^2*c^2+3*a*b*c*d+a^2*d^2)*_
+ x^5+1/7*(b*c+a*d)*(b^2*c^2+8*a*b*c*d+a^2*d^2)*x^7+1/3*b*d*_
+ (b^2*c^2+3*a*b*c*d+a^2*d^2)*x^9+3/11*b^2*d^2*(b*c+a*d)*x^11+_
+ 1/13*b^3*d^3*x^13
+--R
+--R
+--R (2)
+--R 1 3 3 13 3 2 3 3 3 2 11 1 2 3 2 2 1 3 2 9
+--R -- b d x + (-- a b d + -- b c d )x + (- a b d + a b c d + - b c d)x
+--R 13 11 11 3 3
+--R +
+--R 1 3 3 9 2 2 9 2 2 1 3 3 7
+--R (- a d + - a b c d + - a b c d + - b c )x
+--R 7 7 7 7
+--R +
+--R 3 3 2 9 2 2 3 2 3 5 3 2 2 3 3 3 3
+--R (- a c d + - a b c d + - a b c )x + (a c d + a b c )x + a c x
+--R 5 5 5
+--R Type: Polynomial(Fraction(Integer))
+--E 79
+
+--S 80 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 3 3 13 3 2 3 3 3 2 11 1 2 3 2 2 1 3 2 9
+--R -- b d x + (-- a b d + -- b c d )x + (- a b d + a b c d + - b c d)x
+--R 13 11 11 3 3
+--R +
+--R 1 3 3 9 2 2 9 2 2 1 3 3 7
+--R (- a d + - a b c d + - a b c d + - b c )x
+--R 7 7 7 7
+--R +
+--R 3 3 2 9 2 2 3 2 3 5 3 2 2 3 3 3 3
+--R (- a c d + - a b c d + - a b c )x + (a c d + a b c )x + a c x
+--R 5 5 5
+--R Type: Polynomial(Fraction(Integer))
+--E 80
+
+--S 81 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 81
+
+--S 82 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 82
+
+)clear all
+
+--S 83 of 994
+t0:=(a+b*x^2)^3*(c+d*x^2)^2
+--R
+--R
+--R (1)
+--R 3 2 10 2 2 3 8 2 2 2 3 2 6
+--R b d x + (3a b d + 2b c d)x + (3a b d + 6a b c d + b c )x
+--R +
+--R 3 2 2 2 2 4 3 2 2 2 3 2
+--R (a d + 6a b c d + 3a b c )x + (2a c d + 3a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 83
+
+--S 84 of 994
+r0:=a^3*c^2*x+1/3*a^2*c*(3*b*c+2*a*d)*x^3+1/5*a*(3*b^2*c^2+6*a*b*c*d+_
+ a^2*d^2)*x^5+1/7*b*(b^2*c^2+6*a*b*c*d+3*a^2*d^2)*x^7+_
+ 1/9*b^2*d*(2*b*c+3*a*d)*x^9+1/11*b^3*d^2*x^11
+--R
+--R
+--R (2)
+--R 1 3 2 11 1 2 2 2 3 9 3 2 2 6 2 1 3 2 7
+--R -- b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x
+--R 11 3 9 7 7 7
+--R +
+--R 1 3 2 6 2 3 2 2 5 2 3 2 2 3 3 2
+--R (- a d + - a b c d + - a b c )x + (- a c d + a b c )x + a c x
+--R 5 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 84
+
+--S 85 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 3 2 11 1 2 2 2 3 9 3 2 2 6 2 1 3 2 7
+--R -- b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x
+--R 11 3 9 7 7 7
+--R +
+--R 1 3 2 6 2 3 2 2 5 2 3 2 2 3 3 2
+--R (- a d + - a b c d + - a b c )x + (- a c d + a b c )x + a c x
+--R 5 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 85
+
+--S 86 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 86
+
+--S 87 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 87
+
+)clear all
+
+--S 88 of 994
+t0:=(a+b*x^2)^3*(c+d*x^2)
+--R
+--R
+--R (1)
+--R 3 8 2 3 6 2 2 4 3 2 2 3
+--R b d x + (3a b d + b c)x + (3a b d + 3a b c)x + (a d + 3a b c)x + a c
+--R Type: Polynomial(Integer)
+--E 88
+
+--S 89 of 994
+r0:=a^3*c*x+1/3*a^2*(3*b*c+a*d)*x^3+3/5*a*b*(b*c+a*d)*x^5+_
+ 1/7*b^2*(b*c+3*a*d)*x^7+1/9*b^3*d*x^9
+--R
+--R
+--R (2)
+--R 1 3 9 3 2 1 3 7 3 2 3 2 5 1 3 2 3
+--R - b d x + (- a b d + - b c)x + (- a b d + - a b c)x + (- a d + a b c)x
+--R 9 7 7 5 5 3
+--R +
+--R 3
+--R a c x
+--R Type: Polynomial(Fraction(Integer))
+--E 89
+
+--S 90 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 3 9 3 2 1 3 7 3 2 3 2 5 1 3 2 3
+--R - b d x + (- a b d + - b c)x + (- a b d + - a b c)x + (- a d + a b c)x
+--R 9 7 7 5 5 3
+--R +
+--R 3
+--R a c x
+--R Type: Polynomial(Fraction(Integer))
+--E 90
+
+--S 91 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 91
+
+--S 92 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 92
+
+)clear all
+
+--S 93 of 994
+t0:=(a+b*x^2)^3/(c+d*x^2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 93
+
+--S 94 of 994
+r0:=b*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*x/d^3-1/3*b^2*(b*c-3*a*d)*x^3/d^2+_
+ 1/5*b^3*x^5/d-(b*c-a*d)^3*atan(x*sqrt(d)/sqrt(c))/(d^(7/2)*sqrt(c))
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|d
+--R (15a d - 45a b c d + 45a b c d - 15b c )atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 5 2 2 3 3 2 2 2 3 2
+--R (3b d x + (15a b d - 5b c d)x + (45a b d - 45a b c d + 15b c )x)
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 3 +-+ +-+
+--R 15d \|c \|d
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 3 2 2 2 2 3 3
+--R (15a d - 45a b c d + 45a b c d - 15b c )
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 3 2 5 2 2 3 3 2 2 2 3 2
+--R (6b d x + (30a b d - 10b c d)x + (90a b d - 90a b c d + 30b c )x)
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 3 +-----+
+--R 30d \|- c d
+--R ,
+--R
+--R +---+
+--R 3 3 2 2 2 2 3 3 x\|c d
+--R (15a d - 45a b c d + 45a b c d - 15b c )atan(-------)
+--R c
+--R +
+--R 3 2 5 2 2 3 3 2 2 2 3 2
+--R (3b d x + (15a b d - 5b c d)x + (45a b d - 45a b c d + 15b c )x)
+--R *
+--R +---+
+--R \|c d
+--R /
+--R 3 +---+
+--R 15d \|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 95
+
+--S 96 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|c \|d
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|d
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-----+ +-+ +-+
+--R 2d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|c d
+--R (a d - 3a b c d + 3a b c d - b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|d
+--R (- a d + 3a b c d - 3a b c d + b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-+ +-+ +---+
+--R d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 98
+
+--S 99 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 99
+
+)clear all
+
+--S 100 of 994
+t0:=(a+b*x^2)^3/(c+d*x^2)^2
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 100
+
+--S 101 of 994
+r0:=-b^2*(2*b*c-3*a*d)*x/d^3+1/3*b^3*x^3/d^2-1/2*(b*c-a*d)^3*_
+ x/(c*d^3*(c+d*x^2))+1/2*(b*c-a*d)^2*(5*b*c+a*d)*atan(x*sqrt(d)/_
+ sqrt(c))/(c^(3/2)*d^(7/2))
+--R
+--R
+--R (2)
+--R 3 4 2 3 2 2 2 3 3 2 3 3 2 2 2
+--R (3a d + 9a b c d - 27a b c d + 15b c d)x + 3a c d + 9a b c d
+--R +
+--R 2 3 3 4
+--R - 27a b c d + 15b c
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 5 2 2 3 2 3
+--R 2b c d x + (18a b c d - 10b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (3a d - 9a b c d + 27a b c d - 15b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 4 2 2 3 +-+ +-+
+--R (6c d x + 6c d )\|c \|d
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 4 2 3 2 2 2 3 3 2 3 3 2 2 2
+--R (3a d + 9a b c d - 27a b c d + 15b c d)x + 3a c d + 9a b c d
+--R +
+--R 2 3 3 4
+--R - 27a b c d + 15b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 3 2 5 2 2 3 2 3
+--R 4b c d x + (36a b c d - 20b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (6a d - 18a b c d + 54a b c d - 30b c )x
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 4 2 2 3 +-----+
+--R (12c d x + 12c d )\|- c d
+--R ,
+--R
+--R 3 4 2 3 2 2 2 3 3 2 3 3 2 2 2
+--R (3a d + 9a b c d - 27a b c d + 15b c d)x + 3a c d + 9a b c d
+--R +
+--R 2 3 3 4
+--R - 27a b c d + 15b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 3 2 5 2 2 3 2 3
+--R 2b c d x + (18a b c d - 10b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (3a d - 9a b c d + 27a b c d - 15b c )x
+--R *
+--R +---+
+--R \|c d
+--R /
+--R 4 2 2 3 +---+
+--R (6c d x + 6c d )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 102
+
+--S 103 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (a d + 3a b c d - 9a b c d + 5b c )\|c \|d
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|d
+--R (- 2a d - 6a b c d + 18a b c d - 10b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4c d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 103
+
+--S 104 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|c d
+--R (a d + 3a b c d - 9a b c d + 5b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|d
+--R (- a d - 3a b c d + 9a b c d - 5b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-+ +-+ +---+
+--R 2c d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 105
+
+--S 106 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 106
+
+)clear all
+
+--S 107 of 994
+t0:=(a+b*x^2)^3/(c+d*x^2)^3
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 107
+
+--S 108 of 994
+r0:=b^3*x/d^3-1/4*(b*c-a*d)^3*x/(c*d^3*(c+d*x^2)^2)+3/8*(b*c-a*d)^2*_
+ (3*b*c+a*d)*x/(c^2*d^3*(c+d*x^2))-3/8*(b*c-a*d)*(4*b^2*c^2+_
+ (b*c+a*d)^2)*atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*d^(7/2))
+--R
+--R
+--R (2)
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (3a d + 3a b c d + 9a b c d - 15b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3 2 3 2
+--R (6a c d + 6a b c d + 18a b c d - 30b c d)x + 3a c d + 3a b c d
+--R +
+--R 2 4 3 5
+--R 9a b c d - 15b c
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 2 5 3 4 2 3 2 2 2 3 3 3
+--R 8b c d x + (3a d + 3a b c d - 15a b c d + 25b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (5a c d - 3a b c d - 9a b c d + 15b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 2 5 4 3 4 2 4 3 +-+ +-+
+--R (8c d x + 16c d x + 8c d )\|c \|d
+--R Type: Expression(Integer)
+--E 108
+
+--S 109 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (3a d + 3a b c d + 9a b c d - 15b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (6a c d + 6a b c d + 18a b c d - 30b c d)x + 3a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 3a b c d + 9a b c d - 15b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 3 2 2 5 3 4 2 3 2 2 2 3 3 3
+--R 16b c d x + (6a d + 6a b c d - 30a b c d + 50b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (10a c d - 6a b c d - 18a b c d + 30b c )x
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 2 5 4 3 4 2 4 3 +-----+
+--R (16c d x + 32c d x + 16c d )\|- c d
+--R ,
+--R
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (3a d + 3a b c d + 9a b c d - 15b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (6a c d + 6a b c d + 18a b c d - 30b c d)x + 3a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 3a b c d + 9a b c d - 15b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 3 2 2 5 3 4 2 3 2 2 2 3 3 3
+--R 8b c d x + (3a d + 3a b c d - 15a b c d + 25b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (5a c d - 3a b c d - 9a b c d + 15b c )x
+--R *
+--R +---+
+--R \|c d
+--R /
+--R 2 5 4 3 4 2 4 3 +---+
+--R (8c d x + 16c d x + 8c d )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 109
+
+--S 110 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (3a d + 3a b c d + 9a b c d - 15b c )\|c \|d
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|d
+--R (- 6a d - 6a b c d - 18a b c d + 30b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 3 +-----+ +-+ +-+
+--R 16c d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 110
+
+--S 111 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|c d
+--R (3a d + 3a b c d + 9a b c d - 15b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|d
+--R (- 3a d - 3a b c d - 9a b c d + 15b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 3 +-+ +-+ +---+
+--R 8c d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 113
+
+)clear all
+
+--S 114 of 994
+t0:=(c+d*x^2)^4/(a+b*x^2)
+--R
+--R
+--R 4 8 3 6 2 2 4 3 2 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R (1) ---------------------------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 114
+
+--S 115 of 994
+r0:=d*(2*b*c-a*d)*(2*b^2*c^2-2*a*b*c*d+a^2*d^2)*x/b^4+1/3*d^2*(6*b^2*c^2-_
+ 4*a*b*c*d+a^2*d^2)*x^3/b^3+1/5*d^3*(4*b*c-a*d)*x^5/b^2+_
+ 1/7*d^4*x^7/b+(b*c-a*d)^4*atan(x*sqrt(b)/sqrt(a))/(b^(9/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R +-+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 x\|b
+--R (105a d - 420a b c d + 630a b c d - 420a b c d + 105b c )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 4 7 2 4 3 3 5
+--R 15b d x + (- 21a b d + 84b c d )x
+--R +
+--R 2 4 2 3 3 2 2 3
+--R (35a b d - 140a b c d + 210b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3
+--R (- 105a d + 420a b c d - 630a b c d + 420b c d)x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 4 +-+ +-+
+--R 105b \|a \|b
+--R Type: Expression(Integer)
+--E 115
+
+--S 116 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (105a d - 420a b c d + 630a b c d - 420a b c d + 105b c )
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 4 7 2 4 3 3 5
+--R 30b d x + (- 42a b d + 168b c d )x
+--R +
+--R 2 4 2 3 3 2 2 3
+--R (70a b d - 280a b c d + 420b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3
+--R (- 210a d + 840a b c d - 1260a b c d + 840b c d)x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 4 +-----+
+--R 210b \|- a b
+--R ,
+--R
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (105a d - 420a b c d + 630a b c d - 420a b c d + 105b c )
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 3 4 7 2 4 3 3 5
+--R 15b d x + (- 21a b d + 84b c d )x
+--R +
+--R 2 4 2 3 3 2 2 3
+--R (35a b d - 140a b c d + 210b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3
+--R (- 105a d + 420a b c d - 630a b c d + 420b c d)x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 4 +---+
+--R 105b \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 116
+
+--S 117 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+ +-+
+--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----+ x\|b
+--R (- 2a d + 8a b c d - 12a b c d + 8a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-----+ +-+ +-+
+--R 2b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 118
+
+--S 119 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+ +-+ x\|a b
+--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +---+ x\|b
+--R (- a d + 4a b c d - 6a b c d + 4a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+ +-+ +---+
+--R b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 994
+t0:=(c+d*x^2)^3/(a+b*x^2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 121
+
+--S 122 of 994
+r0:=d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x/b^3+1/3*d^2*(3*b*c-a*d)*x^3/b^2+_
+ 1/5*d^3*x^5/b+(b*c-a*d)^3*atan(x*sqrt(b)/sqrt(a))/(b^(7/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|b
+--R (- 15a d + 45a b c d - 45a b c d + 15b c )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 5 3 2 2 3 2 3 2 2 2
+--R (3b d x + (- 5a b d + 15b c d )x + (15a d - 45a b c d + 45b c d)x)
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 3 +-+ +-+
+--R 15b \|a \|b
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 3 2 2 2 2 3 3
+--R (15a d - 45a b c d + 45a b c d - 15b c )
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 5 3 2 2 3
+--R 6b d x + (- 10a b d + 30b c d )x
+--R +
+--R 2 3 2 2 2
+--R (30a d - 90a b c d + 90b c d)x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 3 +-----+
+--R 30b \|- a b
+--R ,
+--R
+--R +---+
+--R 3 3 2 2 2 2 3 3 x\|a b
+--R (- 15a d + 45a b c d - 45a b c d + 15b c )atan(-------)
+--R a
+--R +
+--R 2 3 5 3 2 2 3
+--R 3b d x + (- 5a b d + 15b c d )x
+--R +
+--R 2 3 2 2 2
+--R (15a d - 45a b c d + 45b c d)x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 3 +---+
+--R 15b \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 123
+
+--S 124 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (2a d - 6a b c d + 6a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 2b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 125
+
+--S 126 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (- a d + 3a b c d - 3a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (a d - 3a b c d + 3a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+ +-+ +---+
+--R b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 127
+
+)clear all
+
+--S 128 of 994
+t0:=(c+d*x^2)^2/(a+b*x^2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 128
+
+--S 129 of 994
+r0:=d*(2*b*c-a*d)*x/b^2+1/3*d^2*x^3/b+(b*c-a*d)^2*atan(x*sqrt(b)/_
+ sqrt(a))/(b^(5/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 x\|b
+--R (3a d - 6a b c d + 3b c )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 +-+ +-+
+--R (b d x + (- 3a d + 6b c d)x)\|a \|b
+--R /
+--R 2 +-+ +-+
+--R 3b \|a \|b
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 2 (b x - a)\|- a b + 2a b x
+--R (3a d - 6a b c d + 3b c )log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 2 +-----+
+--R (2b d x + (- 6a d + 12b c d)x)\|- a b
+--R /
+--R 2 +-----+
+--R 6b \|- a b
+--R ,
+--R
+--R +---+
+--R 2 2 2 2 x\|a b
+--R (3a d - 6a b c d + 3b c )atan(-------)
+--R a
+--R +
+--R 2 3 2 +---+
+--R (b d x + (- 3a d + 6b c d)x)\|a b
+--R /
+--R 2 +---+
+--R 3b \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 130
+
+--S 131 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d - 2a b c d + b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (- 2a d + 4a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 2b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (a d - 2a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- a d + 2a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+ +-+ +---+
+--R b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 133
+
+--S 134 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 134
+
+)clear all
+
+--S 135 of 994
+t0:=(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 135
+
+--S 136 of 994
+r0:=d*x/b+(b*c-a*d)*atan(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))
+--R
+--R
+--R +-+
+--R x\|b +-+ +-+
+--R (- a d + b c)atan(-----) + d x\|a \|b
+--R +-+
+--R \|a
+--R (2) --------------------------------------
+--R +-+ +-+
+--R b\|a \|b
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x +-----+
+--R (a d - b c)log(---------------------------) + 2d x\|- a b
+--R 2
+--R b x + a
+--R [----------------------------------------------------------,
+--R +-----+
+--R 2b\|- a b
+--R +---+
+--R x\|a b +---+
+--R (- a d + b c)atan(-------) + d x\|a b
+--R a
+--R --------------------------------------]
+--R +---+
+--R b\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 137
+
+--S 138 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b - 2a b x
+--R (a d - b c)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (2a d - 2b c)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-----+ +-+ +-+
+--R 2b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 138
+
+--S 139 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (- a d + b c)\|a \|b atan(-------) + (a d - b c)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 140
+
+--S 141 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 141
+
+)clear all
+
+--S 142 of 994
+t0:=1/((a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R 4 2
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 142
+
+--S 143 of 994
+r0:=atan(x*sqrt(b)/sqrt(a))*sqrt(b)/((b*c-a*d)*sqrt(a))-_
+ atan(x*sqrt(d)/sqrt(c))*sqrt(d)/((b*c-a*d)*sqrt(c))
+--R
+--R
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R \|a \|d atan(-----) - \|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R (2) -----------------------------------------
+--R +-+ +-+
+--R (a d - b c)\|a \|c
+--R Type: Expression(Integer)
+--E 143
+
+--S 144 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+
+--R | d 2 | b 2
+--R +---+ 2c x |- - + d x - c +---+ - 2a x |- - + b x - a
+--R | d \| c | b \| a
+--R |- - log(---------------------) + |- - log(-----------------------)
+--R \| c 2 \| a 2
+--R d x + c b x + a
+--R [---------------------------------------------------------------------,
+--R 2a d - 2b c
+--R +---+ +-+
+--R | b 2 |d
+--R +---+ - 2a x |- - + b x - a +-+ c |-
+--R | b \| a |d \|c
+--R |- - log(-----------------------) - 2 |- atan(-----)
+--R \| a 2 \|c d x
+--R b x + a
+--R -----------------------------------------------------,
+--R 2a d - 2b c
+--R +---+ +-+
+--R | d 2 |b
+--R +---+ 2c x |- - + d x - c +-+ a |-
+--R | d \| c |b \|a
+--R |- - log(---------------------) + 2 |- atan(-----)
+--R \| c 2 \|a b x
+--R d x + c
+--R ---------------------------------------------------,
+--R 2a d - 2b c
+--R +-+ +-+
+--R |d |b
+--R +-+ c |- +-+ a |-
+--R |d \|c |b \|a
+--R - |- atan(-----) + |- atan(-----)
+--R \|c d x \|a b x
+--R -----------------------------------]
+--R a d - b c
+--R Type: Union(List(Expression(Integer)),...)
+--E 144
+
+--S 145 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d +-+ +-+ \| c
+--R |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R | b +-+ +-+ \| a +-+ +-+ x\|d
+--R |- - \|a \|c log(-----------------------) - 2\|a \|d atan(-----)
+--R \| a 2 +-+
+--R b x + a \|c
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R 2\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-+ +-+
+--R (2a d - 2b c)\|a \|c
+--R Type: Expression(Integer)
+--E 145
+
+--S 146 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R | b +-+ +-+ \| a +-+ +-+ x\|d
+--R |- - \|a \|c log(-----------------------) - 2\|a \|d atan(-----)
+--R \| a 2 +-+
+--R b x + a \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- +-+
+--R +-+ +-+ |d \|c +-+ +-+ x\|b
+--R - 2\|a \|c |- atan(-----) + 2\|b \|c atan(-----)
+--R \|c d x +-+
+--R \|a
+--R /
+--R +-+ +-+
+--R (2a d - 2b c)\|a \|c
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 148
+
+)clear all
+
+--S 149 of 994
+t0:=1/((a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 149
+
+--S 150 of 994
+r0:=-1/2*d*x/(c*(b*c-a*d)*(c+d*x^2))+b^(3/2)*atan(x*sqrt(b)/sqrt(a))/_
+ ((b*c-a*d)^2*sqrt(a))-1/2*(3*b*c-a*d)*atan(x*sqrt(d)/sqrt(c))*_
+ sqrt(d)/(c^(3/2)*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 +-+ +-+ x\|d
+--R ((a d - 3b c d)x + a c d - 3b c )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b 2 +-+ +-+
+--R (2b c d x + 2b c )\|b \|c atan(-----) + (a d - b c d)x\|a \|c
+--R +-+
+--R \|a
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4 +-+ +-+
+--R ((2a c d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c )\|a \|c
+--R Type: Expression(Integer)
+--E 150
+
+--S 151 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b \| a
+--R (2b c d x + 2b c ) |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 | d \| c
+--R ((a d - 3b c d)x + a c d - 3b c ) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2
+--R (2a d - 2b c d)x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (4a c d - 8a b c d + 4b c d)x + 4a c d - 8a b c d + 4b c
+--R ,
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b \| a
+--R (b c d x + b c ) |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 |d \|c 2
+--R ((- a d + 3b c d)x - a c d + 3b c ) |- atan(-----) + (a d - b c d)x
+--R \|c d x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (2a c d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c
+--R ,
+--R
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 | d \| c
+--R ((a d - 3b c d)x + a c d - 3b c ) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 |b \|a 2
+--R (- 4b c d x - 4b c ) |- atan(-----) + (2a d - 2b c d)x
+--R \|a b x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (4a c d - 8a b c d + 4b c d)x + 4a c d - 8a b c d + 4b c
+--R ,
+--R
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 |d \|c
+--R ((- a d + 3b c d)x - a c d + 3b c ) |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 |b \|a 2
+--R (- 2b c d x - 2b c ) |- atan(-----) + (a d - b c d)x
+--R \|a b x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (2a c d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 151
+
+--S 152 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R 2b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d +-+ +-+ \| c
+--R (a d - 3b c) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R (- 2a d + 6b c)\|a \|d atan(-----) - 4b c\|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 2 2 2 2 3 +-+ +-+
+--R (4a c d - 8a b c d + 4b c )\|a \|c
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 153
+
+--S 154 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ +-+ c |-
+--R +-+ +-+ x\|d +-+ +-+ |d \|c
+--R (- a d + 3b c)\|a \|d atan(-----) + (- a d + 3b c)\|a \|c |- atan(-----)
+--R +-+ \|c d x
+--R \|c
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R - 2b c\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 2 2 3 +-+ +-+
+--R (2a c d - 4a b c d + 2b c )\|a \|c
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 994
+t0:=1/((a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R -----------------------------------------------------------------------------
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 156
+
+--S 157 of 994
+r0:=-1/4*d*x/(c*(b*c-a*d)*(c+d*x^2)^2)-1/8*d*(7*b*c-3*a*d)*x/_
+ (c^2*(b*c-a*d)^2*(c+d*x^2))+b^(5/2)*atan(x*sqrt(b)/sqrt(a))/_
+ ((b*c-a*d)^3*sqrt(a))-1/8*(15*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*_
+ atan(x*sqrt(d)/sqrt(c))*sqrt(d)/(c^(5/2)*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (3a d - 10a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (6a c d - 20a b c d + 30b c d)x + 3a c d - 10a b c d + 15b c
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 4 2 3 2 2 4 +-+ +-+ x\|b
+--R (- 8b c d x - 16b c d x - 8b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R ((3a d - 10a b c d + 7b c d )x + (5a c d - 14a b c d + 9b c d)x)
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3 2 5 2
+--R (16a c d - 48a b c d + 48a b c d - 16b c d)x + 8a c d - 24a b c d
+--R +
+--R 2 6 3 7
+--R 24a b c d - 8b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 4
+--R (3a d - 10a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (6a c d - 20a b c d + 30b c d)x + 3a c d - 10a b c d + 15b c
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 4 2 3 2 2 4 | b \| a
+--R (8b c d x + 16b c d x + 8b c ) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R (6a d - 20a b c d + 14b c d )x + (10a c d - 28a b c d + 18b c d)x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (16a c d - 48a b c d + 48a b c d - 16b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3
+--R (32a c d - 96a b c d + 96a b c d - 32b c d)x + 16a c d
+--R +
+--R 2 5 2 2 6 3 7
+--R - 48a b c d + 48a b c d - 16b c
+--R ,
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 4 2 3 2 2 4 | b \| a
+--R (4b c d x + 8b c d x + 4b c ) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 3a d + 10a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 6a c d + 20a b c d - 30b c d)x - 3a c d + 10a b c d - 15b c
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R (3a d - 10a b c d + 7b c d )x + (5a c d - 14a b c d + 9b c d)x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3 2 5 2
+--R (16a c d - 48a b c d + 48a b c d - 16b c d)x + 8a c d - 24a b c d
+--R +
+--R 2 6 3 7
+--R 24a b c d - 8b c
+--R ,
+--R
+--R 2 4 3 2 2 2 4
+--R (3a d - 10a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (6a c d - 20a b c d + 30b c d)x + 3a c d - 10a b c d + 15b c
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 2 4 2 3 2 2 4 |b \|a
+--R (16b c d x + 32b c d x + 16b c ) |- atan(-----)
+--R \|a b x
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R (6a d - 20a b c d + 14b c d )x + (10a c d - 28a b c d + 18b c d)x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (16a c d - 48a b c d + 48a b c d - 16b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3
+--R (32a c d - 96a b c d + 96a b c d - 32b c d)x + 16a c d
+--R +
+--R 2 5 2 2 6 3 7
+--R - 48a b c d + 48a b c d - 16b c
+--R ,
+--R
+--R 2 4 3 2 2 2 4
+--R (- 3a d + 10a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 6a c d + 20a b c d - 30b c d)x - 3a c d + 10a b c d - 15b c
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 2 4 2 3 2 2 4 |b \|a
+--R (8b c d x + 16b c d x + 8b c ) |- atan(-----)
+--R \|a b x
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R (3a d - 10a b c d + 7b c d )x + (5a c d - 14a b c d + 9b c d)x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3 2 5 2
+--R (16a c d - 48a b c d + 48a b c d - 16b c d)x + 8a c d - 24a b c d
+--R +
+--R 2 6 3 7
+--R 24a b c d - 8b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 158
+
+--S 159 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 2 | d +-+ +-+ \| c
+--R (3a d - 10a b c d + 15b c ) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R 8b c |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|d
+--R (- 6a d + 20a b c d - 30b c )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R 16b c \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 2 3 2 3 2 2 4 3 5 +-+ +-+
+--R (16a c d - 48a b c d + 48a b c d - 16b c )\|a \|c
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+--S 161 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R 4b c |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|d
+--R (- 3a d + 10a b c d - 15b c )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 2 +-+ +-+ |d \|c
+--R (- 3a d + 10a b c d - 15b c )\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R 8b c \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 2 3 2 3 2 2 4 3 5 +-+ +-+
+--R (8a c d - 24a b c d + 24a b c d - 8b c )\|a \|c
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 162
+
+)clear all
+
+--S 163 of 994
+t0:=(c+d*x^2)^5/(a+b*x^2)^2
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R d x + 5c d x + 10c d x + 10c d x + 5c d x + c
+--R (1) ----------------------------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 163
+
+--S 164 of 994
+r0:=d^2*(10*b^3*c^3-20*a*b^2*c^2*d+15*a^2*b*c*d^2-4*a^3*d^3)*x/b^5+_
+ 1/3*d^3*(10*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*x^3/b^4+1/5*d^4*_
+ (5*b*c-2*a*d)*x^5/b^3+1/7*d^5*x^7/b^2+1/2*(b*c-a*d)^5*x/_
+ (a*b^5*(a+b*x^2))+1/2*(b*c-a*d)^4*(b*c+9*a*d)*atan(x*sqrt(b)/_
+ sqrt(a))/(a^(3/2)*b^(11/2))
+--R
+--R
+--R (2)
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 945a b d - 3675a b c d + 5250a b c d - 3150a b c d
+--R +
+--R 5 4 6 5
+--R 525a b c d + 105b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R 945a d - 3675a b c d + 5250a b c d - 3150a b c d + 525a b c d
+--R +
+--R 5 5
+--R 105a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 5 9 2 3 5 4 4 7
+--R 30a b d x + (- 54a b d + 210a b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 5
+--R (126a b d - 490a b c d + 700a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 3
+--R (- 630a b d + 2450a b c d - 3500a b c d + 2100a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R - 945a d + 3675a b c d - 5250a b c d + 3150a b c d
+--R +
+--R 4 4 5 5
+--R - 525a b c d + 105b c
+--R *
+--R x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 6 2 2 5 +-+ +-+
+--R (210a b x + 210a b )\|a \|b
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 945a b d - 3675a b c d + 5250a b c d - 3150a b c d
+--R +
+--R 5 4 6 5
+--R 525a b c d + 105b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R 945a d - 3675a b c d + 5250a b c d - 3150a b c d + 525a b c d
+--R +
+--R 5 5
+--R 105a b c
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 4 5 9 2 3 5 4 4 7
+--R 60a b d x + (- 108a b d + 420a b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 5
+--R (252a b d - 980a b c d + 1400a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 3
+--R (- 1260a b d + 4900a b c d - 7000a b c d + 4200a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R - 1890a d + 7350a b c d - 10500a b c d + 6300a b c d
+--R +
+--R 4 4 5 5
+--R - 1050a b c d + 210b c
+--R *
+--R x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 6 2 2 5 +-----+
+--R (420a b x + 420a b )\|- a b
+--R ,
+--R
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 945a b d - 3675a b c d + 5250a b c d - 3150a b c d
+--R +
+--R 5 4 6 5
+--R 525a b c d + 105b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R 945a d - 3675a b c d + 5250a b c d - 3150a b c d + 525a b c d
+--R +
+--R 5 5
+--R 105a b c
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 4 5 9 2 3 5 4 4 7
+--R 30a b d x + (- 54a b d + 210a b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 5
+--R (126a b d - 490a b c d + 700a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 3
+--R (- 630a b d + 2450a b c d - 3500a b c d + 2100a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R - 945a d + 3675a b c d - 5250a b c d + 3150a b c d
+--R +
+--R 4 4 5 5
+--R - 525a b c d + 105b c
+--R *
+--R x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 6 2 2 5 +---+
+--R (210a b x + 210a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 165
+
+--S 166 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +-+
+--R (9a d - 35a b c d + 50a b c d - 30a b c d + 5a b c d + b c )\|a
+--R *
+--R 2 +-----+
+--R +-+ (b x - a)\|- a b + 2a b x
+--R \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (- 18a d + 70a b c d - 100a b c d + 60a b c d - 10a b c d - 2b c )
+--R *
+--R +-+
+--R +-----+ x\|b
+--R \|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 +-----+ +-+ +-+
+--R 4a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +-+
+--R (9a d - 35a b c d + 50a b c d - 30a b c d + 5a b c d + b c )\|a
+--R *
+--R +---+
+--R +-+ x\|a b
+--R \|b atan(-------)
+--R a
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (- 9a d + 35a b c d - 50a b c d + 30a b c d - 5a b c d - b c )
+--R *
+--R +-+
+--R +---+ x\|b
+--R \|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 +-+ +-+ +---+
+--R 2a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 168
+
+--S 169 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 169
+
+)clear all
+
+--S 170 of 994
+t0:=(c+d*x^2)^4/(a+b*x^2)^2
+--R
+--R
+--R 4 8 3 6 2 2 4 3 2 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R (1) ---------------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 170
+
+--S 171 of 994
+r0:=d^2*(6*b^2*c^2-8*a*b*c*d+3*a^2*d^2)*x/b^4+2/3*d^3*(2*b*c-a*d)*_
+ x^3/b^3+1/5*d^4*x^5/b^2+1/2*(b*c-a*d)^4*x/(a*b^4*(a+b*x^2))+_
+ 1/2*(b*c-a*d)^3*(b*c+7*a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(9/2))
+--R
+--R
+--R (2)
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2
+--R (- 105a b d + 300a b c d - 270a b c d + 60a b c d + 15b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 105a d + 300a b c d - 270a b c d + 60a b c d + 15a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 4 7 2 2 4 3 3 5
+--R 6a b d x + (- 14a b d + 40a b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 3
+--R (70a b d - 200a b c d + 180a b c d )x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (105a d - 300a b c d + 270a b c d - 60a b c d + 15b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 5 2 2 4 +-+ +-+
+--R (30a b x + 30a b )\|a \|b
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2
+--R (105a b d - 300a b c d + 270a b c d - 60a b c d - 15b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 105a d - 300a b c d + 270a b c d - 60a b c d - 15a b c
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 4 7 2 2 4 3 3 5
+--R 12a b d x + (- 28a b d + 80a b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 3
+--R (140a b d - 400a b c d + 360a b c d )x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (210a d - 600a b c d + 540a b c d - 120a b c d + 30b c )x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 5 2 2 4 +-----+
+--R (60a b x + 60a b )\|- a b
+--R ,
+--R
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2
+--R (- 105a b d + 300a b c d - 270a b c d + 60a b c d + 15b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 105a d + 300a b c d - 270a b c d + 60a b c d + 15a b c
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 3 4 7 2 2 4 3 3 5
+--R 6a b d x + (- 14a b d + 40a b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 3
+--R (70a b d - 200a b c d + 180a b c d )x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (105a d - 300a b c d + 270a b c d - 60a b c d + 15b c )x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 5 2 2 4 +---+
+--R (30a b x + 30a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 172
+
+--S 173 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+ +-+
+--R (7a d - 20a b c d + 18a b c d - 4a b c d - b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----+ x\|b
+--R (14a d - 40a b c d + 36a b c d - 8a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-----+ +-+ +-+
+--R 4a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 173
+
+--S 174 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+ +-+
+--R (- 7a d + 20a b c d - 18a b c d + 4a b c d + b c )\|a \|b
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R +-+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +---+ x\|b
+--R (7a d - 20a b c d + 18a b c d - 4a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+ +-+ +---+
+--R 2a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 175
+
+--S 176 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 176
+
+)clear all
+
+--S 177 of 994
+t0:=(c+d*x^2)^3/(a+b*x^2)^2
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 177
+
+--S 178 of 994
+r0:=d^2*(3*b*c-2*a*d)*x/b^3+1/3*d^3*x^3/b^2+1/2*(b*c-a*d)^3*x/_
+ (a*b^3*(a+b*x^2))+1/2*(b*c-a*d)^2*(b*c+5*a*d)*atan(x*sqrt(b)/_
+ sqrt(a))/(a^(3/2)*b^(7/2))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (15a b d - 27a b c d + 9a b c d + 3b c )x + 15a d - 27a b c d
+--R +
+--R 2 2 2 3 3
+--R 9a b c d + 3a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 5 2 3 2 2 3
+--R 2a b d x + (- 10a b d + 18a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 15a d + 27a b c d - 9a b c d + 3b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 4 2 2 3 +-+ +-+
+--R (6a b x + 6a b )\|a \|b
+--R Type: Expression(Integer)
+--E 178
+
+--S 179 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (15a b d - 27a b c d + 9a b c d + 3b c )x + 15a d - 27a b c d
+--R +
+--R 2 2 2 3 3
+--R 9a b c d + 3a b c
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 5 2 3 2 2 3
+--R 4a b d x + (- 20a b d + 36a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 30a d + 54a b c d - 18a b c d + 6b c )x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 4 2 2 3 +-----+
+--R (12a b x + 12a b )\|- a b
+--R ,
+--R
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (15a b d - 27a b c d + 9a b c d + 3b c )x + 15a d - 27a b c d
+--R +
+--R 2 2 2 3 3
+--R 9a b c d + 3a b c
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 3 5 2 3 2 2 3
+--R 2a b d x + (- 10a b d + 18a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 15a d + 27a b c d - 9a b c d + 3b c )x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 4 2 2 3 +---+
+--R (6a b x + 6a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 179
+
+--S 180 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (5a d - 9a b c d + 3a b c d + b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (- 10a d + 18a b c d - 6a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 180
+
+--S 181 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (5a d - 9a b c d + 3a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (- 5a d + 9a b c d - 3a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+ +-+ +---+
+--R 2a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 183
+
+)clear all
+
+--S 184 of 994
+t0:=(c+d*x^2)^2/(a+b*x^2)^2
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 184
+
+--S 185 of 994
+r0:=d^2*x/b^2+1/2*(b*c-a*d)^2*x/(a*b^2*(a+b*x^2))+1/2*(b*c-a*d)*_
+ (b*c+3*a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(5/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 3 2 2 3 2 2 2 2 x\|b
+--R ((- 3a b d + 2a b c d + b c )x - 3a d + 2a b c d + a b c )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 2 2 2 +-+ +-+
+--R (2a b d x + (3a d - 2a b c d + b c )x)\|a \|b
+--R /
+--R 3 2 2 2 +-+ +-+
+--R (2a b x + 2a b )\|a \|b
+--R Type: Expression(Integer)
+--E 185
+
+--S 186 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((3a b d - 2a b c d - b c )x + 3a d - 2a b c d - a b c )
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 2 2 2 2 +-----+
+--R (4a b d x + (6a d - 4a b c d + 2b c )x)\|- a b
+--R /
+--R 3 2 2 2 +-----+
+--R (4a b x + 4a b )\|- a b
+--R ,
+--R
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 3a b d + 2a b c d + b c )x - 3a d + 2a b c d + a b c )
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 3 2 2 2 2 +---+
+--R (2a b d x + (3a d - 2a b c d + b c )x)\|a b
+--R /
+--R 3 2 2 2 +---+
+--R (2a b x + 2a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 186
+
+--S 187 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b - 2a b x
+--R (3a d - 2a b c d - b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (6a d - 4a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 188
+
+--S 189 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (- 3a d + 2a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (3a d - 2a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+ +-+ +---+
+--R 2a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 994
+t0:=(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 2
+--R d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 191
+
+--S 192 of 994
+r0:=1/2*(b*c-a*d)*x/(a*b*(a+b*x^2))+1/2*(b*c+a*d)*atan(x*sqrt(b)/_
+ sqrt(a))/(a^(3/2)*b^(3/2))
+--R
+--R
+--R +-+
+--R 2 2 2 x\|b +-+ +-+
+--R ((a b d + b c)x + a d + a b c)atan(-----) + (- a d + b c)x\|a \|b
+--R +-+
+--R \|a
+--R (2) -------------------------------------------------------------------
+--R 2 2 2 +-+ +-+
+--R (2a b x + 2a b)\|a \|b
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 (b x - a)\|- a b + 2a b x
+--R ((a b d + b c)x + a d + a b c)log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-----+
+--R (- 2a d + 2b c)x\|- a b
+--R /
+--R 2 2 2 +-----+
+--R (4a b x + 4a b)\|- a b
+--R ,
+--R +---+
+--R 2 2 2 x\|a b +---+
+--R ((a b d + b c)x + a d + a b c)atan(-------) + (- a d + b c)x\|a b
+--R a
+--R -------------------------------------------------------------------]
+--R 2 2 2 +---+
+--R (2a b x + 2a b)\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 193
+
+--S 194 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d + b c)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2a d - 2b c)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-----+ +-+ +-+
+--R 4a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+--S 196 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (a d + b c)\|a \|b atan(-------) + (- a d - b c)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R 2a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 197
+
+)clear all
+
+--S 198 of 994
+t0:=1/((a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 198
+
+--S 199 of 994
+r0:=1/2*b*x/(a*(b*c-a*d)*(a+b*x^2))+1/2*(b*c-3*a*d)*atan(x*sqrt(b)/_
+ sqrt(a))*sqrt(b)/(a^(3/2)*(b*c-a*d)^2)+d^(3/2)*atan(x*sqrt(d)/_
+ sqrt(c))/((b*c-a*d)^2*sqrt(c))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (2a b d x + 2a d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 +-+ +-+ x\|b
+--R ((- 3a b d + b c)x - 3a d + a b c)\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 +-+ +-+
+--R (- a b d + b c)x\|a \|c
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2 +-+ +-+
+--R ((2a b d - 4a b c d + 2a b c )x + 2a d - 4a b c d + 2a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 | d \| c
+--R (2a b d x + 2a d) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 | b \| a
+--R ((3a b d - b c)x + 3a d - a b c) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2
+--R (- 2a b d + 2b c)x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (4a b d - 8a b c d + 4a b c )x + 4a d - 8a b c d + 4a b c
+--R ,
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 | b \| a
+--R ((3a b d - b c)x + 3a d - a b c) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 |d \|c 2
+--R (- 4a b d x - 4a d) |- atan(-----) + (- 2a b d + 2b c)x
+--R \|c d x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (4a b d - 8a b c d + 4a b c )x + 4a d - 8a b c d + 4a b c
+--R ,
+--R
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 | d \| c
+--R (a b d x + a d) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 2 |b \|a 2
+--R ((3a b d - b c)x + 3a d - a b c) |- atan(-----) + (- a b d + b c)x
+--R \|a b x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (2a b d - 4a b c d + 2a b c )x + 2a d - 4a b c d + 2a b c
+--R ,
+--R
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 |d \|c
+--R (- 2a b d x - 2a d) |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 2 |b \|a 2
+--R ((3a b d - b c)x + 3a d - a b c) |- atan(-----) + (- a b d + b c)x
+--R \|a b x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (2a b d - 4a b c d + 2a b c )x + 2a d - 4a b c d + 2a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 200
+
+--S 201 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d +-+ +-+ \| c
+--R 2a d |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R (3a d - b c) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R - 4a d\|a \|d atan(-----) + (6a d - 2b c)\|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 3 2 2 2 2 +-+ +-+
+--R (4a d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R (3a d - b c) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ +-+ c |-
+--R +-+ +-+ x\|d +-+ +-+ |d \|c
+--R - 4a d\|a \|d atan(-----) - 4a d\|a \|c |- atan(-----)
+--R +-+ \|c d x
+--R \|c
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R (6a d - 2b c)\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 2 2 2 2 +-+ +-+
+--R (4a d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 203
+
+--S 204 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 204
+
+)clear all
+
+--S 205 of 994
+t0:=1/((a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 205
+
+--S 206 of 994
+r0:=1/2*d*(b*c+a*d)*x/(a*c*(b*c-a*d)^2*(c+d*x^2))+1/2*b*x/(a*(b*c-a*d)*_
+ (a+b*x^2)*(c+d*x^2))+1/2*b^(3/2)*(b*c-5*a*d)*atan(x*sqrt(b)/_
+ sqrt(a))/(a^(3/2)*(b*c-a*d)^3)+1/2*d^(3/2)*(5*b*c-a*d)*atan(x*_
+ sqrt(d)/sqrt(c))/(c^(3/2)*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 2 3 2 2 4 3 3 2 2 2 2 2 3 2
+--R (a b d - 5a b c d )x + (a d - 4a b c d - 5a b c d)x + a c d
+--R +
+--R 2 2
+--R - 5a b c d
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2 2 2
+--R (5a b c d - b c d)x + (5a b c d + 4a b c d - b c )x + 5a b c d
+--R +
+--R 2 3
+--R - a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3 +-+ +-+
+--R ((a b d - b c d)x + (a d - a b c d + a b c d - b c )x)\|a \|c
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (2a c d - 4a b c d + 4a b c d - 2a b c )x + 2a c d - 6a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 6a b c d - 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 3 2 4 2 2 2 2 3 3 2 2 2
+--R (5a b c d - b c d)x + (5a b c d + 4a b c d - b c )x + 5a b c d
+--R +
+--R 2 3
+--R - a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2 3 2
+--R (a b d - 5a b c d )x + (a d - 4a b c d - 5a b c d)x + a c d
+--R +
+--R 2 2
+--R - 5a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3
+--R (2a b d - 2b c d)x + (2a d - 2a b c d + 2a b c d - 2b c )x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (4a b c d - 12a b c d + 12a b c d - 4a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (4a c d - 8a b c d + 8a b c d - 4a b c )x + 4a c d - 12a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 2 3 2 4 2 2 2 2 3 3 2 2 2
+--R (5a b c d - b c d)x + (5a b c d + 4a b c d - b c )x + 5a b c d
+--R +
+--R 2 3
+--R - a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (- 2a b d + 10a b c d )x + (- 2a d + 8a b c d + 10a b c d)x
+--R +
+--R 3 2 2 2
+--R - 2a c d + 10a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3
+--R (2a b d - 2b c d)x + (2a d - 2a b c d + 2a b c d - 2b c )x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (4a b c d - 12a b c d + 12a b c d - 4a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (4a c d - 8a b c d + 8a b c d - 4a b c )x + 4a c d - 12a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 3 2 2 4 3 3 2 2 2 2 2 3 2
+--R (a b d - 5a b c d )x + (a d - 4a b c d - 5a b c d)x + a c d
+--R +
+--R 2 2
+--R - 5a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (- 10a b c d + 2b c d)x + (- 10a b c d - 8a b c d + 2b c )x
+--R +
+--R 2 2 2 3
+--R - 10a b c d + 2a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3
+--R (2a b d - 2b c d)x + (2a d - 2a b c d + 2a b c d - 2b c )x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (4a b c d - 12a b c d + 12a b c d - 4a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (4a c d - 8a b c d + 8a b c d - 4a b c )x + 4a c d - 12a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (- a b d + 5a b c d )x + (- a d + 4a b c d + 5a b c d)x
+--R +
+--R 3 2 2 2
+--R - a c d + 5a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (- 5a b c d + b c d)x + (- 5a b c d - 4a b c d + b c )x
+--R +
+--R 2 2 2 3
+--R - 5a b c d + a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3
+--R (a b d - b c d)x + (a d - a b c d + a b c d - b c )x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (2a c d - 4a b c d + 4a b c d - 2a b c )x + 2a c d - 6a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 6a b c d - 2a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 207
+
+--S 208 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R (5a b c d - b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 | d +-+ +-+ \| c
+--R (a d - 5a b c d) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (- 2a d + 10a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R (- 10a b c d + 2b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 3 3 2 2 2 2 3 3 4 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 208
+
+--S 209 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R (5a b c d - b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (- 2a d + 10a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 +-+ +-+ |d \|c
+--R (- 2a d + 10a b c d)\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R (- 10a b c d + 2b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 3 3 2 2 2 2 3 3 4 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 210
+
+--S 211 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 211
+
+)clear all
+
+--S 212 of 994
+t0:=1/((a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 212
+
+--S 213 of 994
+r0:=1/4*d*(2*b*c+a*d)*x/(a*c*(b*c-a*d)^2*(c+d*x^2)^2)+1/2*b*x/(a*(b*c-_
+ a*d)*(a+b*x^2)*(c+d*x^2)^2)+1/8*d*(4*b*c-a*d)*(b*c+3*a*d)*x/_
+ (a*c^2*(b*c-a*d)^3*(c+d*x^2))+1/2*b^(5/2)*(b*c-7*a*d)*atan(x*_
+ sqrt(b)/sqrt(a))/(a^(3/2)*(b*c-a*d)^4)+1/8*d^(3/2)*(35*b^2*c^2-_
+ 14*a*b*c*d+3*a^2*d^2)*atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*(b*c-a*d)^4)
+--R
+--R
+--R (2)
+--R 3 5 2 2 4 3 2 3 6
+--R (3a b d - 14a b c d + 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (3a d - 8a b c d + 7a b c d + 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (6a c d - 25a b c d + 56a b c d + 35a b c d)x + 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 14a b c d + 35a b c d
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (- 28a b c d + 4b c d )x + (- 28a b c d - 52a b c d + 8b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (- 56a b c d - 20a b c d + 4b c )x - 28a b c d + 4a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (3a b d - 14a b c d + 7a b c d + 4b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (3a d - 9a b c d - 7a b c d + 5a b c d + 8b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (5a c d - 18a b c d + 13a b c d - 4a b c d + 4b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 7
+--R 16a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 5 8
+--R 8a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 213
+
+--S 214 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 5 2 2 4 3 2 3 6
+--R (3a b d - 14a b c d + 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (3a d - 8a b c d + 7a b c d + 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (6a c d - 25a b c d + 56a b c d + 35a b c d)x + 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 14a b c d + 35a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (28a b c d - 4b c d )x + (28a b c d + 52a b c d - 8b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (56a b c d + 20a b c d - 4b c )x + 28a b c d - 4a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (6a b d - 28a b c d + 14a b c d + 8b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (6a d - 18a b c d - 14a b c d + 10a b c d + 16b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (10a c d - 36a b c d + 26a b c d - 8a b c d + 8b c )x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 5 7
+--R 32a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 32a c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 5 8
+--R 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R ,
+--R
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (14a b c d - 2b c d )x + (14a b c d + 26a b c d - 4b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (28a b c d + 10a b c d - 2b c )x + 14a b c d - 2a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 5 2 2 4 3 2 3 6
+--R (- 3a b d + 14a b c d - 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (- 3a d + 8a b c d - 7a b c d - 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (- 6a c d + 25a b c d - 56a b c d - 35a b c d)x - 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R 14a b c d - 35a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (3a b d - 14a b c d + 7a b c d + 4b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (3a d - 9a b c d - 7a b c d + 5a b c d + 8b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (5a c d - 18a b c d + 13a b c d - 4a b c d + 4b c )x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 7
+--R 16a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 5 8
+--R 8a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R ,
+--R
+--R 3 5 2 2 4 3 2 3 6
+--R (3a b d - 14a b c d + 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (3a d - 8a b c d + 7a b c d + 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (6a c d - 25a b c d + 56a b c d + 35a b c d)x + 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 14a b c d + 35a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (56a b c d - 8b c d )x + (56a b c d + 104a b c d - 16b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (112a b c d + 40a b c d - 8b c )x + 56a b c d - 8a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (6a b d - 28a b c d + 14a b c d + 8b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (6a d - 18a b c d - 14a b c d + 10a b c d + 16b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (10a c d - 36a b c d + 26a b c d - 8a b c d + 8b c )x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 5 7
+--R 32a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 32a c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 5 8
+--R 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R ,
+--R
+--R 3 5 2 2 4 3 2 3 6
+--R (- 3a b d + 14a b c d - 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (- 3a d + 8a b c d - 7a b c d - 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (- 6a c d + 25a b c d - 56a b c d - 35a b c d)x - 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R 14a b c d - 35a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (28a b c d - 4b c d )x + (28a b c d + 52a b c d - 8b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (56a b c d + 20a b c d - 4b c )x + 28a b c d - 4a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (3a b d - 14a b c d + 7a b c d + 4b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (3a d - 9a b c d - 7a b c d + 5a b c d + 8b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (5a c d - 18a b c d + 13a b c d - 4a b c d + 4b c )x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 7
+--R 16a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 5 8
+--R 8a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 214
+
+--S 215 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 3 3 2 2 2 2 | d +-+ +-+ \| c
+--R (3a d - 14a b c d + 35a b c d) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (28a b c d - 4b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 +-+ +-+ x\|d
+--R (- 6a d + 28a b c d - 70a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 3 3 +-+ +-+ x\|b
+--R (56a b c d - 8b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +-+ +-+
+--R (16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 215
+
+--S 216 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (14a b c d - 2b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 +-+ +-+ x\|d
+--R (- 3a d + 14a b c d - 35a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 3 3 2 2 2 2 +-+ +-+ |d \|c
+--R (- 3a d + 14a b c d - 35a b c d)\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 3 3 +-+ +-+ x\|b
+--R (28a b c d - 4b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +-+ +-+
+--R (8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 218
+
+)clear all
+
+--S 219 of 994
+t0:=(c+d*x^2)^5/(a+b*x^2)^3
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R d x + 5c d x + 10c d x + 10c d x + 5c d x + c
+--R (1) ----------------------------------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 219
+
+--S 220 of 994
+r0:=d^3*(10*b^2*c^2-15*a*b*c*d+6*a^2*d^2)*x/b^5+1/3*d^4*(5*b*c-3*a*d)*_
+ x^3/b^4+1/5*d^5*x^5/b^3+1/4*(b*c-a*d)^5*x/(a*b^5*(a+b*x^2)^2)+_
+ 1/8*(b*c-a*d)^4*(3*b*c+17*a*d)*x/(a^2*b^5*(a+b*x^2))+1/8*(b*c-_
+ a*d)^3*(3*b^2*c^2+14*a*b*c*d+63*a^2*d^2)*atan(x*sqrt(b)/sqrt(a))/_
+ (a^(5/2)*b^(11/2))
+--R
+--R
+--R (2)
+--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2
+--R - 945a b d + 2625a b c d - 2250a b c d + 450a b c d
+--R +
+--R 6 4 7 5
+--R 75a b c d + 45b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 5 5 2 4 4 3 2 3 3 4 3 2
+--R - 1890a b d + 5250a b c d - 4500a b c d + 900a b c d
+--R +
+--R 2 5 4 6 5
+--R 150a b c d + 90a b c
+--R *
+--R 2
+--R x
+--R +
+--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4
+--R - 945a d + 2625a b c d - 2250a b c d + 450a b c d + 75a b c d
+--R +
+--R 2 5 5
+--R 45a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 4 5 9 3 3 5 2 4 4 7
+--R 24a b d x + (- 72a b d + 200a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5
+--R (504a b d - 1400a b c d + 1200a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 1575a b d - 4375a b c d + 3750a b c d - 750a b c d
+--R +
+--R 5 4 6 5
+--R 75a b c d + 45b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R 945a d - 2625a b c d + 2250a b c d - 450a b c d - 75a b c d
+--R +
+--R 5 5
+--R 75a b c
+--R *
+--R x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 2 7 4 3 6 2 4 5 +-+ +-+
+--R (120a b x + 240a b x + 120a b )\|a \|b
+--R Type: Expression(Integer)
+--E 220
+
+--S 221 of 994
+--a0:=integrate(t0,x)
+--E 221
+
+--S 222 of 994
+--m0:=a0-r0
+--E 222
+
+--S 223 of 994
+--d0:=D(m0,x)
+--E 223
+
+)clear all
+
+--S 224 of 994
+t0:=(c+d*x^2)^4/(a+b*x^2)^3
+--R
+--R
+--R 4 8 3 6 2 2 4 3 2 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R (1) ---------------------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 224
+
+--S 225 of 994
+r0:=d^3*(4*b*c-3*a*d)*x/b^4+1/3*d^4*x^3/b^3+1/4*(b*c-a*d)^4*x/_
+ (a*b^4*(a+b*x^2)^2)+1/8*(b*c-a*d)^3*(3*b*c+13*a*d)*x/(a^2*b^4*_
+ (a+b*x^2))+1/8*(b*c-a*d)^2*(3*b^2*c^2+10*a*b*c*d+35*a^2*d^2)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(9/2))
+--R
+--R
+--R (2)
+--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 4
+--R (105a b d - 180a b c d + 54a b c d + 12a b c d + 9b c )x
+--R +
+--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 2
+--R (210a b d - 360a b c d + 108a b c d + 24a b c d + 18a b c )x
+--R +
+--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 105a d - 180a b c d + 54a b c d + 12a b c d + 9a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 4 7 3 2 4 2 3 3 5
+--R 8a b d x + (- 56a b d + 96a b c d )x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (- 175a b d + 300a b c d - 90a b c d + 12a b c d + 9b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 105a d + 180a b c d - 54a b c d - 12a b c d + 15a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 2 6 4 3 5 2 4 4 +-+ +-+
+--R (24a b x + 48a b x + 24a b )\|a \|b
+--R Type: Expression(Integer)
+--E 225
+
+--S 226 of 994
+--a0:=integrate(t0,x)
+--E 226
+
+--S 227 of 994
+--m0:=a0-r0
+--E 227
+
+--S 228 of 994
+--d0:=D(m0,x)
+--E 228
+
+)clear all
+
+--S 229 of 994
+t0:=(c+d*x^2)^3/(a+b*x^2)^3
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 229
+
+--S 230 of 994
+r0:=d^3*x/b^3+1/4*(b*c-a*d)^3*x/(a*b^3*(a+b*x^2)^2)+3/8*(b*c-a*d)^2*_
+ (b*c+3*a*d)*x/(a^2*b^3*(a+b*x^2))+3/8*(b*c-a*d)*(4*a^2*d^2+_
+ (b*c+a*d)^2)*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(7/2))
+--R
+--R
+--R (2)
+--R 3 2 3 2 3 2 4 2 5 3 4
+--R (- 15a b d + 9a b c d + 3a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 2 5 3 4 2
+--R (- 30a b d + 18a b c d + 6a b c d + 6a b c )x - 15a d + 9a b c d
+--R +
+--R 3 2 2 2 3 3
+--R 3a b c d + 3a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 3 5 3 3 2 2 2 3 2 4 3 3
+--R 8a b d x + (25a b d - 15a b c d + 3a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (15a d - 9a b c d - 3a b c d + 5a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 2 5 4 3 4 2 4 3 +-+ +-+
+--R (8a b x + 16a b x + 8a b )\|a \|b
+--R Type: Expression(Integer)
+--E 230
+
+--S 231 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 3 2 3 2 4 2 5 3 4
+--R (15a b d - 9a b c d - 3a b c d - 3b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 2 5 3 4 2
+--R (30a b d - 18a b c d - 6a b c d - 6a b c )x + 15a d - 9a b c d
+--R +
+--R 3 2 2 2 3 3
+--R - 3a b c d - 3a b c
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 2 3 5 3 3 2 2 2 3 2 4 3 3
+--R 16a b d x + (50a b d - 30a b c d + 6a b c d + 6b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (30a d - 18a b c d - 6a b c d + 10a b c )x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 2 5 4 3 4 2 4 3 +-----+
+--R (16a b x + 32a b x + 16a b )\|- a b
+--R ,
+--R
+--R 3 2 3 2 3 2 4 2 5 3 4
+--R (- 15a b d + 9a b c d + 3a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 2 5 3
+--R (- 30a b d + 18a b c d + 6a b c d + 6a b c )x - 15a d
+--R +
+--R 4 2 3 2 2 2 3 3
+--R 9a b c d + 3a b c d + 3a b c
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 2 3 5 3 3 2 2 2 3 2 4 3 3
+--R 8a b d x + (25a b d - 15a b c d + 3a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (15a d - 9a b c d - 3a b c d + 5a b c )x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 2 5 4 3 4 2 4 3 +---+
+--R (8a b x + 16a b x + 8a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 231
+
+--S 232 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (15a d - 9a b c d - 3a b c d - 3b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (30a d - 18a b c d - 6a b c d - 6b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 3 +-----+ +-+ +-+
+--R 16a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 233
+
+--S 234 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (- 15a d + 9a b c d + 3a b c d + 3b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (15a d - 9a b c d - 3a b c d - 3b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 3 +-+ +-+ +---+
+--R 8a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 994
+t0:=(c+d*x^2)^2/(a+b*x^2)^3
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 236
+
+--S 237 of 994
+r0:=3/8*(c^2/a^2-d^2/b^2)*x/(a+b*x^2)+1/4*(b*c-a*d)*x*(c+d*x^2)/_
+ (a*b*(a+b*x^2)^2)+1/8*(3*b^2*c^2+2*a*b*c*d+3*a^2*d^2)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(5/2))
+--R
+--R
+--R (2)
+--R 2 2 2 3 4 2 4 3 2 2 2 3 2 2
+--R (3a b d + 2a b c d + 3b c )x + (6a b d + 4a b c d + 6a b c )x
+--R +
+--R 4 2 3 2 2 2
+--R 3a d + 2a b c d + 3a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((- 5a b d + 2a b c d + 3b c )x + (- 3a d - 2a b c d + 5a b c )x)
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 2 4 4 3 3 2 4 2 +-+ +-+
+--R (8a b x + 16a b x + 8a b )\|a \|b
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 2 3 4 2 4 3 2 2 2 3 2 2
+--R (3a b d + 2a b c d + 3b c )x + (6a b d + 4a b c d + 6a b c )x
+--R +
+--R 4 2 3 2 2 2
+--R 3a d + 2a b c d + 3a b c
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 2 2 3 2 3
+--R (- 10a b d + 4a b c d + 6b c )x
+--R +
+--R 3 2 2 2 2
+--R (- 6a d - 4a b c d + 10a b c )x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 2 4 4 3 3 2 4 2 +-----+
+--R (16a b x + 32a b x + 16a b )\|- a b
+--R ,
+--R
+--R 2 2 2 3 4 2 4 3 2 2 2 3 2 2
+--R (3a b d + 2a b c d + 3b c )x + (6a b d + 4a b c d + 6a b c )x
+--R +
+--R 4 2 3 2 2 2
+--R 3a d + 2a b c d + 3a b c
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((- 5a b d + 2a b c d + 3b c )x + (- 3a d - 2a b c d + 5a b c )x)
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 2 4 4 3 3 2 4 2 +---+
+--R (8a b x + 16a b x + 8a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 238
+
+--S 239 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (3a d + 2a b c d + 3b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (- 6a d - 4a b c d - 6b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 +-----+ +-+ +-+
+--R 16a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+--S 241 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (3a d + 2a b c d + 3b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- 3a d - 2a b c d - 3b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 +-+ +-+ +---+
+--R 8a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 242
+
+)clear all
+
+--S 243 of 994
+t0:=(c+d*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 2
+--R d x + c
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 243
+
+--S 244 of 994
+r0:=1/4*(b*c-a*d)*x/(a*b*(a+b*x^2)^2)+1/8*(3*b*c+a*d)*x/(a^2*b*(a+_
+ b*x^2))+1/8*(3*b*c+a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(3/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 4 2 2 2 3 2 x\|b
+--R ((a b d + 3b c)x + (2a b d + 6a b c)x + a d + 3a b c)atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 +-+ +-+
+--R ((a b d + 3b c)x + (- a d + 5a b c)x)\|a \|b
+--R /
+--R 2 3 4 3 2 2 4 +-+ +-+
+--R (8a b x + 16a b x + 8a b)\|a \|b
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 4 2 2 2 3 2
+--R ((a b d + 3b c)x + (2a b d + 6a b c)x + a d + 3a b c)
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 2 +-----+
+--R ((2a b d + 6b c)x + (- 2a d + 10a b c)x)\|- a b
+--R /
+--R 2 3 4 3 2 2 4 +-----+
+--R (16a b x + 32a b x + 16a b)\|- a b
+--R ,
+--R
+--R +---+
+--R 2 3 4 2 2 2 3 2 x\|a b
+--R ((a b d + 3b c)x + (2a b d + 6a b c)x + a d + 3a b c)atan(-------)
+--R a
+--R +
+--R 2 3 2 +---+
+--R ((a b d + 3b c)x + (- a d + 5a b c)x)\|a b
+--R /
+--R 2 3 4 3 2 2 4 +---+
+--R (8a b x + 16a b x + 8a b)\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 245
+
+--S 246 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d + 3b c)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2a d - 6b c)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 16a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (a d + 3b c)\|a \|b atan(-------) + (- a d - 3b c)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 8a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 248
+
+--S 249 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 249
+
+)clear all
+
+--S 250 of 994
+t0:=1/((a+b*x^2)^3*(c+d*x^2))
+--R
+--R
+--R (1)
+--R 1
+--R ------------------------------------------------------------------------
+--R 3 8 2 3 6 2 2 4 3 2 2 3
+--R b d x + (3a b d + b c)x + (3a b d + 3a b c)x + (a d + 3a b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 250
+
+--S 251 of 994
+r0:=1/4*b*x/(a*(b*c-a*d)*(a+b*x^2)^2)+1/8*b*(3*b*c-7*a*d)*x/_
+ (a^2*(b*c-a*d)^2*(a+b*x^2))+1/8*(3*b^2*c^2-10*a*b*c*d+15*_
+ a^2*d^2)*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/(a^(5/2)*(b*c-a*d)^3)-_
+ d^(5/2)*atan(x*sqrt(d)/sqrt(c))/((b*c-a*d)^3*sqrt(c))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 4 3 2 2 4 2 +-+ +-+ x\|d
+--R (8a b d x + 16a b d x + 8a d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 3 4 2 4
+--R (- 15a b d + 10a b c d - 3b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (- 30a b d + 20a b c d - 6a b c )x - 15a d + 10a b c d - 3a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 3 4 2 3
+--R (- 7a b d + 10a b c d - 3b c )x
+--R +
+--R 3 2 2 2 3 2
+--R (- 9a b d + 14a b c d - 5a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (8a b d - 24a b c d + 24a b c d - 8a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2 7 3 6 2
+--R (16a b d - 48a b c d + 48a b c d - 16a b c )x + 8a d - 24a b c d
+--R +
+--R 5 2 2 4 3 3
+--R 24a b c d - 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 4 3 2 2 4 2 | d \| c
+--R (8a b d x + 16a b d x + 8a d ) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 2 2 3 4 2 4
+--R (15a b d - 10a b c d + 3b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (30a b d - 20a b c d + 6a b c )x + 15a d - 10a b c d + 3a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 2 2 3 4 2 3 3 2 2 2 3 2
+--R (- 14a b d + 20a b c d - 6b c )x + (- 18a b d + 28a b c d - 10a b c )x
+--R /
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (16a b d - 48a b c d + 48a b c d - 16a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2 7 3 6 2
+--R (32a b d - 96a b c d + 96a b c d - 32a b c )x + 16a d - 48a b c d
+--R +
+--R 5 2 2 4 3 3
+--R 48a b c d - 16a b c
+--R ,
+--R
+--R 2 2 2 3 4 2 4
+--R (15a b d - 10a b c d + 3b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (30a b d - 20a b c d + 6a b c )x + 15a d - 10a b c d + 3a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 4 3 2 2 4 2 |d \|c
+--R (- 16a b d x - 32a b d x - 16a d ) |- atan(-----)
+--R \|c d x
+--R +
+--R 2 2 2 3 4 2 3 3 2 2 2 3 2
+--R (- 14a b d + 20a b c d - 6b c )x + (- 18a b d + 28a b c d - 10a b c )x
+--R /
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (16a b d - 48a b c d + 48a b c d - 16a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2 7 3 6 2
+--R (32a b d - 96a b c d + 96a b c d - 32a b c )x + 16a d - 48a b c d
+--R +
+--R 5 2 2 4 3 3
+--R 48a b c d - 16a b c
+--R ,
+--R
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 4 3 2 2 4 2 | d \| c
+--R (4a b d x + 8a b d x + 4a d ) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 2 2 3 4 2 4
+--R (15a b d - 10a b c d + 3b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (30a b d - 20a b c d + 6a b c )x + 15a d - 10a b c d + 3a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 2 2 3 4 2 3 3 2 2 2 3 2
+--R (- 7a b d + 10a b c d - 3b c )x + (- 9a b d + 14a b c d - 5a b c )x
+--R /
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (8a b d - 24a b c d + 24a b c d - 8a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2 7 3 6 2
+--R (16a b d - 48a b c d + 48a b c d - 16a b c )x + 8a d - 24a b c d
+--R +
+--R 5 2 2 4 3 3
+--R 24a b c d - 8a b c
+--R ,
+--R
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 4 3 2 2 4 2 |d \|c
+--R (- 8a b d x - 16a b d x - 8a d ) |- atan(-----)
+--R \|c d x
+--R +
+--R 2 2 2 3 4 2 4
+--R (15a b d - 10a b c d + 3b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (30a b d - 20a b c d + 6a b c )x + 15a d - 10a b c d + 3a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 2 2 3 4 2 3 3 2 2 2 3 2
+--R (- 7a b d + 10a b c d - 3b c )x + (- 9a b d + 14a b c d - 5a b c )x
+--R /
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (8a b d - 24a b c d + 24a b c d - 8a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2 7 3 6 2
+--R (16a b d - 48a b c d + 48a b c d - 16a b c )x + 8a d - 24a b c d
+--R +
+--R 5 2 2 4 3 3
+--R 24a b c d - 8a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 252
+
+--S 253 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 | d +-+ +-+ \| c
+--R 8a d |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 2 | b +-+ +-+ \| a
+--R (15a d - 10a b c d + 3b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R - 16a d \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|b
+--R (30a d - 20a b c d + 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 3 4 2 3 2 2 2 3 3 +-+ +-+
+--R (16a d - 48a b c d + 48a b c d - 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 253
+
+--S 254 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 2 | b +-+ +-+ \| a
+--R (15a d - 10a b c d + 3b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ +-+ c |-
+--R 2 2 +-+ +-+ x\|d 2 2 +-+ +-+ |d \|c
+--R - 16a d \|a \|d atan(-----) - 16a d \|a \|c |- atan(-----)
+--R +-+ \|c d x
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|b
+--R (30a d - 20a b c d + 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 3 4 2 3 2 2 2 3 3 +-+ +-+
+--R (16a d - 48a b c d + 48a b c d - 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 255
+
+--S 256 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 256
+
+)clear all
+
+--S 257 of 994
+t0:=1/((a+b*x^2)^3*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 2 10 2 2 3 8 2 2 2 3 2 6
+--R b d x + (3a b d + 2b c d)x + (3a b d + 6a b c d + b c )x
+--R +
+--R 3 2 2 2 2 4 3 2 2 2 3 2
+--R (a d + 6a b c d + 3a b c )x + (2a c d + 3a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 257
+
+--S 258 of 994
+r0:=1/8*d*(b*c-4*a*d)*(3*b*c+a*d)*x/(a^2*c*(b*c-a*d)^3*(c+d*x^2))+_
+ 1/4*b*x/(a*(b*c-a*d)*(a+b*x^2)^2*(c+d*x^2))+3/8*b*(b*c-3*a*d)*_
+ x/(a^2*(b*c-a*d)^2*(a+b*x^2)*(c+d*x^2))+1/8*b^(3/2)*(3*b^2*c^2-_
+ 14*a*b*c*d+35*a^2*d^2)*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-_
+ a*d)^4)-1/2*d^(5/2)*(7*b*c-a*d)*atan(x*sqrt(d)/sqrt(c))/_
+ (c^(3/2)*(b*c-a*d)^4)
+--R
+--R
+--R (2)
+--R 3 2 4 2 3 3 6 4 4 3 2 3 2 3 2 2 4
+--R (4a b d - 28a b c d )x + (8a b d - 52a b c d - 28a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 5 3 4 2 2
+--R (4a d - 20a b c d - 56a b c d )x + 4a c d - 28a b c d
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 3 4 2 2 5 3 6
+--R (35a b c d - 14a b c d + 3b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4 4
+--R (70a b c d + 7a b c d - 8a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 2 4 2 2
+--R (35a b c d + 56a b c d - 25a b c d + 6a b c )x + 35a b c d
+--R +
+--R 3 2 3 2 3 4
+--R - 14a b c d + 3a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 5
+--R (4a b d + 7a b c d - 14a b c d + 3b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (8a b d + 5a b c d - 7a b c d - 9a b c d + 3b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R (4a d - 4a b c d + 13a b c d - 18a b c d + 5a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 6 2 5 5 3 2 4 4 4 3 3 3 5 4 2 2 6 5 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d)x
+--R +
+--R 7 5 6 2 2 4 5 3 3 3 4 4 4 2 3 5 5
+--R 16a b c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 2 6 6
+--R 8a b c
+--R *
+--R 4
+--R x
+--R +
+--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 3 5 6
+--R 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 8 2 4 7 3 3 6 2 4 2 5 3 5 4 4 6
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 258
+
+--S 259 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 3 4 2 2 5 3 6
+--R (35a b c d - 14a b c d + 3b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4 4
+--R (70a b c d + 7a b c d - 8a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 2 4 2 2
+--R (35a b c d + 56a b c d - 25a b c d + 6a b c )x + 35a b c d
+--R +
+--R 3 2 3 2 3 4
+--R - 14a b c d + 3a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 2 4 2 3 3 6 4 4 3 2 3 2 3 2 2 4
+--R (4a b d - 28a b c d )x + (8a b d - 52a b c d - 28a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 5 3 4 2 2
+--R (4a d - 20a b c d - 56a b c d )x + 4a c d - 28a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 5
+--R (8a b d + 14a b c d - 28a b c d + 6b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (16a b d + 10a b c d - 14a b c d - 18a b c d + 6b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R (8a d - 8a b c d + 26a b c d - 36a b c d + 10a b c )x
+--R /
+--R 6 2 5 5 3 2 4 4 4 3 3 3 5 4 2 2 6 5 6
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16a b c d)x
+--R +
+--R 7 5 6 2 2 4 5 3 3 3 4 4 4 2 3 5 5
+--R 32a b c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 2 6 6
+--R 16a b c
+--R *
+--R 4
+--R x
+--R +
+--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 3 5 6
+--R 32a b c
+--R *
+--R 2
+--R x
+--R +
+--R 8 2 4 7 3 3 6 2 4 2 5 3 5 4 4 6
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R ,
+--R
+--R 2 3 3 4 2 2 5 3 6
+--R (35a b c d - 14a b c d + 3b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4 4
+--R (70a b c d + 7a b c d - 8a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 2 4 2 2
+--R (35a b c d + 56a b c d - 25a b c d + 6a b c )x + 35a b c d
+--R +
+--R 3 2 3 2 3 4
+--R - 14a b c d + 3a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 2 4 2 3 3 6
+--R (- 8a b d + 56a b c d )x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4
+--R (- 16a b d + 104a b c d + 56a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 5 3 4 2 2
+--R (- 8a d + 40a b c d + 112a b c d )x - 8a c d + 56a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 5
+--R (8a b d + 14a b c d - 28a b c d + 6b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (16a b d + 10a b c d - 14a b c d - 18a b c d + 6b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R (8a d - 8a b c d + 26a b c d - 36a b c d + 10a b c )x
+--R /
+--R 6 2 5 5 3 2 4 4 4 3 3 3 5 4 2 2 6 5 6
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16a b c d)x
+--R +
+--R 7 5 6 2 2 4 5 3 3 3 4 4 4 2 3 5 5
+--R 32a b c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 2 6 6
+--R 16a b c
+--R *
+--R 4
+--R x
+--R +
+--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 3 5 6
+--R 32a b c
+--R *
+--R 2
+--R x
+--R +
+--R 8 2 4 7 3 3 6 2 4 2 5 3 5 4 4 6
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R ,
+--R
+--R 3 2 4 2 3 3 6 4 4 3 2 3 2 3 2 2 4
+--R (2a b d - 14a b c d )x + (4a b d - 26a b c d - 14a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 5 3 4 2 2
+--R (2a d - 10a b c d - 28a b c d )x + 2a c d - 14a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 3 3 4 2 2 5 3 6
+--R (- 35a b c d + 14a b c d - 3b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4 4
+--R (- 70a b c d - 7a b c d + 8a b c d - 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 2 4 2 2
+--R (- 35a b c d - 56a b c d + 25a b c d - 6a b c )x - 35a b c d
+--R +
+--R 3 2 3 2 3 4
+--R 14a b c d - 3a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 5
+--R (4a b d + 7a b c d - 14a b c d + 3b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (8a b d + 5a b c d - 7a b c d - 9a b c d + 3b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R (4a d - 4a b c d + 13a b c d - 18a b c d + 5a b c )x
+--R /
+--R 6 2 5 5 3 2 4 4 4 3 3 3 5 4 2 2 6 5 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d)x
+--R +
+--R 7 5 6 2 2 4 5 3 3 3 4 4 4 2 3 5 5
+--R 16a b c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 2 6 6
+--R 8a b c
+--R *
+--R 4
+--R x
+--R +
+--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 3 5 6
+--R 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 8 2 4 7 3 3 6 2 4 2 5 3 5 4 4 6
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R ,
+--R
+--R 3 2 4 2 3 3 6
+--R (- 4a b d + 28a b c d )x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4
+--R (- 8a b d + 52a b c d + 28a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 5 3 4 2 2
+--R (- 4a d + 20a b c d + 56a b c d )x - 4a c d + 28a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 3 3 4 2 2 5 3 6
+--R (- 35a b c d + 14a b c d - 3b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4 4
+--R (- 70a b c d - 7a b c d + 8a b c d - 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 2 4 2 2
+--R (- 35a b c d - 56a b c d + 25a b c d - 6a b c )x - 35a b c d
+--R +
+--R 3 2 3 2 3 4
+--R 14a b c d - 3a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 5
+--R (4a b d + 7a b c d - 14a b c d + 3b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (8a b d + 5a b c d - 7a b c d - 9a b c d + 3b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R (4a d - 4a b c d + 13a b c d - 18a b c d + 5a b c )x
+--R /
+--R 6 2 5 5 3 2 4 4 4 3 3 3 5 4 2 2 6 5 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d)x
+--R +
+--R 7 5 6 2 2 4 5 3 3 3 4 4 4 2 3 5 5
+--R 16a b c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 2 6 6
+--R 8a b c
+--R *
+--R 4
+--R x
+--R +
+--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 3 5 6
+--R 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 8 2 4 7 3 3 6 2 4 2 5 3 5 4 4 6
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 259
+
+--S 260 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 2 2 3 3 | b +-+ +-+ \| a
+--R (35a b c d - 14a b c d + 3b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 3 3 2 2 | d +-+ +-+ \| c
+--R (4a d - 28a b c d ) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R 3 3 2 2 +-+ +-+ x\|d
+--R (- 8a d + 56a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 2 3 3 +-+ +-+ x\|b
+--R (- 70a b c d + 28a b c d - 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +-+ +-+
+--R (16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 260
+
+--S 261 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 2 2 3 3 | b +-+ +-+ \| a
+--R (35a b c d - 14a b c d + 3b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 +-+ +-+ x\|d
+--R (- 8a d + 56a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 3 3 2 2 +-+ +-+ |d \|c
+--R (- 8a d + 56a b c d )\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 2 2 3 3 +-+ +-+ x\|b
+--R (- 70a b c d + 28a b c d - 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +-+ +-+
+--R (16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 263
+
+)clear all
+
+--S 264 of 994
+t0:=1/((a+b*x^2)^3*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 3 12 2 3 3 2 10 2 3 2 2 3 2 8
+--R b d x + (3a b d + 3b c d )x + (3a b d + 9a b c d + 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 6 3 2 2 2 2 3 4
+--R (a d + 9a b c d + 9a b c d + b c )x + (3a c d + 9a b c d + 3a b c )x
+--R +
+--R 3 2 2 3 2 3 3
+--R (3a c d + 3a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 264
+
+--S 265 of 994
+r0:=1/8*d*(3*b^2*c^2-13*a*b*c*d-2*a^2*d^2)*x/(a^2*c*(b*c-a*d)^3*_
+ (c+d*x^2)^2)+1/4*b*x/(a*(b*c-a*d)*(a+b*x^2)^2*(c+d*x^2)^2)+_
+ 1/8*b*(3*b*c-11*a*d)*x/(a^2*(b*c-a*d)^2*(a+b*x^2)*(c+d*x^2)^2)+_
+ 3/8*d*(b*c+a*d)*(b^2*c^2-6*a*b*c*d+a^2*d^2)*x/(a^2*c^2*(b*c-_
+ a*d)^4*(c+d*x^2))+3/8*b^(5/2)*(b^2*c^2-6*a*b*c*d+21*a^2*d^2)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-a*d)^5)-3/8*d^(5/2)*_
+ (21*b^2*c^2-6*a*b*c*d+a^2*d^2)*atan(x*sqrt(d)/sqrt(c))/_
+ (c^(5/2)*(b*c-a*d)^5)
+--R
+--R
+--R (2)
+--R 4 2 6 3 3 5 2 4 2 4 8
+--R (3a b d - 18a b c d + 63a b c d )x
+--R +
+--R 5 6 4 2 5 3 3 2 4 2 4 3 3 6
+--R (6a b d - 30a b c d + 90a b c d + 126a b c d )x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 4
+--R (3a d - 6a b c d - 6a b c d + 234a b c d + 63a b c d )x
+--R +
+--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 6 2 4
+--R (6a c d - 30a b c d + 90a b c d + 126a b c d )x + 3a c d
+--R +
+--R 5 3 3 4 2 4 2
+--R - 18a b c d + 63a b c d
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 4 2 4 5 3 3 6 4 2 8
+--R (- 63a b c d + 18a b c d - 3b c d )x
+--R +
+--R 3 3 2 4 2 4 3 3 5 4 2 6 5 6
+--R (- 126a b c d - 90a b c d + 30a b c d - 6b c d)x
+--R +
+--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 4
+--R (- 63a b c d - 234a b c d + 6a b c d + 6a b c d - 3b c )x
+--R +
+--R 4 2 3 3 3 3 4 2 2 4 5 5 6 2 4 2 4 2
+--R (- 126a b c d - 90a b c d + 30a b c d - 6a b c )x - 63a b c d
+--R +
+--R 3 3 5 2 4 6
+--R 18a b c d - 3a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 2 6 3 3 5 5 3 3 6 4 2 7
+--R (3a b d - 18a b c d + 18a b c d - 3b c d )x
+--R +
+--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2
+--R 6a b d - 31a b c d - 9a b c d + 9a b c d + 31a b c d
+--R +
+--R 6 5
+--R - 6b c d
+--R *
+--R 5
+--R x
+--R +
+--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 3
+--R (3a d - 8a b c d - 29a b c d + 29a b c d + 8a b c d - 3b c )x
+--R +
+--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6
+--R (5a c d - 22a b c d + 17a b c d - 17a b c d + 22a b c d - 5a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 3 6 6 3
+--R 8a b c d - 40a b c d + 80a b c d - 80a b c d + 40a b c d
+--R +
+--R 2 7 7 2
+--R - 8a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 8 2 7 7 2 3 6 6 3 4 5 4 5 6 3 3 6 7 2
+--R 16a b c d - 64a b c d + 80a b c d - 80a b c d + 64a b c d
+--R +
+--R 2 7 8
+--R - 16a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 9 2 7 8 3 6 7 2 4 5 6 3 5 4 5 4 6 3
+--R 8a c d - 8a b c d - 72a b c d + 200a b c d - 200a b c d
+--R +
+--R 4 5 7 2 3 6 8 2 7 9
+--R 72a b c d + 8a b c d - 8a b c
+--R *
+--R 4
+--R x
+--R +
+--R 9 3 6 8 4 5 7 2 5 4 5 4 7 2 4 5 8
+--R 16a c d - 64a b c d + 80a b c d - 80a b c d + 64a b c d
+--R +
+--R 3 6 9
+--R - 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 9 4 5 8 5 4 7 2 6 3 6 3 7 2 5 4 8 4 5 9
+--R 8a c d - 40a b c d + 80a b c d - 80a b c d + 40a b c d - 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 265
+
+--S 266 of 994
+--a0:=integrate(t0,x)
+--E 266
+
+--S 267 of 994
+--m0:=a0-r0
+--E 267
+
+--S 268 of 994
+--d0:=D(m0,x)
+--E 268
+
+)clear all
+
+--S 269 of 994
+t0:=(-1+x^2)^3/(1+x^2)^4
+--R
+--R
+--R 6 4 2
+--R x - 3x + 3x - 1
+--R (1) ------------------------
+--R 8 6 4 2
+--R x + 4x + 6x + 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 269
+
+--S 270 of 994
+r0:=-1/3*x*(1-x^2)^2/(1+x^2)^3-2/3*x/(1+x^2)
+--R
+--R
+--R 5 2 3
+--R - x - - x - x
+--R 3
+--R (2) ------------------
+--R 6 4 2
+--R x + 3x + 3x + 1
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 270
+
+--S 271 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 3
+--R - 3x - 2x - 3x
+--R (3) -------------------
+--R 6 4 2
+--R 3x + 9x + 9x + 3
+--R Type: Union(Expression(Integer),...)
+--E 271
+
+--S 272 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 273
+
+)clear all
+
+--S 274 of 994
+t0:=(-1+x^2)^4/(1+x^2)^5
+--R
+--R
+--R 8 6 4 2
+--R x - 4x + 6x - 4x + 1
+--R (1) ---------------------------------
+--R 10 8 6 4 2
+--R x + 5x + 10x + 10x + 5x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 274
+
+--S 275 of 994
+r0:=1/4*x*(1-x^2)^3/(1+x^2)^4+3/8*x*(1-x^2)/(1+x^2)^2+3/8*atan(x)
+--R
+--R
+--R 8 6 4 2 7 5 3
+--R (3x + 12x + 18x + 12x + 3)atan(x) - 5x + 3x - 3x + 5x
+--R (2) ------------------------------------------------------------
+--R 8 6 4 2
+--R 8x + 32x + 48x + 32x + 8
+--R Type: Expression(Integer)
+--E 275
+
+--S 276 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 8 6 4 2 7 5 3
+--R (3x + 12x + 18x + 12x + 3)atan(x) - 5x + 3x - 3x + 5x
+--R (3) ------------------------------------------------------------
+--R 8 6 4 2
+--R 8x + 32x + 48x + 32x + 8
+--R Type: Union(Expression(Integer),...)
+--E 276
+
+--S 277 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 278
+
+)clear all
+
+--S 279 of 994
+t0:=(a+b*x^2)^(1/2)*(c+d*x^2)^3
+--R
+--R
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (1) (d x + 3c d x + 3c d x + c )\|b x + a
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 994
+r0:=1/192*d*(88*b^2*c^2-68*a*b*c*d+15*a^2*d^2)*x*(a+b*x^2)^(3/2)/b^3+_
+ 1/8*d*x*(a+b*x^2)^(3/2)*(c+d*x^2)^2/b+1/48*d*x*(a+b*x^2)^(3/2)*_
+ (c*(8*b*c-a*d)+d*(12*b*c-5*a*d)*x^2)/b^2+1/128*a*(64*b^3*c^3-_
+ 48*a*b^2*c^2*d+24*a^2*b*c*d^2-5*a^3*d^3)*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(7/2)+1/128*(64*b^3*c^3-48*a*b^2*c^2*d+24*_
+ a^2*b*c*d^2-5*a^3*d^3)*x*sqrt(a+b*x^2)/b^3
+--R
+--R
+--R (2)
+--R +-+
+--R 4 3 3 2 2 2 2 3 3 x\|b
+--R (- 15a d + 72a b c d - 144a b c d + 192a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 3 7 2 3 3 2 5
+--R 48b d x + (8a b d + 192b c d )x
+--R +
+--R 2 3 2 2 3 2 3
+--R (- 10a b d + 48a b c d + 288b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (15a d - 72a b c d + 144a b c d + 192b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 3 +-+
+--R 384b \|b
+--R Type: Expression(Integer)
+--E 280
+
+--S 281 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 3 3 3 4 2 2 5 2 6 3 6
+--R (120a b d - 576a b c d + 1152a b c d - 1536a b c )x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (1200a b d - 5760a b c d + 11520a b c d - 15360a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2
+--R (2880a b d - 13824a b c d + 27648a b c d - 36864a b c )x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R 1920a d - 9216a b c d + 18432a b c d - 24576a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 3 3 5 2 2 6 2 7 3 8
+--R (- 15a b d + 72a b c d - 144a b c d + 192a b c )x
+--R +
+--R 5 3 3 4 4 2 3 5 2 2 6 3 6
+--R (- 480a b d + 2304a b c d - 4608a b c d + 6144a b c )x
+--R +
+--R 6 2 3 5 3 2 4 4 2 3 5 3 4
+--R (- 2400a b d + 11520a b c d - 23040a b c d + 30720a b c )x
+--R +
+--R 7 3 6 2 2 5 3 2 4 4 3 2
+--R (- 3840a b d + 18432a b c d - 36864a b c d + 49152a b c )x
+--R +
+--R 8 3 7 2 6 2 2 5 3 3
+--R - 1920a d + 9216a b c d - 18432a b c d + 24576a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 7 3 15 6 3 7 2 13
+--R - 48b d x + (- 1544a b d - 192b c d )x
+--R +
+--R 2 5 3 6 2 7 2 11
+--R (- 7926a b d - 6192a b c d - 288b c d)x
+--R +
+--R 3 4 3 2 5 2 6 2 7 3 9
+--R (- 13263a b d - 32184a b c d - 9360a b c d - 192b c )x
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 7
+--R (- 7072a b d - 54528a b c d - 50688a b c d - 6144a b c )x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 5
+--R (- 864a b d - 25344a b c d - 96768a b c d - 30720a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 3
+--R (- 2560a b d + 12288a b c d - 73728a b c d - 49152a b c )x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (- 1920a d + 9216a b c d - 18432a b c d - 24576a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 7 3 15 6 3 7 2 13
+--R 384b d x + (4288a b d + 1536b c d )x
+--R +
+--R 2 5 3 6 2 7 2 11
+--R (13680a b d + 17280a b c d + 2304b c d)x
+--R +
+--R 3 4 3 2 5 2 6 2 7 3 9
+--R (16776a b d + 55872a b c d + 26496a b c d + 1536b c )x
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 7
+--R (7304a b d + 68160a b c d + 91008a b c d + 16896a b c )x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 5
+--R (1904a b d + 20352a b c d + 131328a b c d + 52224a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 3
+--R (3520a b d - 16896a b c d + 82944a b c d + 61440a b c )x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (1920a d - 9216a b c d + 18432a b c d + 24576a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +-+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b )\|a \|b \|b x + a
+--R +
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +-+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b )\|b
+--R ,
+--R
+--R 4 3 3 3 4 2 2 5 2 6 3 6
+--R (- 240a b d + 1152a b c d - 2304a b c d + 3072a b c )x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (- 2400a b d + 11520a b c d - 23040a b c d + 30720a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2
+--R (- 5760a b d + 27648a b c d - 55296a b c d + 73728a b c )x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R - 3840a d + 18432a b c d - 36864a b c d + 49152a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 3 3 5 2 2 6 2 7 3 8
+--R (30a b d - 144a b c d + 288a b c d - 384a b c )x
+--R +
+--R 5 3 3 4 4 2 3 5 2 2 6 3 6
+--R (960a b d - 4608a b c d + 9216a b c d - 12288a b c )x
+--R +
+--R 6 2 3 5 3 2 4 4 2 3 5 3 4
+--R (4800a b d - 23040a b c d + 46080a b c d - 61440a b c )x
+--R +
+--R 7 3 6 2 2 5 3 2 4 4 3 2
+--R (7680a b d - 36864a b c d + 73728a b c d - 98304a b c )x
+--R +
+--R 8 3 7 2 6 2 2 5 3 3
+--R 3840a d - 18432a b c d + 36864a b c d - 49152a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 7 3 15 6 3 7 2 13
+--R - 48b d x + (- 1544a b d - 192b c d )x
+--R +
+--R 2 5 3 6 2 7 2 11
+--R (- 7926a b d - 6192a b c d - 288b c d)x
+--R +
+--R 3 4 3 2 5 2 6 2 7 3 9
+--R (- 13263a b d - 32184a b c d - 9360a b c d - 192b c )x
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 7
+--R (- 7072a b d - 54528a b c d - 50688a b c d - 6144a b c )x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 5
+--R (- 864a b d - 25344a b c d - 96768a b c d - 30720a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 3
+--R (- 2560a b d + 12288a b c d - 73728a b c d - 49152a b c )x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (- 1920a d + 9216a b c d - 18432a b c d - 24576a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 7 3 15 6 3 7 2 13
+--R 384b d x + (4288a b d + 1536b c d )x
+--R +
+--R 2 5 3 6 2 7 2 11
+--R (13680a b d + 17280a b c d + 2304b c d)x
+--R +
+--R 3 4 3 2 5 2 6 2 7 3 9
+--R (16776a b d + 55872a b c d + 26496a b c d + 1536b c )x
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 7
+--R (7304a b d + 68160a b c d + 91008a b c d + 16896a b c )x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 5
+--R (1904a b d + 20352a b c d + 131328a b c d + 52224a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 3
+--R (3520a b d - 16896a b c d + 82944a b c d + 61440a b c )x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (1920a d - 9216a b c d + 18432a b c d + 24576a b c )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +---+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b )\|- b \|a \|b x + a
+--R +
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +---+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 281
+
+--S 282 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 3 3 2 2 2 2 3 3
+--R (5a d - 24a b c d + 48a b c d - 64a b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 4 3 3 2 2 2 2 3 3 x\|b
+--R (5a d - 24a b c d + 48a b c d - 64a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 128b \|b
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 283
+
+--S 284 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 4 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (5a d - 24a b c d + 48a b c d - 64a b c )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 3 3 2 2 2 2 3 3 +-+
+--R (- 10a d + 48a b c d - 96a b c d + 128a b c )\|b
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 128b \|- b \|b
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 994
+t0:=(a+b*x^2)^(1/2)*(c+d*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (1) (d x + 2c d x + c )\|b x + a
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 994
+r0:=1/24*d*(8*b*c-3*a*d)*x*(a+b*x^2)^(3/2)/b^2+1/6*d*x*(a+b*x^2)^(3/2)*_
+ (c+d*x^2)/b+1/16*a*(8*b^2*c^2-4*a*b*c*d+a^2*d^2)*atanh(x*_
+ sqrt(b)/sqrt(a+b*x^2))/b^(5/2)+1/16*(8*b^2*c^2-4*a*b*c*d+_
+ a^2*d^2)*x*sqrt(a+b*x^2)/b^2
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 2 2 2 x\|b
+--R (3a d - 12a b c d + 24a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 5 2 2 3 2 2 2 2 +-+
+--R (8b d x + (2a b d + 24b c d)x + (- 3a d + 12a b c d + 24b c )x)\|b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 48b \|b
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 2 2 3 4 2 4
+--R (18a b d - 72a b c d + 144a b c )x
+--R +
+--R 4 2 3 2 2 3 2 2 5 2 4
+--R (96a b d - 384a b c d + 768a b c )x + 96a d - 384a b c d
+--R +
+--R 3 2 2
+--R 768a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 2 2 4 5 2 6
+--R (- 3a b d + 12a b c d - 24a b c )x
+--R +
+--R 4 2 2 3 3 2 4 2 4
+--R (- 54a b d + 216a b c d - 432a b c )x
+--R +
+--R 5 2 4 2 3 3 2 2 6 2 5
+--R (- 144a b d + 576a b c d - 1152a b c )x - 96a d + 384a b c d
+--R +
+--R 4 2 2
+--R - 768a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 5 2 11 4 2 5 9
+--R - 8b d x + (- 146a b d - 24b c d)x
+--R +
+--R 2 3 2 4 5 2 7
+--R (- 417a b d - 444a b c d - 24b c )x
+--R +
+--R 3 2 2 2 3 4 2 5
+--R (- 298a b d - 1368a b c d - 432a b c )x
+--R +
+--R 4 2 3 2 2 3 2 3
+--R (80a b d - 1344a b c d - 1152a b c )x
+--R +
+--R 5 2 4 3 2 2
+--R (96a d - 384a b c d - 768a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 5 2 11 4 2 5 9
+--R 48b d x + (316a b d + 144b c d)x
+--R +
+--R 2 3 2 4 5 2 7
+--R (570a b d + 984a b c d + 144b c )x
+--R +
+--R 3 2 2 2 3 4 2 5
+--R (270a b d + 1992a b c d + 912a b c )x
+--R +
+--R 4 2 3 2 2 3 2 3
+--R (- 128a b d + 1536a b c d + 1536a b c )x
+--R +
+--R 5 2 4 3 2 2
+--R (- 96a d + 384a b c d + 768a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +-+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b )\|a \|b \|b x + a
+--R +
+--R 5 6 4 4 2 3 2 3 2 +-+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|b
+--R ,
+--R
+--R 3 2 2 2 3 4 2 4
+--R (36a b d - 144a b c d + 288a b c )x
+--R +
+--R 4 2 3 2 2 3 2 2 5 2 4
+--R (192a b d - 768a b c d + 1536a b c )x + 192a d - 768a b c d
+--R +
+--R 3 2 2
+--R 1536a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 2 2 4 5 2 6
+--R (- 6a b d + 24a b c d - 48a b c )x
+--R +
+--R 4 2 2 3 3 2 4 2 4
+--R (- 108a b d + 432a b c d - 864a b c )x
+--R +
+--R 5 2 4 2 3 3 2 2 6 2 5
+--R (- 288a b d + 1152a b c d - 2304a b c )x - 192a d + 768a b c d
+--R +
+--R 4 2 2
+--R - 1536a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 5 2 11 4 2 5 9
+--R - 8b d x + (- 146a b d - 24b c d)x
+--R +
+--R 2 3 2 4 5 2 7
+--R (- 417a b d - 444a b c d - 24b c )x
+--R +
+--R 3 2 2 2 3 4 2 5
+--R (- 298a b d - 1368a b c d - 432a b c )x
+--R +
+--R 4 2 3 2 2 3 2 3
+--R (80a b d - 1344a b c d - 1152a b c )x
+--R +
+--R 5 2 4 3 2 2
+--R (96a d - 384a b c d - 768a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 2 11 4 2 5 9
+--R 48b d x + (316a b d + 144b c d)x
+--R +
+--R 2 3 2 4 5 2 7
+--R (570a b d + 984a b c d + 144b c )x
+--R +
+--R 3 2 2 2 3 4 2 5
+--R (270a b d + 1992a b c d + 912a b c )x
+--R +
+--R 4 2 3 2 2 3 2 3
+--R (- 128a b d + 1536a b c d + 1536a b c )x
+--R +
+--R 5 2 4 3 2 2
+--R (- 96a d + 384a b c d + 768a b c )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +---+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b )\|- b \|a \|b x + a
+--R +
+--R 5 6 4 4 2 3 2 3 2 +---+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 288
+
+--S 289 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 2 2 2 2
+--R (a d - 4a b c d + 8a b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 2 2 2 2 x\|b
+--R (- a d + 4a b c d - 8a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+--S 291 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 3 2 2 2 2 +---+ x\|b
+--R (- a d + 4a b c d - 8a b c )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 3 2 2 2 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (2a d - 8a b c d + 16a b c )\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 16b \|- b \|b
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 292
+
+)clear all
+
+--S 293 of 994
+t0:=(a+b*x^2)^(1/2)*(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (1) (d x + c)\|b x + a
+--R Type: Expression(Integer)
+--E 293
+
+--S 294 of 994
+r0:=1/4*d*x*(a+b*x^2)^(3/2)/b+1/8*a*(4*b*c-a*d)*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(3/2)+1/8*(4*b*c-a*d)*x*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 x\|b 3 +-+ | 2
+--R (- a d + 4a b c)atanh(-----------) + (2b d x + (a d + 4b c)x)\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R -----------------------------------------------------------------------------
+--R +-+
+--R 8b\|b
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 3 2 +-+ | 2
+--R ((4a b d - 16a b c)x + 8a d - 32a b c)\|a \|b x + a
+--R +
+--R 2 2 3 4 3 2 2 2 4 3
+--R (- a b d + 4a b c)x + (- 8a b d + 32a b c)x - 8a d + 32a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 3 7 2 3 5 2 2 3
+--R - 2b d x + (- 17a b d - 4b c)x + (- 24a b d - 32a b c)x
+--R +
+--R 3 2
+--R (- 8a d - 32a b c)x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 3 7 2 3 5 2 2 3
+--R 8b d x + (28a b d + 16b c)x + (28a b d + 48a b c)x
+--R +
+--R 3 2
+--R (8a d + 32a b c)x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+
+--R (32b x + 64a b)\|a \|b \|b x + a + (- 8b x - 64a b x - 64a b)\|b
+--R ,
+--R
+--R +--------+
+--R 2 2 2 3 2 +-+ | 2
+--R ((- 8a b d + 32a b c)x - 16a d + 64a b c)\|a \|b x + a
+--R +
+--R 2 2 3 4 3 2 2 2 4 3
+--R (2a b d - 8a b c)x + (16a b d - 64a b c)x + 16a d - 64a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 3 7 2 3 5 2 2 3
+--R - 2b d x + (- 17a b d - 4b c)x + (- 24a b d - 32a b c)x
+--R +
+--R 3 2
+--R (- 8a d - 32a b c)x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 3 7 2 3 5 2 2 3
+--R 8b d x + (28a b d + 16b c)x + (28a b d + 48a b c)x
+--R +
+--R 3 2
+--R (8a d + 32a b c)x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 2 2 +---+ +-+ | 2
+--R (32b x + 64a b)\|- b \|a \|b x + a
+--R +
+--R 3 4 2 2 2 +---+
+--R (- 8b x - 64a b x - 64a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 295
+
+--S 296 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2
+--R (a d - 4a b c)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R (a d - 4a b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 8b\|b
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +---+ x\|b
+--R (a d - 4a b c)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 2a d + 8a b c)\|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 8b\|- b \|b
+--R Type: Expression(Integer)
+--E 298
+
+--S 299 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 299
+
+)clear all
+
+--S 300 of 994
+t0:=(a+b*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R (1) \|b x + a
+--R Type: Expression(Integer)
+--E 300
+
+--S 301 of 994
+r0:=1/2*a*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+1/2*x*sqrt(a+b*x^2)
+--R
+--R
+--R +-+ +--------+
+--R x\|b +-+ | 2
+--R a atanh(-----------) + x\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ---------------------------------------
+--R +-+
+--R 2\|b
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2
+--R (2a\|a \|b x + a - a b x - 2a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (- b x - 2a x)\|b \|b x + a + (2b x + 2a x)\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 +-+
+--R 4\|a \|b \|b x + a + (- 2b x - 4a)\|b
+--R ,
+--R
+--R +--------+
+--R +--------+ +---+ | 2 +---+ +-+
+--R +-+ | 2 2 2 \|- b \|b x + a - \|- b \|a
+--R (4a\|a \|b x + a - 2a b x - 4a )atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R 3 +---+ | 2 3 +---+ +-+
+--R (- b x - 2a x)\|- b \|b x + a + (2b x + 2a x)\|- b \|a
+--R /
+--R +--------+
+--R +---+ +-+ | 2 2 +---+
+--R 4\|- b \|a \|b x + a + (- 2b x - 4a)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 302
+
+--S 303 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R - a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 2\|b
+--R Type: Expression(Integer)
+--E 303
+
+--S 304 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a
+--R - a\|- b atanh(-----------) + 2a\|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ------------------------------------------------------------------------
+--R +---+ +-+
+--R 2\|- b \|b
+--R Type: Expression(Integer)
+--E 305
+
+--S 306 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 306
+
+)clear all
+
+--S 307 of 994
+t0:=(a+b*x^2)^(1/2)/(c+d*x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R 2
+--R d x + c
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 994
+r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)/d-atanh(x*sqrt(b*c-a*d)/_
+ (sqrt(c)*sqrt(a+b*x^2)))*sqrt(b*c-a*d)/(d*sqrt(c))
+--R
+--R
+--R +-+ +-----------+
+--R +-+ +-+ x\|b +-----------+ x\|- a d + b c
+--R \|b \|c atanh(-----------) - \|- a d + b c atanh(---------------)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|b x + a \|c \|b x + a
+--R (2) -----------------------------------------------------------------
+--R +-+
+--R d\|c
+--R Type: Expression(Integer)
+--E 308
+
+--S 309 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 2\|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R /
+--R 2d
+--R ,
+--R
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R \|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +-+
+--R |a d - b c \|a
+--R |--------- atan(-------------)
+--R \| c +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R /
+--R d
+--R ,
+--R
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R | 2 +-+
+--R +---+ \|b x + a - \|a
+--R 4\|- b atan(------------------)
+--R +---+
+--R x\|- b
+--R /
+--R 2d
+--R ,
+--R
+--R +--------+
+--R | 2 +-+
+--R +---+ \|b x + a - \|a
+--R 2\|- b atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +-+
+--R |a d - b c \|a
+--R |--------- atan(-------------)
+--R \| c +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R /
+--R d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 309
+
+--S 310 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 2\|b \|c log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+ +-----------+
+--R +-+ +-+ x\|b +-----------+ x\|- a d + b c
+--R - 2\|b \|c atanh(-----------) + 2\|- a d + b c atanh(---------------)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|b x + a \|c \|b x + a
+--R /
+--R +-+
+--R 2d\|c
+--R Type: Expression(Integer)
+--E 310
+
+--S 311 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R \|b \|c log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+ +-----------+
+--R +-+ +-+ x\|b +-----------+ x\|- a d + b c
+--R - \|b \|c atanh(-----------) + \|- a d + b c atanh(---------------)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|b x + a \|c \|b x + a
+--R +
+--R +---------+
+--R +-+ |a d - b c
+--R \|c |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +-+
+--R +-+ |a d - b c \|a
+--R \|c |--------- atan(-------------)
+--R \| c +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R /
+--R +-+
+--R d\|c
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 313
+
+)clear all
+
+--S 314 of 994
+t0:=(a+b*x^2)^(1/2)/(c+d*x^2)^2
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 994
+r0:=1/2*a*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/(c^(3/2)*_
+ sqrt(b*c-a*d))+1/2*x*sqrt(a+b*x^2)/(c*(c+d*x^2))
+--R
+--R
+--R +-----------+ +--------+
+--R 2 x\|- a d + b c +-----------+ +-+ | 2
+--R (a d x + a c)atanh(---------------) + x\|- a d + b c \|c \|b x + a
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R (2) ---------------------------------------------------------------------
+--R 2 2 +-----------+ +-+
+--R (2c d x + 2c )\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 315
+
+--S 316 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R (2a d x + 2a c)\|a \|b x + a - a b d x + (- 2a d - a b c)x
+--R +
+--R 2
+--R - 2a c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +--------+
+--R 3 | 2 | 2
+--R (- 2b x - 4a x)\|- a c d + b c \|b x + a
+--R +
+--R +--------------+
+--R 3 | 2 +-+
+--R (4b x + 4a x)\|- a c d + b c \|a
+--R /
+--R +--------------+ +--------+
+--R 2 2 | 2 +-+ | 2
+--R (8c d x + 8c )\|- a c d + b c \|a \|b x + a
+--R +
+--R +--------------+
+--R 4 2 2 2 | 2
+--R (- 4b c d x + (- 8a c d - 4b c )x - 8a c )\|- a c d + b c
+--R ,
+--R
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R (2a d x + 2a c)\|a \|b x + a - a b d x + (- 2a d - a b c)x
+--R +
+--R 2
+--R - 2a c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R (2a d x + 2a c)\|a \|b x + a - a b d x + (- 2a d - a b c)x
+--R +
+--R 2
+--R - 2a c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R +------------+ +--------+
+--R 3 | 2 | 2
+--R (- b x - 2a x)\|a c d - b c \|b x + a
+--R +
+--R +------------+
+--R 3 +-+ | 2
+--R (2b x + 2a x)\|a \|a c d - b c
+--R /
+--R +------------+ +--------+
+--R 2 2 +-+ | 2 | 2
+--R (4c d x + 4c )\|a \|a c d - b c \|b x + a
+--R +
+--R +------------+
+--R 4 2 2 2 | 2
+--R (- 2b c d x + (- 4a c d - 2b c )x - 4a c )\|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 316
+
+--S 317 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R a\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - 2a\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R | 2 +-----------+ +-+
+--R 4c\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 318
+
+--S 319 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - a\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +-----------+ +-+
+--R a\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R +-----------+ +-+ \|a \|a c d - b c
+--R a\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R +-----------+ +-+ | 2
+--R 2c\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 994
+t0:=(a+b*x^2)^(1/2)/(c+d*x^2)^3
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 994
+r0:=1/8*a*(4*b*c-3*a*d)*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/_
+ (c^(5/2)*(b*c-a*d)^(3/2))+1/4*x*sqrt(a+b*x^2)/(c*(c+d*x^2)^2)+_
+ 1/8*(2*b*c-3*a*d)*x*sqrt(a+b*x^2)/(c^2*(b*c-a*d)*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 3 2 4 2 2 2 2 2 2 3
+--R ((3a d - 4a b c d )x + (6a c d - 8a b c d)x + 3a c d - 4a b c )
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +--------+
+--R 2 3 2 +-----------+ +-+ | 2
+--R ((3a d - 2b c d)x + (5a c d - 4b c )x)\|- a d + b c \|c \|b x + a
+--R /
+--R 2 3 3 2 4 3 2 4 2 4 5
+--R ((8a c d - 8b c d )x + (16a c d - 16b c d)x + 8a c d - 8b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 6 3 3 2 2 2 2 4
+--R (12a b d - 16a b c d )x + (24a d - 8a b c d - 32a b c d)x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (48a c d - 52a b c d - 16a b c )x + 24a c d - 32a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 3 3 2 8 3 3 2 2 2 3 2 6
+--R (- 3a b d + 4a b c d )x + (- 24a b d + 26a b c d + 8a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4
+--R (- 24a d - 16a b c d + 61a b c d + 4a b c )x
+--R +
+--R 4 2 3 2 2 2 3 2 4 2 3 3
+--R (- 48a c d + 40a b c d + 32a b c )x - 24a c d + 32a b c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R 2 2 3 7 2 2 2 3 2 5
+--R (- 6a b d + 4b c d)x + (- 48a b d + 22a b c d + 8b c )x
+--R +
+--R 3 2 2 2 2 3 3 2 2
+--R (- 48a d - 48a b c d + 64a b c )x + (- 80a c d + 64a b c )x
+--R *
+--R +--------------+ +--------+
+--R | 2 | 2
+--R \|- a c d + b c \|b x + a
+--R +
+--R 2 2 3 7 2 2 2 3 2 5
+--R (24a b d - 16b c d)x + (72a b d - 8a b c d - 32b c )x
+--R +
+--R 3 2 2 2 2 3 3 2 2
+--R (48a d + 88a b c d - 96a b c )x + (80a c d - 64a b c )x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 2 3 2 3 2 6 2 2 3 2 4 4
+--R (64a b c d - 64b c d )x + (128a c d - 128b c d)x
+--R +
+--R 2 3 2 4 2 5 2 2 4 5
+--R (256a c d - 192a b c d - 64b c )x + 128a c d - 128a b c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 2 2 3 3 3 2 8
+--R (- 16a b c d + 16b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 6
+--R (- 128a b c d + 96a b c d + 32b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4
+--R (- 128a c d - 128a b c d + 240a b c d + 16b c )x
+--R +
+--R 3 3 2 2 4 2 5 2 3 4 2 5
+--R (- 256a c d + 128a b c d + 128a b c )x - 128a c d + 128a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 2 3 2 2 6 3 3 2 2 2 2 4
+--R (12a b d - 16a b c d )x + (24a d - 8a b c d - 32a b c d)x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (48a c d - 52a b c d - 16a b c )x + 24a c d - 32a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 3 3 2 8 3 3 2 2 2 3 2 6
+--R (- 3a b d + 4a b c d )x + (- 24a b d + 26a b c d + 8a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4
+--R (- 24a d - 16a b c d + 61a b c d + 4a b c )x
+--R +
+--R 4 2 3 2 2 2 3 2 4 2 3 3
+--R (- 48a c d + 40a b c d + 32a b c )x - 24a c d + 32a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 2 3 2 2 6 3 3 2 2 2 2 4
+--R (12a b d - 16a b c d )x + (24a d - 8a b c d - 32a b c d)x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (48a c d - 52a b c d - 16a b c )x + 24a c d - 32a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 3 3 2 8 3 3 2 2 2 3 2 6
+--R (- 3a b d + 4a b c d )x + (- 24a b d + 26a b c d + 8a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4
+--R (- 24a d - 16a b c d + 61a b c d + 4a b c )x
+--R +
+--R 4 2 3 2 2 2 3 2 4 2 3 3
+--R (- 48a c d + 40a b c d + 32a b c )x - 24a c d + 32a b c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 2 3 7 2 2 2 3 2 5
+--R (- 3a b d + 2b c d)x + (- 24a b d + 11a b c d + 4b c )x
+--R +
+--R 3 2 2 2 2 3 3 2 2
+--R (- 24a d - 24a b c d + 32a b c )x + (- 40a c d + 32a b c )x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 2 3 7 2 2 2 3 2 5
+--R (12a b d - 8b c d)x + (36a b d - 4a b c d - 16b c )x
+--R +
+--R 3 2 2 2 2 3 3 2 2
+--R (24a d + 44a b c d - 48a b c )x + (40a c d - 32a b c )x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 2 3 2 3 2 6 2 2 3 2 4 4
+--R (32a b c d - 32b c d )x + (64a c d - 64b c d)x
+--R +
+--R 2 3 2 4 2 5 2 2 4 5
+--R (128a c d - 96a b c d - 32b c )x + 64a c d - 64a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 2 2 3 3 3 2 8 2 2 3 2 3 2 3 4 6
+--R (- 8a b c d + 8b c d )x + (- 64a b c d + 48a b c d + 16b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4
+--R (- 64a c d - 64a b c d + 120a b c d + 8b c )x
+--R +
+--R 3 3 2 2 4 2 5 2 3 4 2 5
+--R (- 128a c d + 64a b c d + 64a b c )x - 64a c d + 64a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 323
+
+--S 324 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----------+ +-+
+--R (3a d - 4a b c)\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (- 6a d + 8a b c)\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 3 | 2 +-----------+ +-+
+--R (16a c d - 16b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 325
+
+--S 326 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (- 3a d + 4a b c)\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 +-----------+ +-+
+--R (3a d - 4a b c)\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 2 +-----------+ +-+ \|a \|a c d - b c
+--R (3a d - 4a b c)\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 3 +-----------+ +-+ | 2
+--R (8a c d - 8b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 327
+
+)clear all
+
+--S 328 of 994
+t0:=(a+b*x^2)^(1/2)/(c+d*x^2)^4
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) ---------------------------------------
+--R 4 8 3 6 2 2 4 3 2 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R Type: Expression(Integer)
+--E 328
+
+--S 329 of 994
+r0:=1/16*a*(8*b^2*c^2-12*a*b*c*d+5*a^2*d^2)*atanh(x*sqrt(b*c-a*d)/_
+ (sqrt(c)*sqrt(a+b*x^2)))/(c^(7/2)*(b*c-a*d)^(5/2))+1/6*x*_
+ sqrt(a+b*x^2)/(c*(c+d*x^2)^3)+1/24*(4*b*c-5*a*d)*x*sqrt(a+_
+ b*x^2)/(c^2*(b*c-a*d)*(c+d*x^2)^2)+1/48*(2*b*c-5*a*d)*(4*b*c-_
+ 3*a*d)*x*sqrt(a+b*x^2)/(c^3*(b*c-a*d)^2*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 3 5 2 4 2 2 3 6
+--R (15a d - 36a b c d + 24a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 4
+--R (45a c d - 108a b c d + 72a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4 2 3 3 2 2 4
+--R (45a c d - 108a b c d + 72a b c d)x + 15a c d - 36a b c d
+--R +
+--R 2 5
+--R 24a b c
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 4 3 2 2 2 5
+--R (15a d - 26a b c d + 8b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4
+--R (40a c d - 70a b c d + 24b c d)x + (33a c d - 60a b c d + 24b c )x
+--R *
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+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|b x + a
+--R /
+--R 2 3 5 4 4 2 5 3 6
+--R (48a c d - 96a b c d + 48b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 4
+--R (144a c d - 288a b c d + 144b c d )x
+--R +
+--R 2 5 3 6 2 2 7 2 2 6 2 7 2 8
+--R (144a c d - 288a b c d + 144b c d)x + 48a c d - 96a b c d + 48b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 5 2 3 4 4 2 3 10
+--R (90a b d - 216a b c d + 144a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 8
+--R (480a b d - 882a b c d + 120a b c d + 432a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R 480a d + 288a b c d - 2418a b c d + 1656a b c d
+--R +
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+--R 432a b c d
+--R *
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+--R x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4
+--R 1440a c d - 2016a b c d - 1062a b c d + 2088a b c d
+--R +
+--R 4 5
+--R 144a b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 2 3 4 3 2 3 2 4 2 3 5 2
+--R (1440a c d - 2976a b c d + 1152a b c d + 768a b c )x
+--R +
+--R 5 3 2 4 4 3 2 5
+--R 480a c d - 1152a b c d + 768a b c
+--R *
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+--R +-+ | 2
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+--R +
+--R 3 3 5 2 4 4 5 2 3 12
+--R (- 15a b d + 36a b c d - 24a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5 3 2 10
+--R (- 270a b d + 603a b c d - 324a b c d - 72a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 720a b d + 918a b c d + 747a b c d - 1188a b c d
+--R +
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+--R - 72a b c d
+--R *
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+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2
+--R - 480a d - 1008a b c d + 3606a b c d - 1527a b c d
+--R +
+--R 2 4 4 5 5
+--R - 1260a b c d - 24a b c
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+--R 6
+--R x
+--R +
+--R 6 4 5 2 3 4 2 3 2 3 3 4
+--R - 1440a c d + 1296a b c d + 2610a b c d - 2808a b c d
+--R +
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+--R - 432a b c
+--R *
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+--R x
+--R +
+--R 6 2 3 5 3 2 4 2 4 3 3 5 2
+--R (- 1440a c d + 2736a b c d - 576a b c d - 1152a b c )x
+--R +
+--R 6 3 2 5 4 4 2 5
+--R - 480a c d + 1152a b c d - 768a b c
+--R *
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+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
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+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
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+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
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+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
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+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
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+--R (- 30a b d + 52a b c d - 16b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 9
+--R (- 540a b d + 856a b c d - 148a b c d - 48b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 1440a b d + 1056a b c d + 1686a b c d - 744a b c d
+--R +
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+--R - 48b c
+--R *
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+--R x
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+--R 5 4 4 3 3 2 2 2 2 3 3
+--R - 960a d - 2176a b c d + 5020a b c d - 144a b c d
+--R +
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+--R - 864a b c
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+--R x
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+--R 5 3 4 2 2 3 2 3 2 3 4 3
+--R (- 2560a c d + 1312a b c d + 4224a b c d - 2304a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4
+--R (- 2112a c d + 3840a b c d - 1536a b c )x
+--R *
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+--R \|- a c d + b c \|b x + a
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+--R (180a b d - 312a b c d + 96b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 9
+--R (1140a b d - 1496a b c d - 232a b c d + 288b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 7
+--R (1920a b d - 288a b c d - 3900a b c d + 1104a b c d + 288b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R 960a d + 3456a b c d - 5940a b c d - 1488a b c d
+--R +
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+--R 1824a b c
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+--R 5
+--R x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 3
+--R (2560a c d - 256a b c d - 6144a b c d + 3072a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4
+--R (2112a c d - 3840a b c d + 1536a b c )x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 2 2 3 5 3 4 4 4 5 3 10
+--R (576a b c d - 1152a b c d + 576b c d )x
+--R +
+--R 3 3 5 2 2 4 4 3 5 3 4 6 2 8
+--R (3072a b c d - 4416a b c d - 384a b c d + 1728b c d )x
+--R +
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2
+--R 3072a c d + 3072a b c d - 13632a b c d + 5760a b c d
+--R +
+--R 4 7
+--R 1728b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7
+--R 9216a c d - 9216a b c d - 8640a b c d + 8064a b c d
+--R +
+--R 4 8
+--R 576b c
+--R *
+--R 4
+--R x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8 2
+--R (9216a c d - 15360a b c d + 3072a b c d + 3072a b c )x
+--R +
+--R 4 6 2 3 7 2 2 8
+--R 3072a c d - 6144a b c d + 3072a b c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 2 3 3 5 4 4 4 5 5 3 12
+--R (- 96a b c d + 192a b c d - 96b c d )x
+--R +
+--R 3 2 3 5 2 3 4 4 4 5 3 5 6 2 10
+--R (- 1728a b c d + 3168a b c d - 1152a b c d - 288b c d )x
+--R +
+--R 4 3 5 3 2 4 4 2 3 5 3 4 6 2
+--R - 4608a b c d + 4032a b c d + 5472a b c d - 4608a b c d
+--R +
+--R 5 7
+--R - 288b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2
+--R - 3072a c d - 7680a b c d + 19392a b c d - 3552a b c d
+--R +
+--R 4 7 5 8
+--R - 4992a b c d - 96b c
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 4 4 5 3 3 2 6 2 2 3 7
+--R - 9216a c d + 4608a b c d + 16704a b c d - 10368a b c d
+--R +
+--R 4 8
+--R - 1728a b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 3 4 6 2 2 3 8 2 5 6 2
+--R (- 9216a c d + 13824a b c d - 4608a b c )x - 3072a c d
+--R +
+--R 4 7 3 2 8
+--R 6144a b c d - 3072a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 3 2 5 2 3 4 4 2 3 10
+--R (90a b d - 216a b c d + 144a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 8
+--R (480a b d - 882a b c d + 120a b c d + 432a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R 480a d + 288a b c d - 2418a b c d + 1656a b c d
+--R +
+--R 4 4
+--R 432a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4
+--R 1440a c d - 2016a b c d - 1062a b c d + 2088a b c d
+--R +
+--R 4 5
+--R 144a b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 2 3 4 3 2 3 2 4 2 3 5 2
+--R (1440a c d - 2976a b c d + 1152a b c d + 768a b c )x
+--R +
+--R 5 3 2 4 4 3 2 5
+--R 480a c d - 1152a b c d + 768a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 5 2 4 4 5 2 3 12
+--R (- 15a b d + 36a b c d - 24a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5 3 2 10
+--R (- 270a b d + 603a b c d - 324a b c d - 72a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 720a b d + 918a b c d + 747a b c d - 1188a b c d
+--R +
+--R 5 4
+--R - 72a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2
+--R - 480a d - 1008a b c d + 3606a b c d - 1527a b c d
+--R +
+--R 2 4 4 5 5
+--R - 1260a b c d - 24a b c
+--R *
+--R 6
+--R x
+--R +
+--R 6 4 5 2 3 4 2 3 2 3 3 4
+--R - 1440a c d + 1296a b c d + 2610a b c d - 2808a b c d
+--R +
+--R 2 4 5
+--R - 432a b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 2 3 5 3 2 4 2 4 3 3 5 2
+--R (- 1440a c d + 2736a b c d - 576a b c d - 1152a b c )x
+--R +
+--R 6 3 2 5 4 4 2 5
+--R - 480a c d + 1152a b c d - 768a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 3 2 5 2 3 4 4 2 3 10
+--R (90a b d - 216a b c d + 144a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 8
+--R (480a b d - 882a b c d + 120a b c d + 432a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R 480a d + 288a b c d - 2418a b c d + 1656a b c d
+--R +
+--R 4 4
+--R 432a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4
+--R 1440a c d - 2016a b c d - 1062a b c d + 2088a b c d
+--R +
+--R 4 5
+--R 144a b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 2 3 4 3 2 3 2 4 2 3 5 2
+--R (1440a c d - 2976a b c d + 1152a b c d + 768a b c )x
+--R +
+--R 5 3 2 4 4 3 2 5
+--R 480a c d - 1152a b c d + 768a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 5 2 4 4 5 2 3 12
+--R (- 15a b d + 36a b c d - 24a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5 3 2 10
+--R (- 270a b d + 603a b c d - 324a b c d - 72a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 720a b d + 918a b c d + 747a b c d - 1188a b c d
+--R +
+--R 5 4
+--R - 72a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2
+--R - 480a d - 1008a b c d + 3606a b c d - 1527a b c d
+--R +
+--R 2 4 4 5 5
+--R - 1260a b c d - 24a b c
+--R *
+--R 6
+--R x
+--R +
+--R 6 4 5 2 3 4 2 3 2 3 3 4
+--R - 1440a c d + 1296a b c d + 2610a b c d - 2808a b c d
+--R +
+--R 2 4 5
+--R - 432a b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 2 3 5 3 2 4 2 4 3 3 5 2
+--R (- 1440a c d + 2736a b c d - 576a b c d - 1152a b c )x
+--R +
+--R 6 3 2 5 4 4 2 5
+--R - 480a c d + 1152a b c d - 768a b c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 3 4 4 3 5 2 2 11
+--R (- 15a b d + 26a b c d - 8b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 9
+--R (- 270a b d + 428a b c d - 74a b c d - 24b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 7
+--R (- 720a b d + 528a b c d + 843a b c d - 372a b c d - 24b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4 5
+--R (- 480a d - 1088a b c d + 2510a b c d - 72a b c d - 432a b c )x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 3
+--R (- 1280a c d + 656a b c d + 2112a b c d - 1152a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4
+--R (- 1056a c d + 1920a b c d - 768a b c )x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 3 4 4 3 5 2 2 11
+--R (90a b d - 156a b c d + 48b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 9
+--R (570a b d - 748a b c d - 116a b c d + 144b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 7
+--R (960a b d - 144a b c d - 1950a b c d + 552a b c d + 144b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4 5
+--R (480a d + 1728a b c d - 2970a b c d - 744a b c d + 912a b c )x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 3
+--R (1280a c d - 128a b c d - 3072a b c d + 1536a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4
+--R (1056a c d - 1920a b c d + 768a b c )x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 2 2 3 5 3 4 4 4 5 3 10
+--R (288a b c d - 576a b c d + 288b c d )x
+--R +
+--R 3 3 5 2 2 4 4 3 5 3 4 6 2 8
+--R (1536a b c d - 2208a b c d - 192a b c d + 864b c d )x
+--R +
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2
+--R 1536a c d + 1536a b c d - 6816a b c d + 2880a b c d
+--R +
+--R 4 7
+--R 864b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7
+--R 4608a c d - 4608a b c d - 4320a b c d + 4032a b c d
+--R +
+--R 4 8
+--R 288b c
+--R *
+--R 4
+--R x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8 2
+--R (4608a c d - 7680a b c d + 1536a b c d + 1536a b c )x
+--R +
+--R 4 6 2 3 7 2 2 8
+--R 1536a c d - 3072a b c d + 1536a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 2 3 3 5 4 4 4 5 5 3 12
+--R (- 48a b c d + 96a b c d - 48b c d )x
+--R +
+--R 3 2 3 5 2 3 4 4 4 5 3 5 6 2 10
+--R (- 864a b c d + 1584a b c d - 576a b c d - 144b c d )x
+--R +
+--R 4 3 5 3 2 4 4 2 3 5 3 4 6 2
+--R - 2304a b c d + 2016a b c d + 2736a b c d - 2304a b c d
+--R +
+--R 5 7
+--R - 144b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2
+--R - 1536a c d - 3840a b c d + 9696a b c d - 1776a b c d
+--R +
+--R 4 7 5 8
+--R - 2496a b c d - 48b c
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 4 4 5 3 3 2 6 2 2 3 7
+--R - 4608a c d + 2304a b c d + 8352a b c d - 5184a b c d
+--R +
+--R 4 8
+--R - 864a b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 3 4 6 2 2 3 8 2 5 6 2
+--R (- 4608a c d + 6912a b c d - 2304a b c )x - 1536a c d
+--R +
+--R 4 7 3 2 8
+--R 3072a b c d - 1536a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 330
+
+--S 331 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 2 2 2 2 +-----------+ +-+
+--R (5a d - 12a b c d + 8a b c )\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 3 2 2 2 2 | 2 x\|- a d + b c
+--R (- 10a d + 24a b c d - 16a b c )\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 3 2 4 2 5 | 2 +-----------+ +-+
+--R (32a c d - 64a b c d + 32b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 3 2 2 2 2 | 2 x\|- a d + b c
+--R (- 5a d + 12a b c d - 8a b c )\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 3 2 2 2 2 +-----------+ +-+
+--R (5a d - 12a b c d + 8a b c )\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 3 2 2 2 2 +-----------+ +-+ \|a \|a c d - b c
+--R (5a d - 12a b c d + 8a b c )\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 3 2 4 2 5 +-----------+ +-+ | 2
+--R (16a c d - 32a b c d + 16b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 333
+
+--S 334 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 334
+
+)clear all
+
+--S 335 of 994
+t0:=(a+b*x^2)^(3/2)*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 3 8 3 2 6 2 2 4 2 3 2
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3
+--R a c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 335
+
+--S 336 of 994
+r0:=1/128*(4*b*c-a*d)*(8*b^2*c^2-2*a*b*c*d+a^2*d^2)*x*(a+b*x^2)^(3/2)/_
+ b^3+1/160*d*(44*b^2*c^2-28*a*b*c*d+5*a^2*d^2)*x*(a+b*x^2)^(5/2)/_
+ b^3+1/10*d*x*(a+b*x^2)^(5/2)*(c+d*x^2)^2/b+1/80*d*x*(a+_
+ b*x^2)^(5/2)*(c*(10*b*c-a*d)+d*(14*b*c-5*a*d)*x^2)/b^2+3/256*_
+ a^2*(4*b*c-a*d)*(8*b^2*c^2-2*a*b*c*d+a^2*d^2)*atanh(x*_
+ sqrt(b)/sqrt(a+b*x^2))/b^(7/2)+3/256*a*(4*b*c-a*d)*(8*b^2*_
+ c^2-2*a*b*c*d+a^2*d^2)*x*sqrt(a+b*x^2)/b^3
+--R
+--R
+--R (2)
+--R +-+
+--R 5 3 4 2 3 2 2 2 3 3 x\|b
+--R (- 15a d + 90a b c d - 240a b c d + 480a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 3 9 3 3 4 2 7
+--R 128b d x + (176a b d + 480b c d )x
+--R +
+--R 2 2 3 3 2 4 2 5
+--R (8a b d + 720a b c d + 640b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 10a b d + 60a b c d + 1120a b c d + 320b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (15a d - 90a b c d + 240a b c d + 800a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 3 +-+
+--R 1280b \|b
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 5 4 3 4 5 2 3 6 2 2 7 3 8
+--R (150a b d - 900a b c d + 2400a b c d - 4800a b c )x
+--R +
+--R 6 3 3 5 4 2 4 5 2 3 6 3 6
+--R (2400a b d - 14400a b c d + 38400a b c d - 76800a b c )x
+--R +
+--R 7 2 3 6 3 2 5 4 2 4 5 3 4
+--R (10080a b d - 60480a b c d + 161280a b c d - 322560a b c )x
+--R +
+--R 8 3 7 2 2 6 3 2 5 4 3 2
+--R (15360a b d - 92160a b c d + 245760a b c d - 491520a b c )x
+--R +
+--R 9 3 8 2 7 2 2 6 3 3
+--R 7680a d - 46080a b c d + 122880a b c d - 245760a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 5 3 4 6 2 3 7 2 2 8 3 10
+--R (- 15a b d + 90a b c d - 240a b c d + 480a b c )x
+--R +
+--R 6 4 3 5 5 2 4 6 2 3 7 3 8
+--R (- 750a b d + 4500a b c d - 12000a b c d + 24000a b c )x
+--R +
+--R 7 3 3 6 4 2 5 5 2 4 6 3 6
+--R (- 6000a b d + 36000a b c d - 96000a b c d + 192000a b c )x
+--R +
+--R 8 2 3 7 3 2 6 4 2 5 5 3 4
+--R (- 16800a b d + 100800a b c d - 268800a b c d + 537600a b c )x
+--R +
+--R 9 3 8 2 2 7 3 2 6 4 3 2
+--R (- 19200a b d + 115200a b c d - 307200a b c d + 614400a b c )x
+--R +
+--R 10 3 9 2 8 2 2 7 3 3
+--R - 7680a d + 46080a b c d - 122880a b c d + 245760a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 9 3 19 8 3 9 2 17
+--R - 128b d x + (- 6576a b d - 480b c d )x
+--R +
+--R 2 7 3 8 2 9 2 15
+--R (- 60008a b d - 24720a b c d - 640b c d)x
+--R +
+--R 3 6 3 2 7 2 8 2 9 3 13
+--R (- 214150a b d - 228060a b c d - 33120a b c d - 320b c )x
+--R +
+--R 4 5 3 3 6 2 2 7 2 8 3 11
+--R (- 363675a b d - 828510a b c d - 312240a b c d - 16800a b c )x
+--R +
+--R 5 4 3 4 5 2 3 6 2
+--R - 296526a b d - 1440300a b c d - 1176800a b c d
+--R +
+--R 2 7 3
+--R - 168000a b c
+--R *
+--R 9
+--R x
+--R +
+--R 6 3 3 5 4 2 4 5 2 3 6 3 7
+--R (- 95152a b d - 1198560a b c d - 2169600a b c d - 678400a b c )x
+--R +
+--R 7 2 3 6 3 2 5 4 2 4 5 3 5
+--R (- 8096a b d - 344640a b c d - 2030080a b c d - 1305600a b c )x
+--R +
+--R 8 3 7 2 2 6 3 2 5 4 3 3
+--R (- 14080a b d + 84480a b c d - 880640a b c d - 1187840a b c )x
+--R +
+--R 9 3 8 2 7 2 2 6 3 3
+--R (- 7680a d + 46080a b c d - 122880a b c d - 409600a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 9 3 19 8 3 9 2 17
+--R 1280b d x + (23520a b d + 4800b c d )x
+--R +
+--R 2 7 3 8 2 9 2 15
+--R (136496a b d + 88800a b c d + 6400b c d)x
+--R +
+--R 3 6 3 2 7 2 8 2 9 3 13
+--R (364780a b d + 522360a b c d + 120000a b c d + 3200b c )x
+--R +
+--R 4 5 3 3 6 2 2 7 2 8 3 11
+--R (500210a b d + 1422420a b c d + 725280a b c d + 62400a b c )x
+--R +
+--R 5 4 3 4 5 2 3 6 2 2 7 3 9
+--R (343670a b d + 1993020a b c d + 2058080a b c d + 402240a b c )x
+--R +
+--R 6 3 3 5 4 2 4 5 2 3 6 3 7
+--R (97920a b d + 1378560a b c d + 3082240a b c d + 1208320a b c )x
+--R +
+--R 7 2 3 6 3 2 5 4 2 4 5 3 5
+--R (14176a b d + 308160a b c d + 2455040a b c d + 1848320a b c )x
+--R +
+--R 8 3 7 2 2 6 3 2 5 4 3 3
+--R (17920a b d - 107520a b c d + 942080a b c d + 1392640a b c )x
+--R +
+--R 9 3 8 2 7 2 2 6 3 3
+--R (7680a d - 46080a b c d + 122880a b c d + 409600a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 7 8 6 6 2 5 4 3 4 2
+--R 12800b x + 204800a b x + 860160a b x + 1310720a b x
+--R +
+--R 4 3
+--R 655360a b
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 8 10 7 8 2 6 6 3 5 4
+--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x
+--R +
+--R 4 4 2 5 3
+--R - 1638400a b x - 655360a b
+--R *
+--R +-+
+--R \|b
+--R ,
+--R
+--R 5 4 3 4 5 2 3 6 2 2 7 3 8
+--R (- 300a b d + 1800a b c d - 4800a b c d + 9600a b c )x
+--R +
+--R 6 3 3 5 4 2 4 5 2 3 6 3 6
+--R (- 4800a b d + 28800a b c d - 76800a b c d + 153600a b c )x
+--R +
+--R 7 2 3 6 3 2 5 4 2
+--R - 20160a b d + 120960a b c d - 322560a b c d
+--R +
+--R 4 5 3
+--R 645120a b c
+--R *
+--R 4
+--R x
+--R +
+--R 8 3 7 2 2 6 3 2
+--R - 30720a b d + 184320a b c d - 491520a b c d
+--R +
+--R 5 4 3
+--R 983040a b c
+--R *
+--R 2
+--R x
+--R +
+--R 9 3 8 2 7 2 2 6 3 3
+--R - 15360a d + 92160a b c d - 245760a b c d + 491520a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 5 3 4 6 2 3 7 2 2 8 3 10
+--R (30a b d - 180a b c d + 480a b c d - 960a b c )x
+--R +
+--R 6 4 3 5 5 2 4 6 2 3 7 3 8
+--R (1500a b d - 9000a b c d + 24000a b c d - 48000a b c )x
+--R +
+--R 7 3 3 6 4 2 5 5 2 4 6 3 6
+--R (12000a b d - 72000a b c d + 192000a b c d - 384000a b c )x
+--R +
+--R 8 2 3 7 3 2 6 4 2 5 5 3 4
+--R (33600a b d - 201600a b c d + 537600a b c d - 1075200a b c )x
+--R +
+--R 9 3 8 2 2 7 3 2 6 4 3 2
+--R (38400a b d - 230400a b c d + 614400a b c d - 1228800a b c )x
+--R +
+--R 10 3 9 2 8 2 2 7 3 3
+--R 15360a d - 92160a b c d + 245760a b c d - 491520a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 9 3 19 8 3 9 2 17
+--R - 128b d x + (- 6576a b d - 480b c d )x
+--R +
+--R 2 7 3 8 2 9 2 15
+--R (- 60008a b d - 24720a b c d - 640b c d)x
+--R +
+--R 3 6 3 2 7 2 8 2 9 3 13
+--R (- 214150a b d - 228060a b c d - 33120a b c d - 320b c )x
+--R +
+--R 4 5 3 3 6 2 2 7 2 8 3 11
+--R (- 363675a b d - 828510a b c d - 312240a b c d - 16800a b c )x
+--R +
+--R 5 4 3 4 5 2 3 6 2
+--R - 296526a b d - 1440300a b c d - 1176800a b c d
+--R +
+--R 2 7 3
+--R - 168000a b c
+--R *
+--R 9
+--R x
+--R +
+--R 6 3 3 5 4 2 4 5 2 3 6 3 7
+--R (- 95152a b d - 1198560a b c d - 2169600a b c d - 678400a b c )x
+--R +
+--R 7 2 3 6 3 2 5 4 2 4 5 3 5
+--R (- 8096a b d - 344640a b c d - 2030080a b c d - 1305600a b c )x
+--R +
+--R 8 3 7 2 2 6 3 2 5 4 3 3
+--R (- 14080a b d + 84480a b c d - 880640a b c d - 1187840a b c )x
+--R +
+--R 9 3 8 2 7 2 2 6 3 3
+--R (- 7680a d + 46080a b c d - 122880a b c d - 409600a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 9 3 19 8 3 9 2 17
+--R 1280b d x + (23520a b d + 4800b c d )x
+--R +
+--R 2 7 3 8 2 9 2 15
+--R (136496a b d + 88800a b c d + 6400b c d)x
+--R +
+--R 3 6 3 2 7 2 8 2 9 3 13
+--R (364780a b d + 522360a b c d + 120000a b c d + 3200b c )x
+--R +
+--R 4 5 3 3 6 2 2 7 2 8 3 11
+--R (500210a b d + 1422420a b c d + 725280a b c d + 62400a b c )x
+--R +
+--R 5 4 3 4 5 2 3 6 2 2 7 3 9
+--R (343670a b d + 1993020a b c d + 2058080a b c d + 402240a b c )x
+--R +
+--R 6 3 3 5 4 2 4 5 2 3 6 3 7
+--R (97920a b d + 1378560a b c d + 3082240a b c d + 1208320a b c )x
+--R +
+--R 7 2 3 6 3 2 5 4 2 4 5 3 5
+--R (14176a b d + 308160a b c d + 2455040a b c d + 1848320a b c )x
+--R +
+--R 8 3 7 2 2 6 3 2 5 4 3 3
+--R (17920a b d - 107520a b c d + 942080a b c d + 1392640a b c )x
+--R +
+--R 9 3 8 2 7 2 2 6 3 3
+--R (7680a d - 46080a b c d + 122880a b c d + 409600a b c )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R 7 8 6 6 2 5 4 3 4 2
+--R 12800b x + 204800a b x + 860160a b x + 1310720a b x
+--R +
+--R 4 3
+--R 655360a b
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 8 10 7 8 2 6 6 3 5 4
+--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x
+--R +
+--R 4 4 2 5 3
+--R - 1638400a b x - 655360a b
+--R *
+--R +---+
+--R \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 337
+
+--S 338 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 5 3 4 2 3 2 2 2 3 3
+--R (3a d - 18a b c d + 48a b c d - 96a b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 5 3 4 2 3 2 2 2 3 3 x\|b
+--R (3a d - 18a b c d + 48a b c d - 96a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 256b \|b
+--R Type: Expression(Integer)
+--E 338
+
+--S 339 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 5 3 4 2 3 2 2 2 3 3 +---+ x\|b
+--R (3a d - 18a b c d + 48a b c d - 96a b c )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 3 4 2 3 2 2 2 3 3 +-+
+--R (- 6a d + 36a b c d - 96a b c d + 192a b c )\|b
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 256b \|- b \|b
+--R Type: Expression(Integer)
+--E 340
+
+--S 341 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 341
+
+)clear all
+
+--S 342 of 994
+t0:=(a+b*x^2)^(3/2)*(c+d*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (1) (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 994
+r0:=1/192*(48*b^2*c^2-16*a*b*c*d+3*a^2*d^2)*x*(a+b*x^2)^(3/2)/b^2+_
+ 1/48*d*(10*b*c-3*a*d)*x*(a+b*x^2)^(5/2)/b^2+1/8*d*x*(a+b*_
+ x^2)^(5/2)*(c+d*x^2)/b+1/128*a^2*(48*b^2*c^2-16*a*b*c*d+3*_
+ a^2*d^2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)+1/128*a*_
+ (48*b^2*c^2-16*a*b*c*d+3*a^2*d^2)*x*sqrt(a+b*x^2)/b^2
+--R
+--R
+--R (2)
+--R +-+
+--R 4 2 3 2 2 2 x\|b
+--R (9a d - 48a b c d + 144a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 7 2 2 3 5
+--R 48b d x + (72a b d + 128b c d)x
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R (6a b d + 224a b c d + 96b c )x + (- 9a d + 48a b c d + 240a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 2 +-+
+--R 384b \|b
+--R Type: Expression(Integer)
+--E 343
+
+--S 344 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 3 2 3 4 2 5 2 6
+--R (72a b d - 384a b c d + 1152a b c )x
+--R +
+--R 5 2 2 4 3 3 4 2 4
+--R (720a b d - 3840a b c d + 11520a b c )x
+--R +
+--R 6 2 5 2 4 3 2 2 7 2
+--R (1728a b d - 9216a b c d + 27648a b c )x + 1152a d
+--R +
+--R 6 5 2 2
+--R - 6144a b c d + 18432a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 2 3 5 2 6 2 8
+--R (- 9a b d + 48a b c d - 144a b c )x
+--R +
+--R 5 3 2 4 4 3 5 2 6
+--R (- 288a b d + 1536a b c d - 4608a b c )x
+--R +
+--R 6 2 2 5 3 4 4 2 4
+--R (- 1440a b d + 7680a b c d - 23040a b c )x
+--R +
+--R 7 2 6 2 5 3 2 2 8 2
+--R (- 2304a b d + 12288a b c d - 36864a b c )x - 1152a d
+--R +
+--R 7 6 2 2
+--R 6144a b c d - 18432a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 7 2 15 6 2 7 13
+--R - 48b d x + (- 1608a b d - 128b c d)x
+--R +
+--R 2 5 2 6 7 2 11
+--R (- 9990a b d - 4320a b c d - 96b c )x
+--R +
+--R 3 4 2 2 5 6 2 9
+--R (- 23991a b d - 27696a b c d - 3312a b c )x
+--R +
+--R 4 3 2 3 4 2 5 2 7
+--R (- 25248a b d - 70144a b c d - 23040a b c )x
+--R +
+--R 5 2 2 4 3 3 4 2 5
+--R (- 9312a b d - 81408a b c d - 62976a b c )x
+--R +
+--R 6 2 5 2 4 3 2 3
+--R (1536a b d - 40960a b c d - 73728a b c )x
+--R +
+--R 7 2 6 5 2 2
+--R (1152a d - 6144a b c d - 30720a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 7 2 15 6 2 7 13
+--R 384b d x + (4800a b d + 1024b c d)x
+--R +
+--R 2 5 2 6 7 2 11
+--R (19440a b d + 13056a b c d + 768b c )x
+--R +
+--R 3 4 2 2 5 6 2 9
+--R (35400a b d + 54912a b c d + 10368a b c )x
+--R +
+--R 4 3 2 3 4 2 5 2 7
+--R (30024a b d + 106112a b c d + 47232a b c )x
+--R +
+--R 5 2 2 4 3 3 4 2 5
+--R (8688a b d + 101120a b c d + 96000a b c )x
+--R +
+--R 6 2 5 2 4 3 2 3
+--R (- 2112a b d + 44032a b c d + 89088a b c )x
+--R +
+--R 7 2 6 5 2 2
+--R (- 1152a d + 6144a b c d + 30720a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 +-+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b )\|a \|b \|b x + a
+--R +
+--R 6 8 5 6 2 4 4 3 3 2 4 2 +-+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b )\|b
+--R ,
+--R
+--R 4 3 2 3 4 2 5 2 6
+--R (144a b d - 768a b c d + 2304a b c )x
+--R +
+--R 5 2 2 4 3 3 4 2 4
+--R (1440a b d - 7680a b c d + 23040a b c )x
+--R +
+--R 6 2 5 2 4 3 2 2 7 2
+--R (3456a b d - 18432a b c d + 55296a b c )x + 2304a d
+--R +
+--R 6 5 2 2
+--R - 12288a b c d + 36864a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 2 3 5 2 6 2 8
+--R (- 18a b d + 96a b c d - 288a b c )x
+--R +
+--R 5 3 2 4 4 3 5 2 6
+--R (- 576a b d + 3072a b c d - 9216a b c )x
+--R +
+--R 6 2 2 5 3 4 4 2 4
+--R (- 2880a b d + 15360a b c d - 46080a b c )x
+--R +
+--R 7 2 6 2 5 3 2 2 8 2
+--R (- 4608a b d + 24576a b c d - 73728a b c )x - 2304a d
+--R +
+--R 7 6 2 2
+--R 12288a b c d - 36864a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 7 2 15 6 2 7 13
+--R - 48b d x + (- 1608a b d - 128b c d)x
+--R +
+--R 2 5 2 6 7 2 11
+--R (- 9990a b d - 4320a b c d - 96b c )x
+--R +
+--R 3 4 2 2 5 6 2 9
+--R (- 23991a b d - 27696a b c d - 3312a b c )x
+--R +
+--R 4 3 2 3 4 2 5 2 7
+--R (- 25248a b d - 70144a b c d - 23040a b c )x
+--R +
+--R 5 2 2 4 3 3 4 2 5
+--R (- 9312a b d - 81408a b c d - 62976a b c )x
+--R +
+--R 6 2 5 2 4 3 2 3
+--R (1536a b d - 40960a b c d - 73728a b c )x
+--R +
+--R 7 2 6 5 2 2
+--R (1152a d - 6144a b c d - 30720a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 7 2 15 6 2 7 13
+--R 384b d x + (4800a b d + 1024b c d)x
+--R +
+--R 2 5 2 6 7 2 11
+--R (19440a b d + 13056a b c d + 768b c )x
+--R +
+--R 3 4 2 2 5 6 2 9
+--R (35400a b d + 54912a b c d + 10368a b c )x
+--R +
+--R 4 3 2 3 4 2 5 2 7
+--R (30024a b d + 106112a b c d + 47232a b c )x
+--R +
+--R 5 2 2 4 3 3 4 2 5
+--R (8688a b d + 101120a b c d + 96000a b c )x
+--R +
+--R 6 2 5 2 4 3 2 3
+--R (- 2112a b d + 44032a b c d + 89088a b c )x
+--R +
+--R 7 2 6 5 2 2
+--R (- 1152a d + 6144a b c d + 30720a b c )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 +---+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b )\|- b \|a \|b x + a
+--R +
+--R 6 8 5 6 2 4 4 3 3 2 4 2 +---+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 344
+
+--S 345 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 2 3 2 2 2
+--R (3a d - 16a b c d + 48a b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 4 2 3 2 2 2 x\|b
+--R (- 3a d + 16a b c d - 48a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 128b \|b
+--R Type: Expression(Integer)
+--E 345
+
+--S 346 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 4 2 3 2 2 2 +---+ x\|b
+--R (- 3a d + 16a b c d - 48a b c )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 4 2 3 2 2 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (6a d - 32a b c d + 96a b c )\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 128b \|- b \|b
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 348
+
+)clear all
+
+--S 349 of 994
+t0:=(a+b*x^2)^(3/2)*(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (1) (b d x + (a d + b c)x + a c)\|b x + a
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 994
+r0:=1/24*(6*b*c-a*d)*x*(a+b*x^2)^(3/2)/b+1/6*d*x*(a+b*x^2)^(5/2)/b+_
+ 1/16*a^2*(6*b*c-a*d)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_
+ 1/16*a*(6*b*c-a*d)*x*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 x\|b
+--R (- 3a d + 18a b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 2 5 2 3 2 +-+ | 2
+--R (8b d x + (14a b d + 12b c)x + (3a d + 30a b c)x)\|b \|b x + a
+--R /
+--R +-+
+--R 48b\|b
+--R Type: Expression(Integer)
+--E 350
+
+--S 351 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 2 3 4 4 3 2 2 5
+--R (18a b d - 108a b c)x + (96a b d - 576a b c)x + 96a d
+--R +
+--R 4
+--R - 576a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 2 4 6 4 2 3 3 4
+--R (- 3a b d + 18a b c)x + (- 54a b d + 324a b c)x
+--R +
+--R 5 4 2 2 6 5
+--R (- 144a b d + 864a b c)x - 96a d + 576a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 5 11 4 5 9 2 3 4 7
+--R - 8b d x + (- 158a b d - 12b c)x + (- 639a b d - 246a b c)x
+--R +
+--R 3 2 2 3 5 4 3 2 3
+--R (- 982a b d - 1116a b c)x + (- 592a b d - 1824a b c)x
+--R +
+--R 5 4
+--R (- 96a d - 960a b c)x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 5 11 4 5 9 2 3 4 7
+--R 48b d x + (388a b d + 72b c)x + (1062a b d + 636a b c)x
+--R +
+--R 3 2 2 3 5 4 3 2 3
+--R (1266a b d + 1908a b c)x + (640a b d + 2304a b c)x
+--R +
+--R 5 4
+--R (96a d + 960a b c)x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 3 4 2 2 2 +-+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b)\|a \|b \|b x + a
+--R +
+--R 4 6 3 4 2 2 2 3 +-+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b)\|b
+--R ,
+--R
+--R 3 2 2 3 4 4 3 2 2 5
+--R (- 36a b d + 216a b c)x + (- 192a b d + 1152a b c)x - 192a d
+--R +
+--R 4
+--R 1152a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 2 4 6 4 2 3 3 4
+--R (6a b d - 36a b c)x + (108a b d - 648a b c)x
+--R +
+--R 5 4 2 2 6 5
+--R (288a b d - 1728a b c)x + 192a d - 1152a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 5 11 4 5 9 2 3 4 7
+--R - 8b d x + (- 158a b d - 12b c)x + (- 639a b d - 246a b c)x
+--R +
+--R 3 2 2 3 5 4 3 2 3
+--R (- 982a b d - 1116a b c)x + (- 592a b d - 1824a b c)x
+--R +
+--R 5 4
+--R (- 96a d - 960a b c)x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 11 4 5 9 2 3 4 7
+--R 48b d x + (388a b d + 72b c)x + (1062a b d + 636a b c)x
+--R +
+--R 3 2 2 3 5 4 3 2 3
+--R (1266a b d + 1908a b c)x + (640a b d + 2304a b c)x
+--R +
+--R 5 4
+--R (96a d + 960a b c)x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 3 4 2 2 2 +---+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b)\|- b \|a \|b x + a
+--R +
+--R 4 6 3 4 2 2 2 3 +---+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 351
+
+--S 352 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 2
+--R (a d - 6a b c)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 2 x\|b
+--R (a d - 6a b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 16b\|b
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 353
+
+--S 354 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 3 2 +---+ x\|b
+--R (a d - 6a b c)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 3 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 2a d + 12a b c)\|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 16b\|- b \|b
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 994
+t0:=(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (1) (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 994
+r0:=1/4*x*(a+b*x^2)^(3/2)+3/8*a^2*atanh(x*sqrt(b)/sqrt(a+b*x^2))/_
+ sqrt(b)+3/8*a*x*sqrt(a+b*x^2)
+--R
+--R
+--R +-+ +--------+
+--R 2 x\|b 3 +-+ | 2
+--R 3a atanh(-----------) + (2b x + 5a x)\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -----------------------------------------------------
+--R +-+
+--R 8\|b
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((12a b x + 24a )\|a \|b x + a - 3a b x - 24a b x - 24a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 3 7 2 5 2 3 3 +-+ | 2
+--R (- 2b x - 21a b x - 56a b x - 40a x)\|b \|b x + a
+--R +
+--R 3 7 2 5 2 3 3 +-+ +-+
+--R (8b x + 44a b x + 76a b x + 40a x)\|a \|b
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 4 2 2 +-+
+--R (32b x + 64a)\|a \|b \|b x + a + (- 8b x - 64a b x - 64a )\|b
+--R ,
+--R
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((24a b x + 48a )\|a \|b x + a - 6a b x - 48a b x - 48a )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R 3 7 2 5 2 3 3 +---+ | 2
+--R (- 2b x - 21a b x - 56a b x - 40a x)\|- b \|b x + a
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+
+--R (8b x + 44a b x + 76a b x + 40a x)\|- b \|a
+--R /
+--R +--------+
+--R 2 +---+ +-+ | 2 2 4 2 2 +---+
+--R (32b x + 64a)\|- b \|a \|b x + a + (- 8b x - 64a b x - 64a )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 358
+
+--S 359 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 2 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R 3a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R - 3a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 8\|b
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+--S 361 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 2 +---+ x\|b 2 +-+ \|- b \|b x + a - \|- b \|a
+--R - 3a \|- b atanh(-----------) + 6a \|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ---------------------------------------------------------------------------
+--R +---+ +-+
+--R 8\|- b \|b
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 362
+
+)clear all
+
+--S 363 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 2
+--R d x + c
+--R Type: Expression(Integer)
+--E 363
+
+--S 364 of 994
+r0:=-1/2*(2*b*c-3*a*d)*atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)/d^2+_
+ (b*c-a*d)^(3/2)*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/_
+ (d^2*sqrt(c))+1/2*b*x*sqrt(a+b*x^2)/d
+--R
+--R
+--R (2)
+--R +-+
+--R +-+ +-+ x\|b
+--R (3a d - 2b c)\|b \|c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+ +--------+
+--R +-----------+ x\|- a d + b c +-+ | 2
+--R (- 2a d + 2b c)\|- a d + b c atanh(---------------) + b d x\|c \|b x + a
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R 2 +-+
+--R 2d \|c
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R (2a d - 2b c) |----------- \|a \|b x + a
+--R \| c
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c
+--R ((- a b d + b c)x - 2a d + 2a b c) |-----------
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2
+--R (6a d - 4b c)\|a \|b \|b x + a
+--R +
+--R 2 2 2 +-+
+--R ((- 3a b d + 2b c)x - 6a d + 4a b c)\|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 2 3 | 2 2 3 +-+
+--R (- b d x - 2a b d x)\|b x + a + (2b d x + 2a b d x)\|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2
+--R 4d \|a \|b x + a - 2b d x - 4a d
+--R ,
+--R
+--R +--------+
+--R +-+ +-+ | 2
+--R (6a d - 4b c)\|a \|b \|b x + a
+--R +
+--R 2 2 2 +-+
+--R ((- 3a b d + 2b c)x - 6a d + 4a b c)\|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R (4a d - 4b c)\|a |--------- \|b x + a
+--R \| c
+--R +
+--R +---------+
+--R 2 2 2 |a d - b c
+--R ((- 2a b d + 2b c)x - 4a d + 4a b c) |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R (4a d - 4b c)\|a |--------- \|b x + a
+--R \| c
+--R +
+--R +---------+
+--R 2 2 2 |a d - b c
+--R ((- 2a b d + 2b c)x - 4a d + 4a b c) |---------
+--R \| c
+--R *
+--R +-+
+--R \|a
+--R atan(-------------)
+--R +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R +
+--R +--------+
+--R 2 3 | 2 2 3 +-+
+--R (- b d x - 2a b d x)\|b x + a + (2b d x + 2a b d x)\|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2
+--R 4d \|a \|b x + a - 2b d x - 4a d
+--R ,
+--R
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R (2a d - 2b c) |----------- \|a \|b x + a
+--R \| c
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c
+--R ((- a b d + b c)x - 2a d + 2a b c) |-----------
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R +---+ +-+ | 2
+--R (12a d - 8b c)\|- b \|a \|b x + a
+--R +
+--R 2 2 2 +---+
+--R ((- 6a b d + 4b c)x - 12a d + 8a b c)\|- b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +--------+
+--R 2 3 | 2 2 3 +-+
+--R (- b d x - 2a b d x)\|b x + a + (2b d x + 2a b d x)\|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2
+--R 4d \|a \|b x + a - 2b d x - 4a d
+--R ,
+--R
+--R +--------+
+--R +---+ +-+ | 2
+--R (12a d - 8b c)\|- b \|a \|b x + a
+--R +
+--R 2 2 2 +---+
+--R ((- 6a b d + 4b c)x - 12a d + 8a b c)\|- b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R (4a d - 4b c)\|a |--------- \|b x + a
+--R \| c
+--R +
+--R +---------+
+--R 2 2 2 |a d - b c
+--R ((- 2a b d + 2b c)x - 4a d + 4a b c) |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R (4a d - 4b c)\|a |--------- \|b x + a
+--R \| c
+--R +
+--R +---------+
+--R 2 2 2 |a d - b c
+--R ((- 2a b d + 2b c)x - 4a d + 4a b c) |---------
+--R \| c
+--R *
+--R +-+
+--R \|a
+--R atan(-------------)
+--R +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R +
+--R +--------+
+--R 2 3 | 2 2 3 +-+
+--R (- b d x - 2a b d x)\|b x + a + (2b d x + 2a b d x)\|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2
+--R 4d \|a \|b x + a - 2b d x - 4a d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 365
+
+--S 366 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R |- a d + b c +-+
+--R (a d - b c) |----------- \|c
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +-+ +-+
+--R (3a d - 2b c)\|b \|c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R (- 3a d + 2b c)\|b \|c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (2a d - 2b c)\|- a d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R 2 +-+
+--R 2d \|c
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+ +-+
+--R (3a d - 2b c)\|b \|c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R (- 3a d + 2b c)\|b \|c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (2a d - 2b c)\|- a d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +---------+
+--R +-+ |a d - b c
+--R (2a d - 2b c)\|c |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +-+
+--R +-+ |a d - b c \|a
+--R (2a d - 2b c)\|c |--------- atan(-------------)
+--R \| c +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R /
+--R 2 +-+
+--R 2d \|c
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 369
+
+)clear all
+
+--S 370 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Expression(Integer)
+--E 370
+
+--S 371 of 994
+r0:=b^(3/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/d^2-1/2*(2*b*c+a*d)*_
+ atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))*sqrt(b*c-a*d)/_
+ (c^(3/2)*d^2)-1/2*(b*c-a*d)*x*sqrt(a+b*x^2)/(c*d*(c+d*x^2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R (2b c d x + 2b c )\|b \|c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 2 2 2 +-----------+ x\|- a d + b c
+--R ((- a d - 2b c d)x - a c d - 2b c )\|- a d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R (a d - b c d)x\|c \|b x + a
+--R /
+--R 3 2 2 2 +-+
+--R (2c d x + 2c d )\|c
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+ +--------+
+--R 2 2 2 |- a d + b c +-+ | 2
+--R ((2a d + 4b c d)x + 2a c d + 4b c ) |----------- \|a \|b x + a
+--R \| c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 2b c d)x + (- 2a d - 5a b c d - 2b c )x - 2a c d
+--R +
+--R 2
+--R - 4a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 +-+ +-+ | 2
+--R (8b c d x + 8b c )\|a \|b \|b x + a
+--R +
+--R 2 4 2 2 2 2 +-+
+--R (- 4b c d x + (- 8a b c d - 4b c )x - 8a b c )\|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 2 2 3 2 2 | 2
+--R ((- 2a b d + 2b c d)x + (- 4a d + 4a b c d)x)\|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a b d - 4b c d)x + (4a d - 4a b c d)x)\|a
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ | 2 3 4 3 2 2 2
+--R (8c d x + 8c d )\|a \|b x + a - 4b c d x + (- 8a c d - 4b c d )x
+--R +
+--R 2 2
+--R - 8a c d
+--R ,
+--R
+--R +--------+
+--R 2 2 +-+ +-+ | 2
+--R (4b c d x + 4b c )\|a \|b \|b x + a
+--R +
+--R 2 4 2 2 2 2 +-+
+--R (- 2b c d x + (- 4a b c d - 2b c )x - 4a b c )\|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +---------+ +--------+
+--R 2 2 2 +-+ |a d - b c | 2
+--R ((2a d + 4b c d)x + 2a c d + 4b c )\|a |--------- \|b x + a
+--R \| c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 2b c d)x + (- 2a d - 5a b c d - 2b c )x - 2a c d
+--R +
+--R 2
+--R - 4a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +--------+
+--R 2 2 2 +-+ |a d - b c | 2
+--R ((2a d + 4b c d)x + 2a c d + 4b c )\|a |--------- \|b x + a
+--R \| c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 2b c d)x + (- 2a d - 5a b c d - 2b c )x - 2a c d
+--R +
+--R 2
+--R - 4a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| c
+--R *
+--R +-+
+--R \|a
+--R atan(-------------)
+--R +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R +
+--R +--------+
+--R 2 2 3 2 2 | 2
+--R ((- a b d + b c d)x + (- 2a d + 2a b c d)x)\|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((2a b d - 2b c d)x + (2a d - 2a b c d)x)\|a
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ | 2 3 4 3 2 2 2
+--R (4c d x + 4c d )\|a \|b x + a - 2b c d x + (- 4a c d - 2b c d )x
+--R +
+--R 2 2
+--R - 4a c d
+--R ,
+--R
+--R +-----------+ +--------+
+--R 2 2 2 |- a d + b c +-+ | 2
+--R ((2a d + 4b c d)x + 2a c d + 4b c ) |----------- \|a \|b x + a
+--R \| c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 2b c d)x + (- 2a d - 5a b c d - 2b c )x - 2a c d
+--R +
+--R 2
+--R - 4a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 +---+ +-+ | 2
+--R (16b c d x + 16b c )\|- b \|a \|b x + a
+--R +
+--R 2 4 2 2 2 2 +---+
+--R (- 8b c d x + (- 16a b c d - 8b c )x - 16a b c )\|- b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +--------+
+--R 2 2 3 2 2 | 2
+--R ((- 2a b d + 2b c d)x + (- 4a d + 4a b c d)x)\|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a b d - 4b c d)x + (4a d - 4a b c d)x)\|a
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ | 2 3 4 3 2 2 2
+--R (8c d x + 8c d )\|a \|b x + a - 4b c d x + (- 8a c d - 4b c d )x
+--R +
+--R 2 2
+--R - 8a c d
+--R ,
+--R
+--R +--------+
+--R 2 2 +---+ +-+ | 2
+--R (8b c d x + 8b c )\|- b \|a \|b x + a
+--R +
+--R 2 4 2 2 2 2 +---+
+--R (- 4b c d x + (- 8a b c d - 4b c )x - 8a b c )\|- b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +---------+ +--------+
+--R 2 2 2 +-+ |a d - b c | 2
+--R ((2a d + 4b c d)x + 2a c d + 4b c )\|a |--------- \|b x + a
+--R \| c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 2b c d)x + (- 2a d - 5a b c d - 2b c )x - 2a c d
+--R +
+--R 2
+--R - 4a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +--------+
+--R 2 2 2 +-+ |a d - b c | 2
+--R ((2a d + 4b c d)x + 2a c d + 4b c )\|a |--------- \|b x + a
+--R \| c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 2b c d)x + (- 2a d - 5a b c d - 2b c )x - 2a c d
+--R +
+--R 2
+--R - 4a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| c
+--R *
+--R +-+
+--R \|a
+--R atan(-------------)
+--R +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R +
+--R +--------+
+--R 2 2 3 2 2 | 2
+--R ((- a b d + b c d)x + (- 2a d + 2a b c d)x)\|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((2a b d - 2b c d)x + (2a d - 2a b c d)x)\|a
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ | 2 3 4 3 2 2 2
+--R (4c d x + 4c d )\|a \|b x + a - 2b c d x + (- 4a c d - 2b c d )x
+--R +
+--R 2 2
+--R - 4a c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 372
+
+--S 373 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R |- a d + b c +-+
+--R (a d + 2b c) |----------- \|c
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 4b c\|b \|c log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R - 4b c\|b \|c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (2a d + 4b c)\|- a d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R 2 +-+
+--R 4c d \|c
+--R Type: Expression(Integer)
+--E 373
+
+--S 374 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 2b c\|b \|c log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R - 2b c\|b \|c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (a d + 2b c)\|- a d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +---------+
+--R +-+ |a d - b c
+--R (a d + 2b c)\|c |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +-+
+--R +-+ |a d - b c \|a
+--R (a d + 2b c)\|c |--------- atan(-------------)
+--R \| c +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R /
+--R 2 +-+
+--R 2c d \|c
+--R Type: Expression(Integer)
+--E 375
+
+--S 376 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 376
+
+)clear all
+
+--S 377 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)^3
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 994
+r0:=3/8*a^2*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/(c^(5/2)*_
+ sqrt(b*c-a*d))-1/4*(b*c-a*d)*x*sqrt(a+b*x^2)/(c*d*(c+d*x^2)^2)+_
+ 1/8*(2*b*c+3*a*d)*x*sqrt(a+b*x^2)/(c^2*d*(c+d*x^2))
+--R
+--R
+--R (2)
+--R +-----------+
+--R 2 2 4 2 2 2 2 x\|- a d + b c
+--R (3a d x + 6a c d x + 3a c )atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +--------+
+--R 3 +-----------+ +-+ | 2
+--R ((3a d + 2b c)x + 5a c x)\|- a d + b c \|c \|b x + a
+--R /
+--R 2 2 4 3 2 4 +-----------+ +-+
+--R (8c d x + 16c d x + 8c )\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 378
+
+--S 379 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 6 3 2 2 4 3 2 2 2
+--R 12a b d x + (24a d + 24a b c d)x + (48a c d + 12a b c )x
+--R +
+--R 3 2
+--R 24a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 2 8 3 2 2 2 6
+--R - 3a b d x + (- 24a b d - 6a b c d)x
+--R +
+--R 4 2 3 2 2 2 4 4 3 2 2
+--R (- 24a d - 48a b c d - 3a b c )x + (- 48a c d - 24a b c )x
+--R +
+--R 4 2
+--R - 24a c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R 2 3 7 2 2 5
+--R (- 6a b d - 4b c)x + (- 48a b d - 42a b c)x
+--R +
+--R 3 2 3 3
+--R (- 48a d - 112a b c)x - 80a c x
+--R *
+--R +--------------+ +--------+
+--R | 2 | 2
+--R \|- a c d + b c \|b x + a
+--R +
+--R 2 3 7 2 2 5 3 2 3
+--R (24a b d + 16b c)x + (72a b d + 88a b c)x + (48a d + 152a b c)x
+--R +
+--R 3
+--R 80a c x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 2 2 6 2 2 3 4 3 4 2
+--R 64b c d x + (128a c d + 128b c d)x + (256a c d + 64b c )x
+--R +
+--R 4
+--R 128a c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 2 2 2 8 2 2 2 3 6
+--R - 16b c d x + (- 128a b c d - 32b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (- 128a c d - 256a b c d - 16b c )x + (- 256a c d - 128a b c )x
+--R +
+--R 2 4
+--R - 128a c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 2 2 6 3 2 2 4 3 2 2 2
+--R 12a b d x + (24a d + 24a b c d)x + (48a c d + 12a b c )x
+--R +
+--R 3 2
+--R 24a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 2 8 3 2 2 2 6
+--R - 3a b d x + (- 24a b d - 6a b c d)x
+--R +
+--R 4 2 3 2 2 2 4 4 3 2 2
+--R (- 24a d - 48a b c d - 3a b c )x + (- 48a c d - 24a b c )x
+--R +
+--R 4 2
+--R - 24a c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 2 2 6 3 2 2 4 3 2 2 2
+--R 12a b d x + (24a d + 24a b c d)x + (48a c d + 12a b c )x
+--R +
+--R 3 2
+--R 24a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 2 8 3 2 2 2 6
+--R - 3a b d x + (- 24a b d - 6a b c d)x
+--R +
+--R 4 2 3 2 2 2 4 4 3 2 2
+--R (- 24a d - 48a b c d - 3a b c )x + (- 48a c d - 24a b c )x
+--R +
+--R 4 2
+--R - 24a c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 3 7 2 2 5
+--R (- 3a b d - 2b c)x + (- 24a b d - 21a b c)x
+--R +
+--R 3 2 3 3
+--R (- 24a d - 56a b c)x - 40a c x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 3 7 2 2 5 3 2 3
+--R (12a b d + 8b c)x + (36a b d + 44a b c)x + (24a d + 76a b c)x
+--R +
+--R 3
+--R 40a c x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 2 2 6 2 2 3 4 3 4 2
+--R 32b c d x + (64a c d + 64b c d)x + (128a c d + 32b c )x
+--R +
+--R 4
+--R 64a c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 2 2 2 8 2 2 2 3 6
+--R - 8b c d x + (- 64a b c d - 16b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (- 64a c d - 128a b c d - 8b c )x + (- 128a c d - 64a b c )x
+--R +
+--R 2 4
+--R - 64a c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 379
+
+--S 380 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----------+ +-+
+--R 3a \|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R - 6a \|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 | 2 +-----------+ +-+
+--R 16c \|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 380
+
+--S 381 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R - 3a \|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 +-----------+ +-+
+--R 3a \|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 2 +-----------+ +-+ \|a \|a c d - b c
+--R 3a \|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 +-----------+ +-+ | 2
+--R 8c \|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 383
+
+)clear all
+
+--S 384 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)^4
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------------------------
+--R 4 8 3 6 2 2 4 3 2 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 994
+r0:=1/16*a^2*(6*b*c-5*a*d)*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*_
+ sqrt(a+b*x^2)))/(c^(7/2)*(b*c-a*d)^(3/2))-1/6*(b*c-a*d)*x*_
+ sqrt(a+b*x^2)/(c*d*(c+d*x^2)^3)+1/24*(2*b*c+5*a*d)*x*_
+ sqrt(a+b*x^2)/(c^2*d*(c+d*x^2)^2)+1/48*(4*b^2*c^2+8*a*b*c*_
+ d-15*a^2*d^2)*x*sqrt(a+b*x^2)/(c^3*d*(b*c-a*d)*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 3 4 2 3 6 3 3 2 2 2 4
+--R (15a d - 18a b c d )x + (45a c d - 54a b c d )x
+--R +
+--R 3 2 2 2 3 2 3 3 2 4
+--R (45a c d - 54a b c d)x + 15a c d - 18a b c
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 3 2 2 2 5 2 2 2 2 3 3
+--R (15a d - 8a b c d - 4b c d)x + (40a c d - 22a b c d - 12b c )x
+--R +
+--R 2 2 3
+--R (33a c d - 30a b c )x
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|b x + a
+--R /
+--R 3 4 4 3 6 4 3 5 2 4
+--R (48a c d - 48b c d )x + (144a c d - 144b c d )x
+--R +
+--R 5 2 6 2 6 7
+--R (144a c d - 144b c d)x + 48a c d - 48b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 385
+
+--S 386 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 4 2 3 3 10
+--R (90a b d - 108a b c d )x
+--R +
+--R 4 4 3 2 3 2 3 2 2 8
+--R (480a b d - 306a b c d - 324a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 6
+--R (480a d + 864a b c d - 1458a b c d - 324a b c d)x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 4
+--R (1440a c d - 288a b c d - 1638a b c d - 108a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4 2 5 3 4 4
+--R (1440a c d - 1248a b c d - 576a b c )x + 480a c d - 576a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 4 2 4 3 12
+--R (- 15a b d + 18a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 4 2 2 10
+--R (- 270a b d + 279a b c d + 54a b c d )x
+--R +
+--R 5 4 4 2 3 3 3 2 2 2 4 3 8
+--R (- 720a b d + 54a b c d + 927a b c d + 54a b c d)x
+--R +
+--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 6
+--R (- 480a d - 1584a b c d + 1782a b c d + 957a b c d + 18a b c )x
+--R +
+--R 6 3 5 2 2 4 2 3 3 3 4 4
+--R (- 1440a c d - 432a b c d + 2322a b c d + 324a b c )x
+--R +
+--R 6 2 2 5 3 4 2 4 2 6 3 5 4
+--R (- 1440a c d + 1008a b c d + 864a b c )x - 480a c d + 576a b c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R 2 3 3 4 2 5 2 11
+--R (- 30a b d + 16a b c d + 8b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 9
+--R (- 540a b d + 208a b c d + 188a b c d + 24b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 7
+--R (- 1440a b d - 672a b c d + 1110a b c d + 492a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3 5
+--R (- 960a d - 3328a b c d + 1180a b c d + 2232a b c )x
+--R +
+--R 5 2 4 2 3 2 3 3
+--R (- 2560a c d - 1760a b c d + 3648a b c )x
+--R +
+--R 5 2 4 3
+--R (- 2112a c d + 1920a b c )x
+--R *
+--R +--------------+ +--------+
+--R | 2 | 2
+--R \|- a c d + b c \|b x + a
+--R +
+--R 2 3 3 4 2 5 2 11
+--R (180a b d - 96a b c d - 48b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 9
+--R (1140a b d - 128a b c d - 568a b c d - 144b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 7
+--R (1920a b d + 2016a b c d - 1788a b c d - 1272a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3 5
+--R (960a d + 4608a b c d - 564a b c d - 3816a b c )x
+--R +
+--R 5 2 4 2 3 2 3 3 5 2 4 3
+--R (2560a c d + 2816a b c d - 4608a b c )x + (2112a c d - 1920a b c )x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 2 3 4 3 4 3 10
+--R (576a b c d - 576b c d )x
+--R +
+--R 2 3 4 2 4 3 3 5 2 8
+--R (3072a b c d - 1344a b c d - 1728b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 6
+--R (3072a c d + 6144a b c d - 7488a b c d - 1728b c d)x
+--R +
+--R 3 4 3 2 6 3 7 4
+--R (9216a c d - 8640a b c d - 576b c )x
+--R +
+--R 3 5 2 2 6 2 7 2 3 6 2 7
+--R (9216a c d - 6144a b c d - 3072a b c )x + 3072a c d - 3072a b c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 3 3 4 4 4 3 12
+--R (- 96a b c d + 96b c d )x
+--R +
+--R 2 2 3 4 3 4 3 4 5 2 10
+--R (- 1728a b c d + 1440a b c d + 288b c d )x
+--R +
+--R 3 3 4 2 2 4 3 3 5 2 4 6 8
+--R (- 4608a b c d - 576a b c d + 4896a b c d + 288b c d)x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6
+--R - 3072a c d - 10752a b c d + 8640a b c d + 5088a b c d
+--R +
+--R 4 7
+--R 96b c
+--R *
+--R 6
+--R x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7 4
+--R (- 9216a c d - 4608a b c d + 12096a b c d + 1728a b c )x
+--R +
+--R 4 5 2 3 6 2 2 7 2 4 6 3 7
+--R (- 9216a c d + 4608a b c d + 4608a b c )x - 3072a c d + 3072a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 3 2 4 2 3 3 10
+--R (90a b d - 108a b c d )x
+--R +
+--R 4 4 3 2 3 2 3 2 2 8
+--R (480a b d - 306a b c d - 324a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 6
+--R (480a d + 864a b c d - 1458a b c d - 324a b c d)x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 4
+--R (1440a c d - 288a b c d - 1638a b c d - 108a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4 2 5 3 4 4
+--R (1440a c d - 1248a b c d - 576a b c )x + 480a c d - 576a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 4 2 4 3 12
+--R (- 15a b d + 18a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 4 2 2 10
+--R (- 270a b d + 279a b c d + 54a b c d )x
+--R +
+--R 5 4 4 2 3 3 3 2 2 2 4 3 8
+--R (- 720a b d + 54a b c d + 927a b c d + 54a b c d)x
+--R +
+--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 6
+--R (- 480a d - 1584a b c d + 1782a b c d + 957a b c d + 18a b c )x
+--R +
+--R 6 3 5 2 2 4 2 3 3 3 4 4
+--R (- 1440a c d - 432a b c d + 2322a b c d + 324a b c )x
+--R +
+--R 6 2 2 5 3 4 2 4 2 6 3 5 4
+--R (- 1440a c d + 1008a b c d + 864a b c )x - 480a c d + 576a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 3 2 4 2 3 3 10
+--R (90a b d - 108a b c d )x
+--R +
+--R 4 4 3 2 3 2 3 2 2 8
+--R (480a b d - 306a b c d - 324a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 6
+--R (480a d + 864a b c d - 1458a b c d - 324a b c d)x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 4
+--R (1440a c d - 288a b c d - 1638a b c d - 108a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4 2 5 3 4 4
+--R (1440a c d - 1248a b c d - 576a b c )x + 480a c d - 576a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 4 2 4 3 12
+--R (- 15a b d + 18a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 4 2 2 10
+--R (- 270a b d + 279a b c d + 54a b c d )x
+--R +
+--R 5 4 4 2 3 3 3 2 2 2 4 3 8
+--R (- 720a b d + 54a b c d + 927a b c d + 54a b c d)x
+--R +
+--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 6
+--R (- 480a d - 1584a b c d + 1782a b c d + 957a b c d + 18a b c )x
+--R +
+--R 6 3 5 2 2 4 2 3 3 3 4 4
+--R (- 1440a c d - 432a b c d + 2322a b c d + 324a b c )x
+--R +
+--R 6 2 2 5 3 4 2 4 2 6 3 5 4
+--R (- 1440a c d + 1008a b c d + 864a b c )x - 480a c d + 576a b c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 3 3 4 2 5 2 11
+--R (- 15a b d + 8a b c d + 4b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 9
+--R (- 270a b d + 104a b c d + 94a b c d + 12b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 7
+--R (- 720a b d - 336a b c d + 555a b c d + 246a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3 5
+--R (- 480a d - 1664a b c d + 590a b c d + 1116a b c )x
+--R +
+--R 5 2 4 2 3 2 3 3
+--R (- 1280a c d - 880a b c d + 1824a b c )x
+--R +
+--R 5 2 4 3
+--R (- 1056a c d + 960a b c )x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 3 3 4 2 5 2 11
+--R (90a b d - 48a b c d - 24b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 9
+--R (570a b d - 64a b c d - 284a b c d - 72b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 7
+--R (960a b d + 1008a b c d - 894a b c d - 636a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3 5
+--R (480a d + 2304a b c d - 282a b c d - 1908a b c )x
+--R +
+--R 5 2 4 2 3 2 3 3 5 2 4 3
+--R (1280a c d + 1408a b c d - 2304a b c )x + (1056a c d - 960a b c )x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 2 3 4 3 4 3 10
+--R (288a b c d - 288b c d )x
+--R +
+--R 2 3 4 2 4 3 3 5 2 8
+--R (1536a b c d - 672a b c d - 864b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 6
+--R (1536a c d + 3072a b c d - 3744a b c d - 864b c d)x
+--R +
+--R 3 4 3 2 6 3 7 4
+--R (4608a c d - 4320a b c d - 288b c )x
+--R +
+--R 3 5 2 2 6 2 7 2 3 6 2 7
+--R (4608a c d - 3072a b c d - 1536a b c )x + 1536a c d - 1536a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 3 3 4 4 4 3 12
+--R (- 48a b c d + 48b c d )x
+--R +
+--R 2 2 3 4 3 4 3 4 5 2 10
+--R (- 864a b c d + 720a b c d + 144b c d )x
+--R +
+--R 3 3 4 2 2 4 3 3 5 2 4 6 8
+--R (- 2304a b c d - 288a b c d + 2448a b c d + 144b c d)x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6
+--R - 1536a c d - 5376a b c d + 4320a b c d + 2544a b c d
+--R +
+--R 4 7
+--R 48b c
+--R *
+--R 6
+--R x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7 4
+--R (- 4608a c d - 2304a b c d + 6048a b c d + 864a b c )x
+--R +
+--R 4 5 2 3 6 2 2 7 2 4 6 3 7
+--R (- 4608a c d + 2304a b c d + 2304a b c )x - 1536a c d + 1536a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 386
+
+--S 387 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 2 +-----------+ +-+
+--R (5a d - 6a b c)\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 3 2 | 2 x\|- a d + b c
+--R (- 10a d + 12a b c)\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 3 4 | 2 +-----------+ +-+
+--R (32a c d - 32b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 388
+
+--S 389 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 3 2 | 2 x\|- a d + b c
+--R (- 5a d + 6a b c)\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 3 2 +-----------+ +-+
+--R (5a d - 6a b c)\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 3 2 +-----------+ +-+ \|a \|a c d - b c
+--R (5a d - 6a b c)\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 3 4 +-----------+ +-+ | 2
+--R (16a c d - 16b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)^5
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ----------------------------------------------------
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R d x + 5c d x + 10c d x + 10c d x + 5c d x + c
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 994
+r0:=1/128*a^2*(48*b^2*c^2-80*a*b*c*d+35*a^2*d^2)*atanh(x*sqrt(b*c-_
+ a*d)/(sqrt(c)*sqrt(a+b*x^2)))/(c^(9/2)*(b*c-a*d)^(5/2))-_
+ 1/8*(b*c-a*d)*x*sqrt(a+b*x^2)/(c*d*(c+d*x^2)^4)+1/48*(2*b*c+_
+ 7*a*d)*x*sqrt(a+b*x^2)/(c^2*d*(c+d*x^2)^3)+1/192*(8*b^2*c^2+_
+ 24*a*b*c*d-35*a^2*d^2)*x*sqrt(a+b*x^2)/(c^3*d*(b*c-a*d)*(c+_
+ d*x^2)^2)+1/384*(16*b^3*c^3+40*a*b^2*c^2*d-170*a^2*b*c*d^2+_
+ 105*a^3*d^3)*x*sqrt(a+b*x^2)/(c^4*d*(b*c-a*d)^2*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 4 6 3 5 2 2 2 4 8
+--R (105a d - 240a b c d + 144a b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 6
+--R (420a c d - 960a b c d + 576a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 4
+--R (630a c d - 1440a b c d + 864a b c d )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 2 4 4 2 3 5
+--R (420a c d - 960a b c d + 576a b c d)x + 105a c d - 240a b c d
+--R +
+--R 2 2 6
+--R 144a b c
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 7
+--R (105a d - 170a b c d + 40a b c d + 16b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 5
+--R (385a c d - 628a b c d + 152a b c d + 64b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 3
+--R (511a c d - 842a b c d + 208a b c d + 96b c )x
+--R +
+--R 3 3 2 2 4 2 5
+--R (279a c d - 528a b c d + 240a b c )x
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|b x + a
+--R /
+--R 2 4 6 5 5 2 6 4 8
+--R (384a c d - 768a b c d + 384b c d )x
+--R +
+--R 2 5 5 6 4 2 7 3 6
+--R (1536a c d - 3072a b c d + 1536b c d )x
+--R +
+--R 2 6 4 7 3 2 8 2 4
+--R (2304a c d - 4608a b c d + 2304b c d )x
+--R +
+--R 2 7 3 8 2 2 9 2 2 8 2 9
+--R (1536a c d - 3072a b c d + 1536b c d)x + 384a c d - 768a b c d
+--R +
+--R 2 10
+--R 384b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 3 6 3 4 5 2 5 2 4 14
+--R (840a b d - 1920a b c d + 1152a b c d )x
+--R +
+--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 12
+--R (8400a b d - 15840a b c d + 3840a b c d + 4608a b c d )x
+--R +
+--R 6 6 5 2 5 4 3 2 4 3 4 3 3
+--R 20160a b d - 12480a b c d - 44112a b c d + 34560a b c d
+--R +
+--R 2 5 4 2
+--R 6912a b c d
+--R *
+--R 10
+--R x
+--R +
+--R 7 6 6 5 5 2 2 4 4 3 3 3
+--R 13440a d + 49920a b c d - 115488a b c d - 1248a b c d
+--R +
+--R 3 4 4 2 2 5 5
+--R 61440a b c d + 4608a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 7 5 6 2 4 5 2 3 3 4 3 4 2
+--R 53760a c d - 1920a b c d - 169152a b c d + 89928a b c d
+--R +
+--R 3 4 5 2 5 6
+--R 44160a b c d + 1152a b c
+--R *
+--R 6
+--R x
+--R +
+--R 7 2 4 6 3 3 5 2 4 2 4 3 5
+--R 80640a c d - 103680a b c d - 65328a b c d + 91392a b c d
+--R +
+--R 3 4 6
+--R 11520a b c
+--R *
+--R 4
+--R x
+--R +
+--R 7 3 3 6 4 2 5 2 5 4 3 6 2
+--R (53760a c d - 102720a b c d + 27648a b c d + 27648a b c )x
+--R +
+--R 7 4 2 6 5 5 2 6
+--R 13440a c d - 30720a b c d + 18432a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 6 3 5 5 2 6 2 4 16
+--R (- 105a b d + 240a b c d - 144a b c d )x
+--R +
+--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 14
+--R (- 3360a b d + 7260a b c d - 3648a b c d - 576a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3
+--R - 16800a b d + 24960a b c d + 7050a b c d - 16992a b c d
+--R +
+--R 2 6 4 2
+--R - 864a b c d
+--R *
+--R 12
+--R x
+--R +
+--R 7 6 6 2 5 5 3 2 4 4 4 3 3
+--R - 26880a b d - 5760a b c d + 96576a b c d - 46500a b c d
+--R +
+--R 3 5 4 2 2 6 5
+--R - 26688a b c d - 576a b c d
+--R *
+--R 10
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+--R (30720a b c d - 49152a b c d + 6144a b c d + 12288b c d )x
+--R +
+--R 4 4 6 3 2 5 5 2 3 6 4 4 7 3
+--R 73728a b c d - 24576a b c d - 153600a b c d + 86016a b c d
+--R +
+--R 5 8 2
+--R 18432b c d
+--R *
+--R 10
+--R x
+--R +
+--R 5 4 6 4 5 5 3 2 6 4 2 3 7 3
+--R 49152a c d + 196608a b c d - 356352a b c d - 61440a b c d
+--R +
+--R 4 8 2 5 9
+--R 159744a b c d + 12288b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 5 5 4 6 4 3 2 7 3 2 3 8 2
+--R 196608a c d + 49152a b c d - 565248a b c d + 199680a b c d
+--R +
+--R 4 9 5 10
+--R 116736a b c d + 3072b c
+--R *
+--R 6
+--R x
+--R +
+--R 5 6 4 4 7 3 3 2 8 2 2 3 9
+--R 294912a c d - 294912a b c d - 264192a b c d + 233472a b c d
+--R +
+--R 4 10
+--R 30720a b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 7 3 4 8 2 3 2 9 2 3 10 2
+--R (196608a c d - 319488a b c d + 49152a b c d + 73728a b c )x
+--R +
+--R 5 8 2 4 9 3 2 10
+--R 49152a c d - 98304a b c d + 49152a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 2 4 4 6 5 5 5 6 6 4 16
+--R (- 384a b c d + 768a b c d - 384b c d )x
+--R +
+--R 3 3 4 6 2 4 5 5 5 6 4 6 7 3 14
+--R (- 12288a b c d + 23040a b c d - 9216a b c d - 1536b c d )x
+--R +
+--R 4 2 4 6 3 3 5 5 2 4 6 4 5 7 3
+--R - 61440a b c d + 73728a b c d + 34560a b c d - 44544a b c d
+--R +
+--R 6 8 2
+--R - 2304b c d
+--R *
+--R 12
+--R x
+--R +
+--R 5 4 6 4 2 5 5 3 3 6 4
+--R - 98304a b c d - 49152a b c d + 319488a b c d
+--R +
+--R 2 4 7 3 5 8 2 6 9
+--R - 99840a b c d - 70656a b c d - 1536b c d
+--R *
+--R 10
+--R x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4
+--R - 49152a c d - 294912a b c d + 368640a b c d
+--R +
+--R 3 3 7 3 2 4 8 2 5 9 6 10
+--R 294912a b c d - 270720a b c d - 48384a b c d - 384b c
+--R *
+--R 8
+--R x
+--R +
+--R 6 5 5 5 6 4 4 2 7 3
+--R - 196608a c d - 196608a b c d + 737280a b c d
+--R +
+--R 3 3 8 2 2 4 9 5 10
+--R - 110592a b c d - 221184a b c d - 12288a b c
+--R *
+--R 6
+--R x
+--R +
+--R 6 6 4 5 7 3 4 2 8 2
+--R - 294912a c d + 196608a b c d + 430080a b c d
+--R +
+--R 3 3 9 2 4 10
+--R - 270336a b c d - 61440a b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 7 3 5 8 2 3 3 10 2 6 8 2
+--R (- 196608a c d + 294912a b c d - 98304a b c )x - 49152a c d
+--R +
+--R 5 9 4 2 10
+--R 98304a b c d - 49152a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 393
+
+--S 394 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 2 3 2 2 2 +-----------+ +-+
+--R (35a d - 80a b c d + 48a b c )\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 4 2 3 2 2 2 | 2 x\|- a d + b c
+--R (- 70a d + 160a b c d - 96a b c )\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 4 2 5 2 6 | 2 +-----------+ +-+
+--R (256a c d - 512a b c d + 256b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 395
+
+--S 396 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 4 2 3 2 2 2 | 2 x\|- a d + b c
+--R (- 35a d + 80a b c d - 48a b c )\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 4 2 3 2 2 2 +-----------+ +-+
+--R (35a d - 80a b c d + 48a b c )\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 4 2 3 2 2 2 +-----------+ +-+ \|a \|a c d - b c
+--R (35a d - 80a b c d + 48a b c )\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 4 2 5 2 6 +-----------+ +-+ | 2
+--R (128a c d - 256a b c d + 128b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 397
+
+)clear all
+
+--S 398 of 994
+t0:=sqrt(1-x^2)/(1+x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|- x + 1
+--R (1) -----------
+--R 2
+--R x + 1
+--R Type: Expression(Integer)
+--E 398
+
+--S 399 of 994
+r0:=-asin(x)+atan(x*sqrt(2)/sqrt(1-x^2))*sqrt(2)
+--R
+--R
+--R +-+
+--R +-+ x\|2
+--R (2) \|2 atan(-----------) - asin(x)
+--R +--------+
+--R | 2
+--R \|- x + 1
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--------+
+--R | 2 2 | 2 2
+--R \|- x + 1 - 1 +-+ (2x + 1)\|- x + 1 - x - 1
+--R 2atan(---------------) - \|2 atan(-----------------------------)
+--R x 3 +-+
+--R x \|2
+--R +
+--R +-+ 1
+--R \|2 atan(-----)
+--R +-+
+--R x\|2
+--R Type: Union(Expression(Integer),...)
+--E 400
+
+--S 401 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 2 2 | 2 2
+--R \|- x + 1 - 1 +-+ (2x + 1)\|- x + 1 - x - 1
+--R 2atan(---------------) - \|2 atan(-----------------------------)
+--R x 3 +-+
+--R x \|2
+--R +
+--R +-+
+--R +-+ x\|2 +-+ 1
+--R - \|2 atan(-----------) + \|2 atan(-----) + asin(x)
+--R +--------+ +-+
+--R | 2 x\|2
+--R \|- x + 1
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 402
+
+)clear all
+
+--S 403 of 994
+t0:=sqrt(1+x^2)/(-1+x^2)
+--R
+--R
+--R +------+
+--R | 2
+--R \|x + 1
+--R (1) ---------
+--R 2
+--R x - 1
+--R Type: Expression(Integer)
+--E 403
+
+--S 404 of 994
+r0:=asinh(x)-atanh(x*sqrt(2)/sqrt(1+x^2))*sqrt(2)
+--R
+--R
+--R +-+
+--R +-+ x\|2
+--R (2) - \|2 atanh(---------) + asinh(x)
+--R +------+
+--R | 2
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+
+--R | 2
+--R - 2log(\|x + 1 - x)
+--R +
+--R +------+
+--R +-+ 3 | 2 2 +-+ 4 2
+--R +-+ (2x\|2 + 2x - 2x)\|x + 1 + (- 2x + 2)\|2 - 2x + x - 3
+--R \|2 log(-------------------------------------------------------------)
+--R +------+
+--R 3 | 2 4 2
+--R (2x - 2x)\|x + 1 - 2x + x + 1
+--R /
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 405
+
+--S 406 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +------+
+--R | 2
+--R - 2log(\|x + 1 - x)
+--R +
+--R +------+
+--R +-+ 3 | 2 2 +-+ 4 2
+--R +-+ (2x\|2 + 2x - 2x)\|x + 1 + (- 2x + 2)\|2 - 2x + x - 3
+--R \|2 log(-------------------------------------------------------------)
+--R +------+
+--R 3 | 2 4 2
+--R (2x - 2x)\|x + 1 - 2x + x + 1
+--R +
+--R +-+
+--R +-+ x\|2
+--R 2\|2 atanh(---------) - 2asinh(x)
+--R +------+
+--R | 2
+--R \|x + 1
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 407
+
+)clear all
+
+--S 408 of 994
+t0:=sqrt(1-x^2)/(-1+2*x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|- x + 1
+--R (1) -----------
+--R 2
+--R 2x - 1
+--R Type: Expression(Integer)
+--E 408
+
+--S 409 of 994
+r0:=-1/2*asin(x)-1/2*atanh(x/sqrt(1-x^2))
+--R
+--R
+--R x
+--R - atanh(-----------) - asin(x)
+--R +--------+
+--R | 2
+--R \|- x + 1
+--R (2) ------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R | 2 2
+--R (x - 1)\|- x + 1 - x - x + 1
+--R - log(-------------------------------)
+--R 2
+--R x
+--R +
+--R +--------+ +--------+
+--R | 2 2 | 2
+--R (- x - 1)\|- x + 1 - x + x + 1 \|- x + 1 - 1
+--R log(---------------------------------) + 4atan(---------------)
+--R 2 x
+--R x
+--R /
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 410
+
+--S 411 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 2
+--R (x - 1)\|- x + 1 - x - x + 1
+--R - log(-------------------------------)
+--R 2
+--R x
+--R +
+--R +--------+
+--R | 2 2
+--R (- x - 1)\|- x + 1 - x + x + 1 x
+--R log(---------------------------------) + 2atanh(-----------)
+--R 2 +--------+
+--R x | 2
+--R \|- x + 1
+--R +
+--R +--------+
+--R | 2
+--R \|- x + 1 - 1
+--R 4atan(---------------) + 2asin(x)
+--R x
+--R /
+--R 4
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 412
+
+)clear all
+
+--S 413 of 994
+t0:=(c+d*x^2)^3/(a+b*x^2)^(1/2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 413
+
+--S 414 of 994
+r0:=1/16*(2*b*c-a*d)*(8*b^2*c^2-8*a*b*c*d+5*a^2*d^2)*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(7/2)+1/48*d*(52*b^2*c^2-52*a*b*c*d+15*a^2*_
+ d^2)*x*sqrt(a+b*x^2)/b^3+1/6*d*x*(c+d*x^2)^2*sqrt(a+b*x^2)/b+_
+ 1/24*d*x*(c*(6*b*c-a*d)+5*d*(2*b*c-a*d)*x^2)*sqrt(a+b*x^2)/b^2
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|b
+--R (- 15a d + 54a b c d - 72a b c d + 48b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 3 5 3 2 2 3
+--R 8b d x + (- 10a b d + 36b c d )x
+--R +
+--R 2 3 2 2 2
+--R (15a d - 54a b c d + 72b c d)x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 3 +-+
+--R 48b \|b
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 3 2 3 2 4 2 5 3 4
+--R (90a b d - 324a b c d + 432a b c d - 288b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 2
+--R (480a b d - 1728a b c d + 2304a b c d - 1536a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3
+--R 480a d - 1728a b c d + 2304a b c d - 1536a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 3 2 4 2 5 2 6 3 6
+--R (- 15a b d + 54a b c d - 72a b c d + 48b c )x
+--R +
+--R 4 2 3 3 3 2 2 4 2 5 3 4
+--R (- 270a b d + 972a b c d - 1296a b c d + 864a b c )x
+--R +
+--R 5 3 4 2 2 3 3 2 2 4 3 2 6 3
+--R (- 720a b d + 2592a b c d - 3456a b c d + 2304a b c )x - 480a d
+--R +
+--R 5 2 4 2 2 3 3 3
+--R 1728a b c d - 2304a b c d + 1536a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 5 3 11 4 3 5 2 9
+--R - 8b d x + (- 134a b d - 36b c d )x
+--R +
+--R 2 3 3 4 2 5 2 7
+--R (- 219a b d - 594a b c d - 72b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5
+--R (- 46a b d - 756a b c d - 1296a b c d)x
+--R +
+--R 4 3 3 2 2 2 3 2 3
+--R (- 400a b d + 1440a b c d - 3456a b c d)x
+--R +
+--R 5 3 4 2 3 2 2
+--R (- 480a d + 1728a b c d - 2304a b c d)x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 5 3 11 4 3 5 2 9
+--R 48b d x + (244a b d + 216b c d )x
+--R +
+--R 2 3 3 4 2 5 2 7
+--R (222a b d + 1044a b c d + 432b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5
+--R (186a b d + 252a b c d + 2736a b c d)x
+--R +
+--R 4 3 3 2 2 2 3 2 3
+--R (640a b d - 2304a b c d + 4608a b c d)x
+--R +
+--R 5 3 4 2 3 2 2
+--R (480a d - 1728a b c d + 2304a b c d)x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +-+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b )\|a \|b \|b x + a
+--R +
+--R 6 6 5 4 2 4 2 3 3 +-+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|b
+--R ,
+--R
+--R 3 2 3 2 3 2 4 2 5 3 4
+--R (- 180a b d + 648a b c d - 864a b c d + 576b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 2
+--R (- 960a b d + 3456a b c d - 4608a b c d + 3072a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3
+--R - 960a d + 3456a b c d - 4608a b c d + 3072a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 3 2 4 2 5 2 6 3 6
+--R (30a b d - 108a b c d + 144a b c d - 96b c )x
+--R +
+--R 4 2 3 3 3 2 2 4 2 5 3 4
+--R (540a b d - 1944a b c d + 2592a b c d - 1728a b c )x
+--R +
+--R 5 3 4 2 2 3 3 2 2 4 3 2 6 3
+--R (1440a b d - 5184a b c d + 6912a b c d - 4608a b c )x + 960a d
+--R +
+--R 5 2 4 2 2 3 3 3
+--R - 3456a b c d + 4608a b c d - 3072a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 5 3 11 4 3 5 2 9
+--R - 8b d x + (- 134a b d - 36b c d )x
+--R +
+--R 2 3 3 4 2 5 2 7
+--R (- 219a b d - 594a b c d - 72b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5
+--R (- 46a b d - 756a b c d - 1296a b c d)x
+--R +
+--R 4 3 3 2 2 2 3 2 3
+--R (- 400a b d + 1440a b c d - 3456a b c d)x
+--R +
+--R 5 3 4 2 3 2 2
+--R (- 480a d + 1728a b c d - 2304a b c d)x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 3 11 4 3 5 2 9
+--R 48b d x + (244a b d + 216b c d )x
+--R +
+--R 2 3 3 4 2 5 2 7
+--R (222a b d + 1044a b c d + 432b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5
+--R (186a b d + 252a b c d + 2736a b c d)x
+--R +
+--R 4 3 3 2 2 2 3 2 3
+--R (640a b d - 2304a b c d + 4608a b c d)x
+--R +
+--R 5 3 4 2 3 2 2
+--R (480a d - 1728a b c d + 2304a b c d)x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +---+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b )\|- b \|a \|b x + a
+--R +
+--R 6 6 5 4 2 4 2 3 3 +---+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 415
+
+--S 416 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (5a d - 18a b c d + 24a b c d - 16b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|b
+--R (5a d - 18a b c d + 24a b c d - 16b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (5a d - 18a b c d + 24a b c d - 16b c )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (- 10a d + 36a b c d - 48a b c d + 32b c )\|b
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 16b \|- b \|b
+--R Type: Expression(Integer)
+--E 418
+
+--S 419 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 419
+
+)clear all
+
+--S 420 of 994
+t0:=(c+d*x^2)^2/(a+b*x^2)^(1/2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 420
+
+--S 421 of 994
+r0:=1/8*(8*b^2*c^2-8*a*b*c*d+3*a^2*d^2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/_
+ b^(5/2)+3/8*d*(2*b*c-a*d)*x*sqrt(a+b*x^2)/b^2+1/4*d*x*(c+d*x^2)*_
+ sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 x\|b
+--R (3a d - 8a b c d + 8b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 2 3 2 +-+ | 2
+--R (2b d x + (- 3a d + 8b c d)x)\|b \|b x + a
+--R /
+--R 2 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 2 3 2 2 3 2 2
+--R (12a b d - 32a b c d + 32b c )x + 24a d - 64a b c d
+--R +
+--R 2 2
+--R 64a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 2 3 4 2 4
+--R (- 3a b d + 8a b c d - 8b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (- 24a b d + 64a b c d - 64a b c )x - 24a d + 64a b c d - 64a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 3 2 7 2 2 3 5 2 2 2 3
+--R - 2b d x + (- 13a b d - 8b c d)x + (8a b d - 64a b c d)x
+--R +
+--R 3 2 2
+--R (24a d - 64a b c d)x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 3 2 7 2 2 3 5 2 2 2 3
+--R 8b d x + (12a b d + 32b c d)x + (- 20a b d + 96a b c d)x
+--R +
+--R 3 2 2
+--R (- 24a d + 64a b c d)x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+
+--R (32b x + 64a b )\|a \|b \|b x + a + (- 8b x - 64a b x - 64a b )\|b
+--R ,
+--R
+--R 2 2 2 3 2 2 3 2 2
+--R (24a b d - 64a b c d + 64b c )x + 48a d - 128a b c d
+--R +
+--R 2 2
+--R 128a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 2 3 4 2 4
+--R (- 6a b d + 16a b c d - 16b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3
+--R (- 48a b d + 128a b c d - 128a b c )x - 48a d + 128a b c d
+--R +
+--R 2 2 2
+--R - 128a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 3 2 7 2 2 3 5 2 2 2 3
+--R - 2b d x + (- 13a b d - 8b c d)x + (8a b d - 64a b c d)x
+--R +
+--R 3 2 2
+--R (24a d - 64a b c d)x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 3 2 7 2 2 3 5 2 2 2 3
+--R 8b d x + (12a b d + 32b c d)x + (- 20a b d + 96a b c d)x
+--R +
+--R 3 2 2
+--R (- 24a d + 64a b c d)x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 3 2 2 +---+ +-+ | 2
+--R (32b x + 64a b )\|- b \|a \|b x + a
+--R +
+--R 4 4 3 2 2 2 +---+
+--R (- 8b x - 64a b x - 64a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 422
+
+--S 423 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2
+--R (3a d - 8a b c d + 8b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 2 2 2 x\|b
+--R (- 3a d + 8a b c d - 8b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 423
+
+--S 424 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- 3a d + 8a b c d - 8b c )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (6a d - 16a b c d + 16b c )\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 8b \|- b \|b
+--R Type: Expression(Integer)
+--E 425
+
+--S 426 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 426
+
+)clear all
+
+--S 427 of 994
+t0:=(c+d*x^2)/(a+b*x^2)^(1/2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 994
+r0:=1/2*(2*b*c-a*d)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+1/2*d*x*_
+ sqrt(a+b*x^2)/b
+--R
+--R
+--R +-+ +--------+
+--R x\|b +-+ | 2
+--R (- a d + 2b c)atanh(-----------) + d x\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -----------------------------------------------------
+--R +-+
+--R 2b\|b
+--R Type: Expression(Integer)
+--E 428
+
+--S 429 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2 2
+--R ((2a d - 4b c)\|a \|b x + a + (- a b d + 2b c)x - 2a d + 4a b c)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (- b d x - 2a d x)\|b \|b x + a + (2b d x + 2a d x)\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 2 +-+
+--R 4b\|a \|b \|b x + a + (- 2b x - 4a b)\|b
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2 2
+--R ((- 4a d + 8b c)\|a \|b x + a + (2a b d - 4b c)x + 4a d - 8a b c)
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R 3 +---+ | 2 3 +---+ +-+
+--R (- b d x - 2a d x)\|- b \|b x + a + (2b d x + 2a d x)\|- b \|a
+--R /
+--R +--------+
+--R +---+ +-+ | 2 2 2 +---+
+--R 4b\|- b \|a \|b x + a + (- 2b x - 4a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 429
+
+--S 430 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R (a d - 2b c)log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R (a d - 2b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 2b\|b
+--R Type: Expression(Integer)
+--E 430
+
+--S 431 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R +---+ x\|b
+--R (a d - 2b c)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R +-+ \|- b \|b x + a - \|- b \|a
+--R (- 2a d + 4b c)\|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 2b\|- b \|b
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 433
+
+)clear all
+
+--S 434 of 994
+t0:=1/(a+b*x^2)^(1/2)
+--R
+--R
+--R 1
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 994
+r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)
+--R
+--R
+--R +-+
+--R x\|b
+--R atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 435
+
+--S 436 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R [-------------------------------------------------------------,
+--R +-+
+--R \|b
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R 2atan(------------------------------)
+--R b x
+--R -------------------------------------]
+--R +---+
+--R \|- b
+--R Type: Union(List(Expression(Integer)),...)
+--E 436
+
+--S 437 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R - atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 438
+
+--S 439 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a
+--R - \|- b atanh(-----------) + 2\|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R (6) ----------------------------------------------------------------------
+--R +---+ +-+
+--R \|- b \|b
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 994
+t0:=1/((a+b*x^2)^(1/2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|b x + a
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 994
+r0:=atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/(sqrt(c)*sqrt(b*c-a*d))
+--R
+--R
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R (2) ----------------------
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R /
+--R +--------------+
+--R | 2
+--R 2\|- a c d + b c
+--R ,
+--R
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 443
+
+--S 444 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - 2\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R | 2 +-----------+ +-+
+--R 2\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+--S 446 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - \|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R +-----------+ +-+ \|a \|a c d - b c
+--R \|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 447
+
+)clear all
+
+--S 448 of 994
+t0:=1/((a+b*x^2)^(1/2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|b x + a
+--R Type: Expression(Integer)
+--E 448
+
+--S 449 of 994
+r0:=1/2*(2*b*c-a*d)*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/_
+ (c^(3/2)*(b*c-a*d)^(3/2))-1/2*d*x*sqrt(a+b*x^2)/(c*(b*c-a*d)*(c+d*x^2))
+--R
+--R
+--R (2)
+--R +-----------+
+--R 2 2 2 x\|- a d + b c
+--R ((a d - 2b c d)x + a c d - 2b c )atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R d x\|- a d + b c \|c \|b x + a
+--R /
+--R 2 2 2 2 3 +-----------+ +-+
+--R ((2a c d - 2b c d)x + 2a c d - 2b c )\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((2a d - 4b c d)x + 2a c d - 4b c )\|a \|b x + a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d + 2b c d)x + (- 2a d + 3a b c d + 2b c )x - 2a c d
+--R +
+--R 2
+--R 4a b c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +--------+
+--R 3 | 2 | 2
+--R (- 2b d x - 4a d x)\|- a c d + b c \|b x + a
+--R +
+--R +--------------+
+--R 3 | 2 +-+
+--R (4b d x + 4a d x)\|- a c d + b c \|a
+--R /
+--R +--------------+ +--------+
+--R 2 2 2 2 3 | 2 +-+ | 2
+--R ((8a c d - 8b c d)x + 8a c d - 8b c )\|- a c d + b c \|a \|b x + a
+--R +
+--R 2 2 2 4 2 2 2 2 3 2
+--R (- 4a b c d + 4b c d)x + (- 8a c d + 4a b c d + 4b c )x
+--R +
+--R 2 2 3
+--R - 8a c d + 8a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((2a d - 4b c d)x + 2a c d - 4b c )\|a \|b x + a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d + 2b c d)x + (- 2a d + 3a b c d + 2b c )x - 2a c d
+--R +
+--R 2
+--R 4a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((2a d - 4b c d)x + 2a c d - 4b c )\|a \|b x + a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d + 2b c d)x + (- 2a d + 3a b c d + 2b c )x - 2a c d
+--R +
+--R 2
+--R 4a b c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R +------------+ +--------+
+--R 3 | 2 | 2
+--R (- b d x - 2a d x)\|a c d - b c \|b x + a
+--R +
+--R +------------+
+--R 3 +-+ | 2
+--R (2b d x + 2a d x)\|a \|a c d - b c
+--R /
+--R +------------+ +--------+
+--R 2 2 2 2 3 +-+ | 2 | 2
+--R ((4a c d - 4b c d)x + 4a c d - 4b c )\|a \|a c d - b c \|b x + a
+--R +
+--R 2 2 2 4 2 2 2 2 3 2
+--R (- 2a b c d + 2b c d)x + (- 4a c d + 2a b c d + 2b c )x
+--R +
+--R 2 2 3
+--R - 4a c d + 4a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 450
+
+--S 451 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R (a d - 2b c)\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R (- 2a d + 4b c)\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 | 2 +-----------+ +-+
+--R (4a c d - 4b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R (- a d + 2b c)\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +-----------+ +-+
+--R (a d - 2b c)\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R +-----------+ +-+ \|a \|a c d - b c
+--R (a d - 2b c)\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 +-----------+ +-+ | 2
+--R (2a c d - 2b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 453
+
+--S 454 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 454
+
+)clear all
+
+--S 455 of 994
+t0:=1/((a+b*x^2)^(1/2)*(c+d*x^2)^3)
+--R
+--R
+--R 1
+--R (1) ------------------------------------------
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (d x + 3c d x + 3c d x + c )\|b x + a
+--R Type: Expression(Integer)
+--E 455
+
+--S 456 of 994
+r0:=1/8*(8*b^2*c^2-8*a*b*c*d+3*a^2*d^2)*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*_
+ sqrt(a+b*x^2)))/(c^(5/2)*(b*c-a*d)^(5/2))-1/4*d*x*sqrt(a+b*x^2)/_
+ (c*(b*c-a*d)*(c+d*x^2)^2)-3/8*d*(2*b*c-a*d)*x*sqrt(a+b*x^2)/_
+ (c^2*(b*c-a*d)^2*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d - 8a b c d + 8b c d )x + (6a c d - 16a b c d + 16b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d - 8a b c d + 8b c
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +--------+
+--R 3 2 3 2 2 +-----------+ +-+ | 2
+--R ((3a d - 6b c d )x + (5a c d - 8b c d)x)\|- a d + b c \|c \|b x + a
+--R /
+--R 2 2 4 3 3 2 4 2 4
+--R (8a c d - 16a b c d + 8b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5 2 6
+--R (16a c d - 32a b c d + 16b c d)x + 8a c d - 16a b c d + 8b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 2 3 3 2 2 6
+--R (12a b d - 32a b c d + 32b c d )x
+--R +
+--R 3 4 2 3 3 3 4
+--R (24a d - 40a b c d + 64b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (48a c d - 116a b c d + 96a b c d + 32b c )x + 24a c d
+--R +
+--R 2 3 2 4
+--R - 64a b c d + 64a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 4 3 3 4 2 2 8
+--R (- 3a b d + 8a b c d - 8b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 6
+--R (- 24a b d + 58a b c d - 48a b c d - 16b c d)x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 24a d + 16a b c d + 61a b c d - 120a b c d - 8b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2
+--R (- 48a c d + 104a b c d - 64a b c d - 64a b c )x - 24a c d
+--R +
+--R 3 3 2 2 4
+--R 64a b c d - 64a b c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R 2 3 3 2 7 2 3 2 2 3 2 5
+--R (- 6a b d + 12b c d )x + (- 48a b d + 86a b c d + 16b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 2 2
+--R (- 48a d + 16a b c d + 128a b c d)x + (- 80a c d + 128a b c d)x
+--R *
+--R +--------------+ +--------+
+--R | 2 | 2
+--R \|- a c d + b c \|b x + a
+--R +
+--R 2 3 3 2 7 2 3 2 2 3 2 5
+--R (24a b d - 48b c d )x + (72a b d - 104a b c d - 64b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 2 2
+--R (48a d + 24a b c d - 192a b c d)x + (80a c d - 128a b c d)x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 2 2 4 2 3 3 3 4 2 6
+--R (64a b c d - 128a b c d + 64b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (128a c d - 128a b c d - 128a b c d + 128b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2 3 4 2
+--R (256a c d - 448a b c d + 128a b c d + 64b c )x + 128a c d
+--R +
+--R 2 5 2 6
+--R - 256a b c d + 128a b c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 2 2 2 4 3 3 3 4 4 2 8
+--R (- 16a b c d + 32a b c d - 16b c d )x
+--R +
+--R 3 2 4 2 2 3 3 3 4 2 4 5 6
+--R (- 128a b c d + 224a b c d - 64a b c d - 32b c d)x
+--R +
+--R 4 2 4 2 2 4 2 3 5 4 6 4
+--R (- 128a c d + 368a b c d - 224a b c d - 16b c )x
+--R +
+--R 4 3 3 3 4 2 3 6 2 4 4 2 3 5
+--R (- 256a c d + 384a b c d - 128a b c )x - 128a c d + 256a b c d
+--R +
+--R 2 2 6
+--R - 128a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 2 4 2 3 3 2 2 6
+--R (12a b d - 32a b c d + 32b c d )x
+--R +
+--R 3 4 2 3 3 3 4
+--R (24a d - 40a b c d + 64b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (48a c d - 116a b c d + 96a b c d + 32b c )x + 24a c d
+--R +
+--R 2 3 2 4
+--R - 64a b c d + 64a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 4 3 3 4 2 2 8
+--R (- 3a b d + 8a b c d - 8b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 6
+--R (- 24a b d + 58a b c d - 48a b c d - 16b c d)x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 24a d + 16a b c d + 61a b c d - 120a b c d - 8b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2
+--R (- 48a c d + 104a b c d - 64a b c d - 64a b c )x - 24a c d
+--R +
+--R 3 3 2 2 4
+--R 64a b c d - 64a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (12a b d - 32a b c d + 32b c d )x
+--R +
+--R 3 4 2 3 3 3 4
+--R (24a d - 40a b c d + 64b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (48a c d - 116a b c d + 96a b c d + 32b c )x + 24a c d
+--R +
+--R 2 3 2 4
+--R - 64a b c d + 64a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 4 3 3 4 2 2 8
+--R (- 3a b d + 8a b c d - 8b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 6
+--R (- 24a b d + 58a b c d - 48a b c d - 16b c d)x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 24a d + 16a b c d + 61a b c d - 120a b c d - 8b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2
+--R (- 48a c d + 104a b c d - 64a b c d - 64a b c )x - 24a c d
+--R +
+--R 3 3 2 2 4
+--R 64a b c d - 64a b c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 3 3 2 7 2 3 2 2 3 2 5
+--R (- 3a b d + 6b c d )x + (- 24a b d + 43a b c d + 8b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 2 2
+--R (- 24a d + 8a b c d + 64a b c d)x + (- 40a c d + 64a b c d)x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 3 3 2 7 2 3 2 2 3 2 5
+--R (12a b d - 24b c d )x + (36a b d - 52a b c d - 32b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 2 2
+--R (24a d + 12a b c d - 96a b c d)x + (40a c d - 64a b c d)x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 2 2 4 2 3 3 3 4 2 6
+--R (32a b c d - 64a b c d + 32b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (64a c d - 64a b c d - 64a b c d + 64b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2 3 4 2
+--R (128a c d - 224a b c d + 64a b c d + 32b c )x + 64a c d
+--R +
+--R 2 5 2 6
+--R - 128a b c d + 64a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 2 2 2 4 3 3 3 4 4 2 8
+--R (- 8a b c d + 16a b c d - 8b c d )x
+--R +
+--R 3 2 4 2 2 3 3 3 4 2 4 5 6
+--R (- 64a b c d + 112a b c d - 32a b c d - 16b c d)x
+--R +
+--R 4 2 4 2 2 4 2 3 5 4 6 4
+--R (- 64a c d + 184a b c d - 112a b c d - 8b c )x
+--R +
+--R 4 3 3 3 4 2 3 6 2 4 4 2 3 5
+--R (- 128a c d + 192a b c d - 64a b c )x - 64a c d + 128a b c d
+--R +
+--R 2 2 6
+--R - 64a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 457
+
+--S 458 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-----------+ +-+
+--R (3a d - 8a b c d + 8b c )\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 2 2 2 2 | 2 x\|- a d + b c
+--R (- 6a d + 16a b c d - 16b c )\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 2 2 3 2 4 | 2 +-----------+ +-+
+--R (16a c d - 32a b c d + 16b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 458
+
+--S 459 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 2 2 2 2 | 2 x\|- a d + b c
+--R (- 3a d + 8a b c d - 8b c )\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 2 2 2 +-----------+ +-+
+--R (3a d - 8a b c d + 8b c )\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 2 2 2 2 +-----------+ +-+ \|a \|a c d - b c
+--R (3a d - 8a b c d + 8b c )\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 2 2 3 2 4 +-----------+ +-+ | 2
+--R (8a c d - 16a b c d + 8b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 460
+
+--S 461 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 461
+
+)clear all
+
+--S 462 of 994
+t0:=(c+d*x^2)^4/(a+b*x^2)^(3/2)
+--R
+--R
+--R 4 8 3 6 2 2 4 3 2 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R (1) ---------------------------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 994
+r0:=1/16*d*(64*b^3*c^3-144*a*b^2*c^2*d+120*a^2*b*c*d^2-35*a^3*d^3)*_
+ atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(9/2)+(b*c-a*d)*x*(c+d*x^2)^3/_
+ (a*b*sqrt(a+b*x^2))-1/48*d*(96*b^3*c^3-352*a*b^2*c^2*d+346*_
+ a^2*b*c*d^2-105*a^3*d^3)*x*sqrt(a+b*x^2)/(a*b^4)-1/6*d*(6*b*c-_
+ 7*a*d)*x*(c+d*x^2)^2*sqrt(a+b*x^2)/(a*b^2)+1/24*d^2*x*(a*c*_
+ (12*b*c-7*a*d)-(24*b^2*c^2-64*a*b*c*d+35*a^2*d^2)*x^2)*_
+ sqrt(a+b*x^2)/(a*b^3)
+--R
+--R
+--R (2)
+--R +--------+
+--R 4 4 3 3 2 2 2 2 3 3 | 2
+--R (- 105a d + 360a b c d - 432a b c d + 192a b c d)\|b x + a
+--R *
+--R +-+
+--R x\|b
+--R atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 4 7 2 2 4 3 3 5
+--R 8a b d x + (- 14a b d + 48a b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 3
+--R (35a b d - 120a b c d + 144a b c d )x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (105a d - 360a b c d + 432a b c d - 192a b c d + 48b c )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R +--------+
+--R 4 +-+ | 2
+--R 48a b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 463
+
+--S 464 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 3 4 3 4 3 2 5 2 2 6 3 6
+--R (735a b d - 2520a b c d + 3024a b c d - 1344a b c d)x
+--R +
+--R 5 2 4 4 3 3 3 4 2 2 2 5 3 4
+--R (5880a b d - 20160a b c d + 24192a b c d - 10752a b c d)x
+--R +
+--R 6 4 5 2 3 4 3 2 2 3 4 3 2
+--R (11760a b d - 40320a b c d + 48384a b c d - 21504a b c d)x
+--R +
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 6720a d - 23040a b c d + 27648a b c d - 12288a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 4 3 5 3 2 6 2 2 7 3 8
+--R (- 105a b d + 360a b c d - 432a b c d + 192a b c d)x
+--R +
+--R 5 3 4 4 4 3 3 5 2 2 2 6 3 6
+--R (- 2625a b d + 9000a b c d - 10800a b c d + 4800a b c d)x
+--R +
+--R 6 2 4 5 3 3 4 4 2 2 3 5 3 4
+--R (- 10920a b d + 37440a b c d - 44928a b c d + 19968a b c d)x
+--R +
+--R 7 4 6 2 3 5 3 2 2 4 4 3 2
+--R (- 15120a b d + 51840a b c d - 62208a b c d + 27648a b c d)x
+--R +
+--R 8 4 7 3 6 2 2 2 5 3 3
+--R - 6720a d + 23040a b c d - 27648a b c d + 12288a b c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 6 4 13 2 5 4 6 3 11
+--R - 8a b d x + (- 178a b d - 48a b c d )x
+--R +
+--R 3 4 4 2 5 3 6 2 2 9
+--R (- 339a b d - 1032a b c d - 144a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7
+--R (- 337a b d - 600a b c d - 3888a b c d + 192a b c d - 48b c )x
+--R +
+--R 5 2 4 4 3 3 3 4 2 2 2 5 3
+--R - 4424a b d + 15168a b c d - 21888a b c d + 4608a b c d
+--R +
+--R 6 4
+--R - 1152a b c
+--R *
+--R 5
+--R x
+--R +
+--R 6 4 5 2 3 4 3 2 2 3 4 3
+--R - 10640a b d + 36480a b c d - 43776a b c d + 15360a b c d
+--R +
+--R 2 5 4
+--R - 3840a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R - 6720a d + 23040a b c d - 27648a b c d + 12288a b c d
+--R +
+--R 3 4 4
+--R - 3072a b c
+--R *
+--R x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 6 4 13 2 5 4 6 3 11
+--R 56a b d x + (350a b d + 336a b c d )x
+--R +
+--R 3 4 4 2 5 3 6 2 2 9
+--R (357a b d + 1848a b c d + 1008a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R 1639a b d - 3864a b c d + 11088a b c d - 1344a b c d
+--R +
+--R 7 4
+--R 336b c
+--R *
+--R 7
+--R x
+--R +
+--R 5 2 4 4 3 3 3 4 2 2 2 5 3
+--R 8904a b d - 30528a b c d + 40320a b c d - 10752a b c d
+--R +
+--R 6 4
+--R 2688a b c
+--R *
+--R 5
+--R x
+--R +
+--R 6 4 5 2 3 4 3 2 2 3 4 3
+--R 14000a b d - 48000a b c d + 57600a b c d - 21504a b c d
+--R +
+--R 2 5 4
+--R 5376a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 6720a d - 23040a b c d + 27648a b c d - 12288a b c d
+--R +
+--R 3 4 4
+--R 3072a b c
+--R *
+--R x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 7 6 2 6 4 3 5 2 4 4 +-+ +-+ | 2
+--R (336a b x + 2688a b x + 5376a b x + 3072a b )\|a \|b \|b x + a
+--R +
+--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +-+
+--R (- 48a b x - 1200a b x - 4992a b x - 6912a b x - 3072a b )\|b
+--R ,
+--R
+--R 4 3 4 3 4 3 2 5 2 2 6 3 6
+--R (- 1470a b d + 5040a b c d - 6048a b c d + 2688a b c d)x
+--R +
+--R 5 2 4 4 3 3 3 4 2 2
+--R - 11760a b d + 40320a b c d - 48384a b c d
+--R +
+--R 2 5 3
+--R 21504a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 4 5 2 3 4 3 2 2
+--R - 23520a b d + 80640a b c d - 96768a b c d
+--R +
+--R 3 4 3
+--R 43008a b c d
+--R *
+--R 2
+--R x
+--R +
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R - 13440a d + 46080a b c d - 55296a b c d + 24576a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 4 3 5 3 2 6 2 2 7 3 8
+--R (210a b d - 720a b c d + 864a b c d - 384a b c d)x
+--R +
+--R 5 3 4 4 4 3 3 5 2 2 2 6 3 6
+--R (5250a b d - 18000a b c d + 21600a b c d - 9600a b c d)x
+--R +
+--R 6 2 4 5 3 3 4 4 2 2 3 5 3 4
+--R (21840a b d - 74880a b c d + 89856a b c d - 39936a b c d)x
+--R +
+--R 7 4 6 2 3 5 3 2 2 4 4 3 2
+--R (30240a b d - 103680a b c d + 124416a b c d - 55296a b c d)x
+--R +
+--R 8 4 7 3 6 2 2 2 5 3 3
+--R 13440a d - 46080a b c d + 55296a b c d - 24576a b c d
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 6 4 13 2 5 4 6 3 11
+--R - 8a b d x + (- 178a b d - 48a b c d )x
+--R +
+--R 3 4 4 2 5 3 6 2 2 9
+--R (- 339a b d - 1032a b c d - 144a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7
+--R (- 337a b d - 600a b c d - 3888a b c d + 192a b c d - 48b c )x
+--R +
+--R 5 2 4 4 3 3 3 4 2 2 2 5 3
+--R - 4424a b d + 15168a b c d - 21888a b c d + 4608a b c d
+--R +
+--R 6 4
+--R - 1152a b c
+--R *
+--R 5
+--R x
+--R +
+--R 6 4 5 2 3 4 3 2 2 3 4 3
+--R - 10640a b d + 36480a b c d - 43776a b c d + 15360a b c d
+--R +
+--R 2 5 4
+--R - 3840a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R - 6720a d + 23040a b c d - 27648a b c d + 12288a b c d
+--R +
+--R 3 4 4
+--R - 3072a b c
+--R *
+--R x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 6 4 13 2 5 4 6 3 11
+--R 56a b d x + (350a b d + 336a b c d )x
+--R +
+--R 3 4 4 2 5 3 6 2 2 9
+--R (357a b d + 1848a b c d + 1008a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R 1639a b d - 3864a b c d + 11088a b c d - 1344a b c d
+--R +
+--R 7 4
+--R 336b c
+--R *
+--R 7
+--R x
+--R +
+--R 5 2 4 4 3 3 3 4 2 2 2 5 3
+--R 8904a b d - 30528a b c d + 40320a b c d - 10752a b c d
+--R +
+--R 6 4
+--R 2688a b c
+--R *
+--R 5
+--R x
+--R +
+--R 6 4 5 2 3 4 3 2 2 3 4 3
+--R 14000a b d - 48000a b c d + 57600a b c d - 21504a b c d
+--R +
+--R 2 5 4
+--R 5376a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 6720a d - 23040a b c d + 27648a b c d - 12288a b c d
+--R +
+--R 3 4 4
+--R 3072a b c
+--R *
+--R x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 7 6 2 6 4 3 5 2 4 4 +---+ +-+ | 2
+--R (336a b x + 2688a b x + 5376a b x + 3072a b )\|- b \|a \|b x + a
+--R +
+--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +---+
+--R (- 48a b x - 1200a b x - 4992a b x - 6912a b x - 3072a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 464
+
+--S 465 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 4 2 3 2 2 2 3 3
+--R (35a d - 120a b c d + 144a b c d - 64b c d)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 4 2 3 2 2 2 3 3 x\|b
+--R (35a d - 120a b c d + 144a b c d - 64b c d)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 465
+
+--S 466 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 3 4 2 3 2 2 2 3 3 +---+ x\|b
+--R (35a d - 120a b c d + 144a b c d - 64b c d)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (- 70a d + 240a b c d - 288a b c d + 128b c d)\|b
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R /
+--R 4 +---+ +-+
+--R 16b \|- b \|b
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 468
+
+)clear all
+
+--S 469 of 994
+t0:=(c+d*x^2)^3/(a+b*x^2)^(3/2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 994
+r0:=3/8*d*(8*b^2*c^2-12*a*b*c*d+5*a^2*d^2)*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(7/2)+(b*c-a*d)*x*(c+d*x^2)^2/(a*b*_
+ sqrt(a+b*x^2))-1/8*d*(8*b*c-5*a*d)*(2*b*c-3*a*d)*x*_
+ sqrt(a+b*x^2)/(a*b^3)+1/4*d^2*x*(a*c-(4*b*c-5*a*d)*x^2)*_
+ sqrt(a+b*x^2)/(a*b^2)
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 3 3 2 2 2 2 | 2 x\|b
+--R (15a d - 36a b c d + 24a b c d)\|b x + a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 3 5 2 3 2 2 3
+--R 2a b d x + (- 5a b d + 12a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 15a d + 36a b c d - 24a b c d + 8b c )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R +--------+
+--R 3 +-+ | 2
+--R 8a b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 470
+
+--S 471 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 3 2 3 2 4 2 4
+--R (75a b d - 180a b c d + 120a b c d)x
+--R +
+--R 4 3 3 2 2 2 3 2 2 5 3
+--R (300a b d - 720a b c d + 480a b c d)x + 240a d
+--R +
+--R 4 2 3 2 2
+--R - 576a b c d + 384a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 3 2 4 2 5 2 6
+--R (- 15a b d + 36a b c d - 24a b c d)x
+--R +
+--R 4 2 3 3 3 2 2 4 2 4
+--R (- 195a b d + 468a b c d - 312a b c d)x
+--R +
+--R 5 3 4 2 2 3 3 2 2 6 3 5 2
+--R (- 420a b d + 1008a b c d - 672a b c d)x - 240a d + 576a b c d
+--R +
+--R 4 2 2
+--R - 384a b c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 4 3 9 2 3 3 4 2 7
+--R - 2a b d x + (- 19a b d - 12a b c d )x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 5
+--R (43a b d - 180a b c d + 24a b c d - 8b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 3
+--R (260a b d - 624a b c d + 288a b c d - 96a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3
+--R (240a d - 576a b c d + 384a b c d - 128a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 4 3 9 2 3 3 4 2 7
+--R 10a b d x + (15a b d + 60a b c d )x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 5
+--R (- 143a b d + 420a b c d - 120a b c d + 40b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 3
+--R (- 380a b d + 912a b c d - 480a b c d + 160a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3
+--R (- 240a d + 576a b c d - 384a b c d + 128a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 5 4 2 4 2 3 3 +-+ +-+ | 2
+--R (40a b x + 160a b x + 128a b )\|a \|b \|b x + a
+--R +
+--R 6 6 2 5 4 3 4 2 4 3 +-+
+--R (- 8a b x - 104a b x - 224a b x - 128a b )\|b
+--R ,
+--R
+--R 3 2 3 2 3 2 4 2 4
+--R (150a b d - 360a b c d + 240a b c d)x
+--R +
+--R 4 3 3 2 2 2 3 2 2 5 3
+--R (600a b d - 1440a b c d + 960a b c d)x + 480a d
+--R +
+--R 4 2 3 2 2
+--R - 1152a b c d + 768a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 3 2 4 2 5 2 6
+--R (- 30a b d + 72a b c d - 48a b c d)x
+--R +
+--R 4 2 3 3 3 2 2 4 2 4
+--R (- 390a b d + 936a b c d - 624a b c d)x
+--R +
+--R 5 3 4 2 2 3 3 2 2 6 3
+--R (- 840a b d + 2016a b c d - 1344a b c d)x - 480a d
+--R +
+--R 5 2 4 2 2
+--R 1152a b c d - 768a b c d
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 4 3 9 2 3 3 4 2 7
+--R - 2a b d x + (- 19a b d - 12a b c d )x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 5
+--R (43a b d - 180a b c d + 24a b c d - 8b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 3
+--R (260a b d - 624a b c d + 288a b c d - 96a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3
+--R (240a d - 576a b c d + 384a b c d - 128a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 4 3 9 2 3 3 4 2 7
+--R 10a b d x + (15a b d + 60a b c d )x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 5
+--R (- 143a b d + 420a b c d - 120a b c d + 40b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 3
+--R (- 380a b d + 912a b c d - 480a b c d + 160a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3
+--R (- 240a d + 576a b c d - 384a b c d + 128a b c )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 5 4 2 4 2 3 3 +---+ +-+ | 2
+--R (40a b x + 160a b x + 128a b )\|- b \|a \|b x + a
+--R +
+--R 6 6 2 5 4 3 4 2 4 3 +---+
+--R (- 8a b x - 104a b x - 224a b x - 128a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 471
+
+--S 472 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 2 2 2
+--R (15a d - 36a b c d + 24b c d)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 3 2 2 2 x\|b
+--R (- 15a d + 36a b c d - 24b c d)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 473
+
+--S 474 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 3 2 2 2 +---+ x\|b
+--R (- 15a d + 36a b c d - 24b c d)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 3 2 2 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (30a d - 72a b c d + 48b c d)\|b atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 8b \|- b \|b
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 475
+
+)clear all
+
+--S 476 of 994
+t0:=(c+d*x^2)^2/(a+b*x^2)^(3/2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 994
+r0a:=1/2*d*(4*b*c-3*a*d)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)+(b*c-a*d)^2*x/(a*b^2*sqrt(a+b*x^2))+1/2*d^2*x*sqrt(a+b*x^2)/b^2
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 2 2 | 2 x\|b
+--R (- 3a d + 4a b c d)\|b x + a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 3 2 2 2 2 +-+
+--R (a b d x + (3a d - 4a b c d + 2b c )x)\|b
+--R /
+--R +--------+
+--R 2 +-+ | 2
+--R 2a b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 994
+r0b:=1/2*d*(4*b*c-3*a*d)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)+(b*c-a*d)*x*(c+d*x^2)/(a*b*sqrt(a+b*x^2))-1/2*d*(2*b*c-3*a*d)*x*sqrt(a+b*x^2)/(a*b^2)
+--R
+--R
+--R (3)
+--R +--------+ +-+
+--R 2 2 | 2 x\|b
+--R (- 3a d + 4a b c d)\|b x + a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 3 2 2 2 2 +-+
+--R (a b d x + (3a d - 4a b c d + 2b c )x)\|b
+--R /
+--R +--------+
+--R 2 +-+ | 2
+--R 2a b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 478
+
+--S 479 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R +--------+
+--R 2 2 2 2 3 2 2 +-+ | 2
+--R ((9a b d - 12a b c d)x + 12a d - 16a b c d)\|a \|b x + a
+--R +
+--R 2 2 2 3 4 3 2 2 2 2 4 2
+--R (- 3a b d + 4a b c d)x + (- 15a b d + 20a b c d)x - 12a d
+--R +
+--R 3
+--R 16a b c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 2 2 5 2 2 2 3 2 3
+--R - a b d x + (- 7a b d + 4a b c d - 2b c )x
+--R +
+--R 3 2 2 2 2
+--R (- 12a d + 16a b c d - 8a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 2 2 5 2 2 2 3 2 3
+--R 3a b d x + (13a b d - 12a b c d + 6b c )x
+--R +
+--R 3 2 2 2 2
+--R (12a d - 16a b c d + 8a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ +-+ | 2 4 4 2 3 2 3 2 +-+
+--R (6a b x + 8a b )\|a \|b \|b x + a + (- 2a b x - 10a b x - 8a b )\|b
+--R ,
+--R
+--R +--------+
+--R 2 2 2 2 3 2 2 +-+ | 2
+--R ((- 18a b d + 24a b c d)x - 24a d + 32a b c d)\|a \|b x + a
+--R +
+--R 2 2 2 3 4 3 2 2 2 2 4 2
+--R (6a b d - 8a b c d)x + (30a b d - 40a b c d)x + 24a d
+--R +
+--R 3
+--R - 32a b c d
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 2 2 5 2 2 2 3 2 3
+--R - a b d x + (- 7a b d + 4a b c d - 2b c )x
+--R +
+--R 3 2 2 2 2
+--R (- 12a d + 16a b c d - 8a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 2 2 5 2 2 2 3 2 3
+--R 3a b d x + (13a b d - 12a b c d + 6b c )x
+--R +
+--R 3 2 2 2 2
+--R (12a d - 16a b c d + 8a b c )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 3 2 2 2 +---+ +-+ | 2
+--R (6a b x + 8a b )\|- b \|a \|b x + a
+--R +
+--R 4 4 2 3 2 3 2 +---+
+--R (- 2a b x - 10a b x - 8a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 479
+
+--S 480 of 994
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 2
+--R (3a d - 4b c d)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R (3a d - 4b c d)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 480
+
+--S 481 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 994
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +-+
+--R 2 +---+ x\|b
+--R (3a d - 4b c d)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 6a d + 8b c d)\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 2b \|- b \|b
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 483
+
+--S 484 of 994
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 2
+--R (3a d - 4b c d)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R (3a d - 4b c d)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 994
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 485
+
+--S 486 of 994
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +-+
+--R 2 +---+ x\|b
+--R (3a d - 4b c d)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 6a d + 8b c d)\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 2b \|- b \|b
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 994
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 487
+
+)clear all
+
+--S 488 of 994
+t0:=(c+d*x^2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 488
+
+--S 489 of 994
+r0:=d*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+(b*c-a*d)*x/(a*b*sqrt(a+b*x^2))
+--R
+--R
+--R +--------+ +-+
+--R | 2 x\|b +-+
+--R a d\|b x + a atanh(-----------) + (- a d + b c)x\|b
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -----------------------------------------------------
+--R +--------+
+--R +-+ | 2
+--R a b\|b \|b x + a
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2
+--R (a d\|a \|b x + a - a b d x - a d)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R (a d - b c)x\|b \|b x + a + (- a d + b c)x\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 2 2 +-+
+--R a b\|a \|b \|b x + a + (- a b x - a b)\|b
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2
+--R (2a d\|a \|b x + a - 2a b d x - 2a d)
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R (a d - b c)x\|- b \|b x + a + (- a d + b c)x\|- b \|a
+--R /
+--R +--------+
+--R +---+ +-+ | 2 2 2 2 +---+
+--R a b\|- b \|a \|b x + a + (- a b x - a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 490
+
+--S 491 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R d log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R - d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a
+--R - d\|- b atanh(-----------) + 2d\|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ------------------------------------------------------------------------
+--R +---+ +-+
+--R b\|- b \|b
+--R Type: Expression(Integer)
+--E 493
+
+--S 494 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 494
+
+)clear all
+
+--S 495 of 994
+t0:=1/(a+b*x^2)^(3/2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 495
+
+--S 496 of 994
+r0:=x/(a*sqrt(a+b*x^2))
+--R
+--R
+--R x
+--R (2) ------------
+--R +--------+
+--R | 2
+--R a\|b x + a
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 2 +-+
+--R - x\|b x + a + x\|a
+--R (3) ------------------------------
+--R +--------+
+--R +-+ | 2 2 2
+--R a\|a \|b x + a - a b x - a
+--R Type: Union(Expression(Integer),...)
+--E 497
+
+--S 498 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 498
+
+--S 499 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 499
+
+)clear all
+
+--S 500 of 994
+t0:=1/((a+b*x^2)^(3/2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b d x + (a d + b c)x + a c)\|b x + a
+--R Type: Expression(Integer)
+--E 500
+
+--S 501 of 994
+r0:=-d*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/((b*c-a*d)^(3/2)*_
+ sqrt(c))+b*x/(a*(b*c-a*d)*sqrt(a+b*x^2))
+--R
+--R
+--R +--------+ +-----------+
+--R | 2 x\|- a d + b c +-----------+ +-+
+--R a d\|b x + a atanh(---------------) - b x\|- a d + b c \|c
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R (2) ------------------------------------------------------------
+--R +--------+
+--R 2 +-----------+ +-+ | 2
+--R (a d - a b c)\|- a d + b c \|c \|b x + a
+--R Type: Expression(Integer)
+--E 501
+
+--S 502 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2
+--R (a d\|a \|b x + a - a b d x - a d)
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +--------+ +--------------+
+--R | 2 | 2 | 2 +-+
+--R 2b x\|- a c d + b c \|b x + a - 2b x\|- a c d + b c \|a
+--R /
+--R +--------------+ +--------+
+--R 2 | 2 +-+ | 2
+--R (2a d - 2a b c)\|- a c d + b c \|a \|b x + a
+--R +
+--R +--------------+
+--R 2 2 2 3 2 | 2
+--R ((- 2a b d + 2a b c)x - 2a d + 2a b c)\|- a c d + b c
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2
+--R (a d\|a \|b x + a - a b d x - a d)
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +--------+ +-+ | 2
+--R +-+ | 2 2 2 \|a \|a c d - b c
+--R (a d\|a \|b x + a - a b d x - a d)atan(-------------------)
+--R (a d - b c)x
+--R +
+--R +------------+ +--------+ +------------+
+--R | 2 | 2 +-+ | 2
+--R b x\|a c d - b c \|b x + a - b x\|a \|a c d - b c
+--R /
+--R +------------+ +--------+
+--R 2 +-+ | 2 | 2
+--R (a d - a b c)\|a \|a c d - b c \|b x + a
+--R +
+--R +------------+
+--R 2 2 2 3 2 | 2
+--R ((- a b d + a b c)x - a d + a b c)\|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 502
+
+--S 503 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R d\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - 2d\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R | 2 +-----------+ +-+
+--R (2a d - 2b c)\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 503
+
+--S 504 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 504
+
+--S 505 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - d\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +-----------+ +-+
+--R d\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R +-----------+ +-+ \|a \|a c d - b c
+--R d\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R +-----------+ +-+ | 2
+--R (a d - b c)\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 505
+
+--S 506 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 506
+
+)clear all
+
+--S 507 of 994
+t0:=1/((a+b*x^2)^(3/2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a
+--R Type: Expression(Integer)
+--E 507
+
+--S 508 of 994
+r0:=-1/2*d*(4*b*c-a*d)*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/_
+ (c^(3/2)*(b*c-a*d)^(5/2))+b*x/(a*(b*c-a*d)*(c+d*x^2)*_
+ sqrt(a+b*x^2))+1/2*d*(2*b*c+a*d)*x*sqrt(a+b*x^2)/(a*c*(b*c-_
+ a*d)^2*(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R 2 3 2 2 2 2 2 | 2
+--R ((a d - 4a b c d )x + a c d - 4a b c d)\|b x + a
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 2 3 2 2 2 2 +-----------+ +-+
+--R ((a b d + 2b c d)x + (a d + 2b c )x)\|- a d + b c \|c
+--R /
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3 2 4
+--R ((2a c d - 4a b c d + 2a b c d)x + 2a c d - 4a b c d + 2a b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|b x + a
+--R Type: Expression(Integer)
+--E 508
+
+--S 509 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (3a b d - 12a b c d )x + (4a d - 13a b c d - 12a b c d)x
+--R +
+--R 3 2 2 2
+--R 4a c d - 16a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 3 3 2 6 3 3 2 2 2 3 2 4
+--R (- a b d + 4a b c d )x + (- 5a b d + 19a b c d + 4a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 2 4 2 3 2
+--R (- 4a d + 11a b c d + 20a b c d)x - 4a c d + 16a b c d
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R 2 2 3 5 2 2 2 3 2 3
+--R (- 2a b d - 4b c d)x + (- 10a b d - 16a b c d - 4b c )x
+--R +
+--R 3 2 2 2
+--R (- 8a d - 16a b c )x
+--R *
+--R +--------------+ +--------+
+--R | 2 | 2
+--R \|- a c d + b c \|b x + a
+--R +
+--R 2 2 3 5 2 2 2 3 2 3
+--R (6a b d + 12b c d)x + (14a b d + 16a b c d + 12b c )x
+--R +
+--R 3 2 2 2
+--R (8a d + 16a b c )x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 3 3 2 2 2 2 3 3 4
+--R (12a b c d - 24a b c d + 12a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2
+--R (16a c d - 20a b c d - 8a b c d + 12a b c )x + 16a c d
+--R +
+--R 3 3 2 2 4
+--R - 32a b c d + 16a b c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 3 2 3 2 3 2 2 4 3 6
+--R (- 4a b c d + 8a b c d - 4a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 20a b c d + 36a b c d - 12a b c d - 4a b c )x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 2 5 2 2
+--R (- 16a c d + 12a b c d + 24a b c d - 20a b c )x - 16a c d
+--R +
+--R 4 3 3 2 4
+--R 32a b c d - 16a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (3a b d - 12a b c d )x + (4a d - 13a b c d - 12a b c d)x
+--R +
+--R 3 2 2 2
+--R 4a c d - 16a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 3 3 2 6 3 3 2 2 2 3 2 4
+--R (- a b d + 4a b c d )x + (- 5a b d + 19a b c d + 4a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 2 4 2 3 2
+--R (- 4a d + 11a b c d + 20a b c d)x - 4a c d + 16a b c d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (3a b d - 12a b c d )x + (4a d - 13a b c d - 12a b c d)x
+--R +
+--R 3 2 2 2
+--R 4a c d - 16a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 3 3 2 6 3 3 2 2 2 3 2 4
+--R (- a b d + 4a b c d )x + (- 5a b d + 19a b c d + 4a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 2 4 2 3 2
+--R (- 4a d + 11a b c d + 20a b c d)x - 4a c d + 16a b c d
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 2 3 5 2 2 2 3 2 3
+--R (- a b d - 2b c d)x + (- 5a b d - 8a b c d - 2b c )x
+--R +
+--R 3 2 2 2
+--R (- 4a d - 8a b c )x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 2 3 5 2 2 2 3 2 3
+--R (3a b d + 6b c d)x + (7a b d + 8a b c d + 6b c )x
+--R +
+--R 3 2 2 2
+--R (4a d + 8a b c )x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 3 3 2 2 2 2 3 3 4
+--R (6a b c d - 12a b c d + 6a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2 3 3
+--R (8a c d - 10a b c d - 4a b c d + 6a b c )x + 8a c d - 16a b c d
+--R +
+--R 2 2 4
+--R 8a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 3 2 3 2 3 2 2 4 3 6
+--R (- 2a b c d + 4a b c d - 2a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 10a b c d + 18a b c d - 6a b c d - 2a b c )x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 2 5 2 2
+--R (- 8a c d + 6a b c d + 12a b c d - 10a b c )x - 8a c d
+--R +
+--R 4 3 3 2 4
+--R 16a b c d - 8a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 509
+
+--S 510 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----------+ +-+
+--R (a d - 4b c d)\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (- 2a d + 8b c d)\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 2 2 2 3 | 2 +-----------+ +-+
+--R (4a c d - 8a b c d + 4b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 510
+
+--S 511 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 511
+
+--S 512 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (- a d + 4b c d)\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 +-----------+ +-+
+--R (a d - 4b c d)\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 2 +-----------+ +-+ \|a \|a c d - b c
+--R (a d - 4b c d)\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 2 2 2 3 +-----------+ +-+ | 2
+--R (2a c d - 4a b c d + 2b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 512
+
+--S 513 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 513
+
+)clear all
+
+--S 514 of 994
+t0:=1/((a+b*x^2)^(3/2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 8 3 2 6 2 2 4 2 3 2
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3
+--R a c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 514
+
+--S 515 of 994
+r0:=-3/8*d*(8*b^2*c^2-4*a*b*c*d+a^2*d^2)*atanh(x*sqrt(b*c-a*d)/_
+ (sqrt(c)*sqrt(a+b*x^2)))/(c^(5/2)*(b*c-a*d)^(7/2))+b*x/_
+ (a*(b*c-a*d)*(c+d*x^2)^2*sqrt(a+b*x^2))+1/4*d*(4*b*c+a*d)*_
+ x*sqrt(a+b*x^2)/(a*c*(b*c-a*d)^2*(c+d*x^2)^2)+1/8*d*(4*b*c-_
+ a*d)*(2*b*c+3*a*d)*x*sqrt(a+b*x^2)/(a*c^2*(b*c-a*d)^3*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 3 5 2 4 2 2 3 4
+--R (3a d - 12a b c d + 24a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 2 3 2 3 2 3 2
+--R (6a c d - 24a b c d + 48a b c d )x + 3a c d - 12a b c d
+--R +
+--R 2 4
+--R 24a b c d
+--R *
+--R +--------+ +-----------+
+--R | 2 x\|- a d + b c
+--R \|b x + a atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 4 2 3 3 2 2 5
+--R (3a b d - 10a b c d - 8b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 3
+--R (3a d - 5a b c d - 12a b c d - 16b c d)x
+--R +
+--R 3 3 2 2 2 3 4
+--R (5a c d - 12a b c d - 8b c )x
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 2 4 4 3
+--R (16a c d - 48a b c d + 48a b c d - 16a b c d)x + 8a c d
+--R +
+--R 3 5 2 2 2 6 3 7
+--R - 24a b c d + 24a b c d - 8a b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|b x + a
+--R Type: Expression(Integer)
+--E 515
+
+--S 516 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 5 2 3 4 4 2 3 8
+--R (15a b d - 60a b c d + 120a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 6
+--R (60a b d - 210a b c d + 360a b c d + 240a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (48a d - 72a b c d - 81a b c d + 900a b c d + 120a b c d)x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 2
+--R (96a c d - 324a b c d + 528a b c d + 480a b c d)x
+--R +
+--R 5 2 3 4 3 2 3 2 4
+--R 48a c d - 192a b c d + 384a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 5 2 4 4 5 2 3 10
+--R (- 3a b d + 12a b c d - 24a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5 3 2 8
+--R (- 39a b d + 150a b c d - 288a b c d - 48a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 84a b d + 258a b c d - 363a b c d - 612a b c d
+--R +
+--R 5 4
+--R - 24a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 4
+--R (- 48a d + 24a b c d + 249a b c d - 1188a b c d - 312a b c d)x
+--R +
+--R 6 4 5 2 3 4 2 3 2 3 3 4 2 6 2 3
+--R (- 96a c d + 300a b c d - 432a b c d - 672a b c d)x - 48a c d
+--R +
+--R 5 3 2 4 2 4
+--R 192a b c d - 384a b c d
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R 2 3 4 4 3 5 2 2 9
+--R (- 6a b d + 20a b c d + 16b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 7
+--R (- 78a b d + 250a b c d + 216a b c d + 32b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5
+--R (- 168a b d + 430a b c d + 568a b c d + 384a b c d + 16b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4 3
+--R (- 96a d + 40a b c d + 672a b c d + 512a b c d + 192a b c )x
+--R +
+--R 5 3 4 2 2 2 3 4
+--R (- 160a c d + 384a b c d + 256a b c )x
+--R *
+--R +--------------+ +--------+
+--R | 2 | 2
+--R \|- a c d + b c \|b x + a
+--R +
+--R 2 3 4 4 3 5 2 2 9
+--R (30a b d - 100a b c d - 80b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 7
+--R (150a b d - 450a b c d - 440a b c d - 160b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5
+--R (216a b d - 470a b c d - 856a b c d - 640a b c d - 80b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4 3
+--R (96a d + 40a b c d - 864a b c d - 512a b c d - 320a b c )x
+--R +
+--R 5 3 4 2 2 2 3 4
+--R (160a c d - 384a b c d - 256a b c )x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 4 2 2 5 3 3 3 4 2 4 4 3 5 5 2 8
+--R (80a b c d - 240a b c d + 240a b c d - 80a b c d )x
+--R +
+--R 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2
+--R 320a b c d - 800a b c d + 480a b c d + 160a b c d
+--R +
+--R 5 6
+--R - 160a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2
+--R 256a c d - 128a b c d - 1072a b c d + 1424a b c d
+--R +
+--R 2 4 6 5 7
+--R - 400a b c d - 80a b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 2
+--R (512a c d - 1216a b c d + 576a b c d + 448a b c d - 320a b c )x
+--R +
+--R 6 4 3 5 5 2 4 2 6 3 3 7
+--R 256a c d - 768a b c d + 768a b c d - 256a b c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 10
+--R (- 16a b c d + 48a b c d - 48a b c d + 16a b c d )x
+--R +
+--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2
+--R - 208a b c d + 592a b c d - 528a b c d + 112a b c d
+--R +
+--R 6 6
+--R 32a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2
+--R - 448a b c d + 928a b c d - 112a b c d - 752a b c d
+--R +
+--R 2 5 6 6 7
+--R 368a b c d + 16a b c
+--R *
+--R 6
+--R x
+--R +
+--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2
+--R - 256a c d - 128a b c d + 1712a b c d - 1808a b c d
+--R +
+--R 3 4 6 2 5 7
+--R 272a b c d + 208a b c
+--R *
+--R 4
+--R x
+--R +
+--R 7 3 4 6 4 3 5 2 5 2 4 3 6
+--R - 512a c d + 1088a b c d - 192a b c d - 832a b c d
+--R +
+--R 3 4 7
+--R 448a b c
+--R *
+--R 2
+--R x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7
+--R - 256a c d + 768a b c d - 768a b c d + 256a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 3 2 5 2 3 4 4 2 3 8
+--R (15a b d - 60a b c d + 120a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 6
+--R (60a b d - 210a b c d + 360a b c d + 240a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (48a d - 72a b c d - 81a b c d + 900a b c d + 120a b c d)x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 2
+--R (96a c d - 324a b c d + 528a b c d + 480a b c d)x
+--R +
+--R 5 2 3 4 3 2 3 2 4
+--R 48a c d - 192a b c d + 384a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 5 2 4 4 5 2 3 10
+--R (- 3a b d + 12a b c d - 24a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5 3 2 8
+--R (- 39a b d + 150a b c d - 288a b c d - 48a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 84a b d + 258a b c d - 363a b c d - 612a b c d
+--R +
+--R 5 4
+--R - 24a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 4
+--R (- 48a d + 24a b c d + 249a b c d - 1188a b c d - 312a b c d)x
+--R +
+--R 6 4 5 2 3 4 2 3 2 3 3 4 2 6 2 3
+--R (- 96a c d + 300a b c d - 432a b c d - 672a b c d)x - 48a c d
+--R +
+--R 5 3 2 4 2 4
+--R 192a b c d - 384a b c d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 3 2 5 2 3 4 4 2 3 8
+--R (15a b d - 60a b c d + 120a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 6
+--R (60a b d - 210a b c d + 360a b c d + 240a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (48a d - 72a b c d - 81a b c d + 900a b c d + 120a b c d)x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 2
+--R (96a c d - 324a b c d + 528a b c d + 480a b c d)x
+--R +
+--R 5 2 3 4 3 2 3 2 4
+--R 48a c d - 192a b c d + 384a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 5 2 4 4 5 2 3 10
+--R (- 3a b d + 12a b c d - 24a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5 3 2 8
+--R (- 39a b d + 150a b c d - 288a b c d - 48a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 84a b d + 258a b c d - 363a b c d - 612a b c d
+--R +
+--R 5 4
+--R - 24a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 4
+--R (- 48a d + 24a b c d + 249a b c d - 1188a b c d - 312a b c d)x
+--R +
+--R 6 4 5 2 3 4 2 3 2 3 3 4 2 6 2 3
+--R (- 96a c d + 300a b c d - 432a b c d - 672a b c d)x - 48a c d
+--R +
+--R 5 3 2 4 2 4
+--R 192a b c d - 384a b c d
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 3 4 4 3 5 2 2 9
+--R (- 3a b d + 10a b c d + 8b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 7
+--R (- 39a b d + 125a b c d + 108a b c d + 16b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5
+--R (- 84a b d + 215a b c d + 284a b c d + 192a b c d + 8b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4 3
+--R (- 48a d + 20a b c d + 336a b c d + 256a b c d + 96a b c )x
+--R +
+--R 5 3 4 2 2 2 3 4
+--R (- 80a c d + 192a b c d + 128a b c )x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 3 4 4 3 5 2 2 9
+--R (15a b d - 50a b c d - 40b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 7
+--R (75a b d - 225a b c d - 220a b c d - 80b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5
+--R (108a b d - 235a b c d - 428a b c d - 320a b c d - 40b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4 3
+--R (48a d + 20a b c d - 432a b c d - 256a b c d - 160a b c )x
+--R +
+--R 5 3 4 2 2 2 3 4
+--R (80a c d - 192a b c d - 128a b c )x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 4 2 2 5 3 3 3 4 2 4 4 3 5 5 2 8
+--R (40a b c d - 120a b c d + 120a b c d - 40a b c d )x
+--R +
+--R 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2
+--R 160a b c d - 400a b c d + 240a b c d + 80a b c d
+--R +
+--R 5 6
+--R - 80a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6
+--R 128a c d - 64a b c d - 536a b c d + 712a b c d - 200a b c d
+--R +
+--R 5 7
+--R - 40a b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 2
+--R (256a c d - 608a b c d + 288a b c d + 224a b c d - 160a b c )x
+--R +
+--R 6 4 3 5 5 2 4 2 6 3 3 7
+--R 128a c d - 384a b c d + 384a b c d - 128a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 10
+--R (- 8a b c d + 24a b c d - 24a b c d + 8a b c d )x
+--R +
+--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2
+--R - 104a b c d + 296a b c d - 264a b c d + 56a b c d
+--R +
+--R 6 6
+--R 16a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2
+--R - 224a b c d + 464a b c d - 56a b c d - 376a b c d
+--R +
+--R 2 5 6 6 7
+--R 184a b c d + 8a b c
+--R *
+--R 6
+--R x
+--R +
+--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2
+--R - 128a c d - 64a b c d + 856a b c d - 904a b c d
+--R +
+--R 3 4 6 2 5 7
+--R 136a b c d + 104a b c
+--R *
+--R 4
+--R x
+--R +
+--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 2
+--R (- 256a c d + 544a b c d - 96a b c d - 416a b c d + 224a b c )x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7
+--R - 128a c d + 384a b c d - 384a b c d + 128a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 516
+
+--S 517 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 2 2 2 +-----------+ +-+
+--R (3a d - 12a b c d + 24b c d)\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 2 3 2 2 2 | 2 x\|- a d + b c
+--R (- 6a d + 24a b c d - 48b c d)\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 3 2 3 2 3 2 2 4 3 5 | 2
+--R (16a c d - 48a b c d + 48a b c d - 16b c )\|- a c d + b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 517
+
+--S 518 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 518
+
+--S 519 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 2 3 2 2 2 | 2 x\|- a d + b c
+--R (- 3a d + 12a b c d - 24b c d)\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 3 2 2 2 +-----------+ +-+
+--R (3a d - 12a b c d + 24b c d)\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 2 3 2 2 2 +-----------+ +-+ \|a \|a c d - b c
+--R (3a d - 12a b c d + 24b c d)\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 3 2 3 2 3 2 2 4 3 5 +-----------+ +-+ | 2
+--R (8a c d - 24a b c d + 24a b c d - 8b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 519
+
+--S 520 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 520
+
+)clear all
+
+--S 521 of 994
+t0:=1/((b*c/d+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R d
+--R (1) -------------------------
+--R +--------+
+--R 2 | 2
+--R (b d x + b c)\|d x + c
+--R Type: Expression(Integer)
+--E 521
+
+--S 522 of 994
+r0:=d*x/(b*c*sqrt(c+d*x^2))
+--R
+--R
+--R d x
+--R (2) --------------
+--R +--------+
+--R | 2
+--R b c\|d x + c
+--R Type: Expression(Integer)
+--E 522
+
+--S 523 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 2 +-+
+--R - d x\|d x + c + d x\|c
+--R (3) ------------------------------------
+--R +--------+
+--R +-+ | 2 2 2
+--R b c\|c \|d x + c - b c d x - b c
+--R Type: Union(Expression(Integer),...)
+--E 523
+
+--S 524 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 524
+
+--S 525 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 525
+
+)clear all
+
+--S 526 of 994
+t0:=1/((1+x^2)*sqrt(1-x^2))
+--R
+--R
+--R 1
+--R (1) -------------------
+--R +--------+
+--R 2 | 2
+--R (x + 1)\|- x + 1
+--R Type: Expression(Integer)
+--E 526
+
+--S 527 of 994
+r0:=atan(x*sqrt(2)/sqrt(1-x^2))/sqrt(2)
+--R
+--R
+--R +-+
+--R x\|2
+--R atan(-----------)
+--R +--------+
+--R | 2
+--R \|- x + 1
+--R (2) -----------------
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 527
+
+--S 528 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 | 2 2 +-+
+--R (2x + 1)\|- x + 1 - x - 1 \|2
+--R - atan(-----------------------------) + atan(----)
+--R 3 +-+ 2x
+--R x \|2
+--R (3) --------------------------------------------------
+--R +-+
+--R \|2
+--R Type: Union(Expression(Integer),...)
+--E 528
+
+--S 529 of 994
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R 2 | 2 2 +-+ +-+
+--R (2x + 1)\|- x + 1 - x - 1 x\|2 \|2
+--R - atan(-----------------------------) - atan(-----------) + atan(----)
+--R 3 +-+ +--------+ 2x
+--R x \|2 | 2
+--R \|- x + 1
+--R (4) ----------------------------------------------------------------------
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 529
+
+--S 530 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 530
+
+)clear all
+
+--S 531 of 994
+t0:=1/((a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 531
+
+--S 532 of 994
+r0:=atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/(sqrt(a)*sqrt(b*c-a*d))
+--R
+--R
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R (2) ---------------------
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 532
+
+--S 533 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 2 | 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )\|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R /
+--R +-----------+
+--R | 2
+--R 2\|a d - a b c
+--R ,
+--R
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R - atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R - atan(--------------------)
+--R (a d - b c)x
+--R /
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 533
+
+--S 534 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - 2\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R 2\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 534
+
+--S 535 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 535
+
+--S 536 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R -
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R +-----------+ +-+ \|- a d + a b c \|c
+--R - \|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - \|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R \|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 536
+
+--S 537 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 537
+
+)clear all
+
+--S 538 of 994
+t0:=(-1+x^2)/(1+x^2)^(3/2)
+--R
+--R
+--R 2
+--R x - 1
+--R (1) -----------------
+--R +------+
+--R 2 | 2
+--R (x + 1)\|x + 1
+--R Type: Expression(Integer)
+--E 538
+
+--S 539 of 994
+r0:=asinh(x)-2*x/sqrt(1+x^2)
+--R
+--R
+--R +------+
+--R | 2
+--R asinh(x)\|x + 1 - 2x
+--R (2) ----------------------
+--R +------+
+--R | 2
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 539
+
+--S 540 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+ +------+
+--R | 2 2 | 2
+--R (- x\|x + 1 + x + 1)log(\|x + 1 - x) + 2
+--R (3) ---------------------------------------------
+--R +------+
+--R | 2 2
+--R x\|x + 1 - x - 1
+--R Type: Union(Expression(Integer),...)
+--E 540
+
+--S 541 of 994
+m0:=a0-r0
+--R
+--R
+--R +------+
+--R | 2
+--R (4) - log(\|x + 1 - x) - asinh(x) - 2
+--R Type: Expression(Integer)
+--E 541
+
+--S 542 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 542
+
+)clear all
+
+--S 543 of 994
+t0:=(a+b*x^2)^(5/2)*(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+ +--------+
+--R 2 4 2 2 | 2 | 2
+--R (1) (b x + 2a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 543
+
+--S 544 of 994
+--r0:=1/7*b*x*(a+b*x^2)^(3/2)*(c+d*x^2)^(3/2)/d-2/35*(2*b*c-5*a*d)*_
+-- x*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/d-1/105*(4*b^2*c^2-13*a*b*c*d-_
+-- 15*a^2*d^2)*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)/d^2+1/105*(8*b^3*c^3-_
+-- 33*a*b^2*c^2*d+58*a^2*b*c*d^2+15*a^3*d^3)*elliptic_e(asin(x*_
+-- sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(a+b*x^2)*sqrt((c+_
+-- d*x^2)/c)/(b*(-d)^(5/2)*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-_
+-- 1/105*a*(b*c-a*d)*(4*b^2*c^2-13*a*b*c*d-15*a^2*d^2)*_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(b*(-d)^(5/2)*sqrt(a+_
+-- b*x^2)*sqrt(c+d*x^2))
+--E 544
+
+--S 545 of 994
+--a0:=integrate(t0,x)
+--E 545
+
+--S 546 of 994
+--m0:=a0-r0
+--E 546
+
+--S 547 of 994
+--d0:=D(m0,x)
+--E 547
+
+)clear all
+
+--S 548 of 994
+t0:=(a+b*x^2)^(3/2)*(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+ +--------+
+--R 2 | 2 | 2
+--R (1) (b x + a)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 548
+
+--S 549 of 994
+--r0:=1/5*b*x*(c+d*x^2)^(3/2)*sqrt(a+b*x^2)/d-2/15*(b*c-3*a*d)*x*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2)/d+1/15*(2*b^2*c^2-7*a*b*c*d-3*_
+-- a^2*d^2)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*_
+-- sqrt(c)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b*(-d)^(3/2)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-1/15*a*(b*c-a*d)*(b*c+3*a*d)*_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(b*(-d)^(3/2)*sqrt(a+_
+-- b*x^2)*sqrt(c+d*x^2))
+--E 549
+
+--S 550 of 994
+--a0:=integrate(t0,x)
+--E 550
+
+--S 551 of 994
+--m0:=a0-r0
+--E 551
+
+--S 552 of 994
+--d0:=D(m0,x)
+--E 552
+
+)clear all
+
+--S 553 of 994
+t0:=(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+ +--------+
+--R | 2 | 2
+--R (1) \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 553
+
+--S 554 of 994
+--r0:=1/3*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)+1/3*(b*c+a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b*sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))+1/3*a*(b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/_
+-- c)/(b*sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 554
+
+--S 555 of 994
+--a0:=integrate(t0,x)
+--E 555
+
+--S 556 of 994
+--m0:=a0-r0
+--E 556
+
+--S 557 of 994
+--d0:=D(m0,x)
+--E 557
+
+)clear all
+
+--S 558 of 994
+t0:=(c+d*x^2)^(1/2)/(a+b*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 558
+
+--S 559 of 994
+--r0:=elliptic_e(asin(x*sqrt(-b)/sqrt(a)),a*d/(b*c))*sqrt(a)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2)/(sqrt(-b)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c))
+--E 559
+
+--S 560 of 994
+--a0:=integrate(t0,x)
+--E 560
+
+--S 561 of 994
+--m0:=a0-r0
+--E 561
+
+--S 562 of 994
+--d0:=D(m0,x)
+--E 562
+
+)clear all
+
+--S 563 of 994
+t0:=(c+d*x^2)^(1/2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 563
+
+--S 564 of 994
+--r0:=x*sqrt(c+d*x^2)/(a*sqrt(a+b*x^2))+elliptic_e(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt(a+b*x^2)*sqrt((c+_
+-- d*x^2)/c)/(a*b*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(b*sqrt(a+b*x^2)*_
+-- sqrt(c+d*x^2))
+--E 564
+
+--S 565 of 994
+--a0:=integrate(t0,x)
+--E 565
+
+--S 566 of 994
+--m0:=a0-r0
+--E 566
+
+--S 567 of 994
+--d0:=D(m0,x)
+--E 567
+
+)clear all
+
+--S 568 of 994
+t0:=(c+d*x^2)^(1/2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 568
+
+--S 569 of 994
+--r0:=1/3*x*sqrt(c+d*x^2)/(a*(a+b*x^2)^(3/2))+1/3*(2*b*c-a*d)*x*_
+-- sqrt(c+d*x^2)/(a^2*(b*c-a*d)*sqrt(a+b*x^2))+1/3*(2*b*c-a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(-d)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a^2*b*(b*c-a*d)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-1/3*elliptic_f(asin(x*_
+-- sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt((c+d*x^2)/c)/(a*b*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 569
+
+--S 570 of 994
+--a0:=integrate(t0,x)
+--E 570
+
+--S 571 of 994
+--m0:=a0-r0
+--E 571
+
+--S 572 of 994
+--d0:=D(m0,x)
+--E 572
+
+)clear all
+
+--S 573 of 994
+t0:=(c+d*x^2)^(1/2)/(a+b*x^2)^(7/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) ------------------------------------------
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (b x + 3a b x + 3a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 573
+
+--S 574 of 994
+--r0:=1/5*x*sqrt(c+d*x^2)/(a*(a+b*x^2)^(5/2))+1/15*(4*b*c-3*a*d)*x*_
+-- sqrt(c+d*x^2)/(a^2*(b*c-a*d)*(a+b*x^2)^(3/2))+1/15*(8*b^2*c^2-_
+-- 13*a*b*c*d+3*a^2*d^2)*x*sqrt(c+d*x^2)/(a^3*(b*c-a*d)^2*sqrt(a+_
+-- b*x^2))+1/15*(8*b^2*c^2-13*a*b*c*d+3*a^2*d^2)*elliptic_e(_
+-- asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt(a+_
+-- b*x^2)*sqrt((c+d*x^2)/c)/(a^3*b*(b*c-a*d)^2*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))-1/15*(4*b*c-3*a*d)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt((c+d*x^2)/c)/(a^2*b*(b*c-a*d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 574
+
+--S 575 of 994
+--a0:=integrate(t0,x)
+--E 575
+
+--S 576 of 994
+--m0:=a0-r0
+--E 576
+
+--S 577 of 994
+--d0:=D(m0,x)
+--E 577
+
+)clear all
+
+--S 578 of 994
+t0:=(a+b*x^2)^(3/2)*(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+ +--------+
+--R 4 2 | 2 | 2
+--R (1) (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 578
+
+--S 579 of 994
+--r0:=2/35*(4*b*c-a*d)*x*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/b+1/7*d*x*(a+_
+-- b*x^2)^(5/2)*sqrt(c+d*x^2)/b+1/35*(9*a*c+b*c^2/d-2*a^2*d/b)*_
+-- x*sqrt(a+b*x^2)*sqrt(c+d*x^2)+2/35*(b*c+a*d)*(b^2*c^2-6*a*b*c*d+_
+-- a^2*d^2)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b^2*(-d)^(3/2)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))-1/35*a*(b*c-a*d)*(b^2*c^2+9*a*b*c*d-2*a^2*d^2)*_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(b^2*(-d)^(3/2)*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 579
+
+--S 580 of 994
+--a0:=integrate(t0,x)
+--E 580
+
+--S 581 of 994
+--m0:=a0-r0
+--E 581
+
+--S 582 of 994
+--d0:=D(m0,x)
+--E 582
+
+)clear all
+
+--S 583 of 994
+t0:=(a+b*x^2)^(1/2)*(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+ +--------+
+--R 2 | 2 | 2
+--R (1) (d x + c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 583
+
+--S 584 of 994
+--r0:=1/5*d*x*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/b+2/15*(3*b*c-a*d)*x*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2)/b+1/15*(3*b^2*c^2+7*a*b*c*d-2*a^2*_
+-- d^2)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b^2*sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))+2/15*a*(b*c-a*d)*(3*b*c-a*d)*elliptic_f(asin(x*_
+-- sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt((a+b*x^2)/a)*_
+-- sqrt((c+d*x^2)/c)/(b^2*sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 584
+
+--S 585 of 994
+--a0:=integrate(t0,x)
+--E 585
+
+--S 586 of 994
+--m0:=a0-r0
+--E 586
+
+--S 587 of 994
+--d0:=D(m0,x)
+--E 587
+
+)clear all
+
+--S 588 of 994
+t0:=(c+d*x^2)^(3/2)/(a+b*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 588
+
+--S 589 of 994
+--r0:=1/3*d*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)/b-2/3*(2*b*c-a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b^2*sqrt((a+b*x^2)/a)*sqrt(c+_
+-- d*x^2))+1/3*(3*b*c-2*a*d)*(b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/_
+-- (b^2*sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 589
+
+--S 590 of 994
+--a0:=integrate(t0,x)
+--E 590
+
+--S 591 of 994
+--m0:=a0-r0
+--E 591
+
+--S 592 of 994
+--d0:=D(m0,x)
+--E 592
+
+)clear all
+
+--S 593 of 994
+t0:=(c+d*x^2)^(3/2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 593
+
+--S 594 of 994
+--r0:=(b*c-a*d)*x*sqrt(c+d*x^2)/(a*b*sqrt(a+b*x^2))+(b*c-2*a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a*b^2*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))-2*(b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/sqrt(c)),_
+-- b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/_
+-- (b^2*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 594
+
+--S 595 of 994
+--a0:=integrate(t0,x)
+--E 595
+
+--S 596 of 994
+--m0:=a0-r0
+--E 596
+
+--S 597 of 994
+--d0:=D(m0,x)
+--E 597
+
+)clear all
+
+--S 598 of 994
+t0:=(c+d*x^2)^(3/2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 598
+
+--S 599 of 994
+--r0:=1/3*(b*c-a*d)*x*sqrt(c+d*x^2)/(a*b*(a+b*x^2)^(3/2))+2/3*(b*c+a*d)*_
+-- x*sqrt(c+d*x^2)/(a^2*b*sqrt(a+b*x^2))+2/3*(b*c+a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(-d)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a^2*b^2*sqrt((a+_
+-- b*x^2)/a)*sqrt(c+d*x^2))-1/3*(b*c+2*a*d)*elliptic_f(asin(x*_
+-- sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt((c+d*x^2)/c)/(a*b^2*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 599
+
+--S 600 of 994
+--a0:=integrate(t0,x)
+--E 600
+
+--S 601 of 994
+--m0:=a0-r0
+--E 601
+
+--S 602 of 994
+--d0:=D(m0,x)
+--E 602
+
+)clear all
+
+--S 603 of 994
+t0:=(c+d*x^2)^(3/2)/(a+b*x^2)^(7/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ------------------------------------------
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (b x + 3a b x + 3a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 603
+
+--S 604 of 994
+--r0:=1/5*(b*c-a*d)*x*sqrt(c+d*x^2)/(a*b*(a+b*x^2)^(5/2))+2/15*(2*b*c+_
+-- a*d)*x*sqrt(c+d*x^2)/(a^2*b*(a+b*x^2)^(3/2))+1/15*(8*b^2*c^2-_
+-- 3*a*b*c*d-2*a^2*d^2)*x*sqrt(c+d*x^2)/(a^3*b*(b*c-a*d)*sqrt(a+_
+-- b*x^2))+1/15*(8*b^2*c^2-3*a*b*c*d-2*a^2*d^2)*elliptic_e(asin(x*_
+-- sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt(a+b*x^2)*_
+-- sqrt((c+d*x^2)/c)/(a^3*b^2*(b*c-a*d)*sqrt((a+b*x^2)/a)*sqrt(c+_
+-- d*x^2))-2/15*(2*b*c+a*d)*elliptic_f(asin(x*sqrt(-d)/sqrt(c)),_
+-- b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/_
+-- (a^2*b^2*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 604
+
+--S 605 of 994
+--a0:=integrate(t0,x)
+--E 605
+
+--S 606 of 994
+--m0:=a0-r0
+--E 606
+
+--S 607 of 994
+--d0:=D(m0,x)
+--E 607
+
+)clear all
+
+--S 608 of 994
+t0:=sqrt(2+b*x^2)*sqrt(3+d*x^2)
+--R
+--R
+--R +--------+ +--------+
+--R | 2 | 2
+--R (1) \|b x + 2 \|d x + 3
+--R Type: Expression(Integer)
+--E 608
+
+--S 609 of 994
+--r0:=1/3*(3*b+2*d)*elliptic_e(asin(x*sqrt(-d)/sqrt(3)),3/2*b/d)*_
+-- sqrt(2)/(b*sqrt(-d))+1/3*(3*b-2*d)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(3)),3/2*b/d)*sqrt(2)/(b*sqrt(-d))+1/3*x*sqrt(2+b*x^2)*sqrt(3+d*x^2)
+--E 609
+
+--S 610 of 994
+--a0:=integrate(t0,x)
+--E 610
+
+--S 611 of 994
+--m0:=a0-r0
+--E 611
+
+--S 612 of 994
+--d0:=D(m0,x)
+--E 612
+
+)clear all
+
+--S 613 of 994
+t0:=sqrt(a+b*x^2)*sqrt(c+d*x^2)
+--R
+--R
+--R +--------+ +--------+
+--R | 2 | 2
+--R (1) \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 613
+
+--S 614 of 994
+--r0:=1/3*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)+1/3*(b*c+a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b*sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))+1/3*a*(b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/_
+-- (b*sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 614
+
+--S 615 of 994
+--a0:=integrate(t0,x)
+--E 615
+
+--S 616 of 994
+--m0:=a0-r0
+--E 616
+
+--S 617 of 994
+--d0:=D(m0,x)
+--E 617
+
+)clear all
+
+--S 618 of 994
+t0:=sqrt(3-6*x^2)*sqrt(2+4*x^2)
+--R
+--R
+--R +---------+ +-------+
+--R | 2 | 2
+--R (1) \|- 6x + 3 \|4x + 2
+--R Type: Expression(Integer)
+--E 618
+
+--S 619 of 994
+--r0:=2*elliptic_f(asin(x*sqrt(2)),-1)/sqrt(3)+x*sqrt(2/3)*_
+-- sqrt(1-2*x^2)*sqrt(1+2*x^2)
+--E 619
+
+--S 620 of 994
+--a0:=integrate(t0,x)
+--E 620
+
+--S 621 of 994
+--m0:=a0-r0
+--E 621
+
+--S 622 of 994
+--d0:=D(m0,x)
+--E 622
+
+)clear all
+
+--S 623 of 994
+t0:=sqrt(2+4*x^2)*sqrt(3+6*x^2)
+--R
+--R
+--R +-------+ +-------+
+--R | 2 | 2
+--R (1) \|4x + 2 \|6x + 3
+--R Type: Expression(Integer)
+--E 623
+
+--S 624 of 994
+r0:=2*x^3*sqrt(2/3)+x*sqrt(6)
+--R
+--R
+--R +-+
+--R 2\|2 3 +-+
+--R (2) ----- x + \|6 x
+--R +-+
+--R \|3
+--R Type: Polynomial(AlgebraicNumber)
+--E 624
+
+--S 625 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+ +-------+
+--R 3 | 2 | 2
+--R (2x + 3x)\|4x + 2 \|6x + 3
+--R (3) ------------------------------
+--R 2
+--R 6x + 3
+--R Type: Union(Expression(Integer),...)
+--E 625
+
+--S 626 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-------+ +-------+
+--R 3 +-+ | 2 | 2 3 +-+ +-+
+--R (2x + 3x)\|3 \|4x + 2 \|6x + 3 + (- 6x - 3x)\|3 \|6
+--R +
+--R 5 3 +-+
+--R (- 12x - 6x )\|2
+--R /
+--R 2 +-+
+--R (6x + 3)\|3
+--R Type: Expression(Integer)
+--E 626
+
+--S 627 of 994
+d0:=D(m0,x)
+--R
+--R
+--R +-------+ +-------+
+--R +-+ 2 +-+ +-+ | 2 | 2 4 2
+--R (- \|6 - 2x \|2 \|3 )\|4x + 2 \|6x + 3 + 24x + 24x + 6
+--R (5) ------------------------------------------------------------
+--R +-------+ +-------+
+--R | 2 | 2
+--R \|4x + 2 \|6x + 3
+--R Type: Expression(Integer)
+--E 627
+
+)clear all
+
+--S 628 of 994
+t0:=(a+b*x^2)^(7/2)/(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (b x + 3a b x + 3a b x + a )\|b x + a
+--R (1) ------------------------------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 628
+
+--S 629 of 994
+--r0:=-6/35*b*(b*c-2*a*d)*x*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/d^2+1/7*b*_
+-- x*(a+b*x^2)^(5/2)*sqrt(c+d*x^2)/d+1/105*b*(24*b^2*c^2-71*a*b*_
+-- c*d+71*a^2*d^2)*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)/d^3+8/105*(b*c-_
+-- 2*a*d)*(6*b^2*c^2-11*a*b*c*d+11*a^2*d^2)*elliptic_e(asin(x*_
+-- sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(a+b*x^2)*sqrt((c+d*_
+-- x^2)/c)/((-d)^(7/2)*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-1/105*_
+-- a*(b*c-a*d)*(24*b^2*c^2-71*a*b*c*d+71*a^2*d^2)*elliptic_f(_
+-- asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt((a+b*x^2)/a)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(7/2)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 629
+
+--S 630 of 994
+--a0:=integrate(t0,x)
+--E 630
+
+--S 631 of 994
+--m0:=a0-r0
+--E 631
+
+--S 632 of 994
+--d0:=D(m0,x)
+--E 632
+
+)clear all
+
+--S 633 of 994
+t0:=(a+b*x^2)^(5/2)/(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 633
+
+--S 634 of 994
+--r0:=1/5*b*x*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/d-4/15*b*(b*c-2*a*d)*x*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2)/d^2+1/15*(8*b^2*c^2-23*a*b*c*d+23*_
+-- a^2*d^2)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*_
+-- sqrt(c)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/((-d)^(5/2)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-4/15*a*(b*c-2*a*d)*(b*c-a*d)*_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/((-d)^(5/2)*sqrt(a+b*x^2)*_
+-- sqrt(c+d*x^2))
+--E 634
+
+--S 635 of 994
+--a0:=integrate(t0,x)
+--E 635
+
+--S 636 of 994
+--m0:=a0-r0
+--E 636
+
+--S 637 of 994
+--d0:=D(m0,x)
+--E 637
+
+)clear all
+
+--S 638 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 638
+
+--S 639 of 994
+--r0:=1/3*b*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)/d+2/3*(b*c-2*a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/((-d)^(3/2)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))-1/3*a*(b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/_
+-- ((-d)^(3/2)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 639
+
+--S 640 of 994
+--a0:=integrate(t0,x)
+--E 640
+
+--S 641 of 994
+--m0:=a0-r0
+--E 641
+
+--S 642 of 994
+--d0:=D(m0,x)
+--E 642
+
+)clear all
+
+--S 643 of 994
+t0:=(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 643
+
+--S 644 of 994
+--r0:=elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))
+--E 644
+
+--S 645 of 994
+--a0:=integrate(t0,x)
+--E 645
+
+--S 646 of 994
+--m0:=a0-r0
+--E 646
+
+--S 647 of 994
+--d0:=D(m0,x)
+--E 647
+
+)clear all
+
+--S 648 of 994
+t0:=1/((a+b*x^2)^(1/2)*(c+d*x^2)^(1/2))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 648
+
+--S 649 of 994
+--r0:=elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 649
+
+--S 650 of 994
+--a0:=integrate(t0,x)
+--E 650
+
+--S 651 of 994
+--m0:=a0-r0
+--E 651
+
+--S 652 of 994
+--d0:=D(m0,x)
+--E 652
+
+)clear all
+
+--S 653 of 994
+t0:=1/((a+b*x^2)^(3/2)*(c+d*x^2)^(1/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R +--------+ +--------+
+--R 2 | 2 | 2
+--R (b x + a)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 653
+
+--S 654 of 994
+--r0:=b*x*sqrt(c+d*x^2)/(a*(b*c-a*d)*sqrt(a+b*x^2))+elliptic_e(_
+-- asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))
+--E 654
+
+--S 655 of 994
+--a0:=integrate(t0,x)
+--E 655
+
+--S 656 of 994
+--m0:=a0-r0
+--E 656
+
+--S 657 of 994
+--d0:=D(m0,x)
+--E 657
+
+)clear all
+
+--S 658 of 994
+t0:=1/((a+b*x^2)^(5/2)*(c+d*x^2)^(1/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------
+--R +--------+ +--------+
+--R 2 4 2 2 | 2 | 2
+--R (b x + 2a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 658
+
+--S 659 of 994
+--r0:=1/3*b*x*sqrt(c+d*x^2)/(a*(b*c-a*d)*(a+b*x^2)^(3/2))+2/3*b*_
+-- (b*c-2*a*d)*x*sqrt(c+d*x^2)/(a^2*(b*c-a*d)^2*sqrt(a+b*x^2))+_
+-- 2/3*(b*c-2*a*d)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*_
+-- sqrt(c)*sqrt(-d)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a^2*(b*c-_
+-- a*d)^2*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-1/3*elliptic_f(_
+-- asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 659
+
+--S 660 of 994
+--a0:=integrate(t0,x)
+--E 660
+
+--S 661 of 994
+--m0:=a0-r0
+--E 661
+
+--S 662 of 994
+--d0:=D(m0,x)
+--E 662
+
+)clear all
+
+--S 663 of 994
+t0:=1/((a+b*x^2)^(7/2)*(c+d*x^2)^(1/2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R +--------+ +--------+
+--R 3 6 2 4 2 2 3 | 2 | 2
+--R (b x + 3a b x + 3a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 663
+
+--S 664 of 994
+--r0:=1/5*b*x*sqrt(c+d*x^2)/(a*(b*c-a*d)*(a+b*x^2)^(5/2))+4/15*b*_
+-- (b*c-2*a*d)*x*sqrt(c+d*x^2)/(a^2*(b*c-a*d)^2*(a+b*x^2)^(3/2))+_
+-- 1/15*b*(8*b^2*c^2-23*a*b*c*d+23*a^2*d^2)*x*sqrt(c+d*x^2)/_
+-- (a^3*(b*c-a*d)^3*sqrt(a+b*x^2))+1/15*(8*b^2*c^2-23*a*b*c*d+_
+-- 23*a^2*d^2)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*_
+-- sqrt(c)*sqrt(-d)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a^3*(b*c-_
+-- a*d)^3*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-4/15*(b*c-2*a*d)*_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)^2*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 664
+
+--S 665 of 994
+--a0:=integrate(t0,x)
+--E 665
+
+--S 666 of 994
+--m0:=a0-r0
+--E 666
+
+--S 667 of 994
+--d0:=D(m0,x)
+--E 667
+
+)clear all
+
+--S 668 of 994
+t0:=(a+b*x^2)^(7/2)/(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (b x + 3a b x + 3a b x + a )\|b x + a
+--R (1) ------------------------------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 668
+
+--S 669 of 994
+--r0:=-(b*c-a*d)*x*(a+b*x^2)^(5/2)/(c*d*sqrt(c+d*x^2))+1/5*b*(6*b*c-_
+-- 5*a*d)*x*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/(c*d^2)-1/15*b*(24*b^2*_
+-- c^2-43*a*b*c*d+15*a^2*d^2)*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)/_
+-- (c*d^3)-1/15*(48*b^3*c^3-128*a*b^2*c^2*d+103*a^2*b*c*d^2-_
+-- 15*a^3*d^3)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/((-d)^(7/2)*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))+1/15*a*(b*c-a*d)*(24*b^2*_
+-- c^2-43*a*b*c*d+15*a^2*d^2)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/_
+-- ((-d)^(7/2)*sqrt(c)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 669
+
+--S 670 of 994
+--a0:=integrate(t0,x)
+--E 670
+
+--S 671 of 994
+--m0:=a0-r0
+--E 671
+
+--S 672 of 994
+--d0:=D(m0,x)
+--E 672
+
+)clear all
+
+--S 673 of 994
+t0:=(a+b*x^2)^(5/2)/(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 673
+
+--S 674 of 994
+--r0:=-(b*c-a*d)*x*(a+b*x^2)^(3/2)/(c*d*sqrt(c+d*x^2))+1/3*b*_
+-- (4*b*c-3*a*d)*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)/(c*d^2)-1/3*_
+-- (8*b^2*c^2-13*a*b*c*d+3*a^2*d^2)*elliptic_e(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/((-d)^(5/2)*_
+-- sqrt(c)*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))+1/3*a*(4*b*c-3*a*d)*_
+-- (b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/((-d)^(5/2)*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 674
+
+--S 675 of 994
+--a0:=integrate(t0,x)
+--E 675
+
+--S 676 of 994
+--m0:=a0-r0
+--E 676
+
+--S 677 of 994
+--d0:=D(m0,x)
+--E 677
+
+)clear all
+
+--S 678 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 678
+
+--S 679 of 994
+--r0:=-(b*c-a*d)*x*sqrt(a+b*x^2)/(c*d*sqrt(c+d*x^2))-(2*b*c-a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(a+b*x^2)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(3/2)*sqrt(c)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))+a*(b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/sqrt(c)),_
+-- b*c/(a*d))*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/((-d)^(3/2)*_
+-- sqrt(c)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 679
+
+--S 680 of 994
+--a0:=integrate(t0,x)
+--E 680
+
+--S 681 of 994
+--m0:=a0-r0
+--E 681
+
+--S 682 of 994
+--d0:=D(m0,x)
+--E 682
+
+)clear all
+
+--S 683 of 994
+t0:=(a+b*x^2)^(1/2)/(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 683
+
+--S 684 of 994
+--r0:=x*sqrt(a+b*x^2)/(c*sqrt(c+d*x^2))-elliptic_e(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(sqrt(c)*_
+-- sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))+a*elliptic_f(_
+-- asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt((a+b*x^2)/a)*_
+-- sqrt((c+d*x^2)/c)/(sqrt(c)*sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 684
+
+--S 685 of 994
+--a0:=integrate(t0,x)
+--E 685
+
+--S 686 of 994
+--m0:=a0-r0
+--E 686
+
+--S 687 of 994
+--d0:=D(m0,x)
+--E 687
+
+)clear all
+
+--S 688 of 994
+t0:=1/((a+b*x^2)^(1/2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R +--------+ +--------+
+--R 2 | 2 | 2
+--R (d x + c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 688
+
+--S 689 of 994
+--r0:=-d*x*sqrt(a+b*x^2)/(c*(b*c-a*d)*sqrt(c+d*x^2))-_
+-- elliptic_e(asin(x*sqrt(-b)/sqrt(a)),a*d/(b*c))*sqrt(a)*_
+-- sqrt(-b)*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2)/(c*(b*c-a*d)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c))
+--E 689
+
+--S 690 of 994
+--a0:=integrate(t0,x)
+--E 690
+
+--S 691 of 994
+--m0:=a0-r0
+--E 691
+
+--S 692 of 994
+--d0:=D(m0,x)
+--E 692
+
+)clear all
+
+--S 693 of 994
+t0:=1/((a+b*x^2)^(3/2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------
+--R +--------+ +--------+
+--R 4 2 | 2 | 2
+--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 693
+
+--S 694 of 994
+--r0:=b*x/(a*(b*c-a*d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))+d*(b*c+a*d)*x*_
+-- sqrt(a+b*x^2)/(a*c*(b*c-a*d)^2*sqrt(c+d*x^2))+(b*c+a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(-d)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)^2*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))+elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt((c+_
+-- d*x^2)/c)/((b*c-a*d)*sqrt(c)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 694
+
+--S 695 of 994
+--a0:=integrate(t0,x)
+--E 695
+
+--S 696 of 994
+--m0:=a0-r0
+--E 696
+
+--S 697 of 994
+--d0:=D(m0,x)
+--E 697
+
+)clear all
+
+--S 698 of 994
+t0:=1/((a+b*x^2)^(5/2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R (1)
+--R 1
+--R --------------------------------------------------------------------------
+--R +--------+ +--------+
+--R 2 6 2 4 2 2 2 | 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 698
+
+--S 699 of 994
+--r0:=1/3*b*x/(a*(b*c-a*d)*(a+b*x^2)^(3/2)*sqrt(c+d*x^2))+2/3*b*(b*c-_
+-- 3*a*d)*x/(a^2*(b*c-a*d)^2*sqrt(a+b*x^2)*sqrt(c+d*x^2))+1/3*_
+-- d*(2*b^2*c^2-7*a*b*c*d-3*a^2*d^2)*x*sqrt(a+b*x^2)/(a^2*c*(b*c-_
+-- a*d)^3*sqrt(c+d*x^2))+1/3*(2*b^2*c^2-7*a*b*c*d-3*a^2*d^2)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(-d)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)^3*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-1/3*(b*c+3*a*d)*_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(-d)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)^2*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 699
+
+--S 700 of 994
+--a0:=integrate(t0,x)
+--E 700
+
+--S 701 of 994
+--m0:=a0-r0
+--E 701
+
+--S 702 of 994
+--d0:=D(m0,x)
+--E 702
+
+)clear all
+
+--S 703 of 994
+t0:=1/(sqrt(2+b*x^2)*sqrt(3+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + 2 \|d x + 3
+--R Type: Expression(Integer)
+--E 703
+
+--S 704 of 994
+--r0:=elliptic_f(asin(x*sqrt(-d)/sqrt(3)),3/2*b/d)/(sqrt(2)*sqrt(-d))
+--E 704
+
+--S 705 of 994
+--a0:=integrate(t0,x)
+--E 705
+
+--S 706 of 994
+--m0:=a0-r0
+--E 706
+
+--S 707 of 994
+--d0:=D(m0,x)
+--E 707
+
+)clear all
+
+--S 708 of 994
+t0:=1/(sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 708
+
+--S 709 of 994
+--r0:=elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 709
+
+--S 710 of 994
+--a0:=integrate(t0,x)
+--E 710
+
+--S 711 of 994
+--m0:=a0-r0
+--E 711
+
+--S 712 of 994
+--d0:=D(m0,x)
+--E 712
+
+)clear all
+
+--S 713 of 994
+t0:=1/(sqrt(4-x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|- x + 4 \|d x + c
+--R Type: Expression(Integer)
+--E 713
+
+--S 714 of 994
+--r0:=elliptic_f(asin(1/2*x),-4*d/c)*sqrt((c+d*x^2)/c)/sqrt(c+d*x^2)
+--E 714
+
+--S 715 of 994
+--a0:=integrate(t0,x)
+--E 715
+
+--S 716 of 994
+--m0:=a0-r0
+--E 716
+
+--S 717 of 994
+--d0:=D(m0,x)
+--E 717
+
+)clear all
+
+--S 718 of 994
+t0:=1/(sqrt(4+x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) --------------------
+--R +------+ +--------+
+--R | 2 | 2
+--R \|x + 4 \|d x + c
+--R Type: Expression(Integer)
+--E 718
+
+--S 719 of 994
+--r0:=-%i*elliptic_f(%i*asinh(1/2*x),4*d/c)*sqrt((c+d*x^2)/c)/sqrt(c+d*x^2)
+--E 719
+
+--S 720 of 994
+--a0:=integrate(t0,x)
+--E 720
+
+--S 721 of 994
+--m0:=a0-r0
+--E 721
+
+--S 722 of 994
+--d0:=D(m0,x)
+--E 722
+
+)clear all
+
+--S 723 of 994
+t0:=1/(sqrt(1-x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+ +-------+
+--R | 2 | 2
+--R \|- x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 723
+
+--S 724 of 994
+--r0:=elliptic_f(asin(x),-3/2)/sqrt(2)
+--E 724
+
+--S 725 of 994
+--a0:=integrate(t0,x)
+--E 725
+
+--S 726 of 994
+--m0:=a0-r0
+--E 726
+
+--S 727 of 994
+--d0:=D(m0,x)
+--E 727
+
+)clear all
+
+--S 728 of 994
+t0:=1/(sqrt(2-3*x^2)*sqrt(1-x^2))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +---------+ +--------+
+--R | 2 | 2
+--R \|- 3x + 2 \|- x + 1
+--R Type: Expression(Integer)
+--E 728
+
+--S 729 of 994
+--r0:=elliptic_f(asin(x),3/2)/sqrt(2)
+--E 729
+
+--S 730 of 994
+--a0:=integrate(t0,x)
+--E 730
+
+--S 731 of 994
+--m0:=a0-r0
+--E 731
+
+--S 732 of 994
+--d0:=D(m0,x)
+--E 732
+
+)clear all
+
+--S 733 of 994
+t0:=1/(sqrt(4-x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+ +-------+
+--R | 2 | 2
+--R \|- x + 4 \|3x + 2
+--R Type: Expression(Integer)
+--E 733
+
+--S 734 of 994
+--r0:=elliptic_f(asin(1/2*x),-6)/sqrt(2)
+--E 734
+
+--S 735 of 994
+--a0:=integrate(t0,x)
+--E 735
+
+--S 736 of 994
+--m0:=a0-r0
+--E 736
+
+--S 737 of 994
+--d0:=D(m0,x)
+--E 737
+
+)clear all
+
+--S 738 of 994
+t0:=1/(sqrt(2-3*x^2)*sqrt(4-x^2))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +---------+ +--------+
+--R | 2 | 2
+--R \|- 3x + 2 \|- x + 4
+--R Type: Expression(Integer)
+--E 738
+
+--S 739 of 994
+--r0:=elliptic_f(asin(1/2*x),6)/sqrt(2)
+--E 739
+
+--S 740 of 994
+--a0:=integrate(t0,x)
+--E 740
+
+--S 741 of 994
+--m0:=a0-r0
+--E 741
+
+--S 742 of 994
+--d0:=D(m0,x)
+--E 742
+
+)clear all
+
+--S 743 of 994
+t0:=1/(sqrt(1-4*x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R +---------+ +-------+
+--R | 2 | 2
+--R \|- 4x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 743
+
+--S 744 of 994
+--r0:=1/2*elliptic_f(asin(2*x),-3/8)/sqrt(2)
+--E 744
+
+--S 745 of 994
+--a0:=integrate(t0,x)
+--E 745
+
+--S 746 of 994
+--m0:=a0-r0
+--E 746
+
+--S 747 of 994
+--d0:=D(m0,x)
+--E 747
+
+)clear all
+
+--S 748 of 994
+t0:=1/(sqrt(1-4*x^2)*sqrt(2-3*x^2))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +---------+ +---------+
+--R | 2 | 2
+--R \|- 4x + 1 \|- 3x + 2
+--R Type: Expression(Integer)
+--E 748
+
+--S 749 of 994
+--r0:=1/2*elliptic_f(asin(2*x),3/8)/sqrt(2)
+--E 749
+
+--S 750 of 994
+--a0:=integrate(t0,x)
+--E 750
+
+--S 751 of 994
+--m0:=a0-r0
+--E 751
+
+--S 752 of 994
+--d0:=D(m0,x)
+--E 752
+
+)clear all
+
+--S 753 of 994
+t0:=1/(sqrt(1+x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------
+--R +------+ +-------+
+--R | 2 | 2
+--R \|x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 753
+
+--S 754 of 994
+--r0:=-%i*elliptic_f(%i*asinh(x),3/2)/sqrt(2)
+--E 754
+
+--S 755 of 994
+--a0:=integrate(t0,x)
+--E 755
+
+--S 756 of 994
+--m0:=a0-r0
+--E 756
+
+--S 757 of 994
+--d0:=D(m0,x)
+--E 757
+
+)clear all
+
+--S 758 of 994
+t0:=1/(sqrt(2-3*x^2)*sqrt(1+x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +---------+ +------+
+--R | 2 | 2
+--R \|- 3x + 2 \|x + 1
+--R Type: Expression(Integer)
+--E 758
+
+--S 759 of 994
+--r0:=elliptic_f(asin(x*sqrt(3/2)),-2/3)/sqrt(3)
+--E 759
+
+--S 760 of 994
+--a0:=integrate(t0,x)
+--E 760
+
+--S 761 of 994
+--m0:=a0-r0
+--E 761
+
+--S 762 of 994
+--d0:=D(m0,x)
+--E 762
+
+)clear all
+
+--S 763 of 994
+t0:=1/(sqrt(4+x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------
+--R +------+ +-------+
+--R | 2 | 2
+--R \|x + 4 \|3x + 2
+--R Type: Expression(Integer)
+--E 763
+
+--S 764 of 994
+--r0:=-%i*elliptic_f(%i*asinh(1/2*x),6)/sqrt(2)
+--E 764
+
+--S 765 of 994
+--a0:=integrate(t0,x)
+--E 765
+
+--S 766 of 994
+--m0:=a0-r0
+--E 766
+
+--S 767 of 994
+--d0:=D(m0,x)
+--E 767
+
+)clear all
+
+--S 768 of 994
+t0:=1/(sqrt(2-3*x^2)*sqrt(4+x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +---------+ +------+
+--R | 2 | 2
+--R \|- 3x + 2 \|x + 4
+--R Type: Expression(Integer)
+--E 768
+
+--S 769 of 994
+--r0:=1/2*elliptic_f(asin(x*sqrt(3/2)),-1/6)/sqrt(3)
+--E 769
+
+--S 770 of 994
+--a0:=integrate(t0,x)
+--E 770
+
+--S 771 of 994
+--m0:=a0-r0
+--E 771
+
+--S 772 of 994
+--d0:=D(m0,x)
+--E 772
+
+)clear all
+
+--S 773 of 994
+t0:=1/(sqrt(2+3*x^2)*sqrt(1+4*x^2))
+--R
+--R
+--R 1
+--R (1) --------------------
+--R +-------+ +-------+
+--R | 2 | 2
+--R \|3x + 2 \|4x + 1
+--R Type: Expression(Integer)
+--E 773
+
+--S 774 of 994
+--r0:=-1/2*%i*elliptic_f(%i*asinh(2*x),3/8)/sqrt(2)
+--E 774
+
+--S 775 of 994
+--a0:=integrate(t0,x)
+--E 775
+
+--S 776 of 994
+--m0:=a0-r0
+--E 776
+
+--S 777 of 994
+--d0:=D(m0,x)
+--E 777
+
+)clear all
+
+--S 778 of 994
+t0:=1/(sqrt(2-3*x^2)*sqrt(1+4*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R +---------+ +-------+
+--R | 2 | 2
+--R \|- 3x + 2 \|4x + 1
+--R Type: Expression(Integer)
+--E 778
+
+--S 779 of 994
+--r0:=elliptic_f(asin(x*sqrt(3/2)),-8/3)/sqrt(3)
+--E 779
+
+--S 780 of 994
+--a0:=integrate(t0,x)
+--E 780
+
+--S 781 of 994
+--m0:=a0-r0
+--E 781
+
+--S 782 of 994
+--d0:=D(m0,x)
+--E 782
+
+)clear all
+
+--S 783 of 994
+t0:=1/(sqrt(1-x^2)*sqrt(-1+2*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+ +-------+
+--R | 2 | 2
+--R \|- x + 1 \|2x - 1
+--R Type: Expression(Integer)
+--E 783
+
+--S 784 of 994
+--r0:=-elliptic_f(acos(x),2),elliptic_f(asin(x),2)*sqrt(1-2*x^2)/sqrt(-1+2*x^2)
+--E 784
+
+--S 785 of 994
+--a0:=integrate(t0,x)
+--E 785
+
+--S 786 of 994
+--m0:=a0-r0
+--E 786
+
+--S 787 of 994
+--d0:=D(m0,x)
+--E 787
+
+)clear all
+
+--S 788 of 994
+t0:=sqrt(2+b*x^2)/sqrt(3+d*x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + 2
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|d x + 3
+--R Type: Expression(Integer)
+--E 788
+
+--S 789 of 994
+--r0:=elliptic_e(asin(x*sqrt(-d)/sqrt(3)),3/2*b/d)*sqrt(2)/sqrt(-d)
+--E 789
+
+--S 790 of 994
+--a0:=integrate(t0,x)
+--E 790
+
+--S 791 of 994
+--m0:=a0-r0
+--E 791
+
+--S 792 of 994
+--d0:=D(m0,x)
+--E 792
+
+)clear all
+
+--S 793 of 994
+t0:=sqrt(a+b*x^2)/sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 793
+
+--S 794 of 994
+--r0:=elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))
+--E 794
+
+--S 795 of 994
+--a0:=integrate(t0,x)
+--E 795
+
+--S 796 of 994
+--m0:=a0-r0
+--E 796
+
+--S 797 of 994
+--d0:=D(m0,x)
+--E 797
+
+)clear all
+
+--S 798 of 994
+t0:=sqrt(-1+3*x^2)/sqrt(2-3*x^2)
+--R
+--R
+--R +-------+
+--R | 2
+--R \|3x - 1
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 3x + 2
+--R Type: Expression(Integer)
+--E 798
+
+--S 799 of 994
+--r0:=elliptic_e(asin(x*sqrt(3/2)),2)*sqrt(-1+3*x^2)/(sqrt(3)*sqrt(1-3*x^2))
+--E 799
+
+--S 800 of 994
+--a0:=integrate(t0,x)
+--E 800
+
+--S 801 of 994
+--m0:=a0-r0
+--E 801
+
+--S 802 of 994
+--d0:=D(m0,x)
+--E 802
+
+)clear all
+
+--S 803 of 994
+t0:=sqrt(1+2*c*x^2/(b-sqrt(b^2-4*a*c)))/sqrt(1+2*c*x^2/(b+sqrt(b^2-4*a*c)))
+--R
+--R
+--R +--------------------------+
+--R | +-----------+
+--R | | 2 2
+--R |\|- 4a c + b - 2c x - b
+--R |--------------------------
+--R | +-----------+
+--R | | 2
+--R \| \|- 4a c + b - b
+--R (1) -----------------------------
+--R +--------------------------+
+--R | +-----------+
+--R | | 2 2
+--R |\|- 4a c + b + 2c x + b
+--R |--------------------------
+--R | +-----------+
+--R | | 2
+--R \| \|- 4a c + b + b
+--R Type: Expression(Integer)
+--E 803
+
+--S 804 of 994
+--r0:=elliptic_e(asin(x*sqrt(2)*sqrt(-c)/sqrt(b+sqrt(b^2-4*a*c))),_
+-- (b+sqrt(b^2-4*a*c))/(b-sqrt(b^2-4*a*c)))*sqrt(b+_
+-- sqrt(b^2-4*a*c))/(sqrt(2)*sqrt(-c))
+--E 804
+
+--S 805 of 994
+--a0:=integrate(t0,x)
+--E 805
+
+--S 806 of 994
+--m0:=a0-r0
+--E 806
+
+--S 807 of 994
+--d0:=D(m0,x)
+--E 807
+
+)clear all
+
+--S 808 of 994
+t0:=(a+b*x^3)*(c+d*x^3)^p
+--R
+--R
+--R 3 3 p
+--R (1) (b x + a)(d x + c)
+--R Type: Expression(Integer)
+--E 808
+
+--S 809 of 994
+--r0:=b*x*(c+d*x^3)^(1+p)/(d*(4+3*p))-(b*c-a*d*(4+3*p))*x*(c+d*x^3)^p*_
+-- hypergeometric(1/3,-p,4/3,-d*x^3/c)/(d*(4+3*p)*((c+d*x^3)/c)^p)
+--E 809
+
+--S 810 of 994
+--a0:=integrate(t0,x)
+--E 810
+
+--S 811 of 994
+--m0:=a0-r0
+--E 811
+
+--S 812 of 994
+--d0:=D(m0,x)
+--E 812
+
+)clear all
+
+--S 813 of 994
+t0:=(a+b*x^3)*(c+d*x^3)^4
+--R
+--R
+--R (1)
+--R 4 15 4 3 12 3 2 2 9
+--R b d x + (a d + 4b c d )x + (4a c d + 6b c d )x
+--R +
+--R 2 2 3 6 3 4 3 4
+--R (6a c d + 4b c d)x + (4a c d + b c )x + a c
+--R Type: Polynomial(Integer)
+--E 813
+
+--S 814 of 994
+r0:=a*c^4*x+1/4*c^3*(b*c+4*a*d)*x^4+2/7*c^2*d*(2*b*c+3*a*d)*x^7+_
+ 1/5*c*d^2*(3*b*c+2*a*d)*x^10+1/13*d^3*(4*b*c+a*d)*x^13+1/16*b*d^4*x^16
+--R
+--R
+--R (2)
+--R 1 4 16 1 4 4 3 13 2 3 3 2 2 10
+--R -- b d x + (-- a d + -- b c d )x + (- a c d + - b c d )x
+--R 16 13 13 5 5
+--R +
+--R 6 2 2 4 3 7 3 1 4 4 4
+--R (- a c d + - b c d)x + (a c d + - b c )x + a c x
+--R 7 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 814
+
+--S 815 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 4 16 1 4 4 3 13 2 3 3 2 2 10
+--R -- b d x + (-- a d + -- b c d )x + (- a c d + - b c d )x
+--R 16 13 13 5 5
+--R +
+--R 6 2 2 4 3 7 3 1 4 4 4
+--R (- a c d + - b c d)x + (a c d + - b c )x + a c x
+--R 7 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 815
+
+--S 816 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 816
+
+--S 817 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 817
+
+)clear all
+
+--S 818 of 994
+t0:=(a+b*x^3)*(c+d*x^3)^3
+--R
+--R
+--R (1)
+--R 3 12 3 2 9 2 2 6 2 3 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3
+--R a c
+--R Type: Polynomial(Integer)
+--E 818
+
+--S 819 of 994
+r0:=a*c^3*x+1/4*c^2*(b*c+3*a*d)*x^4+3/7*c*d*(b*c+a*d)*x^7+_
+ 1/10*d^2*(3*b*c+a*d)*x^10+1/13*b*d^3*x^13
+--R
+--R
+--R (2)
+--R 1 3 13 1 3 3 2 10 3 2 3 2 7
+--R -- b d x + (-- a d + -- b c d )x + (- a c d + - b c d)x
+--R 13 10 10 7 7
+--R +
+--R 3 2 1 3 4 3
+--R (- a c d + - b c )x + a c x
+--R 4 4
+--R Type: Polynomial(Fraction(Integer))
+--E 819
+
+--S 820 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 3 13 1 3 3 2 10 3 2 3 2 7
+--R -- b d x + (-- a d + -- b c d )x + (- a c d + - b c d)x
+--R 13 10 10 7 7
+--R +
+--R 3 2 1 3 4 3
+--R (- a c d + - b c )x + a c x
+--R 4 4
+--R Type: Polynomial(Fraction(Integer))
+--E 820
+
+--S 821 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 821
+
+--S 822 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 822
+
+)clear all
+
+--S 823 of 994
+t0:=(a+b*x^3)*(c+d*x^3)^2
+--R
+--R
+--R 2 9 2 6 2 3 2
+--R (1) b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Polynomial(Integer)
+--E 823
+
+--S 824 of 994
+r0:=a*c^2*x+1/4*c*(b*c+2*a*d)*x^4+1/7*d*(2*b*c+a*d)*x^7+1/10*b*d^2*x^10
+--R
+--R
+--R 1 2 10 1 2 2 7 1 1 2 4 2
+--R (2) -- b d x + (- a d + - b c d)x + (- a c d + - b c )x + a c x
+--R 10 7 7 2 4
+--R Type: Polynomial(Fraction(Integer))
+--E 824
+
+--S 825 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 10 1 2 2 7 1 1 2 4 2
+--R (3) -- b d x + (- a d + - b c d)x + (- a c d + - b c )x + a c x
+--R 10 7 7 2 4
+--R Type: Polynomial(Fraction(Integer))
+--E 825
+
+--S 826 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 826
+
+--S 827 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 827
+
+)clear all
+
+--S 828 of 994
+t0:=(a+b*x^3)*(c+d*x^3)
+--R
+--R
+--R 6 3
+--R (1) b d x + (a d + b c)x + a c
+--R Type: Polynomial(Integer)
+--E 828
+
+--S 829 of 994
+r0:=a*c*x+1/4*(b*c+a*d)*x^4+1/7*b*d*x^7
+--R
+--R
+--R 1 7 1 1 4
+--R (2) - b d x + (- a d + - b c)x + a c x
+--R 7 4 4
+--R Type: Polynomial(Fraction(Integer))
+--E 829
+
+--S 830 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 7 1 1 4
+--R (3) - b d x + (- a d + - b c)x + a c x
+--R 7 4 4
+--R Type: Polynomial(Fraction(Integer))
+--E 830
+
+--S 831 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 831
+
+--S 832 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 832
+
+)clear all
+
+--S 833 of 994
+t0:=(a+b*x^3)/(c+d*x^3)
+--R
+--R
+--R 3
+--R b x + a
+--R (1) --------
+--R 3
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 833
+
+--S 834 of 994
+r0:=b*x/d-1/3*(b*c-a*d)*log(c^(1/3)+d^(1/3)*x)/(c^(2/3)*d^(4/3))+_
+ 1/6*(b*c-a*d)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/_
+ (c^(2/3)*d^(4/3))+(b*c-a*d)*atan((c^(1/3)-2*d^(1/3)*x)/_
+ (c^(1/3)*sqrt(3)))/(c^(2/3)*d^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- a d + b c)\|3 log(x \|d - x\|c \|d + \|c )
+--R +
+--R 3+-+ 3+-+
+--R +-+ 3+-+ 3+-+ 2x\|d - \|c
+--R (2a d - 2b c)\|3 log(x\|d + \|c ) + (6a d - 6b c)atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R +-+3+-+2 3+-+
+--R 6b x\|3 \|c \|d
+--R /
+--R +-+3+-+2 3+-+
+--R 6d\|3 \|c \|d
+--R Type: Expression(Integer)
+--E 834
+
+--S 835 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R +-+ 2 3| 2 3| 2 2
+--R (- a d + b c)\|3 log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R +-+ 3| 2
+--R (2a d - 2b c)\|3 log(x\|c d + c)
+--R +
+--R +---+
+--R +-+3| 2 +-+ +---+
+--R 2x\|3 \|c d - c\|3 +-+3| 2
+--R (6a d - 6b c)atan(--------------------) + 6b x\|3 \|c d
+--R 3c
+--R /
+--R +---+
+--R +-+3| 2
+--R 6d\|3 \|c d
+--R Type: Union(Expression(Integer),...)
+--E 835
+
+--S 836 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- a d + b c)\|3 \|c \|d log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R (2a d - 2b c)\|3 \|c \|d log(x\|c d + c)
+--R +
+--R +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (a d - b c)\|3 \|c d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 3+-+ 3+-+
+--R (- 2a d + 2b c)\|3 \|c d log(x\|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 3+-+2 3+-+ 2x\|3 \|c d - c\|3
+--R (6a d - 6b c)\|c \|d atan(--------------------)
+--R 3c
+--R +
+--R +---+ 3+-+ 3+-+
+--R 3| 2 2x\|d - \|c
+--R (- 6a d + 6b c)\|c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R /
+--R +---+
+--R +-+3+-+2 3+-+3| 2
+--R 6d\|3 \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 836
+
+--S 837 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 837
+
+)clear all
+
+--S 838 of 994
+t0:=(a+b*x^3)/(c+d*x^3)^2
+--R
+--R
+--R 3
+--R b x + a
+--R (1) -------------------
+--R 2 6 3 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 838
+
+--S 839 of 994
+r0:=-1/3*(b*c-a*d)*x/(c*d*(c+d*x^3))+1/9*(b*c+2*a*d)*log(c^(1/3)+_
+ d^(1/3)*x)/(c^(5/3)*d^(4/3))-1/18*(b*c+2*a*d)*log(c^(2/3)-_
+ c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(5/3)*d^(4/3))-1/3*(b*c+_
+ 2*a*d)*atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/_
+ (c^(5/3)*d^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R ((- 2a d - b c d)x - 2a c d - b c )\|3 log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 3 2 +-+ 3+-+ 3+-+
+--R ((4a d + 2b c d)x + 4a c d + 2b c )\|3 log(x\|d + \|c )
+--R +
+--R 3+-+ 3+-+
+--R 2 3 2 2x\|d - \|c
+--R ((12a d + 6b c d)x + 12a c d + 6b c )atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R +-+3+-+2 3+-+
+--R (6a d - 6b c)x\|3 \|c \|d
+--R /
+--R 2 3 2 +-+3+-+2 3+-+
+--R (18c d x + 18c d)\|3 \|c \|d
+--R Type: Expression(Integer)
+--E 839
+
+--S 840 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 2 3 2 +-+ 2 3| 2 3| 2 2
+--R ((- 2a d - b c d)x - 2a c d - b c )\|3 log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R 2 3 2 +-+ 3| 2
+--R ((4a d + 2b c d)x + 4a c d + 2b c )\|3 log(x\|c d + c)
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 3 2 2x\|3 \|c d - c\|3
+--R ((12a d + 6b c d)x + 12a c d + 6b c )atan(--------------------)
+--R 3c
+--R +
+--R +---+
+--R +-+3| 2
+--R (6a d - 6b c)x\|3 \|c d
+--R /
+--R +---+
+--R 2 3 2 +-+3| 2
+--R (18c d x + 18c d)\|3 \|c d
+--R Type: Union(Expression(Integer),...)
+--E 840
+
+--S 841 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- 2a d - b c)\|3 \|c \|d log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R (4a d + 2b c)\|3 \|c \|d log(x\|c d + c)
+--R +
+--R +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (2a d + b c)\|3 \|c d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 3+-+ 3+-+
+--R (- 4a d - 2b c)\|3 \|c d log(x\|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 3+-+2 3+-+ 2x\|3 \|c d - c\|3
+--R (12a d + 6b c)\|c \|d atan(--------------------)
+--R 3c
+--R +
+--R +---+ 3+-+ 3+-+
+--R 3| 2 2x\|d - \|c
+--R (- 12a d - 6b c)\|c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R /
+--R +---+
+--R +-+3+-+2 3+-+3| 2
+--R 18c d\|3 \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 841
+
+--S 842 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 842
+
+)clear all
+
+--S 843 of 994
+t0:=(a+b*x^3)/(c+d*x^3)^3
+--R
+--R
+--R 3
+--R b x + a
+--R (1) -----------------------------
+--R 3 9 2 6 2 3 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 843
+
+--S 844 of 994
+r0:=-1/6*(b*c-a*d)*x/(c*d*(c+d*x^3)^2)+1/18*(b*c+5*a*d)*x/_
+ (c^2*d*(c+d*x^3))+1/27*(b*c+5*a*d)*log(c^(1/3)+d^(1/3)*x)/_
+ (c^(8/3)*d^(4/3))-1/54*(b*c+5*a*d)*log(c^(2/3)-c^(1/3)*d^(1/3)*_
+ x+d^(2/3)*x^2)/(c^(8/3)*d^(4/3))-1/9*(b*c+5*a*d)*_
+ atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(8/3)*d^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 2 6 2 2 3 2 3 +-+
+--R ((- 5a d - b c d )x + (- 10a c d - 2b c d)x - 5a c d - b c )\|3
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|d - x\|c \|d + \|c )
+--R +
+--R 3 2 6 2 2 3 2 3 +-+
+--R ((10a d + 2b c d )x + (20a c d + 4b c d)x + 10a c d + 2b c )\|3
+--R *
+--R 3+-+ 3+-+
+--R log(x\|d + \|c )
+--R +
+--R 3 2 6 2 2 3 2 3
+--R ((30a d + 6b c d )x + (60a c d + 12b c d)x + 30a c d + 6b c )
+--R *
+--R 3+-+ 3+-+
+--R 2x\|d - \|c
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 2 4 2 +-+3+-+2 3+-+
+--R ((15a d + 3b c d)x + (24a c d - 6b c )x)\|3 \|c \|d
+--R /
+--R 2 3 6 3 2 3 4 +-+3+-+2 3+-+
+--R (54c d x + 108c d x + 54c d)\|3 \|c \|d
+--R Type: Expression(Integer)
+--E 844
+
+--S 845 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 6 2 2 3 2 3 +-+
+--R ((- 5a d - b c d )x + (- 10a c d - 2b c d)x - 5a c d - b c )\|3
+--R *
+--R +---+2 +---+
+--R 2 3| 2 3| 2 2
+--R log(x \|c d - c x\|c d + c )
+--R +
+--R 3 2 6 2 2 3 2 3 +-+
+--R ((10a d + 2b c d )x + (20a c d + 4b c d)x + 10a c d + 2b c )\|3
+--R *
+--R +---+
+--R 3| 2
+--R log(x\|c d + c)
+--R +
+--R 3 2 6 2 2 3 2 3
+--R ((30a d + 6b c d )x + (60a c d + 12b c d)x + 30a c d + 6b c )
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|c d - c\|3
+--R atan(--------------------)
+--R 3c
+--R +
+--R +---+
+--R 2 4 2 +-+3| 2
+--R ((15a d + 3b c d)x + (24a c d - 6b c )x)\|3 \|c d
+--R /
+--R +---+
+--R 2 3 6 3 2 3 4 +-+3| 2
+--R (54c d x + 108c d x + 54c d)\|3 \|c d
+--R Type: Union(Expression(Integer),...)
+--E 845
+
+--S 846 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- 5a d - b c)\|3 \|c \|d log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R (10a d + 2b c)\|3 \|c \|d log(x\|c d + c)
+--R +
+--R +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (5a d + b c)\|3 \|c d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 3+-+ 3+-+
+--R (- 10a d - 2b c)\|3 \|c d log(x\|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 3+-+2 3+-+ 2x\|3 \|c d - c\|3
+--R (30a d + 6b c)\|c \|d atan(--------------------)
+--R 3c
+--R +
+--R +---+ 3+-+ 3+-+
+--R 3| 2 2x\|d - \|c
+--R (- 30a d - 6b c)\|c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R /
+--R +---+
+--R 2 +-+3+-+2 3+-+3| 2
+--R 54c d\|3 \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 846
+
+--S 847 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 847
+
+)clear all
+
+--S 848 of 994
+t0:=(a+b*x^3)^2*(c+d*x^3)^p
+--R
+--R
+--R 2 6 3 2 3 p
+--R (1) (b x + 2a b x + a )(d x + c)
+--R Type: Expression(Integer)
+--E 848
+
+--S 849 of 994
+--r0:=-b*(4*b*c-a*d*(10+3*p))*x*(c+d*x^3)^(1+p)/(d^2*(4+3*p)*(7+3*p))+_
+-- b*x*(a+b*x^3)*(c+d*x^3)^(1+p)/(d*(7+3*p))+(4*b^2*c^2-2*a*b*c*_
+-- d*(7+3*p)+a^2*d^2*(28+33*p+9*p^2))*x*(c+d*x^3)^p*_
+-- hypergeometric(1/3,-p,4/3,-d*x^3/c)/(d^2*(4+3*p)*(7+3*p)*((c+d*x^3)/c)^p)
+--E 849
+
+--S 850 of 994
+--a0:=integrate(t0,x)
+--E 850
+
+--S 851 of 994
+--m0:=a0-r0
+--E 851
+
+--S 852 of 994
+--d0:=D(m0,x)
+--E 852
+
+)clear all
+
+--S 853 of 994
+t0:=(a+b*x^3)^2*(c+d*x^3)^3
+--R
+--R
+--R (1)
+--R 2 3 15 3 2 2 12 2 3 2 2 2 9
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 6 2 2 3 3 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 853
+
+--S 854 of 994
+r0:=a^2*c^3*x+1/4*a*c^2*(2*b*c+3*a*d)*x^4+1/7*c*(b^2*c^2+6*a*b*c*d+_
+ 3*a^2*d^2)*x^7+1/10*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^10+_
+ 1/13*b*d^2*(3*b*c+2*a*d)*x^13+1/16*b^2*d^3*x^16
+--R
+--R
+--R (2)
+--R 1 2 3 16 2 3 3 2 2 13
+--R -- b d x + (-- a b d + -- b c d )x
+--R 16 13 13
+--R +
+--R 1 2 3 3 2 3 2 2 10 3 2 2 6 2 1 2 3 7
+--R (-- a d + - a b c d + -- b c d)x + (- a c d + - a b c d + - b c )x
+--R 10 5 10 7 7 7
+--R +
+--R 3 2 2 1 3 4 2 3
+--R (- a c d + - a b c )x + a c x
+--R 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 854
+
+--S 855 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 3 16 2 3 3 2 2 13
+--R -- b d x + (-- a b d + -- b c d )x
+--R 16 13 13
+--R +
+--R 1 2 3 3 2 3 2 2 10 3 2 2 6 2 1 2 3 7
+--R (-- a d + - a b c d + -- b c d)x + (- a c d + - a b c d + - b c )x
+--R 10 5 10 7 7 7
+--R +
+--R 3 2 2 1 3 4 2 3
+--R (- a c d + - a b c )x + a c x
+--R 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 855
+
+--S 856 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 856
+
+--S 857 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 857
+
+)clear all
+
+--S 858 of 994
+t0:=(a+b*x^3)^2*(c+d*x^3)^2
+--R
+--R
+--R (1)
+--R 2 2 12 2 2 9 2 2 2 2 6
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 3 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 858
+
+--S 859 of 994
+r0:=a^2*c^2*x+1/2*a*c*(b*c+a*d)*x^4+1/7*(b^2*c^2+4*a*b*c*d+a^2*d^2)*x^7+_
+ 1/5*b*d*(b*c+a*d)*x^10+1/13*b^2*d^2*x^13
+--R
+--R
+--R (2)
+--R 1 2 2 13 1 2 1 2 10 1 2 2 4 1 2 2 7
+--R -- b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 13 5 5 7 7 7
+--R +
+--R 1 2 1 2 4 2 2
+--R (- a c d + - a b c )x + a c x
+--R 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 859
+
+--S 860 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 2 13 1 2 1 2 10 1 2 2 4 1 2 2 7
+--R -- b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 13 5 5 7 7 7
+--R +
+--R 1 2 1 2 4 2 2
+--R (- a c d + - a b c )x + a c x
+--R 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 860
+
+--S 861 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 861
+
+--S 862 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 862
+
+)clear all
+
+--S 863 of 994
+t0:=(a+b*x^3)^2*(c+d*x^3)
+--R
+--R
+--R 2 9 2 6 2 3 2
+--R (1) b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Polynomial(Integer)
+--E 863
+
+--S 864 of 994
+r0:=a^2*c*x+1/4*a*(2*b*c+a*d)*x^4+1/7*b*(b*c+2*a*d)*x^7+1/10*b^2*d*x^10
+--R
+--R
+--R 1 2 10 2 1 2 7 1 2 1 4 2
+--R (2) -- b d x + (- a b d + - b c)x + (- a d + - a b c)x + a c x
+--R 10 7 7 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 864
+
+--S 865 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 10 2 1 2 7 1 2 1 4 2
+--R (3) -- b d x + (- a b d + - b c)x + (- a d + - a b c)x + a c x
+--R 10 7 7 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 865
+
+--S 866 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 866
+
+--S 867 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 867
+
+)clear all
+
+--S 868 of 994
+t0:=(a+b*x^3)^2/(c+d*x^3)
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 3
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 868
+
+--S 869 of 994
+r0:=-b*(b*c-2*a*d)*x/d^2+1/4*b^2*x^4/d+1/3*(b*c-a*d)^2*log(c^(1/3)+_
+ d^(1/3)*x)/(c^(2/3)*d^(7/3))-1/6*(b*c-a*d)^2*log(c^(2/3)-_
+ c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(2/3)*d^(7/3))-(b*c-a*d)^2*_
+ atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(2/3)*d^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 2a d + 4a b c d - 2b c )\|3 log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 2 2 2 +-+ 3+-+ 3+-+
+--R (4a d - 8a b c d + 4b c )\|3 log(x\|d + \|c )
+--R +
+--R 3+-+ 3+-+
+--R 2 2 2 2 2x\|d - \|c
+--R (12a d - 24a b c d + 12b c )atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 2 4 2 +-+3+-+2 3+-+
+--R (3b d x + (24a b d - 12b c)x)\|3 \|c \|d
+--R /
+--R 2 +-+3+-+2 3+-+
+--R 12d \|3 \|c \|d
+--R Type: Expression(Integer)
+--E 869
+
+--S 870 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 2 2 2 2 +-+ 2 3| 2 3| 2 2
+--R (- 2a d + 4a b c d - 2b c )\|3 log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+ 3| 2
+--R (4a d - 8a b c d + 4b c )\|3 log(x\|c d + c)
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 2 2 2 2x\|3 \|c d - c\|3
+--R (12a d - 24a b c d + 12b c )atan(--------------------)
+--R 3c
+--R +
+--R +---+
+--R 2 4 2 +-+3| 2
+--R (3b d x + (24a b d - 12b c)x)\|3 \|c d
+--R /
+--R +---+
+--R 2 +-+3| 2
+--R 12d \|3 \|c d
+--R Type: Union(Expression(Integer),...)
+--E 870
+
+--S 871 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- a d + 2a b c d - b c )\|3 \|c \|d log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 3| 2
+--R (2a d - 4a b c d + 2b c )\|3 \|c \|d log(x\|c d + c)
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (a d - 2a b c d + b c )\|3 \|c d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 3+-+ 3+-+
+--R (- 2a d + 4a b c d - 2b c )\|3 \|c d log(x\|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 2 2 2 3+-+2 3+-+ 2x\|3 \|c d - c\|3
+--R (6a d - 12a b c d + 6b c )\|c \|d atan(--------------------)
+--R 3c
+--R +
+--R +---+ 3+-+ 3+-+
+--R 2 2 2 2 3| 2 2x\|d - \|c
+--R (- 6a d + 12a b c d - 6b c )\|c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R /
+--R +---+
+--R 2 +-+3+-+2 3+-+3| 2
+--R 6d \|3 \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 871
+
+--S 872 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 872
+
+)clear all
+
+--S 873 of 994
+t0:=(a+b*x^3)^2/(c+d*x^3)^2
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 2 6 3 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 873
+
+--S 874 of 994
+r0:=b^2*x/d^2+1/3*(b*c-a*d)^2*x/(c*d^2*(c+d*x^3))-2/9*(b*c-a*d)*_
+ (2*b*c+a*d)*log(c^(1/3)+d^(1/3)*x)/(c^(5/3)*d^(7/3))+1/9*_
+ (b*c-a*d)*(2*b*c+a*d)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*_
+ x^2)/(c^(5/3)*d^(7/3))+2/3*(b*c-a*d)*(2*b*c+a*d)*_
+ atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(5/3)*d^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+
+--R ((- a d - a b c d + 2b c d)x - a c d - a b c d + 2b c )\|3
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+
+--R ((2a d + 2a b c d - 4b c d)x + 2a c d + 2a b c d - 4b c )\|3
+--R *
+--R 3+-+ 3+-+
+--R log(x\|d + \|c )
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((6a d + 6a b c d - 12b c d)x + 6a c d + 6a b c d - 12b c )
+--R *
+--R 3+-+ 3+-+
+--R 2x\|d - \|c
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 2 4 2 2 2 2 +-+3+-+2 3+-+
+--R (9b c d x + (3a d - 6a b c d + 12b c )x)\|3 \|c \|d
+--R /
+--R 3 3 2 2 +-+3+-+2 3+-+
+--R (9c d x + 9c d )\|3 \|c \|d
+--R Type: Expression(Integer)
+--E 874
+
+--S 875 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+
+--R ((- a d - a b c d + 2b c d)x - a c d - a b c d + 2b c )\|3
+--R *
+--R +---+2 +---+
+--R 2 3| 2 3| 2 2
+--R log(x \|c d - c x\|c d + c )
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+
+--R ((2a d + 2a b c d - 4b c d)x + 2a c d + 2a b c d - 4b c )\|3
+--R *
+--R +---+
+--R 3| 2
+--R log(x\|c d + c)
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((6a d + 6a b c d - 12b c d)x + 6a c d + 6a b c d - 12b c )
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|c d - c\|3
+--R atan(--------------------)
+--R 3c
+--R +
+--R +---+
+--R 2 4 2 2 2 2 +-+3| 2
+--R (9b c d x + (3a d - 6a b c d + 12b c )x)\|3 \|c d
+--R /
+--R +---+
+--R 3 3 2 2 +-+3| 2
+--R (9c d x + 9c d )\|3 \|c d
+--R Type: Union(Expression(Integer),...)
+--E 875
+
+--S 876 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- a d - a b c d + 2b c )\|3 \|c \|d log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 3| 2
+--R (2a d + 2a b c d - 4b c )\|3 \|c \|d log(x\|c d + c)
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (a d + a b c d - 2b c )\|3 \|c d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 3+-+ 3+-+
+--R (- 2a d - 2a b c d + 4b c )\|3 \|c d log(x\|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 2 2 2 3+-+2 3+-+ 2x\|3 \|c d - c\|3
+--R (6a d + 6a b c d - 12b c )\|c \|d atan(--------------------)
+--R 3c
+--R +
+--R +---+ 3+-+ 3+-+
+--R 2 2 2 2 3| 2 2x\|d - \|c
+--R (- 6a d - 6a b c d + 12b c )\|c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R /
+--R +---+
+--R 2 +-+3+-+2 3+-+3| 2
+--R 9c d \|3 \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 876
+
+--S 877 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 877
+
+)clear all
+
+--S 878 of 994
+t0:=(a+b*x^3)^2/(c+d*x^3)^3
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -----------------------------
+--R 3 9 2 6 2 3 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 878
+
+--S 879 of 994
+r0:=-1/6*(b*c-a*d)*x*(a+b*x^3)/(c*d*(c+d*x^3)^2)-1/18*(b*c-a*d)*_
+ (4*b*c+5*a*d)*x/(c^2*d^2*(c+d*x^3))+1/27*(2*b^2*c^2+2*a*b*c*_
+ d+5*a^2*d^2)*log(c^(1/3)+d^(1/3)*x)/(c^(8/3)*d^(7/3))-1/54*_
+ (2*b^2*c^2+2*a*b*c*d+5*a^2*d^2)*log(c^(2/3)-c^(1/3)*d^(1/3)*_
+ x+d^(2/3)*x^2)/(c^(8/3)*d^(7/3))-1/9*(2*b^2*c^2+2*a*b*c*d+_
+ 5*a^2*d^2)*atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/_
+ (c^(8/3)*d^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 6
+--R (- 5a d - 2a b c d - 2b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4
+--R (- 10a c d - 4a b c d - 4b c d)x - 5a c d - 2a b c d - 2b c
+--R *
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 4 3 2 2 2 6 2 3 2 2 2 3 3
+--R (10a d + 4a b c d + 4b c d )x + (20a c d + 8a b c d + 8b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 10a c d + 4a b c d + 4b c
+--R *
+--R +-+ 3+-+ 3+-+
+--R \|3 log(x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 6
+--R (30a d + 12a b c d + 12b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4
+--R (60a c d + 24a b c d + 24b c d)x + 30a c d + 12a b c d + 12b c
+--R *
+--R 3+-+ 3+-+
+--R 2x\|d - \|c
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 2 3 2 2 2 4 2 2 2 2 3
+--R ((15a d + 6a b c d - 21b c d)x + (24a c d - 12a b c d - 12b c )x)
+--R *
+--R +-+3+-+2 3+-+
+--R \|3 \|c \|d
+--R /
+--R 2 4 6 3 3 3 4 2 +-+3+-+2 3+-+
+--R (54c d x + 108c d x + 54c d )\|3 \|c \|d
+--R Type: Expression(Integer)
+--E 879
+
+--S 880 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 2 2 2 6
+--R (- 5a d - 2a b c d - 2b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4
+--R (- 10a c d - 4a b c d - 4b c d)x - 5a c d - 2a b c d - 2b c
+--R *
+--R +---+2 +---+
+--R +-+ 2 3| 2 3| 2 2
+--R \|3 log(x \|c d - c x\|c d + c )
+--R +
+--R 2 4 3 2 2 2 6 2 3 2 2 2 3 3
+--R (10a d + 4a b c d + 4b c d )x + (20a c d + 8a b c d + 8b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 10a c d + 4a b c d + 4b c
+--R *
+--R +---+
+--R +-+ 3| 2
+--R \|3 log(x\|c d + c)
+--R +
+--R 2 4 3 2 2 2 6
+--R (30a d + 12a b c d + 12b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4
+--R (60a c d + 24a b c d + 24b c d)x + 30a c d + 12a b c d + 12b c
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|c d - c\|3
+--R atan(--------------------)
+--R 3c
+--R +
+--R 2 3 2 2 2 4 2 2 2 2 3
+--R ((15a d + 6a b c d - 21b c d)x + (24a c d - 12a b c d - 12b c )x)
+--R *
+--R +---+
+--R +-+3| 2
+--R \|3 \|c d
+--R /
+--R +---+
+--R 2 4 6 3 3 3 4 2 +-+3| 2
+--R (54c d x + 108c d x + 54c d )\|3 \|c d
+--R Type: Union(Expression(Integer),...)
+--E 880
+
+--S 881 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- 5a d - 2a b c d - 2b c )\|3 \|c \|d log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 3| 2
+--R (10a d + 4a b c d + 4b c )\|3 \|c \|d log(x\|c d + c)
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (5a d + 2a b c d + 2b c )\|3 \|c d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 3+-+ 3+-+
+--R (- 10a d - 4a b c d - 4b c )\|3 \|c d log(x\|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 2 2 2 3+-+2 3+-+ 2x\|3 \|c d - c\|3
+--R (30a d + 12a b c d + 12b c )\|c \|d atan(--------------------)
+--R 3c
+--R +
+--R +---+ 3+-+ 3+-+
+--R 2 2 2 2 3| 2 2x\|d - \|c
+--R (- 30a d - 12a b c d - 12b c )\|c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R /
+--R +---+
+--R 2 2 +-+3+-+2 3+-+3| 2
+--R 54c d \|3 \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 881
+
+--S 882 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 882
+
+)clear all
+
+--S 883 of 994
+t0:=(c+d*x^3)^p/(a+b*x^3)
+--R
+--R
+--R 3 p
+--R (d x + c)
+--R (1) -----------
+--R 3
+--R b x + a
+--R Type: Expression(Integer)
+--E 883
+
+--S 884 of 994
+--r0:=x*(c+d*x^3)^p*AppellF1(1/3,1,-p,4/3,-b*x^3/a,-d*x^3/c)/(a*(1+d*x^3/c)^p)
+--E 884
+
+--S 885 of 994
+--a0:=integrate(t0,x)
+--E 885
+
+--S 886 of 994
+--m0:=a0-r0
+--E 886
+
+--S 887 of 994
+--d0:=D(m0,x)
+--E 887
+
+)clear all
+
+--S 888 of 994
+t0:=(c+d*x^3)^4/(a+b*x^3)
+--R
+--R
+--R 4 12 3 9 2 2 6 3 3 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R (1) ----------------------------------------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 888
+
+--S 889 of 994
+r0:=d*(2*b*c-a*d)*(2*b^2*c^2-2*a*b*c*d+a^2*d^2)*x/b^4+1/4*d^2*_
+ (6*b^2*c^2-4*a*b*c*d+a^2*d^2)*x^4/b^3+1/7*d^3*(4*b*c-a*d)*_
+ x^7/b^2+1/10*d^4*x^10/b+1/3*(b*c-a*d)^4*log(a^(1/3)+b^(1/3)*_
+ x)/(a^(2/3)*b^(13/3))-1/6*(b*c-a*d)^4*log(a^(2/3)-a^(1/3)*_
+ b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(13/3))-(b*c-a*d)^4*_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(13/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+
+--R (- 70a d + 280a b c d - 420a b c d + 280a b c d - 70b c )\|3
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+
+--R (140a d - 560a b c d + 840a b c d - 560a b c d + 140b c )\|3
+--R *
+--R 3+-+ 3+-+
+--R log(x\|b + \|a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (420a d - 1680a b c d + 2520a b c d - 1680a b c d + 420b c )
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 3 4 10 2 4 3 3 7
+--R 42b d x + (- 60a b d + 240b c d )x
+--R +
+--R 2 4 2 3 3 2 2 4
+--R (105a b d - 420a b c d + 630b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3
+--R (- 420a d + 1680a b c d - 2520a b c d + 1680b c d)x
+--R *
+--R +-+3+-+2 3+-+
+--R \|3 \|a \|b
+--R /
+--R 4 +-+3+-+2 3+-+
+--R 420b \|3 \|a \|b
+--R Type: Expression(Integer)
+--E 889
+
+--S 890 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+
+--R (- 70a d + 280a b c d - 420a b c d + 280a b c d - 70b c )\|3
+--R *
+--R +---+2 +---+
+--R 2 3| 2 3| 2 2
+--R log(x \|a b - a x\|a b + a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+
+--R (140a d - 560a b c d + 840a b c d - 560a b c d + 140b c )\|3
+--R *
+--R +---+
+--R 3| 2
+--R log(x\|a b + a)
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (420a d - 1680a b c d + 2520a b c d - 1680a b c d + 420b c )
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|a b - a\|3
+--R atan(--------------------)
+--R 3a
+--R +
+--R 3 4 10 2 4 3 3 7
+--R 42b d x + (- 60a b d + 240b c d )x
+--R +
+--R 2 4 2 3 3 2 2 4
+--R (105a b d - 420a b c d + 630b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3
+--R (- 420a d + 1680a b c d - 2520a b c d + 1680b c d)x
+--R *
+--R +---+
+--R +-+3| 2
+--R \|3 \|a b
+--R /
+--R +---+
+--R 4 +-+3| 2
+--R 420b \|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 890
+
+--S 891 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3+-+2 3+-+
+--R (- a d + 4a b c d - 6a b c d + 4a b c d - b c )\|3 \|a \|b
+--R *
+--R +---+2 +---+
+--R 2 3| 2 3| 2 2
+--R log(x \|a b - a x\|a b + a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3+-+2 3+-+
+--R (2a d - 8a b c d + 12a b c d - 8a b c d + 2b c )\|3 \|a \|b
+--R *
+--R +---+
+--R 3| 2
+--R log(x\|a b + a)
+--R +
+--R +---+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3| 2
+--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )\|3 \|a b
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R +---+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3| 2
+--R (- 2a d + 8a b c d - 12a b c d + 8a b c d - 2b c )\|3 \|a b
+--R *
+--R 3+-+ 3+-+
+--R log(x\|b + \|a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 3+-+2 3+-+
+--R (6a d - 24a b c d + 36a b c d - 24a b c d + 6b c )\|a \|b
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|a b - a\|3
+--R atan(--------------------)
+--R 3a
+--R +
+--R +---+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 3| 2
+--R (- 6a d + 24a b c d - 36a b c d + 24a b c d - 6b c )\|a b
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R 4 +-+3+-+2 3+-+3| 2
+--R 6b \|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 891
+
+--S 892 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 892
+
+)clear all
+
+--S 893 of 994
+t0:=(c+d*x^3)^3/(a+b*x^3)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 893
+
+--S 894 of 994
+r0:=d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x/b^3+1/4*d^2*(3*b*c-a*d)*x^4/b^2+_
+ 1/7*d^3*x^7/b+1/3*(b*c-a*d)^3*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*_
+ b^(10/3))-1/6*(b*c-a*d)^3*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*_
+ x^2)/(a^(2/3)*b^(10/3))-(b*c-a*d)^3*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(2/3)*b^(10/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (14a d - 42a b c d + 42a b c d - 14b c )\|3
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 +-+ 3+-+ 3+-+
+--R (- 28a d + 84a b c d - 84a b c d + 28b c )\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 3 2 2 2 2 3 3 2x\|b - \|a
+--R (- 84a d + 252a b c d - 252a b c d + 84b c )atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 3 7 3 2 2 4
+--R 12b d x + (- 21a b d + 63b c d )x
+--R +
+--R 2 3 2 2 2
+--R (84a d - 252a b c d + 252b c d)x
+--R *
+--R +-+3+-+2 3+-+
+--R \|3 \|a \|b
+--R /
+--R 3 +-+3+-+2 3+-+
+--R 84b \|3 \|a \|b
+--R Type: Expression(Integer)
+--E 894
+
+--S 895 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (- 14a d + 42a b c d - 42a b c d + 14b c )\|3
+--R *
+--R +-----+2 +-----+
+--R 2 3| 2 3| 2 2
+--R log(x \|- a b + a x\|- a b + a )
+--R +
+--R +-----+
+--R 3 3 2 2 2 2 3 3 +-+ 3| 2
+--R (28a d - 84a b c d + 84a b c d - 28b c )\|3 log(x\|- a b - a)
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 84a d + 252a b c d - 252a b c d + 84b c )
+--R *
+--R +-----+
+--R +-+3| 2 +-+
+--R 2x\|3 \|- a b + a\|3
+--R atan(----------------------)
+--R 3a
+--R +
+--R 2 3 7 3 2 2 4
+--R 12b d x + (- 21a b d + 63b c d )x
+--R +
+--R 2 3 2 2 2
+--R (84a d - 252a b c d + 252b c d)x
+--R *
+--R +-----+
+--R +-+3| 2
+--R \|3 \|- a b
+--R /
+--R +-----+
+--R 3 +-+3| 2
+--R 84b \|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 895
+
+--S 896 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----+
+--R 3 3 2 2 2 2 3 3 +-+3| 2
+--R (- a d + 3a b c d - 3a b c d + b c )\|3 \|- a b
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-----+
+--R 3 3 2 2 2 2 3 3 +-+3| 2 3+-+ 3+-+
+--R (2a d - 6a b c d + 6a b c d - 2b c )\|3 \|- a b log(x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 +-+3+-+2 3+-+
+--R (- a d + 3a b c d - 3a b c d + b c )\|3 \|a \|b
+--R *
+--R +-----+2 +-----+
+--R 2 3| 2 3| 2 2
+--R log(x \|- a b + a x\|- a b + a )
+--R +
+--R +-----+
+--R 3 3 2 2 2 2 3 3 +-+3+-+2 3+-+ 3| 2
+--R (2a d - 6a b c d + 6a b c d - 2b c )\|3 \|a \|b log(x\|- a b - a)
+--R +
+--R +-----+ 3+-+ 3+-+
+--R 3 3 2 2 2 2 3 3 3| 2 2x\|b - \|a
+--R (6a d - 18a b c d + 18a b c d - 6b c )\|- a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 3 3 2 2 2 2 3 3 3+-+2 3+-+
+--R (- 6a d + 18a b c d - 18a b c d + 6b c )\|a \|b
+--R *
+--R +-----+
+--R +-+3| 2 +-+
+--R 2x\|3 \|- a b + a\|3
+--R atan(----------------------)
+--R 3a
+--R /
+--R +-----+
+--R 3 +-+3| 2 3+-+2 3+-+
+--R 6b \|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 896
+
+--S 897 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 897
+
+)clear all
+
+--S 898 of 994
+t0:=(c+d*x^3)^2/(a+b*x^3)
+--R
+--R
+--R 2 6 3 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 898
+
+--S 899 of 994
+r0:=d*(2*b*c-a*d)*x/b^2+1/4*d^2*x^4/b+1/3*(b*c-a*d)^2*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(2/3)*b^(7/3))-1/6*(b*c-a*d)^2*log(a^(2/3)-_
+ a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(7/3))-(b*c-a*d)^2*_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 2a d + 4a b c d - 2b c )\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 2 2 2 +-+ 3+-+ 3+-+
+--R (4a d - 8a b c d + 4b c )\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 2 2 2 2x\|b - \|a
+--R (12a d - 24a b c d + 12b c )atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 4 2 +-+3+-+2 3+-+
+--R (3b d x + (- 12a d + 24b c d)x)\|3 \|a \|b
+--R /
+--R 2 +-+3+-+2 3+-+
+--R 12b \|3 \|a \|b
+--R Type: Expression(Integer)
+--E 899
+
+--S 900 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 2 2 2 2 +-+ 2 3| 2 3| 2 2
+--R (- 2a d + 4a b c d - 2b c )\|3 log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R 2 2 2 2 +-+ 3| 2
+--R (4a d - 8a b c d + 4b c )\|3 log(x\|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 2 2 2 2x\|3 \|a b - a\|3
+--R (12a d - 24a b c d + 12b c )atan(--------------------)
+--R 3a
+--R +
+--R +---+
+--R 2 4 2 +-+3| 2
+--R (3b d x + (- 12a d + 24b c d)x)\|3 \|a b
+--R /
+--R +---+
+--R 2 +-+3| 2
+--R 12b \|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 900
+
+--S 901 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- a d + 2a b c d - b c )\|3 \|a \|b log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 3| 2
+--R (2a d - 4a b c d + 2b c )\|3 \|a \|b log(x\|a b + a)
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (a d - 2a b c d + b c )\|3 \|a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 3+-+ 3+-+
+--R (- 2a d + 4a b c d - 2b c )\|3 \|a b log(x\|b + \|a )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 2 2 2 3+-+2 3+-+ 2x\|3 \|a b - a\|3
+--R (6a d - 12a b c d + 6b c )\|a \|b atan(--------------------)
+--R 3a
+--R +
+--R +---+ 3+-+ 3+-+
+--R 2 2 2 2 3| 2 2x\|b - \|a
+--R (- 6a d + 12a b c d - 6b c )\|a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R 2 +-+3+-+2 3+-+3| 2
+--R 6b \|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 901
+
+--S 902 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 902
+
+)clear all
+
+--S 903 of 994
+t0:=(c+d*x^3)/(a+b*x^3)
+--R
+--R
+--R 3
+--R d x + c
+--R (1) --------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 903
+
+--S 904 of 994
+r0:=d*x/b+1/3*(b*c-a*d)*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*b^(4/3))-_
+ 1/6*(b*c-a*d)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/_
+ (a^(2/3)*b^(4/3))-(b*c-a*d)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(2/3)*b^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (a d - b c)\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R +-+ 3+-+ 3+-+ 2x\|b - \|a
+--R (- 2a d + 2b c)\|3 log(x\|b + \|a ) + (- 6a d + 6b c)atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +-+3+-+2 3+-+
+--R 6d x\|3 \|a \|b
+--R /
+--R +-+3+-+2 3+-+
+--R 6b\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 904
+
+--S 905 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----+2 +-----+
+--R +-+ 2 3| 2 3| 2 2
+--R (- a d + b c)\|3 log(x \|- a b + a x\|- a b + a )
+--R +
+--R +-----+
+--R +-+ 3| 2
+--R (2a d - 2b c)\|3 log(x\|- a b - a)
+--R +
+--R +-----+
+--R +-+3| 2 +-+ +-----+
+--R 2x\|3 \|- a b + a\|3 +-+3| 2
+--R (- 6a d + 6b c)atan(----------------------) + 6d x\|3 \|- a b
+--R 3a
+--R /
+--R +-----+
+--R +-+3| 2
+--R 6b\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 905
+
+--S 906 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- a d + b c)\|3 \|- a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-----+
+--R +-+3| 2 3+-+ 3+-+
+--R (2a d - 2b c)\|3 \|- a b log(x\|b + \|a )
+--R +
+--R +-----+2 +-----+
+--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- a d + b c)\|3 \|a \|b log(x \|- a b + a x\|- a b + a )
+--R +
+--R +-----+
+--R +-+3+-+2 3+-+ 3| 2
+--R (2a d - 2b c)\|3 \|a \|b log(x\|- a b - a)
+--R +
+--R +-----+ 3+-+ 3+-+
+--R 3| 2 2x\|b - \|a
+--R (6a d - 6b c)\|- a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +-----+
+--R +-+3| 2 +-+
+--R 3+-+2 3+-+ 2x\|3 \|- a b + a\|3
+--R (- 6a d + 6b c)\|a \|b atan(----------------------)
+--R 3a
+--R /
+--R +-----+
+--R +-+3| 2 3+-+2 3+-+
+--R 6b\|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 906
+
+--S 907 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 907
+
+)clear all
+
+--S 908 of 994
+t0:=1/((a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R 6 3
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 908
+
+--S 909 of 994
+r0:=1/3*b^(2/3)*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*(b*c-a*d))-_
+ 1/3*d^(2/3)*log(c^(1/3)+d^(1/3)*x)/(c^(2/3)*(b*c-a*d))-_
+ 1/6*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/_
+ (a^(2/3)*(b*c-a*d))+1/6*d^(2/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+_
+ d^(2/3)*x^2)/(c^(2/3)*(b*c-a*d))-b^(2/3)*atan((a^(1/3)-_
+ 2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*(b*c-a*d)*sqrt(3))+_
+ d^(2/3)*atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/_
+ (c^(2/3)*(b*c-a*d)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R 2\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R +-+3+-+2 3+-+2 3+-+ 3+-+ 3+-+2 3+-+2 2x\|d - \|c
+--R - 2\|3 \|b \|c log(x\|b + \|a + 6\|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|b - \|a
+--R - 6\|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+2 3+-+2
+--R (6a d - 6b c)\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 909
+
+--S 910 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+ |d 2 |d |d 2 2
+--R - \|3 |-- log(c |-- - c d x |-- + d x )
+--R 3| 2 3| 2 3| 2
+--R \|c \|c \|c
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R +-+ |d |d
+--R 2\|3 |-- log(c |-- + d x)
+--R 3| 2 3| 2
+--R \|c \|c
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b 2 | b | b 2 2
+--R - \|3 |- -- log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ +----+ +----+ a\|3 |- -- + 2b x\|3
+--R | 2 | 2 | 2 3| 2
+--R +-+ | b | b | b \| a
+--R 2\|3 |- -- log(- a |- -- + b x - 6 |- -- atan(-----------------------)
+--R 3| 2 3| 2 3| 2 +----+
+--R \| a \| a \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R +--+
+--R | 2
+--R +-+ |d +-+
+--R +--+ c\|3 |-- - 2d x\|3
+--R | 2 3| 2
+--R |d \|c
+--R - 6 |-- atan(---------------------)
+--R 3| 2 +--+
+--R \|c | 2
+--R |d
+--R 3c |--
+--R 3| 2
+--R \|c
+--R /
+--R +-+
+--R (6a d - 6b c)\|3
+--R Type: Union(Expression(Integer),...)
+--E 910
+
+--S 911 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+3+-+2 3+-+2 |d 2 |d |d 2 2
+--R - \|3 \|a \|c |-- log(c |-- - c d x |-- + d x )
+--R 3| 2 3| 2 3| 2
+--R \|c \|c \|c
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R +-+3+-+2 3+-+2 |d |d
+--R 2\|3 \|a \|c |-- log(c |-- + d x)
+--R 3| 2 3| 2
+--R \|c \|c
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R - 2\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R 2\|3 \|b \|c log(x\|b + \|a )
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b 3+-+2 3+-+2 2 | b | b 2 2
+--R - \|3 |- -- \|a \|c log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R +-+ | b 3+-+2 3+-+2 | b
+--R 2\|3 |- -- \|a \|c log(- a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R 3+-+ 3+-+ 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|d - \|c 3+-+2 3+-+2 2x\|b - \|a
+--R - 6\|a \|d atan(------------- + 6\|b \|c atan(-------------)
+--R +-+3+-+ +-+3+-+
+--R \|3 \|c \|3 \|a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- + 2b x\|3
+--R | 2 3| 2
+--R | b 3+-+2 3+-+2 \| a
+--R - 6 |- -- \|a \|c atan(-----------------------)
+--R 3| 2 +----+
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R +--+
+--R | 2
+--R +-+ |d +-+
+--R +--+ c\|3 |-- - 2d x\|3
+--R | 2 3| 2
+--R 3+-+2 3+-+2 |d \|c
+--R - 6\|a \|c |-- atan(---------------------)
+--R 3| 2 +--+
+--R \|c | 2
+--R |d
+--R 3c |--
+--R 3| 2
+--R \|c
+--R /
+--R +-+3+-+2 3+-+2
+--R (6a d - 6b c)\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 911
+
+--S 912 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 912
+
+)clear all
+
+--S 913 of 994
+t0:=1/((a+b*x^3)*(c+d*x^3)^2)
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R 2 9 2 6 2 3 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 913
+
+--S 914 of 994
+r0:=-1/3*d*x/(c*(b*c-a*d)*(c+d*x^3))+1/3*b^(5/3)*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(2/3)*(b*c-a*d)^2)-1/9*d^(2/3)*(5*b*c-2*a*d)*_
+ log(c^(1/3)+d^(1/3)*x)/(c^(5/3)*(b*c-a*d)^2)-1/6*b^(5/3)*_
+ log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*(b*c-_
+ a*d)^2)+1/18*d^(2/3)*(5*b*c-2*a*d)*log(c^(2/3)-c^(1/3)*_
+ d^(1/3)*x+d^(2/3)*x^2)/(c^(5/3)*(b*c-a*d)^2)-b^(5/3)*_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*_
+ (b*c-a*d)^2*sqrt(3))+1/3*d^(2/3)*(5*b*c-2*a*d)*atan((c^(1/3)-_
+ 2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(5/3)*(b*c-a*d)^2*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 3 2 +-+3+-+2 3+-+2
+--R ((- 2a d + 5b c d)x - 2a c d + 5b c )\|3 \|a \|d
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 3 2 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R ((4a d - 10b c d)x + 4a c d - 10b c )\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R 3 2 +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 3b c d x - 3b c )\|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3 2 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R (6b c d x + 6b c )\|3 \|b \|c log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 3 2 3+-+2 3+-+2 2x\|d - \|c
+--R ((12a d - 30b c d)x + 12a c d - 30b c )\|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3 2 3+-+2 3+-+2 2x\|b - \|a
+--R (18b c d x + 18b c )\|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 +-+3+-+2 3+-+2
+--R (6a d - 6b c d)x\|3 \|a \|c
+--R /
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4 +-+
+--R ((18a c d - 36a b c d + 18b c d)x + 18a c d - 36a b c d + 18b c )\|3
+--R *
+--R 3+-+2 3+-+2
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 914
+
+--S 915 of 994
+--a0:=integrate(t0,x)
+--E 915
+
+--S 916 of 994
+--m0:=a0-r0
+--E 916
+
+--S 917 of 994
+--d0:=D(m0,x)
+--E 917
+
+)clear all
+
+--S 918 of 994
+t0:=(c+d*x^3)^p/(a+b*x^3)^2
+--R
+--R
+--R 3 p
+--R (d x + c)
+--R (1) -------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 918
+
+--S 919 of 994
+--r0:=1/3*b*x*(c+d*x^3)^(1+p)/(a*(b*c-a*d)*(a+b*x^3))+1/3*(2*b*c-3*a*d)*_
+-- x*(c+d*x^3)^p*AppellF1(1/3,1,-p,4/3,-b*x^3/a,-d*x^3/c)/_
+-- (a^2*(b*c-a*d)*(1+d*x^3/c)^p)-1/12*b*d*(1+3*p)*x^4*(c+d*x^3)^p*_
+-- AppellF1(4/3,1,-p,7/3,-b*x^3/a,-d*x^3/c)/(a^2*(b*c-a*d)*(1+d*x^3/c)^p)
+--E 919
+
+--S 920 of 994
+--a0:=integrate(t0,x)
+--E 920
+
+--S 921 of 994
+--m0:=a0-r0
+--E 921
+
+--S 922 of 994
+--d0:=D(m0,x)
+--E 922
+
+)clear all
+
+--S 923 of 994
+t0:=(c+d*x^3)^5/(a+b*x^3)^2
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R d x + 5c d x + 10c d x + 10c d x + 5c d x + c
+--R (1) -----------------------------------------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 923
+
+--S 924 of 994
+r0:=d^2*(10*b^3*c^3-20*a*b^2*c^2*d+15*a^2*b*c*d^2-4*a^3*d^3)*x/b^5+_
+ 1/4*d^3*(10*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*x^4/b^4+1/7*d^4*_
+ (5*b*c-2*a*d)*x^7/b^3+1/10*d^5*x^10/b^2+1/3*(b*c-a*d)^5*x/_
+ (a*b^5*(a+b*x^3))+1/9*(b*c-a*d)^4*(2*b*c+13*a*d)*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(5/3)*b^(16/3))-1/18*(b*c-a*d)^4*(2*b*c+13*a*d)*_
+ log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*b^(16/3))-_
+ 1/3*(b*c-a*d)^4*(2*b*c+13*a*d)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(5/3)*b^(16/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 910a b d + 3500a b c d - 4900a b c d + 2800a b c d
+--R +
+--R 5 4 6 5
+--R - 350a b c d - 140b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R - 910a d + 3500a b c d - 4900a b c d + 2800a b c d - 350a b c d
+--R +
+--R 5 5
+--R - 140a b c
+--R *
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 1820a b d - 7000a b c d + 9800a b c d - 5600a b c d
+--R +
+--R 5 4 6 5
+--R 700a b c d + 280b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R 1820a d - 7000a b c d + 9800a b c d - 5600a b c d + 700a b c d
+--R +
+--R 5 5
+--R 280a b c
+--R *
+--R +-+ 3+-+ 3+-+
+--R \|3 log(x\|b + \|a )
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 5460a b d - 21000a b c d + 29400a b c d - 16800a b c d
+--R +
+--R 5 4 6 5
+--R 2100a b c d + 840b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2
+--R 5460a d - 21000a b c d + 29400a b c d - 16800a b c d
+--R +
+--R 2 4 4 5 5
+--R 2100a b c d + 840a b c
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 4 5 13 2 3 5 4 4 10
+--R 126a b d x + (- 234a b d + 900a b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 7
+--R (585a b d - 2250a b c d + 3150a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 4
+--R (- 4095a b d + 15750a b c d - 22050a b c d + 12600a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R - 5460a d + 21000a b c d - 29400a b c d + 16800a b c d
+--R +
+--R 4 4 5 5
+--R - 2100a b c d + 420b c
+--R *
+--R x
+--R *
+--R +-+3+-+2 3+-+
+--R \|3 \|a \|b
+--R /
+--R 6 3 2 5 +-+3+-+2 3+-+
+--R (1260a b x + 1260a b )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 924
+
+--S 925 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 910a b d + 3500a b c d - 4900a b c d + 2800a b c d
+--R +
+--R 5 4 6 5
+--R - 350a b c d - 140b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R - 910a d + 3500a b c d - 4900a b c d + 2800a b c d - 350a b c d
+--R +
+--R 5 5
+--R - 140a b c
+--R *
+--R +---+2 +---+
+--R +-+ 2 3| 2 3| 2 2
+--R \|3 log(x \|a b - a x\|a b + a )
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 1820a b d - 7000a b c d + 9800a b c d - 5600a b c d
+--R +
+--R 5 4 6 5
+--R 700a b c d + 280b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R 1820a d - 7000a b c d + 9800a b c d - 5600a b c d + 700a b c d
+--R +
+--R 5 5
+--R 280a b c
+--R *
+--R +---+
+--R +-+ 3| 2
+--R \|3 log(x\|a b + a)
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 5460a b d - 21000a b c d + 29400a b c d - 16800a b c d
+--R +
+--R 5 4 6 5
+--R 2100a b c d + 840b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2
+--R 5460a d - 21000a b c d + 29400a b c d - 16800a b c d
+--R +
+--R 2 4 4 5 5
+--R 2100a b c d + 840a b c
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|a b - a\|3
+--R atan(--------------------)
+--R 3a
+--R +
+--R 4 5 13 2 3 5 4 4 10
+--R 126a b d x + (- 234a b d + 900a b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 7
+--R (585a b d - 2250a b c d + 3150a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 4
+--R (- 4095a b d + 15750a b c d - 22050a b c d + 12600a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R - 5460a d + 21000a b c d - 29400a b c d + 16800a b c d
+--R +
+--R 4 4 5 5
+--R - 2100a b c d + 420b c
+--R *
+--R x
+--R *
+--R +---+
+--R +-+3| 2
+--R \|3 \|a b
+--R /
+--R +---+
+--R 6 3 2 5 +-+3| 2
+--R (1260a b x + 1260a b )\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 925
+
+--S 926 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (- 13a d + 50a b c d - 70a b c d + 40a b c d - 5a b c d - 2b c )
+--R *
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R \|3 \|a \|b log(x \|a b - a x\|a b + a )
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (26a d - 100a b c d + 140a b c d - 80a b c d + 10a b c d + 4b c )
+--R *
+--R +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R \|3 \|a \|b log(x\|a b + a)
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +-+
+--R (13a d - 50a b c d + 70a b c d - 40a b c d + 5a b c d + 2b c )\|3
+--R *
+--R +---+
+--R 3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (- 26a d + 100a b c d - 140a b c d + 80a b c d - 10a b c d - 4b c )
+--R *
+--R +---+
+--R +-+3| 2 3+-+ 3+-+
+--R \|3 \|a b log(x\|b + \|a )
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (78a d - 300a b c d + 420a b c d - 240a b c d + 30a b c d + 12b c )
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3
+--R \|a \|b atan(--------------------)
+--R 3a
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 78a d + 300a b c d - 420a b c d + 240a b c d - 30a b c d
+--R +
+--R 5 5
+--R - 12b c
+--R *
+--R +---+ 3+-+ 3+-+
+--R 3| 2 2x\|b - \|a
+--R \|a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R 5 +-+3+-+2 3+-+3| 2
+--R 18a b \|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 926
+
+--S 927 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 927
+
+)clear all
+
+--S 928 of 994
+t0:=(c+d*x^3)^4/(a+b*x^3)^2
+--R
+--R
+--R 4 12 3 9 2 2 6 3 3 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R (1) ----------------------------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 928
+
+--S 929 of 994
+r0:=d^2*(6*b^2*c^2-8*a*b*c*d+3*a^2*d^2)*x/b^4+1/2*d^3*(2*b*c-a*d)*_
+ x^4/b^3+1/7*d^4*x^7/b^2+1/3*(b*c-a*d)^4*x/(a*b^4*(a+b*x^3))+_
+ 2/9*(b*c-a*d)^3*(b*c+5*a*d)*log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*_
+ b^(13/3))-1/9*(b*c-a*d)^3*(b*c+5*a*d)*log(a^(2/3)-a^(1/3)*_
+ b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*b^(13/3))-2/3*(b*c-a*d)^3*_
+ (b*c+5*a*d)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_
+ (a^(5/3)*b^(13/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (70a b d - 196a b c d + 168a b c d - 28a b c d - 14b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 70a d - 196a b c d + 168a b c d - 28a b c d - 14a b c
+--R *
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (- 140a b d + 392a b c d - 336a b c d + 56a b c d + 28b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 140a d + 392a b c d - 336a b c d + 56a b c d + 28a b c
+--R *
+--R +-+ 3+-+ 3+-+
+--R \|3 log(x\|b + \|a )
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (- 420a b d + 1176a b c d - 1008a b c d + 168a b c d + 84b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 420a d + 1176a b c d - 1008a b c d + 168a b c d + 84a b c
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 3 4 10 2 2 4 3 3 7
+--R 18a b d x + (- 45a b d + 126a b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4
+--R (315a b d - 882a b c d + 756a b c d )x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (420a d - 1176a b c d + 1008a b c d - 168a b c d + 42b c )x
+--R *
+--R +-+3+-+2 3+-+
+--R \|3 \|a \|b
+--R /
+--R 5 3 2 4 +-+3+-+2 3+-+
+--R (126a b x + 126a b )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 929
+
+--S 930 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (- 70a b d + 196a b c d - 168a b c d + 28a b c d + 14b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 70a d + 196a b c d - 168a b c d + 28a b c d + 14a b c
+--R *
+--R +-----+2 +-----+
+--R +-+ 2 3| 2 3| 2 2
+--R \|3 log(x \|- a b + a x\|- a b + a )
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (140a b d - 392a b c d + 336a b c d - 56a b c d - 28b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 140a d - 392a b c d + 336a b c d - 56a b c d - 28a b c
+--R *
+--R +-----+
+--R +-+ 3| 2
+--R \|3 log(x\|- a b - a)
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (- 420a b d + 1176a b c d - 1008a b c d + 168a b c d + 84b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 420a d + 1176a b c d - 1008a b c d + 168a b c d + 84a b c
+--R *
+--R +-----+
+--R +-+3| 2 +-+
+--R 2x\|3 \|- a b + a\|3
+--R atan(----------------------)
+--R 3a
+--R +
+--R 3 4 10 2 2 4 3 3 7
+--R 18a b d x + (- 45a b d + 126a b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4
+--R (315a b d - 882a b c d + 756a b c d )x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (420a d - 1176a b c d + 1008a b c d - 168a b c d + 42b c )x
+--R *
+--R +-----+
+--R +-+3| 2
+--R \|3 \|- a b
+--R /
+--R +-----+
+--R 5 3 2 4 +-+3| 2
+--R (126a b x + 126a b )\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 930
+
+--S 931 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3| 2
+--R (- 5a d + 14a b c d - 12a b c d + 2a b c d + b c )\|3 \|- a b
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-----+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3| 2
+--R (10a d - 28a b c d + 24a b c d - 4a b c d - 2b c )\|3 \|- a b
+--R *
+--R 3+-+ 3+-+
+--R log(x\|b + \|a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3+-+2 3+-+
+--R (- 5a d + 14a b c d - 12a b c d + 2a b c d + b c )\|3 \|a \|b
+--R *
+--R +-----+2 +-----+
+--R 2 3| 2 3| 2 2
+--R log(x \|- a b + a x\|- a b + a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3+-+2 3+-+
+--R (10a d - 28a b c d + 24a b c d - 4a b c d - 2b c )\|3 \|a \|b
+--R *
+--R +-----+
+--R 3| 2
+--R log(x\|- a b - a)
+--R +
+--R +-----+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 3| 2
+--R (30a d - 84a b c d + 72a b c d - 12a b c d - 6b c )\|- a b
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 3+-+2 3+-+
+--R (- 30a d + 84a b c d - 72a b c d + 12a b c d + 6b c )\|a \|b
+--R *
+--R +-----+
+--R +-+3| 2 +-+
+--R 2x\|3 \|- a b + a\|3
+--R atan(----------------------)
+--R 3a
+--R /
+--R +-----+
+--R 4 +-+3| 2 3+-+2 3+-+
+--R 9a b \|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 931
+
+--S 932 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 932
+
+)clear all
+
+--S 933 of 994
+t0:=(c+d*x^3)^3/(a+b*x^3)^2
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 933
+
+--S 934 of 994
+r0:=d^2*(3*b*c-2*a*d)*x/b^3+1/4*d^3*x^4/b^2+1/3*(b*c-a*d)^3*_
+ x/(a*b^3*(a+b*x^3))+1/9*(b*c-a*d)^2*(2*b*c+7*a*d)*_
+ log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*b^(10/3))-1/18*(b*c-a*d)^2*_
+ (2*b*c+7*a*d)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/_
+ (a^(5/3)*b^(10/3))-1/3*(b*c-a*d)^2*(2*b*c+7*a*d)*_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(10/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 3 4 3 3 2
+--R (- 14a b d + 24a b c d - 6a b c d - 4b c )x - 14a d + 24a b c d
+--R +
+--R 2 2 2 3 3
+--R - 6a b c d - 4a b c
+--R *
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 3 4 3 3 2
+--R (28a b d - 48a b c d + 12a b c d + 8b c )x + 28a d - 48a b c d
+--R +
+--R 2 2 2 3 3
+--R 12a b c d + 8a b c
+--R *
+--R +-+ 3+-+ 3+-+
+--R \|3 log(x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 3 4 3
+--R (84a b d - 144a b c d + 36a b c d + 24b c )x + 84a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 144a b c d + 36a b c d + 24a b c
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 3 7 2 3 2 2 4
+--R 9a b d x + (- 63a b d + 108a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 84a d + 144a b c d - 36a b c d + 12b c )x
+--R *
+--R +-+3+-+2 3+-+
+--R \|3 \|a \|b
+--R /
+--R 4 3 2 3 +-+3+-+2 3+-+
+--R (36a b x + 36a b )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 934
+
+--S 935 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 3 2 4 3 3 4 3 3 2
+--R (- 14a b d + 24a b c d - 6a b c d - 4b c )x - 14a d + 24a b c d
+--R +
+--R 2 2 2 3 3
+--R - 6a b c d - 4a b c
+--R *
+--R +---+2 +---+
+--R +-+ 2 3| 2 3| 2 2
+--R \|3 log(x \|a b - a x\|a b + a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 3 4 3 3 2
+--R (28a b d - 48a b c d + 12a b c d + 8b c )x + 28a d - 48a b c d
+--R +
+--R 2 2 2 3 3
+--R 12a b c d + 8a b c
+--R *
+--R +---+
+--R +-+ 3| 2
+--R \|3 log(x\|a b + a)
+--R +
+--R 3 3 2 2 2 3 2 4 3 3 4 3
+--R (84a b d - 144a b c d + 36a b c d + 24b c )x + 84a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 144a b c d + 36a b c d + 24a b c
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|a b - a\|3
+--R atan(--------------------)
+--R 3a
+--R +
+--R 2 3 7 2 3 2 2 4
+--R 9a b d x + (- 63a b d + 108a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 84a d + 144a b c d - 36a b c d + 12b c )x
+--R *
+--R +---+
+--R +-+3| 2
+--R \|3 \|a b
+--R /
+--R +---+
+--R 4 3 2 3 +-+3| 2
+--R (36a b x + 36a b )\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 935
+
+--S 936 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+3+-+2 3+-+
+--R (- 7a d + 12a b c d - 3a b c d - 2b c )\|3 \|a \|b
+--R *
+--R +---+2 +---+
+--R 2 3| 2 3| 2 2
+--R log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+3+-+2 3+-+ 3| 2
+--R (14a d - 24a b c d + 6a b c d + 4b c )\|3 \|a \|b log(x\|a b + a)
+--R +
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+3| 2
+--R (7a d - 12a b c d + 3a b c d + 2b c )\|3 \|a b
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+3| 2 3+-+ 3+-+
+--R (- 14a d + 24a b c d - 6a b c d - 4b c )\|3 \|a b log(x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 3+-+2 3+-+
+--R (42a d - 72a b c d + 18a b c d + 12b c )\|a \|b
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|a b - a\|3
+--R atan(--------------------)
+--R 3a
+--R +
+--R +---+ 3+-+ 3+-+
+--R 3 3 2 2 2 2 3 3 3| 2 2x\|b - \|a
+--R (- 42a d + 72a b c d - 18a b c d - 12b c )\|a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R 3 +-+3+-+2 3+-+3| 2
+--R 18a b \|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 936
+
+--S 937 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 937
+
+)clear all
+
+--S 938 of 994
+t0:=(c+d*x^3)^2/(a+b*x^3)^2
+--R
+--R
+--R 2 6 3 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 938
+
+--S 939 of 994
+r0:=d^2*x/b^2+1/3*(b*c-a*d)^2*x/(a*b^2*(a+b*x^3))+2/9*(b*c-a*d)*_
+ (b*c+2*a*d)*log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*b^(7/3))-_
+ 1/9*(b*c-a*d)*(b*c+2*a*d)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/(a^(5/3)*b^(7/3))-2/3*(b*c-a*d)*(b*c+2*a*d)*_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 3 3 2 2 2 2 +-+
+--R ((2a b d - a b c d - b c )x + 2a d - a b c d - a b c )\|3
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2 +-+
+--R ((- 4a b d + 2a b c d + 2b c )x - 4a d + 2a b c d + 2a b c )\|3
+--R *
+--R 3+-+ 3+-+
+--R log(x\|b + \|a )
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((- 12a b d + 6a b c d + 6b c )x - 12a d + 6a b c d + 6a b c )
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 4 2 2 2 2 +-+3+-+2 3+-+
+--R (9a b d x + (12a d - 6a b c d + 3b c )x)\|3 \|a \|b
+--R /
+--R 3 3 2 2 +-+3+-+2 3+-+
+--R (9a b x + 9a b )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 939
+
+--S 940 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 3 2 3 3 2 2 2 2 +-+
+--R ((- 2a b d + a b c d + b c )x - 2a d + a b c d + a b c )\|3
+--R *
+--R +-----+2 +-----+
+--R 2 3| 2 3| 2 2
+--R log(x \|- a b + a x\|- a b + a )
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2 +-+
+--R ((4a b d - 2a b c d - 2b c )x + 4a d - 2a b c d - 2a b c )\|3
+--R *
+--R +-----+
+--R 3| 2
+--R log(x\|- a b - a)
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((- 12a b d + 6a b c d + 6b c )x - 12a d + 6a b c d + 6a b c )
+--R *
+--R +-----+
+--R +-+3| 2 +-+
+--R 2x\|3 \|- a b + a\|3
+--R atan(----------------------)
+--R 3a
+--R +
+--R +-----+
+--R 2 4 2 2 2 2 +-+3| 2
+--R (9a b d x + (12a d - 6a b c d + 3b c )x)\|3 \|- a b
+--R /
+--R +-----+
+--R 3 3 2 2 +-+3| 2
+--R (9a b x + 9a b )\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 940
+
+--S 941 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----+
+--R 2 2 2 2 +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 2a d + a b c d + b c )\|3 \|- a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-----+
+--R 2 2 2 2 +-+3| 2 3+-+ 3+-+
+--R (4a d - 2a b c d - 2b c )\|3 \|- a b log(x\|b + \|a )
+--R +
+--R 2 2 2 2 +-+3+-+2 3+-+
+--R (- 2a d + a b c d + b c )\|3 \|a \|b
+--R *
+--R +-----+2 +-----+
+--R 2 3| 2 3| 2 2
+--R log(x \|- a b + a x\|- a b + a )
+--R +
+--R +-----+
+--R 2 2 2 2 +-+3+-+2 3+-+ 3| 2
+--R (4a d - 2a b c d - 2b c )\|3 \|a \|b log(x\|- a b - a)
+--R +
+--R +-----+ 3+-+ 3+-+
+--R 2 2 2 2 3| 2 2x\|b - \|a
+--R (12a d - 6a b c d - 6b c )\|- a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +-----+
+--R +-+3| 2 +-+
+--R 2 2 2 2 3+-+2 3+-+ 2x\|3 \|- a b + a\|3
+--R (- 12a d + 6a b c d + 6b c )\|a \|b atan(----------------------)
+--R 3a
+--R /
+--R +-----+
+--R 2 +-+3| 2 3+-+2 3+-+
+--R 9a b \|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 941
+
+--S 942 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 942
+
+)clear all
+
+--S 943 of 994
+t0:=(c+d*x^3)/(a+b*x^3)^2
+--R
+--R
+--R 3
+--R d x + c
+--R (1) -------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 943
+
+--S 944 of 994
+r0:=1/3*(b*c-a*d)*x/(a*b*(a+b*x^3))+1/9*(2*b*c+a*d)*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(5/3)*b^(4/3))-1/18*(2*b*c+a*d)*log(a^(2/3)-_
+ a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*b^(4/3))-1/3*(2*b*c+_
+ a*d)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*_
+ b^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R ((- a b d - 2b c)x - a d - 2a b c)\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 3 2 +-+ 3+-+ 3+-+
+--R ((2a b d + 4b c)x + 2a d + 4a b c)\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 3 2 2x\|b - \|a
+--R ((6a b d + 12b c)x + 6a d + 12a b c)atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +-+3+-+2 3+-+
+--R (- 6a d + 6b c)x\|3 \|a \|b
+--R /
+--R 2 3 2 +-+3+-+2 3+-+
+--R (18a b x + 18a b)\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 944
+
+--S 945 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 2 3 2 +-+ 2 3| 2 3| 2 2
+--R ((- a b d - 2b c)x - a d - 2a b c)\|3 log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R 2 3 2 +-+ 3| 2
+--R ((2a b d + 4b c)x + 2a d + 4a b c)\|3 log(x\|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 3 2 2x\|3 \|a b - a\|3
+--R ((6a b d + 12b c)x + 6a d + 12a b c)atan(--------------------)
+--R 3a
+--R +
+--R +---+
+--R +-+3| 2
+--R (- 6a d + 6b c)x\|3 \|a b
+--R /
+--R +---+
+--R 2 3 2 +-+3| 2
+--R (18a b x + 18a b)\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 945
+
+--S 946 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- a d - 2b c)\|3 \|a \|b log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R (2a d + 4b c)\|3 \|a \|b log(x\|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (a d + 2b c)\|3 \|a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +---+
+--R +-+3| 2 3+-+ 3+-+
+--R (- 2a d - 4b c)\|3 \|a b log(x\|b + \|a )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3
+--R (6a d + 12b c)\|a \|b atan(--------------------)
+--R 3a
+--R +
+--R +---+ 3+-+ 3+-+
+--R 3| 2 2x\|b - \|a
+--R (- 6a d - 12b c)\|a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R +-+3+-+2 3+-+3| 2
+--R 18a b\|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 946
+
+--S 947 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 947
+
+)clear all
+
+--S 948 of 994
+t0:=1/((a+b*x^3)^2*(c+d*x^3))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------
+--R 2 9 2 6 2 3 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 948
+
+--S 949 of 994
+r0:=1/3*b*x/(a*(b*c-a*d)*(a+b*x^3))+1/9*b^(2/3)*(2*b*c-5*a*d)*_
+ log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*(b*c-a*d)^2)+1/3*d^(5/3)*_
+ log(c^(1/3)+d^(1/3)*x)/(c^(2/3)*(b*c-a*d)^2)-1/18*b^(2/3)*_
+ (2*b*c-5*a*d)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/_
+ (a^(5/3)*(b*c-a*d)^2)-1/6*d^(5/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*_
+ x+d^(2/3)*x^2)/(c^(2/3)*(b*c-a*d)^2)-1/3*b^(2/3)*(2*b*c-_
+ 5*a*d)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_
+ (a^(5/3)*(b*c-a*d)^2*sqrt(3))-d^(5/3)*atan((c^(1/3)-_
+ 2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(2/3)*(b*c-a*d)^2*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 2 +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 3a b d x - 3a d)\|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R 3 2 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R (6a b d x + 6a d)\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R 2 3 2 +-+3+-+2 3+-+2
+--R ((5a b d - 2b c)x + 5a d - 2a b c)\|3 \|b \|c
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 3 2 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R ((- 10a b d + 4b c)x - 10a d + 4a b c)\|3 \|b \|c log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 2 3+-+2 3+-+2 2x\|d - \|c
+--R (18a b d x + 18a d)\|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 2 3 2 3+-+2 3+-+2 2x\|b - \|a
+--R ((- 30a b d + 12b c)x - 30a d + 12a b c)\|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 +-+3+-+2 3+-+2
+--R (- 6a b d + 6b c)x\|3 \|a \|c
+--R /
+--R 3 2 2 2 3 2 3 4 2 3 2 2 2 +-+
+--R ((18a b d - 36a b c d + 18a b c )x + 18a d - 36a b c d + 18a b c )\|3
+--R *
+--R 3+-+2 3+-+2
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 949
+
+--S 950 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R 3 2 +-+ |d 2 |d |d 2 2
+--R (- 3a b d x - 3a d)\|3 |-- log(c |-- - c d x |-- + d x )
+--R 3| 2 3| 2 3| 2
+--R \|c \|c \|c
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R 3 2 +-+ |d |d
+--R (6a b d x + 6a d)\|3 |-- log(c |-- + d x)
+--R 3| 2 3| 2
+--R \|c \|c
+--R +
+--R +----+
+--R | 2
+--R 2 3 2 +-+ | b
+--R ((- 5a b d + 2b c)x - 5a d + 2a b c)\|3 |- --
+--R 3| 2
+--R \| a
+--R *
+--R +----+2 +----+
+--R | 2 | 2
+--R 2 | b | b 2 2
+--R log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R 2 3 2 +-+ | b | b
+--R ((10a b d - 4b c)x + 10a d - 4a b c)\|3 |- -- log(- a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R +----+
+--R | 2
+--R 2 3 2 | b
+--R ((- 30a b d + 12b c)x - 30a d + 12a b c) |- --
+--R 3| 2
+--R \| a
+--R *
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R a\|3 |- -- + 2b x\|3
+--R 3| 2
+--R \| a
+--R atan(-----------------------)
+--R +----+
+--R | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R +--+
+--R | 2
+--R +-+ |d +-+
+--R +--+ c\|3 |-- - 2d x\|3
+--R | 2 3| 2
+--R 3 2 |d \|c
+--R (- 18a b d x - 18a d) |-- atan(---------------------)
+--R 3| 2 +--+
+--R \|c | 2
+--R |d
+--R 3c |--
+--R 3| 2
+--R \|c
+--R +
+--R 2 +-+
+--R (- 6a b d + 6b c)x\|3
+--R /
+--R 3 2 2 2 3 2 3 4 2 3 2 2 2 +-+
+--R ((18a b d - 36a b c d + 18a b c )x + 18a d - 36a b c d + 18a b c )\|3
+--R Type: Union(Expression(Integer),...)
+--E 950
+
+--S 951 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+3+-+2 3+-+2 |d 2 |d |d 2 2
+--R - 3a d\|3 \|a \|c |-- log(c |-- - c d x |-- + d x )
+--R 3| 2 3| 2 3| 2
+--R \|c \|c \|c
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R +-+3+-+2 3+-+2 |d |d
+--R 6a d\|3 \|a \|c |-- log(c |-- + d x)
+--R 3| 2 3| 2
+--R \|c \|c
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R 3a d\|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R - 6a d\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 5a d + 2b c)\|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R (10a d - 4b c)\|3 \|b \|c log(x\|b + \|a )
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b 3+-+2 3+-+2 2 | b | b 2 2
+--R (- 5a d + 2b c)\|3 |- -- \|a \|c log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R +-+ | b 3+-+2 3+-+2 | b
+--R (10a d - 4b c)\|3 |- -- \|a \|c log(- a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|d - \|c
+--R - 18a d \|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|b - \|a
+--R (30a d - 12b c)\|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- + 2b x\|3
+--R | 2 3| 2
+--R | b 3+-+2 3+-+2 \| a
+--R (- 30a d + 12b c) |- -- \|a \|c atan(-----------------------)
+--R 3| 2 +----+
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R +--+
+--R | 2
+--R +-+ |d +-+
+--R +--+ c\|3 |-- - 2d x\|3
+--R | 2 3| 2
+--R 3+-+2 3+-+2 |d \|c
+--R - 18a d \|a \|c |-- atan(---------------------)
+--R 3| 2 +--+
+--R \|c | 2
+--R |d
+--R 3c |--
+--R 3| 2
+--R \|c
+--R /
+--R 3 2 2 2 2 +-+3+-+2 3+-+2
+--R (18a d - 36a b c d + 18a b c )\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 951
+
+--S 952 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 952
+
+)clear all
+
+--S 953 of 994
+t0:=1/((a+b*x^3)^2*(c+d*x^3)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 12 2 2 9 2 2 2 2 6
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 3 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 953
+
+--S 954 of 994
+r0:=1/3*d*(b*c+a*d)*x/(a*c*(b*c-a*d)^2*(c+d*x^3))+1/3*b*x/_
+ (a*(b*c-a*d)*(a+b*x^3)*(c+d*x^3))+2/9*b^(5/3)*(b*c-4*a*d)*_
+ log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*(b*c-a*d)^3)+2/9*d^(5/3)*_
+ (4*b*c-a*d)*log(c^(1/3)+d^(1/3)*x)/(c^(5/3)*(b*c-a*d)^3)-_
+ 1/9*b^(5/3)*(b*c-4*a*d)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/(a^(5/3)*(b*c-a*d)^3)-1/9*d^(5/3)*(4*b*c-a*d)*_
+ log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(5/3)*(b*c-_
+ a*d)^3)-2/3*b^(5/3)*(b*c-4*a*d)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(5/3)*(b*c-a*d)^3*sqrt(3))-_
+ 2/3*d^(5/3)*(4*b*c-a*d)*atan((c^(1/3)-2*d^(1/3)*x)/_
+ (c^(1/3)*sqrt(3)))/(c^(5/3)*(b*c-a*d)^3*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 3 2 2 6 3 3 2 2 2 2 3 3 2
+--R (- a b d + 4a b c d )x + (- a d + 3a b c d + 4a b c d)x - a c d
+--R +
+--R 2 2
+--R 4a b c d
+--R *
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 3 2 2 6 3 3 2 2 2 2 3 3 2
+--R (2a b d - 8a b c d )x + (2a d - 6a b c d - 8a b c d)x + 2a c d
+--R +
+--R 2 2
+--R - 8a b c d
+--R *
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R \|3 \|a \|d log(x\|d + \|c )
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 3
+--R (- 4a b c d + b c d)x + (- 4a b c d - 3a b c d + b c )x
+--R +
+--R 2 2 2 3
+--R - 4a b c d + a b c
+--R *
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 3 2 2
+--R (8a b c d - 2b c d)x + (8a b c d + 6a b c d - 2b c )x + 8a b c d
+--R +
+--R 2 3
+--R - 2a b c
+--R *
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R \|3 \|b \|c log(x\|b + \|a )
+--R +
+--R 2 3 2 2 6 3 3 2 2 2 2 3
+--R (6a b d - 24a b c d )x + (6a d - 18a b c d - 24a b c d)x
+--R +
+--R 3 2 2 2
+--R 6a c d - 24a b c d
+--R *
+--R 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|d - \|c
+--R \|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 3
+--R (24a b c d - 6b c d)x + (24a b c d + 18a b c d - 6b c )x
+--R +
+--R 2 2 2 3
+--R 24a b c d - 6a b c
+--R *
+--R 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|b - \|a
+--R \|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 3 3 2 4 3 3 2 2 2 2 3 3 +-+
+--R ((3a b d - 3b c d)x + (3a d - 3a b c d + 3a b c d - 3b c )x)\|3
+--R *
+--R 3+-+2 3+-+2
+--R \|a \|c
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 6
+--R (9a b c d - 27a b c d + 27a b c d - 9a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 3 5 2 3 4 3 2
+--R (9a c d - 18a b c d + 18a b c d - 9a b c )x + 9a c d - 27a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 27a b c d - 9a b c
+--R *
+--R +-+3+-+2 3+-+2
+--R \|3 \|a \|c
+--R Type: Expression(Integer)
+--E 954
+
+--S 955 of 994
+--a0:=integrate(t0,x)
+--E 955
+
+--S 956 of 994
+--m0:=a0-r0
+--E 956
+
+--S 957 of 994
+--d0:=D(m0,x)
+--E 957
+
+)clear all
+
+--S 958 of 994
+t0:=(a+b/x^2)/(c+d/x^2)
+--R
+--R
+--R 2
+--R a x + b
+--R (1) --------
+--R 2
+--R c x + d
+--R Type: Fraction(Polynomial(Integer))
+--E 958
+
+--S 959 of 994
+r0:=a*x/c+(b*c-a*d)*atan(x*sqrt(c)/sqrt(d))/(c^(3/2)*sqrt(d))
+--R
+--R
+--R +-+
+--R x\|c +-+ +-+
+--R (- a d + b c)atan(-----) + a x\|c \|d
+--R +-+
+--R \|d
+--R (2) --------------------------------------
+--R +-+ +-+
+--R c\|c \|d
+--R Type: Expression(Integer)
+--E 959
+
+--S 960 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R (c x - d)\|- c d - 2c d x +-----+
+--R (a d - b c)log(---------------------------) + 2a x\|- c d
+--R 2
+--R c x + d
+--R [----------------------------------------------------------,
+--R +-----+
+--R 2c\|- c d
+--R +---+
+--R x\|c d +---+
+--R (- a d + b c)atan(-------) + a x\|c d
+--R d
+--R --------------------------------------]
+--R +---+
+--R c\|c d
+--R Type: Union(List(Expression(Integer)),...)
+--E 960
+
+--S 961 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (c x - d)\|- c d - 2c d x
+--R (a d - b c)\|c \|d log(---------------------------)
+--R 2
+--R c x + d
+--R +
+--R +-+
+--R +-----+ x\|c
+--R (2a d - 2b c)\|- c d atan(-----)
+--R +-+
+--R \|d
+--R /
+--R +-----+ +-+ +-+
+--R 2c\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 961
+
+--S 962 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 962
+
+--S 963 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|c d +---+ x\|c
+--R (- a d + b c)\|c \|d atan(-------) + (a d - b c)\|c d atan(-----)
+--R d +-+
+--R \|d
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R c\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 963
+
+--S 964 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 964
+
+)clear all
+
+--S 965 of 994
+t0:=(a+b/x^3)/(c+d/x^3)
+--R
+--R
+--R 3
+--R a x + b
+--R (1) --------
+--R 3
+--R c x + d
+--R Type: Fraction(Polynomial(Integer))
+--E 965
+
+--S 966 of 994
+r0:=a*x/c+1/3*(b*c-a*d)*log(d^(1/3)+c^(1/3)*x)/(c^(4/3)*d^(2/3))-_
+ 1/6*(b*c-a*d)*log(d^(2/3)-c^(1/3)*d^(1/3)*x+c^(2/3)*x^2)/_
+ (c^(4/3)*d^(2/3))-(b*c-a*d)*atan((d^(1/3)-2*c^(1/3)*x)/_
+ (d^(1/3)*sqrt(3)))/(c^(4/3)*d^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 3+-+2 3+-+3+-+ 2 3+-+2
+--R (a d - b c)\|3 log(\|d - x\|c \|d + x \|c )
+--R +
+--R 3+-+ 3+-+
+--R +-+ 3+-+ 3+-+ \|d - 2x\|c
+--R (- 2a d + 2b c)\|3 log(\|d + x\|c ) + (6a d - 6b c)atan(-------------)
+--R +-+3+-+
+--R \|3 \|d
+--R +
+--R +-+3+-+3+-+2
+--R 6a x\|3 \|c \|d
+--R /
+--R +-+3+-+3+-+2
+--R 6c\|3 \|c \|d
+--R Type: Expression(Integer)
+--E 966
+
+--S 967 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+2 +------+
+--R +-+ 2 3| 2 3| 2 2
+--R (- a d + b c)\|3 log(x \|- c d + d x\|- c d + d )
+--R +
+--R +------+
+--R +-+ 3| 2
+--R (2a d - 2b c)\|3 log(x\|- c d - d)
+--R +
+--R +------+
+--R +-+3| 2 +-+ +------+
+--R 2x\|3 \|- c d + d\|3 +-+3| 2
+--R (- 6a d + 6b c)atan(-----------------------) + 6a x\|3 \|- c d
+--R 3d
+--R /
+--R +------+
+--R +-+3| 2
+--R 6c\|3 \|- c d
+--R Type: Union(Expression(Integer),...)
+--E 967
+
+--S 968 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +------+
+--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2
+--R (- a d + b c)\|3 \|- c d log(\|d - x\|c \|d + x \|c )
+--R +
+--R +------+
+--R +-+3| 2 3+-+ 3+-+
+--R (2a d - 2b c)\|3 \|- c d log(\|d + x\|c )
+--R +
+--R +------+2 +------+
+--R +-+3+-+3+-+2 2 3| 2 3| 2 2
+--R (- a d + b c)\|3 \|c \|d log(x \|- c d + d x\|- c d + d )
+--R +
+--R +------+
+--R +-+3+-+3+-+2 3| 2
+--R (2a d - 2b c)\|3 \|c \|d log(x\|- c d - d)
+--R +
+--R +------+
+--R +-+3| 2 +-+
+--R 3+-+3+-+2 2x\|3 \|- c d + d\|3
+--R (- 6a d + 6b c)\|c \|d atan(-----------------------)
+--R 3d
+--R +
+--R +------+ 3+-+ 3+-+
+--R 3| 2 \|d - 2x\|c
+--R (- 6a d + 6b c)\|- c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|d
+--R /
+--R +------+
+--R +-+3| 2 3+-+3+-+2
+--R 6c\|3 \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 968
+
+--S 969 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 969
+
+)clear all
+
+--S 970 of 994
+t0:=(a+b*sqrt(x))/(c+d*sqrt(x))
+--R
+--R
+--R +-+
+--R b\|x + a
+--R (1) ---------
+--R +-+
+--R d\|x + c
+--R Type: Expression(Integer)
+--E 970
+
+--S 971 of 994
+r0:=b*x/d+2*c*(b*c-a*d)*log(c+d*sqrt(x))/d^3-2*(b*c-a*d)*sqrt(x)/d^2
+--R
+--R
+--R 2 +-+ 2 +-+ 2
+--R (- 2a c d + 2b c )log(d\|x + c) + (2a d - 2b c d)\|x + b d x
+--R (2) ---------------------------------------------------------------
+--R 3
+--R d
+--R Type: Expression(Integer)
+--E 971
+
+--S 972 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+ 2 +-+ 2
+--R (- 2a c d + 2b c )log(d\|x + c) + (2a d - 2b c d)\|x + b d x
+--R (3) ---------------------------------------------------------------
+--R 3
+--R d
+--R Type: Union(Expression(Integer),...)
+--E 972
+
+--S 973 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 973
+
+--S 974 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 974
+
+)clear all
+
+--S 975 of 994
+t0:=(-1+x^(1/3))/(1+x^(1/3))
+--R
+--R
+--R 3+-+
+--R \|x - 1
+--R (1) --------
+--R 3+-+
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 975
+
+--S 976 of 994
+r0:=6*x^(1/3)-3*x^(2/3)+x-6*log(1+x^(1/3))
+--R
+--R
+--R 3+-+ 3+-+2 3+-+
+--R (2) - 6log(\|x + 1) - 3\|x + 6\|x + x
+--R Type: Expression(Integer)
+--E 976
+
+--S 977 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 3+-+ 3+-+2 3+-+
+--R (3) - 6log(\|x + 1) - 3\|x + 6\|x + x
+--R Type: Union(Expression(Integer),...)
+--E 977
+
+--S 978 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 978
+
+--S 979 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 979
+
+)clear all
+
+--S 980 of 994
+t0:=(1+1/x^(1/3))/(-1+1/x^(1/3))
+--R
+--R
+--R 3+-+
+--R - \|x - 1
+--R (1) ----------
+--R 3+-+
+--R \|x - 1
+--R Type: Expression(Integer)
+--E 980
+
+--S 981 of 994
+r0:=-6*x^(1/3)-3*x^(2/3)-x-6*log(1-x^(1/3))
+--R
+--R
+--R 3+-+ 3+-+2 3+-+
+--R (2) - 6log(- \|x + 1) - 3\|x - 6\|x - x
+--R Type: Expression(Integer)
+--E 981
+
+--S 982 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 3+-+ 3+-+2 3+-+
+--R (3) - 6log(\|x - 1) - 3\|x - 6\|x - x
+--R Type: Union(Expression(Integer),...)
+--E 982
+
+--S 983 of 994
+m0:=a0-r0
+--R
+--R
+--R 3+-+ 3+-+
+--R (4) - 6log(\|x - 1) + 6log(- \|x + 1)
+--R Type: Expression(Integer)
+--E 983
+
+--S 984 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 984
+
+)clear all
+
+--S 985 of 994
+t0:=(1+x^(2/3))/(-1+x^(2/3))
+--R
+--R
+--R 3+-+2
+--R \|x + 1
+--R (1) ---------
+--R 3+-+2
+--R \|x - 1
+--R Type: Expression(Integer)
+--E 985
+
+--S 986 of 994
+r0:=6*x^(1/3)+x-6*atanh(x^(1/3))
+--R
+--R
+--R 3+-+ 3+-+
+--R (2) - 6atanh(\|x ) + 6\|x + x
+--R Type: Expression(Integer)
+--E 986
+
+--S 987 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 3+-+ 3+-+ 3+-+
+--R (3) - 3log(\|x + 1) + 3log(\|x - 1) + 6\|x + x
+--R Type: Union(Expression(Integer),...)
+--E 987
+
+--S 988 of 994
+m0:=a0-r0
+--R
+--R
+--R 3+-+ 3+-+ 3+-+
+--R (4) - 3log(\|x + 1) + 3log(\|x - 1) + 6atanh(\|x )
+--R Type: Expression(Integer)
+--E 988
+
+--S 989 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 989
+
+)clear all
+
+--S 990 of 994
+t0:=(-16+x^(3/4))/(16+x^(3/4))
+--R
+--R
+--R 4+-+3
+--R \|x - 16
+--R (1) ----------
+--R 4+-+3
+--R \|x + 16
+--R Type: Expression(Integer)
+--E 990
+
+--S 991 of 994
+r0:=-128*x^(1/4)+x+256/3*2^(1/3)*log(2*2^(1/3)+x^(1/4))-128/3*2^(1/3)*_
+ log(4*2^(2/3)-2*2^(1/3)*x^(1/4)+sqrt(x))-256*2^(1/3)*_
+ atan((2^(1/3)-x^(1/4))/(2^(1/3)*sqrt(3)))/sqrt(3)
+--R
+--R
+--R (2)
+--R 3+-+ +-+ 4+-+ 3+-+
+--R 256\|2 \|3 log(\|x + 2\|2 )
+--R +
+--R 4+-+ 3+-+
+--R 3+-+ +-+ 3+-+4+-+ +-+ 3+-+2 3+-+ \|x - \|2
+--R - 128\|2 \|3 log(- 2\|2 \|x + \|x + 4\|2 ) + 768\|2 atan(-----------)
+--R 3+-+ +-+
+--R \|2 \|3
+--R +
+--R +-+4+-+ +-+
+--R - 384\|3 \|x + 3x\|3
+--R /
+--R +-+
+--R 3\|3
+--R Type: Expression(Integer)
+--E 991
+
+--S 992 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3+-+ +-+ 4+-+2 3+-+4+-+ 3+-+2
+--R - 128\|2 \|3 log(\|x - 2\|2 \|x + 4\|2 )
+--R +
+--R +-+4+-+ 3+-+ +-+
+--R 3+-+ +-+ 4+-+ 3+-+ 3+-+ \|3 \|x - \|2 \|3
+--R 256\|2 \|3 log(\|x + 2\|2 ) + 768\|2 atan(-------------------)
+--R 3+-+
+--R 3\|2
+--R +
+--R +-+4+-+ +-+
+--R - 384\|3 \|x + 3x\|3
+--R /
+--R +-+
+--R 3\|3
+--R Type: Union(Expression(Integer),...)
+--E 992
+
+--S 993 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3+-+ +-+ 4+-+2 3+-+4+-+ 3+-+2
+--R - 128\|2 \|3 log(\|x - 2\|2 \|x + 4\|2 )
+--R +
+--R 3+-+ +-+ 3+-+4+-+ +-+ 3+-+2
+--R 128\|2 \|3 log(- 2\|2 \|x + \|x + 4\|2 )
+--R +
+--R +-+4+-+ 3+-+ +-+ 4+-+ 3+-+
+--R 3+-+ \|3 \|x - \|2 \|3 3+-+ \|x - \|2
+--R 768\|2 atan(-------------------) - 768\|2 atan(-----------)
+--R 3+-+ 3+-+ +-+
+--R 3\|2 \|2 \|3
+--R /
+--R +-+
+--R 3\|3
+--R Type: Expression(Integer)
+--E 993
+
+--S 994 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3+-+2 +-+ 3+-+ 4+-+3
+--R ((- 64x \|2 - 20480)\|x + 3584x\|2 )\|x
+--R +
+--R 3+-+ +-+ 3+-+2 4+-+2
+--R ((16384\|2 + 1024x)\|x - 8192x \|2 )\|x
+--R +
+--R 3+-+ +-+ 2 3+-+2 4+-+ 3+-+2 +-+ 3+-+
+--R (- 3584x\|2 \|x + 64x \|2 + 20480x)\|x + 8192x \|2 \|x - 16384x\|2
+--R +
+--R 2
+--R - 1024x
+--R /
+--R 3+-+2 2 3+-+ +-+ 2 4+-+3
+--R ((2496x \|2 + 6x \|2)\|x + 336x )\|x
+--R +
+--R 2 3+-+2 +-+ 2 3+-+ 3 4+-+2
+--R ((- 48x \|2 - 6912x)\|x - 576x \|2 - 3x )\|x
+--R +
+--R 3+-+ 2 +-+ 2 3+-+2 3 3+-+4+-+
+--R ((6144x\|2 + 432x )\|x + 576x \|2 + 18x \|2)\|x
+--R +
+--R 3+-+2 2 3+-+ +-+ 3 3+-+2 2
+--R (- 3072x \|2 - 1248x \|2)\|x - 72x \|2 - 768x
+--R Type: Expression(Integer)
+--E 994
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich5.input.pdf b/src/axiom-website/CATS/rich5.input.pdf
new file mode 100644
index 0000000..2457659
Binary files /dev/null and b/src/axiom-website/CATS/rich5.input.pdf differ
diff --git a/src/axiom-website/CATS/rich6a.input.pamphlet b/src/axiom-website/CATS/rich6a.input.pamphlet
new file mode 100644
index 0000000..6da82f5
--- /dev/null
+++ b/src/axiom-website/CATS/rich6a.input.pamphlet
@@ -0,0 +1,28754 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich6a.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p (c+d x^n)^q|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 260 supplied "optimal results".
+\item 318 matching answers.
+\item 58 cases where Axiom supplied 2 results.
+\item 0 cases that Axiom failed to integrate.
+\item 0 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich6a.output
+)spool rich6a.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 1406
+t0:=x^m*(a+b*x^2)*(A+B*x^2)
+--R
+--R
+--R 4 2 m
+--R (1) (B b x + (A b + B a)x + A a)x
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 1406
+r0:=a*A*x^(1+m)/(1+m)+(A*b+a*B)*x^(3+m)/(3+m)+b*B*x^(5+m)/(5+m)
+--R
+--R
+--R (2)
+--R 2 m + 5
+--R (B b m + 4B b m + 3B b)x
+--R +
+--R 2 m + 3
+--R ((A b + B a)m + (6A b + 6B a)m + 5A b + 5B a)x
+--R +
+--R 2 m + 1
+--R (A a m + 8A a m + 15A a)x
+--R /
+--R 3 2
+--R m + 9m + 23m + 15
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5
+--R (B b m + 4B b m + 3B b)x
+--R +
+--R 2 3
+--R ((A b + B a)m + (6A b + 6B a)m + 5A b + 5B a)x
+--R +
+--R 2
+--R (A a m + 8A a m + 15A a)x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 3 2
+--R m + 9m + 23m + 15
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 5
+--R (B b m + 4B b m + 3B b)x
+--R +
+--R 2 3
+--R ((A b + B a)m + (6A b + 6B a)m + 5A b + 5B a)x
+--R +
+--R 2
+--R (A a m + 8A a m + 15A a)x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 2 m + 5
+--R (- B b m - 4B b m - 3B b)x
+--R +
+--R 2 m + 3
+--R ((- A b - B a)m + (- 6A b - 6B a)m - 5A b - 5B a)x
+--R +
+--R 2 m + 1
+--R (- A a m - 8A a m - 15A a)x
+--R /
+--R 3 2
+--R m + 9m + 23m + 15
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 1406
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 1406
+t0:=x^2*(a+b*x^2)*(A+B*x^2)
+--R
+--R
+--R 6 4 2
+--R (1) B b x + (A b + B a)x + A a x
+--R Type: Polynomial(Integer)
+--E 6
+
+--S 7 of 1406
+r0:=1/3*a*A*x^3+1/5*(A*b+a*B)*x^5+1/7*b*B*x^7
+--R
+--R
+--R 1 7 1 1 5 1 3
+--R (2) - B b x + (- A b + - B a)x + - A a x
+--R 7 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 7
+
+--S 8 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 7 1 1 5 1 3
+--R (3) - B b x + (- A b + - B a)x + - A a x
+--R 7 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 8
+
+--S 9 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 9
+
+--S 10 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 10
+
+)clear all
+
+--S 11 of 1406
+t0:=x*(a+b*x^2)*(A+B*x^2)
+--R
+--R
+--R 5 3
+--R (1) B b x + (A b + B a)x + A a x
+--R Type: Polynomial(Integer)
+--E 11
+
+--S 12 of 1406
+r0:=1/2*a*A*x^2+1/4*(A*b+a*B)*x^4+1/6*b*B*x^6
+--R
+--R
+--R 1 6 1 1 4 1 2
+--R (2) - B b x + (- A b + - B a)x + - A a x
+--R 6 4 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 12
+
+--S 13 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 6 1 1 4 1 2
+--R (3) - B b x + (- A b + - B a)x + - A a x
+--R 6 4 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 13
+
+--S 14 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 14
+
+--S 15 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 15
+
+)clear all
+
+--S 16 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)
+--R
+--R
+--R 4 2
+--R (1) B b x + (A b + B a)x + A a
+--R Type: Polynomial(Integer)
+--E 16
+
+--S 17 of 1406
+r0:=a*A*x+1/3*(A*b+a*B)*x^3+1/5*b*B*x^5
+--R
+--R
+--R 1 5 1 1 3
+--R (2) - B b x + (- A b + - B a)x + A a x
+--R 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 17
+
+--S 18 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 1 1 3
+--R (3) - B b x + (- A b + - B a)x + A a x
+--R 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 18
+
+--S 19 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 19
+
+--S 20 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 20
+
+)clear all
+
+--S 21 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 21
+
+--S 22 of 1406
+r0:=1/2*(A*b+a*B)*x^2+1/4*b*B*x^4+a*A*log(x)
+--R
+--R
+--R 4 2
+--R 4A a log(x) + B b x + (2A b + 2B a)x
+--R (2) --------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R 4A a log(x) + B b x + (2A b + 2B a)x
+--R (3) --------------------------------------
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^2
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 26
+
+--S 27 of 1406
+r0:=-a*A/x+(A*b+a*B)*x+1/3*b*B*x^3
+--R
+--R
+--R 4 2
+--R B b x + (3A b + 3B a)x - 3A a
+--R (2) -------------------------------
+--R 3x
+--R Type: Fraction(Polynomial(Integer))
+--E 27
+
+--S 28 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R B b x + (3A b + 3B a)x - 3A a
+--R (3) -------------------------------
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 28
+
+--S 29 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 30
+
+)clear all
+
+--S 31 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^3
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 31
+
+--S 32 of 1406
+r0:=-1/2*a*A/x^2+1/2*b*B*x^2+(A*b+a*B)*log(x)
+--R
+--R
+--R 2 4
+--R (2A b + 2B a)x log(x) + B b x - A a
+--R (2) ------------------------------------
+--R 2
+--R 2x
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4
+--R (2A b + 2B a)x log(x) + B b x - A a
+--R (3) ------------------------------------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^4
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 36
+
+--S 37 of 1406
+r0:=-1/3*a*A/x^3+(-A*b-a*B)/x+b*B*x
+--R
+--R
+--R 4 2 1
+--R B b x + (- A b - B a)x - - A a
+--R 3
+--R (2) --------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 37
+
+--S 38 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R 3B b x + (- 3A b - 3B a)x - A a
+--R (3) ---------------------------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^5
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 41
+
+--S 42 of 1406
+r0:=-1/4*a*A/x^4+1/2*(-A*b-a*B)/x^2+b*B*log(x)
+--R
+--R
+--R 4 2
+--R 4B b x log(x) + (- 2A b - 2B a)x - A a
+--R (2) ---------------------------------------
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R 4B b x log(x) + (- 2A b - 2B a)x - A a
+--R (3) ---------------------------------------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^6
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 46
+
+--S 47 of 1406
+r0:=-1/5*a*A/x^5+1/3*(-A*b-a*B)/x^3-b*B/x
+--R
+--R
+--R 4 1 1 2 1
+--R - B b x + (- - A b - - B a)x - - A a
+--R 3 3 5
+--R (2) --------------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 47
+
+--S 48 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R - 15B b x + (- 5A b - 5B a)x - 3A a
+--R (3) -------------------------------------
+--R 5
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^7
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 51
+
+--S 52 of 1406
+r0:=-1/6*a*A/x^6+1/4*(-A*b-a*B)/x^4-1/2*b*B/x^2
+--R
+--R
+--R 1 4 1 1 2 1
+--R - - B b x + (- - A b - - B a)x - - A a
+--R 2 4 4 6
+--R (2) ----------------------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 52
+
+--S 53 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R - 6B b x + (- 3A b - 3B a)x - 2A a
+--R (3) ------------------------------------
+--R 6
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 1406
+t0:=x^m*(a+b*x^2)^2*(A+B*x^2)
+--R
+--R
+--R 2 6 2 4 2 2 2 m
+--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )x
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 1406
+r0:=a^2*A*x^(1+m)/(1+m)+a*(2*A*b+a*B)*x^(3+m)/(3+m)+b*(A*b+2*a*B)*_
+ x^(5+m)/(5+m)+b^2*B*x^(7+m)/(7+m)
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 m + 7
+--R (B b m + 9B b m + 23B b m + 15B b )x
+--R +
+--R 2 3 2 2 2
+--R (A b + 2B a b)m + (11A b + 22B a b)m + (31A b + 62B a b)m
+--R +
+--R 2
+--R 21A b + 42B a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 2 3 2 2 2
+--R (2A a b + B a )m + (26A a b + 13B a )m + (94A a b + 47B a )m
+--R +
+--R 2
+--R 70A a b + 35B a
+--R *
+--R m + 3
+--R x
+--R +
+--R 2 3 2 2 2 2 m + 1
+--R (A a m + 15A a m + 71A a m + 105A a )x
+--R /
+--R 4 3 2
+--R m + 16m + 86m + 176m + 105
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 2 7
+--R (B b m + 9B b m + 23B b m + 15B b )x
+--R +
+--R 2 3 2 2 2
+--R (A b + 2B a b)m + (11A b + 22B a b)m + (31A b + 62B a b)m
+--R +
+--R 2
+--R 21A b + 42B a b
+--R *
+--R 5
+--R x
+--R +
+--R 2 3 2 2 2
+--R (2A a b + B a )m + (26A a b + 13B a )m + (94A a b + 47B a )m
+--R +
+--R 2
+--R 70A a b + 35B a
+--R *
+--R 3
+--R x
+--R +
+--R 2 3 2 2 2 2
+--R (A a m + 15A a m + 71A a m + 105A a )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 4 3 2
+--R m + 16m + 86m + 176m + 105
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 2 2 2 2 7
+--R (B b m + 9B b m + 23B b m + 15B b )x
+--R +
+--R 2 3 2 2 2
+--R (A b + 2B a b)m + (11A b + 22B a b)m + (31A b + 62B a b)m
+--R +
+--R 2
+--R 21A b + 42B a b
+--R *
+--R 5
+--R x
+--R +
+--R 2 3 2 2 2
+--R (2A a b + B a )m + (26A a b + 13B a )m + (94A a b + 47B a )m
+--R +
+--R 2
+--R 70A a b + 35B a
+--R *
+--R 3
+--R x
+--R +
+--R 2 3 2 2 2 2
+--R (A a m + 15A a m + 71A a m + 105A a )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 2 3 2 2 2 2 m + 7
+--R (- B b m - 9B b m - 23B b m - 15B b )x
+--R +
+--R 2 3 2 2 2
+--R (- A b - 2B a b)m + (- 11A b - 22B a b)m + (- 31A b - 62B a b)m
+--R +
+--R 2
+--R - 21A b - 42B a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 2 3 2 2 2
+--R (- 2A a b - B a )m + (- 26A a b - 13B a )m + (- 94A a b - 47B a )m
+--R +
+--R 2
+--R - 70A a b - 35B a
+--R *
+--R m + 3
+--R x
+--R +
+--R 2 3 2 2 2 2 m + 1
+--R (- A a m - 15A a m - 71A a m - 105A a )x
+--R /
+--R 4 3 2
+--R m + 16m + 86m + 176m + 105
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 1406
+t0:=x^2*(a+b*x^2)^2*(A+B*x^2)
+--R
+--R
+--R 2 8 2 6 2 4 2 2
+--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 61
+
+--S 62 of 1406
+r0:=1/3*a^2*A*x^3+1/5*a*(2*A*b+a*B)*x^5+1/7*b*(A*b+2*a*B)*x^7+1/9*b^2*B*x^9
+--R
+--R
+--R 1 2 9 1 2 2 7 2 1 2 5 1 2 3
+--R (2) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x
+--R 9 7 7 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 62
+
+--S 63 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 9 1 2 2 7 2 1 2 5 1 2 3
+--R (3) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x
+--R 9 7 7 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 63
+
+--S 64 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 64
+
+--S 65 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 65
+
+)clear all
+
+--S 66 of 1406
+t0:=x*(a+b*x^2)^2*(A+B*x^2)
+--R
+--R
+--R 2 7 2 5 2 3 2
+--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 66
+
+--S 67 of 1406
+r0:=1/6*(A*b-a*B)*(a+b*x^2)^3/b^2+1/8*B*(a+b*x^2)^4/b^2
+--R
+--R
+--R (2)
+--R 1 4 8 1 4 1 3 6 1 3 1 2 2 4 1 2 2 2
+--R - B b x + (- A b + - B a b )x + (- A a b + - B a b )x + - A a b x
+--R 8 6 3 2 4 2
+--R +
+--R 1 3 1 4
+--R - A a b - -- B a
+--R 6 24
+--R /
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 67
+
+--S 68 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 8 1 2 1 6 1 1 2 4 1 2 2
+--R (3) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x
+--R 8 6 3 2 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 68
+
+--S 69 of 1406
+m0:=a0-r0
+--R
+--R
+--R 1 3 1 4
+--R - - A a b + -- B a
+--R 6 24
+--R (4) -------------------
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 69
+
+--S 70 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 70
+
+)clear all
+
+--S 71 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R Type: Polynomial(Integer)
+--E 71
+
+--S 72 of 1406
+r0:=a^2*A*x+1/3*a*(2*A*b+a*B)*x^3+1/5*b*(A*b+2*a*B)*x^5+1/7*b^2*B*x^7
+--R
+--R
+--R 1 2 7 1 2 2 5 2 1 2 3 2
+--R (2) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + A a x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 72
+
+--S 73 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 7 1 2 2 5 2 1 2 3 2
+--R (3) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + A a x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 73
+
+--S 74 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 74
+
+--S 75 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 75
+
+)clear all
+
+--S 76 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 76
+
+--S 77 of 1406
+r0:=a*A*b*x^2+1/4*A*b^2*x^4+1/6*B*(a+b*x^2)^3/b+a^2*A*log(x)
+--R
+--R
+--R (2)
+--R 2 3 6 3 2 4 2 2 2
+--R 12A a b log(x) + 2B b x + (3A b + 6B a b )x + (12A a b + 6B a b)x
+--R +
+--R 3
+--R 2B a
+--R /
+--R 12b
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 6 2 4 2 2
+--R 12A a log(x) + 2B b x + (3A b + 6B a b)x + (12A a b + 6B a )x
+--R (3) -----------------------------------------------------------------
+--R 12
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 1406
+m0:=a0-r0
+--R
+--R
+--R 3
+--R B a
+--R (4) - ----
+--R 6b
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^2
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 81
+
+--S 82 of 1406
+r0:=-a^2*A/x+a*(2*A*b+a*B)*x+1/3*b*(A*b+2*a*B)*x^3+1/5*b^2*B*x^5
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 3B b x + (5A b + 10B a b)x + (30A a b + 15B a )x - 15A a
+--R (2) -------------------------------------------------------------
+--R 15x
+--R Type: Fraction(Polynomial(Integer))
+--E 82
+
+--S 83 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 3B b x + (5A b + 10B a b)x + (30A a b + 15B a )x - 15A a
+--R (3) -------------------------------------------------------------
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^3
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 86
+
+--S 87 of 1406
+r0:=-1/2*a^2*A/x^2+1/2*b*(A*b+2*a*B)*x^2+1/4*b^2*B*x^4+a*(2*A*b+a*B)*log(x)
+--R
+--R
+--R 2 2 2 6 2 4 2
+--R (8A a b + 4B a )x log(x) + B b x + (2A b + 4B a b)x - 2A a
+--R (2) --------------------------------------------------------------
+--R 2
+--R 4x
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 6 2 4 2
+--R (8A a b + 4B a )x log(x) + B b x + (2A b + 4B a b)x - 2A a
+--R (3) --------------------------------------------------------------
+--R 2
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^4
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 91
+
+--S 92 of 1406
+r0:=-1/3*a^2*A/x^3-a*(2*A*b+a*B)/x+b*(A*b+2*a*B)*x+1/3*b^2*B*x^3
+--R
+--R
+--R 1 2 6 2 4 2 2 1 2
+--R - B b x + (A b + 2B a b)x + (- 2A a b - B a )x - - A a
+--R 3 3
+--R (2) -----------------------------------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 92
+
+--S 93 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (3A b + 6B a b)x + (- 6A a b - 3B a )x - A a
+--R (3) ---------------------------------------------------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^5
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 96
+
+--S 97 of 1406
+r0:=-1/4*a^2*A/x^4-1/2*a*(2*A*b+a*B)/x^2+1/2*b^2*B*x^2+b*(A*b+2*a*B)*log(x)
+--R
+--R
+--R 2 4 2 6 2 2 2
+--R (4A b + 8B a b)x log(x) + 2B b x + (- 4A a b - 2B a )x - A a
+--R (2) ----------------------------------------------------------------
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 6 2 2 2
+--R (4A b + 8B a b)x log(x) + 2B b x + (- 4A a b - 2B a )x - A a
+--R (3) ----------------------------------------------------------------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^6
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 101
+
+--S 102 of 1406
+r0:=-1/5*a^2*A/x^5-1/3*a*(2*A*b+a*B)/x^3-b*(A*b+2*a*B)/x+b^2*B*x
+--R
+--R
+--R 2 6 2 4 2 1 2 2 1 2
+--R B b x + (- A b - 2B a b)x + (- - A a b - - B a )x - - A a
+--R 3 3 5
+--R (2) --------------------------------------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 102
+
+--S 103 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 15B b x + (- 15A b - 30B a b)x + (- 10A a b - 5B a )x - 3A a
+--R (3) -----------------------------------------------------------------
+--R 5
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^7
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 106
+
+--S 107 of 1406
+r0:=-1/4*a^2*B/x^4-a*b*B/x^2-1/6*A*(a+b*x^2)^3/(a*x^6)+b^2*B*log(x)
+--R
+--R
+--R (2)
+--R 2 6 3 6 2 2 4
+--R 12B a b x log(x) - 2A b x + (- 6A a b - 12B a b)x
+--R +
+--R 2 3 2 3
+--R (- 6A a b - 3B a )x - 2A a
+--R /
+--R 6
+--R 12a x
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 12B b x log(x) + (- 6A b - 12B a b)x + (- 6A a b - 3B a )x - 2A a
+--R (3) ---------------------------------------------------------------------
+--R 6
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 1406
+m0:=a0-r0
+--R
+--R
+--R 3
+--R A b
+--R (4) ----
+--R 6a
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^8
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 111
+
+--S 112 of 1406
+r0:=-1/7*a^2*A/x^7-1/5*a*(2*A*b+a*B)/x^5-1/3*b*(A*b+2*a*B)/x^3-b^2*B/x
+--R
+--R
+--R 2 6 1 2 2 4 2 1 2 2 1 2
+--R - B b x + (- - A b - - B a b)x + (- - A a b - - B a )x - - A a
+--R 3 3 5 5 7
+--R (2) -------------------------------------------------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 112
+
+--S 113 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R - 105B b x + (- 35A b - 70B a b)x + (- 42A a b - 21B a )x - 15A a
+--R (3) ----------------------------------------------------------------------
+--R 7
+--R 105x
+--R Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^9
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 116
+
+--S 117 of 1406
+r0:=-1/8*A*(a+b*x^2)^3/(a*x^8)+1/24*(A*b-4*a*B)*(a+b*x^2)^3/(a^2*x^6)
+--R
+--R
+--R (2)
+--R 1 4 1 3 8 1 2 2 6 1 2 2 1 3 4
+--R (-- A b - - B a b )x - - B a b x + (- - A a b - - B a b)x
+--R 24 6 2 4 2
+--R +
+--R 1 3 1 4 2 1 4
+--R (- - A a b - - B a )x - - A a
+--R 3 6 8
+--R /
+--R 2 8
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 117
+
+--S 118 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R - 12B b x + (- 6A b - 12B a b)x + (- 8A a b - 4B a )x - 3A a
+--R (3) -----------------------------------------------------------------
+--R 8
+--R 24x
+--R Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 1406
+m0:=a0-r0
+--R
+--R
+--R 4 3
+--R - A b + 4B a b
+--R (4) ----------------
+--R 2
+--R 24a
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 1406
+t0:=x^m*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R *
+--R m
+--R x
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 1406
+r0:=a^5*A*x^(1+m)/(1+m)+a^4*(5*A*b+a*B)*x^(3+m)/(3+m)+5*a^3*b*_
+ (2*A*b+a*B)*x^(5+m)/(5+m)+10*a^2*b^2*(A*b+a*B)*x^(7+m)/_
+ (7+m)+5*a*b^3*(A*b+2*a*B)*x^(9+m)/(9+m)+b^4*(A*b+5*a*B)*_
+ x^(11+m)/(11+m)+b^5*B*x^(13+m)/(13+m)
+--R
+--R
+--R (2)
+--R 5 6 5 5 5 4 5 3 5 2 5
+--R B b m + 36B b m + 505B b m + 3480B b m + 12139B b m + 19524B b m
+--R +
+--R 5
+--R 10395B b
+--R *
+--R m + 13
+--R x
+--R +
+--R 5 4 6 5 4 5
+--R (A b + 5B a b )m + (38A b + 190B a b )m
+--R +
+--R 5 4 4 5 4 3
+--R (555A b + 2775B a b )m + (3940A b + 19700B a b )m
+--R +
+--R 5 4 2 5 4 5
+--R (14039A b + 70195B a b )m + (22902A b + 114510B a b )m + 12285A b
+--R +
+--R 4
+--R 61425B a b
+--R *
+--R m + 11
+--R x
+--R +
+--R 4 2 3 6 4 2 3 5
+--R (5A a b + 10B a b )m + (200A a b + 400B a b )m
+--R +
+--R 4 2 3 4 4 2 3 3
+--R (3065A a b + 6130B a b )m + (22640A a b + 45280B a b )m
+--R +
+--R 4 2 3 2 4 2 3
+--R (83135A a b + 166270B a b )m + (138440A a b + 276880B a b )m
+--R +
+--R 4 2 3
+--R 75075A a b + 150150B a b
+--R *
+--R m + 9
+--R x
+--R +
+--R 2 3 3 2 6 2 3 3 2 5
+--R (10A a b + 10B a b )m + (420A a b + 420B a b )m
+--R +
+--R 2 3 3 2 4 2 3 3 2 3
+--R (6790A a b + 6790B a b )m + (52920A a b + 52920B a b )m
+--R +
+--R 2 3 3 2 2 2 3 3 2
+--R (203350A a b + 203350B a b )m + (349860A a b + 349860B a b )m
+--R +
+--R 2 3 3 2
+--R 193050A a b + 193050B a b
+--R *
+--R m + 7
+--R x
+--R +
+--R 3 2 4 6 3 2 4 5
+--R (10A a b + 5B a b)m + (440A a b + 220B a b)m
+--R +
+--R 3 2 4 4 3 2 4 3
+--R (7530A a b + 3765B a b)m + (62800A a b + 31400B a b)m
+--R +
+--R 3 2 4 2 3 2 4
+--R (259790A a b + 129895B a b)m + (474360A a b + 237180B a b)m
+--R +
+--R 3 2 4
+--R 270270A a b + 135135B a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 4 5 6 4 5 5 4 5 4
+--R (5A a b + B a )m + (230A a b + 46B a )m + (4175A a b + 835B a )m
+--R +
+--R 4 5 3 4 5 2
+--R (37700A a b + 7540B a )m + (173795A a b + 34759B a )m
+--R +
+--R 4 5 4 5
+--R (365270A a b + 73054B a )m + 225225A a b + 45045B a
+--R *
+--R m + 3
+--R x
+--R +
+--R 5 6 5 5 5 4 5 3 5 2
+--R A a m + 48A a m + 925A a m + 9120A a m + 48259A a m
+--R +
+--R 5 5
+--R 129072A a m + 135135A a
+--R *
+--R m + 1
+--R x
+--R /
+--R 7 6 5 4 3 2
+--R m + 49m + 973m + 10045m + 57379m + 177331m + 264207m + 135135
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 6 5 5 5 4 5 3 5 2
+--R B b m + 36B b m + 505B b m + 3480B b m + 12139B b m
+--R +
+--R 5 5
+--R 19524B b m + 10395B b
+--R *
+--R 13
+--R x
+--R +
+--R 5 4 6 5 4 5
+--R (A b + 5B a b )m + (38A b + 190B a b )m
+--R +
+--R 5 4 4 5 4 3
+--R (555A b + 2775B a b )m + (3940A b + 19700B a b )m
+--R +
+--R 5 4 2 5 4
+--R (14039A b + 70195B a b )m + (22902A b + 114510B a b )m
+--R +
+--R 5 4
+--R 12285A b + 61425B a b
+--R *
+--R 11
+--R x
+--R +
+--R 4 2 3 6 4 2 3 5
+--R (5A a b + 10B a b )m + (200A a b + 400B a b )m
+--R +
+--R 4 2 3 4 4 2 3 3
+--R (3065A a b + 6130B a b )m + (22640A a b + 45280B a b )m
+--R +
+--R 4 2 3 2 4 2 3
+--R (83135A a b + 166270B a b )m + (138440A a b + 276880B a b )m
+--R +
+--R 4 2 3
+--R 75075A a b + 150150B a b
+--R *
+--R 9
+--R x
+--R +
+--R 2 3 3 2 6 2 3 3 2 5
+--R (10A a b + 10B a b )m + (420A a b + 420B a b )m
+--R +
+--R 2 3 3 2 4 2 3 3 2 3
+--R (6790A a b + 6790B a b )m + (52920A a b + 52920B a b )m
+--R +
+--R 2 3 3 2 2 2 3 3 2
+--R (203350A a b + 203350B a b )m + (349860A a b + 349860B a b )m
+--R +
+--R 2 3 3 2
+--R 193050A a b + 193050B a b
+--R *
+--R 7
+--R x
+--R +
+--R 3 2 4 6 3 2 4 5
+--R (10A a b + 5B a b)m + (440A a b + 220B a b)m
+--R +
+--R 3 2 4 4 3 2 4 3
+--R (7530A a b + 3765B a b)m + (62800A a b + 31400B a b)m
+--R +
+--R 3 2 4 2 3 2 4
+--R (259790A a b + 129895B a b)m + (474360A a b + 237180B a b)m
+--R +
+--R 3 2 4
+--R 270270A a b + 135135B a b
+--R *
+--R 5
+--R x
+--R +
+--R 4 5 6 4 5 5 4 5 4
+--R (5A a b + B a )m + (230A a b + 46B a )m + (4175A a b + 835B a )m
+--R +
+--R 4 5 3 4 5 2
+--R (37700A a b + 7540B a )m + (173795A a b + 34759B a )m
+--R +
+--R 4 5 4 5
+--R (365270A a b + 73054B a )m + 225225A a b + 45045B a
+--R *
+--R 3
+--R x
+--R +
+--R 5 6 5 5 5 4 5 3 5 2
+--R A a m + 48A a m + 925A a m + 9120A a m + 48259A a m
+--R +
+--R 5 5
+--R 129072A a m + 135135A a
+--R *
+--R x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 7 6 5 4 3 2
+--R m + 49m + 973m + 10045m + 57379m + 177331m + 264207m + 135135
+--R Type: Union(Expression(Integer),...)
+--E 123
+
+--S 124 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 6 5 5 5 4 5 3 5 2
+--R B b m + 36B b m + 505B b m + 3480B b m + 12139B b m
+--R +
+--R 5 5
+--R 19524B b m + 10395B b
+--R *
+--R 13
+--R x
+--R +
+--R 5 4 6 5 4 5
+--R (A b + 5B a b )m + (38A b + 190B a b )m
+--R +
+--R 5 4 4 5 4 3
+--R (555A b + 2775B a b )m + (3940A b + 19700B a b )m
+--R +
+--R 5 4 2 5 4
+--R (14039A b + 70195B a b )m + (22902A b + 114510B a b )m
+--R +
+--R 5 4
+--R 12285A b + 61425B a b
+--R *
+--R 11
+--R x
+--R +
+--R 4 2 3 6 4 2 3 5
+--R (5A a b + 10B a b )m + (200A a b + 400B a b )m
+--R +
+--R 4 2 3 4 4 2 3 3
+--R (3065A a b + 6130B a b )m + (22640A a b + 45280B a b )m
+--R +
+--R 4 2 3 2 4 2 3
+--R (83135A a b + 166270B a b )m + (138440A a b + 276880B a b )m
+--R +
+--R 4 2 3
+--R 75075A a b + 150150B a b
+--R *
+--R 9
+--R x
+--R +
+--R 2 3 3 2 6 2 3 3 2 5
+--R (10A a b + 10B a b )m + (420A a b + 420B a b )m
+--R +
+--R 2 3 3 2 4 2 3 3 2 3
+--R (6790A a b + 6790B a b )m + (52920A a b + 52920B a b )m
+--R +
+--R 2 3 3 2 2 2 3 3 2
+--R (203350A a b + 203350B a b )m + (349860A a b + 349860B a b )m
+--R +
+--R 2 3 3 2
+--R 193050A a b + 193050B a b
+--R *
+--R 7
+--R x
+--R +
+--R 3 2 4 6 3 2 4 5
+--R (10A a b + 5B a b)m + (440A a b + 220B a b)m
+--R +
+--R 3 2 4 4 3 2 4 3
+--R (7530A a b + 3765B a b)m + (62800A a b + 31400B a b)m
+--R +
+--R 3 2 4 2 3 2 4
+--R (259790A a b + 129895B a b)m + (474360A a b + 237180B a b)m
+--R +
+--R 3 2 4
+--R 270270A a b + 135135B a b
+--R *
+--R 5
+--R x
+--R +
+--R 4 5 6 4 5 5
+--R (5A a b + B a )m + (230A a b + 46B a )m
+--R +
+--R 4 5 4 4 5 3
+--R (4175A a b + 835B a )m + (37700A a b + 7540B a )m
+--R +
+--R 4 5 2 4 5
+--R (173795A a b + 34759B a )m + (365270A a b + 73054B a )m
+--R +
+--R 4 5
+--R 225225A a b + 45045B a
+--R *
+--R 3
+--R x
+--R +
+--R 5 6 5 5 5 4 5 3 5 2
+--R A a m + 48A a m + 925A a m + 9120A a m + 48259A a m
+--R +
+--R 5 5
+--R 129072A a m + 135135A a
+--R *
+--R x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 5 6 5 5 5 4 5 3 5 2
+--R - B b m - 36B b m - 505B b m - 3480B b m - 12139B b m
+--R +
+--R 5 5
+--R - 19524B b m - 10395B b
+--R *
+--R m + 13
+--R x
+--R +
+--R 5 4 6 5 4 5
+--R (- A b - 5B a b )m + (- 38A b - 190B a b )m
+--R +
+--R 5 4 4 5 4 3
+--R (- 555A b - 2775B a b )m + (- 3940A b - 19700B a b )m
+--R +
+--R 5 4 2 5 4
+--R (- 14039A b - 70195B a b )m + (- 22902A b - 114510B a b )m
+--R +
+--R 5 4
+--R - 12285A b - 61425B a b
+--R *
+--R m + 11
+--R x
+--R +
+--R 4 2 3 6 4 2 3 5
+--R (- 5A a b - 10B a b )m + (- 200A a b - 400B a b )m
+--R +
+--R 4 2 3 4 4 2 3 3
+--R (- 3065A a b - 6130B a b )m + (- 22640A a b - 45280B a b )m
+--R +
+--R 4 2 3 2 4 2 3
+--R (- 83135A a b - 166270B a b )m + (- 138440A a b - 276880B a b )m
+--R +
+--R 4 2 3
+--R - 75075A a b - 150150B a b
+--R *
+--R m + 9
+--R x
+--R +
+--R 2 3 3 2 6 2 3 3 2 5
+--R (- 10A a b - 10B a b )m + (- 420A a b - 420B a b )m
+--R +
+--R 2 3 3 2 4 2 3 3 2 3
+--R (- 6790A a b - 6790B a b )m + (- 52920A a b - 52920B a b )m
+--R +
+--R 2 3 3 2 2 2 3 3 2
+--R (- 203350A a b - 203350B a b )m + (- 349860A a b - 349860B a b )m
+--R +
+--R 2 3 3 2
+--R - 193050A a b - 193050B a b
+--R *
+--R m + 7
+--R x
+--R +
+--R 3 2 4 6 3 2 4 5
+--R (- 10A a b - 5B a b)m + (- 440A a b - 220B a b)m
+--R +
+--R 3 2 4 4 3 2 4 3
+--R (- 7530A a b - 3765B a b)m + (- 62800A a b - 31400B a b)m
+--R +
+--R 3 2 4 2 3 2 4
+--R (- 259790A a b - 129895B a b)m + (- 474360A a b - 237180B a b)m
+--R +
+--R 3 2 4
+--R - 270270A a b - 135135B a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 4 5 6 4 5 5
+--R (- 5A a b - B a )m + (- 230A a b - 46B a )m
+--R +
+--R 4 5 4 4 5 3
+--R (- 4175A a b - 835B a )m + (- 37700A a b - 7540B a )m
+--R +
+--R 4 5 2 4 5
+--R (- 173795A a b - 34759B a )m + (- 365270A a b - 73054B a )m
+--R +
+--R 4 5
+--R - 225225A a b - 45045B a
+--R *
+--R m + 3
+--R x
+--R +
+--R 5 6 5 5 5 4 5 3 5 2
+--R - A a m - 48A a m - 925A a m - 9120A a m - 48259A a m
+--R +
+--R 5 5
+--R - 129072A a m - 135135A a
+--R *
+--R m + 1
+--R x
+--R /
+--R 7 6 5 4 3 2
+--R m + 49m + 973m + 10045m + 57379m + 177331m + 264207m + 135135
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 1406
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 1406
+t0:=x^9*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 21 5 4 19 4 2 3 17
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 15 3 2 4 13 4 5 11
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x
+--R +
+--R 5 9
+--R A a x
+--R Type: Polynomial(Integer)
+--E 126
+
+--S 127 of 1406
+r0:=1/10*a^5*A*x^10+1/12*a^4*(5*A*b+a*B)*x^12+5/14*a^3*b*(2*A*b+a*B)*_
+ x^14+5/8*a^2*b^2*(A*b+a*B)*x^16+5/18*a*b^3*(A*b+2*a*B)*x^18+_
+ 1/20*b^4*(A*b+5*a*B)*x^20+1/22*b^5*B*x^22
+--R
+--R
+--R (2)
+--R 1 5 22 1 5 1 4 20 5 4 5 2 3 18
+--R -- B b x + (-- A b + - B a b )x + (-- A a b + - B a b )x
+--R 22 20 4 18 9
+--R +
+--R 5 2 3 5 3 2 16 5 3 2 5 4 14
+--R (- A a b + - B a b )x + (- A a b + -- B a b)x
+--R 8 8 7 14
+--R +
+--R 5 4 1 5 12 1 5 10
+--R (-- A a b + -- B a )x + -- A a x
+--R 12 12 10
+--R Type: Polynomial(Fraction(Integer))
+--E 127
+
+--S 128 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 22 1 5 1 4 20 5 4 5 2 3 18
+--R -- B b x + (-- A b + - B a b )x + (-- A a b + - B a b )x
+--R 22 20 4 18 9
+--R +
+--R 5 2 3 5 3 2 16 5 3 2 5 4 14
+--R (- A a b + - B a b )x + (- A a b + -- B a b)x
+--R 8 8 7 14
+--R +
+--R 5 4 1 5 12 1 5 10
+--R (-- A a b + -- B a )x + -- A a x
+--R 12 12 10
+--R Type: Polynomial(Fraction(Integer))
+--E 128
+
+--S 129 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 129
+
+--S 130 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 130
+
+)clear all
+
+--S 131 of 1406
+t0:=x^8*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 20 5 4 18 4 2 3 16
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 14 3 2 4 12 4 5 10
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x
+--R +
+--R 5 8
+--R A a x
+--R Type: Polynomial(Integer)
+--E 131
+
+--S 132 of 1406
+r0:=1/9*a^5*A*x^9+1/11*a^4*(5*A*b+a*B)*x^11+5/13*a^3*b*(2*A*b+a*B)*x^13+_
+ 2/3*a^2*b^2*(A*b+a*B)*x^15+5/17*a*b^3*(A*b+2*a*B)*x^17+_
+ 1/19*b^4*(A*b+5*a*B)*x^19+1/21*b^5*B*x^21
+--R
+--R
+--R (2)
+--R 1 5 21 1 5 5 4 19 5 4 10 2 3 17
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + -- B a b )x
+--R 21 19 19 17 17
+--R +
+--R 2 2 3 2 3 2 15 10 3 2 5 4 13
+--R (- A a b + - B a b )x + (-- A a b + -- B a b)x
+--R 3 3 13 13
+--R +
+--R 5 4 1 5 11 1 5 9
+--R (-- A a b + -- B a )x + - A a x
+--R 11 11 9
+--R Type: Polynomial(Fraction(Integer))
+--E 132
+
+--S 133 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 21 1 5 5 4 19 5 4 10 2 3 17
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + -- B a b )x
+--R 21 19 19 17 17
+--R +
+--R 2 2 3 2 3 2 15 10 3 2 5 4 13
+--R (- A a b + - B a b )x + (-- A a b + -- B a b)x
+--R 3 3 13 13
+--R +
+--R 5 4 1 5 11 1 5 9
+--R (-- A a b + -- B a )x + - A a x
+--R 11 11 9
+--R Type: Polynomial(Fraction(Integer))
+--E 133
+
+--S 134 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 134
+
+--S 135 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 135
+
+)clear all
+
+--S 136 of 1406
+t0:=x^7*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 19 5 4 17 4 2 3 15
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 13 3 2 4 11 4 5 9
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x
+--R +
+--R 5 7
+--R A a x
+--R Type: Polynomial(Integer)
+--E 136
+
+--S 137 of 1406
+r0:=1/8*a^5*A*x^8+1/10*a^4*(5*A*b+a*B)*x^10+5/12*a^3*b*(2*A*b+a*B)*x^12+_
+ 5/7*a^2*b^2*(A*b+a*B)*x^14+5/16*a*b^3*(A*b+2*a*B)*x^16+_
+ 1/18*b^4*(A*b+5*a*B)*x^18+1/20*b^5*B*x^20
+--R
+--R
+--R (2)
+--R 1 5 20 1 5 5 4 18 5 4 5 2 3 16
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + - B a b )x
+--R 20 18 18 16 8
+--R +
+--R 5 2 3 5 3 2 14 5 3 2 5 4 12
+--R (- A a b + - B a b )x + (- A a b + -- B a b)x
+--R 7 7 6 12
+--R +
+--R 1 4 1 5 10 1 5 8
+--R (- A a b + -- B a )x + - A a x
+--R 2 10 8
+--R Type: Polynomial(Fraction(Integer))
+--E 137
+
+--S 138 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 20 1 5 5 4 18 5 4 5 2 3 16
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + - B a b )x
+--R 20 18 18 16 8
+--R +
+--R 5 2 3 5 3 2 14 5 3 2 5 4 12
+--R (- A a b + - B a b )x + (- A a b + -- B a b)x
+--R 7 7 6 12
+--R +
+--R 1 4 1 5 10 1 5 8
+--R (- A a b + -- B a )x + - A a x
+--R 2 10 8
+--R Type: Polynomial(Fraction(Integer))
+--E 138
+
+--S 139 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 139
+
+--S 140 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 140
+
+)clear all
+
+--S 141 of 1406
+t0:=x^6*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 18 5 4 16 4 2 3 14
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 12 3 2 4 10 4 5 8
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x
+--R +
+--R 5 6
+--R A a x
+--R Type: Polynomial(Integer)
+--E 141
+
+--S 142 of 1406
+r0:=1/7*a^5*A*x^7+1/9*a^4*(5*A*b+a*B)*x^9+5/11*a^3*b*(2*A*b+a*B)*x^11+_
+ 10/13*a^2*b^2*(A*b+a*B)*x^13+1/3*a*b^3*(A*b+2*a*B)*x^15+_
+ 1/17*b^4*(A*b+5*a*B)*x^17+1/19*b^5*B*x^19
+--R
+--R
+--R (2)
+--R 1 5 19 1 5 5 4 17 1 4 2 2 3 15
+--R -- B b x + (-- A b + -- B a b )x + (- A a b + - B a b )x
+--R 19 17 17 3 3
+--R +
+--R 10 2 3 10 3 2 13 10 3 2 5 4 11
+--R (-- A a b + -- B a b )x + (-- A a b + -- B a b)x
+--R 13 13 11 11
+--R +
+--R 5 4 1 5 9 1 5 7
+--R (- A a b + - B a )x + - A a x
+--R 9 9 7
+--R Type: Polynomial(Fraction(Integer))
+--E 142
+
+--S 143 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 19 1 5 5 4 17 1 4 2 2 3 15
+--R -- B b x + (-- A b + -- B a b )x + (- A a b + - B a b )x
+--R 19 17 17 3 3
+--R +
+--R 10 2 3 10 3 2 13 10 3 2 5 4 11
+--R (-- A a b + -- B a b )x + (-- A a b + -- B a b)x
+--R 13 13 11 11
+--R +
+--R 5 4 1 5 9 1 5 7
+--R (- A a b + - B a )x + - A a x
+--R 9 9 7
+--R Type: Polynomial(Fraction(Integer))
+--E 143
+
+--S 144 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 144
+
+--S 145 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 145
+
+)clear all
+
+--S 146 of 1406
+t0:=x^5*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 17 5 4 15 4 2 3 13
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 11 3 2 4 9 4 5 7 5 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 146
+
+--S 147 of 1406
+r0:=1/12*a^2*(A*b-a*B)*(a+b*x^2)^6/b^4-1/14*a*(2*A*b-3*a*B)*(a+b*x^2)^7/_
+ b^4+1/16*(A*b-3*a*B)*(a+b*x^2)^8/b^4+1/18*B*(a+b*x^2)^9/b^4
+--R
+--R
+--R (2)
+--R 1 9 18 1 9 5 8 16 5 8 5 2 7 14
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + - B a b )x
+--R 18 16 16 14 7
+--R +
+--R 5 2 7 5 3 6 12 3 6 1 4 5 10
+--R (- A a b + - B a b )x + (A a b + - B a b )x
+--R 6 6 2
+--R +
+--R 5 4 5 1 5 4 8 1 5 4 6 1 8 1 9
+--R (- A a b + - B a b )x + - A a b x + --- A a b - ---- B a
+--R 8 8 6 336 1008
+--R /
+--R 4
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 147
+
+--S 148 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 18 1 5 5 4 16 5 4 5 2 3 14
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + - B a b )x
+--R 18 16 16 14 7
+--R +
+--R 5 2 3 5 3 2 12 3 2 1 4 10 5 4 1 5 8
+--R (- A a b + - B a b )x + (A a b + - B a b)x + (- A a b + - B a )x
+--R 6 6 2 8 8
+--R +
+--R 1 5 6
+--R - A a x
+--R 6
+--R Type: Polynomial(Fraction(Integer))
+--E 148
+
+--S 149 of 1406
+m0:=a0-r0
+--R
+--R
+--R 1 8 1 9
+--R - --- A a b + ---- B a
+--R 336 1008
+--R (4) -----------------------
+--R 4
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 149
+
+--S 150 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 150
+
+)clear all
+
+--S 151 of 1406
+t0:=x^4*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 16 5 4 14 4 2 3 12
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 10 3 2 4 8 4 5 6 5 4
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 151
+
+--S 152 of 1406
+r0:=1/5*a^5*A*x^5+1/7*a^4*(5*A*b+a*B)*x^7+5/9*a^3*b*(2*A*b+a*B)*x^9+_
+ 10/11*a^2*b^2*(A*b+a*B)*x^11+5/13*a*b^3*(A*b+2*a*B)*x^13+_
+ 1/15*b^4*(A*b+5*a*B)*x^15+1/17*b^5*B*x^17
+--R
+--R
+--R (2)
+--R 1 5 17 1 5 1 4 15 5 4 10 2 3 13
+--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x
+--R 17 15 3 13 13
+--R +
+--R 10 2 3 10 3 2 11 10 3 2 5 4 9 5 4 1 5 7
+--R (-- A a b + -- B a b )x + (-- A a b + - B a b)x + (- A a b + - B a )x
+--R 11 11 9 9 7 7
+--R +
+--R 1 5 5
+--R - A a x
+--R 5
+--R Type: Polynomial(Fraction(Integer))
+--E 152
+
+--S 153 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 17 1 5 1 4 15 5 4 10 2 3 13
+--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x
+--R 17 15 3 13 13
+--R +
+--R 10 2 3 10 3 2 11 10 3 2 5 4 9 5 4 1 5 7
+--R (-- A a b + -- B a b )x + (-- A a b + - B a b)x + (- A a b + - B a )x
+--R 11 11 9 9 7 7
+--R +
+--R 1 5 5
+--R - A a x
+--R 5
+--R Type: Polynomial(Fraction(Integer))
+--E 153
+
+--S 154 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 154
+
+--S 155 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 155
+
+)clear all
+
+--S 156 of 1406
+t0:=x^3*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 15 5 4 13 4 2 3 11
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 9 3 2 4 7 4 5 5 5 3
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 156
+
+--S 157 of 1406
+r0:=-1/12*a*(A*b-a*B)*(a+b*x^2)^6/b^3+1/14*(A*b-2*a*B)*(a+b*x^2)^7/b^3+_
+ 1/16*B*(a+b*x^2)^8/b^3
+--R
+--R
+--R (2)
+--R 1 8 16 1 8 5 7 14 5 7 5 2 6 12
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + - B a b )x
+--R 16 14 14 12 6
+--R +
+--R 2 6 3 5 10 5 3 5 5 4 4 8 5 4 4 1 5 3 6
+--R (A a b + B a b )x + (- A a b + - B a b )x + (- A a b + - B a b )x
+--R 4 8 6 6
+--R +
+--R 1 5 3 4 1 7 1 8
+--R - A a b x - -- A a b + --- B a
+--R 4 84 336
+--R /
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 157
+
+--S 158 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 16 1 5 5 4 14 5 4 5 2 3 12
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + - B a b )x
+--R 16 14 14 12 6
+--R +
+--R 2 3 3 2 10 5 3 2 5 4 8 5 4 1 5 6
+--R (A a b + B a b )x + (- A a b + - B a b)x + (- A a b + - B a )x
+--R 4 8 6 6
+--R +
+--R 1 5 4
+--R - A a x
+--R 4
+--R Type: Polynomial(Fraction(Integer))
+--E 158
+
+--S 159 of 1406
+m0:=a0-r0
+--R
+--R
+--R 1 7 1 8
+--R -- A a b - --- B a
+--R 84 336
+--R (4) -------------------
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 159
+
+--S 160 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 160
+
+)clear all
+
+--S 161 of 1406
+t0:=x^2*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 14 5 4 12 4 2 3 10
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 8 3 2 4 6 4 5 4 5 2
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 161
+
+--S 162 of 1406
+r0:=1/3*a^5*A*x^3+1/5*a^4*(5*A*b+a*B)*x^5+5/7*a^3*b*(2*A*b+a*B)*x^7+_
+ 10/9*a^2*b^2*(A*b+a*B)*x^9+5/11*a*b^3*(A*b+2*a*B)*x^11+_
+ 1/13*b^4*(A*b+5*a*B)*x^13+1/15*b^5*B*x^15
+--R
+--R
+--R (2)
+--R 1 5 15 1 5 5 4 13 5 4 10 2 3 11
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + -- B a b )x
+--R 15 13 13 11 11
+--R +
+--R 10 2 3 10 3 2 9 10 3 2 5 4 7 4 1 5 5
+--R (-- A a b + -- B a b )x + (-- A a b + - B a b)x + (A a b + - B a )x
+--R 9 9 7 7 5
+--R +
+--R 1 5 3
+--R - A a x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 162
+
+--S 163 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 15 1 5 5 4 13 5 4 10 2 3 11
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + -- B a b )x
+--R 15 13 13 11 11
+--R +
+--R 10 2 3 10 3 2 9 10 3 2 5 4 7 4 1 5 5
+--R (-- A a b + -- B a b )x + (-- A a b + - B a b)x + (A a b + - B a )x
+--R 9 9 7 7 5
+--R +
+--R 1 5 3
+--R - A a x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 163
+
+--S 164 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 164
+
+--S 165 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 165
+
+)clear all
+
+--S 166 of 1406
+t0:=x*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 13 5 4 11 4 2 3 9
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 7 3 2 4 5 4 5 3 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 166
+
+--S 167 of 1406
+r0:=1/12*(A*b-a*B)*(a+b*x^2)^6/b^2+1/14*B*(a+b*x^2)^7/b^2
+--R
+--R
+--R (2)
+--R 1 7 14 1 7 5 6 12 1 6 2 5 10
+--R -- B b x + (-- A b + -- B a b )x + (- A a b + B a b )x
+--R 14 12 12 2
+--R +
+--R 5 2 5 5 3 4 8 5 3 4 5 4 3 6
+--R (- A a b + - B a b )x + (- A a b + - B a b )x
+--R 4 4 3 6
+--R +
+--R 5 4 3 1 5 2 4 1 5 2 2 1 6 1 7
+--R (- A a b + - B a b )x + - A a b x + -- A a b - -- B a
+--R 4 4 2 12 84
+--R /
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 167
+
+--S 168 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 14 1 5 5 4 12 1 4 2 3 10
+--R -- B b x + (-- A b + -- B a b )x + (- A a b + B a b )x
+--R 14 12 12 2
+--R +
+--R 5 2 3 5 3 2 8 5 3 2 5 4 6 5 4 1 5 4
+--R (- A a b + - B a b )x + (- A a b + - B a b)x + (- A a b + - B a )x
+--R 4 4 3 6 4 4
+--R +
+--R 1 5 2
+--R - A a x
+--R 2
+--R Type: Polynomial(Fraction(Integer))
+--E 168
+
+--S 169 of 1406
+m0:=a0-r0
+--R
+--R
+--R 1 6 1 7
+--R - -- A a b + -- B a
+--R 12 84
+--R (4) --------------------
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 169
+
+--S 170 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 170
+
+)clear all
+
+--S 171 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R Type: Polynomial(Integer)
+--E 171
+
+--S 172 of 1406
+r0:=a^5*A*x+1/3*a^4*(5*A*b+a*B)*x^3+a^3*b*(2*A*b+a*B)*x^5+_
+ 10/7*a^2*b^2*(A*b+a*B)*x^7+5/9*a*b^3*(A*b+2*a*B)*x^9+_
+ 1/11*b^4*(A*b+5*a*B)*x^11+1/13*b^5*B*x^13
+--R
+--R
+--R (2)
+--R 1 5 13 1 5 5 4 11 5 4 10 2 3 9
+--R -- B b x + (-- A b + -- B a b )x + (- A a b + -- B a b )x
+--R 13 11 11 9 9
+--R +
+--R 10 2 3 10 3 2 7 3 2 4 5 5 4 1 5 3
+--R (-- A a b + -- B a b )x + (2A a b + B a b)x + (- A a b + - B a )x
+--R 7 7 3 3
+--R +
+--R 5
+--R A a x
+--R Type: Polynomial(Fraction(Integer))
+--E 172
+
+--S 173 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 13 1 5 5 4 11 5 4 10 2 3 9
+--R -- B b x + (-- A b + -- B a b )x + (- A a b + -- B a b )x
+--R 13 11 11 9 9
+--R +
+--R 10 2 3 10 3 2 7 3 2 4 5 5 4 1 5 3
+--R (-- A a b + -- B a b )x + (2A a b + B a b)x + (- A a b + - B a )x
+--R 7 7 3 3
+--R +
+--R 5
+--R A a x
+--R Type: Polynomial(Fraction(Integer))
+--E 173
+
+--S 174 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 174
+
+--S 175 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 175
+
+)clear all
+
+--S 176 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 176
+
+--S 177 of 1406
+r0:=5/2*a^4*A*b*x^2+5/2*a^3*A*b^2*x^4+5/3*a^2*A*b^3*x^6+5/8*a*A*b^4*x^8+_
+ 1/10*A*b^5*x^10+1/12*B*(a+b*x^2)^6/b+a^5*A*log(x)
+--R
+--R
+--R (2)
+--R 5 6 12 6 5 10
+--R 120A a b log(x) + 10B b x + (12A b + 60B a b )x
+--R +
+--R 5 2 4 8 2 4 3 3 6
+--R (75A a b + 150B a b )x + (200A a b + 200B a b )x
+--R +
+--R 3 3 4 2 4 4 2 5 2 6
+--R (300A a b + 150B a b )x + (300A a b + 60B a b)x + 10B a
+--R /
+--R 120b
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 5 12 5 4 10
+--R 120A a log(x) + 10B b x + (12A b + 60B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (75A a b + 150B a b )x + (200A a b + 200B a b )x
+--R +
+--R 3 2 4 4 4 5 2
+--R (300A a b + 150B a b)x + (300A a b + 60B a )x
+--R /
+--R 120
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 1406
+m0:=a0-r0
+--R
+--R
+--R 6
+--R B a
+--R (4) - ----
+--R 12b
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^2
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 181
+
+--S 182 of 1406
+r0:=-a^5*A/x+a^4*(5*A*b+a*B)*x+5/3*a^3*b*(2*A*b+a*B)*x^3+_
+ 2*a^2*b^2*(A*b+a*B)*x^5+5/7*a*b^3*(A*b+2*a*B)*x^7+_
+ 1/9*b^4*(A*b+5*a*B)*x^9+1/11*b^5*B*x^11
+--R
+--R
+--R (2)
+--R 5 12 5 4 10 4 2 3 8
+--R 63B b x + (77A b + 385B a b )x + (495A a b + 990B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (1386A a b + 1386B a b )x + (2310A a b + 1155B a b)x
+--R +
+--R 4 5 2 5
+--R (3465A a b + 693B a )x - 693A a
+--R /
+--R 693x
+--R Type: Fraction(Polynomial(Integer))
+--E 182
+
+--S 183 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R 63B b x + (77A b + 385B a b )x + (495A a b + 990B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (1386A a b + 1386B a b )x + (2310A a b + 1155B a b)x
+--R +
+--R 4 5 2 5
+--R (3465A a b + 693B a )x - 693A a
+--R /
+--R 693x
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^3
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 186
+
+--S 187 of 1406
+r0:=-1/2*a^5*A/x^2+5/2*a^3*b*(2*A*b+a*B)*x^2+5/2*a^2*b^2*(A*b+a*B)*x^4+_
+ 5/6*a*b^3*(A*b+2*a*B)*x^6+1/8*b^4*(A*b+5*a*B)*x^8+1/10*b^5*B*x^10+_
+ a^4*(5*A*b+a*B)*log(x)
+--R
+--R
+--R (2)
+--R 4 5 2 5 12 5 4 10
+--R (600A a b + 120B a )x log(x) + 12B b x + (15A b + 75B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (100A a b + 200B a b )x + (300A a b + 300B a b )x
+--R +
+--R 3 2 4 4 5
+--R (600A a b + 300B a b)x - 60A a
+--R /
+--R 2
+--R 120x
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 5 2 5 12 5 4 10
+--R (600A a b + 120B a )x log(x) + 12B b x + (15A b + 75B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (100A a b + 200B a b )x + (300A a b + 300B a b )x
+--R +
+--R 3 2 4 4 5
+--R (600A a b + 300B a b)x - 60A a
+--R /
+--R 2
+--R 120x
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^4
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 191
+
+--S 192 of 1406
+r0:=-1/3*a^5*A/x^3-a^4*(5*A*b+a*B)/x+5*a^3*b*(2*A*b+a*B)*x+_
+ 10/3*a^2*b^2*(A*b+a*B)*x^3+a*b^3*(A*b+2*a*B)*x^5+_
+ 1/7*b^4*(A*b+5*a*B)*x^7+1/9*b^5*B*x^9
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 4 2 3 8
+--R - B b x + (- A b + - B a b )x + (A a b + 2B a b )x
+--R 9 7 7
+--R +
+--R 10 2 3 10 3 2 6 3 2 4 4 4 5 2
+--R (-- A a b + -- B a b )x + (10A a b + 5B a b)x + (- 5A a b - B a )x
+--R 3 3
+--R +
+--R 1 5
+--R - - A a
+--R 3
+--R /
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 192
+
+--S 193 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R 7B b x + (9A b + 45B a b )x + (63A a b + 126B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (210A a b + 210B a b )x + (630A a b + 315B a b)x
+--R +
+--R 4 5 2 5
+--R (- 315A a b - 63B a )x - 21A a
+--R /
+--R 3
+--R 63x
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^5
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 196
+
+--S 197 of 1406
+r0:=-1/4*a^5*A/x^4-1/2*a^4*(5*A*b+a*B)/x^2+5*a^2*b^2*(A*b+a*B)*x^2+_
+ 5/4*a*b^3*(A*b+2*a*B)*x^4+1/6*b^4*(A*b+5*a*B)*x^6+_
+ 1/8*b^5*B*x^8+5*a^3*b*(2*A*b+a*B)*log(x)
+--R
+--R
+--R (2)
+--R 3 2 4 4 5 12 5 4 10
+--R (240A a b + 120B a b)x log(x) + 3B b x + (4A b + 20B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (30A a b + 60B a b )x + (120A a b + 120B a b )x
+--R +
+--R 4 5 2 5
+--R (- 60A a b - 12B a )x - 6A a
+--R /
+--R 4
+--R 24x
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 4 5 12 5 4 10
+--R (240A a b + 120B a b)x log(x) + 3B b x + (4A b + 20B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (30A a b + 60B a b )x + (120A a b + 120B a b )x
+--R +
+--R 4 5 2 5
+--R (- 60A a b - 12B a )x - 6A a
+--R /
+--R 4
+--R 24x
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^6
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 201
+
+--S 202 of 1406
+r0:=-1/5*a^5*A/x^5-1/3*a^4*(5*A*b+a*B)/x^3-5*a^3*b*(2*A*b+a*B)/x+_
+ 10*a^2*b^2*(A*b+a*B)*x+5/3*a*b^3*(A*b+2*a*B)*x^3+_
+ 1/5*b^4*(A*b+5*a*B)*x^5+1/7*b^5*B*x^7
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 4 10 5 4 10 2 3 8
+--R - B b x + (- A b + B a b )x + (- A a b + -- B a b )x
+--R 7 5 3 3
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (10A a b + 10B a b )x + (- 10A a b - 5B a b)x
+--R +
+--R 5 4 1 5 2 1 5
+--R (- - A a b - - B a )x - - A a
+--R 3 3 5
+--R /
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 202
+
+--S 203 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R 15B b x + (21A b + 105B a b )x + (175A a b + 350B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (1050A a b + 1050B a b )x + (- 1050A a b - 525B a b)x
+--R +
+--R 4 5 2 5
+--R (- 175A a b - 35B a )x - 21A a
+--R /
+--R 5
+--R 105x
+--R Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^7
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 206
+
+--S 207 of 1406
+r0:=-1/6*a^5*A/x^6-1/4*a^4*(5*A*b+a*B)/x^4-5/2*a^3*b*(2*A*b+a*B)/x^2+_
+ 5/2*a*b^3*(A*b+2*a*B)*x^2+1/4*b^4*(A*b+5*a*B)*x^4+1/6*b^5*B*x^6+_
+ 10*a^2*b^2*(A*b+a*B)*log(x)
+--R
+--R
+--R (2)
+--R 2 3 3 2 6 5 12 5 4 10
+--R (120A a b + 120B a b )x log(x) + 2B b x + (3A b + 15B a b )x
+--R +
+--R 4 2 3 8 3 2 4 4
+--R (30A a b + 60B a b )x + (- 60A a b - 30B a b)x
+--R +
+--R 4 5 2 5
+--R (- 15A a b - 3B a )x - 2A a
+--R /
+--R 6
+--R 12x
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 3 2 6 5 12 5 4 10
+--R (120A a b + 120B a b )x log(x) + 2B b x + (3A b + 15B a b )x
+--R +
+--R 4 2 3 8 3 2 4 4
+--R (30A a b + 60B a b )x + (- 60A a b - 30B a b)x
+--R +
+--R 4 5 2 5
+--R (- 15A a b - 3B a )x - 2A a
+--R /
+--R 6
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 208
+
+--S 209 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 210
+
+)clear all
+
+--S 211 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^8
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 211
+
+--S 212 of 1406
+r0:=-1/7*a^5*A/x^7-1/5*a^4*(5*A*b+a*B)/x^5-5/3*a^3*b*(2*A*b+a*B)/x^3-_
+ 10*a^2*b^2*(A*b+a*B)/x+5*a*b^3*(A*b+2*a*B)*x+_
+ 1/3*b^4*(A*b+5*a*B)*x^3+1/5*b^5*B*x^5
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 4 2 3 8
+--R - B b x + (- A b + - B a b )x + (5A a b + 10B a b )x
+--R 5 3 3
+--R +
+--R 2 3 3 2 6 10 3 2 5 4 4
+--R (- 10A a b - 10B a b )x + (- -- A a b - - B a b)x
+--R 3 3
+--R +
+--R 4 1 5 2 1 5
+--R (- A a b - - B a )x - - A a
+--R 5 7
+--R /
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 212
+
+--S 213 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R 21B b x + (35A b + 175B a b )x + (525A a b + 1050B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 1050A a b - 1050B a b )x + (- 350A a b - 175B a b)x
+--R +
+--R 4 5 2 5
+--R (- 105A a b - 21B a )x - 15A a
+--R /
+--R 7
+--R 105x
+--R Type: Union(Expression(Integer),...)
+--E 213
+
+--S 214 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 215
+
+)clear all
+
+--S 216 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^9
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 216
+
+--S 217 of 1406
+r0:=-1/8*a^5*A/x^8-1/6*a^4*(5*A*b+a*B)/x^6-5/4*a^3*b*(2*A*b+a*B)/x^4-_
+ 5*a^2*b^2*(A*b+a*B)/x^2+1/2*b^4*(A*b+5*a*B)*x^2+1/4*b^5*B*x^4+_
+ 5*a*b^3*(A*b+2*a*B)*log(x)
+--R
+--R
+--R (2)
+--R 4 2 3 8 5 12 5 4 10
+--R (120A a b + 240B a b )x log(x) + 6B b x + (12A b + 60B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 120A a b - 120B a b )x + (- 60A a b - 30B a b)x
+--R +
+--R 4 5 2 5
+--R (- 20A a b - 4B a )x - 3A a
+--R /
+--R 8
+--R 24x
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 3 8 5 12 5 4 10
+--R (120A a b + 240B a b )x log(x) + 6B b x + (12A b + 60B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 120A a b - 120B a b )x + (- 60A a b - 30B a b)x
+--R +
+--R 4 5 2 5
+--R (- 20A a b - 4B a )x - 3A a
+--R /
+--R 8
+--R 24x
+--R Type: Union(Expression(Integer),...)
+--E 218
+
+--S 219 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 220
+
+)clear all
+
+--S 221 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^10
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 221
+
+--S 222 of 1406
+r0:=-1/9*a^5*A/x^9-1/7*a^4*(5*A*b+a*B)/x^7-a^3*b*(2*A*b+a*B)/x^5-_
+ 10/3*a^2*b^2*(A*b+a*B)/x^3-5*a*b^3*(A*b+2*a*B)/x+_
+ b^4*(A*b+5*a*B)*x+1/3*b^5*B*x^3
+--R
+--R
+--R (2)
+--R 1 5 12 5 4 10 4 2 3 8
+--R - B b x + (A b + 5B a b )x + (- 5A a b - 10B a b )x
+--R 3
+--R +
+--R 10 2 3 10 3 2 6 3 2 4 4
+--R (- -- A a b - -- B a b )x + (- 2A a b - B a b)x
+--R 3 3
+--R +
+--R 5 4 1 5 2 1 5
+--R (- - A a b - - B a )x - - A a
+--R 7 7 9
+--R /
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 222
+
+--S 223 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R 21B b x + (63A b + 315B a b )x + (- 315A a b - 630B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 210A a b - 210B a b )x + (- 126A a b - 63B a b)x
+--R +
+--R 4 5 2 5
+--R (- 45A a b - 9B a )x - 7A a
+--R /
+--R 9
+--R 63x
+--R Type: Union(Expression(Integer),...)
+--E 223
+
+--S 224 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 225
+
+)clear all
+
+--S 226 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^11
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 226
+
+--S 227 of 1406
+r0:=-1/10*a^5*A/x^10-1/8*a^4*(5*A*b+a*B)/x^8-5/6*a^3*b*(2*A*b+a*B)/x^6-_
+ 5/2*a^2*b^2*(A*b+a*B)/x^4-5/2*a*b^3*(A*b+2*a*B)/x^2+_
+ 1/2*b^5*B*x^2+b^4*(A*b+5*a*B)*log(x)
+--R
+--R
+--R (2)
+--R 5 4 10 5 12 4 2 3 8
+--R (120A b + 600B a b )x log(x) + 60B b x + (- 300A a b - 600B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 300A a b - 300B a b )x + (- 200A a b - 100B a b)x
+--R +
+--R 4 5 2 5
+--R (- 75A a b - 15B a )x - 12A a
+--R /
+--R 10
+--R 120x
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 10 5 12 4 2 3 8
+--R (120A b + 600B a b )x log(x) + 60B b x + (- 300A a b - 600B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 300A a b - 300B a b )x + (- 200A a b - 100B a b)x
+--R +
+--R 4 5 2 5
+--R (- 75A a b - 15B a )x - 12A a
+--R /
+--R 10
+--R 120x
+--R Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^12
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 12
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 231
+
+--S 232 of 1406
+r0:=-1/11*a^5*A/x^11-1/9*a^4*(5*A*b+a*B)/x^9-5/7*a^3*b*(2*A*b+a*B)/x^7-_
+ 2*a^2*b^2*(A*b+a*B)/x^5-5/3*a*b^3*(A*b+2*a*B)/x^3-_
+ b^4*(A*b+5*a*B)/x+b^5*B*x
+--R
+--R
+--R (2)
+--R 5 12 5 4 10 5 4 10 2 3 8
+--R B b x + (- A b - 5B a b )x + (- - A a b - -- B a b )x
+--R 3 3
+--R +
+--R 2 3 3 2 6 10 3 2 5 4 4
+--R (- 2A a b - 2B a b )x + (- -- A a b - - B a b)x
+--R 7 7
+--R +
+--R 5 4 1 5 2 1 5
+--R (- - A a b - - B a )x - -- A a
+--R 9 9 11
+--R /
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 232
+
+--S 233 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R 693B b x + (- 693A b - 3465B a b )x + (- 1155A a b - 2310B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 1386A a b - 1386B a b )x + (- 990A a b - 495B a b)x
+--R +
+--R 4 5 2 5
+--R (- 385A a b - 77B a )x - 63A a
+--R /
+--R 11
+--R 693x
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^13
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 13
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 236
+
+--S 237 of 1406
+r0:=-1/10*a^5*B/x^10-5/8*a^4*b*B/x^8-5/3*a^3*b^2*B/x^6-5/2*a^2*b^3*B/x^4-_
+ 5/2*a*b^4*B/x^2-1/12*A*(a+b*x^2)^6/(a*x^12)+b^5*B*log(x)
+--R
+--R
+--R (2)
+--R 5 12 6 12 5 2 4 10
+--R 120B a b x log(x) - 10A b x + (- 60A a b - 300B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 150A a b - 300B a b )x + (- 200A a b - 200B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (- 150A a b - 75B a b)x + (- 60A a b - 12B a )x - 10A a
+--R /
+--R 12
+--R 120a x
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R 120B b x log(x) + (- 60A b - 300B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 150A a b - 300B a b )x + (- 200A a b - 200B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 150A a b - 75B a b)x + (- 60A a b - 12B a )x - 10A a
+--R /
+--R 12
+--R 120x
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 1406
+m0:=a0-r0
+--R
+--R
+--R 6
+--R A b
+--R (4) ----
+--R 12a
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^14
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 14
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 241
+
+--S 242 of 1406
+r0:=-1/13*a^5*A/x^13-1/11*a^4*(5*A*b+a*B)/x^11-5/9*a^3*b*_
+ (2*A*b+a*B)/x^9-10/7*a^2*b^2*(A*b+a*B)/x^7-a*b^3*_
+ (A*b+2*a*B)/x^5-1/3*b^4*(A*b+5*a*B)/x^3-b^5*B/x
+--R
+--R
+--R (2)
+--R 5 12 1 5 5 4 10 4 2 3 8
+--R - B b x + (- - A b - - B a b )x + (- A a b - 2B a b )x
+--R 3 3
+--R +
+--R 10 2 3 10 3 2 6 10 3 2 5 4 4
+--R (- -- A a b - -- B a b )x + (- -- A a b - - B a b)x
+--R 7 7 9 9
+--R +
+--R 5 4 1 5 2 1 5
+--R (- -- A a b - -- B a )x - -- A a
+--R 11 11 13
+--R /
+--R 13
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 242
+
+--S 243 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 9009B b x + (- 3003A b - 15015B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 9009A a b - 18018B a b )x + (- 12870A a b - 12870B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 10010A a b - 5005B a b)x + (- 4095A a b - 819B a )x - 693A a
+--R /
+--R 13
+--R 9009x
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^15
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 15
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 246
+
+--S 247 of 1406
+r0:=-1/14*A*(a+b*x^2)^6/(a*x^14)+1/84*(A*b-7*a*B)*(a+b*x^2)^6/(a^2*x^12)
+--R
+--R
+--R (2)
+--R 1 7 1 6 14 1 2 5 12 1 2 5 5 3 4 10
+--R (-- A b - -- B a b )x - - B a b x + (- - A a b - - B a b )x
+--R 84 12 2 4 4
+--R +
+--R 5 3 4 5 4 3 8 5 4 3 5 5 2 6
+--R (- - A a b - - B a b )x + (- - A a b - - B a b )x
+--R 6 3 4 4
+--R +
+--R 5 2 1 6 4 5 6 1 7 2 1 7
+--R (- A a b - - B a b)x + (- -- A a b - -- B a )x - -- A a
+--R 2 12 12 14
+--R /
+--R 2 14
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 247
+
+--S 248 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R - 42B b x + (- 21A b - 105B a b )x + (- 70A a b - 140B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 105A a b - 105B a b )x + (- 84A a b - 42B a b)x
+--R +
+--R 4 5 2 5
+--R (- 35A a b - 7B a )x - 6A a
+--R /
+--R 14
+--R 84x
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 1406
+m0:=a0-r0
+--R
+--R
+--R 7 6
+--R - A b + 7B a b
+--R (4) ----------------
+--R 2
+--R 84a
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^16
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 16
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 251
+
+--S 252 of 1406
+r0:=-1/15*a^5*A/x^15-1/13*a^4*(5*A*b+a*B)/x^13-5/11*a^3*b*(2*A*b+a*B)/_
+ x^11-10/9*a^2*b^2*(A*b+a*B)/x^9-5/7*a*b^3*(A*b+2*a*B)/x^7-_
+ 1/5*b^4*(A*b+5*a*B)/x^5-1/3*b^5*B/x^3
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 4 10 5 4 10 2 3 8
+--R - - B b x + (- - A b - B a b )x + (- - A a b - -- B a b )x
+--R 3 5 7 7
+--R +
+--R 10 2 3 10 3 2 6 10 3 2 5 4 4
+--R (- -- A a b - -- B a b )x + (- -- A a b - -- B a b)x
+--R 9 9 11 11
+--R +
+--R 5 4 1 5 2 1 5
+--R (- -- A a b - -- B a )x - -- A a
+--R 13 13 15
+--R /
+--R 15
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 252
+
+--S 253 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 15015B b x + (- 9009A b - 45045B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 32175A a b - 64350B a b )x + (- 50050A a b - 50050B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 40950A a b - 20475B a b)x + (- 17325A a b - 3465B a )x - 3003A a
+--R /
+--R 15
+--R 45045x
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^17
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 17
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 256
+
+--S 257 of 1406
+r0:=-1/16*A*(a+b*x^2)^6/(a*x^16)+1/56*(A*b-4*a*B)*(a+b*x^2)^6/_
+ (a^2*x^14)-1/336*b*(A*b-4*a*B)*(a+b*x^2)^6/(a^3*x^12)
+--R
+--R
+--R (2)
+--R 1 8 1 7 16 1 3 5 12 1 3 5 5 4 4 10
+--R (- --- A b + -- B a b )x - - B a b x + (- - A a b - - B a b )x
+--R 336 84 4 6 6
+--R +
+--R 5 4 4 5 5 3 8 5 3 6 2 6
+--R (- - A a b - - B a b )x + (- A a b - B a b )x
+--R 8 4
+--R +
+--R 5 6 2 5 7 4 5 7 1 8 2 1 8
+--R (- - A a b - -- B a b)x + (- -- A a b - -- B a )x - -- A a
+--R 6 12 14 14 16
+--R /
+--R 3 16
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 257
+
+--S 258 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R - 84B b x + (- 56A b - 280B a b )x + (- 210A a b - 420B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 336A a b - 336B a b )x + (- 280A a b - 140B a b)x
+--R +
+--R 4 5 2 5
+--R (- 120A a b - 24B a )x - 21A a
+--R /
+--R 16
+--R 336x
+--R Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 1406
+m0:=a0-r0
+--R
+--R
+--R 8 7
+--R A b - 4B a b
+--R (4) --------------
+--R 3
+--R 336a
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^18
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 18
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 261
+
+--S 262 of 1406
+r0:=-1/17*a^5*A/x^17-1/15*a^4*(5*A*b+a*B)/x^15-5/13*a^3*b*_
+ (2*A*b+a*B)/x^13-10/11*a^2*b^2*(A*b+a*B)/x^11-_
+ 5/9*a*b^3*(A*b+2*a*B)/x^9-1/7*b^4*(A*b+5*a*B)/x^7-1/5*b^5*B/x^5
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 5 4 10 2 3 8
+--R - - B b x + (- - A b - - B a b )x + (- - A a b - -- B a b )x
+--R 5 7 7 9 9
+--R +
+--R 10 2 3 10 3 2 6 10 3 2 5 4 4
+--R (- -- A a b - -- B a b )x + (- -- A a b - -- B a b)x
+--R 11 11 13 13
+--R +
+--R 1 4 1 5 2 1 5
+--R (- - A a b - -- B a )x - -- A a
+--R 3 15 17
+--R /
+--R 17
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 262
+
+--S 263 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 153153B b x + (- 109395A b - 546975B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 425425A a b - 850850B a b )x + (- 696150A a b - 696150B a b )x
+--R +
+--R 3 2 4 4 4 5 2
+--R (- 589050A a b - 294525B a b)x + (- 255255A a b - 51051B a )x
+--R +
+--R 5
+--R - 45045A a
+--R /
+--R 17
+--R 765765x
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^19
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 19
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 266
+
+--S 267 of 1406
+r0:=-1/18*a^5*A/x^18-1/16*a^4*(5*A*b+a*B)/x^16-5/14*a^3*b*_
+ (2*A*b+a*B)/x^14-5/6*a^2*b^2*(A*b+a*B)/x^12-1/2*a*b^3*_
+ (A*b+2*a*B)/x^10-1/8*b^4*(A*b+5*a*B)/x^8-1/6*b^5*B/x^6
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 1 4 2 3 8
+--R - - B b x + (- - A b - - B a b )x + (- - A a b - B a b )x
+--R 6 8 8 2
+--R +
+--R 5 2 3 5 3 2 6 5 3 2 5 4 4
+--R (- - A a b - - B a b )x + (- - A a b - -- B a b)x
+--R 6 6 7 14
+--R +
+--R 5 4 1 5 2 1 5
+--R (- -- A a b - -- B a )x - -- A a
+--R 16 16 18
+--R /
+--R 18
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 267
+
+--S 268 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R - 168B b x + (- 126A b - 630B a b )x + (- 504A a b - 1008B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 840A a b - 840B a b )x + (- 720A a b - 360B a b)x
+--R +
+--R 4 5 2 5
+--R (- 315A a b - 63B a )x - 56A a
+--R /
+--R 18
+--R 1008x
+--R Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^20
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 20
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 271
+
+--S 272 of 1406
+r0:=-1/19*a^5*A/x^19-1/17*a^4*(5*A*b+a*B)/x^17-1/3*a^3*b*_
+ (2*A*b+a*B)/x^15-10/13*a^2*b^2*(A*b+a*B)/x^13-5/11*a*b^3*_
+ (A*b+2*a*B)/x^11-1/9*b^4*(A*b+5*a*B)/x^9-1/7*b^5*B/x^7
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 5 4 10 2 3 8
+--R - - B b x + (- - A b - - B a b )x + (- -- A a b - -- B a b )x
+--R 7 9 9 11 11
+--R +
+--R 10 2 3 10 3 2 6 2 3 2 1 4 4
+--R (- -- A a b - -- B a b )x + (- - A a b - - B a b)x
+--R 13 13 3 3
+--R +
+--R 5 4 1 5 2 1 5
+--R (- -- A a b - -- B a )x - -- A a
+--R 17 17 19
+--R /
+--R 19
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 272
+
+--S 273 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 415701B b x + (- 323323A b - 1616615B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 1322685A a b - 2645370B a b )x + (- 2238390A a b - 2238390B a b )x
+--R +
+--R 3 2 4 4 4 5 2
+--R (- 1939938A a b - 969969B a b)x + (- 855855A a b - 171171B a )x
+--R +
+--R 5
+--R - 153153A a
+--R /
+--R 19
+--R 2909907x
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^21
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 21
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 276
+
+--S 277 of 1406
+r0:=-1/20*a^5*A/x^20-1/18*a^4*(5*A*b+a*B)/x^18-5/16*a^3*b*_
+ (2*A*b+a*B)/x^16-5/7*a^2*b^2*(A*b+a*B)/x^14-5/12*a*b^3*_
+ (A*b+2*a*B)/x^12-1/10*b^4*(A*b+5*a*B)/x^10-1/8*b^5*B/x^8
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 1 4 10 5 4 5 2 3 8
+--R - - B b x + (- -- A b - - B a b )x + (- -- A a b - - B a b )x
+--R 8 10 2 12 6
+--R +
+--R 5 2 3 5 3 2 6 5 3 2 5 4 4
+--R (- - A a b - - B a b )x + (- - A a b - -- B a b)x
+--R 7 7 8 16
+--R +
+--R 5 4 1 5 2 1 5
+--R (- -- A a b - -- B a )x - -- A a
+--R 18 18 20
+--R /
+--R 20
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 277
+
+--S 278 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 630B b x + (- 504A b - 2520B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 2100A a b - 4200B a b )x + (- 3600A a b - 3600B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 3150A a b - 1575B a b)x + (- 1400A a b - 280B a )x - 252A a
+--R /
+--R 20
+--R 5040x
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^22
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 22
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 281
+
+--S 282 of 1406
+r0:=-1/21*a^5*A/x^21-1/19*a^4*(5*A*b+a*B)/x^19-5/17*a^3*b*_
+ (2*A*b+a*B)/x^17-2/3*a^2*b^2*(A*b+a*B)/x^15-5/13*a*b^3*_
+ (A*b+2*a*B)/x^13-1/11*b^4*(A*b+5*a*B)/x^11-1/9*b^5*B/x^9
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 5 4 10 2 3 8
+--R - - B b x + (- -- A b - -- B a b )x + (- -- A a b - -- B a b )x
+--R 9 11 11 13 13
+--R +
+--R 2 2 3 2 3 2 6 10 3 2 5 4 4
+--R (- - A a b - - B a b )x + (- -- A a b - -- B a b)x
+--R 3 3 17 17
+--R +
+--R 5 4 1 5 2 1 5
+--R (- -- A a b - -- B a )x - -- A a
+--R 19 19 21
+--R /
+--R 21
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 282
+
+--S 283 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 323323B b x + (- 264537A b - 1322685B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 1119195A a b - 2238390B a b )x + (- 1939938A a b - 1939938B a b )x
+--R +
+--R 3 2 4 4 4 5 2
+--R (- 1711710A a b - 855855B a b)x + (- 765765A a b - 153153B a )x
+--R +
+--R 5
+--R - 138567A a
+--R /
+--R 21
+--R 2909907x
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^23
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 23
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 286
+
+--S 287 of 1406
+r0:=-1/22*a^5*A/x^22-1/20*a^4*(5*A*b+a*B)/x^20-5/18*a^3*b*_
+ (2*A*b+a*B)/x^18-5/8*a^2*b^2*(A*b+a*B)/x^16-5/14*a*b^3*_
+ (A*b+2*a*B)/x^14-1/12*b^4*(A*b+5*a*B)/x^12-1/10*b^5*B/x^10
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 5 4 5 2 3 8
+--R - -- B b x + (- -- A b - -- B a b )x + (- -- A a b - - B a b )x
+--R 10 12 12 14 7
+--R +
+--R 5 2 3 5 3 2 6 5 3 2 5 4 4
+--R (- - A a b - - B a b )x + (- - A a b - -- B a b)x
+--R 8 8 9 18
+--R +
+--R 1 4 1 5 2 1 5
+--R (- - A a b - -- B a )x - -- A a
+--R 4 20 22
+--R /
+--R 22
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 287
+
+--S 288 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 2772B b x + (- 2310A b - 11550B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 9900A a b - 19800B a b )x + (- 17325A a b - 17325B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 15400A a b - 7700B a b)x + (- 6930A a b - 1386B a )x - 1260A a
+--R /
+--R 22
+--R 27720x
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 1406
+t0:=x^6*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 8 6
+--R B x + A x
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 291
+
+--S 292 of 1406
+r0:=a^2*(A*b-a*B)*x/b^4-1/3*a*(A*b-a*B)*x^3/b^3+1/5*(A*b-a*B)*x^5/b^2+_
+ 1/7*B*x^7/b-a^(5/2)*(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))/b^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 +-+ x\|b
+--R (- 105A a b + 105B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 15B b x + (21A b - 21B a b )x + (- 35A a b + 35B a b)x
+--R +
+--R 2 3
+--R (105A a b - 105B a )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 4 +-+
+--R 105b \|b
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 3 | a \| b 3 7
+--R (105A a b - 105B a ) |- - log(-----------------------) + 30B b x
+--R \| b 2
+--R b x + a
+--R +
+--R 3 2 5 2 2 3 2 3
+--R (42A b - 42B a b )x + (- 70A a b + 70B a b)x + (210A a b - 210B a )x
+--R /
+--R 4
+--R 210b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 3 |a \|b 3 7 3 2 5
+--R (105A a b - 105B a ) |- atan(----) + 15B b x + (21A b - 21B a b )x
+--R \|b x
+--R +
+--R 2 2 3 2 3
+--R (- 35A a b + 35B a b)x + (105A a b - 105B a )x
+--R /
+--R 4
+--R 105b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 293
+
+--S 294 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 3 | a +-+ \| b
+--R (A a b - B a ) |- - \|b log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 3 +-+ x\|b
+--R (2A a b - 2B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+--S 296 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 3 +-+ x\|b 2 3 |a +-+ \|b
+--R (A a b - B a )\|a atan(-----) + (A a b - B a ) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ----------------------------------------------------------------
+--R 4 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 297
+
+)clear all
+
+--S 298 of 1406
+t0:=x^5*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 7 5
+--R B x + A x
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 298
+
+--S 299 of 1406
+r0:=-1/2*a*(A*b-a*B)*x^2/b^3+1/4*(A*b-a*B)*x^4/b^2+1/6*B*x^6/b+_
+ 1/2*a^2*(A*b-a*B)*log(a+b*x^2)/b^4
+--R
+--R
+--R (2)
+--R 2 3 2 3 6 3 2 4
+--R (6A a b - 6B a )log(b x + a) + 2B b x + (3A b - 3B a b )x
+--R +
+--R 2 2 2
+--R (- 6A a b + 6B a b)x
+--R /
+--R 4
+--R 12b
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 3 6 3 2 4
+--R (6A a b - 6B a )log(b x + a) + 2B b x + (3A b - 3B a b )x
+--R +
+--R 2 2 2
+--R (- 6A a b + 6B a b)x
+--R /
+--R 4
+--R 12b
+--R Type: Union(Expression(Integer),...)
+--E 300
+
+--S 301 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 302
+
+)clear all
+
+--S 303 of 1406
+t0:=x^4*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 6 4
+--R B x + A x
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 303
+
+--S 304 of 1406
+r0:=-a*(A*b-a*B)*x/b^3+1/3*(A*b-a*B)*x^3/b^2+1/5*B*x^5/b+_
+ a^(3/2)*(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))/b^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 +-+ x\|b
+--R (15A a b - 15B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 5 2 3 2 +-+
+--R (3B b x + (5A b - 5B a b)x + (- 15A a b + 15B a )x)\|b
+--R /
+--R 3 +-+
+--R 15b \|b
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 | a \| b 2 5
+--R (15A a b - 15B a ) |- - log(---------------------) + 6B b x
+--R \| b 2
+--R b x + a
+--R +
+--R 2 3 2
+--R (10A b - 10B a b)x + (- 30A a b + 30B a )x
+--R /
+--R 3
+--R 30b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 |a \|b 2 5 2 3
+--R (- 15A a b + 15B a ) |- atan(----) + 3B b x + (5A b - 5B a b)x
+--R \|b x
+--R +
+--R 2
+--R (- 15A a b + 15B a )x
+--R /
+--R 3
+--R 15b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 305
+
+--S 306 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 | a +-+ \| b
+--R (A a b - B a ) |- - \|b log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R (- 2A a b + 2B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 +-+ x\|b 2 |a +-+ \|b
+--R (- A a b + B a )\|a atan(-----) + (- A a b + B a ) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) --------------------------------------------------------------------
+--R 3 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 308
+
+--S 309 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 309
+
+)clear all
+
+--S 310 of 1406
+t0:=x^3*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 5 3
+--R B x + A x
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 310
+
+--S 311 of 1406
+r0:=1/2*(A*b-a*B)*x^2/b^2+1/4*B*x^4/b-1/2*a*(A*b-a*B)*log(a+b*x^2)/b^3
+--R
+--R
+--R 2 2 2 4 2 2
+--R (- 2A a b + 2B a )log(b x + a) + B b x + (2A b - 2B a b)x
+--R (2) -------------------------------------------------------------
+--R 3
+--R 4b
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 4 2 2
+--R (- 2A a b + 2B a )log(b x + a) + B b x + (2A b - 2B a b)x
+--R (3) -------------------------------------------------------------
+--R 3
+--R 4b
+--R Type: Union(Expression(Integer),...)
+--E 312
+
+--S 313 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 313
+
+--S 314 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 314
+
+)clear all
+
+--S 315 of 1406
+t0:=x^2*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 4 2
+--R B x + A x
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 315
+
+--S 316 of 1406
+r0:=(A*b-a*B)*x/b^2+1/3*B*x^3/b-(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))*_
+ sqrt(a)/b^(5/2)
+--R
+--R
+--R +-+
+--R +-+ x\|b 3 +-+
+--R (- 3A b + 3B a)\|a atan(-----) + (B b x + (3A b - 3B a)x)\|b
+--R +-+
+--R \|a
+--R (2) --------------------------------------------------------------
+--R 2 +-+
+--R 3b \|b
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R | a \| b 3
+--R (3A b - 3B a) |- - log(-----------------------) + 2B b x + (6A b - 6B a)x
+--R \| b 2
+--R b x + a
+--R [--------------------------------------------------------------------------,
+--R 2
+--R 6b
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b 3
+--R (3A b - 3B a) |- atan(----) + B b x + (3A b - 3B a)x
+--R \|b x
+--R -----------------------------------------------------]
+--R 2
+--R 3b
+--R Type: Union(List(Expression(Integer)),...)
+--E 317
+
+--S 318 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R | a +-+ \| b
+--R (A b - B a) |- - \|b log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ x\|b
+--R (2A b - 2B a)\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 318
+
+--S 319 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R (A b - B a)\|a atan(-----) + (A b - B a) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ----------------------------------------------------------
+--R 2 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 320
+
+--S 321 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 321
+
+)clear all
+
+--S 322 of 1406
+t0:=x*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 3
+--R B x + A x
+--R (1) ----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 322
+
+--S 323 of 1406
+r0:=1/2*B*x^2/b+1/2*(A*b-a*B)*log(a+b*x^2)/b^2
+--R
+--R
+--R 2 2
+--R (A b - B a)log(b x + a) + B b x
+--R (2) ---------------------------------
+--R 2
+--R 2b
+--R Type: Expression(Integer)
+--E 323
+
+--S 324 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R (A b - B a)log(b x + a) + B b x
+--R (3) ---------------------------------
+--R 2
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 324
+
+--S 325 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 325
+
+--S 326 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 326
+
+)clear all
+
+--S 327 of 1406
+t0:=(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 327
+
+--S 328 of 1406
+r0:=B*x/b+(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))
+--R
+--R
+--R +-+
+--R x\|b +-+ +-+
+--R (A b - B a)atan(-----) + B x\|a \|b
+--R +-+
+--R \|a
+--R (2) ------------------------------------
+--R +-+ +-+
+--R b\|a \|b
+--R Type: Expression(Integer)
+--E 328
+
+--S 329 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x +-----+
+--R (A b - B a)log(---------------------------) + 2B x\|- a b
+--R 2
+--R b x + a
+--R [----------------------------------------------------------,
+--R +-----+
+--R 2b\|- a b
+--R +---+
+--R x\|a b +---+
+--R (A b - B a)atan(-------) + B x\|a b
+--R a
+--R ------------------------------------]
+--R +---+
+--R b\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 329
+
+--S 330 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (A b - B a)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2A b + 2B a)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-----+ +-+ +-+
+--R 2b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 330
+
+--S 331 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (A b - B a)\|a \|b atan(-------) + (- A b + B a)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 333
+
+)clear all
+
+--S 334 of 1406
+t0:=(A+B*x^2)/(a-b*x^2)
+--R
+--R
+--R 2
+--R - B x - A
+--R (1) ----------
+--R 2
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 334
+
+--S 335 of 1406
+r0:=-B*x/b+(A*b+a*B)*atanh(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))
+--R
+--R
+--R +-+
+--R x\|b +-+ +-+
+--R (A b + B a)atanh(-----) - B x\|a \|b
+--R +-+
+--R \|a
+--R (2) -------------------------------------
+--R +-+ +-+
+--R b\|a \|b
+--R Type: Expression(Integer)
+--E 335
+
+--S 336 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +---+
+--R (b x + a)\|a b + 2a b x +---+
+--R (A b + B a)log(-------------------------) - 2B x\|a b
+--R 2
+--R b x - a
+--R [------------------------------------------------------,
+--R +---+
+--R 2b\|a b
+--R +-----+
+--R x\|- a b +-----+
+--R (A b + B a)atan(---------) - B x\|- a b
+--R a
+--R ----------------------------------------]
+--R +-----+
+--R b\|- a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 336
+
+--S 337 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +---+
+--R +-+ +-+ (b x + a)\|a b + 2a b x
+--R (A b + B a)\|a \|b log(-------------------------)
+--R 2
+--R b x - a
+--R +
+--R +-+
+--R +---+ x\|b
+--R (- 2A b - 2B a)\|a b atanh(-----)
+--R +-+
+--R \|a
+--R /
+--R +-+ +-+ +---+
+--R 2b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 338
+
+--S 339 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-----+
+--R +-----+ x\|b +-+ +-+ x\|- a b
+--R (- A b - B a)\|- a b atanh(-----) + (A b + B a)\|a \|b atan(---------)
+--R +-+ a
+--R \|a
+--R (6) ----------------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 1406
+t0:=(A+B*x^2)/(x*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ----------
+--R 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 341
+
+--S 342 of 1406
+r0:=A*log(x)/a-1/2*(A*b-a*B)*log(a+b*x^2)/(a*b)
+--R
+--R
+--R 2
+--R (- A b + B a)log(b x + a) + 2A b log(x)
+--R (2) ----------------------------------------
+--R 2a b
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (- A b + B a)log(b x + a) + 2A b log(x)
+--R (3) ----------------------------------------
+--R 2a b
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 1406
+t0:=(A+B*x^2)/(x^2*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------
+--R 4 2
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 346
+
+--S 347 of 1406
+r0:=-A/(a*x)-(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b))
+--R
+--R
+--R +-+
+--R x\|b +-+ +-+
+--R (- A b + B a)x atan(-----) - A\|a \|b
+--R +-+
+--R \|a
+--R (2) --------------------------------------
+--R +-+ +-+
+--R a x\|a \|b
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x +-----+
+--R (A b - B a)x log(---------------------------) - 2A\|- a b
+--R 2
+--R b x + a
+--R [----------------------------------------------------------,
+--R +-----+
+--R 2a x\|- a b
+--R +---+
+--R x\|a b +---+
+--R (- A b + B a)x atan(-------) - A\|a b
+--R a
+--R --------------------------------------]
+--R +---+
+--R a x\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 348
+
+--S 349 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b - 2a b x
+--R (A b - B a)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (2A b - 2B a)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-----+ +-+ +-+
+--R 2a\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+--S 351 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (- A b + B a)\|a \|b atan(-------) + (A b - B a)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R a\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 352
+
+)clear all
+
+--S 353 of 1406
+t0:=(A+B*x^2)/(x^3*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------
+--R 5 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 353
+
+--S 354 of 1406
+r0:=-1/2*A/(a*x^2)-(A*b-a*B)*log(x)/a^2+1/2*(A*b-a*B)*log(a+b*x^2)/a^2
+--R
+--R
+--R 2 2 2
+--R (A b - B a)x log(b x + a) + (- 2A b + 2B a)x log(x) - A a
+--R (2) ----------------------------------------------------------
+--R 2 2
+--R 2a x
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R (A b - B a)x log(b x + a) + (- 2A b + 2B a)x log(x) - A a
+--R (3) ----------------------------------------------------------
+--R 2 2
+--R 2a x
+--R Type: Union(Expression(Integer),...)
+--E 355
+
+--S 356 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 357
+
+)clear all
+
+--S 358 of 1406
+t0:=(A+B*x^2)/(x^4*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------
+--R 6 4
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 358
+
+--S 359 of 1406
+r0:=-1/3*A/(a*x^3)+(A*b-a*B)/(a^2*x)+(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))*_
+ sqrt(b)/a^(5/2)
+--R
+--R
+--R +-+
+--R 3 +-+ x\|b 2 +-+
+--R (3A b - 3B a)x \|b atan(-----) + ((3A b - 3B a)x - A a)\|a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------------------------
+--R 2 3 +-+
+--R 3a x \|a
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 | b \| a 2
+--R (3A b - 3B a)x |- - log(---------------------) + (6A b - 6B a)x - 2A a
+--R \| a 2
+--R b x + a
+--R [------------------------------------------------------------------------,
+--R 2 3
+--R 6a x
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 |b \|a 2
+--R (- 3A b + 3B a)x |- atan(-----) + (3A b - 3B a)x - A a
+--R \|a b x
+--R --------------------------------------------------------]
+--R 2 3
+--R 3a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 360
+
+--S 361 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b +-+ \| a
+--R (A b - B a) |- - \|a log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ x\|b
+--R (- 2A b + 2B a)\|b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R (- A b + B a)\|b atan(-----) + (- A b + B a)\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) ---------------------------------------------------------------
+--R 2 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 363
+
+--S 364 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 364
+
+)clear all
+
+--S 365 of 1406
+t0:=(A+B*x^2)/(x^5*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------
+--R 7 5
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 365
+
+--S 366 of 1406
+r0:=-1/4*A/(a*x^4)+1/2*(A*b-a*B)/(a^2*x^2)+b*(A*b-a*B)*log(x)/a^3-_
+ 1/2*b*(A*b-a*B)*log(a+b*x^2)/a^3
+--R
+--R
+--R (2)
+--R 2 4 2 2 4
+--R (- 2A b + 2B a b)x log(b x + a) + (4A b - 4B a b)x log(x)
+--R +
+--R 2 2 2
+--R (2A a b - 2B a )x - A a
+--R /
+--R 3 4
+--R 4a x
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 4
+--R (- 2A b + 2B a b)x log(b x + a) + (4A b - 4B a b)x log(x)
+--R +
+--R 2 2 2
+--R (2A a b - 2B a )x - A a
+--R /
+--R 3 4
+--R 4a x
+--R Type: Union(Expression(Integer),...)
+--E 367
+
+--S 368 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 369
+
+)clear all
+
+--S 370 of 1406
+t0:=(A+B*x^2)/(x^6*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------
+--R 8 6
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 370
+
+--S 371 of 1406
+r0:=-1/5*A/(a*x^5)+1/3*(A*b-a*B)/(a^2*x^3)-b*(A*b-a*B)/(a^3*x)-_
+ b^(3/2)*(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))/a^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 5 +-+ x\|b
+--R (- 15A b + 15B a b)x \|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+
+--R ((- 15A b + 15B a b)x + (5A a b - 5B a )x - 3A a )\|a
+--R /
+--R 3 5 +-+
+--R 15a x \|a
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 5 | b \| a
+--R (15A b - 15B a b)x |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 4 2 2 2
+--R (- 30A b + 30B a b)x + (10A a b - 10B a )x - 6A a
+--R /
+--R 3 5
+--R 30a x
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 5 |b \|a 2 4
+--R (15A b - 15B a b)x |- atan(-----) + (- 15A b + 15B a b)x
+--R \|a b x
+--R +
+--R 2 2 2
+--R (5A a b - 5B a )x - 3A a
+--R /
+--R 3 5
+--R 15a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 372
+
+--S 373 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 | b +-+ \| a
+--R (A b - B a b) |- - \|a log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R (2A b - 2B a b)\|b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 373
+
+--S 374 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R 2 +-+ x\|b 2 +-+ |b \|a
+--R (A b - B a b)\|b atan(-----) + (A b - B a b)\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R 3 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 375
+
+--S 376 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 376
+
+)clear all
+
+--S 377 of 1406
+t0:=(A+B*x^2)/(x^7*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------
+--R 9 7
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 377
+
+--S 378 of 1406
+r0:=-1/6*A/(a*x^6)+1/4*(A*b-a*B)/(a^2*x^4)-1/2*b*(A*b-a*B)/(a^3*x^2)-_
+ b^2*(A*b-a*B)*log(x)/a^4+1/2*b^2*(A*b-a*B)*log(a+b*x^2)/a^4
+--R
+--R
+--R (2)
+--R 3 2 6 2 3 2 6
+--R (6A b - 6B a b )x log(b x + a) + (- 12A b + 12B a b )x log(x)
+--R +
+--R 2 2 4 2 3 2 3
+--R (- 6A a b + 6B a b)x + (3A a b - 3B a )x - 2A a
+--R /
+--R 4 6
+--R 12a x
+--R Type: Expression(Integer)
+--E 378
+
+--S 379 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 6 2 3 2 6
+--R (6A b - 6B a b )x log(b x + a) + (- 12A b + 12B a b )x log(x)
+--R +
+--R 2 2 4 2 3 2 3
+--R (- 6A a b + 6B a b)x + (3A a b - 3B a )x - 2A a
+--R /
+--R 4 6
+--R 12a x
+--R Type: Union(Expression(Integer),...)
+--E 379
+
+--S 380 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 380
+
+--S 381 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 381
+
+)clear all
+
+--S 382 of 1406
+t0:=(A+B*x^2)/(x^8*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ------------
+--R 10 8
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 382
+
+--S 383 of 1406
+r0:=-1/7*A/(a*x^7)+1/5*(A*b-a*B)/(a^2*x^5)-1/3*b*(A*b-a*B)/(a^3*x^3)+_
+ b^2*(A*b-a*B)/(a^4*x)+b^(5/2)*(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))/a^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 7 +-+ x\|b
+--R (105A b - 105B a b )x \|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 2 6 2 2 4
+--R (105A b - 105B a b )x + (- 35A a b + 35B a b)x
+--R +
+--R 2 3 2 3
+--R (21A a b - 21B a )x - 15A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 7 +-+
+--R 105a x \|a
+--R Type: Expression(Integer)
+--E 383
+
+--S 384 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 2 7 | b \| a
+--R (105A b - 105B a b )x |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 2 6 2 2 4
+--R (210A b - 210B a b )x + (- 70A a b + 70B a b)x
+--R +
+--R 2 3 2 3
+--R (42A a b - 42B a )x - 30A a
+--R /
+--R 4 7
+--R 210a x
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 2 7 |b \|a 3 2 6
+--R (- 105A b + 105B a b )x |- atan(-----) + (105A b - 105B a b )x
+--R \|a b x
+--R +
+--R 2 2 4 2 3 2 3
+--R (- 35A a b + 35B a b)x + (21A a b - 21B a )x - 15A a
+--R /
+--R 4 7
+--R 105a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 384
+
+--S 385 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 2 | b +-+ \| a
+--R (A b - B a b ) |- - \|a log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 2 +-+ x\|b
+--R (- 2A b + 2B a b )\|b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 385
+
+--S 386 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R 3 2 +-+ x\|b 3 2 +-+ |b \|a
+--R (- A b + B a b )\|b atan(-----) + (- A b + B a b )\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R -----------------------------------------------------------------------
+--R 4 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 388
+
+)clear all
+
+--S 389 of 1406
+t0:=x^9*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 11 9
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 389
+
+--S 390 of 1406
+r0:=1/2*a^2*(3*A*b-4*a*B)*x^2/b^5-1/4*a*(2*A*b-3*a*B)*x^4/b^4+_
+ 1/6*(A*b-2*a*B)*x^6/b^3+1/8*B*x^8/b^2-1/2*a^4*(A*b-a*B)/_
+ (b^6*(a+b*x^2))-1/2*a^3*(4*A*b-5*a*B)*log(a+b*x^2)/b^6
+--R
+--R
+--R (2)
+--R 3 2 4 2 4 5 2 5 10
+--R ((- 48A a b + 60B a b)x - 48A a b + 60B a )log(b x + a) + 3B b x
+--R +
+--R 5 4 8 4 2 3 6 2 3 3 2 4
+--R (4A b - 5B a b )x + (- 8A a b + 10B a b )x + (24A a b - 30B a b )x
+--R +
+--R 3 2 4 2 4 5
+--R (36A a b - 48B a b)x - 12A a b + 12B a
+--R /
+--R 7 2 6
+--R 24b x + 24a b
+--R Type: Expression(Integer)
+--E 390
+
+--S 391 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 2 4 5 2 5 10
+--R ((- 48A a b + 60B a b)x - 48A a b + 60B a )log(b x + a) + 3B b x
+--R +
+--R 5 4 8 4 2 3 6 2 3 3 2 4
+--R (4A b - 5B a b )x + (- 8A a b + 10B a b )x + (24A a b - 30B a b )x
+--R +
+--R 3 2 4 2 4 5
+--R (36A a b - 48B a b)x - 12A a b + 12B a
+--R /
+--R 7 2 6
+--R 24b x + 24a b
+--R Type: Union(Expression(Integer),...)
+--E 391
+
+--S 392 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 393
+
+)clear all
+
+--S 394 of 1406
+t0:=x^8*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 10 8
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 394
+
+--S 395 of 1406
+r0:=1/2*a^2*(7*A*b-9*a*B)*x/b^5-1/6*a*(7*A*b-9*a*B)*x^3/b^4+_
+ 1/10*(7*A*b-9*a*B)*x^5/b^3-1/14*(7*A*b-9*a*B)*x^7/(a*b^2)+_
+ 1/2*(A*b-a*B)*x^9/(a*b*(a+b*x^2))-1/2*a^(5/2)*(7*A*b-9*a*B)*_
+ atan(x*sqrt(b)/sqrt(a))/b^(11/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 3 2 3 4 +-+ x\|b
+--R ((- 735A a b + 945B a b)x - 735A a b + 945B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 30B b x + (42A b - 54B a b )x + (- 98A a b + 126B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (490A a b - 630B a b)x + (735A a b - 945B a )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 6 2 5 +-+
+--R (210b x + 210a b )\|b
+--R Type: Expression(Integer)
+--E 395
+
+--S 396 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 2 2 3 2 3 4 | a
+--R ((735A a b - 945B a b)x + 735A a b - 945B a ) |- -
+--R \| b
+--R *
+--R +---+
+--R | a 2
+--R - 2b x |- - + b x - a
+--R \| b
+--R log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 60B b x + (84A b - 108B a b )x + (- 196A a b + 252B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (980A a b - 1260B a b)x + (1470A a b - 1890B a )x
+--R /
+--R 6 2 5
+--R 420b x + 420a b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 3 2 3 4 |a \|b
+--R ((735A a b - 945B a b)x + 735A a b - 945B a ) |- atan(----)
+--R \|b x
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 30B b x + (42A b - 54B a b )x + (- 98A a b + 126B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (490A a b - 630B a b)x + (735A a b - 945B a )x
+--R /
+--R 6 2 5
+--R 210b x + 210a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 396
+
+--S 397 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 3 | a +-+ \| b
+--R (7A a b - 9B a ) |- - \|b log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 3 +-+ x\|b
+--R (14A a b - 18B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 398
+
+--S 399 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 3 +-+ x\|b 2 3 |a +-+ \|b
+--R (7A a b - 9B a )\|a atan(-----) + (7A a b - 9B a ) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) --------------------------------------------------------------------
+--R 5 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 1406
+t0:=x^7*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 9 7
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 401
+
+--S 402 of 1406
+r0:=-1/2*a*(2*A*b-3*a*B)*x^2/b^4+1/4*(A*b-2*a*B)*x^4/b^3+1/6*B*x^6/b^2+_
+ 1/2*a^3*(A*b-a*B)/(b^5*(a+b*x^2))+1/2*a^2*(3*A*b-4*a*B)*log(a+b*x^2)/b^5
+--R
+--R
+--R (2)
+--R 2 2 3 2 3 4 2 4 8
+--R ((18A a b - 24B a b)x + 18A a b - 24B a )log(b x + a) + 2B b x
+--R +
+--R 4 3 6 3 2 2 4 2 2 3 2
+--R (3A b - 4B a b )x + (- 9A a b + 12B a b )x + (- 12A a b + 18B a b)x
+--R +
+--R 3 4
+--R 6A a b - 6B a
+--R /
+--R 6 2 5
+--R 12b x + 12a b
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 3 2 3 4 2 4 8
+--R ((18A a b - 24B a b)x + 18A a b - 24B a )log(b x + a) + 2B b x
+--R +
+--R 4 3 6 3 2 2 4 2 2 3 2
+--R (3A b - 4B a b )x + (- 9A a b + 12B a b )x + (- 12A a b + 18B a b)x
+--R +
+--R 3 4
+--R 6A a b - 6B a
+--R /
+--R 6 2 5
+--R 12b x + 12a b
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 1406
+t0:=x^6*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 8 6
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 406
+
+--S 407 of 1406
+r0:=-1/2*a*(5*A*b-7*a*B)*x/b^4+1/6*(5*A*b-7*a*B)*x^3/b^3-_
+ 1/10*(5*A*b-7*a*B)*x^5/(a*b^2)+1/2*(A*b-a*B)*x^7/(a*b*(a+b*x^2))+_
+ 1/2*a^(3/2)*(5*A*b-7*a*B)*atan(x*sqrt(b)/sqrt(a))/b^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 3 +-+ x\|b
+--R ((75A a b - 105B a b)x + 75A a b - 105B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 6B b x + (10A b - 14B a b )x + (- 50A a b + 70B a b)x
+--R +
+--R 2 3
+--R (- 75A a b + 105B a )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 5 2 4 +-+
+--R (30b x + 30a b )\|b
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 2 2 2 2 3 | a
+--R ((75A a b - 105B a b)x + 75A a b - 105B a ) |- -
+--R \| b
+--R *
+--R +---+
+--R | a 2
+--R 2b x |- - + b x - a
+--R \| b
+--R log(---------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 12B b x + (20A b - 28B a b )x + (- 100A a b + 140B a b)x
+--R +
+--R 2 3
+--R (- 150A a b + 210B a )x
+--R /
+--R 5 2 4
+--R 60b x + 60a b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 2 2 3 |a \|b 3 7
+--R ((- 75A a b + 105B a b)x - 75A a b + 105B a ) |- atan(----) + 6B b x
+--R \|b x
+--R +
+--R 3 2 5 2 2 3 2 3
+--R (10A b - 14B a b )x + (- 50A a b + 70B a b)x + (- 75A a b + 105B a )x
+--R /
+--R 5 2 4
+--R 30b x + 30a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 408
+
+--S 409 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 | a +-+ \| b
+--R (5A a b - 7B a ) |- - \|b log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R (- 10A a b + 14B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 410
+
+--S 411 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 +-+ x\|b 2 |a +-+ \|b
+--R (- 5A a b + 7B a )\|a atan(-----) + (- 5A a b + 7B a ) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R ------------------------------------------------------------------------
+--R 4 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 412
+
+)clear all
+
+--S 413 of 1406
+t0:=x^5*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 7 5
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 413
+
+--S 414 of 1406
+r0:=1/2*(A*b-2*a*B)*x^2/b^3+1/4*B*x^4/b^2-1/2*a^2*(A*b-a*B)/_
+ (b^4*(a+b*x^2))-1/2*a*(2*A*b-3*a*B)*log(a+b*x^2)/b^4
+--R
+--R
+--R (2)
+--R 2 2 2 2 3 2 3 6
+--R ((- 4A a b + 6B a b)x - 4A a b + 6B a )log(b x + a) + B b x
+--R +
+--R 3 2 4 2 2 2 2 3
+--R (2A b - 3B a b )x + (2A a b - 4B a b)x - 2A a b + 2B a
+--R /
+--R 5 2 4
+--R 4b x + 4a b
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 3 2 3 6
+--R ((- 4A a b + 6B a b)x - 4A a b + 6B a )log(b x + a) + B b x
+--R +
+--R 3 2 4 2 2 2 2 3
+--R (2A b - 3B a b )x + (2A a b - 4B a b)x - 2A a b + 2B a
+--R /
+--R 5 2 4
+--R 4b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 415
+
+--S 416 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 417
+
+)clear all
+
+--S 418 of 1406
+t0:=x^4*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 6 4
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 418
+
+--S 419 of 1406
+r0:=1/2*(3*A*b-5*a*B)*x/b^3-1/6*(3*A*b-5*a*B)*x^3/(a*b^2)+_
+ 1/2*(A*b-a*B)*x^5/(a*b*(a+b*x^2))-1/2*(3*A*b-5*a*B)*_
+ atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 +-+ x\|b
+--R ((- 9A b + 15B a b)x - 9A a b + 15B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 5 2 3 2 +-+
+--R (2B b x + (6A b - 10B a b)x + (9A a b - 15B a )x)\|b
+--R /
+--R 4 2 3 +-+
+--R (6b x + 6a b )\|b
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 2 2 2 | a
+--R ((9A b - 15B a b)x + 9A a b - 15B a ) |- -
+--R \| b
+--R *
+--R +---+
+--R | a 2
+--R - 2b x |- - + b x - a
+--R \| b
+--R log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 5 2 3 2
+--R 4B b x + (12A b - 20B a b)x + (18A a b - 30B a )x
+--R /
+--R 4 2 3
+--R 12b x + 12a b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 2 |a \|b 2 5
+--R ((9A b - 15B a b)x + 9A a b - 15B a ) |- atan(----) + 2B b x
+--R \|b x
+--R +
+--R 2 3 2
+--R (6A b - 10B a b)x + (9A a b - 15B a )x
+--R /
+--R 4 2 3
+--R 6b x + 6a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 420
+
+--S 421 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R | a +-+ \| b
+--R (3A b - 5B a) |- - \|b log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ x\|b
+--R (6A b - 10B a)\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R (3A b - 5B a)\|a atan(-----) + (3A b - 5B a) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) --------------------------------------------------------------
+--R 3 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 423
+
+--S 424 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 424
+
+)clear all
+
+--S 425 of 1406
+t0:=x^3*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 5 3
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 425
+
+--S 426 of 1406
+r0:=1/2*B*x^2/b^2+1/2*a*(A*b-a*B)/(b^3*(a+b*x^2))+1/2*(A*b-2*a*B)*_
+ log(a+b*x^2)/b^3
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 4 2
+--R ((A b - 2B a b)x + A a b - 2B a )log(b x + a) + B b x + B a b x
+--R +
+--R 2
+--R A a b - B a
+--R /
+--R 4 2 3
+--R 2b x + 2a b
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 4 2
+--R ((A b - 2B a b)x + A a b - 2B a )log(b x + a) + B b x + B a b x
+--R +
+--R 2
+--R A a b - B a
+--R /
+--R 4 2 3
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 427
+
+--S 428 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 428
+
+--S 429 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 429
+
+)clear all
+
+--S 430 of 1406
+t0:=x^2*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 4 2
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 430
+
+--S 431 of 1406
+r0a:=3/2*B*x/b^2-1/2*x*(A+B*x^2)/(b*(a+b*x^2))+1/2*(A*b-3*a*B)*_
+ atan(x*sqrt(b)/sqrt(a))/(b^(5/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 x\|b
+--R ((A b - 3B a b)x + A a b - 3B a )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 +-+ +-+
+--R (2B b x + (- A b + 3B a)x)\|a \|b
+--R /
+--R 3 2 2 +-+ +-+
+--R (2b x + 2a b )\|a \|b
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 1406
+r0b:=-1/2*(A*b-3*a*B)*x/(a*b^2)+1/2*(A*b-a*B)*x^3/(a*b*(a+b*x^2))+_
+ 1/2*(A*b-3*a*B)*atan(x*sqrt(b)/sqrt(a))/(b^(5/2)*sqrt(a))
+--R
+--R
+--R (3)
+--R +-+
+--R 2 2 2 x\|b
+--R ((A b - 3B a b)x + A a b - 3B a )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 +-+ +-+
+--R (2B b x + (- A b + 3B a)x)\|a \|b
+--R /
+--R 3 2 2 +-+ +-+
+--R (2b x + 2a b )\|a \|b
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 +-----+
+--R 2 2 2 (b x - a)\|- a b + 2a b x
+--R ((A b - 3B a b)x + A a b - 3B a )log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 +-----+
+--R (4B b x + (- 2A b + 6B a)x)\|- a b
+--R /
+--R 3 2 2 +-----+
+--R (4b x + 4a b )\|- a b
+--R ,
+--R
+--R +---+
+--R 2 2 2 x\|a b
+--R ((A b - 3B a b)x + A a b - 3B a )atan(-------)
+--R a
+--R +
+--R 3 +---+
+--R (2B b x + (- A b + 3B a)x)\|a b
+--R /
+--R 3 2 2 +---+
+--R (2b x + 2a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 433
+
+--S 434 of 1406
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (A b - 3B a)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2A b + 6B a)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 435
+
+--S 436 of 1406
+m0b:=a0.2-r0a
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (A b - 3B a)\|a \|b atan(-------) + (- A b + 3B a)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (7) -------------------------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 2b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 1406
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (A b - 3B a)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2A b + 6B a)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 438
+
+--S 439 of 1406
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 1406
+m0d:=a0.2-r0b
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (A b - 3B a)\|a \|b atan(-------) + (- A b + 3B a)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (11) -------------------------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 2b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 440
+
+--S 441 of 1406
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 441
+
+)clear all
+
+--S 442 of 1406
+t0:=x*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 3
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 442
+
+--S 443 of 1406
+r0:=1/2*(-A*b+a*B)/(b^2*(a+b*x^2))+1/2*B*log(a+b*x^2)/b^2
+--R
+--R
+--R 2 2
+--R (B b x + B a)log(b x + a) - A b + B a
+--R (2) ---------------------------------------
+--R 3 2 2
+--R 2b x + 2a b
+--R Type: Expression(Integer)
+--E 443
+
+--S 444 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R (B b x + B a)log(b x + a) - A b + B a
+--R (3) ---------------------------------------
+--R 3 2 2
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 444
+
+--S 445 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 445
+
+--S 446 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 446
+
+)clear all
+
+--S 447 of 1406
+t0:=(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 447
+
+--S 448 of 1406
+r0:=1/2*(A*b-a*B)*x/(a*b*(a+b*x^2))+1/2*(A*b+a*B)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(3/2))
+--R
+--R
+--R +-+
+--R 2 2 2 x\|b +-+ +-+
+--R ((A b + B a b)x + A a b + B a )atan(-----) + (A b - B a)x\|a \|b
+--R +-+
+--R \|a
+--R (2) -------------------------------------------------------------------
+--R 2 2 2 +-+ +-+
+--R (2a b x + 2a b)\|a \|b
+--R Type: Expression(Integer)
+--E 448
+
+--S 449 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 (b x - a)\|- a b + 2a b x
+--R ((A b + B a b)x + A a b + B a )log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-----+
+--R (2A b - 2B a)x\|- a b
+--R /
+--R 2 2 2 +-----+
+--R (4a b x + 4a b)\|- a b
+--R ,
+--R +---+
+--R 2 2 2 x\|a b +---+
+--R ((A b + B a b)x + A a b + B a )atan(-------) + (A b - B a)x\|a b
+--R a
+--R -------------------------------------------------------------------]
+--R 2 2 2 +---+
+--R (2a b x + 2a b)\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 449
+
+--S 450 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (A b + B a)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2A b - 2B a)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-----+ +-+ +-+
+--R 4a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 450
+
+--S 451 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (A b + B a)\|a \|b atan(-------) + (- A b - B a)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R 2a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 453
+
+)clear all
+
+--S 454 of 1406
+t0:=(A+B*x^2)/(x*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) --------------------
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 454
+
+--S 455 of 1406
+r0:=1/2*(A*b-a*B)/(a*b*(a+b*x^2))+A*log(x)/a^2-1/2*A*log(a+b*x^2)/a^2
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2
+--R (- A b x - A a b)log(b x + a) + (2A b x + 2A a b)log(x) + A a b - B a
+--R -------------------------------------------------------------------------
+--R 2 2 2 3
+--R 2a b x + 2a b
+--R Type: Expression(Integer)
+--E 455
+
+--S 456 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2
+--R (- A b x - A a b)log(b x + a) + (2A b x + 2A a b)log(x) + A a b - B a
+--R -------------------------------------------------------------------------
+--R 2 2 2 3
+--R 2a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 456
+
+--S 457 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 458
+
+)clear all
+
+--S 459 of 1406
+t0:=(A+B*x^2)/(x^2*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ---------------------
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 459
+
+--S 460 of 1406
+r0:=1/2*(-3*A*b+a*B)/(a^2*b*x)+1/2*(A*b-a*B)/(a*b*x*(a+b*x^2))-_
+ 1/2*(3*A*b-a*B)*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*sqrt(b))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 2 x\|b
+--R ((- 3A b + B a b)x + (- 3A a b + B a )x)atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 +-+ +-+
+--R ((- 3A b + B a)x - 2A a)\|a \|b
+--R /
+--R 2 3 3 +-+ +-+
+--R (2a b x + 2a x)\|a \|b
+--R Type: Expression(Integer)
+--E 460
+
+--S 461 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 3 2 (b x - a)\|- a b - 2a b x
+--R ((3A b - B a b)x + (3A a b - B a )x)log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 +-----+
+--R ((- 6A b + 2B a)x - 4A a)\|- a b
+--R /
+--R 2 3 3 +-----+
+--R (4a b x + 4a x)\|- a b
+--R ,
+--R
+--R +---+
+--R 2 3 2 x\|a b
+--R ((- 3A b + B a b)x + (- 3A a b + B a )x)atan(-------)
+--R a
+--R +
+--R 2 +---+
+--R ((- 3A b + B a)x - 2A a)\|a b
+--R /
+--R 2 3 3 +---+
+--R (2a b x + 2a x)\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 461
+
+--S 462 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b - 2a b x
+--R (3A b - B a)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (6A b - 2B a)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4a \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 463
+
+--S 464 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (- 3A b + B a)\|a \|b atan(-------) + (3A b - B a)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 2a \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 465
+
+)clear all
+
+--S 466 of 1406
+t0:=(A+B*x^2)/(x^3*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ---------------------
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 466
+
+--S 467 of 1406
+r0:=1/2*(-2*A*b+a*B)/(a^2*b*x^2)+1/2*(A*b-a*B)/(a*b*x^2*(a+b*x^2))-_
+ (2*A*b-a*B)*log(x)/a^3+1/2*(2*A*b-a*B)*log(a+b*x^2)/a^3
+--R
+--R
+--R (2)
+--R 2 4 2 2 2
+--R ((2A b - B a b)x + (2A a b - B a )x )log(b x + a)
+--R +
+--R 2 4 2 2 2 2
+--R ((- 4A b + 2B a b)x + (- 4A a b + 2B a )x )log(x) + (- 2A a b + B a )x
+--R +
+--R 2
+--R - A a
+--R /
+--R 3 4 4 2
+--R 2a b x + 2a x
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 2
+--R ((2A b - B a b)x + (2A a b - B a )x )log(b x + a)
+--R +
+--R 2 4 2 2 2 2
+--R ((- 4A b + 2B a b)x + (- 4A a b + 2B a )x )log(x) + (- 2A a b + B a )x
+--R +
+--R 2
+--R - A a
+--R /
+--R 3 4 4 2
+--R 2a b x + 2a x
+--R Type: Union(Expression(Integer),...)
+--E 468
+
+--S 469 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 470
+
+)clear all
+
+--S 471 of 1406
+t0:=(A+B*x^2)/(x^4*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ---------------------
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 471
+
+--S 472 of 1406
+r0:=1/6*(-5*A*b+3*a*B)/(a^2*b*x^3)+1/2*(5*A*b-3*a*B)/(a^3*x)+_
+ 1/2*(A*b-a*B)/(a*b*x^3*(a+b*x^2))+1/2*(5*A*b-3*a*B)*_
+ atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 5 2 3 +-+ x\|b
+--R ((15A b - 9B a b)x + (15A a b - 9B a )x )\|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+
+--R ((15A b - 9B a b)x + (10A a b - 6B a )x - 2A a )\|a
+--R /
+--R 3 5 4 3 +-+
+--R (6a b x + 6a x )\|a
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 2 5 2 3 | b
+--R ((15A b - 9B a b)x + (15A a b - 9B a )x ) |- -
+--R \| a
+--R *
+--R +---+
+--R | b 2
+--R 2a x |- - + b x - a
+--R \| a
+--R log(---------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 4 2 2 2
+--R (30A b - 18B a b)x + (20A a b - 12B a )x - 4A a
+--R /
+--R 3 5 4 3
+--R 12a b x + 12a x
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 5 2 3 |b \|a
+--R ((- 15A b + 9B a b)x + (- 15A a b + 9B a )x ) |- atan(-----)
+--R \|a b x
+--R +
+--R 2 4 2 2 2
+--R (15A b - 9B a b)x + (10A a b - 6B a )x - 2A a
+--R /
+--R 3 5 4 3
+--R 6a b x + 6a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 473
+
+--S 474 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b +-+ \| a
+--R (5A b - 3B a) |- - \|a log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ x\|b
+--R (- 10A b + 6B a)\|b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 475
+
+--S 476 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R (- 5A b + 3B a)\|b atan(-----) + (- 5A b + 3B a)\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -------------------------------------------------------------------
+--R 3 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 477
+
+)clear all
+
+--S 478 of 1406
+t0:=(A+B*x^2)/(x^5*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ---------------------
+--R 2 9 7 2 5
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 478
+
+--S 479 of 1406
+r0:=1/4*(-3*A*b+2*a*B)/(a^2*b*x^4)+1/2*(3*A*b-2*a*B)/(a^3*x^2)+_
+ 1/2*(A*b-a*B)/(a*b*x^4*(a+b*x^2))+b*(3*A*b-2*a*B)*log(x)/a^4-_
+ 1/2*b*(3*A*b-2*a*B)*log(a+b*x^2)/a^4
+--R
+--R
+--R (2)
+--R 3 2 6 2 2 4 2
+--R ((- 6A b + 4B a b )x + (- 6A a b + 4B a b)x )log(b x + a)
+--R +
+--R 3 2 6 2 2 4
+--R ((12A b - 8B a b )x + (12A a b - 8B a b)x )log(x)
+--R +
+--R 2 2 4 2 3 2 3
+--R (6A a b - 4B a b)x + (3A a b - 2B a )x - A a
+--R /
+--R 4 6 5 4
+--R 4a b x + 4a x
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 6 2 2 4 2
+--R ((- 6A b + 4B a b )x + (- 6A a b + 4B a b)x )log(b x + a)
+--R +
+--R 3 2 6 2 2 4
+--R ((12A b - 8B a b )x + (12A a b - 8B a b)x )log(x)
+--R +
+--R 2 2 4 2 3 2 3
+--R (6A a b - 4B a b)x + (3A a b - 2B a )x - A a
+--R /
+--R 4 6 5 4
+--R 4a b x + 4a x
+--R Type: Union(Expression(Integer),...)
+--E 480
+
+--S 481 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 482
+
+)clear all
+
+--S 483 of 1406
+t0:=(A+B*x^2)/(x^6*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ----------------------
+--R 2 10 8 2 6
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 483
+
+--S 484 of 1406
+r0:=1/10*(-7*A*b+5*a*B)/(a^2*b*x^5)+1/6*(7*A*b-5*a*B)/(a^3*x^3)-_
+ 1/2*b*(7*A*b-5*a*B)/(a^4*x)+1/2*(A*b-a*B)/(a*b*x^5*(a+b*x^2))-_
+ 1/2*b^(3/2)*(7*A*b-5*a*B)*atan(x*sqrt(b)/sqrt(a))/a^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 7 2 2 5 +-+ x\|b
+--R ((- 105A b + 75B a b )x + (- 105A a b + 75B a b)x )\|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 2 6 2 2 4
+--R (- 105A b + 75B a b )x + (- 70A a b + 50B a b)x
+--R +
+--R 2 3 2 3
+--R (14A a b - 10B a )x - 6A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 7 5 5 +-+
+--R (30a b x + 30a x )\|a
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 3 2 7 2 2 5 | b
+--R ((105A b - 75B a b )x + (105A a b - 75B a b)x ) |- -
+--R \| a
+--R *
+--R +---+
+--R | b 2
+--R - 2a x |- - + b x - a
+--R \| a
+--R log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 2 6 2 2 4
+--R (- 210A b + 150B a b )x + (- 140A a b + 100B a b)x
+--R +
+--R 2 3 2 3
+--R (28A a b - 20B a )x - 12A a
+--R /
+--R 4 7 5 5
+--R 60a b x + 60a x
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 2 7 2 2 5 |b \|a
+--R ((105A b - 75B a b )x + (105A a b - 75B a b)x ) |- atan(-----)
+--R \|a b x
+--R +
+--R 3 2 6 2 2 4
+--R (- 105A b + 75B a b )x + (- 70A a b + 50B a b)x
+--R +
+--R 2 3 2 3
+--R (14A a b - 10B a )x - 6A a
+--R /
+--R 4 7 5 5
+--R 30a b x + 30a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 485
+
+--S 486 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 | b +-+ \| a
+--R (7A b - 5B a b) |- - \|a log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R (14A b - 10B a b)\|b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R 2 +-+ x\|b 2 +-+ |b \|a
+--R (7A b - 5B a b)\|b atan(-----) + (7A b - 5B a b)\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) ---------------------------------------------------------------------
+--R 4 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 488
+
+--S 489 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 489
+
+)clear all
+
+--S 490 of 1406
+t0:=(A+B*x^2)/(x^7*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ----------------------
+--R 2 11 9 2 7
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 490
+
+--S 491 of 1406
+r0:=1/6*(-4*A*b+3*a*B)/(a^2*b*x^6)+1/4*(4*A*b-3*a*B)/(a^3*x^4)-_
+ 1/2*b*(4*A*b-3*a*B)/(a^4*x^2)+1/2*(A*b-a*B)/(a*b*x^6*(a+b*x^2))-_
+ b^2*(4*A*b-3*a*B)*log(x)/a^5+1/2*b^2*(4*A*b-3*a*B)*log(a+b*x^2)/a^5
+--R
+--R
+--R (2)
+--R 4 3 8 3 2 2 6 2
+--R ((24A b - 18B a b )x + (24A a b - 18B a b )x )log(b x + a)
+--R +
+--R 4 3 8 3 2 2 6
+--R ((- 48A b + 36B a b )x + (- 48A a b + 36B a b )x )log(x)
+--R +
+--R 3 2 2 6 2 2 3 4 3 4 2
+--R (- 24A a b + 18B a b )x + (- 12A a b + 9B a b)x + (4A a b - 3B a )x
+--R +
+--R 4
+--R - 2A a
+--R /
+--R 5 8 6 6
+--R 12a b x + 12a x
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 8 3 2 2 6 2
+--R ((24A b - 18B a b )x + (24A a b - 18B a b )x )log(b x + a)
+--R +
+--R 4 3 8 3 2 2 6
+--R ((- 48A b + 36B a b )x + (- 48A a b + 36B a b )x )log(x)
+--R +
+--R 3 2 2 6 2 2 3 4 3 4 2
+--R (- 24A a b + 18B a b )x + (- 12A a b + 9B a b)x + (4A a b - 3B a )x
+--R +
+--R 4
+--R - 2A a
+--R /
+--R 5 8 6 6
+--R 12a b x + 12a x
+--R Type: Union(Expression(Integer),...)
+--E 492
+
+--S 493 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 493
+
+--S 494 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 494
+
+)clear all
+
+--S 495 of 1406
+t0:=x^11*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 13 11
+--R B x + A x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 495
+
+--S 496 of 1406
+r0:=a^2*(3*A*b-5*a*B)*x^2/b^6-3/4*a*(A*b-2*a*B)*x^4/b^5+1/6*_
+ (A*b-3*a*B)*x^6/b^4+1/8*B*x^8/b^3+1/4*a^5*(A*b-a*B)/(b^7*_
+ (a+b*x^2)^2)-1/2*a^4*(5*A*b-6*a*B)/(b^7*(a+b*x^2))-_
+ 5/2*a^3*(2*A*b-3*a*B)*log(a+b*x^2)/b^7
+--R
+--R
+--R (2)
+--R 3 3 4 2 4 4 2 5 2 5
+--R (- 120A a b + 180B a b )x + (- 240A a b + 360B a b)x - 120A a b
+--R +
+--R 6
+--R 180B a
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 6 12 6 5 10 5 2 4 8
+--R 3B b x + (4A b - 6B a b )x + (- 10A a b + 15B a b )x
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (40A a b - 60B a b )x + (126A a b - 204B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (12A a b - 48B a b)x - 54A a b + 66B a
+--R /
+--R 9 4 8 2 2 7
+--R 24b x + 48a b x + 24a b
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 4 2 4 4 2 5 2 5
+--R (- 120A a b + 180B a b )x + (- 240A a b + 360B a b)x - 120A a b
+--R +
+--R 6
+--R 180B a
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 6 12 6 5 10 5 2 4 8
+--R 3B b x + (4A b - 6B a b )x + (- 10A a b + 15B a b )x
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (40A a b - 60B a b )x + (126A a b - 204B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (12A a b - 48B a b)x - 54A a b + 66B a
+--R /
+--R 9 4 8 2 2 7
+--R 24b x + 48a b x + 24a b
+--R Type: Union(Expression(Integer),...)
+--E 497
+
+--S 498 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 498
+
+--S 499 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 499
+
+)clear all
+
+--S 500 of 1406
+t0:=x^10*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 12 10
+--R B x + A x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 500
+
+--S 501 of 1406
+r0:=9/8*a^2*(7*A*b-11*a*B)*x/b^6-3/8*a*(7*A*b-11*a*B)*x^3/b^5+_
+ 9/40*(7*A*b-11*a*B)*x^5/b^4-9/56*(7*A*b-11*a*B)*x^7/(a*b^3)+_
+ 1/4*(A*b-a*B)*x^11/(a*b*(a+b*x^2)^2)+1/8*(7*A*b-11*a*B)*x^9/_
+ (a*b^2*(a+b*x^2))-9/8*a^(5/2)*(7*A*b-11*a*B)*_
+ atan(x*sqrt(b)/sqrt(a))/b^(13/2)
+--R
+--R
+--R (2)
+--R 2 3 3 2 4 3 2 4 2
+--R (- 2205A a b + 3465B a b )x + (- 4410A a b + 6930B a b)x
+--R +
+--R 4 5
+--R - 2205A a b + 3465B a
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R 40B b x + (56A b - 88B a b )x + (- 168A a b + 264B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (1176A a b - 1848B a b )x + (3675A a b - 5775B a b)x
+--R +
+--R 4 5
+--R (2205A a b - 3465B a )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 8 4 7 2 2 6 +-+
+--R (280b x + 560a b x + 280a b )\|b
+--R Type: Expression(Integer)
+--E 501
+
+--S 502 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 3 2 4 3 2 4 2
+--R (2205A a b - 3465B a b )x + (4410A a b - 6930B a b)x
+--R +
+--R 4 5
+--R 2205A a b - 3465B a
+--R *
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R | a \| b
+--R |- - log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R 80B b x + (112A b - 176B a b )x + (- 336A a b + 528B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (2352A a b - 3696B a b )x + (7350A a b - 11550B a b)x
+--R +
+--R 4 5
+--R (4410A a b - 6930B a )x
+--R /
+--R 8 4 7 2 2 6
+--R 560b x + 1120a b x + 560a b
+--R ,
+--R
+--R 2 3 3 2 4 3 2 4 2
+--R (2205A a b - 3465B a b )x + (4410A a b - 6930B a b)x
+--R +
+--R 4 5
+--R 2205A a b - 3465B a
+--R *
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b
+--R |- atan(----)
+--R \|b x
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R 40B b x + (56A b - 88B a b )x + (- 168A a b + 264B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (1176A a b - 1848B a b )x + (3675A a b - 5775B a b)x
+--R +
+--R 4 5
+--R (2205A a b - 3465B a )x
+--R /
+--R 8 4 7 2 2 6
+--R 280b x + 560a b x + 280a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 502
+
+--S 503 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 3 | a +-+ \| b
+--R (63A a b - 99B a ) |- - \|b log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 3 +-+ x\|b
+--R (126A a b - 198B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 6 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 503
+
+--S 504 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 504
+
+--S 505 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 3 +-+ x\|b 2 3 |a +-+ \|b
+--R (63A a b - 99B a )\|a atan(-----) + (63A a b - 99B a ) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R ------------------------------------------------------------------------
+--R 6 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 505
+
+--S 506 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 506
+
+)clear all
+
+--S 507 of 1406
+t0:=x^9*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 11 9
+--R B x + A x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 507
+
+--S 508 of 1406
+r0:=-3/2*a*(A*b-2*a*B)*x^2/b^5+1/4*(A*b-3*a*B)*x^4/b^4+1/6*B*x^6/b^3-_
+ 1/4*a^4*(A*b-a*B)/(b^6*(a+b*x^2)^2)+1/2*a^3*(4*A*b-5*a*B)/_
+ (b^6*(a+b*x^2))+a^2*(3*A*b-5*a*B)*log(a+b*x^2)/b^6
+--R
+--R
+--R (2)
+--R 2 3 3 2 4 3 2 4 2 4 5
+--R ((36A a b - 60B a b )x + (72A a b - 120B a b)x + 36A a b - 60B a )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 5 10 5 4 8 4 2 3 6
+--R 2B b x + (3A b - 5B a b )x + (- 12A a b + 20B a b )x
+--R +
+--R 2 3 3 2 4 3 2 4 2 4 5
+--R (- 33A a b + 63B a b )x + (6A a b + 6B a b)x + 21A a b - 27B a
+--R /
+--R 8 4 7 2 2 6
+--R 12b x + 24a b x + 12a b
+--R Type: Expression(Integer)
+--E 508
+
+--S 509 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 3 2 4 3 2 4 2 4 5
+--R ((36A a b - 60B a b )x + (72A a b - 120B a b)x + 36A a b - 60B a )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 5 10 5 4 8 4 2 3 6
+--R 2B b x + (3A b - 5B a b )x + (- 12A a b + 20B a b )x
+--R +
+--R 2 3 3 2 4 3 2 4 2 4 5
+--R (- 33A a b + 63B a b )x + (6A a b + 6B a b)x + 21A a b - 27B a
+--R /
+--R 8 4 7 2 2 6
+--R 12b x + 24a b x + 12a b
+--R Type: Union(Expression(Integer),...)
+--E 509
+
+--S 510 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 510
+
+--S 511 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 511
+
+)clear all
+
+--S 512 of 1406
+t0:=x^8*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 10 8
+--R B x + A x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 512
+
+--S 513 of 1406
+r0:=-7/8*a*(5*A*b-9*a*B)*x/b^5+7/24*(5*A*b-9*a*B)*x^3/b^4-_
+ 7/40*(5*A*b-9*a*B)*x^5/(a*b^3)+1/4*(A*b-a*B)*x^9/(a*b*(a+b*x^2)^2)+_
+ 1/8*(5*A*b-9*a*B)*x^7/(a*b^2*(a+b*x^2))+7/8*a^(3/2)*_
+ (5*A*b-9*a*B)*atan(x*sqrt(b)/sqrt(a))/b^(11/2)
+--R
+--R
+--R (2)
+--R 3 2 2 4 2 2 3 2 3
+--R (525A a b - 945B a b )x + (1050A a b - 1890B a b)x + 525A a b
+--R +
+--R 4
+--R - 945B a
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 24B b x + (40A b - 72B a b )x + (- 280A a b + 504B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (- 875A a b + 1575B a b)x + (- 525A a b + 945B a )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 7 4 6 2 2 5 +-+
+--R (120b x + 240a b x + 120a b )\|b
+--R Type: Expression(Integer)
+--E 513
+
+--S 514 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 2 4 2 2 3 2 3
+--R (525A a b - 945B a b )x + (1050A a b - 1890B a b)x + 525A a b
+--R +
+--R 4
+--R - 945B a
+--R *
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a \| b
+--R |- - log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 48B b x + (80A b - 144B a b )x + (- 560A a b + 1008B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (- 1750A a b + 3150B a b)x + (- 1050A a b + 1890B a )x
+--R /
+--R 7 4 6 2 2 5
+--R 240b x + 480a b x + 240a b
+--R ,
+--R
+--R 3 2 2 4 2 2 3 2
+--R (- 525A a b + 945B a b )x + (- 1050A a b + 1890B a b)x
+--R +
+--R 3 4
+--R - 525A a b + 945B a
+--R *
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b
+--R |- atan(----)
+--R \|b x
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 24B b x + (40A b - 72B a b )x + (- 280A a b + 504B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (- 875A a b + 1575B a b)x + (- 525A a b + 945B a )x
+--R /
+--R 7 4 6 2 2 5
+--R 120b x + 240a b x + 120a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 514
+
+--S 515 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 | a +-+ \| b
+--R (35A a b - 63B a ) |- - \|b log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R (- 70A a b + 126B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 515
+
+--S 516 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 516
+
+--S 517 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 +-+ x\|b 2 |a +-+ \|b
+--R (- 35A a b + 63B a )\|a atan(-----) + (- 35A a b + 63B a ) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R ----------------------------------------------------------------------------
+--R 5 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 517
+
+--S 518 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 518
+
+)clear all
+
+--S 519 of 1406
+t0:=x^7*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 9 7
+--R B x + A x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 519
+
+--S 520 of 1406
+r0:=1/2*(A*b-3*a*B)*x^2/b^4+1/4*B*x^4/b^3+1/4*a^3*(A*b-a*B)/_
+ (b^5*(a+b*x^2)^2)-1/2*a^2*(3*A*b-4*a*B)/(b^5*(a+b*x^2))-_
+ 3/2*a*(A*b-2*a*B)*log(a+b*x^2)/b^5
+--R
+--R
+--R (2)
+--R 3 2 2 4 2 2 3 2 3 4
+--R ((- 6A a b + 12B a b )x + (- 12A a b + 24B a b)x - 6A a b + 12B a )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 4 8 4 3 6 3 2 2 4
+--R B b x + (2A b - 4B a b )x + (4A a b - 11B a b )x
+--R +
+--R 2 2 3 2 3 4
+--R (- 4A a b + 2B a b)x - 5A a b + 7B a
+--R /
+--R 7 4 6 2 2 5
+--R 4b x + 8a b x + 4a b
+--R Type: Expression(Integer)
+--E 520
+
+--S 521 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2 4 2 2 3 2 3 4
+--R ((- 6A a b + 12B a b )x + (- 12A a b + 24B a b)x - 6A a b + 12B a )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 4 8 4 3 6 3 2 2 4
+--R B b x + (2A b - 4B a b )x + (4A a b - 11B a b )x
+--R +
+--R 2 2 3 2 3 4
+--R (- 4A a b + 2B a b)x - 5A a b + 7B a
+--R /
+--R 7 4 6 2 2 5
+--R 4b x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 521
+
+--S 522 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 522
+
+--S 523 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 523
+
+)clear all
+
+--S 524 of 1406
+t0:=x^6*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 8 6
+--R B x + A x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 524
+
+--S 525 of 1406
+r0:=5/8*(3*A*b-7*a*B)*x/b^4-5/24*(3*A*b-7*a*B)*x^3/(a*b^3)+_
+ 1/4*(A*b-a*B)*x^7/(a*b*(a+b*x^2)^2)+1/8*(3*A*b-7*a*B)*x^5/_
+ (a*b^2*(a+b*x^2))-5/8*(3*A*b-7*a*B)*atan(x*sqrt(b)/sqrt(a))*_
+ sqrt(a)/b^(9/2)
+--R
+--R
+--R (2)
+--R 3 2 4 2 2 2 2
+--R (- 45A b + 105B a b )x + (- 90A a b + 210B a b)x - 45A a b
+--R +
+--R 3
+--R 105B a
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 8B b x + (24A b - 56B a b )x + (75A a b - 175B a b)x
+--R +
+--R 2 3
+--R (45A a b - 105B a )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 6 4 5 2 2 4 +-+
+--R (24b x + 48a b x + 24a b )\|b
+--R Type: Expression(Integer)
+--E 525
+
+--S 526 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 4 2 2 2 2
+--R (45A b - 105B a b )x + (90A a b - 210B a b)x + 45A a b
+--R +
+--R 3
+--R - 105B a
+--R *
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R | a \| b
+--R |- - log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 16B b x + (48A b - 112B a b )x + (150A a b - 350B a b)x
+--R +
+--R 2 3
+--R (90A a b - 210B a )x
+--R /
+--R 6 4 5 2 2 4
+--R 48b x + 96a b x + 48a b
+--R ,
+--R
+--R 3 2 4 2 2 2 2
+--R (45A b - 105B a b )x + (90A a b - 210B a b)x + 45A a b
+--R +
+--R 3
+--R - 105B a
+--R *
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b
+--R |- atan(----)
+--R \|b x
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 8B b x + (24A b - 56B a b )x + (75A a b - 175B a b)x
+--R +
+--R 2 3
+--R (45A a b - 105B a )x
+--R /
+--R 6 4 5 2 2 4
+--R 24b x + 48a b x + 24a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 526
+
+--S 527 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R | a +-+ \| b
+--R (15A b - 35B a) |- - \|b log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ x\|b
+--R (30A b - 70B a)\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 527
+
+--S 528 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 528
+
+--S 529 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R (15A b - 35B a)\|a atan(-----) + (15A b - 35B a) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ------------------------------------------------------------------
+--R 4 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 529
+
+--S 530 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 530
+
+)clear all
+
+--S 531 of 1406
+t0:=x^5*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 7 5
+--R B x + A x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 531
+
+--S 532 of 1406
+r0:=1/2*B*x^2/b^3-1/4*a^2*(A*b-a*B)/(b^4*(a+b*x^2)^2)+_
+ 1/2*a*(2*A*b-3*a*B)/(b^4*(a+b*x^2))+1/2*(A*b-3*a*B)*log(a+b*x^2)/b^4
+--R
+--R
+--R (2)
+--R 3 2 4 2 2 2 2 3
+--R ((2A b - 6B a b )x + (4A a b - 12B a b)x + 2A a b - 6B a )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 3 6 2 4 2 2 2 2 3
+--R 2B b x + 4B a b x + (4A a b - 4B a b)x + 3A a b - 5B a
+--R /
+--R 6 4 5 2 2 4
+--R 4b x + 8a b x + 4a b
+--R Type: Expression(Integer)
+--E 532
+
+--S 533 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 2 2 2 2 3
+--R ((2A b - 6B a b )x + (4A a b - 12B a b)x + 2A a b - 6B a )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 3 6 2 4 2 2 2 2 3
+--R 2B b x + 4B a b x + (4A a b - 4B a b)x + 3A a b - 5B a
+--R /
+--R 6 4 5 2 2 4
+--R 4b x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 533
+
+--S 534 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 534
+
+--S 535 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 535
+
+)clear all
+
+--S 536 of 1406
+t0:=x^4*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 6 4
+--R B x + A x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 536
+
+--S 537 of 1406
+r0:=-3/8*(A*b-5*a*B)*x/(a*b^3)+1/4*(A*b-a*B)*x^5/(a*b*(a+b*x^2)^2)+_
+ 1/8*(A*b-5*a*B)*x^3/(a*b^2*(a+b*x^2))+3/8*(A*b-5*a*B)*_
+ atan(x*sqrt(b)/sqrt(a))/(b^(7/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R 3 2 4 2 2 2 2 3
+--R ((3A b - 15B a b )x + (6A a b - 30B a b)x + 3A a b - 15B a )
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 5 2 3 2 +-+ +-+
+--R (8B b x + (- 5A b + 25B a b)x + (- 3A a b + 15B a )x)\|a \|b
+--R /
+--R 5 4 4 2 2 3 +-+ +-+
+--R (8b x + 16a b x + 8a b )\|a \|b
+--R Type: Expression(Integer)
+--E 537
+
+--S 538 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 4 2 2 2 2 3
+--R ((3A b - 15B a b )x + (6A a b - 30B a b)x + 3A a b - 15B a )
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 5 2 3 2 +-----+
+--R (16B b x + (- 10A b + 50B a b)x + (- 6A a b + 30B a )x)\|- a b
+--R /
+--R 5 4 4 2 2 3 +-----+
+--R (16b x + 32a b x + 16a b )\|- a b
+--R ,
+--R
+--R 3 2 4 2 2 2 2 3
+--R ((3A b - 15B a b )x + (6A a b - 30B a b)x + 3A a b - 15B a )
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 5 2 3 2 +---+
+--R (8B b x + (- 5A b + 25B a b)x + (- 3A a b + 15B a )x)\|a b
+--R /
+--R 5 4 4 2 2 3 +---+
+--R (8b x + 16a b x + 8a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 538
+
+--S 539 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (3A b - 15B a)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 6A b + 30B a)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 16b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 539
+
+--S 540 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 540
+
+--S 541 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (3A b - 15B a)\|a \|b atan(-------) + (- 3A b + 15B a)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R -----------------------------------------------------------------------
+--R 3 +-+ +-+ +---+
+--R 8b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 541
+
+--S 542 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 542
+
+)clear all
+
+--S 543 of 1406
+t0:=x^3*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 5 3
+--R B x + A x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 543
+
+--S 544 of 1406
+r0:=1/4*a*(A*b-a*B)/(b^3*(a+b*x^2)^2)+1/2*(-A*b+2*a*B)/(b^3*(a+b*x^2))+_
+ 1/2*B*log(a+b*x^2)/b^3
+--R
+--R
+--R (2)
+--R 2 4 2 2 2 2 2
+--R (2B b x + 4B a b x + 2B a )log(b x + a) + (- 2A b + 4B a b)x - A a b
+--R +
+--R 2
+--R 3B a
+--R /
+--R 5 4 4 2 2 3
+--R 4b x + 8a b x + 4a b
+--R Type: Expression(Integer)
+--E 544
+
+--S 545 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 2 2 2
+--R (2B b x + 4B a b x + 2B a )log(b x + a) + (- 2A b + 4B a b)x - A a b
+--R +
+--R 2
+--R 3B a
+--R /
+--R 5 4 4 2 2 3
+--R 4b x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 545
+
+--S 546 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 546
+
+--S 547 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 547
+
+)clear all
+
+--S 548 of 1406
+t0:=x^2*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 4 2
+--R B x + A x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 548
+
+--S 549 of 1406
+r0a:=1/8*(A*b-3*a*B)*x/(a*b^2*(a+b*x^2))-1/4*x*(A+B*x^2)/(b*(a+b*x^2)^2)+1/8*(A*b+3*a*B)*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(5/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 4 2 2 2 2 3 x\|b
+--R ((A b + 3B a b )x + (2A a b + 6B a b)x + A a b + 3B a )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 +-+ +-+
+--R ((A b - 5B a b)x + (- A a b - 3B a )x)\|a \|b
+--R /
+--R 4 4 2 3 2 3 2 +-+ +-+
+--R (8a b x + 16a b x + 8a b )\|a \|b
+--R Type: Expression(Integer)
+--E 549
+
+--S 550 of 1406
+r0b:=1/4*(A*b-a*B)*x^3/(a*b*(a+b*x^2)^2)-1/8*(A*b+3*a*B)*x/(a*b^2*(a+b*x^2))+1/8*(A*b+3*a*B)*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(5/2))
+--R
+--R
+--R (3)
+--R +-+
+--R 3 2 4 2 2 2 2 3 x\|b
+--R ((A b + 3B a b )x + (2A a b + 6B a b)x + A a b + 3B a )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 +-+ +-+
+--R ((A b - 5B a b)x + (- A a b - 3B a )x)\|a \|b
+--R /
+--R 4 4 2 3 2 3 2 +-+ +-+
+--R (8a b x + 16a b x + 8a b )\|a \|b
+--R Type: Expression(Integer)
+--E 550
+
+--S 551 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 3 2 4 2 2 2 2 3
+--R ((A b + 3B a b )x + (2A a b + 6B a b)x + A a b + 3B a )
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 2 +-----+
+--R ((2A b - 10B a b)x + (- 2A a b - 6B a )x)\|- a b
+--R /
+--R 4 4 2 3 2 3 2 +-----+
+--R (16a b x + 32a b x + 16a b )\|- a b
+--R ,
+--R
+--R 3 2 4 2 2 2 2 3
+--R ((A b + 3B a b )x + (2A a b + 6B a b)x + A a b + 3B a )
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 3 2 +---+
+--R ((A b - 5B a b)x + (- A a b - 3B a )x)\|a b
+--R /
+--R 4 4 2 3 2 3 2 +---+
+--R (8a b x + 16a b x + 8a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 551
+
+--S 552 of 1406
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (A b + 3B a)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2A b - 6B a)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 16a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 552
+
+--S 553 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 553
+
+--S 554 of 1406
+m0b:=a0.2-r0a
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (A b + 3B a)\|a \|b atan(-------) + (- A b - 3B a)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (7) -------------------------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 8a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 554
+
+--S 555 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 555
+
+--S 556 of 1406
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (A b + 3B a)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2A b - 6B a)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 16a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 556
+
+--S 557 of 1406
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 557
+
+--S 558 of 1406
+m0d:=a0.2-r0b
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (A b + 3B a)\|a \|b atan(-------) + (- A b - 3B a)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (11) -------------------------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 8a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 558
+
+--S 559 of 1406
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 559
+
+)clear all
+
+--S 560 of 1406
+t0:=x*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 3
+--R B x + A x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 560
+
+--S 561 of 1406
+r0:=-1/4*(A+B*x^2)^2/((A*b-a*B)*(a+b*x^2)^2)
+--R
+--R
+--R 1 2 4 1 2 1 2
+--R - - B x - - A B x - - A
+--R 4 2 4
+--R (2) -------------------------------------------------------
+--R 3 2 4 2 2 2 2 3
+--R (A b - B a b )x + (2A a b - 2B a b)x + A a b - B a
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 561
+
+--S 562 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 2B b x - A b - B a
+--R (3) -----------------------
+--R 4 4 3 2 2 2
+--R 4b x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 562
+
+--S 563 of 1406
+m0:=a0-r0
+--R
+--R
+--R 2
+--R B
+--R (4) ---------------
+--R 3 2
+--R 4A b - 4B a b
+--R Type: Expression(Integer)
+--E 563
+
+--S 564 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 564
+
+)clear all
+
+--S 565 of 1406
+t0:=(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 565
+
+--S 566 of 1406
+r0:=1/4*(A*b-a*B)*x/(a*b*(a+b*x^2)^2)+1/8*(3*A*b+a*B)*x/(a^2*b*(a+b*x^2))+_
+ 1/8*(3*A*b+a*B)*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(3/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 4 2 2 2 2 3 x\|b
+--R ((3A b + B a b )x + (6A a b + 2B a b)x + 3A a b + B a )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 +-+ +-+
+--R ((3A b + B a b)x + (5A a b - B a )x)\|a \|b
+--R /
+--R 2 3 4 3 2 2 4 +-+ +-+
+--R (8a b x + 16a b x + 8a b)\|a \|b
+--R Type: Expression(Integer)
+--E 566
+
+--S 567 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 4 2 2 2 2 3
+--R ((3A b + B a b )x + (6A a b + 2B a b)x + 3A a b + B a )
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 2 +-----+
+--R ((6A b + 2B a b)x + (10A a b - 2B a )x)\|- a b
+--R /
+--R 2 3 4 3 2 2 4 +-----+
+--R (16a b x + 32a b x + 16a b)\|- a b
+--R ,
+--R
+--R 3 2 4 2 2 2 2 3
+--R ((3A b + B a b )x + (6A a b + 2B a b)x + 3A a b + B a )
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 3 2 +---+
+--R ((3A b + B a b)x + (5A a b - B a )x)\|a b
+--R /
+--R 2 3 4 3 2 2 4 +---+
+--R (8a b x + 16a b x + 8a b)\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 567
+
+--S 568 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (3A b + B a)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 6A b - 2B a)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 16a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 568
+
+--S 569 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 569
+
+--S 570 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (3A b + B a)\|a \|b atan(-------) + (- 3A b - B a)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 8a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 570
+
+--S 571 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 571
+
+)clear all
+
+--S 572 of 1406
+t0:=(A+B*x^2)/(x*(a+b*x^2)^3)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ------------------------------
+--R 3 7 2 5 2 3 3
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 572
+
+--S 573 of 1406
+r0:=1/4*(A*b-a*B)/(a*b*(a+b*x^2)^2)+1/2*A/(a^2*(a+b*x^2))+A*log(x)/a^3-_
+ 1/2*A*log(a+b*x^2)/a^3
+--R
+--R
+--R (2)
+--R 3 4 2 2 2 2
+--R (- 2A b x - 4A a b x - 2A a b)log(b x + a)
+--R +
+--R 3 4 2 2 2 2 2 2 3
+--R (4A b x + 8A a b x + 4A a b)log(x) + 2A a b x + 3A a b - B a
+--R /
+--R 3 3 4 4 2 2 5
+--R 4a b x + 8a b x + 4a b
+--R Type: Expression(Integer)
+--E 573
+
+--S 574 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 4 2 2 2 2
+--R (- 2A b x - 4A a b x - 2A a b)log(b x + a)
+--R +
+--R 3 4 2 2 2 2 2 2 3
+--R (4A b x + 8A a b x + 4A a b)log(x) + 2A a b x + 3A a b - B a
+--R /
+--R 3 3 4 4 2 2 5
+--R 4a b x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 574
+
+--S 575 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 575
+
+--S 576 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 576
+
+)clear all
+
+--S 577 of 1406
+t0:=(A+B*x^2)/(x^2*(a+b*x^2)^3)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------------------------
+--R 3 8 2 6 2 4 3 2
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 577
+
+--S 578 of 1406
+r0:=-3/8*(5*A*b-a*B)/(a^3*b*x)+1/4*(A*b-a*B)/(a*b*x*(a+b*x^2)^2)+_
+ 1/8*(5*A*b-a*B)/(a^2*b*x*(a+b*x^2))-3/8*(5*A*b-a*B)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(7/2)*sqrt(b))
+--R
+--R
+--R (2)
+--R 3 2 5 2 2 3
+--R (- 15A b + 3B a b )x + (- 30A a b + 6B a b)x
+--R +
+--R 2 3
+--R (- 15A a b + 3B a )x
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+ +-+
+--R ((- 15A b + 3B a b)x + (- 25A a b + 5B a )x - 8A a )\|a \|b
+--R /
+--R 3 2 5 4 3 5 +-+ +-+
+--R (8a b x + 16a b x + 8a x)\|a \|b
+--R Type: Expression(Integer)
+--E 578
+
+--S 579 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 5 2 2 3 2 3
+--R ((15A b - 3B a b )x + (30A a b - 6B a b)x + (15A a b - 3B a )x)
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 4 2 2 2 +-----+
+--R ((- 30A b + 6B a b)x + (- 50A a b + 10B a )x - 16A a )\|- a b
+--R /
+--R 3 2 5 4 3 5 +-----+
+--R (16a b x + 32a b x + 16a x)\|- a b
+--R ,
+--R
+--R 3 2 5 2 2 3
+--R (- 15A b + 3B a b )x + (- 30A a b + 6B a b)x
+--R +
+--R 2 3
+--R (- 15A a b + 3B a )x
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 4 2 2 2 +---+
+--R ((- 15A b + 3B a b)x + (- 25A a b + 5B a )x - 8A a )\|a b
+--R /
+--R 3 2 5 4 3 5 +---+
+--R (8a b x + 16a b x + 8a x)\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 579
+
+--S 580 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b - 2a b x
+--R (15A b - 3B a)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (30A b - 6B a)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 16a \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 580
+
+--S 581 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 581
+
+--S 582 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (- 15A b + 3B a)\|a \|b atan(-------) + (15A b - 3B a)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R -----------------------------------------------------------------------
+--R 3 +-+ +-+ +---+
+--R 8a \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 582
+
+--S 583 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 583
+
+)clear all
+
+--S 584 of 1406
+t0:=(A+B*x^2)/(x^3*(a+b*x^2)^3)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------------------------
+--R 3 9 2 7 2 5 3 3
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 584
+
+--S 585 of 1406
+r0:=1/2*(-3*A*b+a*B)/(a^3*b*x^2)+1/4*(A*b-a*B)/(a*b*x^2*(a+b*x^2)^2)+_
+ 1/4*(3*A*b-a*B)/(a^2*b*x^2*(a+b*x^2))-(3*A*b-a*B)*log(x)/a^4+_
+ 1/2*(3*A*b-a*B)*log(a+b*x^2)/a^4
+--R
+--R
+--R (2)
+--R 3 2 6 2 2 4 2 3 2
+--R ((6A b - 2B a b )x + (12A a b - 4B a b)x + (6A a b - 2B a )x )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 3 2 6 2 2 4
+--R (- 12A b + 4B a b )x + (- 24A a b + 8B a b)x
+--R +
+--R 2 3 2
+--R (- 12A a b + 4B a )x
+--R *
+--R log(x)
+--R +
+--R 2 2 4 2 3 2 3
+--R (- 6A a b + 2B a b)x + (- 9A a b + 3B a )x - 2A a
+--R /
+--R 4 2 6 5 4 6 2
+--R 4a b x + 8a b x + 4a x
+--R Type: Expression(Integer)
+--E 585
+
+--S 586 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 6 2 2 4 2 3 2
+--R ((6A b - 2B a b )x + (12A a b - 4B a b)x + (6A a b - 2B a )x )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 3 2 6 2 2 4
+--R (- 12A b + 4B a b )x + (- 24A a b + 8B a b)x
+--R +
+--R 2 3 2
+--R (- 12A a b + 4B a )x
+--R *
+--R log(x)
+--R +
+--R 2 2 4 2 3 2 3
+--R (- 6A a b + 2B a b)x + (- 9A a b + 3B a )x - 2A a
+--R /
+--R 4 2 6 5 4 6 2
+--R 4a b x + 8a b x + 4a x
+--R Type: Union(Expression(Integer),...)
+--E 586
+
+--S 587 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 587
+
+--S 588 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 588
+
+)clear all
+
+--S 589 of 1406
+t0:=(A+B*x^2)/(x^4*(a+b*x^2)^3)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) --------------------------------
+--R 3 10 2 8 2 6 3 4
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 589
+
+--S 590 of 1406
+r0:=-5/24*(7*A*b-3*a*B)/(a^3*b*x^3)+5/8*(7*A*b-3*a*B)/(a^4*x)+_
+ 1/4*(A*b-a*B)/(a*b*x^3*(a+b*x^2)^2)+1/8*(7*A*b-3*a*B)/_
+ (a^2*b*x^3*(a+b*x^2))+5/8*(7*A*b-3*a*B)*atan(x*sqrt(b)/_
+ sqrt(a))*sqrt(b)/a^(9/2)
+--R
+--R
+--R (2)
+--R 3 2 7 2 2 5
+--R (105A b - 45B a b )x + (210A a b - 90B a b)x
+--R +
+--R 2 3 3
+--R (105A a b - 45B a )x
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 2 6 2 2 4
+--R (105A b - 45B a b )x + (175A a b - 75B a b)x
+--R +
+--R 2 3 2 3
+--R (56A a b - 24B a )x - 8A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 2 7 5 5 6 3 +-+
+--R (24a b x + 48a b x + 24a x )\|a
+--R Type: Expression(Integer)
+--E 590
+
+--S 591 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 7 2 2 5
+--R (105A b - 45B a b )x + (210A a b - 90B a b)x
+--R +
+--R 2 3 3
+--R (105A a b - 45B a )x
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 2 6 2 2 4
+--R (210A b - 90B a b )x + (350A a b - 150B a b)x
+--R +
+--R 2 3 2 3
+--R (112A a b - 48B a )x - 16A a
+--R /
+--R 4 2 7 5 5 6 3
+--R 48a b x + 96a b x + 48a x
+--R ,
+--R
+--R 3 2 7 2 2 5
+--R (- 105A b + 45B a b )x + (- 210A a b + 90B a b)x
+--R +
+--R 2 3 3
+--R (- 105A a b + 45B a )x
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 3 2 6 2 2 4 2 3 2
+--R (105A b - 45B a b )x + (175A a b - 75B a b)x + (56A a b - 24B a )x
+--R +
+--R 3
+--R - 8A a
+--R /
+--R 4 2 7 5 5 6 3
+--R 24a b x + 48a b x + 24a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 591
+
+--S 592 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b +-+ \| a
+--R (35A b - 15B a) |- - \|a log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ x\|b
+--R (- 70A b + 30B a)\|b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 592
+
+--S 593 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 593
+
+--S 594 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R (- 35A b + 15B a)\|b atan(-----) + (- 35A b + 15B a)\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R -----------------------------------------------------------------------
+--R 4 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 594
+
+--S 595 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 595
+
+)clear all
+
+--S 596 of 1406
+t0:=(A+B*x^2)/(x^5*(a+b*x^2)^3)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) --------------------------------
+--R 3 11 2 9 2 7 3 5
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 596
+
+--S 597 of 1406
+r0:=-3/4*(2*A*b-a*B)/(a^3*b*x^4)+3/2*(2*A*b-a*B)/(a^4*x^2)+_
+ 1/4*(A*b-a*B)/(a*b*x^4*(a+b*x^2)^2)+1/2*(2*A*b-a*B)/_
+ (a^2*b*x^4*(a+b*x^2))+3*b*(2*A*b-a*B)*log(x)/a^5-3/2*b*_
+ (2*A*b-a*B)*log(a+b*x^2)/a^5
+--R
+--R
+--R (2)
+--R 4 3 8 3 2 2 6
+--R (- 12A b + 6B a b )x + (- 24A a b + 12B a b )x
+--R +
+--R 2 2 3 4
+--R (- 12A a b + 6B a b)x
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 4 3 8 3 2 2 6
+--R (24A b - 12B a b )x + (48A a b - 24B a b )x
+--R +
+--R 2 2 3 4
+--R (24A a b - 12B a b)x
+--R *
+--R log(x)
+--R +
+--R 3 2 2 6 2 2 3 4 3 4 2 4
+--R (12A a b - 6B a b )x + (18A a b - 9B a b)x + (4A a b - 2B a )x - A a
+--R /
+--R 5 2 8 6 6 7 4
+--R 4a b x + 8a b x + 4a x
+--R Type: Expression(Integer)
+--E 597
+
+--S 598 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 8 3 2 2 6
+--R (- 12A b + 6B a b )x + (- 24A a b + 12B a b )x
+--R +
+--R 2 2 3 4
+--R (- 12A a b + 6B a b)x
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 4 3 8 3 2 2 6
+--R (24A b - 12B a b )x + (48A a b - 24B a b )x
+--R +
+--R 2 2 3 4
+--R (24A a b - 12B a b)x
+--R *
+--R log(x)
+--R +
+--R 3 2 2 6 2 2 3 4 3 4 2 4
+--R (12A a b - 6B a b )x + (18A a b - 9B a b)x + (4A a b - 2B a )x - A a
+--R /
+--R 5 2 8 6 6 7 4
+--R 4a b x + 8a b x + 4a x
+--R Type: Union(Expression(Integer),...)
+--E 598
+
+--S 599 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 599
+
+--S 600 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 600
+
+)clear all
+
+--S 601 of 1406
+t0:=(A+B*x^2)/(x^6*(a+b*x^2)^3)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ---------------------------------
+--R 3 12 2 10 2 8 3 6
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 601
+
+--S 602 of 1406
+r0:=-7/40*(9*A*b-5*a*B)/(a^3*b*x^5)+7/24*(9*A*b-5*a*B)/(a^4*x^3)-_
+ 7/8*b*(9*A*b-5*a*B)/(a^5*x)+1/4*(A*b-a*B)/(a*b*x^5*(a+b*x^2)^2)+_
+ 1/8*(9*A*b-5*a*B)/(a^2*b*x^5*(a+b*x^2))-7/8*b^(3/2)*_
+ (9*A*b-5*a*B)*atan(x*sqrt(b)/sqrt(a))/a^(11/2)
+--R
+--R
+--R (2)
+--R 4 3 9 3 2 2 7
+--R (- 945A b + 525B a b )x + (- 1890A a b + 1050B a b )x
+--R +
+--R 2 2 3 5
+--R (- 945A a b + 525B a b)x
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 3 8 3 2 2 6
+--R (- 945A b + 525B a b )x + (- 1575A a b + 875B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (- 504A a b + 280B a b)x + (72A a b - 40B a )x - 24A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 5 2 9 6 7 7 5 +-+
+--R (120a b x + 240a b x + 120a x )\|a
+--R Type: Expression(Integer)
+--E 602
+
+--S 603 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 3 9 3 2 2 7
+--R (945A b - 525B a b )x + (1890A a b - 1050B a b )x
+--R +
+--R 2 2 3 5
+--R (945A a b - 525B a b)x
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 4 3 8 3 2 2 6
+--R (- 1890A b + 1050B a b )x + (- 3150A a b + 1750B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (- 1008A a b + 560B a b)x + (144A a b - 80B a )x - 48A a
+--R /
+--R 5 2 9 6 7 7 5
+--R 240a b x + 480a b x + 240a x
+--R ,
+--R
+--R 4 3 9 3 2 2 7
+--R (945A b - 525B a b )x + (1890A a b - 1050B a b )x
+--R +
+--R 2 2 3 5
+--R (945A a b - 525B a b)x
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 4 3 8 3 2 2 6
+--R (- 945A b + 525B a b )x + (- 1575A a b + 875B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (- 504A a b + 280B a b)x + (72A a b - 40B a )x - 24A a
+--R /
+--R 5 2 9 6 7 7 5
+--R 120a b x + 240a b x + 120a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 603
+
+--S 604 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 | b +-+ \| a
+--R (63A b - 35B a b) |- - \|a log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R (126A b - 70B a b)\|b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 604
+
+--S 605 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 605
+
+--S 606 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R 2 +-+ x\|b 2 +-+ |b \|a
+--R (63A b - 35B a b)\|b atan(-----) + (63A b - 35B a b)\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R -------------------------------------------------------------------------
+--R 5 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 606
+
+--S 607 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 607
+
+)clear all
+
+--S 608 of 1406
+t0:=(A+B*x^2)/(x^7*(a+b*x^2)^3)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ---------------------------------
+--R 3 13 2 11 2 9 3 7
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 608
+
+--S 609 of 1406
+r0:=1/3*(-5*A*b+3*a*B)/(a^3*b*x^6)+1/2*(5*A*b-3*a*B)/(a^4*x^4)-_
+ b*(5*A*b-3*a*B)/(a^5*x^2)+1/4*(A*b-a*B)/(a*b*x^6*(a+b*x^2)^2)+_
+ 1/4*(5*A*b-3*a*B)/(a^2*b*x^6*(a+b*x^2))-2*b^2*(5*A*b-3*a*B)*_
+ log(x)/a^6+b^2*(5*A*b-3*a*B)*log(a+b*x^2)/a^6
+--R
+--R
+--R (2)
+--R 5 4 10 4 2 3 8
+--R (60A b - 36B a b )x + (120A a b - 72B a b )x
+--R +
+--R 2 3 3 2 6
+--R (60A a b - 36B a b )x
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 5 4 10 4 2 3 8
+--R (- 120A b + 72B a b )x + (- 240A a b + 144B a b )x
+--R +
+--R 2 3 3 2 6
+--R (- 120A a b + 72B a b )x
+--R *
+--R log(x)
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 60A a b + 36B a b )x + (- 90A a b + 54B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 20A a b + 12B a b)x + (5A a b - 3B a )x - 2A a
+--R /
+--R 6 2 10 7 8 8 6
+--R 12a b x + 24a b x + 12a x
+--R Type: Expression(Integer)
+--E 609
+
+--S 610 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 10 4 2 3 8
+--R (60A b - 36B a b )x + (120A a b - 72B a b )x
+--R +
+--R 2 3 3 2 6
+--R (60A a b - 36B a b )x
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 5 4 10 4 2 3 8
+--R (- 120A b + 72B a b )x + (- 240A a b + 144B a b )x
+--R +
+--R 2 3 3 2 6
+--R (- 120A a b + 72B a b )x
+--R *
+--R log(x)
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 60A a b + 36B a b )x + (- 90A a b + 54B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 20A a b + 12B a b)x + (5A a b - 3B a )x - 2A a
+--R /
+--R 6 2 10 7 8 8 6
+--R 12a b x + 24a b x + 12a x
+--R Type: Union(Expression(Integer),...)
+--E 610
+
+--S 611 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 611
+
+--S 612 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 612
+
+)clear all
+
+--S 613 of 1406
+t0:=(a+b*x^2)/(1+x^2)
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R 2
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 613
+
+--S 614 of 1406
+r0:=b*x+(a-b)*atan(x)
+--R
+--R
+--R (2) (- b + a)atan(x) + b x
+--R Type: Expression(Integer)
+--E 614
+
+--S 615 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3) (- b + a)atan(x) + b x
+--R Type: Union(Expression(Integer),...)
+--E 615
+
+--S 616 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 616
+
+--S 617 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 617
+
+)clear all
+
+--S 618 of 1406
+t0:=(a+b*x^2)/(1-x^2)
+--R
+--R
+--R 2
+--R - b x - a
+--R (1) ----------
+--R 2
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 618
+
+--S 619 of 1406
+r0:=-b*x+(a+b)*atanh(x)
+--R
+--R
+--R (2) (b + a)atanh(x) - b x
+--R Type: Expression(Integer)
+--E 619
+
+--S 620 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (b + a)log(x + 1) + (- b - a)log(x - 1) - 2b x
+--R (3) ----------------------------------------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 620
+
+--S 621 of 1406
+m0:=a0-r0
+--R
+--R
+--R (b + a)log(x + 1) + (- b - a)log(x - 1) + (- 2b - 2a)atanh(x)
+--R (4) -------------------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 621
+
+--S 622 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 622
+
+)clear all
+
+--S 623 of 1406
+t0:=(1+x^2)/(-1+x^2)^2
+--R
+--R
+--R 2
+--R x + 1
+--R (1) ------------
+--R 4 2
+--R x - 2x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 623
+
+--S 624 of 1406
+r0:=x/(1-x^2)
+--R
+--R
+--R x
+--R (2) - ------
+--R 2
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 624
+
+--S 625 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R x
+--R (3) - ------
+--R 2
+--R x - 1
+--R Type: Union(Expression(Integer),...)
+--E 625
+
+--S 626 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 626
+
+--S 627 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 627
+
+)clear all
+
+--S 628 of 1406
+t0:=(1-x^2)/(1+x^2)^2
+--R
+--R
+--R 2
+--R - x + 1
+--R (1) ------------
+--R 4 2
+--R x + 2x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 628
+
+--S 629 of 1406
+r0:=x/(1+x^2)
+--R
+--R
+--R x
+--R (2) ------
+--R 2
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 629
+
+--S 630 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R x
+--R (3) ------
+--R 2
+--R x + 1
+--R Type: Union(Expression(Integer),...)
+--E 630
+
+--S 631 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 631
+
+--S 632 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 632
+
+)clear all
+
+--S 633 of 1406
+t0:=(3+2*x^2)/(1+x^2)^2
+--R
+--R
+--R 2
+--R 2x + 3
+--R (1) ------------
+--R 4 2
+--R x + 2x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 633
+
+--S 634 of 1406
+r0:=1/2*x/(1+x^2)+5/2*atan(x)
+--R
+--R
+--R 2
+--R (5x + 5)atan(x) + x
+--R (2) --------------------
+--R 2
+--R 2x + 2
+--R Type: Expression(Integer)
+--E 634
+
+--S 635 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (5x + 5)atan(x) + x
+--R (3) --------------------
+--R 2
+--R 2x + 2
+--R Type: Union(Expression(Integer),...)
+--E 635
+
+--S 636 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 636
+
+--S 637 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 637
+
+)clear all
+
+--S 638 of 1406
+t0:=(-2+x^2)/(1+x^2)^2
+--R
+--R
+--R 2
+--R x - 2
+--R (1) ------------
+--R 4 2
+--R x + 2x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 638
+
+--S 639 of 1406
+r0:=-3/2*x/(1+x^2)-1/2*atan(x)
+--R
+--R
+--R 2
+--R (- x - 1)atan(x) - 3x
+--R (2) ----------------------
+--R 2
+--R 2x + 2
+--R Type: Expression(Integer)
+--E 639
+
+--S 640 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (- x - 1)atan(x) - 3x
+--R (3) ----------------------
+--R 2
+--R 2x + 2
+--R Type: Union(Expression(Integer),...)
+--E 640
+
+--S 641 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 641
+
+--S 642 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 642
+
+)clear all
+
+--S 643 of 1406
+t0:=(3+x^2)/(1+x^2)^2
+--R
+--R
+--R 2
+--R x + 3
+--R (1) ------------
+--R 4 2
+--R x + 2x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 643
+
+--S 644 of 1406
+r0:=x/(1+x^2)+2*atan(x)
+--R
+--R
+--R 2
+--R (2x + 2)atan(x) + x
+--R (2) --------------------
+--R 2
+--R x + 1
+--R Type: Expression(Integer)
+--E 644
+
+--S 645 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (2x + 2)atan(x) + x
+--R (3) --------------------
+--R 2
+--R x + 1
+--R Type: Union(Expression(Integer),...)
+--E 645
+
+--S 646 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 646
+
+--S 647 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 647
+
+)clear all
+
+--S 648 of 1406
+t0:=(a+b*x^2)/(-a+b*x^2)^2
+--R
+--R
+--R 2
+--R b x + a
+--R (1) -------------------
+--R 2 4 2 2
+--R b x - 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 648
+
+--S 649 of 1406
+r0:=x/(a-b*x^2)
+--R
+--R
+--R x
+--R (2) - --------
+--R 2
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 649
+
+--S 650 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R x
+--R (3) - --------
+--R 2
+--R b x - a
+--R Type: Union(Expression(Integer),...)
+--E 650
+
+--S 651 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 651
+
+--S 652 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 652
+
+)clear all
+
+--S 653 of 1406
+t0:=(a+b*x^2)/(a-b*x^2)^2
+--R
+--R
+--R 2
+--R b x + a
+--R (1) -------------------
+--R 2 4 2 2
+--R b x - 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 653
+
+--S 654 of 1406
+r0:=x/(a-b*x^2)
+--R
+--R
+--R x
+--R (2) - --------
+--R 2
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 654
+
+--S 655 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R x
+--R (3) - --------
+--R 2
+--R b x - a
+--R Type: Union(Expression(Integer),...)
+--E 655
+
+--S 656 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 656
+
+--S 657 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 657
+
+)clear all
+
+--S 658 of 1406
+t0:=(1+x^2)/(16+x^2)^3
+--R
+--R
+--R 2
+--R x + 1
+--R (1) ------------------------
+--R 6 4 2
+--R x + 48x + 768x + 4096
+--R Type: Fraction(Polynomial(Integer))
+--E 658
+
+--S 659 of 1406
+r0:=-15/64*x/(16+x^2)^2+19/2048*x/(16+x^2)+19/8192*atan(1/4*x)
+--R
+--R
+--R 4 2 x 3
+--R (19x + 608x + 4864)atan(-) + 76x - 704x
+--R 4
+--R (2) ------------------------------------------
+--R 4 2
+--R 8192x + 262144x + 2097152
+--R Type: Expression(Integer)
+--E 659
+
+--S 660 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2 x 3
+--R (19x + 608x + 4864)atan(-) + 76x - 704x
+--R 4
+--R (3) ------------------------------------------
+--R 4 2
+--R 8192x + 262144x + 2097152
+--R Type: Union(Expression(Integer),...)
+--E 660
+
+--S 661 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 661
+
+--S 662 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 662
+
+)clear all
+
+--S 663 of 1406
+t0:=(1+2*x^2)/(x^5*(1+x^2)^3)
+--R
+--R
+--R 2
+--R 2x + 1
+--R (1) --------------------
+--R 11 9 7 5
+--R x + 3x + 3x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 663
+
+--S 664 of 1406
+r0:=(-1/4)/(x^4*(1+x^2)^2)
+--R
+--R
+--R 1
+--R -
+--R 4
+--R (2) - -------------
+--R 8 6 4
+--R x + 2x + x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 664
+
+--S 665 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - ---------------
+--R 8 6 4
+--R 4x + 8x + 4x
+--R Type: Union(Expression(Integer),...)
+--E 665
+
+--S 666 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 666
+
+--S 667 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 667
+
+)clear all
+
+--S 668 of 1406
+t0:=(1-x^2)^2/(-1+x^2)^2
+--R
+--R
+--R (1) 1
+--R Type: Fraction(Polynomial(Integer))
+--E 668
+
+--S 669 of 1406
+r0:=x
+--R
+--R
+--R (2) x
+--R Type: Variable(x)
+--E 669
+
+--S 670 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3) x
+--R Type: Union(Expression(Integer),...)
+--E 670
+
+--S 671 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 671
+
+--S 672 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 672
+
+)clear all
+
+--S 673 of 1406
+t0:=(-1+x^2)/(-2*x+x^3)
+--R
+--R
+--R 2
+--R x - 1
+--R (1) -------
+--R 3
+--R x - 2x
+--R Type: Fraction(Polynomial(Integer))
+--E 673
+
+--S 674 of 1406
+r0:=1/2*log(x)+1/4*log(2-x^2)
+--R
+--R
+--R 2
+--R 2log(x) + log(- x + 2)
+--R (2) -----------------------
+--R 4
+--R Type: Expression(Integer)
+--E 674
+
+--S 675 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R log(x - 2) + 2log(x)
+--R (3) ---------------------
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 675
+
+--S 676 of 1406
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R log(x - 2) - log(- x + 2)
+--R (4) ---------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 676
+
+--S 677 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 677
+
+)clear all
+
+--S 678 of 1406
+t0:=(1+x^2)/(3*x+x^3)
+--R
+--R
+--R 2
+--R x + 1
+--R (1) -------
+--R 3
+--R x + 3x
+--R Type: Fraction(Polynomial(Integer))
+--E 678
+
+--S 679 of 1406
+r0a:=1/3*log(x*(3+x^2))
+--R
+--R
+--R 3
+--R log(x + 3x)
+--R (2) ------------
+--R 3
+--R Type: Expression(Integer)
+--E 679
+
+--S 680 of 1406
+r0b:=1/3*log(x)+1/3*log(3+x^2)
+--R
+--R
+--R 2
+--R log(x + 3) + log(x)
+--R (3) --------------------
+--R 3
+--R Type: Expression(Integer)
+--E 680
+
+--S 681 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R log(x + 3x)
+--R (4) ------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 681
+
+--S 682 of 1406
+m0a:=a0-r0a
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 682
+
+--S 683 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 683
+
+--S 684 of 1406
+m0b:=a0-r0b
+--R
+--R
+--R 3 2
+--R log(x + 3x) - log(x + 3) - log(x)
+--R (7) -----------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 684
+
+--S 685 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 685
+
+)clear all
+
+--S 686 of 1406
+t0:=(a+3*b*x^2)/(a*x+b*x^3)
+--R
+--R
+--R 2
+--R 3b x + a
+--R (1) ----------
+--R 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 686
+
+--S 687 of 1406
+r0a:=log(x*(a+b*x^2))
+--R
+--R
+--R 3
+--R (2) log(b x + a x)
+--R Type: Expression(Integer)
+--E 687
+
+--S 688 of 1406
+r0b:=log(x)+log(a+b*x^2)
+--R
+--R
+--R 2
+--R (3) log(b x + a) + log(x)
+--R Type: Expression(Integer)
+--E 688
+
+--S 689 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R (4) log(b x + a x)
+--R Type: Union(Expression(Integer),...)
+--E 689
+
+--S 690 of 1406
+m0a:=a0-r0a
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 690
+
+--S 691 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 691
+
+--S 692 of 1406
+m0b:=a0-r0b
+--R
+--R
+--R 3 2
+--R (7) log(b x + a x) - log(b x + a) - log(x)
+--R Type: Expression(Integer)
+--E 692
+
+--S 693 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 693
+
+)clear all
+
+--S 694 of 1406
+t0:=x^5*(A+B*x^2)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 7 5 | 2
+--R (1) (B x + A x )\|b x + a
+--R Type: Expression(Integer)
+--E 694
+
+--S 695 of 1406
+r0:=1/3*a^2*(A*b-a*B)*(a+b*x^2)^(3/2)/b^4-1/5*a*(2*A*b-3*a*B)*_
+ (a+b*x^2)^(5/2)/b^4+1/7*(A*b-3*a*B)*(a+b*x^2)^(7/2)/b^4+_
+ 1/9*B*(a+b*x^2)^(9/2)/b^4
+--R
+--R
+--R (2)
+--R 4 8 4 3 6 3 2 2 4
+--R 35B b x + (45A b + 5B a b )x + (9A a b - 6B a b )x
+--R +
+--R 2 2 3 2 3 4
+--R (- 12A a b + 8B a b)x + 24A a b - 16B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4
+--R 315b
+--R Type: Expression(Integer)
+--E 695
+
+--S 696 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 16 4 2 3 14
+--R - 315B a b x + (- 405A a b - 4245B a b )x
+--R +
+--R 2 3 3 2 12 3 2 4 10
+--R (- 5481A a b - 15666B a b )x + (- 20412A a b - 21672B a b)x
+--R +
+--R 4 5 8 5 6
+--R (- 28560A a b - 10080B a )x - 13440A a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 18 5 4 16 4 2 3 14
+--R 35B b x + (45A b + 1440B a b )x + (1854A a b + 9999B a b )x
+--R +
+--R 2 3 3 2 12 3 2 4 10
+--R (12957A a b + 25242B a b )x + (33012A a b + 26712B a b)x
+--R +
+--R 4 5 8 5 6
+--R (35280A a b + 10080B a )x + 13440A a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a
+--R Type: Union(Expression(Integer),...)
+--E 696
+
+--S 697 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 5 5 4 8 5 4 6 3 6
+--R (24A a b - 16B a b )x + (960A a b - 640B a b )x
+--R +
+--R 6 3 7 2 4 7 2 8 2 8
+--R (5760A a b - 3840B a b )x + (10752A a b - 7168B a b)x + 6144A a b
+--R +
+--R 9
+--R - 4096B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 5 5 4 8 5 4 6 3 6
+--R (- 216A a b + 144B a b )x + (- 2880A a b + 1920B a b )x
+--R +
+--R 6 3 7 2 4 7 2 8 2
+--R (- 10368A a b + 6912B a b )x + (- 13824A a b + 9216B a b)x
+--R +
+--R 8 9
+--R - 6144A a b + 4096B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 8 8 7 6 2 6 4 3 5 2 4 4 +-+
+--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 8 8 2 7 6 3 6 4 4 5 2 5 4
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a b
+--R Type: Expression(Integer)
+--E 697
+
+--S 698 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 698
+
+)clear all
+
+--S 699 of 1406
+t0:=x^4*(A+B*x^2)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 6 4 | 2
+--R (1) (B x + A x )\|b x + a
+--R Type: Expression(Integer)
+--E 699
+
+--S 700 of 1406
+r0:=1/8*B*x^5*(a+b*x^2)^(3/2)/b+1/128*a^3*(8*A*b-5*a*B)*_
+ atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(7/2)-1/128*a^2*(8*A*b-_
+ 5*a*B)*x*sqrt(a+b*x^2)/b^3+1/192*a*(8*A*b-5*a*B)*x^3*_
+ sqrt(a+b*x^2)/b^2+1/48*(8*A*b-5*a*B)*x^5*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 3 4 x\|b
+--R (24A a b - 15B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 48B b x + (64A b + 8B a b )x + (16A a b - 10B a b)x
+--R +
+--R 2 3
+--R (- 24A a b + 15B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 3 +-+
+--R 384b \|b
+--R Type: Expression(Integer)
+--E 700
+
+--S 701 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 4 4 3 6 4 3 5 2 4
+--R (192A a b - 120B a b )x + (1920A a b - 1200B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (4608A a b - 2880B a b)x + 3072A a b - 1920B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 5 4 4 8 4 4 5 3 6
+--R (- 24A a b + 15B a b )x + (- 768A a b + 480B a b )x
+--R +
+--R 5 3 6 2 4 6 2 7 2
+--R (- 3840A a b + 2400B a b )x + (- 6144A a b + 3840B a b)x
+--R +
+--R 7 8
+--R - 3072A a b + 1920B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 7 15 7 6 13
+--R - 48B b x + (- 64A b - 1544B a b )x
+--R +
+--R 6 2 5 11 2 5 3 4 9
+--R (- 2064A a b - 7926B a b )x + (- 10728A a b - 13263B a b )x
+--R +
+--R 3 4 4 3 7 4 3 5 2 5
+--R (- 18176A a b - 7072B a b )x + (- 8448A a b - 864B a b )x
+--R +
+--R 5 2 6 3 6 7
+--R (4096A a b - 2560B a b)x + (3072A a b - 1920B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 7 15 7 6 13
+--R 384B b x + (512A b + 4288B a b )x
+--R +
+--R 6 2 5 11 2 5 3 4 9
+--R (5760A a b + 13680B a b )x + (18624A a b + 16776B a b )x
+--R +
+--R 3 4 4 3 7 4 3 5 2 5
+--R (22720A a b + 7304B a b )x + (6784A a b + 1904B a b )x
+--R +
+--R 5 2 6 3 6 7
+--R (- 5632A a b + 3520B a b)x + (- 3072A a b + 1920B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +-+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b )\|a \|b \|b x + a
+--R +
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +-+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b )\|b
+--R ,
+--R
+--R 3 4 4 3 6 4 3 5 2 4
+--R (384A a b - 240B a b )x + (3840A a b - 2400B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (9216A a b - 5760B a b)x + 6144A a b - 3840B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 5 4 4 8 4 4 5 3 6
+--R (- 48A a b + 30B a b )x + (- 1536A a b + 960B a b )x
+--R +
+--R 5 3 6 2 4 6 2 7 2
+--R (- 7680A a b + 4800B a b )x + (- 12288A a b + 7680B a b)x
+--R +
+--R 7 8
+--R - 6144A a b + 3840B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 7 15 7 6 13
+--R - 48B b x + (- 64A b - 1544B a b )x
+--R +
+--R 6 2 5 11 2 5 3 4 9
+--R (- 2064A a b - 7926B a b )x + (- 10728A a b - 13263B a b )x
+--R +
+--R 3 4 4 3 7 4 3 5 2 5
+--R (- 18176A a b - 7072B a b )x + (- 8448A a b - 864B a b )x
+--R +
+--R 5 2 6 3 6 7
+--R (4096A a b - 2560B a b)x + (3072A a b - 1920B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 7 15 7 6 13
+--R 384B b x + (512A b + 4288B a b )x
+--R +
+--R 6 2 5 11 2 5 3 4 9
+--R (5760A a b + 13680B a b )x + (18624A a b + 16776B a b )x
+--R +
+--R 3 4 4 3 7 4 3 5 2 5
+--R (22720A a b + 7304B a b )x + (6784A a b + 1904B a b )x
+--R +
+--R 5 2 6 3 6 7
+--R (- 5632A a b + 3520B a b)x + (- 3072A a b + 1920B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +---+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b )\|- b \|a \|b x + a
+--R +
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +---+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 701
+
+--S 702 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 4
+--R (8A a b - 5B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 4 x\|b
+--R (- 8A a b + 5B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 128b \|b
+--R Type: Expression(Integer)
+--E 702
+
+--S 703 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 703
+
+--S 704 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 3 4 +---+ x\|b
+--R (- 8A a b + 5B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 3 4 +-+ \|- b \|b x + a - \|- b \|a
+--R (16A a b - 10B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 128b \|- b \|b
+--R Type: Expression(Integer)
+--E 704
+
+--S 705 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 705
+
+)clear all
+
+--S 706 of 1406
+t0:=x^3*(A+B*x^2)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 5 3 | 2
+--R (1) (B x + A x )\|b x + a
+--R Type: Expression(Integer)
+--E 706
+
+--S 707 of 1406
+r0:=-1/3*a*(A*b-a*B)*(a+b*x^2)^(3/2)/b^3+1/5*(A*b-2*a*B)*_
+ (a+b*x^2)^(5/2)/b^3+1/7*B*(a+b*x^2)^(7/2)/b^3
+--R
+--R
+--R (2)
+--R 3 6 3 2 4 2 2 2 2
+--R 15B b x + (21A b + 3B a b )x + (7A a b - 4B a b)x - 14A a b
+--R +
+--R 3
+--R 8B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3
+--R 105b
+--R Type: Expression(Integer)
+--E 707
+
+--S 708 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 12 3 2 2 10
+--R - 105B a b x + (- 147A a b - 861B a b )x
+--R +
+--R 2 2 3 8 3 4 6 4 4
+--R (- 1225A a b - 1820B a b)x + (- 2660A a b - 1120B a )x - 1680A a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 14 4 3 12 3 2 2 10
+--R 15B b x + (21A b + 378B a b )x + (532A a b + 1631B a b )x
+--R +
+--R 2 2 3 8 3 4 6 4 4
+--R (2345A a b + 2380B a b)x + (3500A a b + 1120B a )x + 1680A a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (105b x + 2520a b x + 8400a b x + 6720a )\|a \|b x + a - 735a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 5880a b x - 11760a b x - 6720a
+--R Type: Union(Expression(Integer),...)
+--E 708
+
+--S 709 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 4 4 3 6 4 3 5 2 4
+--R (- 14A a b + 8B a b )x + (- 336A a b + 192B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (- 1120A a b + 640B a b)x - 896A a b + 512B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 4 4 3 6 4 3 5 2 4
+--R (98A a b - 56B a b )x + (784A a b - 448B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (1568A a b - 896B a b)x + 896A a b - 512B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +-+ | 2 6 6
+--R (105b x + 2520a b x + 8400a b x + 6720a b )\|a \|b x + a - 735a b x
+--R +
+--R 2 5 4 3 4 2 4 3
+--R - 5880a b x - 11760a b x - 6720a b
+--R Type: Expression(Integer)
+--E 709
+
+--S 710 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 710
+
+)clear all
+
+--S 711 of 1406
+t0:=x^2*(A+B*x^2)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (1) (B x + A x )\|b x + a
+--R Type: Expression(Integer)
+--E 711
+
+--S 712 of 1406
+r0:=1/6*B*x^3*(a+b*x^2)^(3/2)/b-1/16*a^2*(2*A*b-a*B)*_
+ atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)+1/16*a*(2*A*b-a*B)*_
+ x*sqrt(a+b*x^2)/b^2+1/8*(2*A*b-a*B)*x^3*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 x\|b
+--R (- 6A a b + 3B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 2 5 2 3 2 +-+ | 2
+--R (8B b x + (12A b + 2B a b)x + (6A a b - 3B a )x)\|b \|b x + a
+--R /
+--R 2 +-+
+--R 48b \|b
+--R Type: Expression(Integer)
+--E 712
+
+--S 713 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 3 2 4 3 2 4 2 4
+--R (36A a b - 18B a b )x + (192A a b - 96B a b)x + 192A a b
+--R +
+--R 5
+--R - 96B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (- 6A a b + 3B a b )x + (- 108A a b + 54B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (- 288A a b + 144B a b)x - 192A a b + 96B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R - 8B b x + (- 12A b - 146B a b )x + (- 222A a b - 417B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (- 684A a b - 298B a b )x + (- 672A a b + 80B a b)x
+--R +
+--R 4 5
+--R (- 192A a b + 96B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R 48B b x + (72A b + 316B a b )x + (492A a b + 570B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (996A a b + 270B a b )x + (768A a b - 128B a b)x
+--R +
+--R 4 5
+--R (192A a b - 96B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +-+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b )\|a \|b \|b x + a
+--R +
+--R 5 6 4 4 2 3 2 3 2 +-+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|b
+--R ,
+--R
+--R 2 3 3 2 4 3 2 4 2
+--R (- 72A a b + 36B a b )x + (- 384A a b + 192B a b)x
+--R +
+--R 4 5
+--R - 384A a b + 192B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (12A a b - 6B a b )x + (216A a b - 108B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (576A a b - 288B a b)x + 384A a b - 192B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R - 8B b x + (- 12A b - 146B a b )x + (- 222A a b - 417B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (- 684A a b - 298B a b )x + (- 672A a b + 80B a b)x
+--R +
+--R 4 5
+--R (- 192A a b + 96B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R 48B b x + (72A b + 316B a b )x + (492A a b + 570B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (996A a b + 270B a b )x + (768A a b - 128B a b)x
+--R +
+--R 4 5
+--R (192A a b - 96B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +---+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b )\|- b \|a \|b x + a
+--R +
+--R 5 6 4 4 2 3 2 3 2 +---+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 713
+
+--S 714 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3
+--R (2A a b - B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 3 x\|b
+--R (2A a b - B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 714
+
+--S 715 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 715
+
+--S 716 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 3 +---+ x\|b
+--R (2A a b - B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 3 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 4A a b + 2B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 16b \|- b \|b
+--R Type: Expression(Integer)
+--E 716
+
+--S 717 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 717
+
+)clear all
+
+--S 718 of 1406
+t0:=x*(A+B*x^2)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 3 | 2
+--R (1) (B x + A x)\|b x + a
+--R Type: Expression(Integer)
+--E 718
+
+--S 719 of 1406
+r0:=1/3*(A*b-a*B)*(a+b*x^2)^(3/2)/b^2+1/5*B*(a+b*x^2)^(5/2)/b^2
+--R
+--R
+--R +--------+
+--R 2 4 2 2 2 | 2
+--R (3B b x + (5A b + B a b)x + 5A a b - 2B a )\|b x + a
+--R (2) ---------------------------------------------------------
+--R 2
+--R 15b
+--R Type: Expression(Integer)
+--E 719
+
+--S 720 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 8 2 2 6 2 3 4
+--R - 15B a b x + (- 25A a b - 65B a b)x + (- 120A a b - 60B a )x
+--R +
+--R 3 2
+--R - 120A a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 10 3 2 8 2 2 6
+--R 3B b x + (5A b + 40B a b )x + (70A a b + 95B a b)x
+--R +
+--R 2 3 4 3 2
+--R (180A a b + 60B a )x + 120A a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a
+--R Type: Union(Expression(Integer),...)
+--E 720
+
+--S 721 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 3 2 4 3 2 4 2 4 5
+--R ((5A a b - 2B a b )x + (60A a b - 24B a b)x + 80A a b - 32B a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 3 3 2 4 3 2 4 2 4
+--R (- 25A a b + 10B a b )x + (- 100A a b + 40B a b)x - 80A a b
+--R +
+--R 5
+--R 32B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +-+ | 2 4 4 2 3 2
+--R (15b x + 180a b x + 240a b )\|a \|b x + a - 75a b x - 300a b x
+--R +
+--R 3 2
+--R - 240a b
+--R Type: Expression(Integer)
+--E 721
+
+--S 722 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 722
+
+)clear all
+
+--S 723 of 1406
+t0:=(A+B*x^2)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (1) (B x + A)\|b x + a
+--R Type: Expression(Integer)
+--E 723
+
+--S 724 of 1406
+r0:=1/4*B*x*(a+b*x^2)^(3/2)/b+1/8*a*(4*A*b-a*B)*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(3/2)+1/8*(4*A*b-a*B)*x*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 x\|b 3 +-+ | 2
+--R (4A a b - B a )atanh(-----------) + (2B b x + (4A b + B a)x)\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R ----------------------------------------------------------------------------
+--R +-+
+--R 8b\|b
+--R Type: Expression(Integer)
+--E 724
+
+--S 725 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((16A a b - 4B a b)x + 32A a b - 8B a )\|a \|b x + a
+--R +
+--R 3 2 2 4 2 2 3 2 3 4
+--R (- 4A a b + B a b )x + (- 32A a b + 8B a b)x - 32A a b + 8B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R - 2B b x + (- 4A b - 17B a b )x + (- 32A a b - 24B a b)x
+--R +
+--R 2 3
+--R (- 32A a b - 8B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 8B b x + (16A b + 28B a b )x + (48A a b + 28B a b)x
+--R +
+--R 2 3
+--R (32A a b + 8B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+
+--R (32b x + 64a b)\|a \|b \|b x + a + (- 8b x - 64a b x - 64a b)\|b
+--R ,
+--R
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((32A a b - 8B a b)x + 64A a b - 16B a )\|a \|b x + a
+--R +
+--R 3 2 2 4 2 2 3 2 3 4
+--R (- 8A a b + 2B a b )x + (- 64A a b + 16B a b)x - 64A a b + 16B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 3 7 3 2 5 2 2 3
+--R - 2B b x + (- 4A b - 17B a b )x + (- 32A a b - 24B a b)x
+--R +
+--R 2 3
+--R (- 32A a b - 8B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 8B b x + (16A b + 28B a b )x + (48A a b + 28B a b)x
+--R +
+--R 2 3
+--R (32A a b + 8B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 2 2 +---+ +-+ | 2
+--R (32b x + 64a b)\|- b \|a \|b x + a
+--R +
+--R 3 4 2 2 2 +---+
+--R (- 8b x - 64a b x - 64a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 725
+
+--S 726 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2
+--R (4A a b - B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R (- 4A a b + B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 8b\|b
+--R Type: Expression(Integer)
+--E 726
+
+--S 727 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 727
+
+--S 728 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +---+ x\|b
+--R (- 4A a b + B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (8A a b - 2B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 8b\|- b \|b
+--R Type: Expression(Integer)
+--E 728
+
+--S 729 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 729
+
+)clear all
+
+--S 730 of 1406
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R x
+--R Type: Expression(Integer)
+--E 730
+
+--S 731 of 1406
+r0:=1/3*B*(a+b*x^2)^(3/2)/b-A*atanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+_
+ A*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R +-+ \|b x + a 2 | 2
+--R - 3A b\|a atanh(-----------) + (B b x + 3A b + B a)\|b x + a
+--R +-+
+--R \|a
+--R (2) ---------------------------------------------------------------
+--R 3b
+--R Type: Expression(Integer)
+--E 731
+
+--S 732 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R ((3A a b x + 12A a )\|b x + a + (- 9A a b x - 12A a )\|a )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 2 2 | 2
+--R (- 3B a b x + (- 6A a b - 6B a )x )\|b x + a
+--R +
+--R 2 6 2 4 2 2 +-+
+--R (B b x + (3A b + 6B a b)x + (6A a b + 6B a )x )\|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a
+--R Type: Union(Expression(Integer),...)
+--E 732
+
+--S 733 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 2 | 2 2 2 2 +-+
+--R ((3A a b x + 12A a b)\|b x + a + (- 9A a b x - 12A a b)\|a )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 2 | 2 2 2 2 +-+
+--R ((3A a b x + 12A a b)\|b x + a + (- 9A a b x - 12A a b)\|a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 2 2 2 3 | 2
+--R ((3A a b + B a b)x + 12A a b + 4B a )\|b x + a
+--R +
+--R 2 2 2 2 3 +-+
+--R ((- 9A a b - 3B a b)x - 12A a b - 4B a )\|a
+--R /
+--R +--------+
+--R 2 2 +-+ | 2 2 2 2
+--R (3b x + 12a b)\|a \|b x + a - 9a b x - 12a b
+--R Type: Expression(Integer)
+--E 733
+
+--S 734 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 734
+
+)clear all
+
+--S 735 of 1406
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x^2
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 735
+
+--S 736 of 1406
+r0:=-A*(a+b*x^2)^(3/2)/(a*x)+1/2*(2*A*b+a*B)*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/sqrt(b)+1/2*(2*A*b+a*B)*x*sqrt(a+b*x^2)/a
+--R
+--R
+--R +-+ +--------+
+--R x\|b 2 +-+ | 2
+--R (2A b + B a)x atanh(-----------) + (B x - 2A)\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -------------------------------------------------------------
+--R +-+
+--R 2x\|b
+--R Type: Expression(Integer)
+--E 736
+
+--S 737 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 3 2 | 2
+--R ((2A b + B a b)x + (8A a b + 4B a )x)\|b x + a
+--R +
+--R 2 3 2 +-+
+--R ((- 6A b - 3B a b)x + (- 8A a b - 4B a )x)\|a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 4 2 +-+ +-+ | 2
+--R (- 3B b x + (6A b - 4B a)x + 8A a)\|a \|b \|b x + a
+--R +
+--R 2 6 2 4 2 2 2 +-+
+--R (B b x + (- 2A b + 5B a b)x + (- 10A a b + 4B a )x - 8A a )\|b
+--R /
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (2b x + 8a x)\|b \|b x + a + (- 6b x - 8a x)\|a \|b
+--R ,
+--R
+--R +--------+
+--R 2 3 2 | 2
+--R ((4A b + 2B a b)x + (16A a b + 8B a )x)\|b x + a
+--R +
+--R 2 3 2 +-+
+--R ((- 12A b - 6B a b)x + (- 16A a b - 8B a )x)\|a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R 4 2 +---+ +-+ | 2
+--R (- 3B b x + (6A b - 4B a)x + 8A a)\|- b \|a \|b x + a
+--R +
+--R 2 6 2 4 2 2 2 +---+
+--R (B b x + (- 2A b + 5B a b)x + (- 10A a b + 4B a )x - 8A a )\|- b
+--R /
+--R +--------+
+--R 3 +---+ | 2 3 +---+ +-+
+--R (2b x + 8a x)\|- b \|b x + a + (- 6b x - 8a x)\|- b \|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 737
+
+--S 738 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R (2A b + B a)log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R (- 2A b - B a)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 2\|b
+--R Type: Expression(Integer)
+--E 738
+
+--S 739 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 739
+
+--S 740 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R +---+ x\|b
+--R (- 2A b - B a)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R +-+ \|- b \|b x + a - \|- b \|a
+--R (4A b + 2B a)\|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 2\|- b \|b
+--R Type: Expression(Integer)
+--E 740
+
+--S 741 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 741
+
+)clear all
+
+--S 742 of 1406
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x^3
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 742
+
+--S 743 of 1406
+r0:=-1/2*A*(a+b*x^2)^(3/2)/(a*x^2)-1/2*(A*b+2*a*B)*_
+ atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)+1/2*(A*b+2*a*B)*sqrt(a+b*x^2)/a
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 2 \|b x + a 2 +-+ | 2
+--R (- A b - 2B a)x atanh(-----------) + (2B x - A)\|a \|b x + a
+--R +-+
+--R \|a
+--R (2) ---------------------------------------------------------------
+--R 2 +-+
+--R 2x \|a
+--R Type: Expression(Integer)
+--E 743
+
+--S 744 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 | 2
+--R ((A b + 2B a b)x + (4A a b + 8B a )x )\|b x + a
+--R +
+--R 2 4 2 2 +-+
+--R ((- 3A b - 6B a b)x + (- 4A a b - 8B a )x )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 2 2 | 2
+--R (- 4B a b x + 3A a b x + 4A a )\|b x + a
+--R +
+--R 2 6 2 4 2 2 +-+
+--R (2B b x + (- A b + 4B a b)x - 5A a b x - 4A a )\|a
+--R /
+--R +--------+
+--R 4 2 +-+ | 2 4 2 2
+--R (2b x + 8a x )\|a \|b x + a - 6a b x - 8a x
+--R Type: Union(Expression(Integer),...)
+--E 744
+
+--S 745 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|b x + a - \|a \|b x + a
+--R (A b + 2B a)log(------------------) + (A b + 2B a)atanh(-----------) + 2B a
+--R x +-+
+--R \|a
+--R ---------------------------------------------------------------------------
+--R +-+
+--R 2\|a
+--R Type: Expression(Integer)
+--E 745
+
+--S 746 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 746
+
+)clear all
+
+--S 747 of 1406
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x^4
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 747
+
+--S 748 of 1406
+r0:=-1/3*A*(a+b*x^2)^(3/2)/(a*x^3)+B*atanh(x*sqrt(b)/sqrt(a+b*x^2))*_
+ sqrt(b)-B*sqrt(a+b*x^2)/x
+--R
+--R
+--R +-+ +--------+
+--R 3 +-+ x\|b 2 | 2
+--R 3B a x \|b atanh(-----------) + ((- A b - 3B a)x - A a)\|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -------------------------------------------------------------------
+--R 3
+--R 3a x
+--R Type: Expression(Integer)
+--E 748
+
+--S 749 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 5 2 3 +-+ | 2
+--R (3B a b x + 12B a x )\|b \|b x + a
+--R +
+--R 5 2 3 +-+ +-+
+--R (- 9B a b x - 12B a x )\|a \|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R ((3A b + 9B a b)x + (7A a b + 12B a )x + 4A a )\|a \|b x + a
+--R +
+--R 3 2 6 2 2 4 2 3 2
+--R (- A b - 3B a b )x + (- 6A a b - 15B a b)x + (- 9A a b - 12B a )x
+--R +
+--R 3
+--R - 4A a
+--R /
+--R +--------+
+--R 5 2 3 | 2 5 2 3 +-+
+--R (3a b x + 12a x )\|b x + a + (- 9a b x - 12a x )\|a
+--R ,
+--R
+--R +--------+
+--R 5 2 3 +---+ | 2
+--R (6B a b x + 24B a x )\|- b \|b x + a
+--R +
+--R 5 2 3 +---+ +-+
+--R (- 18B a b x - 24B a x )\|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R ((3A b + 9B a b)x + (7A a b + 12B a )x + 4A a )\|a \|b x + a
+--R +
+--R 3 2 6 2 2 4 2 3 2
+--R (- A b - 3B a b )x + (- 6A a b - 15B a b)x + (- 9A a b - 12B a )x
+--R +
+--R 3
+--R - 4A a
+--R /
+--R +--------+
+--R 5 2 3 | 2 5 2 3 +-+
+--R (3a b x + 12a x )\|b x + a + (- 9a b x - 12a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 749
+
+--S 750 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R B\|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ x\|b
+--R - B\|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 750
+
+--S 751 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 751
+
+--S 752 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R +-+ x\|b +---+ \|b x + a - \|a
+--R (6) - B\|b atanh(-----------) + 2B\|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 752
+
+--S 753 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 753
+
+)clear all
+
+--S 754 of 1406
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x^5
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 754
+
+--S 755 of 1406
+r0:=-1/4*A*(a+b*x^2)^(3/2)/(a*x^4)+1/8*b*(A*b-4*a*B)*_
+ atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)+1/8*(A*b-4*a*B)*_
+ sqrt(a+b*x^2)/(a*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 4 \|b x + a
+--R (A b - 4B a b)x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R ((- A b - 4B a)x - 2A a)\|a \|b x + a
+--R /
+--R 4 +-+
+--R 8a x \|a
+--R Type: Expression(Integer)
+--E 755
+
+--S 756 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 2 2 6 2 2 3 4 | 2
+--R ((- 4A a b + 16B a b )x + (- 8A a b + 32B a b)x )\|b x + a
+--R +
+--R 4 3 8 3 2 2 6
+--R (A b - 4B a b )x + (8A a b - 32B a b )x
+--R +
+--R 2 2 3 4
+--R (8A a b - 32B a b)x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 3 2 2 6 2 2 3 4 3 4 2
+--R (A a b + 4B a b )x + (10A a b + 32B a b)x + (24A a b + 32B a )x
+--R +
+--R 4
+--R 16A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 2 6 2 2 3 4
+--R (- 4A a b - 16B a b )x + (- 20A a b - 48B a b)x
+--R +
+--R 3 4 2 4
+--R (- 32A a b - 32B a )x - 16A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 2 6 3 4 +-+ | 2 2 2 8 3 6 4 4
+--R (32a b x + 64a x )\|a \|b x + a - 8a b x - 64a b x - 64a x
+--R Type: Union(Expression(Integer),...)
+--E 756
+
+--S 757 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 2 \|b x + a - \|a
+--R (- A b + 4B a b)log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 2 \|b x + a
+--R (- A b + 4B a b)atanh(-----------)
+--R +-+
+--R \|a
+--R /
+--R +-+
+--R 8a\|a
+--R Type: Expression(Integer)
+--E 757
+
+--S 758 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 758
+
+)clear all
+
+--S 759 of 1406
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x^6
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 759
+
+--S 760 of 1406
+r0:=-1/5*A*(a+b*x^2)^(3/2)/(a*x^5)+1/15*(2*A*b-5*a*B)*(a+b*x^2)^(3/2)/(a^2*x^3)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 2 | 2
+--R ((2A b - 5B a b)x + (- A a b - 5B a )x - 3A a )\|b x + a
+--R (2) -------------------------------------------------------------
+--R 2 5
+--R 15a x
+--R Type: Expression(Integer)
+--E 760
+
+--S 761 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 8 3 2 2 6
+--R (- 10A b + 25B a b )x + (- 35A a b + 125B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (3A a b + 180B a b)x + (76A a b + 80B a )x + 48A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 4 10 4 2 3 8 2 3 3 2 6
+--R (2A b - 5B a b )x + (25A a b - 70B a b )x + (40A a b - 205B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 35A a b - 220B a b)x + (- 100A a b - 80B a )x - 48A a
+--R /
+--R +--------+
+--R 2 2 9 3 7 4 5 | 2
+--R (15a b x + 180a b x + 240a x )\|b x + a
+--R +
+--R 2 2 9 3 7 4 5 +-+
+--R (- 75a b x - 300a b x - 240a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 761
+
+--S 762 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 762
+
+--S 763 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 763
+
+)clear all
+
+--S 764 of 1406
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x^7
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 764
+
+--S 765 of 1406
+r0:=-1/6*A*(a+b*x^2)^(3/2)/(a*x^6)-1/16*b^2*(A*b-2*a*B)*_
+ atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)+1/8*(A*b-2*a*B)*_
+ sqrt(a+b*x^2)/(a*x^4)+1/16*b*(A*b-2*a*B)*sqrt(a+b*x^2)/(a^2*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 3 2 6 \|b x + a
+--R (- 3A b + 6B a b )x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R ((3A b - 6B a b)x + (- 2A a b - 12B a )x - 8A a )\|a \|b x + a
+--R /
+--R 2 6 +-+
+--R 48a x \|a
+--R Type: Expression(Integer)
+--E 765
+
+--S 766 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 2 4 10 2 4 3 3 8
+--R (18A a b - 36B a b )x + (96A a b - 192B a b )x
+--R +
+--R 3 3 4 2 6
+--R (96A a b - 192B a b )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 5 12 5 2 4 10
+--R (- 3A b + 6B a b )x + (- 54A a b + 108B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 144A a b + 288B a b )x + (- 96A a b + 192B a b )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 2 4 10 2 4 3 3 8
+--R (- 3A a b + 6B a b )x + (- 52A a b + 120B a b )x
+--R +
+--R 3 3 4 2 6 4 2 5 4
+--R (- 100A a b + 504B a b )x + (144A a b + 768B a b)x
+--R +
+--R 5 6 2 6
+--R (448A a b + 384B a )x + 256A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 2 4 10 2 4 3 3 8
+--R (18A a b - 36B a b )x + (102A a b - 300B a b )x
+--R +
+--R 3 3 4 2 6 4 2 5 4
+--R (68A a b - 840B a b )x + (- 336A a b - 960B a b)x
+--R +
+--R 5 6 2 6
+--R (- 576A a b - 384B a )x - 256A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 2 10 4 8 5 6 +-+ | 2 3 3 12
+--R (288a b x + 1536a b x + 1536a x )\|a \|b x + a - 48a b x
+--R +
+--R 4 2 10 5 8 6 6
+--R - 864a b x - 2304a b x - 1536a x
+--R Type: Union(Expression(Integer),...)
+--E 766
+
+--S 767 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 3 2 \|b x + a - \|a 3 2 \|b x + a
+--R (A b - 2B a b )log(------------------) + (A b - 2B a b )atanh(-----------)
+--R x +-+
+--R \|a
+--R ----------------------------------------------------------------------------
+--R 2 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 767
+
+--S 768 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 768
+
+)clear all
+
+--S 769 of 1406
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x^8
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 769
+
+--S 770 of 1406
+r0:=-1/7*A*(a+b*x^2)^(3/2)/(a*x^7)+1/35*(4*A*b-7*a*B)*_
+ (a+b*x^2)^(3/2)/(a^2*x^5)-2/105*b*(4*A*b-7*a*B)*(a+b*x^2)^(3/2)/(a^3*x^3)
+--R
+--R
+--R (2)
+--R 3 2 6 2 2 4 2 3 2
+--R (- 8A b + 14B a b )x + (4A a b - 7B a b)x + (- 3A a b - 21B a )x
+--R +
+--R 3
+--R - 15A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 7
+--R 105a x
+--R Type: Expression(Integer)
+--E 770
+
+--S 771 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 12 5 2 4 10
+--R (56A b - 98B a b )x + (420A a b - 735B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (693A a b - 1029B a b )x + (337A a b + 1064B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (920A a b + 2800B a b)x + (1872A a b + 1344B a )x + 960A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 6 14 6 2 5 12
+--R (- 8A b + 14B a b )x + (- 196A a b + 343B a b )x
+--R +
+--R 2 5 3 4 10 3 4 4 3 8
+--R (- 735A a b + 1260B a b )x + (- 826A a b + 763B a b )x
+--R +
+--R 4 3 5 2 6 5 2 6 4
+--R (- 623A a b - 2296B a b )x + (- 1736A a b - 3472B a b)x
+--R +
+--R 6 7 2 7
+--R (- 2352A a b - 1344B a )x - 960A a
+--R /
+--R +--------+
+--R 3 3 13 4 2 11 5 9 6 7 | 2
+--R (105a b x + 2520a b x + 8400a b x + 6720a x )\|b x + a
+--R +
+--R 3 3 13 4 2 11 5 9 6 7 +-+
+--R (- 735a b x - 5880a b x - 11760a b x - 6720a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 771
+
+--S 772 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 772
+
+--S 773 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 773
+
+)clear all
+
+--S 774 of 1406
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x^9
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R 9
+--R x
+--R Type: Expression(Integer)
+--E 774
+
+--S 775 of 1406
+r0:=-1/8*A*(a+b*x^2)^(3/2)/(a*x^8)+1/128*b^3*(5*A*b-8*a*B)*_
+ atanh(sqrt(a+b*x^2)/sqrt(a))/a^(7/2)+1/48*(5*A*b-8*a*B)*_
+ sqrt(a+b*x^2)/(a*x^6)+1/192*b*(5*A*b-8*a*B)*sqrt(a+b*x^2)/_
+ (a^2*x^4)-1/128*b^2*(5*A*b-8*a*B)*sqrt(a+b*x^2)/(a^3*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 4 3 8 \|b x + a
+--R (15A b - 24B a b )x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 3 2 6 2 2 4
+--R (- 15A b + 24B a b )x + (10A a b - 16B a b)x
+--R +
+--R 2 3 2 3
+--R (- 8A a b - 64B a )x - 48A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R /
+--R 3 8 +-+
+--R 384a x \|a
+--R Type: Expression(Integer)
+--E 775
+
+--S 776 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 2 6 14 2 6 3 5 12
+--R (- 120A a b + 192B a b )x + (- 1200A a b + 1920B a b )x
+--R +
+--R 3 5 4 4 10 4 4 5 3 8
+--R (- 2880A a b + 4608B a b )x + (- 1920A a b + 3072B a b )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 8 7 16 7 2 6 14
+--R (15A b - 24B a b )x + (480A a b - 768B a b )x
+--R +
+--R 2 6 3 5 12 3 5 4 4 10
+--R (2400A a b - 3840B a b )x + (3840A a b - 6144B a b )x
+--R +
+--R 4 4 5 3 8
+--R (1920A a b - 3072B a b )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 7 2 6 14 2 6 3 5 12
+--R (15A a b - 24B a b )x + (470A a b - 752B a b )x
+--R +
+--R 3 5 4 4 10 4 4 5 3 8
+--R (2088A a b - 3264B a b )x + (2544A a b - 1536B a b )x
+--R +
+--R 5 3 6 2 6 6 2 7 4
+--R (2176A a b + 11264B a b )x + (8448A a b + 18432B a b)x
+--R +
+--R 7 8 2 8
+--R (13312A a b + 8192B a )x + 6144A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 2 6 14 2 6 3 5 12
+--R (- 120A a b + 192B a b )x + (- 1240A a b + 1984B a b )x
+--R +
+--R 3 5 4 4 10 4 4 5 3 8
+--R (- 3264A a b + 4608B a b )x + (- 3168A a b - 2304B a b )x
+--R +
+--R 5 3 6 2 6 6 2 7 4
+--R (- 5120A a b - 19456B a b )x + (- 14336A a b - 22528B a b)x
+--R +
+--R 7 8 2 8
+--R (- 16384A a b - 8192B a )x - 6144A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 4 3 14 5 2 12 6 10 7 8 +-+ | 2
+--R (3072a b x + 30720a b x + 73728a b x + 49152a x )\|a \|b x + a
+--R +
+--R 4 4 16 5 3 14 6 2 12 7 10 8 8
+--R - 384a b x - 12288a b x - 61440a b x - 98304a b x - 49152a x
+--R Type: Union(Expression(Integer),...)
+--E 776
+
+--S 777 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 4 3 \|b x + a - \|a
+--R (- 5A b + 8B a b )log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 4 3 \|b x + a
+--R (- 5A b + 8B a b )atanh(-----------)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+
+--R 128a \|a
+--R Type: Expression(Integer)
+--E 777
+
+--S 778 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 778
+
+)clear all
+
+--S 779 of 1406
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x^10
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R 10
+--R x
+--R Type: Expression(Integer)
+--E 779
+
+--S 780 of 1406
+r0:=-1/9*A*(a+b*x^2)^(3/2)/(a*x^9)+1/21*(2*A*b-3*a*B)*(a+b*x^2)^(3/2)/_
+ (a^2*x^7)-4/105*b*(2*A*b-3*a*B)*(a+b*x^2)^(3/2)/(a^3*x^5)+_
+ 8/315*b^2*(2*A*b-3*a*B)*(a+b*x^2)^(3/2)/(a^4*x^3)
+--R
+--R
+--R (2)
+--R 4 3 8 3 2 2 6 2 2 3 4
+--R (16A b - 24B a b )x + (- 8A a b + 12B a b )x + (6A a b - 9B a b)x
+--R +
+--R 3 4 2 4
+--R (- 5A a b - 45B a )x - 35A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4 9
+--R 315a x
+--R Type: Expression(Integer)
+--E 780
+
+--S 781 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 16 7 2 6 14
+--R (- 144A b + 216B a b )x + (- 1848A a b + 2772B a b )x
+--R +
+--R 2 6 3 5 12 3 5 4 4 10
+--R (- 6006A a b + 9009B a b )x + (- 6435A a b + 10125B a b )x
+--R +
+--R 4 4 5 3 8 5 3 6 2 6
+--R (- 1165A a b + 8520B a b )x + (4952A a b + 21552B a b )x
+--R +
+--R 6 2 7 4 7 8 2 8
+--R (16464A a b + 28224B a b)x + (21440A a b + 11520B a )x + 8960A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 8 18 8 2 7 16
+--R (16A b - 24B a b )x + (648A a b - 972B a b )x
+--R +
+--R 2 7 3 6 14 3 6 4 5 12
+--R (4158A a b - 6237B a b )x + (9009A a b - 13566B a b )x
+--R +
+--R 4 5 5 4 10 5 4 6 3 8
+--R (7200A a b - 13005B a b )x + (- 243A a b - 16488B a b )x
+--R +
+--R 6 3 7 2 6 7 2 8 4
+--R (- 11064A a b - 34224B a b )x + (- 26064A a b - 33984B a b)x
+--R +
+--R 8 9 2 9
+--R (- 25920A a b - 11520B a )x - 8960A a
+--R /
+--R 4 4 17 5 3 15 6 2 13 7 11 8 9
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 4 17 5 3 15 6 2 13 7 11
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 8 9
+--R - 80640a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 781
+
+--S 782 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 782
+
+--S 783 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 783
+
+)clear all
+
+--S 784 of 1406
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x^11
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R 11
+--R x
+--R Type: Expression(Integer)
+--E 784
+
+--S 785 of 1406
+r0:=-1/10*A*(a+b*x^2)^(3/2)/(a*x^10)-1/256*b^4*(7*A*b-10*a*B)*_
+ atanh(sqrt(a+b*x^2)/sqrt(a))/a^(9/2)+1/80*(7*A*b-10*a*B)*_
+ sqrt(a+b*x^2)/(a*x^8)+1/480*b*(7*A*b-10*a*B)*sqrt(a+b*x^2)/_
+ (a^2*x^6)-1/384*b^2*(7*A*b-10*a*B)*sqrt(a+b*x^2)/(a^3*x^4)+_
+ 1/256*b^3*(7*A*b-10*a*B)*sqrt(a+b*x^2)/(a^4*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 5 4 10 \|b x + a
+--R (- 105A b + 150B a b )x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 3 8 3 2 2 6
+--R (105A b - 150B a b )x + (- 70A a b + 100B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (56A a b - 80B a b)x + (- 48A a b - 480B a )x - 384A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R /
+--R 4 10 +-+
+--R 3840a x \|a
+--R Type: Expression(Integer)
+--E 785
+
+--S 786 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 2 8 18 2 8 3 7 16
+--R (1050A a b - 1500B a b )x + (16800A a b - 24000B a b )x
+--R +
+--R 3 7 4 6 14
+--R (70560A a b - 100800B a b )x
+--R +
+--R 4 6 5 5 12 5 5 6 4 10
+--R (107520A a b - 153600B a b )x + (53760A a b - 76800B a b )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 10 9 20 9 2 8 18
+--R (- 105A b + 150B a b )x + (- 5250A a b + 7500B a b )x
+--R +
+--R 2 8 3 7 16
+--R (- 42000A a b + 60000B a b )x
+--R +
+--R 3 7 4 6 14
+--R (- 117600A a b + 168000B a b )x
+--R +
+--R 4 6 5 5 12
+--R (- 134400A a b + 192000B a b )x
+--R +
+--R 5 5 6 4 10
+--R (- 53760A a b + 76800B a b )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 9 2 8 18 2 8 3 7 16
+--R (- 105A a b + 150B a b )x + (- 5180A a b + 7400B a b )x
+--R +
+--R 3 7 4 6 14 4 6 5 5 12
+--R (- 38556A a b + 55080B a b )x + (- 92352A a b + 132480B a b )x
+--R +
+--R 5 5 6 4 10 6 4 7 3 8
+--R (- 75616A a b + 136000B a b )x + (11520A a b + 230400B a b )x
+--R +
+--R 7 3 8 2 6 8 2 9 4
+--R (171520A a b + 588800B a b )x + (462848A a b + 655360B a b)x
+--R +
+--R 9 10 2 10
+--R (516096A a b + 245760B a )x + 196608A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 2 8 18 2 8 3 7 16
+--R (1050A a b - 1500B a b )x + (17150A a b - 24500B a b )x
+--R +
+--R 3 7 4 6 14 4 6 5 5 12
+--R (76020A a b - 108600B a b )x + (128880A a b - 189600B a b )x
+--R +
+--R 5 5 6 4 10 6 4 7 3 8
+--R (77152A a b - 208960B a b )x + (- 64000A a b - 458240B a b )x
+--R +
+--R 7 3 8 2 6 8 2 9 4
+--R (- 350720A a b - 885760B a b )x + (- 696320A a b - 778240B a b)x
+--R +
+--R 9 10 2 10
+--R (- 614400A a b - 245760B a )x - 196608A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 5 4 18 6 3 16 7 2 14 8 12
+--R 38400a b x + 614400a b x + 2580480a b x + 3932160a b x
+--R +
+--R 9 10
+--R 1966080a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 5 20 6 4 18 7 3 16 8 2 14
+--R - 3840a b x - 192000a b x - 1536000a b x - 4300800a b x
+--R +
+--R 9 12 10 10
+--R - 4915200a b x - 1966080a x
+--R Type: Union(Expression(Integer),...)
+--E 786
+
+--S 787 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 5 4 \|b x + a - \|a
+--R (7A b - 10B a b )log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 5 4 \|b x + a
+--R (7A b - 10B a b )atanh(-----------)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 256a \|a
+--R Type: Expression(Integer)
+--E 787
+
+--S 788 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 788
+
+)clear all
+
+--S 789 of 1406
+t0:=x^5*(a+b*x^2)^(3/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 9 7 5 | 2
+--R (1) (B b x + (A b + B a)x + A a x )\|b x + a
+--R Type: Expression(Integer)
+--E 789
+
+--S 790 of 1406
+r0:=1/5*a^2*(A*b-a*B)*(a+b*x^2)^(5/2)/b^4-1/7*a*(2*A*b-3*a*B)*_
+ (a+b*x^2)^(7/2)/b^4+1/9*(A*b-3*a*B)*(a+b*x^2)^(9/2)/b^4+_
+ 1/11*B*(a+b*x^2)^(11/2)/b^4
+--R
+--R
+--R (2)
+--R 5 10 5 4 8 4 2 3 6
+--R 315B b x + (385A b + 420B a b )x + (550A a b + 15B a b )x
+--R +
+--R 2 3 3 2 4 3 2 4 2 4 5
+--R (33A a b - 18B a b )x + (- 44A a b + 24B a b)x + 88A a b - 48B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4
+--R 3465b
+--R Type: Expression(Integer)
+--E 790
+
+--S 791 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 20 6 2 5 18
+--R - 3465B a b x + (- 4235A a b - 73920B a b )x
+--R +
+--R 2 5 3 4 16
+--R (- 90750A a b - 480645B a b )x
+--R +
+--R 3 4 4 3 14
+--R (- 595683A a b - 1407582B a b )x
+--R +
+--R 4 3 5 2 12
+--R (- 1768536A a b - 2084544B a b )x
+--R +
+--R 5 2 6 10 6 7 8
+--R (- 2664816A a b - 1530144B a b)x + (- 1995840A a b - 443520B a )x
+--R +
+--R 7 6
+--R - 591360A a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 22 7 6 20
+--R 315B b x + (385A b + 19635B a b )x
+--R +
+--R 6 2 5 18 2 5 3 4 16
+--R (24035A a b + 220935B a b )x + (272283A a b + 1002177B a b )x
+--R +
+--R 3 4 4 3 14
+--R (1248489A a b + 2286306B a b )x
+--R +
+--R 4 3 5 2 12
+--R (2888424A a b + 2794176B a b )x
+--R +
+--R 5 2 6 10 6 7 8
+--R (3588816A a b + 1751904B a b)x + (2291520A a b + 443520B a )x
+--R +
+--R 7 6
+--R 591360A a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 5 10 4 8 2 3 6 3 2 4
+--R 3465b x + 207900a b x + 1940400a b x + 6209280a b x
+--R +
+--R 4 2 5
+--R 7983360a b x + 3548160a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4
+--R - 38115a b x - 762300a b x - 4268880a b x - 9757440a b x
+--R +
+--R 5 2 6
+--R - 9757440a b x - 3548160a
+--R Type: Union(Expression(Integer),...)
+--E 791
+
+--S 792 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 6 6 5 10 6 5 7 4 8
+--R (88A a b - 48B a b )x + (5280A a b - 2880B a b )x
+--R +
+--R 7 4 8 3 6 8 3 9 2 4
+--R (49280A a b - 26880B a b )x + (157696A a b - 86016B a b )x
+--R +
+--R 9 2 10 2 10 11
+--R (202752A a b - 110592B a b)x + 90112A a b - 49152B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 6 6 5 10 6 5 7 4 8
+--R (- 968A a b + 528B a b )x + (- 19360A a b + 10560B a b )x
+--R +
+--R 7 4 8 3 6 8 3 9 2 4
+--R (- 108416A a b + 59136B a b )x + (- 247808A a b + 135168B a b )x
+--R +
+--R 9 2 10 2 10 11
+--R (- 247808A a b + 135168B a b)x - 90112A a b + 49152B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 9 10 8 8 2 7 6 3 6 4
+--R 3465b x + 207900a b x + 1940400a b x + 6209280a b x
+--R +
+--R 4 5 2 5 4
+--R 7983360a b x + 3548160a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 10 2 8 8 3 7 6 4 6 4
+--R - 38115a b x - 762300a b x - 4268880a b x - 9757440a b x
+--R +
+--R 5 5 2 6 4
+--R - 9757440a b x - 3548160a b
+--R Type: Expression(Integer)
+--E 792
+
+--S 793 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 793
+
+)clear all
+
+--S 794 of 1406
+t0:=x^4*(a+b*x^2)^(3/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 8 6 4 | 2
+--R (1) (B b x + (A b + B a)x + A a x )\|b x + a
+--R Type: Expression(Integer)
+--E 794
+
+--S 795 of 1406
+r0:=1/16*(2*A*b-a*B)*x^5*(a+b*x^2)^(3/2)/b+1/10*B*x^5*(a+b*x^2)^(5/2)/b+_
+ 3/256*a^4*(2*A*b-a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(7/2)-_
+ 3/256*a^3*(2*A*b-a*B)*x*sqrt(a+b*x^2)/b^3+1/128*a^2*_
+ (2*A*b-a*B)*x^3*sqrt(a+b*x^2)/b^2+1/32*a*(2*A*b-a*B)*x^5*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 4 5 x\|b
+--R (30A a b - 15B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 128B b x + (160A b + 176B a b )x + (240A a b + 8B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (20A a b - 10B a b)x + (- 30A a b + 15B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 3 +-+
+--R 1280b \|b
+--R Type: Expression(Integer)
+--E 795
+
+--S 796 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 5 5 4 8 5 4 6 3 6
+--R (300A a b - 150B a b )x + (4800A a b - 2400B a b )x
+--R +
+--R 6 3 7 2 4 7 2 8 2
+--R (20160A a b - 10080B a b )x + (30720A a b - 15360B a b)x
+--R +
+--R 8 9
+--R 15360A a b - 7680B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 6 5 5 10 5 5 6 4 8
+--R (- 30A a b + 15B a b )x + (- 1500A a b + 750B a b )x
+--R +
+--R 6 4 7 3 6 7 3 8 2 4
+--R (- 12000A a b + 6000B a b )x + (- 33600A a b + 16800B a b )x
+--R +
+--R 8 2 9 2 9 10
+--R (- 38400A a b + 19200B a b)x - 15360A a b + 7680B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 9 19 9 8 17
+--R - 128B b x + (- 160A b - 6576B a b )x
+--R +
+--R 8 2 7 15 2 7 3 6 13
+--R (- 8240A a b - 60008B a b )x + (- 76020A a b - 214150B a b )x
+--R +
+--R 3 6 4 5 11
+--R (- 276170A a b - 363675B a b )x
+--R +
+--R 4 5 5 4 9
+--R (- 480100A a b - 296526B a b )x
+--R +
+--R 5 4 6 3 7 6 3 7 2 5
+--R (- 399520A a b - 95152B a b )x + (- 114880A a b - 8096B a b )x
+--R +
+--R 7 2 8 3 8 9
+--R (28160A a b - 14080B a b)x + (15360A a b - 7680B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 9 19 9 8 17
+--R 1280B b x + (1600A b + 23520B a b )x
+--R +
+--R 8 2 7 15 2 7 3 6 13
+--R (29600A a b + 136496B a b )x + (174120A a b + 364780B a b )x
+--R +
+--R 3 6 4 5 11 4 5 5 4 9
+--R (474140A a b + 500210B a b )x + (664340A a b + 343670B a b )x
+--R +
+--R 5 4 6 3 7 6 3 7 2 5
+--R (459520A a b + 97920B a b )x + (102720A a b + 14176B a b )x
+--R +
+--R 7 2 8 3 8 9
+--R (- 35840A a b + 17920B a b)x + (- 15360A a b + 7680B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 7 8 6 6 2 5 4 3 4 2
+--R 12800b x + 204800a b x + 860160a b x + 1310720a b x
+--R +
+--R 4 3
+--R 655360a b
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 8 10 7 8 2 6 6 3 5 4
+--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x
+--R +
+--R 4 4 2 5 3
+--R - 1638400a b x - 655360a b
+--R *
+--R +-+
+--R \|b
+--R ,
+--R
+--R 4 5 5 4 8 5 4 6 3 6
+--R (600A a b - 300B a b )x + (9600A a b - 4800B a b )x
+--R +
+--R 6 3 7 2 4 7 2 8 2
+--R (40320A a b - 20160B a b )x + (61440A a b - 30720B a b)x
+--R +
+--R 8 9
+--R 30720A a b - 15360B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 6 5 5 10 5 5 6 4 8
+--R (- 60A a b + 30B a b )x + (- 3000A a b + 1500B a b )x
+--R +
+--R 6 4 7 3 6 7 3 8 2 4
+--R (- 24000A a b + 12000B a b )x + (- 67200A a b + 33600B a b )x
+--R +
+--R 8 2 9 2 9 10
+--R (- 76800A a b + 38400B a b)x - 30720A a b + 15360B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 9 19 9 8 17
+--R - 128B b x + (- 160A b - 6576B a b )x
+--R +
+--R 8 2 7 15 2 7 3 6 13
+--R (- 8240A a b - 60008B a b )x + (- 76020A a b - 214150B a b )x
+--R +
+--R 3 6 4 5 11
+--R (- 276170A a b - 363675B a b )x
+--R +
+--R 4 5 5 4 9
+--R (- 480100A a b - 296526B a b )x
+--R +
+--R 5 4 6 3 7 6 3 7 2 5
+--R (- 399520A a b - 95152B a b )x + (- 114880A a b - 8096B a b )x
+--R +
+--R 7 2 8 3 8 9
+--R (28160A a b - 14080B a b)x + (15360A a b - 7680B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 9 19 9 8 17
+--R 1280B b x + (1600A b + 23520B a b )x
+--R +
+--R 8 2 7 15 2 7 3 6 13
+--R (29600A a b + 136496B a b )x + (174120A a b + 364780B a b )x
+--R +
+--R 3 6 4 5 11 4 5 5 4 9
+--R (474140A a b + 500210B a b )x + (664340A a b + 343670B a b )x
+--R +
+--R 5 4 6 3 7 6 3 7 2 5
+--R (459520A a b + 97920B a b )x + (102720A a b + 14176B a b )x
+--R +
+--R 7 2 8 3 8 9
+--R (- 35840A a b + 17920B a b)x + (- 15360A a b + 7680B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R 7 8 6 6 2 5 4 3 4 2
+--R 12800b x + 204800a b x + 860160a b x + 1310720a b x
+--R +
+--R 4 3
+--R 655360a b
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 8 10 7 8 2 6 6 3 5 4
+--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x
+--R +
+--R 4 4 2 5 3
+--R - 1638400a b x - 655360a b
+--R *
+--R +---+
+--R \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 796
+
+--S 797 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 5
+--R (6A a b - 3B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 4 5 x\|b
+--R (- 6A a b + 3B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 256b \|b
+--R Type: Expression(Integer)
+--E 797
+
+--S 798 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 798
+
+--S 799 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 4 5 +---+ x\|b
+--R (- 6A a b + 3B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 4 5 +-+ \|- b \|b x + a - \|- b \|a
+--R (12A a b - 6B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 256b \|- b \|b
+--R Type: Expression(Integer)
+--E 799
+
+--S 800 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 800
+
+)clear all
+
+--S 801 of 1406
+t0:=x^3*(a+b*x^2)^(3/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 7 5 3 | 2
+--R (1) (B b x + (A b + B a)x + A a x )\|b x + a
+--R Type: Expression(Integer)
+--E 801
+
+--S 802 of 1406
+r0:=-1/5*a*(A*b-a*B)*(a+b*x^2)^(5/2)/b^3+1/7*(A*b-2*a*B)*_
+ (a+b*x^2)^(7/2)/b^3+1/9*B*(a+b*x^2)^(9/2)/b^3
+--R
+--R
+--R (2)
+--R 4 8 4 3 6 3 2 2 4
+--R 35B b x + (45A b + 50B a b )x + (72A a b + 3B a b )x
+--R +
+--R 2 2 3 2 3 4
+--R (9A a b - 4B a b)x - 18A a b + 8B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3
+--R 315b
+--R Type: Expression(Integer)
+--E 802
+
+--S 803 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 16 5 2 4 14
+--R - 315B a b x + (- 405A a b - 4650B a b )x
+--R +
+--R 2 4 3 3 12 3 3 4 2 10
+--R (- 6048A a b - 21147B a b )x + (- 28161A a b - 42084B a b )x
+--R +
+--R 4 2 5 8 5 6 6
+--R (- 57960A a b - 38640B a b)x + (- 55440A a b - 13440B a )x
+--R +
+--R 6 4
+--R - 20160A a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 18 6 5 16 5 2 4 14
+--R 35B b x + (45A b + 1485B a b )x + (1917A a b + 11853B a b )x
+--R +
+--R 2 4 3 3 12 3 3 4 2 10
+--R (15561A a b + 38199B a b )x + (51471A a b + 59724B a b )x
+--R +
+--R 4 2 5 8 5 6 6 6 4
+--R (83160A a b + 45360B a b)x + (65520A a b + 13440B a )x + 20160A a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a
+--R Type: Union(Expression(Integer),...)
+--E 803
+
+--S 804 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 5 5 4 8 5 4 6 3 6
+--R (- 18A a b + 8B a b )x + (- 720A a b + 320B a b )x
+--R +
+--R 6 3 7 2 4 7 2 8 2
+--R (- 4320A a b + 1920B a b )x + (- 8064A a b + 3584B a b)x
+--R +
+--R 8 9
+--R - 4608A a b + 2048B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 5 5 4 8 5 4 6 3 6
+--R (162A a b - 72B a b )x + (2160A a b - 960B a b )x
+--R +
+--R 6 3 7 2 4 7 2 8 2 8
+--R (7776A a b - 3456B a b )x + (10368A a b - 4608B a b)x + 4608A a b
+--R +
+--R 9
+--R - 2048B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +-+
+--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 8 2 6 6 3 5 4 4 4 2 5 3
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a b
+--R Type: Expression(Integer)
+--E 804
+
+--S 805 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 805
+
+)clear all
+
+--S 806 of 1406
+t0:=x^2*(a+b*x^2)^(3/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 6 4 2 | 2
+--R (1) (B b x + (A b + B a)x + A a x )\|b x + a
+--R Type: Expression(Integer)
+--E 806
+
+--S 807 of 1406
+r0:=1/48*(8*A*b-3*a*B)*x^3*(a+b*x^2)^(3/2)/b+1/8*B*x^3*_
+ (a+b*x^2)^(5/2)/b-1/128*a^3*(8*A*b-3*a*B)*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(5/2)+1/128*a^2*(8*A*b-3*a*B)*x*_
+ sqrt(a+b*x^2)/b^2+1/64*a*(8*A*b-3*a*B)*x^3*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 3 4 x\|b
+--R (- 24A a b + 9B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 48B b x + (64A b + 72B a b )x + (112A a b + 6B a b)x
+--R +
+--R 2 3
+--R (24A a b - 9B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 2 +-+
+--R 384b \|b
+--R Type: Expression(Integer)
+--E 807
+
+--S 808 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 4 4 3 6 4 3 5 2 4
+--R (192A a b - 72B a b )x + (1920A a b - 720B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (4608A a b - 1728B a b)x + 3072A a b - 1152B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 5 4 4 8 4 4 5 3 6
+--R (- 24A a b + 9B a b )x + (- 768A a b + 288B a b )x
+--R +
+--R 5 3 6 2 4 6 2 7 2
+--R (- 3840A a b + 1440B a b )x + (- 6144A a b + 2304B a b)x
+--R +
+--R 7 8
+--R - 3072A a b + 1152B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 7 15 7 6 13
+--R - 48B b x + (- 64A b - 1608B a b )x
+--R +
+--R 6 2 5 11 2 5 3 4 9
+--R (- 2160A a b - 9990B a b )x + (- 13848A a b - 23991B a b )x
+--R +
+--R 3 4 4 3 7 4 3 5 2 5
+--R (- 35072A a b - 25248B a b )x + (- 40704A a b - 9312B a b )x
+--R +
+--R 5 2 6 3 6 7
+--R (- 20480A a b + 1536B a b)x + (- 3072A a b + 1152B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 7 15 7 6 13
+--R 384B b x + (512A b + 4800B a b )x
+--R +
+--R 6 2 5 11 2 5 3 4 9
+--R (6528A a b + 19440B a b )x + (27456A a b + 35400B a b )x
+--R +
+--R 3 4 4 3 7 4 3 5 2 5
+--R (53056A a b + 30024B a b )x + (50560A a b + 8688B a b )x
+--R +
+--R 5 2 6 3 6 7
+--R (22016A a b - 2112B a b)x + (3072A a b - 1152B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 +-+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b )\|a \|b \|b x + a
+--R +
+--R 6 8 5 6 2 4 4 3 3 2 4 2 +-+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b )\|b
+--R ,
+--R
+--R 3 4 4 3 6 4 3 5 2 4
+--R (- 384A a b + 144B a b )x + (- 3840A a b + 1440B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (- 9216A a b + 3456B a b)x - 6144A a b + 2304B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 5 4 4 8 4 4 5 3 6
+--R (48A a b - 18B a b )x + (1536A a b - 576B a b )x
+--R +
+--R 5 3 6 2 4 6 2 7 2
+--R (7680A a b - 2880B a b )x + (12288A a b - 4608B a b)x
+--R +
+--R 7 8
+--R 6144A a b - 2304B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 7 15 7 6 13
+--R - 48B b x + (- 64A b - 1608B a b )x
+--R +
+--R 6 2 5 11 2 5 3 4 9
+--R (- 2160A a b - 9990B a b )x + (- 13848A a b - 23991B a b )x
+--R +
+--R 3 4 4 3 7 4 3 5 2 5
+--R (- 35072A a b - 25248B a b )x + (- 40704A a b - 9312B a b )x
+--R +
+--R 5 2 6 3 6 7
+--R (- 20480A a b + 1536B a b)x + (- 3072A a b + 1152B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 7 15 7 6 13
+--R 384B b x + (512A b + 4800B a b )x
+--R +
+--R 6 2 5 11 2 5 3 4 9
+--R (6528A a b + 19440B a b )x + (27456A a b + 35400B a b )x
+--R +
+--R 3 4 4 3 7 4 3 5 2 5
+--R (53056A a b + 30024B a b )x + (50560A a b + 8688B a b )x
+--R +
+--R 5 2 6 3 6 7
+--R (22016A a b - 2112B a b)x + (3072A a b - 1152B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 +---+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b )\|- b \|a \|b x + a
+--R +
+--R 6 8 5 6 2 4 4 3 3 2 4 2 +---+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 808
+
+--S 809 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 4
+--R (8A a b - 3B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 4 x\|b
+--R (8A a b - 3B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 128b \|b
+--R Type: Expression(Integer)
+--E 809
+
+--S 810 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 810
+
+--S 811 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 3 4 +---+ x\|b
+--R (8A a b - 3B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 3 4 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 16A a b + 6B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 128b \|- b \|b
+--R Type: Expression(Integer)
+--E 811
+
+--S 812 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 812
+
+)clear all
+
+--S 813 of 1406
+t0:=x*(a+b*x^2)^(3/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 5 3 | 2
+--R (1) (B b x + (A b + B a)x + A a x)\|b x + a
+--R Type: Expression(Integer)
+--E 813
+
+--S 814 of 1406
+r0:=1/5*(A*b-a*B)*(a+b*x^2)^(5/2)/b^2+1/7*B*(a+b*x^2)^(7/2)/b^2
+--R
+--R
+--R (2)
+--R 3 6 3 2 4 2 2 2 2 3
+--R (5B b x + (7A b + 8B a b )x + (14A a b + B a b)x + 7A a b - 2B a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2
+--R 35b
+--R Type: Expression(Integer)
+--E 814
+
+--S 815 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 12 4 2 3 10
+--R - 35B a b x + (- 49A a b - 336B a b )x
+--R +
+--R 2 3 3 2 8 3 2 4 6
+--R (- 490A a b - 1015B a b )x + (- 1610A a b - 1260B a b)x
+--R +
+--R 4 5 4 5 2
+--R (- 2240A a b - 560B a )x - 1120A a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 14 5 4 12 4 2 3 10
+--R 5B b x + (7A b + 133B a b )x + (189A a b + 721B a b )x
+--R +
+--R 2 3 3 2 8 3 2 4 6
+--R (1085A a b + 1575B a b )x + (2590A a b + 1540B a b)x
+--R +
+--R 4 5 4 5 2
+--R (2800A a b + 560B a )x + 1120A a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (35b x + 840a b x + 2800a b x + 2240a )\|a \|b x + a - 245a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 1960a b x - 3920a b x - 2240a
+--R Type: Union(Expression(Integer),...)
+--E 815
+
+--S 816 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 4 4 3 6 4 3 5 2 4
+--R (7A a b - 2B a b )x + (168A a b - 48B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (560A a b - 160B a b)x + 448A a b - 128B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 4 4 3 6 4 3 5 2 4
+--R (- 49A a b + 14B a b )x + (- 392A a b + 112B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (- 784A a b + 224B a b)x - 448A a b + 128B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 +-+ | 2 5 6
+--R (35b x + 840a b x + 2800a b x + 2240a b )\|a \|b x + a - 245a b x
+--R +
+--R 2 4 4 3 3 2 4 2
+--R - 1960a b x - 3920a b x - 2240a b
+--R Type: Expression(Integer)
+--E 816
+
+--S 817 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 817
+
+)clear all
+
+--S 818 of 1406
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (1) (B b x + (A b + B a)x + A a)\|b x + a
+--R Type: Expression(Integer)
+--E 818
+
+--S 819 of 1406
+r0:=1/24*(6*A*b-a*B)*x*(a+b*x^2)^(3/2)/b+1/6*B*x*(a+b*x^2)^(5/2)/b+_
+ 1/16*a^2*(6*A*b-a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_
+ 1/16*a*(6*A*b-a*B)*x*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 x\|b
+--R (18A a b - 3B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 2 5 2 3 2 +-+ | 2
+--R (8B b x + (12A b + 14B a b)x + (30A a b + 3B a )x)\|b \|b x + a
+--R /
+--R +-+
+--R 48b\|b
+--R Type: Expression(Integer)
+--E 819
+
+--S 820 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 3 2 4 3 2 4 2 4
+--R (108A a b - 18B a b )x + (576A a b - 96B a b)x + 576A a b
+--R +
+--R 5
+--R - 96B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (- 18A a b + 3B a b )x + (- 324A a b + 54B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (- 864A a b + 144B a b)x - 576A a b + 96B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R - 8B b x + (- 12A b - 158B a b )x + (- 246A a b - 639B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (- 1116A a b - 982B a b )x + (- 1824A a b - 592B a b)x
+--R +
+--R 4 5
+--R (- 960A a b - 96B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R 48B b x + (72A b + 388B a b )x + (636A a b + 1062B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (1908A a b + 1266B a b )x + (2304A a b + 640B a b)x
+--R +
+--R 4 5
+--R (960A a b + 96B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 3 4 2 2 2 +-+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b)\|a \|b \|b x + a
+--R +
+--R 4 6 3 4 2 2 2 3 +-+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b)\|b
+--R ,
+--R
+--R 2 3 3 2 4 3 2 4 2
+--R (216A a b - 36B a b )x + (1152A a b - 192B a b)x
+--R +
+--R 4 5
+--R 1152A a b - 192B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (- 36A a b + 6B a b )x + (- 648A a b + 108B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (- 1728A a b + 288B a b)x - 1152A a b + 192B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R - 8B b x + (- 12A b - 158B a b )x + (- 246A a b - 639B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (- 1116A a b - 982B a b )x + (- 1824A a b - 592B a b)x
+--R +
+--R 4 5
+--R (- 960A a b - 96B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R 48B b x + (72A b + 388B a b )x + (636A a b + 1062B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (1908A a b + 1266B a b )x + (2304A a b + 640B a b)x
+--R +
+--R 4 5
+--R (960A a b + 96B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 3 4 2 2 2 +---+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b)\|- b \|a \|b x + a
+--R +
+--R 4 6 3 4 2 2 2 3 +---+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 820
+
+--S 821 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3
+--R (6A a b - B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 3 x\|b
+--R (- 6A a b + B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 16b\|b
+--R Type: Expression(Integer)
+--E 821
+
+--S 822 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 822
+
+--S 823 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 3 +---+ x\|b
+--R (- 6A a b + B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 3 +-+ \|- b \|b x + a - \|- b \|a
+--R (12A a b - 2B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 16b\|- b \|b
+--R Type: Expression(Integer)
+--E 823
+
+--S 824 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 824
+
+)clear all
+
+--S 825 of 1406
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 825
+
+--S 826 of 1406
+r0:=1/3*A*(a+b*x^2)^(3/2)+1/5*B*(a+b*x^2)^(5/2)/b-a^(3/2)*A*_
+ atanh(sqrt(a+b*x^2)/sqrt(a))+a*A*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R +-+ \|b x + a
+--R - 15A a b\|a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 4 2 2 2 | 2
+--R (3B b x + (5A b + 6B a b)x + 20A a b + 3B a )\|b x + a
+--R /
+--R 15b
+--R Type: Expression(Integer)
+--E 826
+
+--S 827 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 2 4 3 2 4 | 2
+--R (15A a b x + 180A a b x + 240A a )\|b x + a
+--R +
+--R 2 2 4 3 2 4 +-+
+--R (- 75A a b x - 300A a b x - 240A a )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 3 8 3 2 2 6 2 2 3 4
+--R - 15B a b x + (- 25A a b - 90B a b )x + (- 180A a b - 180B a b)x
+--R +
+--R 3 4 2
+--R (- 240A a b - 120B a )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 10 4 3 8 3 2 2 6
+--R 3B b x + (5A b + 45B a b )x + (85A a b + 165B a b )x
+--R +
+--R 2 2 3 4 3 4 2
+--R (300A a b + 240B a b)x + (240A a b + 120B a )x
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a
+--R Type: Union(Expression(Integer),...)
+--E 827
+
+--S 828 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 3 4 3 2 2 4 | 2
+--R (15A a b x + 180A a b x + 240A a b)\|b x + a
+--R +
+--R 2 3 4 3 2 2 4 +-+
+--R (- 75A a b x - 300A a b x - 240A a b)\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 3 4 3 2 2 4 | 2
+--R (15A a b x + 180A a b x + 240A a b)\|b x + a
+--R +
+--R 2 3 4 3 2 2 4 +-+
+--R (- 75A a b x - 300A a b x - 240A a b)\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 3 3 2 4 3 2 4 2 4 5
+--R ((20A a b + 3B a b )x + (240A a b + 36B a b)x + 320A a b + 48B a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 3 3 2 4 3 2 4 2 4
+--R (- 100A a b - 15B a b )x + (- 400A a b - 60B a b)x - 320A a b
+--R +
+--R 5
+--R - 48B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 4 2 2 2 +-+ | 2 3 4 2 2 2
+--R (15b x + 180a b x + 240a b)\|a \|b x + a - 75a b x - 300a b x
+--R +
+--R 3
+--R - 240a b
+--R Type: Expression(Integer)
+--E 828
+
+--S 829 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 829
+
+)clear all
+
+--S 830 of 1406
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x^2
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 830
+
+--S 831 of 1406
+r0:=1/4*(4*A*b+a*B)*x*(a+b*x^2)^(3/2)/a-A*(a+b*x^2)^(5/2)/(a*x)+_
+ 3/8*a*(4*A*b+a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+_
+ 3/8*(4*A*b+a*B)*x*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 x\|b
+--R (12A a b + 3B a )x atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 4 2 +-+ | 2
+--R (2B b x + (4A b + 5B a)x - 8A a)\|b \|b x + a
+--R /
+--R +-+
+--R 8x\|b
+--R Type: Expression(Integer)
+--E 831
+
+--S 832 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 2 5 2 2 3 3
+--R (12A a b + 3B a b )x + (144A a b + 36B a b)x
+--R +
+--R 3 4
+--R (192A a b + 48B a )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 2 5 2 2 3 3
+--R (- 60A a b - 15B a b )x + (- 240A a b - 60B a b)x
+--R +
+--R 3 4
+--R (- 192A a b - 48B a )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 3 8 3 2 6 2 2 4
+--R - 10B b x + (- 20A b - 65B a b )x + (- 40A a b - 132B a b)x
+--R +
+--R 2 3 2 3
+--R (96A a b - 80B a )x + 128A a
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 4 10 4 3 8 3 2 2 6
+--R 2B b x + (4A b + 31B a b )x + (44A a b + 121B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (8A a b + 172B a b)x + (- 160A a b + 80B a )x - 128A a
+--R *
+--R +-+
+--R \|b
+--R /
+--R +--------+
+--R 2 5 3 2 +-+ | 2
+--R (8b x + 96a b x + 128a x)\|b \|b x + a
+--R +
+--R 2 5 3 2 +-+ +-+
+--R (- 40b x - 160a b x - 128a x)\|a \|b
+--R ,
+--R
+--R 3 2 2 5 2 2 3 3
+--R (24A a b + 6B a b )x + (288A a b + 72B a b)x
+--R +
+--R 3 4
+--R (384A a b + 96B a )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 2 5 2 2 3 3
+--R (- 120A a b - 30B a b )x + (- 480A a b - 120B a b)x
+--R +
+--R 3 4
+--R (- 384A a b - 96B a )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 3 8 3 2 6 2 2 4
+--R - 10B b x + (- 20A b - 65B a b )x + (- 40A a b - 132B a b)x
+--R +
+--R 2 3 2 3
+--R (96A a b - 80B a )x + 128A a
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 4 10 4 3 8 3 2 2 6
+--R 2B b x + (4A b + 31B a b )x + (44A a b + 121B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (8A a b + 172B a b)x + (- 160A a b + 80B a )x - 128A a
+--R *
+--R +---+
+--R \|- b
+--R /
+--R +--------+
+--R 2 5 3 2 +---+ | 2
+--R (8b x + 96a b x + 128a x)\|- b \|b x + a
+--R +
+--R 2 5 3 2 +---+ +-+
+--R (- 40b x - 160a b x - 128a x)\|- b \|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 832
+
+--S 833 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2
+--R (12A a b + 3B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R (- 12A a b - 3B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 8\|b
+--R Type: Expression(Integer)
+--E 833
+
+--S 834 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 834
+
+--S 835 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +---+ x\|b
+--R (- 12A a b - 3B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (24A a b + 6B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 8\|- b \|b
+--R Type: Expression(Integer)
+--E 835
+
+--S 836 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 836
+
+)clear all
+
+--S 837 of 1406
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x^3
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 837
+
+--S 838 of 1406
+r0:=1/6*(3*A*b+2*a*B)*(a+b*x^2)^(3/2)/a-1/2*A*(a+b*x^2)^(5/2)/(a*x^2)-_
+ 1/2*(3*A*b+2*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+_
+ 1/2*(3*A*b+2*a*B)*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 +-+ \|b x + a
+--R (- 9A b - 6B a)x \|a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 4 2 | 2
+--R (2B b x + (6A b + 8B a)x - 3A a)\|b x + a
+--R /
+--R 2
+--R 6x
+--R Type: Expression(Integer)
+--E 838
+
+--S 839 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2 6 2 2 3 4
+--R (9A a b + 6B a b )x + (108A a b + 72B a b)x
+--R +
+--R 3 4 2
+--R (144A a b + 96B a )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 2 6 2 2 3 4
+--R (- 45A a b - 30B a b )x + (- 180A a b - 120B a b)x
+--R +
+--R 3 4 2
+--R (- 144A a b - 96B a )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 3 8 3 2 2 6 2 2 3 4
+--R - 10B a b x + (- 24A a b - 72B a b )x + (- 33A a b - 96B a b)x
+--R +
+--R 3 2 4
+--R 60A a b x + 48A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 10 4 3 8 3 2 2 6
+--R 2B b x + (6A b + 34B a b )x + (45A a b + 120B a b )x
+--R +
+--R 2 2 3 4 3 2 4
+--R (9A a b + 96B a b)x - 84A a b x - 48A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 2 6 4 2 2 +-+ | 2 2 6 2 4 3 2
+--R (6b x + 72a b x + 96a x )\|a \|b x + a - 30a b x - 120a b x - 96a x
+--R Type: Union(Expression(Integer),...)
+--E 839
+
+--S 840 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 2 2 4 2 2 3 2 3
+--R (9A a b + 6B a b )x + (108A a b + 72B a b)x + 144A a b
+--R +
+--R 4
+--R 96B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (- 45A a b - 30B a b )x + (- 180A a b - 120B a b)x - 144A a b
+--R +
+--R 4
+--R - 96B a
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (9A a b + 6B a b )x + (108A a b + 72B a b)x + 144A a b
+--R +
+--R 4
+--R 96B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (- 45A a b - 30B a b )x + (- 180A a b - 120B a b)x - 144A a b
+--R +
+--R 4
+--R - 96B a
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 3 2 2 4 2 2 3 2 3 4
+--R ((6A a b + 8B a b )x + (72A a b + 96B a b)x + 96A a b + 128B a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (- 30A a b - 40B a b )x + (- 120A a b - 160B a b)x - 96A a b
+--R +
+--R 4
+--R - 128B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (6b x + 72a b x + 96a )\|a \|b x + a - 30a b x - 120a b x - 96a
+--R Type: Expression(Integer)
+--E 840
+
+--S 841 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 841
+
+)clear all
+
+--S 842 of 1406
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x^4
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 842
+
+--S 843 of 1406
+r0:=-1/3*(2*A*b+3*a*B)*(a+b*x^2)^(3/2)/(a*x)-1/3*A*(a+b*x^2)^(5/2)/_
+ (a*x^3)+1/2*(2*A*b+3*a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))*_
+ sqrt(b)+1/2*b*(2*A*b+3*a*B)*x*sqrt(a+b*x^2)/a
+--R
+--R
+--R (2)
+--R +-+
+--R 3 +-+ x\|b
+--R (6A b + 9B a)x \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 4 2 | 2
+--R (3B b x + (- 8A b - 6B a)x - 2A a)\|b x + a
+--R /
+--R 3
+--R 6x
+--R Type: Expression(Integer)
+--E 843
+
+--S 844 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 7 2 2 5
+--R (6A b + 9B a b )x + (72A a b + 108B a b)x
+--R +
+--R 2 3 3
+--R (96A a b + 144B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 3 2 7 2 2 5
+--R (- 30A b - 45B a b )x + (- 120A a b - 180B a b)x
+--R +
+--R 2 3 3
+--R (- 96A a b - 144B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 3 8 3 2 6 2 2 4
+--R - 15B b x + (40A b - 30B a b )x + (170A a b + 72B a b)x
+--R +
+--R 2 3 2 3
+--R (168A a b + 96B a )x + 32A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 10 4 3 8 3 2 2 6
+--R 3B b x + (- 8A b + 33B a b )x + (- 106A a b + 6B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (- 250A a b - 120B a b)x + (- 184A a b - 96B a )x - 32A a
+--R /
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (6b x + 72a b x + 96a x )\|b x + a
+--R +
+--R 2 7 5 2 3 +-+
+--R (- 30b x - 120a b x - 96a x )\|a
+--R ,
+--R
+--R 3 2 7 2 2 5
+--R (12A b + 18B a b )x + (144A a b + 216B a b)x
+--R +
+--R 2 3 3
+--R (192A a b + 288B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 3 2 7 2 2 5
+--R (- 60A b - 90B a b )x + (- 240A a b - 360B a b)x
+--R +
+--R 2 3 3
+--R (- 192A a b - 288B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R 3 8 3 2 6 2 2 4
+--R - 15B b x + (40A b - 30B a b )x + (170A a b + 72B a b)x
+--R +
+--R 2 3 2 3
+--R (168A a b + 96B a )x + 32A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 10 4 3 8 3 2 2 6
+--R 3B b x + (- 8A b + 33B a b )x + (- 106A a b + 6B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (- 250A a b - 120B a b)x + (- 184A a b - 96B a )x - 32A a
+--R /
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (6b x + 72a b x + 96a x )\|b x + a
+--R +
+--R 2 7 5 2 3 +-+
+--R (- 30b x - 120a b x - 96a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 844
+
+--S 845 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R (2A b + 3B a)\|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ x\|b
+--R (- 2A b - 3B a)\|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 845
+
+--S 846 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 846
+
+--S 847 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R +-+ x\|b
+--R (- 2A b - 3B a)\|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R | 2 +-+
+--R +---+ \|b x + a - \|a
+--R (4A b + 6B a)\|- b atan(------------------)
+--R +---+
+--R x\|- b
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 847
+
+--S 848 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 848
+
+)clear all
+
+--S 849 of 1406
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x^5
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 849
+
+--S 850 of 1406
+r0:=-1/8*(A*b+4*a*B)*(a+b*x^2)^(3/2)/(a*x^2)-1/4*A*(a+b*x^2)^(5/2)/_
+ (a*x^4)-3/8*b*(A*b+4*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))/_
+ sqrt(a)+3/8*b*(A*b+4*a*B)*sqrt(a+b*x^2)/a
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 4 \|b x + a
+--R (- 3A b - 12B a b)x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 4 2 +-+ | 2
+--R (8B b x + (- 5A b - 4B a)x - 2A a)\|a \|b x + a
+--R /
+--R 4 +-+
+--R 8x \|a
+--R Type: Expression(Integer)
+--E 850
+
+--S 851 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 8 3 2 2 6
+--R (3A b + 12B a b )x + (36A a b + 144B a b )x
+--R +
+--R 2 2 3 4
+--R (48A a b + 192B a b)x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 3 8 3 2 2 6
+--R (- 15A b - 60B a b )x + (- 60A a b - 240B a b )x
+--R +
+--R 2 2 3 4
+--R (- 48A a b - 192B a b)x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 3 8 3 2 2 6 2 2 3 4
+--R - 32B a b x + (25A a b - 44B a b )x + (110A a b + 80B a b)x
+--R +
+--R 3 4 2 4
+--R (120A a b + 64B a )x + 32A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 10 4 3 8 3 2 2 6
+--R 8B b x + (- 5A b + 60B a b )x + (- 67A a b + 12B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (- 166A a b - 112B a b)x + (- 136A a b - 64B a )x - 32A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 2 8 6 2 4 +-+ | 2 2 8 2 6
+--R (8b x + 96a b x + 128a x )\|a \|b x + a - 40a b x - 160a b x
+--R +
+--R 3 4
+--R - 128a x
+--R Type: Union(Expression(Integer),...)
+--E 851
+
+--S 852 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 2 \|b x + a - \|a
+--R (3A b + 12B a b)log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 2 \|b x + a
+--R (3A b + 12B a b)atanh(-----------) + 8B a b
+--R +-+
+--R \|a
+--R /
+--R +-+
+--R 8\|a
+--R Type: Expression(Integer)
+--E 852
+
+--S 853 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 853
+
+)clear all
+
+--S 854 of 1406
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x^6
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 854
+
+--S 855 of 1406
+r0:=-1/3*B*(a+b*x^2)^(3/2)/x^3-1/5*A*(a+b*x^2)^(5/2)/(a*x^5)+_
+ b^(3/2)*B*atanh(x*sqrt(b)/sqrt(a+b*x^2))-b*B*sqrt(a+b*x^2)/x
+--R
+--R
+--R (2)
+--R +-+
+--R 5 +-+ x\|b
+--R 15B a b x \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 2 4 2 2 2 | 2
+--R ((- 3A b - 20B a b)x + (- 6A a b - 5B a )x - 3A a )\|b x + a
+--R /
+--R 5
+--R 15a x
+--R Type: Expression(Integer)
+--E 855
+
+--S 856 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 9 2 2 7 3 5 +-+ | 2
+--R (15B a b x + 180B a b x + 240B a b x )\|b \|b x + a
+--R +
+--R 3 9 2 2 7 3 5 +-+ +-+
+--R (- 75B a b x - 300B a b x - 240B a b x )\|a \|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 4 3 8 3 2 2 6
+--R (15A b + 100B a b )x + (90A a b + 425B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (183A a b + 420B a b)x + (156A a b + 80B a )x + 48A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 4 10 4 2 3 8
+--R (- 3A b - 20B a b )x + (- 45A a b - 265B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 165A a b - 625B a b )x + (- 255A a b - 460B a b)x
+--R +
+--R 4 5 2 5
+--R (- 180A a b - 80B a )x - 48A a
+--R /
+--R +--------+
+--R 2 9 2 7 3 5 | 2
+--R (15a b x + 180a b x + 240a x )\|b x + a
+--R +
+--R 2 9 2 7 3 5 +-+
+--R (- 75a b x - 300a b x - 240a x )\|a
+--R ,
+--R
+--R +--------+
+--R 3 9 2 2 7 3 5 +---+ | 2
+--R (30B a b x + 360B a b x + 480B a b x )\|- b \|b x + a
+--R +
+--R 3 9 2 2 7 3 5 +---+ +-+
+--R (- 150B a b x - 600B a b x - 480B a b x )\|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R 4 3 8 3 2 2 6
+--R (15A b + 100B a b )x + (90A a b + 425B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (183A a b + 420B a b)x + (156A a b + 80B a )x + 48A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 4 10 4 2 3 8
+--R (- 3A b - 20B a b )x + (- 45A a b - 265B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 165A a b - 625B a b )x + (- 255A a b - 460B a b)x
+--R +
+--R 4 5 2 5
+--R (- 180A a b - 80B a )x - 48A a
+--R /
+--R +--------+
+--R 2 9 2 7 3 5 | 2
+--R (15a b x + 180a b x + 240a x )\|b x + a
+--R +
+--R 2 9 2 7 3 5 +-+
+--R (- 75a b x - 300a b x - 240a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 856
+
+--S 857 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R B b\|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ x\|b
+--R - B b\|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 857
+
+--S 858 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 858
+
+--S 859 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R +-+ x\|b +---+ \|b x + a - \|a
+--R (6) - B b\|b atanh(-----------) + 2B b\|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 859
+
+--S 860 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 860
+
+)clear all
+
+--S 861 of 1406
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x^7
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 861
+
+--S 862 of 1406
+r0:=1/24*(A*b-6*a*B)*(a+b*x^2)^(3/2)/(a*x^4)-1/6*A*(a+b*x^2)^(5/2)/_
+ (a*x^6)+1/16*b^2*(A*b-6*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)+_
+ 1/16*b*(A*b-6*a*B)*sqrt(a+b*x^2)/(a*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 3 2 6 \|b x + a
+--R (3A b - 18B a b )x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R ((- 3A b - 30B a b)x + (- 14A a b - 12B a )x - 8A a )\|a \|b x + a
+--R /
+--R 6 +-+
+--R 48a x \|a
+--R Type: Expression(Integer)
+--E 862
+
+--S 863 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 2 4 10 2 4 3 3 8
+--R (- 18A a b + 108B a b )x + (- 96A a b + 576B a b )x
+--R +
+--R 3 3 4 2 6
+--R (- 96A a b + 576B a b )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 5 12 5 2 4 10
+--R (3A b - 18B a b )x + (54A a b - 324B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (144A a b - 864B a b )x + (96A a b - 576B a b )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 2 4 10 2 4 3 3 8
+--R (3A a b + 30B a b )x + (68A a b + 552B a b )x
+--R +
+--R 3 3 4 2 6 4 2 5 4
+--R (404A a b + 1656B a b )x + (912A a b + 1536B a b)x
+--R +
+--R 5 6 2 6
+--R (832A a b + 384B a )x + 256A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 2 4 10 2 4 3 3 8
+--R (- 18A a b - 180B a b )x + (- 198A a b - 1212B a b )x
+--R +
+--R 3 3 4 2 6 4 2 5 4
+--R (- 772A a b - 2376B a b )x + (- 1296A a b - 1728B a b)x
+--R +
+--R 5 6 2 6
+--R (- 960A a b - 384B a )x - 256A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 2 2 10 3 8 4 6 +-+ | 2 2 3 12
+--R (288a b x + 1536a b x + 1536a x )\|a \|b x + a - 48a b x
+--R +
+--R 3 2 10 4 8 5 6
+--R - 864a b x - 2304a b x - 1536a x
+--R Type: Union(Expression(Integer),...)
+--E 863
+
+--S 864 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 3 2 \|b x + a - \|a
+--R (- A b + 6B a b )log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 3 2 \|b x + a
+--R (- A b + 6B a b )atanh(-----------)
+--R +-+
+--R \|a
+--R /
+--R +-+
+--R 16a\|a
+--R Type: Expression(Integer)
+--E 864
+
+--S 865 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 865
+
+)clear all
+
+--S 866 of 1406
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x^8
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 866
+
+--S 867 of 1406
+r0:=-1/7*A*(a+b*x^2)^(5/2)/(a*x^7)+1/35*(2*A*b-7*a*B)*(a+b*x^2)^(5/2)/(a^2*x^5)
+--R
+--R
+--R (2)
+--R 3 2 6 2 2 4 2 3 2
+--R (2A b - 7B a b )x + (- A a b - 14B a b)x + (- 8A a b - 7B a )x
+--R +
+--R 3
+--R - 5A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 7
+--R 35a x
+--R Type: Expression(Integer)
+--E 867
+
+--S 868 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 12 5 2 4 10
+--R (- 14A b + 49B a b )x + (- 105A a b + 490B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 112A a b + 1617B a b )x + (467A a b + 2408B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (1240A a b + 1680B a b)x + (1072A a b + 448B a )x + 320A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 6 14 6 2 5 12
+--R (2A b - 7B a b )x + (49A a b - 189B a b )x
+--R +
+--R 2 5 3 4 10 3 4 4 3 8
+--R (175A a b - 1085B a b )x + (- 21A a b - 2639B a b )x
+--R +
+--R 4 3 5 2 6 5 2 6 4
+--R (- 973A a b - 3192B a b )x + (- 1736A a b - 1904B a b)x
+--R +
+--R 6 7 2 7
+--R (- 1232A a b - 448B a )x - 320A a
+--R /
+--R +--------+
+--R 2 3 13 3 2 11 4 9 5 7 | 2
+--R (35a b x + 840a b x + 2800a b x + 2240a x )\|b x + a
+--R +
+--R 2 3 13 3 2 11 4 9 5 7 +-+
+--R (- 245a b x - 1960a b x - 3920a b x - 2240a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 868
+
+--S 869 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 869
+
+--S 870 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 870
+
+)clear all
+
+--S 871 of 1406
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x^9
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R 9
+--R x
+--R Type: Expression(Integer)
+--E 871
+
+--S 872 of 1406
+r0:=1/48*(3*A*b-8*a*B)*(a+b*x^2)^(3/2)/(a*x^6)-1/8*A*(a+b*x^2)^(5/2)/_
+ (a*x^8)-1/128*b^3*(3*A*b-8*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))/_
+ a^(5/2)+1/64*b*(3*A*b-8*a*B)*sqrt(a+b*x^2)/(a*x^4)+_
+ 1/128*b^2*(3*A*b-8*a*B)*sqrt(a+b*x^2)/(a^2*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 4 3 8 \|b x + a
+--R (- 9A b + 24B a b )x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 3 2 6 2 2 4
+--R (9A b - 24B a b )x + (- 6A a b - 112B a b)x
+--R +
+--R 2 3 2 3
+--R (- 72A a b - 64B a )x - 48A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R /
+--R 2 8 +-+
+--R 384a x \|a
+--R Type: Expression(Integer)
+--E 872
+
+--S 873 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 2 6 14 2 6 3 5 12
+--R (72A a b - 192B a b )x + (720A a b - 1920B a b )x
+--R +
+--R 3 5 4 4 10 4 4 5 3 8
+--R (1728A a b - 4608B a b )x + (1152A a b - 3072B a b )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 8 7 16 7 2 6 14
+--R (- 9A b + 24B a b )x + (- 288A a b + 768B a b )x
+--R +
+--R 2 6 3 5 12 3 5 4 4 10
+--R (- 1440A a b + 3840B a b )x + (- 2304A a b + 6144B a b )x
+--R +
+--R 4 4 5 3 8
+--R (- 1152A a b + 3072B a b )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 7 2 6 14 2 6 3 5 12
+--R (- 9A a b + 24B a b )x + (- 282A a b + 880B a b )x
+--R +
+--R 3 5 4 4 10 4 4 5 3 8
+--R (- 1176A a b + 7488B a b )x + (1008A a b + 26112B a b )x
+--R +
+--R 5 3 6 2 6 6 2 7 4
+--R (13440A a b + 41984B a b )x + (26880A a b + 30720B a b)x
+--R +
+--R 7 8 2 8
+--R (21504A a b + 8192B a )x + 6144A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 2 6 14 2 6 3 5 12
+--R (72A a b - 192B a b )x + (744A a b - 3008B a b )x
+--R +
+--R 3 5 4 4 10 4 4 5 3 8
+--R (1344A a b - 16896B a b )x + (- 5472A a b - 43776B a b )x
+--R +
+--R 5 3 6 2 6 6 2 7 4
+--R (- 24576A a b - 56320B a b )x + (- 36864A a b - 34816B a b)x
+--R +
+--R 7 8 2 8
+--R (- 24576A a b - 8192B a )x - 6144A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 3 14 4 2 12 5 10 6 8 +-+ | 2
+--R (3072a b x + 30720a b x + 73728a b x + 49152a x )\|a \|b x + a
+--R +
+--R 3 4 16 4 3 14 5 2 12 6 10 7 8
+--R - 384a b x - 12288a b x - 61440a b x - 98304a b x - 49152a x
+--R Type: Union(Expression(Integer),...)
+--E 873
+
+--S 874 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 4 3 \|b x + a - \|a
+--R (3A b - 8B a b )log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 4 3 \|b x + a
+--R (3A b - 8B a b )atanh(-----------)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+
+--R 128a \|a
+--R Type: Expression(Integer)
+--E 874
+
+--S 875 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 875
+
+)clear all
+
+--S 876 of 1406
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x^10
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R 10
+--R x
+--R Type: Expression(Integer)
+--E 876
+
+--S 877 of 1406
+r0:=-1/9*A*(a+b*x^2)^(5/2)/(a*x^9)+1/63*(4*A*b-9*a*B)*(a+b*x^2)^(5/2)/_
+ (a^2*x^7)-2/315*b*(4*A*b-9*a*B)*(a+b*x^2)^(5/2)/(a^3*x^5)
+--R
+--R
+--R (2)
+--R 4 3 8 3 2 2 6
+--R (- 8A b + 18B a b )x + (4A a b - 9B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (- 3A a b - 72B a b)x + (- 50A a b - 45B a )x - 35A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 9
+--R 315a x
+--R Type: Expression(Integer)
+--E 877
+
+--S 878 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 16 7 2 6 14
+--R (72A b - 162B a b )x + (924A a b - 2079B a b )x
+--R +
+--R 2 6 3 5 12 3 5 4 4 10
+--R (3003A a b - 6048B a b )x + (3690A a b + 2565B a b )x
+--R +
+--R 4 4 5 3 8 5 3 6 2 6
+--R (7355A a b + 37080B a b )x + (26504A a b + 63216B a b )x
+--R +
+--R 6 2 7 4 7 8 2 8
+--R (44688A a b + 44352B a b)x + (32960A a b + 11520B a )x + 8960A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 8 18 8 2 7 16
+--R (- 8A b + 18B a b )x + (- 324A a b + 729B a b )x
+--R +
+--R 2 7 3 6 14 3 6 4 5 12
+--R (- 2079A a b + 4599B a b )x + (- 4557A a b + 6867B a b )x
+--R +
+--R 4 5 5 4 10 5 4 6 3 8
+--R (- 5805A a b - 15525B a b )x + (- 16731A a b - 63864B a b )x
+--R +
+--R 6 3 7 2 6 7 2 8 4
+--R (- 45288A a b - 83952B a b )x + (- 60048A a b - 50112B a b)x
+--R +
+--R 8 9 2 9
+--R (- 37440A a b - 11520B a )x - 8960A a
+--R /
+--R 3 4 17 4 3 15 5 2 13 6 11 7 9
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 4 17 4 3 15 5 2 13 6 11
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 7 9
+--R - 80640a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 878
+
+--S 879 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 879
+
+--S 880 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 880
+
+)clear all
+
+--S 881 of 1406
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x^11
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R 11
+--R x
+--R Type: Expression(Integer)
+--E 881
+
+--S 882 of 1406
+r0:=1/16*(A*b-2*a*B)*(a+b*x^2)^(3/2)/(a*x^8)-1/10*A*(a+b*x^2)^(5/2)/_
+ (a*x^10)+3/256*b^4*(A*b-2*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))/_
+ a^(7/2)+1/32*b*(A*b-2*a*B)*sqrt(a+b*x^2)/(a*x^6)+1/128*b^2*_
+ (A*b-2*a*B)*sqrt(a+b*x^2)/(a^2*x^4)-3/256*b^3*(A*b-2*a*B)*_
+ sqrt(a+b*x^2)/(a^3*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 5 4 10 \|b x + a
+--R (15A b - 30B a b )x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 3 8 3 2 2 6
+--R (- 15A b + 30B a b )x + (10A a b - 20B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (- 8A a b - 240B a b)x + (- 176A a b - 160B a )x - 128A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R /
+--R 3 10 +-+
+--R 1280a x \|a
+--R Type: Expression(Integer)
+--E 882
+
+--S 883 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 2 8 18 2 8 3 7 16
+--R (- 150A a b + 300B a b )x + (- 2400A a b + 4800B a b )x
+--R +
+--R 3 7 4 6 14
+--R (- 10080A a b + 20160B a b )x
+--R +
+--R 4 6 5 5 12 5 5 6 4 10
+--R (- 15360A a b + 30720B a b )x + (- 7680A a b + 15360B a b )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 10 9 20 9 2 8 18
+--R (15A b - 30B a b )x + (750A a b - 1500B a b )x
+--R +
+--R 2 8 3 7 16 3 7 4 6 14
+--R (6000A a b - 12000B a b )x + (16800A a b - 33600B a b )x
+--R +
+--R 4 6 5 5 12 5 5 6 4 10
+--R (19200A a b - 38400B a b )x + (7680A a b - 15360B a b )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 9 2 8 18 2 8 3 7 16
+--R (15A a b - 30B a b )x + (740A a b - 1480B a b )x
+--R +
+--R 3 7 4 6 14 4 6 5 5 12
+--R (5508A a b - 10760B a b )x + (13376A a b - 13440B a b )x
+--R +
+--R 5 5 6 4 10 6 4 7 3 8
+--R (20128A a b + 88000B a b )x + (80640A a b + 343040B a b )x
+--R +
+--R 7 3 8 2 6 8 2 9 4
+--R (253440A a b + 496640B a b )x + (372736A a b + 327680B a b)x
+--R +
+--R 9 10 2 10
+--R (253952A a b + 81920B a )x + 65536A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 2 8 18 2 8 3 7 16
+--R (- 150A a b + 300B a b )x + (- 2450A a b + 4900B a b )x
+--R +
+--R 3 7 4 6 14 4 6 5 5 12
+--R (- 10860A a b + 19160B a b )x + (- 20240A a b - 8160B a b )x
+--R +
+--R 5 5 6 4 10 6 4 7 3 8
+--R (- 43936A a b - 214720B a b )x + (- 174080A a b - 555520B a b )x
+--R +
+--R 7 3 8 2 6 8 2 9 4
+--R (- 412160A a b - 650240B a b )x + (- 491520A a b - 368640B a b)x
+--R +
+--R 9 10 2 10
+--R (- 286720A a b - 81920B a )x - 65536A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 4 18 5 3 16 6 2 14 7 12
+--R 12800a b x + 204800a b x + 860160a b x + 1310720a b x
+--R +
+--R 8 10
+--R 655360a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 5 20 5 4 18 6 3 16 7 2 14
+--R - 1280a b x - 64000a b x - 512000a b x - 1433600a b x
+--R +
+--R 8 12 9 10
+--R - 1638400a b x - 655360a x
+--R Type: Union(Expression(Integer),...)
+--E 883
+
+--S 884 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 5 4 \|b x + a - \|a
+--R (- 3A b + 6B a b )log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 5 4 \|b x + a
+--R (- 3A b + 6B a b )atanh(-----------)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+
+--R 256a \|a
+--R Type: Expression(Integer)
+--E 884
+
+--S 885 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 885
+
+)clear all
+
+--S 886 of 1406
+t0:=x^5*(a+b*x^2)^(5/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 2 11 2 9 2 7 2 5 | 2
+--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x )\|b x + a
+--R Type: Expression(Integer)
+--E 886
+
+--S 887 of 1406
+r0:=1/7*a^2*(A*b-a*B)*(a+b*x^2)^(7/2)/b^4-1/9*a*(2*A*b-3*a*B)*_
+ (a+b*x^2)^(9/2)/b^4+1/11*(A*b-3*a*B)*(a+b*x^2)^(11/2)/b^4+_
+ 1/13*B*(a+b*x^2)^(13/2)/b^4
+--R
+--R
+--R (2)
+--R 6 12 6 5 10 5 2 4 8
+--R 693B b x + (819A b + 1701B a b )x + (2093A a b + 1113B a b )x
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (1469A a b + 15B a b )x + (39A a b - 18B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (- 52A a b + 24B a b)x + 104A a b - 48B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4
+--R 9009b
+--R Type: Expression(Integer)
+--E 887
+
+--S 888 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 8 2 7 22
+--R - 9009B a b x + (- 10647A a b - 274365B a b )x
+--R +
+--R 2 7 3 6 20
+--R (- 325325A a b - 2651649B a b )x
+--R +
+--R 3 6 4 5 18
+--R (- 3165877A a b - 12277551B a b )x
+--R +
+--R 4 5 5 4 16
+--R (- 14806935A a b - 31760586B a b )x
+--R +
+--R 5 4 6 3 14
+--R (- 38815920A a b - 48679488B a b )x
+--R +
+--R 6 3 7 2 12
+--R (- 60492432A a b - 44108064B a b )x
+--R +
+--R 7 2 8 10
+--R (- 55927872A a b - 21909888B a b)x
+--R +
+--R 8 9 8 9 6
+--R (- 28444416A a b - 4612608B a )x - 6150144A a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 26 9 8 24
+--R 693B b x + (819A b + 60606B a b )x
+--R +
+--R 8 2 7 22 2 7 3 6 20
+--R (71708A a b + 980070B a b )x + (1165450A a b + 6644352B a b )x
+--R +
+--R 3 6 4 5 18
+--R (7965100A a b + 24099933B a b )x
+--R +
+--R 4 5 5 4 16
+--R (29205891A a b + 51776010B a b )x
+--R +
+--R 5 4 6 3 14
+--R (63608688A a b + 68283072B a b )x
+--R +
+--R 6 3 7 2 12
+--R (85285200A a b + 54486432B a b )x
+--R +
+--R 7 2 8 10 8 9 8
+--R (69381312A a b + 24216192B a b)x + (31519488A a b + 4612608B a )x
+--R +
+--R 9 6
+--R 6150144A a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 6 12 5 10 2 4 8 3 3 6
+--R 9009b x + 756756a b x + 10090080a b x + 48432384a b x
+--R +
+--R 4 2 4 5 2 6
+--R 103783680a b x + 101477376a b x + 36900864a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 12 2 5 10 3 4 8 4 3 6
+--R - 117117a b x - 3279276a b x - 26234208a b x - 89945856a b x
+--R +
+--R 5 2 4 6 2 7
+--R - 149909760a b x - 119927808a b x - 36900864a
+--R Type: Union(Expression(Integer),...)
+--E 888
+
+--S 889 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 6 7 7 6 12 7 6 8 5 10
+--R (104A a b - 48B a b )x + (8736A a b - 4032B a b )x
+--R +
+--R 8 5 9 4 8 9 4 10 3 6
+--R (116480A a b - 53760B a b )x + (559104A a b - 258048B a b )x
+--R +
+--R 10 3 11 2 4
+--R (1198080A a b - 552960B a b )x
+--R +
+--R 11 2 12 2 12 13
+--R (1171456A a b - 540672B a b)x + 425984A a b - 196608B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 7 7 6 12 7 6 8 5 10
+--R (- 1352A a b + 624B a b )x + (- 37856A a b + 17472B a b )x
+--R +
+--R 8 5 9 4 8
+--R (- 302848A a b + 139776B a b )x
+--R +
+--R 9 4 10 3 6
+--R (- 1038336A a b + 479232B a b )x
+--R +
+--R 10 3 11 2 4
+--R (- 1730560A a b + 798720B a b )x
+--R +
+--R 11 2 12 2 12 13
+--R (- 1384448A a b + 638976B a b)x - 425984A a b + 196608B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 10 12 9 10 2 8 8 3 7 6
+--R 9009b x + 756756a b x + 10090080a b x + 48432384a b x
+--R +
+--R 4 6 4 5 5 2 6 4
+--R 103783680a b x + 101477376a b x + 36900864a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 10 12 2 9 10 3 8 8 4 7 6
+--R - 117117a b x - 3279276a b x - 26234208a b x - 89945856a b x
+--R +
+--R 5 6 4 6 5 2 7 4
+--R - 149909760a b x - 119927808a b x - 36900864a b
+--R Type: Expression(Integer)
+--E 889
+
+--S 890 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 890
+
+)clear all
+
+--S 891 of 1406
+t0:=x^4*(a+b*x^2)^(5/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 2 10 2 8 2 6 2 4 | 2
+--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x )\|b x + a
+--R Type: Expression(Integer)
+--E 891
+
+--S 892 of 1406
+r0:=1/192*a*(12*A*b-5*a*B)*x^5*(a+b*x^2)^(3/2)/b+1/120*(12*A*b-5*a*B)*_
+ x^5*(a+b*x^2)^(5/2)/b+1/12*B*x^5*(a+b*x^2)^(7/2)/b+1/1024*_
+ a^5*(12*A*b-5*a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(7/2)-_
+ 1/1024*a^4*(12*A*b-5*a*B)*x*sqrt(a+b*x^2)/b^3+1/1536*a^3*_
+ (12*A*b-5*a*B)*x^3*sqrt(a+b*x^2)/b^2+1/384*a^2*(12*A*b-5*a*B)*_
+ x^5*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 5 6 x\|b
+--R (180A a b - 75B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R 1280B b x + (1536A b + 3200B a b )x + (4032A a b + 2160B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (2976A a b + 40B a b )x + (120A a b - 50B a b)x
+--R +
+--R 4 5
+--R (- 180A a b + 75B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 3 +-+
+--R 15360b \|b
+--R Type: Expression(Integer)
+--E 892
+
+--S 893 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 5 6 6 5 10 6 5 7 4 8
+--R (2160A a b - 900B a b )x + (50400A a b - 21000B a b )x
+--R +
+--R 7 4 8 3 6
+--R (322560A a b - 134400B a b )x
+--R +
+--R 8 3 9 2 4
+--R (829440A a b - 345600B a b )x
+--R +
+--R 9 2 10 2 10 11
+--R (921600A a b - 384000B a b)x + 368640A a b - 153600B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 7 6 6 12 6 6 7 5 10
+--R (- 180A a b + 75B a b )x + (- 12960A a b + 5400B a b )x
+--R +
+--R 7 5 8 4 8
+--R (- 151200A a b + 63000B a b )x
+--R +
+--R 8 4 9 3 6
+--R (- 645120A a b + 268800B a b )x
+--R +
+--R 9 3 10 2 4
+--R (- 1244160A a b + 518400B a b )x
+--R +
+--R 10 2 11 2 11 12
+--R (- 1105920A a b + 460800B a b)x - 368640A a b + 153600B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 11 23 11 10 21
+--R - 1280B b x + (- 1536A b - 95360B a b )x
+--R +
+--R 10 2 9 19
+--R (- 114624A a b - 1307760B a b )x
+--R +
+--R 2 9 3 8 17
+--R (- 1583520A a b - 7431080B a b )x
+--R +
+--R 3 8 4 7 15
+--R (- 9106296A a b - 22133390B a b )x
+--R +
+--R 4 7 5 6 13
+--R (- 27575820A a b - 37754235B a b )x
+--R +
+--R 5 6 6 5 11
+--R (- 48060192A a b - 37318920B a b )x
+--R +
+--R 6 5 7 4 9
+--R (- 48767328A a b - 19984920B a b )x
+--R +
+--R 7 4 8 3 7
+--R (- 26726400A a b - 4592640B a b )x
+--R +
+--R 8 3 9 2 5
+--R (- 5587968A a b - 293120B a b )x
+--R +
+--R 9 2 10 3 10 11
+--R (860160A a b - 358400B a b)x + (368640A a b - 153600B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 11 23 11 10 21
+--R 15360B b x + (18432A b + 412160B a b )x
+--R +
+--R 10 2 9 19
+--R (496896A a b + 3612480B a b )x
+--R +
+--R 2 9 3 8 17
+--R (4395648A a b + 15453600B a b )x
+--R +
+--R 3 8 4 7 15
+--R (19055136A a b + 37418440B a b )x
+--R +
+--R 4 7 5 6 13
+--R (46946160A a b + 54197820B a b )x
+--R +
+--R 5 6 6 5 11
+--R (69475824A a b + 46745820B a b )x
+--R +
+--R 6 5 7 4 9
+--R (61392672A a b + 22261000B a b )x
+--R +
+--R 7 4 8 3 7
+--R (29604864A a b + 4704000B a b )x
+--R +
+--R 8 3 9 2 5
+--R (5203968A a b + 453120B a b )x
+--R +
+--R 9 2 10 3 10 11
+--R (- 1044480A a b + 435200B a b)x + (- 368640A a b + 153600B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 8 10 7 8 2 6 6 3 5 4
+--R 184320b x + 4300800a b x + 27525120a b x + 70778880a b x
+--R +
+--R 4 4 2 5 3
+--R 78643200a b x + 31457280a b
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 9 12 8 10 2 7 8 3 6 6
+--R - 15360b x - 1105920a b x - 12902400a b x - 55050240a b x
+--R +
+--R 4 5 4 5 4 2 6 3
+--R - 106168320a b x - 94371840a b x - 31457280a b
+--R *
+--R +-+
+--R \|b
+--R ,
+--R
+--R 5 6 6 5 10 6 5 7 4 8
+--R (4320A a b - 1800B a b )x + (100800A a b - 42000B a b )x
+--R +
+--R 7 4 8 3 6
+--R (645120A a b - 268800B a b )x
+--R +
+--R 8 3 9 2 4
+--R (1658880A a b - 691200B a b )x
+--R +
+--R 9 2 10 2 10 11
+--R (1843200A a b - 768000B a b)x + 737280A a b - 307200B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 7 6 6 12 6 6 7 5 10
+--R (- 360A a b + 150B a b )x + (- 25920A a b + 10800B a b )x
+--R +
+--R 7 5 8 4 8
+--R (- 302400A a b + 126000B a b )x
+--R +
+--R 8 4 9 3 6
+--R (- 1290240A a b + 537600B a b )x
+--R +
+--R 9 3 10 2 4
+--R (- 2488320A a b + 1036800B a b )x
+--R +
+--R 10 2 11 2 11 12
+--R (- 2211840A a b + 921600B a b)x - 737280A a b + 307200B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 11 23 11 10 21
+--R - 1280B b x + (- 1536A b - 95360B a b )x
+--R +
+--R 10 2 9 19
+--R (- 114624A a b - 1307760B a b )x
+--R +
+--R 2 9 3 8 17
+--R (- 1583520A a b - 7431080B a b )x
+--R +
+--R 3 8 4 7 15
+--R (- 9106296A a b - 22133390B a b )x
+--R +
+--R 4 7 5 6 13
+--R (- 27575820A a b - 37754235B a b )x
+--R +
+--R 5 6 6 5 11
+--R (- 48060192A a b - 37318920B a b )x
+--R +
+--R 6 5 7 4 9
+--R (- 48767328A a b - 19984920B a b )x
+--R +
+--R 7 4 8 3 7
+--R (- 26726400A a b - 4592640B a b )x
+--R +
+--R 8 3 9 2 5
+--R (- 5587968A a b - 293120B a b )x
+--R +
+--R 9 2 10 3 10 11
+--R (860160A a b - 358400B a b)x + (368640A a b - 153600B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 11 23 11 10 21
+--R 15360B b x + (18432A b + 412160B a b )x
+--R +
+--R 10 2 9 19
+--R (496896A a b + 3612480B a b )x
+--R +
+--R 2 9 3 8 17
+--R (4395648A a b + 15453600B a b )x
+--R +
+--R 3 8 4 7 15
+--R (19055136A a b + 37418440B a b )x
+--R +
+--R 4 7 5 6 13
+--R (46946160A a b + 54197820B a b )x
+--R +
+--R 5 6 6 5 11
+--R (69475824A a b + 46745820B a b )x
+--R +
+--R 6 5 7 4 9
+--R (61392672A a b + 22261000B a b )x
+--R +
+--R 7 4 8 3 7
+--R (29604864A a b + 4704000B a b )x
+--R +
+--R 8 3 9 2 5
+--R (5203968A a b + 453120B a b )x
+--R +
+--R 9 2 10 3 10 11
+--R (- 1044480A a b + 435200B a b)x + (- 368640A a b + 153600B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R 8 10 7 8 2 6 6 3 5 4
+--R 184320b x + 4300800a b x + 27525120a b x + 70778880a b x
+--R +
+--R 4 4 2 5 3
+--R 78643200a b x + 31457280a b
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 9 12 8 10 2 7 8 3 6 6
+--R - 15360b x - 1105920a b x - 12902400a b x - 55050240a b x
+--R +
+--R 4 5 4 5 4 2 6 3
+--R - 106168320a b x - 94371840a b x - 31457280a b
+--R *
+--R +---+
+--R \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 893
+
+--S 894 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 5 6
+--R (12A a b - 5B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 5 6 x\|b
+--R (- 12A a b + 5B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 1024b \|b
+--R Type: Expression(Integer)
+--E 894
+
+--S 895 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 895
+
+--S 896 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 5 6 +---+ x\|b
+--R (- 12A a b + 5B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 5 6 +-+ \|- b \|b x + a - \|- b \|a
+--R (24A a b - 10B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 1024b \|- b \|b
+--R Type: Expression(Integer)
+--E 896
+
+--S 897 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 897
+
+)clear all
+
+--S 898 of 1406
+t0:=x^3*(a+b*x^2)^(5/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 2 9 2 7 2 5 2 3 | 2
+--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x )\|b x + a
+--R Type: Expression(Integer)
+--E 898
+
+--S 899 of 1406
+r0:=-1/7*a*(A*b-a*B)*(a+b*x^2)^(7/2)/b^3+1/9*(A*b-2*a*B)*_
+ (a+b*x^2)^(9/2)/b^3+1/11*B*(a+b*x^2)^(11/2)/b^3
+--R
+--R
+--R (2)
+--R 5 10 5 4 8 4 2 3 6
+--R 63B b x + (77A b + 161B a b )x + (209A a b + 113B a b )x
+--R +
+--R 2 3 3 2 4 3 2 4 2 4 5
+--R (165A a b + 3B a b )x + (11A a b - 4B a b)x - 22A a b + 8B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3
+--R 693b
+--R Type: Expression(Integer)
+--E 899
+
+--S 900 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 20 7 2 6 18
+--R - 693B a b x + (- 847A a b - 15631B a b )x
+--R +
+--R 2 6 3 5 16
+--R (- 19239A a b - 114279B a b )x
+--R +
+--R 3 5 4 4 14
+--R (- 142659A a b - 400653B a b )x
+--R +
+--R 4 4 5 3 12
+--R (- 510741A a b - 770616B a b )x
+--R +
+--R 5 3 6 2 10
+--R (- 1010856A a b - 838992B a b )x
+--R +
+--R 6 2 7 8 7 8 6
+--R (- 1142064A a b - 487872B a b)x + (- 694848A a b - 118272B a )x
+--R +
+--R 8 4
+--R - 177408A a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 8 22 8 7 20 7 2 6 18
+--R 63B b x + (77A b + 4004B a b )x + (4906A a b + 48994B a b )x
+--R +
+--R 2 6 3 5 16 3 5 4 4 14
+--R (60654A a b + 254892B a b )x + (320760A a b + 706959B a b )x
+--R +
+--R 4 4 5 3 12
+--R (909909A a b + 1136520B a b )x
+--R +
+--R 5 3 6 2 10 6 2 7 8
+--R (1506120A a b + 1068144B a b )x + (1467312A a b + 547008B a b)x
+--R +
+--R 7 8 6 8 4
+--R (783552A a b + 118272B a )x + 177408A a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 5 10 4 8 2 3 6 3 2 4 4 2
+--R 693b x + 41580a b x + 388080a b x + 1241856a b x + 1596672a b x
+--R +
+--R 5
+--R 709632a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4
+--R - 7623a b x - 152460a b x - 853776a b x - 1951488a b x
+--R +
+--R 5 2 6
+--R - 1951488a b x - 709632a
+--R Type: Union(Expression(Integer),...)
+--E 900
+
+--S 901 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 6 6 5 10 6 5 7 4 8
+--R (- 22A a b + 8B a b )x + (- 1320A a b + 480B a b )x
+--R +
+--R 7 4 8 3 6 8 3 9 2 4
+--R (- 12320A a b + 4480B a b )x + (- 39424A a b + 14336B a b )x
+--R +
+--R 9 2 10 2 10 11
+--R (- 50688A a b + 18432B a b)x - 22528A a b + 8192B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 6 6 5 10 6 5 7 4 8
+--R (242A a b - 88B a b )x + (4840A a b - 1760B a b )x
+--R +
+--R 7 4 8 3 6 8 3 9 2 4
+--R (27104A a b - 9856B a b )x + (61952A a b - 22528B a b )x
+--R +
+--R 9 2 10 2 10 11
+--R (61952A a b - 22528B a b)x + 22528A a b - 8192B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 8 10 7 8 2 6 6 3 5 4 4 4 2
+--R 693b x + 41580a b x + 388080a b x + 1241856a b x + 1596672a b x
+--R +
+--R 5 3
+--R 709632a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 8 10 2 7 8 3 6 6 4 5 4
+--R - 7623a b x - 152460a b x - 853776a b x - 1951488a b x
+--R +
+--R 5 4 2 6 3
+--R - 1951488a b x - 709632a b
+--R Type: Expression(Integer)
+--E 901
+
+--S 902 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 902
+
+)clear all
+
+--S 903 of 1406
+t0:=x^2*(a+b*x^2)^(5/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 2 8 2 6 2 4 2 2 | 2
+--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x )\|b x + a
+--R Type: Expression(Integer)
+--E 903
+
+--S 904 of 1406
+r0:=1/96*a*(10*A*b-3*a*B)*x^3*(a+b*x^2)^(3/2)/b+1/80*(10*A*b-3*a*B)*_
+ x^3*(a+b*x^2)^(5/2)/b+1/10*B*x^3*(a+b*x^2)^(7/2)/b-_
+ 1/256*a^4*(10*A*b-3*a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)+_
+ 1/256*a^3*(10*A*b-3*a*B)*x*sqrt(a+b*x^2)/b^2+1/128*a^2*_
+ (10*A*b-3*a*B)*x^3*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 4 5 x\|b
+--R (- 150A a b + 45B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 384B b x + (480A b + 1008B a b )x + (1360A a b + 744B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (1180A a b + 30B a b)x + (150A a b - 45B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 2 +-+
+--R 3840b \|b
+--R Type: Expression(Integer)
+--E 904
+
+--S 905 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 5 5 4 8 5 4 6 3 6
+--R (1500A a b - 450B a b )x + (24000A a b - 7200B a b )x
+--R +
+--R 6 3 7 2 4 7 2 8 2
+--R (100800A a b - 30240B a b )x + (153600A a b - 46080B a b)x
+--R +
+--R 8 9
+--R 76800A a b - 23040B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 6 5 5 10 5 5 6 4 8
+--R (- 150A a b + 45B a b )x + (- 7500A a b + 2250B a b )x
+--R +
+--R 6 4 7 3 6 7 3 8 2 4
+--R (- 60000A a b + 18000B a b )x + (- 168000A a b + 50400B a b )x
+--R +
+--R 8 2 9 2 9 10
+--R (- 192000A a b + 57600B a b)x - 76800A a b + 23040B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 9 19 9 8 17
+--R - 384B b x + (- 480A b - 20208B a b )x
+--R +
+--R 8 2 7 15
+--R (- 25360A a b - 204744B a b )x
+--R +
+--R 2 7 3 6 13
+--R (- 261180A a b - 870510B a b )x
+--R +
+--R 3 6 4 5 11
+--R (- 1140750A a b - 1919535B a b )x
+--R +
+--R 4 5 5 4 9
+--R (- 2617100A a b - 2329878B a b )x
+--R +
+--R 5 4 6 3 7
+--R (- 3368160A a b - 1484016B a b )x
+--R +
+--R 6 3 7 2 5
+--R (- 2374720A a b - 368928B a b )x
+--R +
+--R 7 2 8 3 8 9
+--R (- 796160A a b + 42240B a b)x + (- 76800A a b + 23040B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 9 19 9 8 17
+--R 3840B b x + (4800A b + 75360B a b )x
+--R +
+--R 8 2 7 15 2 7 3 6 13
+--R (95200A a b + 498288B a b )x + (642360A a b + 1616700B a b )x
+--R +
+--R 3 6 4 5 11
+--R (2147700A a b + 2923050B a b )x
+--R +
+--R 4 5 5 4 9
+--R (4051100A a b + 3024030B a b )x
+--R +
+--R 5 4 6 3 7
+--R (4460800A a b + 1672320B a b )x
+--R +
+--R 6 3 7 2 5 7 2 8 3
+--R (2763200A a b + 350688B a b )x + (834560A a b - 53760B a b)x
+--R +
+--R 8 9
+--R (76800A a b - 23040B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 6 8 5 6 2 4 4 3 3 2
+--R 38400b x + 614400a b x + 2580480a b x + 3932160a b x
+--R +
+--R 4 2
+--R 1966080a b
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 7 10 6 8 2 5 6 3 4 4
+--R - 3840b x - 192000a b x - 1536000a b x - 4300800a b x
+--R +
+--R 4 3 2 5 2
+--R - 4915200a b x - 1966080a b
+--R *
+--R +-+
+--R \|b
+--R ,
+--R
+--R 4 5 5 4 8 5 4 6 3 6
+--R (- 3000A a b + 900B a b )x + (- 48000A a b + 14400B a b )x
+--R +
+--R 6 3 7 2 4
+--R (- 201600A a b + 60480B a b )x
+--R +
+--R 7 2 8 2 8 9
+--R (- 307200A a b + 92160B a b)x - 153600A a b + 46080B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 6 5 5 10 5 5 6 4 8
+--R (300A a b - 90B a b )x + (15000A a b - 4500B a b )x
+--R +
+--R 6 4 7 3 6 7 3 8 2 4
+--R (120000A a b - 36000B a b )x + (336000A a b - 100800B a b )x
+--R +
+--R 8 2 9 2 9 10
+--R (384000A a b - 115200B a b)x + 153600A a b - 46080B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 9 19 9 8 17
+--R - 384B b x + (- 480A b - 20208B a b )x
+--R +
+--R 8 2 7 15
+--R (- 25360A a b - 204744B a b )x
+--R +
+--R 2 7 3 6 13
+--R (- 261180A a b - 870510B a b )x
+--R +
+--R 3 6 4 5 11
+--R (- 1140750A a b - 1919535B a b )x
+--R +
+--R 4 5 5 4 9
+--R (- 2617100A a b - 2329878B a b )x
+--R +
+--R 5 4 6 3 7
+--R (- 3368160A a b - 1484016B a b )x
+--R +
+--R 6 3 7 2 5
+--R (- 2374720A a b - 368928B a b )x
+--R +
+--R 7 2 8 3 8 9
+--R (- 796160A a b + 42240B a b)x + (- 76800A a b + 23040B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 9 19 9 8 17
+--R 3840B b x + (4800A b + 75360B a b )x
+--R +
+--R 8 2 7 15 2 7 3 6 13
+--R (95200A a b + 498288B a b )x + (642360A a b + 1616700B a b )x
+--R +
+--R 3 6 4 5 11
+--R (2147700A a b + 2923050B a b )x
+--R +
+--R 4 5 5 4 9
+--R (4051100A a b + 3024030B a b )x
+--R +
+--R 5 4 6 3 7
+--R (4460800A a b + 1672320B a b )x
+--R +
+--R 6 3 7 2 5 7 2 8 3
+--R (2763200A a b + 350688B a b )x + (834560A a b - 53760B a b)x
+--R +
+--R 8 9
+--R (76800A a b - 23040B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R 6 8 5 6 2 4 4 3 3 2
+--R 38400b x + 614400a b x + 2580480a b x + 3932160a b x
+--R +
+--R 4 2
+--R 1966080a b
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 7 10 6 8 2 5 6 3 4 4
+--R - 3840b x - 192000a b x - 1536000a b x - 4300800a b x
+--R +
+--R 4 3 2 5 2
+--R - 4915200a b x - 1966080a b
+--R *
+--R +---+
+--R \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 905
+
+--S 906 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 5
+--R (10A a b - 3B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 4 5 x\|b
+--R (10A a b - 3B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 256b \|b
+--R Type: Expression(Integer)
+--E 906
+
+--S 907 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 907
+
+--S 908 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 4 5 +---+ x\|b
+--R (10A a b - 3B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 4 5 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 20A a b + 6B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 256b \|- b \|b
+--R Type: Expression(Integer)
+--E 908
+
+--S 909 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 909
+
+)clear all
+
+--S 910 of 1406
+t0:=x*(a+b*x^2)^(5/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 2 7 2 5 2 3 2 | 2
+--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x)\|b x + a
+--R Type: Expression(Integer)
+--E 910
+
+--S 911 of 1406
+r0:=1/7*(A*b-a*B)*(a+b*x^2)^(7/2)/b^2+1/9*B*(a+b*x^2)^(9/2)/b^2
+--R
+--R
+--R (2)
+--R 4 8 4 3 6 3 2 2 4
+--R 7B b x + (9A b + 19B a b )x + (27A a b + 15B a b )x
+--R +
+--R 2 2 3 2 3 4
+--R (27A a b + B a b)x + 9A a b - 2B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2
+--R 63b
+--R Type: Expression(Integer)
+--E 911
+
+--S 912 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 16 6 2 5 14
+--R - 63B a b x + (- 81A a b - 1011B a b )x
+--R +
+--R 2 5 3 4 12 3 4 4 3 10
+--R (- 1323A a b - 5439B a b )x + (- 7371A a b - 14049B a b )x
+--R +
+--R 4 3 5 2 8 5 2 6 6
+--R (- 20160A a b - 19320B a b )x + (- 30240A a b - 13776B a b)x
+--R +
+--R 6 7 4 7 2
+--R (- 24192A a b - 4032B a )x - 8064A a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 18 7 6 16 6 2 5 14
+--R 7B b x + (9A b + 306B a b )x + (396A a b + 2754B a b )x
+--R +
+--R 2 5 3 4 12 3 4 4 3 10
+--R (3654A a b + 10752B a b )x + (14868A a b + 22239B a b )x
+--R +
+--R 4 3 5 2 8 5 2 6 6
+--R (32760A a b + 25704B a b )x + (41328A a b + 15792B a b)x
+--R +
+--R 6 7 4 7 2
+--R (28224A a b + 4032B a )x + 8064A a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (63b x + 2520a b x + 15120a b x + 28224a b x + 16128a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 567a b x - 7560a b x - 27216a b x - 36288a b x - 16128a
+--R Type: Union(Expression(Integer),...)
+--E 912
+
+--S 913 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 5 5 4 8 5 4 6 3 6
+--R (9A a b - 2B a b )x + (360A a b - 80B a b )x
+--R +
+--R 6 3 7 2 4 7 2 8 2 8
+--R (2160A a b - 480B a b )x + (4032A a b - 896B a b)x + 2304A a b
+--R +
+--R 9
+--R - 512B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 5 5 4 8 5 4 6 3 6
+--R (- 81A a b + 18B a b )x + (- 1080A a b + 240B a b )x
+--R +
+--R 6 3 7 2 4 7 2 8 2
+--R (- 3888A a b + 864B a b )x + (- 5184A a b + 1152B a b)x
+--R +
+--R 8 9
+--R - 2304A a b + 512B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 6 8 5 6 2 4 4 3 3 2 4 2 +-+
+--R (63b x + 2520a b x + 15120a b x + 28224a b x + 16128a b )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 8 2 5 6 3 4 4 4 3 2 5 2
+--R - 567a b x - 7560a b x - 27216a b x - 36288a b x - 16128a b
+--R Type: Expression(Integer)
+--E 913
+
+--S 914 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 914
+
+)clear all
+
+--S 915 of 1406
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R Type: Expression(Integer)
+--E 915
+
+--S 916 of 1406
+r0:=5/192*a*(8*A*b-a*B)*x*(a+b*x^2)^(3/2)/b+1/48*(8*A*b-a*B)*x*_
+ (a+b*x^2)^(5/2)/b+1/8*B*x*(a+b*x^2)^(7/2)/b+5/128*a^3*_
+ (8*A*b-a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_
+ 5/128*a^2*(8*A*b-a*B)*x*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 3 4 x\|b
+--R (120A a b - 15B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 48B b x + (64A b + 136B a b )x + (208A a b + 118B a b)x
+--R +
+--R 2 3
+--R (264A a b + 15B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R +-+
+--R 384b\|b
+--R Type: Expression(Integer)
+--E 916
+
+--S 917 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 4 4 3 6 4 3 5 2 4
+--R (960A a b - 120B a b )x + (9600A a b - 1200B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (23040A a b - 2880B a b)x + 15360A a b - 1920B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 5 4 4 8 4 4 5 3 6
+--R (- 120A a b + 15B a b )x + (- 3840A a b + 480B a b )x
+--R +
+--R 5 3 6 2 4 6 2 7 2
+--R (- 19200A a b + 2400B a b )x + (- 30720A a b + 3840B a b)x
+--R +
+--R 7 8
+--R - 15360A a b + 1920B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 7 15 7 6 13
+--R - 48B b x + (- 64A b - 1672B a b )x
+--R +
+--R 6 2 5 11 2 5 3 4 9
+--R (- 2256A a b - 12150B a b )x + (- 17160A a b - 37839B a b )x
+--R +
+--R 3 4 4 3 7 4 3 5 2 5
+--R (- 58112A a b - 60320B a b )x + (- 103680A a b - 50016B a b )x
+--R +
+--R 5 2 6 3 6 7
+--R (- 94208A a b - 18944B a b)x + (- 33792A a b - 1920B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 7 15 7 6 13
+--R 384B b x + (512A b + 5312B a b )x
+--R +
+--R 6 2 5 11 2 5 3 4 9
+--R (7296A a b + 25968B a b )x + (37824A a b + 62856B a b )x
+--R +
+--R 3 4 4 3 7 4 3 5 2 5
+--R (100288A a b + 83080B a b )x + (146560A a b + 59248B a b )x
+--R +
+--R 5 2 6 3 6 7
+--R (111104A a b + 19904B a b)x + (33792A a b + 1920B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 4 6 3 4 2 2 2 3 +-+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b)\|a \|b \|b x + a
+--R +
+--R 5 8 4 6 2 3 4 3 2 2 4 +-+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b)\|b
+--R ,
+--R
+--R 3 4 4 3 6 4 3 5 2 4
+--R (1920A a b - 240B a b )x + (19200A a b - 2400B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (46080A a b - 5760B a b)x + 30720A a b - 3840B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 5 4 4 8 4 4 5 3 6
+--R (- 240A a b + 30B a b )x + (- 7680A a b + 960B a b )x
+--R +
+--R 5 3 6 2 4 6 2 7 2
+--R (- 38400A a b + 4800B a b )x + (- 61440A a b + 7680B a b)x
+--R +
+--R 7 8
+--R - 30720A a b + 3840B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 7 15 7 6 13
+--R - 48B b x + (- 64A b - 1672B a b )x
+--R +
+--R 6 2 5 11 2 5 3 4 9
+--R (- 2256A a b - 12150B a b )x + (- 17160A a b - 37839B a b )x
+--R +
+--R 3 4 4 3 7 4 3 5 2 5
+--R (- 58112A a b - 60320B a b )x + (- 103680A a b - 50016B a b )x
+--R +
+--R 5 2 6 3 6 7
+--R (- 94208A a b - 18944B a b)x + (- 33792A a b - 1920B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 7 15 7 6 13
+--R 384B b x + (512A b + 5312B a b )x
+--R +
+--R 6 2 5 11 2 5 3 4 9
+--R (7296A a b + 25968B a b )x + (37824A a b + 62856B a b )x
+--R +
+--R 3 4 4 3 7 4 3 5 2 5
+--R (100288A a b + 83080B a b )x + (146560A a b + 59248B a b )x
+--R +
+--R 5 2 6 3 6 7
+--R (111104A a b + 19904B a b)x + (33792A a b + 1920B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 4 6 3 4 2 2 2 3 +---+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b)\|- b \|a \|b x + a
+--R +
+--R 5 8 4 6 2 3 4 3 2 2 4 +---+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 917
+
+--S 918 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 4
+--R (40A a b - 5B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 4 x\|b
+--R (- 40A a b + 5B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 128b\|b
+--R Type: Expression(Integer)
+--E 918
+
+--S 919 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 919
+
+--S 920 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 3 4 +---+ x\|b
+--R (- 40A a b + 5B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 3 4 +-+ \|- b \|b x + a - \|- b \|a
+--R (80A a b - 10B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 128b\|- b \|b
+--R Type: Expression(Integer)
+--E 920
+
+--S 921 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 921
+
+)clear all
+
+--S 922 of 1406
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 922
+
+--S 923 of 1406
+r0:=1/3*a*A*(a+b*x^2)^(3/2)+1/5*A*(a+b*x^2)^(5/2)+_
+ 1/7*B*(a+b*x^2)^(7/2)/b-a^(5/2)*A*atanh(sqrt(a+b*x^2)/_
+ sqrt(a))+a^2*A*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 +-+ \|b x + a
+--R - 105A a b\|a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 3 6 3 2 4 2 2 2 2
+--R 15B b x + (21A b + 45B a b )x + (77A a b + 45B a b)x + 161A a b
+--R +
+--R 3
+--R 15B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 105b
+--R Type: Expression(Integer)
+--E 923
+
+--S 924 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 3 6 4 2 4 5 2 6 | 2
+--R (105A a b x + 2520A a b x + 8400A a b x + 6720A a )\|b x + a
+--R +
+--R 3 3 6 4 2 4 5 2 6 +-+
+--R (- 735A a b x - 5880A a b x - 11760A a b x - 6720A a )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 12 5 2 4 10
+--R - 105B a b x + (- 147A a b - 1155B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 1715A a b - 4515B a b )x + (- 7630A a b - 8610B a b )x
+--R +
+--R 4 2 5 4 5 6 2
+--R (- 15120A a b - 8400B a b)x + (- 10080A a b - 3360B a )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 14 6 5 12 5 2 4 10
+--R 15B b x + (21A b + 420B a b )x + (602A a b + 2730B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (4270A a b + 7980B a b )x + (13930A a b + 12390B a b )x
+--R +
+--R 4 2 5 4 5 6 2
+--R (20160A a b + 10080B a b)x + (10080A a b + 3360B a )x
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (105b x + 2520a b x + 8400a b x + 6720a )\|a \|b x + a - 735a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 5880a b x - 11760a b x - 6720a
+--R Type: Union(Expression(Integer),...)
+--E 924
+
+--S 925 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 4 6 4 3 4 5 2 2 6 | 2
+--R (105A a b x + 2520A a b x + 8400A a b x + 6720A a b)\|b x + a
+--R +
+--R 3 4 6 4 3 4 5 2 2 6 +-+
+--R (- 735A a b x - 5880A a b x - 11760A a b x - 6720A a b)\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 3 4 6 4 3 4 5 2 2 6 | 2
+--R (105A a b x + 2520A a b x + 8400A a b x + 6720A a b)\|b x + a
+--R +
+--R 3 4 6 4 3 4 5 2 2 6 +-+
+--R (- 735A a b x - 5880A a b x - 11760A a b x - 6720A a b)\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 3 4 4 3 6 4 3 5 2 4
+--R (161A a b + 15B a b )x + (3864A a b + 360B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (12880A a b + 1200B a b)x + 10304A a b + 960B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 4 4 3 6 4 3 5 2 4
+--R (- 1127A a b - 105B a b )x + (- 9016A a b - 840B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (- 18032A a b - 1680B a b)x - 10304A a b - 960B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 4 6 3 4 2 2 2 3 +-+ | 2 4 6
+--R (105b x + 2520a b x + 8400a b x + 6720a b)\|a \|b x + a - 735a b x
+--R +
+--R 2 3 4 3 2 2 4
+--R - 5880a b x - 11760a b x - 6720a b
+--R Type: Expression(Integer)
+--E 925
+
+--S 926 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 926
+
+)clear all
+
+--S 927 of 1406
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x^2
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 927
+
+--S 928 of 1406
+r0:=5/24*(6*A*b+a*B)*x*(a+b*x^2)^(3/2)+1/6*(6*A*b+a*B)*x*_
+ (a+b*x^2)^(5/2)/a-A*(a+b*x^2)^(7/2)/(a*x)+5/16*a^2*_
+ (6*A*b+a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+_
+ 5/16*a*(6*A*b+a*B)*x*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 x\|b
+--R (90A a b + 15B a )x atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 6 2 4 2 2 2 +-+
+--R (8B b x + (12A b + 26B a b)x + (54A a b + 33B a )x - 48A a )\|b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 48x\|b
+--R Type: Expression(Integer)
+--E 928
+
+--S 929 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 3 7 3 3 4 2 5
+--R (90A a b + 15B a b )x + (2160A a b + 360B a b )x
+--R +
+--R 4 2 5 3 5 6
+--R (7200A a b + 1200B a b)x + (5760A a b + 960B a )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 4 3 3 7 3 3 4 2 5
+--R (- 630A a b - 105B a b )x + (- 5040A a b - 840B a b )x
+--R +
+--R 4 2 5 3 5 6
+--R (- 10080A a b - 1680B a b)x + (- 5760A a b - 960B a )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 5 12 5 4 10
+--R - 56B b x + (- 84A b - 630B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 1050A a b - 2583B a b )x + (- 4032A a b - 5272B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 4128A a b - 5360B a b)x + (1920A a b - 2112B a )x + 3072A a
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 6 14 6 5 12 5 2 4 10
+--R 8B b x + (12A b + 226B a b )x + (354A a b + 1515B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (2550A a b + 4681B a b )x + (6144A a b + 7688B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (3552A a b + 6416B a b)x + (- 3456A a b + 2112B a )x - 3072A a
+--R *
+--R +-+
+--R \|b
+--R /
+--R +--------+
+--R 3 7 2 5 2 3 3 +-+ | 2
+--R (48b x + 1152a b x + 3840a b x + 3072a x)\|b \|b x + a
+--R +
+--R 3 7 2 5 2 3 3 +-+ +-+
+--R (- 336b x - 2688a b x - 5376a b x - 3072a x)\|a \|b
+--R ,
+--R
+--R 2 4 3 3 7 3 3 4 2 5
+--R (180A a b + 30B a b )x + (4320A a b + 720B a b )x
+--R +
+--R 4 2 5 3 5 6
+--R (14400A a b + 2400B a b)x + (11520A a b + 1920B a )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 4 3 3 7 3 3 4 2 5
+--R (- 1260A a b - 210B a b )x + (- 10080A a b - 1680B a b )x
+--R +
+--R 4 2 5 3 5 6
+--R (- 20160A a b - 3360B a b)x + (- 11520A a b - 1920B a )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 5 12 5 4 10
+--R - 56B b x + (- 84A b - 630B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 1050A a b - 2583B a b )x + (- 4032A a b - 5272B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 4128A a b - 5360B a b)x + (1920A a b - 2112B a )x + 3072A a
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 6 14 6 5 12 5 2 4 10
+--R 8B b x + (12A b + 226B a b )x + (354A a b + 1515B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (2550A a b + 4681B a b )x + (6144A a b + 7688B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (3552A a b + 6416B a b)x + (- 3456A a b + 2112B a )x - 3072A a
+--R *
+--R +---+
+--R \|- b
+--R /
+--R +--------+
+--R 3 7 2 5 2 3 3 +---+ | 2
+--R (48b x + 1152a b x + 3840a b x + 3072a x)\|- b \|b x + a
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+
+--R (- 336b x - 2688a b x - 5376a b x - 3072a x)\|- b \|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 929
+
+--S 930 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3
+--R (30A a b + 5B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 3 x\|b
+--R (- 30A a b - 5B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 16\|b
+--R Type: Expression(Integer)
+--E 930
+
+--S 931 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 931
+
+--S 932 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 3 +---+ x\|b
+--R (- 30A a b - 5B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 3 +-+ \|- b \|b x + a - \|- b \|a
+--R (60A a b + 10B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 16\|- b \|b
+--R Type: Expression(Integer)
+--E 932
+
+--S 933 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 933
+
+)clear all
+
+--S 934 of 1406
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x^3
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 934
+
+--S 935 of 1406
+r0:=1/6*(5*A*b+2*a*B)*(a+b*x^2)^(3/2)+1/10*(5*A*b+2*a*B)*_
+ (a+b*x^2)^(5/2)/a-1/2*A*(a+b*x^2)^(7/2)/(a*x^2)-1/2*a^(3/2)*_
+ (5*A*b+2*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))+1/2*a*_
+ (5*A*b+2*a*B)*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 2 +-+ \|b x + a
+--R (- 75A a b - 30B a )x \|a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (6B b x + (10A b + 22B a b)x + (70A a b + 46B a )x - 15A a )\|b x + a
+--R /
+--R 2
+--R 30x
+--R Type: Expression(Integer)
+--E 935
+
+--S 936 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 3 8 3 3 4 2 6
+--R (75A a b + 30B a b )x + (1800A a b + 720B a b )x
+--R +
+--R 4 2 5 4 5 6 2
+--R (6000A a b + 2400B a b)x + (4800A a b + 1920B a )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 525A a b - 210B a b )x + (- 4200A a b - 1680B a b )x
+--R +
+--R 4 2 5 4 5 6 2
+--R (- 8400A a b - 3360B a b)x + (- 4800A a b - 1920B a )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 12 5 2 4 10
+--R - 42B a b x + (- 70A a b - 490B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 980A a b - 2180B a b )x + (- 3255A a b - 4320B a b )x
+--R +
+--R 4 2 5 4 5 2 6
+--R (- 2040A a b - 2880B a b)x + 1680A a b x + 960A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 14 6 5 12 5 2 4 10
+--R 6B b x + (10A b + 172B a b )x + (320A a b + 1220B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (2285A a b + 3980B a b )x + (4425A a b + 5760B a b )x
+--R +
+--R 4 2 5 4 5 2 6
+--R (1320A a b + 2880B a b)x - 2160A a b x - 960A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 8 2 6 2 4 3 2 +-+ | 2 3 8
+--R (30b x + 720a b x + 2400a b x + 1920a x )\|a \|b x + a - 210a b x
+--R +
+--R 2 2 6 3 4 4 2
+--R - 1680a b x - 3360a b x - 1920a x
+--R Type: Union(Expression(Integer),...)
+--E 936
+
+--S 937 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 4 3 3 6 3 3 4 2 4
+--R (75A a b + 30B a b )x + (1800A a b + 720B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (6000A a b + 2400B a b)x + 4800A a b + 1920B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (- 525A a b - 210B a b )x + (- 4200A a b - 1680B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (- 8400A a b - 3360B a b)x - 4800A a b - 1920B a
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (75A a b + 30B a b )x + (1800A a b + 720B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (6000A a b + 2400B a b)x + 4800A a b + 1920B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (- 525A a b - 210B a b )x + (- 4200A a b - 1680B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (- 8400A a b - 3360B a b)x - 4800A a b - 1920B a
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (70A a b + 46B a b )x + (1680A a b + 1104B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (5600A a b + 3680B a b)x + 4480A a b + 2944B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (- 490A a b - 322B a b )x + (- 3920A a b - 2576B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (- 7840A a b - 5152B a b)x - 4480A a b - 2944B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (30b x + 720a b x + 2400a b x + 1920a )\|a \|b x + a - 210a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 1680a b x - 3360a b x - 1920a
+--R Type: Expression(Integer)
+--E 937
+
+--S 938 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 938
+
+)clear all
+
+--S 939 of 1406
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x^4
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 939
+
+--S 940 of 1406
+r0:=5/12*b*(4*A*b+3*a*B)*x*(a+b*x^2)^(3/2)/a-1/3*(4*A*b+3*a*B)*_
+ (a+b*x^2)^(5/2)/(a*x)-1/3*A*(a+b*x^2)^(7/2)/(a*x^3)+5/8*_
+ a*(4*A*b+3*a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)+_
+ 5/8*b*(4*A*b+3*a*B)*x*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 +-+ x\|b
+--R (60A a b + 45B a )x \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 6 2 4 2 2 2
+--R (6B b x + (12A b + 27B a b)x + (- 56A a b - 24B a )x - 8A a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3
+--R 24x
+--R Type: Expression(Integer)
+--E 940
+
+--S 941 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 2 3 9 2 3 3 2 7
+--R (60A a b + 45B a b )x + (1440A a b + 1080B a b )x
+--R +
+--R 3 2 4 5 4 5 3
+--R (4800A a b + 3600B a b)x + (3840A a b + 2880B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 4 2 3 9 2 3 3 2 7
+--R (- 420A a b - 315B a b )x + (- 3360A a b - 2520B a b )x
+--R +
+--R 3 2 4 5 4 5 3
+--R (- 6720A a b - 5040B a b)x + (- 3840A a b - 2880B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 5 12 5 4 10
+--R - 42B b x + (- 84A b - 525B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 280A a b - 2016B a b )x + (1848A a b - 2064B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (5952A a b + 960B a b)x + (4480A a b + 1536B a )x + 512A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 14 6 5 12 5 2 4 10
+--R 6B b x + (12A b + 177B a b )x + (244A a b + 1275B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 160A a b + 3072B a b )x + (- 4296A a b + 1776B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (- 8128A a b - 1728B a b)x + (- 4736A a b - 1536B a )x - 512A a
+--R /
+--R +--------+
+--R 3 9 2 7 2 5 3 3 | 2
+--R (24b x + 576a b x + 1920a b x + 1536a x )\|b x + a
+--R +
+--R 3 9 2 7 2 5 3 3 +-+
+--R (- 168b x - 1344a b x - 2688a b x - 1536a x )\|a
+--R ,
+--R
+--R 4 2 3 9 2 3 3 2 7
+--R (120A a b + 90B a b )x + (2880A a b + 2160B a b )x
+--R +
+--R 3 2 4 5 4 5 3
+--R (9600A a b + 7200B a b)x + (7680A a b + 5760B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 4 2 3 9 2 3 3 2 7
+--R (- 840A a b - 630B a b )x + (- 6720A a b - 5040B a b )x
+--R +
+--R 3 2 4 5 4 5 3
+--R (- 13440A a b - 10080B a b)x + (- 7680A a b - 5760B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R 5 12 5 4 10
+--R - 42B b x + (- 84A b - 525B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 280A a b - 2016B a b )x + (1848A a b - 2064B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (5952A a b + 960B a b)x + (4480A a b + 1536B a )x + 512A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 14 6 5 12 5 2 4 10
+--R 6B b x + (12A b + 177B a b )x + (244A a b + 1275B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 160A a b + 3072B a b )x + (- 4296A a b + 1776B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (- 8128A a b - 1728B a b)x + (- 4736A a b - 1536B a )x - 512A a
+--R /
+--R +--------+
+--R 3 9 2 7 2 5 3 3 | 2
+--R (24b x + 576a b x + 1920a b x + 1536a x )\|b x + a
+--R +
+--R 3 9 2 7 2 5 3 3 +-+
+--R (- 168b x - 1344a b x - 2688a b x - 1536a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 941
+
+--S 942 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-+
+--R (20A a b + 15B a )\|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R (- 20A a b - 15B a )\|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 8
+--R Type: Expression(Integer)
+--E 942
+
+--S 943 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 943
+
+--S 944 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +-+ x\|b
+--R (- 20A a b - 15B a )\|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R | 2 +-+
+--R 2 +---+ \|b x + a - \|a
+--R (40A a b + 30B a )\|- b atan(------------------)
+--R +---+
+--R x\|- b
+--R /
+--R 8
+--R Type: Expression(Integer)
+--E 944
+
+--S 945 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 945
+
+)clear all
+
+--S 946 of 1406
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x^5
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 946
+
+--S 947 of 1406
+r0:=5/24*b*(3*A*b+4*a*B)*(a+b*x^2)^(3/2)/a-1/8*(3*A*b+4*a*B)*_
+ (a+b*x^2)^(5/2)/(a*x^2)-1/4*A*(a+b*x^2)^(7/2)/(a*x^4)-_
+ 5/8*b*(3*A*b+4*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))*_
+ sqrt(a)+5/8*b*(3*A*b+4*a*B)*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 4 +-+ \|b x + a
+--R (- 45A b - 60B a b)x \|a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 6 2 4 2 2 2
+--R (8B b x + (24A b + 56B a b)x + (- 27A a b - 12B a )x - 6A a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4
+--R 24x
+--R Type: Expression(Integer)
+--E 947
+
+--S 948 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 2 4 10 2 4 3 3 8
+--R (45A a b + 60B a b )x + (1080A a b + 1440B a b )x
+--R +
+--R 3 3 4 2 6 4 2 5 4
+--R (3600A a b + 4800B a b )x + (2880A a b + 3840B a b)x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 2 4 10 2 4 3 3 8
+--R (- 315A a b - 420B a b )x + (- 2520A a b - 3360B a b )x
+--R +
+--R 3 3 4 2 6 4 2 5 4
+--R (- 5040A a b - 6720B a b )x + (- 2880A a b - 3840B a b)x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 12 5 2 4 10
+--R - 56B a b x + (- 144A a b - 784B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 579A a b - 2604B a b )x + (786A a b - 1632B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (3360A a b + 1344B a b)x + (2400A a b + 768B a )x + 384A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 14 6 5 12 5 2 4 10
+--R 8B b x + (24A b + 256B a b )x + (405A a b + 1828B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (471A a b + 3540B a b )x + (- 2190A a b + 1056B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (- 4512A a b - 1728B a b)x + (- 2592A a b - 768B a )x - 384A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 10 2 8 2 6 3 4 +-+ | 2 3 10
+--R (24b x + 576a b x + 1920a b x + 1536a x )\|a \|b x + a - 168a b x
+--R +
+--R 2 2 8 3 6 4 4
+--R - 1344a b x - 2688a b x - 1536a x
+--R Type: Union(Expression(Integer),...)
+--E 948
+
+--S 949 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 2 4 6 2 4 3 3 4
+--R (45A a b + 60B a b )x + (1080A a b + 1440B a b )x
+--R +
+--R 3 3 4 2 2 4 2 5
+--R (3600A a b + 4800B a b )x + 2880A a b + 3840B a b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 2 4 6 2 4 3 3 4
+--R (- 315A a b - 420B a b )x + (- 2520A a b - 3360B a b )x
+--R +
+--R 3 3 4 2 2 4 2 5
+--R (- 5040A a b - 6720B a b )x - 2880A a b - 3840B a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 2 4 6 2 4 3 3 4
+--R (45A a b + 60B a b )x + (1080A a b + 1440B a b )x
+--R +
+--R 3 3 4 2 2 4 2 5
+--R (3600A a b + 4800B a b )x + 2880A a b + 3840B a b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 2 4 6 2 4 3 3 4
+--R (- 315A a b - 420B a b )x + (- 2520A a b - 3360B a b )x
+--R +
+--R 3 3 4 2 2 4 2 5
+--R (- 5040A a b - 6720B a b )x - 2880A a b - 3840B a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 5 2 4 6 2 4 3 3 4
+--R (24A a b + 56B a b )x + (576A a b + 1344B a b )x
+--R +
+--R 3 3 4 2 2 4 2 5
+--R (1920A a b + 4480B a b )x + 1536A a b + 3584B a b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 2 4 6 2 4 3 3 4
+--R (- 168A a b - 392B a b )x + (- 1344A a b - 3136B a b )x
+--R +
+--R 3 3 4 2 2 4 2 5
+--R (- 2688A a b - 6272B a b )x - 1536A a b - 3584B a b
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (24b x + 576a b x + 1920a b x + 1536a )\|a \|b x + a - 168a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 1344a b x - 2688a b x - 1536a
+--R Type: Expression(Integer)
+--E 949
+
+--S 950 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 950
+
+)clear all
+
+--S 951 of 1406
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x^6
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 951
+
+--S 952 of 1406
+r0:=-1/3*b*(2*A*b+5*a*B)*(a+b*x^2)^(3/2)/(a*x)-1/15*(2*A*b+5*a*B)*_
+ (a+b*x^2)^(5/2)/(a*x^3)-1/5*A*(a+b*x^2)^(7/2)/(a*x^5)+_
+ 1/2*b^(3/2)*(2*A*b+5*a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))+_
+ 1/2*b^2*(2*A*b+5*a*B)*x*sqrt(a+b*x^2)/a
+--R
+--R
+--R (2)
+--R +-+
+--R 2 5 +-+ x\|b
+--R (30A b + 75B a b)x \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 6 2 4 2 2 2
+--R (15B b x + (- 46A b - 70B a b)x + (- 22A a b - 10B a )x - 6A a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 5
+--R 30x
+--R Type: Expression(Integer)
+--E 952
+
+--S 953 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 5 4 11 4 2 3 9
+--R (30A b + 75B a b )x + (720A a b + 1800B a b )x
+--R +
+--R 2 3 3 2 7 3 2 4 5
+--R (2400A a b + 6000B a b )x + (1920A a b + 4800B a b)x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 5 4 11 4 2 3 9
+--R (- 210A b - 525B a b )x + (- 1680A a b - 4200B a b )x
+--R +
+--R 2 3 3 2 7 3 2 4 5
+--R (- 3360A a b - 8400B a b )x + (- 1920A a b - 4800B a b)x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 5 12 5 4 10
+--R - 105B b x + (322A b - 350B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (2730A a b + 2310B a b )x + (6426A a b + 7440B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (5744A a b + 5600B a b)x + (2080A a b + 640B a )x + 384A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 14 6 5 12 5 2 4 10
+--R 15B b x + (- 46A b + 305B a b )x + (- 1172A a b - 200B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 5340A a b - 5370B a b )x + (- 9062A a b - 10160B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (- 6736A a b - 5920B a b)x + (- 2272A a b - 640B a )x - 384A a
+--R /
+--R +--------+
+--R 3 11 2 9 2 7 3 5 | 2
+--R (30b x + 720a b x + 2400a b x + 1920a x )\|b x + a
+--R +
+--R 3 11 2 9 2 7 3 5 +-+
+--R (- 210b x - 1680a b x - 3360a b x - 1920a x )\|a
+--R ,
+--R
+--R 5 4 11 4 2 3 9
+--R (60A b + 150B a b )x + (1440A a b + 3600B a b )x
+--R +
+--R 2 3 3 2 7 3 2 4 5
+--R (4800A a b + 12000B a b )x + (3840A a b + 9600B a b)x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 4 11 4 2 3 9
+--R (- 420A b - 1050B a b )x + (- 3360A a b - 8400B a b )x
+--R +
+--R 2 3 3 2 7 3 2 4 5
+--R (- 6720A a b - 16800B a b )x + (- 3840A a b - 9600B a b)x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R 5 12 5 4 10
+--R - 105B b x + (322A b - 350B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (2730A a b + 2310B a b )x + (6426A a b + 7440B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (5744A a b + 5600B a b)x + (2080A a b + 640B a )x + 384A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 14 6 5 12 5 2 4 10
+--R 15B b x + (- 46A b + 305B a b )x + (- 1172A a b - 200B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 5340A a b - 5370B a b )x + (- 9062A a b - 10160B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (- 6736A a b - 5920B a b)x + (- 2272A a b - 640B a )x - 384A a
+--R /
+--R +--------+
+--R 3 11 2 9 2 7 3 5 | 2
+--R (30b x + 720a b x + 2400a b x + 1920a x )\|b x + a
+--R +
+--R 3 11 2 9 2 7 3 5 +-+
+--R (- 210b x - 1680a b x - 3360a b x - 1920a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 953
+
+--S 954 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-+
+--R (2A b + 5B a b)\|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R (- 2A b - 5B a b)\|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 954
+
+--S 955 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 955
+
+--S 956 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +-+ x\|b
+--R (- 2A b - 5B a b)\|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R | 2 +-+
+--R 2 +---+ \|b x + a - \|a
+--R (4A b + 10B a b)\|- b atan(------------------)
+--R +---+
+--R x\|- b
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 956
+
+--S 957 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 957
+
+)clear all
+
+--S 958 of 1406
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x^7
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 958
+
+--S 959 of 1406
+r0:=-5/48*b*(A*b+6*a*B)*(a+b*x^2)^(3/2)/(a*x^2)-1/24*(A*b+6*a*B)*_
+ (a+b*x^2)^(5/2)/(a*x^4)-1/6*A*(a+b*x^2)^(7/2)/(a*x^6)-_
+ 5/16*b^2*(A*b+6*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)+_
+ 5/16*b^2*(A*b+6*a*B)*sqrt(a+b*x^2)/a
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 3 2 6 \|b x + a
+--R (- 15A b - 90B a b )x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 6 2 4 2 2 2
+--R (48B b x + (- 33A b - 54B a b)x + (- 26A a b - 12B a )x - 8A a )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R /
+--R 6 +-+
+--R 48x \|a
+--R Type: Expression(Integer)
+--E 959
+
+--S 960 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 12 5 2 4 10
+--R (15A b + 90B a b )x + (360A a b + 2160B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (1200A a b + 7200B a b )x + (960A a b + 5760B a b )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 5 12 5 2 4 10
+--R (- 105A b - 630B a b )x + (- 840A a b - 5040B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 1680A a b - 10080B a b )x + (- 960A a b - 5760B a b )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 12 5 2 4 10
+--R - 288B a b x + (231A a b - 1158B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (2030A a b + 1572B a b )x + (5208A a b + 6720B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (5472A a b + 4800B a b)x + (2560A a b + 768B a )x + 512A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 14 6 5 12 5 2 4 10
+--R 48B b x + (- 33A b + 810B a b )x + (- 851A a b + 942B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 4090A a b - 4380B a b )x + (- 7656A a b - 9024B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (- 6688A a b - 5184B a b)x + (- 2816A a b - 768B a )x - 512A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 12 2 10 2 8 3 6 +-+ | 2
+--R (48b x + 1152a b x + 3840a b x + 3072a x )\|a \|b x + a
+--R +
+--R 3 12 2 2 10 3 8 4 6
+--R - 336a b x - 2688a b x - 5376a b x - 3072a x
+--R Type: Union(Expression(Integer),...)
+--E 960
+
+--S 961 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 3 2 \|b x + a - \|a
+--R (5A b + 30B a b )log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 3 2 \|b x + a 2
+--R (5A b + 30B a b )atanh(-----------) + 16B a b
+--R +-+
+--R \|a
+--R /
+--R +-+
+--R 16\|a
+--R Type: Expression(Integer)
+--E 961
+
+--S 962 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 962
+
+)clear all
+
+--S 963 of 1406
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x^8
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 963
+
+--S 964 of 1406
+r0:=-1/3*b*B*(a+b*x^2)^(3/2)/x^3-1/5*B*(a+b*x^2)^(5/2)/x^5-_
+ 1/7*A*(a+b*x^2)^(7/2)/(a*x^7)+b^(5/2)*B*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))-b^2*B*sqrt(a+b*x^2)/x
+--R
+--R
+--R (2)
+--R +-+
+--R 2 7 +-+ x\|b
+--R 105B a b x \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 6 2 2 4
+--R (- 15A b - 161B a b )x + (- 45A a b - 77B a b)x
+--R +
+--R 2 3 2 3
+--R (- 45A a b - 21B a )x - 15A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 7
+--R 105a x
+--R Type: Expression(Integer)
+--E 964
+
+--S 965 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 5 13 2 4 11 3 3 9 4 2 7 +-+
+--R (105B a b x + 2520B a b x + 8400B a b x + 6720B a b x )\|b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 13 2 4 11 3 3 9 4 2 7
+--R (- 735B a b x - 5880B a b x - 11760B a b x - 6720B a b x )
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 6 5 12 5 2 4 10
+--R (105A b + 1127B a b )x + (1155A a b + 9555B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (4515A a b + 22491B a b )x + (8625A a b + 20104B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (8760A a b + 7280B a b)x + (4560A a b + 1344B a )x + 960A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 6 14 6 2 5 12
+--R (- 15A b - 161B a b )x + (- 420A a b - 4102B a b )x
+--R +
+--R 2 5 3 4 10 3 4 4 3 8
+--R (- 2730A a b - 18690B a b )x + (- 7980A a b - 31717B a b )x
+--R +
+--R 4 3 5 2 6 5 2 6 4
+--R (- 12495A a b - 23576B a b )x + (- 10920A a b - 7952B a b)x
+--R +
+--R 6 7 2 7
+--R (- 5040A a b - 1344B a )x - 960A a
+--R /
+--R +--------+
+--R 3 13 2 2 11 3 9 4 7 | 2
+--R (105a b x + 2520a b x + 8400a b x + 6720a x )\|b x + a
+--R +
+--R 3 13 2 2 11 3 9 4 7 +-+
+--R (- 735a b x - 5880a b x - 11760a b x - 6720a x )\|a
+--R ,
+--R
+--R 5 13 2 4 11 3 3 9 4 2 7
+--R (210B a b x + 5040B a b x + 16800B a b x + 13440B a b x )
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 13 2 4 11 3 3 9
+--R - 1470B a b x - 11760B a b x - 23520B a b x
+--R +
+--R 4 2 7
+--R - 13440B a b x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R 6 5 12 5 2 4 10
+--R (105A b + 1127B a b )x + (1155A a b + 9555B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (4515A a b + 22491B a b )x + (8625A a b + 20104B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (8760A a b + 7280B a b)x + (4560A a b + 1344B a )x + 960A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 6 14 6 2 5 12
+--R (- 15A b - 161B a b )x + (- 420A a b - 4102B a b )x
+--R +
+--R 2 5 3 4 10 3 4 4 3 8
+--R (- 2730A a b - 18690B a b )x + (- 7980A a b - 31717B a b )x
+--R +
+--R 4 3 5 2 6 5 2 6 4
+--R (- 12495A a b - 23576B a b )x + (- 10920A a b - 7952B a b)x
+--R +
+--R 6 7 2 7
+--R (- 5040A a b - 1344B a )x - 960A a
+--R /
+--R +--------+
+--R 3 13 2 2 11 3 9 4 7 | 2
+--R (105a b x + 2520a b x + 8400a b x + 6720a x )\|b x + a
+--R +
+--R 3 13 2 2 11 3 9 4 7 +-+
+--R (- 735a b x - 5880a b x - 11760a b x - 6720a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 965
+
+--S 966 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R 2 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R B b \|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R - B b \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 966
+
+--S 967 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 967
+
+--S 968 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R 2 +-+ x\|b 2 +---+ \|b x + a - \|a
+--R (6) - B b \|b atanh(-----------) + 2B b \|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 968
+
+--S 969 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 969
+
+)clear all
+
+--S 970 of 1406
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x^9
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R 9
+--R x
+--R Type: Expression(Integer)
+--E 970
+
+--S 971 of 1406
+r0:=5/192*b*(A*b-8*a*B)*(a+b*x^2)^(3/2)/(a*x^4)+1/48*(A*b-8*a*B)*_
+ (a+b*x^2)^(5/2)/(a*x^6)-1/8*A*(a+b*x^2)^(7/2)/(a*x^8)+_
+ 5/128*b^3*(A*b-8*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)+_
+ 5/128*b^2*(A*b-8*a*B)*sqrt(a+b*x^2)/(a*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 4 3 8 \|b x + a
+--R (15A b - 120B a b )x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 3 2 6 2 2 4
+--R (- 15A b - 264B a b )x + (- 118A a b - 208B a b)x
+--R +
+--R 2 3 2 3
+--R (- 136A a b - 64B a )x - 48A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R /
+--R 8 +-+
+--R 384a x \|a
+--R Type: Expression(Integer)
+--E 971
+
+--S 972 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 2 6 14 2 6 3 5 12
+--R (- 120A a b + 960B a b )x + (- 1200A a b + 9600B a b )x
+--R +
+--R 3 5 4 4 10 4 4 5 3 8
+--R (- 2880A a b + 23040B a b )x + (- 1920A a b + 15360B a b )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 8 7 16 7 2 6 14
+--R (15A b - 120B a b )x + (480A a b - 3840B a b )x
+--R +
+--R 2 6 3 5 12 3 5 4 4 10
+--R (2400A a b - 19200B a b )x + (3840A a b - 30720B a b )x
+--R +
+--R 4 4 5 3 8
+--R (1920A a b - 15360B a b )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 7 2 6 14 2 6 3 5 12
+--R (15A a b + 264B a b )x + (598A a b + 8656B a b )x
+--R +
+--R 3 5 4 4 10 4 4 5 3 8
+--R (6312A a b + 48960B a b )x + (27120A a b + 102912B a b )x
+--R +
+--R 5 3 6 2 6 6 2 7 4
+--R (55424A a b + 97280B a b )x + (57600A a b + 43008B a b)x
+--R +
+--R 7 8 2 8
+--R (29696A a b + 8192B a )x + 6144A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 2 6 14 2 6 3 5 12
+--R (- 120A a b - 2112B a b )x + (- 2264A a b - 24896B a b )x
+--R +
+--R 3 5 4 4 10 4 4 5 3 8
+--R (- 15552A a b - 90624B a b )x + (- 49248A a b - 146688B a b )x
+--R +
+--R 5 3 6 2 6 6 2 7 4
+--R (- 80896A a b - 117760B a b )x + (- 71680A a b - 47104B a b)x
+--R +
+--R 7 8 2 8
+--R (- 32768A a b - 8192B a )x - 6144A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 2 3 14 3 2 12 4 10 5 8 +-+ | 2
+--R (3072a b x + 30720a b x + 73728a b x + 49152a x )\|a \|b x + a
+--R +
+--R 2 4 16 3 3 14 4 2 12 5 10 6 8
+--R - 384a b x - 12288a b x - 61440a b x - 98304a b x - 49152a x
+--R Type: Union(Expression(Integer),...)
+--E 972
+
+--S 973 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 4 3 \|b x + a - \|a
+--R (- 5A b + 40B a b )log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 4 3 \|b x + a
+--R (- 5A b + 40B a b )atanh(-----------)
+--R +-+
+--R \|a
+--R /
+--R +-+
+--R 128a\|a
+--R Type: Expression(Integer)
+--E 973
+
+--S 974 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 974
+
+)clear all
+
+--S 975 of 1406
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x^10
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R 10
+--R x
+--R Type: Expression(Integer)
+--E 975
+
+--S 976 of 1406
+r0:=-1/9*A*(a+b*x^2)^(7/2)/(a*x^9)+1/63*(2*A*b-9*a*B)*(a+b*x^2)^(7/2)/(a^2*x^7)
+--R
+--R
+--R (2)
+--R 4 3 8 3 2 2 6
+--R (2A b - 9B a b )x + (- A a b - 27B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (- 15A a b - 27B a b)x + (- 19A a b - 9B a )x - 7A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 9
+--R 63a x
+--R Type: Expression(Integer)
+--E 976
+
+--S 977 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 16 7 2 6 14
+--R (- 18A b + 81B a b )x + (- 231A a b + 1323B a b )x
+--R +
+--R 2 6 3 5 12 3 5 4 4 10
+--R (- 609A a b + 7371B a b )x + (1251A a b + 20169B a b )x
+--R +
+--R 4 4 5 3 8 5 3 6 2 6
+--R (8887A a b + 30600B a b )x + (17944A a b + 26352B a b )x
+--R +
+--R 6 2 7 4 7 8 2 8
+--R (17808A a b + 12096B a b)x + (8896A a b + 2304B a )x + 1792A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 8 18 8 2 7 16
+--R (2A b - 9B a b )x + (81A a b - 396B a b )x
+--R +
+--R 2 7 3 6 14 3 6 4 5 12
+--R (504A a b - 3654B a b )x + (462A a b - 14868B a b )x
+--R +
+--R 4 5 5 4 10 5 4 6 3 8
+--R (- 4266A a b - 32841B a b )x + (- 16119A a b - 42408B a b )x
+--R +
+--R 6 3 7 2 6 7 2 8 4
+--R (- 25848A a b - 32112B a b )x + (- 22032A a b - 13248B a b)x
+--R +
+--R 8 9 2 9
+--R (- 9792A a b - 2304B a )x - 1792A a
+--R /
+--R 2 4 17 3 3 15 4 2 13 5 11 6 9
+--R (63a b x + 2520a b x + 15120a b x + 28224a b x + 16128a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 4 17 3 3 15 4 2 13 5 11 6 9 +-+
+--R (- 567a b x - 7560a b x - 27216a b x - 36288a b x - 16128a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 977
+
+--S 978 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 978
+
+--S 979 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 979
+
+)clear all
+
+--S 980 of 1406
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x^11
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R 11
+--R x
+--R Type: Expression(Integer)
+--E 980
+
+--S 981 of 1406
+r0:=1/96*b*(3*A*b-10*a*B)*(a+b*x^2)^(3/2)/(a*x^6)+1/80*(3*A*b-10*a*B)*_
+ (a+b*x^2)^(5/2)/(a*x^8)-1/10*A*(a+b*x^2)^(7/2)/(a*x^10)-_
+ 1/256*b^4*(3*A*b-10*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)+_
+ 1/128*b^2*(3*A*b-10*a*B)*sqrt(a+b*x^2)/(a*x^4)+_
+ 1/256*b^3*(3*A*b-10*a*B)*sqrt(a+b*x^2)/(a^2*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 5 4 10 \|b x + a
+--R (- 45A b + 150B a b )x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 3 8 3 2 2 6
+--R (45A b - 150B a b )x + (- 30A a b - 1180B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (- 744A a b - 1360B a b)x + (- 1008A a b - 480B a )x - 384A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R /
+--R 2 10 +-+
+--R 3840a x \|a
+--R Type: Expression(Integer)
+--E 981
+
+--S 982 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 2 8 18 2 8 3 7 16
+--R (450A a b - 1500B a b )x + (7200A a b - 24000B a b )x
+--R +
+--R 3 7 4 6 14 4 6 5 5 12
+--R (30240A a b - 100800B a b )x + (46080A a b - 153600B a b )x
+--R +
+--R 5 5 6 4 10
+--R (23040A a b - 76800B a b )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 10 9 20 9 2 8 18
+--R (- 45A b + 150B a b )x + (- 2250A a b + 7500B a b )x
+--R +
+--R 2 8 3 7 16
+--R (- 18000A a b + 60000B a b )x
+--R +
+--R 3 7 4 6 14
+--R (- 50400A a b + 168000B a b )x
+--R +
+--R 4 6 5 5 12
+--R (- 57600A a b + 192000B a b )x
+--R +
+--R 5 5 6 4 10
+--R (- 23040A a b + 76800B a b )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 9 2 8 18 2 8 3 7 16
+--R (- 45A a b + 150B a b )x + (- 2220A a b + 8680B a b )x
+--R +
+--R 3 7 4 6 14 4 6 5 5 12
+--R (- 15756A a b + 120360B a b )x + (- 192A a b + 708480B a b )x
+--R +
+--R 5 5 6 4 10 6 4 7 3 8
+--R (324384A a b + 2081600B a b )x + (1271040A a b + 3302400B a b )x
+--R +
+--R 7 3 8 2 6 8 2 9 4
+--R (2250240A a b + 2882560B a b )x + (2101248A a b + 1310720B a b)x
+--R +
+--R 9 10 2 10
+--R (1007616A a b + 245760B a )x + 196608A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 2 8 18 2 8 3 7 16
+--R (450A a b - 1500B a b )x + (7350A a b - 37300B a b )x
+--R +
+--R 3 7 4 6 14 4 6 5 5 12
+--R (24900A a b - 339000B a b )x + (- 85200A a b - 1472160B a b )x
+--R +
+--R 5 5 6 4 10
+--R (- 775968A a b - 3444800B a b )x
+--R +
+--R 6 4 7 3 8
+--R (- 2188800A a b - 4595200B a b )x
+--R +
+--R 7 3 8 2 6
+--R (- 3187200A a b - 3507200B a b )x
+--R +
+--R 8 2 9 4 9 10 2
+--R (- 2580480A a b - 1433600B a b)x + (- 1105920A a b - 245760B a )x
+--R +
+--R 10
+--R - 196608A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 3 4 18 4 3 16 5 2 14 6 12
+--R 38400a b x + 614400a b x + 2580480a b x + 3932160a b x
+--R +
+--R 7 10
+--R 1966080a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 5 20 4 4 18 5 3 16 6 2 14
+--R - 3840a b x - 192000a b x - 1536000a b x - 4300800a b x
+--R +
+--R 7 12 8 10
+--R - 4915200a b x - 1966080a x
+--R Type: Union(Expression(Integer),...)
+--E 982
+
+--S 983 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 5 4 \|b x + a - \|a
+--R (3A b - 10B a b )log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 5 4 \|b x + a
+--R (3A b - 10B a b )atanh(-----------)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+
+--R 256a \|a
+--R Type: Expression(Integer)
+--E 983
+
+--S 984 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 984
+
+)clear all
+
+--S 985 of 1406
+t0:=x^5*(A+B*x^2)/sqrt(a+b*x^2)
+--R
+--R
+--R 7 5
+--R B x + A x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 985
+
+--S 986 of 1406
+r0:=-1/3*a*(2*A*b-3*a*B)*(a+b*x^2)^(3/2)/b^4+1/5*(A*b-3*a*B)*_
+ (a+b*x^2)^(5/2)/b^4+1/7*B*(a+b*x^2)^(7/2)/b^4+_
+ a^2*(A*b-a*B)*sqrt(a+b*x^2)/b^4
+--R
+--R
+--R (2)
+--R 3 6 3 2 4 2 2 2 2
+--R 15B b x + (21A b - 18B a b )x + (- 28A a b + 24B a b)x + 56A a b
+--R +
+--R 3
+--R - 48B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4
+--R 105b
+--R Type: Expression(Integer)
+--E 986
+
+--S 987 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 12 2 2 10
+--R - 105B a b x + (- 147A a b - 714B a b)x
+--R +
+--R 2 3 8 3 6
+--R (- 980A a b - 840B a )x - 1120A a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 14 3 2 12 2 2 10
+--R 15B b x + (21A b + 357B a b )x + (497A a b + 1134B a b)x
+--R +
+--R 2 3 8 3 6
+--R (1540A a b + 840B a )x + 1120A a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (105b x + 2520a b x + 8400a b x + 6720a )\|a \|b x + a - 735a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 5880a b x - 11760a b x - 6720a
+--R Type: Union(Expression(Integer),...)
+--E 987
+
+--S 988 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 4 4 3 6 4 3 5 2 4
+--R (56A a b - 48B a b )x + (1344A a b - 1152B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (4480A a b - 3840B a b)x + 3584A a b - 3072B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 4 4 3 6 4 3 5 2 4
+--R (- 392A a b + 336B a b )x + (- 3136A a b + 2688B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (- 6272A a b + 5376B a b)x - 3584A a b + 3072B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 7 6 6 4 2 5 2 3 4 +-+ | 2 7 6
+--R (105b x + 2520a b x + 8400a b x + 6720a b )\|a \|b x + a - 735a b x
+--R +
+--R 2 6 4 3 5 2 4 4
+--R - 5880a b x - 11760a b x - 6720a b
+--R Type: Expression(Integer)
+--E 988
+
+--S 989 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 989
+
+)clear all
+
+--S 990 of 1406
+t0:=x^4*(A+B*x^2)/sqrt(a+b*x^2)
+--R
+--R
+--R 6 4
+--R B x + A x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 990
+
+--S 991 of 1406
+r0:=1/16*a^2*(6*A*b-5*a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(7/2)-_
+ 1/16*a*(6*A*b-5*a*B)*x*sqrt(a+b*x^2)/b^3+_
+ 1/24*(6*A*b-5*a*B)*x^3*sqrt(a+b*x^2)/b^2+1/6*B*x^5*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 x\|b
+--R (18A a b - 15B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 2 5 2 3 2 +-+ | 2
+--R (8B b x + (12A b - 10B a b)x + (- 18A a b + 15B a )x)\|b \|b x + a
+--R /
+--R 3 +-+
+--R 48b \|b
+--R Type: Expression(Integer)
+--E 991
+
+--S 992 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 3 2 4 3 2 4 2 4
+--R (108A a b - 90B a b )x + (576A a b - 480B a b)x + 576A a b
+--R +
+--R 5
+--R - 480B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (- 18A a b + 15B a b )x + (- 324A a b + 270B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (- 864A a b + 720B a b)x - 576A a b + 480B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R - 8B b x + (- 12A b - 134B a b )x + (- 198A a b - 219B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (- 252A a b - 46B a b )x + (480A a b - 400B a b)x
+--R +
+--R 4 5
+--R (576A a b - 480B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R 48B b x + (72A b + 244B a b )x + (348A a b + 222B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (84A a b + 186B a b )x + (- 768A a b + 640B a b)x
+--R +
+--R 4 5
+--R (- 576A a b + 480B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +-+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b )\|a \|b \|b x + a
+--R +
+--R 6 6 5 4 2 4 2 3 3 +-+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|b
+--R ,
+--R
+--R 2 3 3 2 4 3 2 4 2
+--R (216A a b - 180B a b )x + (1152A a b - 960B a b)x
+--R +
+--R 4 5
+--R 1152A a b - 960B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (- 36A a b + 30B a b )x + (- 648A a b + 540B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (- 1728A a b + 1440B a b)x - 1152A a b + 960B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R - 8B b x + (- 12A b - 134B a b )x + (- 198A a b - 219B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (- 252A a b - 46B a b )x + (480A a b - 400B a b)x
+--R +
+--R 4 5
+--R (576A a b - 480B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 11 5 4 9 4 2 3 7
+--R 48B b x + (72A b + 244B a b )x + (348A a b + 222B a b )x
+--R +
+--R 2 3 3 2 5 3 2 4 3
+--R (84A a b + 186B a b )x + (- 768A a b + 640B a b)x
+--R +
+--R 4 5
+--R (- 576A a b + 480B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +---+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b )\|- b \|a \|b x + a
+--R +
+--R 6 6 5 4 2 4 2 3 3 +---+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 992
+
+--S 993 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3
+--R (6A a b - 5B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 3 x\|b
+--R (- 6A a b + 5B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 993
+
+--S 994 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 994
+
+--S 995 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 3 +---+ x\|b
+--R (- 6A a b + 5B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 3 +-+ \|- b \|b x + a - \|- b \|a
+--R (12A a b - 10B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 16b \|- b \|b
+--R Type: Expression(Integer)
+--E 995
+
+--S 996 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 996
+
+)clear all
+
+--S 997 of 1406
+t0:=x^3*(A+B*x^2)/sqrt(a+b*x^2)
+--R
+--R
+--R 5 3
+--R B x + A x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 997
+
+--S 998 of 1406
+r0:=1/3*(A*b-2*a*B)*(a+b*x^2)^(3/2)/b^3+1/5*B*(a+b*x^2)^(5/2)/b^3-_
+ a*(A*b-a*B)*sqrt(a+b*x^2)/b^3
+--R
+--R
+--R +--------+
+--R 2 4 2 2 2 | 2
+--R (3B b x + (5A b - 4B a b)x - 10A a b + 8B a )\|b x + a
+--R (2) -----------------------------------------------------------
+--R 3
+--R 15b
+--R Type: Expression(Integer)
+--E 998
+
+--S 999 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 8 2 6 2 4 | 2
+--R (- 15B a b x + (- 25A a b - 40B a )x - 60A a x )\|b x + a
+--R +
+--R 2 10 2 8 2 6 2 4 +-+
+--R (3B b x + (5A b + 35B a b)x + (55A a b + 40B a )x + 60A a x )\|a
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a
+--R Type: Union(Expression(Integer),...)
+--E 999
+
+--S 1000 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 3 2 4 3 2 4 2 4
+--R (- 10A a b + 8B a b )x + (- 120A a b + 96B a b)x - 160A a b
+--R +
+--R 5
+--R 128B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 3 3 2 4 3 2 4 2 4
+--R (50A a b - 40B a b )x + (200A a b - 160B a b)x + 160A a b
+--R +
+--R 5
+--R - 128B a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +-+ | 2 5 4 2 4 2
+--R (15b x + 180a b x + 240a b )\|a \|b x + a - 75a b x - 300a b x
+--R +
+--R 3 3
+--R - 240a b
+--R Type: Expression(Integer)
+--E 1000
+
+--S 1001 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1001
+
+)clear all
+
+--S 1002 of 1406
+t0:=x^2*(A+B*x^2)/sqrt(a+b*x^2)
+--R
+--R
+--R 4 2
+--R B x + A x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 1002
+
+--S 1003 of 1406
+r0:=-1/8*a*(4*A*b-3*a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)+_
+ 1/8*(4*A*b-3*a*B)*x*sqrt(a+b*x^2)/b^2+1/4*B*x^3*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 2 x\|b
+--R (- 4A a b + 3B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 3 +-+ | 2
+--R (2B b x + (4A b - 3B a)x)\|b \|b x + a
+--R /
+--R 2 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 1003
+
+--S 1004 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((16A a b - 12B a b)x + 32A a b - 24B a )\|a \|b x + a
+--R +
+--R 3 2 2 4 2 2 3 2 3 4
+--R (- 4A a b + 3B a b )x + (- 32A a b + 24B a b)x - 32A a b + 24B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R - 2B b x + (- 4A b - 13B a b )x + (- 32A a b + 8B a b)x
+--R +
+--R 2 3
+--R (- 32A a b + 24B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 8B b x + (16A b + 12B a b )x + (48A a b - 20B a b)x
+--R +
+--R 2 3
+--R (32A a b - 24B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+
+--R (32b x + 64a b )\|a \|b \|b x + a + (- 8b x - 64a b x - 64a b )\|b
+--R ,
+--R
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((- 32A a b + 24B a b)x - 64A a b + 48B a )\|a \|b x + a
+--R +
+--R 3 2 2 4 2 2 3 2 3 4
+--R (8A a b - 6B a b )x + (64A a b - 48B a b)x + 64A a b - 48B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 3 7 3 2 5 2 2 3
+--R - 2B b x + (- 4A b - 13B a b )x + (- 32A a b + 8B a b)x
+--R +
+--R 2 3
+--R (- 32A a b + 24B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 8B b x + (16A b + 12B a b )x + (48A a b - 20B a b)x
+--R +
+--R 2 3
+--R (32A a b - 24B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 3 2 2 +---+ +-+ | 2
+--R (32b x + 64a b )\|- b \|a \|b x + a
+--R +
+--R 4 4 3 2 2 2 +---+
+--R (- 8b x - 64a b x - 64a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1004
+
+--S 1005 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2
+--R (4A a b - 3B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R (4A a b - 3B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 1005
+
+--S 1006 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1006
+
+--S 1007 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +---+ x\|b
+--R (4A a b - 3B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 8A a b + 6B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 8b \|- b \|b
+--R Type: Expression(Integer)
+--E 1007
+
+--S 1008 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1008
+
+)clear all
+
+--S 1009 of 1406
+t0:=x*(A+B*x^2)/sqrt(a+b*x^2)
+--R
+--R
+--R 3
+--R B x + A x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 1009
+
+--S 1010 of 1406
+r0:=1/3*B*(a+b*x^2)^(3/2)/b^2+(A*b-a*B)*sqrt(a+b*x^2)/b^2
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B b x + 3A b - 2B a)\|b x + a
+--R (2) ---------------------------------
+--R 2
+--R 3b
+--R Type: Expression(Integer)
+--E 1010
+
+--S 1011 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 2 | 2 6 4 2 +-+
+--R (- 3B a x - 6A a x )\|b x + a + (B b x + (3A b + 3B a)x + 6A a x )\|a
+--R ---------------------------------------------------------------------------
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a
+--R Type: Union(Expression(Integer),...)
+--E 1011
+
+--S 1012 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 2 2 3 | 2
+--R ((3A a b - 2B a b)x + 12A a b - 8B a )\|b x + a
+--R +
+--R 2 2 2 2 3 +-+
+--R ((- 9A a b + 6B a b)x - 12A a b + 8B a )\|a
+--R /
+--R +--------+
+--R 3 2 2 +-+ | 2 3 2 2 2
+--R (3b x + 12a b )\|a \|b x + a - 9a b x - 12a b
+--R Type: Expression(Integer)
+--E 1012
+
+--S 1013 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1013
+
+)clear all
+
+--S 1014 of 1406
+t0:=(A+B*x^2)/sqrt(a+b*x^2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 1014
+
+--S 1015 of 1406
+r0:=1/2*(2*A*b-a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_
+ 1/2*B*x*sqrt(a+b*x^2)/b
+--R
+--R
+--R +-+ +--------+
+--R x\|b +-+ | 2
+--R (2A b - B a)atanh(-----------) + B x\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ---------------------------------------------------
+--R +-+
+--R 2b\|b
+--R Type: Expression(Integer)
+--E 1015
+
+--S 1016 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2 2
+--R ((4A b - 2B a)\|a \|b x + a + (- 2A b + B a b)x - 4A a b + 2B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (- B b x - 2B a x)\|b \|b x + a + (2B b x + 2B a x)\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 2 +-+
+--R 4b\|a \|b \|b x + a + (- 2b x - 4a b)\|b
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2
+--R (8A b - 4B a)\|a \|b x + a + (- 4A b + 2B a b)x - 8A a b
+--R +
+--R 2
+--R 4B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R 3 +---+ | 2 3 +---+ +-+
+--R (- B b x - 2B a x)\|- b \|b x + a + (2B b x + 2B a x)\|- b \|a
+--R /
+--R +--------+
+--R +---+ +-+ | 2 2 2 +---+
+--R 4b\|- b \|a \|b x + a + (- 2b x - 4a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1016
+
+--S 1017 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R (2A b - B a)log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R (- 2A b + B a)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 2b\|b
+--R Type: Expression(Integer)
+--E 1017
+
+--S 1018 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1018
+
+--S 1019 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R +---+ x\|b
+--R (- 2A b + B a)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R +-+ \|- b \|b x + a - \|- b \|a
+--R (4A b - 2B a)\|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 2b\|- b \|b
+--R Type: Expression(Integer)
+--E 1019
+
+--S 1020 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1020
+
+)clear all
+
+--S 1021 of 1406
+t0:=(A+B*x^2)/(x*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ------------
+--R +--------+
+--R | 2
+--R x\|b x + a
+--R Type: Expression(Integer)
+--E 1021
+
+--S 1022 of 1406
+r0:=-A*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)+B*sqrt(a+b*x^2)/b
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R \|b x + a +-+ | 2
+--R - A b atanh(-----------) + B\|a \|b x + a
+--R +-+
+--R \|a
+--R (2) -------------------------------------------
+--R +-+
+--R b\|a
+--R Type: Expression(Integer)
+--E 1022
+
+--S 1023 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 2 +-+
+--R | 2 +-+ \|b x + a - \|a 2 +-+
+--R (A\|b x + a - A\|a )log(------------------) + B x \|a
+--R x
+--R (3) --------------------------------------------------------
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R Type: Union(Expression(Integer),...)
+--E 1023
+
+--S 1024 of 1406
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|b x + a - \|a \|b x + a
+--R A b log(------------------) + A b atanh(-----------) + B a
+--R x +-+
+--R \|a
+--R (4) ----------------------------------------------------------
+--R +-+
+--R b\|a
+--R Type: Expression(Integer)
+--E 1024
+
+--S 1025 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1025
+
+)clear all
+
+--S 1026 of 1406
+t0:=(A+B*x^2)/(x^2*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------
+--R +--------+
+--R 2 | 2
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 1026
+
+--S 1027 of 1406
+r0:=B*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)-A*sqrt(a+b*x^2)/(a*x)
+--R
+--R
+--R +-+ +--------+
+--R x\|b +-+ | 2
+--R B a x atanh(-----------) - A\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -------------------------------------------
+--R +-+
+--R a x\|b
+--R Type: Expression(Integer)
+--E 1027
+
+--S 1028 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R | 2 +-+
+--R (B a x\|b x + a - B a x\|a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R +-+ +-+ | 2 2 +-+
+--R A\|a \|b \|b x + a + (- A b x - A a)\|b
+--R /
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R a x\|b \|b x + a - a x\|a \|b
+--R ,
+--R
+--R +--------+
+--R +--------+ +---+ | 2 +---+ +-+
+--R | 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (2B a x\|b x + a - 2B a x\|a )atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R +---+ +-+ | 2 2 +---+
+--R A\|- b \|a \|b x + a + (- A b x - A a)\|- b
+--R /
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R a x\|- b \|b x + a - a x\|- b \|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1028
+
+--S 1029 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R B log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R - B atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1029
+
+--S 1030 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1030
+
+--S 1031 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a
+--R - B\|- b atanh(-----------) + 2B\|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ------------------------------------------------------------------------
+--R +---+ +-+
+--R \|- b \|b
+--R Type: Expression(Integer)
+--E 1031
+
+--S 1032 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1032
+
+)clear all
+
+--S 1033 of 1406
+t0:=(A+B*x^2)/(x^3*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------
+--R +--------+
+--R 3 | 2
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 1033
+
+--S 1034 of 1406
+r0:=1/2*(A*b-2*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-_
+ 1/2*A*sqrt(a+b*x^2)/(a*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 2 \|b x + a +-+ | 2
+--R (A b - 2B a)x atanh(-----------) - A\|a \|b x + a
+--R +-+
+--R \|a
+--R (2) ---------------------------------------------------
+--R 2 +-+
+--R 2a x \|a
+--R Type: Expression(Integer)
+--E 1034
+
+--S 1035 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 2 | 2
+--R (- 2A a b + 4B a )x \|b x + a
+--R +
+--R 2 4 2 2 +-+
+--R ((A b - 2B a b)x + (2A a b - 4B a )x )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R (A a b x + 2A a )\|b x + a + (- 2A a b x - 2A a )\|a
+--R /
+--R +--------+
+--R 2 2 +-+ | 2 2 4 3 2
+--R 4a x \|a \|b x + a - 2a b x - 4a x
+--R Type: Union(Expression(Integer),...)
+--E 1035
+
+--S 1036 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|b x + a - \|a \|b x + a
+--R (- A b + 2B a)log(------------------) + (- A b + 2B a)atanh(-----------)
+--R x +-+
+--R \|a
+--R ------------------------------------------------------------------------
+--R +-+
+--R 2a\|a
+--R Type: Expression(Integer)
+--E 1036
+
+--S 1037 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1037
+
+)clear all
+
+--S 1038 of 1406
+t0:=(A+B*x^2)/(x^4*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------
+--R +--------+
+--R 4 | 2
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 1038
+
+--S 1039 of 1406
+r0:=-1/3*A*sqrt(a+b*x^2)/(a*x^3)+1/3*(2*A*b-3*a*B)*sqrt(a+b*x^2)/(a^2*x)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R ((2A b - 3B a)x - A a)\|b x + a
+--R (2) ----------------------------------
+--R 2 3
+--R 3a x
+--R Type: Expression(Integer)
+--E 1039
+
+--S 1040 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R ((- 6A b + 9B a b)x + (- 5A a b + 12B a )x + 4A a )\|a \|b x + a
+--R +
+--R 3 2 6 2 2 4 2 3 2 3
+--R (2A b - 3B a b )x + (9A a b - 15B a b)x + (3A a b - 12B a )x - 4A a
+--R /
+--R +--------+
+--R 2 5 3 3 | 2 2 5 3 3 +-+
+--R (3a b x + 12a x )\|b x + a + (- 9a b x - 12a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 1040
+
+--S 1041 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1041
+
+--S 1042 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1042
+
+)clear all
+
+--S 1043 of 1406
+t0:=(A+B*x^2)/(x^5*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------
+--R +--------+
+--R 5 | 2
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 1043
+
+--S 1044 of 1406
+r0:=-1/8*b*(3*A*b-4*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-_
+ 1/4*A*sqrt(a+b*x^2)/(a*x^4)+1/8*(3*A*b-4*a*B)*sqrt(a+b*x^2)/(a^2*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 4 \|b x + a
+--R (- 3A b + 4B a b)x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R ((3A b - 4B a)x - 2A a)\|a \|b x + a
+--R /
+--R 2 4 +-+
+--R 8a x \|a
+--R Type: Expression(Integer)
+--E 1044
+
+--S 1045 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 2 2 6 2 2 3 4 | 2
+--R ((12A a b - 16B a b )x + (24A a b - 32B a b)x )\|b x + a
+--R +
+--R 4 3 8 3 2 2 6
+--R (- 3A b + 4B a b )x + (- 24A a b + 32B a b )x
+--R +
+--R 2 2 3 4
+--R (- 24A a b + 32B a b)x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 3 2 2 6 2 2 3 4
+--R (- 3A a b + 4B a b )x + (- 22A a b + 32B a b)x
+--R +
+--R 3 4 2 4
+--R (- 8A a b + 32B a )x + 16A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 2 6 2 2 3 4 4 2 4 +-+
+--R ((12A a b - 16B a b )x + (28A a b - 48B a b)x - 32B a x - 16A a )\|a
+--R /
+--R +--------+
+--R 3 6 4 4 +-+ | 2 3 2 8 4 6 5 4
+--R (32a b x + 64a x )\|a \|b x + a - 8a b x - 64a b x - 64a x
+--R Type: Union(Expression(Integer),...)
+--E 1045
+
+--S 1046 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 2 \|b x + a - \|a 2 \|b x + a
+--R (3A b - 4B a b)log(------------------) + (3A b - 4B a b)atanh(-----------)
+--R x +-+
+--R \|a
+--R ----------------------------------------------------------------------------
+--R 2 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 1046
+
+--S 1047 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1047
+
+)clear all
+
+--S 1048 of 1406
+t0:=(A+B*x^2)/(x^6*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------
+--R +--------+
+--R 6 | 2
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 1048
+
+--S 1049 of 1406
+r0:=-1/5*A*sqrt(a+b*x^2)/(a*x^5)+1/15*(4*A*b-5*a*B)*_
+ sqrt(a+b*x^2)/(a^2*x^3)-2/15*b*(4*A*b-5*a*B)*sqrt(a+b*x^2)/(a^3*x)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 2 | 2
+--R ((- 8A b + 10B a b)x + (4A a b - 5B a )x - 3A a )\|b x + a
+--R (2) ---------------------------------------------------------------
+--R 3 5
+--R 15a x
+--R Type: Expression(Integer)
+--E 1049
+
+--S 1050 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 8 3 2 2 6
+--R (40A b - 50B a b )x + (140A a b - 175B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (63A a b - 60B a b)x + (- 4A a b + 80B a )x + 48A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 4 10 4 2 3 8
+--R (- 8A b + 10B a b )x + (- 100A a b + 125B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 175A a b + 215B a b )x + (- 55A a b + 20B a b)x
+--R +
+--R 4 5 2 5
+--R (- 20A a b - 80B a )x - 48A a
+--R /
+--R +--------+
+--R 3 2 9 4 7 5 5 | 2
+--R (15a b x + 180a b x + 240a x )\|b x + a
+--R +
+--R 3 2 9 4 7 5 5 +-+
+--R (- 75a b x - 300a b x - 240a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 1050
+
+--S 1051 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1051
+
+--S 1052 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1052
+
+)clear all
+
+--S 1053 of 1406
+t0:=(A+B*x^2)/(x^7*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------
+--R +--------+
+--R 7 | 2
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 1053
+
+--S 1054 of 1406
+r0:=1/16*b^2*(5*A*b-6*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(7/2)-_
+ 1/6*A*sqrt(a+b*x^2)/(a*x^6)+1/24*(5*A*b-6*a*B)*sqrt(a+b*x^2)/_
+ (a^2*x^4)-1/16*b*(5*A*b-6*a*B)*sqrt(a+b*x^2)/(a^3*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 3 2 6 \|b x + a
+--R (15A b - 18B a b )x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R ((- 15A b + 18B a b)x + (10A a b - 12B a )x - 8A a )\|a \|b x + a
+--R /
+--R 3 6 +-+
+--R 48a x \|a
+--R Type: Expression(Integer)
+--E 1054
+
+--S 1055 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 2 4 10 2 4 3 3 8
+--R (- 90A a b + 108B a b )x + (- 480A a b + 576B a b )x
+--R +
+--R 3 3 4 2 6
+--R (- 480A a b + 576B a b )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 5 12 5 2 4 10
+--R (15A b - 18B a b )x + (270A a b - 324B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (720A a b - 864B a b )x + (480A a b - 576B a b )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 2 4 10 2 4 3 3 8
+--R (15A a b - 18B a b )x + (260A a b - 312B a b )x
+--R +
+--R 3 3 4 2 6 4 2 4 5 6 2
+--R (548A a b - 648B a b )x + 144A a b x + (64A a b + 384B a )x
+--R +
+--R 6
+--R 256A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 2 4 10 2 4 3 3 8
+--R (- 90A a b + 108B a b )x + (- 510A a b + 612B a b )x
+--R +
+--R 3 3 4 2 6 4 2 5 4
+--R (- 628A a b + 696B a b )x + (- 144A a b - 192B a b)x
+--R +
+--R 5 6 2 6
+--R (- 192A a b - 384B a )x - 256A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 4 2 10 5 8 6 6 +-+ | 2 4 3 12
+--R (288a b x + 1536a b x + 1536a x )\|a \|b x + a - 48a b x
+--R +
+--R 5 2 10 6 8 7 6
+--R - 864a b x - 2304a b x - 1536a x
+--R Type: Union(Expression(Integer),...)
+--E 1055
+
+--S 1056 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 3 2 \|b x + a - \|a
+--R (- 5A b + 6B a b )log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 3 2 \|b x + a
+--R (- 5A b + 6B a b )atanh(-----------)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 1056
+
+--S 1057 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1057
+
+)clear all
+
+--S 1058 of 1406
+t0:=(A+B*x^2)/(x^8*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------
+--R +--------+
+--R 8 | 2
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 1058
+
+--S 1059 of 1406
+r0:=-1/7*A*sqrt(a+b*x^2)/(a*x^7)+1/35*(6*A*b-7*a*B)*sqrt(a+b*x^2)/_
+ (a^2*x^5)-4/105*b*(6*A*b-7*a*B)*sqrt(a+b*x^2)/(a^3*x^3)+_
+ 8/105*b^2*(6*A*b-7*a*B)*sqrt(a+b*x^2)/(a^4*x)
+--R
+--R
+--R (2)
+--R 3 2 6 2 2 4 2 3 2
+--R (48A b - 56B a b )x + (- 24A a b + 28B a b)x + (18A a b - 21B a )x
+--R +
+--R 3
+--R - 15A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4 7
+--R 105a x
+--R Type: Expression(Integer)
+--E 1059
+
+--S 1060 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 12 5 2 4 10
+--R (- 336A b + 392B a b )x + (- 2520A a b + 2940B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 4158A a b + 4851B a b )x + (- 1287A a b + 1624B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (360A a b + 560B a b)x + (528A a b + 1344B a )x + 960A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 6 14 6 2 5 12
+--R (48A b - 56B a b )x + (1176A a b - 1372B a b )x
+--R +
+--R 2 5 3 4 10 3 4 4 3 8
+--R (4410A a b - 5145B a b )x + (4851A a b - 5677B a b )x
+--R +
+--R 4 3 5 2 6 5 2 6 4
+--R (1113A a b - 1736B a b )x + (- 504A a b - 1232B a b)x
+--R +
+--R 6 7 2 7
+--R (- 1008A a b - 1344B a )x - 960A a
+--R /
+--R +--------+
+--R 4 3 13 5 2 11 6 9 7 7 | 2
+--R (105a b x + 2520a b x + 8400a b x + 6720a x )\|b x + a
+--R +
+--R 4 3 13 5 2 11 6 9 7 7 +-+
+--R (- 735a b x - 5880a b x - 11760a b x - 6720a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 1060
+
+--S 1061 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1061
+
+--S 1062 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1062
+
+)clear all
+
+--S 1063 of 1406
+t0:=x^6*(A+B*x^2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 8 6
+--R B x + A x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 1063
+
+--S 1064 of 1406
+r0:=5/16*a^2*(6*A*b-7*a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(9/2)+_
+ (A*b-a*B)*x^7/(a*b*sqrt(a+b*x^2))-5/16*a*(6*A*b-7*a*B)*x*_
+ sqrt(a+b*x^2)/b^4+5/24*(6*A*b-7*a*B)*x^3*sqrt(a+b*x^2)/b^3-_
+ 1/6*(6*A*b-7*a*B)*x^5*sqrt(a+b*x^2)/(a*b^2)
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 2 3 | 2 x\|b
+--R (90A a b - 105B a )\|b x + a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 8B b x + (12A b - 14B a b )x + (- 30A a b + 35B a b)x
+--R +
+--R 2 3
+--R (- 90A a b + 105B a )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R +--------+
+--R 4 +-+ | 2
+--R 48b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 1064
+
+--S 1065 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 3 6 3 3 4 2 4
+--R (630A a b - 735B a b )x + (5040A a b - 5880B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (10080A a b - 11760B a b)x + 5760A a b - 6720B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 5 3 4 8 3 4 4 3 6
+--R (- 90A a b + 105B a b )x + (- 2250A a b + 2625B a b )x
+--R +
+--R 4 3 5 2 4 5 2 6 2
+--R (- 9360A a b + 10920B a b )x + (- 12960A a b + 15120B a b)x
+--R +
+--R 6 7
+--R - 5760A a b + 6720B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 6 13 6 5 11
+--R - 8B b x + (- 12A b - 178B a b )x
+--R +
+--R 5 2 4 9 2 4 3 3 7
+--R (- 258A a b - 339B a b )x + (- 150A a b - 337B a b )x
+--R +
+--R 3 3 4 2 5 4 2 5 3
+--R (3792A a b - 4424B a b )x + (9120A a b - 10640B a b)x
+--R +
+--R 5 6
+--R (5760A a b - 6720B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 6 13 6 5 11 5 2 4 9
+--R 56B b x + (84A b + 350B a b )x + (462A a b + 357B a b )x
+--R +
+--R 2 4 3 3 7 3 3 4 2 5
+--R (- 966A a b + 1639B a b )x + (- 7632A a b + 8904B a b )x
+--R +
+--R 4 2 5 3 5 6
+--R (- 12000A a b + 14000B a b)x + (- 5760A a b + 6720B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 7 6 6 4 2 5 2 3 4 +-+ +-+ | 2
+--R (336b x + 2688a b x + 5376a b x + 3072a b )\|a \|b \|b x + a
+--R +
+--R 8 8 7 6 2 6 4 3 5 2 4 4 +-+
+--R (- 48b x - 1200a b x - 4992a b x - 6912a b x - 3072a b )\|b
+--R ,
+--R
+--R 2 4 3 3 6 3 3 4 2 4
+--R (1260A a b - 1470B a b )x + (10080A a b - 11760B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (20160A a b - 23520B a b)x + 11520A a b - 13440B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 5 3 4 8 3 4 4 3 6
+--R (- 180A a b + 210B a b )x + (- 4500A a b + 5250B a b )x
+--R +
+--R 4 3 5 2 4 5 2 6 2
+--R (- 18720A a b + 21840B a b )x + (- 25920A a b + 30240B a b)x
+--R +
+--R 6 7
+--R - 11520A a b + 13440B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 6 13 6 5 11
+--R - 8B b x + (- 12A b - 178B a b )x
+--R +
+--R 5 2 4 9 2 4 3 3 7
+--R (- 258A a b - 339B a b )x + (- 150A a b - 337B a b )x
+--R +
+--R 3 3 4 2 5 4 2 5 3
+--R (3792A a b - 4424B a b )x + (9120A a b - 10640B a b)x
+--R +
+--R 5 6
+--R (5760A a b - 6720B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 6 13 6 5 11 5 2 4 9
+--R 56B b x + (84A b + 350B a b )x + (462A a b + 357B a b )x
+--R +
+--R 2 4 3 3 7 3 3 4 2 5
+--R (- 966A a b + 1639B a b )x + (- 7632A a b + 8904B a b )x
+--R +
+--R 4 2 5 3 5 6
+--R (- 12000A a b + 14000B a b)x + (- 5760A a b + 6720B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 7 6 6 4 2 5 2 3 4 +---+ +-+ | 2
+--R (336b x + 2688a b x + 5376a b x + 3072a b )\|- b \|a \|b x + a
+--R +
+--R 8 8 7 6 2 6 4 3 5 2 4 4 +---+
+--R (- 48b x - 1200a b x - 4992a b x - 6912a b x - 3072a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1065
+
+--S 1066 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3
+--R (30A a b - 35B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 3 x\|b
+--R (- 30A a b + 35B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 1066
+
+--S 1067 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1067
+
+--S 1068 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 3 +---+ x\|b
+--R (- 30A a b + 35B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 3 +-+ \|- b \|b x + a - \|- b \|a
+--R (60A a b - 70B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R 4 +---+ +-+
+--R 16b \|- b \|b
+--R Type: Expression(Integer)
+--E 1068
+
+--S 1069 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1069
+
+)clear all
+
+--S 1070 of 1406
+t0:=x^5*(A+B*x^2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 7 5
+--R B x + A x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 1070
+
+--S 1071 of 1406
+r0:=1/3*(A*b-3*a*B)*(a+b*x^2)^(3/2)/b^4+1/5*B*(a+b*x^2)^(5/2)/b^4-_
+ a^2*(A*b-a*B)/(b^4*sqrt(a+b*x^2))-a*(2*A*b-3*a*B)*sqrt(a+b*x^2)/b^4
+--R
+--R
+--R (2)
+--R 3 6 3 2 4 2 2 2 2 3
+--R 3B b x + (5A b - 6B a b )x + (- 20A a b + 24B a b)x - 40A a b + 48B a
+--R ---------------------------------------------------------------------------
+--R +--------+
+--R 4 | 2
+--R 15b \|b x + a
+--R Type: Expression(Integer)
+--E 1071
+
+--S 1072 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 10 2 8 2 6 | 2
+--R (- 18B a b x + (- 30A a b - 60B a )x - 80A a x )\|b x + a
+--R +
+--R 2 12 2 10 2 8 2 6 +-+
+--R (3B b x + (5A b + 48B a b)x + (70A a b + 60B a )x + 80A a x )\|a
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (15b x + 270a b x + 720a b x + 480a )\|a \|b x + a - 90a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 570a b x - 960a b x - 480a
+--R Type: Union(Expression(Integer),...)
+--E 1072
+
+--S 1073 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 3 2 4 3 2 4 2
+--R (- 240A a b + 288B a b )x + (- 1280A a b + 1536B a b)x
+--R +
+--R 4 5
+--R - 1280A a b + 1536B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 4 3 3 6 3 3 4 2 4
+--R (40A a b - 48B a b )x + (720A a b - 864B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (1920A a b - 2304B a b)x + 1280A a b - 1536B a
+--R /
+--R +--------+
+--R 6 4 2 5 2 3 4 | 2
+--R (90a b x + 480a b x + 480a b )\|b x + a
+--R +
+--R 7 6 6 4 2 5 2 3 4 +-+
+--R (- 15b x - 270a b x - 720a b x - 480a b )\|a
+--R Type: Expression(Integer)
+--E 1073
+
+--S 1074 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1074
+
+)clear all
+
+--S 1075 of 1406
+t0:=x^4*(A+B*x^2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 6 4
+--R B x + A x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 1075
+
+--S 1076 of 1406
+r0:=-3/8*a*(4*A*b-5*a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(7/2)+_
+ (A*b-a*B)*x^5/(a*b*sqrt(a+b*x^2))+3/8*(4*A*b-5*a*B)*x*_
+ sqrt(a+b*x^2)/b^3-1/4*(4*A*b-5*a*B)*x^3*sqrt(a+b*x^2)/(a*b^2)
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 2 | 2 x\|b
+--R (- 12A a b + 15B a )\|b x + a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 5 2 3 2 +-+
+--R (2B b x + (4A b - 5B a b)x + (12A a b - 15B a )x)\|b
+--R /
+--R +--------+
+--R 3 +-+ | 2
+--R 8b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 1076
+
+--S 1077 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 2 4 2 2 3 2 3
+--R (60A a b - 75B a b )x + (240A a b - 300B a b)x + 192A a b
+--R +
+--R 4
+--R - 240B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 2 3 6 2 3 3 2 4
+--R (- 12A a b + 15B a b )x + (- 156A a b + 195B a b )x
+--R +
+--R 3 2 4 2 4 5
+--R (- 336A a b + 420B a b)x - 192A a b + 240B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R - 2B b x + (- 4A b - 19B a b )x + (- 60A a b + 43B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (- 208A a b + 260B a b)x + (- 192A a b + 240B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 10B b x + (20A b + 15B a b )x + (140A a b - 143B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (304A a b - 380B a b)x + (192A a b - 240B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +-+ +-+ | 2
+--R (40b x + 160a b x + 128a b )\|a \|b \|b x + a
+--R +
+--R 6 6 5 4 2 4 2 3 3 +-+
+--R (- 8b x - 104a b x - 224a b x - 128a b )\|b
+--R ,
+--R
+--R 3 2 2 4 2 2 3 2
+--R (- 120A a b + 150B a b )x + (- 480A a b + 600B a b)x
+--R +
+--R 3 4
+--R - 384A a b + 480B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 2 3 6 2 3 3 2 4
+--R (24A a b - 30B a b )x + (312A a b - 390B a b )x
+--R +
+--R 3 2 4 2 4 5
+--R (672A a b - 840B a b)x + 384A a b - 480B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R - 2B b x + (- 4A b - 19B a b )x + (- 60A a b + 43B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (- 208A a b + 260B a b)x + (- 192A a b + 240B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 10B b x + (20A b + 15B a b )x + (140A a b - 143B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (304A a b - 380B a b)x + (192A a b - 240B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +---+ +-+ | 2
+--R (40b x + 160a b x + 128a b )\|- b \|a \|b x + a
+--R +
+--R 6 6 5 4 2 4 2 3 3 +---+
+--R (- 8b x - 104a b x - 224a b x - 128a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1077
+
+--S 1078 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2
+--R (12A a b - 15B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R (12A a b - 15B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 1078
+
+--S 1079 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1079
+
+--S 1080 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +---+ x\|b
+--R (12A a b - 15B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 24A a b + 30B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 8b \|- b \|b
+--R Type: Expression(Integer)
+--E 1080
+
+--S 1081 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1081
+
+)clear all
+
+--S 1082 of 1406
+t0:=x^3*(A+B*x^2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 5 3
+--R B x + A x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 1082
+
+--S 1083 of 1406
+r0:=1/3*B*(a+b*x^2)^(3/2)/b^3+a*(A*b-a*B)/(b^3*sqrt(a+b*x^2))+_
+ (A*b-2*a*B)*sqrt(a+b*x^2)/b^3
+--R
+--R
+--R 2 4 2 2 2
+--R B b x + (3A b - 4B a b)x + 6A a b - 8B a
+--R (2) --------------------------------------------
+--R +--------+
+--R 3 | 2
+--R 3b \|b x + a
+--R Type: Expression(Integer)
+--E 1083
+
+--S 1084 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 6 4 | 2 8 6 4 +-+
+--R (- 4B a x - 6A a x )\|b x + a + (B b x + (3A b + 4B a)x + 6A a x )\|a
+--R ---------------------------------------------------------------------------
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (3b x + 24a b x + 24a )\|a \|b x + a - 12a b x - 36a b x - 24a
+--R Type: Union(Expression(Integer),...)
+--E 1084
+
+--S 1085 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((24A a b - 32B a b)x + 48A a b - 64B a )\|a \|b x + a
+--R +
+--R 3 2 2 4 2 2 3 2 3 4
+--R (- 6A a b + 8B a b )x + (- 48A a b + 64B a b)x - 48A a b + 64B a
+--R /
+--R +--------+
+--R 4 2 2 3 | 2 5 4 4 2 2 3 +-+
+--R (12a b x + 24a b )\|b x + a + (- 3b x - 24a b x - 24a b )\|a
+--R Type: Expression(Integer)
+--E 1085
+
+--S 1086 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1086
+
+)clear all
+
+--S 1087 of 1406
+t0:=x^2*(A+B*x^2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 4 2
+--R B x + A x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 1087
+
+--S 1088 of 1406
+r0a:=1/2*(2*A*b-3*a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-x*(A+B*x^2)/(b*sqrt(a+b*x^2))+3/2*B*x*sqrt(a+b*x^2)/b^2
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R | 2 x\|b 3 +-+
+--R (2A b - 3B a)\|b x + a atanh(-----------) + (B b x + (- 2A b + 3B a)x)\|b
+--R +--------+
+--R | 2
+--R \|b x + a
+--R ----------------------------------------------------------------------------
+--R +--------+
+--R 2 +-+ | 2
+--R 2b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 1088
+
+--S 1089 of 1406
+r0b:=1/2*(2*A*b-3*a*B)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)+(A*b-a*B)*x^3/(a*b*sqrt(a+b*x^2))-1/2*(2*A*b-3*a*B)*x*sqrt(a+b*x^2)/(a*b^2)
+--R
+--R
+--R (3)
+--R +--------+ +-+
+--R | 2 x\|b 3 +-+
+--R (2A b - 3B a)\|b x + a atanh(-----------) + (B b x + (- 2A b + 3B a)x)\|b
+--R +--------+
+--R | 2
+--R \|b x + a
+--R ----------------------------------------------------------------------------
+--R +--------+
+--R 2 +-+ | 2
+--R 2b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 1089
+
+--S 1090 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((6A b - 9B a b)x + 8A a b - 12B a )\|a \|b x + a
+--R +
+--R 3 2 4 2 2 2 2 3
+--R (- 2A b + 3B a b )x + (- 10A a b + 15B a b)x - 8A a b + 12B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 2 5 2 3 2 +-+ | 2
+--R (- B b x + (2A b - 7B a b)x + (8A a b - 12B a )x)\|b \|b x + a
+--R +
+--R 2 5 2 3 2 +-+ +-+
+--R (3B b x + (- 6A b + 13B a b)x + (- 8A a b + 12B a )x)\|a \|b
+--R /
+--R +--------+
+--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+
+--R (6b x + 8a b )\|a \|b \|b x + a + (- 2b x - 10a b x - 8a b )\|b
+--R ,
+--R
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((12A b - 18B a b)x + 16A a b - 24B a )\|a \|b x + a
+--R +
+--R 3 2 4 2 2 2 2 3
+--R (- 4A b + 6B a b )x + (- 20A a b + 30B a b)x - 16A a b + 24B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R 2 5 2 3 2 +---+ | 2
+--R (- B b x + (2A b - 7B a b)x + (8A a b - 12B a )x)\|- b \|b x + a
+--R +
+--R 2 5 2 3 2 +---+ +-+
+--R (3B b x + (- 6A b + 13B a b)x + (- 8A a b + 12B a )x)\|- b \|a
+--R /
+--R +--------+
+--R 3 2 2 +---+ +-+ | 2 4 4 3 2 2 2 +---+
+--R (6b x + 8a b )\|- b \|a \|b x + a + (- 2b x - 10a b x - 8a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1090
+
+--S 1091 of 1406
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R (2A b - 3B a)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R (- 2A b + 3B a)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 1091
+
+--S 1092 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 1092
+
+--S 1093 of 1406
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +-+
+--R +---+ x\|b
+--R (- 2A b + 3B a)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R +-+ \|- b \|b x + a - \|- b \|a
+--R (4A b - 6B a)\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 2b \|- b \|b
+--R Type: Expression(Integer)
+--E 1093
+
+--S 1094 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 1094
+
+--S 1095 of 1406
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R (2A b - 3B a)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R (- 2A b + 3B a)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 1095
+
+--S 1096 of 1406
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 1096
+
+--S 1097 of 1406
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +-+
+--R +---+ x\|b
+--R (- 2A b + 3B a)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R +-+ \|- b \|b x + a - \|- b \|a
+--R (4A b - 6B a)\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 2b \|- b \|b
+--R Type: Expression(Integer)
+--E 1097
+
+--S 1098 of 1406
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 1098
+
+)clear all
+
+--S 1099 of 1406
+t0:=x*(A+B*x^2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 3
+--R B x + A x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 1099
+
+--S 1100 of 1406
+r0:=(-A*b+a*B)/(b^2*sqrt(a+b*x^2))+B*sqrt(a+b*x^2)/b^2
+--R
+--R
+--R 2
+--R B b x - A b + 2B a
+--R (2) -------------------
+--R +--------+
+--R 2 | 2
+--R b \|b x + a
+--R Type: Expression(Integer)
+--E 1100
+
+--S 1101 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 | 2 4 2 +-+
+--R - A x \|b x + a + (B x + A x )\|a
+--R (3) ------------------------------------------
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (b x + 2a)\|a \|b x + a - 2a b x - 2a
+--R Type: Union(Expression(Integer),...)
+--E 1101
+
+--S 1102 of 1406
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 2 2 2
+--R (- 2A b + 4B a)\|a \|b x + a + (A b - 2B a b)x + 2A a b - 4B a
+--R (4) -------------------------------------------------------------------
+--R +--------+
+--R 2 | 2 3 2 2 +-+
+--R 2a b \|b x + a + (- b x - 2a b )\|a
+--R Type: Expression(Integer)
+--E 1102
+
+--S 1103 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1103
+
+)clear all
+
+--S 1104 of 1406
+t0:=(A+B*x^2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 1104
+
+--S 1105 of 1406
+r0:=B*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+(A*b-a*B)*x/(a*b*sqrt(a+b*x^2))
+--R
+--R
+--R +--------+ +-+
+--R | 2 x\|b +-+
+--R B a\|b x + a atanh(-----------) + (A b - B a)x\|b
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ---------------------------------------------------
+--R +--------+
+--R +-+ | 2
+--R a b\|b \|b x + a
+--R Type: Expression(Integer)
+--E 1105
+
+--S 1106 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2
+--R (B a\|a \|b x + a - B a b x - B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R (- A b + B a)x\|b \|b x + a + (A b - B a)x\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 2 2 +-+
+--R a b\|a \|b \|b x + a + (- a b x - a b)\|b
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2
+--R (2B a\|a \|b x + a - 2B a b x - 2B a )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R (- A b + B a)x\|- b \|b x + a + (A b - B a)x\|- b \|a
+--R /
+--R +--------+
+--R +---+ +-+ | 2 2 2 2 +---+
+--R a b\|- b \|a \|b x + a + (- a b x - a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1106
+
+--S 1107 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R B log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R - B atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 1107
+
+--S 1108 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1108
+
+--S 1109 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a
+--R - B\|- b atanh(-----------) + 2B\|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ------------------------------------------------------------------------
+--R +---+ +-+
+--R b\|- b \|b
+--R Type: Expression(Integer)
+--E 1109
+
+--S 1110 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1110
+
+)clear all
+
+--S 1111 of 1406
+t0:=(A+B*x^2)/(x*(a+b*x^2)^(3/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------------------
+--R +--------+
+--R 3 | 2
+--R (b x + a x)\|b x + a
+--R Type: Expression(Integer)
+--E 1111
+
+--S 1112 of 1406
+r0:=-A*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)+(A*b-a*B)/(a*b*sqrt(a+b*x^2))
+--R
+--R
+--R +--------+
+--R +--------+ | 2
+--R | 2 \|b x + a +-+
+--R - A b\|b x + a atanh(-----------) + (A b - B a)\|a
+--R +-+
+--R \|a
+--R (2) ----------------------------------------------------
+--R +--------+
+--R +-+ | 2
+--R a b\|a \|b x + a
+--R Type: Expression(Integer)
+--E 1112
+
+--S 1113 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +--------+ | 2 +-+
+--R | 2 2 +-+ \|b x + a - \|a
+--R (A a\|b x + a + (- A b x - A a)\|a )log(------------------)
+--R x
+--R +
+--R 2 +-+
+--R (- A b + B a)x \|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 3
+--R a \|a \|b x + a - a b x - a
+--R Type: Union(Expression(Integer),...)
+--E 1113
+
+--S 1114 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +--------+ | 2 +-+
+--R | 2 +-+ \|b x + a - \|a
+--R (A b\|b x + a - A b\|a )log(------------------)
+--R x
+--R +
+--R +--------+
+--R +--------+ | 2 +--------+
+--R | 2 +-+ \|b x + a | 2
+--R (A b\|b x + a - A b\|a )atanh(-----------) + (A b - B a)\|b x + a
+--R +-+
+--R \|a
+--R +
+--R +-+
+--R (- A b + B a)\|a
+--R /
+--R +--------+
+--R +-+ | 2 2
+--R a b\|a \|b x + a - a b
+--R Type: Expression(Integer)
+--E 1114
+
+--S 1115 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1115
+
+)clear all
+
+--S 1116 of 1406
+t0:=(A+B*x^2)/(x^2*(a+b*x^2)^(3/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1116
+
+--S 1117 of 1406
+r0:=-A/(a*x*sqrt(a+b*x^2))-(2*A*b-a*B)*x/(a^2*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R (- 2A b + B a)x - A a
+--R (2) ----------------------
+--R +--------+
+--R 2 | 2
+--R a x\|b x + a
+--R Type: Expression(Integer)
+--E 1117
+
+--S 1118 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 +-+ | 2 2 4
+--R ((4A b - 2B a)x + 2A a)\|a \|b x + a + (- 2A b + B a b)x
+--R +
+--R 2 2 2
+--R (- 5A a b + 2B a )x - 2A a
+--R /
+--R +--------+
+--R 2 3 3 | 2 2 3 3 +-+
+--R (a b x + 2a x)\|b x + a + (- 2a b x - 2a x)\|a
+--R Type: Union(Expression(Integer),...)
+--E 1118
+
+--S 1119 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1119
+
+--S 1120 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1120
+
+)clear all
+
+--S 1121 of 1406
+t0:=(A+B*x^2)/(x^3*(a+b*x^2)^(3/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ------------------------
+--R +--------+
+--R 5 3 | 2
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1121
+
+--S 1122 of 1406
+r0:=1/2*(3*A*b-2*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)+_
+ 1/2*(-3*A*b+2*a*B)/(a^2*sqrt(a+b*x^2))-1/2*A/(a*x^2*sqrt(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ | 2
+--R 2 | 2 \|b x + a 2 +-+
+--R (3A b - 2B a)x \|b x + a atanh(-----------) + ((- 3A b + 2B a)x - A a)\|a
+--R +-+
+--R \|a
+--R ----------------------------------------------------------------------------
+--R +--------+
+--R 2 2 +-+ | 2
+--R 2a x \|a \|b x + a
+--R Type: Expression(Integer)
+--E 1122
+
+--S 1123 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 2 4 2 3 2 | 2
+--R ((- 9A a b + 6B a b)x + (- 12A a b + 8B a )x )\|b x + a
+--R +
+--R 3 2 6 2 2 4
+--R (3A b - 2B a b )x + (15A a b - 10B a b)x
+--R +
+--R 2 3 2
+--R (12A a b - 8B a )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 4 2 2 3 | 2
+--R ((- 3A a b + 4B a b)x + 5A a b x + 4A a )\|b x + a
+--R +
+--R 3 2 6 2 2 4 2 2 3 +-+
+--R ((2A b - 2B a b )x + (A a b - 4B a b)x - 7A a b x - 4A a )\|a
+--R /
+--R +--------+
+--R 3 4 4 2 +-+ | 2 3 2 6 4 4 5 2
+--R (6a b x + 8a x )\|a \|b x + a - 2a b x - 10a b x - 8a x
+--R Type: Union(Expression(Integer),...)
+--E 1123
+
+--S 1124 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 2 | 2
+--R ((- 3A b + 2B a b)x - 12A a b + 8B a )\|b x + a
+--R +
+--R 2 2 2 +-+
+--R ((9A b - 6B a b)x + 12A a b - 8B a )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 2 | 2
+--R ((- 3A b + 2B a b)x - 12A a b + 8B a )\|b x + a
+--R +
+--R 2 2 2 +-+
+--R ((9A b - 6B a b)x + 12A a b - 8B a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 2 2 | 2
+--R ((- 2A b + 2B a b)x - 8A a b + 8B a )\|b x + a
+--R +
+--R 2 2 2 +-+
+--R ((6A b - 6B a b)x + 8A a b - 8B a )\|a
+--R /
+--R +--------+
+--R 2 2 3 +-+ | 2 3 2 4
+--R (2a b x + 8a )\|a \|b x + a - 6a b x - 8a
+--R Type: Expression(Integer)
+--E 1124
+
+--S 1125 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1125
+
+)clear all
+
+--S 1126 of 1406
+t0:=(A+B*x^2)/(x^4*(a+b*x^2)^(3/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ------------------------
+--R +--------+
+--R 6 4 | 2
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1126
+
+--S 1127 of 1406
+r0:=-1/3*A/(a*x^3*sqrt(a+b*x^2))+1/3*(-4*A*b+3*a*B)/(a^2*x*_
+ sqrt(a+b*x^2))+2/3*(4*A*b-3*a*B)*sqrt(a+b*x^2)/(a^3*x)
+--R
+--R
+--R 2 4 2 2 2
+--R (8A b - 6B a b)x + (4A a b - 3B a )x - A a
+--R (2) ----------------------------------------------
+--R +--------+
+--R 3 3 | 2
+--R 3a x \|b x + a
+--R Type: Expression(Integer)
+--E 1127
+
+--S 1128 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 6 2 2 4
+--R (- 32A b + 24B a b )x + (- 80A a b + 60B a b)x
+--R +
+--R 2 3 2 3
+--R (- 28A a b + 24B a )x + 8A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 3 8 3 2 2 6 2 2 3 4
+--R (8A b - 6B a b )x + (68A a b - 51B a b )x + (95A a b - 72B a b)x
+--R +
+--R 3 4 2 4
+--R (24A a b - 24B a )x - 8A a
+--R /
+--R +--------+
+--R 3 2 7 4 5 5 3 | 2
+--R (3a b x + 24a b x + 24a x )\|b x + a
+--R +
+--R 3 2 7 4 5 5 3 +-+
+--R (- 12a b x - 36a b x - 24a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 1128
+
+--S 1129 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1129
+
+--S 1130 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1130
+
+)clear all
+
+--S 1131 of 1406
+t0:=(A+B*x^2)/(x^5*(a+b*x^2)^(3/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ------------------------
+--R +--------+
+--R 7 5 | 2
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1131
+
+--S 1132 of 1406
+r0:=-3/8*b*(5*A*b-4*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(7/2)-_
+ 1/4*A/(a*x^4*sqrt(a+b*x^2))+1/4*(-5*A*b+4*a*B)/(a^2*x^2*_
+ sqrt(a+b*x^2))+3/8*(5*A*b-4*a*B)*sqrt(a+b*x^2)/(a^3*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ | 2
+--R 2 4 | 2 \|b x + a
+--R (- 15A b + 12B a b)x \|b x + a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+
+--R ((15A b - 12B a b)x + (5A a b - 4B a )x - 2A a )\|a
+--R /
+--R +--------+
+--R 3 4 +-+ | 2
+--R 8a x \|a \|b x + a
+--R Type: Expression(Integer)
+--E 1132
+
+--S 1133 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 3 8 2 3 3 2 6
+--R (75A a b - 60B a b )x + (300A a b - 240B a b )x
+--R +
+--R 3 2 4 4
+--R (240A a b - 192B a b)x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 4 10 4 2 3 8
+--R (- 15A b + 12B a b )x + (- 195A a b + 156B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 420A a b + 336B a b )x + (- 240A a b + 192B a b)x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (25A a b - 28B a b )x + (- 25A a b - 12B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 170A a b + 112B a b)x + (- 56A a b + 64B a )x + 32A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 4 10 4 2 3 8
+--R (- 8A b + 8B a b )x + (- 29A a b + 44B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (101A a b - 36B a b )x + (202A a b - 144B a b)x
+--R +
+--R 4 5 2 5
+--R (40A a b - 64B a )x - 32A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 4 2 8 5 6 6 4 +-+ | 2 4 3 10 5 2 8
+--R (40a b x + 160a b x + 128a x )\|a \|b x + a - 8a b x - 104a b x
+--R +
+--R 6 6 7 4
+--R - 224a b x - 128a x
+--R Type: Union(Expression(Integer),...)
+--E 1133
+
+--S 1134 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 3 4 3 2 2 2 2 2
+--R (15A b - 12B a b )x + (180A a b - 144B a b )x + 240A a b
+--R +
+--R 3
+--R - 192B a b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 3 4 3 2 2 2 2 2
+--R (- 75A b + 60B a b )x + (- 300A a b + 240B a b )x - 240A a b
+--R +
+--R 3
+--R 192B a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 4 3 4 3 2 2 2 2 2
+--R (15A b - 12B a b )x + (180A a b - 144B a b )x + 240A a b
+--R +
+--R 3
+--R - 192B a b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 3 4 3 2 2 2 2 2
+--R (- 75A b + 60B a b )x + (- 300A a b + 240B a b )x - 240A a b
+--R +
+--R 3
+--R 192B a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 3 4 3 2 2 2 2 2 3
+--R ((8A b - 8B a b )x + (96A a b - 96B a b )x + 128A a b - 128B a b)
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 3 4 3 2 2 2 2 2
+--R (- 40A b + 40B a b )x + (- 160A a b + 160B a b )x - 128A a b
+--R +
+--R 3
+--R 128B a b
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 2 4 4 2 5 +-+ | 2 4 2 4 5 2 6
+--R (8a b x + 96a b x + 128a )\|a \|b x + a - 40a b x - 160a b x - 128a
+--R Type: Expression(Integer)
+--E 1134
+
+--S 1135 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1135
+
+)clear all
+
+--S 1136 of 1406
+t0:=(A+B*x^2)/(x^6*(a+b*x^2)^(3/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ------------------------
+--R +--------+
+--R 8 6 | 2
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1136
+
+--S 1137 of 1406
+r0:=-1/5*A/(a*x^5*sqrt(a+b*x^2))+1/5*(-6*A*b+5*a*B)/(a^2*x^3*_
+ sqrt(a+b*x^2))+4/15*(6*A*b-5*a*B)*sqrt(a+b*x^2)/(a^3*x^3)-_
+ 8/15*b*(6*A*b-5*a*B)*sqrt(a+b*x^2)/(a^4*x)
+--R
+--R
+--R (2)
+--R 3 2 6 2 2 4 2 3 2
+--R (- 48A b + 40B a b )x + (- 24A a b + 20B a b)x + (6A a b - 5B a )x
+--R +
+--R 3
+--R - 3A a
+--R /
+--R +--------+
+--R 4 5 | 2
+--R 15a x \|b x + a
+--R Type: Expression(Integer)
+--E 1137
+
+--S 1138 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 10 4 2 3 8
+--R (288A b - 240B a b )x + (1680A a b - 1400B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (2268A a b - 1890B a b )x + (594A a b - 480B a b)x
+--R +
+--R 4 5 2 5
+--R (- 96A a b + 160B a )x + 96A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 5 12 5 2 4 10
+--R (- 48A b + 40B a b )x + (- 888A a b + 740B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 2730A a b + 2275B a b )x + (- 2583A a b + 2150B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (- 534A a b + 400B a b)x + (48A a b - 160B a )x - 96A a
+--R /
+--R +--------+
+--R 4 3 11 5 2 9 6 7 7 5 | 2
+--R (15a b x + 270a b x + 720a b x + 480a x )\|b x + a
+--R +
+--R 4 3 11 5 2 9 6 7 7 5 +-+
+--R (- 90a b x - 570a b x - 960a b x - 480a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 1138
+
+--S 1139 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1139
+
+--S 1140 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1140
+
+)clear all
+
+--S 1141 of 1406
+t0:=(A+B*x^2)/(x^7*(a+b*x^2)^(3/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ------------------------
+--R +--------+
+--R 9 7 | 2
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1141
+
+--S 1142 of 1406
+r0:=5/16*b^2*(7*A*b-6*a*B)*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(9/2)-_
+ 1/6*A/(a*x^6*sqrt(a+b*x^2))+1/6*(-7*A*b+6*a*B)/(a^2*x^4*_
+ sqrt(a+b*x^2))+5/24*(7*A*b-6*a*B)*sqrt(a+b*x^2)/(a^3*x^4)-_
+ 5/16*b*(7*A*b-6*a*B)*sqrt(a+b*x^2)/(a^4*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ | 2
+--R 3 2 6 | 2 \|b x + a
+--R (105A b - 90B a b )x \|b x + a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 3 2 6 2 2 4
+--R (- 105A b + 90B a b )x + (- 35A a b + 30B a b)x
+--R +
+--R 2 3 2 3
+--R (14A a b - 12B a )x - 8A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 4 6 +-+ | 2
+--R 48a x \|a \|b x + a
+--R Type: Expression(Integer)
+--E 1142
+
+--S 1143 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 2 5 12 2 5 3 4 10
+--R (- 735A a b + 630B a b )x + (- 5880A a b + 5040B a b )x
+--R +
+--R 3 4 4 3 8 4 3 5 2 6
+--R (- 11760A a b + 10080B a b )x + (- 6720A a b + 5760B a b )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 6 14 6 2 5 12
+--R (105A b - 90B a b )x + (2625A a b - 2250B a b )x
+--R +
+--R 2 5 3 4 10 3 4 4 3 8
+--R (10920A a b - 9360B a b )x + (15120A a b - 12960B a b )x
+--R +
+--R 4 3 5 2 6
+--R (6720A a b - 5760B a b )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 6 2 5 12 2 5 3 4 10
+--R (- 231A a b + 246B a b )x + (- 133A a b + 498B a b )x
+--R +
+--R 3 4 4 3 8 4 3 5 2 6
+--R (3850A a b - 2532B a b )x + (6120A a b - 4800B a b )x
+--R +
+--R 5 2 6 4 6 7 2 7
+--R (1312A a b - 960B a b)x + (- 256A a b + 768B a )x + 512A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 6 14 6 2 5 12
+--R (48A b - 48B a b )x + (465A a b - 570B a b )x
+--R +
+--R 2 5 3 4 10 3 4 4 3 8
+--R (- 1133A a b + 258B a b )x + (- 6710A a b + 4764B a b )x
+--R +
+--R 4 3 5 2 6 5 2 6 4
+--R (- 6840A a b + 5376B a b )x + (- 1120A a b + 576B a b)x
+--R +
+--R 7 2 7
+--R - 768B a x - 512A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 5 3 12 6 2 10 7 8 8 6 +-+ | 2
+--R (336a b x + 2688a b x + 5376a b x + 3072a x )\|a \|b x + a
+--R +
+--R 5 4 14 6 3 12 7 2 10 8 8 9 6
+--R - 48a b x - 1200a b x - 4992a b x - 6912a b x - 3072a x
+--R Type: Union(Expression(Integer),...)
+--E 1143
+
+--S 1144 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 6 5 6 5 2 4 4
+--R (- 35A b + 30B a b )x + (- 840A a b + 720B a b )x
+--R +
+--R 2 4 3 3 2 3 3 4 2
+--R (- 2800A a b + 2400B a b )x - 2240A a b + 1920B a b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 5 6 5 2 4 4
+--R (245A b - 210B a b )x + (1960A a b - 1680B a b )x
+--R +
+--R 2 4 3 3 2 3 3 4 2
+--R (3920A a b - 3360B a b )x + 2240A a b - 1920B a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 6 5 6 5 2 4 4
+--R (- 35A b + 30B a b )x + (- 840A a b + 720B a b )x
+--R +
+--R 2 4 3 3 2 3 3 4 2
+--R (- 2800A a b + 2400B a b )x - 2240A a b + 1920B a b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 5 6 5 2 4 4
+--R (245A b - 210B a b )x + (1960A a b - 1680B a b )x
+--R +
+--R 2 4 3 3 2 3 3 4 2
+--R (3920A a b - 3360B a b )x + 2240A a b - 1920B a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 6 5 6 5 2 4 4
+--R (- 16A b + 16B a b )x + (- 384A a b + 384B a b )x
+--R +
+--R 2 4 3 3 2 3 3 4 2
+--R (- 1280A a b + 1280B a b )x - 1024A a b + 1024B a b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 5 6 5 2 4 4
+--R (112A b - 112B a b )x + (896A a b - 896B a b )x
+--R +
+--R 2 4 3 3 2 3 3 4 2
+--R (1792A a b - 1792B a b )x + 1024A a b - 1024B a b
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 +-+ | 2 5 3 6
+--R (16a b x + 384a b x + 1280a b x + 1024a )\|a \|b x + a - 112a b x
+--R +
+--R 6 2 4 7 2 8
+--R - 896a b x - 1792a b x - 1024a
+--R Type: Expression(Integer)
+--E 1144
+
+--S 1145 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1145
+
+)clear all
+
+--S 1146 of 1406
+t0:=(A+B*x^2)/(x^8*(a+b*x^2)^(3/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------------------
+--R +--------+
+--R 10 8 | 2
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1146
+
+--S 1147 of 1406
+r0:=-1/7*A/(a*x^7*sqrt(a+b*x^2))+1/7*(-8*A*b+7*a*B)/(a^2*x^5*_
+ sqrt(a+b*x^2))+6/35*(8*A*b-7*a*B)*sqrt(a+b*x^2)/(a^3*x^5)-_
+ 8/35*b*(8*A*b-7*a*B)*sqrt(a+b*x^2)/(a^4*x^3)+16/35*b^2*_
+ (8*A*b-7*a*B)*sqrt(a+b*x^2)/(a^5*x)
+--R
+--R
+--R (2)
+--R 4 3 8 3 2 2 6
+--R (128A b - 112B a b )x + (64A a b - 56B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (- 16A a b + 14B a b)x + (8A a b - 7B a )x - 5A a
+--R /
+--R +--------+
+--R 5 7 | 2
+--R 35a x \|b x + a
+--R Type: Expression(Integer)
+--E 1147
+
+--S 1148 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 14 6 2 5 12
+--R (- 1024A b + 896B a b )x + (- 10752A a b + 9408B a b )x
+--R +
+--R 2 5 3 4 10 3 4 4 3 8
+--R (- 29568A a b + 25872B a b )x + (- 27456A a b + 24024B a b )x
+--R +
+--R 4 3 5 2 6 5 2 6 4
+--R (- 5720A a b + 5040B a b )x + (912A a b - 448B a b)x
+--R +
+--R 6 7 2 7
+--R (- 64A a b + 896B a )x + 640A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 8 7 16 7 2 6 14
+--R (128A b - 112B a b )x + (4160A a b - 3640B a b )x
+--R +
+--R 2 6 3 5 12 3 5 4 4 10
+--R (22512A a b - 19698B a b )x + (42504A a b - 37191B a b )x
+--R +
+--R 4 4 5 3 8 5 3 6 2 6 6 2 4
+--R (30459A a b - 26656B a b )x + (5216A a b - 4704B a b )x - 800A a b x
+--R +
+--R 7 8 2 8
+--R (- 256A a b - 896B a )x - 640A a
+--R /
+--R 5 4 15 6 3 13 7 2 11 8 9 9 7
+--R (35a b x + 1120a b x + 5600a b x + 8960a b x + 4480a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 4 15 6 3 13 7 2 11 8 9 9 7 +-+
+--R (- 280a b x - 3080a b x - 9520a b x - 11200a b x - 4480a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 1148
+
+--S 1149 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1149
+
+--S 1150 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1150
+
+)clear all
+
+--S 1151 of 1406
+t0:=x^7*(A+B*x^2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 9 7
+--R B x + A x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1151
+
+--S 1152 of 1406
+r0:=1/3*a^3*(A*b-a*B)/(b^5*(a+b*x^2)^(3/2))+1/3*(A*b-4*a*B)*_
+ (a+b*x^2)^(3/2)/b^5+1/5*B*(a+b*x^2)^(5/2)/b^5-a^2*(3*A*b-_
+ 4*a*B)/(b^5*sqrt(a+b*x^2))-3*a*(A*b-2*a*B)*sqrt(a+b*x^2)/b^5
+--R
+--R
+--R (2)
+--R 4 8 4 3 6 3 2 2 4
+--R 3B b x + (5A b - 8B a b )x + (- 30A a b + 48B a b )x
+--R +
+--R 2 2 3 2 3 4
+--R (- 120A a b + 192B a b)x - 80A a b + 128B a
+--R /
+--R +--------+
+--R 6 2 5 | 2
+--R (15b x + 15a b )\|b x + a
+--R Type: Expression(Integer)
+--E 1152
+
+--S 1153 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 14 2 2 12
+--R - 24B a b x + (- 40A a b - 176B a b)x
+--R +
+--R 2 3 10 3 8
+--R (- 240A a b - 192B a )x - 240A a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 16 3 2 14 2 2 12
+--R 3B b x + (5A b + 88B a b )x + (130A a b + 272B a b)x
+--R +
+--R 2 3 10 3 8
+--R (360A a b + 192B a )x + 240A a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R (15b x + 495a b x + 2880a b x + 6240a b x + 5760a b x + 1920a )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6
+--R - 120a b x - 1440a b x - 5400a b x - 8880a b x - 6720a b x - 1920a
+--R Type: Union(Expression(Integer),...)
+--E 1153
+
+--S 1154 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 4 3 3 6 3 3 4 2 4
+--R (- 640A a b + 1024B a b )x + (- 6400A a b + 10240B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (- 15360A a b + 24576B a b)x - 10240A a b + 16384B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 5 3 4 8 3 4 4 3 6
+--R (80A a b - 128B a b )x + (2560A a b - 4096B a b )x
+--R +
+--R 4 3 5 2 4 5 2 6 2 6
+--R (12800A a b - 20480B a b )x + (20480A a b - 32768B a b)x + 10240A a b
+--R +
+--R 7
+--R - 16384B a
+--R /
+--R +--------+
+--R 8 6 2 7 4 3 6 2 4 5 | 2
+--R (120a b x + 1200a b x + 2880a b x + 1920a b )\|b x + a
+--R +
+--R 9 8 8 6 2 7 4 3 6 2 4 5 +-+
+--R (- 15b x - 480a b x - 2400a b x - 3840a b x - 1920a b )\|a
+--R Type: Expression(Integer)
+--E 1154
+
+--S 1155 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1155
+
+)clear all
+
+--S 1156 of 1406
+t0:=x^6*(A+B*x^2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 8 6
+--R B x + A x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1156
+
+--S 1157 of 1406
+r0:=1/3*(A*b-a*B)*x^7/(a*b*(a+b*x^2)^(3/2))-5/8*a*(4*A*b-7*a*B)*_
+ atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(9/2)+1/3*(4*A*b-7*a*B)*_
+ x^5/(a*b^2*sqrt(a+b*x^2))+5/8*(4*A*b-7*a*B)*x*_
+ sqrt(a+b*x^2)/b^4-5/12*(4*A*b-7*a*B)*x^3*sqrt(a+b*x^2)/(a*b^3)
+--R
+--R
+--R (2)
+--R +--------+
+--R 2 2 2 2 3 | 2
+--R ((- 60A a b + 105B a b)x - 60A a b + 105B a )\|b x + a
+--R *
+--R +-+
+--R x\|b
+--R atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 6B b x + (12A b - 21B a b )x + (80A a b - 140B a b)x
+--R +
+--R 2 3
+--R (60A a b - 105B a )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R +--------+
+--R 5 2 4 +-+ | 2
+--R (24b x + 24a b )\|b \|b x + a
+--R Type: Expression(Integer)
+--E 1157
+
+--S 1158 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 5 2 4 8 2 4 3 3 6
+--R (420A a b - 735B a b )x + (3780A a b - 6615B a b )x
+--R +
+--R 3 3 4 2 4 4 2 5 2
+--R (10080A a b - 17640B a b )x + (10560A a b - 18480B a b)x
+--R +
+--R 5 6
+--R 3840A a b - 6720B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 2 5 10 2 5 3 4 8
+--R (- 60A a b + 105B a b )x + (- 1560A a b + 2730B a b )x
+--R +
+--R 3 4 4 3 6 4 3 5 2 4
+--R (- 7740A a b + 13545B a b )x + (- 14880A a b + 26040B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (- 12480A a b + 21840B a b)x - 3840A a b + 6720B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 6 13 6 5 11
+--R - 6B b x + (- 12A b - 123B a b )x
+--R +
+--R 5 2 4 9 2 4 3 3 7
+--R (- 368A a b + 164B a b )x + (- 2940A a b + 4761B a b )x
+--R +
+--R 3 3 4 2 5 4 2 5 3
+--R (- 8608A a b + 15064B a b )x + (- 9920A a b + 17360B a b)x
+--R +
+--R 5 6
+--R (- 3840A a b + 6720B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 6 13 6 5 11 5 2 4 9
+--R 42B b x + (84A b + 189B a b )x + (1232A a b - 1484B a b )x
+--R +
+--R 2 4 3 3 7 3 3 4 2 5
+--R (6244A a b - 10543B a b )x + (13088A a b - 22904B a b )x
+--R +
+--R 4 2 5 3 5 6
+--R (11840A a b - 20720B a b)x + (3840A a b - 6720B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 8 8 7 6 2 6 4 3 5 2 4 4 +-+ +-+
+--R (168b x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|a \|b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 10 8 8 2 7 6 3 6 4 4 5 2
+--R - 24b x - 624a b x - 3096a b x - 5952a b x - 4992a b x
+--R +
+--R 5 4
+--R - 1536a b
+--R *
+--R +-+
+--R \|b
+--R ,
+--R
+--R 5 2 4 8 2 4 3 3 6
+--R (- 840A a b + 1470B a b )x + (- 7560A a b + 13230B a b )x
+--R +
+--R 3 3 4 2 4
+--R (- 20160A a b + 35280B a b )x
+--R +
+--R 4 2 5 2 5 6
+--R (- 21120A a b + 36960B a b)x - 7680A a b + 13440B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 2 5 10 2 5 3 4 8
+--R (120A a b - 210B a b )x + (3120A a b - 5460B a b )x
+--R +
+--R 3 4 4 3 6 4 3 5 2 4
+--R (15480A a b - 27090B a b )x + (29760A a b - 52080B a b )x
+--R +
+--R 5 2 6 2 6 7
+--R (24960A a b - 43680B a b)x + 7680A a b - 13440B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 6 13 6 5 11
+--R - 6B b x + (- 12A b - 123B a b )x
+--R +
+--R 5 2 4 9 2 4 3 3 7
+--R (- 368A a b + 164B a b )x + (- 2940A a b + 4761B a b )x
+--R +
+--R 3 3 4 2 5 4 2 5 3
+--R (- 8608A a b + 15064B a b )x + (- 9920A a b + 17360B a b)x
+--R +
+--R 5 6
+--R (- 3840A a b + 6720B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 6 13 6 5 11 5 2 4 9
+--R 42B b x + (84A b + 189B a b )x + (1232A a b - 1484B a b )x
+--R +
+--R 2 4 3 3 7 3 3 4 2 5
+--R (6244A a b - 10543B a b )x + (13088A a b - 22904B a b )x
+--R +
+--R 4 2 5 3 5 6
+--R (11840A a b - 20720B a b)x + (3840A a b - 6720B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R 8 8 7 6 2 6 4 3 5 2 4 4 +---+ +-+
+--R (168b x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|- b \|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 10 8 8 2 7 6 3 6 4 4 5 2
+--R - 24b x - 624a b x - 3096a b x - 5952a b x - 4992a b x
+--R +
+--R 5 4
+--R - 1536a b
+--R *
+--R +---+
+--R \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1158
+
+--S 1159 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2
+--R (20A a b - 35B a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R (20A a b - 35B a )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 1159
+
+--S 1160 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1160
+
+--S 1161 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +---+ x\|b
+--R (20A a b - 35B a )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 40A a b + 70B a )\|b atan(------------------------------)
+--R b x
+--R /
+--R 4 +---+ +-+
+--R 8b \|- b \|b
+--R Type: Expression(Integer)
+--E 1161
+
+--S 1162 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1162
+
+)clear all
+
+--S 1163 of 1406
+t0:=x^5*(A+B*x^2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 7 5
+--R B x + A x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1163
+
+--S 1164 of 1406
+r0:=-1/3*a^2*(A*b-a*B)/(b^4*(a+b*x^2)^(3/2))+1/3*B*(a+b*x^2)^(3/2)/b^4+_
+ a*(2*A*b-3*a*B)/(b^4*sqrt(a+b*x^2))+(A*b-3*a*B)*sqrt(a+b*x^2)/b^4
+--R
+--R
+--R (2)
+--R 3 6 3 2 4 2 2 2 2 3
+--R B b x + (3A b - 6B a b )x + (12A a b - 24B a b)x + 8A a b - 16B a
+--R -----------------------------------------------------------------------
+--R +--------+
+--R 5 2 4 | 2
+--R (3b x + 3a b )\|b x + a
+--R Type: Expression(Integer)
+--E 1164
+
+--S 1165 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 10 2 8 2 6 | 2
+--R (- 6B a b x + (- 10A a b - 12B a )x - 16A a x )\|b x + a
+--R +
+--R 2 12 2 10 2 8 2 6 +-+
+--R (B b x + (3A b + 12B a b)x + (18A a b + 12B a )x + 16A a x )\|a
+--R /
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (3b x + 57a b x + 198a b x + 240a b x + 96a )\|a \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 18a b x - 132a b x - 306a b x - 288a b x - 96a
+--R Type: Union(Expression(Integer),...)
+--E 1165
+
+--S 1166 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 2 2 4 2 2 3 2 3
+--R (48A a b - 96B a b )x + (256A a b - 512B a b)x + 256A a b
+--R +
+--R 4
+--R - 512B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 2 3 6 2 3 3 2 4
+--R (- 8A a b + 16B a b )x + (- 144A a b + 288B a b )x
+--R +
+--R 3 2 4 2 4 5
+--R (- 384A a b + 768B a b)x - 256A a b + 512B a
+--R /
+--R +--------+
+--R 6 4 2 5 2 3 4 | 2
+--R (18a b x + 96a b x + 96a b )\|b x + a
+--R +
+--R 7 6 6 4 2 5 2 3 4 +-+
+--R (- 3b x - 54a b x - 144a b x - 96a b )\|a
+--R Type: Expression(Integer)
+--E 1166
+
+--S 1167 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1167
+
+)clear all
+
+--S 1168 of 1406
+t0:=x^4*(A+B*x^2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 6 4
+--R B x + A x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1168
+
+--S 1169 of 1406
+r0:=1/3*(A*b-a*B)*x^5/(a*b*(a+b*x^2)^(3/2))+1/2*(2*A*b-5*a*B)*_
+ atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(7/2)+1/3*(2*A*b-5*a*B)*_
+ x^3/(a*b^2*sqrt(a+b*x^2))-1/2*(2*A*b-5*a*B)*x*sqrt(a+b*x^2)/(a*b^3)
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 2 2 2 | 2 x\|b
+--R ((6A b - 15B a b)x + 6A a b - 15B a )\|b x + a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 5 2 3 2 +-+
+--R (3B b x + (- 8A b + 20B a b)x + (- 6A a b + 15B a )x)\|b
+--R /
+--R +--------+
+--R 4 2 3 +-+ | 2
+--R (6b x + 6a b )\|b \|b x + a
+--R Type: Expression(Integer)
+--E 1169
+
+--S 1170 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 3 6 3 2 2 4
+--R (30A b - 75B a b )x + (150A a b - 375B a b )x
+--R +
+--R 2 2 3 2 3 4
+--R (216A a b - 540B a b)x + 96A a b - 240B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 4 8 4 2 3 6
+--R (- 6A b + 15B a b )x + (- 84A a b + 210B a b )x
+--R +
+--R 2 3 3 2 4 3 2 4 2 4
+--R (- 246A a b + 615B a b )x + (- 264A a b + 660B a b)x - 96A a b
+--R +
+--R 5
+--R 240B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R - 3B b x + (8A b - 56B a b )x + (102A a b - 303B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (200A a b - 500B a b)x + (96A a b - 240B a )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 15B b x + (- 40A b + 160B a b )x + (- 190A a b + 523B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (- 248A a b + 620B a b)x + (- 96A a b + 240B a )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +-+ +-+ | 2
+--R (30b x + 150a b x + 216a b x + 96a b )\|a \|b \|b x + a
+--R +
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +-+
+--R (- 6b x - 84a b x - 246a b x - 264a b x - 96a b )\|b
+--R ,
+--R
+--R 4 3 6 3 2 2 4
+--R (60A b - 150B a b )x + (300A a b - 750B a b )x
+--R +
+--R 2 2 3 2 3 4
+--R (432A a b - 1080B a b)x + 192A a b - 480B a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 4 8 4 2 3 6
+--R (- 12A b + 30B a b )x + (- 168A a b + 420B a b )x
+--R +
+--R 2 3 3 2 4 3 2 4 2
+--R (- 492A a b + 1230B a b )x + (- 528A a b + 1320B a b)x
+--R +
+--R 4 5
+--R - 192A a b + 480B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R - 3B b x + (8A b - 56B a b )x + (102A a b - 303B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (200A a b - 500B a b)x + (96A a b - 240B a )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 15B b x + (- 40A b + 160B a b )x + (- 190A a b + 523B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (- 248A a b + 620B a b)x + (- 96A a b + 240B a )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +---+ +-+ | 2
+--R (30b x + 150a b x + 216a b x + 96a b )\|- b \|a \|b x + a
+--R +
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +---+
+--R (- 6b x - 84a b x - 246a b x - 264a b x - 96a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1170
+
+--S 1171 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R (2A b - 5B a)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R (- 2A b + 5B a)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 1171
+
+--S 1172 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1172
+
+--S 1173 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R +---+ x\|b
+--R (- 2A b + 5B a)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R +-+ \|- b \|b x + a - \|- b \|a
+--R (4A b - 10B a)\|b atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 2b \|- b \|b
+--R Type: Expression(Integer)
+--E 1173
+
+--S 1174 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1174
+
+)clear all
+
+--S 1175 of 1406
+t0:=x^3*(A+B*x^2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 5 3
+--R B x + A x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1175
+
+--S 1176 of 1406
+r0:=1/3*a*(A*b-a*B)/(b^3*(a+b*x^2)^(3/2))+(-A*b+2*a*B)/(b^3*_
+ sqrt(a+b*x^2))+B*sqrt(a+b*x^2)/b^3
+--R
+--R
+--R 2 4 2 2 2
+--R 3B b x + (- 3A b + 12B a b)x - 2A a b + 8B a
+--R (2) ------------------------------------------------
+--R +--------+
+--R 4 2 3 | 2
+--R (3b x + 3a b )\|b x + a
+--R Type: Expression(Integer)
+--E 1176
+
+--S 1177 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 6 4 | 2
+--R ((- 2A b - 4B a)x - 6A a x )\|b x + a
+--R +
+--R 8 6 4 +-+
+--R (3B b x + (5A b + 4B a)x + 6A a x )\|a
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6 2 2 4
+--R (3b x + 27a b x + 48a b x + 24a )\|a \|b x + a - 12a b x - 48a b x
+--R +
+--R 3 2 4
+--R - 60a b x - 24a
+--R Type: Union(Expression(Integer),...)
+--E 1177
+
+--S 1178 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((- 8A b + 32B a b)x - 16A a b + 64B a )\|a \|b x + a
+--R +
+--R 3 2 4 2 2 2 2 3
+--R (2A b - 8B a b )x + (16A a b - 64B a b)x + 16A a b - 64B a
+--R /
+--R +--------+
+--R 4 2 2 3 | 2 5 4 4 2 2 3 +-+
+--R (12a b x + 24a b )\|b x + a + (- 3b x - 24a b x - 24a b )\|a
+--R Type: Expression(Integer)
+--E 1178
+
+--S 1179 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1179
+
+)clear all
+
+--S 1180 of 1406
+t0:=x^2*(A+B*x^2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 4 2
+--R B x + A x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1180
+
+--S 1181 of 1406
+r0:=1/3*(A*b-a*B)*x^3/(a*b*(a+b*x^2)^(3/2))+B*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(5/2)-B*x/(b^2*sqrt(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 2 2 | 2 x\|b
+--R (3B a b x + 3B a )\|b x + a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 3 2 +-+
+--R ((A b - 4B a b)x - 3B a x)\|b
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ | 2
+--R (3a b x + 3a b )\|b \|b x + a
+--R Type: Expression(Integer)
+--E 1181
+
+--S 1182 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 4 2 2 3 +-+ | 2 3 6
+--R (9B a b x + 21B a b x + 12B a )\|a \|b x + a - 3B a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 18B a b x - 27B a b x - 12B a
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 3 2 5 2 2 3 3 +-+
+--R ((- A b + 4B a b )x + (- 4A a b + 19B a b)x + 12B a x)\|b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 5 2 2 3 3 +-+ +-+
+--R ((3A b - 12B a b )x + (4A a b - 25B a b)x - 12B a x)\|a \|b
+--R /
+--R +--------+
+--R 4 4 2 3 2 3 2 +-+ +-+ | 2
+--R (9a b x + 21a b x + 12a b )\|a \|b \|b x + a
+--R +
+--R 5 6 2 4 4 3 3 2 4 2 +-+
+--R (- 3a b x - 18a b x - 27a b x - 12a b )\|b
+--R ,
+--R
+--R +--------+
+--R 2 4 2 2 3 +-+ | 2 3 6
+--R (18B a b x + 42B a b x + 24B a )\|a \|b x + a - 6B a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 36B a b x - 54B a b x - 24B a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 3 2 5 2 2 3 3 +---+
+--R ((- A b + 4B a b )x + (- 4A a b + 19B a b)x + 12B a x)\|- b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 5 2 2 3 3 +---+ +-+
+--R ((3A b - 12B a b )x + (4A a b - 25B a b)x - 12B a x)\|- b \|a
+--R /
+--R +--------+
+--R 4 4 2 3 2 3 2 +---+ +-+ | 2
+--R (9a b x + 21a b x + 12a b )\|- b \|a \|b x + a
+--R +
+--R 5 6 2 4 4 3 3 2 4 2 +---+
+--R (- 3a b x - 18a b x - 27a b x - 12a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1182
+
+--S 1183 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R B log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R - B atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 1183
+
+--S 1184 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1184
+
+--S 1185 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a
+--R - B\|- b atanh(-----------) + 2B\|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ------------------------------------------------------------------------
+--R 2 +---+ +-+
+--R b \|- b \|b
+--R Type: Expression(Integer)
+--E 1185
+
+--S 1186 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1186
+
+)clear all
+
+--S 1187 of 1406
+t0:=x*(A+B*x^2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 3
+--R B x + A x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1187
+
+--S 1188 of 1406
+r0:=1/3*(-A*b+a*B)/(b^2*(a+b*x^2)^(3/2))-B/(b^2*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R - 3B b x - A b - 2B a
+--R (2) --------------------------
+--R +--------+
+--R 3 2 2 | 2
+--R (3b x + 3a b )\|b x + a
+--R Type: Expression(Integer)
+--E 1188
+
+--S 1189 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 | 2
+--R ((- 3A a b - 3B a )x - 6A a x )\|b x + a
+--R +
+--R 2 6 2 4 2 2 +-+
+--R ((A b + 2B a b)x + (6A a b + 3B a )x + 6A a x )\|a
+--R /
+--R +--------+
+--R 2 2 4 3 2 4 +-+ | 2 2 3 6 3 2 4
+--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x
+--R +
+--R 4 2 5
+--R - 27a b x - 12a
+--R Type: Union(Expression(Integer),...)
+--E 1189
+
+--S 1190 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((- A b - 2B a b)x - 4A a b - 8B a )\|a \|b x + a
+--R +
+--R 2 2 2 2 3
+--R (3A a b + 6B a b)x + 4A a b + 8B a
+--R /
+--R +--------+
+--R 2 3 2 3 2 | 2 2 3 2 3 2 +-+
+--R (3a b x + 12a b )\|b x + a + (- 9a b x - 12a b )\|a
+--R Type: Expression(Integer)
+--E 1190
+
+--S 1191 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1191
+
+)clear all
+
+--S 1192 of 1406
+t0:=(A+B*x^2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1192
+
+--S 1193 of 1406
+r0:=1/3*(A*b-a*B)*x/(a*b*(a+b*x^2)^(3/2))+1/3*(2*A*b+a*B)*x/(a^2*b*_
+ sqrt(a+b*x^2))
+--R
+--R
+--R 3
+--R (2A b + B a)x + 3A a x
+--R (2) --------------------------
+--R +--------+
+--R 2 2 3 | 2
+--R (3a b x + 3a )\|b x + a
+--R Type: Expression(Integer)
+--E 1193
+
+--S 1194 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 5 2 3 2 | 2
+--R ((- 2A b - B a b)x + (- 11A a b - 4B a )x - 12A a x)\|b x + a
+--R +
+--R 2 5 2 3 2 +-+
+--R ((6A b + 3B a b)x + (17A a b + 4B a )x + 12A a x)\|a
+--R /
+--R +--------+
+--R 2 2 4 3 2 4 +-+ | 2 2 3 6 3 2 4
+--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x
+--R +
+--R 4 2 5
+--R - 27a b x - 12a
+--R Type: Union(Expression(Integer),...)
+--E 1194
+
+--S 1195 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1195
+
+--S 1196 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1196
+
+)clear all
+
+--S 1197 of 1406
+t0:=(A+B*x^2)/(x*(a+b*x^2)^(5/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ---------------------------------
+--R +--------+
+--R 2 5 3 2 | 2
+--R (b x + 2a b x + a x)\|b x + a
+--R Type: Expression(Integer)
+--E 1197
+
+--S 1198 of 1406
+r0:=1/3*(A*b-a*B)/(a*b*(a+b*x^2)^(3/2))-A*atanh(sqrt(a+b*x^2)/sqrt(a))/_
+ a^(5/2)+A/(a^2*sqrt(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ | 2
+--R 2 2 | 2 \|b x + a
+--R (- 3A b x - 3A a b)\|b x + a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 +-+
+--R (3A b x + 4A a b - B a )\|a
+--R /
+--R +--------+
+--R 2 2 2 3 +-+ | 2
+--R (3a b x + 3a b)\|a \|b x + a
+--R Type: Expression(Integer)
+--E 1198
+
+--S 1199 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 3 | 2
+--R (9A a b x + 21A a b x + 12A a )\|b x + a
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (- 3A b x - 18A a b x - 27A a b x - 12A a )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 4 2 3 2 | 2
+--R ((9A a b - 3B a b)x + (12A a b - 6B a )x )\|b x + a
+--R +
+--R 3 2 6 2 2 4
+--R (- 4A b + B a b )x + (- 15A a b + 6B a b)x
+--R +
+--R 2 3 2
+--R (- 12A a b + 6B a )x
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4
+--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x
+--R +
+--R 5 2 6
+--R - 27a b x - 12a
+--R Type: Union(Expression(Integer),...)
+--E 1199
+
+--S 1200 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R ((3A b x + 12A a b)\|b x + a + (- 9A b x - 12A a b)\|a )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R ((3A b x + 12A a b)\|b x + a + (- 9A b x - 12A a b)\|a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 2 2 | 2
+--R ((4A b - B a b)x + 16A a b - 4B a )\|b x + a
+--R +
+--R 2 2 2 +-+
+--R ((- 12A b + 3B a b)x - 16A a b + 4B a )\|a
+--R /
+--R +--------+
+--R 2 2 2 3 +-+ | 2 3 2 2 4
+--R (3a b x + 12a b)\|a \|b x + a - 9a b x - 12a b
+--R Type: Expression(Integer)
+--E 1200
+
+--S 1201 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1201
+
+)clear all
+
+--S 1202 of 1406
+t0:=(A+B*x^2)/(x^2*(a+b*x^2)^(5/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ----------------------------------
+--R +--------+
+--R 2 6 4 2 2 | 2
+--R (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1202
+
+--S 1203 of 1406
+r0:=-A/(a*x*(a+b*x^2)^(3/2))-1/3*(4*A*b-a*B)*x/(a^2*(a+b*x^2)^(3/2))-_
+ 2/3*(4*A*b-a*B)*x/(a^3*sqrt(a+b*x^2))
+--R
+--R
+--R 2 4 2 2 2
+--R (- 8A b + 2B a b)x + (- 12A a b + 3B a )x - 3A a
+--R (2) ----------------------------------------------------
+--R +--------+
+--R 3 3 4 | 2
+--R (3a b x + 3a x)\|b x + a
+--R Type: Expression(Integer)
+--E 1203
+
+--S 1204 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 6 2 2 4
+--R (32A b - 8B a b )x + (112A a b - 28B a b)x
+--R +
+--R 2 3 2 3
+--R (108A a b - 24B a )x + 24A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 3 8 3 2 2 6
+--R (- 8A b + 2B a b )x + (- 76A a b + 19B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (- 163A a b + 40B a b)x + (- 120A a b + 24B a )x - 24A a
+--R /
+--R +--------+
+--R 3 3 7 4 2 5 5 3 6 | 2
+--R (3a b x + 27a b x + 48a b x + 24a x)\|b x + a
+--R +
+--R 3 3 7 4 2 5 5 3 6 +-+
+--R (- 12a b x - 48a b x - 60a b x - 24a x)\|a
+--R Type: Union(Expression(Integer),...)
+--E 1204
+
+--S 1205 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1205
+
+--S 1206 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1206
+
+)clear all
+
+--S 1207 of 1406
+t0:=(A+B*x^2)/(x^3*(a+b*x^2)^(5/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ----------------------------------
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1207
+
+--S 1208 of 1406
+r0:=1/6*(-5*A*b+2*a*B)/(a^2*(a+b*x^2)^(3/2))-1/2*A/(a*x^2*_
+ (a+b*x^2)^(3/2))+1/2*(5*A*b-2*a*B)*atanh(sqrt(a+b*x^2)/_
+ sqrt(a))/a^(7/2)+1/2*(-5*A*b+2*a*B)/(a^3*sqrt(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ | 2
+--R 2 4 2 2 | 2 \|b x + a
+--R ((15A b - 6B a b)x + (15A a b - 6B a )x )\|b x + a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+
+--R ((- 15A b + 6B a b)x + (- 20A a b + 8B a )x - 3A a )\|a
+--R /
+--R +--------+
+--R 3 4 4 2 +-+ | 2
+--R (6a b x + 6a x )\|a \|b x + a
+--R Type: Expression(Integer)
+--E 1208
+
+--S 1209 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 3 8 2 3 3 2 6
+--R (- 75A a b + 30B a b )x + (- 375A a b + 150B a b )x
+--R +
+--R 3 2 4 4 4 5 2
+--R (- 540A a b + 216B a b)x + (- 240A a b + 96B a )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 4 10 4 2 3 8
+--R (15A b - 6B a b )x + (210A a b - 84B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (615A a b - 246B a b )x + (660A a b - 264B a b)x
+--R +
+--R 4 5 2
+--R (240A a b - 96B a )x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 55A a b + 34B a b )x + (- 150A a b + 120B a b )x
+--R +
+--R 3 2 4 4 4 2 5
+--R (- 21A a b + 96B a b)x + 132A a b x + 48A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 4 10 4 2 3 8
+--R (14A b - 8B a b )x + (121A a b - 82B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 2
+--R (174A a b - 168B a b )x + (- 39A a b - 96B a b)x - 156A a b x
+--R +
+--R 5
+--R - 48A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 4 3 8 5 2 6 6 4 7 2 +-+ | 2 4 4 10
+--R (30a b x + 150a b x + 216a b x + 96a x )\|a \|b x + a - 6a b x
+--R +
+--R 5 3 8 6 2 6 7 4 8 2
+--R - 84a b x - 246a b x - 264a b x - 96a x
+--R Type: Union(Expression(Integer),...)
+--E 1209
+
+--S 1210 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 2 4 2 2 2 2
+--R (- 15A b + 6B a b )x + (- 180A a b + 72B a b)x - 240A a b
+--R +
+--R 3
+--R 96B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 4 2 2 2 2
+--R (75A b - 30B a b )x + (300A a b - 120B a b)x + 240A a b
+--R +
+--R 3
+--R - 96B a
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 15A b + 6B a b )x + (- 180A a b + 72B a b)x - 240A a b
+--R +
+--R 3
+--R 96B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 4 2 2 2 2
+--R (75A b - 30B a b )x + (300A a b - 120B a b)x + 240A a b
+--R +
+--R 3
+--R - 96B a
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 14A b + 8B a b )x + (- 168A a b + 96B a b)x - 224A a b
+--R +
+--R 3
+--R 128B a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 4 2 2 2 2 3 +-+
+--R ((70A b - 40B a b )x + (280A a b - 160B a b)x + 224A a b - 128B a )\|a
+--R /
+--R +--------+
+--R 3 2 4 4 2 5 +-+ | 2 4 2 4 5 2 6
+--R (6a b x + 72a b x + 96a )\|a \|b x + a - 30a b x - 120a b x - 96a
+--R Type: Expression(Integer)
+--E 1210
+
+--S 1211 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1211
+
+)clear all
+
+--S 1212 of 1406
+t0:=(A+B*x^2)/(x^4*(a+b*x^2)^(5/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ----------------------------------
+--R +--------+
+--R 2 8 6 2 4 | 2
+--R (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1212
+
+--S 1213 of 1406
+r0:=-1/3*A/(a*x^3*(a+b*x^2)^(3/2))+1/3*(-2*A*b+a*B)/(a^2*x*_
+ (a+b*x^2)^(3/2))-4/3*(2*A*b-a*B)/(a^3*x*sqrt(a+b*x^2))+_
+ 8/3*(2*A*b-a*B)*sqrt(a+b*x^2)/(a^4*x)
+--R
+--R
+--R (2)
+--R 3 2 6 2 2 4 2 3 2 3
+--R (16A b - 8B a b )x + (24A a b - 12B a b)x + (6A a b - 3B a )x - A a
+--R -------------------------------------------------------------------------
+--R +--------+
+--R 4 5 5 3 | 2
+--R (3a b x + 3a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1213
+
+--S 1214 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 10 4 2 3 8
+--R (- 96A b + 48B a b )x + (- 656A a b + 328B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 1316A a b + 658B a b )x + (- 954A a b + 480B a b)x
+--R +
+--R 4 5 2 5
+--R (- 160A a b + 96B a )x + 32A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 5 12 5 2 4 10
+--R (16A b - 8B a b )x + (312A a b - 156B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (1206A a b - 603B a b )x + (1771A a b - 886B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (1038A a b - 528B a b)x + (144A a b - 96B a )x - 32A a
+--R /
+--R +--------+
+--R 4 4 11 5 3 9 6 2 7 7 5 8 3 | 2
+--R (3a b x + 57a b x + 198a b x + 240a b x + 96a x )\|b x + a
+--R +
+--R 4 4 11 5 3 9 6 2 7 7 5 8 3 +-+
+--R (- 18a b x - 132a b x - 306a b x - 288a b x - 96a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 1214
+
+--S 1215 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1215
+
+--S 1216 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1216
+
+)clear all
+
+--S 1217 of 1406
+t0:=(A+B*x^2)/(x^5*(a+b*x^2)^(5/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ----------------------------------
+--R +--------+
+--R 2 9 7 2 5 | 2
+--R (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1217
+
+--S 1218 of 1406
+r0:=-1/4*A/(a*x^4*(a+b*x^2)^(3/2))+1/12*(-7*A*b+4*a*B)/(a^2*x^2*_
+ (a+b*x^2)^(3/2))-5/8*b*(7*A*b-4*a*B)*atanh(sqrt(a+b*x^2)/_
+ sqrt(a))/a^(9/2)-5/12*(7*A*b-4*a*B)/(a^3*x^2*sqrt(a+b*x^2))+_
+ 5/8*(7*A*b-4*a*B)*sqrt(a+b*x^2)/(a^4*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R 3 2 6 2 2 4 | 2
+--R ((- 105A b + 60B a b )x + (- 105A a b + 60B a b)x )\|b x + a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 3 2 6 2 2 4
+--R (105A b - 60B a b )x + (140A a b - 80B a b)x
+--R +
+--R 2 3 2 3
+--R (21A a b - 12B a )x - 6A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 4 6 5 4 +-+ | 2
+--R (24a b x + 24a x )\|a \|b x + a
+--R Type: Expression(Integer)
+--E 1218
+
+--S 1219 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 2 5 12 2 5 3 4 10
+--R (735A a b - 420B a b )x + (6615A a b - 3780B a b )x
+--R +
+--R 3 4 4 3 8 4 3 5 2 6
+--R (17640A a b - 10080B a b )x + (18480A a b - 10560B a b )x
+--R +
+--R 5 2 6 4
+--R (6720A a b - 3840B a b)x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 6 14 6 2 5 12
+--R (- 105A b + 60B a b )x + (- 2730A a b + 1560B a b )x
+--R +
+--R 2 5 3 4 10 3 4 4 3 8
+--R (- 13545A a b + 7740B a b )x + (- 26040A a b + 14880B a b )x
+--R +
+--R 4 3 5 2 6 5 2 6 4
+--R (- 21840A a b + 12480B a b )x + (- 6720A a b + 3840B a b)x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 6 2 5 12 2 5 3 4 10
+--R (455A a b - 332B a b )x + (2380A a b - 2008B a b )x
+--R +
+--R 3 4 4 3 8 4 3 5 2 6
+--R (1659A a b - 2676B a b )x + (- 4338A a b + 672B a b )x
+--R +
+--R 5 2 6 4 6 7 2 7
+--R (- 5376A a b + 2496B a b)x + (- 864A a b + 768B a )x + 384A a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 6 14 6 2 5 12
+--R (- 80A b + 56B a b )x + (- 1345A a b + 1036B a b )x
+--R +
+--R 2 5 3 4 10 3 4 4 3 8
+--R (- 3460A a b + 3304B a b )x + (- 93A a b + 2604B a b )x
+--R +
+--R 4 3 5 2 6 5 2 6 4
+--R (6894A a b - 1824B a b )x + (5856A a b - 2880B a b)x
+--R +
+--R 6 7 2 7
+--R (672A a b - 768B a )x - 384A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 5 4 12 6 3 10 7 2 8 8 6 9 4 +-+
+--R (168a b x + 1512a b x + 4032a b x + 4224a b x + 1536a x )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 5 14 6 4 12 7 3 10 8 2 8 9 6
+--R - 24a b x - 624a b x - 3096a b x - 5952a b x - 4992a b x
+--R +
+--R 10 4
+--R - 1536a x
+--R Type: Union(Expression(Integer),...)
+--E 1219
+
+--S 1220 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 4 6 4 2 3 4
+--R (105A b - 60B a b )x + (2520A a b - 1440B a b )x
+--R +
+--R 2 3 3 2 2 3 2 4
+--R (8400A a b - 4800B a b )x + 6720A a b - 3840B a b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 4 6 4 2 3 4
+--R (- 735A b + 420B a b )x + (- 5880A a b + 3360B a b )x
+--R +
+--R 2 3 3 2 2 3 2 4
+--R (- 11760A a b + 6720B a b )x - 6720A a b + 3840B a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 4 6 4 2 3 4
+--R (105A b - 60B a b )x + (2520A a b - 1440B a b )x
+--R +
+--R 2 3 3 2 2 3 2 4
+--R (8400A a b - 4800B a b )x + 6720A a b - 3840B a b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 4 6 4 2 3 4
+--R (- 735A b + 420B a b )x + (- 5880A a b + 3360B a b )x
+--R +
+--R 2 3 3 2 2 3 2 4
+--R (- 11760A a b + 6720B a b )x - 6720A a b + 3840B a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 5 4 6 4 2 3 4
+--R (80A b - 56B a b )x + (1920A a b - 1344B a b )x
+--R +
+--R 2 3 3 2 2 3 2 4
+--R (6400A a b - 4480B a b )x + 5120A a b - 3584B a b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 4 6 4 2 3 4
+--R (- 560A b + 392B a b )x + (- 4480A a b + 3136B a b )x
+--R +
+--R 2 3 3 2 2 3 2 4
+--R (- 8960A a b + 6272B a b )x - 5120A a b + 3584B a b
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 +-+ | 2 5 3 6
+--R (24a b x + 576a b x + 1920a b x + 1536a )\|a \|b x + a - 168a b x
+--R +
+--R 6 2 4 7 2 8
+--R - 1344a b x - 2688a b x - 1536a
+--R Type: Expression(Integer)
+--E 1220
+
+--S 1221 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1221
+
+)clear all
+
+--S 1222 of 1406
+t0:=(A+B*x^2)/(x^6*(a+b*x^2)^(5/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------------------------------
+--R +--------+
+--R 2 10 8 2 6 | 2
+--R (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1222
+
+--S 1223 of 1406
+r0:=-1/5*A/(a*x^5*(a+b*x^2)^(3/2))+1/15*(-8*A*b+5*a*B)/(a^2*x^3*_
+ (a+b*x^2)^(3/2))-2/5*(8*A*b-5*a*B)/(a^3*x^3*sqrt(a+b*x^2))+_
+ 8/15*(8*A*b-5*a*B)*sqrt(a+b*x^2)/(a^4*x^3)-16/15*b*_
+ (8*A*b-5*a*B)*sqrt(a+b*x^2)/(a^5*x)
+--R
+--R
+--R (2)
+--R 4 3 8 3 2 2 6
+--R (- 128A b + 80B a b )x + (- 192A a b + 120B a b )x
+--R +
+--R 2 2 3 4 3 4 2 4
+--R (- 48A a b + 30B a b)x + (8A a b - 5B a )x - 3A a
+--R /
+--R +--------+
+--R 5 7 6 5 | 2
+--R (15a b x + 15a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1223
+
+--S 1224 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 14 6 2 5 12
+--R (1024A b - 640B a b )x + (11776A a b - 7360B a b )x
+--R +
+--R 2 5 3 4 10 3 4 4 3 8
+--R (40320A a b - 25200B a b )x + (57024A a b - 35640B a b )x
+--R +
+--R 4 3 5 2 6 5 2 6 4
+--R (33176A a b - 20720B a b )x + (4848A a b - 2880B a b)x
+--R +
+--R 6 7 2 7
+--R (- 448A a b + 640B a )x + 384A a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 8 7 16 7 2 6 14
+--R (- 128A b + 80B a b )x + (- 4288A a b + 2680B a b )x
+--R +
+--R 2 6 3 5 12 3 5 4 4 10
+--R (- 26672A a b + 16670B a b )x + (- 65016A a b + 40635B a b )x
+--R +
+--R 4 4 5 3 8 5 3 6 2 6
+--R (- 72963A a b + 45600B a b )x + (- 35680A a b + 22240B a b )x
+--R +
+--R 6 2 7 4 7 8 2 8
+--R (- 4576A a b + 2560B a b)x + (256A a b - 640B a )x - 384A a
+--R /
+--R 5 5 15 6 4 13 7 3 11 8 2 9 9 7
+--R 15a b x + 495a b x + 2880a b x + 6240a b x + 5760a b x
+--R +
+--R 10 5
+--R 1920a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 5 15 6 4 13 7 3 11 8 2 9 9 7
+--R - 120a b x - 1440a b x - 5400a b x - 8880a b x - 6720a b x
+--R +
+--R 10 5
+--R - 1920a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 1224
+
+--S 1225 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1225
+
+--S 1226 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1226
+
+)clear all
+
+--S 1227 of 1406
+t0:=x^(7/2)*(a+b*x^2)*(A+B*x^2)
+--R
+--R
+--R 7 5 3 +-+
+--R (1) (B b x + (A b + B a)x + A a x )\|x
+--R Type: Expression(Integer)
+--E 1227
+
+--S 1228 of 1406
+r0:=2/9*a*A*x^(9/2)+2/13*(A*b+a*B)*x^(13/2)+2/17*b*B*x^(17/2)
+--R
+--R
+--R 8 6 4 +-+
+--R (234B b x + (306A b + 306B a)x + 442A a x )\|x
+--R (2) -------------------------------------------------
+--R 1989
+--R Type: Expression(Integer)
+--E 1228
+
+--S 1229 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 8 6 4 +-+
+--R (234B b x + (306A b + 306B a)x + 442A a x )\|x
+--R (3) -------------------------------------------------
+--R 1989
+--R Type: Union(Expression(Integer),...)
+--E 1229
+
+--S 1230 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1230
+
+--S 1231 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1231
+
+)clear all
+
+--S 1232 of 1406
+t0:=x^(5/2)*(a+b*x^2)*(A+B*x^2)
+--R
+--R
+--R 6 4 2 +-+
+--R (1) (B b x + (A b + B a)x + A a x )\|x
+--R Type: Expression(Integer)
+--E 1232
+
+--S 1233 of 1406
+r0:=2/7*a*A*x^(7/2)+2/11*(A*b+a*B)*x^(11/2)+2/15*b*B*x^(15/2)
+--R
+--R
+--R 7 5 3 +-+
+--R (154B b x + (210A b + 210B a)x + 330A a x )\|x
+--R (2) -------------------------------------------------
+--R 1155
+--R Type: Expression(Integer)
+--E 1233
+
+--S 1234 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 7 5 3 +-+
+--R (154B b x + (210A b + 210B a)x + 330A a x )\|x
+--R (3) -------------------------------------------------
+--R 1155
+--R Type: Union(Expression(Integer),...)
+--E 1234
+
+--S 1235 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1235
+
+--S 1236 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1236
+
+)clear all
+
+--S 1237 of 1406
+t0:=x^(3/2)*(a+b*x^2)*(A+B*x^2)
+--R
+--R
+--R 5 3 +-+
+--R (1) (B b x + (A b + B a)x + A a x)\|x
+--R Type: Expression(Integer)
+--E 1237
+
+--S 1238 of 1406
+r0:=2/5*a*A*x^(5/2)+2/9*(A*b+a*B)*x^(9/2)+2/13*b*B*x^(13/2)
+--R
+--R
+--R 6 4 2 +-+
+--R (90B b x + (130A b + 130B a)x + 234A a x )\|x
+--R (2) ------------------------------------------------
+--R 585
+--R Type: Expression(Integer)
+--E 1238
+
+--S 1239 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 4 2 +-+
+--R (90B b x + (130A b + 130B a)x + 234A a x )\|x
+--R (3) ------------------------------------------------
+--R 585
+--R Type: Union(Expression(Integer),...)
+--E 1239
+
+--S 1240 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1240
+
+--S 1241 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1241
+
+)clear all
+
+--S 1242 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)*sqrt(x)
+--R
+--R
+--R 4 2 +-+
+--R (1) (B b x + (A b + B a)x + A a)\|x
+--R Type: Expression(Integer)
+--E 1242
+
+--S 1243 of 1406
+r0:=2/3*a*A*x^(3/2)+2/7*(A*b+a*B)*x^(7/2)+2/11*b*B*x^(11/2)
+--R
+--R
+--R 5 3 +-+
+--R (42B b x + (66A b + 66B a)x + 154A a x)\|x
+--R (2) ---------------------------------------------
+--R 231
+--R Type: Expression(Integer)
+--E 1243
+
+--S 1244 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 3 +-+
+--R (42B b x + (66A b + 66B a)x + 154A a x)\|x
+--R (3) ---------------------------------------------
+--R 231
+--R Type: Union(Expression(Integer),...)
+--E 1244
+
+--S 1245 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1245
+
+--S 1246 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1246
+
+)clear all
+
+--S 1247 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/sqrt(x)
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1247
+
+--S 1248 of 1406
+r0:=2/5*(A*b+a*B)*x^(5/2)+2/9*b*B*x^(9/2)+2*a*A*sqrt(x)
+--R
+--R
+--R 4 2 +-+
+--R (10B b x + (18A b + 18B a)x + 90A a)\|x
+--R (2) ------------------------------------------
+--R 45
+--R Type: Expression(Integer)
+--E 1248
+
+--S 1249 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2 +-+
+--R (10B b x + (18A b + 18B a)x + 90A a)\|x
+--R (3) ------------------------------------------
+--R 45
+--R Type: Union(Expression(Integer),...)
+--E 1249
+
+--S 1250 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1250
+
+--S 1251 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1251
+
+)clear all
+
+--S 1252 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^(3/2)
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 1252
+
+--S 1253 of 1406
+r0:=2/3*(A*b+a*B)*x^(3/2)+2/7*b*B*x^(7/2)-2*a*A/sqrt(x)
+--R
+--R
+--R 4 2
+--R 6B b x + (14A b + 14B a)x - 42A a
+--R (2) -----------------------------------
+--R +-+
+--R 21\|x
+--R Type: Expression(Integer)
+--E 1253
+
+--S 1254 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R 6B b x + (14A b + 14B a)x - 42A a
+--R (3) -----------------------------------
+--R +-+
+--R 21\|x
+--R Type: Union(Expression(Integer),...)
+--E 1254
+
+--S 1255 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1255
+
+--S 1256 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1256
+
+)clear all
+
+--S 1257 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^(5/2)
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1257
+
+--S 1258 of 1406
+r0:=-2/3*a*A/x^(3/2)+2/5*b*B*x^(5/2)+2*(A*b+a*B)*sqrt(x)
+--R
+--R
+--R 4 2
+--R 6B b x + (30A b + 30B a)x - 10A a
+--R (2) -----------------------------------
+--R +-+
+--R 15x\|x
+--R Type: Expression(Integer)
+--E 1258
+
+--S 1259 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R 6B b x + (30A b + 30B a)x - 10A a
+--R (3) -----------------------------------
+--R +-+
+--R 15x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1259
+
+--S 1260 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1260
+
+--S 1261 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1261
+
+)clear all
+
+--S 1262 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^(7/2)
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1262
+
+--S 1263 of 1406
+r0:=-2/5*a*A/x^(5/2)+2/3*b*B*x^(3/2)-2*(A*b+a*B)/sqrt(x)
+--R
+--R
+--R 4 2
+--R 10B b x + (- 30A b - 30B a)x - 6A a
+--R (2) -------------------------------------
+--R 2 +-+
+--R 15x \|x
+--R Type: Expression(Integer)
+--E 1263
+
+--S 1264 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R 10B b x + (- 30A b - 30B a)x - 6A a
+--R (3) -------------------------------------
+--R 2 +-+
+--R 15x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1264
+
+--S 1265 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1265
+
+--S 1266 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1266
+
+)clear all
+
+--S 1267 of 1406
+t0:=x^(7/2)*(a+b*x^2)^2*(A+B*x^2)
+--R
+--R
+--R 2 9 2 7 2 5 2 3 +-+
+--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x )\|x
+--R Type: Expression(Integer)
+--E 1267
+
+--S 1268 of 1406
+r0:=2/9*a^2*A*x^(9/2)+2/13*a*(2*A*b+a*B)*x^(13/2)+2/17*b*(A*b+2*a*B)*_
+ x^(17/2)+2/21*b^2*B*x^(21/2)
+--R
+--R
+--R (2)
+--R 2 10 2 8 2 6
+--R 1326B b x + (1638A b + 3276B a b)x + (4284A a b + 2142B a )x
+--R +
+--R 2 4
+--R 3094A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 13923
+--R Type: Expression(Integer)
+--E 1268
+
+--S 1269 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 10 2 8 2 6
+--R 1326B b x + (1638A b + 3276B a b)x + (4284A a b + 2142B a )x
+--R +
+--R 2 4
+--R 3094A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 13923
+--R Type: Union(Expression(Integer),...)
+--E 1269
+
+--S 1270 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1270
+
+--S 1271 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1271
+
+)clear all
+
+--S 1272 of 1406
+t0:=x^(5/2)*(a+b*x^2)^2*(A+B*x^2)
+--R
+--R
+--R 2 8 2 6 2 4 2 2 +-+
+--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x )\|x
+--R Type: Expression(Integer)
+--E 1272
+
+--S 1273 of 1406
+r0:=2/7*a^2*A*x^(7/2)+2/11*a*(2*A*b+a*B)*x^(11/2)+2/15*b*(A*b+2*a*B)*_
+ x^(15/2)+2/19*b^2*B*x^(19/2)
+--R
+--R
+--R (2)
+--R 2 9 2 7 2 5
+--R 2310B b x + (2926A b + 5852B a b)x + (7980A a b + 3990B a )x
+--R +
+--R 2 3
+--R 6270A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 21945
+--R Type: Expression(Integer)
+--E 1273
+
+--S 1274 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 9 2 7 2 5
+--R 2310B b x + (2926A b + 5852B a b)x + (7980A a b + 3990B a )x
+--R +
+--R 2 3
+--R 6270A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 21945
+--R Type: Union(Expression(Integer),...)
+--E 1274
+
+--S 1275 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1275
+
+--S 1276 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1276
+
+)clear all
+
+--S 1277 of 1406
+t0:=x^(3/2)*(a+b*x^2)^2*(A+B*x^2)
+--R
+--R
+--R 2 7 2 5 2 3 2 +-+
+--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x)\|x
+--R Type: Expression(Integer)
+--E 1277
+
+--S 1278 of 1406
+r0:=2/5*a^2*A*x^(5/2)+2/9*a*(2*A*b+a*B)*x^(9/2)+2/13*b*(A*b+2*a*B)*_
+ x^(13/2)+2/17*b^2*B*x^(17/2)
+--R
+--R
+--R (2)
+--R 2 8 2 6 2 4
+--R 1170B b x + (1530A b + 3060B a b)x + (4420A a b + 2210B a )x
+--R +
+--R 2 2
+--R 3978A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 9945
+--R Type: Expression(Integer)
+--E 1278
+
+--S 1279 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 8 2 6 2 4
+--R 1170B b x + (1530A b + 3060B a b)x + (4420A a b + 2210B a )x
+--R +
+--R 2 2
+--R 3978A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 9945
+--R Type: Union(Expression(Integer),...)
+--E 1279
+
+--S 1280 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1280
+
+--S 1281 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1281
+
+)clear all
+
+--S 1282 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)*sqrt(x)
+--R
+--R
+--R 2 6 2 4 2 2 2 +-+
+--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|x
+--R Type: Expression(Integer)
+--E 1282
+
+--S 1283 of 1406
+r0:=2/3*a^2*A*x^(3/2)+2/7*a*(2*A*b+a*B)*x^(7/2)+2/11*b*(A*b+2*a*B)*_
+ x^(11/2)+2/15*b^2*B*x^(15/2)
+--R
+--R
+--R (2)
+--R 2 7 2 5 2 3 2 +-+
+--R (154B b x + (210A b + 420B a b)x + (660A a b + 330B a )x + 770A a x)\|x
+--R ----------------------------------------------------------------------------
+--R 1155
+--R Type: Expression(Integer)
+--E 1283
+
+--S 1284 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 7 2 5 2 3 2 +-+
+--R (154B b x + (210A b + 420B a b)x + (660A a b + 330B a )x + 770A a x)\|x
+--R ----------------------------------------------------------------------------
+--R 1155
+--R Type: Union(Expression(Integer),...)
+--E 1284
+
+--S 1285 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1285
+
+--S 1286 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1286
+
+)clear all
+
+--S 1287 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/sqrt(x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1287
+
+--S 1288 of 1406
+r0:=2/5*a*(2*A*b+a*B)*x^(5/2)+2/9*b*(A*b+2*a*B)*x^(9/2)+2/13*b^2*B*_
+ x^(13/2)+2*a^2*A*sqrt(x)
+--R
+--R
+--R (2)
+--R 2 6 2 4 2 2 2 +-+
+--R (90B b x + (130A b + 260B a b)x + (468A a b + 234B a )x + 1170A a )\|x
+--R ---------------------------------------------------------------------------
+--R 585
+--R Type: Expression(Integer)
+--E 1288
+
+--S 1289 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 2 4 2 2 2 +-+
+--R (90B b x + (130A b + 260B a b)x + (468A a b + 234B a )x + 1170A a )\|x
+--R ---------------------------------------------------------------------------
+--R 585
+--R Type: Union(Expression(Integer),...)
+--E 1289
+
+--S 1290 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1290
+
+--S 1291 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1291
+
+)clear all
+
+--S 1292 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^(3/2)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 1292
+
+--S 1293 of 1406
+r0:=2/3*a*(2*A*b+a*B)*x^(3/2)+2/7*b*(A*b+2*a*B)*x^(7/2)+2/11*b^2*B*_
+ x^(11/2)-2*a^2*A/sqrt(x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 42B b x + (66A b + 132B a b)x + (308A a b + 154B a )x - 462A a
+--R (2) -------------------------------------------------------------------
+--R +-+
+--R 231\|x
+--R Type: Expression(Integer)
+--E 1293
+
+--S 1294 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 42B b x + (66A b + 132B a b)x + (308A a b + 154B a )x - 462A a
+--R (3) -------------------------------------------------------------------
+--R +-+
+--R 231\|x
+--R Type: Union(Expression(Integer),...)
+--E 1294
+
+--S 1295 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1295
+
+--S 1296 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1296
+
+)clear all
+
+--S 1297 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^(5/2)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1297
+
+--S 1298 of 1406
+r0:=-2/3*a^2*A/x^(3/2)+2/5*b*(A*b+2*a*B)*x^(5/2)+2/9*b^2*B*x^(9/2)+_
+ 2*a*(2*A*b+a*B)*sqrt(x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 10B b x + (18A b + 36B a b)x + (180A a b + 90B a )x - 30A a
+--R (2) ----------------------------------------------------------------
+--R +-+
+--R 45x\|x
+--R Type: Expression(Integer)
+--E 1298
+
+--S 1299 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 10B b x + (18A b + 36B a b)x + (180A a b + 90B a )x - 30A a
+--R (3) ----------------------------------------------------------------
+--R +-+
+--R 45x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1299
+
+--S 1300 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1300
+
+--S 1301 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1301
+
+)clear all
+
+--S 1302 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^(7/2)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1302
+
+--S 1303 of 1406
+r0:=-2/5*a^2*A/x^(5/2)+2/3*b*(A*b+2*a*B)*x^(3/2)+2/7*b^2*B*x^(7/2)-_
+ 2*a*(2*A*b+a*B)/sqrt(x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 30B b x + (70A b + 140B a b)x + (- 420A a b - 210B a )x - 42A a
+--R (2) --------------------------------------------------------------------
+--R 2 +-+
+--R 105x \|x
+--R Type: Expression(Integer)
+--E 1303
+
+--S 1304 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 30B b x + (70A b + 140B a b)x + (- 420A a b - 210B a )x - 42A a
+--R (3) --------------------------------------------------------------------
+--R 2 +-+
+--R 105x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1304
+
+--S 1305 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1305
+
+--S 1306 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1306
+
+)clear all
+
+--S 1307 of 1406
+t0:=x^(7/2)*(a+b*x^2)^3*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 3 11 3 2 9 2 2 7 2 3 5
+--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x
+--R +
+--R 3 3
+--R A a x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1307
+
+--S 1308 of 1406
+r0:=2/9*a^3*A*x^(9/2)+2/13*a^2*(3*A*b+a*B)*x^(13/2)+6/17*a*b*(A*b+a*B)*_
+ x^(17/2)+2/21*b^2*(A*b+3*a*B)*x^(21/2)+2/25*b^3*B*x^(25/2)
+--R
+--R
+--R (2)
+--R 3 12 3 2 10
+--R 27846B b x + (33150A b + 99450B a b )x
+--R +
+--R 2 2 8 2 3 6
+--R (122850A a b + 122850B a b)x + (160650A a b + 53550B a )x
+--R +
+--R 3 4
+--R 77350A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 348075
+--R Type: Expression(Integer)
+--E 1308
+
+--S 1309 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 12 3 2 10
+--R 27846B b x + (33150A b + 99450B a b )x
+--R +
+--R 2 2 8 2 3 6
+--R (122850A a b + 122850B a b)x + (160650A a b + 53550B a )x
+--R +
+--R 3 4
+--R 77350A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 348075
+--R Type: Union(Expression(Integer),...)
+--E 1309
+
+--S 1310 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1310
+
+--S 1311 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1311
+
+)clear all
+
+--S 1312 of 1406
+t0:=x^(5/2)*(a+b*x^2)^3*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 3 10 3 2 8 2 2 6 2 3 4
+--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x
+--R +
+--R 3 2
+--R A a x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1312
+
+--S 1313 of 1406
+r0:=2/7*a^3*A*x^(7/2)+2/11*a^2*(3*A*b+a*B)*x^(11/2)+2/5*a*b*(A*b+a*B)*_
+ x^(15/2)+2/19*b^2*(A*b+3*a*B)*x^(19/2)+2/23*b^3*B*x^(23/2)
+--R
+--R
+--R (2)
+--R 3 11 3 2 9
+--R 14630B b x + (17710A b + 53130B a b )x
+--R +
+--R 2 2 7 2 3 5 3 3
+--R (67298A a b + 67298B a b)x + (91770A a b + 30590B a )x + 48070A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 168245
+--R Type: Expression(Integer)
+--E 1313
+
+--S 1314 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 11 3 2 9
+--R 14630B b x + (17710A b + 53130B a b )x
+--R +
+--R 2 2 7 2 3 5 3 3
+--R (67298A a b + 67298B a b)x + (91770A a b + 30590B a )x + 48070A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 168245
+--R Type: Union(Expression(Integer),...)
+--E 1314
+
+--S 1315 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1315
+
+--S 1316 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1316
+
+)clear all
+
+--S 1317 of 1406
+t0:=x^(3/2)*(a+b*x^2)^3*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 3 9 3 2 7 2 2 5 2 3 3
+--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x
+--R +
+--R 3
+--R A a x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1317
+
+--S 1318 of 1406
+r0:=2/5*a^3*A*x^(5/2)+2/9*a^2*(3*A*b+a*B)*x^(9/2)+6/13*a*b*(A*b+a*B)*_
+ x^(13/2)+2/17*b^2*(A*b+3*a*B)*x^(17/2)+2/21*b^3*B*x^(21/2)
+--R
+--R
+--R (2)
+--R 3 10 3 2 8 2 2 6
+--R 6630B b x + (8190A b + 24570B a b )x + (32130A a b + 32130B a b)x
+--R +
+--R 2 3 4 3 2
+--R (46410A a b + 15470B a )x + 27846A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 69615
+--R Type: Expression(Integer)
+--E 1318
+
+--S 1319 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 10 3 2 8 2 2 6
+--R 6630B b x + (8190A b + 24570B a b )x + (32130A a b + 32130B a b)x
+--R +
+--R 2 3 4 3 2
+--R (46410A a b + 15470B a )x + 27846A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 69615
+--R Type: Union(Expression(Integer),...)
+--E 1319
+
+--S 1320 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1320
+
+--S 1321 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1321
+
+)clear all
+
+--S 1322 of 1406
+t0:=(a+b*x^2)^3*(A+B*x^2)*sqrt(x)
+--R
+--R
+--R (1)
+--R 3 8 3 2 6 2 2 4 2 3 2
+--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x
+--R +
+--R 3
+--R A a
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1322
+
+--S 1323 of 1406
+r0:=2/3*a^3*A*x^(3/2)+2/7*a^2*(3*A*b+a*B)*x^(7/2)+6/11*a*b*(A*b+a*B)*_
+ x^(11/2)+2/15*b^2*(A*b+3*a*B)*x^(15/2)+2/19*b^3*B*x^(19/2)
+--R
+--R
+--R (2)
+--R 3 9 3 2 7 2 2 5
+--R 2310B b x + (2926A b + 8778B a b )x + (11970A a b + 11970B a b)x
+--R +
+--R 2 3 3 3
+--R (18810A a b + 6270B a )x + 14630A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 21945
+--R Type: Expression(Integer)
+--E 1323
+
+--S 1324 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 9 3 2 7 2 2 5
+--R 2310B b x + (2926A b + 8778B a b )x + (11970A a b + 11970B a b)x
+--R +
+--R 2 3 3 3
+--R (18810A a b + 6270B a )x + 14630A a x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 21945
+--R Type: Union(Expression(Integer),...)
+--E 1324
+
+--S 1325 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1325
+
+--S 1326 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1326
+
+)clear all
+
+--S 1327 of 1406
+t0:=(a+b*x^2)^3*(A+B*x^2)/sqrt(x)
+--R
+--R
+--R (1)
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a
+--R -----------------------------------------------------------------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1327
+
+--S 1328 of 1406
+r0:=2/5*a^2*(3*A*b+a*B)*x^(5/2)+2/3*a*b*(A*b+a*B)*x^(9/2)+_
+ 2/13*b^2*(A*b+3*a*B)*x^(13/2)+2/17*b^3*B*x^(17/2)+2*a^3*A*sqrt(x)
+--R
+--R
+--R (2)
+--R 3 8 3 2 6 2 2 4
+--R 390B b x + (510A b + 1530B a b )x + (2210A a b + 2210B a b)x
+--R +
+--R 2 3 2 3
+--R (3978A a b + 1326B a )x + 6630A a
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3315
+--R Type: Expression(Integer)
+--E 1328
+
+--S 1329 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 8 3 2 6 2 2 4
+--R 390B b x + (510A b + 1530B a b )x + (2210A a b + 2210B a b)x
+--R +
+--R 2 3 2 3
+--R (3978A a b + 1326B a )x + 6630A a
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3315
+--R Type: Union(Expression(Integer),...)
+--E 1329
+
+--S 1330 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1330
+
+--S 1331 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1331
+
+)clear all
+
+--S 1332 of 1406
+t0:=(a+b*x^2)^3*(A+B*x^2)/x^(3/2)
+--R
+--R
+--R (1)
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a
+--R -----------------------------------------------------------------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 1332
+
+--S 1333 of 1406
+r0:=2/3*a^2*(3*A*b+a*B)*x^(3/2)+6/7*a*b*(A*b+a*B)*x^(7/2)+_
+ 2/11*b^2*(A*b+3*a*B)*x^(11/2)+2/15*b^3*B*x^(15/2)-2*a^3*A/sqrt(x)
+--R
+--R
+--R (2)
+--R 3 8 3 2 6 2 2 4
+--R 154B b x + (210A b + 630B a b )x + (990A a b + 990B a b)x
+--R +
+--R 2 3 2 3
+--R (2310A a b + 770B a )x - 2310A a
+--R /
+--R +-+
+--R 1155\|x
+--R Type: Expression(Integer)
+--E 1333
+
+--S 1334 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 8 3 2 6 2 2 4
+--R 154B b x + (210A b + 630B a b )x + (990A a b + 990B a b)x
+--R +
+--R 2 3 2 3
+--R (2310A a b + 770B a )x - 2310A a
+--R /
+--R +-+
+--R 1155\|x
+--R Type: Union(Expression(Integer),...)
+--E 1334
+
+--S 1335 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1335
+
+--S 1336 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1336
+
+)clear all
+
+--S 1337 of 1406
+t0:=(a+b*x^2)^3*(A+B*x^2)/x^(5/2)
+--R
+--R
+--R (1)
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a
+--R -----------------------------------------------------------------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1337
+
+--S 1338 of 1406
+r0:=-2/3*a^3*A/x^(3/2)+6/5*a*b*(A*b+a*B)*x^(5/2)+2/9*b^2*(A*b+3*a*B)*_
+ x^(9/2)+2/13*b^3*B*x^(13/2)+2*a^2*(3*A*b+a*B)*sqrt(x)
+--R
+--R
+--R (2)
+--R 3 8 3 2 6 2 2 4
+--R 90B b x + (130A b + 390B a b )x + (702A a b + 702B a b)x
+--R +
+--R 2 3 2 3
+--R (3510A a b + 1170B a )x - 390A a
+--R /
+--R +-+
+--R 585x\|x
+--R Type: Expression(Integer)
+--E 1338
+
+--S 1339 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 8 3 2 6 2 2 4
+--R 90B b x + (130A b + 390B a b )x + (702A a b + 702B a b)x
+--R +
+--R 2 3 2 3
+--R (3510A a b + 1170B a )x - 390A a
+--R /
+--R +-+
+--R 585x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1339
+
+--S 1340 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1340
+
+--S 1341 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1341
+
+)clear all
+
+--S 1342 of 1406
+t0:=(a+b*x^2)^3*(A+B*x^2)/x^(7/2)
+--R
+--R
+--R (1)
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a
+--R -----------------------------------------------------------------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1342
+
+--S 1343 of 1406
+r0:=-2/5*a^3*A/x^(5/2)+2*a*b*(A*b+a*B)*x^(3/2)+2/7*b^2*(A*b+3*a*B)*_
+ x^(7/2)+2/11*b^3*B*x^(11/2)-2*a^2*(3*A*b+a*B)/sqrt(x)
+--R
+--R
+--R (2)
+--R 3 8 3 2 6 2 2 4
+--R 70B b x + (110A b + 330B a b )x + (770A a b + 770B a b)x
+--R +
+--R 2 3 2 3
+--R (- 2310A a b - 770B a )x - 154A a
+--R /
+--R 2 +-+
+--R 385x \|x
+--R Type: Expression(Integer)
+--E 1343
+
+--S 1344 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 8 3 2 6 2 2 4
+--R 70B b x + (110A b + 330B a b )x + (770A a b + 770B a b)x
+--R +
+--R 2 3 2 3
+--R (- 2310A a b - 770B a )x - 154A a
+--R /
+--R 2 +-+
+--R 385x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1344
+
+--S 1345 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1345
+
+--S 1346 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1346
+
+)clear all
+
+--S 1347 of 1406
+t0:=x^(7/2)*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 5 3 +-+
+--R (B x + A x )\|x
+--R (1) -----------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1347
+
+--S 1348 of 1406
+r0:=2/5*(A*b-a*B)*x^(5/2)/b^2+2/9*B*x^(9/2)/b-a^(5/4)*(A*b-a*B)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(13/4)*sqrt(2))+_
+ a^(5/4)*(A*b-a*B)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (b^(13/4)*sqrt(2))-1/2*a^(5/4)*(A*b-a*B)*log(sqrt(a)+x*_
+ sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(13/4)*sqrt(2))+_
+ 1/2*a^(5/4)*(A*b-a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(b^(13/4)*sqrt(2))-2*a*(A*b-a*B)*sqrt(x)/b^3
+--R
+--R
+--R (2)
+--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (45A a b - 45B a )\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 45A a b + 45B a )\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ \|2 \|b \|x + \|a
+--R (90A a b - 90B a )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ \|2 \|b \|x - \|a
+--R (90A a b - 90B a )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+4+-+ +-+
+--R (20B b x + (36A b - 36B a b)x - 180A a b + 180B a )\|2 \|b \|x
+--R /
+--R 3 +-+4+-+
+--R 90b \|2 \|b
+--R Type: Expression(Integer)
+--E 1348
+
+--S 1349 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------------------------------------------+
+--R | 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R 3 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 45b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R *
+--R log
+--R 2 +-+
+--R (A a b - B a )\|x
+--R +
+--R +--------------------------------------------------+
+--R | 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R 3 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R 3 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 45b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R *
+--R log
+--R 2 +-+
+--R (A a b - B a )\|x
+--R +
+--R +--------------------------------------------------+
+--R | 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R 3 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 2b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R 3 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 90b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R *
+--R +--------------------------------------------------+
+--R | 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R 3 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R atan(--------------------------------------------------------)
+--R 2 +-+
+--R (A a b - B a )\|x
+--R +
+--R 2 4 2 2 2 +-+
+--R (10B b x + (18A b - 18B a b)x - 90A a b + 90B a )\|x
+--R /
+--R 3
+--R 45b
+--R Type: Union(Expression(Integer),...)
+--E 1349
+
+--S 1350 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- A a b + B a )\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------------------------------------------------+
+--R | 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R 3 +-+ |- A a b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+
+--R 2b \|2 |-------------------------------------------------- \|b
+--R 4| 13
+--R \| 16b
+--R *
+--R log
+--R 2 +-+
+--R (A a b - B a )\|x
+--R +
+--R +--------------------------------------------------+
+--R | 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R 3 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R 3 +-+ |- A a b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+
+--R 2b \|2 |-------------------------------------------------- \|b
+--R 4| 13
+--R \| 16b
+--R *
+--R log
+--R 2 +-+
+--R (A a b - B a )\|x
+--R +
+--R +--------------------------------------------------+
+--R | 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R 3 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 2b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R +
+--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (A a b - B a )\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ \|2 \|b \|x + \|a
+--R (- 2A a b + 2B a )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ \|2 \|b \|x - \|a
+--R (- 2A a b + 2B a )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R 3 +-+ |- A a b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+
+--R 4b \|2 |-------------------------------------------------- \|b
+--R 4| 13
+--R \| 16b
+--R *
+--R +--------------------------------------------------+
+--R | 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R 3 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R atan(--------------------------------------------------------)
+--R 2 +-+
+--R (A a b - B a )\|x
+--R /
+--R 3 +-+4+-+
+--R 2b \|2 \|b
+--R Type: Expression(Integer)
+--E 1350
+
+--S 1351 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1351
+
+)clear all
+
+--S 1352 of 1406
+t0:=x^(5/2)*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 4 2 +-+
+--R (B x + A x )\|x
+--R (1) -----------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1352
+
+--S 1353 of 1406
+r0:=2/3*(A*b-a*B)*x^(3/2)/b^2+2/7*B*x^(7/2)/b+a^(3/4)*(A*b-a*B)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(11/4)*sqrt(2))-_
+ a^(3/4)*(A*b-a*B)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (b^(11/4)*sqrt(2))-1/2*a^(3/4)*(A*b-a*B)*log(sqrt(a)+x*_
+ sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(11/4)*sqrt(2))+_
+ 1/2*a^(3/4)*(A*b-a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(b^(11/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (21A b - 21B a)\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 21A b + 21B a)\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 \|2 \|b \|x + \|a
+--R (- 42A b + 42B a)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 \|2 \|b \|x - \|a
+--R (- 42A b + 42B a)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+4+-+3 +-+
+--R (12B b x + (28A b - 28B a)x)\|2 \|b \|x
+--R /
+--R 2 +-+4+-+3
+--R 42b \|2 \|b
+--R Type: Expression(Integer)
+--E 1353
+
+--S 1354 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +--------------------------------------------------+
+--R | 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R 2 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 21b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R *
+--R log
+--R 3 2 3 2 3 2 2 4 3 5 +-+
+--R (A a b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R 8 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 8b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R +
+--R +--------------------------------------------------+
+--R | 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R 2 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 21b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R *
+--R log
+--R 3 2 3 2 3 2 2 4 3 5 +-+
+--R (A a b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R 8 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 8b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R 2 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 42b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R *
+--R +--------------------------------------------------+3
+--R | 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R 8 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 8b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R atan(---------------------------------------------------------)
+--R 3 2 3 2 3 2 2 4 3 5 +-+
+--R (A a b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R 3 +-+
+--R (6B b x + (14A b - 14B a)x)\|x
+--R /
+--R 2
+--R 21b
+--R Type: Union(Expression(Integer),...)
+--E 1354
+
+--S 1355 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- A b + B a)\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R 2 +-+ |- A a b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+3
+--R 2b \|2 |-------------------------------------------------- \|b
+--R 4| 11
+--R \| 16b
+--R *
+--R log
+--R 3 2 3 2 3 2 2 4 3 5 +-+
+--R (A a b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R 8 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 8b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R +
+--R +--------------------------------------------------+
+--R | 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R 2 +-+ |- A a b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+3
+--R 2b \|2 |-------------------------------------------------- \|b
+--R 4| 11
+--R \| 16b
+--R *
+--R log
+--R 3 2 3 2 3 2 2 4 3 5 +-+
+--R (A a b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R 8 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 8b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R +
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (A b - B a)\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 \|2 \|b \|x + \|a
+--R (2A b - 2B a)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 \|2 \|b \|x - \|a
+--R (2A b - 2B a)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R 2 +-+ |- A a b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+3
+--R 4b \|2 |-------------------------------------------------- \|b
+--R 4| 11
+--R \| 16b
+--R *
+--R +--------------------------------------------------+3
+--R | 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R 8 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 8b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R atan(---------------------------------------------------------)
+--R 3 2 3 2 3 2 2 4 3 5 +-+
+--R (A a b - 3A B a b + 3A B a b - B a )\|x
+--R /
+--R 2 +-+4+-+3
+--R 2b \|2 \|b
+--R Type: Expression(Integer)
+--E 1355
+
+--S 1356 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1356
+
+)clear all
+
+--S 1357 of 1406
+t0:=x^(3/2)*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 3 +-+
+--R (B x + A x)\|x
+--R (1) ----------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1357
+
+--S 1358 of 1406
+r0:=2/5*B*x^(5/2)/b+a^(1/4)*(A*b-a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(b^(9/4)*sqrt(2))-a^(1/4)*(A*b-a*B)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*sqrt(2))+1/2*a^(1/4)*(A*b-_
+ a*B)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (b^(9/4)*sqrt(2))-1/2*a^(1/4)*(A*b-a*B)*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(9/4)*sqrt(2))+2*(A*b-_
+ a*B)*sqrt(x)/b^2
+--R
+--R
+--R (2)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5A b + 5B a)\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5A b - 5B a)\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a
+--R (- 10A b + 10B a)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x - \|a
+--R (- 10A b + 10B a)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+ +-+
+--R (4B b x + 20A b - 20B a)\|2 \|b \|x
+--R /
+--R 2 +-+4+-+
+--R 10b \|2 \|b
+--R Type: Expression(Integer)
+--E 1358
+
+--S 1359 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R 2 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 5b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R *
+--R log
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R 2 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R +
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R 2 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 5b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R *
+--R log
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R 2 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 2b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R +
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R 2 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 10b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R *
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R 2 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R atan(--------------------------------------------------------)
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R 2 +-+
+--R (2B b x + 10A b - 10B a)\|x
+--R /
+--R 2
+--R 5b
+--R Type: Union(Expression(Integer),...)
+--E 1359
+
+--S 1360 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (A b - B a)\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R 2 +-+ |- A a b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+
+--R 2b \|2 |-------------------------------------------------- \|b
+--R 4| 9
+--R \| 16b
+--R *
+--R log
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R 2 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R +
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R 2 +-+ |- A a b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+
+--R 2b \|2 |-------------------------------------------------- \|b
+--R 4| 9
+--R \| 16b
+--R *
+--R log
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R 2 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 2b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- A b + B a)\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a
+--R (2A b - 2B a)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x - \|a
+--R (2A b - 2B a)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R 2 +-+ |- A a b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+
+--R 4b \|2 |-------------------------------------------------- \|b
+--R 4| 9
+--R \| 16b
+--R *
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R 2 |- A a b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R atan(--------------------------------------------------------)
+--R +-+
+--R (A b - B a)\|x
+--R /
+--R 2 +-+4+-+
+--R 2b \|2 \|b
+--R Type: Expression(Integer)
+--E 1360
+
+--S 1361 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1361
+
+)clear all
+
+--S 1362 of 1406
+t0:=(A+B*x^2)*sqrt(x)/(a+b*x^2)
+--R
+--R
+--R 2 +-+
+--R (B x + A)\|x
+--R (1) --------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1362
+
+--S 1363 of 1406
+r0:=2/3*B*x^(3/2)/b-(A*b-a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(1/4)*b^(7/4)*sqrt(2))+(A*b-a*B)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(1/4)*b^(7/4)*sqrt(2))+1/2*(A*b-a*B)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*_
+ b^(7/4)*sqrt(2))-1/2*(A*b-a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(7/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3A b + 3B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (3A b - 3B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (6A b - 6B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a +-+4+-+4+-+3 +-+
+--R (6A b - 6B a)atan(-------------------) + 4B x\|2 \|a \|b \|x
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+4+-+3
+--R 6b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1363
+
+--S 1364 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 3b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 5 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 8a b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 3b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 5 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 8a b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 6b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R *
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 5 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 8a b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R atan(---------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R +-+
+--R 2B x\|x
+--R /
+--R 3b
+--R Type: Union(Expression(Integer),...)
+--E 1364
+
+--S 1365 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (A b - B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+4+-+3
+--R 2b\|2 |------------------------------------------------ \|a \|b
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 5 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 8a b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+4+-+3
+--R 2b\|2 |------------------------------------------------ \|a \|b
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 5 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 8a b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- A b + B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 2A b + 2B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 2A b + 2B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+4+-+3
+--R 4b\|2 |------------------------------------------------ \|a \|b
+--R 4| 7
+--R \| 16a b
+--R *
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 5 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 8a b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R atan(---------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a )\|x
+--R /
+--R +-+4+-+4+-+3
+--R 2b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1365
+
+--S 1366 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1366
+
+)clear all
+
+--S 1367 of 1406
+t0:=(A+B*x^2)/((a+b*x^2)*sqrt(x))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) --------------
+--R 2 +-+
+--R (b x + a)\|x
+--R Type: Expression(Integer)
+--E 1367
+
+--S 1368 of 1406
+r0:=-(A*b-a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(5/4)*_
+ sqrt(2))+(A*b-a*B)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(3/4)*b^(5/4)*sqrt(2))-1/2*(A*b-a*B)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(5/4)*sqrt(2))+_
+ 1/2*(A*b-a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(3/4)*b^(5/4)*sqrt(2))+2*B*sqrt(x)/b
+--R
+--R
+--R (2)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (A b - B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- A b + B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (2A b - 2B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a +-+4+-+3 4+-+ +-+
+--R (2A b - 2B a)atan(-------------------) + 4B\|2 \|a \|b \|x
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+3 4+-+
+--R 2b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1368
+
+--S 1369 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2a b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 2a b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R *
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2a b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R atan(-------------------------------------------------------)
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R +-+
+--R 2B\|x
+--R /
+--R b
+--R Type: Union(Expression(Integer),...)
+--E 1369
+
+--S 1370 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- A b + B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+3 4+-+
+--R 2b\|2 |------------------------------------------------ \|a \|b
+--R 4| 3 5
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2a b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+3 4+-+
+--R 2b\|2 |------------------------------------------------ \|a \|b
+--R 4| 3 5
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 2a b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (A b - B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 2A b + 2B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 2A b + 2B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+3 4+-+
+--R 4b\|2 |------------------------------------------------ \|a \|b
+--R 4| 3 5
+--R \| 16a b
+--R *
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2a b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R atan(-------------------------------------------------------)
+--R +-+
+--R (A b - B a)\|x
+--R /
+--R +-+4+-+3 4+-+
+--R 2b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1370
+
+--S 1371 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1371
+
+)clear all
+
+--S 1372 of 1406
+t0:=(A+B*x^2)/(x^(3/2)*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ----------------
+--R 3 +-+
+--R (b x + a x)\|x
+--R Type: Expression(Integer)
+--E 1372
+
+--S 1373 of 1406
+r0:=(A*b-a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(3/4)*_
+ sqrt(2))-(A*b-a*B)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(5/4)*b^(3/4)*sqrt(2))-1/2*(A*b-a*B)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(3/4)*sqrt(2))+_
+ 1/2*(A*b-a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(5/4)*b^(3/4)*sqrt(2))-2*A/(a*sqrt(x))
+--R
+--R
+--R (2)
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (A b - B a)\|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- A b + B a)\|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x + \|a
+--R (- 2A b + 2B a)\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x - \|a +-+4+-+4+-+3
+--R (- 2A b + 2B a)\|x atan(-------------------) - 4A\|2 \|a \|b
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+4+-+3 +-+
+--R 2a\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1373
+
+--S 1374 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a +-+
+--R a |------------------------------------------------ \|x
+--R 4| 5 3
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 8a b |------------------------------------------------
+--R 4| 5 3
+--R \| 16a b
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a +-+
+--R a |------------------------------------------------ \|x
+--R 4| 5 3
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 8a b |------------------------------------------------
+--R 4| 5 3
+--R \| 16a b
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a +-+
+--R 2a |------------------------------------------------ \|x
+--R 4| 5 3
+--R \| 16a b
+--R *
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 8a b |------------------------------------------------
+--R 4| 5 3
+--R \| 16a b
+--R atan(---------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R - 2A
+--R /
+--R +-+
+--R a\|x
+--R Type: Union(Expression(Integer),...)
+--E 1374
+
+--S 1375 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- A b + B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+4+-+3
+--R 2a\|2 |------------------------------------------------ \|a \|b
+--R 4| 5 3
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 8a b |------------------------------------------------
+--R 4| 5 3
+--R \| 16a b
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+4+-+3
+--R 2a\|2 |------------------------------------------------ \|a \|b
+--R 4| 5 3
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 8a b |------------------------------------------------
+--R 4| 5 3
+--R \| 16a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (A b - B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (2A b - 2B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (2A b - 2B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+4+-+3
+--R 4a\|2 |------------------------------------------------ \|a \|b
+--R 4| 5 3
+--R \| 16a b
+--R *
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 8a b |------------------------------------------------
+--R 4| 5 3
+--R \| 16a b
+--R atan(---------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a )\|x
+--R /
+--R +-+4+-+4+-+3
+--R 2a\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1375
+
+--S 1376 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1376
+
+)clear all
+
+--S 1377 of 1406
+t0:=(A+B*x^2)/(x^(5/2)*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------------
+--R 4 2 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1377
+
+--S 1378 of 1406
+r0:=-2/3*A/(a*x^(3/2))+(A*b-a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(7/4)*b^(1/4)*sqrt(2))-(A*b-a*B)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(7/4)*b^(1/4)*sqrt(2))+1/2*(A*b-a*B)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*_
+ b^(1/4)*sqrt(2))-1/2*(A*b-a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(1/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3A b + 3B a)x\|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (3A b - 3B a)x\|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x + \|a
+--R (- 6A b + 6B a)x\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x - \|a +-+4+-+3 4+-+
+--R (- 6A b + 6B a)x\|x atan(-------------------) - 4A\|2 \|a \|b
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+3 4+-+ +-+
+--R 6a x\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1378
+
+--S 1379 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a +-+
+--R 3a x |------------------------------------------------ \|x
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2a |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a +-+
+--R 3a x |------------------------------------------------ \|x
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 2a |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 4A B a b - 6A B a b + 4A B a b - B a +-+
+--R 6a x |------------------------------------------------ \|x
+--R 4| 7
+--R \| 16a b
+--R *
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2a |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R atan(------------------------------------------------------)
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R - 2A
+--R /
+--R +-+
+--R 3a x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1379
+
+--S 1380 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (A b - B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+3 4+-+
+--R 2a\|2 |------------------------------------------------ \|a \|b
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2a |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+3 4+-+
+--R 2a\|2 |------------------------------------------------ \|a \|b
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (A b - B a)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R - 2a |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- A b + B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (2A b - 2B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (2A b - 2B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a 4+-+3 4+-+
+--R 4a\|2 |------------------------------------------------ \|a \|b
+--R 4| 7
+--R \| 16a b
+--R *
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a
+--R 2a |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R atan(------------------------------------------------------)
+--R +-+
+--R (A b - B a)\|x
+--R /
+--R +-+4+-+3 4+-+
+--R 2a\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1380
+
+--S 1381 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1381
+
+)clear all
+
+--S 1382 of 1406
+t0:=(A+B*x^2)/(x^(7/2)*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------------
+--R 5 3 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1382
+
+--S 1383 of 1406
+r0:=-2/5*A/(a*x^(5/2))-b^(1/4)*(A*b-a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(9/4)*sqrt(2))+b^(1/4)*(A*b-a*B)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*sqrt(2))+1/2*b^(1/4)*(A*b-_
+ a*B)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(9/4)*sqrt(2))-1/2*b^(1/4)*(A*b-a*B)*log(sqrt(a)+x*_
+ sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+_
+ 2*(A*b-a*B)/(a^2*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5A b + 5B a)x \|b \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5A b - 5B a)x \|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ +-+ \|2 \|b \|x + \|a
+--R (10A b - 10B a)x \|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ +-+ \|2 \|b \|x - \|a
+--R (10A b - 10B a)x \|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+
+--R ((20A b - 20B a)x - 4A a)\|2 \|a
+--R /
+--R 2 2 +-+4+-+ +-+
+--R 10a x \|2 \|a \|x
+--R Type: Expression(Integer)
+--E 1383
+
+--S 1384 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------------------------------------------+
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 2 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a b +-+
+--R 5a x |-------------------------------------------------- \|x
+--R 4| 9
+--R \| 16a
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a b)\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 7 |- A b + 4A B a b - 6A B a b + 4A B a b - B a b
+--R 8a |--------------------------------------------------
+--R 4| 9
+--R \| 16a
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 2 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a b +-+
+--R 5a x |-------------------------------------------------- \|x
+--R 4| 9
+--R \| 16a
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a b)\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 7 |- A b + 4A B a b - 6A B a b + 4A B a b - B a b
+--R - 8a |--------------------------------------------------
+--R 4| 9
+--R \| 16a
+--R +
+--R +--------------------------------------------------+
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 2 2 |- A b + 4A B a b - 6A B a b + 4A B a b - B a b +-+
+--R 10a x |-------------------------------------------------- \|x
+--R 4| 9
+--R \| 16a
+--R *
+--R +--------------------------------------------------+3
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 7 |- A b + 4A B a b - 6A B a b + 4A B a b - B a b
+--R 8a |--------------------------------------------------
+--R 4| 9
+--R \| 16a
+--R atan(---------------------------------------------------------)
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a b)\|x
+--R +
+--R 2
+--R (10A b - 10B a)x - 2A a
+--R /
+--R 2 2 +-+
+--R 5a x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1384
+
+--S 1385 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (A b - B a)\|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------------------------------------------------+
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 2 +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a b 4+-+
+--R 2a \|2 |-------------------------------------------------- \|a
+--R 4| 9
+--R \| 16a
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a b)\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 7 |- A b + 4A B a b - 6A B a b + 4A B a b - B a b
+--R 8a |--------------------------------------------------
+--R 4| 9
+--R \| 16a
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 2 +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a b 4+-+
+--R 2a \|2 |-------------------------------------------------- \|a
+--R 4| 9
+--R \| 16a
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a b)\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 7 |- A b + 4A B a b - 6A B a b + 4A B a b - B a b
+--R - 8a |--------------------------------------------------
+--R 4| 9
+--R \| 16a
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- A b + B a)\|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a
+--R (- 2A b + 2B a)\|b atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x - \|a
+--R (- 2A b + 2B a)\|b atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------------------------------------------------+
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 2 +-+ |- A b + 4A B a b - 6A B a b + 4A B a b - B a b 4+-+
+--R 4a \|2 |-------------------------------------------------- \|a
+--R 4| 9
+--R \| 16a
+--R *
+--R +--------------------------------------------------+3
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 7 |- A b + 4A B a b - 6A B a b + 4A B a b - B a b
+--R 8a |--------------------------------------------------
+--R 4| 9
+--R \| 16a
+--R atan(---------------------------------------------------------)
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (A b - 3A B a b + 3A B a b - B a b)\|x
+--R /
+--R 2 +-+4+-+
+--R 2a \|2 \|a
+--R Type: Expression(Integer)
+--E 1385
+
+--S 1386 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1386
+
+)clear all
+
+--S 1387 of 1406
+t0:=x^(7/2)*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 5 3 +-+
+--R (B x + A x )\|x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1387
+
+--S 1388 of 1406
+r0:=-1/10*(5*A*b-9*a*B)*x^(5/2)/(a*b^2)+1/2*(A*b-a*B)*x^(9/2)/(a*b*(a+_
+ b*x^2))+1/4*a^(1/4)*(5*A*b-9*a*B)*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(b^(13/4)*sqrt(2))-1/4*a^(1/4)*(5*A*b-9*a*B)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(13/4)*sqrt(2))+_
+ 1/8*a^(1/4)*(5*A*b-9*a*B)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(b^(13/4)*sqrt(2))-1/8*a^(1/4)*(5*A*b-9*a*B)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (b^(13/4)*sqrt(2))+1/2*(5*A*b-9*a*B)*sqrt(x)/b^3
+--R
+--R
+--R (2)
+--R 2 2 2 4+-+
+--R ((- 25A b + 45B a b)x - 25A a b + 45B a )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 4+-+
+--R ((25A b - 45B a b)x + 25A a b - 45B a )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+ \|2 \|b \|x + \|a
+--R ((- 50A b + 90B a b)x - 50A a b + 90B a )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+ \|2 \|b \|x - \|a
+--R ((- 50A b + 90B a b)x - 50A a b + 90B a )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+4+-+ +-+
+--R (16B b x + (80A b - 144B a b)x + 100A a b - 180B a )\|2 \|b \|x
+--R /
+--R 4 2 3 +-+4+-+
+--R (40b x + 40a b )\|2 \|b
+--R Type: Expression(Integer)
+--E 1388
+
+--S 1389 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 3
+--R (- 10b x - 10a b )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R |- 625A a b + 4500A B a b - 12150A B a b + 14580A B a b - 6561B a
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096b
+--R *
+--R log
+--R +-+
+--R (5A b - 9B a)\|x
+--R +
+--R 3
+--R 8b
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4
+--R - 625A a b + 4500A B a b - 12150A B a b + 14580A B a b
+--R +
+--R 4 5
+--R - 6561B a
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 4 2 3
+--R (10b x + 10a b )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R |- 625A a b + 4500A B a b - 12150A B a b + 14580A B a b - 6561B a
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096b
+--R *
+--R log
+--R +-+
+--R (5A b - 9B a)\|x
+--R +
+--R -
+--R 3
+--R 8b
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2
+--R - 625A a b + 4500A B a b - 12150A B a b
+--R +
+--R 3 4 4 5
+--R 14580A B a b - 6561B a
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 4 2 3
+--R (20b x + 20a b )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R |- 625A a b + 4500A B a b - 12150A B a b + 14580A B a b - 6561B a
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096b
+--R *
+--R atan
+--R 3
+--R 8b
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4
+--R - 625A a b + 4500A B a b - 12150A B a b + 14580A B a b
+--R +
+--R 4 5
+--R - 6561B a
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R /
+--R +-+
+--R (5A b - 9B a)\|x
+--R +
+--R 2 4 2 2 2 +-+
+--R (4B b x + (20A b - 36B a b)x + 25A a b - 45B a )\|x
+--R /
+--R 4 2 3
+--R 10b x + 10a b
+--R Type: Union(Expression(Integer),...)
+--E 1389
+
+--S 1390 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5A b - 9B a)\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 3 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4
+--R - 625A a b + 4500A B a b - 12150A B a b + 14580A B a b
+--R +
+--R 4 5
+--R - 6561B a
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R +-+
+--R (5A b - 9B a)\|x
+--R +
+--R 3
+--R 8b
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2
+--R - 625A a b + 4500A B a b - 12150A B a b
+--R +
+--R 3 4 4 5
+--R 14580A B a b - 6561B a
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 3 +-+
+--R 8b \|2
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R |- 625A a b + 4500A B a b - 12150A B a b + 14580A B a b - 6561B a
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096b
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R +-+
+--R (5A b - 9B a)\|x
+--R +
+--R -
+--R 3
+--R 8b
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2
+--R - 625A a b + 4500A B a b - 12150A B a b
+--R +
+--R 3 4 4 5
+--R 14580A B a b - 6561B a
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5A b + 9B a)\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a
+--R (10A b - 18B a)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x - \|a
+--R (10A b - 18B a)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+
+--R 16b \|2
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R |- 625A a b + 4500A B a b - 12150A B a b + 14580A B a b - 6561B a
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096b
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R atan
+--R 3
+--R 8b
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4
+--R - 625A a b + 4500A B a b - 12150A B a b + 14580A B a b
+--R +
+--R 4 5
+--R - 6561B a
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R /
+--R +-+
+--R (5A b - 9B a)\|x
+--R /
+--R 3 +-+4+-+
+--R 8b \|2 \|b
+--R Type: Expression(Integer)
+--E 1390
+
+--S 1391 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1391
+
+)clear all
+
+--S 1392 of 1406
+t0:=x^(5/2)*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 4 2 +-+
+--R (B x + A x )\|x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1392
+
+--S 1393 of 1406
+r0:=-1/6*(3*A*b-7*a*B)*x^(3/2)/(a*b^2)+1/2*(A*b-a*B)*x^(7/2)/(a*b*_
+ (a+b*x^2))-1/4*(3*A*b-7*a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(1/4)*b^(11/4)*sqrt(2))+1/4*(3*A*b-7*a*B)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(11/4)*_
+ sqrt(2))+1/8*(3*A*b-7*a*B)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(11/4)*sqrt(2))-_
+ 1/8*(3*A*b-7*a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(1/4)*b^(11/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2
+--R ((- 9A b + 21B a b)x - 9A a b + 21B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2
+--R ((9A b - 21B a b)x + 9A a b - 21B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x + \|a
+--R ((18A b - 42B a b)x + 18A a b - 42B a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x - \|a
+--R ((18A b - 42B a b)x + 18A a b - 42B a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+4+-+4+-+3 +-+
+--R (16B b x + (- 12A b + 28B a)x)\|2 \|a \|b \|x
+--R /
+--R 3 2 2 +-+4+-+4+-+3
+--R (24b x + 24a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1393
+
+--S 1394 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2
+--R (6b x + 6a b )
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b + 756A B a b - 2646A B a b + 4116A B a b - 2401B a
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27A b - 189A B a b + 441A B a b - 343B a )\|x
+--R +
+--R 8
+--R 512a b
+--R *
+--R +--------------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b + 756A B a b - 2646A B a b + 4116A B a b - 2401B a
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R +
+--R 3 2 2
+--R (- 6b x - 6a b )
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b + 756A B a b - 2646A B a b + 4116A B a b - 2401B a
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27A b - 189A B a b + 441A B a b - 343B a )\|x
+--R +
+--R -
+--R 8
+--R 512a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 81A b + 756A B a b - 2646A B a b + 4116A B a b
+--R +
+--R 4 4
+--R - 2401B a
+--R /
+--R 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 2
+--R (12b x + 12a b )
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b + 756A B a b - 2646A B a b + 4116A B a b - 2401B a
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R *
+--R atan
+--R 8
+--R 512a b
+--R *
+--R +--------------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b + 756A B a b - 2646A B a b + 4116A B a b - 2401B a
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27A b - 189A B a b + 441A B a b - 343B a )\|x
+--R +
+--R 3 +-+
+--R (4B b x + (- 3A b + 7B a)x)\|x
+--R /
+--R 3 2 2
+--R 6b x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 1394
+
+--S 1395 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (3A b - 7B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 8b \|2
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b + 756A B a b - 2646A B a b + 4116A B a b - 2401B a 4+-+
+--R |-------------------------------------------------------------- \|a
+--R 4| 11
+--R \| 4096a b
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27A b - 189A B a b + 441A B a b - 343B a )\|x
+--R +
+--R 8
+--R 512a b
+--R *
+--R +--------------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b + 756A B a b - 2646A B a b + 4116A B a b - 2401B a
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R +
+--R -
+--R 2 +-+
+--R 8b \|2
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b + 756A B a b - 2646A B a b + 4116A B a b - 2401B a
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27A b - 189A B a b + 441A B a b - 343B a )\|x
+--R +
+--R -
+--R 8
+--R 512a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 81A b + 756A B a b - 2646A B a b
+--R +
+--R 3 3 4 4
+--R 4116A B a b - 2401B a
+--R /
+--R 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3A b + 7B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 6A b + 14B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 6A b + 14B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+
+--R 16b \|2
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b + 756A B a b - 2646A B a b + 4116A B a b - 2401B a 4+-+
+--R |-------------------------------------------------------------- \|a
+--R 4| 11
+--R \| 4096a b
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R atan
+--R 8
+--R 512a b
+--R *
+--R +--------------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b + 756A B a b - 2646A B a b + 4116A B a b - 2401B a
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27A b - 189A B a b + 441A B a b - 343B a )\|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 8b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1395
+
+--S 1396 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1396
+
+)clear all
+
+--S 1397 of 1406
+t0:=x^(3/2)*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 3 +-+
+--R (B x + A x)\|x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1397
+
+--S 1398 of 1406
+r0:=1/2*(A*b-a*B)*x^(5/2)/(a*b*(a+b*x^2))-1/4*(A*b-5*a*B)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(9/4)*_
+ sqrt(2))+1/4*(A*b-5*a*B)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(3/4)*b^(9/4)*sqrt(2))-1/8*(A*b-5*a*B)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(9/4)*_
+ sqrt(2))+1/8*(A*b-5*a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(9/4)*sqrt(2))-1/2*_
+ (A*b-5*a*B)*sqrt(x)/(a*b^2)
+--R
+--R
+--R (2)
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((A b - 5B a b)x + A a b - 5B a )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2
+--R ((- A b + 5B a b)x - A a b + 5B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x + \|a
+--R ((2A b - 10B a b)x + 2A a b - 10B a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x - \|a
+--R ((2A b - 10B a b)x + 2A a b - 10B a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+3 4+-+ +-+
+--R (16B b x - 4A b + 20B a)\|2 \|a \|b \|x
+--R /
+--R 3 2 2 +-+4+-+3 4+-+
+--R (8b x + 8a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1398
+
+--S 1399 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2
+--R (2b x + 2a b )
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 20A B a b - 150A B a b + 500A B a b - 625B a
+--R |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R *
+--R log
+--R +-+
+--R (A b - 5B a)\|x
+--R +
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- A b + 20A B a b - 150A B a b + 500A B a b - 625B a
+--R 8a b |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R +
+--R 3 2 2
+--R (- 2b x - 2a b )
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 20A B a b - 150A B a b + 500A B a b - 625B a
+--R |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R *
+--R log
+--R +-+
+--R (A b - 5B a)\|x
+--R +
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- A b + 20A B a b - 150A B a b + 500A B a b - 625B a
+--R - 8a b |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R +
+--R 3 2 2
+--R (- 4b x - 4a b )
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 20A B a b - 150A B a b + 500A B a b - 625B a
+--R |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- A b + 20A B a b - 150A B a b + 500A B a b - 625B a
+--R 8a b |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R atan(----------------------------------------------------------------)
+--R +-+
+--R (A b - 5B a)\|x
+--R +
+--R 2 +-+
+--R (4B b x - A b + 5B a)\|x
+--R /
+--R 3 2 2
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 1399
+
+--S 1400 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- A b + 5B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- A b + 20A B a b - 150A B a b + 500A B a b - 625B a 4+-+3
+--R 8b \|2 |-------------------------------------------------------- \|a
+--R 4| 3 9
+--R \| 4096a b
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R +-+
+--R (A b - 5B a)\|x
+--R +
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- A b + 20A B a b - 150A B a b + 500A B a b - 625B a
+--R 8a b |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R +
+--R -
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- A b + 20A B a b - 150A B a b + 500A B a b - 625B a
+--R 8b \|2 |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (A b - 5B a)\|x
+--R +
+--R -
+--R 2
+--R 8a b
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b + 20A B a b - 150A B a b + 500A B a b - 625B a
+--R |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (A b - 5B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 2A b + 10B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 2A b + 10B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- A b + 20A B a b - 150A B a b + 500A B a b - 625B a
+--R 16b \|2 |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- A b + 20A B a b - 150A B a b + 500A B a b - 625B a
+--R 8a b |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R atan(----------------------------------------------------------------)
+--R +-+
+--R (A b - 5B a)\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 8b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1400
+
+--S 1401 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1401
+
+)clear all
+
+--S 1402 of 1406
+t0:=(A+B*x^2)*sqrt(x)/(a+b*x^2)^2
+--R
+--R
+--R 2 +-+
+--R (B x + A)\|x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1402
+
+--S 1403 of 1406
+r0:=1/2*(A*b-a*B)*x^(3/2)/(a*b*(a+b*x^2))-1/4*(A*b+3*a*B)*atan(1-b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(7/4)*sqrt(2))+1/4*(A*b+_
+ 3*a*B)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*_
+ b^(7/4)*sqrt(2))+1/8*(A*b+3*a*B)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(7/4)*sqrt(2))-_
+ 1/8*(A*b+3*a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(5/4)*b^(7/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((- A b - 3B a b)x - A a b - 3B a )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((A b + 3B a b)x + A a b + 3B a )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x + \|a
+--R ((2A b + 6B a b)x + 2A a b + 6B a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x - \|a
+--R ((2A b + 6B a b)x + 2A a b + 6B a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+4+-+3 +-+
+--R (4A b - 4B a)x\|2 \|a \|b \|x
+--R /
+--R 2 2 2 +-+4+-+4+-+3
+--R (8a b x + 8a b)\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1403
+
+--S 1404 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2
+--R (2a b x + 2a b)
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b - 12A B a b - 54A B a b - 108A B a b - 81B a
+--R |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b + 9A B a b + 27A B a b + 27B a )\|x
+--R +
+--R +------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 5 |- A b - 12A B a b - 54A B a b - 108A B a b - 81B a
+--R 512a b |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R +
+--R 2 2 2
+--R (- 2a b x - 2a b)
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b - 12A B a b - 54A B a b - 108A B a b - 81B a
+--R |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b + 9A B a b + 27A B a b + 27B a )\|x
+--R +
+--R +------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 5 |- A b - 12A B a b - 54A B a b - 108A B a b - 81B a
+--R - 512a b |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R +
+--R 2 2 2
+--R (4a b x + 4a b)
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b - 12A B a b - 54A B a b - 108A B a b - 81B a
+--R |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R *
+--R +------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 5 |- A b - 12A B a b - 54A B a b - 108A B a b - 81B a
+--R 512a b |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R atan(-----------------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b + 9A B a b + 27A B a b + 27B a )\|x
+--R +
+--R +-+
+--R (A b - B a)x\|x
+--R /
+--R 2 2 2
+--R 2a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 1404
+
+--S 1405 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (A b + 3B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b - 12A B a b - 54A B a b - 108A B a b - 81B a 4+-+
+--R 8a b\|2 |------------------------------------------------------ \|a
+--R 4| 5 7
+--R \| 4096a b
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b + 9A B a b + 27A B a b + 27B a )\|x
+--R +
+--R +------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 5 |- A b - 12A B a b - 54A B a b - 108A B a b - 81B a
+--R 512a b |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R +
+--R -
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b - 12A B a b - 54A B a b - 108A B a b - 81B a
+--R 8a b\|2 |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b + 9A B a b + 27A B a b + 27B a )\|x
+--R +
+--R -
+--R 4 5
+--R 512a b
+--R *
+--R +------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- A b - 12A B a b - 54A B a b - 108A B a b - 81B a
+--R |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- A b - 3B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 2A b - 6B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 2A b - 6B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- A b - 12A B a b - 54A B a b - 108A B a b - 81B a 4+-+
+--R 16a b\|2 |------------------------------------------------------ \|a
+--R 4| 5 7
+--R \| 4096a b
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R +------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 5 |- A b - 12A B a b - 54A B a b - 108A B a b - 81B a
+--R 512a b |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R atan(-----------------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (A b + 9A B a b + 27A B a b + 27B a )\|x
+--R /
+--R +-+4+-+4+-+3
+--R 8a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1405
+
+--S 1406 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1406
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich6a.input.pdf b/src/axiom-website/CATS/rich6a.input.pdf
new file mode 100644
index 0000000..911fca1
Binary files /dev/null and b/src/axiom-website/CATS/rich6a.input.pdf differ
diff --git a/src/axiom-website/CATS/rich6b.input.pamphlet b/src/axiom-website/CATS/rich6b.input.pamphlet
new file mode 100644
index 0000000..02c61c4
--- /dev/null
+++ b/src/axiom-website/CATS/rich6b.input.pamphlet
@@ -0,0 +1,36709 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich6b.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p (c+d x^n)^q|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 259 supplied "optimal results".
+\item 266 matching answers.
+\item 55 cases where Axiom supplied 2 results.
+\item 0 cases that Axiom failed to integrate.
+\item 48 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich6b.output
+)spool rich6b.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 1397
+t0:=(A+B*x^2)/((a+b*x^2)^2*sqrt(x))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------------------
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 1397
+r0:=-1/4*(3*A*b+a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*_
+ b^(5/4)*sqrt(2))+1/4*(3*A*b+a*B)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(7/4)*b^(5/4)*sqrt(2))-1/8*(3*A*b+a*B)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(5/4)*_
+ sqrt(2))+1/8*(3*A*b+a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(7/4)*b^(5/4)*sqrt(2))+1/2*(A*b-a*B)*_
+ sqrt(x)/(a*b*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((3A b + B a b)x + 3A a b + B a )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2
+--R ((- 3A b - B a b)x - 3A a b - B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x + \|a
+--R ((6A b + 2B a b)x + 6A a b + 2B a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x - \|a
+--R ((6A b + 2B a b)x + 6A a b + 2B a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+3 4+-+ +-+
+--R (4A b - 4B a)\|2 \|a \|b \|x
+--R /
+--R 2 2 2 +-+4+-+3 4+-+
+--R (8a b x + 8a b)\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2
+--R (2a b x + 2a b)
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 108A B a b - 54A B a b - 12A B a b - B a
+--R |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R *
+--R log
+--R +-+
+--R (3A b + B a)\|x
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- 81A b - 108A B a b - 54A B a b - 12A B a b - B a
+--R 8a b |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R +
+--R 2 2 2
+--R (- 2a b x - 2a b)
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 108A B a b - 54A B a b - 12A B a b - B a
+--R |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R *
+--R log
+--R +-+
+--R (3A b + B a)\|x
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- 81A b - 108A B a b - 54A B a b - 12A B a b - B a
+--R - 8a b |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R +
+--R 2 2 2
+--R (- 4a b x - 4a b)
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 108A B a b - 54A B a b - 12A B a b - B a
+--R |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- 81A b - 108A B a b - 54A B a b - 12A B a b - B a
+--R 8a b |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R atan(-------------------------------------------------------------)
+--R +-+
+--R (3A b + B a)\|x
+--R +
+--R +-+
+--R (A b - B a)\|x
+--R /
+--R 2 2 2
+--R 2a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3A b - B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- 81A b - 108A B a b - 54A B a b - 12A B a b - B a 4+-+3
+--R 8a b\|2 |------------------------------------------------------ \|a
+--R 4| 7 5
+--R \| 4096a b
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R +-+
+--R (3A b + B a)\|x
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- 81A b - 108A B a b - 54A B a b - 12A B a b - B a
+--R 8a b |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R +
+--R -
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- 81A b - 108A B a b - 54A B a b - 12A B a b - B a
+--R 8a b\|2 |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (3A b + B a)\|x
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- 81A b - 108A B a b - 54A B a b - 12A B a b - B a
+--R - 8a b |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (3A b + B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 6A b - 2B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 6A b - 2B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- 81A b - 108A B a b - 54A B a b - 12A B a b - B a
+--R 16a b\|2 |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- 81A b - 108A B a b - 54A B a b - 12A B a b - B a
+--R 8a b |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R atan(-------------------------------------------------------------)
+--R +-+
+--R (3A b + B a)\|x
+--R /
+--R +-+4+-+3 4+-+
+--R 8a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 1397
+t0:=(A+B*x^2)/(x^(3/2)*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) --------------------------
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 1397
+r0:=1/4*(5*A*b-a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*_
+ b^(3/4)*sqrt(2))-1/4*(5*A*b-a*B)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(9/4)*b^(3/4)*sqrt(2))-1/8*(5*A*b-a*B)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*b^(3/4)*_
+ sqrt(2))+1/8*(5*A*b-a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(9/4)*b^(3/4)*sqrt(2))+1/2*(-5*A*b+a*B)/_
+ (a^2*b*sqrt(x))+1/2*(A*b-a*B)/(a*b*(a+b*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 2 2 +-+
+--R ((5A b - B a b)x + 5A a b - B a )\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 +-+
+--R ((- 5A b + B a b)x - 5A a b + B a )\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 +-+ \|2 \|b \|x + \|a
+--R ((- 10A b + 2B a b)x - 10A a b + 2B a )\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 +-+ \|2 \|b \|x - \|a
+--R ((- 10A b + 2B a b)x - 10A a b + 2B a )\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+4+-+3
+--R ((- 20A b + 4B a)x - 16A a)\|2 \|a \|b
+--R /
+--R 2 2 3 +-+4+-+4+-+3 +-+
+--R (8a b x + 8a )\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 3
+--R (- 2a b x - 2a )
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b + 500A B a b - 150A B a b + 20A B a b - B a +-+
+--R |-------------------------------------------------------- \|x
+--R 4| 9 3
+--R \| 4096a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (125A b - 75A B a b + 15A B a b - B a )\|x
+--R +
+--R +--------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 7 2 |- 625A b + 500A B a b - 150A B a b + 20A B a b - B a
+--R 512a b |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R +
+--R 2 2 3
+--R (2a b x + 2a )
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b + 500A B a b - 150A B a b + 20A B a b - B a +-+
+--R |-------------------------------------------------------- \|x
+--R 4| 9 3
+--R \| 4096a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (125A b - 75A B a b + 15A B a b - B a )\|x
+--R +
+--R -
+--R 7 2
+--R 512a b
+--R *
+--R +--------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b + 500A B a b - 150A B a b + 20A B a b - B a
+--R |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R +
+--R 2 2 3
+--R (- 4a b x - 4a )
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b + 500A B a b - 150A B a b + 20A B a b - B a +-+
+--R |-------------------------------------------------------- \|x
+--R 4| 9 3
+--R \| 4096a b
+--R *
+--R +--------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 7 2 |- 625A b + 500A B a b - 150A B a b + 20A B a b - B a
+--R 512a b |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R atan(-------------------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (125A b - 75A B a b + 15A B a b - B a )\|x
+--R +
+--R 2
+--R (- 5A b + B a)x - 4A a
+--R /
+--R 2 2 3 +-+
+--R (2a b x + 2a )\|x
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5A b + B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- 625A b + 500A B a b - 150A B a b + 20A B a b - B a
+--R 8a \|2 |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (125A b - 75A B a b + 15A B a b - B a )\|x
+--R +
+--R 7 2
+--R 512a b
+--R *
+--R +--------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b + 500A B a b - 150A B a b + 20A B a b - B a
+--R |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R +
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- 625A b + 500A B a b - 150A B a b + 20A B a b - B a 4+-+
+--R 8a \|2 |-------------------------------------------------------- \|a
+--R 4| 9 3
+--R \| 4096a b
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (125A b - 75A B a b + 15A B a b - B a )\|x
+--R +
+--R -
+--R 7 2
+--R 512a b
+--R *
+--R +--------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b + 500A B a b - 150A B a b + 20A B a b - B a
+--R |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (5A b - B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (10A b - 2B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (10A b - 2B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- 625A b + 500A B a b - 150A B a b + 20A B a b - B a
+--R 16a \|2 |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 7 2
+--R 512a b
+--R *
+--R +--------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b + 500A B a b - 150A B a b + 20A B a b - B a
+--R |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (125A b - 75A B a b + 15A B a b - B a )\|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 8a \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 1397
+t0:=(A+B*x^2)/(x^(5/2)*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ---------------------------
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 1397
+r0:=1/6*(-7*A*b+3*a*B)/(a^2*b*x^(3/2))+1/2*(A*b-a*B)/(a*b*x^(3/2)*_
+ (a+b*x^2))+1/4*(7*A*b-3*a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(11/4)*b^(1/4)*sqrt(2))-1/4*(7*A*b-3*a*B)*atan(1+_
+ b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*b^(1/4)*sqrt(2))+_
+ 1/8*(7*A*b-3*a*B)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(11/4)*b^(1/4)*sqrt(2))-1/8*(7*A*b-3*a*B)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*_
+ b^(1/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 3 2 +-+
+--R ((- 21A b + 9B a b)x + (- 21A a b + 9B a )x)\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 3 2 +-+
+--R ((21A b - 9B a b)x + (21A a b - 9B a )x)\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 3 2 +-+
+--R ((- 42A b + 18B a b)x + (- 42A a b + 18B a )x)\|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 +-+
+--R ((- 42A b + 18B a b)x + (- 42A a b + 18B a )x)\|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+3 4+-+
+--R ((- 28A b + 12B a)x - 16A a)\|2 \|a \|b
+--R /
+--R 2 3 3 +-+4+-+3 4+-+ +-+
+--R (24a b x + 24a x)\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 3
+--R (- 6a b x - 6a x)
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401A b + 4116A B a b - 2646A B a b + 756A B a b - 81B a +-+
+--R |-------------------------------------------------------------- \|x
+--R 4| 11
+--R \| 4096a b
+--R *
+--R log
+--R +-+
+--R (7A b - 3B a)\|x
+--R +
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 3 |- 2401A b + 4116A B a b - 2646A B a b + 756A B a b - 81B a
+--R 8a |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R +
+--R 2 3 3
+--R (6a b x + 6a x)
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401A b + 4116A B a b - 2646A B a b + 756A B a b - 81B a +-+
+--R |-------------------------------------------------------------- \|x
+--R 4| 11
+--R \| 4096a b
+--R *
+--R log
+--R +-+
+--R (7A b - 3B a)\|x
+--R +
+--R -
+--R 3
+--R 8a
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 2401A b + 4116A B a b - 2646A B a b + 756A B a b
+--R +
+--R 4 4
+--R - 81B a
+--R /
+--R 11
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 2 3 3
+--R (12a b x + 12a x)
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401A b + 4116A B a b - 2646A B a b + 756A B a b - 81B a +-+
+--R |-------------------------------------------------------------- \|x
+--R 4| 11
+--R \| 4096a b
+--R *
+--R atan
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 3 |- 2401A b + 4116A B a b - 2646A B a b + 756A B a b - 81B a
+--R 8a |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R --------------------------------------------------------------------
+--R +-+
+--R (7A b - 3B a)\|x
+--R +
+--R 2
+--R (- 7A b + 3B a)x - 4A a
+--R /
+--R 2 3 3 +-+
+--R (6a b x + 6a x)\|x
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (7A b - 3B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 2 +-+
+--R 8a \|2
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401A b + 4116A B a b - 2646A B a b + 756A B a b - 81B a
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (7A b - 3B a)\|x
+--R +
+--R 3
+--R 8a
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 2401A b + 4116A B a b - 2646A B a b + 756A B a b
+--R +
+--R 4 4
+--R - 81B a
+--R /
+--R 11
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 2 +-+
+--R 8a \|2
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401A b + 4116A B a b - 2646A B a b + 756A B a b - 81B a 4+-+3
+--R |-------------------------------------------------------------- \|a
+--R 4| 11
+--R \| 4096a b
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R +-+
+--R (7A b - 3B a)\|x
+--R +
+--R -
+--R 3
+--R 8a
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 2401A b + 4116A B a b - 2646A B a b + 756A B a b
+--R +
+--R 4 4
+--R - 81B a
+--R /
+--R 11
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 7A b + 3B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (14A b - 6B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (14A b - 6B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+
+--R 16a \|2
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401A b + 4116A B a b - 2646A B a b + 756A B a b - 81B a 4+-+3
+--R |-------------------------------------------------------------- \|a
+--R 4| 11
+--R \| 4096a b
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R atan
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 3 |- 2401A b + 4116A B a b - 2646A B a b + 756A B a b - 81B a
+--R 8a |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R --------------------------------------------------------------------
+--R +-+
+--R (7A b - 3B a)\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 8a \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 1397
+t0:=(A+B*x^2)/(x^(7/2)*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ---------------------------
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 1397
+r0:=1/10*(-9*A*b+5*a*B)/(a^2*b*x^(5/2))+1/2*(A*b-a*B)/(a*b*x^(5/2)*_
+ (a+b*x^2))-1/4*b^(1/4)*(9*A*b-5*a*B)*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(13/4)*sqrt(2))+1/4*b^(1/4)*(9*A*b-5*a*B)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*sqrt(2))+_
+ 1/8*b^(1/4)*(9*A*b-5*a*B)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))-1/8*b^(1/4)*(9*A*b-5*a*B)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*_
+ sqrt(2))+1/2*(9*A*b-5*a*B)/(a^3*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 4 2 2 4+-+ +-+
+--R ((- 45A b + 25B a b)x + (- 45A a b + 25B a )x )\|b \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 2 4+-+ +-+
+--R ((45A b - 25B a b)x + (45A a b - 25B a )x )\|b \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 2 4+-+ +-+
+--R ((90A b - 50B a b)x + (90A a b - 50B a )x )\|b \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 4+-+ +-+
+--R ((90A b - 50B a b)x + (90A a b - 50B a )x )\|b \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+4+-+
+--R ((180A b - 100B a b)x + (144A a b - 80B a )x - 16A a )\|2 \|a
+--R /
+--R 3 4 4 2 +-+4+-+ +-+
+--R (40a b x + 40a x )\|2 \|a \|x
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 4 4 2
+--R (10a b x + 10a x )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R |- 6561A b + 14580A B a b - 12150A B a b + 4500A B a b - 625B a b
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096a
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (729A b - 1215A B a b + 675A B a b - 125B a b)\|x
+--R +
+--R 10
+--R 512a
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 6561A b + 14580A B a b - 12150A B a b
+--R +
+--R 3 3 2 4 4
+--R 4500A B a b - 625B a b
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 4 4 2
+--R (- 10a b x - 10a x )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R |- 6561A b + 14580A B a b - 12150A B a b + 4500A B a b - 625B a b
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096a
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (729A b - 1215A B a b + 675A B a b - 125B a b)\|x
+--R +
+--R -
+--R 10
+--R 512a
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 6561A b + 14580A B a b - 12150A B a b
+--R +
+--R 3 3 2 4 4
+--R 4500A B a b - 625B a b
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 4 4 2
+--R (20a b x + 20a x )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R |- 6561A b + 14580A B a b - 12150A B a b + 4500A B a b - 625B a b
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096a
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 10
+--R 512a
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 6561A b + 14580A B a b - 12150A B a b
+--R +
+--R 3 3 2 4 4
+--R 4500A B a b - 625B a b
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (729A b - 1215A B a b + 675A B a b - 125B a b)\|x
+--R +
+--R 2 4 2 2 2
+--R (45A b - 25B a b)x + (36A a b - 20B a )x - 4A a
+--R /
+--R 3 4 4 2 +-+
+--R (10a b x + 10a x )\|x
+--R Type: Union(Expression(Integer),...)
+--E 18
+
+--S 19 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (9A b - 5B a)\|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 +-+
+--R 8a \|2
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R |- 6561A b + 14580A B a b - 12150A B a b + 4500A B a b - 625B a b
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096a
+--R *
+--R 4+-+
+--R \|a
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (729A b - 1215A B a b + 675A B a b - 125B a b)\|x
+--R +
+--R 10
+--R 512a
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 6561A b + 14580A B a b - 12150A B a b
+--R +
+--R 3 3 2 4 4
+--R 4500A B a b - 625B a b
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 3 +-+
+--R 8a \|2
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R - 6561A b + 14580A B a b - 12150A B a b + 4500A B a b
+--R +
+--R 4 4
+--R - 625B a b
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|a
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (729A b - 1215A B a b + 675A B a b - 125B a b)\|x
+--R +
+--R -
+--R 10
+--R 512a
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 6561A b + 14580A B a b - 12150A B a b
+--R +
+--R 3 3 2 4 4
+--R 4500A B a b - 625B a b
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 9A b + 5B a)\|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a
+--R (- 18A b + 10B a)\|b atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x - \|a
+--R (- 18A b + 10B a)\|b atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+
+--R 16a \|2
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R |- 6561A b + 14580A B a b - 12150A B a b + 4500A B a b - 625B a b
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096a
+--R *
+--R 4+-+
+--R \|a
+--R *
+--R atan
+--R 10
+--R 512a
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 6561A b + 14580A B a b - 12150A B a b
+--R +
+--R 3 3 2 4 4
+--R 4500A B a b - 625B a b
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (729A b - 1215A B a b + 675A B a b - 125B a b)\|x
+--R /
+--R 3 +-+4+-+
+--R 8a \|2 \|a
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 20
+
+)clear all
+
+--S 21 of 1397
+t0:=x^(7/2)*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 5 3 +-+
+--R (B x + A x )\|x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 1397
+r0:=1/4*(A*b-a*B)*x^(9/2)/(a*b*(a+b*x^2)^2)+1/16*(A*b-9*a*B)*x^(5/2)/_
+ (a*b^2*(a+b*x^2))-5/32*(A*b-9*a*B)*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(3/4)*b^(13/4)*sqrt(2))+5/32*(A*b-9*a*B)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(13/4)*_
+ sqrt(2))-5/64*(A*b-9*a*B)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(3/4)*b^(13/4)*sqrt(2))+5/64*(A*b-9*a*B)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*_
+ b^(13/4)*sqrt(2))-5/16*(A*b-9*a*B)*sqrt(x)/(a*b^3)
+--R
+--R
+--R (2)
+--R 3 2 4 2 2 2 2 3
+--R ((5A b - 45B a b )x + (10A a b - 90B a b)x + 5A a b - 45B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((- 5A b + 45B a b )x + (- 10A a b + 90B a b)x - 5A a b + 45B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((10A b - 90B a b )x + (20A a b - 180B a b)x + 10A a b - 90B a )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((10A b - 90B a b )x + (20A a b - 180B a b)x + 10A a b - 90B a )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+4+-+3 4+-+ +-+
+--R (128B b x + (- 36A b + 324B a b)x - 20A a b + 180B a )\|2 \|a \|b \|x
+--R /
+--R 5 4 4 2 2 3 +-+4+-+3 4+-+
+--R (64b x + 128a b x + 64a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 4 2 2 3
+--R (16b x + 32a b x + 16a b )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 625A b + 22500A B a b - 303750A B a b + 1822500A B a b
+--R +
+--R 4 4
+--R - 4100625B a
+--R /
+--R 3 13
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R (5A b - 45B a)\|x
+--R +
+--R 3
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 625A b + 22500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 1822500A B a b - 4100625B a
+--R /
+--R 3 13
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R 5 4 4 2 2 3
+--R (- 16b x - 32a b x - 16a b )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 625A b + 22500A B a b - 303750A B a b + 1822500A B a b
+--R +
+--R 4 4
+--R - 4100625B a
+--R /
+--R 3 13
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R (5A b - 45B a)\|x
+--R +
+--R -
+--R 3
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 625A b + 22500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 1822500A B a b - 4100625B a
+--R /
+--R 3 13
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R 5 4 4 2 2 3
+--R (- 32b x - 64a b x - 32a b )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 625A b + 22500A B a b - 303750A B a b + 1822500A B a b
+--R +
+--R 4 4
+--R - 4100625B a
+--R /
+--R 3 13
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R atan
+--R 3
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 625A b + 22500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 1822500A B a b - 4100625B a
+--R /
+--R 3 13
+--R 16777216a b
+--R ,
+--R 4
+--R /
+--R +-+
+--R (5A b - 45B a)\|x
+--R +
+--R 2 4 2 2 2 +-+
+--R (32B b x + (- 9A b + 81B a b)x - 5A a b + 45B a )\|x
+--R /
+--R 5 4 4 2 2 3
+--R 16b x + 32a b x + 16a b
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5A b + 45B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 +-+
+--R 64b \|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 625A b + 22500A B a b - 303750A B a b + 1822500A B a b
+--R +
+--R 4 4
+--R - 4100625B a
+--R /
+--R 3 13
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (5A b - 45B a)\|x
+--R +
+--R 3
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 625A b + 22500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 1822500A B a b - 4100625B a
+--R /
+--R 3 13
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R -
+--R 3 +-+
+--R 64b \|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 625A b + 22500A B a b - 303750A B a b + 1822500A B a b
+--R +
+--R 4 4
+--R - 4100625B a
+--R /
+--R 3 13
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (5A b - 45B a)\|x
+--R +
+--R -
+--R 3
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 625A b + 22500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 1822500A B a b - 4100625B a
+--R /
+--R 3 13
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (5A b - 45B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 10A b + 90B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 10A b + 90B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 3 +-+
+--R 128b \|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 625A b + 22500A B a b - 303750A B a b + 1822500A B a b
+--R +
+--R 4 4
+--R - 4100625B a
+--R /
+--R 3 13
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 3
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 625A b + 22500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 1822500A B a b - 4100625B a
+--R /
+--R 3 13
+--R 16777216a b
+--R ,
+--R 4
+--R /
+--R +-+
+--R (5A b - 45B a)\|x
+--R /
+--R 3 +-+4+-+3 4+-+
+--R 64b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 1397
+t0:=x^(5/2)*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 4 2 +-+
+--R (B x + A x )\|x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 1397
+r0:=1/4*(A*b-a*B)*x^(7/2)/(a*b*(a+b*x^2)^2)-1/16*(A*b+7*a*B)*x^(3/2)/_
+ (a*b^2*(a+b*x^2))-3/32*(A*b+7*a*B)*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(5/4)*b^(11/4)*sqrt(2))+3/32*(A*b+7*a*B)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(11/4)*_
+ sqrt(2))+3/64*(A*b+7*a*B)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(5/4)*b^(11/4)*sqrt(2))-3/64*(A*b+7*a*B)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*_
+ b^(11/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 2 4 2 2 2 2 3
+--R ((- 3A b - 21B a b )x + (- 6A a b - 42B a b)x - 3A a b - 21B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((3A b + 21B a b )x + (6A a b + 42B a b)x + 3A a b + 21B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((6A b + 42B a b )x + (12A a b + 84B a b)x + 6A a b + 42B a )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((6A b + 42B a b )x + (12A a b + 84B a b)x + 6A a b + 42B a )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 +-+4+-+4+-+3 +-+
+--R ((12A b - 44B a b)x + (- 4A a b - 28B a )x)\|2 \|a \|b \|x
+--R /
+--R 4 4 2 3 2 3 2 +-+4+-+4+-+3
+--R (64a b x + 128a b x + 64a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 2 3 2 3 2
+--R (16a b x + 32a b x + 16a b )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 2268A B a b - 23814A B a b - 111132A B a b - 194481B a
+--R |--------------------------------------------------------------------
+--R 4| 5 11
+--R \| 16777216a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27A b + 567A B a b + 3969A B a b + 9261B a )\|x
+--R +
+--R 4 8
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 81A b - 2268A B a b - 23814A B a b - 111132A B a b
+--R +
+--R 4 4
+--R - 194481B a
+--R /
+--R 5 11
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 4 2 3 2 3 2
+--R (- 16a b x - 32a b x - 16a b )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 2268A B a b - 23814A B a b - 111132A B a b - 194481B a
+--R |--------------------------------------------------------------------
+--R 4| 5 11
+--R \| 16777216a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27A b + 567A B a b + 3969A B a b + 9261B a )\|x
+--R +
+--R -
+--R 4 8
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 81A b - 2268A B a b - 23814A B a b
+--R +
+--R 3 3 4 4
+--R - 111132A B a b - 194481B a
+--R /
+--R 5 11
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 4 2 3 2 3 2
+--R (32a b x + 64a b x + 32a b )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 2268A B a b - 23814A B a b - 111132A B a b - 194481B a
+--R |--------------------------------------------------------------------
+--R 4| 5 11
+--R \| 16777216a b
+--R *
+--R atan
+--R 4 8
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 81A b - 2268A B a b - 23814A B a b - 111132A B a b
+--R +
+--R 4 4
+--R - 194481B a
+--R /
+--R 5 11
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27A b + 567A B a b + 3969A B a b + 9261B a )\|x
+--R +
+--R 2 3 2 +-+
+--R ((3A b - 11B a b)x + (- A a b - 7B a )x)\|x
+--R /
+--R 4 4 2 3 2 3 2
+--R 16a b x + 32a b x + 16a b
+--R Type: Union(Expression(Integer),...)
+--E 28
+
+--S 29 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (3A b + 21B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 64a b \|2
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 2268A B a b - 23814A B a b - 111132A B a b - 194481B a
+--R |--------------------------------------------------------------------
+--R 4| 5 11
+--R \| 16777216a b
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27A b + 567A B a b + 3969A B a b + 9261B a )\|x
+--R +
+--R 4 8
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 81A b - 2268A B a b - 23814A B a b - 111132A B a b
+--R +
+--R 4 4
+--R - 194481B a
+--R /
+--R 5 11
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2 +-+
+--R 64a b \|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 81A b - 2268A B a b - 23814A B a b - 111132A B a b
+--R +
+--R 4 4
+--R - 194481B a
+--R /
+--R 5 11
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27A b + 567A B a b + 3969A B a b + 9261B a )\|x
+--R +
+--R -
+--R 4 8
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 81A b - 2268A B a b - 23814A B a b
+--R +
+--R 3 3 4 4
+--R - 111132A B a b - 194481B a
+--R /
+--R 5 11
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3A b - 21B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 6A b - 42B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 6A b - 42B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+
+--R 128a b \|2
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 2268A B a b - 23814A B a b - 111132A B a b - 194481B a
+--R |--------------------------------------------------------------------
+--R 4| 5 11
+--R \| 16777216a b
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 4 8
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 81A b - 2268A B a b - 23814A B a b - 111132A B a b
+--R +
+--R 4 4
+--R - 194481B a
+--R /
+--R 5 11
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27A b + 567A B a b + 3969A B a b + 9261B a )\|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 64a b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 30
+
+)clear all
+
+--S 31 of 1397
+t0:=x^(3/2)*(A+B*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 3 +-+
+--R (B x + A x)\|x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 1397
+r0:=1/4*(A*b-a*B)*x^(5/2)/(a*b*(a+b*x^2)^2)-1/32*(3*A*b+5*a*B)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(9/4)*sqrt(2))+_
+ 1/32*(3*A*b+5*a*B)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(7/4)*b^(9/4)*sqrt(2))-1/64*(3*A*b+5*a*B)*log(sqrt(a)+x*_
+ sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(9/4)*_
+ sqrt(2))+1/64*(3*A*b+5*a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(9/4)*sqrt(2))-1/16*(3*A*b+_
+ 5*a*B)*sqrt(x)/(a*b^2*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 3 2 4 2 2 2 2 3
+--R ((3A b + 5B a b )x + (6A a b + 10B a b)x + 3A a b + 5B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((- 3A b - 5B a b )x + (- 6A a b - 10B a b)x - 3A a b - 5B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((6A b + 10B a b )x + (12A a b + 20B a b)x + 6A a b + 10B a )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((6A b + 10B a b )x + (12A a b + 20B a b)x + 6A a b + 10B a )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 +-+4+-+3 4+-+ +-+
+--R ((4A b - 36B a b)x - 12A a b - 20B a )\|2 \|a \|b \|x
+--R /
+--R 4 4 2 3 2 3 2 +-+4+-+3 4+-+
+--R (64a b x + 128a b x + 64a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 2 3 2 3 2
+--R (16a b x + 32a b x + 16a b )
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 540A B a b - 1350A B a b - 1500A B a b - 625B a
+--R |-------------------------------------------------------------
+--R 4| 7 9
+--R \| 16777216a b
+--R *
+--R log
+--R +-+
+--R (3A b + 5B a)\|x
+--R +
+--R 2 2
+--R 64a b
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 540A B a b - 1350A B a b - 1500A B a b - 625B a
+--R |-------------------------------------------------------------
+--R 4| 7 9
+--R \| 16777216a b
+--R +
+--R 4 4 2 3 2 3 2
+--R (- 16a b x - 32a b x - 16a b )
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 540A B a b - 1350A B a b - 1500A B a b - 625B a
+--R |-------------------------------------------------------------
+--R 4| 7 9
+--R \| 16777216a b
+--R *
+--R log
+--R +-+
+--R (3A b + 5B a)\|x
+--R +
+--R -
+--R 2 2
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 81A b - 540A B a b - 1350A B a b - 1500A B a b
+--R +
+--R 4 4
+--R - 625B a
+--R /
+--R 7 9
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R 4 4 2 3 2 3 2
+--R (- 32a b x - 64a b x - 32a b )
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 540A B a b - 1350A B a b - 1500A B a b - 625B a
+--R |-------------------------------------------------------------
+--R 4| 7 9
+--R \| 16777216a b
+--R *
+--R atan
+--R 2 2
+--R 64a b
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 540A B a b - 1350A B a b - 1500A B a b - 625B a
+--R |-------------------------------------------------------------
+--R 4| 7 9
+--R \| 16777216a b
+--R /
+--R +-+
+--R (3A b + 5B a)\|x
+--R +
+--R 2 2 2 +-+
+--R ((A b - 9B a b)x - 3A a b - 5B a )\|x
+--R /
+--R 4 4 2 3 2 3 2
+--R 16a b x + 32a b x + 16a b
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3A b - 5B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 64a b \|2
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 540A B a b - 1350A B a b - 1500A B a b - 625B a 4+-+3
+--R |------------------------------------------------------------- \|a
+--R 4| 7 9
+--R \| 16777216a b
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R +-+
+--R (3A b + 5B a)\|x
+--R +
+--R 2 2
+--R 64a b
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 540A B a b - 1350A B a b - 1500A B a b - 625B a
+--R |-------------------------------------------------------------
+--R 4| 7 9
+--R \| 16777216a b
+--R +
+--R -
+--R 2 +-+
+--R 64a b \|2
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 540A B a b - 1350A B a b - 1500A B a b - 625B a
+--R |-------------------------------------------------------------
+--R 4| 7 9
+--R \| 16777216a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (3A b + 5B a)\|x
+--R +
+--R -
+--R 2 2
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 81A b - 540A B a b - 1350A B a b - 1500A B a b
+--R +
+--R 4 4
+--R - 625B a
+--R /
+--R 7 9
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (3A b + 5B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 6A b - 10B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 6A b - 10B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 2 +-+
+--R 128a b \|2
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81A b - 540A B a b - 1350A B a b - 1500A B a b - 625B a
+--R |-------------------------------------------------------------
+--R 4| 7 9
+--R \| 16777216a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 2 2
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 81A b - 540A B a b - 1350A B a b - 1500A B a b
+--R +
+--R 4 4
+--R - 625B a
+--R /
+--R 7 9
+--R 16777216a b
+--R ,
+--R 4
+--R /
+--R +-+
+--R (3A b + 5B a)\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 64a b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 1397
+t0:=(A+B*x^2)*sqrt(x)/(a+b*x^2)^3
+--R
+--R
+--R 2 +-+
+--R (B x + A)\|x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 1397
+r0:=1/4*(A*b-a*B)*x^(3/2)/(a*b*(a+b*x^2)^2)+1/16*(5*A*b+3*a*B)*_
+ x^(3/2)/(a^2*b*(a+b*x^2))-1/32*(5*A*b+3*a*B)*atan(1-b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*b^(7/4)*sqrt(2))+1/32*(5*A*b+_
+ 3*a*B)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*b^(7/4)*_
+ sqrt(2))+1/64*(5*A*b+3*a*B)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*b^(7/4)*sqrt(2))-1/64*(5*A*b+_
+ 3*a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(9/4)*b^(7/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 2 4 2 2 2 2 3
+--R ((- 5A b - 3B a b )x + (- 10A a b - 6B a b)x - 5A a b - 3B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((5A b + 3B a b )x + (10A a b + 6B a b)x + 5A a b + 3B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((10A b + 6B a b )x + (20A a b + 12B a b)x + 10A a b + 6B a )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((10A b + 6B a b )x + (20A a b + 12B a b)x + 10A a b + 6B a )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 +-+4+-+4+-+3 +-+
+--R ((20A b + 12B a b)x + (36A a b - 4B a )x)\|2 \|a \|b \|x
+--R /
+--R 2 3 4 3 2 2 4 +-+4+-+4+-+3
+--R (64a b x + 128a b x + 64a b)\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 4 3 2 2 4
+--R (16a b x + 32a b x + 16a b)
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b - 1500A B a b - 1350A B a b - 540A B a b - 81B a
+--R |-------------------------------------------------------------
+--R 4| 9 7
+--R \| 16777216a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (125A b + 225A B a b + 135A B a b + 27B a )\|x
+--R +
+--R 7 5
+--R 262144a b
+--R *
+--R +-------------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b - 1500A B a b - 1350A B a b - 540A B a b - 81B a
+--R |-------------------------------------------------------------
+--R 4| 9 7
+--R \| 16777216a b
+--R +
+--R 2 3 4 3 2 2 4
+--R (- 16a b x - 32a b x - 16a b)
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b - 1500A B a b - 1350A B a b - 540A B a b - 81B a
+--R |-------------------------------------------------------------
+--R 4| 9 7
+--R \| 16777216a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (125A b + 225A B a b + 135A B a b + 27B a )\|x
+--R +
+--R -
+--R 7 5
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 625A b - 1500A B a b - 1350A B a b - 540A B a b
+--R +
+--R 4 4
+--R - 81B a
+--R /
+--R 9 7
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 3 4 3 2 2 4
+--R (32a b x + 64a b x + 32a b)
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b - 1500A B a b - 1350A B a b - 540A B a b - 81B a
+--R |-------------------------------------------------------------
+--R 4| 9 7
+--R \| 16777216a b
+--R *
+--R atan
+--R 7 5
+--R 262144a b
+--R *
+--R +-------------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b - 1500A B a b - 1350A B a b - 540A B a b - 81B a
+--R |-------------------------------------------------------------
+--R 4| 9 7
+--R \| 16777216a b
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (125A b + 225A B a b + 135A B a b + 27B a )\|x
+--R +
+--R 2 3 2 +-+
+--R ((5A b + 3B a b)x + (9A a b - B a )x)\|x
+--R /
+--R 2 3 4 3 2 2 4
+--R 16a b x + 32a b x + 16a b
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (5A b + 3B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 64a b\|2
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b - 1500A B a b - 1350A B a b - 540A B a b - 81B a 4+-+
+--R |------------------------------------------------------------- \|a
+--R 4| 9 7
+--R \| 16777216a b
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (125A b + 225A B a b + 135A B a b + 27B a )\|x
+--R +
+--R 7 5
+--R 262144a b
+--R *
+--R +-------------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b - 1500A B a b - 1350A B a b - 540A B a b - 81B a
+--R |-------------------------------------------------------------
+--R 4| 9 7
+--R \| 16777216a b
+--R +
+--R -
+--R 2 +-+
+--R 64a b\|2
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b - 1500A B a b - 1350A B a b - 540A B a b - 81B a 4+-+
+--R |------------------------------------------------------------- \|a
+--R 4| 9 7
+--R \| 16777216a b
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (125A b + 225A B a b + 135A B a b + 27B a )\|x
+--R +
+--R -
+--R 7 5
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 625A b - 1500A B a b - 1350A B a b
+--R +
+--R 3 3 4 4
+--R - 540A B a b - 81B a
+--R /
+--R 9 7
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5A b - 3B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 10A b - 6B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 10A b - 6B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+
+--R 128a b\|2
+--R *
+--R +-------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b - 1500A B a b - 1350A B a b - 540A B a b - 81B a 4+-+
+--R |------------------------------------------------------------- \|a
+--R 4| 9 7
+--R \| 16777216a b
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R atan
+--R 7 5
+--R 262144a b
+--R *
+--R +-------------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625A b - 1500A B a b - 1350A B a b - 540A B a b - 81B a
+--R |-------------------------------------------------------------
+--R 4| 9 7
+--R \| 16777216a b
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (125A b + 225A B a b + 135A B a b + 27B a )\|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 64a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 1397
+t0:=(A+B*x^2)/((a+b*x^2)^3*sqrt(x))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------------------------------
+--R 3 6 2 4 2 2 3 +-+
+--R (b x + 3a b x + 3a b x + a )\|x
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 1397
+r0:=-3/32*(7*A*b+a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*_
+ b^(5/4)*sqrt(2))+3/32*(7*A*b+a*B)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(11/4)*b^(5/4)*sqrt(2))-3/64*(7*A*b+a*B)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*b^(5/4)*_
+ sqrt(2))+3/64*(7*A*b+a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(11/4)*b^(5/4)*sqrt(2))+1/4*(A*b-a*B)*_
+ sqrt(x)/(a*b*(a+b*x^2)^2)+1/16*(7*A*b+a*B)*sqrt(x)/(a^2*b*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 3 2 4 2 2 2 2 3
+--R ((21A b + 3B a b )x + (42A a b + 6B a b)x + 21A a b + 3B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((- 21A b - 3B a b )x + (- 42A a b - 6B a b)x - 21A a b - 3B a )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((42A b + 6B a b )x + (84A a b + 12B a b)x + 42A a b + 6B a )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((42A b + 6B a b )x + (84A a b + 12B a b)x + 42A a b + 6B a )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 +-+4+-+3 4+-+ +-+
+--R ((28A b + 4B a b)x + 44A a b - 12B a )\|2 \|a \|b \|x
+--R /
+--R 2 3 4 3 2 2 4 +-+4+-+3 4+-+
+--R (64a b x + 128a b x + 64a b)\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 4 3 2 2 4
+--R (16a b x + 32a b x + 16a b)
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 194481A b - 111132A B a b - 23814A B a b - 2268A B a b - 81B a
+--R |--------------------------------------------------------------------
+--R 4| 11 5
+--R \| 16777216a b
+--R *
+--R log
+--R +-+
+--R (21A b + 3B a)\|x
+--R +
+--R 3
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 194481A b - 111132A B a b - 23814A B a b
+--R +
+--R 3 3 4 4
+--R - 2268A B a b - 81B a
+--R /
+--R 11 5
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R 2 3 4 3 2 2 4
+--R (- 16a b x - 32a b x - 16a b)
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 194481A b - 111132A B a b - 23814A B a b - 2268A B a b - 81B a
+--R |--------------------------------------------------------------------
+--R 4| 11 5
+--R \| 16777216a b
+--R *
+--R log
+--R +-+
+--R (21A b + 3B a)\|x
+--R +
+--R -
+--R 3
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 194481A b - 111132A B a b - 23814A B a b
+--R +
+--R 3 3 4 4
+--R - 2268A B a b - 81B a
+--R /
+--R 11 5
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R 2 3 4 3 2 2 4
+--R (- 32a b x - 64a b x - 32a b)
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 194481A b - 111132A B a b - 23814A B a b - 2268A B a b - 81B a
+--R |--------------------------------------------------------------------
+--R 4| 11 5
+--R \| 16777216a b
+--R *
+--R atan
+--R 3
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 194481A b - 111132A B a b - 23814A B a b
+--R +
+--R 3 3 4 4
+--R - 2268A B a b - 81B a
+--R /
+--R 11 5
+--R 16777216a b
+--R ,
+--R 4
+--R /
+--R +-+
+--R (21A b + 3B a)\|x
+--R +
+--R 2 2 2 +-+
+--R ((7A b + B a b)x + 11A a b - 3B a )\|x
+--R /
+--R 2 3 4 3 2 2 4
+--R 16a b x + 32a b x + 16a b
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 21A b - 3B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 64a b\|2
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 194481A b - 111132A B a b - 23814A B a b - 2268A B a b - 81B a
+--R |--------------------------------------------------------------------
+--R 4| 11 5
+--R \| 16777216a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (21A b + 3B a)\|x
+--R +
+--R 3
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 194481A b - 111132A B a b - 23814A B a b
+--R +
+--R 3 3 4 4
+--R - 2268A B a b - 81B a
+--R /
+--R 11 5
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R -
+--R 2 +-+
+--R 64a b\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 194481A b - 111132A B a b - 23814A B a b - 2268A B a b
+--R +
+--R 4 4
+--R - 81B a
+--R /
+--R 11 5
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (21A b + 3B a)\|x
+--R +
+--R -
+--R 3
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 194481A b - 111132A B a b - 23814A B a b
+--R +
+--R 3 3 4 4
+--R - 2268A B a b - 81B a
+--R /
+--R 11 5
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (21A b + 3B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 42A b - 6B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 42A b - 6B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 2 +-+
+--R 128a b\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 194481A b - 111132A B a b - 23814A B a b - 2268A B a b
+--R +
+--R 4 4
+--R - 81B a
+--R /
+--R 11 5
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 3
+--R 64a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 194481A b - 111132A B a b - 23814A B a b
+--R +
+--R 3 3 4 4
+--R - 2268A B a b - 81B a
+--R /
+--R 11 5
+--R 16777216a b
+--R ,
+--R 4
+--R /
+--R +-+
+--R (21A b + 3B a)\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 64a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 1397
+t0:=(A+B*x^2)/(x^(3/2)*(a+b*x^2)^3)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ------------------------------------
+--R 3 7 2 5 2 3 3 +-+
+--R (b x + 3a b x + 3a b x + a x)\|x
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 1397
+r0:=5/32*(9*A*b-a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*_
+ b^(3/4)*sqrt(2))-5/32*(9*A*b-a*B)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(13/4)*b^(3/4)*sqrt(2))-5/64*(9*A*b-a*B)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*b^(3/4)*_
+ sqrt(2))+5/64*(9*A*b-a*B)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(13/4)*b^(3/4)*sqrt(2))-5/16*(9*A*b-a*B)/(a^3*_
+ b*sqrt(x))+1/4*(A*b-a*B)/(a*b*(a+b*x^2)^2*sqrt(x))+1/16*(9*A*b-_
+ a*B)/(a^2*b*(a+b*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 3 2 4 2 2 2 2 3 +-+
+--R ((45A b - 5B a b )x + (90A a b - 10B a b)x + 45A a b - 5B a )\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((- 45A b + 5B a b )x + (- 90A a b + 10B a b)x - 45A a b + 5B a )
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 90A b + 10B a b )x + (- 180A a b + 20B a b)x - 90A a b
+--R +
+--R 3
+--R 10B a
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x + \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 90A b + 10B a b )x + (- 180A a b + 20B a b)x - 90A a b
+--R +
+--R 3
+--R 10B a
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x - \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+4+-+4+-+3
+--R ((- 180A b + 20B a b)x + (- 324A a b + 36B a )x - 128A a )\|2 \|a \|b
+--R /
+--R 3 2 4 4 2 5 +-+4+-+4+-+3 +-+
+--R (64a b x + 128a b x + 64a )\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 4 2 5
+--R (- 16a b x - 32a b x - 16a )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 4100625A b + 1822500A B a b - 303750A B a b + 22500A B a b
+--R +
+--R 4 4
+--R - 625B a
+--R /
+--R 13 3
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (91125A b - 30375A B a b + 3375A B a b - 125B a )\|x
+--R +
+--R 10 2
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 4100625A b + 1822500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 22500A B a b - 625B a
+--R /
+--R 13 3
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 4 4 2 5
+--R (16a b x + 32a b x + 16a )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 4100625A b + 1822500A B a b - 303750A B a b + 22500A B a b
+--R +
+--R 4 4
+--R - 625B a
+--R /
+--R 13 3
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (91125A b - 30375A B a b + 3375A B a b - 125B a )\|x
+--R +
+--R -
+--R 10 2
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 4100625A b + 1822500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 22500A B a b - 625B a
+--R /
+--R 13 3
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 4 4 2 5
+--R (- 32a b x - 64a b x - 32a )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 4100625A b + 1822500A B a b - 303750A B a b + 22500A B a b
+--R +
+--R 4 4
+--R - 625B a
+--R /
+--R 13 3
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 10 2
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 4100625A b + 1822500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 22500A B a b - 625B a
+--R /
+--R 13 3
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (91125A b - 30375A B a b + 3375A B a b - 125B a )\|x
+--R +
+--R 2 4 2 2 2
+--R (- 45A b + 5B a b)x + (- 81A a b + 9B a )x - 32A a
+--R /
+--R 3 2 4 4 2 5 +-+
+--R (16a b x + 32a b x + 16a )\|x
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 45A b + 5B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 3 +-+
+--R 64a \|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 4100625A b + 1822500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 22500A B a b - 625B a
+--R /
+--R 13 3
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (91125A b - 30375A B a b + 3375A B a b - 125B a )\|x
+--R +
+--R 10 2
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 4100625A b + 1822500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 22500A B a b - 625B a
+--R /
+--R 13 3
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 +-+
+--R 64a \|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 4100625A b + 1822500A B a b - 303750A B a b + 22500A B a b
+--R +
+--R 4 4
+--R - 625B a
+--R /
+--R 13 3
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (91125A b - 30375A B a b + 3375A B a b - 125B a )\|x
+--R +
+--R -
+--R 10 2
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 4100625A b + 1822500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 22500A B a b - 625B a
+--R /
+--R 13 3
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (45A b - 5B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (90A b - 10B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (90A b - 10B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 3 +-+
+--R 128a \|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 4100625A b + 1822500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 22500A B a b - 625B a
+--R /
+--R 13 3
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 10 2
+--R 262144a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 4100625A b + 1822500A B a b - 303750A B a b
+--R +
+--R 3 3 4 4
+--R 22500A B a b - 625B a
+--R /
+--R 13 3
+--R 16777216a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (91125A b - 30375A B a b + 3375A B a b - 125B a )\|x
+--R /
+--R 3 +-+4+-+4+-+3
+--R 64a \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 1397
+t0:=(A+B*x^2)/(x^(5/2)*(a+b*x^2)^3)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------------------------------
+--R 3 8 2 6 2 4 3 2 +-+
+--R (b x + 3a b x + 3a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 1397
+r0:=-7/48*(11*A*b-3*a*B)/(a^3*b*x^(3/2))+1/4*(A*b-a*B)/(a*b*x^(3/2)*_
+ (a+b*x^2)^2)+1/16*(11*A*b-3*a*B)/(a^2*b*x^(3/2)*(a+b*x^2))+7/32*_
+ (11*A*b-3*a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(15/4)*_
+ b^(1/4)*sqrt(2))-7/32*(11*A*b-3*a*B)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(15/4)*b^(1/4)*sqrt(2))+7/64*(11*A*b-3*a*B)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(15/4)*_
+ b^(1/4)*sqrt(2))-7/64*(11*A*b-3*a*B)*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(15/4)*b^(1/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 2 5 2 2 3
+--R (- 231A b + 63B a b )x + (- 462A a b + 126B a b)x
+--R +
+--R 2 3
+--R (- 231A a b + 63B a )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 5 2 2 3
+--R (231A b - 63B a b )x + (462A a b - 126B a b)x
+--R +
+--R 2 3
+--R (231A a b - 63B a )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 5 2 2 3
+--R (- 462A b + 126B a b )x + (- 924A a b + 252B a b)x
+--R +
+--R 2 3
+--R (- 462A a b + 126B a )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x + \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 5 2 2 3
+--R (- 462A b + 126B a b )x + (- 924A a b + 252B a b)x
+--R +
+--R 2 3
+--R (- 462A a b + 126B a )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x - \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+4+-+3 4+-+
+--R ((- 308A b + 84B a b)x + (- 484A a b + 132B a )x - 128A a )\|2 \|a \|b
+--R /
+--R 3 2 5 4 3 5 +-+4+-+3 4+-+ +-+
+--R (192a b x + 384a b x + 192a x)\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 5 4 3 5
+--R (- 48a b x - 96a b x - 48a x)
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 35153041A b + 38348772A B a b - 15688134A B a b
+--R +
+--R 3 3 4 4
+--R 2852388A B a b - 194481B a
+--R /
+--R 15
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R +-+
+--R (77A b - 21B a)\|x
+--R +
+--R 4
+--R 64a
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 35153041A b + 38348772A B a b - 15688134A B a b
+--R +
+--R 3 3 4 4
+--R 2852388A B a b - 194481B a
+--R /
+--R 15
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R 3 2 5 4 3 5
+--R (48a b x + 96a b x + 48a x)
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 35153041A b + 38348772A B a b - 15688134A B a b
+--R +
+--R 3 3 4 4
+--R 2852388A B a b - 194481B a
+--R /
+--R 15
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R +-+
+--R (77A b - 21B a)\|x
+--R +
+--R -
+--R 4
+--R 64a
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 35153041A b + 38348772A B a b - 15688134A B a b
+--R +
+--R 3 3 4 4
+--R 2852388A B a b - 194481B a
+--R /
+--R 15
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R 3 2 5 4 3 5
+--R (96a b x + 192a b x + 96a x)
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 35153041A b + 38348772A B a b - 15688134A B a b
+--R +
+--R 3 3 4 4
+--R 2852388A B a b - 194481B a
+--R /
+--R 15
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 4
+--R 64a
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 35153041A b + 38348772A B a b - 15688134A B a b
+--R +
+--R 3 3 4 4
+--R 2852388A B a b - 194481B a
+--R /
+--R 15
+--R 16777216a b
+--R ,
+--R 4
+--R /
+--R +-+
+--R (77A b - 21B a)\|x
+--R +
+--R 2 4 2 2 2
+--R (- 77A b + 21B a b)x + (- 121A a b + 33B a )x - 32A a
+--R /
+--R 3 2 5 4 3 5 +-+
+--R (48a b x + 96a b x + 48a x)\|x
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (77A b - 21B a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 3 +-+
+--R 64a \|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 35153041A b + 38348772A B a b - 15688134A B a b
+--R +
+--R 3 3 4 4
+--R 2852388A B a b - 194481B a
+--R /
+--R 15
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (77A b - 21B a)\|x
+--R +
+--R 4
+--R 64a
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 35153041A b + 38348772A B a b - 15688134A B a b
+--R +
+--R 3 3 4 4
+--R 2852388A B a b - 194481B a
+--R /
+--R 15
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R 3 +-+
+--R 64a \|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 35153041A b + 38348772A B a b - 15688134A B a b
+--R +
+--R 3 3 4 4
+--R 2852388A B a b - 194481B a
+--R /
+--R 15
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (77A b - 21B a)\|x
+--R +
+--R -
+--R 4
+--R 64a
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 35153041A b + 38348772A B a b - 15688134A B a b
+--R +
+--R 3 3 4 4
+--R 2852388A B a b - 194481B a
+--R /
+--R 15
+--R 16777216a b
+--R ,
+--R 4
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 77A b + 21B a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (154A b - 42B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (154A b - 42B a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+
+--R 128a \|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 35153041A b + 38348772A B a b - 15688134A B a b
+--R +
+--R 3 3 4 4
+--R 2852388A B a b - 194481B a
+--R /
+--R 15
+--R 16777216a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 4
+--R 64a
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 35153041A b + 38348772A B a b - 15688134A B a b
+--R +
+--R 3 3 4 4
+--R 2852388A B a b - 194481B a
+--R /
+--R 15
+--R 16777216a b
+--R ,
+--R 4
+--R /
+--R +-+
+--R (77A b - 21B a)\|x
+--R /
+--R 3 +-+4+-+3 4+-+
+--R 64a \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 1397
+t0:=(A+B*x^2)/(x^(7/2)*(a+b*x^2)^3)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------------------------------
+--R 3 9 2 7 2 5 3 3 +-+
+--R (b x + 3a b x + 3a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 1397
+r0:=-9/80*(13*A*b-5*a*B)/(a^3*b*x^(5/2))+1/4*(A*b-a*B)/(a*b*x^(5/2)*_
+ (a+b*x^2)^2)+1/16*(13*A*b-5*a*B)/(a^2*b*x^(5/2)*(a+b*x^2))-9/32*_
+ b^(1/4)*(13*A*b-5*a*B)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(17/4)*sqrt(2))+9/32*b^(1/4)*(13*A*b-5*a*B)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(17/4)*sqrt(2))+9/64*b^(1/4)*(13*A*b-_
+ 5*a*B)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(17/4)*sqrt(2))-9/64*b^(1/4)*(13*A*b-5*a*B)*log(sqrt(a)+x*_
+ sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(17/4)*sqrt(2))+_
+ 9/16*(13*A*b-5*a*B)/(a^4*sqrt(x))
+--R
+--R
+--R (2)
+--R 3 2 6 2 2 4
+--R (- 585A b + 225B a b )x + (- 1170A a b + 450B a b)x
+--R +
+--R 2 3 2
+--R (- 585A a b + 225B a )x
+--R *
+--R 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 6 2 2 4
+--R (585A b - 225B a b )x + (1170A a b - 450B a b)x
+--R +
+--R 2 3 2
+--R (585A a b - 225B a )x
+--R *
+--R 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 6 2 2 4
+--R (1170A b - 450B a b )x + (2340A a b - 900B a b)x
+--R +
+--R 2 3 2
+--R (1170A a b - 450B a )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ +-+ \|2 \|b \|x + \|a
+--R \|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 6 2 2 4
+--R (1170A b - 450B a b )x + (2340A a b - 900B a b)x
+--R +
+--R 2 3 2
+--R (1170A a b - 450B a )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ +-+ \|2 \|b \|x - \|a
+--R \|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 6 2 2 4
+--R (2340A b - 900B a b )x + (4212A a b - 1620B a b)x
+--R +
+--R 2 3 2 3
+--R (1664A a b - 640B a )x - 128A a
+--R *
+--R +-+4+-+
+--R \|2 \|a
+--R /
+--R 4 2 6 5 4 6 2 +-+4+-+ +-+
+--R (320a b x + 640a b x + 320a x )\|2 \|a \|x
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 6 5 4 6 2
+--R (80a b x + 160a b x + 80a x )
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 187388721A b + 288290340A B a b - 166321350A B a b
+--R +
+--R 3 3 2 4 4
+--R 42646500A B a b - 4100625B a b
+--R /
+--R 17
+--R 16777216a
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (1601613A b - 1848015A B a b + 710775A B a b - 91125B a b)\|x
+--R +
+--R 13
+--R 262144a
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 187388721A b + 288290340A B a b - 166321350A B a b
+--R +
+--R 3 3 2 4 4
+--R 42646500A B a b - 4100625B a b
+--R /
+--R 17
+--R 16777216a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 2 6 5 4 6 2
+--R (- 80a b x - 160a b x - 80a x )
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 187388721A b + 288290340A B a b - 166321350A B a b
+--R +
+--R 3 3 2 4 4
+--R 42646500A B a b - 4100625B a b
+--R /
+--R 17
+--R 16777216a
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (1601613A b - 1848015A B a b + 710775A B a b - 91125B a b)\|x
+--R +
+--R -
+--R 13
+--R 262144a
+--R *
+--R ROOT
+--R 4 5 3 4
+--R - 187388721A b + 288290340A B a b
+--R +
+--R 2 2 2 3 3 3 2 4 4
+--R - 166321350A B a b + 42646500A B a b - 4100625B a b
+--R /
+--R 17
+--R 16777216a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 2 6 5 4 6 2
+--R (160a b x + 320a b x + 160a x )
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 187388721A b + 288290340A B a b - 166321350A B a b
+--R +
+--R 3 3 2 4 4
+--R 42646500A B a b - 4100625B a b
+--R /
+--R 17
+--R 16777216a
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 13
+--R 262144a
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 187388721A b + 288290340A B a b - 166321350A B a b
+--R +
+--R 3 3 2 4 4
+--R 42646500A B a b - 4100625B a b
+--R /
+--R 17
+--R 16777216a
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (1601613A b - 1848015A B a b + 710775A B a b - 91125B a b)\|x
+--R +
+--R 3 2 6 2 2 4
+--R (585A b - 225B a b )x + (1053A a b - 405B a b)x
+--R +
+--R 2 3 2 3
+--R (416A a b - 160B a )x - 32A a
+--R /
+--R 4 2 6 5 4 6 2 +-+
+--R (80a b x + 160a b x + 80a x )\|x
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (117A b - 45B a)\|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 +-+
+--R 64a \|2
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 187388721A b + 288290340A B a b - 166321350A B a b
+--R +
+--R 3 3 2 4 4
+--R 42646500A B a b - 4100625B a b
+--R /
+--R 17
+--R 16777216a
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|a
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (1601613A b - 1848015A B a b + 710775A B a b - 91125B a b)\|x
+--R +
+--R 13
+--R 262144a
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 187388721A b + 288290340A B a b - 166321350A B a b
+--R +
+--R 3 3 2 4 4
+--R 42646500A B a b - 4100625B a b
+--R /
+--R 17
+--R 16777216a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 4 +-+
+--R 64a \|2
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 187388721A b + 288290340A B a b - 166321350A B a b
+--R +
+--R 3 3 2 4 4
+--R 42646500A B a b - 4100625B a b
+--R /
+--R 17
+--R 16777216a
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|a
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3
+--R (1601613A b - 1848015A B a b + 710775A B a b - 91125B a b)
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 13
+--R 262144a
+--R *
+--R ROOT
+--R 4 5 3 4
+--R - 187388721A b + 288290340A B a b
+--R +
+--R 2 2 2 3 3 3 2
+--R - 166321350A B a b + 42646500A B a b
+--R +
+--R 4 4
+--R - 4100625B a b
+--R /
+--R 17
+--R 16777216a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 117A b + 45B a)\|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a
+--R (- 234A b + 90B a)\|b atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x - \|a
+--R (- 234A b + 90B a)\|b atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 +-+
+--R 128a \|2
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 187388721A b + 288290340A B a b - 166321350A B a b
+--R +
+--R 3 3 2 4 4
+--R 42646500A B a b - 4100625B a b
+--R /
+--R 17
+--R 16777216a
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|a
+--R *
+--R atan
+--R 13
+--R 262144a
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3
+--R - 187388721A b + 288290340A B a b - 166321350A B a b
+--R +
+--R 3 3 2 4 4
+--R 42646500A B a b - 4100625B a b
+--R /
+--R 17
+--R 16777216a
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (1601613A b - 1848015A B a b + 710775A B a b - 91125B a b)\|x
+--R /
+--R 4 +-+4+-+
+--R 64a \|2 \|a
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 1397
+t0:=x^(7/2)*(A+B*x^2)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 5 3 +-+ | 2
+--R (1) (B x + A x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 1397
+--r0:=2/15*B*x^(9/2)*(a+b*x^2)^(3/2)/b+4/385*a*(5*A*b-3*a*B)*x^(5/2)*_
+-- sqrt(a+b*x^2)/b^2+2/55*(5*A*b-3*a*B)*x^(9/2)*sqrt(a+b*x^2)/b-_
+-- 4/231*a^2*(5*A*b-3*a*B)*sqrt(x)*sqrt(a+b*x^2)/b^3-4/231*_
+-- a^(13/4)*(5*A*b-3*a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/_
+-- a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(13/4)*sqrt(a+b*x^2))
+--E 62
+
+--S 63 of 1397
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 1397
+--m0:=a0-r0
+--E 64
+
+--S 65 of 1397
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 1397
+t0:=x^(5/2)*(A+B*x^2)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 4 2 +-+ | 2
+--R (1) (B x + A x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 1397
+--r0:=2/13*B*x^(7/2)*(a+b*x^2)^(3/2)/b+4/585*a*(13*A*b-7*a*B)*x^(3/2)*_
+-- sqrt(a+b*x^2)/b^2+2/117*(13*A*b-7*a*B)*x^(7/2)*sqrt(a+b*x^2)/b-_
+-- 4/195*a^(11/4)*(13*A*b-7*a*B)*elliptic_e(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(11/4)*_
+-- sqrt(a+b*x^2))+4/195*a^(11/4)*(13*A*b-7*a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/((-b)^(11/4)*sqrt(a+b*x^2))
+--E 67
+
+--S 68 of 1397
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 1397
+--m0:=a0-r0
+--E 69
+
+--S 70 of 1397
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 1397
+t0:=x^(3/2)*(A+B*x^2)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 3 +-+ | 2
+--R (1) (B x + A x)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 1397
+--r0:=2/11*B*x^(5/2)*(a+b*x^2)^(3/2)/b+2/77*(11*A*b-5*a*B)*x^(5/2)*_
+-- sqrt(a+b*x^2)/b+4/231*a*(11*A*b-5*a*B)*sqrt(x)*sqrt(a+b*x^2)/_
+-- b^2-4/231*a^(9/4)*(11*A*b-5*a*B)*elliptic_f(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2))
+--E 72
+
+--S 73 of 1397
+--a0:=integrate(t0,x)
+--E 73
+
+--S 74 of 1397
+--m0:=a0-r0
+--E 74
+
+--S 75 of 1397
+--d0:=D(m0,x)
+--E 75
+
+)clear all
+
+--S 76 of 1397
+t0:=(A+B*x^2)*sqrt(x)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 +-+ | 2
+--R (1) (B x + A)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 1397
+--r0:=2/9*B*x^(3/2)*(a+b*x^2)^(3/2)/b+2/15*(3*A*b-a*B)*x^(3/2)*_
+-- sqrt(a+b*x^2)/b-4/15*a^(7/4)*(3*A*b-a*B)*elliptic_e(_
+-- asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+-- ((-b)^(7/4)*sqrt(a+b*x^2))+4/15*a^(7/4)*(3*A*b-a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))
+--E 77
+
+--S 78 of 1397
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 1397
+--m0:=a0-r0
+--E 79
+
+--S 80 of 1397
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 1397
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/sqrt(x)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 1397
+--r0:=2/7*B*(a+b*x^2)^(3/2)*sqrt(x)/b+2/21*(7*A*b-a*B)*sqrt(x)*_
+-- sqrt(a+b*x^2)/b-4/21*a^(5/4)*(7*A*b-a*B)*elliptic_f(_
+-- asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+-- ((-b)^(5/4)*sqrt(a+b*x^2))
+--E 82
+
+--S 83 of 1397
+--a0:=integrate(t0,x)
+--E 83
+
+--S 84 of 1397
+--m0:=a0-r0
+--E 84
+
+--S 85 of 1397
+--d0:=D(m0,x)
+--E 85
+
+)clear all
+
+--S 86 of 1397
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x^(3/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 1397
+--r0:=-2*A*(a+b*x^2)^(3/2)/(a*sqrt(x))+2/5*(5*A*b+a*B)*x^(3/2)*_
+-- sqrt(a+b*x^2)/a+4/5*a^(3/4)*(5*A*b+a*B)*elliptic_e(_
+-- asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+-- ((-b)^(3/4)*sqrt(a+b*x^2))-4/5*a^(3/4)*(5*A*b+a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))
+--E 87
+
+--S 88 of 1397
+--a0:=integrate(t0,x)
+--E 88
+
+--S 89 of 1397
+--m0:=a0-r0
+--E 89
+
+--S 90 of 1397
+--d0:=D(m0,x)
+--E 90
+
+)clear all
+
+--S 91 of 1397
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x^(5/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 1397
+--r0:=-2/3*A*(a+b*x^2)^(3/2)/(a*x^(3/2))+2/3*(A*b+a*B)*sqrt(x)*_
+-- sqrt(a+b*x^2)/a+4/3*a^(1/4)*(A*b+a*B)*elliptic_f(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(1/4)*sqrt(a+b*x^2))
+--E 92
+
+--S 93 of 1397
+--a0:=integrate(t0,x)
+--E 93
+
+--S 94 of 1397
+--m0:=a0-r0
+--E 94
+
+--S 95 of 1397
+--d0:=D(m0,x)
+--E 95
+
+)clear all
+
+--S 96 of 1397
+t0:=(A+B*x^2)*sqrt(a+b*x^2)/x^(7/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (B x + A)\|b x + a
+--R (1) ---------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 1397
+--r0:=-2/5*A*(a+b*x^2)^(3/2)/(a*x^(5/2))-2/5*(A*b+5*a*B)*_
+-- sqrt(a+b*x^2)/(a*sqrt(x))-4/5*(-b)^(1/4)*(A*b+5*a*B)*_
+-- elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/(a^(1/4)*sqrt(a+b*x^2))+4/5*(-b)^(1/4)*(A*b+5*a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*_
+-- x^2)/a)/(a^(1/4)*sqrt(a+b*x^2))
+--E 97
+
+--S 98 of 1397
+--a0:=integrate(t0,x)
+--E 98
+
+--S 99 of 1397
+--m0:=a0-r0
+--E 99
+
+--S 100 of 1397
+--d0:=D(m0,x)
+--E 100
+
+)clear all
+
+--S 101 of 1397
+t0:=x^(7/2)*(a+b*x^2)^(3/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 7 5 3 +-+ | 2
+--R (1) (B b x + (A b + B a)x + A a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 1397
+--r0:=2/285*(19*A*b-9*a*B)*x^(9/2)*(a+b*x^2)^(3/2)/b+2/19*B*x^(9/2)*_
+-- (a+b*x^2)^(5/2)/b+8/7315*a^2*(19*A*b-9*a*B)*x^(5/2)*_
+-- sqrt(a+b*x^2)/b^2+4/1045*a*(19*A*b-9*a*B)*x^(9/2)*_
+-- sqrt(a+b*x^2)/b-8/4389*a^3*(19*A*b-9*a*B)*sqrt(x)*_
+-- sqrt(a+b*x^2)/b^3-8/4389*a^(17/4)*(19*A*b-9*a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/((-b)^(13/4)*sqrt(a+b*x^2))
+--E 102
+
+--S 103 of 1397
+--a0:=integrate(t0,x)
+--E 103
+
+--S 104 of 1397
+--m0:=a0-r0
+--E 104
+
+--S 105 of 1397
+--d0:=D(m0,x)
+--E 105
+
+)clear all
+
+--S 106 of 1397
+t0:=x^(5/2)*(a+b*x^2)^(3/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 6 4 2 +-+ | 2
+--R (1) (B b x + (A b + B a)x + A a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 1397
+--r0:=2/221*(17*A*b-7*a*B)*x^(7/2)*(a+b*x^2)^(3/2)/b+2/17*B*x^(7/2)*_
+-- (a+b*x^2)^(5/2)/b+8/3315*a^2*(17*A*b-7*a*B)*x^(3/2)*_
+-- sqrt(a+b*x^2)/b^2+4/663*a*(17*A*b-7*a*B)*x^(7/2)*sqrt(a+b*x^2)/b-_
+-- 8/1105*a^(15/4)*(17*A*b-7*a*B)*elliptic_e(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(11/4)*_
+-- sqrt(a+b*x^2))+8/1105*a^(15/4)*(17*A*b-7*a*B)*elliptic_f(_
+-- asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+-- ((-b)^(11/4)*sqrt(a+b*x^2))
+--E 107
+
+--S 108 of 1397
+--a0:=integrate(t0,x)
+--E 108
+
+--S 109 of 1397
+--m0:=a0-r0
+--E 109
+
+--S 110 of 1397
+--d0:=D(m0,x)
+--E 110
+
+)clear all
+
+--S 111 of 1397
+t0:=x^(3/2)*(a+b*x^2)^(3/2)*(A+B*x^2)
+--R
+--R
+--R +--------+
+--R 5 3 +-+ | 2
+--R (1) (B b x + (A b + B a)x + A a x)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 1397
+--r0:=2/33*(3*A*b-a*B)*x^(5/2)*(a+b*x^2)^(3/2)/b+2/15*B*x^(5/2)*_
+-- (a+b*x^2)^(5/2)/b+4/77*a*(3*A*b-a*B)*x^(5/2)*sqrt(a+b*x^2)/b+_
+-- 8/231*a^2*(3*A*b-a*B)*sqrt(x)*sqrt(a+b*x^2)/b^2-8/231*a^(13/4)*_
+-- (3*A*b-a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2))
+--E 112
+
+--S 113 of 1397
+--a0:=integrate(t0,x)
+--E 113
+
+--S 114 of 1397
+--m0:=a0-r0
+--E 114
+
+--S 115 of 1397
+--d0:=D(m0,x)
+--E 115
+
+)clear all
+
+--S 116 of 1397
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)*sqrt(x)
+--R
+--R
+--R +--------+
+--R 4 2 +-+ | 2
+--R (1) (B b x + (A b + B a)x + A a)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 1397
+--r0:=2/117*(13*A*b-3*a*B)*x^(3/2)*(a+b*x^2)^(3/2)/b+2/13*B*x^(3/2)*_
+-- (a+b*x^2)^(5/2)/b+4/195*a*(13*A*b-3*a*B)*x^(3/2)*sqrt(a+b*x^2)/b-_
+-- 8/195*a^(11/4)*(13*A*b-3*a*B)*elliptic_e(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))+_
+-- 8/195*a^(11/4)*(13*A*b-3*a*B)*elliptic_f(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))
+--E 117
+
+--S 118 of 1397
+--a0:=integrate(t0,x)
+--E 118
+
+--S 119 of 1397
+--m0:=a0-r0
+--E 119
+
+--S 120 of 1397
+--d0:=D(m0,x)
+--E 120
+
+)clear all
+
+--S 121 of 1397
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/sqrt(x)
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 1397
+--r0:=2/77*(11*A*b-a*B)*(a+b*x^2)^(3/2)*sqrt(x)/b+2/11*B*(a+_
+-- b*x^2)^(5/2)*sqrt(x)/b+4/77*a*(11*A*b-a*B)*sqrt(x)*sqrt(a+_
+-- b*x^2)/b-8/77*a^(9/4)*(11*A*b-a*B)*elliptic_f(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2))
+--E 122
+
+--S 123 of 1397
+--a0:=integrate(t0,x)
+--E 123
+
+--S 124 of 1397
+--m0:=a0-r0
+--E 124
+
+--S 125 of 1397
+--d0:=D(m0,x)
+--E 125
+
+)clear all
+
+--S 126 of 1397
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x^(3/2)
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 1397
+--r0:=2/9*(9*A*b+a*B)*x^(3/2)*(a+b*x^2)^(3/2)/a-2*A*(a+b*x^2)^(5/2)/(a*_
+-- sqrt(x))+4/15*(9*A*b+a*B)*x^(3/2)*sqrt(a+b*x^2)+8/15*a^(7/4)*_
+-- (9*A*b+a*B)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))-8/15*a^(7/4)*_
+-- (9*A*b+a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))
+--E 127
+
+--S 128 of 1397
+--a0:=integrate(t0,x)
+--E 128
+
+--S 129 of 1397
+--m0:=a0-r0
+--E 129
+
+--S 130 of 1397
+--d0:=D(m0,x)
+--E 130
+
+)clear all
+
+--S 131 of 1397
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x^(5/2)
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 1397
+--r0:=-2/3*A*(a+b*x^2)^(5/2)/(a*x^(3/2))+2/21*(7*A*b+3*a*B)*(a+_
+-- b*x^2)^(3/2)*sqrt(x)/a+4/21*(7*A*b+3*a*B)*sqrt(x)*sqrt(a+_
+-- b*x^2)+8/21*a^(5/4)*(7*A*b+3*a*B)*elliptic_f(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(1/4)*sqrt(a+b*x^2))
+--E 132
+
+--S 133 of 1397
+--a0:=integrate(t0,x)
+--E 133
+
+--S 134 of 1397
+--m0:=a0-r0
+--E 134
+
+--S 135 of 1397
+--d0:=D(m0,x)
+--E 135
+
+)clear all
+
+--S 136 of 1397
+t0:=(a+b*x^2)^(3/2)*(A+B*x^2)/x^(7/2)
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|b x + a
+--R (1) -----------------------------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 1397
+--r0:=-2/5*A*(a+b*x^2)^(5/2)/(a*x^(5/2))-2*(A*b+a*B)*(a+b*x^2)^(3/2)/_
+-- (a*sqrt(x))+12/5*b*(A*b+a*B)*x^(3/2)*sqrt(a+b*x^2)/a-24/5*_
+-- a^(3/4)*(-b)^(1/4)*(A*b+a*B)*elliptic_e(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)+24/5*_
+-- a^(3/4)*(-b)^(1/4)*(A*b+a*B)*elliptic_f(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)
+--E 137
+
+--S 138 of 1397
+--a0:=integrate(t0,x)
+--E 138
+
+--S 139 of 1397
+--m0:=a0-r0
+--E 139
+
+--S 140 of 1397
+--d0:=D(m0,x)
+--E 140
+
+)clear all
+
+--S 141 of 1397
+t0:=x^(7/2)*(a+b*x^2)^(5/2)*(A+B*x^2)
+--R
+--R
+--R (1)
+--R +--------+
+--R 2 9 2 7 2 5 2 3 +-+ | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 1397
+--r0:=4/1311*a*(23*A*b-9*a*B)*x^(9/2)*(a+b*x^2)^(3/2)/b+2/437*(23*A*b-_
+-- 9*a*B)*x^(9/2)*(a+b*x^2)^(5/2)/b+2/23*B*x^(9/2)*(a+b*x^2)^(7/2)/b+_
+-- 16/33649*a^3*(23*A*b-9*a*B)*x^(5/2)*sqrt(a+b*x^2)/b^2+8/4807*_
+-- a^2*(23*A*b-9*a*B)*x^(9/2)*sqrt(a+b*x^2)/b-80/100947*a^4*(23*A*_
+-- b-9*a*B)*sqrt(x)*sqrt(a+b*x^2)/b^3-80/100947*a^(21/4)*(23*A*b-_
+-- 9*a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/((-b)^(13/4)*sqrt(a+b*x^2))
+--E 142
+
+--S 143 of 1397
+--a0:=integrate(t0,x)
+--E 143
+
+--S 144 of 1397
+--m0:=a0-r0
+--E 144
+
+--S 145 of 1397
+--d0:=D(m0,x)
+--E 145
+
+)clear all
+
+--S 146 of 1397
+t0:=x^(5/2)*(a+b*x^2)^(5/2)*(A+B*x^2)
+--R
+--R
+--R (1)
+--R +--------+
+--R 2 8 2 6 2 4 2 2 +-+ | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 1397
+--r0:=20/663*a*(3*A*b-a*B)*x^(7/2)*(a+b*x^2)^(3/2)/b+2/51*(3*A*b-_
+-- a*B)*x^(7/2)*(a+b*x^2)^(5/2)/b+2/21*B*x^(7/2)*(a+b*x^2)^(7/2)/b+_
+-- 16/1989*a^3*(3*A*b-a*B)*x^(3/2)*sqrt(a+b*x^2)/b^2+40/1989*a^2*_
+-- (3*A*b-a*B)*x^(7/2)*sqrt(a+b*x^2)/b-16/663*a^(19/4)*(3*A*b-a*B)*_
+-- elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/((-b)^(11/4)*sqrt(a+b*x^2))+16/663*a^(19/4)*(3*A*b-_
+-- a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/((-b)^(11/4)*sqrt(a+b*x^2))
+--E 147
+
+--S 148 of 1397
+--a0:=integrate(t0,x)
+--E 148
+
+--S 149 of 1397
+--m0:=a0-r0
+--E 149
+
+--S 150 of 1397
+--d0:=D(m0,x)
+--E 150
+
+)clear all
+
+--S 151 of 1397
+t0:=x^(3/2)*(a+b*x^2)^(5/2)*(A+B*x^2)
+--R
+--R
+--R (1)
+--R +--------+
+--R 2 7 2 5 2 3 2 +-+ | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 1397
+--r0:=4/627*a*(19*A*b-5*a*B)*x^(5/2)*(a+b*x^2)^(3/2)/b+2/285*(19*A*b-_
+-- 5*a*B)*x^(5/2)*(a+b*x^2)^(5/2)/b+2/19*B*x^(5/2)*(a+b*x^2)^(7/2)/b+_
+-- 8/1463*a^2*(19*A*b-5*a*B)*x^(5/2)*sqrt(a+b*x^2)/b+16/4389*a^3*_
+-- (19*A*b-5*a*B)*sqrt(x)*sqrt(a+b*x^2)/b^2-16/4389*a^(17/4)*_
+-- (19*A*b-5*a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2))
+--E 152
+
+--S 153 of 1397
+--a0:=integrate(t0,x)
+--E 153
+
+--S 154 of 1397
+--m0:=a0-r0
+--E 154
+
+--S 155 of 1397
+--d0:=D(m0,x)
+--E 155
+
+)clear all
+
+--S 156 of 1397
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)*sqrt(x)
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 +-+ | 2
+--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 1397
+--r0:=20/1989*a*(17*A*b-3*a*B)*x^(3/2)*(a+b*x^2)^(3/2)/b+2/221*_
+-- (17*A*b-3*a*B)*x^(3/2)*(a+b*x^2)^(5/2)/b+2/17*B*x^(3/2)*(a+b*_
+-- x^2)^(7/2)/b+8/663*a^2*(17*A*b-3*a*B)*x^(3/2)*sqrt(a+b*x^2)/b-_
+-- 16/663*a^(15/4)*(17*A*b-3*a*B)*elliptic_e(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*_
+-- x^2))+16/663*a^(15/4)*(17*A*b-3*a*B)*elliptic_f(_
+-- asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+-- ((-b)^(7/4)*sqrt(a+b*x^2))
+--E 157
+
+--S 158 of 1397
+--a0:=integrate(t0,x)
+--E 158
+
+--S 159 of 1397
+--m0:=a0-r0
+--E 159
+
+--S 160 of 1397
+--d0:=D(m0,x)
+--E 160
+
+)clear all
+
+--S 161 of 1397
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/sqrt(x)
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 1397
+--r0:=4/231*a*(15*A*b-a*B)*(a+b*x^2)^(3/2)*sqrt(x)/b+2/165*(15*A*b-_
+-- a*B)*(a+b*x^2)^(5/2)*sqrt(x)/b+2/15*B*(a+b*x^2)^(7/2)*sqrt(x)/b+_
+-- 8/231*a^2*(15*A*b-a*B)*sqrt(x)*sqrt(a+b*x^2)/b-16/231*a^(13/4)*_
+-- (15*A*b-a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2))
+--E 162
+
+--S 163 of 1397
+--a0:=integrate(t0,x)
+--E 163
+
+--S 164 of 1397
+--m0:=a0-r0
+--E 164
+
+--S 165 of 1397
+--d0:=D(m0,x)
+--E 165
+
+)clear all
+
+--S 166 of 1397
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x^(3/2)
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 1397
+--r0:=20/117*(13*A*b+a*B)*x^(3/2)*(a+b*x^2)^(3/2)+2/13*(13*A*b+a*B)*_
+-- x^(3/2)*(a+b*x^2)^(5/2)/a-2*A*(a+b*x^2)^(7/2)/(a*sqrt(x))+_
+-- 8/39*a*(13*A*b+a*B)*x^(3/2)*sqrt(a+b*x^2)+16/39*a^(11/4)*(13*A*_
+-- b+a*B)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))-16/39*a^(11/4)*(13*A*b+_
+-- a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))
+--E 167
+
+--S 168 of 1397
+--a0:=integrate(t0,x)
+--E 168
+
+--S 169 of 1397
+--m0:=a0-r0
+--E 169
+
+--S 170 of 1397
+--d0:=D(m0,x)
+--E 170
+
+)clear all
+
+--S 171 of 1397
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x^(5/2)
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 1397
+--r0:=-2/3*A*(a+b*x^2)^(7/2)/(a*x^(3/2))+20/231*(11*A*b+3*a*B)*_
+-- (a+b*x^2)^(3/2)*sqrt(x)+2/33*(11*A*b+3*a*B)*(a+b*x^2)^(5/2)*_
+-- sqrt(x)/a+40/231*a*(11*A*b+3*a*B)*sqrt(x)*sqrt(a+b*x^2)+_
+-- 80/231*a^(9/4)*(11*A*b+3*a*B)*elliptic_f(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(1/4)*sqrt(a+b*x^2))
+--E 172
+
+--S 173 of 1397
+--a0:=integrate(t0,x)
+--E 173
+
+--S 174 of 1397
+--m0:=a0-r0
+--E 174
+
+--S 175 of 1397
+--d0:=D(m0,x)
+--E 175
+
+)clear all
+
+--S 176 of 1397
+t0:=(a+b*x^2)^(5/2)*(A+B*x^2)/x^(7/2)
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a
+--R (1) ------------------------------------------------------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 1397
+--r0:=4/9*b*(9*A*b+5*a*B)*x^(3/2)*(a+b*x^2)^(3/2)/a-2/5*A*(a+_
+-- b*x^2)^(7/2)/(a*x^(5/2))-2/5*(9*A*b+5*a*B)*(a+b*x^2)^(5/2)/(a*_
+-- sqrt(x))+8/15*b*(9*A*b+5*a*B)*x^(3/2)*sqrt(a+b*x^2)-16/15*_
+-- a^(7/4)*(-b)^(1/4)*(9*A*b+5*a*B)*elliptic_e(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)+16/15*_
+-- a^(7/4)*(-b)^(1/4)*(9*A*b+5*a*B)*elliptic_f(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)
+--E 177
+
+--S 178 of 1397
+--a0:=integrate(t0,x)
+--E 178
+
+--S 179 of 1397
+--m0:=a0-r0
+--E 179
+
+--S 180 of 1397
+--d0:=D(m0,x)
+--E 180
+
+)clear all
+
+--S 181 of 1397
+t0:=x^(7/2)*(A+B*x^2)/sqrt(a+b*x^2)
+--R
+--R
+--R 5 3 +-+
+--R (B x + A x )\|x
+--R (1) -----------------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 1397
+--r0:=2/77*(11*A*b-9*a*B)*x^(5/2)*sqrt(a+b*x^2)/b^2+2/11*B*x^(9/2)*_
+-- sqrt(a+b*x^2)/b-10/231*a*(11*A*b-9*a*B)*sqrt(x)*sqrt(a+b*_
+-- x^2)/b^3-10/231*a^(9/4)*(11*A*b-9*a*B)*elliptic_f(_
+-- asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+-- ((-b)^(13/4)*sqrt(a+b*x^2))
+--E 182
+
+--S 183 of 1397
+--a0:=integrate(t0,x)
+--E 183
+
+--S 184 of 1397
+--m0:=a0-r0
+--E 184
+
+--S 185 of 1397
+--d0:=D(m0,x)
+--E 185
+
+)clear all
+
+--S 186 of 1397
+t0:=x^(5/2)*(A+B*x^2)/sqrt(a+b*x^2)
+--R
+--R
+--R 4 2 +-+
+--R (B x + A x )\|x
+--R (1) -----------------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 1397
+--r0:=2/45*(9*A*b-7*a*B)*x^(3/2)*sqrt(a+b*x^2)/b^2+2/9*B*x^(7/2)*_
+-- sqrt(a+b*x^2)/b-2/15*a^(7/4)*(9*A*b-7*a*B)*elliptic_e(_
+-- asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+-- ((-b)^(11/4)*sqrt(a+b*x^2))+2/15*a^(7/4)*(9*A*b-7*a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/((-b)^(11/4)*sqrt(a+b*x^2))
+--E 187
+
+--S 188 of 1397
+--a0:=integrate(t0,x)
+--E 188
+
+--S 189 of 1397
+--m0:=a0-r0
+--E 189
+
+--S 190 of 1397
+--d0:=D(m0,x)
+--E 190
+
+)clear all
+
+--S 191 of 1397
+t0:=x^(3/2)*(A+B*x^2)/sqrt(a+b*x^2)
+--R
+--R
+--R 3 +-+
+--R (B x + A x)\|x
+--R (1) ----------------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 1397
+--r0:=2/7*B*x^(5/2)*sqrt(a+b*x^2)/b+2/21*(7*A*b-5*a*B)*sqrt(x)*_
+-- sqrt(a+b*x^2)/b^2-2/21*a^(5/4)*(7*A*b-5*a*B)*elliptic_f(_
+-- asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+-- ((-b)^(9/4)*sqrt(a+b*x^2))
+--E 192
+
+--S 193 of 1397
+--a0:=integrate(t0,x)
+--E 193
+
+--S 194 of 1397
+--m0:=a0-r0
+--E 194
+
+--S 195 of 1397
+--d0:=D(m0,x)
+--E 195
+
+)clear all
+
+--S 196 of 1397
+t0:=(A+B*x^2)*sqrt(x)/sqrt(a+b*x^2)
+--R
+--R
+--R 2 +-+
+--R (B x + A)\|x
+--R (1) --------------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 1397
+--r0:=2/5*B*x^(3/2)*sqrt(a+b*x^2)/b-2/5*a^(3/4)*(5*A*b-3*a*B)*_
+-- elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))+2/5*a^(3/4)*_
+-- (5*A*b-3*a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))
+--E 197
+
+--S 198 of 1397
+--a0:=integrate(t0,x)
+--E 198
+
+--S 199 of 1397
+--m0:=a0-r0
+--E 199
+
+--S 200 of 1397
+--d0:=D(m0,x)
+--E 200
+
+)clear all
+
+--S 201 of 1397
+t0:=(A+B*x^2)/(sqrt(x)*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ---------------
+--R +--------+
+--R +-+ | 2
+--R \|x \|b x + a
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 1397
+--r0:=2/3*B*sqrt(x)*sqrt(a+b*x^2)/b-2/3*a^(1/4)*(3*A*b-a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2))
+--E 202
+
+--S 203 of 1397
+--a0:=integrate(t0,x)
+--E 203
+
+--S 204 of 1397
+--m0:=a0-r0
+--E 204
+
+--S 205 of 1397
+--d0:=D(m0,x)
+--E 205
+
+)clear all
+
+--S 206 of 1397
+t0:=(A+B*x^2)/(x^(3/2)*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ----------------
+--R +--------+
+--R +-+ | 2
+--R x\|x \|b x + a
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 1397
+--r0:=-2*A*sqrt(a+b*x^2)/(a*sqrt(x))+2*(A*b+a*B)*_
+-- elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/(a^(1/4)*(-b)^(3/4)*sqrt(a+b*x^2))-_
+-- 2*(A*b+a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/(a^(1/4)*(-b)^(3/4)*sqrt(a+b*x^2))
+--E 207
+
+--S 208 of 1397
+--a0:=integrate(t0,x)
+--E 208
+
+--S 209 of 1397
+--m0:=a0-r0
+--E 209
+
+--S 210 of 1397
+--d0:=D(m0,x)
+--E 210
+
+)clear all
+
+--S 211 of 1397
+t0:=(A+B*x^2)/(x^(5/2)*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------------
+--R +--------+
+--R 2 +-+ | 2
+--R x \|x \|b x + a
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 1397
+--r0:=-2/3*A*sqrt(a+b*x^2)/(a*x^(3/2))-2/3*(A*b-3*a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/(a^(3/4)*(-b)^(1/4)*sqrt(a+b*x^2))
+--E 212
+
+--S 213 of 1397
+--a0:=integrate(t0,x)
+--E 213
+
+--S 214 of 1397
+--m0:=a0-r0
+--E 214
+
+--S 215 of 1397
+--d0:=D(m0,x)
+--E 215
+
+)clear all
+
+--S 216 of 1397
+t0:=(A+B*x^2)/(x^(7/2)*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------------
+--R +--------+
+--R 3 +-+ | 2
+--R x \|x \|b x + a
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 1397
+--r0:=-2/5*A*sqrt(a+b*x^2)/(a*x^(5/2))+2/5*(3*A*b-5*a*B)*_
+-- sqrt(a+b*x^2)/(a^2*sqrt(x))+2/5*(-b)^(1/4)*(3*A*b-5*a*B)*_
+-- elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/(a^(5/4)*sqrt(a+b*x^2))-2/5*(-b)^(1/4)*(3*A*b-_
+-- 5*a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/(a^(5/4)*sqrt(a+b*x^2))
+--E 217
+
+--S 218 of 1397
+--a0:=integrate(t0,x)
+--E 218
+
+--S 219 of 1397
+--m0:=a0-r0
+--E 219
+
+--S 220 of 1397
+--d0:=D(m0,x)
+--E 220
+
+)clear all
+
+--S 221 of 1397
+t0:=x^(7/2)*(A+B*x^2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 5 3 +-+
+--R (B x + A x )\|x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 1397
+--r0:=(A*b-a*B)*x^(9/2)/(a*b*sqrt(a+b*x^2))-1/7*(7*A*b-9*a*B)*_
+-- x^(5/2)*sqrt(a+b*x^2)/(a*b^2)+5/21*(7*A*b-9*a*B)*sqrt(x)*_
+-- sqrt(a+b*x^2)/b^3+5/21*a^(5/4)*(7*A*b-9*a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/((-b)^(13/4)*sqrt(a+b*x^2))
+--E 222
+
+--S 223 of 1397
+--a0:=integrate(t0,x)
+--E 223
+
+--S 224 of 1397
+--m0:=a0-r0
+--E 224
+
+--S 225 of 1397
+--d0:=D(m0,x)
+--E 225
+
+)clear all
+
+--S 226 of 1397
+t0:=x^(5/2)*(A+B*x^2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 4 2 +-+
+--R (B x + A x )\|x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 1397
+--r0:=(A*b-a*B)*x^(7/2)/(a*b*sqrt(a+b*x^2))-1/5*(5*A*b-7*a*B)*_
+-- x^(3/2)*sqrt(a+b*x^2)/(a*b^2)+3/5*a^(3/4)*(5*A*b-7*a*B)*_
+-- elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/((-b)^(11/4)*sqrt(a+b*x^2))-3/5*a^(3/4)*(5*A*b-_
+-- 7*a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/((-b)^(11/4)*sqrt(a+b*x^2))
+--E 227
+
+--S 228 of 1397
+--a0:=integrate(t0,x)
+--E 228
+
+--S 229 of 1397
+--m0:=a0-r0
+--E 229
+
+--S 230 of 1397
+--d0:=D(m0,x)
+--E 230
+
+)clear all
+
+--S 231 of 1397
+t0:=x^(3/2)*(A+B*x^2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 3 +-+
+--R (B x + A x)\|x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 1397
+--r0:=(A*b-a*B)*x^(5/2)/(a*b*sqrt(a+b*x^2))-1/3*(3*A*b-5*a*B)*_
+-- sqrt(x)*sqrt(a+b*x^2)/(a*b^2)+1/3*a^(1/4)*(3*A*b-5*a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2))
+--E 232
+
+--S 233 of 1397
+--a0:=integrate(t0,x)
+--E 233
+
+--S 234 of 1397
+--m0:=a0-r0
+--E 234
+
+--S 235 of 1397
+--d0:=D(m0,x)
+--E 235
+
+)clear all
+
+--S 236 of 1397
+t0:=(A+B*x^2)*sqrt(x)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 2 +-+
+--R (B x + A)\|x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 1397
+--r0:=(A*b-a*B)*x^(3/2)/(a*b*sqrt(a+b*x^2))+(A*b-3*a*B)*_
+-- elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/(a^(1/4)*(-b)^(7/4)*sqrt(a+b*x^2))-(A*b-3*a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/(a^(1/4)*(-b)^(7/4)*sqrt(a+b*x^2))
+--E 237
+
+--S 238 of 1397
+--a0:=integrate(t0,x)
+--E 238
+
+--S 239 of 1397
+--m0:=a0-r0
+--E 239
+
+--S 240 of 1397
+--d0:=D(m0,x)
+--E 240
+
+)clear all
+
+--S 241 of 1397
+t0:=(A+B*x^2)/((a+b*x^2)^(3/2)*sqrt(x))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------------------
+--R +--------+
+--R 2 +-+ | 2
+--R (b x + a)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 1397
+--r0:=(A*b-a*B)*sqrt(x)/(a*b*sqrt(a+b*x^2))-(A*b+a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/(a^(3/4)*(-b)^(5/4)*sqrt(a+b*x^2))
+--E 242
+
+--S 243 of 1397
+--a0:=integrate(t0,x)
+--E 243
+
+--S 244 of 1397
+--m0:=a0-r0
+--E 244
+
+--S 245 of 1397
+--d0:=D(m0,x)
+--E 245
+
+)clear all
+
+--S 246 of 1397
+t0:=(A+B*x^2)/(x^(3/2)*(a+b*x^2)^(3/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ---------------------------
+--R +--------+
+--R 3 +-+ | 2
+--R (b x + a x)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 1397
+--r0:=-(3*A*b-a*B)*x^(3/2)/(a^2*sqrt(a+b*x^2))-2*A/(a*sqrt(x)*_
+-- sqrt(a+b*x^2))+(3*A*b-a*B)*elliptic_e(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(5/4)*(-b)^(3/4)*_
+-- sqrt(a+b*x^2))-(3*A*b-a*B)*elliptic_f(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(5/4)*(-b)^(3/4)*_
+-- sqrt(a+b*x^2))
+--E 247
+
+--S 248 of 1397
+--a0:=integrate(t0,x)
+--E 248
+
+--S 249 of 1397
+--m0:=a0-r0
+--E 249
+
+--S 250 of 1397
+--d0:=D(m0,x)
+--E 250
+
+)clear all
+
+--S 251 of 1397
+t0:=(A+B*x^2)/(x^(5/2)*(a+b*x^2)^(3/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ----------------------------
+--R +--------+
+--R 4 2 +-+ | 2
+--R (b x + a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 1397
+--r0:=-2/3*A/(a*x^(3/2)*sqrt(a+b*x^2))-1/3*(5*A*b-3*a*B)*sqrt(x)/_
+-- (a^2*sqrt(a+b*x^2))-1/3*(5*A*b-3*a*B)*elliptic_f(_
+-- asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+-- (a^(7/4)*(-b)^(1/4)*sqrt(a+b*x^2))
+--E 252
+
+--S 253 of 1397
+--a0:=integrate(t0,x)
+--E 253
+
+--S 254 of 1397
+--m0:=a0-r0
+--E 254
+
+--S 255 of 1397
+--d0:=D(m0,x)
+--E 255
+
+)clear all
+
+--S 256 of 1397
+t0:=(A+B*x^2)/(x^(7/2)*(a+b*x^2)^(3/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ----------------------------
+--R +--------+
+--R 5 3 +-+ | 2
+--R (b x + a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 1397
+--r0:=-2/5*A/(a*x^(5/2)*sqrt(a+b*x^2))+1/5*(-7*A*b+5*a*B)/(a^2*_
+-- sqrt(x)*sqrt(a+b*x^2))+3/5*(7*A*b-5*a*B)*sqrt(a+b*x^2)/(a^3*_
+-- sqrt(x))+3/5*(-b)^(1/4)*(7*A*b-5*a*B)*elliptic_e(_
+-- asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+-- (a^(9/4)*sqrt(a+b*x^2))-3/5*(-b)^(1/4)*(7*A*b-5*a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/(a^(9/4)*sqrt(a+b*x^2))
+--E 257
+
+--S 258 of 1397
+--a0:=integrate(t0,x)
+--E 258
+
+--S 259 of 1397
+--m0:=a0-r0
+--E 259
+
+--S 260 of 1397
+--d0:=D(m0,x)
+--E 260
+
+)clear all
+
+--S 261 of 1397
+t0:=x^(7/2)*(A+B*x^2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 5 3 +-+
+--R (B x + A x )\|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 1397
+--r0:=1/3*(A*b-a*B)*x^(9/2)/(a*b*(a+b*x^2)^(3/2))+1/2*(A*b-3*a*B)*_
+-- x^(5/2)/(a*b^2*sqrt(a+b*x^2))-5/6*(A*b-3*a*B)*sqrt(x)*sqrt(a+_
+-- b*x^2)/(a*b^3)-5/6*a^(1/4)*(A*b-3*a*B)*elliptic_f(_
+-- asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+-- ((-b)^(13/4)*sqrt(a+b*x^2))
+--E 262
+
+--S 263 of 1397
+--a0:=integrate(t0,x)
+--E 263
+
+--S 264 of 1397
+--m0:=a0-r0
+--E 264
+
+--S 265 of 1397
+--d0:=D(m0,x)
+--E 265
+
+)clear all
+
+--S 266 of 1397
+t0:=x^(5/2)*(A+B*x^2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 4 2 +-+
+--R (B x + A x )\|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 1397
+--r0:=1/3*(A*b-a*B)*x^(7/2)/(a*b*(a+b*x^2)^(3/2))+1/6*(A*b-7*a*B)*_
+-- x^(3/2)/(a*b^2*sqrt(a+b*x^2))-1/2*(A*b-7*a*B)*_
+-- elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/(a^(1/4)*(-b)^(11/4)*sqrt(a+b*x^2))+_
+-- 1/2*(A*b-7*a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/(a^(1/4)*(-b)^(11/4)*sqrt(a+b*x^2))
+--E 267
+
+--S 268 of 1397
+--a0:=integrate(t0,x)
+--E 268
+
+--S 269 of 1397
+--m0:=a0-r0
+--E 269
+
+--S 270 of 1397
+--d0:=D(m0,x)
+--E 270
+
+)clear all
+
+--S 271 of 1397
+t0:=x^(3/2)*(A+B*x^2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 3 +-+
+--R (B x + A x)\|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 1397
+--r0:=1/3*(A*b-a*B)*x^(5/2)/(a*b*(a+b*x^2)^(3/2))-1/6*(A*b+5*a*B)*_
+-- sqrt(x)/(a*b^2*sqrt(a+b*x^2))+1/6*(A*b+5*a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/(a^(3/4)*(-b)^(9/4)*sqrt(a+b*x^2))
+--E 272
+
+--S 273 of 1397
+--a0:=integrate(t0,x)
+--E 273
+
+--S 274 of 1397
+--m0:=a0-r0
+--E 274
+
+--S 275 of 1397
+--d0:=D(m0,x)
+--E 275
+
+)clear all
+
+--S 276 of 1397
+t0:=(A+B*x^2)*sqrt(x)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 2 +-+
+--R (B x + A)\|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 1397
+--r0:=1/3*(A*b-a*B)*x^(3/2)/(a*b*(a+b*x^2)^(3/2))+1/2*(A*b+a*B)*_
+-- x^(3/2)/(a^2*b*sqrt(a+b*x^2))+1/2*(A*b+a*B)*_
+-- elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/(a^(5/4)*(-b)^(7/4)*sqrt(a+b*x^2))-_
+-- 1/2*(A*b+a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/(a^(5/4)*(-b)^(7/4)*sqrt(a+b*x^2))
+--E 277
+
+--S 278 of 1397
+--a0:=integrate(t0,x)
+--E 278
+
+--S 279 of 1397
+--m0:=a0-r0
+--E 279
+
+--S 280 of 1397
+--d0:=D(m0,x)
+--E 280
+
+)clear all
+
+--S 281 of 1397
+t0:=(A+B*x^2)/((a+b*x^2)^(5/2)*sqrt(x))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ------------------------------------
+--R +--------+
+--R 2 4 2 2 +-+ | 2
+--R (b x + 2a b x + a )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 1397
+--r0:=1/3*(A*b-a*B)*sqrt(x)/(a*b*(a+b*x^2)^(3/2))+1/6*(5*A*b+a*B)*_
+-- sqrt(x)/(a^2*b*sqrt(a+b*x^2))-1/6*(5*A*b+a*B)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/(a^(7/4)*(-b)^(5/4)*sqrt(a+b*x^2))
+--E 282
+
+--S 283 of 1397
+--a0:=integrate(t0,x)
+--E 283
+
+--S 284 of 1397
+--m0:=a0-r0
+--E 284
+
+--S 285 of 1397
+--d0:=D(m0,x)
+--E 285
+
+)clear all
+
+--S 286 of 1397
+t0:=(A+B*x^2)/(x^(3/2)*(a+b*x^2)^(5/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -------------------------------------
+--R +--------+
+--R 2 5 3 2 +-+ | 2
+--R (b x + 2a b x + a x)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 1397
+--r0:=-1/3*(7*A*b-a*B)*x^(3/2)/(a^2*(a+b*x^2)^(3/2))-_
+-- 2*A/(a*(a+b*x^2)^(3/2)*sqrt(x))-1/2*(7*A*b-a*B)*x^(3/2)/_
+-- (a^3*sqrt(a+b*x^2))+1/2*(7*A*b-a*B)*elliptic_e(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(9/4)*(-b)^(3/4)*_
+-- sqrt(a+b*x^2))-1/2*(7*A*b-a*B)*elliptic_f(asin((-b)^(1/4)*_
+-- sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(9/4)*(-b)^(3/4)*_
+-- sqrt(a+b*x^2))
+--E 287
+
+--S 288 of 1397
+--a0:=integrate(t0,x)
+--E 288
+
+--S 289 of 1397
+--m0:=a0-r0
+--E 289
+
+--S 290 of 1397
+--d0:=D(m0,x)
+--E 290
+
+)clear all
+
+--S 291 of 1397
+t0:=(A+B*x^2)/(x^(5/2)*(a+b*x^2)^(5/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) --------------------------------------
+--R +--------+
+--R 2 6 4 2 2 +-+ | 2
+--R (b x + 2a b x + a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 1397
+--r0:=-2/3*A/(a*x^(3/2)*(a+b*x^2)^(3/2))-1/3*(3*A*b-a*B)*sqrt(x)/_
+-- (a^2*(a+b*x^2)^(3/2))-5/6*(3*A*b-a*B)*sqrt(x)/(a^3*sqrt(a+_
+-- b*x^2))-5/6*(3*A*b-a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/_
+-- a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(11/4)*(-b)^(1/4)*sqrt(a+b*x^2))
+--E 292
+
+--S 293 of 1397
+--a0:=integrate(t0,x)
+--E 293
+
+--S 294 of 1397
+--m0:=a0-r0
+--E 294
+
+--S 295 of 1397
+--d0:=D(m0,x)
+--E 295
+
+)clear all
+
+--S 296 of 1397
+t0:=(A+B*x^2)/(x^(7/2)*(a+b*x^2)^(5/2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) --------------------------------------
+--R +--------+
+--R 2 7 5 2 3 +-+ | 2
+--R (b x + 2a b x + a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 1397
+--r0:=-2/5*A/(a*x^(5/2)*(a+b*x^2)^(3/2))+1/15*(-11*A*b+5*a*B)/_
+-- (a^2*(a+b*x^2)^(3/2)*sqrt(x))-7/30*(11*A*b-5*a*B)/(a^3*_
+-- sqrt(x)*sqrt(a+b*x^2))+7/10*(11*A*b-5*a*B)*sqrt(a+b*x^2)/_
+-- (a^4*sqrt(x))+7/10*(-b)^(1/4)*(11*A*b-5*a*B)*_
+-- elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+-- b*x^2)/a)/(a^(13/4)*sqrt(a+b*x^2))-7/10*(-b)^(1/4)*(11*A*b-_
+-- 5*a*B)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+-- sqrt((a+b*x^2)/a)/(a^(13/4)*sqrt(a+b*x^2))
+--E 297
+
+--S 298 of 1397
+--a0:=integrate(t0,x)
+--E 298
+
+--S 299 of 1397
+--m0:=a0-r0
+--E 299
+
+--S 300 of 1397
+--d0:=D(m0,x)
+--E 300
+
+)clear all
+
+--S 301 of 1397
+t0:=x^3*(a*c+b*c*x^2)/(a+b*x^2)
+--R
+--R
+--R 3
+--R (1) c x
+--R Type: Fraction(Polynomial(Integer))
+--E 301
+
+--S 302 of 1397
+r0:=1/4*c*x^4
+--R
+--R
+--R 1 4
+--R (2) - c x
+--R 4
+--R Type: Polynomial(Fraction(Integer))
+--E 302
+
+--S 303 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R c x
+--R (3) ----
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 303
+
+--S 304 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 305
+
+)clear all
+
+--S 306 of 1397
+t0:=x^2*(a*c+b*c*x^2)/(a+b*x^2)
+--R
+--R
+--R 2
+--R (1) c x
+--R Type: Fraction(Polynomial(Integer))
+--E 306
+
+--S 307 of 1397
+r0:=1/3*c*x^3
+--R
+--R
+--R 1 3
+--R (2) - c x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 307
+
+--S 308 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R c x
+--R (3) ----
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 308
+
+--S 309 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 310
+
+)clear all
+
+--S 311 of 1397
+t0:=x*(a*c+b*c*x^2)/(a+b*x^2)
+--R
+--R
+--R (1) c x
+--R Type: Fraction(Polynomial(Integer))
+--E 311
+
+--S 312 of 1397
+r0:=1/2*c*x^2
+--R
+--R
+--R 1 2
+--R (2) - c x
+--R 2
+--R Type: Polynomial(Fraction(Integer))
+--E 312
+
+--S 313 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R c x
+--R (3) ----
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 313
+
+--S 314 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 1397
+t0:=(a*c+b*c*x^2)/(a+b*x^2)
+--R
+--R
+--R (1) c
+--R Type: Fraction(Polynomial(Integer))
+--E 316
+
+--S 317 of 1397
+r0:=c*x
+--R
+--R
+--R (2) c x
+--R Type: Polynomial(Integer)
+--E 317
+
+--S 318 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3) c x
+--R Type: Union(Expression(Integer),...)
+--E 318
+
+--S 319 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 1397
+t0:=(a*c+b*c*x^2)/(x*(a+b*x^2))
+--R
+--R
+--R c
+--R (1) -
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 321
+
+--S 322 of 1397
+r0:=c*log(x)
+--R
+--R
+--R (2) c log(x)
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3) c log(x)
+--R Type: Union(Expression(Integer),...)
+--E 323
+
+--S 324 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 325
+
+)clear all
+
+--S 326 of 1397
+t0:=(a*c+b*c*x^2)/(x^2*(a+b*x^2))
+--R
+--R
+--R c
+--R (1) --
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 326
+
+--S 327 of 1397
+r0:=-c/x
+--R
+--R
+--R c
+--R (2) - -
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 327
+
+--S 328 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R c
+--R (3) - -
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 328
+
+--S 329 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 1397
+t0:=(a*c+b*c*x^2)/(x^3*(a+b*x^2))
+--R
+--R
+--R c
+--R (1) --
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 331
+
+--S 332 of 1397
+r0:=-1/2*c/x^2
+--R
+--R
+--R 1
+--R - c
+--R 2
+--R (2) - ---
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 332
+
+--S 333 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R c
+--R (3) - ---
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 333
+
+--S 334 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 1397
+t0:=x^3*(a*c+b*c*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 3
+--R c x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 336
+
+--S 337 of 1397
+r0:=1/2*c*x^2/b-1/2*a*c*log(a+b*x^2)/b^2
+--R
+--R
+--R 2 2
+--R - a c log(b x + a) + b c x
+--R (2) ----------------------------
+--R 2
+--R 2b
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R - a c log(b x + a) + b c x
+--R (3) ----------------------------
+--R 2
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 338
+
+--S 339 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 1397
+t0:=x^2*(a*c+b*c*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 2
+--R c x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 341
+
+--S 342 of 1397
+r0:=c*x/b-c*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2)
+--R
+--R
+--R +-+
+--R +-+ x\|b +-+
+--R - c\|a atan(-----) + c x\|b
+--R +-+
+--R \|a
+--R (2) ----------------------------
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R +---+
+--R | a 2 +-+
+--R +---+ - 2b x |- - + b x - a |a
+--R | a \| b +-+ |-
+--R c |- - log(-----------------------) + 2c x |a \|b
+--R \| b 2 c |- atan(----) + c x
+--R b x + a \|b x
+--R (3) [------------------------------------------,---------------------]
+--R 2b b
+--R Type: Union(List(Expression(Integer)),...)
+--E 343
+
+--S 344 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a +-+
+--R | a +-+ \| b +-+ x\|b
+--R c |- - \|b log(-----------------------) + 2c\|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------
+--R +-+
+--R 2b\|b
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+--S 346 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R c\|a atan(-----) + c |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) --------------------------------------
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 347
+
+)clear all
+
+--S 348 of 1397
+t0:=x*(a*c+b*c*x^2)/(a+b*x^2)^2
+--R
+--R
+--R c x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 348
+
+--S 349 of 1397
+r0:=1/2*c*log(a+b*x^2)/b
+--R
+--R
+--R 2
+--R c log(b x + a)
+--R (2) ---------------
+--R 2b
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R c log(b x + a)
+--R (3) ---------------
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 350
+
+--S 351 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 352
+
+)clear all
+
+--S 353 of 1397
+t0:=(a*c+b*c*x^2)/(a+b*x^2)^2
+--R
+--R
+--R c
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 353
+
+--S 354 of 1397
+r0:=c*atan(x*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b))
+--R
+--R
+--R +-+
+--R x\|b
+--R c atan(-----)
+--R +-+
+--R \|a
+--R (2) -------------
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x +---+
+--R c log(---------------------------) x\|a b
+--R 2 c atan(-------)
+--R b x + a a
+--R (3) [----------------------------------,---------------]
+--R +-----+ +---+
+--R 2\|- a b \|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 355
+
+--S 356 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R c\|a \|b log(---------------------------) - 2c\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 2\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R c\|a \|b atan(-------) - c\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------
+--R +-+ +-+ +---+
+--R \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 358
+
+--S 359 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 359
+
+)clear all
+
+--S 360 of 1397
+t0:=(a*c+b*c*x^2)/(x*(a+b*x^2)^2)
+--R
+--R
+--R c
+--R (1) ----------
+--R 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 360
+
+--S 361 of 1397
+r0:=c*log(x)/a-1/2*c*log(a+b*x^2)/a
+--R
+--R
+--R 2
+--R - c log(b x + a) + 2c log(x)
+--R (2) -----------------------------
+--R 2a
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - c log(b x + a) + 2c log(x)
+--R (3) -----------------------------
+--R 2a
+--R Type: Union(Expression(Integer),...)
+--E 362
+
+--S 363 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 363
+
+--S 364 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 364
+
+)clear all
+
+--S 365 of 1397
+t0:=(a*c+b*c*x^2)/(x^2*(a+b*x^2)^2)
+--R
+--R
+--R c
+--R (1) -----------
+--R 4 2
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 365
+
+--S 366 of 1397
+r0:=-c/(a*x)-c*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2)
+--R
+--R
+--R +-+
+--R +-+ x\|b +-+
+--R - c x\|b atan(-----) - c\|a
+--R +-+
+--R \|a
+--R (2) ----------------------------
+--R +-+
+--R a x\|a
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R +---+
+--R | b 2 +-+
+--R +---+ - 2a x |- - + b x - a |b
+--R | b \| a +-+ a |-
+--R c x |- - log(-----------------------) - 2c |b \|a
+--R \| a 2 c x |- atan(-----) - c
+--R b x + a \|a b x
+--R (3) [------------------------------------------,----------------------]
+--R 2a x a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 367
+
+--S 368 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R | b +-+ \| a +-+ x\|b
+--R c |- - \|a log(-----------------------) + 2c\|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------
+--R +-+
+--R 2a\|a
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R c\|b atan(-----) + c\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) ---------------------------------------
+--R +-+
+--R a\|a
+--R Type: Expression(Integer)
+--E 370
+
+--S 371 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 371
+
+)clear all
+
+--S 372 of 1397
+t0:=(a*c+b*c*x^2)/(x^3*(a+b*x^2)^2)
+--R
+--R
+--R c
+--R (1) -----------
+--R 5 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 372
+
+--S 373 of 1397
+r0:=-1/2*c/(a*x^2)-b*c*log(x)/a^2+1/2*b*c*log(a+b*x^2)/a^2
+--R
+--R
+--R 2 2 2
+--R b c x log(b x + a) - 2b c x log(x) - a c
+--R (2) -----------------------------------------
+--R 2 2
+--R 2a x
+--R Type: Expression(Integer)
+--E 373
+
+--S 374 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R b c x log(b x + a) - 2b c x log(x) - a c
+--R (3) -----------------------------------------
+--R 2 2
+--R 2a x
+--R Type: Union(Expression(Integer),...)
+--E 374
+
+--S 375 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 375
+
+--S 376 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 376
+
+)clear all
+
+--S 377 of 1397
+t0:=x^3*(a*c+b*c*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 3
+--R c x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 377
+
+--S 378 of 1397
+r0:=1/2*a*c/(b^2*(a+b*x^2))+1/2*c*log(a+b*x^2)/b^2
+--R
+--R
+--R 2 2
+--R (b c x + a c)log(b x + a) + a c
+--R (2) ---------------------------------
+--R 3 2 2
+--R 2b x + 2a b
+--R Type: Expression(Integer)
+--E 378
+
+--S 379 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R (b c x + a c)log(b x + a) + a c
+--R (3) ---------------------------------
+--R 3 2 2
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 379
+
+--S 380 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 380
+
+--S 381 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 381
+
+)clear all
+
+--S 382 of 1397
+t0:=x^2*(a*c+b*c*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 2
+--R c x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 382
+
+--S 383 of 1397
+r0:=-1/2*c*x/(b*(a+b*x^2))+1/2*c*atan(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))
+--R
+--R
+--R +-+
+--R 2 x\|b +-+ +-+
+--R (b c x + a c)atan(-----) - c x\|a \|b
+--R +-+
+--R \|a
+--R (2) ---------------------------------------
+--R 2 2 +-+ +-+
+--R (2b x + 2a b)\|a \|b
+--R Type: Expression(Integer)
+--E 383
+
+--S 384 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R 2 (b x - a)\|- a b + 2a b x +-----+
+--R (b c x + a c)log(---------------------------) - 2c x\|- a b
+--R 2
+--R b x + a
+--R [-------------------------------------------------------------,
+--R 2 2 +-----+
+--R (4b x + 4a b)\|- a b
+--R +---+
+--R 2 x\|a b +---+
+--R (b c x + a c)atan(-------) - c x\|a b
+--R a
+--R ---------------------------------------]
+--R 2 2 +---+
+--R (2b x + 2a b)\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 384
+
+--S 385 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R c\|a \|b log(---------------------------) - 2c\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 4b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 385
+
+--S 386 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R c\|a \|b atan(-------) - c\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------
+--R +-+ +-+ +---+
+--R 2b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 388
+
+)clear all
+
+--S 389 of 1397
+t0:=x*(a*c+b*c*x^2)/(a+b*x^2)^3
+--R
+--R
+--R c x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 389
+
+--S 390 of 1397
+r0:=-1/2*c/(b*(a+b*x^2))
+--R
+--R
+--R 1
+--R - c
+--R 2
+--R (2) - ----------
+--R 2 2
+--R b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 390
+
+--S 391 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R c
+--R (3) - ------------
+--R 2 2
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 391
+
+--S 392 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 393
+
+)clear all
+
+--S 394 of 1397
+t0:=(a*c+b*c*x^2)/(a+b*x^2)^3
+--R
+--R
+--R c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 394
+
+--S 395 of 1397
+r0:=1/2*c*x/(a*(a+b*x^2))+1/2*c*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b))
+--R
+--R
+--R +-+
+--R 2 x\|b +-+ +-+
+--R (b c x + a c)atan(-----) + c x\|a \|b
+--R +-+
+--R \|a
+--R (2) ---------------------------------------
+--R 2 2 +-+ +-+
+--R (2a b x + 2a )\|a \|b
+--R Type: Expression(Integer)
+--E 395
+
+--S 396 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R 2 (b x - a)\|- a b + 2a b x +-----+
+--R (b c x + a c)log(---------------------------) + 2c x\|- a b
+--R 2
+--R b x + a
+--R [-------------------------------------------------------------,
+--R 2 2 +-----+
+--R (4a b x + 4a )\|- a b
+--R +---+
+--R 2 x\|a b +---+
+--R (b c x + a c)atan(-------) + c x\|a b
+--R a
+--R ---------------------------------------]
+--R 2 2 +---+
+--R (2a b x + 2a )\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 396
+
+--S 397 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R c\|a \|b log(---------------------------) - 2c\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 4a\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 398
+
+--S 399 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R c\|a \|b atan(-------) - c\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------
+--R +-+ +-+ +---+
+--R 2a\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 1397
+t0:=(a*c+b*c*x^2)/(x*(a+b*x^2)^3)
+--R
+--R
+--R c
+--R (1) --------------------
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 401
+
+--S 402 of 1397
+r0:=1/2*c/(a*(a+b*x^2))+c*log(x)/a^2-1/2*c*log(a+b*x^2)/a^2
+--R
+--R
+--R 2 2 2
+--R (- b c x - a c)log(b x + a) + (2b c x + 2a c)log(x) + a c
+--R (2) ------------------------------------------------------------
+--R 2 2 3
+--R 2a b x + 2a
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R (- b c x - a c)log(b x + a) + (2b c x + 2a c)log(x) + a c
+--R (3) ------------------------------------------------------------
+--R 2 2 3
+--R 2a b x + 2a
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 1397
+t0:=(a*c+b*c*x^2)/(x^2*(a+b*x^2)^3)
+--R
+--R
+--R c
+--R (1) ---------------------
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 406
+
+--S 407 of 1397
+r0:=-3/2*c/(a^2*x)+1/2*c/(a*x*(a+b*x^2))-3/2*c*atan(x*_
+ sqrt(b)/sqrt(a))*sqrt(b)/a^(5/2)
+--R
+--R
+--R +-+
+--R 3 +-+ x\|b 2 +-+
+--R (- 3b c x - 3a c x)\|b atan(-----) + (- 3b c x - 2a c)\|a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------------------------
+--R 2 3 3 +-+
+--R (2a b x + 2a x)\|a
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 3 | b \| a 2
+--R (3b c x + 3a c x) |- - log(-----------------------) - 6b c x - 4a c
+--R \| a 2
+--R b x + a
+--R [---------------------------------------------------------------------,
+--R 2 3 3
+--R 4a b x + 4a x
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 |b \|a 2
+--R (3b c x + 3a c x) |- atan(-----) - 3b c x - 2a c
+--R \|a b x
+--R --------------------------------------------------]
+--R 2 3 3
+--R 2a b x + 2a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 408
+
+--S 409 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R | b +-+ \| a +-+ x\|b
+--R 3c |- - \|a log(-----------------------) + 6c\|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) ------------------------------------------------------------
+--R 2 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 410
+
+--S 411 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R 3c\|b atan(-----) + 3c\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -----------------------------------------
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 412
+
+)clear all
+
+--S 413 of 1397
+t0:=(a*c+b*c*x^2)/(x^3*(a+b*x^2)^3)
+--R
+--R
+--R c
+--R (1) ---------------------
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 413
+
+--S 414 of 1397
+r0:=-c/(a^2*x^2)+1/2*c/(a*x^2*(a+b*x^2))-2*b*c*log(x)/a^3+b*c*log(a+b*x^2)/a^3
+--R
+--R
+--R (2)
+--R 2 4 2 2 2 4 2
+--R (2b c x + 2a b c x )log(b x + a) + (- 4b c x - 4a b c x )log(x)
+--R +
+--R 2 2
+--R - 2a b c x - a c
+--R /
+--R 3 4 4 2
+--R 2a b x + 2a x
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 2 4 2
+--R (2b c x + 2a b c x )log(b x + a) + (- 4b c x - 4a b c x )log(x)
+--R +
+--R 2 2
+--R - 2a b c x - a c
+--R /
+--R 3 4 4 2
+--R 2a b x + 2a x
+--R Type: Union(Expression(Integer),...)
+--E 415
+
+--S 416 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 417
+
+)clear all
+
+--S 418 of 1397
+t0:=x^m*(a+b*x^2)^2*(c+d*x^2)
+--R
+--R
+--R 2 6 2 4 2 2 2 m
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)x
+--R Type: Expression(Integer)
+--E 418
+
+--S 419 of 1397
+r0:=a^2*c*x^(1+m)/(1+m)+a*(2*b*c+a*d)*x^(3+m)/(3+m)+b*(b*c+2*a*d)*_
+ x^(5+m)/(5+m)+b^2*d*x^(7+m)/(7+m)
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 m + 7
+--R (b d m + 9b d m + 23b d m + 15b d)x
+--R +
+--R 2 3 2 2 2
+--R (2a b d + b c)m + (22a b d + 11b c)m + (62a b d + 31b c)m + 42a b d
+--R +
+--R 2
+--R 21b c
+--R *
+--R m + 5
+--R x
+--R +
+--R 2 3 2 2 2 2
+--R (a d + 2a b c)m + (13a d + 26a b c)m + (47a d + 94a b c)m + 35a d
+--R +
+--R 70a b c
+--R *
+--R m + 3
+--R x
+--R +
+--R 2 3 2 2 2 2 m + 1
+--R (a c m + 15a c m + 71a c m + 105a c)x
+--R /
+--R 4 3 2
+--R m + 16m + 86m + 176m + 105
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 2 7
+--R (b d m + 9b d m + 23b d m + 15b d)x
+--R +
+--R 2 3 2 2 2
+--R (2a b d + b c)m + (22a b d + 11b c)m + (62a b d + 31b c)m
+--R +
+--R 2
+--R 42a b d + 21b c
+--R *
+--R 5
+--R x
+--R +
+--R 2 3 2 2 2 2
+--R (a d + 2a b c)m + (13a d + 26a b c)m + (47a d + 94a b c)m + 35a d
+--R +
+--R 70a b c
+--R *
+--R 3
+--R x
+--R +
+--R 2 3 2 2 2 2
+--R (a c m + 15a c m + 71a c m + 105a c)x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 4 3 2
+--R m + 16m + 86m + 176m + 105
+--R Type: Union(Expression(Integer),...)
+--E 420
+
+--S 421 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 2 2 2 2 7
+--R (b d m + 9b d m + 23b d m + 15b d)x
+--R +
+--R 2 3 2 2 2
+--R (2a b d + b c)m + (22a b d + 11b c)m + (62a b d + 31b c)m
+--R +
+--R 2
+--R 42a b d + 21b c
+--R *
+--R 5
+--R x
+--R +
+--R 2 3 2 2 2
+--R (a d + 2a b c)m + (13a d + 26a b c)m + (47a d + 94a b c)m
+--R +
+--R 2
+--R 35a d + 70a b c
+--R *
+--R 3
+--R x
+--R +
+--R 2 3 2 2 2 2
+--R (a c m + 15a c m + 71a c m + 105a c)x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 2 3 2 2 2 2 m + 7
+--R (- b d m - 9b d m - 23b d m - 15b d)x
+--R +
+--R 2 3 2 2 2
+--R (- 2a b d - b c)m + (- 22a b d - 11b c)m + (- 62a b d - 31b c)m
+--R +
+--R 2
+--R - 42a b d - 21b c
+--R *
+--R m + 5
+--R x
+--R +
+--R 2 3 2 2 2
+--R (- a d - 2a b c)m + (- 13a d - 26a b c)m + (- 47a d - 94a b c)m
+--R +
+--R 2
+--R - 35a d - 70a b c
+--R *
+--R m + 3
+--R x
+--R +
+--R 2 3 2 2 2 2 m + 1
+--R (- a c m - 15a c m - 71a c m - 105a c)x
+--R /
+--R 4 3 2
+--R m + 16m + 86m + 176m + 105
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 422
+
+)clear all
+
+--S 423 of 1397
+t0:=x^4*(a+b*x^2)^2*(c+d*x^2)
+--R
+--R
+--R 2 10 2 8 2 6 2 4
+--R (1) b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x
+--R Type: Polynomial(Integer)
+--E 423
+
+--S 424 of 1397
+r0:=1/5*a^2*c*x^5+1/7*a*(2*b*c+a*d)*x^7+1/9*b*(b*c+2*a*d)*x^9+1/11*b^2*d*x^11
+--R
+--R
+--R 1 2 11 2 1 2 9 1 2 2 7 1 2 5
+--R (2) -- b d x + (- a b d + - b c)x + (- a d + - a b c)x + - a c x
+--R 11 9 9 7 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 424
+
+--S 425 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 11 2 1 2 9 1 2 2 7 1 2 5
+--R (3) -- b d x + (- a b d + - b c)x + (- a d + - a b c)x + - a c x
+--R 11 9 9 7 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 425
+
+--S 426 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 426
+
+--S 427 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 427
+
+)clear all
+
+--S 428 of 1397
+t0:=x^3*(a+b*x^2)^2*(c+d*x^2)
+--R
+--R
+--R 2 9 2 7 2 5 2 3
+--R (1) b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x
+--R Type: Polynomial(Integer)
+--E 428
+
+--S 429 of 1397
+r0:=1/4*a^2*c*x^4+1/6*a*(2*b*c+a*d)*x^6+1/8*b*(b*c+2*a*d)*x^8+1/10*b^2*d*x^10
+--R
+--R
+--R 1 2 10 1 1 2 8 1 2 1 6 1 2 4
+--R (2) -- b d x + (- a b d + - b c)x + (- a d + - a b c)x + - a c x
+--R 10 4 8 6 3 4
+--R Type: Polynomial(Fraction(Integer))
+--E 429
+
+--S 430 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 10 1 1 2 8 1 2 1 6 1 2 4
+--R (3) -- b d x + (- a b d + - b c)x + (- a d + - a b c)x + - a c x
+--R 10 4 8 6 3 4
+--R Type: Polynomial(Fraction(Integer))
+--E 430
+
+--S 431 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 431
+
+--S 432 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 432
+
+)clear all
+
+--S 433 of 1397
+t0:=x^2*(a+b*x^2)^2*(c+d*x^2)
+--R
+--R
+--R 2 8 2 6 2 4 2 2
+--R (1) b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x
+--R Type: Polynomial(Integer)
+--E 433
+
+--S 434 of 1397
+r0:=1/3*a^2*c*x^3+1/5*a*(2*b*c+a*d)*x^5+1/7*b*(b*c+2*a*d)*x^7+1/9*b^2*d*x^9
+--R
+--R
+--R 1 2 9 2 1 2 7 1 2 2 5 1 2 3
+--R (2) - b d x + (- a b d + - b c)x + (- a d + - a b c)x + - a c x
+--R 9 7 7 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 434
+
+--S 435 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 9 2 1 2 7 1 2 2 5 1 2 3
+--R (3) - b d x + (- a b d + - b c)x + (- a d + - a b c)x + - a c x
+--R 9 7 7 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 435
+
+--S 436 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 436
+
+--S 437 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 437
+
+)clear all
+
+--S 438 of 1397
+t0:=x*(a+b*x^2)^2*(c+d*x^2)
+--R
+--R
+--R 2 7 2 5 2 3 2
+--R (1) b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x
+--R Type: Polynomial(Integer)
+--E 438
+
+--S 439 of 1397
+r0:=1/6*(b*c-a*d)*(a+b*x^2)^3/b^2+1/8*d*(a+b*x^2)^4/b^2
+--R
+--R
+--R (2)
+--R 1 4 8 1 3 1 4 6 1 2 2 1 3 4 1 2 2 2
+--R - b d x + (- a b d + - b c)x + (- a b d + - a b c)x + - a b c x
+--R 8 3 6 4 2 2
+--R +
+--R 1 4 1 3
+--R - -- a d + - a b c
+--R 24 6
+--R /
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 439
+
+--S 440 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 8 1 1 2 6 1 2 1 4 1 2 2
+--R (3) - b d x + (- a b d + - b c)x + (- a d + - a b c)x + - a c x
+--R 8 3 6 4 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 440
+
+--S 441 of 1397
+m0:=a0-r0
+--R
+--R
+--R 1 4 1 3
+--R -- a d - - a b c
+--R 24 6
+--R (4) ----------------
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 441
+
+--S 442 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 442
+
+)clear all
+
+--S 443 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R (1) b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Polynomial(Integer)
+--E 443
+
+--S 444 of 1397
+r0:=a^2*c*x+1/3*a*(2*b*c+a*d)*x^3+1/5*b*(b*c+2*a*d)*x^5+1/7*b^2*d*x^7
+--R
+--R
+--R 1 2 7 2 1 2 5 1 2 2 3 2
+--R (2) - b d x + (- a b d + - b c)x + (- a d + - a b c)x + a c x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 444
+
+--S 445 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 7 2 1 2 5 1 2 2 3 2
+--R (3) - b d x + (- a b d + - b c)x + (- a d + - a b c)x + a c x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 445
+
+--S 446 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 446
+
+--S 447 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 447
+
+)clear all
+
+--S 448 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)/x
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R (1) --------------------------------------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 448
+
+--S 449 of 1397
+r0:=a*b*c*x^2+1/4*b^2*c*x^4+1/6*d*(a+b*x^2)^3/b+a^2*c*log(x)
+--R
+--R
+--R (2)
+--R 2 3 6 2 3 4 2 2 2 3
+--R 12a b c log(x) + 2b d x + (6a b d + 3b c)x + (6a b d + 12a b c)x + 2a d
+--R --------------------------------------------------------------------------
+--R 12b
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 6 2 4 2 2
+--R 12a c log(x) + 2b d x + (6a b d + 3b c)x + (6a d + 12a b c)x
+--R (3) ---------------------------------------------------------------
+--R 12
+--R Type: Union(Expression(Integer),...)
+--E 450
+
+--S 451 of 1397
+m0:=a0-r0
+--R
+--R
+--R 3
+--R a d
+--R (4) - ---
+--R 6b
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 452
+
+)clear all
+
+--S 453 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)/x^2
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R (1) --------------------------------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 453
+
+--S 454 of 1397
+r0:=-a^2*c/x+a*(2*b*c+a*d)*x+1/3*b*(b*c+2*a*d)*x^3+1/5*b^2*d*x^5
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 3b d x + (10a b d + 5b c)x + (15a d + 30a b c)x - 15a c
+--R (2) ----------------------------------------------------------
+--R 15x
+--R Type: Fraction(Polynomial(Integer))
+--E 454
+
+--S 455 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 3b d x + (10a b d + 5b c)x + (15a d + 30a b c)x - 15a c
+--R (3) ----------------------------------------------------------
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 455
+
+--S 456 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 457
+
+)clear all
+
+--S 458 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)/x^3
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R (1) --------------------------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 458
+
+--S 459 of 1397
+r0:=-1/2*a^2*c/x^2+1/2*b*(b*c+2*a*d)*x^2+1/4*b^2*d*x^4+a*(2*b*c+a*d)*log(x)
+--R
+--R
+--R 2 2 2 6 2 4 2
+--R (4a d + 8a b c)x log(x) + b d x + (4a b d + 2b c)x - 2a c
+--R (2) -----------------------------------------------------------
+--R 2
+--R 4x
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 6 2 4 2
+--R (4a d + 8a b c)x log(x) + b d x + (4a b d + 2b c)x - 2a c
+--R (3) -----------------------------------------------------------
+--R 2
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 460
+
+--S 461 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 462
+
+)clear all
+
+--S 463 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)/x^4
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R (1) --------------------------------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 463
+
+--S 464 of 1397
+r0:=-1/3*a^2*c/x^3-a*(2*b*c+a*d)/x+b*(b*c+2*a*d)*x+1/3*b^2*d*x^3
+--R
+--R
+--R 1 2 6 2 4 2 2 1 2
+--R - b d x + (2a b d + b c)x + (- a d - 2a b c)x - - a c
+--R 3 3
+--R (2) --------------------------------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 464
+
+--S 465 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R b d x + (6a b d + 3b c)x + (- 3a d - 6a b c)x - a c
+--R (3) ------------------------------------------------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 465
+
+--S 466 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 467
+
+)clear all
+
+--S 468 of 1397
+t0:=x^m*(a+b*x^2)^2*(c+d*x^2)^2
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R m
+--R x
+--R Type: Expression(Integer)
+--E 468
+
+--S 469 of 1397
+r0:=a^2*c^2*x^(1+m)/(1+m)+2*a*c*(b*c+a*d)*x^(3+m)/(3+m)+(b^2*c^2+_
+ 4*a*b*c*d+a^2*d^2)*x^(5+m)/(5+m)+2*b*d*(b*c+a*d)*x^(7+m)/(7+m)+_
+ b^2*d^2*x^(9+m)/(9+m)
+--R
+--R
+--R (2)
+--R 2 2 4 2 2 3 2 2 2 2 2 2 2 m + 9
+--R (b d m + 16b d m + 86b d m + 176b d m + 105b d )x
+--R +
+--R 2 2 4 2 2 3
+--R (2a b d + 2b c d)m + (36a b d + 36b c d)m
+--R +
+--R 2 2 2 2 2 2
+--R (208a b d + 208b c d)m + (444a b d + 444b c d)m + 270a b d
+--R +
+--R 2
+--R 270b c d
+--R *
+--R m + 7
+--R x
+--R +
+--R 2 2 2 2 4 2 2 2 2 3
+--R (a d + 4a b c d + b c )m + (20a d + 80a b c d + 20b c )m
+--R +
+--R 2 2 2 2 2
+--R (130a d + 520a b c d + 130b c )m
+--R +
+--R 2 2 2 2 2 2 2 2
+--R (300a d + 1200a b c d + 300b c )m + 189a d + 756a b c d + 189b c
+--R *
+--R m + 5
+--R x
+--R +
+--R 2 2 4 2 2 3
+--R (2a c d + 2a b c )m + (44a c d + 44a b c )m
+--R +
+--R 2 2 2 2 2 2
+--R (328a c d + 328a b c )m + (916a c d + 916a b c )m + 630a c d
+--R +
+--R 2
+--R 630a b c
+--R *
+--R m + 3
+--R x
+--R +
+--R 2 2 4 2 2 3 2 2 2 2 2 2 2 m + 1
+--R (a c m + 24a c m + 206a c m + 744a c m + 945a c )x
+--R /
+--R 5 4 3 2
+--R m + 25m + 230m + 950m + 1689m + 945
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 4 2 2 3 2 2 2 2 2 2 2 9
+--R (b d m + 16b d m + 86b d m + 176b d m + 105b d )x
+--R +
+--R 2 2 4 2 2 3
+--R (2a b d + 2b c d)m + (36a b d + 36b c d)m
+--R +
+--R 2 2 2 2 2 2
+--R (208a b d + 208b c d)m + (444a b d + 444b c d)m + 270a b d
+--R +
+--R 2
+--R 270b c d
+--R *
+--R 7
+--R x
+--R +
+--R 2 2 2 2 4 2 2 2 2 3
+--R (a d + 4a b c d + b c )m + (20a d + 80a b c d + 20b c )m
+--R +
+--R 2 2 2 2 2
+--R (130a d + 520a b c d + 130b c )m
+--R +
+--R 2 2 2 2 2 2 2 2
+--R (300a d + 1200a b c d + 300b c )m + 189a d + 756a b c d + 189b c
+--R *
+--R 5
+--R x
+--R +
+--R 2 2 4 2 2 3
+--R (2a c d + 2a b c )m + (44a c d + 44a b c )m
+--R +
+--R 2 2 2 2 2 2
+--R (328a c d + 328a b c )m + (916a c d + 916a b c )m + 630a c d
+--R +
+--R 2
+--R 630a b c
+--R *
+--R 3
+--R x
+--R +
+--R 2 2 4 2 2 3 2 2 2 2 2 2 2
+--R (a c m + 24a c m + 206a c m + 744a c m + 945a c )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 5 4 3 2
+--R m + 25m + 230m + 950m + 1689m + 945
+--R Type: Union(Expression(Integer),...)
+--E 470
+
+--S 471 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 4 2 2 3 2 2 2 2 2 2 2 9
+--R (b d m + 16b d m + 86b d m + 176b d m + 105b d )x
+--R +
+--R 2 2 4 2 2 3
+--R (2a b d + 2b c d)m + (36a b d + 36b c d)m
+--R +
+--R 2 2 2 2 2 2
+--R (208a b d + 208b c d)m + (444a b d + 444b c d)m + 270a b d
+--R +
+--R 2
+--R 270b c d
+--R *
+--R 7
+--R x
+--R +
+--R 2 2 2 2 4 2 2 2 2 3
+--R (a d + 4a b c d + b c )m + (20a d + 80a b c d + 20b c )m
+--R +
+--R 2 2 2 2 2
+--R (130a d + 520a b c d + 130b c )m
+--R +
+--R 2 2 2 2 2 2 2 2
+--R (300a d + 1200a b c d + 300b c )m + 189a d + 756a b c d + 189b c
+--R *
+--R 5
+--R x
+--R +
+--R 2 2 4 2 2 3
+--R (2a c d + 2a b c )m + (44a c d + 44a b c )m
+--R +
+--R 2 2 2 2 2 2
+--R (328a c d + 328a b c )m + (916a c d + 916a b c )m + 630a c d
+--R +
+--R 2
+--R 630a b c
+--R *
+--R 3
+--R x
+--R +
+--R 2 2 4 2 2 3 2 2 2 2 2 2 2
+--R (a c m + 24a c m + 206a c m + 744a c m + 945a c )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 2 2 4 2 2 3 2 2 2 2 2 2 2 m + 9
+--R (- b d m - 16b d m - 86b d m - 176b d m - 105b d )x
+--R +
+--R 2 2 4 2 2 3
+--R (- 2a b d - 2b c d)m + (- 36a b d - 36b c d)m
+--R +
+--R 2 2 2 2 2 2
+--R (- 208a b d - 208b c d)m + (- 444a b d - 444b c d)m - 270a b d
+--R +
+--R 2
+--R - 270b c d
+--R *
+--R m + 7
+--R x
+--R +
+--R 2 2 2 2 4 2 2 2 2 3
+--R (- a d - 4a b c d - b c )m + (- 20a d - 80a b c d - 20b c )m
+--R +
+--R 2 2 2 2 2
+--R (- 130a d - 520a b c d - 130b c )m
+--R +
+--R 2 2 2 2 2 2 2 2
+--R (- 300a d - 1200a b c d - 300b c )m - 189a d - 756a b c d - 189b c
+--R *
+--R m + 5
+--R x
+--R +
+--R 2 2 4 2 2 3
+--R (- 2a c d - 2a b c )m + (- 44a c d - 44a b c )m
+--R +
+--R 2 2 2 2 2 2
+--R (- 328a c d - 328a b c )m + (- 916a c d - 916a b c )m - 630a c d
+--R +
+--R 2
+--R - 630a b c
+--R *
+--R m + 3
+--R x
+--R +
+--R 2 2 4 2 2 3 2 2 2 2 2 2 2 m + 1
+--R (- a c m - 24a c m - 206a c m - 744a c m - 945a c )x
+--R /
+--R 5 4 3 2
+--R m + 25m + 230m + 950m + 1689m + 945
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 472
+
+)clear all
+
+--S 473 of 1397
+t0:=x^4*(a+b*x^2)^2*(c+d*x^2)^2
+--R
+--R
+--R (1)
+--R 2 2 12 2 2 10 2 2 2 2 8
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 6 2 2 4
+--R (2a c d + 2a b c )x + a c x
+--R Type: Polynomial(Integer)
+--E 473
+
+--S 474 of 1397
+r0:=1/5*a^2*c^2*x^5+2/7*a*c*(b*c+a*d)*x^7+1/9*(b^2*c^2+4*a*b*c*d+_
+ a^2*d^2)*x^9+2/11*b*d*(b*c+a*d)*x^11+1/13*b^2*d^2*x^13
+--R
+--R
+--R (2)
+--R 1 2 2 13 2 2 2 2 11 1 2 2 4 1 2 2 9
+--R -- b d x + (-- a b d + -- b c d)x + (- a d + - a b c d + - b c )x
+--R 13 11 11 9 9 9
+--R +
+--R 2 2 2 2 7 1 2 2 5
+--R (- a c d + - a b c )x + - a c x
+--R 7 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 474
+
+--S 475 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 2 13 2 2 2 2 11 1 2 2 4 1 2 2 9
+--R -- b d x + (-- a b d + -- b c d)x + (- a d + - a b c d + - b c )x
+--R 13 11 11 9 9 9
+--R +
+--R 2 2 2 2 7 1 2 2 5
+--R (- a c d + - a b c )x + - a c x
+--R 7 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 475
+
+--S 476 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 476
+
+--S 477 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 477
+
+)clear all
+
+--S 478 of 1397
+t0:=x^3*(a+b*x^2)^2*(c+d*x^2)^2
+--R
+--R
+--R (1)
+--R 2 2 11 2 2 9 2 2 2 2 7
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 5 2 2 3
+--R (2a c d + 2a b c )x + a c x
+--R Type: Polynomial(Integer)
+--E 478
+
+--S 479 of 1397
+r0:=1/4*a^2*c^2*x^4+1/3*a*c*(b*c+a*d)*x^6+1/8*(b^2*c^2+4*a*b*c*d+_
+ a^2*d^2)*x^8+1/5*b*d*(b*c+a*d)*x^10+1/12*b^2*d^2*x^12
+--R
+--R
+--R (2)
+--R 1 2 2 12 1 2 1 2 10 1 2 2 1 1 2 2 8
+--R -- b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 12 5 5 8 2 8
+--R +
+--R 1 2 1 2 6 1 2 2 4
+--R (- a c d + - a b c )x + - a c x
+--R 3 3 4
+--R Type: Polynomial(Fraction(Integer))
+--E 479
+
+--S 480 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 2 12 1 2 1 2 10 1 2 2 1 1 2 2 8
+--R -- b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 12 5 5 8 2 8
+--R +
+--R 1 2 1 2 6 1 2 2 4
+--R (- a c d + - a b c )x + - a c x
+--R 3 3 4
+--R Type: Polynomial(Fraction(Integer))
+--E 480
+
+--S 481 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 481
+
+--S 482 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 482
+
+)clear all
+
+--S 483 of 1397
+t0:=x^2*(a+b*x^2)^2*(c+d*x^2)^2
+--R
+--R
+--R (1)
+--R 2 2 10 2 2 8 2 2 2 2 6
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 4 2 2 2
+--R (2a c d + 2a b c )x + a c x
+--R Type: Polynomial(Integer)
+--E 483
+
+--S 484 of 1397
+r0:=1/3*a^2*c^2*x^3+2/5*a*c*(b*c+a*d)*x^5+1/7*(b^2*c^2+4*a*b*c*d+_
+ a^2*d^2)*x^7+2/9*b*d*(b*c+a*d)*x^9+1/11*b^2*d^2*x^11
+--R
+--R
+--R (2)
+--R 1 2 2 11 2 2 2 2 9 1 2 2 4 1 2 2 7
+--R -- b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 11 9 9 7 7 7
+--R +
+--R 2 2 2 2 5 1 2 2 3
+--R (- a c d + - a b c )x + - a c x
+--R 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 484
+
+--S 485 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 2 11 2 2 2 2 9 1 2 2 4 1 2 2 7
+--R -- b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 11 9 9 7 7 7
+--R +
+--R 2 2 2 2 5 1 2 2 3
+--R (- a c d + - a b c )x + - a c x
+--R 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 485
+
+--S 486 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 486
+
+--S 487 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 487
+
+)clear all
+
+--S 488 of 1397
+t0:=x*(a+b*x^2)^2*(c+d*x^2)^2
+--R
+--R
+--R (1)
+--R 2 2 9 2 2 7 2 2 2 2 5
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 3 2 2
+--R (2a c d + 2a b c )x + a c x
+--R Type: Polynomial(Integer)
+--E 488
+
+--S 489 of 1397
+r0:=1/6*(b*c-a*d)^2*(a+b*x^2)^3/b^3+1/4*d*(b*c-a*d)*(a+b*x^2)^4/b^3+_
+ 1/10*d^2*(a+b*x^2)^5/b^3
+--R
+--R
+--R (2)
+--R 1 5 2 10 1 4 2 1 5 8 1 2 3 2 2 4 1 5 2 6
+--R -- b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x
+--R 10 4 4 6 3 6
+--R +
+--R 1 2 3 1 4 2 4 1 2 3 2 2 1 5 2 1 4 1 3 2 2
+--R (- a b c d + - a b c )x + - a b c x + -- a d - -- a b c d + - a b c
+--R 2 2 2 60 12 6
+--R /
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 489
+
+--S 490 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 2 10 1 2 1 2 8 1 2 2 2 1 2 2 6
+--R -- b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 10 4 4 6 3 6
+--R +
+--R 1 2 1 2 4 1 2 2 2
+--R (- a c d + - a b c )x + - a c x
+--R 2 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 490
+
+--S 491 of 1397
+m0:=a0-r0
+--R
+--R
+--R 1 5 2 1 4 1 3 2 2
+--R - -- a d + -- a b c d - - a b c
+--R 60 12 6
+--R (4) ---------------------------------
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 491
+
+--S 492 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 492
+
+)clear all
+
+--S 493 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^2
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 493
+
+--S 494 of 1397
+r0:=a^2*c^2*x+2/3*a*c*(b*c+a*d)*x^3+1/5*(b^2*c^2+4*a*b*c*d+a^2*d^2)*_
+ x^5+2/7*b*d*(b*c+a*d)*x^7+1/9*b^2*d^2*x^9
+--R
+--R
+--R (2)
+--R 1 2 2 9 2 2 2 2 7 1 2 2 4 1 2 2 5
+--R - b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 9 7 7 5 5 5
+--R +
+--R 2 2 2 2 3 2 2
+--R (- a c d + - a b c )x + a c x
+--R 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 494
+
+--S 495 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 2 9 2 2 2 2 7 1 2 2 4 1 2 2 5
+--R - b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 9 7 7 5 5 5
+--R +
+--R 2 2 2 2 3 2 2
+--R (- a c d + - a b c )x + a c x
+--R 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 495
+
+--S 496 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 496
+
+--S 497 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 497
+
+)clear all
+
+--S 498 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^2/x
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R /
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 498
+
+--S 499 of 1397
+r0:=a*c*(b*c+a*d)*x^2+1/4*(b^2*c^2+4*a*b*c*d+a^2*d^2)*x^4+_
+ 1/3*b*d*(b*c+a*d)*x^6+1/8*b^2*d^2*x^8+a^2*c^2*log(x)
+--R
+--R
+--R (2)
+--R 2 2 2 2 8 2 2 6
+--R 24a c log(x) + 3b d x + (8a b d + 8b c d)x
+--R +
+--R 2 2 2 2 4 2 2 2
+--R (6a d + 24a b c d + 6b c )x + (24a c d + 24a b c )x
+--R /
+--R 24
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 8 2 2 6
+--R 24a c log(x) + 3b d x + (8a b d + 8b c d)x
+--R +
+--R 2 2 2 2 4 2 2 2
+--R (6a d + 24a b c d + 6b c )x + (24a c d + 24a b c )x
+--R /
+--R 24
+--R Type: Union(Expression(Integer),...)
+--E 500
+
+--S 501 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 501
+
+--S 502 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 502
+
+)clear all
+
+--S 503 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^2/x^2
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R /
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 503
+
+--S 504 of 1397
+r0:=-a^2*c^2/x+2*a*c*(b*c+a*d)*x+1/3*(b^2*c^2+4*a*b*c*d+a^2*d^2)*x^3+_
+ 2/5*b*d*(b*c+a*d)*x^5+1/7*b^2*d^2*x^7
+--R
+--R
+--R (2)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R 15b d x + (42a b d + 42b c d)x + (35a d + 140a b c d + 35b c )x
+--R +
+--R 2 2 2 2 2
+--R (210a c d + 210a b c )x - 105a c
+--R /
+--R 105x
+--R Type: Fraction(Polynomial(Integer))
+--E 504
+
+--S 505 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R 15b d x + (42a b d + 42b c d)x + (35a d + 140a b c d + 35b c )x
+--R +
+--R 2 2 2 2 2
+--R (210a c d + 210a b c )x - 105a c
+--R /
+--R 105x
+--R Type: Union(Expression(Integer),...)
+--E 505
+
+--S 506 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 506
+
+--S 507 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 507
+
+)clear all
+
+--S 508 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^2/x^3
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R /
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 508
+
+--S 509 of 1397
+r0:=-1/2*a^2*c^2/x^2+1/2*(b^2*c^2+4*a*b*c*d+a^2*d^2)*x^2+_
+ 1/2*b*d*(b*c+a*d)*x^4+1/6*b^2*d^2*x^6+2*a*c*(b*c+a*d)*log(x)
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 8 2 2 6
+--R (12a c d + 12a b c )x log(x) + b d x + (3a b d + 3b c d)x
+--R +
+--R 2 2 2 2 4 2 2
+--R (3a d + 12a b c d + 3b c )x - 3a c
+--R /
+--R 2
+--R 6x
+--R Type: Expression(Integer)
+--E 509
+
+--S 510 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 8 2 2 6
+--R (12a c d + 12a b c )x log(x) + b d x + (3a b d + 3b c d)x
+--R +
+--R 2 2 2 2 4 2 2
+--R (3a d + 12a b c d + 3b c )x - 3a c
+--R /
+--R 2
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 510
+
+--S 511 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 511
+
+--S 512 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 512
+
+)clear all
+
+--S 513 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^2/x^4
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R /
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 513
+
+--S 514 of 1397
+r0:=-1/3*a^2*c^2/x^3-2*a*c*(b*c+a*d)/x+(b^2*c^2+4*a*b*c*d+a^2*d^2)*x+_
+ 2/3*b*d*(b*c+a*d)*x^3+1/5*b^2*d^2*x^5
+--R
+--R
+--R (2)
+--R 1 2 2 8 2 2 2 2 6 2 2 2 2 4
+--R - b d x + (- a b d + - b c d)x + (a d + 4a b c d + b c )x
+--R 5 3 3
+--R +
+--R 2 2 2 1 2 2
+--R (- 2a c d - 2a b c )x - - a c
+--R 3
+--R /
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 514
+
+--S 515 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R 3b d x + (10a b d + 10b c d)x + (15a d + 60a b c d + 15b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 30a c d - 30a b c )x - 5a c
+--R /
+--R 3
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 515
+
+--S 516 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 516
+
+--S 517 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 517
+
+)clear all
+
+--S 518 of 1397
+t0:=x^m*(a+b*x^2)^2*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R *
+--R m
+--R x
+--R Type: Expression(Integer)
+--E 518
+
+--S 519 of 1397
+r0:=a^2*c^3*x^(1+m)/(1+m)+a*c^2*(2*b*c+3*a*d)*x^(3+m)/(3+m)+c*(b^2*c^2+_
+ 6*a*b*c*d+3*a^2*d^2)*x^(5+m)/(5+m)+d*(3*b^2*c^2+6*a*b*c*d+_
+ a^2*d^2)*x^(7+m)/(7+m)+b*d^2*(3*b*c+2*a*d)*x^(9+m)/(9+m)+_
+ b^2*d^3*x^(11+m)/(11+m)
+--R
+--R
+--R (2)
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 2 3 m + 11
+--R (b d m + 25b d m + 230b d m + 950b d m + 1689b d m + 945b d )x
+--R +
+--R 3 2 2 5 3 2 2 4
+--R (2a b d + 3b c d )m + (54a b d + 81b c d )m
+--R +
+--R 3 2 2 3 3 2 2 2
+--R (524a b d + 786b c d )m + (2244a b d + 3366b c d )m
+--R +
+--R 3 2 2 3 2 2
+--R (4082a b d + 6123b c d )m + 2310a b d + 3465b c d
+--R *
+--R m + 9
+--R x
+--R +
+--R 2 3 2 2 2 5 2 3 2 2 2 4
+--R (a d + 6a b c d + 3b c d)m + (29a d + 174a b c d + 87b c d)m
+--R +
+--R 2 3 2 2 2 3
+--R (302a d + 1812a b c d + 906b c d)m
+--R +
+--R 2 3 2 2 2 2
+--R (1366a d + 8196a b c d + 4098b c d)m
+--R +
+--R 2 3 2 2 2 2 3 2
+--R (2577a d + 15462a b c d + 7731b c d)m + 1485a d + 8910a b c d
+--R +
+--R 2 2
+--R 4455b c d
+--R *
+--R m + 7
+--R x
+--R +
+--R 2 2 2 2 3 5 2 2 2 2 3 4
+--R (3a c d + 6a b c d + b c )m + (93a c d + 186a b c d + 31b c )m
+--R +
+--R 2 2 2 2 3 3
+--R (1050a c d + 2100a b c d + 350b c )m
+--R +
+--R 2 2 2 2 3 2
+--R (5190a c d + 10380a b c d + 1730b c )m
+--R +
+--R 2 2 2 2 3 2 2 2
+--R (10467a c d + 20934a b c d + 3489b c )m + 6237a c d + 12474a b c d
+--R +
+--R 2 3
+--R 2079b c
+--R *
+--R m + 5
+--R x
+--R +
+--R 2 2 3 5 2 2 3 4
+--R (3a c d + 2a b c )m + (99a c d + 66a b c )m
+--R +
+--R 2 2 3 3 2 2 3 2
+--R (1218a c d + 812a b c )m + (6786a c d + 4524a b c )m
+--R +
+--R 2 2 3 2 2 3
+--R (16059a c d + 10706a b c )m + 10395a c d + 6930a b c
+--R *
+--R m + 3
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 2 3 m + 1
+--R (a c m + 35a c m + 470a c m + 3010a c m + 9129a c m + 10395a c )x
+--R /
+--R 6 5 4 3 2
+--R m + 36m + 505m + 3480m + 12139m + 19524m + 10395
+--R Type: Expression(Integer)
+--E 519
+
+--S 520 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 2 3 11
+--R (b d m + 25b d m + 230b d m + 950b d m + 1689b d m + 945b d )x
+--R +
+--R 3 2 2 5 3 2 2 4
+--R (2a b d + 3b c d )m + (54a b d + 81b c d )m
+--R +
+--R 3 2 2 3 3 2 2 2
+--R (524a b d + 786b c d )m + (2244a b d + 3366b c d )m
+--R +
+--R 3 2 2 3 2 2
+--R (4082a b d + 6123b c d )m + 2310a b d + 3465b c d
+--R *
+--R 9
+--R x
+--R +
+--R 2 3 2 2 2 5 2 3 2 2 2 4
+--R (a d + 6a b c d + 3b c d)m + (29a d + 174a b c d + 87b c d)m
+--R +
+--R 2 3 2 2 2 3
+--R (302a d + 1812a b c d + 906b c d)m
+--R +
+--R 2 3 2 2 2 2
+--R (1366a d + 8196a b c d + 4098b c d)m
+--R +
+--R 2 3 2 2 2 2 3 2
+--R (2577a d + 15462a b c d + 7731b c d)m + 1485a d + 8910a b c d
+--R +
+--R 2 2
+--R 4455b c d
+--R *
+--R 7
+--R x
+--R +
+--R 2 2 2 2 3 5 2 2 2 2 3 4
+--R (3a c d + 6a b c d + b c )m + (93a c d + 186a b c d + 31b c )m
+--R +
+--R 2 2 2 2 3 3
+--R (1050a c d + 2100a b c d + 350b c )m
+--R +
+--R 2 2 2 2 3 2
+--R (5190a c d + 10380a b c d + 1730b c )m
+--R +
+--R 2 2 2 2 3 2 2
+--R (10467a c d + 20934a b c d + 3489b c )m + 6237a c d
+--R +
+--R 2 2 3
+--R 12474a b c d + 2079b c
+--R *
+--R 5
+--R x
+--R +
+--R 2 2 3 5 2 2 3 4
+--R (3a c d + 2a b c )m + (99a c d + 66a b c )m
+--R +
+--R 2 2 3 3 2 2 3 2
+--R (1218a c d + 812a b c )m + (6786a c d + 4524a b c )m
+--R +
+--R 2 2 3 2 2 3
+--R (16059a c d + 10706a b c )m + 10395a c d + 6930a b c
+--R *
+--R 3
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 2 3
+--R (a c m + 35a c m + 470a c m + 3010a c m + 9129a c m + 10395a c )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 6 5 4 3 2
+--R m + 36m + 505m + 3480m + 12139m + 19524m + 10395
+--R Type: Union(Expression(Integer),...)
+--E 520
+
+--S 521 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 2 3 11
+--R (b d m + 25b d m + 230b d m + 950b d m + 1689b d m + 945b d )x
+--R +
+--R 3 2 2 5 3 2 2 4
+--R (2a b d + 3b c d )m + (54a b d + 81b c d )m
+--R +
+--R 3 2 2 3 3 2 2 2
+--R (524a b d + 786b c d )m + (2244a b d + 3366b c d )m
+--R +
+--R 3 2 2 3 2 2
+--R (4082a b d + 6123b c d )m + 2310a b d + 3465b c d
+--R *
+--R 9
+--R x
+--R +
+--R 2 3 2 2 2 5
+--R (a d + 6a b c d + 3b c d)m
+--R +
+--R 2 3 2 2 2 4
+--R (29a d + 174a b c d + 87b c d)m
+--R +
+--R 2 3 2 2 2 3
+--R (302a d + 1812a b c d + 906b c d)m
+--R +
+--R 2 3 2 2 2 2
+--R (1366a d + 8196a b c d + 4098b c d)m
+--R +
+--R 2 3 2 2 2 2 3 2
+--R (2577a d + 15462a b c d + 7731b c d)m + 1485a d + 8910a b c d
+--R +
+--R 2 2
+--R 4455b c d
+--R *
+--R 7
+--R x
+--R +
+--R 2 2 2 2 3 5
+--R (3a c d + 6a b c d + b c )m
+--R +
+--R 2 2 2 2 3 4
+--R (93a c d + 186a b c d + 31b c )m
+--R +
+--R 2 2 2 2 3 3
+--R (1050a c d + 2100a b c d + 350b c )m
+--R +
+--R 2 2 2 2 3 2
+--R (5190a c d + 10380a b c d + 1730b c )m
+--R +
+--R 2 2 2 2 3 2 2
+--R (10467a c d + 20934a b c d + 3489b c )m + 6237a c d
+--R +
+--R 2 2 3
+--R 12474a b c d + 2079b c
+--R *
+--R 5
+--R x
+--R +
+--R 2 2 3 5 2 2 3 4
+--R (3a c d + 2a b c )m + (99a c d + 66a b c )m
+--R +
+--R 2 2 3 3 2 2 3 2
+--R (1218a c d + 812a b c )m + (6786a c d + 4524a b c )m
+--R +
+--R 2 2 3 2 2 3
+--R (16059a c d + 10706a b c )m + 10395a c d + 6930a b c
+--R *
+--R 3
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 2 3
+--R (a c m + 35a c m + 470a c m + 3010a c m + 9129a c m + 10395a c )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 2 3
+--R (- b d m - 25b d m - 230b d m - 950b d m - 1689b d m - 945b d )
+--R *
+--R m + 11
+--R x
+--R +
+--R 3 2 2 5 3 2 2 4
+--R (- 2a b d - 3b c d )m + (- 54a b d - 81b c d )m
+--R +
+--R 3 2 2 3 3 2 2 2
+--R (- 524a b d - 786b c d )m + (- 2244a b d - 3366b c d )m
+--R +
+--R 3 2 2 3 2 2
+--R (- 4082a b d - 6123b c d )m - 2310a b d - 3465b c d
+--R *
+--R m + 9
+--R x
+--R +
+--R 2 3 2 2 2 5
+--R (- a d - 6a b c d - 3b c d)m
+--R +
+--R 2 3 2 2 2 4
+--R (- 29a d - 174a b c d - 87b c d)m
+--R +
+--R 2 3 2 2 2 3
+--R (- 302a d - 1812a b c d - 906b c d)m
+--R +
+--R 2 3 2 2 2 2
+--R (- 1366a d - 8196a b c d - 4098b c d)m
+--R +
+--R 2 3 2 2 2 2 3 2
+--R (- 2577a d - 15462a b c d - 7731b c d)m - 1485a d - 8910a b c d
+--R +
+--R 2 2
+--R - 4455b c d
+--R *
+--R m + 7
+--R x
+--R +
+--R 2 2 2 2 3 5
+--R (- 3a c d - 6a b c d - b c )m
+--R +
+--R 2 2 2 2 3 4
+--R (- 93a c d - 186a b c d - 31b c )m
+--R +
+--R 2 2 2 2 3 3
+--R (- 1050a c d - 2100a b c d - 350b c )m
+--R +
+--R 2 2 2 2 3 2
+--R (- 5190a c d - 10380a b c d - 1730b c )m
+--R +
+--R 2 2 2 2 3 2 2
+--R (- 10467a c d - 20934a b c d - 3489b c )m - 6237a c d
+--R +
+--R 2 2 3
+--R - 12474a b c d - 2079b c
+--R *
+--R m + 5
+--R x
+--R +
+--R 2 2 3 5 2 2 3 4
+--R (- 3a c d - 2a b c )m + (- 99a c d - 66a b c )m
+--R +
+--R 2 2 3 3 2 2 3 2
+--R (- 1218a c d - 812a b c )m + (- 6786a c d - 4524a b c )m
+--R +
+--R 2 2 3 2 2 3
+--R (- 16059a c d - 10706a b c )m - 10395a c d - 6930a b c
+--R *
+--R m + 3
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 2 3
+--R (- a c m - 35a c m - 470a c m - 3010a c m - 9129a c m - 10395a c )
+--R *
+--R m + 1
+--R x
+--R /
+--R 6 5 4 3 2
+--R m + 36m + 505m + 3480m + 12139m + 19524m + 10395
+--R Type: Expression(Integer)
+--E 521
+
+--S 522 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 522
+
+)clear all
+
+--S 523 of 1397
+t0:=x^4*(a+b*x^2)^2*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 2 3 14 3 2 2 12 2 3 2 2 2 10
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 8 2 2 3 6 2 3 4
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R Type: Polynomial(Integer)
+--E 523
+
+--S 524 of 1397
+r0:=1/5*a^2*c^3*x^5+1/7*a*c^2*(2*b*c+3*a*d)*x^7+1/9*c*(b^2*c^2+_
+ 6*a*b*c*d+3*a^2*d^2)*x^9+1/11*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*_
+ x^11+1/13*b*d^2*(3*b*c+2*a*d)*x^13+1/15*b^2*d^3*x^15
+--R
+--R
+--R (2)
+--R 1 2 3 15 2 3 3 2 2 13
+--R -- b d x + (-- a b d + -- b c d )x
+--R 15 13 13
+--R +
+--R 1 2 3 6 2 3 2 2 11 1 2 2 2 2 1 2 3 9
+--R (-- a d + -- a b c d + -- b c d)x + (- a c d + - a b c d + - b c )x
+--R 11 11 11 3 3 9
+--R +
+--R 3 2 2 2 3 7 1 2 3 5
+--R (- a c d + - a b c )x + - a c x
+--R 7 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 524
+
+--S 525 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 3 15 2 3 3 2 2 13
+--R -- b d x + (-- a b d + -- b c d )x
+--R 15 13 13
+--R +
+--R 1 2 3 6 2 3 2 2 11 1 2 2 2 2 1 2 3 9
+--R (-- a d + -- a b c d + -- b c d)x + (- a c d + - a b c d + - b c )x
+--R 11 11 11 3 3 9
+--R +
+--R 3 2 2 2 3 7 1 2 3 5
+--R (- a c d + - a b c )x + - a c x
+--R 7 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 525
+
+--S 526 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 526
+
+--S 527 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 527
+
+)clear all
+
+--S 528 of 1397
+t0:=x^3*(a+b*x^2)^2*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 2 3 13 3 2 2 11 2 3 2 2 2 9
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 7 2 2 3 5 2 3 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R Type: Polynomial(Integer)
+--E 528
+
+--S 529 of 1397
+r0:=-1/8*c*(b*c-a*d)^2*(c+d*x^2)^4/d^4+1/10*(b*c-a*d)*(3*b*c-a*d)*_
+ (c+d*x^2)^5/d^4-1/12*b*(3*b*c-2*a*d)*(c+d*x^2)^6/d^4+_
+ 1/14*b^2*(c+d*x^2)^7/d^4
+--R
+--R
+--R (2)
+--R 1 2 7 14 1 7 1 2 6 12
+--R -- b d x + (- a b d + - b c d )x
+--R 14 6 4
+--R +
+--R 1 2 7 3 6 3 2 2 5 10
+--R (-- a d + - a b c d + -- b c d )x
+--R 10 5 10
+--R +
+--R 3 2 6 3 2 5 1 2 3 4 8 1 2 2 5 1 3 4 6
+--R (- a c d + - a b c d + - b c d )x + (- a c d + - a b c d )x
+--R 8 4 8 2 3
+--R +
+--R 1 2 3 4 4 1 2 5 2 1 6 1 2 7
+--R - a c d x - -- a c d + -- a b c d - --- b c
+--R 4 40 60 280
+--R /
+--R 4
+--R d
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 529
+
+--S 530 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 3 14 1 3 1 2 2 12
+--R -- b d x + (- a b d + - b c d )x
+--R 14 6 4
+--R +
+--R 1 2 3 3 2 3 2 2 10 3 2 2 3 2 1 2 3 8
+--R (-- a d + - a b c d + -- b c d)x + (- a c d + - a b c d + - b c )x
+--R 10 5 10 8 4 8
+--R +
+--R 1 2 2 1 3 6 1 2 3 4
+--R (- a c d + - a b c )x + - a c x
+--R 2 3 4
+--R Type: Polynomial(Fraction(Integer))
+--E 530
+
+--S 531 of 1397
+m0:=a0-r0
+--R
+--R
+--R 1 2 5 2 1 6 1 2 7
+--R -- a c d - -- a b c d + --- b c
+--R 40 60 280
+--R (4) ---------------------------------
+--R 4
+--R d
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 531
+
+--S 532 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 532
+
+)clear all
+
+--S 533 of 1397
+t0:=x^2*(a+b*x^2)^2*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 2 3 12 3 2 2 10 2 3 2 2 2 8
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 6 2 2 3 4 2 3 2
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R Type: Polynomial(Integer)
+--E 533
+
+--S 534 of 1397
+r0:=1/3*a^2*c^3*x^3+1/5*a*c^2*(2*b*c+3*a*d)*x^5+1/7*c*(b^2*c^2+_
+ 6*a*b*c*d+3*a^2*d^2)*x^7+1/9*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^9+_
+ 1/11*b*d^2*(3*b*c+2*a*d)*x^11+1/13*b^2*d^3*x^13
+--R
+--R
+--R (2)
+--R 1 2 3 13 2 3 3 2 2 11 1 2 3 2 2 1 2 2 9
+--R -- b d x + (-- a b d + -- b c d )x + (- a d + - a b c d + - b c d)x
+--R 13 11 11 9 3 3
+--R +
+--R 3 2 2 6 2 1 2 3 7 3 2 2 2 3 5 1 2 3 3
+--R (- a c d + - a b c d + - b c )x + (- a c d + - a b c )x + - a c x
+--R 7 7 7 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 534
+
+--S 535 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 3 13 2 3 3 2 2 11 1 2 3 2 2 1 2 2 9
+--R -- b d x + (-- a b d + -- b c d )x + (- a d + - a b c d + - b c d)x
+--R 13 11 11 9 3 3
+--R +
+--R 3 2 2 6 2 1 2 3 7 3 2 2 2 3 5 1 2 3 3
+--R (- a c d + - a b c d + - b c )x + (- a c d + - a b c )x + - a c x
+--R 7 7 7 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 535
+
+--S 536 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 536
+
+--S 537 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 537
+
+)clear all
+
+--S 538 of 1397
+t0:=x*(a+b*x^2)^2*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 2 3 11 3 2 2 9 2 3 2 2 2 7
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 5 2 2 3 3 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R Type: Polynomial(Integer)
+--E 538
+
+--S 539 of 1397
+r0:=1/8*(b*c-a*d)^2*(c+d*x^2)^4/d^3-1/5*b*(b*c-a*d)*(c+d*x^2)^5/d^3+_
+ 1/12*b^2*(c+d*x^2)^6/d^3
+--R
+--R
+--R (2)
+--R 1 2 6 12 1 6 3 2 5 10
+--R -- b d x + (- a b d + -- b c d )x
+--R 12 5 10
+--R +
+--R 1 2 6 3 5 3 2 2 4 8 1 2 5 2 4 1 2 3 3 6
+--R (- a d + - a b c d + - b c d )x + (- a c d + a b c d + - b c d )x
+--R 8 4 8 2 6
+--R +
+--R 3 2 2 4 1 3 3 4 1 2 3 3 2 1 2 4 2 1 5 1 2 6
+--R (- a c d + - a b c d )x + - a c d x + - a c d - -- a b c d + --- b c
+--R 4 2 2 8 20 120
+--R /
+--R 3
+--R d
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 539
+
+--S 540 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 3 12 1 3 3 2 2 10 1 2 3 3 2 3 2 2 8
+--R -- b d x + (- a b d + -- b c d )x + (- a d + - a b c d + - b c d)x
+--R 12 5 10 8 4 8
+--R +
+--R 1 2 2 2 1 2 3 6 3 2 2 1 3 4 1 2 3 2
+--R (- a c d + a b c d + - b c )x + (- a c d + - a b c )x + - a c x
+--R 2 6 4 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 540
+
+--S 541 of 1397
+m0:=a0-r0
+--R
+--R
+--R 1 2 4 2 1 5 1 2 6
+--R - - a c d + -- a b c d - --- b c
+--R 8 20 120
+--R (4) ----------------------------------
+--R 3
+--R d
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 541
+
+--S 542 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 542
+
+)clear all
+
+--S 543 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 543
+
+--S 544 of 1397
+r0:=a^2*c^3*x+1/3*a*c^2*(2*b*c+3*a*d)*x^3+1/5*c*(b^2*c^2+6*a*b*c*d+_
+ 3*a^2*d^2)*x^5+1/7*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^7+_
+ 1/9*b*d^2*(3*b*c+2*a*d)*x^9+1/11*b^2*d^3*x^11
+--R
+--R
+--R (2)
+--R 1 2 3 11 2 3 1 2 2 9 1 2 3 6 2 3 2 2 7
+--R -- b d x + (- a b d + - b c d )x + (- a d + - a b c d + - b c d)x
+--R 11 9 3 7 7 7
+--R +
+--R 3 2 2 6 2 1 2 3 5 2 2 2 3 3 2 3
+--R (- a c d + - a b c d + - b c )x + (a c d + - a b c )x + a c x
+--R 5 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 544
+
+--S 545 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 3 11 2 3 1 2 2 9 1 2 3 6 2 3 2 2 7
+--R -- b d x + (- a b d + - b c d )x + (- a d + - a b c d + - b c d)x
+--R 11 9 3 7 7 7
+--R +
+--R 3 2 2 6 2 1 2 3 5 2 2 2 3 3 2 3
+--R (- a c d + - a b c d + - b c )x + (a c d + - a b c )x + a c x
+--R 5 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 545
+
+--S 546 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 546
+
+--S 547 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 547
+
+)clear all
+
+--S 548 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^3/x
+--R
+--R
+--R (1)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R /
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 548
+
+--S 549 of 1397
+r0:=1/2*a*c^2*(2*b*c+3*a*d)*x^2+1/4*c*(b^2*c^2+6*a*b*c*d+3*a^2*d^2)*x^4+_
+ 1/6*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^6+1/8*b*d^2*(3*b*c+2*a*d)*_
+ x^8+1/10*b^2*d^3*x^10+a^2*c^3*log(x)
+--R
+--R
+--R (2)
+--R 2 3 2 3 10 3 2 2 8
+--R 120a c log(x) + 12b d x + (30a b d + 45b c d )x
+--R +
+--R 2 3 2 2 2 6 2 2 2 2 3 4
+--R (20a d + 120a b c d + 60b c d)x + (90a c d + 180a b c d + 30b c )x
+--R +
+--R 2 2 3 2
+--R (180a c d + 120a b c )x
+--R /
+--R 120
+--R Type: Expression(Integer)
+--E 549
+
+--S 550 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 3 10 3 2 2 8
+--R 120a c log(x) + 12b d x + (30a b d + 45b c d )x
+--R +
+--R 2 3 2 2 2 6 2 2 2 2 3 4
+--R (20a d + 120a b c d + 60b c d)x + (90a c d + 180a b c d + 30b c )x
+--R +
+--R 2 2 3 2
+--R (180a c d + 120a b c )x
+--R /
+--R 120
+--R Type: Union(Expression(Integer),...)
+--E 550
+
+--S 551 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 551
+
+--S 552 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 552
+
+)clear all
+
+--S 553 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^3/x^2
+--R
+--R
+--R (1)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R /
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 553
+
+--S 554 of 1397
+r0:=-a^2*c^3/x+a*c^2*(2*b*c+3*a*d)*x+1/3*c*(b^2*c^2+6*a*b*c*d+3*a^2*d^2)*_
+ x^3+1/5*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^5+1/7*b*d^2*(3*b*c+_
+ 2*a*d)*x^7+1/9*b^2*d^3*x^9
+--R
+--R
+--R (2)
+--R 2 3 10 3 2 2 8
+--R 35b d x + (90a b d + 135b c d )x
+--R +
+--R 2 3 2 2 2 6
+--R (63a d + 378a b c d + 189b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (315a c d + 630a b c d + 105b c )x + (945a c d + 630a b c )x - 315a c
+--R /
+--R 315x
+--R Type: Fraction(Polynomial(Integer))
+--E 554
+
+--S 555 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 10 3 2 2 8
+--R 35b d x + (90a b d + 135b c d )x
+--R +
+--R 2 3 2 2 2 6
+--R (63a d + 378a b c d + 189b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (315a c d + 630a b c d + 105b c )x + (945a c d + 630a b c )x - 315a c
+--R /
+--R 315x
+--R Type: Union(Expression(Integer),...)
+--E 555
+
+--S 556 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 556
+
+--S 557 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 557
+
+)clear all
+
+--S 558 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^3/x^3
+--R
+--R
+--R (1)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R /
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 558
+
+--S 559 of 1397
+r0:=-1/2*a^2*c^3/x^2+1/2*c*(b^2*c^2+6*a*b*c*d+3*a^2*d^2)*x^2+1/4*d*_
+ (3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^4+1/6*b*d^2*(3*b*c+2*a*d)*x^6+_
+ 1/8*b^2*d^3*x^8+a*c^2*(2*b*c+3*a*d)*log(x)
+--R
+--R
+--R (2)
+--R 2 2 3 2 2 3 10 3 2 2 8
+--R (72a c d + 48a b c )x log(x) + 3b d x + (8a b d + 12b c d )x
+--R +
+--R 2 3 2 2 2 6 2 2 2 2 3 4
+--R (6a d + 36a b c d + 18b c d)x + (36a c d + 72a b c d + 12b c )x
+--R +
+--R 2 3
+--R - 12a c
+--R /
+--R 2
+--R 24x
+--R Type: Expression(Integer)
+--E 559
+
+--S 560 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 3 2 2 3 10 3 2 2 8
+--R (72a c d + 48a b c )x log(x) + 3b d x + (8a b d + 12b c d )x
+--R +
+--R 2 3 2 2 2 6 2 2 2 2 3 4
+--R (6a d + 36a b c d + 18b c d)x + (36a c d + 72a b c d + 12b c )x
+--R +
+--R 2 3
+--R - 12a c
+--R /
+--R 2
+--R 24x
+--R Type: Union(Expression(Integer),...)
+--E 560
+
+--S 561 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 561
+
+--S 562 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 562
+
+)clear all
+
+--S 563 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^3/x^4
+--R
+--R
+--R (1)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R /
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 563
+
+--S 564 of 1397
+r0:=-1/3*a^2*c^3/x^3-a*c^2*(2*b*c+3*a*d)/x+c*(b^2*c^2+6*a*b*c*d+_
+ 3*a^2*d^2)*x+1/3*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^3+_
+ 1/5*b*d^2*(3*b*c+2*a*d)*x^5+1/7*b^2*d^3*x^7
+--R
+--R
+--R (2)
+--R 1 2 3 10 2 3 3 2 2 8 1 2 3 2 2 2 6
+--R - b d x + (- a b d + - b c d )x + (- a d + 2a b c d + b c d)x
+--R 7 5 5 3
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 1 2 3
+--R (3a c d + 6a b c d + b c )x + (- 3a c d - 2a b c )x - - a c
+--R 3
+--R /
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 564
+
+--S 565 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R 15b d x + (42a b d + 63b c d )x + (35a d + 210a b c d + 105b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (315a c d + 630a b c d + 105b c )x + (- 315a c d - 210a b c )x - 35a c
+--R /
+--R 3
+--R 105x
+--R Type: Union(Expression(Integer),...)
+--E 565
+
+--S 566 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 566
+
+--S 567 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 567
+
+)clear all
+
+--S 568 of 1397
+t0:=x^4*(a+b*x^2)^2/(c+d*x^2)
+--R
+--R
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 568
+
+--S 569 of 1397
+r0:=-c*(b*c-a*d)^2*x/d^4+1/3*(b*c-a*d)^2*x^3/d^3-1/5*b*(b*c-2*a*d)*_
+ x^5/d^2+1/7*b^2*x^7/d+c^(3/2)*(b*c-a*d)^2*atan(x*sqrt(d)/sqrt(c))/d^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 3 +-+ x\|d
+--R (105a c d - 210a b c d + 105b c )\|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 7 3 2 2 5
+--R 15b d x + (42a b d - 21b c d )x
+--R +
+--R 2 3 2 2 2 3
+--R (35a d - 70a b c d + 35b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 105a c d + 210a b c d - 105b c )x
+--R *
+--R +-+
+--R \|d
+--R /
+--R 4 +-+
+--R 105d \|d
+--R Type: Expression(Integer)
+--E 569
+
+--S 570 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | c 2
+--R +---+ 2d x |- - + d x - c
+--R 2 2 2 2 3 | c \| d
+--R (105a c d - 210a b c d + 105b c ) |- - log(---------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 3 2 2 2 3
+--R 30b d x + (84a b d - 42b c d )x + (70a d - 140a b c d + 70b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 210a c d + 420a b c d - 210b c )x
+--R /
+--R 4
+--R 210d
+--R ,
+--R
+--R +-+
+--R |c
+--R +-+ |-
+--R 2 2 2 2 3 |c \|d 2 3 7
+--R (- 105a c d + 210a b c d - 105b c ) |- atan(----) + 15b d x
+--R \|d x
+--R +
+--R 3 2 2 5 2 3 2 2 2 3
+--R (42a b d - 21b c d )x + (35a d - 70a b c d + 35b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 105a c d + 210a b c d - 105b c )x
+--R /
+--R 4
+--R 105d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 570
+
+--S 571 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | c 2
+--R +---+ 2d x |- - + d x - c
+--R 2 2 2 2 3 | c +-+ \| d
+--R (a c d - 2a b c d + b c ) |- - \|d log(---------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 3 +-+ x\|d
+--R (- 2a c d + 4a b c d - 2b c )\|c atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 4 +-+
+--R 2d \|d
+--R Type: Expression(Integer)
+--E 571
+
+--S 572 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 572
+
+--S 573 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 3 +-+ x\|d
+--R (- a c d + 2a b c d - b c )\|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |c
+--R +-+ |-
+--R 2 2 2 2 3 |c +-+ \|d
+--R (- a c d + 2a b c d - b c ) |- \|d atan(----)
+--R \|d x
+--R /
+--R 4 +-+
+--R d \|d
+--R Type: Expression(Integer)
+--E 573
+
+--S 574 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 574
+
+)clear all
+
+--S 575 of 1397
+t0:=x^3*(a+b*x^2)^2/(c+d*x^2)
+--R
+--R
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 575
+
+--S 576 of 1397
+r0:=1/2*(b*c-a*d)^2*x^2/d^3-1/4*b*(b*c-2*a*d)*x^4/d^2+1/6*b^2*x^6/d-_
+ 1/2*c*(b*c-a*d)^2*log(c+d*x^2)/d^4
+--R
+--R
+--R (2)
+--R 2 2 2 2 3 2 2 3 6
+--R (- 6a c d + 12a b c d - 6b c )log(d x + c) + 2b d x
+--R +
+--R 3 2 2 4 2 3 2 2 2 2
+--R (6a b d - 3b c d )x + (6a d - 12a b c d + 6b c d)x
+--R /
+--R 4
+--R 12d
+--R Type: Expression(Integer)
+--E 576
+
+--S 577 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 3 2 2 3 6
+--R (- 6a c d + 12a b c d - 6b c )log(d x + c) + 2b d x
+--R +
+--R 3 2 2 4 2 3 2 2 2 2
+--R (6a b d - 3b c d )x + (6a d - 12a b c d + 6b c d)x
+--R /
+--R 4
+--R 12d
+--R Type: Union(Expression(Integer),...)
+--E 577
+
+--S 578 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 578
+
+--S 579 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 579
+
+)clear all
+
+--S 580 of 1397
+t0:=x^2*(a+b*x^2)^2/(c+d*x^2)
+--R
+--R
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 580
+
+--S 581 of 1397
+r0:=(b*c-a*d)^2*x/d^3-1/3*b*(b*c-2*a*d)*x^3/d^2+1/5*b^2*x^5/d-_
+ (b*c-a*d)^2*atan(x*sqrt(d)/sqrt(c))*sqrt(c)/d^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 +-+ x\|d
+--R (- 15a d + 30a b c d - 15b c )\|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 5 2 2 3 2 2 2 2 +-+
+--R (3b d x + (10a b d - 5b c d)x + (15a d - 30a b c d + 15b c )x)\|d
+--R /
+--R 3 +-+
+--R 15d \|d
+--R Type: Expression(Integer)
+--E 581
+
+--S 582 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R 2 2 2 2 | c \| d
+--R (15a d - 30a b c d + 15b c ) |- - log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R 2 2 5 2 2 3 2 2 2 2
+--R 6b d x + (20a b d - 10b c d)x + (30a d - 60a b c d + 30b c )x
+--R /
+--R 3
+--R 30d
+--R ,
+--R
+--R +-+
+--R |c
+--R +-+ |-
+--R 2 2 2 2 |c \|d 2 2 5
+--R (15a d - 30a b c d + 15b c ) |- atan(----) + 3b d x
+--R \|d x
+--R +
+--R 2 2 3 2 2 2 2
+--R (10a b d - 5b c d)x + (15a d - 30a b c d + 15b c )x
+--R /
+--R 3
+--R 15d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 582
+
+--S 583 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R 2 2 2 2 | c +-+ \| d
+--R (a d - 2a b c d + b c ) |- - \|d log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ x\|d
+--R (2a d - 4a b c d + 2b c )\|c atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-+
+--R 2d \|d
+--R Type: Expression(Integer)
+--E 583
+
+--S 584 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 584
+
+--S 585 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 +-+ x\|d
+--R (a d - 2a b c d + b c )\|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |c
+--R +-+ |-
+--R 2 2 2 2 |c +-+ \|d
+--R (a d - 2a b c d + b c ) |- \|d atan(----)
+--R \|d x
+--R /
+--R 3 +-+
+--R d \|d
+--R Type: Expression(Integer)
+--E 585
+
+--S 586 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 586
+
+)clear all
+
+--S 587 of 1397
+t0:=x*(a+b*x^2)^2/(c+d*x^2)
+--R
+--R
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R (1) --------------------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 587
+
+--S 588 of 1397
+r0:=-1/2*b*(b*c-a*d)*x^2/d^2+1/4*(a+b*x^2)^2/d+1/2*(b*c-a*d)^2*_
+ log(c+d*x^2)/d^3
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2 2 4 2 2 2
+--R (2a d - 4a b c d + 2b c )log(d x + c) + b d x + (4a b d - 2b c d)x
+--R +
+--R 2 2
+--R a d
+--R /
+--R 3
+--R 4d
+--R Type: Expression(Integer)
+--E 588
+
+--S 589 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2 2 4 2 2 2
+--R (2a d - 4a b c d + 2b c )log(d x + c) + b d x + (4a b d - 2b c d)x
+--R -----------------------------------------------------------------------
+--R 3
+--R 4d
+--R Type: Union(Expression(Integer),...)
+--E 589
+
+--S 590 of 1397
+m0:=a0-r0
+--R
+--R
+--R 2
+--R a
+--R (4) - --
+--R 4d
+--R Type: Expression(Integer)
+--E 590
+
+--S 591 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 591
+
+)clear all
+
+--S 592 of 1397
+t0:=(a+b*x^2)^2/(c+d*x^2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 592
+
+--S 593 of 1397
+r0:=-b*(b*c-2*a*d)*x/d^2+1/3*b^2*x^3/d+(b*c-a*d)^2*_
+ atan(x*sqrt(d)/sqrt(c))/(d^(5/2)*sqrt(c))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 x\|d 2 3 2 +-+ +-+
+--R (3a d - 6a b c d + 3b c )atan(-----) + (b d x + (6a b d - 3b c)x)\|c \|d
+--R +-+
+--R \|c
+--R ---------------------------------------------------------------------------
+--R 2 +-+ +-+
+--R 3d \|c \|d
+--R Type: Expression(Integer)
+--E 593
+
+--S 594 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 2 (d x - c)\|- c d + 2c d x
+--R (3a d - 6a b c d + 3b c )log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 +-----+
+--R (2b d x + (12a b d - 6b c)x)\|- c d
+--R /
+--R 2 +-----+
+--R 6d \|- c d
+--R ,
+--R +---+
+--R 2 2 2 2 x\|c d 2 3 2 +---+
+--R (3a d - 6a b c d + 3b c )atan(-------) + (b d x + (6a b d - 3b c)x)\|c d
+--R c
+--R ---------------------------------------------------------------------------]
+--R 2 +---+
+--R 3d \|c d
+--R Type: Union(List(Expression(Integer)),...)
+--E 594
+
+--S 595 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d - 2a b c d + b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 2a d + 4a b c d - 2b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-----+ +-+ +-+
+--R 2d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 595
+
+--S 596 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 596
+
+--S 597 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (a d - 2a b c d + b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- a d + 2a b c d - b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-+ +-+ +---+
+--R d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 597
+
+--S 598 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 598
+
+)clear all
+
+--S 599 of 1397
+t0:=(a+b*x^2)^2/(x*(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 3
+--R d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 599
+
+--S 600 of 1397
+r0:=1/2*b^2*x^2/d+a^2*log(x)/c-1/2*(b*c-a*d)^2*log(c+d*x^2)/(c*d^2)
+--R
+--R
+--R 2 2 2 2 2 2 2 2 2
+--R (- a d + 2a b c d - b c )log(d x + c) + 2a d log(x) + b c d x
+--R (2) ----------------------------------------------------------------
+--R 2
+--R 2c d
+--R Type: Expression(Integer)
+--E 600
+
+--S 601 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 2 2 2 2 2 2
+--R (- a d + 2a b c d - b c )log(d x + c) + 2a d log(x) + b c d x
+--R (3) ----------------------------------------------------------------
+--R 2
+--R 2c d
+--R Type: Union(Expression(Integer),...)
+--E 601
+
+--S 602 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 602
+
+--S 603 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 603
+
+)clear all
+
+--S 604 of 1397
+t0:=(a+b*x^2)^2/(x^2*(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 4 2
+--R d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 604
+
+--S 605 of 1397
+r0:=-a^2/(c*x)+b^2*x/d-(b*c-a*d)^2*atan(x*sqrt(d)/sqrt(c))/(c^(3/2)*d^(3/2))
+--R
+--R
+--R +-+
+--R 2 2 2 2 x\|d 2 2 2 +-+ +-+
+--R (- a d + 2a b c d - b c )x atan(-----) + (b c x - a d)\|c \|d
+--R +-+
+--R \|c
+--R (2) ----------------------------------------------------------------
+--R +-+ +-+
+--R c d x\|c \|d
+--R Type: Expression(Integer)
+--E 605
+
+--S 606 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 2 (d x - c)\|- c d - 2c d x
+--R (a d - 2a b c d + b c )x log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 2 2 +-----+
+--R (2b c x - 2a d)\|- c d
+--R /
+--R +-----+
+--R 2c d x\|- c d
+--R ,
+--R +---+
+--R 2 2 2 2 x\|c d 2 2 2 +---+
+--R (- a d + 2a b c d - b c )x atan(-------) + (b c x - a d)\|c d
+--R c
+--R ----------------------------------------------------------------]
+--R +---+
+--R c d x\|c d
+--R Type: Union(List(Expression(Integer)),...)
+--E 606
+
+--S 607 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d - 2c d x
+--R (a d - 2a b c d + b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (2a d - 4a b c d + 2b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R +-----+ +-+ +-+
+--R 2c d\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 607
+
+--S 608 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 608
+
+--S 609 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (- a d + 2a b c d - b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (a d - 2a b c d + b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R +-+ +-+ +---+
+--R c d\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 609
+
+--S 610 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 610
+
+)clear all
+
+--S 611 of 1397
+t0:=(a+b*x^2)^2/(x^3*(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 5 3
+--R d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 611
+
+--S 612 of 1397
+r0:=-1/2*a^2/(c*x^2)+a*(2*b*c-a*d)*log(x)/c^2+1/2*(b*c-a*d)^2*_
+ log(c+d*x^2)/(c^2*d)
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2 2 2 2
+--R (a d - 2a b c d + b c )x log(d x + c) + (- 2a d + 4a b c d)x log(x)
+--R +
+--R 2
+--R - a c d
+--R /
+--R 2 2
+--R 2c d x
+--R Type: Expression(Integer)
+--E 612
+
+--S 613 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2 2 2 2
+--R (a d - 2a b c d + b c )x log(d x + c) + (- 2a d + 4a b c d)x log(x)
+--R +
+--R 2
+--R - a c d
+--R /
+--R 2 2
+--R 2c d x
+--R Type: Union(Expression(Integer),...)
+--E 613
+
+--S 614 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 614
+
+--S 615 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 615
+
+)clear all
+
+--S 616 of 1397
+t0:=(a+b*x^2)^2/(x^4*(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 6 4
+--R d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 616
+
+--S 617 of 1397
+r0:=-1/3*a^2/(c*x^3)-a*(2*b*c-a*d)/(c^2*x)+(b*c-a*d)^2*_
+ atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*sqrt(d))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 3 x\|d 2 2 2 +-+ +-+
+--R (3a d - 6a b c d + 3b c )x atan(-----) + ((3a d - 6a b c)x - a c)\|c \|d
+--R +-+
+--R \|c
+--R ---------------------------------------------------------------------------
+--R 2 3 +-+ +-+
+--R 3c x \|c \|d
+--R Type: Expression(Integer)
+--E 617
+
+--S 618 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 2 3 (d x - c)\|- c d + 2c d x
+--R (3a d - 6a b c d + 3b c )x log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 2 2 +-----+
+--R ((6a d - 12a b c)x - 2a c)\|- c d
+--R /
+--R 2 3 +-----+
+--R 6c x \|- c d
+--R ,
+--R +---+
+--R 2 2 2 2 3 x\|c d 2 2 2 +---+
+--R (3a d - 6a b c d + 3b c )x atan(-------) + ((3a d - 6a b c)x - a c)\|c d
+--R c
+--R ---------------------------------------------------------------------------]
+--R 2 3 +---+
+--R 3c x \|c d
+--R Type: Union(List(Expression(Integer)),...)
+--E 618
+
+--S 619 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d - 2a b c d + b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 2a d + 4a b c d - 2b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-----+ +-+ +-+
+--R 2c \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 619
+
+--S 620 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 620
+
+--S 621 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (a d - 2a b c d + b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- a d + 2a b c d - b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-+ +-+ +---+
+--R c \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 621
+
+--S 622 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 622
+
+)clear all
+
+--S 623 of 1397
+t0:=(a+b*x^2)^2/(x^5*(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 7 5
+--R d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 623
+
+--S 624 of 1397
+r0:=-1/4*a^2/(c*x^4)-1/2*a*(2*b*c-a*d)/(c^2*x^2)+(b*c-a*d)^2*_
+ log(x)/c^3-1/2*(b*c-a*d)^2*log(c+d*x^2)/c^3
+--R
+--R
+--R (2)
+--R 2 2 2 2 4 2
+--R (- 2a d + 4a b c d - 2b c )x log(d x + c)
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R (4a d - 8a b c d + 4b c )x log(x) + (2a c d - 4a b c )x - a c
+--R /
+--R 3 4
+--R 4c x
+--R Type: Expression(Integer)
+--E 624
+
+--S 625 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 4 2
+--R (- 2a d + 4a b c d - 2b c )x log(d x + c)
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R (4a d - 8a b c d + 4b c )x log(x) + (2a c d - 4a b c )x - a c
+--R /
+--R 3 4
+--R 4c x
+--R Type: Union(Expression(Integer),...)
+--E 625
+
+--S 626 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 626
+
+--S 627 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 627
+
+)clear all
+
+--S 628 of 1397
+t0:=(a+b*x^2)^2/(x^6*(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 8 6
+--R d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 628
+
+--S 629 of 1397
+r0:=-1/5*a^2/(c*x^5)-1/3*a*(2*b*c-a*d)/(c^2*x^3)-(b*c-a*d)^2/(c^3*x)-_
+ (b*c-a*d)^2*atan(x*sqrt(d)/sqrt(c))*sqrt(d)/c^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 5 +-+ x\|d
+--R (- 15a d + 30a b c d - 15b c )x \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2 4 2 2 2 2 2 +-+
+--R ((- 15a d + 30a b c d - 15b c )x + (5a c d - 10a b c )x - 3a c )\|c
+--R /
+--R 3 5 +-+
+--R 15c x \|c
+--R Type: Expression(Integer)
+--E 629
+
+--S 630 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R 2 2 2 2 5 | d \| c
+--R (15a d - 30a b c d + 15b c )x |- - log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R (- 30a d + 60a b c d - 30b c )x + (10a c d - 20a b c )x - 6a c
+--R /
+--R 3 5
+--R 30c x
+--R ,
+--R
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 2 5 |d \|c
+--R (15a d - 30a b c d + 15b c )x |- atan(-----)
+--R \|c d x
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R (- 15a d + 30a b c d - 15b c )x + (5a c d - 10a b c )x - 3a c
+--R /
+--R 3 5
+--R 15c x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 630
+
+--S 631 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R 2 2 2 2 | d +-+ \| c
+--R (a d - 2a b c d + b c ) |- - \|c log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ x\|d
+--R (2a d - 4a b c d + 2b c )\|d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-+
+--R 2c \|c
+--R Type: Expression(Integer)
+--E 631
+
+--S 632 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 632
+
+--S 633 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 +-+ x\|d
+--R (a d - 2a b c d + b c )\|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 2 +-+ |d \|c
+--R (a d - 2a b c d + b c )\|c |- atan(-----)
+--R \|c d x
+--R /
+--R 3 +-+
+--R c \|c
+--R Type: Expression(Integer)
+--E 633
+
+--S 634 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 634
+
+)clear all
+
+--S 635 of 1397
+t0:=(a+b*x^2)^2/(x^7*(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 9 7
+--R d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 635
+
+--S 636 of 1397
+r0:=-1/6*a^2/(c*x^6)-1/4*a*(2*b*c-a*d)/(c^2*x^4)-_
+ 1/2*(b*c-a*d)^2/(c^3*x^2)-d*(b*c-a*d)^2*log(x)/c^4+_
+ 1/2*d*(b*c-a*d)^2*log(c+d*x^2)/c^4
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 6 2
+--R (6a d - 12a b c d + 6b c d)x log(d x + c)
+--R +
+--R 2 3 2 2 2 6
+--R (- 12a d + 24a b c d - 12b c d)x log(x)
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (- 6a c d + 12a b c d - 6b c )x + (3a c d - 6a b c )x - 2a c
+--R /
+--R 4 6
+--R 12c x
+--R Type: Expression(Integer)
+--E 636
+
+--S 637 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 6 2
+--R (6a d - 12a b c d + 6b c d)x log(d x + c)
+--R +
+--R 2 3 2 2 2 6
+--R (- 12a d + 24a b c d - 12b c d)x log(x)
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (- 6a c d + 12a b c d - 6b c )x + (3a c d - 6a b c )x - 2a c
+--R /
+--R 4 6
+--R 12c x
+--R Type: Union(Expression(Integer),...)
+--E 637
+
+--S 638 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 638
+
+--S 639 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 639
+
+)clear all
+
+--S 640 of 1397
+t0:=x^4*(a+b*x^2)^2/(c+d*x^2)^2
+--R
+--R
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 640
+
+--S 641 of 1397
+r0a:=(3*b^2*c^2-4*a*b*c*d+a^2*d^2)*x/d^4-2/3*b*(b*c-a*d)*x^3/d^3+_
+ 1/5*b^2*x^5/d^2+1/2*c*(b*c-a*d)^2*x/(d^4*(c+d*x^2))-_
+ 1/2*(7*b*c-3*a*d)*(b*c-a*d)*atan(x*sqrt(d)/sqrt(c))*_
+ sqrt(c)/d^(9/2)
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2
+--R (- 45a d + 150a b c d - 105b c d)x - 45a c d + 150a b c d
+--R +
+--R 2 3
+--R - 105b c
+--R *
+--R +-+
+--R +-+ x\|d
+--R \|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 7 3 2 2 5
+--R 6b d x + (20a b d - 14b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (30a d - 100a b c d + 70b c d)x + (45a c d - 150a b c d + 105b c )x
+--R *
+--R +-+
+--R \|d
+--R /
+--R 5 2 4 +-+
+--R (30d x + 30c d )\|d
+--R Type: Expression(Integer)
+--E 641
+
+--S 642 of 1397
+r0b:=(b*c-a*d)*(3*b*c-a*d)*x/d^4-2/3*b*(b*c-a*d)*_
+ x^3/d^3+1/5*b^2*x^5/d^2+1/2*c*(b*c-a*d)^2*x/(d^4*(c+d*x^2))+_
+ 1/2*(b*c-a*d)^2*atan(x*sqrt(d)/sqrt(c))*sqrt(c)/d^(9/2)-_
+ 2*(b*c-a*d)*(2*b*c-a*d)*atan(x*sqrt(d)/sqrt(c))*sqrt(c)/d^(9/2)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 2 2 2 2
+--R (- 45a d + 150a b c d - 105b c d)x - 45a c d + 150a b c d
+--R +
+--R 2 3
+--R - 105b c
+--R *
+--R +-+
+--R +-+ x\|d
+--R \|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 7 3 2 2 5
+--R 6b d x + (20a b d - 14b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (30a d - 100a b c d + 70b c d)x + (45a c d - 150a b c d + 105b c )x
+--R *
+--R +-+
+--R \|d
+--R /
+--R 5 2 4 +-+
+--R (30d x + 30c d )\|d
+--R Type: Expression(Integer)
+--E 642
+
+--S 643 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 3 2 2 2 2 2 2 2
+--R (45a d - 150a b c d + 105b c d)x + 45a c d - 150a b c d
+--R +
+--R 2 3
+--R 105b c
+--R *
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R | c \| d
+--R |- - log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R 2 3 7 3 2 2 5
+--R 12b d x + (40a b d - 28b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (60a d - 200a b c d + 140b c d)x + (90a c d - 300a b c d + 210b c )x
+--R /
+--R 5 2 4
+--R 60d x + 60c d
+--R ,
+--R
+--R 2 3 2 2 2 2 2 2 2
+--R (45a d - 150a b c d + 105b c d)x + 45a c d - 150a b c d
+--R +
+--R 2 3
+--R 105b c
+--R *
+--R +-+
+--R |c
+--R +-+ |-
+--R |c \|d
+--R |- atan(----)
+--R \|d x
+--R +
+--R 2 3 7 3 2 2 5 2 3 2 2 2 3
+--R 6b d x + (20a b d - 14b c d )x + (30a d - 100a b c d + 70b c d)x
+--R +
+--R 2 2 2 2 3
+--R (45a c d - 150a b c d + 105b c )x
+--R /
+--R 5 2 4
+--R 30d x + 30c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 643
+
+--S 644 of 1397
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R 2 2 2 2 | c +-+ \| d
+--R (3a d - 10a b c d + 7b c ) |- - \|d log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ x\|d
+--R (6a d - 20a b c d + 14b c )\|c atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 4 +-+
+--R 4d \|d
+--R Type: Expression(Integer)
+--E 644
+
+--S 645 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 645
+
+--S 646 of 1397
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +-+
+--R 2 2 2 2 +-+ x\|d
+--R (3a d - 10a b c d + 7b c )\|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |c
+--R +-+ |-
+--R 2 2 2 2 |c +-+ \|d
+--R (3a d - 10a b c d + 7b c ) |- \|d atan(----)
+--R \|d x
+--R /
+--R 4 +-+
+--R 2d \|d
+--R Type: Expression(Integer)
+--E 646
+
+--S 647 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 647
+
+--S 648 of 1397
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R 2 2 2 2 | c +-+ \| d
+--R (3a d - 10a b c d + 7b c ) |- - \|d log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ x\|d
+--R (6a d - 20a b c d + 14b c )\|c atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 4 +-+
+--R 4d \|d
+--R Type: Expression(Integer)
+--E 648
+
+--S 649 of 1397
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 649
+
+--S 650 of 1397
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +-+
+--R 2 2 2 2 +-+ x\|d
+--R (3a d - 10a b c d + 7b c )\|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |c
+--R +-+ |-
+--R 2 2 2 2 |c +-+ \|d
+--R (3a d - 10a b c d + 7b c ) |- \|d atan(----)
+--R \|d x
+--R /
+--R 4 +-+
+--R 2d \|d
+--R Type: Expression(Integer)
+--E 650
+
+--S 651 of 1397
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 651
+
+)clear all
+
+--S 652 of 1397
+t0:=x^3*(a+b*x^2)^2/(c+d*x^2)^2
+--R
+--R
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 652
+
+--S 653 of 1397
+r0:=-b*(b*c-a*d)*x^2/d^3+1/4*b^2*x^4/d^2+1/2*c*(b*c-a*d)^2/(d^4*(c+_
+ d*x^2))+1/2*(b*c-a*d)*(3*b*c-a*d)*log(c+d*x^2)/d^4
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((2a d - 8a b c d + 6b c d)x + 2a c d - 8a b c d + 6b c )
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 2 3 6 3 2 2 4 2 2 2 2 2 2
+--R b d x + (4a b d - 3b c d )x + (4a b c d - 4b c d)x + 2a c d
+--R +
+--R 2 2 3
+--R - 4a b c d + 2b c
+--R /
+--R 5 2 4
+--R 4d x + 4c d
+--R Type: Expression(Integer)
+--E 653
+
+--S 654 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((2a d - 8a b c d + 6b c d)x + 2a c d - 8a b c d + 6b c )
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 2 3 6 3 2 2 4 2 2 2 2 2 2
+--R b d x + (4a b d - 3b c d )x + (4a b c d - 4b c d)x + 2a c d
+--R +
+--R 2 2 3
+--R - 4a b c d + 2b c
+--R /
+--R 5 2 4
+--R 4d x + 4c d
+--R Type: Union(Expression(Integer),...)
+--E 654
+
+--S 655 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 655
+
+--S 656 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 656
+
+)clear all
+
+--S 657 of 1397
+t0:=x^2*(a+b*x^2)^2/(c+d*x^2)^2
+--R
+--R
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 657
+
+--S 658 of 1397
+r0a:=-2*b*(b*c-a*d)*x/d^3+1/3*b^2*x^3/d^2-1/2*(b*c-a*d)^2*x/(d^3*(c+_
+ d*x^2))+1/2*(5*b^2*c^2-6*a*b*c*d+a^2*d^2)*atan(x*sqrt(d)/sqrt(c))/_
+ (d^(7/2)*sqrt(c))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d - 18a b c d + 15b c d)x + 3a c d - 18a b c d + 15b c )
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 5 2 2 3 2 2 2 2
+--R (2b d x + (12a b d - 10b c d)x + (- 3a d + 18a b c d - 15b c )x)
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 4 2 3 +-+ +-+
+--R (6d x + 6c d )\|c \|d
+--R Type: Expression(Integer)
+--E 658
+
+--S 659 of 1397
+r0b:=-2*b*(b*c-a*d)*x/d^3+1/3*b^2*x^3/d^2-1/2*(b*c-_
+ a*d)^2*x/(d^3*(c+d*x^2))-1/2*(b*c-a*d)^2*atan(x*sqrt(d)/sqrt(c))/_
+ (d^(7/2)*sqrt(c))+(b*c-a*d)*(3*b*c-a*d)*atan(x*sqrt(d)/sqrt(c))/_
+ (d^(7/2)*sqrt(c))
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d - 18a b c d + 15b c d)x + 3a c d - 18a b c d + 15b c )
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 5 2 2 3 2 2 2 2
+--R (2b d x + (12a b d - 10b c d)x + (- 3a d + 18a b c d - 15b c )x)
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 4 2 3 +-+ +-+
+--R (6d x + 6c d )\|c \|d
+--R Type: Expression(Integer)
+--E 659
+
+--S 660 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d - 18a b c d + 15b c d)x + 3a c d - 18a b c d + 15b c )
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 2 5 2 2 3 2 2 2 2
+--R (4b d x + (24a b d - 20b c d)x + (- 6a d + 36a b c d - 30b c )x)
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 4 2 3 +-----+
+--R (12d x + 12c d )\|- c d
+--R ,
+--R
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d - 18a b c d + 15b c d)x + 3a c d - 18a b c d + 15b c )
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 2 5 2 2 3 2 2 2 2
+--R (2b d x + (12a b d - 10b c d)x + (- 3a d + 18a b c d - 15b c )x)
+--R *
+--R +---+
+--R \|c d
+--R /
+--R 4 2 3 +---+
+--R (6d x + 6c d )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 660
+
+--S 661 of 1397
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d - 6a b c d + 5b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 2a d + 12a b c d - 10b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 661
+
+--S 662 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 662
+
+--S 663 of 1397
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (a d - 6a b c d + 5b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- a d + 6a b c d - 5b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-+ +-+ +---+
+--R 2d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 663
+
+--S 664 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 664
+
+--S 665 of 1397
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d - 6a b c d + 5b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 2a d + 12a b c d - 10b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 665
+
+--S 666 of 1397
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 666
+
+--S 667 of 1397
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (a d - 6a b c d + 5b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- a d + 6a b c d - 5b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-+ +-+ +---+
+--R 2d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 667
+
+--S 668 of 1397
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 668
+
+)clear all
+
+--S 669 of 1397
+t0:=x*(a+b*x^2)^2/(c+d*x^2)^2
+--R
+--R
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R (1) --------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 669
+
+--S 670 of 1397
+r0:=1/2*b^2*x^2/d^2-1/2*(b*c-a*d)^2/(d^3*(c+d*x^2))-b*(b*c-a*d)*_
+ log(c+d*x^2)/d^3
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2 2 2 4
+--R ((2a b d - 2b c d)x + 2a b c d - 2b c )log(d x + c) + b d x
+--R +
+--R 2 2 2 2 2 2
+--R b c d x - a d + 2a b c d - b c
+--R /
+--R 4 2 3
+--R 2d x + 2c d
+--R Type: Expression(Integer)
+--E 670
+
+--S 671 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2 2 2 4
+--R ((2a b d - 2b c d)x + 2a b c d - 2b c )log(d x + c) + b d x
+--R +
+--R 2 2 2 2 2 2
+--R b c d x - a d + 2a b c d - b c
+--R /
+--R 4 2 3
+--R 2d x + 2c d
+--R Type: Union(Expression(Integer),...)
+--E 671
+
+--S 672 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 672
+
+--S 673 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 673
+
+)clear all
+
+--S 674 of 1397
+t0:=(a+b*x^2)^2/(c+d*x^2)^2
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 674
+
+--S 675 of 1397
+r0:=b^2*x/d^2+1/2*(b*c-a*d)^2*x/(c*d^2*(c+d*x^2))-1/2*(b*c-a*d)*_
+ (3*b*c+a*d)*atan(x*sqrt(d)/sqrt(c))/(c^(3/2)*d^(5/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 2 2 2 2 2 2 2 2 3 x\|d
+--R ((a d + 2a b c d - 3b c d)x + a c d + 2a b c d - 3b c )atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 +-+ +-+
+--R (2b c d x + (a d - 2a b c d + 3b c )x)\|c \|d
+--R /
+--R 3 2 2 2 +-+ +-+
+--R (2c d x + 2c d )\|c \|d
+--R Type: Expression(Integer)
+--E 675
+
+--S 676 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((a d + 2a b c d - 3b c d)x + a c d + 2a b c d - 3b c )
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 2 2 2 +-----+
+--R (4b c d x + (2a d - 4a b c d + 6b c )x)\|- c d
+--R /
+--R 3 2 2 2 +-----+
+--R (4c d x + 4c d )\|- c d
+--R ,
+--R
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((a d + 2a b c d - 3b c d)x + a c d + 2a b c d - 3b c )
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 2 2 2 2 +---+
+--R (2b c d x + (a d - 2a b c d + 3b c )x)\|c d
+--R /
+--R 3 2 2 2 +---+
+--R (2c d x + 2c d )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 676
+
+--S 677 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d + 2a b c d - 3b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 2a d - 4a b c d + 6b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4c d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 677
+
+--S 678 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 678
+
+--S 679 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (a d + 2a b c d - 3b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- a d - 2a b c d + 3b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-+ +-+ +---+
+--R 2c d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 679
+
+--S 680 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 680
+
+)clear all
+
+--S 681 of 1397
+t0:=(a+b*x^2)^2/(x*(c+d*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) --------------------
+--R 2 5 3 2
+--R d x + 2c d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 681
+
+--S 682 of 1397
+r0:=1/2*(b*c-a*d)^2/(c*d^2*(c+d*x^2))+a^2*log(x)/c^2-_
+ 1/2*(a^2/c^2-b^2/d^2)*log(c+d*x^2)
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 3 2
+--R ((- a d + b c d)x - a c d + b c )log(d x + c)
+--R +
+--R 2 3 2 2 2 2 2 2 2 3
+--R (2a d x + 2a c d )log(x) + a c d - 2a b c d + b c
+--R /
+--R 2 3 2 3 2
+--R 2c d x + 2c d
+--R Type: Expression(Integer)
+--E 682
+
+--S 683 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 2 2 2 3 2
+--R ((- a d + b c d)x - a c d + b c )log(d x + c)
+--R +
+--R 2 3 2 2 2 2 2 2 2 3
+--R (2a d x + 2a c d )log(x) + a c d - 2a b c d + b c
+--R /
+--R 2 3 2 3 2
+--R 2c d x + 2c d
+--R Type: Union(Expression(Integer),...)
+--E 683
+
+--S 684 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 684
+
+--S 685 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 685
+
+)clear all
+
+--S 686 of 1397
+t0:=(a+b*x^2)^2/(x^2*(c+d*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ---------------------
+--R 2 6 4 2 2
+--R d x + 2c d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 686
+
+--S 687 of 1397
+r0a:=-a^2/(c^2*x)-1/2*(b*c-a*d)^2*x/(c^2*d*(c+d*x^2))+_
+ 1/2*(b^2*c^2+2*a*b*c*d-3*a^2*d^2)*atan(x*sqrt(d)/sqrt(c))/_
+ (c^(5/2)*d^(3/2))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((- 3a d + 2a b c d + b c d)x + (- 3a c d + 2a b c d + b c )x)
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2 2 2 +-+ +-+
+--R ((- 3a d + 2a b c d - b c )x - 2a c d)\|c \|d
+--R /
+--R 2 2 3 3 +-+ +-+
+--R (2c d x + 2c d x)\|c \|d
+--R Type: Expression(Integer)
+--E 687
+
+--S 688 of 1397
+r0b:=-a^2/(c^2*x)-1/2*(b*c-a*d)^2*x/(c^2*d*_
+ (c+d*x^2))-1/2*(b*c-a*d)^2*atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*_
+ d^(3/2))+(b*c-a*d)*(b*c+a*d)*atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*d^(3/2))
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((- 3a d + 2a b c d + b c d)x + (- 3a c d + 2a b c d + b c )x)
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2 2 2 +-+ +-+
+--R ((- 3a d + 2a b c d - b c )x - 2a c d)\|c \|d
+--R /
+--R 2 2 3 3 +-+ +-+
+--R (2c d x + 2c d x)\|c \|d
+--R Type: Expression(Integer)
+--E 688
+
+--S 689 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((3a d - 2a b c d - b c d)x + (3a c d - 2a b c d - b c )x)
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d - 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 2 2 2 2 2 +-----+
+--R ((- 6a d + 4a b c d - 2b c )x - 4a c d)\|- c d
+--R /
+--R 2 2 3 3 +-----+
+--R (4c d x + 4c d x)\|- c d
+--R ,
+--R
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((- 3a d + 2a b c d + b c d)x + (- 3a c d + 2a b c d + b c )x)
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 2 2 2 2 2 +---+
+--R ((- 3a d + 2a b c d - b c )x - 2a c d)\|c d
+--R /
+--R 2 2 3 3 +---+
+--R (2c d x + 2c d x)\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 689
+
+--S 690 of 1397
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d - 2c d x
+--R (3a d - 2a b c d - b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (6a d - 4a b c d - 2b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4c d\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 690
+
+--S 691 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 691
+
+--S 692 of 1397
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (- 3a d + 2a b c d + b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (3a d - 2a b c d - b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-+ +-+ +---+
+--R 2c d\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 692
+
+--S 693 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 693
+
+--S 694 of 1397
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d - 2c d x
+--R (3a d - 2a b c d - b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (6a d - 4a b c d - 2b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4c d\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 694
+
+--S 695 of 1397
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 695
+
+--S 696 of 1397
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (- 3a d + 2a b c d + b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (3a d - 2a b c d - b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-+ +-+ +---+
+--R 2c d\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 696
+
+--S 697 of 1397
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 697
+
+)clear all
+
+--S 698 of 1397
+t0:=(a+b*x^2)^2/(x^3*(c+d*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ---------------------
+--R 2 7 5 2 3
+--R d x + 2c d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 698
+
+--S 699 of 1397
+r0:=-1/2*a^2/(c^2*x^2)-1/2*(b*c-a*d)^2/(c^2*d*(c+d*x^2))+_
+ 2*a*(b*c-a*d)*log(x)/c^3-a*(b*c-a*d)*log(c+d*x^2)/c^3
+--R
+--R
+--R (2)
+--R 2 3 2 4 2 2 2 2 2
+--R ((2a d - 2a b c d )x + (2a c d - 2a b c d)x )log(d x + c)
+--R +
+--R 2 3 2 4 2 2 2 2
+--R ((- 4a d + 4a b c d )x + (- 4a c d + 4a b c d)x )log(x)
+--R +
+--R 2 2 2 2 3 2 2 2
+--R (- 2a c d + 2a b c d - b c )x - a c d
+--R /
+--R 3 2 4 4 2
+--R 2c d x + 2c d x
+--R Type: Expression(Integer)
+--E 699
+
+--S 700 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 4 2 2 2 2 2
+--R ((2a d - 2a b c d )x + (2a c d - 2a b c d)x )log(d x + c)
+--R +
+--R 2 3 2 4 2 2 2 2
+--R ((- 4a d + 4a b c d )x + (- 4a c d + 4a b c d)x )log(x)
+--R +
+--R 2 2 2 2 3 2 2 2
+--R (- 2a c d + 2a b c d - b c )x - a c d
+--R /
+--R 3 2 4 4 2
+--R 2c d x + 2c d x
+--R Type: Union(Expression(Integer),...)
+--E 700
+
+--S 701 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 701
+
+--S 702 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 702
+
+)clear all
+
+--S 703 of 1397
+t0:=(a+b*x^2)^2/(x^4*(c+d*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ---------------------
+--R 2 8 6 2 4
+--R d x + 2c d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 703
+
+--S 704 of 1397
+r0a:=-1/3*a^2/(c^2*x^3)-2*a*(b*c-a*d)/(c^3*x)+1/2*(b*c-a*d)^2*_
+ x/(c^3*(c+d*x^2))+1/2*(b^2*c^2-6*a*b*c*d+5*a^2*d^2)*atan(x*_
+ sqrt(d)/sqrt(c))/(c^(7/2)*sqrt(d))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 5 2 2 2 2 3 3
+--R ((15a d - 18a b c d + 3b c d)x + (15a c d - 18a b c d + 3b c )x )
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2 4 2 2 2 2 2 +-+ +-+
+--R ((15a d - 18a b c d + 3b c )x + (10a c d - 12a b c )x - 2a c )\|c \|d
+--R /
+--R 3 5 4 3 +-+ +-+
+--R (6c d x + 6c x )\|c \|d
+--R Type: Expression(Integer)
+--E 704
+
+--S 705 of 1397
+r0b:=-1/3*a^2/(c^2*x^3)-_
+ 2*a*(b*c-a*d)/(c^3*x)+1/2*(b*c-a*d)^2*x/(c^3*(c+d*x^2))+_
+ 1/2*(b*c-a*d)^2*atan(x*sqrt(d)/sqrt(c))/(c^(7/2)*sqrt(d))-_
+ 2*a*(b*c-a*d)*atan(x*sqrt(d)/sqrt(c))*sqrt(d)/c^(7/2)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 5 2 2 2 2 3 3
+--R ((15a d - 18a b c d + 3b c d)x + (15a c d - 18a b c d + 3b c )x )
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2 4 2 2 2 2 2 +-+ +-+
+--R ((15a d - 18a b c d + 3b c )x + (10a c d - 12a b c )x - 2a c )\|c \|d
+--R /
+--R 3 5 4 3 +-+ +-+
+--R (6c d x + 6c x )\|c \|d
+--R Type: Expression(Integer)
+--E 705
+
+--S 706 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 3 2 2 2 5 2 2 2 2 3 3
+--R ((15a d - 18a b c d + 3b c d)x + (15a c d - 18a b c d + 3b c )x )
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 2 2 2 4 2 2 2 2 2 +-----+
+--R ((30a d - 36a b c d + 6b c )x + (20a c d - 24a b c )x - 4a c )\|- c d
+--R /
+--R 3 5 4 3 +-----+
+--R (12c d x + 12c x )\|- c d
+--R ,
+--R
+--R 2 3 2 2 2 5 2 2 2 2 3 3
+--R ((15a d - 18a b c d + 3b c d)x + (15a c d - 18a b c d + 3b c )x )
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 2 2 2 4 2 2 2 2 2 +---+
+--R ((15a d - 18a b c d + 3b c )x + (10a c d - 12a b c )x - 2a c )\|c d
+--R /
+--R 3 5 4 3 +---+
+--R (6c d x + 6c x )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 706
+
+--S 707 of 1397
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (5a d - 6a b c d + b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 10a d + 12a b c d - 2b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4c \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 707
+
+--S 708 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 708
+
+--S 709 of 1397
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (5a d - 6a b c d + b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 5a d + 6a b c d - b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-+ +-+ +---+
+--R 2c \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 709
+
+--S 710 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 710
+
+--S 711 of 1397
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (5a d - 6a b c d + b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 10a d + 12a b c d - 2b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4c \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 711
+
+--S 712 of 1397
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 712
+
+--S 713 of 1397
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (5a d - 6a b c d + b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 5a d + 6a b c d - b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-+ +-+ +---+
+--R 2c \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 713
+
+--S 714 of 1397
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 714
+
+)clear all
+
+--S 715 of 1397
+t0:=x^4*(a+b*x^2)^2/(c+d*x^2)^3
+--R
+--R
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 715
+
+--S 716 of 1397
+r0:=-1/8*(35*b^2*c^2-30*a*b*c*d+3*a^2*d^2)*x/(c*d^4)+1/24*(35*b^2*c^2-_
+ 30*a*b*c*d+3*a^2*d^2)*x^3/(c^2*d^3)+1/4*(b*c-a*d)^2*x^5/_
+ (c*d^2*(c+d*x^2)^2)-1/8*(b*c-a*d)*(9*b*c-a*d)*x^5/(c^2*d^2*_
+ (c+d*x^2))+1/8*(35*b^2*c^2-30*a*b*c*d+3*a^2*d^2)*atan(x*_
+ sqrt(d)/sqrt(c))/(d^(9/2)*sqrt(c))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (9a d - 90a b c d + 105b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (18a c d - 180a b c d + 210b c d)x + 9a c d - 90a b c d + 105b c
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 7 3 2 2 5
+--R 8b d x + (48a b d - 56b c d )x
+--R +
+--R 2 3 2 2 2 3
+--R (- 15a d + 150a b c d - 175b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 9a c d + 90a b c d - 105b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 6 4 5 2 2 4 +-+ +-+
+--R (24d x + 48c d x + 24c d )\|c \|d
+--R Type: Expression(Integer)
+--E 716
+
+--S 717 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 4
+--R (9a d - 90a b c d + 105b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (18a c d - 180a b c d + 210b c d)x + 9a c d - 90a b c d + 105b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 7 3 2 2 5
+--R 16b d x + (96a b d - 112b c d )x
+--R +
+--R 2 3 2 2 2 3
+--R (- 30a d + 300a b c d - 350b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 18a c d + 180a b c d - 210b c )x
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 6 4 5 2 2 4 +-----+
+--R (48d x + 96c d x + 48c d )\|- c d
+--R ,
+--R
+--R 2 4 3 2 2 2 4
+--R (9a d - 90a b c d + 105b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (18a c d - 180a b c d + 210b c d)x + 9a c d - 90a b c d + 105b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 7 3 2 2 5
+--R 8b d x + (48a b d - 56b c d )x
+--R +
+--R 2 3 2 2 2 3
+--R (- 15a d + 150a b c d - 175b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 9a c d + 90a b c d - 105b c )x
+--R *
+--R +---+
+--R \|c d
+--R /
+--R 6 4 5 2 2 4 +---+
+--R (24d x + 48c d x + 24c d )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 717
+
+--S 718 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (3a d - 30a b c d + 35b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 6a d + 60a b c d - 70b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 4 +-----+ +-+ +-+
+--R 16d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 718
+
+--S 719 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 719
+
+--S 720 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (3a d - 30a b c d + 35b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 3a d + 30a b c d - 35b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 4 +-+ +-+ +---+
+--R 8d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 720
+
+--S 721 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 721
+
+)clear all
+
+--S 722 of 1397
+t0:=x^3*(a+b*x^2)^2/(c+d*x^2)^3
+--R
+--R
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 722
+
+--S 723 of 1397
+r0:=1/2*b^2*x^2/d^3+1/4*c*(b*c-a*d)^2/(d^4*(c+d*x^2)^2)-1/2*(b*c-a*d)*_
+ (3*b*c-a*d)/(d^4*(c+d*x^2))-1/2*b*(3*b*c-2*a*d)*log(c+d*x^2)/d^4
+--R
+--R
+--R (2)
+--R 3 2 2 4 2 2 2 2 2 2 3
+--R ((4a b d - 6b c d )x + (8a b c d - 12b c d)x + 4a b c d - 6b c )
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 2 3 6 2 2 4 2 3 2 2 2 2 2 2
+--R 2b d x + 4b c d x + (- 2a d + 8a b c d - 4b c d)x - a c d
+--R +
+--R 2 2 3
+--R 6a b c d - 5b c
+--R /
+--R 6 4 5 2 2 4
+--R 4d x + 8c d x + 4c d
+--R Type: Expression(Integer)
+--E 723
+
+--S 724 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2 4 2 2 2 2 2 2 3
+--R ((4a b d - 6b c d )x + (8a b c d - 12b c d)x + 4a b c d - 6b c )
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 2 3 6 2 2 4 2 3 2 2 2 2 2 2
+--R 2b d x + 4b c d x + (- 2a d + 8a b c d - 4b c d)x - a c d
+--R +
+--R 2 2 3
+--R 6a b c d - 5b c
+--R /
+--R 6 4 5 2 2 4
+--R 4d x + 8c d x + 4c d
+--R Type: Union(Expression(Integer),...)
+--E 724
+
+--S 725 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 725
+
+--S 726 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 726
+
+)clear all
+
+--S 727 of 1397
+t0:=x^2*(a+b*x^2)^2/(c+d*x^2)^3
+--R
+--R
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 727
+
+--S 728 of 1397
+r0:=-1/8*(6*a*b-15*b^2*c/d+a^2*d/c)*x/(c*d^2)+1/4*(b*c-a*d)^2*x^3/_
+ (c*d^2*(c+d*x^2)^2)-1/8*(b*c-a*d)*(7*b*c+a*d)*x^3/(c^2*d^2*(c+_
+ d*x^2))-1/8*(15*b^2*c^2-6*a*b*c*d-a^2*d^2)*atan(x*sqrt(d)/_
+ sqrt(c))/(c^(3/2)*d^(7/2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (a d + 6a b c d - 15b c d )x + (2a c d + 12a b c d - 30b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R a c d + 6a b c d - 15b c
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 5 2 3 2 2 2 3
+--R 8b c d x + (a d - 10a b c d + 25b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- a c d - 6a b c d + 15b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 5 4 2 4 2 3 3 +-+ +-+
+--R (8c d x + 16c d x + 8c d )\|c \|d
+--R Type: Expression(Integer)
+--E 728
+
+--S 729 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 4
+--R (a d + 6a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (2a c d + 12a b c d - 30b c d)x + a c d + 6a b c d - 15b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 2 5 2 3 2 2 2 3
+--R 16b c d x + (2a d - 20a b c d + 50b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 2a c d - 12a b c d + 30b c )x
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 5 4 2 4 2 3 3 +-----+
+--R (16c d x + 32c d x + 16c d )\|- c d
+--R ,
+--R
+--R 2 4 3 2 2 2 4
+--R (a d + 6a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (2a c d + 12a b c d - 30b c d)x + a c d + 6a b c d - 15b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 2 5 2 3 2 2 2 3
+--R 8b c d x + (a d - 10a b c d + 25b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- a c d - 6a b c d + 15b c )x
+--R *
+--R +---+
+--R \|c d
+--R /
+--R 5 4 2 4 2 3 3 +---+
+--R (8c d x + 16c d x + 8c d )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 729
+
+--S 730 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d + 6a b c d - 15b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 2a d - 12a b c d + 30b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-----+ +-+ +-+
+--R 16c d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 730
+
+--S 731 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 731
+
+--S 732 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (a d + 6a b c d - 15b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- a d - 6a b c d + 15b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-+ +-+ +---+
+--R 8c d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 732
+
+--S 733 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 733
+
+)clear all
+
+--S 734 of 1397
+t0:=x*(a+b*x^2)^2/(c+d*x^2)^3
+--R
+--R
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 734
+
+--S 735 of 1397
+r0:=-1/4*(b*c-a*d)^2/(d^3*(c+d*x^2)^2)+b*(b*c-a*d)/(d^3*(c+d*x^2))+_
+ 1/2*b^2*log(c+d*x^2)/d^3
+--R
+--R
+--R (2)
+--R 2 2 4 2 2 2 2 2 2 2 2
+--R (2b d x + 4b c d x + 2b c )log(d x + c) + (- 4a b d + 4b c d)x
+--R +
+--R 2 2 2 2
+--R - a d - 2a b c d + 3b c
+--R /
+--R 5 4 4 2 2 3
+--R 4d x + 8c d x + 4c d
+--R Type: Expression(Integer)
+--E 735
+
+--S 736 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 4 2 2 2 2 2 2 2 2
+--R (2b d x + 4b c d x + 2b c )log(d x + c) + (- 4a b d + 4b c d)x
+--R +
+--R 2 2 2 2
+--R - a d - 2a b c d + 3b c
+--R /
+--R 5 4 4 2 2 3
+--R 4d x + 8c d x + 4c d
+--R Type: Union(Expression(Integer),...)
+--E 736
+
+--S 737 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 737
+
+--S 738 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 738
+
+)clear all
+
+--S 739 of 1397
+t0:=(a+b*x^2)^2/(c+d*x^2)^3
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 739
+
+--S 740 of 1397
+r0:=-1/4*(b*c-a*d)*x*(a+b*x^2)/(c*d*(c+d*x^2)^2)+3/8*(a^2/c^2-b^2/d^2)*x/_
+ (c+d*x^2)+1/8*(3*b^2*c^2+2*a*b*c*d+3*a^2*d^2)*atan(x*sqrt(d)/_
+ sqrt(c))/(c^(5/2)*d^(5/2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 2a b c d + 3b c d )x + (6a c d + 4a b c d + 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 2a b c d + 3b c
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+ +-+
+--R ((3a d + 2a b c d - 5b c d)x + (5a c d - 2a b c d - 3b c )x)\|c \|d
+--R /
+--R 2 4 4 3 3 2 4 2 +-+ +-+
+--R (8c d x + 16c d x + 8c d )\|c \|d
+--R Type: Expression(Integer)
+--E 740
+
+--S 741 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 2a b c d + 3b c d )x + (6a c d + 4a b c d + 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 2a b c d + 3b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((6a d + 4a b c d - 10b c d)x + (10a c d - 4a b c d - 6b c )x)
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 2 4 4 3 3 2 4 2 +-----+
+--R (16c d x + 32c d x + 16c d )\|- c d
+--R ,
+--R
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 2a b c d + 3b c d )x + (6a c d + 4a b c d + 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 2a b c d + 3b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +---+
+--R ((3a d + 2a b c d - 5b c d)x + (5a c d - 2a b c d - 3b c )x)\|c d
+--R /
+--R 2 4 4 3 3 2 4 2 +---+
+--R (8c d x + 16c d x + 8c d )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 741
+
+--S 742 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (3a d + 2a b c d + 3b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 6a d - 4a b c d - 6b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 2 +-----+ +-+ +-+
+--R 16c d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 742
+
+--S 743 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 743
+
+--S 744 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (3a d + 2a b c d + 3b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 3a d - 2a b c d - 3b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 2 +-+ +-+ +---+
+--R 8c d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 744
+
+--S 745 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 745
+
+)clear all
+
+--S 746 of 1397
+t0:=(a+b*x^2)^2/(x*(c+d*x^2)^3)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ------------------------------
+--R 3 7 2 5 2 3 3
+--R d x + 3c d x + 3c d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 746
+
+--S 747 of 1397
+r0:=1/4*(b*c-a*d)^2/(c*d^2*(c+d*x^2)^2)+1/2*(a^2/c^2-b^2/d^2)/_
+ (c+d*x^2)+a^2*log(x)/c^3-1/2*a^2*log(c+d*x^2)/c^3
+--R
+--R
+--R (2)
+--R 2 4 4 2 3 2 2 2 2 2
+--R (- 2a d x - 4a c d x - 2a c d )log(d x + c)
+--R +
+--R 2 4 4 2 3 2 2 2 2 2 3 2 3 2 2 2 2
+--R (4a d x + 8a c d x + 4a c d )log(x) + (2a c d - 2b c d)x + 3a c d
+--R +
+--R 3 2 4
+--R - 2a b c d - b c
+--R /
+--R 3 4 4 4 3 2 5 2
+--R 4c d x + 8c d x + 4c d
+--R Type: Expression(Integer)
+--E 747
+
+--S 748 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 4 2 3 2 2 2 2 2
+--R (- 2a d x - 4a c d x - 2a c d )log(d x + c)
+--R +
+--R 2 4 4 2 3 2 2 2 2 2 3 2 3 2 2 2 2
+--R (4a d x + 8a c d x + 4a c d )log(x) + (2a c d - 2b c d)x + 3a c d
+--R +
+--R 3 2 4
+--R - 2a b c d - b c
+--R /
+--R 3 4 4 4 3 2 5 2
+--R 4c d x + 8c d x + 4c d
+--R Type: Union(Expression(Integer),...)
+--E 748
+
+--S 749 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 749
+
+--S 750 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 750
+
+)clear all
+
+--S 751 of 1397
+t0:=(a+b*x^2)^2/(x^2*(c+d*x^2)^3)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------------------
+--R 3 8 2 6 2 4 3 2
+--R d x + 3c d x + 3c d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 751
+
+--S 752 of 1397
+r0:=-a^2/(c*x*(c+d*x^2)^2)+1/4*(2*a*b-b^2*c/d-5*a^2*d/c)*x/(c*(c+_
+ d*x^2)^2)+1/8*(b^2*c^2+3*a*d*(2*b*c-5*a*d))*x/(c^3*d*(c+d*x^2))+_
+ 1/8*(b^2*c^2+3*a*d*(2*b*c-5*a*d))*atan(x*sqrt(d)/sqrt(c))/_
+ (c^(7/2)*d^(3/2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 5
+--R (- 15a d + 6a b c d + b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4
+--R (- 30a c d + 12a b c d + 2b c d)x + (- 15a c d + 6a b c d + b c )x
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 4 2 2 2 2 3 2
+--R (- 15a d + 6a b c d + b c d)x + (- 25a c d + 10a b c d - b c )x
+--R +
+--R 2 2
+--R - 8a c d
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 3 3 5 4 2 3 5 +-+ +-+
+--R (8c d x + 16c d x + 8c d x)\|c \|d
+--R Type: Expression(Integer)
+--E 752
+
+--S 753 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 5
+--R (15a d - 6a b c d - b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4
+--R (30a c d - 12a b c d - 2b c d)x + (15a c d - 6a b c d - b c )x
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d - 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 2 2 4
+--R (- 30a d + 12a b c d + 2b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2
+--R (- 50a c d + 20a b c d - 2b c )x - 16a c d
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 3 3 5 4 2 3 5 +-----+
+--R (16c d x + 32c d x + 16c d x)\|- c d
+--R ,
+--R
+--R 2 4 3 2 2 2 5
+--R (- 15a d + 6a b c d + b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (- 30a c d + 12a b c d + 2b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (- 15a c d + 6a b c d + b c )x
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 2 2 2 4
+--R (- 15a d + 6a b c d + b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2
+--R (- 25a c d + 10a b c d - b c )x - 8a c d
+--R *
+--R +---+
+--R \|c d
+--R /
+--R 3 3 5 4 2 3 5 +---+
+--R (8c d x + 16c d x + 8c d x)\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 753
+
+--S 754 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d - 2c d x
+--R (15a d - 6a b c d - b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (30a d - 12a b c d - 2b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-----+ +-+ +-+
+--R 16c d\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 754
+
+--S 755 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 755
+
+--S 756 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (- 15a d + 6a b c d + b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (15a d - 6a b c d - b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-+ +-+ +---+
+--R 8c d\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 756
+
+--S 757 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 757
+
+)clear all
+
+--S 758 of 1397
+t0:=(a+b*x^2)^2/(x^3*(c+d*x^2)^3)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------------------
+--R 3 9 2 7 2 5 3 3
+--R d x + 3c d x + 3c d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 758
+
+--S 759 of 1397
+r0:=-1/2*a^2/(c^3*x^2)-1/4*(b*c-a*d)^2/(c^2*d*(c+d*x^2)^2)+a*(b*c-a*d)/_
+ (c^3*(c+d*x^2))+a*(2*b*c-3*a*d)*log(x)/c^4-1/2*a*(2*b*c-3*a*d)*_
+ log(c+d*x^2)/c^4
+--R
+--R
+--R (2)
+--R 2 4 3 6 2 3 2 2 4
+--R (6a d - 4a b c d )x + (12a c d - 8a b c d )x
+--R +
+--R 2 2 2 3 2
+--R (6a c d - 4a b c d)x
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 2 4 3 6 2 3 2 2 4
+--R (- 12a d + 8a b c d )x + (- 24a c d + 16a b c d )x
+--R +
+--R 2 2 2 3 2
+--R (- 12a c d + 8a b c d)x
+--R *
+--R log(x)
+--R +
+--R 2 3 2 2 4 2 2 2 3 2 4 2 2 3
+--R (- 6a c d + 4a b c d )x + (- 9a c d + 6a b c d - b c )x - 2a c d
+--R /
+--R 4 3 6 5 2 4 6 2
+--R 4c d x + 8c d x + 4c d x
+--R Type: Expression(Integer)
+--E 759
+
+--S 760 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 6 2 3 2 2 4
+--R (6a d - 4a b c d )x + (12a c d - 8a b c d )x
+--R +
+--R 2 2 2 3 2
+--R (6a c d - 4a b c d)x
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 2 4 3 6 2 3 2 2 4
+--R (- 12a d + 8a b c d )x + (- 24a c d + 16a b c d )x
+--R +
+--R 2 2 2 3 2
+--R (- 12a c d + 8a b c d)x
+--R *
+--R log(x)
+--R +
+--R 2 3 2 2 4 2 2 2 3 2 4 2 2 3
+--R (- 6a c d + 4a b c d )x + (- 9a c d + 6a b c d - b c )x - 2a c d
+--R /
+--R 4 3 6 5 2 4 6 2
+--R 4c d x + 8c d x + 4c d x
+--R Type: Union(Expression(Integer),...)
+--E 760
+
+--S 761 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 761
+
+--S 762 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 762
+
+)clear all
+
+--S 763 of 1397
+t0:=(a+b*x^2)^2/(x^4*(c+d*x^2)^3)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) --------------------------------
+--R 3 10 2 8 2 6 3 4
+--R d x + 3c d x + 3c d x + c x
+--R Type: Fraction(Polynomial(Integer))
+--E 763
+
+--S 764 of 1397
+r0:=1/8*(3*b^2*c^2-5*a*d*(6*b*c-7*a*d))/(c^4*d*x)-1/3*a^2/(c*x^3*_
+ (c+d*x^2)^2)+1/12*(-3*b^2*c^2+6*a*b*c*d-7*a^2*d^2)/(c^2*d*x*_
+ (c+d*x^2)^2)+1/24*(-3*b^2*c^2+5*a*d*(6*b*c-7*a*d))/(c^3*d*x*_
+ (c+d*x^2))+1/8*(3*b^2*c^2-5*a*d*(6*b*c-7*a*d))*atan(x*sqrt(d)/_
+ sqrt(c))/(c^(9/2)*sqrt(d))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 7
+--R (105a d - 90a b c d + 9b c d )x
+--R +
+--R 2 3 2 2 2 3 5
+--R (210a c d - 180a b c d + 18b c d)x
+--R +
+--R 2 2 2 3 2 4 3
+--R (105a c d - 90a b c d + 9b c )x
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 6
+--R (105a d - 90a b c d + 9b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (175a c d - 150a b c d + 15b c )x + (56a c d - 48a b c )x - 8a c
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 4 2 7 5 5 6 3 +-+ +-+
+--R (24c d x + 48c d x + 24c x )\|c \|d
+--R Type: Expression(Integer)
+--E 764
+
+--S 765 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 7
+--R (105a d - 90a b c d + 9b c d )x
+--R +
+--R 2 3 2 2 2 3 5
+--R (210a c d - 180a b c d + 18b c d)x
+--R +
+--R 2 2 2 3 2 4 3
+--R (105a c d - 90a b c d + 9b c )x
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 2 2 6
+--R (210a d - 180a b c d + 18b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (350a c d - 300a b c d + 30b c )x + (112a c d - 96a b c )x
+--R +
+--R 2 3
+--R - 16a c
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 4 2 7 5 5 6 3 +-----+
+--R (48c d x + 96c d x + 48c x )\|- c d
+--R ,
+--R
+--R 2 4 3 2 2 2 7
+--R (105a d - 90a b c d + 9b c d )x
+--R +
+--R 2 3 2 2 2 3 5
+--R (210a c d - 180a b c d + 18b c d)x
+--R +
+--R 2 2 2 3 2 4 3
+--R (105a c d - 90a b c d + 9b c )x
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 2 2 2 6
+--R (105a d - 90a b c d + 9b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (175a c d - 150a b c d + 15b c )x + (56a c d - 48a b c )x - 8a c
+--R *
+--R +---+
+--R \|c d
+--R /
+--R 4 2 7 5 5 6 3 +---+
+--R (24c d x + 48c d x + 24c x )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 765
+
+--S 766 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (35a d - 30a b c d + 3b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 70a d + 60a b c d - 6b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 4 +-----+ +-+ +-+
+--R 16c \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 766
+
+--S 767 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 767
+
+--S 768 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (35a d - 30a b c d + 3b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 35a d + 30a b c d - 3b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 4 +-+ +-+ +---+
+--R 8c \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 768
+
+--S 769 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 769
+
+)clear all
+
+--S 770 of 1397
+t0:=x^4*(a+b*x^2)^2*sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 8 6 2 4 | 2
+--R (1) (b x + 2a b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 770
+
+--S 771 of 1397
+r0:=-1/80*b*(7*b*c-20*a*d)*x^5*(c+d*x^2)^(3/2)/d^2+1/10*b^2*x^7*_
+ (c+d*x^2)^(3/2)/d+1/256*c^3*(16*a^2*d^2+b*c*(7*b*c-20*a*d))*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))/d^(9/2)-1/256*c^2*(16*a^2*d^2+_
+ b*c*(7*b*c-20*a*d))*x*sqrt(c+d*x^2)/d^4+1/384*c*(16*a^2*d^2+_
+ b*c*(7*b*c-20*a*d))*x^3*sqrt(c+d*x^2)/d^3+1/96*(16*a^2*d^2+_
+ b*c*(7*b*c-20*a*d))*x^5*sqrt(c+d*x^2)/d^2
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 2 4 2 5 x\|d
+--R (240a c d - 300a b c d + 105b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 9 4 2 3 7
+--R 384b d x + (960a b d + 48b c d )x
+--R +
+--R 2 4 3 2 2 2 5
+--R (640a d + 160a b c d - 56b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (160a c d - 200a b c d + 70b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (- 240a c d + 300a b c d - 105b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R 4 +-+
+--R 3840d \|d
+--R Type: Expression(Integer)
+--E 771
+
+--S 772 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 6 4 5 2 5 4 8
+--R (2400a c d - 3000a b c d + 1050b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 6
+--R (38400a c d - 48000a b c d + 16800b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 4
+--R (161280a c d - 201600a b c d + 70560b c d )x
+--R +
+--R 2 6 3 7 2 2 8 2 2 7 2
+--R (245760a c d - 307200a b c d + 107520b c d)x + 122880a c d
+--R +
+--R 8 2 9
+--R - 153600a b c d + 53760b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 3 7 4 6 2 5 5 10
+--R (- 240a c d + 300a b c d - 105b c d )x
+--R +
+--R 2 4 6 5 5 2 6 4 8
+--R (- 12000a c d + 15000a b c d - 5250b c d )x
+--R +
+--R 2 5 5 6 4 2 7 3 6
+--R (- 96000a c d + 120000a b c d - 42000b c d )x
+--R +
+--R 2 6 4 7 3 2 8 2 4
+--R (- 268800a c d + 336000a b c d - 117600b c d )x
+--R +
+--R 2 7 3 8 2 2 9 2 2 8 2
+--R (- 307200a c d + 384000a b c d - 134400b c d)x - 122880a c d
+--R +
+--R 9 2 10
+--R 153600a b c d - 53760b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 9 19 9 2 8 17
+--R - 384b d x + (- 960a b d - 19248b c d )x
+--R +
+--R 2 9 8 2 2 7 15
+--R (- 640a d - 48160a b c d - 155944b c d )x
+--R +
+--R 2 8 2 7 2 3 6 13
+--R (- 32160a c d - 391800a b c d - 446550b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 11
+--R (- 263760a c d - 1129500a b c d - 526275b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 9
+--R (- 768800a c d - 1343000a b c d - 218078b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 7
+--R (- 902400a c d - 592320a b c d + 10704b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 5
+--R (- 263680a c d - 161920a b c d + 56672b c d )x
+--R +
+--R 2 6 3 7 2 2 8 3
+--R (225280a c d - 281600a b c d + 98560b c d)x
+--R +
+--R 2 7 2 8 2 9
+--R (122880a c d - 153600a b c d + 53760b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 9 19 9 2 8 17
+--R 3840b d x + (9600a b d + 65760b c d )x
+--R +
+--R 2 9 8 2 2 7 15
+--R (6400a d + 164800a b c d + 327088b c d )x
+--R +
+--R 2 8 2 7 2 3 6 13
+--R (110400a c d + 823920a b c d + 682380b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 11
+--R (557280a c d + 1730280a b c d + 635490b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 9
+--R (1177760a c d + 1630520a b c d + 215750b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 7
+--R (1054720a c d + 647680a b c d - 30080b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 5
+--R (166400a c d + 283520a b c d - 99232b c d )x
+--R +
+--R 2 6 3 7 2 2 8 3
+--R (- 286720a c d + 358400a b c d - 125440b c d)x
+--R +
+--R 2 7 2 8 2 9
+--R (- 122880a c d + 153600a b c d - 53760b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 8 8 7 6 2 6 4 3 5 2
+--R 38400d x + 614400c d x + 2580480c d x + 3932160c d x
+--R +
+--R 4 4
+--R 1966080c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 9 10 8 8 2 7 6 3 6 4
+--R - 3840d x - 192000c d x - 1536000c d x - 4300800c d x
+--R +
+--R 4 5 2 5 4
+--R - 4915200c d x - 1966080c d
+--R *
+--R +-+
+--R \|d
+--R ,
+--R
+--R 2 3 6 4 5 2 5 4 8
+--R (4800a c d - 6000a b c d + 2100b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 6
+--R (76800a c d - 96000a b c d + 33600b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 4
+--R (322560a c d - 403200a b c d + 141120b c d )x
+--R +
+--R 2 6 3 7 2 2 8 2 2 7 2
+--R (491520a c d - 614400a b c d + 215040b c d)x + 245760a c d
+--R +
+--R 8 2 9
+--R - 307200a b c d + 107520b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 3 7 4 6 2 5 5 10
+--R (- 480a c d + 600a b c d - 210b c d )x
+--R +
+--R 2 4 6 5 5 2 6 4 8
+--R (- 24000a c d + 30000a b c d - 10500b c d )x
+--R +
+--R 2 5 5 6 4 2 7 3 6
+--R (- 192000a c d + 240000a b c d - 84000b c d )x
+--R +
+--R 2 6 4 7 3 2 8 2 4
+--R (- 537600a c d + 672000a b c d - 235200b c d )x
+--R +
+--R 2 7 3 8 2 2 9 2 2 8 2
+--R (- 614400a c d + 768000a b c d - 268800b c d)x - 245760a c d
+--R +
+--R 9 2 10
+--R 307200a b c d - 107520b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 9 19 9 2 8 17
+--R - 384b d x + (- 960a b d - 19248b c d )x
+--R +
+--R 2 9 8 2 2 7 15
+--R (- 640a d - 48160a b c d - 155944b c d )x
+--R +
+--R 2 8 2 7 2 3 6 13
+--R (- 32160a c d - 391800a b c d - 446550b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 11
+--R (- 263760a c d - 1129500a b c d - 526275b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 9
+--R (- 768800a c d - 1343000a b c d - 218078b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 7
+--R (- 902400a c d - 592320a b c d + 10704b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 5
+--R (- 263680a c d - 161920a b c d + 56672b c d )x
+--R +
+--R 2 6 3 7 2 2 8 3
+--R (225280a c d - 281600a b c d + 98560b c d)x
+--R +
+--R 2 7 2 8 2 9
+--R (122880a c d - 153600a b c d + 53760b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 9 19 9 2 8 17
+--R 3840b d x + (9600a b d + 65760b c d )x
+--R +
+--R 2 9 8 2 2 7 15
+--R (6400a d + 164800a b c d + 327088b c d )x
+--R +
+--R 2 8 2 7 2 3 6 13
+--R (110400a c d + 823920a b c d + 682380b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 11
+--R (557280a c d + 1730280a b c d + 635490b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 9
+--R (1177760a c d + 1630520a b c d + 215750b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 7
+--R (1054720a c d + 647680a b c d - 30080b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 5
+--R (166400a c d + 283520a b c d - 99232b c d )x
+--R +
+--R 2 6 3 7 2 2 8 3
+--R (- 286720a c d + 358400a b c d - 125440b c d)x
+--R +
+--R 2 7 2 8 2 9
+--R (- 122880a c d + 153600a b c d - 53760b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R 8 8 7 6 2 6 4 3 5 2
+--R 38400d x + 614400c d x + 2580480c d x + 3932160c d x
+--R +
+--R 4 4
+--R 1966080c d
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 9 10 8 8 2 7 6 3 6 4
+--R - 3840d x - 192000c d x - 1536000c d x - 4300800c d x
+--R +
+--R 4 5 2 5 4
+--R - 4915200c d x - 1966080c d
+--R *
+--R +---+
+--R \|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 772
+
+--S 773 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 2 4 2 5
+--R (16a c d - 20a b c d + 7b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 3 2 4 2 5 x\|d
+--R (- 16a c d + 20a b c d - 7b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4 +-+
+--R 256d \|d
+--R Type: Expression(Integer)
+--E 773
+
+--S 774 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 774
+
+--S 775 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 3 2 4 2 5 +---+ x\|d
+--R (- 16a c d + 20a b c d - 7b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 3 2 4 2 5 +-+ \|- d \|d x + c - \|- d \|c
+--R (32a c d - 40a b c d + 14b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 4 +---+ +-+
+--R 256d \|- d \|d
+--R Type: Expression(Integer)
+--E 775
+
+--S 776 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 776
+
+)clear all
+
+--S 777 of 1397
+t0:=x^3*(a+b*x^2)^2*sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (1) (b x + 2a b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 777
+
+--S 778 of 1397
+r0:=-1/3*c*(b*c-a*d)^2*(c+d*x^2)^(3/2)/d^4+1/5*(b*c-a*d)*(3*b*c-a*d)*_
+ (c+d*x^2)^(5/2)/d^4-1/7*b*(3*b*c-2*a*d)*(c+d*x^2)^(7/2)/d^4+_
+ 1/9*b^2*(c+d*x^2)^(9/2)/d^4
+--R
+--R
+--R (2)
+--R 2 4 8 4 2 3 6 2 4 3 2 2 2 4
+--R 35b d x + (90a b d + 5b c d )x + (63a d + 18a b c d - 6b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (21a c d - 24a b c d + 8b c d)x - 42a c d + 48a b c d - 16b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4
+--R 315d
+--R Type: Expression(Integer)
+--E 778
+
+--S 779 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 16 4 2 2 3 14
+--R - 315b c d x + (- 810a b c d - 4245b c d )x
+--R +
+--R 2 4 2 3 2 3 2 12
+--R (- 567a c d - 10962a b c d - 15666b c d )x
+--R +
+--R 2 2 3 3 2 2 4 10
+--R (- 7749a c d - 40824a b c d - 21672b c d)x
+--R +
+--R 2 3 2 4 2 5 8
+--R (- 29400a c d - 57120a b c d - 10080b c )x
+--R +
+--R 2 4 5 6 2 5 4
+--R (- 42000a c d - 26880a b c )x - 20160a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 18 5 2 4 16
+--R 35b d x + (90a b d + 1440b c d )x
+--R +
+--R 2 5 4 2 2 3 14
+--R (63a d + 3708a b c d + 9999b c d )x
+--R +
+--R 2 4 2 3 2 3 2 12
+--R (2604a c d + 25914a b c d + 25242b c d )x
+--R +
+--R 2 2 3 3 2 2 4 10
+--R (18459a c d + 66024a b c d + 26712b c d)x
+--R +
+--R 2 3 2 4 2 5 8
+--R (47880a c d + 70560a b c d + 10080b c )x
+--R +
+--R 2 4 5 6 2 5 4
+--R (52080a c d + 26880a b c )x + 20160a c x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (315d x + 12600c d x + 75600c d x + 141120c d x + 80640c )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 2835c d x - 37800c d x - 136080c d x - 181440c d x - 80640c
+--R Type: Union(Expression(Integer),...)
+--E 779
+
+--S 780 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 6 4 5 2 5 4 8
+--R (- 42a c d + 48a b c d - 16b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 6
+--R (- 1680a c d + 1920a b c d - 640b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 4
+--R (- 10080a c d + 11520a b c d - 3840b c d )x
+--R +
+--R 2 6 3 7 2 2 8 2 2 7 2
+--R (- 18816a c d + 21504a b c d - 7168b c d)x - 10752a c d
+--R +
+--R 8 2 9
+--R 12288a b c d - 4096b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 6 4 5 2 5 4 8
+--R (378a c d - 432a b c d + 144b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 6
+--R (5040a c d - 5760a b c d + 1920b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 4
+--R (18144a c d - 20736a b c d + 6912b c d )x
+--R +
+--R 2 6 3 7 2 2 8 2 2 7 2
+--R (24192a c d - 27648a b c d + 9216b c d)x + 10752a c d
+--R +
+--R 8 2 9
+--R - 12288a b c d + 4096b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 8 8 7 6 2 6 4 3 5 2 4 4 +-+
+--R (315d x + 12600c d x + 75600c d x + 141120c d x + 80640c d )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 8 8 2 7 6 3 6 4 4 5 2 5 4
+--R - 2835c d x - 37800c d x - 136080c d x - 181440c d x - 80640c d
+--R Type: Expression(Integer)
+--E 780
+
+--S 781 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 781
+
+)clear all
+
+--S 782 of 1397
+t0:=x^2*(a+b*x^2)^2*sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 6 4 2 2 | 2
+--R (1) (b x + 2a b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 782
+
+--S 783 of 1397
+r0:=-1/48*b*(5*b*c-16*a*d)*x^3*(c+d*x^2)^(3/2)/d^2+1/8*b^2*x^5*_
+ (c+d*x^2)^(3/2)/d-1/128*c^2*(16*a^2*d^2+b*c*(5*b*c-16*a*d))*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))/d^(7/2)+1/128*c*(16*a^2*d^2+b*_
+ c*(5*b*c-16*a*d))*x*sqrt(c+d*x^2)/d^3+1/64*(16*a^2*d^2+_
+ b*c*(5*b*c-16*a*d))*x^3*sqrt(c+d*x^2)/d^2
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 3 2 4 x\|d
+--R (- 48a c d + 48a b c d - 15b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 7 3 2 2 5
+--R 48b d x + (128a b d + 8b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (96a d + 32a b c d - 10b c d)x + (48a c d - 48a b c d + 15b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R 3 +-+
+--R 384d \|d
+--R Type: Expression(Integer)
+--E 783
+
+--S 784 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 5 3 4 2 4 3 6
+--R (384a c d - 384a b c d + 120b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (3840a c d - 3840a b c d + 1200b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (9216a c d - 9216a b c d + 2880b c d)x + 6144a c d
+--R +
+--R 6 2 7
+--R - 6144a b c d + 1920b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 2 6 3 5 2 4 4 8
+--R (- 48a c d + 48a b c d - 15b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 6
+--R (- 1536a c d + 1536a b c d - 480b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 4
+--R (- 7680a c d + 7680a b c d - 2400b c d )x
+--R +
+--R 2 5 3 6 2 2 7 2 2 6 2
+--R (- 12288a c d + 12288a b c d - 3840b c d)x - 6144a c d
+--R +
+--R 7 2 8
+--R 6144a b c d - 1920b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 7 15 7 2 6 13
+--R - 48b d x + (- 128a b d - 1544b c d )x
+--R +
+--R 2 7 6 2 2 5 11
+--R (- 96a d - 4128a b c d - 7926b c d )x
+--R +
+--R 2 6 2 5 2 3 4 9
+--R (- 3120a c d - 21456a b c d - 13263b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 7
+--R (- 16896a c d - 36352a b c d - 7072b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 5
+--R (- 32256a c d - 16896a b c d - 864b c d )x
+--R +
+--R 2 4 3 5 2 2 6 3
+--R (- 24576a c d + 8192a b c d - 2560b c d)x
+--R +
+--R 2 5 2 6 2 7
+--R (- 6144a c d + 6144a b c d - 1920b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 7 15 7 2 6 13
+--R 384b d x + (1024a b d + 4288b c d )x
+--R +
+--R 2 7 6 2 2 5 11
+--R (768a d + 11520a b c d + 13680b c d )x
+--R +
+--R 2 6 2 5 2 3 4 9
+--R (8832a c d + 37248a b c d + 16776b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 7
+--R (30336a c d + 45440a b c d + 7304b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 5
+--R (43776a c d + 13568a b c d + 1904b c d )x
+--R +
+--R 2 4 3 5 2 2 6 3
+--R (27648a c d - 11264a b c d + 3520b c d)x
+--R +
+--R 2 5 2 6 2 7
+--R (6144a c d - 6144a b c d + 1920b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +-+ +-+ | 2
+--R (3072d x + 30720c d x + 73728c d x + 49152c d )\|c \|d \|d x + c
+--R +
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +-+
+--R (- 384d x - 12288c d x - 61440c d x - 98304c d x - 49152c d )\|d
+--R ,
+--R
+--R 2 2 5 3 4 2 4 3 6
+--R (- 768a c d + 768a b c d - 240b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (- 7680a c d + 7680a b c d - 2400b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (- 18432a c d + 18432a b c d - 5760b c d)x - 12288a c d
+--R +
+--R 6 2 7
+--R 12288a b c d - 3840b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 2 6 3 5 2 4 4 8
+--R (96a c d - 96a b c d + 30b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 6
+--R (3072a c d - 3072a b c d + 960b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 4
+--R (15360a c d - 15360a b c d + 4800b c d )x
+--R +
+--R 2 5 3 6 2 2 7 2 2 6 2
+--R (24576a c d - 24576a b c d + 7680b c d)x + 12288a c d
+--R +
+--R 7 2 8
+--R - 12288a b c d + 3840b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 7 15 7 2 6 13
+--R - 48b d x + (- 128a b d - 1544b c d )x
+--R +
+--R 2 7 6 2 2 5 11
+--R (- 96a d - 4128a b c d - 7926b c d )x
+--R +
+--R 2 6 2 5 2 3 4 9
+--R (- 3120a c d - 21456a b c d - 13263b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 7
+--R (- 16896a c d - 36352a b c d - 7072b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 5
+--R (- 32256a c d - 16896a b c d - 864b c d )x
+--R +
+--R 2 4 3 5 2 2 6 3
+--R (- 24576a c d + 8192a b c d - 2560b c d)x
+--R +
+--R 2 5 2 6 2 7
+--R (- 6144a c d + 6144a b c d - 1920b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 7 15 7 2 6 13
+--R 384b d x + (1024a b d + 4288b c d )x
+--R +
+--R 2 7 6 2 2 5 11
+--R (768a d + 11520a b c d + 13680b c d )x
+--R +
+--R 2 6 2 5 2 3 4 9
+--R (8832a c d + 37248a b c d + 16776b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 7
+--R (30336a c d + 45440a b c d + 7304b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 5
+--R (43776a c d + 13568a b c d + 1904b c d )x
+--R +
+--R 2 4 3 5 2 2 6 3
+--R (27648a c d - 11264a b c d + 3520b c d)x
+--R +
+--R 2 5 2 6 2 7
+--R (6144a c d - 6144a b c d + 1920b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +---+ +-+ | 2
+--R (3072d x + 30720c d x + 73728c d x + 49152c d )\|- d \|c \|d x + c
+--R +
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +---+
+--R (- 384d x - 12288c d x - 61440c d x - 98304c d x - 49152c d )\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 784
+
+--S 785 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 3 2 4
+--R (16a c d - 16a b c d + 5b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 3 2 4 x\|d
+--R (16a c d - 16a b c d + 5b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 +-+
+--R 128d \|d
+--R Type: Expression(Integer)
+--E 785
+
+--S 786 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 786
+
+--S 787 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 3 2 4 +---+ x\|d
+--R (16a c d - 16a b c d + 5b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 3 2 4 +-+ \|- d \|d x + c - \|- d \|c
+--R (- 32a c d + 32a b c d - 10b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 3 +---+ +-+
+--R 128d \|- d \|d
+--R Type: Expression(Integer)
+--E 787
+
+--S 788 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 788
+
+)clear all
+
+--S 789 of 1397
+t0:=x*(a+b*x^2)^2*sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 5 3 2 | 2
+--R (1) (b x + 2a b x + a x)\|d x + c
+--R Type: Expression(Integer)
+--E 789
+
+--S 790 of 1397
+r0:=1/3*(b*c-a*d)^2*(c+d*x^2)^(3/2)/d^3-2/5*b*(b*c-a*d)*_
+ (c+d*x^2)^(5/2)/d^3+1/7*b^2*(c+d*x^2)^(7/2)/d^3
+--R
+--R
+--R (2)
+--R 2 3 6 3 2 2 4 2 3 2 2 2 2
+--R 15b d x + (42a b d + 3b c d )x + (35a d + 14a b c d - 4b c d)x
+--R +
+--R 2 2 2 2 3
+--R 35a c d - 28a b c d + 8b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3
+--R 105d
+--R Type: Expression(Integer)
+--E 790
+
+--S 791 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 12 3 2 2 2 10
+--R - 105b c d x + (- 294a b c d - 861b c d )x
+--R +
+--R 2 3 2 2 2 3 8
+--R (- 245a c d - 2450a b c d - 1820b c d)x
+--R +
+--R 2 2 2 3 2 4 6
+--R (- 2170a c d - 5320a b c d - 1120b c )x
+--R +
+--R 2 3 4 4 2 4 2
+--R (- 5040a c d - 3360a b c )x - 3360a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 14 4 2 3 12
+--R 15b d x + (42a b d + 378b c d )x
+--R +
+--R 2 4 3 2 2 2 10
+--R (35a d + 1064a b c d + 1631b c d )x
+--R +
+--R 2 3 2 2 2 3 8
+--R (910a c d + 4690a b c d + 2380b c d)x
+--R +
+--R 2 2 2 3 2 4 6 2 3 4 4
+--R (4270a c d + 7000a b c d + 1120b c )x + (6720a c d + 3360a b c )x
+--R +
+--R 2 4 2
+--R 3360a c x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (105d x + 2520c d x + 8400c d x + 6720c )\|c \|d x + c - 735c d x
+--R +
+--R 2 2 4 3 2 4
+--R - 5880c d x - 11760c d x - 6720c
+--R Type: Union(Expression(Integer),...)
+--E 791
+
+--S 792 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 5 3 4 2 4 3 6
+--R (35a c d - 28a b c d + 8b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (840a c d - 672a b c d + 192b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2 6
+--R (2800a c d - 2240a b c d + 640b c d)x + 2240a c d - 1792a b c d
+--R +
+--R 2 7
+--R 512b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (- 245a c d + 196a b c d - 56b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (- 1960a c d + 1568a b c d - 448b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2 6
+--R (- 3920a c d + 3136a b c d - 896b c d)x - 2240a c d + 1792a b c d
+--R +
+--R 2 7
+--R - 512b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +-+ | 2 6 6
+--R (105d x + 2520c d x + 8400c d x + 6720c d )\|c \|d x + c - 735c d x
+--R +
+--R 2 5 4 3 4 2 4 3
+--R - 5880c d x - 11760c d x - 6720c d
+--R Type: Expression(Integer)
+--E 792
+
+--S 793 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 793
+
+)clear all
+
+--S 794 of 1397
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (1) (b x + 2a b x + a )\|d x + c
+--R Type: Expression(Integer)
+--E 794
+
+--S 795 of 1397
+r0:=-1/24*b*(3*b*c-8*a*d)*x*(c+d*x^2)^(3/2)/d^2+1/6*b*x*(a+b*x^2)*_
+ (c+d*x^2)^(3/2)/d+1/16*c*(b^2*c^2-4*a*b*c*d+8*a^2*d^2)*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))/d^(5/2)+1/16*(b^2*c^2-_
+ 4*a*b*c*d+8*a^2*d^2)*x*sqrt(c+d*x^2)/d^2
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 3 x\|d
+--R (24a c d - 12a b c d + 3b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 5 2 2 3 2 2 2 2 +-+
+--R (8b d x + (24a b d + 2b c d)x + (24a d + 12a b c d - 3b c )x)\|d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2 +-+
+--R 48d \|d
+--R Type: Expression(Integer)
+--E 795
+
+--S 796 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 2 3 2 3 2 4
+--R (144a c d - 72a b c d + 18b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (768a c d - 384a b c d + 96b c d)x + 768a c d - 384a b c d
+--R +
+--R 2 5
+--R 96b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 24a c d + 12a b c d - 3b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 432a c d + 216a b c d - 54b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5
+--R (- 1152a c d + 576a b c d - 144b c d)x - 768a c d + 384a b c d
+--R +
+--R 2 6
+--R - 96b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 5 11 5 2 4 9
+--R - 8b d x + (- 24a b d - 146b c d )x
+--R +
+--R 2 5 4 2 2 3 7
+--R (- 24a d - 444a b c d - 417b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (- 432a c d - 1368a b c d - 298b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3
+--R (- 1152a c d - 1344a b c d + 80b c d)x
+--R +
+--R 2 3 2 4 2 5
+--R (- 768a c d - 384a b c d + 96b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 5 11 5 2 4 9
+--R 48b d x + (144a b d + 316b c d )x
+--R +
+--R 2 5 4 2 2 3 7
+--R (144a d + 984a b c d + 570b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (912a c d + 1992a b c d + 270b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3
+--R (1536a c d + 1536a b c d - 128b c d)x
+--R +
+--R 2 3 2 4 2 5
+--R (768a c d + 384a b c d - 96b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +-+ +-+ | 2
+--R (288d x + 1536c d x + 1536c d )\|c \|d \|d x + c
+--R +
+--R 5 6 4 4 2 3 2 3 2 +-+
+--R (- 48d x - 864c d x - 2304c d x - 1536c d )\|d
+--R ,
+--R
+--R 2 4 2 3 2 3 2 4
+--R (288a c d - 144a b c d + 36b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (1536a c d - 768a b c d + 192b c d)x + 1536a c d
+--R +
+--R 4 2 5
+--R - 768a b c d + 192b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 48a c d + 24a b c d - 6b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 864a c d + 432a b c d - 108b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (- 2304a c d + 1152a b c d - 288b c d)x - 1536a c d
+--R +
+--R 5 2 6
+--R 768a b c d - 192b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 5 11 5 2 4 9
+--R - 8b d x + (- 24a b d - 146b c d )x
+--R +
+--R 2 5 4 2 2 3 7
+--R (- 24a d - 444a b c d - 417b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (- 432a c d - 1368a b c d - 298b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3
+--R (- 1152a c d - 1344a b c d + 80b c d)x
+--R +
+--R 2 3 2 4 2 5
+--R (- 768a c d - 384a b c d + 96b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 5 11 5 2 4 9
+--R 48b d x + (144a b d + 316b c d )x
+--R +
+--R 2 5 4 2 2 3 7
+--R (144a d + 984a b c d + 570b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (912a c d + 1992a b c d + 270b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3
+--R (1536a c d + 1536a b c d - 128b c d)x
+--R +
+--R 2 3 2 4 2 5
+--R (768a c d + 384a b c d - 96b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +---+ +-+ | 2
+--R (288d x + 1536c d x + 1536c d )\|- d \|c \|d x + c
+--R +
+--R 5 6 4 4 2 3 2 3 2 +---+
+--R (- 48d x - 864c d x - 2304c d x - 1536c d )\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 796
+
+--S 797 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 3
+--R (8a c d - 4a b c d + b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 3 x\|d
+--R (- 8a c d + 4a b c d - b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2 +-+
+--R 16d \|d
+--R Type: Expression(Integer)
+--E 797
+
+--S 798 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 798
+
+--S 799 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 3 +---+ x\|d
+--R (- 8a c d + 4a b c d - b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 2 3 +-+ \|- d \|d x + c - \|- d \|c
+--R (16a c d - 8a b c d + 2b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 2 +---+ +-+
+--R 16d \|- d \|d
+--R Type: Expression(Integer)
+--E 799
+
+--S 800 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 800
+
+)clear all
+
+--S 801 of 1397
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)/x
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R (1) --------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 801
+
+--S 802 of 1397
+r0:=-2/15*b*(b*c-5*a*d)*(c+d*x^2)^(3/2)/d^2+1/5*b^2*x^2*_
+ (c+d*x^2)^(3/2)/d-a^2*atanh(sqrt(c+d*x^2)/sqrt(c))*sqrt(c)+_
+ a^2*sqrt(c+d*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 2 +-+ \|d x + c
+--R - 15a d \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 4 2 2 2 2 2 2 2 | 2
+--R (3b d x + (10a b d + b c d)x + 15a d + 10a b c d - 2b c )\|d x + c
+--R /
+--R 2
+--R 15d
+--R Type: Expression(Integer)
+--E 802
+
+--S 803 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 2 4 2 2 2 2 3 | 2
+--R (15a c d x + 180a c d x + 240a c )\|d x + c
+--R +
+--R 2 2 4 2 2 2 2 3 +-+
+--R (- 75a c d x - 300a c d x - 240a c )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 8 2 2 2 6
+--R - 15b c d x + (- 50a b c d - 65b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (- 60a c d - 240a b c d - 60b c )x + (- 120a c d - 240a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 10 3 2 2 8
+--R 3b d x + (10a b d + 40b c d )x
+--R +
+--R 2 3 2 2 2 6
+--R (15a d + 140a b c d + 95b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (120a c d + 360a b c d + 60b c )x + (120a c d + 240a b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (15d x + 180c d x + 240c )\|c \|d x + c - 75c d x - 300c d x - 240c
+--R Type: Union(Expression(Integer),...)
+--E 803
+
+--S 804 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 4 4 2 2 3 2 2 3 2 | 2
+--R (15a c d x + 180a c d x + 240a c d )\|d x + c
+--R +
+--R 2 4 4 2 2 3 2 2 3 2 +-+
+--R (- 75a c d x - 300a c d x - 240a c d )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 4 4 2 2 3 2 2 3 2 | 2
+--R (15a c d x + 180a c d x + 240a c d )\|d x + c
+--R +
+--R 2 4 4 2 2 3 2 2 3 2 +-+
+--R (- 75a c d x - 300a c d x - 240a c d )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (15a c d + 10a b c d - 2b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (180a c d + 120a b c d - 24b c d)x + 240a c d + 160a b c d - 32b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 75a c d - 50a b c d + 10b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (- 300a c d - 200a b c d + 40b c d)x - 240a c d - 160a b c d
+--R +
+--R 2 5
+--R 32b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +-+ | 2 4 4 2 3 2
+--R (15d x + 180c d x + 240c d )\|c \|d x + c - 75c d x - 300c d x
+--R +
+--R 3 2
+--R - 240c d
+--R Type: Expression(Integer)
+--E 804
+
+--S 805 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 805
+
+)clear all
+
+--S 806 of 1397
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)/x^2
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R (1) --------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 806
+
+--S 807 of 1397
+r0:=-a^2*(c+d*x^2)^(3/2)/(c*x)+1/4*b^2*x*(c+d*x^2)^(3/2)/d-_
+ 1/8*(b^2*c^2-8*a*d*(b*c+a*d))*atanh(x*sqrt(d)/_
+ sqrt(c+d*x^2))/d^(3/2)-1/8*(b^2*c^2-8*a*d*(b*c+a*d))*x*_
+ sqrt(c+d*x^2)/(c*d)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 x\|d
+--R (8a d + 8a b c d - b c )x atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R (2b d x + (8a b d + b c)x - 8a d)\|d \|d x + c
+--R /
+--R +-+
+--R 8d x\|d
+--R Type: Expression(Integer)
+--E 807
+
+--S 808 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 5
+--R (8a d + 8a b c d - b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (96a c d + 96a b c d - 12b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (128a c d + 128a b c d - 16b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 2 5
+--R (- 40a d - 40a b c d + 5b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (- 160a c d - 160a b c d + 20b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (- 128a c d - 128a b c d + 16b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 3 8 3 2 2 6
+--R - 10b d x + (- 40a b d - 45b c d )x
+--R +
+--R 2 3 2 2 2 4
+--R (40a d - 160a b c d - 52b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2
+--R (160a c d - 128a b c d - 16b c )x + 128a c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 2 4 10 4 2 3 8
+--R 2b d x + (8a b d + 27b c d )x
+--R +
+--R 2 4 3 2 2 2 6
+--R (- 8a d + 104a b c d + 69b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 104a c d + 224a b c d + 60b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3
+--R (- 224a c d + 128a b c d + 16b c )x - 128a c d
+--R *
+--R +-+
+--R \|d
+--R /
+--R +--------+
+--R 3 5 2 3 2 +-+ | 2
+--R (8d x + 96c d x + 128c d x)\|d \|d x + c
+--R +
+--R 3 5 2 3 2 +-+ +-+
+--R (- 40d x - 160c d x - 128c d x)\|c \|d
+--R ,
+--R
+--R 2 4 3 2 2 2 5
+--R (16a d + 16a b c d - 2b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (192a c d + 192a b c d - 24b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (256a c d + 256a b c d - 32b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 2 5
+--R (- 80a d - 80a b c d + 10b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (- 320a c d - 320a b c d + 40b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (- 256a c d - 256a b c d + 32b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 3 8 3 2 2 6
+--R - 10b d x + (- 40a b d - 45b c d )x
+--R +
+--R 2 3 2 2 2 4
+--R (40a d - 160a b c d - 52b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2
+--R (160a c d - 128a b c d - 16b c )x + 128a c d
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 2 4 10 4 2 3 8
+--R 2b d x + (8a b d + 27b c d )x
+--R +
+--R 2 4 3 2 2 2 6
+--R (- 8a d + 104a b c d + 69b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 104a c d + 224a b c d + 60b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3
+--R (- 224a c d + 128a b c d + 16b c )x - 128a c d
+--R *
+--R +---+
+--R \|- d
+--R /
+--R +--------+
+--R 3 5 2 3 2 +---+ | 2
+--R (8d x + 96c d x + 128c d x)\|- d \|d x + c
+--R +
+--R 3 5 2 3 2 +---+ +-+
+--R (- 40d x - 160c d x - 128c d x)\|- d \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 808
+
+--S 809 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2
+--R (8a d + 8a b c d - b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 x\|d
+--R (- 8a d - 8a b c d + b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R +-+
+--R 8d\|d
+--R Type: Expression(Integer)
+--E 809
+
+--S 810 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 810
+
+--S 811 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 8a d - 8a b c d + b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 2 +-+ \|- d \|d x + c - \|- d \|c
+--R (16a d + 16a b c d - 2b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R +---+ +-+
+--R 8d\|- d \|d
+--R Type: Expression(Integer)
+--E 811
+
+--S 812 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 812
+
+)clear all
+
+--S 813 of 1397
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)/x^3
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R (1) --------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 813
+
+--S 814 of 1397
+r0:=1/3*b^2*(c+d*x^2)^(3/2)/d-1/2*a^2*(c+d*x^2)^(3/2)/(c*x^2)-_
+ 1/2*a*(4*b*c+a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))/sqrt(c)+_
+ 1/2*a*(4*b*c+a*d)*sqrt(c+d*x^2)/c
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 2 2 \|d x + c
+--R (- 3a d - 12a b c d)x atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R (2b d x + (12a b d + 2b c)x - 3a d)\|c \|d x + c
+--R /
+--R 2 +-+
+--R 6d x \|c
+--R Type: Expression(Integer)
+--E 814
+
+--S 815 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 6 2 2 2 4
+--R (3a d + 12a b c d )x + (36a c d + 144a b c d)x
+--R +
+--R 2 2 3 2
+--R (48a c d + 192a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 2 6 2 2 2 4
+--R (- 15a d - 60a b c d )x + (- 60a c d - 240a b c d)x
+--R +
+--R 2 2 3 2
+--R (- 48a c d - 192a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 8 2 2 2 6
+--R - 10b c d x + (- 48a b c d - 48b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 2 2 3
+--R (15a c d - 96a b c d - 48b c )x + 60a c d x + 48a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 10 3 2 2 8
+--R 2b d x + (12a b d + 28b c d )x
+--R +
+--R 2 3 2 2 2 6
+--R (- 3a d + 96a b c d + 72b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 2 2 3
+--R (- 39a c d + 96a b c d + 48b c )x - 84a c d x - 48a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 2 6 4 2 2 +-+ | 2 2 6 2 4 3 2
+--R (6d x + 72c d x + 96c x )\|c \|d x + c - 30c d x - 120c d x - 96c x
+--R Type: Union(Expression(Integer),...)
+--E 815
+
+--S 816 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 2 2 \|d x + c - \|c
+--R (3a d + 12a b c d)log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 2 2 \|d x + c 2 2
+--R (3a d + 12a b c d)atanh(-----------) + 12a b c d + 2b c
+--R +-+
+--R \|c
+--R /
+--R +-+
+--R 6d\|c
+--R Type: Expression(Integer)
+--E 816
+
+--S 817 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 817
+
+)clear all
+
+--S 818 of 1397
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)/x^4
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R (1) --------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 818
+
+--S 819 of 1397
+r0:=-1/3*a^2*(c+d*x^2)^(3/2)/(c*x^3)-2*a*b*(c+d*x^2)^(3/2)/(c*x)+_
+ 1/2*b*(b*c+4*a*d)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/sqrt(d)+_
+ 1/2*b*(b*c+4*a*d)*x*sqrt(c+d*x^2)/c
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 3 x\|d
+--R (12a b c d + 3b c )x atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R (3b c x + (- 2a d - 12a b c)x - 2a c)\|d \|d x + c
+--R /
+--R 3 +-+
+--R 6c x \|d
+--R Type: Expression(Integer)
+--E 819
+
+--S 820 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 2 2 7 2 2 2 3 5
+--R (12a b c d + 3b c d )x + (144a b c d + 36b c d)x
+--R +
+--R 3 2 4 3
+--R (192a b c d + 48b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 2 7 2 2 2 3 5
+--R (- 60a b c d - 15b c d )x + (- 240a b c d - 60b c d)x
+--R +
+--R 3 2 4 3
+--R (- 192a b c d - 48b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 2 8 2 3 2 2 2 6
+--R - 15b c d x + (10a d + 60a b c d - 60b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (50a c d + 240a b c d - 48b c )x + (72a c d + 192a b c )x + 32a c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 2 3 10 2 4 3 2 2 2 8
+--R 3b c d x + (- 2a d - 12a b c d + 39b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (- 28a c d - 156a b c d + 84b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (- 82a c d - 336a b c d + 48b c )x + (- 88a c d - 192a b c )x
+--R +
+--R 2 4
+--R - 32a c
+--R *
+--R +-+
+--R \|d
+--R /
+--R +--------+
+--R 2 7 2 5 3 3 +-+ | 2
+--R (6c d x + 72c d x + 96c x )\|d \|d x + c
+--R +
+--R 2 7 2 5 3 3 +-+ +-+
+--R (- 30c d x - 120c d x - 96c x )\|c \|d
+--R ,
+--R
+--R 3 2 2 2 7 2 2 2 3 5
+--R (24a b c d + 6b c d )x + (288a b c d + 72b c d)x
+--R +
+--R 3 2 4 3
+--R (384a b c d + 96b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 2 7 2 2 2 3 5
+--R (- 120a b c d - 30b c d )x + (- 480a b c d - 120b c d)x
+--R +
+--R 3 2 4 3
+--R (- 384a b c d - 96b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 2 8 2 3 2 2 2 6
+--R - 15b c d x + (10a d + 60a b c d - 60b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (50a c d + 240a b c d - 48b c )x + (72a c d + 192a b c )x + 32a c
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 2 3 10 2 4 3 2 2 2 8
+--R 3b c d x + (- 2a d - 12a b c d + 39b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (- 28a c d - 156a b c d + 84b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (- 82a c d - 336a b c d + 48b c )x + (- 88a c d - 192a b c )x
+--R +
+--R 2 4
+--R - 32a c
+--R *
+--R +---+
+--R \|- d
+--R /
+--R +--------+
+--R 2 7 2 5 3 3 +---+ | 2
+--R (6c d x + 72c d x + 96c x )\|- d \|d x + c
+--R +
+--R 2 7 2 5 3 3 +---+ +-+
+--R (- 30c d x - 120c d x - 96c x )\|- d \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 820
+
+--S 821 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2
+--R (4a b d + b c)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 x\|d
+--R (- 4a b d - b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R +-+
+--R 2\|d
+--R Type: Expression(Integer)
+--E 821
+
+--S 822 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 822
+
+--S 823 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +---+ x\|d
+--R (- 4a b d - b c)\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- d \|d x + c - \|- d \|c
+--R (8a b d + 2b c)\|d atan(------------------------------)
+--R d x
+--R /
+--R +---+ +-+
+--R 2\|- d \|d
+--R Type: Expression(Integer)
+--E 823
+
+--S 824 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 824
+
+)clear all
+
+--S 825 of 1397
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)/x^5
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R (1) --------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 825
+
+--S 826 of 1397
+r0:=-1/4*a^2*(c+d*x^2)^(3/2)/(c*x^4)-1/8*a*(8*b*c-a*d)*_
+ (c+d*x^2)^(3/2)/(c^2*x^2)-1/8*(8*b^2*c^2+a*d*(8*b*c-a*d))*_
+ atanh(sqrt(c+d*x^2)/sqrt(c))/c^(3/2)+1/8*(8*b^2*c^2+_
+ a*d*(8*b*c-a*d))*sqrt(c+d*x^2)/c^2
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 2 2 2 4 \|d x + c
+--R (a d - 8a b c d - 8b c )x atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R (8b c x + (- a d - 8a b c)x - 2a c)\|c \|d x + c
+--R /
+--R 4 +-+
+--R 8c x \|c
+--R Type: Expression(Integer)
+--E 826
+
+--S 827 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 2 2 2 8
+--R (- a d + 8a b c d + 8b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (- 12a c d + 96a b c d + 96b c d)x
+--R +
+--R 2 2 2 3 2 4 4
+--R (- 16a c d + 128a b c d + 128b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 2 8
+--R (5a d - 40a b c d - 40b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (20a c d - 160a b c d - 160b c d)x
+--R +
+--R 2 2 2 3 2 4 4
+--R (16a c d - 128a b c d - 128b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 2 8 2 3 2 2 2 3 6
+--R - 32b c d x + (5a c d + 40a b c d - 64b c d)x
+--R +
+--R 2 2 2 3 4 2 3 4 2 2 4
+--R (30a c d + 160a b c d)x + (56a c d + 128a b c )x + 32a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 10 2 4 3 2 2 2 8
+--R 8b c d x + (- a d - 8a b c d + 64b c d )x
+--R +
+--R 2 3 2 2 2 3 6 2 2 2 3 4
+--R (- 15a c d - 104a b c d + 64b c d)x + (- 54a c d - 224a b c d)x
+--R +
+--R 2 3 4 2 2 4
+--R (- 72a c d - 128a b c )x - 32a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 2 8 2 6 3 4 +-+ | 2 2 2 8 3 6
+--R (8c d x + 96c d x + 128c x )\|c \|d x + c - 40c d x - 160c d x
+--R +
+--R 4 4
+--R - 128c x
+--R Type: Union(Expression(Integer),...)
+--E 827
+
+--S 828 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 2 2 2 2 \|d x + c - \|c
+--R (- a d + 8a b c d + 8b c )log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 2 2 2 2 \|d x + c 2 2
+--R (- a d + 8a b c d + 8b c )atanh(-----------) + 8b c
+--R +-+
+--R \|c
+--R /
+--R +-+
+--R 8c\|c
+--R Type: Expression(Integer)
+--E 828
+
+--S 829 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 829
+
+)clear all
+
+--S 830 of 1397
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)/x^6
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R (1) --------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 830
+
+--S 831 of 1397
+r0:=-1/5*a^2*(c+d*x^2)^(3/2)/(c*x^5)-2/15*a*(5*b*c-a*d)*_
+ (c+d*x^2)^(3/2)/(c^2*x^3)+b^2*atanh(x*sqrt(d)/sqrt(c+d*x^2))*_
+ sqrt(d)-b^2*sqrt(c+d*x^2)/x
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 5 +-+ x\|d
+--R 15b c x \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R ((2a d - 10a b c d - 15b c )x + (- a c d - 10a b c )x - 3a c )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2 5
+--R 15c x
+--R Type: Expression(Integer)
+--E 831
+
+--S 832 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 9 2 3 7 2 4 5 +-+ | 2
+--R (15b c d x + 180b c d x + 240b c x )\|d \|d x + c
+--R +
+--R 2 2 2 9 2 3 7 2 4 5 +-+ +-+
+--R (- 75b c d x - 300b c d x - 240b c x )\|c \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 4 3 2 2 2 8
+--R (- 10a d + 50a b c d + 75b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (- 35a c d + 250a b c d + 300b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2 2 4
+--R (3a c d + 360a b c d + 240b c )x + (76a c d + 160a b c )x + 48a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 4 2 2 3 10
+--R (2a d - 10a b c d - 15b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (25a c d - 140a b c d - 195b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (40a c d - 410a b c d - 420b c d)x
+--R +
+--R 2 3 2 4 2 5 4 2 4 5 2
+--R (- 35a c d - 440a b c d - 240b c )x + (- 100a c d - 160a b c )x
+--R +
+--R 2 5
+--R - 48a c
+--R /
+--R +--------+
+--R 2 2 9 3 7 4 5 | 2
+--R (15c d x + 180c d x + 240c x )\|d x + c
+--R +
+--R 2 2 9 3 7 4 5 +-+
+--R (- 75c d x - 300c d x - 240c x )\|c
+--R ,
+--R
+--R +--------+
+--R 2 2 2 9 2 3 7 2 4 5 +---+ | 2
+--R (30b c d x + 360b c d x + 480b c x )\|- d \|d x + c
+--R +
+--R 2 2 2 9 2 3 7 2 4 5 +---+ +-+
+--R (- 150b c d x - 600b c d x - 480b c x )\|- d \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 2 4 3 2 2 2 8
+--R (- 10a d + 50a b c d + 75b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (- 35a c d + 250a b c d + 300b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2 2 4
+--R (3a c d + 360a b c d + 240b c )x + (76a c d + 160a b c )x + 48a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 4 2 2 3 10
+--R (2a d - 10a b c d - 15b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (25a c d - 140a b c d - 195b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (40a c d - 410a b c d - 420b c d)x
+--R +
+--R 2 3 2 4 2 5 4 2 4 5 2
+--R (- 35a c d - 440a b c d - 240b c )x + (- 100a c d - 160a b c )x
+--R +
+--R 2 5
+--R - 48a c
+--R /
+--R +--------+
+--R 2 2 9 3 7 4 5 | 2
+--R (15c d x + 180c d x + 240c x )\|d x + c
+--R +
+--R 2 2 9 3 7 4 5 +-+
+--R (- 75c d x - 300c d x - 240c x )\|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 832
+
+--S 833 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R 2 +-+ (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R b \|d log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 +-+ x\|d
+--R - b \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 833
+
+--S 834 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 834
+
+--S 835 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R 2 +-+ x\|d 2 +---+ \|d x + c - \|c
+--R (6) - b \|d atanh(-----------) + 2b \|- d atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- d
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 835
+
+--S 836 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 836
+
+)clear all
+
+--S 837 of 1397
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)/x^7
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R (1) --------------------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 837
+
+--S 838 of 1397
+r0:=-1/6*a^2*(c+d*x^2)^(3/2)/(c*x^6)-1/8*a*(4*b*c-a*d)*(c+d*x^2)^(3/2)/_
+ (c^2*x^4)-1/16*d*(8*b^2*c^2-4*a*b*c*d+a^2*d^2)*atanh(_
+ sqrt(c+d*x^2)/sqrt(c))/c^(5/2)-1/16*(8*b^2*c^2-4*a*b*c*d+_
+ a^2*d^2)*sqrt(c+d*x^2)/(c^2*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 3 2 2 2 6 \|d x + c
+--R (- 3a d + 12a b c d - 24b c d)x atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2 4 2 2 2 2 2 +-+
+--R ((3a d - 12a b c d - 24b c )x + (- 2a c d - 24a b c )x - 8a c )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2 6 +-+
+--R 48c x \|c
+--R Type: Expression(Integer)
+--E 838
+
+--S 839 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 2 4 2 3 3 10
+--R (18a c d - 72a b c d + 144b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (96a c d - 384a b c d + 768b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (96a c d - 384a b c d + 768b c d)x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 5 2 2 4 12
+--R (- 3a d + 12a b c d - 24b c d )x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (- 54a c d + 216a b c d - 432b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (- 144a c d + 576a b c d - 1152b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (- 96a c d + 384a b c d - 768b c d)x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (- 3a c d + 12a b c d + 24b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (- 52a c d + 240a b c d + 432b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (- 100a c d + 1008a b c d + 1152b c d)x
+--R +
+--R 2 4 2 5 2 6 4 2 5 6 2
+--R (144a c d + 1536a b c d + 768b c )x + (448a c d + 768a b c )x
+--R +
+--R 2 6
+--R 256a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (18a c d - 72a b c d - 144b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (102a c d - 600a b c d - 912b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (68a c d - 1680a b c d - 1536b c d)x
+--R +
+--R 2 4 2 5 2 6 4 2 5 6 2
+--R (- 336a c d - 1920a b c d - 768b c )x + (- 576a c d - 768a b c )x
+--R +
+--R 2 6
+--R - 256a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 2 10 4 8 5 6 +-+ | 2 3 3 12
+--R (288c d x + 1536c d x + 1536c x )\|c \|d x + c - 48c d x
+--R +
+--R 4 2 10 5 8 6 6
+--R - 864c d x - 2304c d x - 1536c x
+--R Type: Union(Expression(Integer),...)
+--E 839
+
+--S 840 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 2 3 2 2 2 \|d x + c - \|c
+--R (a d - 4a b c d + 8b c d)log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 2 3 2 2 2 \|d x + c
+--R (a d - 4a b c d + 8b c d)atanh(-----------)
+--R +-+
+--R \|c
+--R /
+--R 2 +-+
+--R 16c \|c
+--R Type: Expression(Integer)
+--E 840
+
+--S 841 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 841
+
+)clear all
+
+--S 842 of 1397
+t0:=x^4*(a+b*x^2)^2*(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 10 2 8 2 6 2 4 | 2
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|d x + c
+--R Type: Expression(Integer)
+--E 842
+
+--S 843 of 1397
+r0:=1/192*(24*a^2*d^2+b*c*(7*b*c-24*a*d))*x^5*(c+d*x^2)^(3/2)/d^2-_
+ 1/120*b*(7*b*c-24*a*d)*x^5*(c+d*x^2)^(5/2)/d^2+1/12*b^2*x^7*_
+ (c+d*x^2)^(5/2)/d+1/1024*c^4*(24*a^2*d^2+b*c*(7*b*c-24*a*d))*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))/d^(9/2)-1/1024*c^3*(24*a^2*d^2+_
+ b*c*(7*b*c-24*a*d))*x*sqrt(c+d*x^2)/d^4+1/1536*c^2*(24*a^2*d^2+_
+ b*c*(7*b*c-24*a*d))*x^3*sqrt(c+d*x^2)/d^3+1/384*c*(24*a^2*d^2+_
+ b*c*(7*b*c-24*a*d))*x^5*sqrt(c+d*x^2)/d^2
+--R
+--R
+--R (2)
+--R +-+
+--R 2 4 2 5 2 6 x\|d
+--R (360a c d - 360a b c d + 105b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 11 5 2 4 9
+--R 1280b d x + (3072a b d + 1664b c d )x
+--R +
+--R 2 5 4 2 2 3 7
+--R (1920a d + 4224a b c d + 48b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (2880a c d + 192a b c d - 56b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3
+--R (240a c d - 240a b c d + 70b c d)x
+--R +
+--R 2 3 2 4 2 5
+--R (- 360a c d + 360a b c d - 105b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R 4 +-+
+--R 15360d \|d
+--R Type: Expression(Integer)
+--E 843
+
+--S 844 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 7 5 6 2 6 5 10
+--R (4320a c d - 4320a b c d + 1260b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 8
+--R (100800a c d - 100800a b c d + 29400b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 6
+--R (645120a c d - 645120a b c d + 188160b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 4
+--R (1658880a c d - 1658880a b c d + 483840b c d )x
+--R +
+--R 2 8 3 9 2 2 10 2
+--R (1843200a c d - 1843200a b c d + 537600b c d)x
+--R +
+--R 2 9 2 10 2 11
+--R 737280a c d - 737280a b c d + 215040b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 8 5 7 2 6 6 12
+--R (- 360a c d + 360a b c d - 105b c d )x
+--R +
+--R 2 5 7 6 6 2 7 5 10
+--R (- 25920a c d + 25920a b c d - 7560b c d )x
+--R +
+--R 2 6 6 7 5 2 8 4 8
+--R (- 302400a c d + 302400a b c d - 88200b c d )x
+--R +
+--R 2 7 5 8 4 2 9 3 6
+--R (- 1290240a c d + 1290240a b c d - 376320b c d )x
+--R +
+--R 2 8 4 9 3 2 10 2 4
+--R (- 2488320a c d + 2488320a b c d - 725760b c d )x
+--R +
+--R 2 9 3 10 2 2 11 2
+--R (- 2211840a c d + 2211840a b c d - 645120b c d)x
+--R +
+--R 2 10 2 11 2 12
+--R - 737280a c d + 737280a b c d - 215040b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 11 23 11 2 10 21
+--R - 1280b d x + (- 3072a b d - 93824b c d )x
+--R +
+--R 2 11 10 2 2 9 19
+--R (- 1920a d - 225408a b c d - 1195056b c d )x
+--R +
+--R 2 10 2 9 2 3 8 17
+--R (- 141120a c d - 2884800a b c d - 5988680b c d )x
+--R +
+--R 2 2 9 3 8 2 4 7 15
+--R (- 1820400a c d - 14571792a b c d - 14847494b c d )x
+--R +
+--R 2 3 8 4 7 2 5 6 13
+--R (- 9317400a c d - 36516840a b c d - 19495815b c d )x
+--R +
+--R 2 4 7 5 6 2 6 5 11
+--R (- 23768640a c d - 48583104a b c d - 13027368b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 9
+--R (- 32260800a c d - 33013056a b c d - 3478392b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 7
+--R (- 21995520a c d - 9461760a b c d + 138240b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 5
+--R (- 4884480a c d - 1406976a b c d + 410368b c d )x
+--R +
+--R 2 8 3 9 2 2 10 3
+--R (1720320a c d - 1720320a b c d + 501760b c d)x
+--R +
+--R 2 9 2 10 2 11
+--R (737280a c d - 737280a b c d + 215040b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 11 23 11 2 10 21
+--R 15360b d x + (36864a b d + 393728b c d )x
+--R +
+--R 2 11 10 2 2 9 19
+--R (23040a d + 947712a b c d + 3138624b c d )x
+--R +
+--R 2 10 2 9 2 3 8 17
+--R (595200a c d + 7600896a b c d + 11653152b c d )x
+--R +
+--R 2 2 9 3 8 2 4 7 15
+--R (4822080a c d + 28466112a b c d + 23185384b c d )x
+--R +
+--R 2 3 8 4 7 2 5 6 13
+--R (18321120a c d + 57250080a b c d + 25572780b c d )x
+--R +
+--R 2 4 7 5 6 2 6 5 11
+--R (37501920a c d + 63947808a b c d + 14771916b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 9
+--R (42569280a c d + 37646784a b c d + 3437608b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 7
+--R (24606720a c d + 9996288a b c d - 294144b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 5
+--R (4116480a c d + 2174976a b c d - 634368b c d )x
+--R +
+--R 2 8 3 9 2 2 10 3
+--R (- 2088960a c d + 2088960a b c d - 609280b c d)x
+--R +
+--R 2 9 2 10 2 11
+--R (- 737280a c d + 737280a b c d - 215040b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 9 10 8 8 2 7 6 3 6 4
+--R 184320d x + 4300800c d x + 27525120c d x + 70778880c d x
+--R +
+--R 4 5 2 5 4
+--R 78643200c d x + 31457280c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 10 12 9 10 2 8 8 3 7 6
+--R - 15360d x - 1105920c d x - 12902400c d x - 55050240c d x
+--R +
+--R 4 6 4 5 5 2 6 4
+--R - 106168320c d x - 94371840c d x - 31457280c d
+--R *
+--R +-+
+--R \|d
+--R ,
+--R
+--R 2 4 7 5 6 2 6 5 10
+--R (8640a c d - 8640a b c d + 2520b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 8
+--R (201600a c d - 201600a b c d + 58800b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 6
+--R (1290240a c d - 1290240a b c d + 376320b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 4
+--R (3317760a c d - 3317760a b c d + 967680b c d )x
+--R +
+--R 2 8 3 9 2 2 10 2
+--R (3686400a c d - 3686400a b c d + 1075200b c d)x
+--R +
+--R 2 9 2 10 2 11
+--R 1474560a c d - 1474560a b c d + 430080b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 8 5 7 2 6 6 12
+--R (- 720a c d + 720a b c d - 210b c d )x
+--R +
+--R 2 5 7 6 6 2 7 5 10
+--R (- 51840a c d + 51840a b c d - 15120b c d )x
+--R +
+--R 2 6 6 7 5 2 8 4 8
+--R (- 604800a c d + 604800a b c d - 176400b c d )x
+--R +
+--R 2 7 5 8 4 2 9 3 6
+--R (- 2580480a c d + 2580480a b c d - 752640b c d )x
+--R +
+--R 2 8 4 9 3 2 10 2 4
+--R (- 4976640a c d + 4976640a b c d - 1451520b c d )x
+--R +
+--R 2 9 3 10 2 2 11 2
+--R (- 4423680a c d + 4423680a b c d - 1290240b c d)x
+--R +
+--R 2 10 2 11 2 12
+--R - 1474560a c d + 1474560a b c d - 430080b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 11 23 11 2 10 21
+--R - 1280b d x + (- 3072a b d - 93824b c d )x
+--R +
+--R 2 11 10 2 2 9 19
+--R (- 1920a d - 225408a b c d - 1195056b c d )x
+--R +
+--R 2 10 2 9 2 3 8 17
+--R (- 141120a c d - 2884800a b c d - 5988680b c d )x
+--R +
+--R 2 2 9 3 8 2 4 7 15
+--R (- 1820400a c d - 14571792a b c d - 14847494b c d )x
+--R +
+--R 2 3 8 4 7 2 5 6 13
+--R (- 9317400a c d - 36516840a b c d - 19495815b c d )x
+--R +
+--R 2 4 7 5 6 2 6 5 11
+--R (- 23768640a c d - 48583104a b c d - 13027368b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 9
+--R (- 32260800a c d - 33013056a b c d - 3478392b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 7
+--R (- 21995520a c d - 9461760a b c d + 138240b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 5
+--R (- 4884480a c d - 1406976a b c d + 410368b c d )x
+--R +
+--R 2 8 3 9 2 2 10 3
+--R (1720320a c d - 1720320a b c d + 501760b c d)x
+--R +
+--R 2 9 2 10 2 11
+--R (737280a c d - 737280a b c d + 215040b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 11 23 11 2 10 21
+--R 15360b d x + (36864a b d + 393728b c d )x
+--R +
+--R 2 11 10 2 2 9 19
+--R (23040a d + 947712a b c d + 3138624b c d )x
+--R +
+--R 2 10 2 9 2 3 8 17
+--R (595200a c d + 7600896a b c d + 11653152b c d )x
+--R +
+--R 2 2 9 3 8 2 4 7 15
+--R (4822080a c d + 28466112a b c d + 23185384b c d )x
+--R +
+--R 2 3 8 4 7 2 5 6 13
+--R (18321120a c d + 57250080a b c d + 25572780b c d )x
+--R +
+--R 2 4 7 5 6 2 6 5 11
+--R (37501920a c d + 63947808a b c d + 14771916b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 9
+--R (42569280a c d + 37646784a b c d + 3437608b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 7
+--R (24606720a c d + 9996288a b c d - 294144b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 5
+--R (4116480a c d + 2174976a b c d - 634368b c d )x
+--R +
+--R 2 8 3 9 2 2 10 3
+--R (- 2088960a c d + 2088960a b c d - 609280b c d)x
+--R +
+--R 2 9 2 10 2 11
+--R (- 737280a c d + 737280a b c d - 215040b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R 9 10 8 8 2 7 6 3 6 4
+--R 184320d x + 4300800c d x + 27525120c d x + 70778880c d x
+--R +
+--R 4 5 2 5 4
+--R 78643200c d x + 31457280c d
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 10 12 9 10 2 8 8 3 7 6
+--R - 15360d x - 1105920c d x - 12902400c d x - 55050240c d x
+--R +
+--R 4 6 4 5 5 2 6 4
+--R - 106168320c d x - 94371840c d x - 31457280c d
+--R *
+--R +---+
+--R \|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 844
+
+--S 845 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 4 2 5 2 6
+--R (24a c d - 24a b c d + 7b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 4 2 5 2 6 x\|d
+--R (- 24a c d + 24a b c d - 7b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4 +-+
+--R 1024d \|d
+--R Type: Expression(Integer)
+--E 845
+
+--S 846 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 846
+
+--S 847 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 4 2 5 2 6 +---+ x\|d
+--R (- 24a c d + 24a b c d - 7b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 4 2 5 2 6 +-+ \|- d \|d x + c - \|- d \|c
+--R (48a c d - 48a b c d + 14b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 4 +---+ +-+
+--R 1024d \|- d \|d
+--R Type: Expression(Integer)
+--E 847
+
+--S 848 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 848
+
+)clear all
+
+--S 849 of 1397
+t0:=x^3*(a+b*x^2)^2*(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 9 2 7 2 5 2 3 | 2
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|d x + c
+--R Type: Expression(Integer)
+--E 849
+
+--S 850 of 1397
+r0:=-1/5*c*(b*c-a*d)^2*(c+d*x^2)^(5/2)/d^4+1/7*(b*c-a*d)*(3*b*c-a*d)*_
+ (c+d*x^2)^(7/2)/d^4-1/9*b*(3*b*c-2*a*d)*(c+d*x^2)^(9/2)/d^4+_
+ 1/11*b^2*(c+d*x^2)^(11/2)/d^4
+--R
+--R
+--R (2)
+--R 2 5 10 5 2 4 8
+--R 315b d x + (770a b d + 420b c d )x
+--R +
+--R 2 5 4 2 2 3 6
+--R (495a d + 1100a b c d + 15b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (792a c d + 66a b c d - 18b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (99a c d - 88a b c d + 24b c d)x - 198a c d + 176a b c d - 48b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4
+--R 3465d
+--R Type: Expression(Integer)
+--E 850
+
+--S 851 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 20 6 2 2 5 18
+--R - 3465b c d x + (- 8470a b c d - 73920b c d )x
+--R +
+--R 2 6 2 5 2 3 4 16
+--R (- 5445a c d - 181500a b c d - 480645b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 14
+--R (- 117612a c d - 1191366a b c d - 1407582b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 12
+--R (- 785169a c d - 3537072a b c d - 2084544b c d )x
+--R +
+--R 2 4 3 5 2 2 6 10
+--R (- 2389464a c d - 5329632a b c d - 1530144b c d)x
+--R +
+--R 2 5 2 6 2 7 8
+--R (- 3714480a c d - 3991680a b c d - 443520b c )x
+--R +
+--R 2 6 7 6 2 7 4
+--R (- 2882880a c d - 1182720a b c )x - 887040a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 7 22 7 2 6 20
+--R 315b d x + (770a b d + 19635b c d )x
+--R +
+--R 2 7 6 2 2 5 18
+--R (495a d + 48070a b c d + 220935b c d )x
+--R +
+--R 2 6 2 5 2 3 4 16
+--R (30987a c d + 544566a b c d + 1002177b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 14
+--R (355311a c d + 2496978a b c d + 2286306b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 12
+--R (1661121a c d + 5776848a b c d + 2794176b c d )x
+--R +
+--R 2 4 3 5 2 2 6 10
+--R (3941784a c d + 7177632a b c d + 1751904b c d)x
+--R +
+--R 2 5 2 6 2 7 8
+--R (5045040a c d + 4583040a b c d + 443520b c )x
+--R +
+--R 2 6 7 6 2 7 4
+--R (3326400a c d + 1182720a b c )x + 887040a c x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 5 10 4 8 2 3 6 3 2 4
+--R 3465d x + 207900c d x + 1940400c d x + 6209280c d x
+--R +
+--R 4 2 5
+--R 7983360c d x + 3548160c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4
+--R - 38115c d x - 762300c d x - 4268880c d x - 9757440c d x
+--R +
+--R 5 2 6
+--R - 9757440c d x - 3548160c
+--R Type: Union(Expression(Integer),...)
+--E 851
+
+--S 852 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 4 7 5 6 2 6 5 10
+--R (- 198a c d + 176a b c d - 48b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 8
+--R (- 11880a c d + 10560a b c d - 2880b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 6
+--R (- 110880a c d + 98560a b c d - 26880b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 4
+--R (- 354816a c d + 315392a b c d - 86016b c d )x
+--R +
+--R 2 8 3 9 2 2 10 2 2 9 2
+--R (- 456192a c d + 405504a b c d - 110592b c d)x - 202752a c d
+--R +
+--R 10 2 11
+--R 180224a b c d - 49152b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 7 5 6 2 6 5 10
+--R (2178a c d - 1936a b c d + 528b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 8
+--R (43560a c d - 38720a b c d + 10560b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 6
+--R (243936a c d - 216832a b c d + 59136b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 4
+--R (557568a c d - 495616a b c d + 135168b c d )x
+--R +
+--R 2 8 3 9 2 2 10 2 2 9 2
+--R (557568a c d - 495616a b c d + 135168b c d)x + 202752a c d
+--R +
+--R 10 2 11
+--R - 180224a b c d + 49152b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 9 10 8 8 2 7 6 3 6 4
+--R 3465d x + 207900c d x + 1940400c d x + 6209280c d x
+--R +
+--R 4 5 2 5 4
+--R 7983360c d x + 3548160c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 9 10 2 8 8 3 7 6 4 6 4
+--R - 38115c d x - 762300c d x - 4268880c d x - 9757440c d x
+--R +
+--R 5 5 2 6 4
+--R - 9757440c d x - 3548160c d
+--R Type: Expression(Integer)
+--E 852
+
+--S 853 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 853
+
+)clear all
+
+--S 854 of 1397
+t0:=x^2*(a+b*x^2)^2*(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 8 2 6 2 4 2 2 | 2
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|d x + c
+--R Type: Expression(Integer)
+--E 854
+
+--S 855 of 1397
+r0:=1/96*(16*a^2*d^2+3*b*c*(b*c-4*a*d))*x^3*(c+d*x^2)^(3/2)/d^2-_
+ 1/16*b*(b*c-4*a*d)*x^3*(c+d*x^2)^(5/2)/d^2+1/10*b^2*x^5*(c+_
+ d*x^2)^(5/2)/d-1/256*c^3*(16*a^2*d^2+3*b*c*(b*c-4*a*d))*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))/d^(7/2)+1/256*c^2*(16*a^2*d^2+_
+ 3*b*c*(b*c-4*a*d))*x*sqrt(c+d*x^2)/d^3+1/128*c*(16*a^2*d^2+_
+ 3*b*c*(b*c-4*a*d))*x^3*sqrt(c+d*x^2)/d^2
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 2 4 2 5 x\|d
+--R (- 240a c d + 180a b c d - 45b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 9 4 2 3 7
+--R 384b d x + (960a b d + 528b c d )x
+--R +
+--R 2 4 3 2 2 2 5
+--R (640a d + 1440a b c d + 24b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (1120a c d + 120a b c d - 30b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (240a c d - 180a b c d + 45b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R 3 +-+
+--R 3840d \|d
+--R Type: Expression(Integer)
+--E 855
+
+--S 856 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 6 4 5 2 5 4 8
+--R (2400a c d - 1800a b c d + 450b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 6
+--R (38400a c d - 28800a b c d + 7200b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 4
+--R (161280a c d - 120960a b c d + 30240b c d )x
+--R +
+--R 2 6 3 7 2 2 8 2 2 7 2
+--R (245760a c d - 184320a b c d + 46080b c d)x + 122880a c d
+--R +
+--R 8 2 9
+--R - 92160a b c d + 23040b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 3 7 4 6 2 5 5 10
+--R (- 240a c d + 180a b c d - 45b c d )x
+--R +
+--R 2 4 6 5 5 2 6 4 8
+--R (- 12000a c d + 9000a b c d - 2250b c d )x
+--R +
+--R 2 5 5 6 4 2 7 3 6
+--R (- 96000a c d + 72000a b c d - 18000b c d )x
+--R +
+--R 2 6 4 7 3 2 8 2 4
+--R (- 268800a c d + 201600a b c d - 50400b c d )x
+--R +
+--R 2 7 3 8 2 2 9 2 2 8 2
+--R (- 307200a c d + 230400a b c d - 57600b c d)x - 122880a c d
+--R +
+--R 9 2 10
+--R 92160a b c d - 23040b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 9 19 9 2 8 17
+--R - 384b d x + (- 960a b d - 19728b c d )x
+--R +
+--R 2 9 8 2 2 7 15
+--R (- 640a d - 49440a b c d - 180024b c d )x
+--R +
+--R 2 8 2 7 2 3 6 13
+--R (- 33120a c d - 456120a b c d - 642450b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 11
+--R (- 312240a c d - 1657020a b c d - 1091025b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 9
+--R (- 1176800a c d - 2880600a b c d - 889578b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 7
+--R (- 2169600a c d - 2397120a b c d - 285456b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 5
+--R (- 2030080a c d - 689280a b c d - 24288b c d )x
+--R +
+--R 2 6 3 7 2 2 8 3
+--R (- 880640a c d + 168960a b c d - 42240b c d)x
+--R +
+--R 2 7 2 8 2 9
+--R (- 122880a c d + 92160a b c d - 23040b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 9 19 9 2 8 17
+--R 3840b d x + (9600a b d + 70560b c d )x
+--R +
+--R 2 9 8 2 2 7 15
+--R (6400a d + 177600a b c d + 409488b c d )x
+--R +
+--R 2 8 2 7 2 3 6 13
+--R (120000a c d + 1044720a b c d + 1094340b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 11
+--R (725280a c d + 2844840a b c d + 1500630b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 9
+--R (2058080a c d + 3986040a b c d + 1031010b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 7
+--R (3082240a c d + 2757120a b c d + 293760b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 5
+--R (2455040a c d + 616320a b c d + 42528b c d )x
+--R +
+--R 2 6 3 7 2 2 8 3
+--R (942080a c d - 215040a b c d + 53760b c d)x
+--R +
+--R 2 7 2 8 2 9
+--R (122880a c d - 92160a b c d + 23040b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 7 8 6 6 2 5 4 3 4 2
+--R 38400d x + 614400c d x + 2580480c d x + 3932160c d x
+--R +
+--R 4 3
+--R 1966080c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 8 10 7 8 2 6 6 3 5 4
+--R - 3840d x - 192000c d x - 1536000c d x - 4300800c d x
+--R +
+--R 4 4 2 5 3
+--R - 4915200c d x - 1966080c d
+--R *
+--R +-+
+--R \|d
+--R ,
+--R
+--R 2 3 6 4 5 2 5 4 8
+--R (- 4800a c d + 3600a b c d - 900b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 6
+--R (- 76800a c d + 57600a b c d - 14400b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 4
+--R (- 322560a c d + 241920a b c d - 60480b c d )x
+--R +
+--R 2 6 3 7 2 2 8 2 2 7 2
+--R (- 491520a c d + 368640a b c d - 92160b c d)x - 245760a c d
+--R +
+--R 8 2 9
+--R 184320a b c d - 46080b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 3 7 4 6 2 5 5 10
+--R (480a c d - 360a b c d + 90b c d )x
+--R +
+--R 2 4 6 5 5 2 6 4 8
+--R (24000a c d - 18000a b c d + 4500b c d )x
+--R +
+--R 2 5 5 6 4 2 7 3 6
+--R (192000a c d - 144000a b c d + 36000b c d )x
+--R +
+--R 2 6 4 7 3 2 8 2 4
+--R (537600a c d - 403200a b c d + 100800b c d )x
+--R +
+--R 2 7 3 8 2 2 9 2 2 8 2
+--R (614400a c d - 460800a b c d + 115200b c d)x + 245760a c d
+--R +
+--R 9 2 10
+--R - 184320a b c d + 46080b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 9 19 9 2 8 17
+--R - 384b d x + (- 960a b d - 19728b c d )x
+--R +
+--R 2 9 8 2 2 7 15
+--R (- 640a d - 49440a b c d - 180024b c d )x
+--R +
+--R 2 8 2 7 2 3 6 13
+--R (- 33120a c d - 456120a b c d - 642450b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 11
+--R (- 312240a c d - 1657020a b c d - 1091025b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 9
+--R (- 1176800a c d - 2880600a b c d - 889578b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 7
+--R (- 2169600a c d - 2397120a b c d - 285456b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 5
+--R (- 2030080a c d - 689280a b c d - 24288b c d )x
+--R +
+--R 2 6 3 7 2 2 8 3
+--R (- 880640a c d + 168960a b c d - 42240b c d)x
+--R +
+--R 2 7 2 8 2 9
+--R (- 122880a c d + 92160a b c d - 23040b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 9 19 9 2 8 17
+--R 3840b d x + (9600a b d + 70560b c d )x
+--R +
+--R 2 9 8 2 2 7 15
+--R (6400a d + 177600a b c d + 409488b c d )x
+--R +
+--R 2 8 2 7 2 3 6 13
+--R (120000a c d + 1044720a b c d + 1094340b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 11
+--R (725280a c d + 2844840a b c d + 1500630b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 9
+--R (2058080a c d + 3986040a b c d + 1031010b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 7
+--R (3082240a c d + 2757120a b c d + 293760b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 5
+--R (2455040a c d + 616320a b c d + 42528b c d )x
+--R +
+--R 2 6 3 7 2 2 8 3
+--R (942080a c d - 215040a b c d + 53760b c d)x
+--R +
+--R 2 7 2 8 2 9
+--R (122880a c d - 92160a b c d + 23040b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R 7 8 6 6 2 5 4 3 4 2
+--R 38400d x + 614400c d x + 2580480c d x + 3932160c d x
+--R +
+--R 4 3
+--R 1966080c d
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 8 10 7 8 2 6 6 3 5 4
+--R - 3840d x - 192000c d x - 1536000c d x - 4300800c d x
+--R +
+--R 4 4 2 5 3
+--R - 4915200c d x - 1966080c d
+--R *
+--R +---+
+--R \|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 856
+
+--S 857 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 2 4 2 5
+--R (16a c d - 12a b c d + 3b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 3 2 4 2 5 x\|d
+--R (16a c d - 12a b c d + 3b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 +-+
+--R 256d \|d
+--R Type: Expression(Integer)
+--E 857
+
+--S 858 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 858
+
+--S 859 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 3 2 4 2 5 +---+ x\|d
+--R (16a c d - 12a b c d + 3b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 3 2 4 2 5 +-+ \|- d \|d x + c - \|- d \|c
+--R (- 32a c d + 24a b c d - 6b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 3 +---+ +-+
+--R 256d \|- d \|d
+--R Type: Expression(Integer)
+--E 859
+
+--S 860 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 860
+
+)clear all
+
+--S 861 of 1397
+t0:=x*(a+b*x^2)^2*(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 7 2 5 2 3 2 | 2
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x)\|d x + c
+--R Type: Expression(Integer)
+--E 861
+
+--S 862 of 1397
+r0:=1/5*(b*c-a*d)^2*(c+d*x^2)^(5/2)/d^3-2/7*b*(b*c-a*d)*_
+ (c+d*x^2)^(7/2)/d^3+1/9*b^2*(c+d*x^2)^(9/2)/d^3
+--R
+--R
+--R (2)
+--R 2 4 8 4 2 3 6 2 4 3 2 2 2 4
+--R 35b d x + (90a b d + 50b c d )x + (63a d + 144a b c d + 3b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (126a c d + 18a b c d - 4b c d)x + 63a c d - 36a b c d + 8b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3
+--R 315d
+--R Type: Expression(Integer)
+--E 862
+
+--S 863 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 16 5 2 2 4 14
+--R - 315b c d x + (- 810a b c d - 4650b c d )x
+--R +
+--R 2 5 2 4 2 3 3 12
+--R (- 567a c d - 12096a b c d - 21147b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 10
+--R (- 8694a c d - 56322a b c d - 42084b c d )x
+--R +
+--R 2 3 3 4 2 2 5 8
+--R (- 42840a c d - 115920a b c d - 38640b c d)x
+--R +
+--R 2 4 2 5 2 6 6
+--R (- 95760a c d - 110880a b c d - 13440b c )x
+--R +
+--R 2 5 6 4 2 6 2
+--R (- 100800a c d - 40320a b c )x - 40320a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 18 6 2 5 16
+--R 35b d x + (90a b d + 1485b c d )x
+--R +
+--R 2 6 5 2 2 4 14
+--R (63a d + 3834a b c d + 11853b c d )x
+--R +
+--R 2 5 2 4 2 3 3 12
+--R (2709a c d + 31122a b c d + 38199b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 10
+--R (22869a c d + 102942a b c d + 59724b c d )x
+--R +
+--R 2 3 3 4 2 2 5 8
+--R (80640a c d + 166320a b c d + 45360b c d)x
+--R +
+--R 2 4 2 5 2 6 6
+--R (141120a c d + 131040a b c d + 13440b c )x
+--R +
+--R 2 5 6 4 2 6 2
+--R (120960a c d + 40320a b c )x + 40320a c x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (315d x + 12600c d x + 75600c d x + 141120c d x + 80640c )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 2835c d x - 37800c d x - 136080c d x - 181440c d x - 80640c
+--R Type: Union(Expression(Integer),...)
+--E 863
+
+--S 864 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 6 4 5 2 5 4 8
+--R (63a c d - 36a b c d + 8b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 6
+--R (2520a c d - 1440a b c d + 320b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 4
+--R (15120a c d - 8640a b c d + 1920b c d )x
+--R +
+--R 2 6 3 7 2 2 8 2 2 7 2
+--R (28224a c d - 16128a b c d + 3584b c d)x + 16128a c d
+--R +
+--R 8 2 9
+--R - 9216a b c d + 2048b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 6 4 5 2 5 4 8
+--R (- 567a c d + 324a b c d - 72b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 6
+--R (- 7560a c d + 4320a b c d - 960b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 4
+--R (- 27216a c d + 15552a b c d - 3456b c d )x
+--R +
+--R 2 6 3 7 2 2 8 2 2 7 2
+--R (- 36288a c d + 20736a b c d - 4608b c d)x - 16128a c d
+--R +
+--R 8 2 9
+--R 9216a b c d - 2048b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +-+
+--R (315d x + 12600c d x + 75600c d x + 141120c d x + 80640c d )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 7 8 2 6 6 3 5 4 4 4 2 5 3
+--R - 2835c d x - 37800c d x - 136080c d x - 181440c d x - 80640c d
+--R Type: Expression(Integer)
+--E 864
+
+--S 865 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 865
+
+)clear all
+
+--S 866 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 866
+
+--S 867 of 1397
+r0:=1/128*c^2*(3*b^2*c^2-16*a*b*c*d+48*a^2*d^2)*atanh(x*sqrt(d)/_
+ sqrt(c+d*x^2))/d^(5/2)-1/384*(9*b^3*c^3+30*a*b^2*c^2*d-_
+ 176*a^2*b*c*d^2+32*a^3*d^3)*x*sqrt(c+d*x^2)/(b*d^2)+1/48*_
+ (9*b*c-2*a*d)*x*(a+b*x^2)^2*sqrt(c+d*x^2)/b+1/8*d*x*(a+_
+ b*x^2)^3*sqrt(c+d*x^2)/b+1/192*x*(a*c*(39*b*c-4*a*d)+_
+ (3*b^2*c^2+40*a*b*c*d-8*a^2*d^2)*x^2)*sqrt(c+d*x^2)/d
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 3 2 4 x\|d
+--R (144a c d - 48a b c d + 9b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 7 3 2 2 5
+--R 48b d x + (128a b d + 72b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (96a d + 224a b c d + 6b c d)x + (240a c d + 48a b c d - 9b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R 2 +-+
+--R 384d \|d
+--R Type: Expression(Integer)
+--E 867
+
+--S 868 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 5 3 4 2 4 3 6
+--R (1152a c d - 384a b c d + 72b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (11520a c d - 3840a b c d + 720b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (27648a c d - 9216a b c d + 1728b c d)x + 18432a c d
+--R +
+--R 6 2 7
+--R - 6144a b c d + 1152b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 2 6 3 5 2 4 4 8
+--R (- 144a c d + 48a b c d - 9b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 6
+--R (- 4608a c d + 1536a b c d - 288b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 4
+--R (- 23040a c d + 7680a b c d - 1440b c d )x
+--R +
+--R 2 5 3 6 2 2 7 2 2 6 2
+--R (- 36864a c d + 12288a b c d - 2304b c d)x - 18432a c d
+--R +
+--R 7 2 8
+--R 6144a b c d - 1152b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 7 15 7 2 6 13
+--R - 48b d x + (- 128a b d - 1608b c d )x
+--R +
+--R 2 7 6 2 2 5 11
+--R (- 96a d - 4320a b c d - 9990b c d )x
+--R +
+--R 2 6 2 5 2 3 4 9
+--R (- 3312a c d - 27696a b c d - 23991b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 7
+--R (- 23040a c d - 70144a b c d - 25248b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 5
+--R (- 62976a c d - 81408a b c d - 9312b c d )x
+--R +
+--R 2 4 3 5 2 2 6 3
+--R (- 73728a c d - 40960a b c d + 1536b c d)x
+--R +
+--R 2 5 2 6 2 7
+--R (- 30720a c d - 6144a b c d + 1152b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 7 15 7 2 6 13
+--R 384b d x + (1024a b d + 4800b c d )x
+--R +
+--R 2 7 6 2 2 5 11
+--R (768a d + 13056a b c d + 19440b c d )x
+--R +
+--R 2 6 2 5 2 3 4 9
+--R (10368a c d + 54912a b c d + 35400b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 7
+--R (47232a c d + 106112a b c d + 30024b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 5
+--R (96000a c d + 101120a b c d + 8688b c d )x
+--R +
+--R 2 4 3 5 2 2 6 3
+--R (89088a c d + 44032a b c d - 2112b c d)x
+--R +
+--R 2 5 2 6 2 7
+--R (30720a c d + 6144a b c d - 1152b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 +-+ +-+ | 2
+--R (3072d x + 30720c d x + 73728c d x + 49152c d )\|c \|d \|d x + c
+--R +
+--R 6 8 5 6 2 4 4 3 3 2 4 2 +-+
+--R (- 384d x - 12288c d x - 61440c d x - 98304c d x - 49152c d )\|d
+--R ,
+--R
+--R 2 2 5 3 4 2 4 3 6
+--R (2304a c d - 768a b c d + 144b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (23040a c d - 7680a b c d + 1440b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (55296a c d - 18432a b c d + 3456b c d)x + 36864a c d
+--R +
+--R 6 2 7
+--R - 12288a b c d + 2304b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 2 6 3 5 2 4 4 8
+--R (- 288a c d + 96a b c d - 18b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 6
+--R (- 9216a c d + 3072a b c d - 576b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 4
+--R (- 46080a c d + 15360a b c d - 2880b c d )x
+--R +
+--R 2 5 3 6 2 2 7 2 2 6 2
+--R (- 73728a c d + 24576a b c d - 4608b c d)x - 36864a c d
+--R +
+--R 7 2 8
+--R 12288a b c d - 2304b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 7 15 7 2 6 13
+--R - 48b d x + (- 128a b d - 1608b c d )x
+--R +
+--R 2 7 6 2 2 5 11
+--R (- 96a d - 4320a b c d - 9990b c d )x
+--R +
+--R 2 6 2 5 2 3 4 9
+--R (- 3312a c d - 27696a b c d - 23991b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 7
+--R (- 23040a c d - 70144a b c d - 25248b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 5
+--R (- 62976a c d - 81408a b c d - 9312b c d )x
+--R +
+--R 2 4 3 5 2 2 6 3
+--R (- 73728a c d - 40960a b c d + 1536b c d)x
+--R +
+--R 2 5 2 6 2 7
+--R (- 30720a c d - 6144a b c d + 1152b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 7 15 7 2 6 13
+--R 384b d x + (1024a b d + 4800b c d )x
+--R +
+--R 2 7 6 2 2 5 11
+--R (768a d + 13056a b c d + 19440b c d )x
+--R +
+--R 2 6 2 5 2 3 4 9
+--R (10368a c d + 54912a b c d + 35400b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 7
+--R (47232a c d + 106112a b c d + 30024b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 5
+--R (96000a c d + 101120a b c d + 8688b c d )x
+--R +
+--R 2 4 3 5 2 2 6 3
+--R (89088a c d + 44032a b c d - 2112b c d)x
+--R +
+--R 2 5 2 6 2 7
+--R (30720a c d + 6144a b c d - 1152b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 +---+ +-+ | 2
+--R (3072d x + 30720c d x + 73728c d x + 49152c d )\|- d \|c \|d x + c
+--R +
+--R 6 8 5 6 2 4 4 3 3 2 4 2 +---+
+--R (- 384d x - 12288c d x - 61440c d x - 98304c d x - 49152c d )\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 868
+
+--S 869 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 3 2 4
+--R (48a c d - 16a b c d + 3b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 3 2 4 x\|d
+--R (- 48a c d + 16a b c d - 3b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2 +-+
+--R 128d \|d
+--R Type: Expression(Integer)
+--E 869
+
+--S 870 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 870
+
+--S 871 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 3 2 4 +---+ x\|d
+--R (- 48a c d + 16a b c d - 3b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 3 2 4 +-+ \|- d \|d x + c - \|- d \|c
+--R (96a c d - 32a b c d + 6b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 2 +---+ +-+
+--R 128d \|- d \|d
+--R Type: Expression(Integer)
+--E 871
+
+--S 872 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 872
+
+)clear all
+
+--S 873 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(3/2)/x
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R (1) ---------------------------------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 873
+
+--S 874 of 1397
+r0:=1/3*a^2*(c+d*x^2)^(3/2)-2/35*b*(b*c-7*a*d)*(c+d*x^2)^(5/2)/d^2+_
+ 1/7*b^2*x^2*(c+d*x^2)^(5/2)/d-a^2*c^(3/2)*atanh(sqrt(c+d*x^2)/_
+ sqrt(c))+a^2*c*sqrt(c+d*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 2 +-+ \|d x + c
+--R - 105a c d \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 6 3 2 2 4 2 3 2 2 2 2
+--R 15b d x + (42a b d + 24b c d )x + (35a d + 84a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3
+--R 140a c d + 42a b c d - 6b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2
+--R 105d
+--R Type: Expression(Integer)
+--E 874
+
+--S 875 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 2 3 6 2 3 2 4 2 4 2 2 5 | 2
+--R (105a c d x + 2520a c d x + 8400a c d x + 6720a c )\|d x + c
+--R +
+--R 2 2 3 6 2 3 2 4 2 4 2 2 5 +-+
+--R (- 735a c d x - 5880a c d x - 11760a c d x - 6720a c )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 4 12 4 2 2 3 10
+--R - 105b c d x + (- 294a b c d - 1008b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (- 245a c d - 2940a b c d - 3045b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (- 2800a c d - 9660a b c d - 3780b c d)x
+--R +
+--R 2 3 2 4 2 5 4
+--R (- 8400a c d - 13440a b c d - 1680b c )x
+--R +
+--R 2 4 5 2
+--R (- 6720a c d - 6720a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 14 5 2 4 12
+--R 15b d x + (42a b d + 399b c d )x
+--R +
+--R 2 5 4 2 2 3 10
+--R (35a d + 1134a b c d + 2163b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (1015a c d + 6510a b c d + 4725b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (6160a c d + 15540a b c d + 4620b c d)x
+--R +
+--R 2 3 2 4 2 5 4 2 4 5 2
+--R (11760a c d + 16800a b c d + 1680b c )x + (6720a c d + 6720a b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (105d x + 2520c d x + 8400c d x + 6720c )\|c \|d x + c - 735c d x
+--R +
+--R 2 2 4 3 2 4
+--R - 5880c d x - 11760c d x - 6720c
+--R Type: Union(Expression(Integer),...)
+--E 875
+
+--S 876 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 5 6 2 3 4 4 2 4 3 2 2 5 2 | 2
+--R (105a c d x + 2520a c d x + 8400a c d x + 6720a c d )\|d x + c
+--R +
+--R 2 2 5 6 2 3 4 4 2 4 3 2 2 5 2 +-+
+--R (- 735a c d x - 5880a c d x - 11760a c d x - 6720a c d )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 5 6 2 3 4 4 2 4 3 2 2 5 2 | 2
+--R (105a c d x + 2520a c d x + 8400a c d x + 6720a c d )\|d x + c
+--R +
+--R 2 2 5 6 2 3 4 4 2 4 3 2 2 5 2 +-+
+--R (- 735a c d x - 5880a c d x - 11760a c d x - 6720a c d )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (140a c d + 42a b c d - 6b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (3360a c d + 1008a b c d - 144b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2 6
+--R (11200a c d + 3360a b c d - 480b c d)x + 8960a c d + 2688a b c d
+--R +
+--R 2 7
+--R - 384b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (- 980a c d - 294a b c d + 42b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (- 7840a c d - 2352a b c d + 336b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (- 15680a c d - 4704a b c d + 672b c d)x - 8960a c d
+--R +
+--R 6 2 7
+--R - 2688a b c d + 384b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 +-+ | 2 5 6
+--R (105d x + 2520c d x + 8400c d x + 6720c d )\|c \|d x + c - 735c d x
+--R +
+--R 2 4 4 3 3 2 4 2
+--R - 5880c d x - 11760c d x - 6720c d
+--R Type: Expression(Integer)
+--E 876
+
+--S 877 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 877
+
+)clear all
+
+--S 878 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(3/2)/x^2
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R (1) ---------------------------------------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 878
+
+--S 879 of 1397
+r0:=-1/24*(b^2*c^2-12*a*d*(b*c+2*a*d))*x*(c+d*x^2)^(3/2)/(c*d)-_
+ a^2*(c+d*x^2)^(5/2)/(c*x)+1/6*b^2*x*(c+d*x^2)^(5/2)/d-_
+ 1/16*c*(b^2*c^2-12*a*d*(b*c+2*a*d))*atanh(x*sqrt(d)/_
+ sqrt(c+d*x^2))/d^(3/2)-1/16*(b^2*c^2-12*a*d*(b*c+2*a*d))*x*_
+ sqrt(c+d*x^2)/d
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 3 x\|d
+--R (72a c d + 36a b c d - 3b c )x atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 4 2 2 2 2 2
+--R 8b d x + (24a b d + 14b c d)x + (24a d + 60a b c d + 3b c )x
+--R +
+--R 2
+--R - 48a c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R +-+
+--R 48d x\|d
+--R Type: Expression(Integer)
+--E 879
+
+--S 880 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 5 2 4 2 3 3 7
+--R (72a c d + 36a b c d - 3b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 5
+--R (1728a c d + 864a b c d - 72b c d )x
+--R +
+--R 2 3 3 4 2 2 5 3
+--R (5760a c d + 2880a b c d - 240b c d)x
+--R +
+--R 2 4 2 5 2 6
+--R (4608a c d + 2304a b c d - 192b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 7
+--R (- 504a c d - 252a b c d + 21b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 5
+--R (- 4032a c d - 2016a b c d + 168b c d )x
+--R +
+--R 2 3 3 4 2 2 5 3
+--R (- 8064a c d - 4032a b c d + 336b c d)x
+--R +
+--R 2 4 2 5 2 6
+--R (- 4608a c d - 2304a b c d + 192b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 5 12 5 2 4 10
+--R - 56b d x + (- 168a b d - 546b c d )x
+--R +
+--R 2 5 4 2 2 3 8
+--R (- 168a d - 1764a b c d - 1701b c d )x
+--R +
+--R 2 4 2 3 2 3 2 6
+--R (- 1008a c d - 6048a b c d - 2248b c d )x
+--R +
+--R 3 2 2 4 4
+--R (- 8256a b c d - 1232b c d)x
+--R +
+--R 2 3 2 4 2 5 2 2 4
+--R (3840a c d - 3840a b c d - 192b c )x + 3072a c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 2 6 14 6 2 5 12
+--R 8b d x + (24a b d + 214b c d )x
+--R +
+--R 2 6 5 2 2 4 10
+--R (24a d + 660a b c d + 1185b c d )x
+--R +
+--R 2 5 2 4 2 3 3 8
+--R (552a c d + 3996a b c d + 2683b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 6
+--R (1296a c d + 9696a b c d + 2840b c d )x
+--R +
+--R 2 3 3 4 2 2 5 4
+--R (- 1536a c d + 10176a b c d + 1328b c d)x
+--R +
+--R 2 4 2 5 2 6 2 2 5
+--R (- 5376a c d + 3840a b c d + 192b c )x - 3072a c d
+--R *
+--R +-+
+--R \|d
+--R /
+--R +--------+
+--R 4 7 3 5 2 2 3 3 +-+ | 2
+--R (48d x + 1152c d x + 3840c d x + 3072c d x)\|d \|d x + c
+--R +
+--R 4 7 3 5 2 2 3 3 +-+ +-+
+--R (- 336d x - 2688c d x - 5376c d x - 3072c d x)\|c \|d
+--R ,
+--R
+--R 2 5 2 4 2 3 3 7
+--R (144a c d + 72a b c d - 6b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 5
+--R (3456a c d + 1728a b c d - 144b c d )x
+--R +
+--R 2 3 3 4 2 2 5 3
+--R (11520a c d + 5760a b c d - 480b c d)x
+--R +
+--R 2 4 2 5 2 6
+--R (9216a c d + 4608a b c d - 384b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 7
+--R (- 1008a c d - 504a b c d + 42b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 5
+--R (- 8064a c d - 4032a b c d + 336b c d )x
+--R +
+--R 2 3 3 4 2 2 5 3
+--R (- 16128a c d - 8064a b c d + 672b c d)x
+--R +
+--R 2 4 2 5 2 6
+--R (- 9216a c d - 4608a b c d + 384b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 5 12 5 2 4 10
+--R - 56b d x + (- 168a b d - 546b c d )x
+--R +
+--R 2 5 4 2 2 3 8
+--R (- 168a d - 1764a b c d - 1701b c d )x
+--R +
+--R 2 4 2 3 2 3 2 6
+--R (- 1008a c d - 6048a b c d - 2248b c d )x
+--R +
+--R 3 2 2 4 4
+--R (- 8256a b c d - 1232b c d)x
+--R +
+--R 2 3 2 4 2 5 2 2 4
+--R (3840a c d - 3840a b c d - 192b c )x + 3072a c d
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 2 6 14 6 2 5 12
+--R 8b d x + (24a b d + 214b c d )x
+--R +
+--R 2 6 5 2 2 4 10
+--R (24a d + 660a b c d + 1185b c d )x
+--R +
+--R 2 5 2 4 2 3 3 8
+--R (552a c d + 3996a b c d + 2683b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 6
+--R (1296a c d + 9696a b c d + 2840b c d )x
+--R +
+--R 2 3 3 4 2 2 5 4
+--R (- 1536a c d + 10176a b c d + 1328b c d)x
+--R +
+--R 2 4 2 5 2 6 2 2 5
+--R (- 5376a c d + 3840a b c d + 192b c )x - 3072a c d
+--R *
+--R +---+
+--R \|- d
+--R /
+--R +--------+
+--R 4 7 3 5 2 2 3 3 +---+ | 2
+--R (48d x + 1152c d x + 3840c d x + 3072c d x)\|- d \|d x + c
+--R +
+--R 4 7 3 5 2 2 3 3 +---+ +-+
+--R (- 336d x - 2688c d x - 5376c d x - 3072c d x)\|- d \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 880
+
+--S 881 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 3
+--R (24a c d + 12a b c d - b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 3 x\|d
+--R (- 24a c d - 12a b c d + b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R +-+
+--R 16d\|d
+--R Type: Expression(Integer)
+--E 881
+
+--S 882 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 882
+
+--S 883 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 3 +---+ x\|d
+--R (- 24a c d - 12a b c d + b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 2 3 +-+ \|- d \|d x + c - \|- d \|c
+--R (48a c d + 24a b c d - 2b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R +---+ +-+
+--R 16d\|- d \|d
+--R Type: Expression(Integer)
+--E 883
+
+--S 884 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 884
+
+)clear all
+
+--S 885 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(3/2)/x^3
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R (1) ---------------------------------------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 885
+
+--S 886 of 1397
+r0:=1/6*a*(4*b*c+3*a*d)*(c+d*x^2)^(3/2)/c+1/5*b^2*(c+d*x^2)^(5/2)/d-_
+ 1/2*a^2*(c+d*x^2)^(5/2)/(c*x^2)-1/2*a*(4*b*c+3*a*d)*atanh(_
+ sqrt(c+d*x^2)/sqrt(c))*sqrt(c)+1/2*a*(4*b*c+3*a*d)*sqrt(c+d*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 2 2 +-+ \|d x + c
+--R (- 45a d - 60a b c d)x \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 6 2 2 4 2 2 2 2 2
+--R 6b d x + (20a b d + 12b c d)x + (30a d + 80a b c d + 6b c )x
+--R +
+--R 2
+--R - 15a c d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2
+--R 30d x
+--R Type: Expression(Integer)
+--E 886
+
+--S 887 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 3 8 2 2 3 3 2 6
+--R (45a c d + 60a b c d )x + (1080a c d + 1440a b c d )x
+--R +
+--R 2 3 2 4 4 2 4 5 2
+--R (3600a c d + 4800a b c d)x + (2880a c d + 3840a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 3 8 2 2 3 3 2 6
+--R (- 315a c d - 420a b c d )x + (- 2520a c d - 3360a b c d )x
+--R +
+--R 2 3 2 4 4 2 4 5 2
+--R (- 5040a c d - 6720a b c d)x + (- 2880a c d - 3840a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 4 12 4 2 2 3 10
+--R - 42b c d x + (- 140a b c d - 420b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (- 180a c d - 1600a b c d - 1380b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (- 855a c d - 4800a b c d - 1920b c d)x
+--R +
+--R 2 3 2 4 2 5 4 2 4 2 2 5
+--R (- 120a c d - 3840a b c d - 960b c )x + 1680a c d x + 960a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 14 5 2 4 12
+--R 6b d x + (20a b d + 162b c d )x
+--R +
+--R 2 5 4 2 2 3 10
+--R (30a d + 580a b c d + 930b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (525a c d + 3520a b c d + 2220b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (1065a c d + 6720a b c d + 2400b c d)x
+--R +
+--R 2 3 2 4 2 5 4 2 4 2 2 5
+--R (- 600a c d + 3840a b c d + 960b c )x - 2160a c d x - 960a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 8 2 6 2 4 3 2 +-+ | 2 3 8
+--R (30d x + 720c d x + 2400c d x + 1920c x )\|c \|d x + c - 210c d x
+--R +
+--R 2 2 6 3 4 4 2
+--R - 1680c d x - 3360c d x - 1920c x
+--R Type: Union(Expression(Integer),...)
+--E 887
+
+--S 888 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 5 2 4 6 2 2 4 3 3 4
+--R (45a c d + 60a b c d )x + (1080a c d + 1440a b c d )x
+--R +
+--R 2 3 3 4 2 2 2 4 2 5
+--R (3600a c d + 4800a b c d )x + 2880a c d + 3840a b c d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 2 4 6 2 2 4 3 3 4
+--R (- 315a c d - 420a b c d )x + (- 2520a c d - 3360a b c d )x
+--R +
+--R 2 3 3 4 2 2 2 4 2 5
+--R (- 5040a c d - 6720a b c d )x - 2880a c d - 3840a b c d
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 5 2 4 6 2 2 4 3 3 4
+--R (45a c d + 60a b c d )x + (1080a c d + 1440a b c d )x
+--R +
+--R 2 3 3 4 2 2 2 4 2 5
+--R (3600a c d + 4800a b c d )x + 2880a c d + 3840a b c d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 2 4 6 2 2 4 3 3 4
+--R (- 315a c d - 420a b c d )x + (- 2520a c d - 3360a b c d )x
+--R +
+--R 2 3 3 4 2 2 2 4 2 5
+--R (- 5040a c d - 6720a b c d )x - 2880a c d - 3840a b c d
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (30a c d + 80a b c d + 6b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (720a c d + 1920a b c d + 144b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5
+--R (2400a c d + 6400a b c d + 480b c d)x + 1920a c d + 5120a b c d
+--R +
+--R 2 6
+--R 384b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 210a c d - 560a b c d - 42b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 1680a c d - 4480a b c d - 336b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5
+--R (- 3360a c d - 8960a b c d - 672b c d)x - 1920a c d - 5120a b c d
+--R +
+--R 2 6
+--R - 384b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 6 3 4 2 2 2 3 +-+ | 2 4 6
+--R (30d x + 720c d x + 2400c d x + 1920c d)\|c \|d x + c - 210c d x
+--R +
+--R 2 3 4 3 2 2 4
+--R - 1680c d x - 3360c d x - 1920c d
+--R Type: Expression(Integer)
+--E 888
+
+--S 889 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 889
+
+)clear all
+
+--S 890 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(3/2)/x^4
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R (1) ---------------------------------------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 890
+
+--S 891 of 1397
+r0:=1/12*(3*b^2*c^2+8*a*d*(3*b*c+a*d))*x*(c+d*x^2)^(3/2)/c^2-_
+ 1/3*a^2*(c+d*x^2)^(5/2)/(c*x^3)-2/3*a*(3*b*c+a*d)*_
+ (c+d*x^2)^(5/2)/(c^2*x)+1/8*(3*b^2*c^2+8*a*d*(3*b*c+a*d))*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))/sqrt(d)+1/8*(3*b^2*c^2+_
+ 8*a*d*(3*b*c+a*d))*x*sqrt(c+d*x^2)/c
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 3 x\|d
+--R (24a d + 72a b c d + 9b c )x atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 2 4 2 2 2 +-+
+--R (6b d x + (24a b d + 15b c)x + (- 32a d - 48a b c)x - 8a c)\|d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 +-+
+--R 24x \|d
+--R Type: Expression(Integer)
+--E 891
+
+--S 892 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 5 4 2 2 3 9
+--R (24a d + 72a b c d + 9b c d )x
+--R +
+--R 2 4 2 3 2 3 2 7
+--R (576a c d + 1728a b c d + 216b c d )x
+--R +
+--R 2 2 3 3 2 2 4 5
+--R (1920a c d + 5760a b c d + 720b c d)x
+--R +
+--R 2 3 2 4 2 5 3
+--R (1536a c d + 4608a b c d + 576b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 4 2 2 3 9
+--R (- 168a d - 504a b c d - 63b c d )x
+--R +
+--R 2 4 2 3 2 3 2 7
+--R (- 1344a c d - 4032a b c d - 504b c d )x
+--R +
+--R 2 2 3 3 2 2 4 5
+--R (- 2688a c d - 8064a b c d - 1008b c d)x
+--R +
+--R 2 3 2 4 2 5 3
+--R (- 1536a c d - 4608a b c d - 576b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 4 12 4 2 3 10
+--R - 42b d x + (- 168a b d - 441b c d )x
+--R +
+--R 2 4 3 2 2 2 8
+--R (224a d - 1008a b c d - 1512b c d )x
+--R +
+--R 2 3 2 3 6 2 2 2 3 2 4 4
+--R (1848a c d - 2064b c d)x + (4032a c d + 3840a b c d - 960b c )x
+--R +
+--R 2 3 4 2 2 4
+--R (2944a c d + 3072a b c )x + 512a c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 2 5 14 5 2 4 12
+--R 6b d x + (24a b d + 165b c d )x
+--R +
+--R 2 5 4 2 2 3 10
+--R (- 32a d + 552a b c d + 999b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (- 808a c d + 1296a b c d + 2424b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (- 3528a c d - 1536a b c d + 2544b c d)x
+--R +
+--R 2 3 2 4 2 5 4
+--R (- 5440a c d - 5376a b c d + 960b c )x
+--R +
+--R 2 4 5 2 2 5
+--R (- 3200a c d - 3072a b c )x - 512a c
+--R *
+--R +-+
+--R \|d
+--R /
+--R +--------+
+--R 3 9 2 7 2 5 3 3 +-+ | 2
+--R (24d x + 576c d x + 1920c d x + 1536c x )\|d \|d x + c
+--R +
+--R 3 9 2 7 2 5 3 3 +-+ +-+
+--R (- 168d x - 1344c d x - 2688c d x - 1536c x )\|c \|d
+--R ,
+--R
+--R 2 5 4 2 2 3 9
+--R (48a d + 144a b c d + 18b c d )x
+--R +
+--R 2 4 2 3 2 3 2 7
+--R (1152a c d + 3456a b c d + 432b c d )x
+--R +
+--R 2 2 3 3 2 2 4 5
+--R (3840a c d + 11520a b c d + 1440b c d)x
+--R +
+--R 2 3 2 4 2 5 3
+--R (3072a c d + 9216a b c d + 1152b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 4 2 2 3 9
+--R (- 336a d - 1008a b c d - 126b c d )x
+--R +
+--R 2 4 2 3 2 3 2 7
+--R (- 2688a c d - 8064a b c d - 1008b c d )x
+--R +
+--R 2 2 3 3 2 2 4 5
+--R (- 5376a c d - 16128a b c d - 2016b c d)x
+--R +
+--R 2 3 2 4 2 5 3
+--R (- 3072a c d - 9216a b c d - 1152b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 4 12 4 2 3 10
+--R - 42b d x + (- 168a b d - 441b c d )x
+--R +
+--R 2 4 3 2 2 2 8
+--R (224a d - 1008a b c d - 1512b c d )x
+--R +
+--R 2 3 2 3 6 2 2 2 3 2 4 4
+--R (1848a c d - 2064b c d)x + (4032a c d + 3840a b c d - 960b c )x
+--R +
+--R 2 3 4 2 2 4
+--R (2944a c d + 3072a b c )x + 512a c
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 2 5 14 5 2 4 12
+--R 6b d x + (24a b d + 165b c d )x
+--R +
+--R 2 5 4 2 2 3 10
+--R (- 32a d + 552a b c d + 999b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (- 808a c d + 1296a b c d + 2424b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (- 3528a c d - 1536a b c d + 2544b c d)x
+--R +
+--R 2 3 2 4 2 5 4
+--R (- 5440a c d - 5376a b c d + 960b c )x
+--R +
+--R 2 4 5 2 2 5
+--R (- 3200a c d - 3072a b c )x - 512a c
+--R *
+--R +---+
+--R \|- d
+--R /
+--R +--------+
+--R 3 9 2 7 2 5 3 3 +---+ | 2
+--R (24d x + 576c d x + 1920c d x + 1536c x )\|- d \|d x + c
+--R +
+--R 3 9 2 7 2 5 3 3 +---+ +-+
+--R (- 168d x - 1344c d x - 2688c d x - 1536c x )\|- d \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 892
+
+--S 893 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2
+--R (8a d + 24a b c d + 3b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 x\|d
+--R (- 8a d - 24a b c d - 3b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R +-+
+--R 8\|d
+--R Type: Expression(Integer)
+--E 893
+
+--S 894 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 894
+
+--S 895 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 8a d - 24a b c d - 3b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 2 +-+ \|- d \|d x + c - \|- d \|c
+--R (16a d + 48a b c d + 6b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R +---+ +-+
+--R 8\|- d \|d
+--R Type: Expression(Integer)
+--E 895
+
+--S 896 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 896
+
+)clear all
+
+--S 897 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(3/2)/x^5
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R (1) ---------------------------------------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 897
+
+--S 898 of 1397
+r0:=1/24*(8*b^2*c^2+3*a*d*(8*b*c+a*d))*(c+d*x^2)^(3/2)/c^2-_
+ 1/4*a^2*(c+d*x^2)^(5/2)/(c*x^4)-1/8*a*(8*b*c+a*d)*_
+ (c+d*x^2)^(5/2)/(c^2*x^2)-1/8*(8*b^2*c^2+3*a*d*(8*b*c+a*d))*_
+ atanh(sqrt(c+d*x^2)/sqrt(c))/sqrt(c)+1/8*(8*b^2*c^2+_
+ 3*a*d*(8*b*c+a*d))*sqrt(c+d*x^2)/c
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 2 2 2 4 \|d x + c
+--R (- 9a d - 72a b c d - 24b c )x atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 6 2 4 2 2 2 +-+
+--R (8b d x + (48a b d + 32b c)x + (- 15a d - 24a b c)x - 6a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4 +-+
+--R 24x \|c
+--R Type: Expression(Integer)
+--E 898
+
+--S 899 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 4 2 2 3 10
+--R (9a d + 72a b c d + 24b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (216a c d + 1728a b c d + 576b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (720a c d + 5760a b c d + 1920b c d)x
+--R +
+--R 2 3 2 4 2 5 4
+--R (576a c d + 4608a b c d + 1536b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 4 2 2 3 10
+--R (- 63a d - 504a b c d - 168b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (- 504a c d - 4032a b c d - 1344b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (- 1008a c d - 8064a b c d - 2688b c d)x
+--R +
+--R 2 3 2 4 2 5 4
+--R (- 576a c d - 4608a b c d - 1536b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 4 12 4 2 2 3 10
+--R - 56b c d x + (- 288a b c d - 640b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (105a c d - 1368a b c d - 1920b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (882a c d - 192a b c d - 1536b c d)x
+--R +
+--R 2 3 2 4 4 2 4 5 2 2 5
+--R (2016a c d + 2688a b c d)x + (1632a c d + 1536a b c )x + 384a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 14 5 2 4 12
+--R 8b d x + (48a b d + 232b c d )x
+--R +
+--R 2 5 4 2 2 3 10
+--R (- 15a d + 840a b c d + 1408b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (- 381a c d + 1704a b c d + 2688b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (- 1710a c d - 960a b c d + 1536b c d)x
+--R +
+--R 2 3 2 4 4 2 4 5 2 2 5
+--R (- 2784a c d - 3456a b c d)x + (- 1824a c d - 1536a b c )x - 384a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 10 2 8 2 6 3 4 +-+ | 2 3 10
+--R (24d x + 576c d x + 1920c d x + 1536c x )\|c \|d x + c - 168c d x
+--R +
+--R 2 2 8 3 6 4 4
+--R - 1344c d x - 2688c d x - 1536c x
+--R Type: Union(Expression(Integer),...)
+--E 899
+
+--S 900 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 2 2 2 2 \|d x + c - \|c
+--R (9a d + 72a b c d + 24b c )log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 2 2 2 2 \|d x + c 2 2
+--R (9a d + 72a b c d + 24b c )atanh(-----------) + 48a b c d + 32b c
+--R +-+
+--R \|c
+--R /
+--R +-+
+--R 24\|c
+--R Type: Expression(Integer)
+--E 900
+
+--S 901 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 901
+
+)clear all
+
+--S 902 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(3/2)/x^6
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R (1) ---------------------------------------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 902
+
+--S 903 of 1397
+r0:=-1/3*b*(3*b*c+4*a*d)*(c+d*x^2)^(3/2)/(c*x)-1/5*a^2*_
+ (c+d*x^2)^(5/2)/(c*x^5)-2/3*a*b*(c+d*x^2)^(5/2)/(c*x^3)+_
+ 1/2*b*(3*b*c+4*a*d)*atanh(x*sqrt(d)/sqrt(c+d*x^2))*sqrt(d)+_
+ 1/2*b*d*(3*b*c+4*a*d)*x*sqrt(c+d*x^2)/c
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 5 +-+ x\|d
+--R (60a b c d + 45b c )x \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 2 2 2 2 4
+--R 15b c d x + (- 6a d - 80a b c d - 30b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 12a c d - 20a b c )x - 6a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 5
+--R 30c x
+--R Type: Expression(Integer)
+--E 903
+
+--S 904 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 2 2 3 11 2 3 2 3 2 9
+--R (60a b c d + 45b c d )x + (1440a b c d + 1080b c d )x
+--R +
+--R 3 2 2 4 7 4 2 5 5
+--R (4800a b c d + 3600b c d)x + (3840a b c d + 2880b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 4 2 2 3 11
+--R (- 420a b c d - 315b c d )x
+--R +
+--R 2 3 2 3 2 9
+--R (- 3360a b c d - 2520b c d )x
+--R +
+--R 3 2 2 4 7 4 2 5 5
+--R (- 6720a b c d - 5040b c d)x + (- 3840a b c d - 2880b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 4 12 2 5 4 2 2 3 10
+--R - 105b c d x + (42a d + 560a b c d - 630b c d )x
+--R +
+--R 2 4 2 3 8
+--R (420a c d + 4620a b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (1386a c d + 10080a b c d + 2400b c d)x
+--R +
+--R 2 3 2 4 2 5 4
+--R (2064a c d + 7360a b c d + 1920b c )x
+--R +
+--R 2 4 5 2 2 5
+--R (1440a c d + 1280a b c )x + 384a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 14 2 6 5 2 2 4 12
+--R 15b c d x + (- 6a d - 80a b c d + 345b c d )x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (- 162a c d - 2020a b c d + 810b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (- 930a c d - 8820a b c d - 960b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (- 2262a c d - 13600a b c d - 3360b c d)x
+--R +
+--R 2 4 2 5 2 6 4
+--R (- 2736a c d - 8000a b c d - 1920b c )x
+--R +
+--R 2 5 6 2 2 6
+--R (- 1632a c d - 1280a b c )x - 384a c
+--R /
+--R +--------+
+--R 3 11 2 2 9 3 7 4 5 | 2
+--R (30c d x + 720c d x + 2400c d x + 1920c x )\|d x + c
+--R +
+--R 3 11 2 2 9 3 7 4 5 +-+
+--R (- 210c d x - 1680c d x - 3360c d x - 1920c x )\|c
+--R ,
+--R
+--R 4 2 2 3 11 2 3 2 3 2 9
+--R (120a b c d + 90b c d )x + (2880a b c d + 2160b c d )x
+--R +
+--R 3 2 2 4 7 4 2 5 5
+--R (9600a b c d + 7200b c d)x + (7680a b c d + 5760b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 4 2 2 3 11
+--R (- 840a b c d - 630b c d )x
+--R +
+--R 2 3 2 3 2 9
+--R (- 6720a b c d - 5040b c d )x
+--R +
+--R 3 2 2 4 7 4 2 5 5
+--R (- 13440a b c d - 10080b c d)x + (- 7680a b c d - 5760b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 2 4 12 2 5 4 2 2 3 10
+--R - 105b c d x + (42a d + 560a b c d - 630b c d )x
+--R +
+--R 2 4 2 3 8
+--R (420a c d + 4620a b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (1386a c d + 10080a b c d + 2400b c d)x
+--R +
+--R 2 3 2 4 2 5 4
+--R (2064a c d + 7360a b c d + 1920b c )x
+--R +
+--R 2 4 5 2 2 5
+--R (1440a c d + 1280a b c )x + 384a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 14 2 6 5 2 2 4 12
+--R 15b c d x + (- 6a d - 80a b c d + 345b c d )x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (- 162a c d - 2020a b c d + 810b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (- 930a c d - 8820a b c d - 960b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (- 2262a c d - 13600a b c d - 3360b c d)x
+--R +
+--R 2 4 2 5 2 6 4
+--R (- 2736a c d - 8000a b c d - 1920b c )x
+--R +
+--R 2 5 6 2 2 6
+--R (- 1632a c d - 1280a b c )x - 384a c
+--R /
+--R +--------+
+--R 3 11 2 2 9 3 7 4 5 | 2
+--R (30c d x + 720c d x + 2400c d x + 1920c x )\|d x + c
+--R +
+--R 3 11 2 2 9 3 7 4 5 +-+
+--R (- 210c d x - 1680c d x - 3360c d x - 1920c x )\|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 904
+
+--S 905 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-+
+--R (4a b d + 3b c)\|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 +-+ x\|d
+--R (- 4a b d - 3b c)\|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 905
+
+--S 906 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 906
+
+--S 907 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +-+ x\|d
+--R (- 4a b d - 3b c)\|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R | 2 +-+
+--R 2 +---+ \|d x + c - \|c
+--R (8a b d + 6b c)\|- d atan(------------------)
+--R +---+
+--R x\|- d
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 907
+
+--S 908 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 908
+
+)clear all
+
+--S 909 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(3/2)/x^7
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R (1) ---------------------------------------------------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 909
+
+--S 910 of 1397
+r0:=-1/48*(24*b^2*c^2+a*d*(12*b*c-a*d))*(c+d*x^2)^(3/2)/(c^2*x^2)-_
+ 1/6*a^2*(c+d*x^2)^(5/2)/(c*x^6)-1/24*a*(12*b*c-a*d)*(c+d*x^2)^(5/2)/_
+ (c^2*x^4)-1/16*d*(24*b^2*c^2+a*d*(12*b*c-a*d))*atanh(sqrt(c+d*x^2)/_
+ sqrt(c))/c^(3/2)+1/16*d*(24*b^2*c^2+a*d*(12*b*c-a*d))*sqrt(c+d*x^2)/c^2
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 3 2 2 2 6 \|d x + c
+--R (3a d - 36a b c d - 72b c d)x atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 6 2 2 2 2 4
+--R 48b c d x + (- 3a d - 60a b c d - 24b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 14a c d - 24a b c )x - 8a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R /
+--R 6 +-+
+--R 48c x \|c
+--R Type: Expression(Integer)
+--E 910
+
+--S 911 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 5 2 2 4 12
+--R (- 3a d + 36a b c d + 72b c d )x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (- 72a c d + 864a b c d + 1728b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (- 240a c d + 2880a b c d + 5760b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (- 192a c d + 2304a b c d + 4608b c d)x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 5 2 2 4 12
+--R (21a d - 252a b c d - 504b c d )x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (168a c d - 2016a b c d - 4032b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (336a c d - 4032a b c d - 8064b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (192a c d - 2304a b c d - 4608b c d)x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 4 12 2 5 2 4 2 3 3 10
+--R - 288b c d x + (21a c d + 420a b c d - 1368b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (266a c d + 3528a b c d - 192b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (1176a c d + 8064a b c d + 2688b c d)x
+--R +
+--R 2 4 2 5 2 6 4 2 5 6 2
+--R (2208a c d + 6528a b c d + 1536b c )x + (1792a c d + 1536a b c )x
+--R +
+--R 2 6
+--R 512a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 14 2 6 5 2 2 4 12
+--R 48b c d x + (- 3a d - 60a b c d + 840b c d )x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (- 89a c d - 1524a b c d + 1704b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (- 670a c d - 6840a b c d - 960b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (- 2088a c d - 11136a b c d - 3456b c d)x
+--R +
+--R 2 4 2 5 2 6 4
+--R (- 3040a c d - 7296a b c d - 1536b c )x
+--R +
+--R 2 5 6 2 2 6
+--R (- 2048a c d - 1536a b c )x - 512a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 12 2 2 10 3 8 4 6 +-+ | 2
+--R (48c d x + 1152c d x + 3840c d x + 3072c x )\|c \|d x + c
+--R +
+--R 2 3 12 3 2 10 4 8 5 6
+--R - 336c d x - 2688c d x - 5376c d x - 3072c x
+--R Type: Union(Expression(Integer),...)
+--E 911
+
+--S 912 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 2 3 2 2 2 \|d x + c - \|c
+--R (- a d + 12a b c d + 24b c d)log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 2 3 2 2 2 \|d x + c 2 2
+--R (- a d + 12a b c d + 24b c d)atanh(-----------) + 16b c d
+--R +-+
+--R \|c
+--R /
+--R +-+
+--R 16c\|c
+--R Type: Expression(Integer)
+--E 912
+
+--S 913 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 913
+
+)clear all
+
+--S 914 of 1397
+t0:=x^3*(a+b*x^2)^2*(c+d*x^2)^(5/2)
+--R
+--R
+--R (1)
+--R 2 2 11 2 2 9 2 2 2 2 7
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 5 2 2 3
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 914
+
+--S 915 of 1397
+r0:=-1/7*c*(b*c-a*d)^2*(c+d*x^2)^(7/2)/d^4+1/9*(b*c-a*d)*(3*b*c-a*d)*_
+ (c+d*x^2)^(9/2)/d^4-1/11*b*(3*b*c-2*a*d)*(c+d*x^2)^(11/2)/d^4+_
+ 1/13*b^2*(c+d*x^2)^(13/2)/d^4
+--R
+--R
+--R (2)
+--R 2 6 12 6 2 5 10
+--R 693b d x + (1638a b d + 1701b c d )x
+--R +
+--R 2 6 5 2 2 4 8
+--R (1001a d + 4186a b c d + 1113b c d )x
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (2717a c d + 2938a b c d + 15b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (2145a c d + 78a b c d - 18b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5 2 6
+--R (143a c d - 104a b c d + 24b c d)x - 286a c d + 208a b c d - 48b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4
+--R 9009d
+--R Type: Expression(Integer)
+--E 915
+
+--S 916 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 8 24 8 2 2 7 22
+--R - 9009b c d x + (- 21294a b c d - 274365b c d )x
+--R +
+--R 2 8 2 7 2 3 6 20
+--R (- 13013a c d - 650650a b c d - 2651649b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 18
+--R (- 399685a c d - 6331754a b c d - 12277551b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 16
+--R (- 3931785a c d - 29613870a b c d - 31760586b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 14
+--R (- 18688527a c d - 77631840a b c d - 48679488b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 12
+--R (- 50078028a c d - 120984864a b c d - 44108064b c d )x
+--R +
+--R 2 6 3 7 2 2 8 10
+--R (- 80288208a c d - 111855744a b c d - 21909888b c d)x
+--R +
+--R 2 7 2 8 2 9 8
+--R (- 76876800a c d - 56888832a b c d - 4612608b c )x
+--R +
+--R 2 8 9 6 2 9 4
+--R (- 40744704a c d - 12300288a b c )x - 9225216a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 9 26 9 2 8 24
+--R 693b d x + (1638a b d + 60606b c d )x
+--R +
+--R 2 9 8 2 2 7 22
+--R (1001a d + 143416a b c d + 980070b c d )x
+--R +
+--R 2 8 2 7 2 3 6 20
+--R (87802a c d + 2330900a b c d + 6644352b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 18
+--R (1438294a c d + 15930200a b c d + 24099933b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 16
+--R (9956232a c d + 58411782a b c d + 51776010b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 14
+--R (37156977a c d + 127217376a b c d + 68283072b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 12
+--R (82798716a c d + 170570400a b c d + 54486432b c d )x
+--R +
+--R 2 6 3 7 2 2 8 10
+--R (114210096a c d + 138762624a b c d + 24216192b c d)x
+--R +
+--R 2 7 2 8 2 9 8
+--R (96096000a c d + 63038976a b c d + 4612608b c )x
+--R +
+--R 2 8 9 6 2 9 4
+--R (45357312a c d + 12300288a b c )x + 9225216a c x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 6 12 5 10 2 4 8 3 3 6
+--R 9009d x + 756756c d x + 10090080c d x + 48432384c d x
+--R +
+--R 4 2 4 5 2 6
+--R 103783680c d x + 101477376c d x + 36900864c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 6 12 2 5 10 3 4 8 4 3 6
+--R - 117117c d x - 3279276c d x - 26234208c d x - 89945856c d x
+--R +
+--R 5 2 4 6 2 7
+--R - 149909760c d x - 119927808c d x - 36900864c
+--R Type: Union(Expression(Integer),...)
+--E 916
+
+--S 917 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 5 8 6 7 2 7 6 12
+--R (- 286a c d + 208a b c d - 48b c d )x
+--R +
+--R 2 6 7 7 6 2 8 5 10
+--R (- 24024a c d + 17472a b c d - 4032b c d )x
+--R +
+--R 2 7 6 8 5 2 9 4 8
+--R (- 320320a c d + 232960a b c d - 53760b c d )x
+--R +
+--R 2 8 5 9 4 2 10 3 6
+--R (- 1537536a c d + 1118208a b c d - 258048b c d )x
+--R +
+--R 2 9 4 10 3 2 11 2 4
+--R (- 3294720a c d + 2396160a b c d - 552960b c d )x
+--R +
+--R 2 10 3 11 2 2 12 2
+--R (- 3221504a c d + 2342912a b c d - 540672b c d)x
+--R +
+--R 2 11 2 12 2 13
+--R - 1171456a c d + 851968a b c d - 196608b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 8 6 7 2 7 6 12
+--R (3718a c d - 2704a b c d + 624b c d )x
+--R +
+--R 2 6 7 7 6 2 8 5 10
+--R (104104a c d - 75712a b c d + 17472b c d )x
+--R +
+--R 2 7 6 8 5 2 9 4 8
+--R (832832a c d - 605696a b c d + 139776b c d )x
+--R +
+--R 2 8 5 9 4 2 10 3 6
+--R (2855424a c d - 2076672a b c d + 479232b c d )x
+--R +
+--R 2 9 4 10 3 2 11 2 4
+--R (4759040a c d - 3461120a b c d + 798720b c d )x
+--R +
+--R 2 10 3 11 2 2 12 2 2 11 2
+--R (3807232a c d - 2768896a b c d + 638976b c d)x + 1171456a c d
+--R +
+--R 12 2 13
+--R - 851968a b c d + 196608b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 10 12 9 10 2 8 8 3 7 6
+--R 9009d x + 756756c d x + 10090080c d x + 48432384c d x
+--R +
+--R 4 6 4 5 5 2 6 4
+--R 103783680c d x + 101477376c d x + 36900864c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 10 12 2 9 10 3 8 8 4 7 6
+--R - 117117c d x - 3279276c d x - 26234208c d x - 89945856c d x
+--R +
+--R 5 6 4 6 5 2 7 4
+--R - 149909760c d x - 119927808c d x - 36900864c d
+--R Type: Expression(Integer)
+--E 917
+
+--S 918 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 918
+
+)clear all
+
+--S 919 of 1397
+t0:=x^2*(a+b*x^2)^2*(c+d*x^2)^(5/2)
+--R
+--R
+--R (1)
+--R 2 2 10 2 2 8 2 2 2 2 6
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 4 2 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 919
+
+--S 920 of 1397
+r0:=1/384*c*(40*a^2*d^2+b*c*(5*b*c-24*a*d))*x^3*(c+d*x^2)^(3/2)/d^2+_
+ 1/320*(40*a^2*d^2+b*c*(5*b*c-24*a*d))*x^3*(c+d*x^2)^(5/2)/d^2-_
+ 1/120*b*(5*b*c-24*a*d)*x^3*(c+d*x^2)^(7/2)/d^2+1/12*b^2*_
+ x^5*(c+d*x^2)^(7/2)/d-1/1024*c^4*(40*a^2*d^2+b*c*(5*b*c-24*a*d))*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))/d^(7/2)+1/1024*c^3*(40*a^2*d^2+_
+ b*c*(5*b*c-24*a*d))*x*sqrt(c+d*x^2)/d^3+1/512*c^2*(40*a^2*d^2+_
+ b*c*(5*b*c-24*a*d))*x^3*sqrt(c+d*x^2)/d^2
+--R
+--R
+--R (2)
+--R +-+
+--R 2 4 2 5 2 6 x\|d
+--R (- 600a c d + 360a b c d - 75b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 11 5 2 4 9
+--R 1280b d x + (3072a b d + 3200b c d )x
+--R +
+--R 2 5 4 2 2 3 7
+--R (1920a d + 8064a b c d + 2160b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (5440a c d + 5952a b c d + 40b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3
+--R (4720a c d + 240a b c d - 50b c d)x
+--R +
+--R 2 3 2 4 2 5
+--R (600a c d - 360a b c d + 75b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R 3 +-+
+--R 15360d \|d
+--R Type: Expression(Integer)
+--E 920
+
+--S 921 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 7 5 6 2 6 5 10
+--R (7200a c d - 4320a b c d + 900b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 8
+--R (168000a c d - 100800a b c d + 21000b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 6
+--R (1075200a c d - 645120a b c d + 134400b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 4
+--R (2764800a c d - 1658880a b c d + 345600b c d )x
+--R +
+--R 2 8 3 9 2 2 10 2
+--R (3072000a c d - 1843200a b c d + 384000b c d)x
+--R +
+--R 2 9 2 10 2 11
+--R 1228800a c d - 737280a b c d + 153600b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 8 5 7 2 6 6 12
+--R (- 600a c d + 360a b c d - 75b c d )x
+--R +
+--R 2 5 7 6 6 2 7 5 10
+--R (- 43200a c d + 25920a b c d - 5400b c d )x
+--R +
+--R 2 6 6 7 5 2 8 4 8
+--R (- 504000a c d + 302400a b c d - 63000b c d )x
+--R +
+--R 2 7 5 8 4 2 9 3 6
+--R (- 2150400a c d + 1290240a b c d - 268800b c d )x
+--R +
+--R 2 8 4 9 3 2 10 2 4
+--R (- 4147200a c d + 2488320a b c d - 518400b c d )x
+--R +
+--R 2 9 3 10 2 2 11 2
+--R (- 3686400a c d + 2211840a b c d - 460800b c d)x
+--R +
+--R 2 10 2 11 2 12
+--R - 1228800a c d + 737280a b c d - 153600b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 11 23 11 2 10 21
+--R - 1280b d x + (- 3072a b d - 95360b c d )x
+--R +
+--R 2 11 10 2 2 9 19
+--R (- 1920a d - 229248a b c d - 1307760b c d )x
+--R +
+--R 2 10 2 9 2 3 8 17
+--R (- 143680a c d - 3167040a b c d - 7431080b c d )x
+--R +
+--R 2 2 9 3 8 2 4 7 15
+--R (- 2009200a c d - 18212592a b c d - 22133390b c d )x
+--R +
+--R 2 3 8 4 7 2 5 6 13
+--R (- 11791320a c d - 55151640a b c d - 37754235b c d )x
+--R +
+--R 2 4 7 5 6 2 6 5 11
+--R (- 36776000a c d - 96120384a b c d - 37318920b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 9
+--R (- 66818240a c d - 97534656a b c d - 19984920b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 7
+--R (- 72130560a c d - 53452800a b c d - 4592640b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 5
+--R (- 44288000a c d - 11175936a b c d - 293120b c d )x
+--R +
+--R 2 8 3 9 2 2 10 3
+--R (- 13352960a c d + 1720320a b c d - 358400b c d)x
+--R +
+--R 2 9 2 10 2 11
+--R (- 1228800a c d + 737280a b c d - 153600b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 11 23 11 2 10 21
+--R 15360b d x + (36864a b d + 412160b c d )x
+--R +
+--R 2 11 10 2 2 9 19
+--R (23040a d + 993792a b c d + 3612480b c d )x
+--R +
+--R 2 10 2 9 2 3 8 17
+--R (625920a c d + 8791296a b c d + 15453600b c d )x
+--R +
+--R 2 2 9 3 8 2 4 7 15
+--R (5623360a c d + 38110272a b c d + 37418440b c d )x
+--R +
+--R 2 3 8 4 7 2 5 6 13
+--R (24945120a c d + 93892320a b c d + 54197820b c d )x
+--R +
+--R 2 4 7 5 6 2 6 5 11
+--R (63448800a c d + 138951648a b c d + 46745820b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 9
+--R (98134080a c d + 122785344a b c d + 22261000b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 7
+--R (92682240a c d + 59209728a b c d + 4704000b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 5
+--R (50810880a c d + 10407936a b c d + 453120b c d )x
+--R +
+--R 2 8 3 9 2 2 10 3
+--R (13967360a c d - 2088960a b c d + 435200b c d)x
+--R +
+--R 2 9 2 10 2 11
+--R (1228800a c d - 737280a b c d + 153600b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 8 10 7 8 2 6 6 3 5 4
+--R 184320d x + 4300800c d x + 27525120c d x + 70778880c d x
+--R +
+--R 4 4 2 5 3
+--R 78643200c d x + 31457280c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 9 12 8 10 2 7 8 3 6 6
+--R - 15360d x - 1105920c d x - 12902400c d x - 55050240c d x
+--R +
+--R 4 5 4 5 4 2 6 3
+--R - 106168320c d x - 94371840c d x - 31457280c d
+--R *
+--R +-+
+--R \|d
+--R ,
+--R
+--R 2 4 7 5 6 2 6 5 10
+--R (- 14400a c d + 8640a b c d - 1800b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 8
+--R (- 336000a c d + 201600a b c d - 42000b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 6
+--R (- 2150400a c d + 1290240a b c d - 268800b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 4
+--R (- 5529600a c d + 3317760a b c d - 691200b c d )x
+--R +
+--R 2 8 3 9 2 2 10 2
+--R (- 6144000a c d + 3686400a b c d - 768000b c d)x
+--R +
+--R 2 9 2 10 2 11
+--R - 2457600a c d + 1474560a b c d - 307200b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 8 5 7 2 6 6 12
+--R (1200a c d - 720a b c d + 150b c d )x
+--R +
+--R 2 5 7 6 6 2 7 5 10
+--R (86400a c d - 51840a b c d + 10800b c d )x
+--R +
+--R 2 6 6 7 5 2 8 4 8
+--R (1008000a c d - 604800a b c d + 126000b c d )x
+--R +
+--R 2 7 5 8 4 2 9 3 6
+--R (4300800a c d - 2580480a b c d + 537600b c d )x
+--R +
+--R 2 8 4 9 3 2 10 2 4
+--R (8294400a c d - 4976640a b c d + 1036800b c d )x
+--R +
+--R 2 9 3 10 2 2 11 2
+--R (7372800a c d - 4423680a b c d + 921600b c d)x
+--R +
+--R 2 10 2 11 2 12
+--R 2457600a c d - 1474560a b c d + 307200b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 11 23 11 2 10 21
+--R - 1280b d x + (- 3072a b d - 95360b c d )x
+--R +
+--R 2 11 10 2 2 9 19
+--R (- 1920a d - 229248a b c d - 1307760b c d )x
+--R +
+--R 2 10 2 9 2 3 8 17
+--R (- 143680a c d - 3167040a b c d - 7431080b c d )x
+--R +
+--R 2 2 9 3 8 2 4 7 15
+--R (- 2009200a c d - 18212592a b c d - 22133390b c d )x
+--R +
+--R 2 3 8 4 7 2 5 6 13
+--R (- 11791320a c d - 55151640a b c d - 37754235b c d )x
+--R +
+--R 2 4 7 5 6 2 6 5 11
+--R (- 36776000a c d - 96120384a b c d - 37318920b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 9
+--R (- 66818240a c d - 97534656a b c d - 19984920b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 7
+--R (- 72130560a c d - 53452800a b c d - 4592640b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 5
+--R (- 44288000a c d - 11175936a b c d - 293120b c d )x
+--R +
+--R 2 8 3 9 2 2 10 3
+--R (- 13352960a c d + 1720320a b c d - 358400b c d)x
+--R +
+--R 2 9 2 10 2 11
+--R (- 1228800a c d + 737280a b c d - 153600b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 11 23 11 2 10 21
+--R 15360b d x + (36864a b d + 412160b c d )x
+--R +
+--R 2 11 10 2 2 9 19
+--R (23040a d + 993792a b c d + 3612480b c d )x
+--R +
+--R 2 10 2 9 2 3 8 17
+--R (625920a c d + 8791296a b c d + 15453600b c d )x
+--R +
+--R 2 2 9 3 8 2 4 7 15
+--R (5623360a c d + 38110272a b c d + 37418440b c d )x
+--R +
+--R 2 3 8 4 7 2 5 6 13
+--R (24945120a c d + 93892320a b c d + 54197820b c d )x
+--R +
+--R 2 4 7 5 6 2 6 5 11
+--R (63448800a c d + 138951648a b c d + 46745820b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 9
+--R (98134080a c d + 122785344a b c d + 22261000b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 7
+--R (92682240a c d + 59209728a b c d + 4704000b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 5
+--R (50810880a c d + 10407936a b c d + 453120b c d )x
+--R +
+--R 2 8 3 9 2 2 10 3
+--R (13967360a c d - 2088960a b c d + 435200b c d)x
+--R +
+--R 2 9 2 10 2 11
+--R (1228800a c d - 737280a b c d + 153600b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R 8 10 7 8 2 6 6 3 5 4
+--R 184320d x + 4300800c d x + 27525120c d x + 70778880c d x
+--R +
+--R 4 4 2 5 3
+--R 78643200c d x + 31457280c d
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 9 12 8 10 2 7 8 3 6 6
+--R - 15360d x - 1105920c d x - 12902400c d x - 55050240c d x
+--R +
+--R 4 5 4 5 4 2 6 3
+--R - 106168320c d x - 94371840c d x - 31457280c d
+--R *
+--R +---+
+--R \|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 921
+
+--S 922 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 4 2 5 2 6
+--R (40a c d - 24a b c d + 5b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 4 2 5 2 6 x\|d
+--R (40a c d - 24a b c d + 5b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 +-+
+--R 1024d \|d
+--R Type: Expression(Integer)
+--E 922
+
+--S 923 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 923
+
+--S 924 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 4 2 5 2 6 +---+ x\|d
+--R (40a c d - 24a b c d + 5b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 4 2 5 2 6 +-+ \|- d \|d x + c - \|- d \|c
+--R (- 80a c d + 48a b c d - 10b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 3 +---+ +-+
+--R 1024d \|- d \|d
+--R Type: Expression(Integer)
+--E 924
+
+--S 925 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 925
+
+)clear all
+
+--S 926 of 1397
+t0:=x*(a+b*x^2)^2*(c+d*x^2)^(5/2)
+--R
+--R
+--R (1)
+--R 2 2 9 2 2 7 2 2 2 2 5
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 3 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 926
+
+--S 927 of 1397
+r0:=1/7*(b*c-a*d)^2*(c+d*x^2)^(7/2)/d^3-2/9*b*(b*c-a*d)*(c+d*x^2)^(9/2)/_
+ d^3+1/11*b^2*(c+d*x^2)^(11/2)/d^3
+--R
+--R
+--R (2)
+--R 2 5 10 5 2 4 8
+--R 63b d x + (154a b d + 161b c d )x
+--R +
+--R 2 5 4 2 2 3 6
+--R (99a d + 418a b c d + 113b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (297a c d + 330a b c d + 3b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (297a c d + 22a b c d - 4b c d)x + 99a c d - 44a b c d + 8b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3
+--R 693d
+--R Type: Expression(Integer)
+--E 927
+
+--S 928 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 7 20 7 2 2 6 18
+--R - 693b c d x + (- 1694a b c d - 15631b c d )x
+--R +
+--R 2 7 2 6 2 3 5 16
+--R (- 1089a c d - 38478a b c d - 114279b c d )x
+--R +
+--R 2 2 6 3 5 2 4 4 14
+--R (- 25047a c d - 285318a b c d - 400653b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 12
+--R (- 190575a c d - 1021482a b c d - 770616b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 10
+--R (- 711018a c d - 2021712a b c d - 838992b c d )x
+--R +
+--R 2 5 3 6 2 2 7 8
+--R (- 1496880a c d - 2284128a b c d - 487872b c d)x
+--R +
+--R 2 6 2 7 2 8 6
+--R (- 1840608a c d - 1389696a b c d - 118272b c )x
+--R +
+--R 2 7 8 4 2 8 2
+--R (- 1241856a c d - 354816a b c )x - 354816a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 8 22 8 2 7 20
+--R 63b d x + (154a b d + 4004b c d )x
+--R +
+--R 2 8 7 2 2 6 18
+--R (99a d + 9812a b c d + 48994b c d )x
+--R +
+--R 2 7 2 6 2 3 5 16
+--R (6336a c d + 121308a b c d + 254892b c d )x
+--R +
+--R 2 2 6 3 5 2 4 4 14
+--R (79794a c d + 641520a b c d + 706959b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 12
+--R (435204a c d + 1819818a b c d + 1136520b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 10
+--R (1293138a c d + 3012240a b c d + 1068144b c d )x
+--R +
+--R 2 5 3 6 2 2 7 8
+--R (2284128a c d + 2934624a b c d + 547008b c d)x
+--R +
+--R 2 6 2 7 2 8 6
+--R (2417184a c d + 1567104a b c d + 118272b c )x
+--R +
+--R 2 7 8 4 2 8 2
+--R (1419264a c d + 354816a b c )x + 354816a c x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 5 10 4 8 2 3 6 3 2 4 4 2
+--R 693d x + 41580c d x + 388080c d x + 1241856c d x + 1596672c d x
+--R +
+--R 5
+--R 709632c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4
+--R - 7623c d x - 152460c d x - 853776c d x - 1951488c d x
+--R +
+--R 5 2 6
+--R - 1951488c d x - 709632c
+--R Type: Union(Expression(Integer),...)
+--E 928
+
+--S 929 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 4 7 5 6 2 6 5 10
+--R (99a c d - 44a b c d + 8b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 8
+--R (5940a c d - 2640a b c d + 480b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 6
+--R (55440a c d - 24640a b c d + 4480b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 4
+--R (177408a c d - 78848a b c d + 14336b c d )x
+--R +
+--R 2 8 3 9 2 2 10 2 2 9 2
+--R (228096a c d - 101376a b c d + 18432b c d)x + 101376a c d
+--R +
+--R 10 2 11
+--R - 45056a b c d + 8192b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 7 5 6 2 6 5 10
+--R (- 1089a c d + 484a b c d - 88b c d )x
+--R +
+--R 2 5 6 6 5 2 7 4 8
+--R (- 21780a c d + 9680a b c d - 1760b c d )x
+--R +
+--R 2 6 5 7 4 2 8 3 6
+--R (- 121968a c d + 54208a b c d - 9856b c d )x
+--R +
+--R 2 7 4 8 3 2 9 2 4
+--R (- 278784a c d + 123904a b c d - 22528b c d )x
+--R +
+--R 2 8 3 9 2 2 10 2 2 9 2
+--R (- 278784a c d + 123904a b c d - 22528b c d)x - 101376a c d
+--R +
+--R 10 2 11
+--R 45056a b c d - 8192b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 8 10 7 8 2 6 6 3 5 4 4 4 2
+--R 693d x + 41580c d x + 388080c d x + 1241856c d x + 1596672c d x
+--R +
+--R 5 3
+--R 709632c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 8 10 2 7 8 3 6 6 4 5 4
+--R - 7623c d x - 152460c d x - 853776c d x - 1951488c d x
+--R +
+--R 5 4 2 6 3
+--R - 1951488c d x - 709632c d
+--R Type: Expression(Integer)
+--E 929
+
+--S 930 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 930
+
+)clear all
+
+--S 931 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(5/2)
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 931
+
+--S 932 of 1397
+r0:=1/10*d*x*(a+b*x^2)^3*(c+d*x^2)^(3/2)/b+1/256*c^3*(3*b^2*c^2-_
+ 20*a*b*c*d+80*a^2*d^2)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/d^(5/2)-_
+ 1/3840*(45*b^4*c^4+474*a*b^3*c^3*d-2072*a^2*b^2*c^2*d^2+736*a^3*_
+ b*c*d^3-128*a^4*d^4)*x*sqrt(c+d*x^2)/(b^2*d^2)+1/480*(93*b^2*c^2-_
+ 38*a*b*c*d+8*a^2*d^2)*x*(a+b*x^2)^2*sqrt(c+d*x^2)/b^2+1/80*d*_
+ (13*b*c-4*a*d)*x*(a+b*x^2)^3*sqrt(c+d*x^2)/b^2+1/1920*x*(a*c*_
+ (387*b^2*c^2-88*a*b*c*d+16*a^2*d^2)+(15*b^3*c^3+436*a*b^2*c^2*d-_
+ 168*a^2*b*c*d^2+32*a^3*d^3)*x^2)*sqrt(c+d*x^2)/(b*d)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 2 4 2 5 x\|d
+--R (1200a c d - 300a b c d + 45b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 9 4 2 3 7
+--R 384b d x + (960a b d + 1008b c d )x
+--R +
+--R 2 4 3 2 2 2 5
+--R (640a d + 2720a b c d + 744b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (2080a c d + 2360a b c d + 30b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (2640a c d + 300a b c d - 45b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R 2 +-+
+--R 3840d \|d
+--R Type: Expression(Integer)
+--E 932
+
+--S 933 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 6 4 5 2 5 4 8
+--R (12000a c d - 3000a b c d + 450b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 6
+--R (192000a c d - 48000a b c d + 7200b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 4
+--R (806400a c d - 201600a b c d + 30240b c d )x
+--R +
+--R 2 6 3 7 2 2 8 2 2 7 2
+--R (1228800a c d - 307200a b c d + 46080b c d)x + 614400a c d
+--R +
+--R 8 2 9
+--R - 153600a b c d + 23040b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 3 7 4 6 2 5 5 10
+--R (- 1200a c d + 300a b c d - 45b c d )x
+--R +
+--R 2 4 6 5 5 2 6 4 8
+--R (- 60000a c d + 15000a b c d - 2250b c d )x
+--R +
+--R 2 5 5 6 4 2 7 3 6
+--R (- 480000a c d + 120000a b c d - 18000b c d )x
+--R +
+--R 2 6 4 7 3 2 8 2 4
+--R (- 1344000a c d + 336000a b c d - 50400b c d )x
+--R +
+--R 2 7 3 8 2 2 9 2 2 8 2
+--R (- 1536000a c d + 384000a b c d - 57600b c d)x - 614400a c d
+--R +
+--R 9 2 10
+--R 153600a b c d - 23040b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 9 19 9 2 8 17
+--R - 384b d x + (- 960a b d - 20208b c d )x
+--R +
+--R 2 9 8 2 2 7 15
+--R (- 640a d - 50720a b c d - 204744b c d )x
+--R +
+--R 2 8 2 7 2 3 6 13
+--R (- 34080a c d - 522360a b c d - 870510b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 11
+--R (- 362640a c d - 2281500a b c d - 1919535b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 9
+--R (- 1680800a c d - 5234200a b c d - 2329878b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 7
+--R (- 4204800a c d - 6736320a b c d - 1484016b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 5
+--R (- 5946880a c d - 4749440a b c d - 368928b c d )x
+--R +
+--R 2 6 3 7 2 2 8 3
+--R (- 4444160a c d - 1592320a b c d + 42240b c d)x
+--R +
+--R 2 7 2 8 2 9
+--R (- 1351680a c d - 153600a b c d + 23040b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 9 19 9 2 8 17
+--R 3840b d x + (9600a b d + 75360b c d )x
+--R +
+--R 2 9 8 2 2 7 15
+--R (6400a d + 190400a b c d + 498288b c d )x
+--R +
+--R 2 8 2 7 2 3 6 13
+--R (129600a c d + 1284720a b c d + 1616700b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 11
+--R (912480a c d + 4295400a b c d + 2923050b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 9
+--R (3264800a c d + 8102200a b c d + 3024030b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 7
+--R (6707200a c d + 8921600a b c d + 1672320b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 5
+--R (8000000a c d + 5526400a b c d + 350688b c d )x
+--R +
+--R 2 6 3 7 2 2 8 3
+--R (5120000a c d + 1669120a b c d - 53760b c d)x
+--R +
+--R 2 7 2 8 2 9
+--R (1351680a c d + 153600a b c d - 23040b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 6 8 5 6 2 4 4 3 3 2
+--R 38400d x + 614400c d x + 2580480c d x + 3932160c d x
+--R +
+--R 4 2
+--R 1966080c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 7 10 6 8 2 5 6 3 4 4
+--R - 3840d x - 192000c d x - 1536000c d x - 4300800c d x
+--R +
+--R 4 3 2 5 2
+--R - 4915200c d x - 1966080c d
+--R *
+--R +-+
+--R \|d
+--R ,
+--R
+--R 2 3 6 4 5 2 5 4 8
+--R (24000a c d - 6000a b c d + 900b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 6
+--R (384000a c d - 96000a b c d + 14400b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 4
+--R (1612800a c d - 403200a b c d + 60480b c d )x
+--R +
+--R 2 6 3 7 2 2 8 2 2 7 2
+--R (2457600a c d - 614400a b c d + 92160b c d)x + 1228800a c d
+--R +
+--R 8 2 9
+--R - 307200a b c d + 46080b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 3 7 4 6 2 5 5 10
+--R (- 2400a c d + 600a b c d - 90b c d )x
+--R +
+--R 2 4 6 5 5 2 6 4 8
+--R (- 120000a c d + 30000a b c d - 4500b c d )x
+--R +
+--R 2 5 5 6 4 2 7 3 6
+--R (- 960000a c d + 240000a b c d - 36000b c d )x
+--R +
+--R 2 6 4 7 3 2 8 2 4
+--R (- 2688000a c d + 672000a b c d - 100800b c d )x
+--R +
+--R 2 7 3 8 2 2 9 2 2 8 2
+--R (- 3072000a c d + 768000a b c d - 115200b c d)x - 1228800a c d
+--R +
+--R 9 2 10
+--R 307200a b c d - 46080b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 9 19 9 2 8 17
+--R - 384b d x + (- 960a b d - 20208b c d )x
+--R +
+--R 2 9 8 2 2 7 15
+--R (- 640a d - 50720a b c d - 204744b c d )x
+--R +
+--R 2 8 2 7 2 3 6 13
+--R (- 34080a c d - 522360a b c d - 870510b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 11
+--R (- 362640a c d - 2281500a b c d - 1919535b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 9
+--R (- 1680800a c d - 5234200a b c d - 2329878b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 7
+--R (- 4204800a c d - 6736320a b c d - 1484016b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 5
+--R (- 5946880a c d - 4749440a b c d - 368928b c d )x
+--R +
+--R 2 6 3 7 2 2 8 3
+--R (- 4444160a c d - 1592320a b c d + 42240b c d)x
+--R +
+--R 2 7 2 8 2 9
+--R (- 1351680a c d - 153600a b c d + 23040b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 9 19 9 2 8 17
+--R 3840b d x + (9600a b d + 75360b c d )x
+--R +
+--R 2 9 8 2 2 7 15
+--R (6400a d + 190400a b c d + 498288b c d )x
+--R +
+--R 2 8 2 7 2 3 6 13
+--R (129600a c d + 1284720a b c d + 1616700b c d )x
+--R +
+--R 2 2 7 3 6 2 4 5 11
+--R (912480a c d + 4295400a b c d + 2923050b c d )x
+--R +
+--R 2 3 6 4 5 2 5 4 9
+--R (3264800a c d + 8102200a b c d + 3024030b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 7
+--R (6707200a c d + 8921600a b c d + 1672320b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 5
+--R (8000000a c d + 5526400a b c d + 350688b c d )x
+--R +
+--R 2 6 3 7 2 2 8 3
+--R (5120000a c d + 1669120a b c d - 53760b c d)x
+--R +
+--R 2 7 2 8 2 9
+--R (1351680a c d + 153600a b c d - 23040b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R 6 8 5 6 2 4 4 3 3 2
+--R 38400d x + 614400c d x + 2580480c d x + 3932160c d x
+--R +
+--R 4 2
+--R 1966080c d
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 7 10 6 8 2 5 6 3 4 4
+--R - 3840d x - 192000c d x - 1536000c d x - 4300800c d x
+--R +
+--R 4 3 2 5 2
+--R - 4915200c d x - 1966080c d
+--R *
+--R +---+
+--R \|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 933
+
+--S 934 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 2 4 2 5
+--R (80a c d - 20a b c d + 3b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 3 2 4 2 5 x\|d
+--R (- 80a c d + 20a b c d - 3b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2 +-+
+--R 256d \|d
+--R Type: Expression(Integer)
+--E 934
+
+--S 935 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 935
+
+--S 936 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 3 2 4 2 5 +---+ x\|d
+--R (- 80a c d + 20a b c d - 3b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 3 2 4 2 5 +-+ \|- d \|d x + c - \|- d \|c
+--R (160a c d - 40a b c d + 6b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 2 +---+ +-+
+--R 256d \|- d \|d
+--R Type: Expression(Integer)
+--E 936
+
+--S 937 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 937
+
+)clear all
+
+--S 938 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(5/2)/x
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R x
+--R Type: Expression(Integer)
+--E 938
+
+--S 939 of 1397
+r0:=1/3*a^2*c*(c+d*x^2)^(3/2)+1/5*a^2*(c+d*x^2)^(5/2)-_
+ 2/63*b*(b*c-9*a*d)*(c+d*x^2)^(7/2)/d^2+1/9*b^2*x^2*_
+ (c+d*x^2)^(7/2)/d-a^2*c^(5/2)*atanh(sqrt(c+d*x^2)/sqrt(c))+_
+ a^2*c^2*sqrt(c+d*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 2 2 +-+ \|d x + c
+--R - 315a c d \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 4 8 4 2 3 6
+--R 35b d x + (90a b d + 95b c d )x
+--R +
+--R 2 4 3 2 2 2 4
+--R (63a d + 270a b c d + 75b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (231a c d + 270a b c d + 5b c d)x + 483a c d + 90a b c d - 10b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2
+--R 315d
+--R Type: Expression(Integer)
+--E 939
+
+--S 940 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 4 8 2 4 3 6 2 5 2 4 2 6 2
+--R 315a c d x + 12600a c d x + 75600a c d x + 141120a c d x
+--R +
+--R 2 7
+--R 80640a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 4 8 2 4 3 6 2 5 2 4 2 6 2
+--R - 2835a c d x - 37800a c d x - 136080a c d x - 181440a c d x
+--R +
+--R 2 7
+--R - 80640a c
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 6 16 6 2 2 5 14
+--R - 315b c d x + (- 810a b c d - 5055b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (- 567a c d - 13230a b c d - 27195b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (- 9639a c d - 73710a b c d - 70245b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 58800a c d - 201600a b c d - 96600b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 174720a c d - 302400a b c d - 68880b c d)x
+--R +
+--R 2 5 2 6 2 7 4
+--R (- 241920a c d - 241920a b c d - 20160b c )x
+--R +
+--R 2 6 7 2
+--R (- 120960a c d - 80640a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 7 18 7 2 6 16
+--R 35b d x + (90a b d + 1530b c d )x
+--R +
+--R 2 7 6 2 2 5 14
+--R (63a d + 3960a b c d + 13770b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (2814a c d + 36540a b c d + 53760b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (27594a c d + 148680a b c d + 111195b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (123480a c d + 327600a b c d + 128520b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (280560a c d + 413280a b c d + 78960b c d)x
+--R +
+--R 2 5 2 6 2 7 4
+--R (302400a c d + 282240a b c d + 20160b c )x
+--R +
+--R 2 6 7 2
+--R (120960a c d + 80640a b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (315d x + 12600c d x + 75600c d x + 141120c d x + 80640c )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 2835c d x - 37800c d x - 136080c d x - 181440c d x - 80640c
+--R Type: Union(Expression(Integer),...)
+--E 940
+
+--S 941 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 6 8 2 4 5 6 2 5 4 4 2 6 3 2
+--R 315a c d x + 12600a c d x + 75600a c d x + 141120a c d x
+--R +
+--R 2 7 2
+--R 80640a c d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 6 8 2 4 5 6 2 5 4 4 2 6 3 2
+--R - 2835a c d x - 37800a c d x - 136080a c d x - 181440a c d x
+--R +
+--R 2 7 2
+--R - 80640a c d
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 6 8 2 4 5 6 2 5 4 4 2 6 3 2
+--R 315a c d x + 12600a c d x + 75600a c d x + 141120a c d x
+--R +
+--R 2 7 2
+--R 80640a c d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 6 8 2 4 5 6 2 5 4 4 2 6 3 2
+--R - 2835a c d x - 37800a c d x - 136080a c d x - 181440a c d x
+--R +
+--R 2 7 2
+--R - 80640a c d
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 6 4 5 2 5 4 8
+--R (483a c d + 90a b c d - 10b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 6
+--R (19320a c d + 3600a b c d - 400b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 4
+--R (115920a c d + 21600a b c d - 2400b c d )x
+--R +
+--R 2 6 3 7 2 2 8 2 2 7 2
+--R (216384a c d + 40320a b c d - 4480b c d)x + 123648a c d
+--R +
+--R 8 2 9
+--R 23040a b c d - 2560b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 6 4 5 2 5 4 8
+--R (- 4347a c d - 810a b c d + 90b c d )x
+--R +
+--R 2 4 5 5 4 2 6 3 6
+--R (- 57960a c d - 10800a b c d + 1200b c d )x
+--R +
+--R 2 5 4 6 3 2 7 2 4
+--R (- 208656a c d - 38880a b c d + 4320b c d )x
+--R +
+--R 2 6 3 7 2 2 8 2 2 7 2
+--R (- 278208a c d - 51840a b c d + 5760b c d)x - 123648a c d
+--R +
+--R 8 2 9
+--R - 23040a b c d + 2560b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 6 8 5 6 2 4 4 3 3 2 4 2 +-+
+--R (315d x + 12600c d x + 75600c d x + 141120c d x + 80640c d )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 6 8 2 5 6 3 4 4 4 3 2 5 2
+--R - 2835c d x - 37800c d x - 136080c d x - 181440c d x - 80640c d
+--R Type: Expression(Integer)
+--E 941
+
+--S 942 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 942
+
+)clear all
+
+--S 943 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(5/2)/x^2
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 943
+
+--S 944 of 1397
+r0:=-5/192*(b^2*c^2-16*a*d*(b*c+3*a*d))*x*(c+d*x^2)^(3/2)/d-_
+ 1/48*(b^2*c^2-16*a*d*(b*c+3*a*d))*x*(c+d*x^2)^(5/2)/(c*d)-_
+ a^2*(c+d*x^2)^(7/2)/(c*x)+1/8*b^2*x*(c+d*x^2)^(7/2)/d-_
+ 5/128*c^2*(b^2*c^2-16*a*d*(b*c+3*a*d))*atanh(x*sqrt(d)/_
+ sqrt(c+d*x^2))/d^(3/2)-5/128*c*(b^2*c^2-16*a*d*(b*c+3*a*d))*_
+ x*sqrt(c+d*x^2)/d
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 3 2 4 x\|d
+--R (720a c d + 240a b c d - 15b c )x atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 8 3 2 2 6
+--R 48b d x + (128a b d + 136b c d )x
+--R +
+--R 2 3 2 2 2 4
+--R (96a d + 416a b c d + 118b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2
+--R (432a c d + 528a b c d + 15b c )x - 384a c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R +-+
+--R 384d x\|d
+--R Type: Expression(Integer)
+--E 944
+
+--S 945 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 6 3 5 2 4 4 9
+--R (720a c d + 240a b c d - 15b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 7
+--R (28800a c d + 9600a b c d - 600b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 5
+--R (172800a c d + 57600a b c d - 3600b c d )x
+--R +
+--R 2 5 3 6 2 2 7 3
+--R (322560a c d + 107520a b c d - 6720b c d)x
+--R +
+--R 2 6 2 7 2 8
+--R (184320a c d + 61440a b c d - 3840b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 3 5 2 4 4 9
+--R (- 6480a c d - 2160a b c d + 135b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 7
+--R (- 86400a c d - 28800a b c d + 1800b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 5
+--R (- 311040a c d - 103680a b c d + 6480b c d )x
+--R +
+--R 2 5 3 6 2 2 7 3
+--R (- 414720a c d - 138240a b c d + 8640b c d)x
+--R +
+--R 2 6 2 7 2 8
+--R (- 184320a c d - 61440a b c d + 3840b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 7 16 7 2 6 14
+--R - 432b d x + (- 1152a b d - 6984b c d )x
+--R +
+--R 2 7 6 2 2 5 12
+--R (- 864a d - 19104a b c d - 38118b c d )x
+--R +
+--R 2 6 2 5 2 3 4 10
+--R (- 15408a c d - 109968a b c d - 100695b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 8
+--R (- 89856a c d - 316800a b c d - 143400b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 6
+--R (- 195840a c d - 500480a b c d - 109264b c d )x
+--R +
+--R 2 4 3 5 2 2 6 4
+--R (- 107520a c d - 410624a b c d - 38848b c d)x
+--R +
+--R 2 5 2 6 2 7 2 2 6
+--R (110592a c d - 135168a b c d - 3840b c )x + 98304a c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 2 8 18 8 2 7 16
+--R 48b d x + (128a b d + 2104b c d )x
+--R +
+--R 2 8 7 2 2 6 14
+--R (96a d + 5664a b c d + 19134b c d )x
+--R +
+--R 2 7 2 6 2 3 5 12
+--R (4368a c d + 53424a b c d + 75957b c d )x
+--R +
+--R 2 2 6 3 5 2 4 4 10
+--R (44208a c d + 226192a b c d + 161015b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 8
+--R (171264a c d + 524160a b c d + 193416b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 6
+--R (257280a c d + 688896a b c d + 128208b c d )x
+--R +
+--R 2 5 3 6 2 2 7 4
+--R (64512a c d + 478208a b c d + 40768b c d)x
+--R +
+--R 2 6 2 7 2 8 2 2 7
+--R (- 159744a c d + 135168a b c d + 3840b c )x - 98304a c d
+--R *
+--R +-+
+--R \|d
+--R /
+--R 5 9 4 7 2 3 5 3 2 3 4 +-+
+--R (384d x + 15360c d x + 92160c d x + 172032c d x + 98304c d x)\|d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 5 9 4 7 2 3 5 3 2 3 4
+--R (- 3456d x - 46080c d x - 165888c d x - 221184c d x - 98304c d x)
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R ,
+--R
+--R 2 2 6 3 5 2 4 4 9
+--R (1440a c d + 480a b c d - 30b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 7
+--R (57600a c d + 19200a b c d - 1200b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 5
+--R (345600a c d + 115200a b c d - 7200b c d )x
+--R +
+--R 2 5 3 6 2 2 7 3
+--R (645120a c d + 215040a b c d - 13440b c d)x
+--R +
+--R 2 6 2 7 2 8
+--R (368640a c d + 122880a b c d - 7680b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 3 5 2 4 4 9
+--R (- 12960a c d - 4320a b c d + 270b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 7
+--R (- 172800a c d - 57600a b c d + 3600b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 5
+--R (- 622080a c d - 207360a b c d + 12960b c d )x
+--R +
+--R 2 5 3 6 2 2 7 3
+--R (- 829440a c d - 276480a b c d + 17280b c d)x
+--R +
+--R 2 6 2 7 2 8
+--R (- 368640a c d - 122880a b c d + 7680b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 7 16 7 2 6 14
+--R - 432b d x + (- 1152a b d - 6984b c d )x
+--R +
+--R 2 7 6 2 2 5 12
+--R (- 864a d - 19104a b c d - 38118b c d )x
+--R +
+--R 2 6 2 5 2 3 4 10
+--R (- 15408a c d - 109968a b c d - 100695b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 8
+--R (- 89856a c d - 316800a b c d - 143400b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 6
+--R (- 195840a c d - 500480a b c d - 109264b c d )x
+--R +
+--R 2 4 3 5 2 2 6 4
+--R (- 107520a c d - 410624a b c d - 38848b c d)x
+--R +
+--R 2 5 2 6 2 7 2 2 6
+--R (110592a c d - 135168a b c d - 3840b c )x + 98304a c d
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 2 8 18 8 2 7 16
+--R 48b d x + (128a b d + 2104b c d )x
+--R +
+--R 2 8 7 2 2 6 14
+--R (96a d + 5664a b c d + 19134b c d )x
+--R +
+--R 2 7 2 6 2 3 5 12
+--R (4368a c d + 53424a b c d + 75957b c d )x
+--R +
+--R 2 2 6 3 5 2 4 4 10
+--R (44208a c d + 226192a b c d + 161015b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 8
+--R (171264a c d + 524160a b c d + 193416b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 6
+--R (257280a c d + 688896a b c d + 128208b c d )x
+--R +
+--R 2 5 3 6 2 2 7 4
+--R (64512a c d + 478208a b c d + 40768b c d)x
+--R +
+--R 2 6 2 7 2 8 2 2 7
+--R (- 159744a c d + 135168a b c d + 3840b c )x - 98304a c d
+--R *
+--R +---+
+--R \|- d
+--R /
+--R 5 9 4 7 2 3 5 3 2 3 4
+--R (384d x + 15360c d x + 92160c d x + 172032c d x + 98304c d x)
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 5 9 4 7 2 3 5 3 2 3 4
+--R (- 3456d x - 46080c d x - 165888c d x - 221184c d x - 98304c d x)
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 945
+
+--S 946 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 3 2 4
+--R (240a c d + 80a b c d - 5b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 3 2 4 x\|d
+--R (- 240a c d - 80a b c d + 5b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R +-+
+--R 128d\|d
+--R Type: Expression(Integer)
+--E 946
+
+--S 947 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 947
+
+--S 948 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 3 2 4 +---+ x\|d
+--R (- 240a c d - 80a b c d + 5b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 3 2 4 +-+ \|- d \|d x + c - \|- d \|c
+--R (480a c d + 160a b c d - 10b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R +---+ +-+
+--R 128d\|- d \|d
+--R Type: Expression(Integer)
+--E 948
+
+--S 949 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 949
+
+)clear all
+
+--S 950 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(5/2)/x^3
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 950
+
+--S 951 of 1397
+r0:=1/6*a*(4*b*c+5*a*d)*(c+d*x^2)^(3/2)+1/10*a*(4*b*c+5*a*d)*_
+ (c+d*x^2)^(5/2)/c+1/7*b^2*(c+d*x^2)^(7/2)/d-1/2*a^2*_
+ (c+d*x^2)^(7/2)/(c*x^2)-1/2*a*c^(3/2)*(4*b*c+5*a*d)*_
+ atanh(sqrt(c+d*x^2)/sqrt(c))+1/2*a*c*(4*b*c+5*a*d)*sqrt(c+d*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 2 2 2 +-+ \|d x + c
+--R (- 525a c d - 420a b c d)x \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 8 3 2 2 6
+--R 30b d x + (84a b d + 90b c d )x
+--R +
+--R 2 3 2 2 2 4
+--R (70a d + 308a b c d + 90b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2
+--R (490a c d + 644a b c d + 30b c )x - 105a c d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2
+--R 210d x
+--R Type: Expression(Integer)
+--E 951
+
+--S 952 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 5 3 4 10 2 3 4 4 3 8
+--R (525a c d + 420a b c d )x + (21000a c d + 16800a b c d )x
+--R +
+--R 2 4 3 5 2 6
+--R (126000a c d + 100800a b c d )x
+--R +
+--R 2 5 2 6 4 2 6 7 2
+--R (235200a c d + 188160a b c d)x + (134400a c d + 107520a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 5 3 4 10
+--R (- 4725a c d - 3780a b c d )x
+--R +
+--R 2 3 4 4 3 8
+--R (- 63000a c d - 50400a b c d )x
+--R +
+--R 2 4 3 5 2 6
+--R (- 226800a c d - 181440a b c d )x
+--R +
+--R 2 5 2 6 4
+--R (- 302400a c d - 241920a b c d)x
+--R +
+--R 2 6 7 2
+--R (- 134400a c d - 107520a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 6 16 6 2 2 5 14
+--R - 270b c d x + (- 756a b c d - 4410b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (- 630a c d - 12852a b c d - 24570b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (- 12320a c d - 78400a b c d - 67200b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 68495a c d - 232960a b c d - 100800b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 121800a c d - 322560a b c d - 80640b c d)x
+--R +
+--R 2 5 2 6 2 7 4 2 6 2
+--R (- 35280a c d - 161280a b c d - 26880b c )x + 60480a c d x
+--R +
+--R 2 7
+--R 26880a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 7 18 7 2 6 16
+--R 30b d x + (84a b d + 1320b c d )x
+--R +
+--R 2 7 6 2 2 5 14
+--R (70a d + 3752a b c d + 12180b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (3360a c d + 36792a b c d + 49560b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (35175a c d + 164640a b c d + 109200b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (122255a c d + 374080a b c d + 137760b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (145320a c d + 403200a b c d + 94080b c d)x
+--R +
+--R 2 5 2 6 2 7 4 2 6 2 2 7
+--R (8400a c d + 161280a b c d + 26880b c )x - 73920a c d x - 26880a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 10 3 8 2 2 6 3 4 4 2 +-+
+--R (210d x + 8400c d x + 50400c d x + 94080c d x + 53760c x )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 10 2 3 8 3 2 6 4 4 5 2
+--R - 1890c d x - 25200c d x - 90720c d x - 120960c d x - 53760c x
+--R Type: Union(Expression(Integer),...)
+--E 952
+
+--S 953 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 6 3 5 8 2 3 5 4 4 6
+--R (525a c d + 420a b c d )x + (21000a c d + 16800a b c d )x
+--R +
+--R 2 4 4 5 3 4
+--R (126000a c d + 100800a b c d )x
+--R +
+--R 2 5 3 6 2 2 2 6 2 7
+--R (235200a c d + 188160a b c d )x + 134400a c d + 107520a b c d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 3 5 8
+--R (- 4725a c d - 3780a b c d )x
+--R +
+--R 2 3 5 4 4 6
+--R (- 63000a c d - 50400a b c d )x
+--R +
+--R 2 4 4 5 3 4
+--R (- 226800a c d - 181440a b c d )x
+--R +
+--R 2 5 3 6 2 2 2 6 2 7
+--R (- 302400a c d - 241920a b c d )x - 134400a c d - 107520a b c d
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 6 3 5 8 2 3 5 4 4 6
+--R (525a c d + 420a b c d )x + (21000a c d + 16800a b c d )x
+--R +
+--R 2 4 4 5 3 4
+--R (126000a c d + 100800a b c d )x
+--R +
+--R 2 5 3 6 2 2 2 6 2 7
+--R (235200a c d + 188160a b c d )x + 134400a c d + 107520a b c d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 3 5 8
+--R (- 4725a c d - 3780a b c d )x
+--R +
+--R 2 3 5 4 4 6
+--R (- 63000a c d - 50400a b c d )x
+--R +
+--R 2 4 4 5 3 4
+--R (- 226800a c d - 181440a b c d )x
+--R +
+--R 2 5 3 6 2 2 2 6 2 7
+--R (- 302400a c d - 241920a b c d )x - 134400a c d - 107520a b c d
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 6 3 5 2 4 4 8
+--R (490a c d + 644a b c d + 30b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 6
+--R (19600a c d + 25760a b c d + 1200b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 4
+--R (117600a c d + 154560a b c d + 7200b c d )x
+--R +
+--R 2 5 3 6 2 2 7 2 2 6 2
+--R (219520a c d + 288512a b c d + 13440b c d)x + 125440a c d
+--R +
+--R 7 2 8
+--R 164864a b c d + 7680b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 3 5 2 4 4 8
+--R (- 4410a c d - 5796a b c d - 270b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 6
+--R (- 58800a c d - 77280a b c d - 3600b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 4
+--R (- 211680a c d - 278208a b c d - 12960b c d )x
+--R +
+--R 2 5 3 6 2 2 7 2 2 6 2
+--R (- 282240a c d - 370944a b c d - 17280b c d)x - 125440a c d
+--R +
+--R 7 2 8
+--R - 164864a b c d - 7680b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 5 8 4 6 2 3 4 3 2 2 4 +-+
+--R (210d x + 8400c d x + 50400c d x + 94080c d x + 53760c d)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 5 8 2 4 6 3 3 4 4 2 2 5
+--R - 1890c d x - 25200c d x - 90720c d x - 120960c d x - 53760c d
+--R Type: Expression(Integer)
+--E 953
+
+--S 954 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 954
+
+)clear all
+
+--S 955 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(5/2)/x^4
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 955
+
+--S 956 of 1397
+r0:=5/24*(b^2*c^2+4*a*d*(3*b*c+2*a*d))*x*(c+d*x^2)^(3/2)/c+_
+ 1/6*(b^2*c^2+4*a*d*(3*b*c+2*a*d))*x*(c+d*x^2)^(5/2)/c^2-_
+ 1/3*a^2*(c+d*x^2)^(7/2)/(c*x^3)-2/3*a*(3*b*c+2*a*d)*_
+ (c+d*x^2)^(7/2)/(c^2*x)+5/16*c*(b^2*c^2+4*a*d*(3*b*c+2*a*d))*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))/sqrt(d)+5/16*(b^2*c^2+4*a*d*_
+ (3*b*c+2*a*d))*x*sqrt(c+d*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 3 3 x\|d
+--R (120a c d + 180a b c d + 15b c )x atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R 8b d x + (24a b d + 26b c d)x + (24a d + 108a b c d + 33b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 112a c d - 96a b c )x - 16a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R 3 +-+
+--R 48x \|d
+--R Type: Expression(Integer)
+--E 956
+
+--S 957 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 6 2 5 2 3 4 11
+--R (120a c d + 180a b c d + 15b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 9
+--R (4800a c d + 7200a b c d + 600b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 7
+--R (28800a c d + 43200a b c d + 3600b c d )x
+--R +
+--R 2 4 3 5 2 2 6 5
+--R (53760a c d + 80640a b c d + 6720b c d)x
+--R +
+--R 2 5 2 6 2 7 3
+--R (30720a c d + 46080a b c d + 3840b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 2 5 2 3 4 11
+--R (- 1080a c d - 1620a b c d - 135b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 9
+--R (- 14400a c d - 21600a b c d - 1800b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 7
+--R (- 51840a c d - 77760a b c d - 6480b c d )x
+--R +
+--R 2 4 3 5 2 2 6 5
+--R (- 69120a c d - 103680a b c d - 8640b c d)x
+--R +
+--R 2 5 2 6 2 7 3
+--R (- 30720a c d - 46080a b c d - 3840b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 6 16 6 2 5 14
+--R - 72b d x + (- 216a b d - 1194b c d )x
+--R +
+--R 2 6 5 2 2 4 12
+--R (- 216a d - 3852a b c d - 6873b c d )x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (- 1872a c d - 22464a b c d - 19800b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (3216a c d - 48960a b c d - 31280b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (36480a c d - 26880a b c d - 25664b c d)x
+--R +
+--R 2 4 2 5 2 6 4
+--R (65280a c d + 27648a b c d - 8448b c )x
+--R +
+--R 2 5 6 2 2 6
+--R (37888a c d + 24576a b c )x + 4096a c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 2 7 18 7 2 6 16
+--R 8b d x + (24a b d + 354b c d )x
+--R +
+--R 2 7 6 2 2 5 14
+--R (24a d + 1092a b c d + 3339b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (872a c d + 11052a b c d + 14137b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (2112a c d + 42816a b c d + 32760b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 15504a c d + 64320a b c d + 43056b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 64640a c d + 16128a b c d + 29888b c d)x
+--R +
+--R 2 5 2 6 2 7 4
+--R (- 83712a c d - 39936a b c d + 8448b c )x
+--R +
+--R 2 6 7 2 2 7
+--R (- 39936a c d - 24576a b c )x - 4096a c
+--R *
+--R +-+
+--R \|d
+--R /
+--R 4 11 3 9 2 2 7 3 5 4 3 +-+
+--R (48d x + 1920c d x + 11520c d x + 21504c d x + 12288c x )\|d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 11 3 9 2 2 7 3 5 4 3 +-+ +-+
+--R (- 432d x - 5760c d x - 20736c d x - 27648c d x - 12288c x )\|c \|d
+--R ,
+--R
+--R 2 6 2 5 2 3 4 11
+--R (240a c d + 360a b c d + 30b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 9
+--R (9600a c d + 14400a b c d + 1200b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 7
+--R (57600a c d + 86400a b c d + 7200b c d )x
+--R +
+--R 2 4 3 5 2 2 6 5
+--R (107520a c d + 161280a b c d + 13440b c d)x
+--R +
+--R 2 5 2 6 2 7 3
+--R (61440a c d + 92160a b c d + 7680b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 2 5 2 3 4 11
+--R (- 2160a c d - 3240a b c d - 270b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 9
+--R (- 28800a c d - 43200a b c d - 3600b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 7
+--R (- 103680a c d - 155520a b c d - 12960b c d )x
+--R +
+--R 2 4 3 5 2 2 6 5
+--R (- 138240a c d - 207360a b c d - 17280b c d)x
+--R +
+--R 2 5 2 6 2 7 3
+--R (- 61440a c d - 92160a b c d - 7680b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 6 16 6 2 5 14
+--R - 72b d x + (- 216a b d - 1194b c d )x
+--R +
+--R 2 6 5 2 2 4 12
+--R (- 216a d - 3852a b c d - 6873b c d )x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (- 1872a c d - 22464a b c d - 19800b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (3216a c d - 48960a b c d - 31280b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (36480a c d - 26880a b c d - 25664b c d)x
+--R +
+--R 2 4 2 5 2 6 4
+--R (65280a c d + 27648a b c d - 8448b c )x
+--R +
+--R 2 5 6 2 2 6
+--R (37888a c d + 24576a b c )x + 4096a c
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 2 7 18 7 2 6 16
+--R 8b d x + (24a b d + 354b c d )x
+--R +
+--R 2 7 6 2 2 5 14
+--R (24a d + 1092a b c d + 3339b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (872a c d + 11052a b c d + 14137b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (2112a c d + 42816a b c d + 32760b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 15504a c d + 64320a b c d + 43056b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 64640a c d + 16128a b c d + 29888b c d)x
+--R +
+--R 2 5 2 6 2 7 4
+--R (- 83712a c d - 39936a b c d + 8448b c )x
+--R +
+--R 2 6 7 2 2 7
+--R (- 39936a c d - 24576a b c )x - 4096a c
+--R *
+--R +---+
+--R \|- d
+--R /
+--R 4 11 3 9 2 2 7 3 5 4 3 +---+
+--R (48d x + 1920c d x + 11520c d x + 21504c d x + 12288c x )\|- d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 11 3 9 2 2 7 3 5 4 3
+--R (- 432d x - 5760c d x - 20736c d x - 27648c d x - 12288c x )
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 957
+
+--S 958 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 3
+--R (40a c d + 60a b c d + 5b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 3 x\|d
+--R (- 40a c d - 60a b c d - 5b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R +-+
+--R 16\|d
+--R Type: Expression(Integer)
+--E 958
+
+--S 959 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 959
+
+--S 960 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 3 +---+ x\|d
+--R (- 40a c d - 60a b c d - 5b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 2 3 +-+ \|- d \|d x + c - \|- d \|c
+--R (80a c d + 120a b c d + 10b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R +---+ +-+
+--R 16\|- d \|d
+--R Type: Expression(Integer)
+--E 960
+
+--S 961 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 961
+
+)clear all
+
+--S 962 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(5/2)/x^5
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 962
+
+--S 963 of 1397
+r0:=1/24*(8*b^2*c^2+5*a*d*(8*b*c+3*a*d))*(c+d*x^2)^(3/2)/c+_
+ 1/40*(8*b^2*c^2+5*a*d*(8*b*c+3*a*d))*(c+d*x^2)^(5/2)/c^2-_
+ 1/4*a^2*(c+d*x^2)^(7/2)/(c*x^4)-1/8*a*(8*b*c+3*a*d)*_
+ (c+d*x^2)^(7/2)/(c^2*x^2)-1/8*(8*b^2*c^2+5*a*d*(8*b*c+3*a*d))*_
+ atanh(sqrt(c+d*x^2)/sqrt(c))*sqrt(c)+1/8*(8*b^2*c^2+5*a*d*_
+ (8*b*c+3*a*d))*sqrt(c+d*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 2 2 2 4 +-+ \|d x + c
+--R (- 225a d - 600a b c d - 120b c )x \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 8 2 2 6
+--R 24b d x + (80a b d + 88b c d)x
+--R +
+--R 2 2 2 2 4 2 2 2
+--R (120a d + 560a b c d + 184b c )x + (- 135a c d - 120a b c )x
+--R +
+--R 2 2
+--R - 30a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4
+--R 120x
+--R Type: Expression(Integer)
+--E 963
+
+--S 964 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 2 5 2 3 4 12
+--R (225a c d + 600a b c d + 120b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (9000a c d + 24000a b c d + 4800b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (54000a c d + 144000a b c d + 28800b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (100800a c d + 268800a b c d + 53760b c d)x
+--R +
+--R 2 5 2 6 2 7 4
+--R (57600a c d + 153600a b c d + 30720b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (- 2025a c d - 5400a b c d - 1080b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (- 27000a c d - 72000a b c d - 14400b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 97200a c d - 259200a b c d - 51840b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 129600a c d - 345600a b c d - 69120b c d)x
+--R +
+--R 2 5 2 6 2 7 4
+--R (- 57600a c d - 153600a b c d - 30720b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 6 16 6 2 2 5 14
+--R - 216b c d x + (- 720a b c d - 3672b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (- 960a c d - 14080a b c d - 22400b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (- 8385a c d - 78280a b c d - 66560b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 6570a c d - 139200a b c d - 92160b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (46560a c d - 40320a b c d - 46080b c d)x
+--R +
+--R 2 5 2 6 4 2 6 7 2
+--R (90720a c d + 69120a b c d)x + (51840a c d + 30720a b c )x
+--R +
+--R 2 7
+--R 7680a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 7 18 7 2 6 16
+--R 24b d x + (80a b d + 1072b c d )x
+--R +
+--R 2 7 6 2 2 5 14
+--R (120a d + 3840a b c d + 10512b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (3705a c d + 40200a b c d + 47040b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (13635a c d + 139720a b c d + 106880b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 8310a c d + 166080a b c d + 115200b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 85920a c d + 9600a b c d + 46080b c d)x
+--R +
+--R 2 5 2 6 4 2 6 7 2
+--R (- 115680a c d - 84480a b c d)x + (- 55680a c d - 30720a b c )x
+--R +
+--R 2 7
+--R - 7680a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 12 3 10 2 2 8 3 6 4 4 +-+
+--R (120d x + 4800c d x + 28800c d x + 53760c d x + 30720c x )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 12 2 3 10 3 2 8 4 6 5 4
+--R - 1080c d x - 14400c d x - 51840c d x - 69120c d x - 30720c x
+--R Type: Union(Expression(Integer),...)
+--E 964
+
+--S 965 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 6 2 5 2 3 4 8
+--R (225a c d + 600a b c d + 120b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (9000a c d + 24000a b c d + 4800b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (54000a c d + 144000a b c d + 28800b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (100800a c d + 268800a b c d + 53760b c d)x + 57600a c d
+--R +
+--R 6 2 7
+--R 153600a b c d + 30720b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 2 5 2 3 4 8
+--R (- 2025a c d - 5400a b c d - 1080b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (- 27000a c d - 72000a b c d - 14400b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (- 97200a c d - 259200a b c d - 51840b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (- 129600a c d - 345600a b c d - 69120b c d)x - 57600a c d
+--R +
+--R 6 2 7
+--R - 153600a b c d - 30720b c
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 6 2 5 2 3 4 8
+--R (225a c d + 600a b c d + 120b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (9000a c d + 24000a b c d + 4800b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (54000a c d + 144000a b c d + 28800b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (100800a c d + 268800a b c d + 53760b c d)x + 57600a c d
+--R +
+--R 6 2 7
+--R 153600a b c d + 30720b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 2 5 2 3 4 8
+--R (- 2025a c d - 5400a b c d - 1080b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (- 27000a c d - 72000a b c d - 14400b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (- 97200a c d - 259200a b c d - 51840b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (- 129600a c d - 345600a b c d - 69120b c d)x - 57600a c d
+--R +
+--R 6 2 7
+--R - 153600a b c d - 30720b c
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 6 2 5 2 3 4 8
+--R (120a c d + 560a b c d + 184b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (4800a c d + 22400a b c d + 7360b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (28800a c d + 134400a b c d + 44160b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (53760a c d + 250880a b c d + 82432b c d)x + 30720a c d
+--R +
+--R 6 2 7
+--R 143360a b c d + 47104b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 2 5 2 3 4 8
+--R (- 1080a c d - 5040a b c d - 1656b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (- 14400a c d - 67200a b c d - 22080b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (- 51840a c d - 241920a b c d - 79488b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (- 69120a c d - 322560a b c d - 105984b c d)x - 30720a c d
+--R +
+--R 6 2 7
+--R - 143360a b c d - 47104b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (120d x + 4800c d x + 28800c d x + 53760c d x + 30720c )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 1080c d x - 14400c d x - 51840c d x - 69120c d x - 30720c
+--R Type: Expression(Integer)
+--E 965
+
+--S 966 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 966
+
+)clear all
+
+--S 967 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(5/2)/x^6
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 967
+
+--S 968 of 1397
+r0:=1/12*d*(15*b^2*c^2+8*a*d*(5*b*c+a*d))*x*(c+d*x^2)^(3/2)/c^2-_
+ 1/15*(15*b^2*c^2+8*a*d*(5*b*c+a*d))*(c+d*x^2)^(5/2)/(c^2*x)-_
+ 1/5*a^2*(c+d*x^2)^(7/2)/(c*x^5)-2/15*a*(5*b*c+a*d)*_
+ (c+d*x^2)^(7/2)/(c^2*x^3)+1/8*(15*b^2*c^2+8*a*d*(5*b*c+a*d))*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))*sqrt(d)+1/8*d*(15*b^2*c^2+8*a*_
+ d*(5*b*c+a*d))*x*sqrt(c+d*x^2)/c
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 5 +-+ x\|d
+--R (120a d + 600a b c d + 225b c )x \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 8 2 2 6
+--R 30b d x + (120a b d + 135b c d)x
+--R +
+--R 2 2 2 2 4 2 2 2
+--R (- 184a d - 560a b c d - 120b c )x + (- 88a c d - 80a b c )x
+--R +
+--R 2 2
+--R - 24a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 5
+--R 120x
+--R Type: Expression(Integer)
+--E 968
+
+--S 969 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 6 5 2 2 4 13
+--R (120a d + 600a b c d + 225b c d )x
+--R +
+--R 2 5 2 4 2 3 3 11
+--R (4800a c d + 24000a b c d + 9000b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 9
+--R (28800a c d + 144000a b c d + 54000b c d )x
+--R +
+--R 2 3 3 4 2 2 5 7
+--R (53760a c d + 268800a b c d + 100800b c d)x
+--R +
+--R 2 4 2 5 2 6 5
+--R (30720a c d + 153600a b c d + 57600b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 6 5 2 2 4 13
+--R (- 1080a d - 5400a b c d - 2025b c d )x
+--R +
+--R 2 5 2 4 2 3 3 11
+--R (- 14400a c d - 72000a b c d - 27000b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 9
+--R (- 51840a c d - 259200a b c d - 97200b c d )x
+--R +
+--R 2 3 3 4 2 2 5 7
+--R (- 69120a c d - 345600a b c d - 129600b c d)x
+--R +
+--R 2 4 2 5 2 6 5
+--R (- 30720a c d - 153600a b c d - 57600b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 6 16 6 2 5 14
+--R - 270b d x + (- 1080a b d - 4815b c d )x
+--R +
+--R 2 6 5 2 2 4 12
+--R (1656a d - 9360a b c d - 28080b c d )x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (22872a c d + 16080a b c d - 61200b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (90264a c d + 182400a b c d - 33600b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (146880a c d + 326400a b c d + 34560b c d)x
+--R +
+--R 2 4 2 5 2 6 4
+--R (108160a c d + 189440a b c d + 30720b c )x
+--R +
+--R 2 5 6 2 2 6
+--R (36352a c d + 20480a b c )x + 6144a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 7 18 7 2 6 16
+--R 30b d x + (120a b d + 1365b c d )x
+--R +
+--R 2 7 6 2 2 5 14
+--R (- 184a d + 4360a b c d + 13815b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (- 7632a c d + 10560a b c d + 53520b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (- 55152a c d - 77520a b c d + 80400b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 152216a c d - 323200a b c d + 20160b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 196800a c d - 418560a b c d - 49920b c d)x
+--R +
+--R 2 5 2 6 2 7 4
+--R (- 125568a c d - 199680a b c d - 30720b c )x
+--R +
+--R 2 6 7 2 2 7
+--R (- 39424a c d - 20480a b c )x - 6144a c
+--R /
+--R 4 13 3 11 2 2 9 3 7 4 5
+--R (120d x + 4800c d x + 28800c d x + 53760c d x + 30720c x )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 13 3 11 2 2 9 3 7 4 5 +-+
+--R (- 1080d x - 14400c d x - 51840c d x - 69120c d x - 30720c x )\|c
+--R ,
+--R
+--R 2 6 5 2 2 4 13
+--R (240a d + 1200a b c d + 450b c d )x
+--R +
+--R 2 5 2 4 2 3 3 11
+--R (9600a c d + 48000a b c d + 18000b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 9
+--R (57600a c d + 288000a b c d + 108000b c d )x
+--R +
+--R 2 3 3 4 2 2 5 7
+--R (107520a c d + 537600a b c d + 201600b c d)x
+--R +
+--R 2 4 2 5 2 6 5
+--R (61440a c d + 307200a b c d + 115200b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 6 5 2 2 4 13
+--R (- 2160a d - 10800a b c d - 4050b c d )x
+--R +
+--R 2 5 2 4 2 3 3 11
+--R (- 28800a c d - 144000a b c d - 54000b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 9
+--R (- 103680a c d - 518400a b c d - 194400b c d )x
+--R +
+--R 2 3 3 4 2 2 5 7
+--R (- 138240a c d - 691200a b c d - 259200b c d)x
+--R +
+--R 2 4 2 5 2 6 5
+--R (- 61440a c d - 307200a b c d - 115200b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 2 6 16 6 2 5 14
+--R - 270b d x + (- 1080a b d - 4815b c d )x
+--R +
+--R 2 6 5 2 2 4 12
+--R (1656a d - 9360a b c d - 28080b c d )x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (22872a c d + 16080a b c d - 61200b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (90264a c d + 182400a b c d - 33600b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (146880a c d + 326400a b c d + 34560b c d)x
+--R +
+--R 2 4 2 5 2 6 4
+--R (108160a c d + 189440a b c d + 30720b c )x
+--R +
+--R 2 5 6 2 2 6
+--R (36352a c d + 20480a b c )x + 6144a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 7 18 7 2 6 16
+--R 30b d x + (120a b d + 1365b c d )x
+--R +
+--R 2 7 6 2 2 5 14
+--R (- 184a d + 4360a b c d + 13815b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (- 7632a c d + 10560a b c d + 53520b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (- 55152a c d - 77520a b c d + 80400b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 152216a c d - 323200a b c d + 20160b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 196800a c d - 418560a b c d - 49920b c d)x
+--R +
+--R 2 5 2 6 2 7 4
+--R (- 125568a c d - 199680a b c d - 30720b c )x
+--R +
+--R 2 6 7 2 2 7
+--R (- 39424a c d - 20480a b c )x - 6144a c
+--R /
+--R 4 13 3 11 2 2 9 3 7 4 5
+--R (120d x + 4800c d x + 28800c d x + 53760c d x + 30720c x )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 13 3 11 2 2 9 3 7 4 5 +-+
+--R (- 1080d x - 14400c d x - 51840c d x - 69120c d x - 30720c x )\|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 969
+
+--S 970 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+
+--R (8a d + 40a b c d + 15b c )\|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ x\|d
+--R (- 8a d - 40a b c d - 15b c )\|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 8
+--R Type: Expression(Integer)
+--E 970
+
+--S 971 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 971
+
+--S 972 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 +-+ x\|d
+--R (- 8a d - 40a b c d - 15b c )\|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R | 2 +-+
+--R 2 2 2 2 +---+ \|d x + c - \|c
+--R (16a d + 80a b c d + 30b c )\|- d atan(------------------)
+--R +---+
+--R x\|- d
+--R /
+--R 8
+--R Type: Expression(Integer)
+--E 972
+
+--S 973 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 973
+
+)clear all
+
+--S 974 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^(5/2)/x^7
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 974
+
+--S 975 of 1397
+r0:=5/48*d*(8*b^2*c^2+a*d*(12*b*c+a*d))*(c+d*x^2)^(3/2)/c^2-_
+ 1/16*(8*b^2*c^2+a*d*(12*b*c+a*d))*(c+d*x^2)^(5/2)/(c^2*x^2)-_
+ 1/6*a^2*(c+d*x^2)^(7/2)/(c*x^6)-1/24*a*(12*b*c+a*d)*_
+ (c+d*x^2)^(7/2)/(c^2*x^4)-5/16*d*(8*b^2*c^2+a*d*(12*b*c+a*d))*_
+ atanh(sqrt(c+d*x^2)/sqrt(c))/sqrt(c)+5/16*d*(8*b^2*c^2+a*d*_
+ (12*b*c+a*d))*sqrt(c+d*x^2)/c
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 3 2 2 2 6 \|d x + c
+--R (- 15a d - 180a b c d - 120b c d)x atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 8 2 2 6
+--R 16b d x + (96a b d + 112b c d)x
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R (- 33a d - 108a b c d - 24b c )x + (- 26a c d - 24a b c )x - 8a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R /
+--R 6 +-+
+--R 48x \|c
+--R Type: Expression(Integer)
+--E 975
+
+--S 976 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 7 6 2 2 5 14
+--R (15a d + 180a b c d + 120b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (600a c d + 7200a b c d + 4800b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (3600a c d + 43200a b c d + 28800b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (6720a c d + 80640a b c d + 53760b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (3840a c d + 46080a b c d + 30720b c d)x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 7 6 2 2 5 14
+--R (- 135a d - 1620a b c d - 1080b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (- 1800a c d - 21600a b c d - 14400b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (- 6480a c d - 77760a b c d - 51840b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 8640a c d - 103680a b c d - 69120b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 3840a c d - 46080a b c d - 30720b c d)x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 6 16 6 2 2 5 14
+--R - 144b c d x + (- 768a b c d - 2816b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (297a c d - 6708a b c d - 15656b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (4194a c d - 5256a b c d - 27840b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (17448a c d + 37248a b c d - 8064b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (31200a c d + 72576a b c d + 13824b c d)x
+--R +
+--R 2 5 2 6 2 7 4
+--R (26880a c d + 41472a b c d + 6144b c )x
+--R +
+--R 2 6 7 2 2 7
+--R (11264a c d + 6144a b c )x + 2048a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 7 18 7 2 6 16
+--R 16b d x + (96a b d + 768b c d )x
+--R +
+--R 2 7 6 2 2 5 14
+--R (- 33a d + 2964a b c d + 8040b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (- 1379a c d + 10908a b c d + 27944b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (- 10314a c d - 6648a b c d + 33216b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 30312a c d - 68736a b c d + 1920b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 43360a c d - 92544a b c d - 16896b c d)x
+--R +
+--R 2 5 2 6 2 7 4
+--R (- 32256a c d - 44544a b c d - 6144b c )x
+--R +
+--R 2 6 7 2 2 7
+--R (- 12288a c d - 6144a b c )x - 2048a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 14 3 12 2 2 10 3 8 4 6 +-+
+--R (48d x + 1920c d x + 11520c d x + 21504c d x + 12288c x )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 14 2 3 12 3 2 10 4 8 5 6
+--R - 432c d x - 5760c d x - 20736c d x - 27648c d x - 12288c x
+--R Type: Union(Expression(Integer),...)
+--E 976
+
+--S 977 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 2 3 2 2 2 \|d x + c - \|c
+--R (15a d + 180a b c d + 120b c d)log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 2 3 2 2 2 \|d x + c 2 2 2
+--R (15a d + 180a b c d + 120b c d)atanh(-----------) + 96a b c d + 112b c d
+--R +-+
+--R \|c
+--R /
+--R +-+
+--R 48\|c
+--R Type: Expression(Integer)
+--E 977
+
+--S 978 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 978
+
+)clear all
+
+--S 979 of 1397
+t0:=x^4*(a+b*x^2)^2/sqrt(c+d*x^2)
+--R
+--R
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 979
+
+--S 980 of 1397
+r0:=1/128*c^2*(48*a^2*d^2+5*b*c*(7*b*c-16*a*d))*atanh(x*sqrt(d)/_
+ sqrt(c+d*x^2))/d^(9/2)-1/128*c*(48*a^2*d^2+5*b*c*(7*b*c-16*a*d))*_
+ x*sqrt(c+d*x^2)/d^4+1/192*(48*a^2*d^2+5*b*c*(7*b*c-16*a*d))*_
+ x^3*sqrt(c+d*x^2)/d^3-1/48*b*(7*b*c-16*a*d)*x^5*sqrt(c+d*x^2)/d^2+_
+ 1/8*b^2*x^7*sqrt(c+d*x^2)/d
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 3 2 4 x\|d
+--R (144a c d - 240a b c d + 105b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 7 3 2 2 5
+--R 48b d x + (128a b d - 56b c d )x
+--R +
+--R 2 3 2 2 2 3
+--R (96a d - 160a b c d + 70b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 144a c d + 240a b c d - 105b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R 4 +-+
+--R 384d \|d
+--R Type: Expression(Integer)
+--E 980
+
+--S 981 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 5 3 4 2 4 3 6
+--R (1152a c d - 1920a b c d + 840b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (11520a c d - 19200a b c d + 8400b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (27648a c d - 46080a b c d + 20160b c d)x + 18432a c d
+--R +
+--R 6 2 7
+--R - 30720a b c d + 13440b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 2 6 3 5 2 4 4 8
+--R (- 144a c d + 240a b c d - 105b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 6
+--R (- 4608a c d + 7680a b c d - 3360b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 4
+--R (- 23040a c d + 38400a b c d - 16800b c d )x
+--R +
+--R 2 5 3 6 2 2 7 2 2 6 2
+--R (- 36864a c d + 61440a b c d - 26880b c d)x - 18432a c d
+--R +
+--R 7 2 8
+--R 30720a b c d - 13440b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 7 15 7 2 6 13
+--R - 48b d x + (- 128a b d - 1480b c d )x
+--R +
+--R 2 7 6 2 2 5 11
+--R (- 96a d - 3936a b c d - 5958b c d )x
+--R +
+--R 2 6 2 5 2 3 4 9
+--R (- 2928a c d - 15600a b c d - 5463b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 7
+--R (- 10752a c d - 14848a b c d + 352b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 5
+--R (- 1536a c d - 13824a b c d + 6048b c d )x
+--R +
+--R 2 4 3 5 2 2 6 3
+--R (24576a c d - 40960a b c d + 17920b c d)x
+--R +
+--R 2 5 2 6 2 7
+--R (18432a c d - 30720a b c d + 13440b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 7 15 7 2 6 13
+--R 384b d x + (1024a b d + 3776b c d )x
+--R +
+--R 2 7 6 2 2 5 11
+--R (768a d + 9984a b c d + 8688b c d )x
+--R +
+--R 2 6 2 5 2 3 4 9
+--R (7296a c d + 22656a b c d + 5448b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 7
+--R (13440a c d + 18560a b c d - 1976b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 5
+--R (- 8448a c d + 30464a b c d - 13328b c d )x
+--R +
+--R 2 4 3 5 2 2 6 3
+--R (- 33792a c d + 56320a b c d - 24640b c d)x
+--R +
+--R 2 5 2 6 2 7
+--R (- 18432a c d + 30720a b c d - 13440b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 7 6 6 4 2 5 2 3 4 +-+ +-+ | 2
+--R (3072d x + 30720c d x + 73728c d x + 49152c d )\|c \|d \|d x + c
+--R +
+--R 8 8 7 6 2 6 4 3 5 2 4 4 +-+
+--R (- 384d x - 12288c d x - 61440c d x - 98304c d x - 49152c d )\|d
+--R ,
+--R
+--R 2 2 5 3 4 2 4 3 6
+--R (2304a c d - 3840a b c d + 1680b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (23040a c d - 38400a b c d + 16800b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (55296a c d - 92160a b c d + 40320b c d)x + 36864a c d
+--R +
+--R 6 2 7
+--R - 61440a b c d + 26880b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 2 6 3 5 2 4 4 8
+--R (- 288a c d + 480a b c d - 210b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 6
+--R (- 9216a c d + 15360a b c d - 6720b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 4
+--R (- 46080a c d + 76800a b c d - 33600b c d )x
+--R +
+--R 2 5 3 6 2 2 7 2 2 6 2
+--R (- 73728a c d + 122880a b c d - 53760b c d)x - 36864a c d
+--R +
+--R 7 2 8
+--R 61440a b c d - 26880b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 7 15 7 2 6 13
+--R - 48b d x + (- 128a b d - 1480b c d )x
+--R +
+--R 2 7 6 2 2 5 11
+--R (- 96a d - 3936a b c d - 5958b c d )x
+--R +
+--R 2 6 2 5 2 3 4 9
+--R (- 2928a c d - 15600a b c d - 5463b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 7
+--R (- 10752a c d - 14848a b c d + 352b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 5
+--R (- 1536a c d - 13824a b c d + 6048b c d )x
+--R +
+--R 2 4 3 5 2 2 6 3
+--R (24576a c d - 40960a b c d + 17920b c d)x
+--R +
+--R 2 5 2 6 2 7
+--R (18432a c d - 30720a b c d + 13440b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 7 15 7 2 6 13
+--R 384b d x + (1024a b d + 3776b c d )x
+--R +
+--R 2 7 6 2 2 5 11
+--R (768a d + 9984a b c d + 8688b c d )x
+--R +
+--R 2 6 2 5 2 3 4 9
+--R (7296a c d + 22656a b c d + 5448b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 7
+--R (13440a c d + 18560a b c d - 1976b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 5
+--R (- 8448a c d + 30464a b c d - 13328b c d )x
+--R +
+--R 2 4 3 5 2 2 6 3
+--R (- 33792a c d + 56320a b c d - 24640b c d)x
+--R +
+--R 2 5 2 6 2 7
+--R (- 18432a c d + 30720a b c d - 13440b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 7 6 6 4 2 5 2 3 4 +---+ +-+ | 2
+--R (3072d x + 30720c d x + 73728c d x + 49152c d )\|- d \|c \|d x + c
+--R +
+--R 8 8 7 6 2 6 4 3 5 2 4 4 +---+
+--R (- 384d x - 12288c d x - 61440c d x - 98304c d x - 49152c d )\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 981
+
+--S 982 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 3 2 4
+--R (48a c d - 80a b c d + 35b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 3 2 4 x\|d
+--R (- 48a c d + 80a b c d - 35b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4 +-+
+--R 128d \|d
+--R Type: Expression(Integer)
+--E 982
+
+--S 983 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 983
+
+--S 984 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 3 2 4 +---+ x\|d
+--R (- 48a c d + 80a b c d - 35b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 3 2 4 +-+ \|- d \|d x + c - \|- d \|c
+--R (96a c d - 160a b c d + 70b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 4 +---+ +-+
+--R 128d \|- d \|d
+--R Type: Expression(Integer)
+--E 984
+
+--S 985 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 985
+
+)clear all
+
+--S 986 of 1397
+t0:=x^3*(a+b*x^2)^2/sqrt(c+d*x^2)
+--R
+--R
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 986
+
+--S 987 of 1397
+r0:=1/3*(b*c-a*d)*(3*b*c-a*d)*(c+d*x^2)^(3/2)/d^4-_
+ 1/5*b*(3*b*c-2*a*d)*(c+d*x^2)^(5/2)/d^4+1/7*b^2*(c+d*x^2)^(7/2)/d^4-_
+ c*(b*c-a*d)^2*sqrt(c+d*x^2)/d^4
+--R
+--R
+--R (2)
+--R 2 3 6 3 2 2 4 2 3 2 2 2 2
+--R 15b d x + (42a b d - 18b c d )x + (35a d - 56a b c d + 24b c d)x
+--R +
+--R 2 2 2 2 3
+--R - 70a c d + 112a b c d - 48b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4
+--R 105d
+--R Type: Expression(Integer)
+--E 987
+
+--S 988 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 12 2 2 2 10
+--R - 105b c d x + (- 294a b c d - 714b c d)x
+--R +
+--R 2 2 2 2 3 8
+--R (- 245a c d - 1960a b c d - 840b c )x
+--R +
+--R 2 2 3 6 2 3 4
+--R (- 1540a c d - 2240a b c )x - 1680a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 14 3 2 2 12
+--R 15b d x + (42a b d + 357b c d )x
+--R +
+--R 2 3 2 2 2 10
+--R (35a d + 994a b c d + 1134b c d)x
+--R +
+--R 2 2 2 2 3 8 2 2 3 6
+--R (805a c d + 3080a b c d + 840b c )x + (2380a c d + 2240a b c )x
+--R +
+--R 2 3 4
+--R 1680a c x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (105d x + 2520c d x + 8400c d x + 6720c )\|c \|d x + c - 735c d x
+--R +
+--R 2 2 4 3 2 4
+--R - 5880c d x - 11760c d x - 6720c
+--R Type: Union(Expression(Integer),...)
+--E 988
+
+--S 989 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 5 3 4 2 4 3 6
+--R (- 70a c d + 112a b c d - 48b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (- 1680a c d + 2688a b c d - 1152b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (- 5600a c d + 8960a b c d - 3840b c d)x - 4480a c d
+--R +
+--R 6 2 7
+--R 7168a b c d - 3072b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (490a c d - 784a b c d + 336b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (3920a c d - 6272a b c d + 2688b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2 6
+--R (7840a c d - 12544a b c d + 5376b c d)x + 4480a c d - 7168a b c d
+--R +
+--R 2 7
+--R 3072b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 7 6 6 4 2 5 2 3 4 +-+ | 2 7 6
+--R (105d x + 2520c d x + 8400c d x + 6720c d )\|c \|d x + c - 735c d x
+--R +
+--R 2 6 4 3 5 2 4 4
+--R - 5880c d x - 11760c d x - 6720c d
+--R Type: Expression(Integer)
+--E 989
+
+--S 990 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 990
+
+)clear all
+
+--S 991 of 1397
+t0:=x^2*(a+b*x^2)^2/sqrt(c+d*x^2)
+--R
+--R
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 991
+
+--S 992 of 1397
+r0:=-1/16*c*(8*a^2*d^2+b*c*(5*b*c-12*a*d))*atanh(x*sqrt(d)/_
+ sqrt(c+d*x^2))/d^(7/2)+1/16*(8*a^2*d^2+b*c*(5*b*c-12*a*d))*x*_
+ sqrt(c+d*x^2)/d^3-1/24*b*(5*b*c-12*a*d)*x^3*sqrt(c+d*x^2)/d^2+_
+ 1/6*b^2*x^5*sqrt(c+d*x^2)/d
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 3 x\|d
+--R (- 24a c d + 36a b c d - 15b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 5 2 2 3 2 2 2 2 +-+
+--R (8b d x + (24a b d - 10b c d)x + (24a d - 36a b c d + 15b c )x)\|d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 +-+
+--R 48d \|d
+--R Type: Expression(Integer)
+--E 992
+
+--S 993 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 2 3 2 3 2 4
+--R (144a c d - 216a b c d + 90b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (768a c d - 1152a b c d + 480b c d)x + 768a c d
+--R +
+--R 4 2 5
+--R - 1152a b c d + 480b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 24a c d + 36a b c d - 15b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 432a c d + 648a b c d - 270b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (- 1152a c d + 1728a b c d - 720b c d)x - 768a c d
+--R +
+--R 5 2 6
+--R 1152a b c d - 480b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 5 11 5 2 4 9
+--R - 8b d x + (- 24a b d - 134b c d )x
+--R +
+--R 2 5 4 2 2 3 7
+--R (- 24a d - 396a b c d - 219b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (- 432a c d - 504a b c d - 46b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3
+--R (- 1152a c d + 960a b c d - 400b c d)x
+--R +
+--R 2 3 2 4 2 5
+--R (- 768a c d + 1152a b c d - 480b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 5 11 5 2 4 9
+--R 48b d x + (144a b d + 244b c d )x
+--R +
+--R 2 5 4 2 2 3 7
+--R (144a d + 696a b c d + 222b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (912a c d + 168a b c d + 186b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3
+--R (1536a c d - 1536a b c d + 640b c d)x
+--R +
+--R 2 3 2 4 2 5
+--R (768a c d - 1152a b c d + 480b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +-+ +-+ | 2
+--R (288d x + 1536c d x + 1536c d )\|c \|d \|d x + c
+--R +
+--R 6 6 5 4 2 4 2 3 3 +-+
+--R (- 48d x - 864c d x - 2304c d x - 1536c d )\|d
+--R ,
+--R
+--R 2 4 2 3 2 3 2 4
+--R (- 288a c d + 432a b c d - 180b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (- 1536a c d + 2304a b c d - 960b c d)x - 1536a c d
+--R +
+--R 4 2 5
+--R 2304a b c d - 960b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (48a c d - 72a b c d + 30b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (864a c d - 1296a b c d + 540b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (2304a c d - 3456a b c d + 1440b c d)x + 1536a c d
+--R +
+--R 5 2 6
+--R - 2304a b c d + 960b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 5 11 5 2 4 9
+--R - 8b d x + (- 24a b d - 134b c d )x
+--R +
+--R 2 5 4 2 2 3 7
+--R (- 24a d - 396a b c d - 219b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (- 432a c d - 504a b c d - 46b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3
+--R (- 1152a c d + 960a b c d - 400b c d)x
+--R +
+--R 2 3 2 4 2 5
+--R (- 768a c d + 1152a b c d - 480b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 5 11 5 2 4 9
+--R 48b d x + (144a b d + 244b c d )x
+--R +
+--R 2 5 4 2 2 3 7
+--R (144a d + 696a b c d + 222b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (912a c d + 168a b c d + 186b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3
+--R (1536a c d - 1536a b c d + 640b c d)x
+--R +
+--R 2 3 2 4 2 5
+--R (768a c d - 1152a b c d + 480b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +---+ +-+ | 2
+--R (288d x + 1536c d x + 1536c d )\|- d \|c \|d x + c
+--R +
+--R 6 6 5 4 2 4 2 3 3 +---+
+--R (- 48d x - 864c d x - 2304c d x - 1536c d )\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 993
+
+--S 994 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 3
+--R (8a c d - 12a b c d + 5b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 3 x\|d
+--R (8a c d - 12a b c d + 5b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 +-+
+--R 16d \|d
+--R Type: Expression(Integer)
+--E 994
+
+--S 995 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 995
+
+--S 996 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 3 +---+ x\|d
+--R (8a c d - 12a b c d + 5b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 2 3 +-+ \|- d \|d x + c - \|- d \|c
+--R (- 16a c d + 24a b c d - 10b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 3 +---+ +-+
+--R 16d \|- d \|d
+--R Type: Expression(Integer)
+--E 996
+
+--S 997 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 997
+
+)clear all
+
+--S 998 of 1397
+t0:=x*(a+b*x^2)^2/sqrt(c+d*x^2)
+--R
+--R
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R (1) --------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 998
+
+--S 999 of 1397
+r0:=-2/3*b*(b*c-a*d)*(c+d*x^2)^(3/2)/d^3+1/5*b^2*(c+d*x^2)^(5/2)/d^3+_
+ (b*c-a*d)^2*sqrt(c+d*x^2)/d^3
+--R
+--R
+--R (2)
+--R +--------+
+--R 2 2 4 2 2 2 2 2 2 2 | 2
+--R (3b d x + (10a b d - 4b c d)x + 15a d - 20a b c d + 8b c )\|d x + c
+--R -------------------------------------------------------------------------
+--R 3
+--R 15d
+--R Type: Expression(Integer)
+--E 999
+
+--S 1000 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 8 2 2 6 2 2 4
+--R - 15b c d x + (- 50a b c d - 40b c )x + (- 60a c d - 120a b c )x
+--R +
+--R 2 2 2
+--R - 120a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 10 2 2 8 2 2 2 2 6
+--R 3b d x + (10a b d + 35b c d)x + (15a d + 110a b c d + 40b c )x
+--R +
+--R 2 2 4 2 2 2
+--R (120a c d + 120a b c )x + 120a c x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (15d x + 180c d x + 240c )\|c \|d x + c - 75c d x - 300c d x - 240c
+--R Type: Union(Expression(Integer),...)
+--E 1000
+
+--S 1001 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 4 2 3 2 3 2 4
+--R (15a c d - 20a b c d + 8b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (180a c d - 240a b c d + 96b c d)x + 240a c d - 320a b c d
+--R +
+--R 2 5
+--R 128b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 75a c d + 100a b c d - 40b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (- 300a c d + 400a b c d - 160b c d)x - 240a c d + 320a b c d
+--R +
+--R 2 5
+--R - 128b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +-+ | 2 5 4 2 4 2
+--R (15d x + 180c d x + 240c d )\|c \|d x + c - 75c d x - 300c d x
+--R +
+--R 3 3
+--R - 240c d
+--R Type: Expression(Integer)
+--E 1001
+
+--S 1002 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1002
+
+)clear all
+
+--S 1003 of 1397
+t0:=(a+b*x^2)^2/sqrt(c+d*x^2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 1003
+
+--S 1004 of 1397
+r0:=1/8*(3*b^2*c^2-8*a*b*c*d+8*a^2*d^2)*atanh(x*sqrt(d)/_
+ sqrt(c+d*x^2))/d^(5/2)-3/8*b*(b*c-2*a*d)*x*sqrt(c+d*x^2)/d^2+_
+ 1/4*b*x*(a+b*x^2)*sqrt(c+d*x^2)/d
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 x\|d
+--R (8a d - 8a b c d + 3b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R 2 3 2 +-+ | 2
+--R (2b d x + (8a b d - 3b c)x)\|d \|d x + c
+--R /
+--R 2 +-+
+--R 8d \|d
+--R Type: Expression(Integer)
+--E 1004
+
+--S 1005 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 2 2 2 2 2
+--R (32a d - 32a b c d + 12b c d)x + 64a c d - 64a b c d
+--R +
+--R 2 3
+--R 24b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 8a d + 8a b c d - 3b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 64a c d + 64a b c d - 24b c d)x - 64a c d + 64a b c d - 24b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R - 2b d x + (- 8a b d - 13b c d )x + (- 64a b c d + 8b c d)x
+--R +
+--R 2 2 3
+--R (- 64a b c d + 24b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 8b d x + (32a b d + 12b c d )x + (96a b c d - 20b c d)x
+--R +
+--R 2 2 3
+--R (64a b c d - 24b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+
+--R (32d x + 64c d )\|c \|d \|d x + c + (- 8d x - 64c d x - 64c d )\|d
+--R ,
+--R
+--R 2 3 2 2 2 2 2 2 2
+--R (64a d - 64a b c d + 24b c d)x + 128a c d - 128a b c d
+--R +
+--R 2 3
+--R 48b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 16a d + 16a b c d - 6b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 128a c d + 128a b c d - 48b c d)x - 128a c d + 128a b c d
+--R +
+--R 2 4
+--R - 48b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R - 2b d x + (- 8a b d - 13b c d )x + (- 64a b c d + 8b c d)x
+--R +
+--R 2 2 3
+--R (- 64a b c d + 24b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 8b d x + (32a b d + 12b c d )x + (96a b c d - 20b c d)x
+--R +
+--R 2 2 3
+--R (64a b c d - 24b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 3 2 2 +---+ +-+ | 2
+--R (32d x + 64c d )\|- d \|c \|d x + c
+--R +
+--R 4 4 3 2 2 2 +---+
+--R (- 8d x - 64c d x - 64c d )\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1005
+
+--S 1006 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2
+--R (8a d - 8a b c d + 3b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 x\|d
+--R (- 8a d + 8a b c d - 3b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2 +-+
+--R 8d \|d
+--R Type: Expression(Integer)
+--E 1006
+
+--S 1007 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1007
+
+--S 1008 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 8a d + 8a b c d - 3b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 2 +-+ \|- d \|d x + c - \|- d \|c
+--R (16a d - 16a b c d + 6b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 2 +---+ +-+
+--R 8d \|- d \|d
+--R Type: Expression(Integer)
+--E 1008
+
+--S 1009 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1009
+
+)clear all
+
+--S 1010 of 1397
+t0:=(a+b*x^2)^2/(x*sqrt(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +--------+
+--R | 2
+--R x\|d x + c
+--R Type: Expression(Integer)
+--E 1010
+
+--S 1011 of 1397
+r0:=-a^2*atanh(sqrt(c+d*x^2)/sqrt(c))/sqrt(c)-2/3*b*(b*c-3*a*d)*_
+ sqrt(c+d*x^2)/d^2+1/3*b^2*x^2*sqrt(c+d*x^2)/d
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 2 2 \|d x + c 2 2 2 +-+ | 2
+--R - 3a d atanh(-----------) + (b d x + 6a b d - 2b c)\|c \|d x + c
+--R +-+
+--R \|c
+--R (2) -------------------------------------------------------------------
+--R 2 +-+
+--R 3d \|c
+--R Type: Expression(Integer)
+--E 1011
+
+--S 1012 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 2 2 | 2 2 2 2 +-+
+--R ((3a d x + 12a c)\|d x + c + (- 9a d x - 12a c)\|c )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 4 2 | 2
+--R (- 3b c x - 12a b c x )\|d x + c
+--R +
+--R 2 6 2 4 2 +-+
+--R (b d x + (6a b d + 3b c)x + 12a b c x )\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (3d x + 12c)\|c \|d x + c - 9c d x - 12c
+--R Type: Union(Expression(Integer),...)
+--E 1012
+
+--S 1013 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 2 2 \|d x + c - \|c 2 2 \|d x + c 2 2
+--R 3a d log(------------------) + 3a d atanh(-----------) + 6a b c d - 2b c
+--R x +-+
+--R \|c
+--R -------------------------------------------------------------------------
+--R 2 +-+
+--R 3d \|c
+--R Type: Expression(Integer)
+--E 1013
+
+--S 1014 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1014
+
+)clear all
+
+--S 1015 of 1397
+t0:=(a+b*x^2)^2/(x^2*sqrt(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +--------+
+--R 2 | 2
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 1015
+
+--S 1016 of 1397
+r0:=-1/2*b*(b*c-4*a*d)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/d^(3/2)-_
+ a^2*sqrt(c+d*x^2)/(c*x)+1/2*b^2*x*sqrt(c+d*x^2)/d
+--R
+--R
+--R +-+ +--------+
+--R 2 2 x\|d 2 2 2 +-+ | 2
+--R (4a b c d - b c )x atanh(-----------) + (b c x - 2a d)\|d \|d x + c
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (2) ----------------------------------------------------------------------
+--R +-+
+--R 2c d x\|d
+--R Type: Expression(Integer)
+--E 1016
+
+--S 1017 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 3 2 2 3 | 2
+--R ((4a b c d - b c d)x + (16a b c d - 4b c )x)\|d x + c
+--R +
+--R 2 2 2 3 2 2 3 +-+
+--R ((- 12a b c d + 3b c d)x + (- 16a b c d + 4b c )x)\|c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +--------+
+--R 2 4 2 2 2 2 2 2 +-+ +-+ | 2
+--R (- 3b c d x + (6a d - 4b c )x + 8a c d)\|c \|d \|d x + c
+--R +
+--R 2 2 6 2 3 2 2 4 2 2 2 3 2 2 2 +-+
+--R (b c d x + (- 2a d + 5b c d)x + (- 10a c d + 4b c )x - 8a c d)\|d
+--R /
+--R +--------+
+--R 2 3 2 +-+ | 2 2 3 2 +-+ +-+
+--R (2c d x + 8c d x)\|d \|d x + c + (- 6c d x - 8c d x)\|c \|d
+--R ,
+--R
+--R +--------+
+--R 2 2 2 3 2 2 3 | 2
+--R ((8a b c d - 2b c d)x + (32a b c d - 8b c )x)\|d x + c
+--R +
+--R 2 2 2 3 2 2 3 +-+
+--R ((- 24a b c d + 6b c d)x + (- 32a b c d + 8b c )x)\|c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R +--------+
+--R 2 4 2 2 2 2 2 2 +---+ +-+ | 2
+--R (- 3b c d x + (6a d - 4b c )x + 8a c d)\|- d \|c \|d x + c
+--R +
+--R 2 2 6 2 3 2 2 4 2 2 2 3 2 2 2 +---+
+--R (b c d x + (- 2a d + 5b c d)x + (- 10a c d + 4b c )x - 8a c d)\|- d
+--R /
+--R +--------+
+--R 2 3 2 +---+ | 2 2 3 2 +---+ +-+
+--R (2c d x + 8c d x)\|- d \|d x + c + (- 6c d x - 8c d x)\|- d \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1017
+
+--S 1018 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2
+--R (4a b d - b c)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 x\|d
+--R (- 4a b d + b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R +-+
+--R 2d\|d
+--R Type: Expression(Integer)
+--E 1018
+
+--S 1019 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1019
+
+--S 1020 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +---+ x\|d
+--R (- 4a b d + b c)\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- d \|d x + c - \|- d \|c
+--R (8a b d - 2b c)\|d atan(------------------------------)
+--R d x
+--R /
+--R +---+ +-+
+--R 2d\|- d \|d
+--R Type: Expression(Integer)
+--E 1020
+
+--S 1021 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1021
+
+)clear all
+
+--S 1022 of 1397
+t0:=(a+b*x^2)^2/(x^3*sqrt(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +--------+
+--R 3 | 2
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 1022
+
+--S 1023 of 1397
+r0:=-1/2*a*(4*b*c-a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))/c^(3/2)+_
+ b^2*sqrt(c+d*x^2)/d-1/2*a^2*sqrt(c+d*x^2)/(c*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 2 2 2 \|d x + c 2 2 2 +-+ | 2
+--R (a d - 4a b c d)x atanh(-----------) + (2b c x - a d)\|c \|d x + c
+--R +-+
+--R \|c
+--R (2) ----------------------------------------------------------------------
+--R 2 +-+
+--R 2c d x \|c
+--R Type: Expression(Integer)
+--E 1023
+
+--S 1024 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 2 4 2 2 2 | 2
+--R ((- a d + 4a b c d)x + (- 4a c d + 16a b c )x )\|d x + c
+--R +
+--R 2 2 4 2 2 2 +-+
+--R ((3a d - 12a b c d)x + (4a c d - 16a b c )x )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 4 2 2 2 2 | 2
+--R (- 4b c x + 3a c d x + 4a c )\|d x + c
+--R +
+--R 2 6 2 2 2 2 4 2 2 2 2 +-+
+--R (2b c d x + (- a d + 4b c )x - 5a c d x - 4a c )\|c
+--R /
+--R +--------+
+--R 4 2 2 +-+ | 2 2 4 3 2
+--R (2c d x + 8c x )\|c \|d x + c - 6c d x - 8c x
+--R Type: Union(Expression(Integer),...)
+--E 1024
+
+--S 1025 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 2 2 \|d x + c - \|c
+--R (- a d + 4a b c d)log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 2 2 \|d x + c 2 2
+--R (- a d + 4a b c d)atanh(-----------) + 2b c
+--R +-+
+--R \|c
+--R /
+--R +-+
+--R 2c d\|c
+--R Type: Expression(Integer)
+--E 1025
+
+--S 1026 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1026
+
+)clear all
+
+--S 1027 of 1397
+t0:=(a+b*x^2)^2/(x^4*sqrt(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +--------+
+--R 4 | 2
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 1027
+
+--S 1028 of 1397
+r0:=b^2*atanh(x*sqrt(d)/sqrt(c+d*x^2))/sqrt(d)-_
+ 1/3*a^2*sqrt(c+d*x^2)/(c*x^3)-2/3*a*(3*b*c-a*d)*sqrt(c+d*x^2)/(c^2*x)
+--R
+--R
+--R +-+ +--------+
+--R 2 2 3 x\|d 2 2 2 +-+ | 2
+--R 3b c x atanh(-----------) + ((2a d - 6a b c)x - a c)\|d \|d x + c
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (2) --------------------------------------------------------------------
+--R 2 3 +-+
+--R 3c x \|d
+--R Type: Expression(Integer)
+--E 1028
+
+--S 1029 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 5 2 3 3 | 2 2 2 5 2 3 3 +-+
+--R ((3b c d x + 12b c x )\|d x + c + (- 9b c d x - 12b c x )\|c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 2 4 2 2 2 2 2 +-+ +-+
+--R ((- 6a d + 18a b c d)x + (- 5a c d + 24a b c )x + 4a c )\|c \|d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 2 6 2 2 2 4
+--R (2a d - 6a b c d )x + (9a c d - 30a b c d)x
+--R +
+--R 2 2 3 2 2 3
+--R (3a c d - 24a b c )x - 4a c
+--R *
+--R +-+
+--R \|d
+--R /
+--R +--------+
+--R 2 5 3 3 +-+ | 2 2 5 3 3 +-+ +-+
+--R (3c d x + 12c x )\|d \|d x + c + (- 9c d x - 12c x )\|c \|d
+--R ,
+--R
+--R +--------+
+--R 2 2 5 2 3 3 | 2 2 2 5 2 3 3 +-+
+--R ((6b c d x + 24b c x )\|d x + c + (- 18b c d x - 24b c x )\|c )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 2 4 2 2 2 2 2 +---+ +-+
+--R ((- 6a d + 18a b c d)x + (- 5a c d + 24a b c )x + 4a c )\|- d \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 2 6 2 2 2 4
+--R (2a d - 6a b c d )x + (9a c d - 30a b c d)x
+--R +
+--R 2 2 3 2 2 3
+--R (3a c d - 24a b c )x - 4a c
+--R *
+--R +---+
+--R \|- d
+--R /
+--R +--------+
+--R 2 5 3 3 +---+ | 2 2 5 3 3 +---+ +-+
+--R (3c d x + 12c x )\|- d \|d x + c + (- 9c d x - 12c x )\|- d \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1029
+
+--S 1030 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 2 (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R b log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 x\|d
+--R - b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R +-+
+--R \|d
+--R Type: Expression(Integer)
+--E 1030
+
+--S 1031 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1031
+
+--S 1032 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 2 +---+ x\|d 2 +-+ \|- d \|d x + c - \|- d \|c
+--R - b \|- d atanh(-----------) + 2b \|d atan(------------------------------)
+--R +--------+ d x
+--R | 2
+--R \|d x + c
+--R --------------------------------------------------------------------------
+--R +---+ +-+
+--R \|- d \|d
+--R Type: Expression(Integer)
+--E 1032
+
+--S 1033 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1033
+
+)clear all
+
+--S 1034 of 1397
+t0:=(a+b*x^2)^2/(x^5*sqrt(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +--------+
+--R 5 | 2
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 1034
+
+--S 1035 of 1397
+r0:=-1/8*(8*b^2*c^2-8*a*b*c*d+3*a^2*d^2)*atanh(sqrt(c+d*x^2)/_
+ sqrt(c))/c^(5/2)-1/4*a^2*sqrt(c+d*x^2)/(c*x^4)-_
+ 1/8*a*(8*b*c-3*a*d)*sqrt(c+d*x^2)/(c^2*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 2 2 2 4 \|d x + c
+--R (- 3a d + 8a b c d - 8b c )x atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((3a d - 8a b c)x - 2a c)\|c \|d x + c
+--R /
+--R 2 4 +-+
+--R 8c x \|c
+--R Type: Expression(Integer)
+--E 1035
+
+--S 1036 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 3 6
+--R (12a c d - 32a b c d + 32b c d)x
+--R +
+--R 2 2 2 3 2 4 4
+--R (24a c d - 64a b c d + 64b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 2 8
+--R (- 3a d + 8a b c d - 8b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (- 24a c d + 64a b c d - 64b c d)x
+--R +
+--R 2 2 2 3 2 4 4
+--R (- 24a c d + 64a b c d - 64b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 6 2 2 2 3 4
+--R (- 3a c d + 8a b c d )x + (- 22a c d + 64a b c d)x
+--R +
+--R 2 3 4 2 2 4
+--R (- 8a c d + 64a b c )x + 16a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 2 2 6 2 2 2 3 4 4 2
+--R (12a c d - 32a b c d )x + (28a c d - 96a b c d)x - 64a b c x
+--R +
+--R 2 4
+--R - 16a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 6 4 4 +-+ | 2 3 2 8 4 6 5 4
+--R (32c d x + 64c x )\|c \|d x + c - 8c d x - 64c d x - 64c x
+--R Type: Union(Expression(Integer),...)
+--E 1036
+
+--S 1037 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 2 2 2 2 \|d x + c - \|c
+--R (3a d - 8a b c d + 8b c )log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 2 2 2 2 \|d x + c
+--R (3a d - 8a b c d + 8b c )atanh(-----------)
+--R +-+
+--R \|c
+--R /
+--R 2 +-+
+--R 8c \|c
+--R Type: Expression(Integer)
+--E 1037
+
+--S 1038 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1038
+
+)clear all
+
+--S 1039 of 1397
+t0:=(a+b*x^2)^2/(x^6*sqrt(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +--------+
+--R 6 | 2
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 1039
+
+--S 1040 of 1397
+r0:=-1/5*a^2*sqrt(c+d*x^2)/(c*x^5)-2/15*a*(5*b*c-2*a*d)*sqrt(c+d*x^2)/_
+ (c^2*x^3)-1/15*(15*b^2*c^2-4*a*d*(5*b*c-2*a*d))*sqrt(c+d*x^2)/(c^3*x)
+--R
+--R
+--R (2)
+--R +--------+
+--R 2 2 2 2 4 2 2 2 2 2 | 2
+--R ((- 8a d + 20a b c d - 15b c )x + (4a c d - 10a b c )x - 3a c )\|d x + c
+--R -----------------------------------------------------------------------------
+--R 3 5
+--R 15c x
+--R Type: Expression(Integer)
+--E 1040
+
+--S 1041 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 2 2 2 8
+--R (40a d - 100a b c d + 75b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (140a c d - 350a b c d + 300b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2 2 4
+--R (63a c d - 120a b c d + 240b c )x + (- 4a c d + 160a b c )x + 48a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 4 2 2 3 10
+--R (- 8a d + 20a b c d - 15b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (- 100a c d + 250a b c d - 195b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (- 175a c d + 430a b c d - 420b c d)x
+--R +
+--R 2 3 2 4 2 5 4 2 4 5 2 2 5
+--R (- 55a c d + 40a b c d - 240b c )x + (- 20a c d - 160a b c )x - 48a c
+--R /
+--R +--------+
+--R 3 2 9 4 7 5 5 | 2
+--R (15c d x + 180c d x + 240c x )\|d x + c
+--R +
+--R 3 2 9 4 7 5 5 +-+
+--R (- 75c d x - 300c d x - 240c x )\|c
+--R Type: Union(Expression(Integer),...)
+--E 1041
+
+--S 1042 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1042
+
+--S 1043 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1043
+
+)clear all
+
+--S 1044 of 1397
+t0:=(a+b*x^2)^2/(x^7*sqrt(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +--------+
+--R 7 | 2
+--R x \|d x + c
+--R Type: Expression(Integer)
+--E 1044
+
+--S 1045 of 1397
+r0:=1/16*d*(8*b^2*c^2-12*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c+d*x^2)/sqrt(c))/_
+ c^(7/2)-1/6*a^2*sqrt(c+d*x^2)/(c*x^6)-1/24*a*(12*b*c-5*a*d)*_
+ sqrt(c+d*x^2)/(c^2*x^4)-1/16*(8*b^2*c^2-12*a*b*c*d+5*a^2*d^2)*_
+ sqrt(c+d*x^2)/(c^3*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 3 2 2 2 6 \|d x + c
+--R (15a d - 36a b c d + 24b c d)x atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R ((- 15a d + 36a b c d - 24b c )x + (10a c d - 24a b c )x - 8a c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R /
+--R 3 6 +-+
+--R 48c x \|c
+--R Type: Expression(Integer)
+--E 1045
+
+--S 1046 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 2 4 2 3 3 10
+--R (- 90a c d + 216a b c d - 144b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (- 480a c d + 1152a b c d - 768b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (- 480a c d + 1152a b c d - 768b c d)x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 5 2 2 4 12
+--R (15a d - 36a b c d + 24b c d )x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (270a c d - 648a b c d + 432b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (720a c d - 1728a b c d + 1152b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (480a c d - 1152a b c d + 768b c d)x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (15a c d - 36a b c d + 24b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (260a c d - 624a b c d + 432b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6 2 4 2 2 6 4
+--R (548a c d - 1296a b c d + 1152b c d)x + (144a c d + 768b c )x
+--R +
+--R 2 5 6 2 2 6
+--R (64a c d + 768a b c )x + 256a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (- 90a c d + 216a b c d - 144b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (- 510a c d + 1224a b c d - 912b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (- 628a c d + 1392a b c d - 1536b c d)x
+--R +
+--R 2 4 2 5 2 6 4 2 5 6 2
+--R (- 144a c d - 384a b c d - 768b c )x + (- 192a c d - 768a b c )x
+--R +
+--R 2 6
+--R - 256a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 2 10 5 8 6 6 +-+ | 2 4 3 12
+--R (288c d x + 1536c d x + 1536c x )\|c \|d x + c - 48c d x
+--R +
+--R 5 2 10 6 8 7 6
+--R - 864c d x - 2304c d x - 1536c x
+--R Type: Union(Expression(Integer),...)
+--E 1046
+
+--S 1047 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 2 3 2 2 2 \|d x + c - \|c
+--R (- 5a d + 12a b c d - 8b c d)log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 2 3 2 2 2 \|d x + c
+--R (- 5a d + 12a b c d - 8b c d)atanh(-----------)
+--R +-+
+--R \|c
+--R /
+--R 3 +-+
+--R 16c \|c
+--R Type: Expression(Integer)
+--E 1047
+
+--S 1048 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1048
+
+)clear all
+
+--S 1049 of 1397
+t0:=x^4*(a+b*x^2)^2/(c+d*x^2)^(3/2)
+--R
+--R
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 1049
+
+--S 1050 of 1397
+r0:=-1/16*c*(35*b^2*c^2-60*a*b*c*d+24*a^2*d^2)*atanh(x*sqrt(d)/_
+ sqrt(c+d*x^2))/d^(9/2)+(b*c-a*d)^2*x^5/(c*d^2*sqrt(c+d*x^2))+_
+ 1/16*(35*b^2*c^2-60*a*b*c*d+24*a^2*d^2)*x*sqrt(c+d*x^2)/d^4-_
+ 1/24*(35*b^2*c^2-60*a*b*c*d+24*a^2*d^2)*x^3*sqrt(c+d*x^2)/_
+ (c*d^3)+1/6*b^2*x^5*sqrt(c+d*x^2)/d^2
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 2 2 2 2 3 | 2 x\|d
+--R (- 72a c d + 180a b c d - 105b c )\|d x + c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 3 2 2 2 3
+--R 8b d x + (24a b d - 14b c d )x + (24a d - 60a b c d + 35b c d)x
+--R +
+--R 2 2 2 2 3
+--R (72a c d - 180a b c d + 105b c )x
+--R *
+--R +-+
+--R \|d
+--R /
+--R +--------+
+--R 4 +-+ | 2
+--R 48d \|d \|d x + c
+--R Type: Expression(Integer)
+--E 1050
+
+--S 1051 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 5 2 4 2 3 3 6
+--R (504a c d - 1260a b c d + 735b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (4032a c d - 10080a b c d + 5880b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (8064a c d - 20160a b c d + 11760b c d)x + 4608a c d
+--R +
+--R 5 2 6
+--R - 11520a b c d + 6720b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 6 2 5 2 3 4 8
+--R (- 72a c d + 180a b c d - 105b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (- 1800a c d + 4500a b c d - 2625b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (- 7488a c d + 18720a b c d - 10920b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (- 10368a c d + 25920a b c d - 15120b c d)x - 4608a c d
+--R +
+--R 6 2 7
+--R 11520a b c d - 6720b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 6 13 6 2 5 11
+--R - 8b d x + (- 24a b d - 178b c d )x
+--R +
+--R 2 6 5 2 2 4 9
+--R (- 24a d - 516a b c d - 339b c d )x
+--R +
+--R 2 5 2 4 2 3 3 7
+--R (- 648a c d - 300a b c d - 337b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 5
+--R (- 3648a c d + 7584a b c d - 4424b c d )x
+--R +
+--R 2 3 3 4 2 2 5 3
+--R (- 7296a c d + 18240a b c d - 10640b c d)x
+--R +
+--R 2 4 2 5 2 6
+--R (- 4608a c d + 11520a b c d - 6720b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 6 13 6 2 5 11
+--R 56b d x + (168a b d + 350b c d )x
+--R +
+--R 2 6 5 2 2 4 9
+--R (168a d + 924a b c d + 357b c d )x
+--R +
+--R 2 5 2 4 2 3 3 7
+--R (1848a c d - 1932a b c d + 1639b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 5
+--R (6720a c d - 15264a b c d + 8904b c d )x
+--R +
+--R 2 3 3 4 2 2 5 3
+--R (9600a c d - 24000a b c d + 14000b c d)x
+--R +
+--R 2 4 2 5 2 6
+--R (4608a c d - 11520a b c d + 6720b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 7 6 6 4 2 5 2 3 4 +-+ +-+ | 2
+--R (336d x + 2688c d x + 5376c d x + 3072c d )\|c \|d \|d x + c
+--R +
+--R 8 8 7 6 2 6 4 3 5 2 4 4 +-+
+--R (- 48d x - 1200c d x - 4992c d x - 6912c d x - 3072c d )\|d
+--R ,
+--R
+--R 2 5 2 4 2 3 3 6
+--R (- 1008a c d + 2520a b c d - 1470b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 8064a c d + 20160a b c d - 11760b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (- 16128a c d + 40320a b c d - 23520b c d)x - 9216a c d
+--R +
+--R 5 2 6
+--R 23040a b c d - 13440b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 6 2 5 2 3 4 8
+--R (144a c d - 360a b c d + 210b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (3600a c d - 9000a b c d + 5250b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (14976a c d - 37440a b c d + 21840b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (20736a c d - 51840a b c d + 30240b c d)x + 9216a c d
+--R +
+--R 6 2 7
+--R - 23040a b c d + 13440b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 6 13 6 2 5 11
+--R - 8b d x + (- 24a b d - 178b c d )x
+--R +
+--R 2 6 5 2 2 4 9
+--R (- 24a d - 516a b c d - 339b c d )x
+--R +
+--R 2 5 2 4 2 3 3 7
+--R (- 648a c d - 300a b c d - 337b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 5
+--R (- 3648a c d + 7584a b c d - 4424b c d )x
+--R +
+--R 2 3 3 4 2 2 5 3
+--R (- 7296a c d + 18240a b c d - 10640b c d)x
+--R +
+--R 2 4 2 5 2 6
+--R (- 4608a c d + 11520a b c d - 6720b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 6 13 6 2 5 11
+--R 56b d x + (168a b d + 350b c d )x
+--R +
+--R 2 6 5 2 2 4 9
+--R (168a d + 924a b c d + 357b c d )x
+--R +
+--R 2 5 2 4 2 3 3 7
+--R (1848a c d - 1932a b c d + 1639b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 5
+--R (6720a c d - 15264a b c d + 8904b c d )x
+--R +
+--R 2 3 3 4 2 2 5 3
+--R (9600a c d - 24000a b c d + 14000b c d)x
+--R +
+--R 2 4 2 5 2 6
+--R (4608a c d - 11520a b c d + 6720b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 7 6 6 4 2 5 2 3 4 +---+ +-+ | 2
+--R (336d x + 2688c d x + 5376c d x + 3072c d )\|- d \|c \|d x + c
+--R +
+--R 8 8 7 6 2 6 4 3 5 2 4 4 +---+
+--R (- 48d x - 1200c d x - 4992c d x - 6912c d x - 3072c d )\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1051
+
+--S 1052 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 3
+--R (24a c d - 60a b c d + 35b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 3 x\|d
+--R (24a c d - 60a b c d + 35b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4 +-+
+--R 16d \|d
+--R Type: Expression(Integer)
+--E 1052
+
+--S 1053 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1053
+
+--S 1054 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 3 +---+ x\|d
+--R (24a c d - 60a b c d + 35b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 2 3 +-+ \|- d \|d x + c - \|- d \|c
+--R (- 48a c d + 120a b c d - 70b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 4 +---+ +-+
+--R 16d \|- d \|d
+--R Type: Expression(Integer)
+--E 1054
+
+--S 1055 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1055
+
+)clear all
+
+--S 1056 of 1397
+t0:=x^3*(a+b*x^2)^2/(c+d*x^2)^(3/2)
+--R
+--R
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 1056
+
+--S 1057 of 1397
+r0:=-1/3*b*(3*b*c-2*a*d)*(c+d*x^2)^(3/2)/d^4+1/5*b^2*(c+d*x^2)^(5/2)/d^4+_
+ c*(b*c-a*d)^2/(d^4*sqrt(c+d*x^2))+(b*c-a*d)*(3*b*c-a*d)*sqrt(c+d*x^2)/d^4
+--R
+--R
+--R (2)
+--R 2 3 6 3 2 2 4 2 3 2 2 2 2
+--R 3b d x + (10a b d - 6b c d )x + (15a d - 40a b c d + 24b c d)x
+--R +
+--R 2 2 2 2 3
+--R 30a c d - 80a b c d + 48b c
+--R /
+--R +--------+
+--R 4 | 2
+--R 15d \|d x + c
+--R Type: Expression(Integer)
+--E 1057
+
+--S 1058 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 10 2 2 8 2 2 6
+--R - 18b c d x + (- 60a b c d - 60b c )x + (- 60a c d - 160a b c )x
+--R +
+--R 2 2 4
+--R - 120a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 12 2 2 10 2 2 2 2 8
+--R 3b d x + (10a b d + 48b c d)x + (15a d + 140a b c d + 60b c )x
+--R +
+--R 2 2 6 2 2 4
+--R (120a c d + 160a b c )x + 120a c x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (15d x + 270c d x + 720c d x + 480c )\|c \|d x + c - 90c d x
+--R +
+--R 2 2 4 3 2 4
+--R - 570c d x - 960c d x - 480c
+--R Type: Union(Expression(Integer),...)
+--E 1058
+
+--S 1059 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 4 2 3 2 3 2 4
+--R (180a c d - 480a b c d + 288b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (960a c d - 2560a b c d + 1536b c d)x + 960a c d - 2560a b c d
+--R +
+--R 2 5
+--R 1536b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 30a c d + 80a b c d - 48b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 540a c d + 1440a b c d - 864b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5
+--R (- 1440a c d + 3840a b c d - 2304b c d)x - 960a c d + 2560a b c d
+--R +
+--R 2 6
+--R - 1536b c
+--R /
+--R +--------+
+--R 6 4 2 5 2 3 4 | 2
+--R (90c d x + 480c d x + 480c d )\|d x + c
+--R +
+--R 7 6 6 4 2 5 2 3 4 +-+
+--R (- 15d x - 270c d x - 720c d x - 480c d )\|c
+--R Type: Expression(Integer)
+--E 1059
+
+--S 1060 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1060
+
+)clear all
+
+--S 1061 of 1397
+t0:=x^2*(a+b*x^2)^2/(c+d*x^2)^(3/2)
+--R
+--R
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 1061
+
+--S 1062 of 1397
+r0:=1/8*(15*b^2*c^2-24*a*b*c*d+8*a^2*d^2)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/_
+ d^(7/2)+(b*c-a*d)^2*x^3/(c*d^2*sqrt(c+d*x^2))-1/8*(15*b^2*c^2-_
+ 24*a*b*c*d+8*a^2*d^2)*x*sqrt(c+d*x^2)/(c*d^3)+1/4*b^2*x^3*_
+ sqrt(c+d*x^2)/d^2
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 2 2 2 2 | 2 x\|d
+--R (8a d - 24a b c d + 15b c )\|d x + c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 5 2 2 3 2 2 2 2 +-+
+--R (2b d x + (8a b d - 5b c d)x + (- 8a d + 24a b c d - 15b c )x)\|d
+--R /
+--R +--------+
+--R 3 +-+ | 2
+--R 8d \|d \|d x + c
+--R Type: Expression(Integer)
+--E 1062
+
+--S 1063 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 4
+--R (40a d - 120a b c d + 75b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (160a c d - 480a b c d + 300b c d)x + 128a c d - 384a b c d
+--R +
+--R 2 4
+--R 240b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 4 2 2 3 6
+--R (- 8a d + 24a b c d - 15b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 104a c d + 312a b c d - 195b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (- 224a c d + 672a b c d - 420b c d)x - 128a c d + 384a b c d
+--R +
+--R 2 5
+--R - 240b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 4 9 4 2 3 7
+--R - 2b d x + (- 8a b d - 19b c d )x
+--R +
+--R 2 4 3 2 2 2 5
+--R (8a d - 120a b c d + 43b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (96a c d - 416a b c d + 260b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (128a c d - 384a b c d + 240b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 4 9 4 2 3 7
+--R 10b d x + (40a b d + 15b c d )x
+--R +
+--R 2 4 3 2 2 2 5
+--R (- 40a d + 280a b c d - 143b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (- 160a c d + 608a b c d - 380b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (- 128a c d + 384a b c d - 240b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +-+ +-+ | 2
+--R (40d x + 160c d x + 128c d )\|c \|d \|d x + c
+--R +
+--R 6 6 5 4 2 4 2 3 3 +-+
+--R (- 8d x - 104c d x - 224c d x - 128c d )\|d
+--R ,
+--R
+--R 2 4 3 2 2 2 4
+--R (80a d - 240a b c d + 150b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (320a c d - 960a b c d + 600b c d)x + 256a c d - 768a b c d
+--R +
+--R 2 4
+--R 480b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 4 2 2 3 6
+--R (- 16a d + 48a b c d - 30b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 208a c d + 624a b c d - 390b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (- 448a c d + 1344a b c d - 840b c d)x - 256a c d + 768a b c d
+--R +
+--R 2 5
+--R - 480b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 4 9 4 2 3 7
+--R - 2b d x + (- 8a b d - 19b c d )x
+--R +
+--R 2 4 3 2 2 2 5
+--R (8a d - 120a b c d + 43b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (96a c d - 416a b c d + 260b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (128a c d - 384a b c d + 240b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 4 9 4 2 3 7
+--R 10b d x + (40a b d + 15b c d )x
+--R +
+--R 2 4 3 2 2 2 5
+--R (- 40a d + 280a b c d - 143b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (- 160a c d + 608a b c d - 380b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (- 128a c d + 384a b c d - 240b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +---+ +-+ | 2
+--R (40d x + 160c d x + 128c d )\|- d \|c \|d x + c
+--R +
+--R 6 6 5 4 2 4 2 3 3 +---+
+--R (- 8d x - 104c d x - 224c d x - 128c d )\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1063
+
+--S 1064 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2
+--R (8a d - 24a b c d + 15b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 x\|d
+--R (- 8a d + 24a b c d - 15b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 +-+
+--R 8d \|d
+--R Type: Expression(Integer)
+--E 1064
+
+--S 1065 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1065
+
+--S 1066 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 8a d + 24a b c d - 15b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 2 +-+ \|- d \|d x + c - \|- d \|c
+--R (16a d - 48a b c d + 30b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 3 +---+ +-+
+--R 8d \|- d \|d
+--R Type: Expression(Integer)
+--E 1066
+
+--S 1067 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1067
+
+)clear all
+
+--S 1068 of 1397
+t0:=x*(a+b*x^2)^2/(c+d*x^2)^(3/2)
+--R
+--R
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 1068
+
+--S 1069 of 1397
+r0:=1/3*b^2*(c+d*x^2)^(3/2)/d^3-(b*c-a*d)^2/(d^3*sqrt(c+d*x^2))-_
+ 2*b*(b*c-a*d)*sqrt(c+d*x^2)/d^3
+--R
+--R
+--R 2 2 4 2 2 2 2 2 2 2
+--R b d x + (6a b d - 4b c d)x - 3a d + 12a b c d - 8b c
+--R (2) ---------------------------------------------------------
+--R +--------+
+--R 3 | 2
+--R 3d \|d x + c
+--R Type: Expression(Integer)
+--E 1069
+
+--S 1070 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 6 2 4 2 2 | 2
+--R (- 4b c x + (- 3a d - 12a b c)x - 12a c x )\|d x + c
+--R +
+--R 2 8 2 6 2 4 2 2 +-+
+--R (b d x + (6a b d + 4b c)x + (9a d + 12a b c)x + 12a c x )\|c
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (3d x + 24c d x + 24c )\|c \|d x + c - 12c d x - 36c d x - 24c
+--R Type: Union(Expression(Integer),...)
+--E 1070
+
+--S 1071 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 12a d + 48a b c d - 32b c d)x - 24a c d + 96a b c d - 64b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d - 12a b c d + 8b c d )x + (24a c d - 96a b c d + 64b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 24a c d - 96a b c d + 64b c
+--R /
+--R +--------+
+--R 4 2 2 3 | 2 5 4 4 2 2 3 +-+
+--R (12c d x + 24c d )\|d x + c + (- 3d x - 24c d x - 24c d )\|c
+--R Type: Expression(Integer)
+--E 1071
+
+--S 1072 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1072
+
+)clear all
+
+--S 1073 of 1397
+t0:=(a+b*x^2)^2/(c+d*x^2)^(3/2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 1073
+
+--S 1074 of 1397
+r0:=-1/2*b*(3*b*c-4*a*d)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/d^(5/2)-_
+ (b*c-a*d)*x*(a+b*x^2)/(c*d*sqrt(c+d*x^2))+1/2*b*(3*b*c-2*a*d)*_
+ x*sqrt(c+d*x^2)/(c*d^2)
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 2 2 | 2 x\|d
+--R (4a b c d - 3b c )\|d x + c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 2 2 2 2 +-+
+--R (b c d x + (2a d - 4a b c d + 3b c )x)\|d
+--R /
+--R +--------+
+--R 2 +-+ | 2
+--R 2c d \|d \|d x + c
+--R Type: Expression(Integer)
+--E 1074
+
+--S 1075 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 2 2 2 3 +-+ | 2
+--R ((12a b c d - 9b c d)x + 16a b c d - 12b c )\|c \|d x + c
+--R +
+--R 3 2 2 2 4 2 2 2 3 2 3
+--R (- 4a b c d + 3b c d )x + (- 20a b c d + 15b c d)x - 16a b c d
+--R +
+--R 2 4
+--R 12b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 2 5 2 3 2 2 2 3
+--R - b c d x + (- 2a d + 4a b c d - 7b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 8a c d + 16a b c d - 12b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 2 5 2 3 2 2 2 3
+--R 3b c d x + (6a d - 12a b c d + 13b c d)x
+--R +
+--R 2 2 2 2 3
+--R (8a c d - 16a b c d + 12b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ +-+ | 2 4 4 2 3 2 3 2 +-+
+--R (6c d x + 8c d )\|c \|d \|d x + c + (- 2c d x - 10c d x - 8c d )\|d
+--R ,
+--R
+--R +--------+
+--R 2 2 2 2 2 2 3 +-+ | 2
+--R ((24a b c d - 18b c d)x + 32a b c d - 24b c )\|c \|d x + c
+--R +
+--R 3 2 2 2 4 2 2 2 3 2 3
+--R (- 8a b c d + 6b c d )x + (- 40a b c d + 30b c d)x - 32a b c d
+--R +
+--R 2 4
+--R 24b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 2 5 2 3 2 2 2 3
+--R - b c d x + (- 2a d + 4a b c d - 7b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 8a c d + 16a b c d - 12b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 2 5 2 3 2 2 2 3
+--R 3b c d x + (6a d - 12a b c d + 13b c d)x
+--R +
+--R 2 2 2 2 3
+--R (8a c d - 16a b c d + 12b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 3 2 2 2 +---+ +-+ | 2
+--R (6c d x + 8c d )\|- d \|c \|d x + c
+--R +
+--R 4 4 2 3 2 3 2 +---+
+--R (- 2c d x - 10c d x - 8c d )\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1075
+
+--S 1076 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2
+--R (4a b d - 3b c)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 x\|d
+--R (- 4a b d + 3b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2 +-+
+--R 2d \|d
+--R Type: Expression(Integer)
+--E 1076
+
+--S 1077 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1077
+
+--S 1078 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +---+ x\|d
+--R (- 4a b d + 3b c)\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- d \|d x + c - \|- d \|c
+--R (8a b d - 6b c)\|d atan(------------------------------)
+--R d x
+--R /
+--R 2 +---+ +-+
+--R 2d \|- d \|d
+--R Type: Expression(Integer)
+--E 1078
+
+--S 1079 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1079
+
+)clear all
+
+--S 1080 of 1397
+t0:=(a+b*x^2)^2/(x*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -----------------------
+--R +--------+
+--R 3 | 2
+--R (d x + c x)\|d x + c
+--R Type: Expression(Integer)
+--E 1080
+
+--S 1081 of 1397
+r0:=-a^2*atanh(sqrt(c+d*x^2)/sqrt(c))/c^(3/2)+(b*c-a*d)^2/_
+ (c*d^2*sqrt(c+d*x^2))+b^2*sqrt(c+d*x^2)/d^2
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ | 2
+--R 2 2 | 2 \|d x + c
+--R - a d \|d x + c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2 2 2 +-+
+--R (b c d x + a d - 2a b c d + 2b c )\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2
+--R c d \|c \|d x + c
+--R Type: Expression(Integer)
+--E 1081
+
+--S 1082 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 2 2 | 2 2 2 2 +-+
+--R ((a d x + 2a c)\|d x + c + (- 2a d x - 2a c)\|c )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 | 2 2 4 2 2 +-+
+--R (a d - 2a b c)x \|d x + c + (b c x + (- a d + 2a b c)x )\|c
+--R /
+--R +--------+
+--R 2 2 +-+ | 2 2 2 3
+--R (c d x + 2c )\|c \|d x + c - 2c d x - 2c
+--R Type: Union(Expression(Integer),...)
+--E 1082
+
+--S 1083 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +--------+ | 2 +-+
+--R 2 2 | 2 2 3 2 2 2 +-+ \|d x + c - \|c
+--R (2a c d \|d x + c + (- a d x - 2a c d )\|c )log(------------------)
+--R x
+--R +
+--R +--------+
+--R +--------+ | 2
+--R 2 2 | 2 2 3 2 2 2 +-+ \|d x + c
+--R (2a c d \|d x + c + (- a d x - 2a c d )\|c )atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 2 2 3 | 2
+--R (2a c d - 4a b c d + 4b c )\|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((- a d + 2a b c d - 2b c d)x - 2a c d + 4a b c d - 4b c )\|c
+--R /
+--R +--------+
+--R 2 2 +-+ | 2 2 3 2 3 2
+--R 2c d \|c \|d x + c - c d x - 2c d
+--R Type: Expression(Integer)
+--E 1083
+
+--S 1084 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1084
+
+)clear all
+
+--S 1085 of 1397
+t0:=(a+b*x^2)^2/(x^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ------------------------
+--R +--------+
+--R 4 2 | 2
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1085
+
+--S 1086 of 1397
+r0:=b^2*atanh(x*sqrt(d)/sqrt(c+d*x^2))/d^(3/2)-a^2/(c*x*sqrt(c+d*x^2))-_
+ (b^2*c^2-2*a*d*(b*c-a*d))*x/(c^2*d*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 2 2 | 2 x\|d
+--R b c x\|d x + c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 2 2 2 +-+
+--R ((- 2a d + 2a b c d - b c )x - a c d)\|d
+--R /
+--R +--------+
+--R 2 +-+ | 2
+--R c d x\|d \|d x + c
+--R Type: Expression(Integer)
+--E 1086
+
+--S 1087 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 3 2 3 | 2 2 2 3 2 3 +-+
+--R ((b c d x + 2b c x)\|d x + c + (- 2b c d x - 2b c x)\|c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +--------+
+--R 2 2 2 2 2 2 +-+ +-+ | 2
+--R ((4a d - 4a b c d + 2b c )x + 2a c d)\|c \|d \|d x + c
+--R +
+--R 2 3 2 2 2 4 2 2 2 2 3 2
+--R (- 2a d + 2a b c d - b c d)x + (- 5a c d + 4a b c d - 2b c )x
+--R +
+--R 2 2
+--R - 2a c d
+--R *
+--R +-+
+--R \|d
+--R /
+--R +--------+
+--R 2 2 3 3 +-+ | 2 2 2 3 3 +-+ +-+
+--R (c d x + 2c d x)\|d \|d x + c + (- 2c d x - 2c d x)\|c \|d
+--R ,
+--R
+--R +--------+
+--R 2 2 3 2 3 | 2 2 2 3 2 3 +-+
+--R ((2b c d x + 4b c x)\|d x + c + (- 4b c d x - 4b c x)\|c )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R +--------+
+--R 2 2 2 2 2 2 +---+ +-+ | 2
+--R ((4a d - 4a b c d + 2b c )x + 2a c d)\|- d \|c \|d x + c
+--R +
+--R 2 3 2 2 2 4 2 2 2 2 3 2
+--R (- 2a d + 2a b c d - b c d)x + (- 5a c d + 4a b c d - 2b c )x
+--R +
+--R 2 2
+--R - 2a c d
+--R *
+--R +---+
+--R \|- d
+--R /
+--R +--------+
+--R 2 2 3 3 +---+ | 2 2 2 3 3 +---+ +-+
+--R (c d x + 2c d x)\|- d \|d x + c + (- 2c d x - 2c d x)\|- d \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1087
+
+--S 1088 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 2 (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R b log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 x\|d
+--R - b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R +-+
+--R d\|d
+--R Type: Expression(Integer)
+--E 1088
+
+--S 1089 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1089
+
+--S 1090 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 2 +---+ x\|d 2 +-+ \|- d \|d x + c - \|- d \|c
+--R - b \|- d atanh(-----------) + 2b \|d atan(------------------------------)
+--R +--------+ d x
+--R | 2
+--R \|d x + c
+--R --------------------------------------------------------------------------
+--R +---+ +-+
+--R d\|- d \|d
+--R Type: Expression(Integer)
+--E 1090
+
+--S 1091 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1091
+
+)clear all
+
+--S 1092 of 1397
+t0:=(a+b*x^2)^2/(x^3*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ------------------------
+--R +--------+
+--R 5 3 | 2
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1092
+
+--S 1093 of 1397
+r0:=-1/2*a*(4*b*c-3*a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))/c^(5/2)+_
+ 1/2*(-2*b^2*c^2+4*a*b*c*d-3*a^2*d^2)/(c^2*d*sqrt(c+d*x^2))-_
+ 1/2*a^2/(c*x^2*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ | 2
+--R 2 2 2 | 2 \|d x + c
+--R (3a d - 4a b c d)x \|d x + c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2 2 2 +-+
+--R ((- 3a d + 4a b c d - 2b c )x - a c d)\|c
+--R /
+--R +--------+
+--R 2 2 +-+ | 2
+--R 2c d x \|c \|d x + c
+--R Type: Expression(Integer)
+--E 1093
+
+--S 1094 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 2 2 4 2 2 3 2 | 2
+--R ((- 9a c d + 12a b c d)x + (- 12a c d + 16a b c )x )\|d x + c
+--R +
+--R 2 3 2 6 2 2 2 4
+--R (3a d - 4a b c d )x + (15a c d - 20a b c d)x
+--R +
+--R 2 2 3 2
+--R (12a c d - 16a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 2 2 3 4 2 2 2 2 3 | 2
+--R ((- 3a c d + 8a b c d - 4b c )x + 5a c d x + 4a c )\|d x + c
+--R +
+--R 2 3 2 2 2 6 2 2 2 2 3 4
+--R (2a d - 4a b c d + 2b c d)x + (a c d - 8a b c d + 4b c )x
+--R +
+--R 2 2 2 2 3
+--R - 7a c d x - 4a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 4 4 2 +-+ | 2 3 2 6 4 4 5 2
+--R (6c d x + 8c x )\|c \|d x + c - 2c d x - 10c d x - 8c x
+--R Type: Union(Expression(Integer),...)
+--E 1094
+
+--S 1095 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 3 2 2 2 2 2 | 2
+--R ((- 3a d + 4a b c d )x - 12a c d + 16a b c d)\|d x + c
+--R +
+--R 2 3 2 2 2 2 2 +-+
+--R ((9a d - 12a b c d )x + 12a c d - 16a b c d)\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 3 2 2 2 2 2 | 2
+--R ((- 3a d + 4a b c d )x - 12a c d + 16a b c d)\|d x + c
+--R +
+--R 2 3 2 2 2 2 2 +-+
+--R ((9a d - 12a b c d )x + 12a c d - 16a b c d)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 2a d + 4a b c d - 2b c d)x - 8a c d + 16a b c d - 8b c )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((6a d - 12a b c d + 6b c d)x + 8a c d - 16a b c d + 8b c )\|c
+--R /
+--R +--------+
+--R 2 2 2 3 +-+ | 2 3 2 2 4
+--R (2c d x + 8c d)\|c \|d x + c - 6c d x - 8c d
+--R Type: Expression(Integer)
+--E 1095
+
+--S 1096 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1096
+
+)clear all
+
+--S 1097 of 1397
+t0:=(a+b*x^2)^2/(x^4*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ------------------------
+--R +--------+
+--R 6 4 | 2
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1097
+
+--S 1098 of 1397
+r0:=-1/3*a^2/(c*x^3*sqrt(c+d*x^2))-2/3*a*(3*b*c-2*a*d)/(c^2*x*_
+ sqrt(c+d*x^2))+1/3*(3*b^2*c^2-4*a*d*(3*b*c-2*a*d))*x/(c^3*sqrt(c+d*x^2))
+--R
+--R
+--R 2 2 2 2 4 2 2 2 2 2
+--R (8a d - 12a b c d + 3b c )x + (4a c d - 6a b c )x - a c
+--R (2) -----------------------------------------------------------
+--R +--------+
+--R 3 3 | 2
+--R 3c x \|d x + c
+--R Type: Expression(Integer)
+--E 1098
+
+--S 1099 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 6
+--R (- 32a d + 48a b c d - 12b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (- 80a c d + 120a b c d - 24b c )x + (- 28a c d + 48a b c )x + 8a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 8 2 3 2 2 2 3 6
+--R (8a d - 12a b c d + 3b c d )x + (68a c d - 102a b c d + 24b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2 2 4
+--R (95a c d - 144a b c d + 24b c )x + (24a c d - 48a b c )x - 8a c
+--R /
+--R +--------+
+--R 3 2 7 4 5 5 3 | 2
+--R (3c d x + 24c d x + 24c x )\|d x + c
+--R +
+--R 3 2 7 4 5 5 3 +-+
+--R (- 12c d x - 36c d x - 24c x )\|c
+--R Type: Union(Expression(Integer),...)
+--E 1099
+
+--S 1100 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1100
+
+--S 1101 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1101
+
+)clear all
+
+--S 1102 of 1397
+t0:=(a+b*x^2)^2/(x^5*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ------------------------
+--R +--------+
+--R 7 5 | 2
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1102
+
+--S 1103 of 1397
+r0:=-1/8*(8*b^2*c^2-3*a*d*(8*b*c-5*a*d))*atanh(sqrt(c+d*x^2)/sqrt(c))/_
+ c^(7/2)+1/8*(8*b^2*c^2-3*a*d*(8*b*c-5*a*d))/(c^3*sqrt(c+d*x^2))-_
+ 1/4*a^2/(c*x^4*sqrt(c+d*x^2))-1/8*a*(8*b*c-5*a*d)/(c^2*x^2*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ | 2
+--R 2 2 2 2 4 | 2 \|d x + c
+--R (- 15a d + 24a b c d - 8b c )x \|d x + c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2 4 2 2 2 2 2 +-+
+--R ((15a d - 24a b c d + 8b c )x + (5a c d - 8a b c )x - 2a c )\|c
+--R /
+--R +--------+
+--R 3 4 +-+ | 2
+--R 8c x \|c \|d x + c
+--R Type: Expression(Integer)
+--E 1103
+
+--S 1104 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 3 2 3 2 8
+--R (75a c d - 120a b c d + 40b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (300a c d - 480a b c d + 160b c d)x
+--R +
+--R 2 3 2 4 2 5 4
+--R (240a c d - 384a b c d + 128b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 4 2 2 3 10
+--R (- 15a d + 24a b c d - 8b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (- 195a c d + 312a b c d - 104b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (- 420a c d + 672a b c d - 224b c d)x
+--R +
+--R 2 3 2 4 2 5 4
+--R (- 240a c d + 384a b c d - 128b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (25a c d - 56a b c d + 32b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6 2 3 2 4 4
+--R (- 25a c d - 24a b c d + 64b c d)x + (- 170a c d + 224a b c d)x
+--R +
+--R 2 4 5 2 2 5
+--R (- 56a c d + 128a b c )x + 32a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 4 2 2 3 10
+--R (- 8a d + 16a b c d - 8b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (- 29a c d + 88a b c d - 64b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6 2 3 2 4 4
+--R (101a c d - 72a b c d - 64b c d)x + (202a c d - 288a b c d)x
+--R +
+--R 2 4 5 2 2 5
+--R (40a c d - 128a b c )x - 32a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 2 8 5 6 6 4 +-+ | 2 4 3 10 5 2 8
+--R (40c d x + 160c d x + 128c x )\|c \|d x + c - 8c d x - 104c d x
+--R +
+--R 6 6 7 4
+--R - 224c d x - 128c x
+--R Type: Union(Expression(Integer),...)
+--E 1104
+
+--S 1105 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 4 3 2 2 2 4
+--R (15a d - 24a b c d + 8b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (180a c d - 288a b c d + 96b c d)x + 240a c d - 384a b c d
+--R +
+--R 2 4
+--R 128b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 75a d + 120a b c d - 40b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 300a c d + 480a b c d - 160b c d)x - 240a c d + 384a b c d
+--R +
+--R 2 4
+--R - 128b c
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 4 3 2 2 2 4
+--R (15a d - 24a b c d + 8b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (180a c d - 288a b c d + 96b c d)x + 240a c d - 384a b c d
+--R +
+--R 2 4
+--R 128b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 75a d + 120a b c d - 40b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 300a c d + 480a b c d - 160b c d)x - 240a c d + 384a b c d
+--R +
+--R 2 4
+--R - 128b c
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 4
+--R (8a d - 16a b c d + 8b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (96a c d - 192a b c d + 96b c d)x + 128a c d - 256a b c d + 128b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 40a d + 80a b c d - 40b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 160a c d + 320a b c d - 160b c d)x - 128a c d + 256a b c d
+--R +
+--R 2 4
+--R - 128b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 2 4 4 2 5 +-+ | 2 4 2 4 5 2 6
+--R (8c d x + 96c d x + 128c )\|c \|d x + c - 40c d x - 160c d x - 128c
+--R Type: Expression(Integer)
+--E 1105
+
+--S 1106 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1106
+
+)clear all
+
+--S 1107 of 1397
+t0:=(a+b*x^2)^2/(x^6*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ------------------------
+--R +--------+
+--R 8 6 | 2
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1107
+
+--S 1108 of 1397
+r0:=-1/5*a^2/(c*x^5*sqrt(c+d*x^2))-2/15*a*(5*b*c-3*a*d)/(c^2*x^3*_
+ sqrt(c+d*x^2))+1/15*(15*b^2*c^2-8*a*d*(5*b*c-3*a*d))/(c^3*x*_
+ sqrt(c+d*x^2))-2/15*(15*b^2*c^2-8*a*d*(5*b*c-3*a*d))*sqrt(c+d*x^2)/(c^4*x)
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 6 2 2 2 2 3 4
+--R (- 48a d + 80a b c d - 30b c d)x + (- 24a c d + 40a b c d - 15b c )x
+--R +
+--R 2 2 3 2 2 3
+--R (6a c d - 10a b c )x - 3a c
+--R /
+--R +--------+
+--R 4 5 | 2
+--R 15c x \|d x + c
+--R Type: Expression(Integer)
+--E 1108
+
+--S 1109 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 4 2 2 3 10
+--R (288a d - 480a b c d + 180b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (1680a c d - 2800a b c d + 1050b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (2268a c d - 3780a b c d + 1440b c d)x
+--R +
+--R 2 3 2 4 2 5 4 2 4 5 2
+--R (594a c d - 960a b c d + 480b c )x + (- 96a c d + 320a b c )x
+--R +
+--R 2 5
+--R 96a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 6 5 2 2 4 12
+--R (- 48a d + 80a b c d - 30b c d )x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (- 888a c d + 1480a b c d - 555b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (- 2730a c d + 4550a b c d - 1710b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (- 2583a c d + 4300a b c d - 1680b c d)x
+--R +
+--R 2 4 2 5 2 6 4 2 5 6 2 2 6
+--R (- 534a c d + 800a b c d - 480b c )x + (48a c d - 320a b c )x - 96a c
+--R /
+--R +--------+
+--R 4 3 11 5 2 9 6 7 7 5 | 2
+--R (15c d x + 270c d x + 720c d x + 480c x )\|d x + c
+--R +
+--R 4 3 11 5 2 9 6 7 7 5 +-+
+--R (- 90c d x - 570c d x - 960c d x - 480c x )\|c
+--R Type: Union(Expression(Integer),...)
+--E 1109
+
+--S 1110 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1110
+
+--S 1111 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1111
+
+)clear all
+
+--S 1112 of 1397
+t0:=(a+b*x^2)^2/(x^7*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ------------------------
+--R +--------+
+--R 9 7 | 2
+--R (d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1112
+
+--S 1113 of 1397
+r0:=1/16*d*(24*b^2*c^2-5*a*d*(12*b*c-7*a*d))*atanh(sqrt(c+d*x^2)/_
+ sqrt(c))/c^(9/2)-1/6*a^2/(c*x^6*sqrt(c+d*x^2))-1/24*a*(12*b*c-_
+ 7*a*d)/(c^2*x^4*sqrt(c+d*x^2))+1/24*(24*b^2*c^2-5*a*d*(12*b*c-_
+ 7*a*d))/(c^3*x^2*sqrt(c+d*x^2))-1/16*(24*b^2*c^2-5*a*d*(12*b*c-_
+ 7*a*d))*sqrt(c+d*x^2)/(c^4*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ | 2
+--R 2 3 2 2 2 6 | 2 \|d x + c
+--R (105a d - 180a b c d + 72b c d)x \|d x + c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 6
+--R (- 105a d + 180a b c d - 72b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (- 35a c d + 60a b c d - 24b c )x + (14a c d - 24a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 6 +-+ | 2
+--R 48c x \|c \|d x + c
+--R Type: Expression(Integer)
+--E 1113
+
+--S 1114 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 2 5 2 3 4 12
+--R (- 735a c d + 1260a b c d - 504b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (- 5880a c d + 10080a b c d - 4032b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 11760a c d + 20160a b c d - 8064b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 6720a c d + 11520a b c d - 4608b c d)x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 7 6 2 2 5 14
+--R (105a d - 180a b c d + 72b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (2625a c d - 4500a b c d + 1800b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (10920a c d - 18720a b c d + 7488b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (15120a c d - 25920a b c d + 10368b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (6720a c d - 11520a b c d + 4608b c d)x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (- 231a c d + 492a b c d - 264b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (- 133a c d + 996a b c d - 936b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (3850a c d - 5064a b c d + 960b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (6120a c d - 9600a b c d + 3456b c d)x
+--R +
+--R 2 5 2 6 2 7 4 2 6 7 2
+--R (1312a c d - 1920a b c d + 1536b c )x + (- 256a c d + 1536a b c )x
+--R +
+--R 2 7
+--R 512a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 7 6 2 2 5 14
+--R (48a d - 96a b c d + 48b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (465a c d - 1140a b c d + 696b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (- 1133a c d + 516a b c d + 792b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 6710a c d + 9528a b c d - 2496b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 6840a c d + 10752a b c d - 4224b c d)x
+--R +
+--R 2 5 2 6 2 7 4 7 2 2 7
+--R (- 1120a c d + 1152a b c d - 1536b c )x - 1536a b c x - 512a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 5 3 12 6 2 10 7 8 8 6 +-+ | 2
+--R (336c d x + 2688c d x + 5376c d x + 3072c x )\|c \|d x + c
+--R +
+--R 5 4 14 6 3 12 7 2 10 8 8 9 6
+--R - 48c d x - 1200c d x - 4992c d x - 6912c d x - 3072c x
+--R Type: Union(Expression(Integer),...)
+--E 1114
+
+--S 1115 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 6 5 2 2 4 6
+--R (- 35a d + 60a b c d - 24b c d )x
+--R +
+--R 2 5 2 4 2 3 3 4
+--R (- 840a c d + 1440a b c d - 576b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 2 2 3 3
+--R (- 2800a c d + 4800a b c d - 1920b c d )x - 2240a c d
+--R +
+--R 4 2 2 5
+--R 3840a b c d - 1536b c d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 5 2 2 4 6
+--R (245a d - 420a b c d + 168b c d )x
+--R +
+--R 2 5 2 4 2 3 3 4
+--R (1960a c d - 3360a b c d + 1344b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 2 2 3 3
+--R (3920a c d - 6720a b c d + 2688b c d )x + 2240a c d
+--R +
+--R 4 2 2 5
+--R - 3840a b c d + 1536b c d
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 6 5 2 2 4 6
+--R (- 35a d + 60a b c d - 24b c d )x
+--R +
+--R 2 5 2 4 2 3 3 4
+--R (- 840a c d + 1440a b c d - 576b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 2 2 3 3
+--R (- 2800a c d + 4800a b c d - 1920b c d )x - 2240a c d
+--R +
+--R 4 2 2 5
+--R 3840a b c d - 1536b c d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 5 2 2 4 6
+--R (245a d - 420a b c d + 168b c d )x
+--R +
+--R 2 5 2 4 2 3 3 4
+--R (1960a c d - 3360a b c d + 1344b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 2 2 3 3
+--R (3920a c d - 6720a b c d + 2688b c d )x + 2240a c d
+--R +
+--R 4 2 2 5
+--R - 3840a b c d + 1536b c d
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 6 5 2 2 4 6
+--R (- 16a d + 32a b c d - 16b c d )x
+--R +
+--R 2 5 2 4 2 3 3 4
+--R (- 384a c d + 768a b c d - 384b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 2 2 3 3
+--R (- 1280a c d + 2560a b c d - 1280b c d )x - 1024a c d
+--R +
+--R 4 2 2 5
+--R 2048a b c d - 1024b c d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 5 2 2 4 6
+--R (112a d - 224a b c d + 112b c d )x
+--R +
+--R 2 5 2 4 2 3 3 4
+--R (896a c d - 1792a b c d + 896b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 2 2 3 3
+--R (1792a c d - 3584a b c d + 1792b c d )x + 1024a c d
+--R +
+--R 4 2 2 5
+--R - 2048a b c d + 1024b c d
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 +-+ | 2 5 3 6
+--R (16c d x + 384c d x + 1280c d x + 1024c )\|c \|d x + c - 112c d x
+--R +
+--R 6 2 4 7 2 8
+--R - 896c d x - 1792c d x - 1024c
+--R Type: Expression(Integer)
+--E 1115
+
+--S 1116 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1116
+
+)clear all
+
+--S 1117 of 1397
+t0:=x^4*(a+b*x^2)^2/(c+d*x^2)^(5/2)
+--R
+--R
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 1117
+
+--S 1118 of 1397
+r0:=1/3*(b*c-a*d)^2*x^5/(c*d^2*(c+d*x^2)^(3/2))+1/8*(35*b^2*c^2-_
+ 40*a*b*c*d+8*a^2*d^2)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/d^(9/2)-_
+ 2/3*(b*c-a*d)*(4*b*c-a*d)*x^5/(c^2*d^2*sqrt(c+d*x^2))-_
+ 1/8*(35*b^2*c^2-40*a*b*c*d+8*a^2*d^2)*x*sqrt(c+d*x^2)/(c*d^4)+_
+ 1/12*(35*b^2*c^2-40*a*b*c*d+8*a^2*d^2)*x^3*sqrt(c+d*x^2)/(c^2*d^3)
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((24a d - 120a b c d + 105b c d)x + 24a c d - 120a b c d + 105b c )
+--R *
+--R +--------+ +-+
+--R | 2 x\|d
+--R \|d x + c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 7 3 2 2 5
+--R 6b d x + (24a b d - 21b c d )x
+--R +
+--R 2 3 2 2 2 3
+--R (- 32a d + 160a b c d - 140b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 24a c d + 120a b c d - 105b c )x
+--R *
+--R +-+
+--R \|d
+--R /
+--R +--------+
+--R 5 2 4 +-+ | 2
+--R (24d x + 24c d )\|d \|d x + c
+--R Type: Expression(Integer)
+--E 1118
+
+--S 1119 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 6 5 2 2 4 8
+--R (168a d - 840a b c d + 735b c d )x
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (1512a c d - 7560a b c d + 6615b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (4032a c d - 20160a b c d + 17640b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (4224a c d - 21120a b c d + 18480b c d)x + 1536a c d
+--R +
+--R 5 2 6
+--R - 7680a b c d + 6720b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 7 6 2 2 5 10
+--R (- 24a d + 120a b c d - 105b c d )x
+--R +
+--R 2 6 2 5 2 3 4 8
+--R (- 624a c d + 3120a b c d - 2730b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (- 3096a c d + 15480a b c d - 13545b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (- 5952a c d + 29760a b c d - 26040b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (- 4992a c d + 24960a b c d - 21840b c d)x - 1536a c d
+--R +
+--R 6 2 7
+--R 7680a b c d - 6720b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 6 13 6 2 5 11
+--R - 6b d x + (- 24a b d - 123b c d )x
+--R +
+--R 2 6 5 2 2 4 9
+--R (32a d - 736a b c d + 164b c d )x
+--R +
+--R 2 5 2 4 2 3 3 7
+--R (792a c d - 5880a b c d + 4761b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 5
+--R (3136a c d - 17216a b c d + 15064b c d )x
+--R +
+--R 2 3 3 4 2 2 5 3
+--R (3968a c d - 19840a b c d + 17360b c d)x
+--R +
+--R 2 4 2 5 2 6
+--R (1536a c d - 7680a b c d + 6720b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 6 13 6 2 5 11
+--R 42b d x + (168a b d + 189b c d )x
+--R +
+--R 2 6 5 2 2 4 9
+--R (- 224a d + 2464a b c d - 1484b c d )x
+--R +
+--R 2 5 2 4 2 3 3 7
+--R (- 1960a c d + 12488a b c d - 10543b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 5
+--R (- 4928a c d + 26176a b c d - 22904b c d )x
+--R +
+--R 2 3 3 4 2 2 5 3
+--R (- 4736a c d + 23680a b c d - 20720b c d)x
+--R +
+--R 2 4 2 5 2 6
+--R (- 1536a c d + 7680a b c d - 6720b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 8 8 7 6 2 6 4 3 5 2 4 4 +-+ +-+
+--R (168d x + 1512c d x + 4032c d x + 4224c d x + 1536c d )\|c \|d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 9 10 8 8 2 7 6 3 6 4 4 5 2
+--R - 24d x - 624c d x - 3096c d x - 5952c d x - 4992c d x
+--R +
+--R 5 4
+--R - 1536c d
+--R *
+--R +-+
+--R \|d
+--R ,
+--R
+--R 2 6 5 2 2 4 8
+--R (336a d - 1680a b c d + 1470b c d )x
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (3024a c d - 15120a b c d + 13230b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (8064a c d - 40320a b c d + 35280b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (8448a c d - 42240a b c d + 36960b c d)x + 3072a c d
+--R +
+--R 5 2 6
+--R - 15360a b c d + 13440b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 7 6 2 2 5 10
+--R (- 48a d + 240a b c d - 210b c d )x
+--R +
+--R 2 6 2 5 2 3 4 8
+--R (- 1248a c d + 6240a b c d - 5460b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (- 6192a c d + 30960a b c d - 27090b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (- 11904a c d + 59520a b c d - 52080b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2
+--R (- 9984a c d + 49920a b c d - 43680b c d)x - 3072a c d
+--R +
+--R 6 2 7
+--R 15360a b c d - 13440b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 6 13 6 2 5 11
+--R - 6b d x + (- 24a b d - 123b c d )x
+--R +
+--R 2 6 5 2 2 4 9
+--R (32a d - 736a b c d + 164b c d )x
+--R +
+--R 2 5 2 4 2 3 3 7
+--R (792a c d - 5880a b c d + 4761b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 5
+--R (3136a c d - 17216a b c d + 15064b c d )x
+--R +
+--R 2 3 3 4 2 2 5 3
+--R (3968a c d - 19840a b c d + 17360b c d)x
+--R +
+--R 2 4 2 5 2 6
+--R (1536a c d - 7680a b c d + 6720b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 6 13 6 2 5 11
+--R 42b d x + (168a b d + 189b c d )x
+--R +
+--R 2 6 5 2 2 4 9
+--R (- 224a d + 2464a b c d - 1484b c d )x
+--R +
+--R 2 5 2 4 2 3 3 7
+--R (- 1960a c d + 12488a b c d - 10543b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 5
+--R (- 4928a c d + 26176a b c d - 22904b c d )x
+--R +
+--R 2 3 3 4 2 2 5 3
+--R (- 4736a c d + 23680a b c d - 20720b c d)x
+--R +
+--R 2 4 2 5 2 6
+--R (- 1536a c d + 7680a b c d - 6720b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R 8 8 7 6 2 6 4 3 5 2 4 4 +---+ +-+
+--R (168d x + 1512c d x + 4032c d x + 4224c d x + 1536c d )\|- d \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 9 10 8 8 2 7 6 3 6 4 4 5 2
+--R - 24d x - 624c d x - 3096c d x - 5952c d x - 4992c d x
+--R +
+--R 5 4
+--R - 1536c d
+--R *
+--R +---+
+--R \|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1119
+
+--S 1120 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2
+--R (8a d - 40a b c d + 35b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 x\|d
+--R (- 8a d + 40a b c d - 35b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4 +-+
+--R 8d \|d
+--R Type: Expression(Integer)
+--E 1120
+
+--S 1121 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1121
+
+--S 1122 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 8a d + 40a b c d - 35b c )\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 2 +-+ \|- d \|d x + c - \|- d \|c
+--R (16a d - 80a b c d + 70b c )\|d atan(------------------------------)
+--R d x
+--R /
+--R 4 +---+ +-+
+--R 8d \|- d \|d
+--R Type: Expression(Integer)
+--E 1122
+
+--S 1123 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1123
+
+)clear all
+
+--S 1124 of 1397
+t0:=x^3*(a+b*x^2)^2/(c+d*x^2)^(5/2)
+--R
+--R
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 1124
+
+--S 1125 of 1397
+r0:=1/3*c*(b*c-a*d)^2/(d^4*(c+d*x^2)^(3/2))+1/3*b^2*(c+d*x^2)^(3/2)/d^4-_
+ (b*c-a*d)*(3*b*c-a*d)/(d^4*sqrt(c+d*x^2))-b*(3*b*c-2*a*d)*_
+ sqrt(c+d*x^2)/d^4
+--R
+--R
+--R (2)
+--R 2 3 6 3 2 2 4 2 3 2 2 2 2
+--R b d x + (6a b d - 6b c d )x + (- 3a d + 24a b c d - 24b c d)x
+--R +
+--R 2 2 2 2 3
+--R - 2a c d + 16a b c d - 16b c
+--R /
+--R +--------+
+--R 5 2 4 | 2
+--R (3d x + 3c d )\|d x + c
+--R Type: Expression(Integer)
+--E 1125
+
+--S 1126 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 10 2 2 2 2 8
+--R - 6b c d x + (- 2a d - 20a b c d - 12b c )x
+--R +
+--R 2 2 6 2 2 4
+--R (- 20a c d - 32a b c )x - 24a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 12 2 2 10 2 2 2 2 8
+--R b d x + (6a b d + 12b c d)x + (9a d + 36a b c d + 12b c )x
+--R +
+--R 2 2 6 2 2 4
+--R (32a c d + 32a b c )x + 24a c x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (3d x + 57c d x + 198c d x + 240c d x + 96c )\|c \|d x + c
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 18c d x - 132c d x - 306c d x - 288c d x - 96c
+--R Type: Union(Expression(Integer),...)
+--E 1126
+
+--S 1127 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 4 3 2 2 2 4
+--R (- 12a d + 96a b c d - 96b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 64a c d + 512a b c d - 512b c d)x - 64a c d + 512a b c d
+--R +
+--R 2 4
+--R - 512b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 4 2 2 3 6
+--R (2a d - 16a b c d + 16b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (36a c d - 288a b c d + 288b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (96a c d - 768a b c d + 768b c d)x + 64a c d - 512a b c d + 512b c
+--R /
+--R +--------+
+--R 6 4 2 5 2 3 4 | 2
+--R (18c d x + 96c d x + 96c d )\|d x + c
+--R +
+--R 7 6 6 4 2 5 2 3 4 +-+
+--R (- 3d x - 54c d x - 144c d x - 96c d )\|c
+--R Type: Expression(Integer)
+--E 1127
+
+--S 1128 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1128
+
+)clear all
+
+--S 1129 of 1397
+t0:=x^2*(a+b*x^2)^2/(c+d*x^2)^(5/2)
+--R
+--R
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 1129
+
+--S 1130 of 1397
+r0:=1/3*(b*c-a*d)^2*x^3/(c*d^2*(c+d*x^2)^(3/2))-1/2*b*(5*b*c-4*a*d)*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))/d^(7/2)-2*b*(b*c-a*d)*x^3/(c*d^2*_
+ sqrt(c+d*x^2))+1/2*b*(5*b*c-4*a*d)*x*sqrt(c+d*x^2)/(c*d^3)
+--R
+--R
+--R (2)
+--R +--------+
+--R 2 2 2 2 2 2 3 | 2
+--R ((12a b c d - 15b c d)x + 12a b c d - 15b c )\|d x + c
+--R *
+--R +-+
+--R x\|d
+--R atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 5 2 3 2 2 2 3
+--R 3b c d x + (2a d - 16a b c d + 20b c d)x
+--R +
+--R 2 2 3
+--R (- 12a b c d + 15b c )x
+--R *
+--R +-+
+--R \|d
+--R /
+--R +--------+
+--R 4 2 2 3 +-+ | 2
+--R (6c d x + 6c d )\|d \|d x + c
+--R Type: Expression(Integer)
+--E 1130
+
+--S 1131 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 2 2 3 6 2 3 2 3 2 4
+--R (60a b c d - 75b c d )x + (300a b c d - 375b c d )x
+--R +
+--R 3 2 2 4 2 4 2 5
+--R (432a b c d - 540b c d)x + 192a b c d - 240b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 5 2 2 4 8 2 4 2 3 3 6
+--R (- 12a b c d + 15b c d )x + (- 168a b c d + 210b c d )x
+--R +
+--R 3 3 2 4 2 4 4 2 2 5 2
+--R (- 492a b c d + 615b c d )x + (- 528a b c d + 660b c d)x
+--R +
+--R 5 2 6
+--R - 192a b c d + 240b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 4 9 2 5 4 2 2 3 7
+--R - 3b c d x + (- 2a d + 16a b c d - 56b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (- 24a c d + 204a b c d - 303b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3 4 2 5
+--R (- 32a c d + 400a b c d - 500b c d)x + (192a b c d - 240b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 4 9 2 5 4 2 2 3 7
+--R 15b c d x + (10a d - 80a b c d + 160b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (40a c d - 380a b c d + 523b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3 4 2 5
+--R (32a c d - 496a b c d + 620b c d)x + (- 192a b c d + 240b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 6 6 2 5 4 3 4 2 4 3 +-+ +-+ | 2
+--R (30c d x + 150c d x + 216c d x + 96c d )\|c \|d \|d x + c
+--R +
+--R 7 8 2 6 6 3 5 4 4 4 2 5 3 +-+
+--R (- 6c d x - 84c d x - 246c d x - 264c d x - 96c d )\|d
+--R ,
+--R
+--R 4 2 2 3 6 2 3 2 3 2 4
+--R (120a b c d - 150b c d )x + (600a b c d - 750b c d )x
+--R +
+--R 3 2 2 4 2 4 2 5
+--R (864a b c d - 1080b c d)x + 384a b c d - 480b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 5 2 2 4 8 2 4 2 3 3 6
+--R (- 24a b c d + 30b c d )x + (- 336a b c d + 420b c d )x
+--R +
+--R 3 3 2 4 2 4 4 2 2 5 2
+--R (- 984a b c d + 1230b c d )x + (- 1056a b c d + 1320b c d)x
+--R +
+--R 5 2 6
+--R - 384a b c d + 480b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 4 9 2 5 4 2 2 3 7
+--R - 3b c d x + (- 2a d + 16a b c d - 56b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (- 24a c d + 204a b c d - 303b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3 4 2 5
+--R (- 32a c d + 400a b c d - 500b c d)x + (192a b c d - 240b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 4 9 2 5 4 2 2 3 7
+--R 15b c d x + (10a d - 80a b c d + 160b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (40a c d - 380a b c d + 523b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3 4 2 5
+--R (32a c d - 496a b c d + 620b c d)x + (- 192a b c d + 240b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 6 6 2 5 4 3 4 2 4 3 +---+ +-+ | 2
+--R (30c d x + 150c d x + 216c d x + 96c d )\|- d \|c \|d x + c
+--R +
+--R 7 8 2 6 6 3 5 4 4 4 2 5 3 +---+
+--R (- 6c d x - 84c d x - 246c d x - 264c d x - 96c d )\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1131
+
+--S 1132 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2
+--R (4a b d - 5b c)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 x\|d
+--R (- 4a b d + 5b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 +-+
+--R 2d \|d
+--R Type: Expression(Integer)
+--E 1132
+
+--S 1133 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1133
+
+--S 1134 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +---+ x\|d
+--R (- 4a b d + 5b c)\|- d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- d \|d x + c - \|- d \|c
+--R (8a b d - 10b c)\|d atan(------------------------------)
+--R d x
+--R /
+--R 3 +---+ +-+
+--R 2d \|- d \|d
+--R Type: Expression(Integer)
+--E 1134
+
+--S 1135 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1135
+
+)clear all
+
+--S 1136 of 1397
+t0:=x*(a+b*x^2)^2/(c+d*x^2)^(5/2)
+--R
+--R
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 1136
+
+--S 1137 of 1397
+r0:=-1/3*(b*c-a*d)^2/(d^3*(c+d*x^2)^(3/2))+2*b*(b*c-a*d)/(d^3*_
+ sqrt(c+d*x^2))+b^2*sqrt(c+d*x^2)/d^3
+--R
+--R
+--R 2 2 4 2 2 2 2 2 2 2
+--R 3b d x + (- 6a b d + 12b c d)x - a d - 4a b c d + 8b c
+--R (2) -----------------------------------------------------------
+--R +--------+
+--R 4 2 3 | 2
+--R (3d x + 3c d )\|d x + c
+--R Type: Expression(Integer)
+--E 1137
+
+--S 1138 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 6 2 2 4 2 2 2
+--R ((- a d - 4a b c d - 4b c )x + (- 9a c d - 12a b c )x - 12a c x )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 8 2 2 2 2 6 2 2 4
+--R 3b c d x + (4a d + 10a b c d + 4b c )x + (15a c d + 12a b c )x
+--R +
+--R 2 2 2
+--R 12a c x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 6 2 2 4 3 2 4 +-+ | 2 2 3 6
+--R (3c d x + 27c d x + 48c d x + 24c )\|c \|d x + c - 12c d x
+--R +
+--R 3 2 4 4 2 5
+--R - 48c d x - 60c d x - 24c
+--R Type: Union(Expression(Integer),...)
+--E 1138
+
+--S 1139 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((- 4a d - 16a b c d + 32b c d)x - 8a c d - 32a b c d + 64b c )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (a d + 4a b c d - 8b c d )x + (8a c d + 32a b c d - 64b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 8a c d + 32a b c d - 64b c
+--R /
+--R +--------+
+--R 2 4 2 3 3 | 2 5 4 2 4 2 3 3 +-+
+--R (12c d x + 24c d )\|d x + c + (- 3c d x - 24c d x - 24c d )\|c
+--R Type: Expression(Integer)
+--E 1139
+
+--S 1140 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1140
+
+)clear all
+
+--S 1141 of 1397
+t0:=(a+b*x^2)^2/(c+d*x^2)^(5/2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 1141
+
+--S 1142 of 1397
+r0:=-1/3*(b*c-a*d)*x*(a+b*x^2)/(c*d*(c+d*x^2)^(3/2))+_
+ b^2*atanh(x*sqrt(d)/sqrt(c+d*x^2))/d^(5/2)-1/3*(b*c-a*d)*_
+ (3*b*c+2*a*d)*x/(c^2*d^2*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 2 2 2 2 3 | 2 x\|d
+--R (3b c d x + 3b c )\|d x + c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 3 +-+
+--R ((2a d + 2a b c d - 4b c d)x + (3a c d - 3b c )x)\|d
+--R /
+--R +--------+
+--R 2 3 2 3 2 +-+ | 2
+--R (3c d x + 3c d )\|d \|d x + c
+--R Type: Expression(Integer)
+--E 1142
+
+--S 1143 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 4 2 3 2 2 4 +-+ | 2 2 2 3 6
+--R (9b c d x + 21b c d x + 12b c )\|c \|d x + c - 3b c d x
+--R +
+--R 2 3 2 4 2 4 2 2 5
+--R - 18b c d x - 27b c d x - 12b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 4 3 2 2 2 5
+--R (- 2a d - 2a b c d + 4b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 2 4
+--R (- 11a c d - 8a b c d + 19b c d)x + (- 12a c d + 12b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 4 3 2 2 2 5
+--R (6a d + 6a b c d - 12b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 2 4
+--R (17a c d + 8a b c d - 25b c d)x + (12a c d - 12b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 2 4 4 3 3 2 4 2 +-+ +-+ | 2
+--R (9c d x + 21c d x + 12c d )\|c \|d \|d x + c
+--R +
+--R 2 5 6 3 4 4 4 3 2 5 2 +-+
+--R (- 3c d x - 18c d x - 27c d x - 12c d )\|d
+--R ,
+--R
+--R +--------+
+--R 2 2 2 4 2 3 2 2 4 +-+ | 2 2 2 3 6
+--R (18b c d x + 42b c d x + 24b c )\|c \|d x + c - 6b c d x
+--R +
+--R 2 3 2 4 2 4 2 2 5
+--R - 36b c d x - 54b c d x - 24b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 4 3 2 2 2 5
+--R (- 2a d - 2a b c d + 4b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 2 4
+--R (- 11a c d - 8a b c d + 19b c d)x + (- 12a c d + 12b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 4 3 2 2 2 5
+--R (6a d + 6a b c d - 12b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 2 4
+--R (17a c d + 8a b c d - 25b c d)x + (12a c d - 12b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 2 4 4 3 3 2 4 2 +---+ +-+ | 2
+--R (9c d x + 21c d x + 12c d )\|- d \|c \|d x + c
+--R +
+--R 2 5 6 3 4 4 4 3 2 5 2 +---+
+--R (- 3c d x - 18c d x - 27c d x - 12c d )\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1143
+
+--S 1144 of 1397
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 2 (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R b log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 x\|d
+--R - b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2 +-+
+--R d \|d
+--R Type: Expression(Integer)
+--E 1144
+
+--S 1145 of 1397
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1145
+
+--S 1146 of 1397
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 2 +---+ x\|d 2 +-+ \|- d \|d x + c - \|- d \|c
+--R - b \|- d atanh(-----------) + 2b \|d atan(------------------------------)
+--R +--------+ d x
+--R | 2
+--R \|d x + c
+--R --------------------------------------------------------------------------
+--R 2 +---+ +-+
+--R d \|- d \|d
+--R Type: Expression(Integer)
+--E 1146
+
+--S 1147 of 1397
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1147
+
+)clear all
+
+--S 1148 of 1397
+t0:=(a+b*x^2)^2/(x*(c+d*x^2)^(5/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ---------------------------------
+--R +--------+
+--R 2 5 3 2 | 2
+--R (d x + 2c d x + c x)\|d x + c
+--R Type: Expression(Integer)
+--E 1148
+
+--S 1149 of 1397
+r0:=1/3*(b*c-a*d)^2/(c*d^2*(c+d*x^2)^(3/2))-a^2*atanh(sqrt(c+d*x^2)/_
+ sqrt(c))/c^(5/2)+(a^2/c^2-b^2/d^2)/sqrt(c+d*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ | 2
+--R 2 3 2 2 2 | 2 \|d x + c
+--R (- 3a d x - 3a c d )\|d x + c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2 3 +-+
+--R ((3a d - 3b c d)x + 4a c d - 2a b c d - 2b c )\|c
+--R /
+--R +--------+
+--R 2 3 2 3 2 +-+ | 2
+--R (3c d x + 3c d )\|c \|d x + c
+--R Type: Expression(Integer)
+--E 1149
+
+--S 1150 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 2 4 2 2 2 2 3 | 2
+--R (9a c d x + 21a c d x + 12a c )\|d x + c
+--R +
+--R 2 3 6 2 2 4 2 2 2 2 3 +-+
+--R (- 3a d x - 18a c d x - 27a c d x - 12a c )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 2 2 3 4 2 2 3 2 | 2
+--R ((9a c d - 6a b c d - 3b c )x + (12a c d - 12a b c )x )\|d x + c
+--R +
+--R 2 3 2 2 2 6 2 2 2 2 3 4
+--R (- 4a d + 2a b c d + 2b c d)x + (- 15a c d + 12a b c d + 3b c )x
+--R +
+--R 2 2 3 2
+--R (- 12a c d + 12a b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4
+--R (9c d x + 21c d x + 12c )\|c \|d x + c - 3c d x - 18c d x
+--R +
+--R 5 2 6
+--R - 27c d x - 12c
+--R Type: Union(Expression(Integer),...)
+--E 1150
+
+--S 1151 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 3 2 2 2 | 2 2 3 2 2 2 +-+
+--R ((3a d x + 12a c d )\|d x + c + (- 9a d x - 12a c d )\|c )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 3 2 2 2 | 2 2 3 2 2 2 +-+
+--R ((3a d x + 12a c d )\|d x + c + (- 9a d x - 12a c d )\|c )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 3 2 2 2 2 2 2 2 2 3 | 2
+--R ((4a d - 2a b c d - 2b c d)x + 16a c d - 8a b c d - 8b c )\|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((- 12a d + 6a b c d + 6b c d)x - 16a c d + 8a b c d + 8b c )\|c
+--R /
+--R +--------+
+--R 2 3 2 3 2 +-+ | 2 3 3 2 4 2
+--R (3c d x + 12c d )\|c \|d x + c - 9c d x - 12c d
+--R Type: Expression(Integer)
+--E 1151
+
+--S 1152 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1152
+
+)clear all
+
+--S 1153 of 1397
+t0:=(a+b*x^2)^2/(x^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ----------------------------------
+--R +--------+
+--R 2 6 4 2 2 | 2
+--R (d x + 2c d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1153
+
+--S 1154 of 1397
+r0:=-a^2/(c*x*(c+d*x^2)^(3/2))-1/3*(b^2*c^2-2*a*d*(b*c-2*a*d))*x/_
+ (c^2*d*(c+d*x^2)^(3/2))+1/3*(b^2*c^2+4*a*d*(b*c-2*a*d))*x/(c^3*_
+ d*sqrt(c+d*x^2))
+--R
+--R
+--R 2 2 2 2 4 2 2 2 2 2
+--R (- 8a d + 4a b c d + b c )x + (- 12a c d + 6a b c )x - 3a c
+--R (2) ---------------------------------------------------------------
+--R +--------+
+--R 3 3 4 | 2
+--R (3c d x + 3c x)\|d x + c
+--R Type: Expression(Integer)
+--E 1154
+
+--S 1155 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 6 2 2 2 2 3 4
+--R (32a d - 16a b c d - 4b c d)x + (112a c d - 56a b c d - 8b c )x
+--R +
+--R 2 2 3 2 2 3
+--R (108a c d - 48a b c )x + 24a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 8 2 3 2 2 2 3 6
+--R (- 8a d + 4a b c d + b c d )x + (- 76a c d + 38a b c d + 8b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2 2 4
+--R (- 163a c d + 80a b c d + 8b c )x + (- 120a c d + 48a b c )x - 24a c
+--R /
+--R +--------+
+--R 3 3 7 4 2 5 5 3 6 | 2
+--R (3c d x + 27c d x + 48c d x + 24c x)\|d x + c
+--R +
+--R 3 3 7 4 2 5 5 3 6 +-+
+--R (- 12c d x - 48c d x - 60c d x - 24c x)\|c
+--R Type: Union(Expression(Integer),...)
+--E 1155
+
+--S 1156 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1156
+
+--S 1157 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1157
+
+)clear all
+
+--S 1158 of 1397
+t0:=(a+b*x^2)^2/(x^3*(c+d*x^2)^(5/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ----------------------------------
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (d x + 2c d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1158
+
+--S 1159 of 1397
+r0:=1/6*(-2*b^2*c^2+4*a*b*c*d-5*a^2*d^2)/(c^2*d*(c+d*x^2)^(3/2))-_
+ 1/2*a^2/(c*x^2*(c+d*x^2)^(3/2))-1/2*a*(4*b*c-5*a*d)*_
+ atanh(sqrt(c+d*x^2)/sqrt(c))/c^(7/2)+1/2*a*(4*b*c-5*a*d)/_
+ (c^3*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R 2 3 2 4 2 2 2 2 | 2
+--R ((15a d - 12a b c d )x + (15a c d - 12a b c d)x )\|d x + c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 4 2 2 2 2 3 2
+--R (- 15a d + 12a b c d )x + (- 20a c d + 16a b c d - 2b c )x
+--R +
+--R 2 2
+--R - 3a c d
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 2 4 4 2 +-+ | 2
+--R (6c d x + 6c d x )\|c \|d x + c
+--R Type: Expression(Integer)
+--E 1159
+
+--S 1160 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 3 8 2 2 3 3 2 6
+--R (- 75a c d + 60a b c d )x + (- 375a c d + 300a b c d )x
+--R +
+--R 2 3 2 4 4 2 4 5 2
+--R (- 540a c d + 432a b c d)x + (- 240a c d + 192a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 4 10 2 4 2 3 8
+--R (15a d - 12a b c d )x + (210a c d - 168a b c d )x
+--R +
+--R 2 2 3 3 2 6 2 3 2 4 4
+--R (615a c d - 492a b c d )x + (660a c d - 528a b c d)x
+--R +
+--R 2 4 5 2
+--R (240a c d - 192a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (- 55a c d + 68a b c d - 10b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (- 150a c d + 240a b c d - 48b c d)x
+--R +
+--R 2 3 2 4 2 5 4 2 4 2 2 5
+--R (- 21a c d + 192a b c d - 48b c )x + 132a c d x + 48a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 4 2 2 3 10
+--R (14a d - 16a b c d + 2b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (121a c d - 164a b c d + 28b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (174a c d - 336a b c d + 72b c d)x
+--R +
+--R 2 3 2 4 2 5 4 2 4 2 2 5
+--R (- 39a c d - 192a b c d + 48b c )x - 156a c d x - 48a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 3 8 5 2 6 6 4 7 2 +-+ | 2 4 4 10
+--R (30c d x + 150c d x + 216c d x + 96c x )\|c \|d x + c - 6c d x
+--R +
+--R 5 3 8 6 2 6 7 4 8 2
+--R - 84c d x - 246c d x - 264c d x - 96c x
+--R Type: Union(Expression(Integer),...)
+--E 1160
+
+--S 1161 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 4 3 4 2 3 2 2 2
+--R (- 15a d + 12a b c d )x + (- 180a c d + 144a b c d )x
+--R +
+--R 2 2 2 3
+--R - 240a c d + 192a b c d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 4 2 3 2 2 2 2 2 2
+--R (75a d - 60a b c d )x + (300a c d - 240a b c d )x + 240a c d
+--R +
+--R 3
+--R - 192a b c d
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 4 3 4 2 3 2 2 2
+--R (- 15a d + 12a b c d )x + (- 180a c d + 144a b c d )x
+--R +
+--R 2 2 2 3
+--R - 240a c d + 192a b c d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 4 2 3 2 2 2 2 2 2
+--R (75a d - 60a b c d )x + (300a c d - 240a b c d )x + 240a c d
+--R +
+--R 3
+--R - 192a b c d
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 14a d + 16a b c d - 2b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 168a c d + 192a b c d - 24b c d)x - 224a c d + 256a b c d
+--R +
+--R 2 4
+--R - 32b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (70a d - 80a b c d + 10b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (280a c d - 320a b c d + 40b c d)x + 224a c d - 256a b c d + 32b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 3 4 4 2 2 5 +-+ | 2 4 3 4 5 2 2 6
+--R (6c d x + 72c d x + 96c d)\|c \|d x + c - 30c d x - 120c d x - 96c d
+--R Type: Expression(Integer)
+--E 1161
+
+--S 1162 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1162
+
+)clear all
+
+--S 1163 of 1397
+t0:=(a+b*x^2)^2/(x^4*(c+d*x^2)^(5/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ----------------------------------
+--R +--------+
+--R 2 8 6 2 4 | 2
+--R (d x + 2c d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1163
+
+--S 1164 of 1397
+r0:=-1/3*a^2/(c*x^3*(c+d*x^2)^(3/2))-2*a*(b*c-a*d)/(c^2*x*(c+d*x^2)^(3/2))+_
+ 1/3*(b^2*c^2-8*a*d*(b*c-a*d))*x/(c^3*(c+d*x^2)^(3/2))+2/3*(b^2*c^2-_
+ 8*a*d*(b*c-a*d))*x/(c^4*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 6 2 2 2 2 3 4
+--R (16a d - 16a b c d + 2b c d)x + (24a c d - 24a b c d + 3b c )x
+--R +
+--R 2 2 3 2 2 3
+--R (6a c d - 6a b c )x - a c
+--R /
+--R +--------+
+--R 4 5 5 3 | 2
+--R (3c d x + 3c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1164
+
+--S 1165 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 4 2 2 3 10
+--R (- 96a d + 96a b c d - 12b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (- 656a c d + 656a b c d - 82b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (- 1316a c d + 1316a b c d - 160b c d)x
+--R +
+--R 2 3 2 4 2 5 4 2 4 5 2
+--R (- 954a c d + 960a b c d - 96b c )x + (- 160a c d + 192a b c )x
+--R +
+--R 2 5
+--R 32a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 6 5 2 2 4 12
+--R (16a d - 16a b c d + 2b c d )x
+--R +
+--R 2 5 2 4 2 3 3 10
+--R (312a c d - 312a b c d + 39b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 8
+--R (1206a c d - 1206a b c d + 150b c d )x
+--R +
+--R 2 3 3 4 2 2 5 6
+--R (1771a c d - 1772a b c d + 208b c d)x
+--R +
+--R 2 4 2 5 2 6 4 2 5 6 2 2 6
+--R (1038a c d - 1056a b c d + 96b c )x + (144a c d - 192a b c )x - 32a c
+--R /
+--R +--------+
+--R 4 4 11 5 3 9 6 2 7 7 5 8 3 | 2
+--R (3c d x + 57c d x + 198c d x + 240c d x + 96c x )\|d x + c
+--R +
+--R 4 4 11 5 3 9 6 2 7 7 5 8 3 +-+
+--R (- 18c d x - 132c d x - 306c d x - 288c d x - 96c x )\|c
+--R Type: Union(Expression(Integer),...)
+--E 1165
+
+--S 1166 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1166
+
+--S 1167 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1167
+
+)clear all
+
+--S 1168 of 1397
+t0:=(a+b*x^2)^2/(x^5*(c+d*x^2)^(5/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ----------------------------------
+--R +--------+
+--R 2 9 7 2 5 | 2
+--R (d x + 2c d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1168
+
+--S 1169 of 1397
+r0:=1/24*(8*b^2*c^2-5*a*d*(8*b*c-7*a*d))/(c^3*(c+d*x^2)^(3/2))-_
+ 1/4*a^2/(c*x^4*(c+d*x^2)^(3/2))-1/8*a*(8*b*c-7*a*d)/(c^2*x^2*_
+ (c+d*x^2)^(3/2))-1/8*(8*b^2*c^2-5*a*d*(8*b*c-7*a*d))*_
+ atanh(sqrt(c+d*x^2)/sqrt(c))/c^(9/2)+1/8*(8*b^2*c^2-5*a*d*(8*b*_
+ c-7*a*d))/(c^4*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 6
+--R (- 105a d + 120a b c d - 24b c d)x
+--R +
+--R 2 2 2 2 3 4
+--R (- 105a c d + 120a b c d - 24b c )x
+--R *
+--R +--------+
+--R +--------+ | 2
+--R | 2 \|d x + c
+--R \|d x + c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 6
+--R (105a d - 120a b c d + 24b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (140a c d - 160a b c d + 32b c )x + (21a c d - 24a b c )x - 6a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 6 5 4 +-+ | 2
+--R (24c d x + 24c x )\|c \|d x + c
+--R Type: Expression(Integer)
+--E 1169
+
+--S 1170 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 2 5 2 3 4 12
+--R (735a c d - 840a b c d + 168b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (6615a c d - 7560a b c d + 1512b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (17640a c d - 20160a b c d + 4032b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (18480a c d - 21120a b c d + 4224b c d)x
+--R +
+--R 2 5 2 6 2 7 4
+--R (6720a c d - 7680a b c d + 1536b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 7 6 2 2 5 14
+--R (- 105a d + 120a b c d - 24b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (- 2730a c d + 3120a b c d - 624b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (- 13545a c d + 15480a b c d - 3096b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 26040a c d + 29760a b c d - 5952b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 21840a c d + 24960a b c d - 4992b c d)x
+--R +
+--R 2 5 2 6 2 7 4
+--R (- 6720a c d + 7680a b c d - 1536b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (455a c d - 664a b c d + 200b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (2380a c d - 4016a b c d + 1408b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (1659a c d - 5352a b c d + 2688b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (- 4338a c d + 1344a b c d + 1536b c d)x
+--R +
+--R 2 5 2 6 4 2 6 7 2 2 7
+--R (- 5376a c d + 4992a b c d)x + (- 864a c d + 1536a b c )x + 384a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 7 6 2 2 5 14
+--R (- 80a d + 112a b c d - 32b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (- 1345a c d + 2072a b c d - 664b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (- 3460a c d + 6608a b c d - 2560b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (- 93a c d + 5208a b c d - 3456b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (6894a c d - 3648a b c d - 1536b c d)x
+--R +
+--R 2 5 2 6 4 2 6 7 2 2 7
+--R (5856a c d - 5760a b c d)x + (672a c d - 1536a b c )x - 384a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 5 4 12 6 3 10 7 2 8 8 6 9 4 +-+
+--R (168c d x + 1512c d x + 4032c d x + 4224c d x + 1536c x )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 5 5 14 6 4 12 7 3 10 8 2 8 9 6
+--R - 24c d x - 624c d x - 3096c d x - 5952c d x - 4992c d x
+--R +
+--R 10 4
+--R - 1536c x
+--R Type: Union(Expression(Integer),...)
+--E 1170
+
+--S 1171 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 5 4 2 2 3 6
+--R (105a d - 120a b c d + 24b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (2520a c d - 2880a b c d + 576b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (8400a c d - 9600a b c d + 1920b c d)x + 6720a c d
+--R +
+--R 4 2 5
+--R - 7680a b c d + 1536b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 4 2 2 3 6
+--R (- 735a d + 840a b c d - 168b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 5880a c d + 6720a b c d - 1344b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (- 11760a c d + 13440a b c d - 2688b c d)x - 6720a c d
+--R +
+--R 4 2 5
+--R 7680a b c d - 1536b c
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 5 4 2 2 3 6
+--R (105a d - 120a b c d + 24b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (2520a c d - 2880a b c d + 576b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (8400a c d - 9600a b c d + 1920b c d)x + 6720a c d
+--R +
+--R 4 2 5
+--R - 7680a b c d + 1536b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 4 2 2 3 6
+--R (- 735a d + 840a b c d - 168b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 5880a c d + 6720a b c d - 1344b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (- 11760a c d + 13440a b c d - 2688b c d)x - 6720a c d
+--R +
+--R 4 2 5
+--R 7680a b c d - 1536b c
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 5 4 2 2 3 6
+--R (80a d - 112a b c d + 32b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (1920a c d - 2688a b c d + 768b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (6400a c d - 8960a b c d + 2560b c d)x + 5120a c d - 7168a b c d
+--R +
+--R 2 5
+--R 2048b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 4 2 2 3 6
+--R (- 560a d + 784a b c d - 224b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 4480a c d + 6272a b c d - 1792b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (- 8960a c d + 12544a b c d - 3584b c d)x - 5120a c d
+--R +
+--R 4 2 5
+--R 7168a b c d - 2048b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 +-+ | 2 5 3 6
+--R (24c d x + 576c d x + 1920c d x + 1536c )\|c \|d x + c - 168c d x
+--R +
+--R 6 2 4 7 2 8
+--R - 1344c d x - 2688c d x - 1536c
+--R Type: Expression(Integer)
+--E 1171
+
+--S 1172 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1172
+
+)clear all
+
+--S 1173 of 1397
+t0:=(a+b*x^2)^2/(x^6*(c+d*x^2)^(5/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -----------------------------------
+--R +--------+
+--R 2 10 8 2 6 | 2
+--R (d x + 2c d x + c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1173
+
+--S 1174 of 1397
+r0:=-1/5*a^2/(c*x^5*(c+d*x^2)^(3/2))-2/15*a*(5*b*c-4*a*d)/(c^2*x^3*_
+ (c+d*x^2)^(3/2))+1/15*(5*b^2*c^2-4*a*d*(5*b*c-4*a*d))/(c^3*x*_
+ (c+d*x^2)^(3/2))+4/15*(5*b^2*c^2-4*a*d*(5*b*c-4*a*d))/(c^4*x*_
+ sqrt(c+d*x^2))-8/15*(5*b^2*c^2-4*a*d*(5*b*c-4*a*d))*sqrt(c+d*x^2)/_
+ (c^5*x)
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 8
+--R (- 128a d + 160a b c d - 40b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (- 192a c d + 240a b c d - 60b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2 2 4
+--R (- 48a c d + 60a b c d - 15b c )x + (8a c d - 10a b c )x - 3a c
+--R /
+--R +--------+
+--R 5 7 6 5 | 2
+--R (15c d x + 15c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1174
+
+--S 1175 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 7 6 2 2 5 14
+--R (1024a d - 1280a b c d + 320b c d )x
+--R +
+--R 2 6 2 5 2 3 4 12
+--R (11776a c d - 14720a b c d + 3680b c d )x
+--R +
+--R 2 2 5 3 4 2 4 3 10
+--R (40320a c d - 50400a b c d + 12600b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 8
+--R (57024a c d - 71280a b c d + 17840b c d )x
+--R +
+--R 2 4 3 5 2 2 6 6
+--R (33176a c d - 41440a b c d + 10560b c d)x
+--R +
+--R 2 5 2 6 2 7 4 2 6 7 2
+--R (4848a c d - 5760a b c d + 1920b c )x + (- 448a c d + 1280a b c )x
+--R +
+--R 2 7
+--R 384a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 8 7 2 2 6 16
+--R (- 128a d + 160a b c d - 40b c d )x
+--R +
+--R 2 7 2 6 2 3 5 14
+--R (- 4288a c d + 5360a b c d - 1340b c d )x
+--R +
+--R 2 2 6 3 5 2 4 4 12
+--R (- 26672a c d + 33340a b c d - 8335b c d )x
+--R +
+--R 2 3 5 4 4 2 5 3 10
+--R (- 65016a c d + 81270a b c d - 20320b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 8
+--R (- 72963a c d + 91200a b c d - 22880b c d )x
+--R +
+--R 2 5 3 6 2 2 7 6
+--R (- 35680a c d + 44480a b c d - 11520b c d)x
+--R +
+--R 2 6 2 7 2 8 4 2 7 8 2
+--R (- 4576a c d + 5120a b c d - 1920b c )x + (256a c d - 1280a b c )x
+--R +
+--R 2 8
+--R - 384a c
+--R /
+--R 5 5 15 6 4 13 7 3 11 8 2 9 9 7
+--R 15c d x + 495c d x + 2880c d x + 6240c d x + 5760c d x
+--R +
+--R 10 5
+--R 1920c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 5 5 15 6 4 13 7 3 11 8 2 9 9 7
+--R - 120c d x - 1440c d x - 5400c d x - 8880c d x - 6720c d x
+--R +
+--R 10 5
+--R - 1920c x
+--R *
+--R +-+
+--R \|c
+--R Type: Union(Expression(Integer),...)
+--E 1175
+
+--S 1176 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1176
+
+--S 1177 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1177
+
+)clear all
+
+--S 1178 of 1397
+t0:=x^(7/2)*(a+b*x^2)^2*(c+d*x^2)
+--R
+--R
+--R 2 9 2 7 2 5 2 3 +-+
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|x
+--R Type: Expression(Integer)
+--E 1178
+
+--S 1179 of 1397
+r0:=2/9*a^2*c*x^(9/2)+2/13*a*(2*b*c+a*d)*x^(13/2)+2/17*b*(b*c+2*a*d)*_
+ x^(17/2)+2/21*b^2*d*x^(21/2)
+--R
+--R
+--R (2)
+--R 2 10 2 8 2 6
+--R 1326b d x + (3276a b d + 1638b c)x + (2142a d + 4284a b c)x
+--R +
+--R 2 4
+--R 3094a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 13923
+--R Type: Expression(Integer)
+--E 1179
+
+--S 1180 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 10 2 8 2 6
+--R 1326b d x + (3276a b d + 1638b c)x + (2142a d + 4284a b c)x
+--R +
+--R 2 4
+--R 3094a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 13923
+--R Type: Union(Expression(Integer),...)
+--E 1180
+
+--S 1181 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1181
+
+--S 1182 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1182
+
+)clear all
+
+--S 1183 of 1397
+t0:=x^(5/2)*(a+b*x^2)^2*(c+d*x^2)
+--R
+--R
+--R 2 8 2 6 2 4 2 2 +-+
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|x
+--R Type: Expression(Integer)
+--E 1183
+
+--S 1184 of 1397
+r0:=2/7*a^2*c*x^(7/2)+2/11*a*(2*b*c+a*d)*x^(11/2)+2/15*b*(b*c+2*a*d)*_
+ x^(15/2)+2/19*b^2*d*x^(19/2)
+--R
+--R
+--R (2)
+--R 2 9 2 7 2 5
+--R 2310b d x + (5852a b d + 2926b c)x + (3990a d + 7980a b c)x
+--R +
+--R 2 3
+--R 6270a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 21945
+--R Type: Expression(Integer)
+--E 1184
+
+--S 1185 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 9 2 7 2 5
+--R 2310b d x + (5852a b d + 2926b c)x + (3990a d + 7980a b c)x
+--R +
+--R 2 3
+--R 6270a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 21945
+--R Type: Union(Expression(Integer),...)
+--E 1185
+
+--S 1186 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1186
+
+--S 1187 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1187
+
+)clear all
+
+--S 1188 of 1397
+t0:=x^(3/2)*(a+b*x^2)^2*(c+d*x^2)
+--R
+--R
+--R 2 7 2 5 2 3 2 +-+
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x)\|x
+--R Type: Expression(Integer)
+--E 1188
+
+--S 1189 of 1397
+r0:=2/5*a^2*c*x^(5/2)+2/9*a*(2*b*c+a*d)*x^(9/2)+2/13*b*(b*c+2*a*d)*_
+ x^(13/2)+2/17*b^2*d*x^(17/2)
+--R
+--R
+--R (2)
+--R 2 8 2 6 2 4
+--R 1170b d x + (3060a b d + 1530b c)x + (2210a d + 4420a b c)x
+--R +
+--R 2 2
+--R 3978a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 9945
+--R Type: Expression(Integer)
+--E 1189
+
+--S 1190 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 8 2 6 2 4
+--R 1170b d x + (3060a b d + 1530b c)x + (2210a d + 4420a b c)x
+--R +
+--R 2 2
+--R 3978a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 9945
+--R Type: Union(Expression(Integer),...)
+--E 1190
+
+--S 1191 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1191
+
+--S 1192 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1192
+
+)clear all
+
+--S 1193 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)*sqrt(x)
+--R
+--R
+--R 2 6 2 4 2 2 2 +-+
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|x
+--R Type: Expression(Integer)
+--E 1193
+
+--S 1194 of 1397
+r0:=2/3*a^2*c*x^(3/2)+2/7*a*(2*b*c+a*d)*x^(7/2)+2/11*b*(b*c+2*a*d)*_
+ x^(11/2)+2/15*b^2*d*x^(15/2)
+--R
+--R
+--R (2)
+--R 2 7 2 5 2 3 2 +-+
+--R (154b d x + (420a b d + 210b c)x + (330a d + 660a b c)x + 770a c x)\|x
+--R --------------------------------------------------------------------------
+--R 1155
+--R Type: Expression(Integer)
+--E 1194
+
+--S 1195 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 7 2 5 2 3 2 +-+
+--R (154b d x + (420a b d + 210b c)x + (330a d + 660a b c)x + 770a c x)\|x
+--R --------------------------------------------------------------------------
+--R 1155
+--R Type: Union(Expression(Integer),...)
+--E 1195
+
+--S 1196 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1196
+
+--S 1197 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1197
+
+)clear all
+
+--S 1198 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)/sqrt(x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R (1) --------------------------------------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1198
+
+--S 1199 of 1397
+r0:=2/5*a*(2*b*c+a*d)*x^(5/2)+2/9*b*(b*c+2*a*d)*x^(9/2)+2/13*b^2*_
+ d*x^(13/2)+2*a^2*c*sqrt(x)
+--R
+--R
+--R (2)
+--R 2 6 2 4 2 2 2 +-+
+--R (90b d x + (260a b d + 130b c)x + (234a d + 468a b c)x + 1170a c)\|x
+--R ------------------------------------------------------------------------
+--R 585
+--R Type: Expression(Integer)
+--E 1199
+
+--S 1200 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 2 4 2 2 2 +-+
+--R (90b d x + (260a b d + 130b c)x + (234a d + 468a b c)x + 1170a c)\|x
+--R ------------------------------------------------------------------------
+--R 585
+--R Type: Union(Expression(Integer),...)
+--E 1200
+
+--S 1201 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1201
+
+--S 1202 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1202
+
+)clear all
+
+--S 1203 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)/x^(3/2)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R (1) --------------------------------------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 1203
+
+--S 1204 of 1397
+r0:=2/3*a*(2*b*c+a*d)*x^(3/2)+2/7*b*(b*c+2*a*d)*x^(7/2)+2/11*b^2*_
+ d*x^(11/2)-2*a^2*c/sqrt(x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 42b d x + (132a b d + 66b c)x + (154a d + 308a b c)x - 462a c
+--R (2) ----------------------------------------------------------------
+--R +-+
+--R 231\|x
+--R Type: Expression(Integer)
+--E 1204
+
+--S 1205 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 42b d x + (132a b d + 66b c)x + (154a d + 308a b c)x - 462a c
+--R (3) ----------------------------------------------------------------
+--R +-+
+--R 231\|x
+--R Type: Union(Expression(Integer),...)
+--E 1205
+
+--S 1206 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1206
+
+--S 1207 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1207
+
+)clear all
+
+--S 1208 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)/x^(5/2)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R (1) --------------------------------------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1208
+
+--S 1209 of 1397
+r0:=-2/3*a^2*c/x^(3/2)+2/5*b*(b*c+2*a*d)*x^(5/2)+2/9*b^2*d*x^(9/2)+_
+ 2*a*(2*b*c+a*d)*sqrt(x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 10b d x + (36a b d + 18b c)x + (90a d + 180a b c)x - 30a c
+--R (2) -------------------------------------------------------------
+--R +-+
+--R 45x\|x
+--R Type: Expression(Integer)
+--E 1209
+
+--S 1210 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 10b d x + (36a b d + 18b c)x + (90a d + 180a b c)x - 30a c
+--R (3) -------------------------------------------------------------
+--R +-+
+--R 45x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1210
+
+--S 1211 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1211
+
+--S 1212 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1212
+
+)clear all
+
+--S 1213 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)/x^(7/2)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R (1) --------------------------------------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1213
+
+--S 1214 of 1397
+r0:=-2/5*a^2*c/x^(5/2)+2/3*b*(b*c+2*a*d)*x^(3/2)+2/7*b^2*d*x^(7/2)-_
+ 2*a*(2*b*c+a*d)/sqrt(x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 30b d x + (140a b d + 70b c)x + (- 210a d - 420a b c)x - 42a c
+--R (2) -----------------------------------------------------------------
+--R 2 +-+
+--R 105x \|x
+--R Type: Expression(Integer)
+--E 1214
+
+--S 1215 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 30b d x + (140a b d + 70b c)x + (- 210a d - 420a b c)x - 42a c
+--R (3) -----------------------------------------------------------------
+--R 2 +-+
+--R 105x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1215
+
+--S 1216 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1216
+
+--S 1217 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1217
+
+)clear all
+
+--S 1218 of 1397
+t0:=x^(7/2)*(a+b*x^2)^2*(c+d*x^2)^2
+--R
+--R
+--R (1)
+--R 2 2 11 2 2 9 2 2 2 2 7
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 5 2 2 3
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1218
+
+--S 1219 of 1397
+r0:=2/9*a^2*c^2*x^(9/2)+4/13*a*c*(b*c+a*d)*x^(13/2)+2/17*(b^2*c^2+_
+ 4*a*b*c*d+a^2*d^2)*x^(17/2)+4/21*b*d*(b*c+a*d)*x^(21/2)+_
+ 2/25*b^2*d^2*x^(25/2)
+--R
+--R
+--R (2)
+--R 2 2 12 2 2 10
+--R 27846b d x + (66300a b d + 66300b c d)x
+--R +
+--R 2 2 2 2 8
+--R (40950a d + 163800a b c d + 40950b c )x
+--R +
+--R 2 2 6 2 2 4
+--R (107100a c d + 107100a b c )x + 77350a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 348075
+--R Type: Expression(Integer)
+--E 1219
+
+--S 1220 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 12 2 2 10
+--R 27846b d x + (66300a b d + 66300b c d)x
+--R +
+--R 2 2 2 2 8
+--R (40950a d + 163800a b c d + 40950b c )x
+--R +
+--R 2 2 6 2 2 4
+--R (107100a c d + 107100a b c )x + 77350a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 348075
+--R Type: Union(Expression(Integer),...)
+--E 1220
+
+--S 1221 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1221
+
+--S 1222 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1222
+
+)clear all
+
+--S 1223 of 1397
+t0:=x^(5/2)*(a+b*x^2)^2*(c+d*x^2)^2
+--R
+--R
+--R (1)
+--R 2 2 10 2 2 8 2 2 2 2 6
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 4 2 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1223
+
+--S 1224 of 1397
+r0:=2/7*a^2*c^2*x^(7/2)+4/11*a*c*(b*c+a*d)*x^(11/2)+2/15*(b^2*c^2+_
+ 4*a*b*c*d+a^2*d^2)*x^(15/2)+4/19*b*d*(b*c+a*d)*x^(19/2)+_
+ 2/23*b^2*d^2*x^(23/2)
+--R
+--R
+--R (2)
+--R 2 2 11 2 2 9
+--R 43890b d x + (106260a b d + 106260b c d)x
+--R +
+--R 2 2 2 2 7
+--R (67298a d + 269192a b c d + 67298b c )x
+--R +
+--R 2 2 5 2 2 3
+--R (183540a c d + 183540a b c )x + 144210a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 504735
+--R Type: Expression(Integer)
+--E 1224
+
+--S 1225 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 11 2 2 9
+--R 43890b d x + (106260a b d + 106260b c d)x
+--R +
+--R 2 2 2 2 7
+--R (67298a d + 269192a b c d + 67298b c )x
+--R +
+--R 2 2 5 2 2 3
+--R (183540a c d + 183540a b c )x + 144210a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 504735
+--R Type: Union(Expression(Integer),...)
+--E 1225
+
+--S 1226 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1226
+
+--S 1227 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1227
+
+)clear all
+
+--S 1228 of 1397
+t0:=x^(3/2)*(a+b*x^2)^2*(c+d*x^2)^2
+--R
+--R
+--R (1)
+--R 2 2 9 2 2 7 2 2 2 2 5
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 3 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1228
+
+--S 1229 of 1397
+r0:=2/5*a^2*c^2*x^(5/2)+4/9*a*c*(b*c+a*d)*x^(9/2)+2/13*(b^2*c^2+_
+ 4*a*b*c*d+a^2*d^2)*x^(13/2)+4/17*b*d*(b*c+a*d)*x^(17/2)+_
+ 2/21*b^2*d^2*x^(21/2)
+--R
+--R
+--R (2)
+--R 2 2 10 2 2 8
+--R 6630b d x + (16380a b d + 16380b c d)x
+--R +
+--R 2 2 2 2 6 2 2 4
+--R (10710a d + 42840a b c d + 10710b c )x + (30940a c d + 30940a b c )x
+--R +
+--R 2 2 2
+--R 27846a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 69615
+--R Type: Expression(Integer)
+--E 1229
+
+--S 1230 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 10 2 2 8
+--R 6630b d x + (16380a b d + 16380b c d)x
+--R +
+--R 2 2 2 2 6 2 2 4
+--R (10710a d + 42840a b c d + 10710b c )x + (30940a c d + 30940a b c )x
+--R +
+--R 2 2 2
+--R 27846a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 69615
+--R Type: Union(Expression(Integer),...)
+--E 1230
+
+--S 1231 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1231
+
+--S 1232 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1232
+
+)clear all
+
+--S 1233 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^2*sqrt(x)
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1233
+
+--S 1234 of 1397
+r0:=2/3*a^2*c^2*x^(3/2)+4/7*a*c*(b*c+a*d)*x^(7/2)+2/11*(b^2*c^2+_
+ 4*a*b*c*d+a^2*d^2)*x^(11/2)+4/15*b*d*(b*c+a*d)*x^(15/2)+_
+ 2/19*b^2*d^2*x^(19/2)
+--R
+--R
+--R (2)
+--R 2 2 9 2 2 7
+--R 2310b d x + (5852a b d + 5852b c d)x
+--R +
+--R 2 2 2 2 5 2 2 3
+--R (3990a d + 15960a b c d + 3990b c )x + (12540a c d + 12540a b c )x
+--R +
+--R 2 2
+--R 14630a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 21945
+--R Type: Expression(Integer)
+--E 1234
+
+--S 1235 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 9 2 2 7
+--R 2310b d x + (5852a b d + 5852b c d)x
+--R +
+--R 2 2 2 2 5 2 2 3
+--R (3990a d + 15960a b c d + 3990b c )x + (12540a c d + 12540a b c )x
+--R +
+--R 2 2
+--R 14630a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 21945
+--R Type: Union(Expression(Integer),...)
+--E 1235
+
+--S 1236 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1236
+
+--S 1237 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1237
+
+)clear all
+
+--S 1238 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^2/sqrt(x)
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R /
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1238
+
+--S 1239 of 1397
+r0:=4/5*a*c*(b*c+a*d)*x^(5/2)+2/9*(b^2*c^2+4*a*b*c*d+a^2*d^2)*x^(9/2)+_
+ 4/13*b*d*(b*c+a*d)*x^(13/2)+2/17*b^2*d^2*x^(17/2)+2*a^2*c^2*sqrt(x)
+--R
+--R
+--R (2)
+--R 2 2 8 2 2 6
+--R 1170b d x + (3060a b d + 3060b c d)x
+--R +
+--R 2 2 2 2 4 2 2 2
+--R (2210a d + 8840a b c d + 2210b c )x + (7956a c d + 7956a b c )x
+--R +
+--R 2 2
+--R 19890a c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 9945
+--R Type: Expression(Integer)
+--E 1239
+
+--S 1240 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 8 2 2 6
+--R 1170b d x + (3060a b d + 3060b c d)x
+--R +
+--R 2 2 2 2 4 2 2 2
+--R (2210a d + 8840a b c d + 2210b c )x + (7956a c d + 7956a b c )x
+--R +
+--R 2 2
+--R 19890a c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 9945
+--R Type: Union(Expression(Integer),...)
+--E 1240
+
+--S 1241 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1241
+
+--S 1242 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1242
+
+)clear all
+
+--S 1243 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^2/x^(3/2)
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R /
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 1243
+
+--S 1244 of 1397
+r0:=4/3*a*c*(b*c+a*d)*x^(3/2)+2/7*(b^2*c^2+4*a*b*c*d+a^2*d^2)*x^(7/2)+_
+ 4/11*b*d*(b*c+a*d)*x^(11/2)+2/15*b^2*d^2*x^(15/2)-2*a^2*c^2/sqrt(x)
+--R
+--R
+--R (2)
+--R 2 2 8 2 2 6
+--R 154b d x + (420a b d + 420b c d)x
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R (330a d + 1320a b c d + 330b c )x + (1540a c d + 1540a b c )x - 2310a c
+--R /
+--R +-+
+--R 1155\|x
+--R Type: Expression(Integer)
+--E 1244
+
+--S 1245 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 8 2 2 6
+--R 154b d x + (420a b d + 420b c d)x
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R (330a d + 1320a b c d + 330b c )x + (1540a c d + 1540a b c )x - 2310a c
+--R /
+--R +-+
+--R 1155\|x
+--R Type: Union(Expression(Integer),...)
+--E 1245
+
+--S 1246 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1246
+
+--S 1247 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1247
+
+)clear all
+
+--S 1248 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^2/x^(5/2)
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R /
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1248
+
+--S 1249 of 1397
+r0:=-2/3*a^2*c^2/x^(3/2)+2/5*(b^2*c^2+4*a*b*c*d+a^2*d^2)*x^(5/2)+_
+ 4/9*b*d*(b*c+a*d)*x^(9/2)+2/13*b^2*d^2*x^(13/2)+4*a*c*(b*c+a*d)*sqrt(x)
+--R
+--R
+--R (2)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R 90b d x + (260a b d + 260b c d)x + (234a d + 936a b c d + 234b c )x
+--R +
+--R 2 2 2 2 2
+--R (2340a c d + 2340a b c )x - 390a c
+--R /
+--R +-+
+--R 585x\|x
+--R Type: Expression(Integer)
+--E 1249
+
+--S 1250 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R 90b d x + (260a b d + 260b c d)x + (234a d + 936a b c d + 234b c )x
+--R +
+--R 2 2 2 2 2
+--R (2340a c d + 2340a b c )x - 390a c
+--R /
+--R +-+
+--R 585x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1250
+
+--S 1251 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1251
+
+--S 1252 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1252
+
+)clear all
+
+--S 1253 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^2/x^(7/2)
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R /
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1253
+
+--S 1254 of 1397
+r0:=-2/5*a^2*c^2/x^(5/2)+2/3*(b^2*c^2+4*a*b*c*d+a^2*d^2)*x^(3/2)+_
+ 4/7*b*d*(b*c+a*d)*x^(7/2)+2/11*b^2*d^2*x^(11/2)-4*a*c*(b*c+a*d)/sqrt(x)
+--R
+--R
+--R (2)
+--R 2 2 8 2 2 6
+--R 210b d x + (660a b d + 660b c d)x
+--R +
+--R 2 2 2 2 4 2 2 2
+--R (770a d + 3080a b c d + 770b c )x + (- 4620a c d - 4620a b c )x
+--R +
+--R 2 2
+--R - 462a c
+--R /
+--R 2 +-+
+--R 1155x \|x
+--R Type: Expression(Integer)
+--E 1254
+
+--S 1255 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 8 2 2 6
+--R 210b d x + (660a b d + 660b c d)x
+--R +
+--R 2 2 2 2 4 2 2 2
+--R (770a d + 3080a b c d + 770b c )x + (- 4620a c d - 4620a b c )x
+--R +
+--R 2 2
+--R - 462a c
+--R /
+--R 2 +-+
+--R 1155x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1255
+
+--S 1256 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1256
+
+--S 1257 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1257
+
+)clear all
+
+--S 1258 of 1397
+t0:=x^(7/2)*(a+b*x^2)^2*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 2 3 13 3 2 2 11 2 3 2 2 2 9
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 7 2 2 3 5 2 3 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1258
+
+--S 1259 of 1397
+r0:=2/9*a^2*c^3*x^(9/2)+2/13*a*c^2*(2*b*c+3*a*d)*x^(13/2)+2/17*c*_
+ (b^2*c^2+6*a*b*c*d+3*a^2*d^2)*x^(17/2)+2/21*d*(3*b^2*c^2+6*a*b*_
+ c*d+a^2*d^2)*x^(21/2)+2/25*b*d^2*(3*b*c+2*a*d)*x^(25/2)+2/29*b^2*_
+ d^3*x^(29/2)
+--R
+--R
+--R (2)
+--R 2 3 14 3 2 2 12
+--R 696150b d x + (1615068a b d + 2422602b c d )x
+--R +
+--R 2 3 2 2 2 10
+--R (961350a d + 5768100a b c d + 2884050b c d)x
+--R +
+--R 2 2 2 2 3 8
+--R (3562650a c d + 7125300a b c d + 1187550b c )x
+--R +
+--R 2 2 3 6 2 3 4
+--R (4658850a c d + 3105900a b c )x + 2243150a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 10094175
+--R Type: Expression(Integer)
+--E 1259
+
+--S 1260 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 14 3 2 2 12
+--R 696150b d x + (1615068a b d + 2422602b c d )x
+--R +
+--R 2 3 2 2 2 10
+--R (961350a d + 5768100a b c d + 2884050b c d)x
+--R +
+--R 2 2 2 2 3 8
+--R (3562650a c d + 7125300a b c d + 1187550b c )x
+--R +
+--R 2 2 3 6 2 3 4
+--R (4658850a c d + 3105900a b c )x + 2243150a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 10094175
+--R Type: Union(Expression(Integer),...)
+--E 1260
+
+--S 1261 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1261
+
+--S 1262 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1262
+
+)clear all
+
+--S 1263 of 1397
+t0:=x^(5/2)*(a+b*x^2)^2*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 2 3 12 3 2 2 10 2 3 2 2 2 8
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 6 2 2 3 4 2 3 2
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1263
+
+--S 1264 of 1397
+r0:=2/7*a^2*c^3*x^(7/2)+2/11*a*c^2*(2*b*c+3*a*d)*x^(11/2)+_
+ 2/15*c*(b^2*c^2+6*a*b*c*d+3*a^2*d^2)*x^(15/2)+_
+ 2/19*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^(19/2)+_
+ 2/23*b*d^2*(3*b*c+2*a*d)*x^(23/2)+2/27*b^2*d^3*x^(27/2)
+--R
+--R
+--R (2)
+--R 2 3 13 3 2 2 11
+--R 336490b d x + (790020a b d + 1185030b c d )x
+--R +
+--R 2 3 2 2 2 9
+--R (478170a d + 2869020a b c d + 1434510b c d)x
+--R +
+--R 2 2 2 2 3 7
+--R (1817046a c d + 3634092a b c d + 605682b c )x
+--R +
+--R 2 2 3 5 2 3 3
+--R (2477790a c d + 1651860a b c )x + 1297890a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 4542615
+--R Type: Expression(Integer)
+--E 1264
+
+--S 1265 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 13 3 2 2 11
+--R 336490b d x + (790020a b d + 1185030b c d )x
+--R +
+--R 2 3 2 2 2 9
+--R (478170a d + 2869020a b c d + 1434510b c d)x
+--R +
+--R 2 2 2 2 3 7
+--R (1817046a c d + 3634092a b c d + 605682b c )x
+--R +
+--R 2 2 3 5 2 3 3
+--R (2477790a c d + 1651860a b c )x + 1297890a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 4542615
+--R Type: Union(Expression(Integer),...)
+--E 1265
+
+--S 1266 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1266
+
+--S 1267 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1267
+
+)clear all
+
+--S 1268 of 1397
+t0:=x^(3/2)*(a+b*x^2)^2*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 2 3 11 3 2 2 9 2 3 2 2 2 7
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 5 2 2 3 3 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1268
+
+--S 1269 of 1397
+r0:=2/5*a^2*c^3*x^(5/2)+2/9*a*c^2*(2*b*c+3*a*d)*x^(9/2)+2/13*c*_
+ (b^2*c^2+6*a*b*c*d+3*a^2*d^2)*x^(13/2)+2/17*d*(3*b^2*c^2+6*a*b*c*d+_
+ a^2*d^2)*x^(17/2)+2/21*b*d^2*(3*b*c+2*a*d)*x^(21/2)+2/25*b^2*d^3*x^(25/2)
+--R
+--R
+--R (2)
+--R 2 3 12 3 2 2 10
+--R 27846b d x + (66300a b d + 99450b c d )x
+--R +
+--R 2 3 2 2 2 8
+--R (40950a d + 245700a b c d + 122850b c d)x
+--R +
+--R 2 2 2 2 3 6
+--R (160650a c d + 321300a b c d + 53550b c )x
+--R +
+--R 2 2 3 4 2 3 2
+--R (232050a c d + 154700a b c )x + 139230a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 348075
+--R Type: Expression(Integer)
+--E 1269
+
+--S 1270 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 12 3 2 2 10
+--R 27846b d x + (66300a b d + 99450b c d )x
+--R +
+--R 2 3 2 2 2 8
+--R (40950a d + 245700a b c d + 122850b c d)x
+--R +
+--R 2 2 2 2 3 6
+--R (160650a c d + 321300a b c d + 53550b c )x
+--R +
+--R 2 2 3 4 2 3 2
+--R (232050a c d + 154700a b c )x + 139230a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 348075
+--R Type: Union(Expression(Integer),...)
+--E 1270
+
+--S 1271 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1271
+
+--S 1272 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1272
+
+)clear all
+
+--S 1273 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^3*sqrt(x)
+--R
+--R
+--R (1)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1273
+
+--S 1274 of 1397
+r0:=2/3*a^2*c^3*x^(3/2)+2/7*a*c^2*(2*b*c+3*a*d)*x^(7/2)+2/11*c*(b^2*c^2+_
+ 6*a*b*c*d+3*a^2*d^2)*x^(11/2)+2/15*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*_
+ x^(15/2)+2/19*b*d^2*(3*b*c+2*a*d)*x^(19/2)+2/23*b^2*d^3*x^(23/2)
+--R
+--R
+--R (2)
+--R 2 3 11 3 2 2 9
+--R 43890b d x + (106260a b d + 159390b c d )x
+--R +
+--R 2 3 2 2 2 7
+--R (67298a d + 403788a b c d + 201894b c d)x
+--R +
+--R 2 2 2 2 3 5
+--R (275310a c d + 550620a b c d + 91770b c )x
+--R +
+--R 2 2 3 3 2 3
+--R (432630a c d + 288420a b c )x + 336490a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 504735
+--R Type: Expression(Integer)
+--E 1274
+
+--S 1275 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 11 3 2 2 9
+--R 43890b d x + (106260a b d + 159390b c d )x
+--R +
+--R 2 3 2 2 2 7
+--R (67298a d + 403788a b c d + 201894b c d)x
+--R +
+--R 2 2 2 2 3 5
+--R (275310a c d + 550620a b c d + 91770b c )x
+--R +
+--R 2 2 3 3 2 3
+--R (432630a c d + 288420a b c )x + 336490a c x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 504735
+--R Type: Union(Expression(Integer),...)
+--E 1275
+
+--S 1276 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1276
+
+--S 1277 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1277
+
+)clear all
+
+--S 1278 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^3/sqrt(x)
+--R
+--R
+--R (1)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R /
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1278
+
+--S 1279 of 1397
+r0:=2/5*a*c^2*(2*b*c+3*a*d)*x^(5/2)+2/9*c*(b^2*c^2+6*a*b*c*d+3*a^2*d^2)*_
+ x^(9/2)+2/13*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^(13/2)+2/17*b*_
+ d^2*(3*b*c+2*a*d)*x^(17/2)+2/21*b^2*d^3*x^(21/2)+2*a^2*c^3*sqrt(x)
+--R
+--R
+--R (2)
+--R 2 3 10 3 2 2 8
+--R 6630b d x + (16380a b d + 24570b c d )x
+--R +
+--R 2 3 2 2 2 6
+--R (10710a d + 64260a b c d + 32130b c d)x
+--R +
+--R 2 2 2 2 3 4
+--R (46410a c d + 92820a b c d + 15470b c )x
+--R +
+--R 2 2 3 2 2 3
+--R (83538a c d + 55692a b c )x + 139230a c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 69615
+--R Type: Expression(Integer)
+--E 1279
+
+--S 1280 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 10 3 2 2 8
+--R 6630b d x + (16380a b d + 24570b c d )x
+--R +
+--R 2 3 2 2 2 6
+--R (10710a d + 64260a b c d + 32130b c d)x
+--R +
+--R 2 2 2 2 3 4
+--R (46410a c d + 92820a b c d + 15470b c )x
+--R +
+--R 2 2 3 2 2 3
+--R (83538a c d + 55692a b c )x + 139230a c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 69615
+--R Type: Union(Expression(Integer),...)
+--E 1280
+
+--S 1281 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1281
+
+--S 1282 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1282
+
+)clear all
+
+--S 1283 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^3/x^(3/2)
+--R
+--R
+--R (1)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R /
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 1283
+
+--S 1284 of 1397
+r0:=2/3*a*c^2*(2*b*c+3*a*d)*x^(3/2)+2/7*c*(b^2*c^2+6*a*b*c*d+3*a^2*d^2)*_
+ x^(7/2)+2/11*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^(11/2)+2/15*b*d^2*_
+ (3*b*c+2*a*d)*x^(15/2)+2/19*b^2*d^3*x^(19/2)-2*a^2*c^3/sqrt(x)
+--R
+--R
+--R (2)
+--R 2 3 10 3 2 2 8
+--R 2310b d x + (5852a b d + 8778b c d )x
+--R +
+--R 2 3 2 2 2 6
+--R (3990a d + 23940a b c d + 11970b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (18810a c d + 37620a b c d + 6270b c )x + (43890a c d + 29260a b c )x
+--R +
+--R 2 3
+--R - 43890a c
+--R /
+--R +-+
+--R 21945\|x
+--R Type: Expression(Integer)
+--E 1284
+
+--S 1285 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 10 3 2 2 8
+--R 2310b d x + (5852a b d + 8778b c d )x
+--R +
+--R 2 3 2 2 2 6
+--R (3990a d + 23940a b c d + 11970b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (18810a c d + 37620a b c d + 6270b c )x + (43890a c d + 29260a b c )x
+--R +
+--R 2 3
+--R - 43890a c
+--R /
+--R +-+
+--R 21945\|x
+--R Type: Union(Expression(Integer),...)
+--E 1285
+
+--S 1286 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1286
+
+--S 1287 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1287
+
+)clear all
+
+--S 1288 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^3/x^(5/2)
+--R
+--R
+--R (1)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R /
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1288
+
+--S 1289 of 1397
+r0:=-2/3*a^2*c^3/x^(3/2)+2/5*c*(b^2*c^2+6*a*b*c*d+3*a^2*d^2)*x^(5/2)+_
+ 2/9*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^(9/2)+_
+ 2/13*b*d^2*(3*b*c+2*a*d)*x^(13/2)+2/17*b^2*d^3*x^(17/2)+_
+ 2*a*c^2*(2*b*c+3*a*d)*sqrt(x)
+--R
+--R
+--R (2)
+--R 2 3 10 3 2 2 8
+--R 1170b d x + (3060a b d + 4590b c d )x
+--R +
+--R 2 3 2 2 2 6
+--R (2210a d + 13260a b c d + 6630b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (11934a c d + 23868a b c d + 3978b c )x + (59670a c d + 39780a b c )x
+--R +
+--R 2 3
+--R - 6630a c
+--R /
+--R +-+
+--R 9945x\|x
+--R Type: Expression(Integer)
+--E 1289
+
+--S 1290 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 10 3 2 2 8
+--R 1170b d x + (3060a b d + 4590b c d )x
+--R +
+--R 2 3 2 2 2 6
+--R (2210a d + 13260a b c d + 6630b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (11934a c d + 23868a b c d + 3978b c )x + (59670a c d + 39780a b c )x
+--R +
+--R 2 3
+--R - 6630a c
+--R /
+--R +-+
+--R 9945x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1290
+
+--S 1291 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1291
+
+--S 1292 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1292
+
+)clear all
+
+--S 1293 of 1397
+t0:=(a+b*x^2)^2*(c+d*x^2)^3/x^(7/2)
+--R
+--R
+--R (1)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R /
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1293
+
+--S 1294 of 1397
+r0:=-2/5*a^2*c^3/x^(5/2)+2/3*c*(b^2*c^2+6*a*b*c*d+3*a^2*d^2)*x^(3/2)+_
+ 2/7*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^(7/2)+_
+ 2/11*b*d^2*(3*b*c+2*a*d)*x^(11/2)+2/15*b^2*d^3*x^(15/2)-_
+ 2*a*c^2*(2*b*c+3*a*d)/sqrt(x)
+--R
+--R
+--R (2)
+--R 2 3 10 3 2 2 8
+--R 154b d x + (420a b d + 630b c d )x
+--R +
+--R 2 3 2 2 2 6
+--R (330a d + 1980a b c d + 990b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (2310a c d + 4620a b c d + 770b c )x + (- 6930a c d - 4620a b c )x
+--R +
+--R 2 3
+--R - 462a c
+--R /
+--R 2 +-+
+--R 1155x \|x
+--R Type: Expression(Integer)
+--E 1294
+
+--S 1295 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 10 3 2 2 8
+--R 154b d x + (420a b d + 630b c d )x
+--R +
+--R 2 3 2 2 2 6
+--R (330a d + 1980a b c d + 990b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (2310a c d + 4620a b c d + 770b c )x + (- 6930a c d - 4620a b c )x
+--R +
+--R 2 3
+--R - 462a c
+--R /
+--R 2 +-+
+--R 1155x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1295
+
+--S 1296 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1296
+
+--S 1297 of 1397
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1297
+
+)clear all
+
+--S 1298 of 1397
+t0:=x^(7/2)*(a+b*x^2)^2/(c+d*x^2)
+--R
+--R
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R (1) ---------------------------
+--R 2
+--R d x + c
+--R Type: Expression(Integer)
+--E 1298
+
+--S 1299 of 1397
+r0:=2/5*(b*c-a*d)^2*x^(5/2)/d^3-2/9*b*(b*c-2*a*d)*x^(9/2)/d^2+2/13*b^2*_
+ x^(13/2)/d-c^(5/4)*(b*c-a*d)^2*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/_
+ c^(1/4))/(d^(17/4)*sqrt(2))+c^(5/4)*(b*c-a*d)^2*atan(1+d^(1/4)*_
+ sqrt(2)*sqrt(x)/c^(1/4))/(d^(17/4)*sqrt(2))-1/2*c^(5/4)*(b*c-a*d)^2*_
+ log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(d^(17/4)*_
+ sqrt(2))+1/2*c^(5/4)*(b*c-a*d)^2*log(sqrt(c)+x*sqrt(d)+c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(d^(17/4)*sqrt(2))-2*c*(b*c-a*d)^2*sqrt(x)/d^4
+--R
+--R
+--R (2)
+--R 2 2 2 2 3 4+-+
+--R (585a c d - 1170a b c d + 585b c )\|c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 2 3 4+-+
+--R (- 585a c d + 1170a b c d - 585b c )\|c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 3 4+-+ \|2 \|d \|x + \|c
+--R (1170a c d - 2340a b c d + 1170b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 3 4+-+ \|2 \|d \|x - \|c
+--R (1170a c d - 2340a b c d + 1170b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 6 3 2 2 4
+--R 180b d x + (520a b d - 260b c d )x
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (468a d - 936a b c d + 468b c d)x - 2340a c d + 4680a b c d
+--R +
+--R 2 3
+--R - 2340b c
+--R *
+--R +-+4+-+ +-+
+--R \|2 \|d \|x
+--R /
+--R 4 +-+4+-+
+--R 1170d \|2 \|d
+--R Type: Expression(Integer)
+--E 1299
+
+--S 1300 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4
+--R 585d
+--R *
+--R ROOT
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5 4 4 9 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 10 3 2 6 11 2 7 12 8 13
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 17
+--R 16d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 3 +-+
+--R (a c d - 2a b c d + b c )\|x
+--R +
+--R 4
+--R 2d
+--R *
+--R ROOT
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2 7 12
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 13
+--R - b c
+--R /
+--R 17
+--R 16d
+--R ,
+--R 4
+--R +
+--R -
+--R 4
+--R 585d
+--R *
+--R ROOT
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5 4 4 9 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 10 3 2 6 11 2 7 12 8 13
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 17
+--R 16d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 3 +-+
+--R (a c d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 4
+--R 2d
+--R *
+--R ROOT
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R - 70a b c d + 56a b c d - 28a b c d
+--R +
+--R 7 12 8 13
+--R 8a b c d - b c
+--R /
+--R 17
+--R 16d
+--R ,
+--R 4
+--R +
+--R -
+--R 4
+--R 1170d
+--R *
+--R ROOT
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5 4 4 9 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 10 3 2 6 11 2 7 12 8 13
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 17
+--R 16d
+--R ,
+--R 4
+--R *
+--R atan
+--R 4
+--R 2d
+--R *
+--R ROOT
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2 7 12
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 13
+--R - b c
+--R /
+--R 17
+--R 16d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 3 +-+
+--R (a c d - 2a b c d + b c )\|x
+--R +
+--R 2 3 6 3 2 2 4
+--R 90b d x + (260a b d - 130b c d )x
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (234a d - 468a b c d + 234b c d)x - 1170a c d + 2340a b c d
+--R +
+--R 2 3
+--R - 1170b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 4
+--R 585d
+--R Type: Union(Expression(Integer),...)
+--E 1300
+
+--S 1301 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 3 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a c d + 2a b c d - b c )\|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4 +-+
+--R 2d \|2
+--R *
+--R ROOT
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5 4 4 9 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 10 3 2 6 11 2 7 12 8 13
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 17
+--R 16d
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|d
+--R *
+--R log
+--R 2 2 2 2 3 +-+
+--R (a c d - 2a b c d + b c )\|x
+--R +
+--R 4
+--R 2d
+--R *
+--R ROOT
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2 7 12
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 13
+--R - b c
+--R /
+--R 17
+--R 16d
+--R ,
+--R 4
+--R +
+--R -
+--R 4 +-+
+--R 2d \|2
+--R *
+--R ROOT
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5 4 4 9 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 10 3 2 6 11 2 7 12 8 13
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 17
+--R 16d
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|d
+--R *
+--R log
+--R 2 2 2 2 3 +-+
+--R (a c d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 4
+--R 2d
+--R *
+--R ROOT
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R - 70a b c d + 56a b c d - 28a b c d
+--R +
+--R 7 12 8 13
+--R 8a b c d - b c
+--R /
+--R 17
+--R 16d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 3 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (a c d - 2a b c d + b c )\|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 3 4+-+ \|2 \|d \|x + \|c
+--R (- 2a c d + 4a b c d - 2b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 3 4+-+ \|2 \|d \|x - \|c
+--R (- 2a c d + 4a b c d - 2b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R -
+--R 4 +-+
+--R 4d \|2
+--R *
+--R ROOT
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5 4 4 9 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 10 3 2 6 11 2 7 12 8 13
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 17
+--R 16d
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|d
+--R *
+--R atan
+--R 4
+--R 2d
+--R *
+--R ROOT
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2 7 12
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 13
+--R - b c
+--R /
+--R 17
+--R 16d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 3 +-+
+--R (a c d - 2a b c d + b c )\|x
+--R /
+--R 4 +-+4+-+
+--R 2d \|2 \|d
+--R Type: Expression(Integer)
+--E 1301
+
+--S 1302 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1302
+
+)clear all
+
+--S 1303 of 1397
+t0:=x^(5/2)*(a+b*x^2)^2/(c+d*x^2)
+--R
+--R
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R (1) ---------------------------
+--R 2
+--R d x + c
+--R Type: Expression(Integer)
+--E 1303
+
+--S 1304 of 1397
+r0:=2/3*(b*c-a*d)^2*x^(3/2)/d^3-2/7*b*(b*c-2*a*d)*x^(7/2)/d^2+_
+ 2/11*b^2*x^(11/2)/d+c^(3/4)*(b*c-a*d)^2*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(d^(15/4)*sqrt(2))-c^(3/4)*(b*c-a*d)^2*atan(1+_
+ d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(d^(15/4)*sqrt(2))-1/2*c^(3/4)*_
+ (b*c-a*d)^2*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (d^(15/4)*sqrt(2))+1/2*c^(3/4)*(b*c-a*d)^2*log(sqrt(c)+x*sqrt(d)+_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(d^(15/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2 2 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (231a d - 462a b c d + 231b c )\|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 2 4+-+3
+--R (- 231a d + 462a b c d - 231b c )\|c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+3 \|2 \|d \|x + \|c
+--R (- 462a d + 924a b c d - 462b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+3 \|2 \|d \|x - \|c
+--R (- 462a d + 924a b c d - 462b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 5 2 2 3
+--R 84b d x + (264a b d - 132b c d)x
+--R +
+--R 2 2 2 2
+--R (308a d - 616a b c d + 308b c )x
+--R *
+--R +-+4+-+3 +-+
+--R \|2 \|d \|x
+--R /
+--R 3 +-+4+-+3
+--R 462d \|2 \|d
+--R Type: Expression(Integer)
+--E 1304
+
+--S 1305 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3
+--R 231d
+--R *
+--R ROOT
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5 4 4 7 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 8 3 2 6 9 2 7 10 8 11
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 15
+--R 16d
+--R ,
+--R 4
+--R *
+--R log
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R a c d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 7 6 8
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 11
+--R 8d
+--R *
+--R ROOT
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 11
+--R - b c
+--R /
+--R 15
+--R 16d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3
+--R 231d
+--R *
+--R ROOT
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5 4 4 7 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 8 3 2 6 9 2 7 10 8 11
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 15
+--R 16d
+--R ,
+--R 4
+--R *
+--R log
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R a c d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 7 6 8
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 11
+--R 8d
+--R *
+--R ROOT
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 11
+--R - b c
+--R /
+--R 15
+--R 16d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 3
+--R 462d
+--R *
+--R ROOT
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5 4 4 7 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 8 3 2 6 9 2 7 10 8 11
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 15
+--R 16d
+--R ,
+--R 4
+--R *
+--R atan
+--R 11
+--R 8d
+--R *
+--R ROOT
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 11
+--R - b c
+--R /
+--R 15
+--R 16d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R a c d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 7 6 8
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 5 2 2 3
+--R 42b d x + (132a b d - 66b c d)x
+--R +
+--R 2 2 2 2
+--R (154a d - 308a b c d + 154b c )x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3
+--R 231d
+--R Type: Union(Expression(Integer),...)
+--E 1305
+
+--S 1306 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )\|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R -
+--R 3 +-+
+--R 2d \|2
+--R *
+--R ROOT
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5 4 4 7 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 8 3 2 6 9 2 7 10 8 11
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 15
+--R 16d
+--R ,
+--R 4
+--R *
+--R 4+-+3
+--R \|d
+--R *
+--R log
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R a c d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 7 6 8
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 11
+--R 8d
+--R *
+--R ROOT
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 11
+--R - b c
+--R /
+--R 15
+--R 16d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 +-+
+--R 2d \|2
+--R *
+--R ROOT
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5 4 4 7 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 8 3 2 6 9 2 7 10 8 11
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 15
+--R 16d
+--R ,
+--R 4
+--R *
+--R 4+-+3
+--R \|d
+--R *
+--R log
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R a c d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 7 6 8
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 11
+--R 8d
+--R *
+--R ROOT
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 11
+--R - b c
+--R /
+--R 15
+--R 16d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )\|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+3 \|2 \|d \|x + \|c
+--R (2a d - 4a b c d + 2b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+3 \|2 \|d \|x - \|c
+--R (2a d - 4a b c d + 2b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R -
+--R 3 +-+
+--R 4d \|2
+--R *
+--R ROOT
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5 4 4 7 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 8 3 2 6 9 2 7 10 8 11
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 15
+--R 16d
+--R ,
+--R 4
+--R *
+--R 4+-+3
+--R \|d
+--R *
+--R atan
+--R 11
+--R 8d
+--R *
+--R ROOT
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 11
+--R - b c
+--R /
+--R 15
+--R 16d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R a c d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 7 6 8
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3 +-+4+-+3
+--R 2d \|2 \|d
+--R Type: Expression(Integer)
+--E 1306
+
+--S 1307 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1307
+
+)clear all
+
+--S 1308 of 1397
+t0:=x^(3/2)*(a+b*x^2)^2/(c+d*x^2)
+--R
+--R
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R (1) --------------------------
+--R 2
+--R d x + c
+--R Type: Expression(Integer)
+--E 1308
+
+--S 1309 of 1397
+r0:=-2/5*b*(b*c-2*a*d)*x^(5/2)/d^2+2/9*b^2*x^(9/2)/d+c^(1/4)*(b*c-a*d)^2*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(d^(13/4)*sqrt(2))-c^(1/4)*_
+ (b*c-a*d)^2*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(d^(13/4)*_
+ sqrt(2))+1/2*c^(1/4)*(b*c-a*d)^2*log(sqrt(c)+x*sqrt(d)-c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(d^(13/4)*sqrt(2))-1/2*c^(1/4)*(b*c-a*d)^2*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(d^(13/4)*_
+ sqrt(2))+2*(b*c-a*d)^2*sqrt(x)/d^3
+--R
+--R
+--R (2)
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 45a d + 90a b c d - 45b c )\|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (45a d - 90a b c d + 45b c )\|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|d \|x + \|c
+--R (- 90a d + 180a b c d - 90b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|d \|x - \|c
+--R (- 90a d + 180a b c d - 90b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R (20b d x + (72a b d - 36b c d)x + 180a d - 360a b c d + 180b c )
+--R *
+--R +-+4+-+ +-+
+--R \|2 \|d \|x
+--R /
+--R 3 +-+4+-+
+--R 90d \|2 \|d
+--R Type: Expression(Integer)
+--E 1309
+
+--S 1310 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3
+--R 45d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 6 3 2 6 7 2 7 8 8 9
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 3
+--R 2d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2 7 8 8 9
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16d
+--R ,
+--R 4
+--R +
+--R 3
+--R 45d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 6 3 2 6 7 2 7 8 8 9
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 3
+--R 2d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2 7 8 8 9
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16d
+--R ,
+--R 4
+--R +
+--R 3
+--R 90d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 6 3 2 6 7 2 7 8 8 9
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16d
+--R ,
+--R 4
+--R *
+--R atan
+--R 3
+--R 2d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2 7 8 8 9
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2 2 4 2 2 2 2 2 2 2 +-+
+--R (10b d x + (36a b d - 18b c d)x + 90a d - 180a b c d + 90b c )\|x
+--R /
+--R 3
+--R 45d
+--R Type: Union(Expression(Integer),...)
+--E 1310
+
+--S 1311 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )\|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R -
+--R 3 +-+
+--R 2d \|2
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 6 3 2 6 7 2 7 8 8 9
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16d
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 3
+--R 2d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2 7 8 8 9
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16d
+--R ,
+--R 4
+--R +
+--R 3 +-+
+--R 2d \|2
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 6 3 2 6 7 2 7 8 8 9
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16d
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 3
+--R 2d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2 7 8 8 9
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )\|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|d \|x + \|c
+--R (2a d - 4a b c d + 2b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|d \|x - \|c
+--R (2a d - 4a b c d + 2b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 +-+
+--R 4d \|2
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4
+--R - a c d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 6 3 2 6 7 2 7 8 8 9
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16d
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|d
+--R *
+--R atan
+--R 3
+--R 2d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R - a c d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2 7 8 8 9
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R /
+--R 3 +-+4+-+
+--R 2d \|2 \|d
+--R Type: Expression(Integer)
+--E 1311
+
+--S 1312 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1312
+
+)clear all
+
+--S 1313 of 1397
+t0:=(a+b*x^2)^2*sqrt(x)/(c+d*x^2)
+--R
+--R
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R (1) -------------------------
+--R 2
+--R d x + c
+--R Type: Expression(Integer)
+--E 1313
+
+--S 1314 of 1397
+r0:=-2/3*b*(b*c-2*a*d)*x^(3/2)/d^2+2/7*b^2*x^(7/2)/d-(b*c-a*d)^2*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(1/4)*d^(11/4)*_
+ sqrt(2))+(b*c-a*d)^2*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(1/4)*d^(11/4)*sqrt(2))+1/2*(b*c-a*d)^2*log(sqrt(c)+x*_
+ sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(1/4)*d^(11/4)*sqrt(2))-_
+ 1/2*(b*c-a*d)^2*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(1/4)*d^(11/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 21a d + 42a b c d - 21b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (21a d - 42a b c d + 21b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (42a d - 84a b c d + 42b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (42a d - 84a b c d + 42b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 +-+4+-+4+-+3 +-+
+--R (12b d x + (56a b d - 28b c)x)\|2 \|c \|d \|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 42d \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1314
+
+--S 1315 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R 21d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 8
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2
+--R 21d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 8
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2
+--R 42d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 8
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 3 2 +-+
+--R (6b d x + (28a b d - 14b c)x)\|x
+--R /
+--R 2
+--R 21d
+--R Type: Union(Expression(Integer),...)
+--E 1315
+
+--S 1316 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 +-+
+--R 2d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 8
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2 +-+
+--R 2d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 8
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 +-+
+--R 4d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R atan
+--R 8
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 2d \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1316
+
+--S 1317 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1317
+
+)clear all
+
+--S 1318 of 1397
+t0:=(a+b*x^2)^2/((c+d*x^2)*sqrt(x))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 2 +-+
+--R (d x + c)\|x
+--R Type: Expression(Integer)
+--E 1318
+
+--S 1319 of 1397
+r0:=2/5*b^2*x^(5/2)/d-(b*c-a*d)^2*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/_
+ c^(1/4))/(c^(3/4)*d^(9/4)*sqrt(2))+(b*c-a*d)^2*atan(1+d^(1/4)*_
+ sqrt(2)*sqrt(x)/c^(1/4))/(c^(3/4)*d^(9/4)*sqrt(2))-1/2*(b*c-a*d)^2*_
+ log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(3/4)*_
+ d^(9/4)*sqrt(2))+1/2*(b*c-a*d)^2*log(sqrt(c)+x*sqrt(d)+c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(3/4)*d^(9/4)*sqrt(2))-_
+ 2*b*(b*c-2*a*d)*sqrt(x)/d^2
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - 10a b c d + 5b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + 10a b c d - 5b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (10a d - 20a b c d + 10b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (10a d - 20a b c d + 10b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 2 +-+4+-+3 4+-+ +-+
+--R (4b d x + 40a b d - 20b c)\|2 \|c \|d \|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 10d \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1319
+
+--S 1320 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R 5d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16c d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2
+--R 2c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16c d
+--R ,
+--R 4
+--R +
+--R -
+--R 2
+--R 5d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16c d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 2
+--R 2c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 3 9
+--R 16c d
+--R ,
+--R 4
+--R +
+--R -
+--R 2
+--R 10d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 2
+--R 2c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2 2 2 +-+
+--R (2b d x + 20a b d - 10b c)\|x
+--R /
+--R 2
+--R 5d
+--R Type: Union(Expression(Integer),...)
+--E 1320
+
+--S 1321 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 +-+
+--R 2d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2
+--R 2c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16c d
+--R ,
+--R 4
+--R +
+--R -
+--R 2 +-+
+--R 2d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 2
+--R 2c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 3 9
+--R 16c d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R -
+--R 2 +-+
+--R 4d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R atan
+--R 2
+--R 2c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 2d \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1321
+
+--S 1322 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1322
+
+)clear all
+
+--S 1323 of 1397
+t0:=(a+b*x^2)^2/(x^(3/2)*(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 3 +-+
+--R (d x + c x)\|x
+--R Type: Expression(Integer)
+--E 1323
+
+--S 1324 of 1397
+r0:=2/3*b^2*x^(3/2)/d+(b*c-a*d)^2*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/_
+ c^(1/4))/(c^(5/4)*d^(7/4)*sqrt(2))-(b*c-a*d)^2*atan(1+d^(1/4)*_
+ sqrt(2)*sqrt(x)/c^(1/4))/(c^(5/4)*d^(7/4)*sqrt(2))-1/2*(b*c-a*d)^2*_
+ log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(5/4)*_
+ d^(7/4)*sqrt(2))+1/2*(b*c-a*d)^2*log(sqrt(c)+x*sqrt(d)+c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(5/4)*d^(7/4)*sqrt(2))-2*a^2/(c*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d - 6a b c d + 3b c )\|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 2 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d + 6a b c d - 3b c )\|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 +-+ \|2 \|d \|x + \|c
+--R (- 6a d + 12a b c d - 6b c )\|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 +-+ \|2 \|d \|x - \|c
+--R (- 6a d + 12a b c d - 6b c )\|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 2 +-+4+-+4+-+3
+--R (4b c x - 12a d)\|2 \|c \|d
+--R /
+--R +-+4+-+4+-+3 +-+
+--R 6c d\|2 \|c \|d \|x
+--R Type: Expression(Integer)
+--E 1324
+
+--S 1325 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 5 7
+--R 16c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 5
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 7
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 5 7
+--R 16c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 5
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 7
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 6c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 5 7
+--R 16c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 4 5
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 7
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 2
+--R 2b c x - 6a d
+--R /
+--R +-+
+--R 3c d\|x
+--R Type: Union(Expression(Integer),...)
+--E 1325
+
+--S 1326 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R -
+--R +-+
+--R 2c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 5 7
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 5
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 7
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R +-+
+--R 2c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 5 7
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 5
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 7
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (2a d - 4a b c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (2a d - 4a b c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R -
+--R +-+
+--R 4c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 5 7
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R atan
+--R 4 5
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 7
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R +-+4+-+4+-+3
+--R 2c d\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1326
+
+--S 1327 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1327
+
+)clear all
+
+--S 1328 of 1397
+t0:=(a+b*x^2)^2/(x^(5/2)*(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 4 2 +-+
+--R (d x + c x )\|x
+--R Type: Expression(Integer)
+--E 1328
+
+--S 1329 of 1397
+r0:=-2/3*a^2/(c*x^(3/2))+(b*c-a*d)^2*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(7/4)*d^(5/4)*sqrt(2))-(b*c-a*d)^2*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(7/4)*d^(5/4)*_
+ sqrt(2))+1/2*(b*c-a*d)^2*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(c^(7/4)*d^(5/4)*sqrt(2))-1/2*(b*c-a*d)^2*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(7/4)*_
+ d^(5/4)*sqrt(2))+2*b^2*sqrt(x)/d
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d + 6a b c d - 3b c )x\|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 2 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d - 6a b c d + 3b c )x\|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 +-+ \|2 \|d \|x + \|c
+--R (- 6a d + 12a b c d - 6b c )x\|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 +-+ \|2 \|d \|x - \|c
+--R (- 6a d + 12a b c d - 6b c )x\|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 2 +-+4+-+3 4+-+
+--R (12b c x - 4a d)\|2 \|c \|d
+--R /
+--R +-+4+-+3 4+-+ +-+
+--R 6c d x\|2 \|c \|d \|x
+--R Type: Expression(Integer)
+--E 1329
+
+--S 1330 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3c d x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2
+--R 2c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16c d
+--R ,
+--R 4
+--R +
+--R 3c d x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 2
+--R 2c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16c d
+--R ,
+--R 4
+--R +
+--R 6c d x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 2
+--R 2c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2 2 2
+--R 6b c x - 2a d
+--R /
+--R +-+
+--R 3c d x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1330
+
+--S 1331 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R -
+--R +-+
+--R 2c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2
+--R 2c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16c d
+--R ,
+--R 4
+--R +
+--R +-+
+--R 2c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 2
+--R 2c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16c d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (2a d - 4a b c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (2a d - 4a b c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+
+--R 4c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R atan
+--R 2
+--R 2c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R /
+--R +-+4+-+3 4+-+
+--R 2c d\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1331
+
+--S 1332 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1332
+
+)clear all
+
+--S 1333 of 1397
+t0:=(a+b*x^2)^2/(x^(7/2)*(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 5 3 +-+
+--R (d x + c x )\|x
+--R Type: Expression(Integer)
+--E 1333
+
+--S 1334 of 1397
+r0:=-2/5*a^2/(c*x^(5/2))-(b*c-a*d)^2*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(9/4)*d^(3/4)*sqrt(2))+(b*c-a*d)^2*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(9/4)*d^(3/4)*_
+ sqrt(2))+1/2*(b*c-a*d)^2*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(c^(9/4)*d^(3/4)*sqrt(2))-1/2*(b*c-a*d)^2*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(9/4)*_
+ d^(3/4)*sqrt(2))-2*a*(2*b*c-a*d)/(c^2*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + 10a b c d - 5b c )x \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 2 2 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - 10a b c d + 5b c )x \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 2 +-+ \|2 \|d \|x + \|c
+--R (10a d - 20a b c d + 10b c )x \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 2 +-+ \|2 \|d \|x - \|c
+--R (10a d - 20a b c d + 10b c )x \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 2 +-+4+-+4+-+3
+--R ((20a d - 40a b c)x - 4a c)\|2 \|c \|d
+--R /
+--R 2 2 +-+4+-+4+-+3 +-+
+--R 10c x \|2 \|c \|d \|x
+--R Type: Expression(Integer)
+--E 1334
+
+--S 1335 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R 5c x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 2
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2 2
+--R 5c x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 2
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 9 3
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2
+--R 10c x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 7 2
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 2
+--R (10a d - 20a b c)x - 2a c
+--R /
+--R 2 2 +-+
+--R 5c x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1335
+
+--S 1336 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 +-+
+--R 2c \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 2
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2 +-+
+--R 2c \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 2
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 9 3
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 +-+
+--R 4c \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R atan
+--R 7 2
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 2c \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1336
+
+--S 1337 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1337
+
+)clear all
+
+--S 1338 of 1397
+t0:=(a+b*x^2)^2/(x^(9/2)*(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 6 4 +-+
+--R (d x + c x )\|x
+--R Type: Expression(Integer)
+--E 1338
+
+--S 1339 of 1397
+r0:=-2/7*a^2/(c*x^(7/2))-2/3*a*(2*b*c-a*d)/(c^2*x^(3/2))-(b*c-a*d)^2*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(11/4)*d^(1/4)*sqrt(2))+_
+ (b*c-a*d)^2*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(11/4)*_
+ d^(1/4)*sqrt(2))-1/2*(b*c-a*d)^2*log(sqrt(c)+x*sqrt(d)-c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(11/4)*d^(1/4)*sqrt(2))+1/2*(b*c-a*d)^2*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(11/4)*_
+ d^(1/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2 2 3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (21a d - 42a b c d + 21b c )x \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 2 3 +-+
+--R (- 21a d + 42a b c d - 21b c )x \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 3 +-+ \|2 \|d \|x + \|c
+--R (42a d - 84a b c d + 42b c )x \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 3 +-+ \|2 \|d \|x - \|c
+--R (42a d - 84a b c d + 42b c )x \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 2 +-+4+-+3 4+-+
+--R ((28a d - 56a b c)x - 12a c)\|2 \|c \|d
+--R /
+--R 2 3 +-+4+-+3 4+-+ +-+
+--R 42c x \|2 \|c \|d \|x
+--R Type: Expression(Integer)
+--E 1339
+
+--S 1340 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3
+--R 21c x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 3
+--R 2c
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R +
+--R -
+--R 2 3
+--R 21c x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 3
+--R 2c
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R +
+--R -
+--R 2 3
+--R 42c x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 3
+--R 2c
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2 2 2
+--R (14a d - 28a b c)x - 6a c
+--R /
+--R 2 3 +-+
+--R 21c x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1340
+
+--S 1341 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 +-+
+--R 2c \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 3
+--R 2c
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R +
+--R -
+--R 2 +-+
+--R 2c \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 3
+--R 2c
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R -
+--R 2 +-+
+--R 4c \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R atan
+--R 3
+--R 2c
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 2c \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1341
+
+--S 1342 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1342
+
+)clear all
+
+--S 1343 of 1397
+t0:=x^(7/2)*(a+b*x^2)^2/(c+d*x^2)^2
+--R
+--R
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R (1) ---------------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Expression(Integer)
+--E 1343
+
+--S 1344 of 1397
+r0:=-1/10*(13*b*c-5*a*d)*(b*c-a*d)*x^(5/2)/(c*d^3)+2/9*b^2*x^(9/2)/d^2+_
+ 1/2*(b*c-a*d)^2*x^(9/2)/(c*d^2*(c+d*x^2))+1/4*c^(1/4)*(13*b*c-5*a*d)*_
+ (b*c-a*d)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(d^(17/4)*sqrt(2))-_
+ 1/4*c^(1/4)*(13*b*c-5*a*d)*(b*c-a*d)*atan(1+d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(d^(17/4)*sqrt(2))+1/8*c^(1/4)*(13*b*c-5*a*d)*_
+ (b*c-a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (d^(17/4)*sqrt(2))-1/8*c^(1/4)*(13*b*c-5*a*d)*(b*c-a*d)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(d^(17/4)*_
+ sqrt(2))+1/2*(13*b*c-5*a*d)*(b*c-a*d)*sqrt(x)/d^4
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2
+--R (- 225a d + 810a b c d - 585b c d)x - 225a c d + 810a b c d
+--R +
+--R 2 3
+--R - 585b c
+--R *
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (225a d - 810a b c d + 585b c d)x + 225a c d - 810a b c d
+--R +
+--R 2 3
+--R 585b c
+--R *
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (- 450a d + 1620a b c d - 1170b c d)x - 450a c d + 1620a b c d
+--R +
+--R 2 3
+--R - 1170b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|d \|x + \|c
+--R \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (- 450a d + 1620a b c d - 1170b c d)x - 450a c d + 1620a b c d
+--R +
+--R 2 3
+--R - 1170b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|d \|x - \|c
+--R \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 6 3 2 2 4
+--R 80b d x + (288a b d - 208b c d )x
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (720a d - 2592a b c d + 1872b c d)x + 900a c d - 3240a b c d
+--R +
+--R 2 3
+--R 2340b c
+--R *
+--R +-+4+-+ +-+
+--R \|2 \|d \|x
+--R /
+--R 5 2 4 +-+4+-+
+--R (360d x + 360c d )\|2 \|d
+--R Type: Expression(Integer)
+--E 1344
+
+--S 1345 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 2 4
+--R (- 90d x - 90c d )
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R - 625a c d + 9000a b c d - 55100a b c d + 186840a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2
+--R - 383046a b c d + 485784a b c d - 372476a b c d
+--R +
+--R 7 8 8 9
+--R 158184a b c d - 28561b c
+--R /
+--R 17
+--R 4096d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (5a d - 18a b c d + 13b c )\|x
+--R +
+--R 4
+--R 8d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6
+--R - 625a c d + 9000a b c d - 55100a b c d
+--R +
+--R 5 3 4 5 4 4 5 4 3 5 6 3
+--R 186840a b c d - 383046a b c d + 485784a b c d
+--R +
+--R 2 6 7 2 7 8 8 9
+--R - 372476a b c d + 158184a b c d - 28561b c
+--R /
+--R 17
+--R 4096d
+--R ,
+--R 4
+--R +
+--R 5 2 4
+--R (90d x + 90c d )
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R - 625a c d + 9000a b c d - 55100a b c d + 186840a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2
+--R - 383046a b c d + 485784a b c d - 372476a b c d
+--R +
+--R 7 8 8 9
+--R 158184a b c d - 28561b c
+--R /
+--R 17
+--R 4096d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (5a d - 18a b c d + 13b c )\|x
+--R +
+--R -
+--R 4
+--R 8d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6
+--R - 625a c d + 9000a b c d - 55100a b c d
+--R +
+--R 5 3 4 5 4 4 5 4 3 5 6 3
+--R 186840a b c d - 383046a b c d + 485784a b c d
+--R +
+--R 2 6 7 2 7 8 8 9
+--R - 372476a b c d + 158184a b c d - 28561b c
+--R /
+--R 17
+--R 4096d
+--R ,
+--R 4
+--R +
+--R 5 2 4
+--R (180d x + 180c d )
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R - 625a c d + 9000a b c d - 55100a b c d + 186840a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2
+--R - 383046a b c d + 485784a b c d - 372476a b c d
+--R +
+--R 7 8 8 9
+--R 158184a b c d - 28561b c
+--R /
+--R 17
+--R 4096d
+--R ,
+--R 4
+--R *
+--R atan
+--R 4
+--R 8d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6
+--R - 625a c d + 9000a b c d - 55100a b c d
+--R +
+--R 5 3 4 5 4 4 5 4 3 5 6 3
+--R 186840a b c d - 383046a b c d + 485784a b c d
+--R +
+--R 2 6 7 2 7 8 8 9
+--R - 372476a b c d + 158184a b c d - 28561b c
+--R /
+--R 17
+--R 4096d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (5a d - 18a b c d + 13b c )\|x
+--R +
+--R 2 3 6 3 2 2 4
+--R 20b d x + (72a b d - 52b c d )x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R (180a d - 648a b c d + 468b c d)x + 225a c d - 810a b c d + 585b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 5 2 4
+--R 90d x + 90c d
+--R Type: Union(Expression(Integer),...)
+--E 1345
+
+--S 1346 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - 18a b c d + 13b c )\|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R -
+--R 4 +-+
+--R 8d \|2
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R - 625a c d + 9000a b c d - 55100a b c d + 186840a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2
+--R - 383046a b c d + 485784a b c d - 372476a b c d
+--R +
+--R 7 8 8 9
+--R 158184a b c d - 28561b c
+--R /
+--R 17
+--R 4096d
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (5a d - 18a b c d + 13b c )\|x
+--R +
+--R 4
+--R 8d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6
+--R - 625a c d + 9000a b c d - 55100a b c d
+--R +
+--R 5 3 4 5 4 4 5 4 3 5 6 3
+--R 186840a b c d - 383046a b c d + 485784a b c d
+--R +
+--R 2 6 7 2 7 8 8 9
+--R - 372476a b c d + 158184a b c d - 28561b c
+--R /
+--R 17
+--R 4096d
+--R ,
+--R 4
+--R +
+--R 4 +-+
+--R 8d \|2
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R - 625a c d + 9000a b c d - 55100a b c d + 186840a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2
+--R - 383046a b c d + 485784a b c d - 372476a b c d
+--R +
+--R 7 8 8 9
+--R 158184a b c d - 28561b c
+--R /
+--R 17
+--R 4096d
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (5a d - 18a b c d + 13b c )\|x
+--R +
+--R -
+--R 4
+--R 8d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6
+--R - 625a c d + 9000a b c d - 55100a b c d
+--R +
+--R 5 3 4 5 4 4 5 4 3 5 6 3
+--R 186840a b c d - 383046a b c d + 485784a b c d
+--R +
+--R 2 6 7 2 7 8 8 9
+--R - 372476a b c d + 158184a b c d - 28561b c
+--R /
+--R 17
+--R 4096d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + 18a b c d - 13b c )\|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|d \|x + \|c
+--R (10a d - 36a b c d + 26b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|d \|x - \|c
+--R (10a d - 36a b c d + 26b c )\|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 4 +-+
+--R 16d \|2
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R - 625a c d + 9000a b c d - 55100a b c d + 186840a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2
+--R - 383046a b c d + 485784a b c d - 372476a b c d
+--R +
+--R 7 8 8 9
+--R 158184a b c d - 28561b c
+--R /
+--R 17
+--R 4096d
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|d
+--R *
+--R atan
+--R 4
+--R 8d
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 2 3 6
+--R - 625a c d + 9000a b c d - 55100a b c d
+--R +
+--R 5 3 4 5 4 4 5 4 3 5 6 3
+--R 186840a b c d - 383046a b c d + 485784a b c d
+--R +
+--R 2 6 7 2 7 8 8 9
+--R - 372476a b c d + 158184a b c d - 28561b c
+--R /
+--R 17
+--R 4096d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (5a d - 18a b c d + 13b c )\|x
+--R /
+--R 4 +-+4+-+
+--R 8d \|2 \|d
+--R Type: Expression(Integer)
+--E 1346
+
+--S 1347 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1347
+
+)clear all
+
+--S 1348 of 1397
+t0:=x^(5/2)*(a+b*x^2)^2/(c+d*x^2)^2
+--R
+--R
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R (1) ---------------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Expression(Integer)
+--E 1348
+
+--S 1349 of 1397
+r0:=-1/6*(11*b*c-3*a*d)*(b*c-a*d)*x^(3/2)/(c*d^3)+2/7*b^2*x^(7/2)/d^2+_
+ 1/2*(b*c-a*d)^2*x^(7/2)/(c*d^2*(c+d*x^2))-1/4*(11*b*c-3*a*d)*_
+ (b*c-a*d)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(1/4)*d^(15/4)*_
+ sqrt(2))+1/4*(11*b*c-3*a*d)*(b*c-a*d)*atan(1+d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(1/4)*d^(15/4)*sqrt(2))+1/8*(11*b*c-3*a*d)*_
+ (b*c-a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(1/4)*d^(15/4)*sqrt(2))-1/8*(11*b*c-3*a*d)*(b*c-a*d)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(1/4)*_
+ d^(15/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2
+--R (- 63a d + 294a b c d - 231b c d)x - 63a c d + 294a b c d
+--R +
+--R 2 3
+--R - 231b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((63a d - 294a b c d + 231b c d)x + 63a c d - 294a b c d + 231b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (126a d - 588a b c d + 462b c d)x + 126a c d - 588a b c d
+--R +
+--R 2 3
+--R 462b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (126a d - 588a b c d + 462b c d)x + 126a c d - 588a b c d
+--R +
+--R 2 3
+--R 462b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 5 2 2 3
+--R 48b d x + (224a b d - 176b c d)x
+--R +
+--R 2 2 2 2
+--R (- 84a d + 392a b c d - 308b c )x
+--R *
+--R +-+4+-+4+-+3 +-+
+--R \|2 \|c \|d \|x
+--R /
+--R 4 2 3 +-+4+-+4+-+3
+--R (168d x + 168c d )\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1349
+
+--S 1350 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 3
+--R (42d x + 42c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d + 1512a b c d - 11772a b c d + 49560a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 122566a b c d + 181720a b c d - 158268a b c d
+--R +
+--R 7 7 8 8
+--R 74536a b c d - 14641b c
+--R /
+--R 15
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 27a d - 378a b c d + 2061a b c d - 5516a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 7557a b c d - 5082a b c d + 1331b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 11
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d + 1512a b c d - 11772a b c d + 49560a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 122566a b c d + 181720a b c d - 158268a b c d
+--R +
+--R 7 7 8 8
+--R 74536a b c d - 14641b c
+--R /
+--R 15
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 2 3
+--R (- 42d x - 42c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d + 1512a b c d - 11772a b c d + 49560a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 122566a b c d + 181720a b c d - 158268a b c d
+--R +
+--R 7 7 8 8
+--R 74536a b c d - 14641b c
+--R /
+--R 15
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 27a d - 378a b c d + 2061a b c d - 5516a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 7557a b c d - 5082a b c d + 1331b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 11
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 81a d + 1512a b c d - 11772a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 49560a b c d - 122566a b c d + 181720a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 158268a b c d + 74536a b c d - 14641b c
+--R /
+--R 15
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 2 3
+--R (84d x + 84c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d + 1512a b c d - 11772a b c d + 49560a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 122566a b c d + 181720a b c d - 158268a b c d
+--R +
+--R 7 7 8 8
+--R 74536a b c d - 14641b c
+--R /
+--R 15
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 11
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d + 1512a b c d - 11772a b c d + 49560a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 122566a b c d + 181720a b c d - 158268a b c d
+--R +
+--R 7 7 8 8
+--R 74536a b c d - 14641b c
+--R /
+--R 15
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 27a d - 378a b c d + 2061a b c d - 5516a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 7557a b c d - 5082a b c d + 1331b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 5 2 2 3 2 2 2 2 +-+
+--R (12b d x + (56a b d - 44b c d)x + (- 21a d + 98a b c d - 77b c )x)\|x
+--R /
+--R 4 2 3
+--R 42d x + 42c d
+--R Type: Union(Expression(Integer),...)
+--E 1350
+
+--S 1351 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d - 14a b c d + 11b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 +-+
+--R 8d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d + 1512a b c d - 11772a b c d + 49560a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 122566a b c d + 181720a b c d - 158268a b c d
+--R +
+--R 7 7 8 8
+--R 74536a b c d - 14641b c
+--R /
+--R 15
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 27a d - 378a b c d + 2061a b c d - 5516a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 7557a b c d - 5082a b c d + 1331b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 11
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d + 1512a b c d - 11772a b c d + 49560a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 122566a b c d + 181720a b c d - 158268a b c d
+--R +
+--R 7 7 8 8
+--R 74536a b c d - 14641b c
+--R /
+--R 15
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 3 +-+
+--R 8d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d + 1512a b c d - 11772a b c d + 49560a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 122566a b c d + 181720a b c d - 158268a b c d
+--R +
+--R 7 7 8 8
+--R 74536a b c d - 14641b c
+--R /
+--R 15
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 27a d - 378a b c d + 2061a b c d - 5516a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 7557a b c d - 5082a b c d + 1331b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 11
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 81a d + 1512a b c d - 11772a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 49560a b c d - 122566a b c d + 181720a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 158268a b c d + 74536a b c d - 14641b c
+--R /
+--R 15
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d + 14a b c d - 11b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 6a d + 28a b c d - 22b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 6a d + 28a b c d - 22b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 +-+
+--R 16d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d + 1512a b c d - 11772a b c d + 49560a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 122566a b c d + 181720a b c d - 158268a b c d
+--R +
+--R 7 7 8 8
+--R 74536a b c d - 14641b c
+--R /
+--R 15
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R atan
+--R 11
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d + 1512a b c d - 11772a b c d + 49560a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 122566a b c d + 181720a b c d - 158268a b c d
+--R +
+--R 7 7 8 8
+--R 74536a b c d - 14641b c
+--R /
+--R 15
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 27a d - 378a b c d + 2061a b c d - 5516a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 7557a b c d - 5082a b c d + 1331b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3 +-+4+-+4+-+3
+--R 8d \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1351
+
+--S 1352 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1352
+
+)clear all
+
+--S 1353 of 1397
+t0:=x^(3/2)*(a+b*x^2)^2/(c+d*x^2)^2
+--R
+--R
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R (1) --------------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Expression(Integer)
+--E 1353
+
+--S 1354 of 1397
+r0:=2/5*b^2*x^(5/2)/d^2+1/2*(b*c-a*d)^2*x^(5/2)/(c*d^2*(c+d*x^2))-_
+ 1/4*(b*c-a*d)*(9*b*c-a*d)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(3/4)*d^(13/4)*sqrt(2))+1/4*(b*c-a*d)*(9*b*c-a*d)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(3/4)*d^(13/4)*_
+ sqrt(2))-1/8*(b*c-a*d)*(9*b*c-a*d)*log(sqrt(c)+x*sqrt(d)-_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(3/4)*d^(13/4)*sqrt(2))+_
+ 1/8*(b*c-a*d)*(9*b*c-a*d)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(c^(3/4)*d^(13/4)*sqrt(2))-1/2*(b*c-a*d)*_
+ (9*b*c-a*d)*sqrt(x)/(c*d^3)
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((5a d - 50a b c d + 45b c d)x + 5a c d - 50a b c d + 45b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 5a d + 50a b c d - 45b c d)x - 5a c d + 50a b c d - 45b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((10a d - 100a b c d + 90b c d)x + 10a c d - 100a b c d + 90b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((10a d - 100a b c d + 90b c d)x + 10a c d - 100a b c d + 90b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R (16b d x + (160a b d - 144b c d)x - 20a d + 200a b c d - 180b c )
+--R *
+--R +-+4+-+3 4+-+ +-+
+--R \|2 \|c \|d \|x
+--R /
+--R 4 2 3 +-+4+-+3 4+-+
+--R (40d x + 40c d )\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1354
+
+--S 1355 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 3
+--R (10d x + 10c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 40a b c d - 636a b c d + 5080a b c d - 21286a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 45720a b c d - 51516a b c d + 29160a b c d - 6561b c
+--R /
+--R 3 13
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 10a b c d + 9b c )\|x
+--R +
+--R 3
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 3 13
+--R 4096c d
+--R ,
+--R 4
+--R +
+--R 4 2 3
+--R (- 10d x - 10c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 40a b c d - 636a b c d + 5080a b c d - 21286a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 45720a b c d - 51516a b c d + 29160a b c d - 6561b c
+--R /
+--R 3 13
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 10a b c d + 9b c )\|x
+--R +
+--R -
+--R 3
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 3 13
+--R 4096c d
+--R ,
+--R 4
+--R +
+--R 4 2 3
+--R (- 20d x - 20c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 40a b c d - 636a b c d + 5080a b c d - 21286a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 45720a b c d - 51516a b c d + 29160a b c d - 6561b c
+--R /
+--R 3 13
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 3
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 3 13
+--R 4096c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 10a b c d + 9b c )\|x
+--R +
+--R 2 2 4 2 2 2 2 2 2 2 +-+
+--R (4b d x + (40a b d - 36b c d)x - 5a d + 50a b c d - 45b c )\|x
+--R /
+--R 4 2 3
+--R 10d x + 10c d
+--R Type: Union(Expression(Integer),...)
+--E 1355
+
+--S 1356 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 10a b c d - 9b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 +-+
+--R 8d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 40a b c d - 636a b c d + 5080a b c d - 21286a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 45720a b c d - 51516a b c d + 29160a b c d - 6561b c
+--R /
+--R 3 13
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 10a b c d + 9b c )\|x
+--R +
+--R 3
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 3 13
+--R 4096c d
+--R ,
+--R 4
+--R +
+--R -
+--R 3 +-+
+--R 8d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 3 13
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 10a b c d + 9b c )\|x
+--R +
+--R -
+--R 3
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 3 13
+--R 4096c d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 10a b c d + 9b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 2a d + 20a b c d - 18b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 2a d + 20a b c d - 18b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R -
+--R 3 +-+
+--R 16d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 3 13
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R atan
+--R 3
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 3 13
+--R 4096c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 10a b c d + 9b c )\|x
+--R /
+--R 3 +-+4+-+3 4+-+
+--R 8d \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1356
+
+--S 1357 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1357
+
+)clear all
+
+--S 1358 of 1397
+t0:=(a+b*x^2)^2*sqrt(x)/(c+d*x^2)^2
+--R
+--R
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R (1) -------------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Expression(Integer)
+--E 1358
+
+--S 1359 of 1397
+r0:=2/3*b^2*x^(3/2)/d^2+1/2*(b*c-a*d)^2*x^(3/2)/(c*d^2*(c+d*x^2))+_
+ 1/4*(b*c-a*d)*(7*b*c+a*d)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(5/4)*d^(11/4)*sqrt(2))-1/4*(b*c-a*d)*(7*b*c+a*d)*atan(1+_
+ d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(5/4)*d^(11/4)*sqrt(2))-1/8*_
+ (b*c-a*d)*(7*b*c+a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(c^(5/4)*d^(11/4)*sqrt(2))+1/8*(b*c-a*d)*(7*b*_
+ c+a*d)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(5/4)*d^(11/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 3a d - 18a b c d + 21b c d)x - 3a c d - 18a b c d + 21b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d + 18a b c d - 21b c d)x + 3a c d + 18a b c d - 21b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((6a d + 36a b c d - 42b c d)x + 6a c d + 36a b c d - 42b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((6a d + 36a b c d - 42b c d)x + 6a c d + 36a b c d - 42b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 +-+4+-+4+-+3 +-+
+--R (16b c d x + (12a d - 24a b c d + 28b c )x)\|2 \|c \|d \|x
+--R /
+--R 3 2 2 2 +-+4+-+4+-+3
+--R (24c d x + 24c d )\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1359
+
+--S 1360 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2 2
+--R (6c d x + 6c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d - 24a b c d - 188a b c d - 360a b c d + 1434a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 2520a b c d - 9212a b c d + 8232a b c d - 2401b c
+--R /
+--R 5 11
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d + 18a b c d + 87a b c d - 36a b c d - 609a b c d
+--R +
+--R 5 5 6 6
+--R 882a b c d - 343b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 8
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1434a b c d + 2520a b c d - 9212a b c d
+--R +
+--R 7 7 8 8
+--R 8232a b c d - 2401b c
+--R /
+--R 5 11
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 2 2
+--R (- 6c d x - 6c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d - 24a b c d - 188a b c d - 360a b c d + 1434a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 2520a b c d - 9212a b c d + 8232a b c d - 2401b c
+--R /
+--R 5 11
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d + 18a b c d + 87a b c d - 36a b c d - 609a b c d
+--R +
+--R 5 5 6 6
+--R 882a b c d - 343b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 8
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1434a b c d + 2520a b c d - 9212a b c d
+--R +
+--R 7 7 8 8
+--R 8232a b c d - 2401b c
+--R /
+--R 5 11
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 2 2
+--R (12c d x + 12c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d - 24a b c d - 188a b c d - 360a b c d + 1434a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 2520a b c d - 9212a b c d + 8232a b c d - 2401b c
+--R /
+--R 5 11
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 4 8
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1434a b c d + 2520a b c d - 9212a b c d
+--R +
+--R 7 7 8 8
+--R 8232a b c d - 2401b c
+--R /
+--R 5 11
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d + 18a b c d + 87a b c d - 36a b c d - 609a b c d
+--R +
+--R 5 5 6 6
+--R 882a b c d - 343b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 3 2 2 2 2 +-+
+--R (4b c d x + (3a d - 6a b c d + 7b c )x)\|x
+--R /
+--R 3 2 2 2
+--R 6c d x + 6c d
+--R Type: Union(Expression(Integer),...)
+--E 1360
+
+--S 1361 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d + 6a b c d - 7b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 +-+
+--R 8c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d - 24a b c d - 188a b c d - 360a b c d + 1434a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 2520a b c d - 9212a b c d + 8232a b c d - 2401b c
+--R /
+--R 5 11
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d + 18a b c d + 87a b c d - 36a b c d - 609a b c d
+--R +
+--R 5 5 6 6
+--R 882a b c d - 343b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 8
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1434a b c d + 2520a b c d - 9212a b c d
+--R +
+--R 7 7 8 8
+--R 8232a b c d - 2401b c
+--R /
+--R 5 11
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2 +-+
+--R 8c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1434a b c d + 2520a b c d - 9212a b c d + 8232a b c d
+--R +
+--R 8 8
+--R - 2401b c
+--R /
+--R 5 11
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d + 18a b c d + 87a b c d - 36a b c d - 609a b c d
+--R +
+--R 5 5 6 6
+--R 882a b c d - 343b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 8
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1434a b c d + 2520a b c d - 9212a b c d
+--R +
+--R 7 7 8 8
+--R 8232a b c d - 2401b c
+--R /
+--R 5 11
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d - 6a b c d + 7b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 2a d - 12a b c d + 14b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 2a d - 12a b c d + 14b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 +-+
+--R 16c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d - 24a b c d - 188a b c d - 360a b c d + 1434a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 2520a b c d - 9212a b c d + 8232a b c d - 2401b c
+--R /
+--R 5 11
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R atan
+--R 4 8
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1434a b c d + 2520a b c d - 9212a b c d
+--R +
+--R 7 7 8 8
+--R 8232a b c d - 2401b c
+--R /
+--R 5 11
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d + 18a b c d + 87a b c d - 36a b c d - 609a b c d
+--R +
+--R 5 5 6 6
+--R 882a b c d - 343b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 8c d \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1361
+
+--S 1362 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1362
+
+)clear all
+
+--S 1363 of 1397
+t0:=(a+b*x^2)^2/((c+d*x^2)^2*sqrt(x))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------------
+--R 2 4 2 2 +-+
+--R (d x + 2c d x + c )\|x
+--R Type: Expression(Integer)
+--E 1363
+
+--S 1364 of 1397
+r0:=1/4*(b*c-a*d)*(5*b*c+3*a*d)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(7/4)*d^(9/4)*sqrt(2))-1/4*(b*c-a*d)*(5*b*c+3*a*d)*atan(1+_
+ d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(7/4)*d^(9/4)*sqrt(2))+1/8*_
+ (b*c-a*d)*(5*b*c+3*a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(c^(7/4)*d^(9/4)*sqrt(2))-1/8*(b*c-a*d)*(5*b*c+_
+ 3*a*d)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(7/4)*d^(9/4)*sqrt(2))+2*b^2*sqrt(x)/d^2+1/2*(b*c-a*d)^2*_
+ sqrt(x)/(c*d^2*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d + 2a b c d - 5b c d)x + 3a c d + 2a b c d - 5b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 3a d - 2a b c d + 5b c d)x - 3a c d - 2a b c d + 5b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((6a d + 4a b c d - 10b c d)x + 6a c d + 4a b c d - 10b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((6a d + 4a b c d - 10b c d)x + 6a c d + 4a b c d - 10b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 2 2 2 2 +-+4+-+3 4+-+ +-+
+--R (16b c d x + 4a d - 8a b c d + 20b c )\|2 \|c \|d \|x
+--R /
+--R 3 2 2 2 +-+4+-+3 4+-+
+--R (8c d x + 8c d )\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1364
+
+--S 1365 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2 2
+--R (2c d x + 2c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d - 646a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 1640a b c d + 900a b c d + 1000a b c d - 625b c
+--R /
+--R 7 9
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (3a d + 2a b c d - 5b c )\|x
+--R +
+--R 2 2
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d - 1640a b c d + 900a b c d + 1000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 7 9
+--R 4096c d
+--R ,
+--R 4
+--R +
+--R 3 2 2 2
+--R (- 2c d x - 2c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d - 646a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 1640a b c d + 900a b c d + 1000a b c d - 625b c
+--R /
+--R 7 9
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (3a d + 2a b c d - 5b c )\|x
+--R +
+--R -
+--R 2 2
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 646a b c d - 1640a b c d + 900a b c d
+--R +
+--R 7 7 8 8
+--R 1000a b c d - 625b c
+--R /
+--R 7 9
+--R 4096c d
+--R ,
+--R 4
+--R +
+--R 3 2 2 2
+--R (- 4c d x - 4c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d - 646a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 1640a b c d + 900a b c d + 1000a b c d - 625b c
+--R /
+--R 7 9
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 2 2
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d - 1640a b c d + 900a b c d + 1000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 7 9
+--R 4096c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (3a d + 2a b c d - 5b c )\|x
+--R +
+--R 2 2 2 2 2 2 +-+
+--R (4b c d x + a d - 2a b c d + 5b c )\|x
+--R /
+--R 3 2 2 2
+--R 2c d x + 2c d
+--R Type: Union(Expression(Integer),...)
+--E 1365
+
+--S 1366 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d - 2a b c d + 5b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 +-+
+--R 8c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d - 646a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 1640a b c d + 900a b c d + 1000a b c d - 625b c
+--R /
+--R 7 9
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (3a d + 2a b c d - 5b c )\|x
+--R +
+--R 2 2
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d - 1640a b c d + 900a b c d + 1000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 7 9
+--R 4096c d
+--R ,
+--R 4
+--R +
+--R -
+--R 2 +-+
+--R 8c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d - 1640a b c d + 900a b c d + 1000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 7 9
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (3a d + 2a b c d - 5b c )\|x
+--R +
+--R -
+--R 2 2
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 646a b c d - 1640a b c d + 900a b c d
+--R +
+--R 7 7 8 8
+--R 1000a b c d - 625b c
+--R /
+--R 7 9
+--R 4096c d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d + 2a b c d - 5b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 6a d - 4a b c d + 10b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 6a d - 4a b c d + 10b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R -
+--R 2 +-+
+--R 16c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d - 1640a b c d + 900a b c d + 1000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 7 9
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R atan
+--R 2 2
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 646a b c d - 1640a b c d + 900a b c d
+--R +
+--R 7 7 8 8
+--R 1000a b c d - 625b c
+--R /
+--R 7 9
+--R 4096c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (3a d + 2a b c d - 5b c )\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 8c d \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1366
+
+--S 1367 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1367
+
+)clear all
+
+--S 1368 of 1397
+t0:=(a+b*x^2)^2/(x^(3/2)*(c+d*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) --------------------------
+--R 2 5 3 2 +-+
+--R (d x + 2c d x + c x)\|x
+--R Type: Expression(Integer)
+--E 1368
+
+--S 1369 of 1397
+r0:=-1/2*(b^2*c^2-2*a*b*c*d+5*a^2*d^2)*x^(3/2)/(c^2*d*(c+d*x^2))-_
+ 1/4*(b*c-a*d)*(3*b*c+5*a*d)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/_
+ c^(1/4))/(c^(9/4)*d^(7/4)*sqrt(2))+1/4*(b*c-a*d)*(3*b*c+5*a*d)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(9/4)*d^(7/4)*sqrt(2))+_
+ 1/8*(b*c-a*d)*(3*b*c+5*a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(c^(9/4)*d^(7/4)*sqrt(2))-1/8*(b*c-a*d)*_
+ (3*b*c+5*a*d)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(9/4)*d^(7/4)*sqrt(2))-2*a^2/(c*(c+d*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((5a d - 2a b c d - 3b c d)x + 5a c d - 2a b c d - 3b c )\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((- 5a d + 2a b c d + 3b c d)x - 5a c d + 2a b c d + 3b c )\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((- 10a d + 4a b c d + 6b c d)x - 10a c d + 4a b c d + 6b c )\|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((- 10a d + 4a b c d + 6b c d)x - 10a c d + 4a b c d + 6b c )\|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 2 2 2 2 +-+4+-+4+-+3
+--R ((- 20a d + 8a b c d - 4b c )x - 16a c d)\|2 \|c \|d
+--R /
+--R 2 2 2 3 +-+4+-+4+-+3 +-+
+--R (8c d x + 8c d)\|2 \|c \|d \|x
+--R Type: Expression(Integer)
+--E 1369
+
+--S 1370 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 3
+--R (- 2c d x - 2c d)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d - 81b c
+--R /
+--R 9 7
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 125a d - 150a b c d - 165a b c d + 172a b c d + 99a b c d
+--R +
+--R 5 5 6 6
+--R - 54a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 5
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d
+--R +
+--R 8 8
+--R - 81b c
+--R /
+--R 9 7
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 3
+--R (2c d x + 2c d)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d - 81b c
+--R /
+--R 9 7
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 125a d - 150a b c d - 165a b c d + 172a b c d + 99a b c d
+--R +
+--R 5 5 6 6
+--R - 54a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 5
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d + 1000a b c d + 900a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 1640a b c d - 646a b c d + 984a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R 324a b c d - 216a b c d - 81b c
+--R /
+--R 9 7
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 3
+--R (- 4c d x - 4c d)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d - 81b c
+--R /
+--R 9 7
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 7 5
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d
+--R +
+--R 8 8
+--R - 81b c
+--R /
+--R 9 7
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 125a d - 150a b c d - 165a b c d + 172a b c d + 99a b c d
+--R +
+--R 5 5 6 6
+--R - 54a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 2 2 2 2
+--R (- 5a d + 2a b c d - b c )x - 4a c d
+--R /
+--R 2 2 2 3 +-+
+--R (2c d x + 2c d)\|x
+--R Type: Union(Expression(Integer),...)
+--E 1370
+
+--S 1371 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + 2a b c d + 3b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R -
+--R 2 +-+
+--R 8c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d - 81b c
+--R /
+--R 9 7
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 125a d - 150a b c d - 165a b c d + 172a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 99a b c d - 54a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 5
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d + 1000a b c d + 900a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 1640a b c d - 646a b c d + 984a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R 324a b c d - 216a b c d - 81b c
+--R /
+--R 9 7
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 +-+
+--R 8c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d - 81b c
+--R /
+--R 9 7
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 125a d - 150a b c d - 165a b c d + 172a b c d + 99a b c d
+--R +
+--R 5 5 6 6
+--R - 54a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 5
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d + 1000a b c d + 900a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 1640a b c d - 646a b c d + 984a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R 324a b c d - 216a b c d - 81b c
+--R /
+--R 9 7
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - 2a b c d - 3b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (10a d - 4a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (10a d - 4a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R -
+--R 2 +-+
+--R 16c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d - 81b c
+--R /
+--R 9 7
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R atan
+--R 7 5
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d + 1000a b c d + 900a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 1640a b c d - 646a b c d + 984a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R 324a b c d - 216a b c d - 81b c
+--R /
+--R 9 7
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 125a d - 150a b c d - 165a b c d + 172a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 99a b c d - 54a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 8c d\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1371
+
+--S 1372 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1372
+
+)clear all
+
+--S 1373 of 1397
+t0:=(a+b*x^2)^2/(x^(5/2)*(c+d*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ---------------------------
+--R 2 6 4 2 2 +-+
+--R (d x + 2c d x + c x )\|x
+--R Type: Expression(Integer)
+--E 1373
+
+--S 1374 of 1397
+r0:=-2/3*a^2/(c*x^(3/2)*(c+d*x^2))-1/4*(b*c-a*d)*(b*c+7*a*d)*atan(1-_
+ d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(11/4)*d^(5/4)*sqrt(2))+1/4*_
+ (b*c-a*d)*(b*c+7*a*d)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(11/4)*d^(5/4)*sqrt(2))-1/8*(b*c-a*d)*(b*c+7*a*d)*log(sqrt(c)+_
+ x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(11/4)*d^(5/4)*_
+ sqrt(2))+1/8*(b*c-a*d)*(b*c+7*a*d)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(11/4)*d^(5/4)*sqrt(2))-1/6*(3*b^2*_
+ c^2-6*a*b*c*d+7*a^2*d^2)*sqrt(x)/(c^2*d*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 3
+--R (- 21a d + 18a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 21a c d + 18a b c d + 3b c )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((21a d - 18a b c d - 3b c d)x + (21a c d - 18a b c d - 3b c )x)
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 3
+--R (- 42a d + 36a b c d + 6b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 42a c d + 36a b c d + 6b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|d \|x + \|c
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 3
+--R (- 42a d + 36a b c d + 6b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 42a c d + 36a b c d + 6b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|d \|x - \|c
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 2 2 2 2 +-+4+-+3 4+-+
+--R ((- 28a d + 24a b c d - 12b c )x - 16a c d)\|2 \|c \|d
+--R /
+--R 2 2 3 3 +-+4+-+3 4+-+ +-+
+--R (24c d x + 24c d x)\|2 \|c \|d \|x
+--R Type: Expression(Integer)
+--E 1374
+
+--S 1375 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 3 3
+--R (- 6c d x - 6c d x)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 11 5
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (7a d - 6a b c d - b c )\|x
+--R +
+--R 3
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 11 5
+--R 4096c d
+--R ,
+--R 4
+--R +
+--R 2 2 3 3
+--R (6c d x + 6c d x)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 11 5
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (7a d - 6a b c d - b c )\|x
+--R +
+--R -
+--R 3
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 2401a d + 8232a b c d - 9212a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 2520a b c d + 1434a b c d - 360a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 188a b c d - 24a b c d - b c
+--R /
+--R 11 5
+--R 4096c d
+--R ,
+--R 4
+--R +
+--R 2 2 3 3
+--R (12c d x + 12c d x)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 11 5
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 3
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 11 5
+--R 4096c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (7a d - 6a b c d - b c )\|x
+--R +
+--R 2 2 2 2 2 2
+--R (- 7a d + 6a b c d - 3b c )x - 4a c d
+--R /
+--R 2 2 3 3 +-+
+--R (6c d x + 6c d x)\|x
+--R Type: Union(Expression(Integer),...)
+--E 1375
+
+--S 1376 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (7a d - 6a b c d - b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R -
+--R 2 +-+
+--R 8c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 11 5
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (7a d - 6a b c d - b c )\|x
+--R +
+--R 3
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 2401a d + 8232a b c d - 9212a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 2520a b c d + 1434a b c d - 360a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 188a b c d - 24a b c d - b c
+--R /
+--R 11 5
+--R 4096c d
+--R ,
+--R 4
+--R +
+--R 2 +-+
+--R 8c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 11 5
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (7a d - 6a b c d - b c )\|x
+--R +
+--R -
+--R 3
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 2401a d + 8232a b c d - 9212a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 2520a b c d + 1434a b c d - 360a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 188a b c d - 24a b c d - b c
+--R /
+--R 11 5
+--R 4096c d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 7a d + 6a b c d + b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (14a d - 12a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (14a d - 12a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 +-+
+--R 16c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 11 5
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R atan
+--R 3
+--R 8c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 11 5
+--R 4096c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (7a d - 6a b c d - b c )\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 8c d\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1376
+
+--S 1377 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1377
+
+)clear all
+
+--S 1378 of 1397
+t0:=(a+b*x^2)^2/(x^(7/2)*(c+d*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ---------------------------
+--R 2 7 5 2 3 +-+
+--R (d x + 2c d x + c x )\|x
+--R Type: Expression(Integer)
+--E 1378
+
+--S 1379 of 1397
+r0:=-2/5*a^2/(c*x^(5/2)*(c+d*x^2))-1/4*(b*c-9*a*d)*(b*c-a*d)*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(13/4)*d^(3/4)*_
+ sqrt(2))+1/4*(b*c-9*a*d)*(b*c-a*d)*atan(1+d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(13/4)*d^(3/4)*sqrt(2))+1/8*(b*c-9*a*d)*_
+ (b*c-a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(13/4)*d^(3/4)*sqrt(2))-1/8*(b*c-9*a*d)*(b*c-a*d)*log(sqrt(c)+_
+ x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(13/4)*d^(3/4)*_
+ sqrt(2))+1/2*(b*c-9*a*d)*(b*c-a*d)/(c^3*d*sqrt(x))+1/10*(-5*b^2*_
+ c^2+10*a*b*c*d-9*a^2*d^2)/(c^2*d*(c+d*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 4
+--R (- 45a d + 50a b c d - 5b c d)x
+--R +
+--R 2 2 2 2 3 2
+--R (- 45a c d + 50a b c d - 5b c )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 4 2 2 2 2 3 2
+--R ((45a d - 50a b c d + 5b c d)x + (45a c d - 50a b c d + 5b c )x )
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 4
+--R (90a d - 100a b c d + 10b c d)x
+--R +
+--R 2 2 2 2 3 2
+--R (90a c d - 100a b c d + 10b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|d \|x + \|c
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 4
+--R (90a d - 100a b c d + 10b c d)x
+--R +
+--R 2 2 2 2 3 2
+--R (90a c d - 100a b c d + 10b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|d \|x - \|c
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R ((180a d - 200a b c d + 20b c )x + (144a c d - 160a b c )x - 16a c )
+--R *
+--R +-+4+-+4+-+3
+--R \|2 \|c \|d
+--R /
+--R 3 4 4 2 +-+4+-+4+-+3 +-+
+--R (40c d x + 40c x )\|2 \|c \|d \|x
+--R Type: Expression(Integer)
+--E 1379
+
+--S 1380 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 4 4 2
+--R (10c d x + 10c x )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 6561a d + 29160a b c d - 51516a b c d + 45720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 21286a b c d + 5080a b c d - 636a b c d + 40a b c d - b c
+--R /
+--R 13 3
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 729a d - 2430a b c d + 2943a b c d - 1540a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 327a b c d - 30a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 2
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 6561a d + 29160a b c d - 51516a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 45720a b c d - 21286a b c d + 5080a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 636a b c d + 40a b c d - b c
+--R /
+--R 13 3
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 4 4 2
+--R (- 10c d x - 10c x )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 6561a d + 29160a b c d - 51516a b c d + 45720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 21286a b c d + 5080a b c d - 636a b c d + 40a b c d - b c
+--R /
+--R 13 3
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 729a d - 2430a b c d + 2943a b c d - 1540a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 327a b c d - 30a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 10 2
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 6561a d + 29160a b c d - 51516a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 45720a b c d - 21286a b c d + 5080a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 636a b c d + 40a b c d - b c
+--R /
+--R 13 3
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 4 4 2
+--R (20c d x + 20c x )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 6561a d + 29160a b c d - 51516a b c d + 45720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 21286a b c d + 5080a b c d - 636a b c d + 40a b c d - b c
+--R /
+--R 13 3
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 10 2
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 6561a d + 29160a b c d - 51516a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 45720a b c d - 21286a b c d + 5080a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 636a b c d + 40a b c d - b c
+--R /
+--R 13 3
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 729a d - 2430a b c d + 2943a b c d - 1540a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 327a b c d - 30a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R (45a d - 50a b c d + 5b c )x + (36a c d - 40a b c )x - 4a c
+--R /
+--R 3 4 4 2 +-+
+--R (10c d x + 10c x )\|x
+--R Type: Union(Expression(Integer),...)
+--E 1380
+
+--S 1381 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (9a d - 10a b c d + b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 +-+
+--R 8c \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 6561a d + 29160a b c d - 51516a b c d + 45720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 21286a b c d + 5080a b c d - 636a b c d + 40a b c d - b c
+--R /
+--R 13 3
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 729a d - 2430a b c d + 2943a b c d - 1540a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 327a b c d - 30a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 2
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 6561a d + 29160a b c d - 51516a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 45720a b c d - 21286a b c d + 5080a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 636a b c d + 40a b c d - b c
+--R /
+--R 13 3
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 3 +-+
+--R 8c \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 6561a d + 29160a b c d - 51516a b c d + 45720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 21286a b c d + 5080a b c d - 636a b c d + 40a b c d - b c
+--R /
+--R 13 3
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 729a d - 2430a b c d + 2943a b c d - 1540a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 327a b c d - 30a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 10 2
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 6561a d + 29160a b c d - 51516a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 45720a b c d - 21286a b c d + 5080a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 636a b c d + 40a b c d - b c
+--R /
+--R 13 3
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 9a d + 10a b c d - b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 18a d + 20a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 18a d + 20a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 +-+
+--R 16c \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 6561a d + 29160a b c d - 51516a b c d + 45720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 21286a b c d + 5080a b c d - 636a b c d + 40a b c d - b c
+--R /
+--R 13 3
+--R 4096c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R atan
+--R 10 2
+--R 512c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 6561a d + 29160a b c d - 51516a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 45720a b c d - 21286a b c d + 5080a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 636a b c d + 40a b c d - b c
+--R /
+--R 13 3
+--R 4096c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 729a d - 2430a b c d + 2943a b c d - 1540a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 327a b c d - 30a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3 +-+4+-+4+-+3
+--R 8c \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1381
+
+--S 1382 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1382
+
+)clear all
+
+--S 1383 of 1397
+t0:=x^(7/2)*(a+b*x^2)^2/(c+d*x^2)^3
+--R
+--R
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Expression(Integer)
+--E 1383
+
+--S 1384 of 1397
+r0:=1/80*(117*b^2*c^2-90*a*b*c*d+5*a^2*d^2)*x^(5/2)/(c^2*d^3)+1/4*_
+ (b*c-a*d)^2*x^(9/2)/(c*d^2*(c+d*x^2)^2)-1/16*(b*c-a*d)*(17*b*c-_
+ a*d)*x^(9/2)/(c^2*d^2*(c+d*x^2))-1/32*(117*b^2*c^2-90*a*b*c*d+5*_
+ a^2*d^2)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(3/4)*_
+ d^(17/4)*sqrt(2))+1/32*(117*b^2*c^2-90*a*b*c*d+5*a^2*d^2)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(3/4)*d^(17/4)*_
+ sqrt(2))-1/64*(117*b^2*c^2-90*a*b*c*d+5*a^2*d^2)*log(sqrt(c)+_
+ x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(3/4)*d^(17/4)*_
+ sqrt(2))+1/64*(117*b^2*c^2-90*a*b*c*d+5*a^2*d^2)*log(sqrt(c)+x*_
+ sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(3/4)*d^(17/4)*_
+ sqrt(2))-1/16*(117*b^2*c^2-90*a*b*c*d+5*a^2*d^2)*sqrt(x)/(c*d^4)
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (25a d - 450a b c d + 585b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (50a c d - 900a b c d + 1170b c d)x + 25a c d - 450a b c d
+--R +
+--R 2 4
+--R 585b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 25a d + 450a b c d - 585b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 50a c d + 900a b c d - 1170b c d)x - 25a c d + 450a b c d
+--R +
+--R 2 4
+--R - 585b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (50a d - 900a b c d + 1170b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (100a c d - 1800a b c d + 2340b c d)x + 50a c d - 900a b c d
+--R +
+--R 2 4
+--R 1170b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 4
+--R (50a d - 900a b c d + 1170b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (100a c d - 1800a b c d + 2340b c d)x + 50a c d - 900a b c d
+--R +
+--R 2 4
+--R 1170b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 6 3 2 2 4
+--R 128b d x + (1280a b d - 1664b c d )x
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (- 180a d + 3240a b c d - 4212b c d)x - 100a c d + 1800a b c d
+--R +
+--R 2 3
+--R - 2340b c
+--R *
+--R +-+4+-+3 4+-+ +-+
+--R \|2 \|c \|d \|x
+--R /
+--R 6 4 5 2 2 4 +-+4+-+3 4+-+
+--R (320d x + 640c d x + 320c d )\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1384
+
+--S 1385 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 4 5 2 2 4
+--R (80d x + 160c d x + 80c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 45000a b c d - 1273500a b c d + 17739000a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 124525350a b c d + 415092600a b c d - 697317660a b c d
+--R +
+--R 7 7 8 8
+--R 576580680a b c d - 187388721b c
+--R /
+--R 3 17
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (5a d - 90a b c d + 117b c )\|x
+--R +
+--R 4
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d + 45000a b c d - 1273500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 17739000a b c d - 124525350a b c d + 415092600a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 697317660a b c d + 576580680a b c d - 187388721b c
+--R /
+--R 3 17
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R 6 4 5 2 2 4
+--R (- 80d x - 160c d x - 80c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 45000a b c d - 1273500a b c d + 17739000a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 124525350a b c d + 415092600a b c d - 697317660a b c d
+--R +
+--R 7 7 8 8
+--R 576580680a b c d - 187388721b c
+--R /
+--R 3 17
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (5a d - 90a b c d + 117b c )\|x
+--R +
+--R -
+--R 4
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d + 45000a b c d - 1273500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4
+--R 17739000a b c d - 124525350a b c d
+--R +
+--R 3 5 5 3 2 6 6 2
+--R 415092600a b c d - 697317660a b c d
+--R +
+--R 7 7 8 8
+--R 576580680a b c d - 187388721b c
+--R /
+--R 3 17
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R 6 4 5 2 2 4
+--R (- 160d x - 320c d x - 160c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 45000a b c d - 1273500a b c d + 17739000a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 124525350a b c d + 415092600a b c d - 697317660a b c d
+--R +
+--R 7 7 8 8
+--R 576580680a b c d - 187388721b c
+--R /
+--R 3 17
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 4
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d + 45000a b c d - 1273500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 17739000a b c d - 124525350a b c d + 415092600a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 697317660a b c d + 576580680a b c d - 187388721b c
+--R /
+--R 3 17
+--R 16777216c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (5a d - 90a b c d + 117b c )\|x
+--R +
+--R 2 3 6 3 2 2 4
+--R 32b d x + (320a b d - 416b c d )x
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (- 45a d + 810a b c d - 1053b c d)x - 25a c d + 450a b c d
+--R +
+--R 2 3
+--R - 585b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 6 4 5 2 2 4
+--R 80d x + 160c d x + 80c d
+--R Type: Union(Expression(Integer),...)
+--E 1385
+
+--S 1386 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + 90a b c d - 117b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4 +-+
+--R 64d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 45000a b c d - 1273500a b c d + 17739000a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 124525350a b c d + 415092600a b c d - 697317660a b c d
+--R +
+--R 7 7 8 8
+--R 576580680a b c d - 187388721b c
+--R /
+--R 3 17
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (5a d - 90a b c d + 117b c )\|x
+--R +
+--R 4
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d + 45000a b c d - 1273500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 17739000a b c d - 124525350a b c d + 415092600a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 697317660a b c d + 576580680a b c d - 187388721b c
+--R /
+--R 3 17
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R -
+--R 4 +-+
+--R 64d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d + 45000a b c d - 1273500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 17739000a b c d - 124525350a b c d + 415092600a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 697317660a b c d + 576580680a b c d - 187388721b c
+--R /
+--R 3 17
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (5a d - 90a b c d + 117b c )\|x
+--R +
+--R -
+--R 4
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d + 45000a b c d - 1273500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4
+--R 17739000a b c d - 124525350a b c d
+--R +
+--R 3 5 5 3 2 6 6 2
+--R 415092600a b c d - 697317660a b c d
+--R +
+--R 7 7 8 8
+--R 576580680a b c d - 187388721b c
+--R /
+--R 3 17
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - 90a b c d + 117b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 10a d + 180a b c d - 234b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 10a d + 180a b c d - 234b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R -
+--R 4 +-+
+--R 128d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d + 45000a b c d - 1273500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 17739000a b c d - 124525350a b c d + 415092600a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 697317660a b c d + 576580680a b c d - 187388721b c
+--R /
+--R 3 17
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R atan
+--R 4
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d + 45000a b c d - 1273500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4
+--R 17739000a b c d - 124525350a b c d
+--R +
+--R 3 5 5 3 2 6 6 2
+--R 415092600a b c d - 697317660a b c d
+--R +
+--R 7 7 8 8
+--R 576580680a b c d - 187388721b c
+--R /
+--R 3 17
+--R 16777216c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (5a d - 90a b c d + 117b c )\|x
+--R /
+--R 4 +-+4+-+3 4+-+
+--R 64d \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1386
+
+--S 1387 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1387
+
+)clear all
+
+--S 1388 of 1397
+t0:=x^(5/2)*(a+b*x^2)^2/(c+d*x^2)^3
+--R
+--R
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Expression(Integer)
+--E 1388
+
+--S 1389 of 1397
+r0:=-1/48*(42*a*b-77*b^2*c/d+3*a^2*d/c)*x^(3/2)/(c*d^2)+1/4*(b*c-a*d)^2*_
+ x^(7/2)/(c*d^2*(c+d*x^2)^2)-1/16*(b*c-a*d)*(15*b*c+a*d)*x^(7/2)/_
+ (c^2*d^2*(c+d*x^2))+1/32*(77*b^2*c^2-42*a*b*c*d-3*a^2*d^2)*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(5/4)*d^(15/4)*sqrt(2))-_
+ 1/32*(77*b^2*c^2-42*a*b*c*d-3*a^2*d^2)*atan(1+d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(5/4)*d^(15/4)*sqrt(2))-1/64*(77*b^2*c^2-_
+ 42*a*b*c*d-3*a^2*d^2)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(5/4)*d^(15/4)*sqrt(2))+1/64*(77*b^2*c^2-42*a*b*c*d-_
+ 3*a^2*d^2)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(5/4)*d^(15/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (- 9a d - 126a b c d + 231b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 18a c d - 252a b c d + 462b c d)x - 9a c d - 126a b c d
+--R +
+--R 2 4
+--R 231b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (9a d + 126a b c d - 231b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (18a c d + 252a b c d - 462b c d)x + 9a c d + 126a b c d - 231b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (18a d + 252a b c d - 462b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (36a c d + 504a b c d - 924b c d)x + 18a c d + 252a b c d - 462b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 4
+--R (18a d + 252a b c d - 462b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (36a c d + 504a b c d - 924b c d)x + 18a c d + 252a b c d - 462b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 5 2 3 2 2 2 3
+--R 128b c d x + (36a d - 264a b c d + 484b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 12a c d - 168a b c d + 308b c )x
+--R *
+--R +-+4+-+4+-+3 +-+
+--R \|2 \|c \|d \|x
+--R /
+--R 5 4 2 4 2 3 3 +-+4+-+4+-+3
+--R (192c d x + 384c d x + 192c d )\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1389
+
+--S 1390 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 2 4 2 3 3
+--R (48c d x + 96c d x + 48c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 4536a b c d - 86940a b c d - 539784a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1457946a b c d + 13854456a b c d - 57274140a b c d
+--R +
+--R 7 7 8 8
+--R 76697544a b c d - 35153041b c
+--R /
+--R 5 15
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 27a d + 1134a b c d + 13797a b c d + 15876a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R - 354123a b c d + 747054a b c d - 456533b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 11
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 81a d - 4536a b c d - 86940a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 539784a b c d + 1457946a b c d + 13854456a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 57274140a b c d + 76697544a b c d - 35153041b c
+--R /
+--R 5 15
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 5 4 2 4 2 3 3
+--R (- 48c d x - 96c d x - 48c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 4536a b c d - 86940a b c d - 539784a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1457946a b c d + 13854456a b c d - 57274140a b c d
+--R +
+--R 7 7 8 8
+--R 76697544a b c d - 35153041b c
+--R /
+--R 5 15
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 27a d + 1134a b c d + 13797a b c d + 15876a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R - 354123a b c d + 747054a b c d - 456533b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 11
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 81a d - 4536a b c d - 86940a b c d
+--R +
+--R 5 3 3 5 4 4 4 4
+--R - 539784a b c d + 1457946a b c d
+--R +
+--R 3 5 5 3 2 6 6 2
+--R 13854456a b c d - 57274140a b c d
+--R +
+--R 7 7 8 8
+--R 76697544a b c d - 35153041b c
+--R /
+--R 5 15
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 5 4 2 4 2 3 3
+--R (96c d x + 192c d x + 96c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 4536a b c d - 86940a b c d - 539784a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1457946a b c d + 13854456a b c d - 57274140a b c d
+--R +
+--R 7 7 8 8
+--R 76697544a b c d - 35153041b c
+--R /
+--R 5 15
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 4 11
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 81a d - 4536a b c d - 86940a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 539784a b c d + 1457946a b c d + 13854456a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 57274140a b c d + 76697544a b c d - 35153041b c
+--R /
+--R 5 15
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 27a d + 1134a b c d + 13797a b c d + 15876a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R - 354123a b c d + 747054a b c d - 456533b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 5 2 3 2 2 2 3
+--R 32b c d x + (9a d - 66a b c d + 121b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 3a c d - 42a b c d + 77b c )x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 5 4 2 4 2 3 3
+--R 48c d x + 96c d x + 48c d
+--R Type: Union(Expression(Integer),...)
+--E 1390
+
+--S 1391 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d + 42a b c d - 77b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 +-+
+--R 64c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 4536a b c d - 86940a b c d - 539784a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1457946a b c d + 13854456a b c d - 57274140a b c d
+--R +
+--R 7 7 8 8
+--R 76697544a b c d - 35153041b c
+--R /
+--R 5 15
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 27a d + 1134a b c d + 13797a b c d + 15876a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R - 354123a b c d + 747054a b c d - 456533b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 11
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 81a d - 4536a b c d - 86940a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 539784a b c d + 1457946a b c d + 13854456a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 57274140a b c d + 76697544a b c d - 35153041b c
+--R /
+--R 5 15
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 3 +-+
+--R 64c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 4536a b c d - 86940a b c d - 539784a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1457946a b c d + 13854456a b c d - 57274140a b c d
+--R +
+--R 7 7 8 8
+--R 76697544a b c d - 35153041b c
+--R /
+--R 5 15
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 27a d + 1134a b c d + 13797a b c d + 15876a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R - 354123a b c d + 747054a b c d - 456533b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 11
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 81a d - 4536a b c d - 86940a b c d
+--R +
+--R 5 3 3 5 4 4 4 4
+--R - 539784a b c d + 1457946a b c d
+--R +
+--R 3 5 5 3 2 6 6 2
+--R 13854456a b c d - 57274140a b c d
+--R +
+--R 7 7 8 8
+--R 76697544a b c d - 35153041b c
+--R /
+--R 5 15
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d - 42a b c d + 77b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 6a d - 84a b c d + 154b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 6a d - 84a b c d + 154b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 +-+
+--R 128c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 4536a b c d - 86940a b c d - 539784a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1457946a b c d + 13854456a b c d - 57274140a b c d
+--R +
+--R 7 7 8 8
+--R 76697544a b c d - 35153041b c
+--R /
+--R 5 15
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R atan
+--R 4 11
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 81a d - 4536a b c d - 86940a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 539784a b c d + 1457946a b c d + 13854456a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 57274140a b c d + 76697544a b c d - 35153041b c
+--R /
+--R 5 15
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 27a d + 1134a b c d + 13797a b c d + 15876a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R - 354123a b c d + 747054a b c d - 456533b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3 +-+4+-+4+-+3
+--R 64c d \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1391
+
+--S 1392 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1392
+
+)clear all
+
+--S 1393 of 1397
+t0:=x^(3/2)*(a+b*x^2)^2/(c+d*x^2)^3
+--R
+--R
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Expression(Integer)
+--E 1393
+
+--S 1394 of 1397
+r0:=1/4*(b*c-a*d)^2*x^(5/2)/(c*d^2*(c+d*x^2)^2)-1/16*(b*c-a*d)*_
+ (13*b*c+3*a*d)*x^(5/2)/(c^2*d^2*(c+d*x^2))+1/32*(45*b^2*c^2-_
+ 10*a*b*c*d-3*a^2*d^2)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(7/4)*d^(13/4)*sqrt(2))-1/32*(45*b^2*c^2-10*a*b*c*d-3*a^2*d^2)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(7/4)*d^(13/4)*sqrt(2))+_
+ 1/64*(45*b^2*c^2-10*a*b*c*d-3*a^2*d^2)*log(sqrt(c)+x*sqrt(d)-_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(7/4)*d^(13/4)*sqrt(2))-_
+ 1/64*(45*b^2*c^2-10*a*b*c*d-3*a^2*d^2)*log(sqrt(c)+x*sqrt(d)+_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(7/4)*d^(13/4)*sqrt(2))-_
+ 1/16*(10*a*b-45*b^2*c/d+3*a^2*d/c)*sqrt(x)/(c*d^2)
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (3a d + 10a b c d - 45b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (6a c d + 20a b c d - 90b c d)x + 3a c d + 10a b c d - 45b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 3a d - 10a b c d + 45b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 6a c d - 20a b c d + 90b c d)x - 3a c d - 10a b c d + 45b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (6a d + 20a b c d - 90b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (12a c d + 40a b c d - 180b c d)x + 6a c d + 20a b c d - 90b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 4
+--R (6a d + 20a b c d - 90b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (12a c d + 40a b c d - 180b c d)x + 6a c d + 20a b c d - 90b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 4 2 3 2 2 2 2 2 2
+--R 128b c d x + (4a d - 72a b c d + 324b c d)x - 12a c d
+--R +
+--R 2 2 3
+--R - 40a b c d + 180b c
+--R *
+--R +-+4+-+3 4+-+ +-+
+--R \|2 \|c \|d \|x
+--R /
+--R 5 4 2 4 2 3 3 +-+4+-+3 4+-+
+--R (64c d x + 128c d x + 64c d )\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1394
+
+--S 1395 of 1397
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 2 4 2 3 3
+--R (16c d x + 32c d x + 16c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 1080a b c d - 540a b c d + 36600a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 42650a b c d - 549000a b c d - 121500a b c d + 3645000a b c d
+--R +
+--R 8 8
+--R - 4100625b c
+--R /
+--R 7 13
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (3a d + 10a b c d - 45b c )\|x
+--R +
+--R 2 3
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 1080a b c d - 540a b c d + 36600a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 42650a b c d - 549000a b c d - 121500a b c d
+--R +
+--R 7 7 8 8
+--R 3645000a b c d - 4100625b c
+--R /
+--R 7 13
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R 5 4 2 4 2 3 3
+--R (- 16c d x - 32c d x - 16c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 1080a b c d - 540a b c d + 36600a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 42650a b c d - 549000a b c d - 121500a b c d + 3645000a b c d
+--R +
+--R 8 8
+--R - 4100625b c
+--R /
+--R 7 13
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (3a d + 10a b c d - 45b c )\|x
+--R +
+--R -
+--R 2 3
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 1080a b c d - 540a b c d + 36600a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 42650a b c d - 549000a b c d - 121500a b c d
+--R +
+--R 7 7 8 8
+--R 3645000a b c d - 4100625b c
+--R /
+--R 7 13
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R 5 4 2 4 2 3 3
+--R (- 32c d x - 64c d x - 32c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 1080a b c d - 540a b c d + 36600a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 42650a b c d - 549000a b c d - 121500a b c d + 3645000a b c d
+--R +
+--R 8 8
+--R - 4100625b c
+--R /
+--R 7 13
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 2 3
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 1080a b c d - 540a b c d + 36600a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 42650a b c d - 549000a b c d - 121500a b c d
+--R +
+--R 7 7 8 8
+--R 3645000a b c d - 4100625b c
+--R /
+--R 7 13
+--R 16777216c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (3a d + 10a b c d - 45b c )\|x
+--R +
+--R 2 2 4 2 3 2 2 2 2 2 2 2
+--R 32b c d x + (a d - 18a b c d + 81b c d)x - 3a c d - 10a b c d
+--R +
+--R 2 3
+--R 45b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 5 4 2 4 2 3 3
+--R 16c d x + 32c d x + 16c d
+--R Type: Union(Expression(Integer),...)
+--E 1395
+
+--S 1396 of 1397
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d - 10a b c d + 45b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 +-+
+--R 64c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 1080a b c d - 540a b c d + 36600a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 42650a b c d - 549000a b c d - 121500a b c d + 3645000a b c d
+--R +
+--R 8 8
+--R - 4100625b c
+--R /
+--R 7 13
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (3a d + 10a b c d - 45b c )\|x
+--R +
+--R 2 3
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 1080a b c d - 540a b c d + 36600a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 42650a b c d - 549000a b c d - 121500a b c d
+--R +
+--R 7 7 8 8
+--R 3645000a b c d - 4100625b c
+--R /
+--R 7 13
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R -
+--R 3 +-+
+--R 64c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 1080a b c d - 540a b c d + 36600a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 42650a b c d - 549000a b c d - 121500a b c d
+--R +
+--R 7 7 8 8
+--R 3645000a b c d - 4100625b c
+--R /
+--R 7 13
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (3a d + 10a b c d - 45b c )\|x
+--R +
+--R -
+--R 2 3
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 81a d - 1080a b c d - 540a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 36600a b c d + 42650a b c d - 549000a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 121500a b c d + 3645000a b c d - 4100625b c
+--R /
+--R 7 13
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d + 10a b c d - 45b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 6a d - 20a b c d + 90b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 6a d - 20a b c d + 90b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R -
+--R 3 +-+
+--R 128c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 1080a b c d - 540a b c d + 36600a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 42650a b c d - 549000a b c d - 121500a b c d
+--R +
+--R 7 7 8 8
+--R 3645000a b c d - 4100625b c
+--R /
+--R 7 13
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R atan
+--R 2 3
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 1080a b c d - 540a b c d + 36600a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 42650a b c d - 549000a b c d - 121500a b c d
+--R +
+--R 7 7 8 8
+--R 3645000a b c d - 4100625b c
+--R /
+--R 7 13
+--R 16777216c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (3a d + 10a b c d - 45b c )\|x
+--R /
+--R 3 +-+4+-+3 4+-+
+--R 64c d \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1396
+
+--S 1397 of 1397
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1397
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
+
diff --git a/src/axiom-website/CATS/rich6b.input.pdf b/src/axiom-website/CATS/rich6b.input.pdf
new file mode 100644
index 0000000..9197bbd
Binary files /dev/null and b/src/axiom-website/CATS/rich6b.input.pdf differ
diff --git a/src/axiom-website/CATS/rich6c.input.pamphlet b/src/axiom-website/CATS/rich6c.input.pamphlet
new file mode 100644
index 0000000..0a7392b
--- /dev/null
+++ b/src/axiom-website/CATS/rich6c.input.pamphlet
@@ -0,0 +1,50528 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich6c.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p (c+d x^n)^q|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 261 supplied "optimal results".
+\item 258 matching answers.
+\item 91 cases where Axiom supplied 2 results.
+\item 12 cases that Axiom failed to integrate.
+\item 82 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich6c.output
+)spool rich6c.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 1475
+t0:=(a+b*x^2)^2*sqrt(x)/(c+d*x^2)^3
+--R
+--R
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 1475
+r0:=1/4*(b*c-a*d)^2*x^(3/2)/(c*d^2*(c+d*x^2)^2)-1/16*(b*c-a*d)*_
+ (11*b*c+5*a*d)*x^(3/2)/(c^2*d^2*(c+d*x^2))-1/32*(21*b^2*c^2+_
+ 6*a*b*c*d+5*a^2*d^2)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(9/4)*d^(11/4)*sqrt(2))+1/32*(21*b^2*c^2+6*a*b*c*d+5*a^2*_
+ d^2)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(9/4)*d^(11/4)*_
+ sqrt(2))+1/64*(21*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*log(sqrt(c)+_
+ x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(9/4)*d^(11/4)*_
+ sqrt(2))-1/64*(21*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*log(sqrt(c)+_
+ x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(9/4)*d^(11/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (- 5a d - 6a b c d - 21b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 10a c d - 12a b c d - 42b c d)x - 5a c d - 6a b c d - 21b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (5a d + 6a b c d + 21b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (10a c d + 12a b c d + 42b c d)x + 5a c d + 6a b c d + 21b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (10a d + 12a b c d + 42b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (20a c d + 24a b c d + 84b c d)x + 10a c d + 12a b c d + 42b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 4
+--R (10a d + 12a b c d + 42b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (20a c d + 24a b c d + 84b c d)x + 10a c d + 12a b c d + 42b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((20a d + 24a b c d - 44b c d)x + (36a c d - 8a b c d - 28b c )x)
+--R *
+--R +-+4+-+4+-+3 +-+
+--R \|2 \|c \|d \|x
+--R /
+--R 2 4 4 3 3 2 4 2 +-+4+-+4+-+3
+--R (64c d x + 128c d x + 64c d )\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 4 3 3 2 4 2
+--R (16c d x + 32c d x + 16c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d - 3000a b c d - 15900a b c d - 42120a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 112806a b c d - 176904a b c d - 280476a b c d
+--R +
+--R 7 7 8 8
+--R - 222264a b c d - 194481b c
+--R /
+--R 9 11
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 125a d + 450a b c d + 2115a b c d + 3996a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 8883a b c d + 7938a b c d + 9261b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 8
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d - 3000a b c d - 15900a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 42120a b c d - 112806a b c d - 176904a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 280476a b c d - 222264a b c d - 194481b c
+--R /
+--R 9 11
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 4 4 3 3 2 4 2
+--R (- 16c d x - 32c d x - 16c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d - 3000a b c d - 15900a b c d - 42120a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 112806a b c d - 176904a b c d - 280476a b c d
+--R +
+--R 7 7 8 8
+--R - 222264a b c d - 194481b c
+--R /
+--R 9 11
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 125a d + 450a b c d + 2115a b c d + 3996a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 8883a b c d + 7938a b c d + 9261b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 8
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d - 3000a b c d - 15900a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 42120a b c d - 112806a b c d - 176904a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 280476a b c d - 222264a b c d - 194481b c
+--R /
+--R 9 11
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 4 4 3 3 2 4 2
+--R (32c d x + 64c d x + 32c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d - 3000a b c d - 15900a b c d - 42120a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 112806a b c d - 176904a b c d - 280476a b c d
+--R +
+--R 7 7 8 8
+--R - 222264a b c d - 194481b c
+--R /
+--R 9 11
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 7 8
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d - 3000a b c d - 15900a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 42120a b c d - 112806a b c d - 176904a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 280476a b c d - 222264a b c d - 194481b c
+--R /
+--R 9 11
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 125a d + 450a b c d + 2115a b c d + 3996a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 8883a b c d + 7938a b c d + 9261b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+
+--R ((5a d + 6a b c d - 11b c d)x + (9a c d - 2a b c d - 7b c )x)\|x
+--R /
+--R 2 4 4 3 3 2 4 2
+--R 16c d x + 32c d x + 16c d
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d + 6a b c d + 21b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 +-+
+--R 64c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d - 3000a b c d - 15900a b c d - 42120a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 112806a b c d - 176904a b c d - 280476a b c d
+--R +
+--R 7 7 8 8
+--R - 222264a b c d - 194481b c
+--R /
+--R 9 11
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 125a d + 450a b c d + 2115a b c d + 3996a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 8883a b c d + 7938a b c d + 9261b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 8
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d - 3000a b c d - 15900a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 42120a b c d - 112806a b c d - 176904a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 280476a b c d - 222264a b c d - 194481b c
+--R /
+--R 9 11
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2 2 +-+
+--R 64c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d - 3000a b c d - 15900a b c d - 42120a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 112806a b c d - 176904a b c d - 280476a b c d
+--R +
+--R 7 7 8 8
+--R - 222264a b c d - 194481b c
+--R /
+--R 9 11
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 125a d + 450a b c d + 2115a b c d + 3996a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 8883a b c d + 7938a b c d + 9261b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 8
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d - 3000a b c d - 15900a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 42120a b c d - 112806a b c d - 176904a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 280476a b c d - 222264a b c d - 194481b c
+--R /
+--R 9 11
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d - 6a b c d - 21b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 10a d - 12a b c d - 42b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 10a d - 12a b c d - 42b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 +-+
+--R 128c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d - 3000a b c d - 15900a b c d - 42120a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 112806a b c d - 176904a b c d - 280476a b c d
+--R +
+--R 7 7 8 8
+--R - 222264a b c d - 194481b c
+--R /
+--R 9 11
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R atan
+--R 7 8
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 625a d - 3000a b c d - 15900a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 42120a b c d - 112806a b c d - 176904a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 280476a b c d - 222264a b c d - 194481b c
+--R /
+--R 9 11
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 125a d + 450a b c d + 2115a b c d + 3996a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 8883a b c d + 7938a b c d + 9261b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 2 2 +-+4+-+4+-+3
+--R 64c d \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 1475
+t0:=(a+b*x^2)^2/((c+d*x^2)^3*sqrt(x))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -----------------------------------
+--R 3 6 2 4 2 2 3 +-+
+--R (d x + 3c d x + 3c d x + c )\|x
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 1475
+r0:=-1/32*(5*b^2*c^2+6*a*b*c*d+21*a^2*d^2)*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(11/4)*d^(9/4)*sqrt(2))+1/32*(5*b^2*c^2+_
+ 6*a*b*c*d+21*a^2*d^2)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(11/4)*d^(9/4)*sqrt(2))-1/64*(5*b^2*c^2+6*a*b*c*d+21*a^2*_
+ d^2)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(11/4)*d^(9/4)*sqrt(2))+1/64*(5*b^2*c^2+6*a*b*c*d+21*a^2*_
+ d^2)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(11/4)*d^(9/4)*sqrt(2))+1/4*(b*c-a*d)^2*sqrt(x)/(c*d^2*_
+ (c+d*x^2)^2)-1/16*(b*c-a*d)*(9*b*c+7*a*d)*sqrt(x)/(c^2*d^2*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (21a d + 6a b c d + 5b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (42a c d + 12a b c d + 10b c d)x + 21a c d + 6a b c d + 5b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 21a d - 6a b c d - 5b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 42a c d - 12a b c d - 10b c d)x - 21a c d - 6a b c d - 5b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (42a d + 12a b c d + 10b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (84a c d + 24a b c d + 20b c d)x + 42a c d + 12a b c d + 10b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 4
+--R (42a d + 12a b c d + 10b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (84a c d + 24a b c d + 20b c d)x + 42a c d + 12a b c d + 10b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((28a d + 8a b c d - 36b c d)x + 44a c d - 24a b c d - 20b c )\|2
+--R *
+--R 4+-+3 4+-+ +-+
+--R \|c \|d \|x
+--R /
+--R 2 4 4 3 3 2 4 2 +-+4+-+3 4+-+
+--R (64c d x + 128c d x + 64c d )\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 4 3 3 2 4 2
+--R (16c d x + 32c d x + 16c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 194481a d - 222264a b c d - 280476a b c d - 176904a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 112806a b c d - 42120a b c d - 15900a b c d - 3000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 11 9
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (21a d + 6a b c d + 5b c )\|x
+--R +
+--R 3 2
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 194481a d - 222264a b c d - 280476a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 176904a b c d - 112806a b c d - 42120a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 15900a b c d - 3000a b c d - 625b c
+--R /
+--R 11 9
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R 2 4 4 3 3 2 4 2
+--R (- 16c d x - 32c d x - 16c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 194481a d - 222264a b c d - 280476a b c d - 176904a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 112806a b c d - 42120a b c d - 15900a b c d - 3000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 11 9
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (21a d + 6a b c d + 5b c )\|x
+--R +
+--R -
+--R 3 2
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 194481a d - 222264a b c d - 280476a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 176904a b c d - 112806a b c d - 42120a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 15900a b c d - 3000a b c d - 625b c
+--R /
+--R 11 9
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R 2 4 4 3 3 2 4 2
+--R (- 32c d x - 64c d x - 32c d )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 194481a d - 222264a b c d - 280476a b c d - 176904a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 112806a b c d - 42120a b c d - 15900a b c d - 3000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 11 9
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 3 2
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 194481a d - 222264a b c d - 280476a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 176904a b c d - 112806a b c d - 42120a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 15900a b c d - 3000a b c d - 625b c
+--R /
+--R 11 9
+--R 16777216c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (21a d + 6a b c d + 5b c )\|x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((7a d + 2a b c d - 9b c d)x + 11a c d - 6a b c d - 5b c )\|x
+--R /
+--R 2 4 4 3 3 2 4 2
+--R 16c d x + 32c d x + 16c d
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 21a d - 6a b c d - 5b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 +-+
+--R 64c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 194481a d - 222264a b c d - 280476a b c d - 176904a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 112806a b c d - 42120a b c d - 15900a b c d - 3000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 11 9
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (21a d + 6a b c d + 5b c )\|x
+--R +
+--R 3 2
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 194481a d - 222264a b c d - 280476a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 176904a b c d - 112806a b c d - 42120a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 15900a b c d - 3000a b c d - 625b c
+--R /
+--R 11 9
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R -
+--R 2 2 +-+
+--R 64c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 194481a d - 222264a b c d - 280476a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 176904a b c d - 112806a b c d - 42120a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 15900a b c d - 3000a b c d - 625b c
+--R /
+--R 11 9
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (21a d + 6a b c d + 5b c )\|x
+--R +
+--R -
+--R 3 2
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 194481a d - 222264a b c d - 280476a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 176904a b c d - 112806a b c d - 42120a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 15900a b c d - 3000a b c d - 625b c
+--R /
+--R 11 9
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (21a d + 6a b c d + 5b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 42a d - 12a b c d - 10b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 42a d - 12a b c d - 10b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R -
+--R 2 2 +-+
+--R 128c d \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 194481a d - 222264a b c d - 280476a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 176904a b c d - 112806a b c d - 42120a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 15900a b c d - 3000a b c d - 625b c
+--R /
+--R 11 9
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R atan
+--R 3 2
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 194481a d - 222264a b c d - 280476a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 176904a b c d - 112806a b c d - 42120a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 15900a b c d - 3000a b c d - 625b c
+--R /
+--R 11 9
+--R 16777216c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (21a d + 6a b c d + 5b c )\|x
+--R /
+--R 2 2 +-+4+-+3 4+-+
+--R 64c d \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 1475
+t0:=(a+b*x^2)^2/(x^(3/2)*(c+d*x^2)^3)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ------------------------------------
+--R 3 7 2 5 2 3 3 +-+
+--R (d x + 3c d x + 3c d x + c x)\|x
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 1475
+r0:=-1/4*(b^2*c^2-2*a*b*c*d+9*a^2*d^2)*x^(3/2)/(c^2*d*(c+d*x^2)^2)+_
+ 1/16*(3*b^2*c^2+5*a*d*(2*b*c-9*a*d))*x^(3/2)/(c^3*d*(c+d*x^2))-_
+ 1/32*(3*b^2*c^2+5*a*d*(2*b*c-9*a*d))*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(13/4)*d^(7/4)*sqrt(2))+1/32*(3*b^2*c^2+_
+ 5*a*d*(2*b*c-9*a*d))*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(13/4)*d^(7/4)*sqrt(2))+1/64*(3*b^2*c^2+5*a*d*(2*b*c-9*a*d))*_
+ log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(13/4)*d^(7/4)*sqrt(2))-1/64*(3*b^2*c^2+5*a*d*(2*b*c-9*a*d))*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(13/4)*d^(7/4)*sqrt(2))-2*a^2/(c*(c+d*x^2)^2*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (45a d - 10a b c d - 3b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (90a c d - 20a b c d - 6b c d)x + 45a c d - 10a b c d - 3b c
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 45a d + 10a b c d + 3b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 90a c d + 20a b c d + 6b c d)x - 45a c d + 10a b c d + 3b c
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 90a d + 20a b c d + 6b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 180a c d + 40a b c d + 12b c d)x - 90a c d + 20a b c d + 6b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|d \|x + \|c
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 90a d + 20a b c d + 6b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 180a c d + 40a b c d + 12b c d)x - 90a c d + 20a b c d + 6b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|d \|x - \|c
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 4
+--R (- 180a d + 40a b c d + 12b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2
+--R (- 324a c d + 72a b c d - 4b c )x - 128a c d
+--R *
+--R +-+4+-+4+-+3
+--R \|2 \|c \|d
+--R /
+--R 3 3 4 4 2 2 5 +-+4+-+4+-+3 +-+
+--R (64c d x + 128c d x + 64c d)\|2 \|c \|d \|x
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 4 4 2 2 5
+--R (- 16c d x - 32c d x - 16c d)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 4100625a d + 3645000a b c d - 121500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 549000a b c d + 42650a b c d + 36600a b c d - 540a b c d
+--R +
+--R 7 7 8 8
+--R - 1080a b c d - 81b c
+--R /
+--R 13 7
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 91125a d - 60750a b c d - 4725a b c d + 7100a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 315a b c d - 270a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 5
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 4100625a d + 3645000a b c d - 121500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 549000a b c d + 42650a b c d + 36600a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 540a b c d - 1080a b c d - 81b c
+--R /
+--R 13 7
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 3 4 4 2 2 5
+--R (16c d x + 32c d x + 16c d)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 4100625a d + 3645000a b c d - 121500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 549000a b c d + 42650a b c d + 36600a b c d - 540a b c d
+--R +
+--R 7 7 8 8
+--R - 1080a b c d - 81b c
+--R /
+--R 13 7
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 91125a d - 60750a b c d - 4725a b c d + 7100a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 315a b c d - 270a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 10 5
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 4100625a d + 3645000a b c d - 121500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 549000a b c d + 42650a b c d + 36600a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 540a b c d - 1080a b c d - 81b c
+--R /
+--R 13 7
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 3 4 4 2 2 5
+--R (- 32c d x - 64c d x - 32c d)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 4100625a d + 3645000a b c d - 121500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 549000a b c d + 42650a b c d + 36600a b c d - 540a b c d
+--R +
+--R 7 7 8 8
+--R - 1080a b c d - 81b c
+--R /
+--R 13 7
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 10 5
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 4100625a d + 3645000a b c d - 121500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 549000a b c d + 42650a b c d + 36600a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 540a b c d - 1080a b c d - 81b c
+--R /
+--R 13 7
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 91125a d - 60750a b c d - 4725a b c d + 7100a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 315a b c d - 270a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 3 2 2 2 4 2 2 2 2 3 2
+--R (- 45a d + 10a b c d + 3b c d)x + (- 81a c d + 18a b c d - b c )x
+--R +
+--R 2 2
+--R - 32a c d
+--R /
+--R 3 3 4 4 2 2 5 +-+
+--R (16c d x + 32c d x + 16c d)\|x
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 45a d + 10a b c d + 3b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R -
+--R 3 +-+
+--R 64c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 4100625a d + 3645000a b c d - 121500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 549000a b c d + 42650a b c d + 36600a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 540a b c d - 1080a b c d - 81b c
+--R /
+--R 13 7
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 91125a d - 60750a b c d - 4725a b c d + 7100a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 315a b c d - 270a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 5
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 4100625a d + 3645000a b c d - 121500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 549000a b c d + 42650a b c d + 36600a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 540a b c d - 1080a b c d - 81b c
+--R /
+--R 13 7
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 +-+
+--R 64c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 4100625a d + 3645000a b c d - 121500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 549000a b c d + 42650a b c d + 36600a b c d - 540a b c d
+--R +
+--R 7 7 8 8
+--R - 1080a b c d - 81b c
+--R /
+--R 13 7
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 91125a d - 60750a b c d - 4725a b c d + 7100a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 315a b c d - 270a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 10 5
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 4100625a d + 3645000a b c d - 121500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 549000a b c d + 42650a b c d + 36600a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 540a b c d - 1080a b c d - 81b c
+--R /
+--R 13 7
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (45a d - 10a b c d - 3b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (90a d - 20a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (90a d - 20a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R -
+--R 3 +-+
+--R 128c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 4100625a d + 3645000a b c d - 121500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 549000a b c d + 42650a b c d + 36600a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 540a b c d - 1080a b c d - 81b c
+--R /
+--R 13 7
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R atan
+--R 10 5
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 4100625a d + 3645000a b c d - 121500a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R - 549000a b c d + 42650a b c d + 36600a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 540a b c d - 1080a b c d - 81b c
+--R /
+--R 13 7
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 91125a d - 60750a b c d - 4725a b c d + 7100a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 315a b c d - 270a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3 +-+4+-+4+-+3
+--R 64c d\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 1475
+t0:=(a+b*x^2)^2/(x^(5/2)*(c+d*x^2)^3)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------------------------
+--R 3 8 2 6 2 4 3 2 +-+
+--R (d x + 3c d x + 3c d x + c x )\|x
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 1475
+r0:=-2/3*a^2/(c*x^(3/2)*(c+d*x^2)^2)-1/32*(3*b^2*c^2+7*a*d*(6*b*c-_
+ 11*a*d))*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(15/4)*_
+ d^(5/4)*sqrt(2))+1/32*(3*b^2*c^2+7*a*d*(6*b*c-11*a*d))*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(15/4)*d^(5/4)*_
+ sqrt(2))-1/64*(3*b^2*c^2+7*a*d*(6*b*c-11*a*d))*log(sqrt(c)+_
+ x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(15/4)*d^(5/4)*_
+ sqrt(2))+1/64*(3*b^2*c^2+7*a*d*(6*b*c-11*a*d))*log(sqrt(c)+_
+ x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(15/4)*d^(5/4)*_
+ sqrt(2))-1/12*(3*b^2*c^2-6*a*b*c*d+11*a^2*d^2)*sqrt(x)/(c^2*_
+ d*(c+d*x^2)^2)+1/48*(3*b^2*c^2+7*a*d*(6*b*c-11*a*d))*sqrt(x)/_
+ (c^3*d*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 5
+--R (- 231a d + 126a b c d + 9b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (- 462a c d + 252a b c d + 18b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (- 231a c d + 126a b c d + 9b c )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 5
+--R (231a d - 126a b c d - 9b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (462a c d - 252a b c d - 18b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (231a c d - 126a b c d - 9b c )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 5
+--R (- 462a d + 252a b c d + 18b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (- 924a c d + 504a b c d + 36b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (- 462a c d + 252a b c d + 18b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|d \|x + \|c
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 5
+--R (- 462a d + 252a b c d + 18b c d )x
+--R +
+--R 2 3 2 2 2 3 3
+--R (- 924a c d + 504a b c d + 36b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R (- 462a c d + 252a b c d + 18b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|d \|x - \|c
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 4
+--R (- 308a d + 168a b c d + 12b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2
+--R (- 484a c d + 264a b c d - 36b c )x - 128a c d
+--R *
+--R +-+4+-+3 4+-+
+--R \|2 \|c \|d
+--R /
+--R 3 3 5 4 2 3 5 +-+4+-+3 4+-+ +-+
+--R (192c d x + 384c d x + 192c d x)\|2 \|c \|d \|x
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 5 4 2 3 5
+--R (- 48c d x - 96c d x - 48c d x)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 35153041a d + 76697544a b c d - 57274140a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 13854456a b c d + 1457946a b c d - 539784a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 86940a b c d - 4536a b c d - 81b c
+--R /
+--R 15 5
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (77a d - 42a b c d - 3b c )\|x
+--R +
+--R 4
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 35153041a d + 76697544a b c d - 57274140a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 13854456a b c d + 1457946a b c d - 539784a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 86940a b c d - 4536a b c d - 81b c
+--R /
+--R 15 5
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R 3 3 5 4 2 3 5
+--R (48c d x + 96c d x + 48c d x)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 35153041a d + 76697544a b c d - 57274140a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 13854456a b c d + 1457946a b c d - 539784a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 86940a b c d - 4536a b c d - 81b c
+--R /
+--R 15 5
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (77a d - 42a b c d - 3b c )\|x
+--R +
+--R -
+--R 4
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 35153041a d + 76697544a b c d - 57274140a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 13854456a b c d + 1457946a b c d - 539784a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 86940a b c d - 4536a b c d - 81b c
+--R /
+--R 15 5
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R 3 3 5 4 2 3 5
+--R (96c d x + 192c d x + 96c d x)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 35153041a d + 76697544a b c d - 57274140a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 13854456a b c d + 1457946a b c d - 539784a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 86940a b c d - 4536a b c d - 81b c
+--R /
+--R 15 5
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 4
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 35153041a d + 76697544a b c d - 57274140a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 13854456a b c d + 1457946a b c d - 539784a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 86940a b c d - 4536a b c d - 81b c
+--R /
+--R 15 5
+--R 16777216c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (77a d - 42a b c d - 3b c )\|x
+--R +
+--R 2 3 2 2 2 4 2 2 2 2 3 2
+--R (- 77a d + 42a b c d + 3b c d)x + (- 121a c d + 66a b c d - 9b c )x
+--R +
+--R 2 2
+--R - 32a c d
+--R /
+--R 3 3 5 4 2 3 5 +-+
+--R (48c d x + 96c d x + 48c d x)\|x
+--R Type: Union(Expression(Integer),...)
+--E 18
+
+--S 19 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (77a d - 42a b c d - 3b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R -
+--R 3 +-+
+--R 64c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 35153041a d + 76697544a b c d - 57274140a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 13854456a b c d + 1457946a b c d - 539784a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 86940a b c d - 4536a b c d - 81b c
+--R /
+--R 15 5
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (77a d - 42a b c d - 3b c )\|x
+--R +
+--R 4
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 35153041a d + 76697544a b c d - 57274140a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 13854456a b c d + 1457946a b c d - 539784a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 86940a b c d - 4536a b c d - 81b c
+--R /
+--R 15 5
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R 3 +-+
+--R 64c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 35153041a d + 76697544a b c d - 57274140a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 13854456a b c d + 1457946a b c d - 539784a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 86940a b c d - 4536a b c d - 81b c
+--R /
+--R 15 5
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (77a d - 42a b c d - 3b c )\|x
+--R +
+--R -
+--R 4
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 35153041a d + 76697544a b c d - 57274140a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 13854456a b c d + 1457946a b c d - 539784a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 86940a b c d - 4536a b c d - 81b c
+--R /
+--R 15 5
+--R 16777216c d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 77a d + 42a b c d + 3b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (154a d - 84a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (154a d - 84a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 +-+
+--R 128c d\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 35153041a d + 76697544a b c d - 57274140a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 13854456a b c d + 1457946a b c d - 539784a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 86940a b c d - 4536a b c d - 81b c
+--R /
+--R 15 5
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R atan
+--R 4
+--R 64c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 35153041a d + 76697544a b c d - 57274140a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 13854456a b c d + 1457946a b c d - 539784a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 86940a b c d - 4536a b c d - 81b c
+--R /
+--R 15 5
+--R 16777216c d
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (77a d - 42a b c d - 3b c )\|x
+--R /
+--R 3 +-+4+-+3 4+-+
+--R 64c d\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 20
+
+)clear all
+
+--S 21 of 1475
+t0:=(a+b*x^2)^2/(x^(7/2)*(c+d*x^2)^3)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------------------------
+--R 3 9 2 7 2 5 3 3 +-+
+--R (d x + 3c d x + 3c d x + c x )\|x
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 1475
+r0:=-2/5*a^2/(c*x^(5/2)*(c+d*x^2)^2)-1/32*(5*b^2*c^2-9*a*d*(10*b*c-_
+ 13*a*d))*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(17/4)*_
+ d^(3/4)*sqrt(2))+1/32*(5*b^2*c^2-9*a*d*(10*b*c-13*a*d))*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(17/4)*d^(3/4)*_
+ sqrt(2))+1/64*(5*b^2*c^2-9*a*d*(10*b*c-13*a*d))*log(sqrt(c)+_
+ x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(17/4)*d^(3/4)*_
+ sqrt(2))-1/64*(5*b^2*c^2-9*a*d*(10*b*c-13*a*d))*log(sqrt(c)+_
+ x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(17/4)*d^(3/4)*_
+ sqrt(2))+1/16*(5*b^2*c^2-9*a*d*(10*b*c-13*a*d))/(c^4*d*sqrt(x))+_
+ 1/20*(-5*b^2*c^2+10*a*b*c*d-13*a^2*d^2)/(c^2*d*(c+d*x^2)^2*_
+ sqrt(x))+1/80*(-5*b^2*c^2+9*a*d*(10*b*c-13*a*d))/(c^3*d*(c+d*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 6
+--R (- 585a d + 450a b c d - 25b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 1170a c d + 900a b c d - 50b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (- 585a c d + 450a b c d - 25b c )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 6
+--R (585a d - 450a b c d + 25b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (1170a c d - 900a b c d + 50b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (585a c d - 450a b c d + 25b c )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 6
+--R (1170a d - 900a b c d + 50b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (2340a c d - 1800a b c d + 100b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (1170a c d - 900a b c d + 50b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|d \|x + \|c
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 6
+--R (1170a d - 900a b c d + 50b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (2340a c d - 1800a b c d + 100b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (1170a c d - 900a b c d + 50b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|d \|x - \|c
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 6
+--R (2340a d - 1800a b c d + 100b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (4212a c d - 3240a b c d + 180b c )x + (1664a c d - 1280a b c )x
+--R +
+--R 2 3
+--R - 128a c
+--R *
+--R +-+4+-+4+-+3
+--R \|2 \|c \|d
+--R /
+--R 4 2 6 5 4 6 2 +-+4+-+4+-+3 +-+
+--R (320c d x + 640c d x + 320c x )\|2 \|c \|d \|x
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 6 5 4 6 2
+--R (80c d x + 160c d x + 80c x )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 187388721a d + 576580680a b c d - 697317660a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 415092600a b c d - 124525350a b c d + 17739000a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 1273500a b c d + 45000a b c d - 625b c
+--R /
+--R 17 3
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4
+--R 1601613a d - 3696030a b c d + 3048435a b c d
+--R +
+--R 3 3 3 3 2 4 4 2 5 5 6 6
+--R - 1044900a b c d + 130275a b c d - 6750a b c d + 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 13 2
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 187388721a d + 576580680a b c d - 697317660a b c d
+--R +
+--R 5 3 3 5 4 4 4 4
+--R 415092600a b c d - 124525350a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7
+--R 17739000a b c d - 1273500a b c d + 45000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 17 3
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 2 6 5 4 6 2
+--R (- 80c d x - 160c d x - 80c x )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 187388721a d + 576580680a b c d - 697317660a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 415092600a b c d - 124525350a b c d + 17739000a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 1273500a b c d + 45000a b c d - 625b c
+--R /
+--R 17 3
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4
+--R 1601613a d - 3696030a b c d + 3048435a b c d
+--R +
+--R 3 3 3 3 2 4 4 2 5 5 6 6
+--R - 1044900a b c d + 130275a b c d - 6750a b c d + 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 13 2
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7
+--R - 187388721a d + 576580680a b c d
+--R +
+--R 6 2 2 6 5 3 3 5
+--R - 697317660a b c d + 415092600a b c d
+--R +
+--R 4 4 4 4 3 5 5 3
+--R - 124525350a b c d + 17739000a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 1273500a b c d + 45000a b c d - 625b c
+--R /
+--R 17 3
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 2 6 5 4 6 2
+--R (160c d x + 320c d x + 160c x )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 187388721a d + 576580680a b c d - 697317660a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 415092600a b c d - 124525350a b c d + 17739000a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 1273500a b c d + 45000a b c d - 625b c
+--R /
+--R 17 3
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 13 2
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 187388721a d + 576580680a b c d - 697317660a b c d
+--R +
+--R 5 3 3 5 4 4 4 4
+--R 415092600a b c d - 124525350a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7
+--R 17739000a b c d - 1273500a b c d + 45000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 17 3
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4
+--R 1601613a d - 3696030a b c d + 3048435a b c d
+--R +
+--R 3 3 3 3 2 4 4 2 5 5 6 6
+--R - 1044900a b c d + 130275a b c d - 6750a b c d + 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 3 2 2 2 6
+--R (585a d - 450a b c d + 25b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (1053a c d - 810a b c d + 45b c )x + (416a c d - 320a b c )x - 32a c
+--R /
+--R 4 2 6 5 4 6 2 +-+
+--R (80c d x + 160c d x + 80c x )\|x
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (117a d - 90a b c d + 5b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4 +-+
+--R 64c \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 187388721a d + 576580680a b c d - 697317660a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 415092600a b c d - 124525350a b c d + 17739000a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 1273500a b c d + 45000a b c d - 625b c
+--R /
+--R 17 3
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4
+--R 1601613a d - 3696030a b c d + 3048435a b c d
+--R +
+--R 3 3 3 3 2 4 4 2 5 5 6 6
+--R - 1044900a b c d + 130275a b c d - 6750a b c d + 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 13 2
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 187388721a d + 576580680a b c d - 697317660a b c d
+--R +
+--R 5 3 3 5 4 4 4 4
+--R 415092600a b c d - 124525350a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7
+--R 17739000a b c d - 1273500a b c d + 45000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 17 3
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 4 +-+
+--R 64c \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 187388721a d + 576580680a b c d - 697317660a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 415092600a b c d - 124525350a b c d + 17739000a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 1273500a b c d + 45000a b c d - 625b c
+--R /
+--R 17 3
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4
+--R 1601613a d - 3696030a b c d + 3048435a b c d
+--R +
+--R 3 3 3 3 2 4 4 2 5 5 6 6
+--R - 1044900a b c d + 130275a b c d - 6750a b c d + 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 13 2
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7
+--R - 187388721a d + 576580680a b c d
+--R +
+--R 6 2 2 6 5 3 3 5
+--R - 697317660a b c d + 415092600a b c d
+--R +
+--R 4 4 4 4 3 5 5 3
+--R - 124525350a b c d + 17739000a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 1273500a b c d + 45000a b c d - 625b c
+--R /
+--R 17 3
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 117a d + 90a b c d - 5b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x + \|c
+--R (- 234a d + 180a b c d - 10b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|d \|x - \|c
+--R (- 234a d + 180a b c d - 10b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 4 +-+
+--R 128c \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 187388721a d + 576580680a b c d - 697317660a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 415092600a b c d - 124525350a b c d + 17739000a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 1273500a b c d + 45000a b c d - 625b c
+--R /
+--R 17 3
+--R 16777216c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R atan
+--R 13 2
+--R 262144c d
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 187388721a d + 576580680a b c d - 697317660a b c d
+--R +
+--R 5 3 3 5 4 4 4 4
+--R 415092600a b c d - 124525350a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7
+--R 17739000a b c d - 1273500a b c d + 45000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 17 3
+--R 16777216c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4
+--R 1601613a d - 3696030a b c d + 3048435a b c d
+--R +
+--R 3 3 3 3 2 4 4 2 5 5 6 6
+--R - 1044900a b c d + 130275a b c d - 6750a b c d + 125b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 4 +-+4+-+4+-+3
+--R 64c \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 1475
+t0:=x^(7/2)*(a+b*x^2)^2*sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 7 5 2 3 +-+ | 2
+--R (1) (b x + 2a b x + a x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 1475
+--r0:=-2/285*b*(13*b*c-38*a*d)*x^(9/2)*(c+d*x^2)^(3/2)/d^2+2/19*b^2*_
+-- x^(13/2)*(c+d*x^2)^(3/2)/d+4/7315*c*(95*a^2*d^2+3*b*c*(13*b*c-_
+-- 38*a*d))*x^(5/2)*sqrt(c+d*x^2)/d^3+2/1045*(95*a^2*d^2+3*b*c*_
+-- (13*b*c-38*a*d))*x^(9/2)*sqrt(c+d*x^2)/d^2-4/4389*c^2*(95*a^2*_
+-- d^2+3*b*c*(13*b*c-38*a*d))*sqrt(x)*sqrt(c+d*x^2)/d^4+4/4389*_
+-- c^(13/4)*(95*a^2*d^2+3*b*c*(13*b*c-38*a*d))*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-d)^(17/4)*sqrt(c+d*x^2))
+--E 27
+
+--S 28 of 1475
+--a0:=integrate(t0,x)
+--E 28
+
+--S 29 of 1475
+--m0:=a0-r0
+--E 29
+
+--S 30 of 1475
+--d0:=D(m0,x)
+--E 30
+
+)clear all
+
+--S 31 of 1475
+t0:=x^(5/2)*(a+b*x^2)^2*sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 6 4 2 2 +-+ | 2
+--R (1) (b x + 2a b x + a x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 1475
+--r0:=-2/221*b*(11*b*c-34*a*d)*x^(7/2)*(c+d*x^2)^(3/2)/d^2+2/17*b^2*_
+-- x^(11/2)*(c+d*x^2)^(3/2)/d+4/9945*c*(221*a^2*d^2+7*b*c*(11*b*c-_
+-- 34*a*d))*x^(3/2)*sqrt(c+d*x^2)/d^3+2/1989*(221*a^2*d^2+7*b*c*_
+-- (11*b*c-34*a*d))*x^(7/2)*sqrt(c+d*x^2)/d^2+4/3315*c^(11/4)*_
+-- (77*b^2*c^2-238*a*b*c*d+221*a^2*d^2)*elliptic_e(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(15/4)*sqrt(c+d*x^2))-_
+-- 4/3315*c^(11/4)*(77*b^2*c^2-238*a*b*c*d+221*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(15/4)*sqrt(c+d*x^2))
+--E 32
+
+--S 33 of 1475
+--a0:=integrate(t0,x)
+--E 33
+
+--S 34 of 1475
+--m0:=a0-r0
+--E 34
+
+--S 35 of 1475
+--d0:=D(m0,x)
+--E 35
+
+)clear all
+
+--S 36 of 1475
+t0:=x^(3/2)*(a+b*x^2)^2*sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 5 3 2 +-+ | 2
+--R (1) (b x + 2a b x + a x)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 1475
+--r0:=-2/55*b*(3*b*c-10*a*d)*x^(5/2)*(c+d*x^2)^(3/2)/d^2+2/15*b^2*_
+-- x^(9/2)*(c+d*x^2)^(3/2)/d+2/77*(11*a^2*d^2+b*c*(3*b*c-10*a*d))*_
+-- x^(5/2)*sqrt(c+d*x^2)/d^2+4/231*c*(11*a^2*d^2+b*c*(3*b*c-_
+-- 10*a*d))*sqrt(x)*sqrt(c+d*x^2)/d^3+4/231*c^(9/4)*(11*a^2*d^2+_
+-- b*c*(3*b*c-10*a*d))*elliptic_f(asin((-d)^(1/4)*sqrt(x)/_
+-- c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(13/4)*sqrt(c+d*x^2))
+--E 37
+
+--S 38 of 1475
+--a0:=integrate(t0,x)
+--E 38
+
+--S 39 of 1475
+--m0:=a0-r0
+--E 39
+
+--S 40 of 1475
+--d0:=D(m0,x)
+--E 40
+
+)clear all
+
+--S 41 of 1475
+t0:=(a+b*x^2)^2*sqrt(x)*sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 +-+ | 2
+--R (1) (b x + 2a b x + a )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 1475
+--r0:=-2/117*b*(7*b*c-26*a*d)*x^(3/2)*(c+d*x^2)^(3/2)/d^2+2/13*b^2*_
+-- x^(7/2)*(c+d*x^2)^(3/2)/d+2/195*(39*a^2*d^2+b*c*(7*b*c-26*a*d))*_
+-- x^(3/2)*sqrt(c+d*x^2)/d^2+4/195*c^(7/4)*(39*a^2*d^2+b*c*(7*b*c-_
+-- 26*a*d))*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(11/4)*sqrt(c+d*x^2))-4/195*c^(7/4)*_
+-- (39*a^2*d^2+b*c*(7*b*c-26*a*d))*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(11/4)*sqrt(c+d*x^2))
+--E 42
+
+--S 43 of 1475
+--a0:=integrate(t0,x)
+--E 43
+
+--S 44 of 1475
+--m0:=a0-r0
+--E 44
+
+--S 45 of 1475
+--d0:=D(m0,x)
+--E 45
+
+)clear all
+
+--S 46 of 1475
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)/sqrt(x)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R (1) --------------------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 1475
+--r0:=2/11*b^2*x^(5/2)*(c+d*x^2)^(3/2)/d-2/77*b*(5*b*c-22*a*d)*_
+-- (c+d*x^2)^(3/2)*sqrt(x)/d^2+2/231*(5*b^2*c^2-22*a*b*c*d+77*_
+-- a^2*d^2)*sqrt(x)*sqrt(c+d*x^2)/d^2+4/231*c^(5/4)*(5*b^2*c^2-_
+-- 22*a*b*c*d+77*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/_
+-- c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(9/4)*sqrt(c+d*x^2))
+--E 47
+
+--S 48 of 1475
+--a0:=integrate(t0,x)
+--E 48
+
+--S 49 of 1475
+--m0:=a0-r0
+--E 49
+
+--S 50 of 1475
+--d0:=D(m0,x)
+--E 50
+
+)clear all
+
+--S 51 of 1475
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)/x^(3/2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R (1) --------------------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 1475
+--r0:=2/9*b^2*x^(3/2)*(c+d*x^2)^(3/2)/d-2*a^2*(c+d*x^2)^(3/2)/_
+-- (c*sqrt(x))-2/15*(b^2*c^2-3*a*d*(2*b*c+5*a*d))*x^(3/2)*sqrt(c+_
+-- d*x^2)/(c*d)+4/15*c^(3/4)*(b^2*c^2-3*a*d*(2*b*c+5*a*d))*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/((-d)^(7/4)*sqrt(c+d*x^2))-4/15*c^(3/4)*(b^2*c^2-3*a*d*(2*b*_
+-- c+5*a*d))*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(7/4)*sqrt(c+d*x^2))
+--E 52
+
+--S 53 of 1475
+--a0:=integrate(t0,x)
+--E 53
+
+--S 54 of 1475
+--m0:=a0-r0
+--E 54
+
+--S 55 of 1475
+--d0:=D(m0,x)
+--E 55
+
+)clear all
+
+--S 56 of 1475
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)/x^(5/2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R (1) --------------------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 1475
+--r0:=-2/3*a^2*(c+d*x^2)^(3/2)/(c*x^(3/2))+2/7*b^2*(c+d*x^2)^(3/2)*_
+-- sqrt(x)/d-2/21*(b^2*c^2-7*a*d*(2*b*c+a*d))*sqrt(x)*sqrt(c+d*x^2)/_
+-- (c*d)+4/21*c^(1/4)*(b^2*c^2-7*a*d*(2*b*c+a*d))*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/((-d)^(5/4)*sqrt(c+d*x^2))
+--E 57
+
+--S 58 of 1475
+--a0:=integrate(t0,x)
+--E 58
+
+--S 59 of 1475
+--m0:=a0-r0
+--E 59
+
+--S 60 of 1475
+--d0:=D(m0,x)
+--E 60
+
+)clear all
+
+--S 61 of 1475
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)/x^(7/2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R (1) --------------------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 1475
+--r0:=-2/5*a^2*(c+d*x^2)^(3/2)/(c*x^(5/2))-2/5*a*(10*b*c+a*d)*_
+-- (c+d*x^2)^(3/2)/(c^2*sqrt(x))+2/5*(b^2*c^2+a*d*(10*b*c+a*d))*_
+-- x^(3/2)*sqrt(c+d*x^2)/c^2+4/5*(b^2*c^2+a*d*(10*b*c+a*d))*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(c^(1/4)*(-d)^(3/4)*sqrt(c+d*x^2))-4/5*(b^2*c^2+a*d*(10*b*_
+-- c+a*d))*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(1/4)*(-d)^(3/4)*sqrt(c+d*x^2))
+--E 62
+
+--S 63 of 1475
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 1475
+--m0:=a0-r0
+--E 64
+
+--S 65 of 1475
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 1475
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)/x^(9/2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R (1) --------------------------------
+--R 4 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 1475
+--r0:=-2/7*a^2*(c+d*x^2)^(3/2)/(c*x^(7/2))-2/21*a*(14*b*c-a*d)*_
+-- (c+d*x^2)^(3/2)/(c^2*x^(3/2))+2/21*(7*b^2*c^2+a*d*(14*b*c-a*d))*_
+-- sqrt(x)*sqrt(c+d*x^2)/c^2+4/21*(7*b^2*c^2+a*d*(14*b*c-a*d))*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(c^(3/4)*(-d)^(1/4)*sqrt(c+d*x^2))
+--E 67
+
+--S 68 of 1475
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 1475
+--m0:=a0-r0
+--E 69
+
+--S 70 of 1475
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 1475
+t0:=(a+b*x^2)^2*sqrt(c+d*x^2)/x^(11/2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R (1) --------------------------------
+--R 5 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 1475
+--r0:=-2/9*a^2*(c+d*x^2)^(3/2)/(c*x^(9/2))-2/15*a*(6*b*c-a*d)*(c+d*_
+-- x^2)^(3/2)/(c^2*x^(5/2))-2/15*(15*b^2*c^2+a*d*(6*b*c-a*d))*_
+-- sqrt(c+d*x^2)/(c^2*sqrt(x))-4/15*(-d)^(1/4)*(15*b^2*c^2+a*d*_
+-- (6*b*c-a*d))*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(5/4)*sqrt(c+d*x^2))+4/15*(-d)^(1/4)*_
+-- (15*b^2*c^2+a*d*(6*b*c-a*d))*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(5/4)*sqrt(c+d*x^2))
+--E 72
+
+--S 73 of 1475
+--a0:=integrate(t0,x)
+--E 73
+
+--S 74 of 1475
+--m0:=a0-r0
+--E 74
+
+--S 75 of 1475
+--d0:=D(m0,x)
+--E 75
+
+)clear all
+
+--S 76 of 1475
+t0:=x^(7/2)*(a+b*x^2)^2*(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 9 2 7 2 5 2 3 +-+ | 2
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 1475
+--r0:=2/6555*(437*a^2*d^2+9*b*c*(13*b*c-46*a*d))*x^(9/2)*(c+d*x^2)^(3/2)/_
+-- d^2-2/437*b*(13*b*c-46*a*d)*x^(9/2)*(c+d*x^2)^(5/2)/d^2+2/23*b^2*_
+-- x^(13/2)*(c+d*x^2)^(5/2)/d+8/168245*c^2*(437*a^2*d^2+9*b*c*(13*_
+-- b*c-46*a*d))*x^(5/2)*sqrt(c+d*x^2)/d^3+4/24035*c*(437*a^2*d^2+9*_
+-- b*c*(13*b*c-46*a*d))*x^(9/2)*sqrt(c+d*x^2)/d^2-8/100947*c^3*_
+-- (437*a^2*d^2+9*b*c*(13*b*c-46*a*d))*sqrt(x)*sqrt(c+d*x^2)/d^4+_
+-- 8/100947*c^(17/4)*(437*a^2*d^2+9*b*c*(13*b*c-46*a*d))*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(17/4)*sqrt(c+d*x^2))
+--E 77
+
+--S 78 of 1475
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 1475
+--m0:=a0-r0
+--E 79
+
+--S 80 of 1475
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 1475
+t0:=x^(5/2)*(a+b*x^2)^2*(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 8 2 6 2 4 2 2 +-+ | 2
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 1475
+--r0:=2/663*(51*a^2*d^2+b*c*(11*b*c-42*a*d))*x^(7/2)*(c+d*x^2)^(3/2)/d^2-_
+-- 2/357*b*(11*b*c-42*a*d)*x^(7/2)*(c+d*x^2)^(5/2)/d^2+2/21*b^2*_
+-- x^(11/2)*(c+d*x^2)^(5/2)/d+8/9945*c^2*(51*a^2*d^2+b*c*_
+-- (11*b*c-42*a*d))*x^(3/2)*sqrt(c+d*x^2)/d^3+4/1989*c*(51*a^2*_
+-- d^2+b*c*(11*b*c-42*a*d))*x^(7/2)*sqrt(c+d*x^2)/d^2+8/3315*_
+-- c^(15/4)*(51*a^2*d^2+b*c*(11*b*c-42*a*d))*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(15/4)*sqrt(c+d*x^2))-8/3315*c^(15/4)*_
+-- (51*a^2*d^2+b*c*(11*b*c-42*a*d))*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(15/4)*sqrt(c+d*x^2))
+--E 82
+
+--S 83 of 1475
+--a0:=integrate(t0,x)
+--E 83
+
+--S 84 of 1475
+--m0:=a0-r0
+--E 84
+
+--S 85 of 1475
+--d0:=D(m0,x)
+--E 85
+
+)clear all
+
+--S 86 of 1475
+t0:=x^(3/2)*(a+b*x^2)^2*(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 7 2 5 2 3 2 +-+ | 2
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 1475
+--r0:=2/627*(57*a^2*d^2+b*c*(9*b*c-38*a*d))*x^(5/2)*(c+d*x^2)^(3/2)/d^2-_
+-- 2/285*b*(9*b*c-38*a*d)*x^(5/2)*(c+d*x^2)^(5/2)/d^2+2/19*b^2*_
+-- x^(9/2)*(c+d*x^2)^(5/2)/d+4/1463*c*(57*a^2*d^2+b*c*(9*b*c-_
+-- 38*a*d))*x^(5/2)*sqrt(c+d*x^2)/d^2+8/4389*c^2*(57*a^2*d^2+b*c*_
+-- (9*b*c-38*a*d))*sqrt(x)*sqrt(c+d*x^2)/d^3+8/4389*c^(13/4)*_
+-- (57*a^2*d^2+b*c*(9*b*c-38*a*d))*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(13/4)*sqrt(c+d*x^2))
+--E 87
+
+--S 88 of 1475
+--a0:=integrate(t0,x)
+--E 88
+
+--S 89 of 1475
+--m0:=a0-r0
+--E 89
+
+--S 90 of 1475
+--d0:=D(m0,x)
+--E 90
+
+)clear all
+
+--S 91 of 1475
+t0:=(a+b*x^2)^2*(c+d*x^2)^(3/2)*sqrt(x)
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 +-+ | 2
+--R (1) (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 1475
+--r0:=2/1989*(221*a^2*d^2+3*b*c*(7*b*c-34*a*d))*x^(3/2)*_
+-- (c+d*x^2)^(3/2)/d^2-2/221*b*(7*b*c-34*a*d)*x^(3/2)*_
+-- (c+d*x^2)^(5/2)/d^2+2/17*b^2*x^(7/2)*(c+d*x^2)^(5/2)/d+_
+-- 4/3315*c*(221*a^2*d^2+3*b*c*(7*b*c-34*a*d))*x^(3/2)*_
+-- sqrt(c+d*x^2)/d^2+8/3315*c^(11/4)*(221*a^2*d^2+3*b*c*_
+-- (7*b*c-34*a*d))*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(11/4)*sqrt(c+d*x^2))-8/3315*c^(11/4)*_
+-- (221*a^2*d^2+3*b*c*(7*b*c-34*a*d))*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(11/4)*sqrt(c+d*x^2))
+--E 92
+
+--S 93 of 1475
+--a0:=integrate(t0,x)
+--E 93
+
+--S 94 of 1475
+--m0:=a0-r0
+--E 94
+
+--S 95 of 1475
+--d0:=D(m0,x)
+--E 95
+
+)clear all
+
+--S 96 of 1475
+t0:=(a+b*x^2)^2*(c+d*x^2)^(3/2)/sqrt(x)
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R (1) ---------------------------------------------------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 1475
+--r0:=2/15*b^2*x^(5/2)*(c+d*x^2)^(5/2)/d+2/231*(33*a^2*d^2+b*c*_
+-- (b*c-6*a*d))*(c+d*x^2)^(3/2)*sqrt(x)/d^2-2/33*b*(b*c-6*a*d)*_
+-- (c+d*x^2)^(5/2)*sqrt(x)/d^2+4/231*c*(33*a^2*d^2+b*c*(b*c-6*a*d))*_
+-- sqrt(x)*sqrt(c+d*x^2)/d^2+8/231*c^(9/4)*(33*a^2*d^2+b*c*(b*c-6*a*d))*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(9/4)*sqrt(c+d*x^2))
+--E 97
+
+--S 98 of 1475
+--a0:=integrate(t0,x)
+--E 98
+
+--S 99 of 1475
+--m0:=a0-r0
+--E 99
+
+--S 100 of 1475
+--d0:=D(m0,x)
+--E 100
+
+)clear all
+
+--S 101 of 1475
+t0:=(a+b*x^2)^2*(c+d*x^2)^(3/2)/x^(3/2)
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R (1) ---------------------------------------------------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 1475
+--r0:=-2/117*(3*b^2*c^2-13*a*d*(2*b*c+9*a*d))*x^(3/2)*(c+d*x^2)^(3/2)/_
+-- (c*d)+2/13*b^2*x^(3/2)*(c+d*x^2)^(5/2)/d-2*a^2*(c+d*x^2)^(5/2)/_
+-- (c*sqrt(x))-4/195*(3*b^2*c^2-13*a*d*(2*b*c+9*a*d))*x^(3/2)*_
+-- sqrt(c+d*x^2)/d+8/195*c^(7/4)*(3*b^2*c^2-13*a*d*(2*b*c+9*a*d))*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/((-d)^(7/4)*sqrt(c+d*x^2))-8/195*c^(7/4)*(3*b^2*c^2-13*a*d*_
+-- (2*b*c+9*a*d))*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(7/4)*sqrt(c+d*x^2))
+--E 102
+
+--S 103 of 1475
+--a0:=integrate(t0,x)
+--E 103
+
+--S 104 of 1475
+--m0:=a0-r0
+--E 104
+
+--S 105 of 1475
+--d0:=D(m0,x)
+--E 105
+
+)clear all
+
+--S 106 of 1475
+t0:=(a+b*x^2)^2*(c+d*x^2)^(3/2)/x^(5/2)
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R (1) ---------------------------------------------------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 1475
+--r0:=-2/3*a^2*(c+d*x^2)^(5/2)/(c*x^(3/2))-2/231*(3*b^2*c^2-11*a*d*_
+-- (6*b*c+7*a*d))*(c+d*x^2)^(3/2)*sqrt(x)/(c*d)+2/11*b^2*_
+-- (c+d*x^2)^(5/2)*sqrt(x)/d-4/231*(3*b^2*c^2-11*a*d*(6*b*c+7*a*d))*_
+-- sqrt(x)*sqrt(c+d*x^2)/d+8/231*c^(5/4)*(3*b^2*c^2-11*a*d*_
+-- (6*b*c+7*a*d))*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(5/4)*sqrt(c+d*x^2))
+--E 107
+
+--S 108 of 1475
+--a0:=integrate(t0,x)
+--E 108
+
+--S 109 of 1475
+--m0:=a0-r0
+--E 109
+
+--S 110 of 1475
+--d0:=D(m0,x)
+--E 110
+
+)clear all
+
+--S 111 of 1475
+t0:=(a+b*x^2)^2*(c+d*x^2)^(3/2)/x^(7/2)
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R (1) ---------------------------------------------------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 1475
+--r0:=2/9*(b^2*c^2+9*a*d*(2*b*c+a*d))*x^(3/2)*(c+d*x^2)^(3/2)/c^2-_
+-- 2/5*a^2*(c+d*x^2)^(5/2)/(c*x^(5/2))-2*a*(2*b*c+a*d)*_
+-- (c+d*x^2)^(5/2)/(c^2*sqrt(x))+4/15*(b^2*c^2+9*a*d*(2*b*c+a*d))*_
+-- x^(3/2)*sqrt(c+d*x^2)/c+8/15*c^(3/4)*(b^2*c^2+9*a*d*(2*b*c+a*d))*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/((-d)^(3/4)*sqrt(c+d*x^2))-8/15*c^(3/4)*(b^2*c^2+9*a*d*(2*b*_
+-- c+a*d))*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(3/4)*sqrt(c+d*x^2))
+--E 112
+
+--S 113 of 1475
+--a0:=integrate(t0,x)
+--E 113
+
+--S 114 of 1475
+--m0:=a0-r0
+--E 114
+
+--S 115 of 1475
+--d0:=D(m0,x)
+--E 115
+
+)clear all
+
+--S 116 of 1475
+t0:=x^(7/2)*(a+b*x^2)^2*(c+d*x^2)^(5/2)
+--R
+--R
+--R (1)
+--R 2 2 11 2 2 9 2 2 2 2 7
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 5 2 2 3
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|x \|d x + c
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 1475
+--r0:=4/3933*c*(69*a^2*d^2+b*c*(13*b*c-54*a*d))*x^(9/2)*(c+d*x^2)^(3/2)/_
+-- d^2+2/1311*(69*a^2*d^2+b*c*(13*b*c-54*a*d))*x^(9/2)*_
+-- (c+d*x^2)^(5/2)/d^2-2/621*b*(13*b*c-54*a*d)*x^(9/2)*_
+-- (c+d*x^2)^(7/2)/d^2+2/27*b^2*x^(13/2)*(c+d*x^2)^(7/2)/d+_
+-- 16/100947*c^3*(69*a^2*d^2+b*c*(13*b*c-54*a*d))*x^(5/2)*_
+-- sqrt(c+d*x^2)/d^3+8/14421*c^2*(69*a^2*d^2+b*c*(13*b*c-54*a*d))*_
+-- x^(9/2)*sqrt(c+d*x^2)/d^2-80/302841*c^4*(69*a^2*d^2+b*c*(13*b*_
+-- c-54*a*d))*sqrt(x)*sqrt(c+d*x^2)/d^4+80/302841*c^(21/4)*(69*_
+-- a^2*d^2+b*c*(13*b*c-54*a*d))*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(17/4)*sqrt(c+d*x^2))
+--E 117
+
+--S 118 of 1475
+--a0:=integrate(t0,x)
+--E 118
+
+--S 119 of 1475
+--m0:=a0-r0
+--E 119
+
+--S 120 of 1475
+--d0:=D(m0,x)
+--E 120
+
+)clear all
+
+--S 121 of 1475
+t0:=x^(5/2)*(a+b*x^2)^2*(c+d*x^2)^(5/2)
+--R
+--R
+--R (1)
+--R 2 2 10 2 2 8 2 2 2 2 6
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 4 2 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|x \|d x + c
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 1475
+--r0:=4/3315*c*(75*a^2*d^2+b*c*(11*b*c-50*a*d))*x^(7/2)*(c+d*x^2)^(3/2)/_
+-- d^2+2/1275*(75*a^2*d^2+b*c*(11*b*c-50*a*d))*x^(7/2)*_
+-- (c+d*x^2)^(5/2)/d^2-2/525*b*(11*b*c-50*a*d)*x^(7/2)*_
+-- (c+d*x^2)^(7/2)/d^2+2/25*b^2*x^(11/2)*(c+d*x^2)^(7/2)/d+_
+-- 16/49725*c^3*(75*a^2*d^2+b*c*(11*b*c-50*a*d))*x^(3/2)*_
+-- sqrt(c+d*x^2)/d^3+8/9945*c^2*(75*a^2*d^2+b*c*(11*b*c-50*a*d))*_
+-- x^(7/2)*sqrt(c+d*x^2)/d^2+16/16575*c^(19/4)*(75*a^2*d^2+b*_
+-- c*(11*b*c-50*a*d))*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(15/4)*sqrt(c+d*x^2))-16/16575*c^(19/4)*_
+-- (75*a^2*d^2+b*c*(11*b*c-50*a*d))*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(15/4)*sqrt(c+d*x^2))
+--E 122
+
+--S 123 of 1475
+--a0:=integrate(t0,x)
+--E 123
+
+--S 124 of 1475
+--m0:=a0-r0
+--E 124
+
+--S 125 of 1475
+--d0:=D(m0,x)
+--E 125
+
+)clear all
+
+--S 126 of 1475
+t0:=x^(3/2)*(a+b*x^2)^2*(c+d*x^2)^(5/2)
+--R
+--R
+--R (1)
+--R 2 2 9 2 2 7 2 2 2 2 5
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 3 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|x \|d x + c
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 1475
+--r0:=4/14421*c*(437*a^2*d^2+5*b*c*(9*b*c-46*a*d))*x^(5/2)*_
+-- (c+d*x^2)^(3/2)/d^2+2/6555*(437*a^2*d^2+5*b*c*(9*b*c-46*a*d))*_
+-- x^(5/2)*(c+d*x^2)^(5/2)/d^2-2/437*b*(9*b*c-46*a*d)*x^(5/2)*_
+-- (c+d*x^2)^(7/2)/d^2+2/23*b^2*x^(9/2)*(c+d*x^2)^(7/2)/d+8/33649*_
+-- c^2*(437*a^2*d^2+5*b*c*(9*b*c-46*a*d))*x^(5/2)*sqrt(c+d*x^2)/d^2+_
+-- 16/100947*c^3*(437*a^2*d^2+5*b*c*(9*b*c-46*a*d))*sqrt(x)*_
+-- sqrt(c+d*x^2)/d^3+16/100947*c^(17/4)*(45*b^2*c^2-230*a*b*c*d+_
+-- 437*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(13/4)*sqrt(c+d*x^2))
+--E 127
+
+--S 128 of 1475
+--a0:=integrate(t0,x)
+--E 128
+
+--S 129 of 1475
+--m0:=a0-r0
+--E 129
+
+--S 130 of 1475
+--d0:=D(m0,x)
+--E 130
+
+)clear all
+
+--S 131 of 1475
+t0:=(a+b*x^2)^2*(c+d*x^2)^(5/2)*sqrt(x)
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|x \|d x + c
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 1475
+--r0:=20/1989*c*(17*a^2*d^2+b*c*(b*c-6*a*d))*x^(3/2)*(c+d*x^2)^(3/2)/d^2+_
+-- 2/221*(17*a^2*d^2+b*c*(b*c-6*a*d))*x^(3/2)*(c+d*x^2)^(5/2)/d^2-_
+-- 2/51*b*(b*c-6*a*d)*x^(3/2)*(c+d*x^2)^(7/2)/d^2+2/21*b^2*x^(7/2)*_
+-- (c+d*x^2)^(7/2)/d+8/663*c^2*(17*a^2*d^2+b*c*(b*c-6*a*d))*x^(3/2)*_
+-- sqrt(c+d*x^2)/d^2+16/663*c^(15/4)*(17*a^2*d^2+b*c*(b*c-6*a*d))*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-d)^(11/4)*sqrt(c+d*x^2))-16/663*c^(15/4)*(17*a^2*d^2+b*c*_
+-- (b*c-6*a*d))*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(11/4)*sqrt(c+d*x^2))
+--E 132
+
+--S 133 of 1475
+--a0:=integrate(t0,x)
+--E 133
+
+--S 134 of 1475
+--m0:=a0-r0
+--E 134
+
+--S 135 of 1475
+--d0:=D(m0,x)
+--E 135
+
+)clear all
+
+--S 136 of 1475
+t0:=(a+b*x^2)^2*(c+d*x^2)^(5/2)/sqrt(x)
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 1475
+--r0:=2/19*b^2*x^(5/2)*(c+d*x^2)^(7/2)/d+4/4389*c*(5*b^2*c^2-38*a*b*c*d+_
+-- 285*a^2*d^2)*(c+d*x^2)^(3/2)*sqrt(x)/d^2+2/3135*(5*b^2*c^2-38*a*_
+-- b*c*d+285*a^2*d^2)*(c+d*x^2)^(5/2)*sqrt(x)/d^2-2/285*b*(5*b*c-_
+-- 38*a*d)*(c+d*x^2)^(7/2)*sqrt(x)/d^2+8/4389*c^2*(5*b^2*c^2-38*a*_
+-- b*c*d+285*a^2*d^2)*sqrt(x)*sqrt(c+d*x^2)/d^2+16/4389*c^(13/4)*_
+-- (5*b^2*c^2-38*a*b*c*d+285*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(9/4)*sqrt(c+d*x^2))
+--E 137
+
+--S 138 of 1475
+--a0:=integrate(t0,x)
+--E 138
+
+--S 139 of 1475
+--m0:=a0-r0
+--E 139
+
+--S 140 of 1475
+--d0:=D(m0,x)
+--E 140
+
+)clear all
+
+--S 141 of 1475
+t0:=(a+b*x^2)^2*(c+d*x^2)^(5/2)/x^(3/2)
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 1475
+--r0:=-20/1989*(3*b^2*c^2-17*a*d*(2*b*c+13*a*d))*x^(3/2)*_
+-- (c+d*x^2)^(3/2)/d-2/221*(3*b^2*c^2-17*a*d*(2*b*c+13*a*d))*_
+-- x^(3/2)*(c+d*x^2)^(5/2)/(c*d)+2/17*b^2*x^(3/2)*(c+d*x^2)^(7/2)/d-_
+-- 2*a^2*(c+d*x^2)^(7/2)/(c*sqrt(x))-8/663*c*(3*b^2*c^2-17*a*d*_
+-- (2*b*c+13*a*d))*x^(3/2)*sqrt(c+d*x^2)/d+16/663*c^(11/4)*(3*b^2*_
+-- c^2-17*a*d*(2*b*c+13*a*d))*elliptic_e(asin((-d)^(1/4)*sqrt(x)/_
+-- c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(7/4)*sqrt(c+d*x^2))-_
+-- 16/663*c^(11/4)*(3*b^2*c^2-17*a*d*(2*b*c+13*a*d))*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/((-d)^(7/4)*sqrt(c+d*x^2))
+--E 142
+
+--S 143 of 1475
+--a0:=integrate(t0,x)
+--E 143
+
+--S 144 of 1475
+--m0:=a0-r0
+--E 144
+
+--S 145 of 1475
+--d0:=D(m0,x)
+--E 145
+
+)clear all
+
+--S 146 of 1475
+t0:=(a+b*x^2)^2*(c+d*x^2)^(5/2)/x^(5/2)
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 1475
+--r0:=-2/3*a^2*(c+d*x^2)^(7/2)/(c*x^(3/2))-4/231*(b^2*c^2-5*a*d*_
+-- (6*b*c+11*a*d))*(c+d*x^2)^(3/2)*sqrt(x)/d-2/165*(b^2*c^2-5*a*_
+-- d*(6*b*c+11*a*d))*(c+d*x^2)^(5/2)*sqrt(x)/(c*d)+2/15*b^2*(c+_
+-- d*x^2)^(7/2)*sqrt(x)/d-8/231*c*(b^2*c^2-5*a*d*(6*b*c+11*a*d))*_
+-- sqrt(x)*sqrt(c+d*x^2)/d+16/231*c^(9/4)*(b^2*c^2-5*a*d*(6*b*c+_
+-- 11*a*d))*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(5/4)*sqrt(c+d*x^2))
+--E 147
+
+--S 148 of 1475
+--a0:=integrate(t0,x)
+--E 148
+
+--S 149 of 1475
+--m0:=a0-r0
+--E 149
+
+--S 150 of 1475
+--d0:=D(m0,x)
+--E 150
+
+)clear all
+
+--S 151 of 1475
+t0:=(a+b*x^2)^2*(c+d*x^2)^(5/2)/x^(7/2)
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 1475
+--r0:=4/117*(5*b^2*c^2+13*a*d*(10*b*c+9*a*d))*x^(3/2)*(c+d*x^2)^(3/2)/c+_
+-- 2/65*(5*b^2*c^2+13*a*d*(10*b*c+9*a*d))*x^(3/2)*(c+d*x^2)^(5/2)/c^2-_
+-- 2/5*a^2*(c+d*x^2)^(7/2)/(c*x^(5/2))-2/5*a*(10*b*c+9*a*d)*_
+-- (c+d*x^2)^(7/2)/(c^2*sqrt(x))+8/195*(5*b^2*c^2+13*a*d*(10*b*c+_
+-- 9*a*d))*x^(3/2)*sqrt(c+d*x^2)+16/195*c^(7/4)*(5*b^2*c^2+13*a*_
+-- d*(10*b*c+9*a*d))*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(3/4)*sqrt(c+d*x^2))-16/195*c^(7/4)*_
+-- (5*b^2*c^2+13*a*d*(10*b*c+9*a*d))*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(3/4)*sqrt(c+d*x^2))
+--E 152
+
+--S 153 of 1475
+--a0:=integrate(t0,x)
+--E 153
+
+--S 154 of 1475
+--m0:=a0-r0
+--E 154
+
+--S 155 of 1475
+--d0:=D(m0,x)
+--E 155
+
+)clear all
+
+--S 156 of 1475
+t0:=x^(7/2)*(a+b*x^2)^2/sqrt(c+d*x^2)
+--R
+--R
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R (1) ---------------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 1475
+--r0:=2/385*(55*a^2*d^2+3*b*c*(13*b*c-30*a*d))*x^(5/2)*sqrt(c+d*x^2)/d^3-_
+-- 2/165*b*(13*b*c-30*a*d)*x^(9/2)*sqrt(c+d*x^2)/d^2+2/15*b^2*_
+-- x^(13/2)*sqrt(c+d*x^2)/d-2/231*c*(55*a^2*d^2+3*b*c*(13*b*c-30*a*d))*_
+-- sqrt(x)*sqrt(c+d*x^2)/d^4+2/231*c^(9/4)*(39*b^2*c^2-90*a*b*c*d+_
+-- 55*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(17/4)*sqrt(c+d*x^2))
+--E 157
+
+--S 158 of 1475
+--a0:=integrate(t0,x)
+--E 158
+
+--S 159 of 1475
+--m0:=a0-r0
+--E 159
+
+--S 160 of 1475
+--d0:=D(m0,x)
+--E 160
+
+)clear all
+
+--S 161 of 1475
+t0:=x^(5/2)*(a+b*x^2)^2/sqrt(c+d*x^2)
+--R
+--R
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R (1) ---------------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 1475
+--r0:=2/585*(117*a^2*d^2+7*b*c*(11*b*c-26*a*d))*x^(3/2)*_
+-- sqrt(c+d*x^2)/d^3-2/117*b*(11*b*c-26*a*d)*x^(7/2)*_
+-- sqrt(c+d*x^2)/d^2+2/13*b^2*x^(11/2)*sqrt(c+d*x^2)/d+_
+-- 2/195*c^(7/4)*(77*b^2*c^2-182*a*b*c*d+117*a^2*d^2)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(15/4)*sqrt(c+d*x^2))-2/195*c^(7/4)*_
+-- (77*b^2*c^2-182*a*b*c*d+117*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(15/4)*sqrt(c+d*x^2))
+--E 162
+
+--S 163 of 1475
+--a0:=integrate(t0,x)
+--E 163
+
+--S 164 of 1475
+--m0:=a0-r0
+--E 164
+
+--S 165 of 1475
+--d0:=D(m0,x)
+--E 165
+
+)clear all
+
+--S 166 of 1475
+t0:=x^(3/2)*(a+b*x^2)^2/sqrt(c+d*x^2)
+--R
+--R
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R (1) --------------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 1475
+--r0:=-2/77*b*(9*b*c-22*a*d)*x^(5/2)*sqrt(c+d*x^2)/d^2+2/11*b^2*_
+-- x^(9/2)*sqrt(c+d*x^2)/d+2/231*(77*a^2*d^2+5*b*c*(9*b*c-22*a*d))*_
+-- sqrt(x)*sqrt(c+d*x^2)/d^3+2/231*c^(5/4)*(45*b^2*c^2-110*a*b*c*_
+-- d+77*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(13/4)*sqrt(c+d*x^2))
+--E 167
+
+--S 168 of 1475
+--a0:=integrate(t0,x)
+--E 168
+
+--S 169 of 1475
+--m0:=a0-r0
+--E 169
+
+--S 170 of 1475
+--d0:=D(m0,x)
+--E 170
+
+)clear all
+
+--S 171 of 1475
+t0:=(a+b*x^2)^2*sqrt(x)/sqrt(c+d*x^2)
+--R
+--R
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R (1) -------------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 1475
+--r0:=-2/45*b*(7*b*c-18*a*d)*x^(3/2)*sqrt(c+d*x^2)/d^2+2/9*b^2*x^(7/2)*_
+-- sqrt(c+d*x^2)/d+2/15*c^(3/4)*(15*a^2*d^2+b*c*(7*b*c-18*a*d))*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(11/4)*sqrt(c+d*x^2))-2/15*c^(3/4)*_
+-- (15*a^2*d^2+b*c*(7*b*c-18*a*d))*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(11/4)*sqrt(c+d*x^2))
+--E 172
+
+--S 173 of 1475
+--a0:=integrate(t0,x)
+--E 173
+
+--S 174 of 1475
+--m0:=a0-r0
+--E 174
+
+--S 175 of 1475
+--d0:=D(m0,x)
+--E 175
+
+)clear all
+
+--S 176 of 1475
+t0:=(a+b*x^2)^2/(sqrt(x)*sqrt(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +--------+
+--R +-+ | 2
+--R \|x \|d x + c
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 1475
+--r0:=2/7*b^2*x^(5/2)*sqrt(c+d*x^2)/d-2/21*b*(5*b*c-14*a*d)*sqrt(x)*_
+-- sqrt(c+d*x^2)/d^2+2/21*c^(1/4)*(5*b^2*c^2-14*a*b*c*d+21*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(9/4)*sqrt(c+d*x^2))
+--E 177
+
+--S 178 of 1475
+--a0:=integrate(t0,x)
+--E 178
+
+--S 179 of 1475
+--m0:=a0-r0
+--E 179
+
+--S 180 of 1475
+--d0:=D(m0,x)
+--E 180
+
+)clear all
+
+--S 181 of 1475
+t0:=(a+b*x^2)^2/(x^(3/2)*sqrt(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +--------+
+--R +-+ | 2
+--R x\|x \|d x + c
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 1475
+--r0:=2/5*b^2*x^(3/2)*sqrt(c+d*x^2)/d-2*a^2*sqrt(c+d*x^2)/(c*sqrt(x))+_
+-- 2/5*(3*b^2*c^2-5*a*d*(2*b*c+a*d))*elliptic_e(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(1/4)*(-d)^(7/4)*_
+-- sqrt(c+d*x^2))-2/5*(3*b^2*c^2-5*a*d*(2*b*c+a*d))*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(1/4)*(-d)^(7/4)*sqrt(c+d*x^2))
+--E 182
+
+--S 183 of 1475
+--a0:=integrate(t0,x)
+--E 183
+
+--S 184 of 1475
+--m0:=a0-r0
+--E 184
+
+--S 185 of 1475
+--d0:=D(m0,x)
+--E 185
+
+)clear all
+
+--S 186 of 1475
+t0:=(a+b*x^2)^2/(x^(5/2)*sqrt(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +--------+
+--R 2 +-+ | 2
+--R x \|x \|d x + c
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 1475
+--r0:=-2/3*a^2*sqrt(c+d*x^2)/(c*x^(3/2))+2/3*b^2*sqrt(x)*sqrt(c+d*x^2)/d+_
+-- 2/3*(b^2*c^2-6*a*b*c*d+a^2*d^2)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(3/4)*(-d)^(5/4)*_
+-- sqrt(c+d*x^2))
+--E 187
+
+--S 188 of 1475
+--a0:=integrate(t0,x)
+--E 188
+
+--S 189 of 1475
+--m0:=a0-r0
+--E 189
+
+--S 190 of 1475
+--d0:=D(m0,x)
+--E 190
+
+)clear all
+
+--S 191 of 1475
+t0:=(a+b*x^2)^2/(x^(7/2)*sqrt(c+d*x^2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +--------+
+--R 3 +-+ | 2
+--R x \|x \|d x + c
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 1475
+--r0:=-2/5*a^2*sqrt(c+d*x^2)/(c*x^(5/2))-2/5*a*(10*b*c-3*a*d)*_
+-- sqrt(c+d*x^2)/(c^2*sqrt(x))+2/5*(5*b^2*c^2+10*a*b*c*d-3*a^2*_
+-- d^2)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(5/4)*(-d)^(3/4)*sqrt(c+d*x^2))-_
+-- 2/5*(5*b^2*c^2+10*a*b*c*d-3*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(5/4)*(-d)^(3/4)*sqrt(c+d*x^2))
+--E 192
+
+--S 193 of 1475
+--a0:=integrate(t0,x)
+--E 193
+
+--S 194 of 1475
+--m0:=a0-r0
+--E 194
+
+--S 195 of 1475
+--d0:=D(m0,x)
+--E 195
+
+)clear all
+
+--S 196 of 1475
+t0:=x^(7/2)*(a+b*x^2)^2/(c+d*x^2)^(3/2)
+--R
+--R
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R (1) ---------------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 1475
+--r0:=(b*c-a*d)^2*x^(9/2)/(c*d^2*sqrt(c+d*x^2))-1/77*(117*b^2*c^2-_
+-- 198*a*b*c*d+77*a^2*d^2)*x^(5/2)*sqrt(c+d*x^2)/(c*d^3)+_
+-- 2/11*b^2*x^(9/2)*sqrt(c+d*x^2)/d^2+5/231*(117*b^2*c^2-_
+-- 198*a*b*c*d+77*a^2*d^2)*sqrt(x)*sqrt(c+d*x^2)/d^4-_
+-- 5/231*c^(5/4)*(117*b^2*c^2-198*a*b*c*d+77*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(17/4)*sqrt(c+d*x^2))
+--E 197
+
+--S 198 of 1475
+--a0:=integrate(t0,x)
+--E 198
+
+--S 199 of 1475
+--m0:=a0-r0
+--E 199
+
+--S 200 of 1475
+--d0:=D(m0,x)
+--E 200
+
+)clear all
+
+--S 201 of 1475
+t0:=x^(5/2)*(a+b*x^2)^2/(c+d*x^2)^(3/2)
+--R
+--R
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R (1) ---------------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 1475
+--r0:=(b*c-a*d)^2*x^(7/2)/(c*d^2*sqrt(c+d*x^2))-1/45*(77*b^2*c^2-_
+-- 126*a*b*c*d+45*a^2*d^2)*x^(3/2)*sqrt(c+d*x^2)/(c*d^3)+2/9*b^2*_
+-- x^(7/2)*sqrt(c+d*x^2)/d^2-1/15*c^(3/4)*(77*b^2*c^2-126*a*b*c*d+_
+-- 45*a^2*d^2)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(15/4)*sqrt(c+d*x^2))+1/15*c^(3/4)*_
+-- (77*b^2*c^2-126*a*b*c*d+45*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(15/4)*sqrt(c+d*x^2))
+--E 202
+
+--S 203 of 1475
+--a0:=integrate(t0,x)
+--E 203
+
+--S 204 of 1475
+--m0:=a0-r0
+--E 204
+
+--S 205 of 1475
+--d0:=D(m0,x)
+--E 205
+
+)clear all
+
+--S 206 of 1475
+t0:=x^(3/2)*(a+b*x^2)^2/(c+d*x^2)^(3/2)
+--R
+--R
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R (1) --------------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 1475
+--r0:=(b*c-a*d)^2*x^(5/2)/(c*d^2*sqrt(c+d*x^2))+2/7*b^2*x^(5/2)*_
+-- sqrt(c+d*x^2)/d^2-1/21*(45*b^2*c^2-70*a*b*c*d+21*a^2*d^2)*_
+-- sqrt(x)*sqrt(c+d*x^2)/(c*d^3)-1/21*c^(1/4)*(45*b^2*c^2-70*a*b*_
+-- c*d+21*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(13/4)*sqrt(c+d*x^2))
+--E 207
+
+--S 208 of 1475
+--a0:=integrate(t0,x)
+--E 208
+
+--S 209 of 1475
+--m0:=a0-r0
+--E 209
+
+--S 210 of 1475
+--d0:=D(m0,x)
+--E 210
+
+)clear all
+
+--S 211 of 1475
+t0:=(a+b*x^2)^2*sqrt(x)/(c+d*x^2)^(3/2)
+--R
+--R
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R (1) -------------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 1475
+--r0:=(b*c-a*d)^2*x^(3/2)/(c*d^2*sqrt(c+d*x^2))+2/5*b^2*x^(3/2)*_
+-- sqrt(c+d*x^2)/d^2-1/5*(21*b^2*c^2-30*a*b*c*d+5*a^2*d^2)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(1/4)*(-d)^(11/4)*sqrt(c+d*x^2))+1/5*_
+-- (21*b^2*c^2-30*a*b*c*d+5*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(1/4)*(-d)^(11/4)*_
+-- sqrt(c+d*x^2))
+--E 212
+
+--S 213 of 1475
+--a0:=integrate(t0,x)
+--E 213
+
+--S 214 of 1475
+--m0:=a0-r0
+--E 214
+
+--S 215 of 1475
+--d0:=D(m0,x)
+--E 215
+
+)clear all
+
+--S 216 of 1475
+t0:=(a+b*x^2)^2/((c+d*x^2)^(3/2)*sqrt(x))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------------
+--R +--------+
+--R 2 +-+ | 2
+--R (d x + c)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 1475
+--r0:=(b*c-a*d)^2*sqrt(x)/(c*d^2*sqrt(c+d*x^2))+2/3*b^2*sqrt(x)*_
+-- sqrt(c+d*x^2)/d^2-1/3*(5*b^2*c^2-6*a*b*c*d-3*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(3/4)*(-d)^(9/4)*sqrt(c+d*x^2))
+--E 217
+
+--S 218 of 1475
+--a0:=integrate(t0,x)
+--E 218
+
+--S 219 of 1475
+--m0:=a0-r0
+--E 219
+
+--S 220 of 1475
+--d0:=D(m0,x)
+--E 220
+
+)clear all
+
+--S 221 of 1475
+t0:=(a+b*x^2)^2/(x^(3/2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ---------------------------
+--R +--------+
+--R 3 +-+ | 2
+--R (d x + c x)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 1475
+--r0:=-(b^2*c^2-2*a*b*c*d+3*a^2*d^2)*x^(3/2)/(c^2*d*sqrt(c+d*x^2))-_
+-- 2*a^2/(c*sqrt(x)*sqrt(c+d*x^2))-(3*b^2*c^2-2*a*b*c*d+3*a^2*d^2)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(5/4)*(-d)^(7/4)*sqrt(c+d*x^2))+_
+-- (3*b^2*c^2-2*a*b*c*d+3*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(5/4)*(-d)^(7/4)*_
+-- sqrt(c+d*x^2))
+--E 222
+
+--S 223 of 1475
+--a0:=integrate(t0,x)
+--E 223
+
+--S 224 of 1475
+--m0:=a0-r0
+--E 224
+
+--S 225 of 1475
+--d0:=D(m0,x)
+--E 225
+
+)clear all
+
+--S 226 of 1475
+t0:=(a+b*x^2)^2/(x^(5/2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ----------------------------
+--R +--------+
+--R 4 2 +-+ | 2
+--R (d x + c x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 1475
+--r0:=-2/3*a^2/(c*x^(3/2)*sqrt(c+d*x^2))-1/3*(3*b^2*c^2-6*a*b*c*d+_
+-- 5*a^2*d^2)*sqrt(x)/(c^2*d*sqrt(c+d*x^2))-1/3*(3*b^2*c^2+a*d*_
+-- (6*b*c-5*a*d))*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(7/4)*(-d)^(5/4)*sqrt(c+d*x^2))
+--E 227
+
+--S 228 of 1475
+--a0:=integrate(t0,x)
+--E 228
+
+--S 229 of 1475
+--m0:=a0-r0
+--E 229
+
+--S 230 of 1475
+--d0:=D(m0,x)
+--E 230
+
+)clear all
+
+--S 231 of 1475
+t0:=(a+b*x^2)^2/(x^(7/2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ----------------------------
+--R +--------+
+--R 5 3 +-+ | 2
+--R (d x + c x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 1475
+--r0:=-2/5*a^2/(c*x^(5/2)*sqrt(c+d*x^2))+1/5*(5*b^2*c^2-3*a*d*_
+-- (10*b*c-7*a*d))*x^(3/2)/(c^3*sqrt(c+d*x^2))-2/5*a*(10*b*c-_
+-- 7*a*d)/(c^2*sqrt(x)*sqrt(c+d*x^2))-1/5*(5*b^2*c^2-3*a*d*(10*b*c-_
+-- 7*a*d))*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(9/4)*(-d)^(3/4)*sqrt(c+d*x^2))+_
+-- 1/5*(5*b^2*c^2-3*a*d*(10*b*c-7*a*d))*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(9/4)*(-d)^(3/4)*_
+-- sqrt(c+d*x^2))
+--E 232
+
+--S 233 of 1475
+--a0:=integrate(t0,x)
+--E 233
+
+--S 234 of 1475
+--m0:=a0-r0
+--E 234
+
+--S 235 of 1475
+--d0:=D(m0,x)
+--E 235
+
+)clear all
+
+--S 236 of 1475
+t0:=x^(7/2)*(a+b*x^2)^2/(c+d*x^2)^(5/2)
+--R
+--R
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 1475
+--r0:=1/3*(b*c-a*d)^2*x^(9/2)/(c*d^2*(c+d*x^2)^(3/2))-1/2*(b*c-a*d)*_
+-- (5*b*c-a*d)*x^(9/2)/(c^2*d^2*sqrt(c+d*x^2))+1/14*(39*b^2*c^2-_
+-- 42*a*b*c*d+7*a^2*d^2)*x^(5/2)*sqrt(c+d*x^2)/(c^2*d^3)-5/42*_
+-- (39*b^2*c^2-42*a*b*c*d+7*a^2*d^2)*sqrt(x)*sqrt(c+d*x^2)/(c*d^4)+_
+-- 5/42*c^(1/4)*(39*b^2*c^2-42*a*b*c*d+7*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(17/4)*sqrt(c+d*x^2))
+--E 237
+
+--S 238 of 1475
+--a0:=integrate(t0,x)
+--E 238
+
+--S 239 of 1475
+--m0:=a0-r0
+--E 239
+
+--S 240 of 1475
+--d0:=D(m0,x)
+--E 240
+
+)clear all
+
+--S 241 of 1475
+t0:=x^(5/2)*(a+b*x^2)^2/(c+d*x^2)^(5/2)
+--R
+--R
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 1475
+--r0:=1/3*(b*c-a*d)^2*x^(7/2)/(c*d^2*(c+d*x^2)^(3/2))-1/6*(b*c-a*d)*_
+-- (13*b*c-a*d)*x^(7/2)/(c^2*d^2*sqrt(c+d*x^2))+1/30*(77*b^2*c^2-_
+-- 70*a*b*c*d+5*a^2*d^2)*x^(3/2)*sqrt(c+d*x^2)/(c^2*d^3)+_
+-- 1/10*(77*b^2*c^2-70*a*b*c*d+5*a^2*d^2)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(1/4)*(-d)^(15/4)*sqrt(c+d*x^2))-_
+-- 1/10*(77*b^2*c^2-70*a*b*c*d+5*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(c^(1/4)*(-d)^(15/4)*sqrt(c+d*x^2))
+--E 242
+
+--S 243 of 1475
+--a0:=integrate(t0,x)
+--E 243
+
+--S 244 of 1475
+--m0:=a0-r0
+--E 244
+
+--S 245 of 1475
+--d0:=D(m0,x)
+--E 245
+
+)clear all
+
+--S 246 of 1475
+t0:=x^(3/2)*(a+b*x^2)^2/(c+d*x^2)^(5/2)
+--R
+--R
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 1475
+--r0:=1/3*(b*c-a*d)^2*x^(5/2)/(c*d^2*(c+d*x^2)^(3/2))-1/6*(b*c-a*d)*_
+-- (11*b*c+a*d)*x^(5/2)/(c^2*d^2*sqrt(c+d*x^2))-1/6*(10*a*b-_
+-- 15*b^2*c/d+a^2*d/c)*sqrt(x)*sqrt(c+d*x^2)/(c*d^2)+_
+-- 1/6*(15*b^2*c^2-10*a*b*c*d-a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(3/4)*(-d)^(13/4)*sqrt(c+d*x^2))
+--E 247
+
+--S 248 of 1475
+--a0:=integrate(t0,x)
+--E 248
+
+--S 249 of 1475
+--m0:=a0-r0
+--E 249
+
+--S 250 of 1475
+--d0:=D(m0,x)
+--E 250
+
+)clear all
+
+--S 251 of 1475
+t0:=(a+b*x^2)^2*sqrt(x)/(c+d*x^2)^(5/2)
+--R
+--R
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 1475
+--r0:=1/3*(b*c-a*d)^2*x^(3/2)/(c*d^2*(c+d*x^2)^(3/2))-1/2*(b*c-a*d)*_
+-- (3*b*c+a*d)*x^(3/2)/(c^2*d^2*sqrt(c+d*x^2))+1/2*(7*b^2*c^2-2*a*_
+-- b*c*d-a^2*d^2)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(5/4)*(-d)^(11/4)*sqrt(c+d*x^2))-1/2*(7*_
+-- b^2*c^2-2*a*b*c*d-a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/_
+-- c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(5/4)*(-d)^(11/4)*sqrt(c+d*x^2))
+--E 252
+
+--S 253 of 1475
+--a0:=integrate(t0,x)
+--E 253
+
+--S 254 of 1475
+--m0:=a0-r0
+--E 254
+
+--S 255 of 1475
+--d0:=D(m0,x)
+--E 255
+
+)clear all
+
+--S 256 of 1475
+t0:=(a+b*x^2)^2/((c+d*x^2)^(5/2)*sqrt(x))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) ------------------------------------
+--R +--------+
+--R 2 4 2 2 +-+ | 2
+--R (d x + 2c d x + c )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 1475
+--r0:=1/3*(b*c-a*d)^2*sqrt(x)/(c*d^2*(c+d*x^2)^(3/2))-1/6*(b*c-a*d)*_
+-- (7*b*c+5*a*d)*sqrt(x)/(c^2*d^2*sqrt(c+d*x^2))+1/6*(5*b^2*c^2+2*_
+-- a*b*c*d+5*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(7/4)*(-d)^(9/4)*sqrt(c+d*x^2))
+--E 257
+
+--S 258 of 1475
+--a0:=integrate(t0,x)
+--E 258
+
+--S 259 of 1475
+--m0:=a0-r0
+--E 259
+
+--S 260 of 1475
+--d0:=D(m0,x)
+--E 260
+
+)clear all
+
+--S 261 of 1475
+t0:=(a+b*x^2)^2/(x^(3/2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------------------------
+--R +--------+
+--R 2 5 3 2 +-+ | 2
+--R (d x + 2c d x + c x)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 1475
+--r0:=-1/3*(b^2*c^2-2*a*b*c*d+7*a^2*d^2)*x^(3/2)/(c^2*d*(c+d*x^2)^(3/2))-_
+-- 2*a^2/(c*(c+d*x^2)^(3/2)*sqrt(x))+1/2*(b^2*c^2+a*d*(2*b*c-7*a*d))*_
+-- x^(3/2)/(c^3*d*sqrt(c+d*x^2))+1/2*(b^2*c^2+a*d*(2*b*c-7*a*d))*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(9/4)*(-d)^(7/4)*sqrt(c+d*x^2))-1/2*_
+-- (b^2*c^2+a*d*(2*b*c-7*a*d))*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(9/4)*(-d)^(7/4)*_
+-- sqrt(c+d*x^2))
+--E 262
+
+--S 263 of 1475
+--a0:=integrate(t0,x)
+--E 263
+
+--S 264 of 1475
+--m0:=a0-r0
+--E 264
+
+--S 265 of 1475
+--d0:=D(m0,x)
+--E 265
+
+)clear all
+
+--S 266 of 1475
+t0:=(a+b*x^2)^2/(x^(5/2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) --------------------------------------
+--R +--------+
+--R 2 6 4 2 2 +-+ | 2
+--R (d x + 2c d x + c x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 1475
+--r0:=-2/3*a^2/(c*x^(3/2)*(c+d*x^2)^(3/2))-1/3*(b^2*c^2-2*a*b*c*d+_
+-- 3*a^2*d^2)*sqrt(x)/(c^2*d*(c+d*x^2)^(3/2))+1/6*(b^2*c^2+5*a*d*_
+-- (2*b*c-3*a*d))*sqrt(x)/(c^3*d*sqrt(c+d*x^2))-1/6*(b^2*c^2+5*a*_
+-- d*(2*b*c-3*a*d))*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(11/4)*(-d)^(5/4)*sqrt(c+d*x^2))
+--E 267
+
+--S 268 of 1475
+--a0:=integrate(t0,x)
+--E 268
+
+--S 269 of 1475
+--m0:=a0-r0
+--E 269
+
+--S 270 of 1475
+--d0:=D(m0,x)
+--E 270
+
+)clear all
+
+--S 271 of 1475
+t0:=(a+b*x^2)^2/(x^(7/2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) --------------------------------------
+--R +--------+
+--R 2 7 5 2 3 +-+ | 2
+--R (d x + 2c d x + c x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 1475
+--r0:=-2/5*a^2/(c*x^(5/2)*(c+d*x^2)^(3/2))+1/15*(5*b^2*c^2-70*a*b*c*d+_
+-- 77*a^2*d^2)*x^(3/2)/(c^3*(c+d*x^2)^(3/2))-2/5*a*(10*b*c-11*a*d)/_
+-- (c^2*(c+d*x^2)^(3/2)*sqrt(x))+1/10*(5*b^2*c^2-70*a*b*c*d+77*a^2*_
+-- d^2)*x^(3/2)/(c^4*sqrt(c+d*x^2))-1/10*(5*b^2*c^2-70*a*b*c*d+77*_
+-- a^2*d^2)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(13/4)*(-d)^(3/4)*sqrt(c+d*x^2))+_
+-- 1/10*(5*b^2*c^2-70*a*b*c*d+77*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(c^(13/4)*(-d)^(3/4)*sqrt(c+d*x^2))
+--E 272
+
+--S 273 of 1475
+--a0:=integrate(t0,x)
+--E 273
+
+--S 274 of 1475
+--m0:=a0-r0
+--E 274
+
+--S 275 of 1475
+--d0:=D(m0,x)
+--E 275
+
+)clear all
+
+--S 276 of 1475
+t0:=x^m*(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R 2 m
+--R (d x + c)x
+--R (1) ------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 1475
+--r0:=d*x^(1+m)/(b*(1+m))+(b*c-a*d)*x^(1+m)*_
+-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-b*x^2/a)/(a*b*(1+m))
+--E 277
+
+--S 278 of 1475
+--a0:=integrate(t0,x)
+--E 278
+
+--S 279 of 1475
+--m0:=a0-r0
+--E 279
+
+--S 280 of 1475
+--d0:=D(m0,x)
+--E 280
+
+)clear all
+
+--S 281 of 1475
+t0:=x^5*(a+b*x^2)/(c+d*x^2)
+--R
+--R
+--R 7 5
+--R b x + a x
+--R (1) -----------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 281
+
+--S 282 of 1475
+r0:=1/2*c*(b*c-a*d)*x^2/d^3-1/4*(b*c-a*d)*x^4/d^2+1/6*b*x^6/d-_
+ 1/2*c^2*(b*c-a*d)*log(c+d*x^2)/d^4
+--R
+--R
+--R (2)
+--R 2 3 2 3 6 3 2 4
+--R (6a c d - 6b c )log(d x + c) + 2b d x + (3a d - 3b c d )x
+--R +
+--R 2 2 2
+--R (- 6a c d + 6b c d)x
+--R /
+--R 4
+--R 12d
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 3 6 3 2 4
+--R (6a c d - 6b c )log(d x + c) + 2b d x + (3a d - 3b c d )x
+--R +
+--R 2 2 2
+--R (- 6a c d + 6b c d)x
+--R /
+--R 4
+--R 12d
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 1475
+t0:=x^4*(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R 6 4
+--R d x + c x
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 286
+
+--S 287 of 1475
+r0:=-a*(b*c-a*d)*x/b^3+1/3*(b*c-a*d)*x^3/b^2+1/5*d*x^5/b+a^(3/2)*_
+ (b*c-a*d)*atan(x*sqrt(b)/sqrt(a))/b^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 +-+ x\|b
+--R (- 15a d + 15a b c)\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 5 2 3 2 +-+
+--R (3b d x + (- 5a b d + 5b c)x + (15a d - 15a b c)x)\|b
+--R /
+--R 3 +-+
+--R 15b \|b
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 | a \| b 2 5
+--R (15a d - 15a b c) |- - log(-----------------------) + 6b d x
+--R \| b 2
+--R b x + a
+--R +
+--R 2 3 2
+--R (- 10a b d + 10b c)x + (30a d - 30a b c)x
+--R /
+--R 3
+--R 30b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 |a \|b 2 5 2 3
+--R (15a d - 15a b c) |- atan(----) + 3b d x + (- 5a b d + 5b c)x
+--R \|b x
+--R +
+--R 2
+--R (15a d - 15a b c)x
+--R /
+--R 3
+--R 15b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 288
+
+--S 289 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 | a +-+ \| b
+--R (a d - a b c) |- - \|b log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R (2a d - 2a b c)\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+--S 291 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 +-+ x\|b 2 |a +-+ \|b
+--R (a d - a b c)\|a atan(-----) + (a d - a b c) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) --------------------------------------------------------------
+--R 3 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 292
+
+)clear all
+
+--S 293 of 1475
+t0:=x^3*(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R 5 3
+--R d x + c x
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 293
+
+--S 294 of 1475
+r0:=1/2*(b*c-a*d)*x^2/b^2+1/4*d*x^4/b-1/2*a*(b*c-a*d)*log(a+b*x^2)/b^3
+--R
+--R
+--R 2 2 2 4 2 2
+--R (2a d - 2a b c)log(b x + a) + b d x + (- 2a b d + 2b c)x
+--R (2) -----------------------------------------------------------
+--R 3
+--R 4b
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 4 2 2
+--R (2a d - 2a b c)log(b x + a) + b d x + (- 2a b d + 2b c)x
+--R (3) -----------------------------------------------------------
+--R 3
+--R 4b
+--R Type: Union(Expression(Integer),...)
+--E 295
+
+--S 296 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 297
+
+)clear all
+
+--S 298 of 1475
+t0:=x^2*(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R 4 2
+--R d x + c x
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 298
+
+--S 299 of 1475
+r0:=(b*c-a*d)*x/b^2+1/3*d*x^3/b-(b*c-a*d)*atan(x*sqrt(b)/sqrt(a))*_
+ sqrt(a)/b^(5/2)
+--R
+--R
+--R +-+
+--R +-+ x\|b 3 +-+
+--R (3a d - 3b c)\|a atan(-----) + (b d x + (- 3a d + 3b c)x)\|b
+--R +-+
+--R \|a
+--R (2) --------------------------------------------------------------
+--R 2 +-+
+--R 3b \|b
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a \| b 3
+--R (3a d - 3b c) |- - log(---------------------) + 2b d x + (- 6a d + 6b c)x
+--R \| b 2
+--R b x + a
+--R [--------------------------------------------------------------------------,
+--R 2
+--R 6b
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b 3
+--R (- 3a d + 3b c) |- atan(----) + b d x + (- 3a d + 3b c)x
+--R \|b x
+--R ---------------------------------------------------------]
+--R 2
+--R 3b
+--R Type: Union(List(Expression(Integer)),...)
+--E 300
+
+--S 301 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a +-+ \| b
+--R (a d - b c) |- - \|b log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ x\|b
+--R (- 2a d + 2b c)\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R (- a d + b c)\|a atan(-----) + (- a d + b c) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) --------------------------------------------------------------
+--R 2 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 303
+
+--S 304 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 304
+
+)clear all
+
+--S 305 of 1475
+t0:=x*(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R 3
+--R d x + c x
+--R (1) ----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 305
+
+--S 306 of 1475
+r0:=1/2*d*x^2/b+1/2*(b*c-a*d)*log(a+b*x^2)/b^2
+--R
+--R
+--R 2 2
+--R (- a d + b c)log(b x + a) + b d x
+--R (2) -----------------------------------
+--R 2
+--R 2b
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R (- a d + b c)log(b x + a) + b d x
+--R (3) -----------------------------------
+--R 2
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 307
+
+--S 308 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 308
+
+--S 309 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 309
+
+)clear all
+
+--S 310 of 1475
+t0:=(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 310
+
+--S 311 of 1475
+r0:=d*x/b+(b*c-a*d)*atan(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))
+--R
+--R
+--R +-+
+--R x\|b +-+ +-+
+--R (- a d + b c)atan(-----) + d x\|a \|b
+--R +-+
+--R \|a
+--R (2) --------------------------------------
+--R +-+ +-+
+--R b\|a \|b
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x +-----+
+--R (a d - b c)log(---------------------------) + 2d x\|- a b
+--R 2
+--R b x + a
+--R [----------------------------------------------------------,
+--R +-----+
+--R 2b\|- a b
+--R +---+
+--R x\|a b +---+
+--R (- a d + b c)atan(-------) + d x\|a b
+--R a
+--R --------------------------------------]
+--R +---+
+--R b\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 312
+
+--S 313 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b - 2a b x
+--R (a d - b c)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (2a d - 2b c)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-----+ +-+ +-+
+--R 2b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 313
+
+--S 314 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (- a d + b c)\|a \|b atan(-------) + (a d - b c)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 315
+
+--S 316 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 316
+
+)clear all
+
+--S 317 of 1475
+t0:=(c+d*x^2)/(x*(a+b*x^2))
+--R
+--R
+--R 2
+--R d x + c
+--R (1) ----------
+--R 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 317
+
+--S 318 of 1475
+r0:=c*log(x)/a-1/2*(b*c-a*d)*log(a+b*x^2)/(a*b)
+--R
+--R
+--R 2
+--R (a d - b c)log(b x + a) + 2b c log(x)
+--R (2) --------------------------------------
+--R 2a b
+--R Type: Expression(Integer)
+--E 318
+
+--S 319 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (a d - b c)log(b x + a) + 2b c log(x)
+--R (3) --------------------------------------
+--R 2a b
+--R Type: Union(Expression(Integer),...)
+--E 319
+
+--S 320 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 320
+
+--S 321 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 321
+
+)clear all
+
+--S 322 of 1475
+t0:=(c+d*x^2)/(x^2*(a+b*x^2))
+--R
+--R
+--R 2
+--R d x + c
+--R (1) -----------
+--R 4 2
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 322
+
+--S 323 of 1475
+r0:=-c/(a*x)-(b*c-a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b))
+--R
+--R
+--R +-+
+--R x\|b +-+ +-+
+--R (a d - b c)x atan(-----) - c\|a \|b
+--R +-+
+--R \|a
+--R (2) ------------------------------------
+--R +-+ +-+
+--R a x\|a \|b
+--R Type: Expression(Integer)
+--E 323
+
+--S 324 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x +-----+
+--R (a d - b c)x log(---------------------------) - 2c\|- a b
+--R 2
+--R b x + a
+--R [----------------------------------------------------------,
+--R +-----+
+--R 2a x\|- a b
+--R +---+
+--R x\|a b +---+
+--R (a d - b c)x atan(-------) - c\|a b
+--R a
+--R ------------------------------------]
+--R +---+
+--R a x\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 324
+
+--S 325 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d - b c)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2a d + 2b c)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-----+ +-+ +-+
+--R 2a\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 325
+
+--S 326 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (a d - b c)\|a \|b atan(-------) + (- a d + b c)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R a\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 328
+
+)clear all
+
+--S 329 of 1475
+t0:=(c+d*x^2)/(x^3*(a+b*x^2))
+--R
+--R
+--R 2
+--R d x + c
+--R (1) -----------
+--R 5 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 329
+
+--S 330 of 1475
+r0:=-1/2*c/(a*x^2)-(b*c-a*d)*log(x)/a^2+1/2*(b*c-a*d)*log(a+b*x^2)/a^2
+--R
+--R
+--R 2 2 2
+--R (- a d + b c)x log(b x + a) + (2a d - 2b c)x log(x) - a c
+--R (2) ----------------------------------------------------------
+--R 2 2
+--R 2a x
+--R Type: Expression(Integer)
+--E 330
+
+--S 331 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R (- a d + b c)x log(b x + a) + (2a d - 2b c)x log(x) - a c
+--R (3) ----------------------------------------------------------
+--R 2 2
+--R 2a x
+--R Type: Union(Expression(Integer),...)
+--E 331
+
+--S 332 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 333
+
+)clear all
+
+--S 334 of 1475
+t0:=(c+d*x^2)/(x^4*(a+b*x^2))
+--R
+--R
+--R 2
+--R d x + c
+--R (1) -----------
+--R 6 4
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 334
+
+--S 335 of 1475
+r0:=-1/3*c/(a*x^3)+(b*c-a*d)/(a^2*x)+(b*c-a*d)*atan(x*sqrt(b)/sqrt(a))*_
+ sqrt(b)/a^(5/2)
+--R
+--R
+--R +-+
+--R 3 +-+ x\|b 2 +-+
+--R (- 3a d + 3b c)x \|b atan(-----) + ((- 3a d + 3b c)x - a c)\|a
+--R +-+
+--R \|a
+--R (2) ----------------------------------------------------------------
+--R 2 3 +-+
+--R 3a x \|a
+--R Type: Expression(Integer)
+--E 335
+
+--S 336 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 3 | b \| a 2
+--R (3a d - 3b c)x |- - log(-----------------------) + (- 6a d + 6b c)x - 2a c
+--R \| a 2
+--R b x + a
+--R [----------------------------------------------------------------------------
+--R 2 3
+--R 6a x
+--R ,
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 |b \|a 2
+--R (3a d - 3b c)x |- atan(-----) + (- 3a d + 3b c)x - a c
+--R \|a b x
+--R --------------------------------------------------------]
+--R 2 3
+--R 3a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 336
+
+--S 337 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b +-+ \| a
+--R (a d - b c) |- - \|a log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ x\|b
+--R (2a d - 2b c)\|b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 338
+
+--S 339 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R (a d - b c)\|b atan(-----) + (a d - b c)\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -----------------------------------------------------------
+--R 2 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 1475
+t0:=x^m*(c+d*x^2)^2/(a+b*x^2)
+--R
+--R
+--R 2 4 2 2 m
+--R (d x + 2c d x + c )x
+--R (1) -----------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 1475
+--r0:=d*(2*b*c-a*d)*x^(1+m)/(b^2*(1+m))+d^2*x^(3+m)/(b*(3+m))+_
+-- (b*c-a*d)^2*x^(1+m)*hypergeometric(1,1/2*(1+m),1/2*(3+m),_
+-- -b*x^2/a)/(a*b^2*(1+m))
+--E 342
+
+--S 343 of 1475
+--a0:=integrate(t0,x)
+--E 343
+
+--S 344 of 1475
+--m0:=a0-r0
+--E 344
+
+--S 345 of 1475
+--d0:=D(m0,x)
+--E 345
+
+)clear all
+
+--S 346 of 1475
+t0:=x^5*(a+b*x^2)^2/(c+d*x^2)
+--R
+--R
+--R 2 9 7 2 5
+--R b x + 2a b x + a x
+--R (1) ---------------------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 346
+
+--S 347 of 1475
+r0:=-1/2*c*(b*c-a*d)^2*x^2/d^4+1/4*(b*c-a*d)^2*x^4/d^3-_
+ 1/6*b*(b*c-2*a*d)*x^6/d^2+1/8*b^2*x^8/d+1/2*c^2*(b*c-a*d)^2*_
+ log(c+d*x^2)/d^5
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 4 2 2 4 8
+--R (12a c d - 24a b c d + 12b c )log(d x + c) + 3b d x
+--R +
+--R 4 2 3 6 2 4 3 2 2 2 4
+--R (8a b d - 4b c d )x + (6a d - 12a b c d + 6b c d )x
+--R +
+--R 2 3 2 2 2 3 2
+--R (- 12a c d + 24a b c d - 12b c d)x
+--R /
+--R 5
+--R 24d
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 3 2 4 2 2 4 8
+--R (12a c d - 24a b c d + 12b c )log(d x + c) + 3b d x
+--R +
+--R 4 2 3 6 2 4 3 2 2 2 4
+--R (8a b d - 4b c d )x + (6a d - 12a b c d + 6b c d )x
+--R +
+--R 2 3 2 2 2 3 2
+--R (- 12a c d + 24a b c d - 12b c d)x
+--R /
+--R 5
+--R 24d
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 1475
+t0:=x^4*(c+d*x^2)^2/(a+b*x^2)
+--R
+--R
+--R 2 8 6 2 4
+--R d x + 2c d x + c x
+--R (1) ---------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 351
+
+--S 352 of 1475
+r0:=-a*(b*c-a*d)^2*x/b^4+1/3*(b*c-a*d)^2*x^3/b^3+1/5*d*(2*b*c-a*d)*_
+ x^5/b^2+1/7*d^2*x^7/b+a^(3/2)*(b*c-a*d)^2*atan(x*sqrt(b)/_
+ sqrt(a))/b^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 2 2 2 +-+ x\|b
+--R (105a d - 210a b c d + 105a b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 2 7 2 2 3 5
+--R 15b d x + (- 21a b d + 42b c d)x
+--R +
+--R 2 2 2 3 2 3
+--R (35a b d - 70a b c d + 35b c )x
+--R +
+--R 3 2 2 2 2
+--R (- 105a d + 210a b c d - 105a b c )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 4 +-+
+--R 105b \|b
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 3 2 2 2 2 | a \| b
+--R (105a d - 210a b c d + 105a b c ) |- - log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 3 2 7 2 2 3 5
+--R 30b d x + (- 42a b d + 84b c d)x
+--R +
+--R 2 2 2 3 2 3
+--R (70a b d - 140a b c d + 70b c )x
+--R +
+--R 3 2 2 2 2
+--R (- 210a d + 420a b c d - 210a b c )x
+--R /
+--R 4
+--R 210b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 3 2 2 2 2 |a \|b 3 2 7
+--R (- 105a d + 210a b c d - 105a b c ) |- atan(----) + 15b d x
+--R \|b x
+--R +
+--R 2 2 3 5 2 2 2 3 2 3
+--R (- 21a b d + 42b c d)x + (35a b d - 70a b c d + 35b c )x
+--R +
+--R 3 2 2 2 2
+--R (- 105a d + 210a b c d - 105a b c )x
+--R /
+--R 4
+--R 105b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 353
+
+--S 354 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 3 2 2 2 2 | a +-+ \| b
+--R (a d - 2a b c d + a b c ) |- - \|b log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 3 2 2 2 2 +-+ x\|b
+--R (- 2a d + 4a b c d - 2a b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 355
+
+--S 356 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 3 2 2 2 2 +-+ x\|b
+--R (- a d + 2a b c d - a b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R 3 2 2 2 2 |a +-+ \|b
+--R (- a d + 2a b c d - a b c ) |- \|b atan(----)
+--R \|b x
+--R /
+--R 4 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 357
+
+)clear all
+
+--S 358 of 1475
+t0:=x^3*(c+d*x^2)^2/(a+b*x^2)
+--R
+--R
+--R 2 7 5 2 3
+--R d x + 2c d x + c x
+--R (1) ---------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 358
+
+--S 359 of 1475
+r0:=1/2*(b*c-a*d)^2*x^2/b^3+1/4*d*(2*b*c-a*d)*x^4/b^2+1/6*d^2*x^6/b-_
+ 1/2*a*(b*c-a*d)^2*log(a+b*x^2)/b^4
+--R
+--R
+--R (2)
+--R 3 2 2 2 2 2 3 2 6
+--R (- 6a d + 12a b c d - 6a b c )log(b x + a) + 2b d x
+--R +
+--R 2 2 3 4 2 2 2 3 2 2
+--R (- 3a b d + 6b c d)x + (6a b d - 12a b c d + 6b c )x
+--R /
+--R 4
+--R 12b
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2 2 2 2 3 2 6
+--R (- 6a d + 12a b c d - 6a b c )log(b x + a) + 2b d x
+--R +
+--R 2 2 3 4 2 2 2 3 2 2
+--R (- 3a b d + 6b c d)x + (6a b d - 12a b c d + 6b c )x
+--R /
+--R 4
+--R 12b
+--R Type: Union(Expression(Integer),...)
+--E 360
+
+--S 361 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 362
+
+)clear all
+
+--S 363 of 1475
+t0:=x^2*(c+d*x^2)^2/(a+b*x^2)
+--R
+--R
+--R 2 6 4 2 2
+--R d x + 2c d x + c x
+--R (1) ---------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 363
+
+--S 364 of 1475
+r0:=(b*c-a*d)^2*x/b^3+1/3*d*(2*b*c-a*d)*x^3/b^2+1/5*d^2*x^5/b-_
+ (b*c-a*d)^2*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 +-+ x\|b
+--R (- 15a d + 30a b c d - 15b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 5 2 2 3 2 2 2 2 +-+
+--R (3b d x + (- 5a b d + 10b c d)x + (15a d - 30a b c d + 15b c )x)\|b
+--R /
+--R 3 +-+
+--R 15b \|b
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 2 2 2 | a \| b
+--R (15a d - 30a b c d + 15b c ) |- - log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 2 2 5 2 2 3 2 2 2 2
+--R 6b d x + (- 10a b d + 20b c d)x + (30a d - 60a b c d + 30b c )x
+--R /
+--R 3
+--R 30b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 2 2 |a \|b 2 2 5
+--R (15a d - 30a b c d + 15b c ) |- atan(----) + 3b d x
+--R \|b x
+--R +
+--R 2 2 3 2 2 2 2
+--R (- 5a b d + 10b c d)x + (15a d - 30a b c d + 15b c )x
+--R /
+--R 3
+--R 15b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 365
+
+--S 366 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 2 2 2 | a +-+ \| b
+--R (a d - 2a b c d + b c ) |- - \|b log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-+ x\|b
+--R (2a d - 4a b c d + 2b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 +-+ x\|b
+--R (a d - 2a b c d + b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 2 2 |a +-+ \|b
+--R (a d - 2a b c d + b c ) |- \|b atan(----)
+--R \|b x
+--R /
+--R 3 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 369
+
+)clear all
+
+--S 370 of 1475
+t0:=x*(c+d*x^2)^2/(a+b*x^2)
+--R
+--R
+--R 2 5 3 2
+--R d x + 2c d x + c x
+--R (1) --------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 370
+
+--S 371 of 1475
+r0:=1/2*d*(b*c-a*d)*x^2/b^2+1/4*(c+d*x^2)^2/b+1/2*(b*c-a*d)^2*_
+ log(a+b*x^2)/b^3
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2 2 4 2 2 2
+--R (2a d - 4a b c d + 2b c )log(b x + a) + b d x + (- 2a b d + 4b c d)x
+--R +
+--R 2 2
+--R b c
+--R /
+--R 3
+--R 4b
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2 2 4 2 2 2
+--R (2a d - 4a b c d + 2b c )log(b x + a) + b d x + (- 2a b d + 4b c d)x
+--R -------------------------------------------------------------------------
+--R 3
+--R 4b
+--R Type: Union(Expression(Integer),...)
+--E 372
+
+--S 373 of 1475
+m0:=a0-r0
+--R
+--R
+--R 2
+--R c
+--R (4) - --
+--R 4b
+--R Type: Expression(Integer)
+--E 373
+
+--S 374 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 374
+
+)clear all
+
+--S 375 of 1475
+t0:=(c+d*x^2)^2/(a+b*x^2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 375
+
+--S 376 of 1475
+r0:=d*(2*b*c-a*d)*x/b^2+1/3*d^2*x^3/b+(b*c-a*d)^2*atan(x*sqrt(b)/_
+ sqrt(a))/(b^(5/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 x\|b
+--R (3a d - 6a b c d + 3b c )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 +-+ +-+
+--R (b d x + (- 3a d + 6b c d)x)\|a \|b
+--R /
+--R 2 +-+ +-+
+--R 3b \|a \|b
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 2 (b x - a)\|- a b + 2a b x
+--R (3a d - 6a b c d + 3b c )log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 2 +-----+
+--R (2b d x + (- 6a d + 12b c d)x)\|- a b
+--R /
+--R 2 +-----+
+--R 6b \|- a b
+--R ,
+--R
+--R +---+
+--R 2 2 2 2 x\|a b
+--R (3a d - 6a b c d + 3b c )atan(-------)
+--R a
+--R +
+--R 2 3 2 +---+
+--R (b d x + (- 3a d + 6b c d)x)\|a b
+--R /
+--R 2 +---+
+--R 3b \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 377
+
+--S 378 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d - 2a b c d + b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (- 2a d + 4a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 2b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 378
+
+--S 379 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (a d - 2a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- a d + 2a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+ +-+ +---+
+--R b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 380
+
+--S 381 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 381
+
+)clear all
+
+--S 382 of 1475
+t0:=(c+d*x^2)^2/(x*(a+b*x^2))
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 382
+
+--S 383 of 1475
+r0:=1/2*d^2*x^2/b+c^2*log(x)/a-1/2*(b*c-a*d)^2*log(a+b*x^2)/(a*b^2)
+--R
+--R
+--R 2 2 2 2 2 2 2 2 2
+--R (- a d + 2a b c d - b c )log(b x + a) + 2b c log(x) + a b d x
+--R (2) ----------------------------------------------------------------
+--R 2
+--R 2a b
+--R Type: Expression(Integer)
+--E 383
+
+--S 384 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 2 2 2 2 2 2
+--R (- a d + 2a b c d - b c )log(b x + a) + 2b c log(x) + a b d x
+--R (3) ----------------------------------------------------------------
+--R 2
+--R 2a b
+--R Type: Union(Expression(Integer),...)
+--E 384
+
+--S 385 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 385
+
+--S 386 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 386
+
+)clear all
+
+--S 387 of 1475
+t0:=(c+d*x^2)^2/(x^2*(a+b*x^2))
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 4 2
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 387
+
+--S 388 of 1475
+r0:=-c^2/(a*x)+d^2*x/b-(b*c-a*d)^2*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(3/2))
+--R
+--R
+--R +-+
+--R 2 2 2 2 x\|b 2 2 2 +-+ +-+
+--R (- a d + 2a b c d - b c )x atan(-----) + (a d x - b c )\|a \|b
+--R +-+
+--R \|a
+--R (2) -----------------------------------------------------------------
+--R +-+ +-+
+--R a b x\|a \|b
+--R Type: Expression(Integer)
+--E 388
+
+--S 389 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 2 (b x - a)\|- a b - 2a b x
+--R (a d - 2a b c d + b c )x log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 2 2 +-----+
+--R (2a d x - 2b c )\|- a b
+--R /
+--R +-----+
+--R 2a b x\|- a b
+--R ,
+--R +---+
+--R 2 2 2 2 x\|a b 2 2 2 +---+
+--R (- a d + 2a b c d - b c )x atan(-------) + (a d x - b c )\|a b
+--R a
+--R -----------------------------------------------------------------]
+--R +---+
+--R a b x\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 389
+
+--S 390 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b - 2a b x
+--R (a d - 2a b c d + b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (2a d - 4a b c d + 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-----+ +-+ +-+
+--R 2a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 390
+
+--S 391 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (- a d + 2a b c d - b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (a d - 2a b c d + b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-+ +-+ +---+
+--R a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 393
+
+)clear all
+
+--S 394 of 1475
+t0:=(c+d*x^2)^2/(x^3*(a+b*x^2))
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 5 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 394
+
+--S 395 of 1475
+r0:=-1/2*c^2/(a*x^2)-c*(b*c-2*a*d)*log(x)/a^2+1/2*(b*c-a*d)^2*_
+ log(a+b*x^2)/(a^2*b)
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2 2 2 2 2
+--R (a d - 2a b c d + b c )x log(b x + a) + (4a b c d - 2b c )x log(x) - a b c
+--R -----------------------------------------------------------------------------
+--R 2 2
+--R 2a b x
+--R Type: Expression(Integer)
+--E 395
+
+--S 396 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2 2 2 2 2
+--R (a d - 2a b c d + b c )x log(b x + a) + (4a b c d - 2b c )x log(x) - a b c
+--R -----------------------------------------------------------------------------
+--R 2 2
+--R 2a b x
+--R Type: Union(Expression(Integer),...)
+--E 396
+
+--S 397 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 398
+
+)clear all
+
+--S 399 of 1475
+t0:=(c+d*x^2)^2/(x^4*(a+b*x^2))
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 6 4
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 399
+
+--S 400 of 1475
+r0:=-1/3*c^2/(a*x^3)+c*(b*c-2*a*d)/(a^2*x)+(b*c-a*d)^2*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*sqrt(b))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 3 x\|b
+--R (3a d - 6a b c d + 3b c )x atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 +-+ +-+
+--R ((- 6a c d + 3b c )x - a c )\|a \|b
+--R /
+--R 2 3 +-+ +-+
+--R 3a x \|a \|b
+--R Type: Expression(Integer)
+--E 400
+
+--S 401 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 2 3 (b x - a)\|- a b + 2a b x
+--R (3a d - 6a b c d + 3b c )x log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 2 2 +-----+
+--R ((- 12a c d + 6b c )x - 2a c )\|- a b
+--R /
+--R 2 3 +-----+
+--R 6a x \|- a b
+--R ,
+--R
+--R +---+
+--R 2 2 2 2 3 x\|a b
+--R (3a d - 6a b c d + 3b c )x atan(-------)
+--R a
+--R +
+--R 2 2 2 +---+
+--R ((- 6a c d + 3b c )x - a c )\|a b
+--R /
+--R 2 3 +---+
+--R 3a x \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 401
+
+--S 402 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d - 2a b c d + b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (- 2a d + 4a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 2a \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 403
+
+--S 404 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (a d - 2a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- a d + 2a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+ +-+ +---+
+--R a \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 1475
+t0:=x^m*(c+d*x^2)^3/(a+b*x^2)
+--R
+--R
+--R 3 6 2 4 2 2 3 m
+--R (d x + 3c d x + 3c d x + c )x
+--R (1) ---------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 1475
+--r0:=d*(a^2*d^2*(15+8*m+m^2)-2*a*b*c*d*(22+11*m+m^2)+b^2*c^2*(37+_
+-- 14*m+m^2))*x^(1+m)/(b^3*(1+m)*(3+m)*(5+m))+d*x^(1+m)*_
+-- (c+d*x^2)^2/(b*(5+m))-d*x^(1+m)*(c*(a*d*(1+m)-b*c*(5+m))+_
+-- d*(a*d*(5+m)-b*c*(9+m))*x^2)/(b^2*(3+m)*(5+m))+(b*c-a*d)^3*_
+-- x^(1+m)*hypergeometric(1,1/2*(1+m),1/2*(3+m),-b*x^2/a)/(a*b^3*(1+m))
+--E 407
+
+--S 408 of 1475
+--a0:=integrate(t0,x)
+--E 408
+
+--S 409 of 1475
+--m0:=a0-r0
+--E 409
+
+--S 410 of 1475
+--d0:=D(m0,x)
+--E 410
+
+)clear all
+
+--S 411 of 1475
+t0:=x^5*(a+b*x^2)^3/(c+d*x^2)
+--R
+--R
+--R 3 11 2 9 2 7 3 5
+--R b x + 3a b x + 3a b x + a x
+--R (1) --------------------------------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 411
+
+--S 412 of 1475
+r0:=1/2*c*(b*c-a*d)^3*x^2/d^5-1/4*(b*c-a*d)^3*x^4/d^4+1/6*b*(b^2*c^2-_
+ 3*a*b*c*d+3*a^2*d^2)*x^6/d^3-1/8*b^2*(b*c-3*a*d)*x^8/d^2+1/10*_
+ b^3*x^10/d-1/2*c^2*(b*c-a*d)^3*log(c+d*x^2)/d^6
+--R
+--R
+--R (2)
+--R 3 2 3 2 3 2 2 4 3 5 2 3 5 10
+--R (60a c d - 180a b c d + 180a b c d - 60b c )log(d x + c) + 12b d x
+--R +
+--R 2 5 3 4 8 2 5 2 4 3 2 3 6
+--R (45a b d - 15b c d )x + (60a b d - 60a b c d + 20b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (30a d - 90a b c d + 90a b c d - 30b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2
+--R (- 60a c d + 180a b c d - 180a b c d + 60b c d)x
+--R /
+--R 6
+--R 120d
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 3 2 3 2 2 4 3 5 2 3 5 10
+--R (60a c d - 180a b c d + 180a b c d - 60b c )log(d x + c) + 12b d x
+--R +
+--R 2 5 3 4 8 2 5 2 4 3 2 3 6
+--R (45a b d - 15b c d )x + (60a b d - 60a b c d + 20b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (30a d - 90a b c d + 90a b c d - 30b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2
+--R (- 60a c d + 180a b c d - 180a b c d + 60b c d)x
+--R /
+--R 6
+--R 120d
+--R Type: Union(Expression(Integer),...)
+--E 413
+
+--S 414 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 415
+
+)clear all
+
+--S 416 of 1475
+t0:=x^4*(c+d*x^2)^3/(a+b*x^2)
+--R
+--R
+--R 3 10 2 8 2 6 3 4
+--R d x + 3c d x + 3c d x + c x
+--R (1) --------------------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 416
+
+--S 417 of 1475
+r0:=-a*(b*c-a*d)^3*x/b^5+1/3*(b*c-a*d)^3*x^3/b^4+1/5*d*(3*b^2*c^2-_
+ 3*a*b*c*d+a^2*d^2)*x^5/b^3+1/7*d^2*(3*b*c-a*d)*x^7/b^2+1/9*d^3*_
+ x^9/b+a^(3/2)*(b*c-a*d)^3*atan(x*sqrt(b)/sqrt(a))/b^(11/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 4 3 3 2 2 2 2 3 3 +-+ x\|b
+--R (- 315a d + 945a b c d - 945a b c d + 315a b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 3 9 3 3 4 2 7
+--R 35b d x + (- 45a b d + 135b c d )x
+--R +
+--R 2 2 3 3 2 4 2 5
+--R (63a b d - 189a b c d + 189b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 105a b d + 315a b c d - 315a b c d + 105b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (315a d - 945a b c d + 945a b c d - 315a b c )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 5 +-+
+--R 315b \|b
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 4 3 3 2 2 2 2 3 3 | a
+--R (315a d - 945a b c d + 945a b c d - 315a b c ) |- -
+--R \| b
+--R *
+--R +---+
+--R | a 2
+--R - 2b x |- - + b x - a
+--R \| b
+--R log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R 4 3 9 3 3 4 2 7
+--R 70b d x + (- 90a b d + 270b c d )x
+--R +
+--R 2 2 3 3 2 4 2 5
+--R (126a b d - 378a b c d + 378b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 210a b d + 630a b c d - 630a b c d + 210b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (630a d - 1890a b c d + 1890a b c d - 630a b c )x
+--R /
+--R 5
+--R 630b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 4 3 3 2 2 2 2 3 3 |a \|b
+--R (315a d - 945a b c d + 945a b c d - 315a b c ) |- atan(----)
+--R \|b x
+--R +
+--R 4 3 9 3 3 4 2 7
+--R 35b d x + (- 45a b d + 135b c d )x
+--R +
+--R 2 2 3 3 2 4 2 5
+--R (63a b d - 189a b c d + 189b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 105a b d + 315a b c d - 315a b c d + 105b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (315a d - 945a b c d + 945a b c d - 315a b c )x
+--R /
+--R 5
+--R 315b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 418
+
+--S 419 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R 4 3 3 2 2 2 2 3 3 | a +-+
+--R (a d - 3a b c d + 3a b c d - a b c ) |- - \|b
+--R \| b
+--R *
+--R +---+
+--R | a 2
+--R - 2b x |- - + b x - a
+--R \| b
+--R log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 4 3 3 2 2 2 2 3 3 +-+ x\|b
+--R (2a d - 6a b c d + 6a b c d - 2a b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 420
+
+--S 421 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 4 3 3 2 2 2 2 3 3 +-+ x\|b
+--R (a d - 3a b c d + 3a b c d - a b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R 4 3 3 2 2 2 2 3 3 |a +-+ \|b
+--R (a d - 3a b c d + 3a b c d - a b c ) |- \|b atan(----)
+--R \|b x
+--R /
+--R 5 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 422
+
+)clear all
+
+--S 423 of 1475
+t0:=x^3*(c+d*x^2)^3/(a+b*x^2)
+--R
+--R
+--R 3 9 2 7 2 5 3 3
+--R d x + 3c d x + 3c d x + c x
+--R (1) -------------------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 423
+
+--S 424 of 1475
+r0:=1/2*(b*c-a*d)^3*x^2/b^4+1/4*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^4/b^3+_
+ 1/6*d^2*(3*b*c-a*d)*x^6/b^2+1/8*d^3*x^8/b-1/2*a*(b*c-a*d)^3*_
+ log(a+b*x^2)/b^5
+--R
+--R
+--R (2)
+--R 4 3 3 2 2 2 2 3 3 2 4 3 8
+--R (12a d - 36a b c d + 36a b c d - 12a b c )log(b x + a) + 3b d x
+--R +
+--R 3 3 4 2 6 2 2 3 3 2 4 2 4
+--R (- 4a b d + 12b c d )x + (6a b d - 18a b c d + 18b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 2
+--R (- 12a b d + 36a b c d - 36a b c d + 12b c )x
+--R /
+--R 5
+--R 24b
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 3 2 2 2 2 3 3 2 4 3 8
+--R (12a d - 36a b c d + 36a b c d - 12a b c )log(b x + a) + 3b d x
+--R +
+--R 3 3 4 2 6 2 2 3 3 2 4 2 4
+--R (- 4a b d + 12b c d )x + (6a b d - 18a b c d + 18b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 2
+--R (- 12a b d + 36a b c d - 36a b c d + 12b c )x
+--R /
+--R 5
+--R 24b
+--R Type: Union(Expression(Integer),...)
+--E 425
+
+--S 426 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 427
+
+)clear all
+
+--S 428 of 1475
+t0:=x^2*(c+d*x^2)^3/(a+b*x^2)
+--R
+--R
+--R 3 8 2 6 2 4 3 2
+--R d x + 3c d x + 3c d x + c x
+--R (1) -------------------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 428
+
+--S 429 of 1475
+r0:=(b*c-a*d)^3*x/b^4+1/3*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^3/b^3+_
+ 1/5*d^2*(3*b*c-a*d)*x^5/b^2+1/7*d^3*x^7/b-(b*c-a*d)^3*atan(x*_
+ sqrt(b)/sqrt(a))*sqrt(a)/b^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-+ x\|b
+--R (105a d - 315a b c d + 315a b c d - 105b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 3 7 2 3 3 2 5
+--R 15b d x + (- 21a b d + 63b c d )x
+--R +
+--R 2 3 2 2 3 2 3
+--R (35a b d - 105a b c d + 105b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 105a d + 315a b c d - 315a b c d + 105b c )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 4 +-+
+--R 105b \|b
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 3 3 2 2 2 2 3 3 | a
+--R (105a d - 315a b c d + 315a b c d - 105b c ) |- -
+--R \| b
+--R *
+--R +---+
+--R | a 2
+--R 2b x |- - + b x - a
+--R \| b
+--R log(---------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 3 7 2 3 3 2 5
+--R 30b d x + (- 42a b d + 126b c d )x
+--R +
+--R 2 3 2 2 3 2 3
+--R (70a b d - 210a b c d + 210b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 210a d + 630a b c d - 630a b c d + 210b c )x
+--R /
+--R 4
+--R 210b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 3 3 2 2 2 2 3 3 |a \|b
+--R (- 105a d + 315a b c d - 315a b c d + 105b c ) |- atan(----)
+--R \|b x
+--R +
+--R 3 3 7 2 3 3 2 5
+--R 15b d x + (- 21a b d + 63b c d )x
+--R +
+--R 2 3 2 2 3 2 3
+--R (35a b d - 105a b c d + 105b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 105a d + 315a b c d - 315a b c d + 105b c )x
+--R /
+--R 4
+--R 105b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 430
+
+--S 431 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 3 3 2 2 2 2 3 3 | a +-+ \| b
+--R (a d - 3a b c d + 3a b c d - b c ) |- - \|b log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-+ x\|b
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-+ x\|b
+--R (- a d + 3a b c d - 3a b c d + b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R 3 3 2 2 2 2 3 3 |a +-+ \|b
+--R (- a d + 3a b c d - 3a b c d + b c ) |- \|b atan(----)
+--R \|b x
+--R /
+--R 4 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 433
+
+--S 434 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 434
+
+)clear all
+
+--S 435 of 1475
+t0:=x*(c+d*x^2)^3/(a+b*x^2)
+--R
+--R
+--R 3 7 2 5 2 3 3
+--R d x + 3c d x + 3c d x + c x
+--R (1) ------------------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 435
+
+--S 436 of 1475
+r0:=1/2*d*(b*c-a*d)^2*x^2/b^3+1/4*(b*c-a*d)*(c+d*x^2)^2/b^2+_
+ 1/6*(c+d*x^2)^3/b+1/2*(b*c-a*d)^3*log(a+b*x^2)/b^4
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 2 3 3 6
+--R (- 6a d + 18a b c d - 18a b c d + 6b c )log(b x + a) + 2b d x
+--R +
+--R 2 3 3 2 4 2 3 2 2 3 2 2 2 2
+--R (- 3a b d + 9b c d )x + (6a b d - 18a b c d + 18b c d)x - 3a b c d
+--R +
+--R 3 3
+--R 5b c
+--R /
+--R 4
+--R 12b
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 2 3 3 2 3 3 6
+--R (- 6a d + 18a b c d - 18a b c d + 6b c )log(b x + a) + 2b d x
+--R +
+--R 2 3 3 2 4 2 3 2 2 3 2 2
+--R (- 3a b d + 9b c d )x + (6a b d - 18a b c d + 18b c d)x
+--R /
+--R 4
+--R 12b
+--R Type: Union(Expression(Integer),...)
+--E 437
+
+--S 438 of 1475
+m0:=a0-r0
+--R
+--R
+--R 2 3
+--R 3a c d - 5b c
+--R (4) --------------
+--R 2
+--R 12b
+--R Type: Expression(Integer)
+--E 438
+
+--S 439 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 439
+
+)clear all
+
+--S 440 of 1475
+t0:=(c+d*x^2)^3/(a+b*x^2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 440
+
+--S 441 of 1475
+r0:=d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x/b^3+1/3*d^2*(3*b*c-a*d)*x^3/b^2+_
+ 1/5*d^3*x^5/b+(b*c-a*d)^3*atan(x*sqrt(b)/sqrt(a))/(b^(7/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|b
+--R (- 15a d + 45a b c d - 45a b c d + 15b c )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 5 3 2 2 3 2 3 2 2 2
+--R (3b d x + (- 5a b d + 15b c d )x + (15a d - 45a b c d + 45b c d)x)
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 3 +-+ +-+
+--R 15b \|a \|b
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 3 2 2 2 2 3 3
+--R (15a d - 45a b c d + 45a b c d - 15b c )
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 5 3 2 2 3
+--R 6b d x + (- 10a b d + 30b c d )x
+--R +
+--R 2 3 2 2 2
+--R (30a d - 90a b c d + 90b c d)x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 3 +-----+
+--R 30b \|- a b
+--R ,
+--R
+--R +---+
+--R 3 3 2 2 2 2 3 3 x\|a b
+--R (- 15a d + 45a b c d - 45a b c d + 15b c )atan(-------)
+--R a
+--R +
+--R 2 3 5 3 2 2 3
+--R 3b d x + (- 5a b d + 15b c d )x
+--R +
+--R 2 3 2 2 2
+--R (15a d - 45a b c d + 45b c d)x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 3 +---+
+--R 15b \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 442
+
+--S 443 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (2a d - 6a b c d + 6a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 2b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 443
+
+--S 444 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (- a d + 3a b c d - 3a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (a d - 3a b c d + 3a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+ +-+ +---+
+--R b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 445
+
+--S 446 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 446
+
+)clear all
+
+--S 447 of 1475
+t0:=(c+d*x^2)^3/(x*(a+b*x^2))
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 447
+
+--S 448 of 1475
+r0:=1/2*d^2*(3*b*c-a*d)*x^2/b^2+1/4*d^3*x^4/b+c^3*log(x)/a-_
+ 1/2*(b*c-a*d)^3*log(a+b*x^2)/(a*b^3)
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 2 3 3
+--R (2a d - 6a b c d + 6a b c d - 2b c )log(b x + a) + 4b c log(x)
+--R +
+--R 2 3 4 2 3 2 2 2
+--R a b d x + (- 2a b d + 6a b c d )x
+--R /
+--R 3
+--R 4a b
+--R Type: Expression(Integer)
+--E 448
+
+--S 449 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 2 3 3 2 3 3
+--R (2a d - 6a b c d + 6a b c d - 2b c )log(b x + a) + 4b c log(x)
+--R +
+--R 2 3 4 2 3 2 2 2
+--R a b d x + (- 2a b d + 6a b c d )x
+--R /
+--R 3
+--R 4a b
+--R Type: Union(Expression(Integer),...)
+--E 449
+
+--S 450 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 450
+
+--S 451 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 451
+
+)clear all
+
+--S 452 of 1475
+t0:=(c+d*x^2)^3/(x^2*(a+b*x^2))
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 4 2
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 452
+
+--S 453 of 1475
+r0:=-c^3/(a*x)+d^2*(3*b*c-a*d)*x/b^2+1/3*d^3*x^3/b-(b*c-a*d)^3*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(5/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|b
+--R (3a d - 9a b c d + 9a b c d - 3b c )x atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 4 2 3 2 2 2 3 +-+ +-+
+--R (a b d x + (- 3a d + 9a b c d )x - 3b c )\|a \|b
+--R /
+--R 2 +-+ +-+
+--R 3a b x\|a \|b
+--R Type: Expression(Integer)
+--E 453
+
+--S 454 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 3 2 2 2 2 3 3
+--R (3a d - 9a b c d + 9a b c d - 3b c )x
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 4 2 3 2 2 2 3 +-----+
+--R (2a b d x + (- 6a d + 18a b c d )x - 6b c )\|- a b
+--R /
+--R 2 +-----+
+--R 6a b x\|- a b
+--R ,
+--R
+--R +---+
+--R 3 3 2 2 2 2 3 3 x\|a b
+--R (3a d - 9a b c d + 9a b c d - 3b c )x atan(-------)
+--R a
+--R +
+--R 3 4 2 3 2 2 2 3 +---+
+--R (a b d x + (- 3a d + 9a b c d )x - 3b c )\|a b
+--R /
+--R 2 +---+
+--R 3a b x\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 454
+
+--S 455 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 2a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 455
+
+--S 456 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (a d - 3a b c d + 3a b c d - b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (- a d + 3a b c d - 3a b c d + b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+ +-+ +---+
+--R a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 458
+
+)clear all
+
+--S 459 of 1475
+t0:=(c+d*x^2)^3/(x^3*(a+b*x^2))
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 5 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 459
+
+--S 460 of 1475
+r0:=-1/2*c^3/(a*x^2)+1/2*d^3*x^2/b-c^2*(b*c-3*a*d)*log(x)/a^2+_
+ 1/2*(b*c-a*d)^3*log(a+b*x^2)/(a^2*b^2)
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 2 2
+--R (- a d + 3a b c d - 3a b c d + b c )x log(b x + a)
+--R +
+--R 2 2 3 3 2 2 3 4 2 3
+--R (6a b c d - 2b c )x log(x) + a b d x - a b c
+--R /
+--R 2 2 2
+--R 2a b x
+--R Type: Expression(Integer)
+--E 460
+
+--S 461 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 2 3 3 2 2
+--R (- a d + 3a b c d - 3a b c d + b c )x log(b x + a)
+--R +
+--R 2 2 3 3 2 2 3 4 2 3
+--R (6a b c d - 2b c )x log(x) + a b d x - a b c
+--R /
+--R 2 2 2
+--R 2a b x
+--R Type: Union(Expression(Integer),...)
+--E 461
+
+--S 462 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 463
+
+)clear all
+
+--S 464 of 1475
+t0:=(c+d*x^2)^3/(x^4*(a+b*x^2))
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 6 4
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 464
+
+--S 465 of 1475
+r0:=-1/3*c^3/(a*x^3)+c^2*(b*c-3*a*d)/(a^2*x)+d^3*x/b+(b*c-a*d)^3*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(3/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 2 2 2 2 3 3 3 x\|b
+--R (- 3a d + 9a b c d - 9a b c d + 3b c )x atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 4 2 2 3 2 3 +-+ +-+
+--R (3a d x + (- 9a b c d + 3b c )x - a b c )\|a \|b
+--R /
+--R 2 3 +-+ +-+
+--R 3a b x \|a \|b
+--R Type: Expression(Integer)
+--E 465
+
+--S 466 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 3 2 2 2 2 3 3 3
+--R (3a d - 9a b c d + 9a b c d - 3b c )x
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 4 2 2 3 2 3 +-----+
+--R (6a d x + (- 18a b c d + 6b c )x - 2a b c )\|- a b
+--R /
+--R 2 3 +-----+
+--R 6a b x \|- a b
+--R ,
+--R
+--R +---+
+--R 3 3 2 2 2 2 3 3 3 x\|a b
+--R (- 3a d + 9a b c d - 9a b c d + 3b c )x atan(-------)
+--R a
+--R +
+--R 2 3 4 2 2 3 2 3 +---+
+--R (3a d x + (- 9a b c d + 3b c )x - a b c )\|a b
+--R /
+--R 2 3 +---+
+--R 3a b x \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 466
+
+--S 467 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (2a d - 6a b c d + 6a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 2a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 468
+
+--S 469 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (- a d + 3a b c d - 3a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (a d - 3a b c d + 3a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+ +-+ +---+
+--R a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 470
+
+)clear all
+
+--S 471 of 1475
+t0:=x^5/((a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 5
+--R x
+--R (1) ----------------------------
+--R 4 2
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 471
+
+--S 472 of 1475
+r0:=1/2*x^2/(b*d)+1/2*a^2*log(a+b*x^2)/(b^2*(b*c-a*d))-_
+ 1/2*c^2*log(c+d*x^2)/(d^2*(b*c-a*d))
+--R
+--R
+--R 2 2 2 2 2 2 2 2 2
+--R b c log(d x + c) - a d log(b x + a) + (a b d - b c d)x
+--R (2) ----------------------------------------------------------
+--R 2 3 3 2
+--R 2a b d - 2b c d
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 2 2 2 2 2 2
+--R b c log(d x + c) - a d log(b x + a) + (a b d - b c d)x
+--R (3) ----------------------------------------------------------
+--R 2 3 3 2
+--R 2a b d - 2b c d
+--R Type: Union(Expression(Integer),...)
+--E 473
+
+--S 474 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 475
+
+)clear all
+
+--S 476 of 1475
+t0:=x^4/((a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 4
+--R x
+--R (1) ----------------------------
+--R 4 2
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 476
+
+--S 477 of 1475
+r0:=x/(b*d)+a^(3/2)*atan(x*sqrt(b)/sqrt(a))/(b^(3/2)*(b*c-a*d))-_
+ c^(3/2)*atan(x*sqrt(d)/sqrt(c))/(d^(3/2)*(b*c-a*d))
+--R
+--R
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b +-+ +-+
+--R b c\|b \|c atan(-----) - a d\|a \|d atan(-----) + (a d - b c)x\|b \|d
+--R +-+ +-+
+--R \|c \|a
+--R (2) ----------------------------------------------------------------------
+--R 2 2 +-+ +-+
+--R (a b d - b c d)\|b \|d
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | c 2
+--R +---+ 2d x |- - + d x - c
+--R | c \| d
+--R b c |- - log(---------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R | a \| b
+--R a d |- - log(-----------------------) + (2a d - 2b c)x
+--R \| b 2
+--R b x + a
+--R /
+--R 2 2
+--R 2a b d - 2b c d
+--R ,
+--R +---+ +-+
+--R | c 2 |a
+--R +---+ 2d x |- - + d x - c +-+ |-
+--R | c \| d |a \|b
+--R b c |- - log(---------------------) + 2a d |- atan(----) + (2a d - 2b c)x
+--R \| d 2 \|b x
+--R d x + c
+--R -------------------------------------------------------------------------,
+--R 2 2
+--R 2a b d - 2b c d
+--R +---+ +-+
+--R | a 2 |c
+--R +---+ - 2b x |- - + b x - a +-+ |-
+--R | a \| b |c \|d
+--R a d |- - log(-----------------------) - 2b c |- atan(----) + (2a d - 2b c)x
+--R \| b 2 \|d x
+--R b x + a
+--R ---------------------------------------------------------------------------,
+--R 2 2
+--R 2a b d - 2b c d
+--R +-+ +-+
+--R |a |c
+--R +-+ |- +-+ |-
+--R |a \|b |c \|d
+--R a d |- atan(----) - b c |- atan(----) + (a d - b c)x
+--R \|b x \|d x
+--R ----------------------------------------------------]
+--R 2 2
+--R a b d - b c d
+--R Type: Union(List(Expression(Integer)),...)
+--E 478
+
+--S 479 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | c 2
+--R +---+ 2d x |- - + d x - c
+--R | c +-+ +-+ \| d
+--R b c |- - \|b \|d log(---------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a +-+
+--R | a +-+ +-+ \| b +-+ +-+ x\|d
+--R a d |- - \|b \|d log(-----------------------) - 2b c\|b \|c atan(-----)
+--R \| b 2 +-+
+--R b x + a \|c
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R 2a d\|a \|d atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 +-+ +-+
+--R (2a b d - 2b c d)\|b \|d
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 480
+
+--S 481 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | c 2
+--R +---+ 2d x |- - + d x - c +-+
+--R | c +-+ +-+ \| d +-+ +-+ x\|d
+--R b c |- - \|b \|d log(---------------------) - 2b c\|b \|c atan(-----)
+--R \| d 2 +-+
+--R d x + c \|c
+--R +
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ +-+ x\|b |a +-+ +-+ \|b
+--R 2a d\|a \|d atan(-----) + 2a d |- \|b \|d atan(----)
+--R +-+ \|b x
+--R \|a
+--R /
+--R 2 2 +-+ +-+
+--R (2a b d - 2b c d)\|b \|d
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 482
+
+)clear all
+
+--S 483 of 1475
+t0:=x^3/((a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 3
+--R x
+--R (1) ----------------------------
+--R 4 2
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 483
+
+--S 484 of 1475
+r0:=-1/2*a*log(a+b*x^2)/(b*(b*c-a*d))+1/2*c*log(c+d*x^2)/(d*(b*c-a*d))
+--R
+--R
+--R 2 2
+--R - b c log(d x + c) + a d log(b x + a)
+--R (2) ---------------------------------------
+--R 2 2
+--R 2a b d - 2b c d
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R - b c log(d x + c) + a d log(b x + a)
+--R (3) ---------------------------------------
+--R 2 2
+--R 2a b d - 2b c d
+--R Type: Union(Expression(Integer),...)
+--E 485
+
+--S 486 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 487
+
+)clear all
+
+--S 488 of 1475
+t0:=x^2/((a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------------
+--R 4 2
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 488
+
+--S 489 of 1475
+r0:=-atan(x*sqrt(b)/sqrt(a))*sqrt(a)/((b*c-a*d)*sqrt(b))+_
+ atan(x*sqrt(d)/sqrt(c))*sqrt(c)/((b*c-a*d)*sqrt(d))
+--R
+--R
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R - \|b \|c atan(-----) + \|a \|d atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R (2) -------------------------------------------
+--R +-+ +-+
+--R (a d - b c)\|b \|d
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+
+--R | a 2 | c 2
+--R +---+ 2b x |- - + b x - a +---+ - 2d x |- - + d x - c
+--R | a \| b | c \| d
+--R |- - log(---------------------) + |- - log(-----------------------)
+--R \| b 2 \| d 2
+--R b x + a d x + c
+--R [---------------------------------------------------------------------,
+--R 2a d - 2b c
+--R +---+ +-+
+--R | c 2 |a
+--R +---+ - 2d x |- - + d x - c +-+ |-
+--R | c \| d |a \|b
+--R |- - log(-----------------------) - 2 |- atan(----)
+--R \| d 2 \|b x
+--R d x + c
+--R ----------------------------------------------------,
+--R 2a d - 2b c
+--R +---+ +-+
+--R | a 2 |c
+--R +---+ 2b x |- - + b x - a +-+ |-
+--R | a \| b |c \|d
+--R |- - log(---------------------) + 2 |- atan(----)
+--R \| b 2 \|d x
+--R b x + a
+--R --------------------------------------------------,
+--R 2a d - 2b c
+--R +-+ +-+
+--R |a |c
+--R +-+ |- +-+ |-
+--R |a \|b |c \|d
+--R - |- atan(----) + |- atan(----)
+--R \|b x \|d x
+--R ---------------------------------]
+--R a d - b c
+--R Type: Union(List(Expression(Integer)),...)
+--E 490
+
+--S 491 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a +-+ +-+ \| b
+--R |- - \|b \|d log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c +-+
+--R | c +-+ +-+ \| d +-+ +-+ x\|d
+--R |- - \|b \|d log(-----------------------) + 2\|b \|c atan(-----)
+--R \| d 2 +-+
+--R d x + c \|c
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R - 2\|a \|d atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-+ +-+
+--R (2a d - 2b c)\|b \|d
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c +-+
+--R | c +-+ +-+ \| d +-+ +-+ x\|d
+--R |- - \|b \|d log(-----------------------) + 2\|b \|c atan(-----)
+--R \| d 2 +-+
+--R d x + c \|c
+--R +
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ +-+ x\|b |a +-+ +-+ \|b
+--R - 2\|a \|d atan(-----) - 2 |- \|b \|d atan(----)
+--R +-+ \|b x
+--R \|a
+--R /
+--R +-+ +-+
+--R (2a d - 2b c)\|b \|d
+--R Type: Expression(Integer)
+--E 493
+
+--S 494 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 494
+
+)clear all
+
+--S 495 of 1475
+t0:=x/((a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R x
+--R (1) ----------------------------
+--R 4 2
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 495
+
+--S 496 of 1475
+r0:=1/2*log(a+b*x^2)/(b*c-a*d)-1/2*log(c+d*x^2)/(b*c-a*d)
+--R
+--R
+--R 2 2
+--R log(d x + c) - log(b x + a)
+--R (2) -----------------------------
+--R 2a d - 2b c
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R log(d x + c) - log(b x + a)
+--R (3) -----------------------------
+--R 2a d - 2b c
+--R Type: Union(Expression(Integer),...)
+--E 497
+
+--S 498 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 498
+
+--S 499 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 499
+
+)clear all
+
+--S 500 of 1475
+t0:=1/((a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R 4 2
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 500
+
+--S 501 of 1475
+r0:=atan(x*sqrt(b)/sqrt(a))*sqrt(b)/((b*c-a*d)*sqrt(a))-_
+ atan(x*sqrt(d)/sqrt(c))*sqrt(d)/((b*c-a*d)*sqrt(c))
+--R
+--R
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R \|a \|d atan(-----) - \|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R (2) -----------------------------------------
+--R +-+ +-+
+--R (a d - b c)\|a \|c
+--R Type: Expression(Integer)
+--E 501
+
+--S 502 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+
+--R | d 2 | b 2
+--R +---+ 2c x |- - + d x - c +---+ - 2a x |- - + b x - a
+--R | d \| c | b \| a
+--R |- - log(---------------------) + |- - log(-----------------------)
+--R \| c 2 \| a 2
+--R d x + c b x + a
+--R [---------------------------------------------------------------------,
+--R 2a d - 2b c
+--R +---+ +-+
+--R | b 2 |d
+--R +---+ - 2a x |- - + b x - a +-+ c |-
+--R | b \| a |d \|c
+--R |- - log(-----------------------) - 2 |- atan(-----)
+--R \| a 2 \|c d x
+--R b x + a
+--R -----------------------------------------------------,
+--R 2a d - 2b c
+--R +---+ +-+
+--R | d 2 |b
+--R +---+ 2c x |- - + d x - c +-+ a |-
+--R | d \| c |b \|a
+--R |- - log(---------------------) + 2 |- atan(-----)
+--R \| c 2 \|a b x
+--R d x + c
+--R ---------------------------------------------------,
+--R 2a d - 2b c
+--R +-+ +-+
+--R |d |b
+--R +-+ c |- +-+ a |-
+--R |d \|c |b \|a
+--R - |- atan(-----) + |- atan(-----)
+--R \|c d x \|a b x
+--R -----------------------------------]
+--R a d - b c
+--R Type: Union(List(Expression(Integer)),...)
+--E 502
+
+--S 503 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d +-+ +-+ \| c
+--R |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R | b +-+ +-+ \| a +-+ +-+ x\|d
+--R |- - \|a \|c log(-----------------------) - 2\|a \|d atan(-----)
+--R \| a 2 +-+
+--R b x + a \|c
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R 2\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-+ +-+
+--R (2a d - 2b c)\|a \|c
+--R Type: Expression(Integer)
+--E 503
+
+--S 504 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 504
+
+--S 505 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R | b +-+ +-+ \| a +-+ +-+ x\|d
+--R |- - \|a \|c log(-----------------------) - 2\|a \|d atan(-----)
+--R \| a 2 +-+
+--R b x + a \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- +-+
+--R +-+ +-+ |d \|c +-+ +-+ x\|b
+--R - 2\|a \|c |- atan(-----) + 2\|b \|c atan(-----)
+--R \|c d x +-+
+--R \|a
+--R /
+--R +-+ +-+
+--R (2a d - 2b c)\|a \|c
+--R Type: Expression(Integer)
+--E 505
+
+--S 506 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 506
+
+)clear all
+
+--S 507 of 1475
+t0:=1/(x*(a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ------------------------------
+--R 5 3
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 507
+
+--S 508 of 1475
+r0:=log(x)/(a*c)-1/2*b*log(a+b*x^2)/(a*(b*c-a*d))+_
+ 1/2*d*log(c+d*x^2)/(c*(b*c-a*d))
+--R
+--R
+--R 2 2
+--R - a d log(d x + c) + b c log(b x + a) + (2a d - 2b c)log(x)
+--R (2) -------------------------------------------------------------
+--R 2 2
+--R 2a c d - 2a b c
+--R Type: Expression(Integer)
+--E 508
+
+--S 509 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R - a d log(d x + c) + b c log(b x + a) + (2a d - 2b c)log(x)
+--R (3) -------------------------------------------------------------
+--R 2 2
+--R 2a c d - 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 509
+
+--S 510 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 510
+
+--S 511 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 511
+
+)clear all
+
+--S 512 of 1475
+t0:=1/(x^2*(a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 6 4 2
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 512
+
+--S 513 of 1475
+r0:=(-1)/(a*c*x)-b^(3/2)*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*(b*c-a*d))+_
+ d^(3/2)*atan(x*sqrt(d)/sqrt(c))/(c^(3/2)*(b*c-a*d))
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b +-+ +-+
+--R - a d x\|a \|d atan(-----) + b c x\|b \|c atan(-----) + (- a d + b c)\|a \|c
+--R +-+ +-+
+--R \|c \|a
+--R -----------------------------------------------------------------------------
+--R 2 2 +-+ +-+
+--R (a c d - a b c )x\|a \|c
+--R Type: Expression(Integer)
+--E 513
+
+--S 514 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R b c x |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R | d \| c
+--R a d x |- - log(-----------------------) - 2a d + 2b c
+--R \| c 2
+--R d x + c
+--R /
+--R 2 2
+--R (2a c d - 2a b c )x
+--R ,
+--R +---+ +-+
+--R | b 2 |d
+--R +---+ 2a x |- - + b x - a +-+ c |-
+--R | b \| a |d \|c
+--R b c x |- - log(---------------------) + 2a d x |- atan(-----) - 2a d + 2b c
+--R \| a 2 \|c d x
+--R b x + a
+--R ---------------------------------------------------------------------------,
+--R 2 2
+--R (2a c d - 2a b c )x
+--R
+--R +---+ +-+
+--R | d 2 |b
+--R +---+ - 2c x |- - + d x - c +-+ a |-
+--R | d \| c |b \|a
+--R a d x |- - log(-----------------------) - 2b c x |- atan(-----) - 2a d
+--R \| c 2 \|a b x
+--R d x + c
+--R +
+--R 2b c
+--R /
+--R 2 2
+--R (2a c d - 2a b c )x
+--R ,
+--R +-+ +-+
+--R |d |b
+--R +-+ c |- +-+ a |-
+--R |d \|c |b \|a
+--R a d x |- atan(-----) - b c x |- atan(-----) - a d + b c
+--R \|c d x \|a b x
+--R -------------------------------------------------------]
+--R 2 2
+--R (a c d - a b c )x
+--R Type: Union(List(Expression(Integer)),...)
+--E 514
+
+--S 515 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c +-+
+--R | d +-+ +-+ \| c +-+ +-+ x\|d
+--R a d |- - \|a \|c log(-----------------------) + 2a d\|a \|d atan(-----)
+--R \| c 2 +-+
+--R d x + c \|c
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R - 2b c\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 +-+ +-+
+--R (2a c d - 2a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 515
+
+--S 516 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 516
+
+--S 517 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a +-+
+--R | b +-+ +-+ \| a +-+ +-+ x\|d
+--R b c |- - \|a \|c log(---------------------) + 2a d\|a \|d atan(-----)
+--R \| a 2 +-+
+--R b x + a \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- +-+
+--R +-+ +-+ |d \|c +-+ +-+ x\|b
+--R 2a d\|a \|c |- atan(-----) - 2b c\|b \|c atan(-----)
+--R \|c d x +-+
+--R \|a
+--R /
+--R 2 2 +-+ +-+
+--R (2a c d - 2a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 517
+
+--S 518 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 518
+
+)clear all
+
+--S 519 of 1475
+t0:=1/(x^3*(a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 7 5 3
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 519
+
+--S 520 of 1475
+r0:=(-1/2)/(a*c*x^2)-(b*c+a*d)*log(x)/(a^2*c^2)+_
+ 1/2*b^2*log(a+b*x^2)/(a^2*(b*c-a*d))-1/2*d^2*log(c+d*x^2)/(c^2*(b*c-a*d))
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2 2 2 2 2 2 2 2
+--R a d x log(d x + c) - b c x log(b x + a) + (- 2a d + 2b c )x log(x)
+--R +
+--R 2 2
+--R - a c d + a b c
+--R /
+--R 3 2 2 3 2
+--R (2a c d - 2a b c )x
+--R Type: Expression(Integer)
+--E 520
+
+--S 521 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2 2 2 2 2 2 2 2
+--R a d x log(d x + c) - b c x log(b x + a) + (- 2a d + 2b c )x log(x)
+--R +
+--R 2 2
+--R - a c d + a b c
+--R /
+--R 3 2 2 3 2
+--R (2a c d - 2a b c )x
+--R Type: Union(Expression(Integer),...)
+--E 521
+
+--S 522 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 522
+
+--S 523 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 523
+
+)clear all
+
+--S 524 of 1475
+t0:=1/(x^4*(a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 8 6 4
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 524
+
+--S 525 of 1475
+r0:=(-1/3)/(a*c*x^3)+(b*c+a*d)/(a^2*c^2*x)+b^(5/2)*atan(x*_
+ sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-a*d))-d^(5/2)*atan(x*sqrt(d)/_
+ sqrt(c))/(c^(5/2)*(b*c-a*d))
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R 2 2 3 +-+ +-+ x\|d 2 2 3 +-+ +-+ x\|b
+--R 3a d x \|a \|d atan(-----) - 3b c x \|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R +
+--R 2 2 2 2 2 2 2 +-+ +-+
+--R ((3a d - 3b c )x - a c d + a b c )\|a \|c
+--R /
+--R 3 2 2 3 3 +-+ +-+
+--R (3a c d - 3a b c )x \|a \|c
+--R Type: Expression(Integer)
+--E 525
+
+--S 526 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 3 | d \| c
+--R 3a d x |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 | b \| a 2 2 2 2 2 2
+--R 3b c x |- - log(-----------------------) + (6a d - 6b c )x - 2a c d
+--R \| a 2
+--R b x + a
+--R +
+--R 2
+--R 2a b c
+--R /
+--R 3 2 2 3 3
+--R (6a c d - 6a b c )x
+--R ,
+--R
+--R +---+ +-+
+--R | b 2 |d
+--R +---+ - 2a x |- - + b x - a +-+ c |-
+--R 2 2 3 | b \| a 2 2 3 |d \|c
+--R 3b c x |- - log(-----------------------) - 6a d x |- atan(-----)
+--R \| a 2 \|c d x
+--R b x + a
+--R +
+--R 2 2 2 2 2 2 2
+--R (6a d - 6b c )x - 2a c d + 2a b c
+--R /
+--R 3 2 2 3 3
+--R (6a c d - 6a b c )x
+--R ,
+--R
+--R +---+ +-+
+--R | d 2 |b
+--R +---+ 2c x |- - + d x - c +-+ a |-
+--R 2 2 3 | d \| c 2 2 3 |b \|a
+--R 3a d x |- - log(---------------------) + 6b c x |- atan(-----)
+--R \| c 2 \|a b x
+--R d x + c
+--R +
+--R 2 2 2 2 2 2 2
+--R (6a d - 6b c )x - 2a c d + 2a b c
+--R /
+--R 3 2 2 3 3
+--R (6a c d - 6a b c )x
+--R ,
+--R
+--R +-+ +-+
+--R |d |b
+--R +-+ c |- +-+ a |-
+--R 2 2 3 |d \|c 2 2 3 |b \|a 2 2 2 2 2
+--R - 3a d x |- atan(-----) + 3b c x |- atan(-----) + (3a d - 3b c )x
+--R \|c d x \|a b x
+--R +
+--R 2 2
+--R - a c d + a b c
+--R /
+--R 3 2 2 3 3
+--R (3a c d - 3a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 526
+
+--S 527 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 | d +-+ +-+ \| c
+--R a d |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R 2 2 | b +-+ +-+ \| a 2 2 +-+ +-+ x\|d
+--R b c |- - \|a \|c log(-----------------------) - 2a d \|a \|d atan(-----)
+--R \| a 2 +-+
+--R b x + a \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R 2b c \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 2 2 3 +-+ +-+
+--R (2a c d - 2a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 527
+
+--S 528 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 528
+
+--S 529 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R 2 2 | b +-+ +-+ \| a 2 2 +-+ +-+ x\|d
+--R b c |- - \|a \|c log(-----------------------) - 2a d \|a \|d atan(-----)
+--R \| a 2 +-+
+--R b x + a \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- +-+
+--R 2 2 +-+ +-+ |d \|c 2 2 +-+ +-+ x\|b
+--R - 2a d \|a \|c |- atan(-----) + 2b c \|b \|c atan(-----)
+--R \|c d x +-+
+--R \|a
+--R /
+--R 3 2 2 3 +-+ +-+
+--R (2a c d - 2a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 529
+
+--S 530 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 530
+
+)clear all
+
+--S 531 of 1475
+t0:=1/(x^5*(a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 9 7 5
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 531
+
+--S 532 of 1475
+r0:=(-1/4)/(a*c*x^4)+1/2*(b*c+a*d)/(a^2*c^2*x^2)+(b^2*c^2+a*b*c*d+_
+ a^2*d^2)*log(x)/(a^3*c^3)-1/2*b^3*log(a+b*x^2)/(a^3*(b*c-a*d))+_
+ 1/2*d^3*log(c+d*x^2)/(c^3*(b*c-a*d))
+--R
+--R
+--R (2)
+--R 3 3 4 2 3 3 4 2 3 3 3 3 4
+--R - 2a d x log(d x + c) + 2b c x log(b x + a) + (4a d - 4b c )x log(x)
+--R +
+--R 3 2 2 3 2 3 2 2 3
+--R (2a c d - 2a b c )x - a c d + a b c
+--R /
+--R 4 3 3 4 4
+--R (4a c d - 4a b c )x
+--R Type: Expression(Integer)
+--E 532
+
+--S 533 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 4 2 3 3 4 2 3 3 3 3 4
+--R - 2a d x log(d x + c) + 2b c x log(b x + a) + (4a d - 4b c )x log(x)
+--R +
+--R 3 2 2 3 2 3 2 2 3
+--R (2a c d - 2a b c )x - a c d + a b c
+--R /
+--R 4 3 3 4 4
+--R (4a c d - 4a b c )x
+--R Type: Union(Expression(Integer),...)
+--E 533
+
+--S 534 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 534
+
+--S 535 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 535
+
+)clear all
+
+--S 536 of 1475
+t0:=1/(x^6*(a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 10 8 6
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 536
+
+--S 537 of 1475
+r0:=(-1/5)/(a*c*x^5)+1/3*(b*c+a*d)/(a^2*c^2*x^3)+(-b^2*c^2-a*b*c*d-_
+ a^2*d^2)/(a^3*c^3*x)-b^(7/2)*atan(x*sqrt(b)/sqrt(a))/(a^(7/2)*_
+ (b*c-a*d))+d^(7/2)*atan(x*sqrt(d)/sqrt(c))/(c^(7/2)*(b*c-a*d))
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R 3 3 5 +-+ +-+ x\|d 3 3 5 +-+ +-+ x\|b
+--R - 15a d x \|a \|d atan(-----) + 15b c x \|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R +
+--R 3 3 3 3 4 3 2 2 3 2 3 2 2 3 +-+ +-+
+--R ((- 15a d + 15b c )x + (5a c d - 5a b c )x - 3a c d + 3a b c )\|a \|c
+--R /
+--R 4 3 3 4 5 +-+ +-+
+--R (15a c d - 15a b c )x \|a \|c
+--R Type: Expression(Integer)
+--E 537
+
+--S 538 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 5 | b \| a
+--R 15b c x |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R 3 3 5 | d \| c 3 3 3 3 4
+--R 15a d x |- - log(-----------------------) + (- 30a d + 30b c )x
+--R \| c 2
+--R d x + c
+--R +
+--R 3 2 2 3 2 3 2 2 3
+--R (10a c d - 10a b c )x - 6a c d + 6a b c
+--R /
+--R 4 3 3 4 5
+--R (30a c d - 30a b c )x
+--R ,
+--R
+--R +---+ +-+
+--R | b 2 |d
+--R +---+ 2a x |- - + b x - a +-+ c |-
+--R 3 3 5 | b \| a 3 3 5 |d \|c
+--R 15b c x |- - log(---------------------) + 30a d x |- atan(-----)
+--R \| a 2 \|c d x
+--R b x + a
+--R +
+--R 3 3 3 3 4 3 2 2 3 2 3 2 2 3
+--R (- 30a d + 30b c )x + (10a c d - 10a b c )x - 6a c d + 6a b c
+--R /
+--R 4 3 3 4 5
+--R (30a c d - 30a b c )x
+--R ,
+--R
+--R +---+ +-+
+--R | d 2 |b
+--R +---+ - 2c x |- - + d x - c +-+ a |-
+--R 3 3 5 | d \| c 3 3 5 |b \|a
+--R 15a d x |- - log(-----------------------) - 30b c x |- atan(-----)
+--R \| c 2 \|a b x
+--R d x + c
+--R +
+--R 3 3 3 3 4 3 2 2 3 2 3 2 2 3
+--R (- 30a d + 30b c )x + (10a c d - 10a b c )x - 6a c d + 6a b c
+--R /
+--R 4 3 3 4 5
+--R (30a c d - 30a b c )x
+--R ,
+--R
+--R +-+ +-+
+--R |d |b
+--R +-+ c |- +-+ a |-
+--R 3 3 5 |d \|c 3 3 5 |b \|a
+--R 15a d x |- atan(-----) - 15b c x |- atan(-----)
+--R \|c d x \|a b x
+--R +
+--R 3 3 3 3 4 3 2 2 3 2 3 2 2 3
+--R (- 15a d + 15b c )x + (5a c d - 5a b c )x - 3a c d + 3a b c
+--R /
+--R 4 3 3 4 5
+--R (15a c d - 15a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 538
+
+--S 539 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 | b +-+ +-+ \| a
+--R b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c +-+
+--R 3 3 | d +-+ +-+ \| c 3 3 +-+ +-+ x\|d
+--R a d |- - \|a \|c log(-----------------------) + 2a d \|a \|d atan(-----)
+--R \| c 2 +-+
+--R d x + c \|c
+--R +
+--R +-+
+--R 3 3 +-+ +-+ x\|b
+--R - 2b c \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 3 3 4 +-+ +-+
+--R (2a c d - 2a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 539
+
+--S 540 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 540
+
+--S 541 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a +-+
+--R 3 3 | b +-+ +-+ \| a 3 3 +-+ +-+ x\|d
+--R b c |- - \|a \|c log(---------------------) + 2a d \|a \|d atan(-----)
+--R \| a 2 +-+
+--R b x + a \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- +-+
+--R 3 3 +-+ +-+ |d \|c 3 3 +-+ +-+ x\|b
+--R 2a d \|a \|c |- atan(-----) - 2b c \|b \|c atan(-----)
+--R \|c d x +-+
+--R \|a
+--R /
+--R 4 3 3 4 +-+ +-+
+--R (2a c d - 2a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 541
+
+--S 542 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 542
+
+)clear all
+
+--S 543 of 1475
+t0:=1/(x^7*(a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 11 9 7
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 543
+
+--S 544 of 1475
+r0:=(-1/6)/(a*c*x^6)+1/4*(b*c+a*d)/(a^2*c^2*x^4)+1/2*(-b^2*c^2-a*b*c*d-_
+ a^2*d^2)/(a^3*c^3*x^2)-(b*c+a*d)*(b^2*c^2+a^2*d^2)*log(x)/(a^4*_
+ c^4)+1/2*b^4*log(a+b*x^2)/(a^4*(b*c-a*d))-1/2*d^4*log(c+d*x^2)/_
+ (c^4*(b*c-a*d))
+--R
+--R
+--R (2)
+--R 4 4 6 2 4 4 6 2 4 4 4 4 6
+--R 6a d x log(d x + c) - 6b c x log(b x + a) + (- 12a d + 12b c )x log(x)
+--R +
+--R 4 3 3 4 4 4 2 2 2 2 4 2 4 3 3 4
+--R (- 6a c d + 6a b c )x + (3a c d - 3a b c )x - 2a c d + 2a b c
+--R /
+--R 5 4 4 5 6
+--R (12a c d - 12a b c )x
+--R Type: Expression(Integer)
+--E 544
+
+--S 545 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 6 2 4 4 6 2 4 4 4 4 6
+--R 6a d x log(d x + c) - 6b c x log(b x + a) + (- 12a d + 12b c )x log(x)
+--R +
+--R 4 3 3 4 4 4 2 2 2 2 4 2 4 3 3 4
+--R (- 6a c d + 6a b c )x + (3a c d - 3a b c )x - 2a c d + 2a b c
+--R /
+--R 5 4 4 5 6
+--R (12a c d - 12a b c )x
+--R Type: Union(Expression(Integer),...)
+--E 545
+
+--S 546 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 546
+
+--S 547 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 547
+
+)clear all
+
+--S 548 of 1475
+t0:=x^5/((a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 5
+--R x
+--R (1) --------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 548
+
+--S 549 of 1475
+r0:=-1/2*a^2/(b^2*(b*c-a*d)*(a+b*x^2))-1/2*a*(2*b*c-a*d)*log(a+b*x^2)/_
+ (b^2*(b*c-a*d)^2)+1/2*c^2*log(c+d*x^2)/(d*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R 3 2 2 2 2 2
+--R (b c x + a b c )log(d x + c)
+--R +
+--R 2 2 2 2 3 2 2 2 3 2 2
+--R ((a b d - 2a b c d)x + a d - 2a b c d)log(b x + a) + a d - a b c d
+--R /
+--R 2 3 3 4 2 5 2 2 3 2 3 2 3 2 4 2
+--R (2a b d - 4a b c d + 2b c d)x + 2a b d - 4a b c d + 2a b c d
+--R Type: Expression(Integer)
+--E 549
+
+--S 550 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2 2 2 2
+--R (b c x + a b c )log(d x + c)
+--R +
+--R 2 2 2 2 3 2 2 2 3 2 2
+--R ((a b d - 2a b c d)x + a d - 2a b c d)log(b x + a) + a d - a b c d
+--R /
+--R 2 3 3 4 2 5 2 2 3 2 3 2 3 2 4 2
+--R (2a b d - 4a b c d + 2b c d)x + 2a b d - 4a b c d + 2a b c d
+--R Type: Union(Expression(Integer),...)
+--E 550
+
+--S 551 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 551
+
+--S 552 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 552
+
+)clear all
+
+--S 553 of 1475
+t0:=x^4/((a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 4
+--R x
+--R (1) -----------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 553
+
+--S 554 of 1475
+r0a:=-1/2*c*x/(d*(b*c-a*d)*(c+d*x^2))+a^(3/2)*atan(x*sqrt(b)/sqrt(a))/_
+ ((b*c-a*d)^2*sqrt(b))+1/2*(b*c-3*a*d)*atan(x*sqrt(d)/sqrt(c))*_
+ sqrt(c)/(d^(3/2)*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 +-+ +-+ x\|d
+--R ((- 3a d + b c d)x - 3a c d + b c )\|b \|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b 2 +-+ +-+
+--R (2a d x + 2a c d)\|a \|d atan(-----) + (a c d - b c )x\|b \|d
+--R +-+
+--R \|a
+--R /
+--R 2 4 3 2 2 2 2 2 3 2 2 2 3 +-+ +-+
+--R ((2a d - 4a b c d + 2b c d )x + 2a c d - 4a b c d + 2b c d)\|b \|d
+--R Type: Expression(Integer)
+--E 554
+
+--S 555 of 1475
+r0b:=-1/2*c*x/(d*(b*c-a*d)*(c+d*x^2))+_
+ a^(3/2)*atan(x*sqrt(b)/sqrt(a))/((b*c-a*d)^2*sqrt(b))+(b*c-2*a*d)*_
+ atan(x*sqrt(d)/sqrt(c))*sqrt(c)/(d^(3/2)*(b*c-a*d)^2)-_
+ 1/2*atan(x*sqrt(d)/sqrt(c))*sqrt(c)/(d^(3/2)*(b*c-a*d))
+--R
+--R
+--R (3)
+--R +-+
+--R 2 2 2 +-+ +-+ x\|d
+--R ((- 3a d + b c d)x - 3a c d + b c )\|b \|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b 2 +-+ +-+
+--R (2a d x + 2a c d)\|a \|d atan(-----) + (a c d - b c )x\|b \|d
+--R +-+
+--R \|a
+--R /
+--R 2 4 3 2 2 2 2 2 3 2 2 2 3 +-+ +-+
+--R ((2a d - 4a b c d + 2b c d )x + 2a c d - 4a b c d + 2b c d)\|b \|d
+--R Type: Expression(Integer)
+--E 555
+
+--S 556 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 2 | a \| b
+--R (2a d x + 2a c d) |- - log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R 2 2 2 | c \| d
+--R ((3a d - b c d)x + 3a c d - b c ) |- - log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R 2
+--R (2a c d - 2b c )x
+--R /
+--R 2 4 3 2 2 2 2 2 3 2 2 2 3
+--R (4a d - 8a b c d + 4b c d )x + 4a c d - 8a b c d + 4b c d
+--R ,
+--R
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R 2 2 2 | c \| d
+--R ((3a d - b c d)x + 3a c d - b c ) |- - log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 |a \|b 2
+--R (- 4a d x - 4a c d) |- atan(----) + (2a c d - 2b c )x
+--R \|b x
+--R /
+--R 2 4 3 2 2 2 2 2 3 2 2 2 3
+--R (4a d - 8a b c d + 4b c d )x + 4a c d - 8a b c d + 4b c d
+--R ,
+--R
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 2 | a \| b
+--R (a d x + a c d) |- - log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R |c
+--R +-+ |-
+--R 2 2 2 |c \|d 2
+--R ((3a d - b c d)x + 3a c d - b c ) |- atan(----) + (a c d - b c )x
+--R \|d x
+--R /
+--R 2 4 3 2 2 2 2 2 3 2 2 2 3
+--R (2a d - 4a b c d + 2b c d )x + 2a c d - 4a b c d + 2b c d
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 |a \|b
+--R (- 2a d x - 2a c d) |- atan(----)
+--R \|b x
+--R +
+--R +-+
+--R |c
+--R +-+ |-
+--R 2 2 2 |c \|d 2
+--R ((3a d - b c d)x + 3a c d - b c ) |- atan(----) + (a c d - b c )x
+--R \|d x
+--R /
+--R 2 4 3 2 2 2 2 2 3 2 2 2 3
+--R (2a d - 4a b c d + 2b c d )x + 2a c d - 4a b c d + 2b c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 556
+
+--S 557 of 1475
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a +-+ +-+ \| b
+--R 2a d |- - \|b \|d log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R | c +-+ +-+ \| d
+--R (3a d - b c) |- - \|b \|d log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R (6a d - 2b c)\|b \|c atan(-----) - 4a d\|a \|d atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 2 3 2 2 2 +-+ +-+
+--R (4a d - 8a b c d + 4b c d)\|b \|d
+--R Type: Expression(Integer)
+--E 557
+
+--S 558 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 558
+
+--S 559 of 1475
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R | c +-+ +-+ \| d
+--R (3a d - b c) |- - \|b \|d log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R (6a d - 2b c)\|b \|c atan(-----) - 4a d\|a \|d atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R |a +-+ +-+ \|b
+--R - 4a d |- \|b \|d atan(----)
+--R \|b x
+--R /
+--R 2 3 2 2 2 +-+ +-+
+--R (4a d - 8a b c d + 4b c d)\|b \|d
+--R Type: Expression(Integer)
+--E 559
+
+--S 560 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 560
+
+--S 561 of 1475
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a +-+ +-+ \| b
+--R 2a d |- - \|b \|d log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R | c +-+ +-+ \| d
+--R (3a d - b c) |- - \|b \|d log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R (6a d - 2b c)\|b \|c atan(-----) - 4a d\|a \|d atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 2 3 2 2 2 +-+ +-+
+--R (4a d - 8a b c d + 4b c d)\|b \|d
+--R Type: Expression(Integer)
+--E 561
+
+--S 562 of 1475
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 562
+
+--S 563 of 1475
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R | c +-+ +-+ \| d
+--R (3a d - b c) |- - \|b \|d log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R (6a d - 2b c)\|b \|c atan(-----) - 4a d\|a \|d atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R |a +-+ +-+ \|b
+--R - 4a d |- \|b \|d atan(----)
+--R \|b x
+--R /
+--R 2 3 2 2 2 +-+ +-+
+--R (4a d - 8a b c d + 4b c d)\|b \|d
+--R Type: Expression(Integer)
+--E 563
+
+--S 564 of 1475
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 564
+
+)clear all
+
+--S 565 of 1475
+t0:=x^3/((a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 3
+--R x
+--R (1) -----------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 565
+
+--S 566 of 1475
+r0:=-1/2*c/(d*(b*c-a*d)*(c+d*x^2))-1/2*a*log(a+b*x^2)/(b*c-a*d)^2+_
+ 1/2*a*log(c+d*x^2)/(b*c-a*d)^2
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2
+--R (a d x + a c d)log(d x + c) + (- a d x - a c d)log(b x + a) + a c d
+--R +
+--R 2
+--R - b c
+--R /
+--R 2 4 3 2 2 2 2 2 3 2 2 2 3
+--R (2a d - 4a b c d + 2b c d )x + 2a c d - 4a b c d + 2b c d
+--R Type: Expression(Integer)
+--E 566
+
+--S 567 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2
+--R (a d x + a c d)log(d x + c) + (- a d x - a c d)log(b x + a) + a c d
+--R +
+--R 2
+--R - b c
+--R /
+--R 2 4 3 2 2 2 2 2 3 2 2 2 3
+--R (2a d - 4a b c d + 2b c d )x + 2a c d - 4a b c d + 2b c d
+--R Type: Union(Expression(Integer),...)
+--E 567
+
+--S 568 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 568
+
+--S 569 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 569
+
+)clear all
+
+--S 570 of 1475
+t0:=x^2/((a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 2
+--R x
+--R (1) -----------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 570
+
+--S 571 of 1475
+r0a:=1/2*x/((b*c-a*d)*(c+d*x^2))-atan(x*sqrt(b)/sqrt(a))*sqrt(a)*_
+ sqrt(b)/(b*c-a*d)^2+1/2*(b*c+a*d)*atan(x*sqrt(d)/sqrt(c))/_
+ ((b*c-a*d)^2*sqrt(c)*sqrt(d))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 x\|d
+--R ((a d + b c d)x + a c d + b c )atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 +-+ +-+ +-+ +-+ x\|b +-+ +-+
+--R (- 2d x - 2c)\|a \|b \|c \|d atan(-----) + (- a d + b c)x\|c \|d
+--R +-+
+--R \|a
+--R /
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+ +-+
+--R ((2a d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c )\|c \|d
+--R Type: Expression(Integer)
+--E 571
+
+--S 572 of 1475
+r0b:=1/2*x/((b*c-a*d)*(c+d*x^2))-_
+ atan(x*sqrt(b)/sqrt(a))*sqrt(a)*sqrt(b)/(b*c-a*d)^2+1/2*_
+ atan(x*sqrt(d)/sqrt(c))/((b*c-a*d)*sqrt(c)*sqrt(d))+a*_
+ atan(x*sqrt(d)/sqrt(c))*sqrt(d)/((b*c-a*d)^2*sqrt(c))
+--R
+--R
+--R (3)
+--R +-+
+--R 2 2 2 x\|d
+--R ((a d + b c d)x + a c d + b c )atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 +-+ +-+ +-+ +-+ x\|b +-+ +-+
+--R (- 2d x - 2c)\|a \|b \|c \|d atan(-----) + (- a d + b c)x\|c \|d
+--R +-+
+--R \|a
+--R /
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+ +-+
+--R ((2a d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c )\|c \|d
+--R Type: Expression(Integer)
+--E 572
+
+--S 573 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 +-----+
+--R 2 2 2 (d x - c)\|- c d + 2c d x
+--R ((a d + b c d)x + a c d + b c )log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-----+ 2
+--R 2 +-----+ +-----+ - 2x\|- a b + b x - a
+--R (2d x + 2c)\|- c d \|- a b log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R +-----+
+--R (- 2a d + 2b c)x\|- c d
+--R /
+--R 2 3 2 2 2 2 2 2 2 2 3 +-----+
+--R ((4a d - 8a b c d + 4b c d)x + 4a c d - 8a b c d + 4b c )\|- c d
+--R ,
+--R
+--R +-----+ 2
+--R 2 +-----+ +---+ - 2x\|- a b + b x - a
+--R (d x + c)\|- a b \|c d log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R +---+
+--R 2 2 2 x\|c d +---+
+--R ((a d + b c d)x + a c d + b c )atan(-------) + (- a d + b c)x\|c d
+--R c
+--R /
+--R 2 3 2 2 2 2 2 2 2 2 3 +---+
+--R ((2a d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c )\|c d
+--R ,
+--R
+--R 2 +-----+
+--R 2 2 2 (d x - c)\|- c d + 2c d x
+--R ((a d + b c d)x + a c d + b c )log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +---+
+--R 2 +-----+ +---+ \|a b +-----+
+--R (4d x + 4c)\|- c d \|a b atan(------) + (- 2a d + 2b c)x\|- c d
+--R b x
+--R /
+--R 2 3 2 2 2 2 2 2 2 2 3 +-----+
+--R ((4a d - 8a b c d + 4b c d)x + 4a c d - 8a b c d + 4b c )\|- c d
+--R ,
+--R
+--R +---+
+--R 2 2 2 x\|c d
+--R ((a d + b c d)x + a c d + b c )atan(-------)
+--R c
+--R +
+--R +---+
+--R 2 +---+ +---+ \|a b +---+
+--R (2d x + 2c)\|a b \|c d atan(------) + (- a d + b c)x\|c d
+--R b x
+--R /
+--R 2 3 2 2 2 2 2 2 2 2 3 +---+
+--R ((2a d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 573
+
+--S 574 of 1475
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 2 +-----+
+--R +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d + b c)\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-----+ 2
+--R +-----+ +-----+ +-+ +-+ - 2x\|- a b + b x - a
+--R 2\|- c d \|- a b \|c \|d log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+ +-+
+--R +-----+ x\|d +-----+ +-+ +-+ +-+ +-+ x\|b
+--R (- 2a d - 2b c)\|- c d atan(-----) + 4\|- c d \|a \|b \|c \|d atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 2 2 2 2 +-----+ +-+ +-+
+--R (4a d - 8a b c d + 4b c )\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 574
+
+--S 575 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 575
+
+--S 576 of 1475
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +-----+ 2
+--R +-----+ +-+ +-+ +---+ - 2x\|- a b + b x - a
+--R \|- a b \|c \|d \|c d log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R +---+ +-+
+--R +-+ +-+ x\|c d +---+ x\|d
+--R (a d + b c)\|c \|d atan(-------) + (- a d - b c)\|c d atan(-----)
+--R c +-+
+--R \|c
+--R +
+--R +-+
+--R +-+ +-+ +-+ +-+ +---+ x\|b
+--R 2\|a \|b \|c \|d \|c d atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 2 2 +-+ +-+ +---+
+--R (2a d - 4a b c d + 2b c )\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 576
+
+--S 577 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 577
+
+--S 578 of 1475
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 2 +-----+
+--R +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d + b c)\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-----+ 2
+--R +-----+ +-----+ +-+ +-+ - 2x\|- a b + b x - a
+--R 2\|- c d \|- a b \|c \|d log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+ +-+
+--R +-----+ x\|d +-----+ +-+ +-+ +-+ +-+ x\|b
+--R (- 2a d - 2b c)\|- c d atan(-----) + 4\|- c d \|a \|b \|c \|d atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 2 2 2 2 +-----+ +-+ +-+
+--R (4a d - 8a b c d + 4b c )\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 578
+
+--S 579 of 1475
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 579
+
+--S 580 of 1475
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +-----+ 2
+--R +-----+ +-+ +-+ +---+ - 2x\|- a b + b x - a
+--R \|- a b \|c \|d \|c d log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R +---+ +-+
+--R +-+ +-+ x\|c d +---+ x\|d
+--R (a d + b c)\|c \|d atan(-------) + (- a d - b c)\|c d atan(-----)
+--R c +-+
+--R \|c
+--R +
+--R +-+
+--R +-+ +-+ +-+ +-+ +---+ x\|b
+--R 2\|a \|b \|c \|d \|c d atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 2 2 +-+ +-+ +---+
+--R (2a d - 4a b c d + 2b c )\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 580
+
+--S 581 of 1475
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 581
+
+)clear all
+
+--S 582 of 1475
+t0:=x/((a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R x
+--R (1) -----------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 582
+
+--S 583 of 1475
+r0:=1/2/((b*c-a*d)*(c+d*x^2))+1/2*b*log(a+b*x^2)/(b*c-a*d)^2-_
+ 1/2*b*log(c+d*x^2)/(b*c-a*d)^2
+--R
+--R
+--R (2)
+--R 2 2 2 2
+--R (- b d x - b c)log(d x + c) + (b d x + b c)log(b x + a) - a d + b c
+--R -----------------------------------------------------------------------
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R (2a d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c
+--R Type: Expression(Integer)
+--E 583
+
+--S 584 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2
+--R (- b d x - b c)log(d x + c) + (b d x + b c)log(b x + a) - a d + b c
+--R -----------------------------------------------------------------------
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R (2a d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c
+--R Type: Union(Expression(Integer),...)
+--E 584
+
+--S 585 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 585
+
+--S 586 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 586
+
+)clear all
+
+--S 587 of 1475
+t0:=1/((a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 587
+
+--S 588 of 1475
+r0:=-1/2*d*x/(c*(b*c-a*d)*(c+d*x^2))+b^(3/2)*atan(x*sqrt(b)/sqrt(a))/_
+ ((b*c-a*d)^2*sqrt(a))-1/2*(3*b*c-a*d)*atan(x*sqrt(d)/sqrt(c))*_
+ sqrt(d)/(c^(3/2)*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 +-+ +-+ x\|d
+--R ((a d - 3b c d)x + a c d - 3b c )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b 2 +-+ +-+
+--R (2b c d x + 2b c )\|b \|c atan(-----) + (a d - b c d)x\|a \|c
+--R +-+
+--R \|a
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4 +-+ +-+
+--R ((2a c d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c )\|a \|c
+--R Type: Expression(Integer)
+--E 588
+
+--S 589 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b \| a
+--R (2b c d x + 2b c ) |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 | d \| c
+--R ((a d - 3b c d)x + a c d - 3b c ) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2
+--R (2a d - 2b c d)x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (4a c d - 8a b c d + 4b c d)x + 4a c d - 8a b c d + 4b c
+--R ,
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b \| a
+--R (b c d x + b c ) |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 |d \|c 2
+--R ((- a d + 3b c d)x - a c d + 3b c ) |- atan(-----) + (a d - b c d)x
+--R \|c d x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (2a c d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c
+--R ,
+--R
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 | d \| c
+--R ((a d - 3b c d)x + a c d - 3b c ) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 |b \|a 2
+--R (- 4b c d x - 4b c ) |- atan(-----) + (2a d - 2b c d)x
+--R \|a b x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (4a c d - 8a b c d + 4b c d)x + 4a c d - 8a b c d + 4b c
+--R ,
+--R
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 |d \|c
+--R ((- a d + 3b c d)x - a c d + 3b c ) |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 |b \|a 2
+--R (- 2b c d x - 2b c ) |- atan(-----) + (a d - b c d)x
+--R \|a b x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (2a c d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 589
+
+--S 590 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R 2b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d +-+ +-+ \| c
+--R (a d - 3b c) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R (- 2a d + 6b c)\|a \|d atan(-----) - 4b c\|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 2 2 2 2 3 +-+ +-+
+--R (4a c d - 8a b c d + 4b c )\|a \|c
+--R Type: Expression(Integer)
+--E 590
+
+--S 591 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 591
+
+--S 592 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ +-+ c |-
+--R +-+ +-+ x\|d +-+ +-+ |d \|c
+--R (- a d + 3b c)\|a \|d atan(-----) + (- a d + 3b c)\|a \|c |- atan(-----)
+--R +-+ \|c d x
+--R \|c
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R - 2b c\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 2 2 3 +-+ +-+
+--R (2a c d - 4a b c d + 2b c )\|a \|c
+--R Type: Expression(Integer)
+--E 592
+
+--S 593 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 593
+
+)clear all
+
+--S 594 of 1475
+t0:=1/(x*(a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------------
+--R 2 7 2 5 2 3 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 594
+
+--S 595 of 1475
+r0:=-1/2*d/(c*(b*c-a*d)*(c+d*x^2))+log(x)/(a*c^2)-1/2*b^2*log(a+b*x^2)/_
+ (a*(b*c-a*d)^2)+1/2*d*(2*b*c-a*d)*log(c+d*x^2)/(c^2*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 2
+--R ((- a d + 2a b c d )x - a c d + 2a b c d)log(d x + c)
+--R +
+--R 2 2 2 2 3 2
+--R (- b c d x - b c )log(b x + a)
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((2a d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c )log(x)
+--R +
+--R 2 2 2
+--R a c d - a b c d
+--R /
+--R 3 2 3 2 3 2 2 4 2 3 3 2 2 4 2 5
+--R (2a c d - 4a b c d + 2a b c d)x + 2a c d - 4a b c d + 2a b c
+--R Type: Expression(Integer)
+--E 595
+
+--S 596 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 2 2 2
+--R ((- a d + 2a b c d )x - a c d + 2a b c d)log(d x + c)
+--R +
+--R 2 2 2 2 3 2
+--R (- b c d x - b c )log(b x + a)
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((2a d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c )log(x)
+--R +
+--R 2 2 2
+--R a c d - a b c d
+--R /
+--R 3 2 3 2 3 2 2 4 2 3 3 2 2 4 2 5
+--R (2a c d - 4a b c d + 2a b c d)x + 2a c d - 4a b c d + 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 596
+
+--S 597 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 597
+
+--S 598 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 598
+
+)clear all
+
+--S 599 of 1475
+t0:=1/(x^2*(a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------
+--R 2 8 2 6 2 4 2 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 599
+
+--S 600 of 1475
+r0a:=(-1)/(a*c^2*x)+1/2*d^2*x/(c^2*(b*c-a*d)*(c+d*x^2))-b^(5/2)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*(b*c-a*d)^2)+1/2*d^(3/2)*(5*b*_
+ c-3*a*d)*atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 2 3 2 2 2 +-+ +-+ x\|d
+--R ((- 3a d + 5a b c d )x + (- 3a c d + 5a b c d)x)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 3 2 3 +-+ +-+ x\|b
+--R (- 2b c d x - 2b c x)\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+ +-+
+--R ((- 3a d + 5a b c d - 2b c d)x - 2a c d + 4a b c d - 2b c )\|a \|c
+--R /
+--R 3 2 3 2 3 2 2 4 3 3 3 2 2 4 2 5
+--R ((2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x)
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 600
+
+--S 601 of 1475
+r0b:=(-1)/(a*c^2*x)+1/2*d^2*x/(c^2*(b*c-a*d)*(c+d*x^2))-b^(5/2)*atan(x*_
+ sqrt(b)/sqrt(a))/(a^(3/2)*(b*c-a*d)^2)+1/2*d^(3/2)*atan(x*_
+ sqrt(d)/sqrt(c))/(c^(5/2)*(b*c-a*d))+d^(3/2)*(2*b*c-a*d)*_
+ atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*(b*c-a*d)^2)
+--R
+--R
+--R (3)
+--R +-+
+--R 2 3 2 3 2 2 2 +-+ +-+ x\|d
+--R ((- 3a d + 5a b c d )x + (- 3a c d + 5a b c d)x)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 3 2 3 +-+ +-+ x\|b
+--R (- 2b c d x - 2b c x)\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+ +-+
+--R ((- 3a d + 5a b c d - 2b c d)x - 2a c d + 4a b c d - 2b c )\|a \|c
+--R /
+--R 3 2 3 2 3 2 2 4 3 3 3 2 2 4 2 5
+--R ((2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x)
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 601
+
+--S 602 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R +---+
+--R 2 3 2 3 2 2 2 | d
+--R ((3a d - 5a b c d )x + (3a c d - 5a b c d)x) |- -
+--R \| c
+--R *
+--R +---+
+--R | d 2
+--R - 2c x |- - + d x - c
+--R \| c
+--R log(-----------------------)
+--R 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 2 3 | b \| a
+--R (2b c d x + 2b c x) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R (- 6a d + 10a b c d - 4b c d)x - 4a c d + 8a b c d - 4b c
+--R /
+--R 3 2 3 2 3 2 2 4 3 3 3 2 2 4 2 5
+--R (4a c d - 8a b c d + 4a b c d)x + (4a c d - 8a b c d + 4a b c )x
+--R ,
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 2 3 | b \| a
+--R (b c d x + b c x) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 3 2 3 2 2 2 |d \|c
+--R ((3a d - 5a b c d )x + (3a c d - 5a b c d)x) |- atan(-----)
+--R \|c d x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R (- 3a d + 5a b c d - 2b c d)x - 2a c d + 4a b c d - 2b c
+--R /
+--R 3 2 3 2 3 2 2 4 3 3 3 2 2 4 2 5
+--R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x
+--R ,
+--R
+--R +---+
+--R 2 3 2 3 2 2 2 | d
+--R ((3a d - 5a b c d )x + (3a c d - 5a b c d)x) |- -
+--R \| c
+--R *
+--R +---+
+--R | d 2
+--R - 2c x |- - + d x - c
+--R \| c
+--R log(-----------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 3 2 3 |b \|a 2 3 2 2 2 2
+--R (4b c d x + 4b c x) |- atan(-----) + (- 6a d + 10a b c d - 4b c d)x
+--R \|a b x
+--R +
+--R 2 2 2 2 3
+--R - 4a c d + 8a b c d - 4b c
+--R /
+--R 3 2 3 2 3 2 2 4 3 3 3 2 2 4 2 5
+--R (4a c d - 8a b c d + 4a b c d)x + (4a c d - 8a b c d + 4a b c )x
+--R ,
+--R
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 3 2 3 2 2 2 |d \|c
+--R ((3a d - 5a b c d )x + (3a c d - 5a b c d)x) |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 3 2 3 |b \|a 2 3 2 2 2 2
+--R (2b c d x + 2b c x) |- atan(-----) + (- 3a d + 5a b c d - 2b c d)x
+--R \|a b x
+--R +
+--R 2 2 2 2 3
+--R - 2a c d + 4a b c d - 2b c
+--R /
+--R 3 2 3 2 3 2 2 4 3 3 3 2 2 4 2 5
+--R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 602
+
+--S 603 of 1475
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R 2 2 | d +-+ +-+ \| c
+--R (3a d - 5a b c d) |- - \|a \|c log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R 2b c |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+ +-+
+--R 2 2 +-+ +-+ x\|d 2 2 +-+ +-+ x\|b
+--R (6a d - 10a b c d)\|a \|d atan(-----) + 4b c \|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 3 2 2 2 3 2 4 +-+ +-+
+--R (4a c d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 603
+
+--S 604 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 604
+
+--S 605 of 1475
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R b c |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (3a d - 5a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- +-+
+--R 2 2 +-+ +-+ |d \|c 2 2 +-+ +-+ x\|b
+--R (3a d - 5a b c d)\|a \|c |- atan(-----) + 2b c \|b \|c atan(-----)
+--R \|c d x +-+
+--R \|a
+--R /
+--R 3 2 2 2 3 2 4 +-+ +-+
+--R (2a c d - 4a b c d + 2a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 605
+
+--S 606 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 606
+
+--S 607 of 1475
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R 2 2 | d +-+ +-+ \| c
+--R (3a d - 5a b c d) |- - \|a \|c log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R 2b c |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+ +-+
+--R 2 2 +-+ +-+ x\|d 2 2 +-+ +-+ x\|b
+--R (6a d - 10a b c d)\|a \|d atan(-----) + 4b c \|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 3 2 2 2 3 2 4 +-+ +-+
+--R (4a c d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 607
+
+--S 608 of 1475
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 608
+
+--S 609 of 1475
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R b c |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (3a d - 5a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- +-+
+--R 2 2 +-+ +-+ |d \|c 2 2 +-+ +-+ x\|b
+--R (3a d - 5a b c d)\|a \|c |- atan(-----) + 2b c \|b \|c atan(-----)
+--R \|c d x +-+
+--R \|a
+--R /
+--R 3 2 2 2 3 2 4 +-+ +-+
+--R (2a c d - 4a b c d + 2a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 609
+
+--S 610 of 1475
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 610
+
+)clear all
+
+--S 611 of 1475
+t0:=1/(x^3*(a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------
+--R 2 9 2 7 2 5 2 3
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 611
+
+--S 612 of 1475
+r0:=(-1/2)/(a*c^2*x^2)+1/2*d^2/(c^2*(b*c-a*d)*(c+d*x^2))-(b*c+2*a*d)*_
+ log(x)/(a^2*c^3)+1/2*b^3*log(a+b*x^2)/(a^2*(b*c-a*d)^2)-1/2*d^2*_
+ (3*b*c-2*a*d)*log(c+d*x^2)/(c^3*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R 3 4 2 3 4 3 3 2 2 2 2 2
+--R ((2a d - 3a b c d )x + (2a c d - 3a b c d )x )log(d x + c)
+--R +
+--R 3 3 4 3 4 2 2
+--R (b c d x + b c x )log(b x + a)
+--R +
+--R 3 4 2 3 3 3 4 3 3 2 2 2 3 4 2
+--R ((- 4a d + 6a b c d - 2b c d)x + (- 4a c d + 6a b c d - 2b c )x )
+--R *
+--R log(x)
+--R +
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3 2 4
+--R (- 2a c d + 3a b c d - a b c d)x - a c d + 2a b c d - a b c
+--R /
+--R 4 3 3 3 4 2 2 2 5 4 4 4 2 3 5 2 2 6 2
+--R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x
+--R Type: Expression(Integer)
+--E 612
+
+--S 613 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 4 2 3 4 3 3 2 2 2 2 2
+--R ((2a d - 3a b c d )x + (2a c d - 3a b c d )x )log(d x + c)
+--R +
+--R 3 3 4 3 4 2 2
+--R (b c d x + b c x )log(b x + a)
+--R +
+--R 3 4 2 3 3 3 4 3 3 2 2 2 3 4 2
+--R ((- 4a d + 6a b c d - 2b c d)x + (- 4a c d + 6a b c d - 2b c )x )
+--R *
+--R log(x)
+--R +
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3 2 4
+--R (- 2a c d + 3a b c d - a b c d)x - a c d + 2a b c d - a b c
+--R /
+--R 4 3 3 3 4 2 2 2 5 4 4 4 2 3 5 2 2 6 2
+--R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x
+--R Type: Union(Expression(Integer),...)
+--E 613
+
+--S 614 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 614
+
+--S 615 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 615
+
+)clear all
+
+--S 616 of 1475
+t0:=1/(x^4*(a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------------
+--R 2 10 2 8 2 6 2 4
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 616
+
+--S 617 of 1475
+r0a:=(-1/3)/(a*c^2*x^3)+(b*c+2*a*d)/(a^2*c^3*x)-1/2*d^3*x/(c^3*(b*c-_
+ a*d)*(c+d*x^2))+b^(7/2)*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-_
+ a*d)^2)-1/2*d^(5/2)*(7*b*c-5*a*d)*atan(x*sqrt(d)/sqrt(c))/_
+ (c^(7/2)*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 4 2 3 5 3 3 2 2 2 3 +-+ +-+ x\|d
+--R ((15a d - 21a b c d )x + (15a c d - 21a b c d )x )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 3 3 5 3 4 3 +-+ +-+ x\|b
+--R (6b c d x + 6b c x )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 4 2 3 3 3 4
+--R (15a d - 21a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (10a c d - 14a b c d - 2a b c d + 6b c )x - 2a c d + 4a b c d
+--R +
+--R 2 4
+--R - 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 4 3 3 3 4 2 2 2 5 5 4 4 2 3 5 2 2 6 3
+--R ((6a c d - 12a b c d + 6a b c d)x + (6a c d - 12a b c d + 6a b c )x )
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 617
+
+--S 618 of 1475
+r0b:=(-1/3)/(a*c^2*x^3)+(b*c+2*a*d)/(a^2*c^3*x)-_
+ 1/2*d^3*x/(c^3*(b*c-a*d)*(c+d*x^2))+b^(7/2)*atan(x*sqrt(b)/_
+ sqrt(a))/(a^(5/2)*(b*c-a*d)^2)-d^(5/2)*(3*b*c-2*a*d)*atan(x*_
+ sqrt(d)/sqrt(c))/(c^(7/2)*(b*c-a*d)^2)-1/2*d^(5/2)*atan(x*_
+ sqrt(d)/sqrt(c))/(c^(7/2)*(b*c-a*d))
+--R
+--R
+--R (3)
+--R +-+
+--R 3 4 2 3 5 3 3 2 2 2 3 +-+ +-+ x\|d
+--R ((15a d - 21a b c d )x + (15a c d - 21a b c d )x )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 3 3 5 3 4 3 +-+ +-+ x\|b
+--R (6b c d x + 6b c x )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 4 2 3 3 3 4
+--R (15a d - 21a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (10a c d - 14a b c d - 2a b c d + 6b c )x - 2a c d + 4a b c d
+--R +
+--R 2 4
+--R - 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 4 3 3 3 4 2 2 2 5 5 4 4 2 3 5 2 2 6 3
+--R ((6a c d - 12a b c d + 6a b c d)x + (6a c d - 12a b c d + 6a b c )x )
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 618
+
+--S 619 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 5 3 4 3 | b \| a
+--R (6b c d x + 6b c x ) |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R 3 4 2 3 5 3 3 2 2 2 3 | d
+--R ((15a d - 21a b c d )x + (15a c d - 21a b c d )x ) |- -
+--R \| c
+--R *
+--R +---+
+--R | d 2
+--R 2c x |- - + d x - c
+--R \| c
+--R log(---------------------)
+--R 2
+--R d x + c
+--R +
+--R 3 4 2 3 3 3 4
+--R (30a d - 42a b c d + 12b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (20a c d - 28a b c d - 4a b c d + 12b c )x - 4a c d + 8a b c d
+--R +
+--R 2 4
+--R - 4a b c
+--R /
+--R 4 3 3 3 4 2 2 2 5 5
+--R (12a c d - 24a b c d + 12a b c d)x
+--R +
+--R 4 4 2 3 5 2 2 6 3
+--R (12a c d - 24a b c d + 12a b c )x
+--R ,
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 5 3 4 3 | b \| a
+--R (3b c d x + 3b c x ) |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 4 2 3 5 3 3 2 2 2 3 |d
+--R ((- 15a d + 21a b c d )x + (- 15a c d + 21a b c d )x ) |-
+--R \|c
+--R *
+--R +-+
+--R |d
+--R c |-
+--R \|c
+--R atan(-----)
+--R d x
+--R +
+--R 3 4 2 3 3 3 4
+--R (15a d - 21a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (10a c d - 14a b c d - 2a b c d + 6b c )x - 2a c d + 4a b c d
+--R +
+--R 2 4
+--R - 2a b c
+--R /
+--R 4 3 3 3 4 2 2 2 5 5 4 4 2 3 5 2 2 6 3
+--R (6a c d - 12a b c d + 6a b c d)x + (6a c d - 12a b c d + 6a b c )x
+--R ,
+--R
+--R +---+
+--R 3 4 2 3 5 3 3 2 2 2 3 | d
+--R ((15a d - 21a b c d )x + (15a c d - 21a b c d )x ) |- -
+--R \| c
+--R *
+--R +---+
+--R | d 2
+--R 2c x |- - + d x - c
+--R \| c
+--R log(---------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 3 5 3 4 3 |b \|a
+--R (- 12b c d x - 12b c x ) |- atan(-----)
+--R \|a b x
+--R +
+--R 3 4 2 3 3 3 4
+--R (30a d - 42a b c d + 12b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (20a c d - 28a b c d - 4a b c d + 12b c )x - 4a c d + 8a b c d
+--R +
+--R 2 4
+--R - 4a b c
+--R /
+--R 4 3 3 3 4 2 2 2 5 5
+--R (12a c d - 24a b c d + 12a b c d)x
+--R +
+--R 4 4 2 3 5 2 2 6 3
+--R (12a c d - 24a b c d + 12a b c )x
+--R ,
+--R
+--R +-+
+--R 3 4 2 3 5 3 3 2 2 2 3 |d
+--R ((- 15a d + 21a b c d )x + (- 15a c d + 21a b c d )x ) |-
+--R \|c
+--R *
+--R +-+
+--R |d
+--R c |-
+--R \|c
+--R atan(-----)
+--R d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 3 5 3 4 3 |b \|a
+--R (- 6b c d x - 6b c x ) |- atan(-----)
+--R \|a b x
+--R +
+--R 3 4 2 3 3 3 4
+--R (15a d - 21a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (10a c d - 14a b c d - 2a b c d + 6b c )x - 2a c d + 4a b c d
+--R +
+--R 2 4
+--R - 2a b c
+--R /
+--R 4 3 3 3 4 2 2 2 5 5 4 4 2 3 5 2 2 6 3
+--R (6a c d - 12a b c d + 6a b c d)x + (6a c d - 12a b c d + 6a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 619
+
+--S 620 of 1475
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 | b +-+ +-+ \| a
+--R 2b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 3 3 2 2 | d +-+ +-+ \| c
+--R (5a d - 7a b c d ) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R 3 3 2 2 +-+ +-+ x\|d 3 3 +-+ +-+ x\|b
+--R (- 10a d + 14a b c d )\|a \|d atan(-----) - 4b c \|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 4 3 2 3 4 2 2 5 +-+ +-+
+--R (4a c d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 620
+
+--S 621 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 621
+
+--S 622 of 1475
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 | b +-+ +-+ \| a
+--R b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 +-+ +-+ x\|d
+--R (- 5a d + 7a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- +-+
+--R 3 3 2 2 +-+ +-+ |d \|c 3 3 +-+ +-+ x\|b
+--R (- 5a d + 7a b c d )\|a \|c |- atan(-----) - 2b c \|b \|c atan(-----)
+--R \|c d x +-+
+--R \|a
+--R /
+--R 4 3 2 3 4 2 2 5 +-+ +-+
+--R (2a c d - 4a b c d + 2a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 622
+
+--S 623 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 623
+
+--S 624 of 1475
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 | b +-+ +-+ \| a
+--R 2b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 3 3 2 2 | d +-+ +-+ \| c
+--R (5a d - 7a b c d ) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R 3 3 2 2 +-+ +-+ x\|d 3 3 +-+ +-+ x\|b
+--R (- 10a d + 14a b c d )\|a \|d atan(-----) - 4b c \|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 4 3 2 3 4 2 2 5 +-+ +-+
+--R (4a c d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 624
+
+--S 625 of 1475
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 625
+
+--S 626 of 1475
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 | b +-+ +-+ \| a
+--R b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 +-+ +-+ x\|d
+--R (- 5a d + 7a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- +-+
+--R 3 3 2 2 +-+ +-+ |d \|c 3 3 +-+ +-+ x\|b
+--R (- 5a d + 7a b c d )\|a \|c |- atan(-----) - 2b c \|b \|c atan(-----)
+--R \|c d x +-+
+--R \|a
+--R /
+--R 4 3 2 3 4 2 2 5 +-+ +-+
+--R (2a c d - 4a b c d + 2a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 626
+
+--S 627 of 1475
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 627
+
+)clear all
+
+--S 628 of 1475
+t0:=x^5/((a+b*x^2)^3*(c+d*x^2))
+--R
+--R
+--R (1)
+--R 5
+--R x
+--R ------------------------------------------------------------------------
+--R 3 8 2 3 6 2 2 4 3 2 2 3
+--R b d x + (3a b d + b c)x + (3a b d + 3a b c)x + (a d + 3a b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 628
+
+--S 629 of 1475
+r0:=-1/4*a^2/(b^2*(b*c-a*d)*(a+b*x^2)^2)+1/2*a*(2*b*c-a*d)/(b^2*_
+ (b*c-a*d)^2*(a+b*x^2))+1/2*c^2*log(a+b*x^2)/(b*c-a*d)^3-_
+ 1/2*c^2*log(c+d*x^2)/(b*c-a*d)^3
+--R
+--R
+--R (2)
+--R 4 2 4 3 2 2 2 2 2 2
+--R (2b c x + 4a b c x + 2a b c )log(d x + c)
+--R +
+--R 4 2 4 3 2 2 2 2 2 2
+--R (- 2b c x - 4a b c x - 2a b c )log(b x + a)
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (- 2a b d + 6a b c d - 4a b c )x - a d + 4a b c d - 3a b c
+--R /
+--R 3 4 3 2 5 2 6 2 7 3 4
+--R (4a b d - 12a b c d + 12a b c d - 4b c )x
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 2 5 2 3 4 3 2
+--R (8a b d - 24a b c d + 24a b c d - 8a b c )x + 4a b d - 12a b c d
+--R +
+--R 3 4 2 2 5 3
+--R 12a b c d - 4a b c
+--R Type: Expression(Integer)
+--E 629
+
+--S 630 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 4 3 2 2 2 2 2 2
+--R (2b c x + 4a b c x + 2a b c )log(d x + c)
+--R +
+--R 4 2 4 3 2 2 2 2 2 2
+--R (- 2b c x - 4a b c x - 2a b c )log(b x + a)
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (- 2a b d + 6a b c d - 4a b c )x - a d + 4a b c d - 3a b c
+--R /
+--R 3 4 3 2 5 2 6 2 7 3 4
+--R (4a b d - 12a b c d + 12a b c d - 4b c )x
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 2 5 2 3 4 3 2
+--R (8a b d - 24a b c d + 24a b c d - 8a b c )x + 4a b d - 12a b c d
+--R +
+--R 3 4 2 2 5 3
+--R 12a b c d - 4a b c
+--R Type: Union(Expression(Integer),...)
+--E 630
+
+--S 631 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 631
+
+--S 632 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 632
+
+)clear all
+
+--S 633 of 1475
+t0:=x^4/((a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 4
+--R x
+--R -----------------------------------------------------------------------------
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 633
+
+--S 634 of 1475
+r0:=-1/4*c*x/(d*(b*c-a*d)*(c+d*x^2)^2)+1/8*(b*c-5*a*d)*x/(d*(b*c-a*d)^2*_
+ (c+d*x^2))+a^(3/2)*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/(b*c-a*d)^3+_
+ 1/8*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*atan(x*sqrt(d)/sqrt(c))/_
+ (d^(3/2)*(b*c-a*d)^3*sqrt(c))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 6a b c d - b c d )x + (6a c d + 12a b c d - 2b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 6a b c d - b c
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 3 4 2 2 2 +-+ +-+ +-+ +-+ x\|b
+--R (- 8a d x - 16a c d x - 8a c d)\|a \|b \|c \|d atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+ +-+
+--R ((- 5a d + 6a b c d - b c d)x + (- 3a c d + 2a b c d + b c )x)\|c \|d
+--R /
+--R 3 6 2 5 2 2 4 3 3 3 4
+--R (8a d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 2 3 2 4
+--R (16a c d - 48a b c d + 48a b c d - 16b c d )x + 8a c d
+--R +
+--R 2 3 3 2 4 2 3 5
+--R - 24a b c d + 24a b c d - 8b c d
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R Type: Expression(Integer)
+--E 634
+
+--S 635 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 6a b c d - b c d )x + (6a c d + 12a b c d - 2b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 6a b c d - b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 3 4 2 2 2 +-----+ +-----+
+--R (8a d x + 16a c d x + 8a c d)\|- c d \|- a b
+--R *
+--R +-----+ 2
+--R - 2x\|- a b + b x - a
+--R log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 2 2 2 3
+--R (- 10a d + 12a b c d - 2b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 6a c d + 4a b c d + 2b c )x
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 3 6 2 5 2 2 4 3 3 3 4
+--R (16a d - 48a b c d + 48a b c d - 16b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 2 3 2 4
+--R (32a c d - 96a b c d + 96a b c d - 32b c d )x + 16a c d
+--R +
+--R 2 3 3 2 4 2 3 5
+--R - 48a b c d + 48a b c d - 16b c d
+--R *
+--R +-----+
+--R \|- c d
+--R ,
+--R
+--R 3 4 2 2 2 +-----+ +---+
+--R (4a d x + 8a c d x + 4a c d)\|- a b \|c d
+--R *
+--R +-----+ 2
+--R - 2x\|- a b + b x - a
+--R log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 6a b c d - b c d )x + (6a c d + 12a b c d - 2b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 6a b c d - b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +---+
+--R ((- 5a d + 6a b c d - b c d)x + (- 3a c d + 2a b c d + b c )x)\|c d
+--R /
+--R 3 6 2 5 2 2 4 3 3 3 4
+--R (8a d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 2 3 2 4
+--R (16a c d - 48a b c d + 48a b c d - 16b c d )x + 8a c d
+--R +
+--R 2 3 3 2 4 2 3 5
+--R - 24a b c d + 24a b c d - 8b c d
+--R *
+--R +---+
+--R \|c d
+--R ,
+--R
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 6a b c d - b c d )x + (6a c d + 12a b c d - 2b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 6a b c d - b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +---+
+--R 3 4 2 2 2 +-----+ +---+ \|a b
+--R (16a d x + 32a c d x + 16a c d)\|- c d \|a b atan(------)
+--R b x
+--R +
+--R 2 3 2 2 2 3
+--R (- 10a d + 12a b c d - 2b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 6a c d + 4a b c d + 2b c )x
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 3 6 2 5 2 2 4 3 3 3 4
+--R (16a d - 48a b c d + 48a b c d - 16b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 2 3 2 4
+--R (32a c d - 96a b c d + 96a b c d - 32b c d )x + 16a c d
+--R +
+--R 2 3 3 2 4 2 3 5
+--R - 48a b c d + 48a b c d - 16b c d
+--R *
+--R +-----+
+--R \|- c d
+--R ,
+--R
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 6a b c d - b c d )x + (6a c d + 12a b c d - 2b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 6a b c d - b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R +---+
+--R 3 4 2 2 2 +---+ +---+ \|a b
+--R (8a d x + 16a c d x + 8a c d)\|a b \|c d atan(------)
+--R b x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +---+
+--R ((- 5a d + 6a b c d - b c d)x + (- 3a c d + 2a b c d + b c )x)\|c d
+--R /
+--R 3 6 2 5 2 2 4 3 3 3 4
+--R (8a d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 2 3 2 4
+--R (16a c d - 48a b c d + 48a b c d - 16b c d )x + 8a c d
+--R +
+--R 2 3 3 2 4 2 3 5
+--R - 24a b c d + 24a b c d - 8b c d
+--R *
+--R +---+
+--R \|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 635
+
+--S 636 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (3a d + 6a b c d - b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-----+ 2
+--R +-----+ +-----+ +-+ +-+ - 2x\|- a b + b x - a
+--R 8a d\|- c d \|- a b \|c \|d log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 6a d - 12a b c d + 2b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R +-----+ +-+ +-+ +-+ +-+ x\|b
+--R 16a d\|- c d \|a \|b \|c \|d atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 4 2 3 2 2 2 3 3 +-----+ +-+ +-+
+--R (16a d - 48a b c d + 48a b c d - 16b c d)\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 636
+
+--S 637 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 637
+
+--S 638 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----+ 2
+--R +-----+ +-+ +-+ +---+ - 2x\|- a b + b x - a
+--R 4a d\|- a b \|c \|d \|c d log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (3a d + 6a b c d - b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 3a d - 6a b c d + b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R +-+ +-+ +-+ +-+ +---+ x\|b
+--R 8a d\|a \|b \|c \|d \|c d atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 4 2 3 2 2 2 3 3 +-+ +-+ +---+
+--R (8a d - 24a b c d + 24a b c d - 8b c d)\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 638
+
+--S 639 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 639
+
+)clear all
+
+--S 640 of 1475
+t0:=x^3/((a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 3
+--R x
+--R -----------------------------------------------------------------------------
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 640
+
+--S 641 of 1475
+r0:=-1/4*c/(d*(b*c-a*d)*(c+d*x^2)^2)-1/2*a/((b*c-a*d)^2*(c+d*x^2))-_
+ 1/2*a*b*log(a+b*x^2)/(b*c-a*d)^3+1/2*a*b*log(c+d*x^2)/(b*c-a*d)^3
+--R
+--R
+--R (2)
+--R 3 4 2 2 2 2
+--R (- 2a b d x - 4a b c d x - 2a b c d)log(d x + c)
+--R +
+--R 3 4 2 2 2 2
+--R (2a b d x + 4a b c d x + 2a b c d)log(b x + a)
+--R +
+--R 2 3 2 2 2 2 2 3
+--R (- 2a d + 2a b c d )x - a c d + b c
+--R /
+--R 3 6 2 5 2 2 4 3 3 3 4
+--R (4a d - 12a b c d + 12a b c d - 4b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 2 3 2 4 2 3 3
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x + 4a c d - 12a b c d
+--R +
+--R 2 4 2 3 5
+--R 12a b c d - 4b c d
+--R Type: Expression(Integer)
+--E 641
+
+--S 642 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 4 2 2 2 2
+--R (- 2a b d x - 4a b c d x - 2a b c d)log(d x + c)
+--R +
+--R 3 4 2 2 2 2
+--R (2a b d x + 4a b c d x + 2a b c d)log(b x + a)
+--R +
+--R 2 3 2 2 2 2 2 3
+--R (- 2a d + 2a b c d )x - a c d + b c
+--R /
+--R 3 6 2 5 2 2 4 3 3 3 4
+--R (4a d - 12a b c d + 12a b c d - 4b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 2 3 2 4 2 3 3
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x + 4a c d - 12a b c d
+--R +
+--R 2 4 2 3 5
+--R 12a b c d - 4b c d
+--R Type: Union(Expression(Integer),...)
+--E 642
+
+--S 643 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 643
+
+--S 644 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 644
+
+)clear all
+
+--S 645 of 1475
+t0:=x^2/((a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 2
+--R x
+--R -----------------------------------------------------------------------------
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 645
+
+--S 646 of 1475
+r0:=1/4*x/((b*c-a*d)*(c+d*x^2)^2)+1/8*(3*b*c+a*d)*x/(c*(b*c-a*d)^2*_
+ (c+d*x^2))-b^(3/2)*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/(b*c-a*d)^3+_
+ 1/8*(3*b^2*c^2+6*a*b*c*d-a^2*d^2)*atan(x*sqrt(d)/sqrt(c))/_
+ (c^(3/2)*(b*c-a*d)^3*sqrt(d))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (a d - 6a b c d - 3b c d )x + (2a c d - 12a b c d - 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R a c d - 6a b c d - 3b c
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 4 2 2 3 +-+ +-+ +-+ +-+ x\|b
+--R (8b c d x + 16b c d x + 8b c )\|a \|b \|c \|d atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+ +-+
+--R ((a d + 2a b c d - 3b c d)x + (- a c d + 6a b c d - 5b c )x)\|c \|d
+--R /
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2 3 3 3 2 4 2
+--R (16a c d - 48a b c d + 48a b c d - 16b c d)x + 8a c d - 24a b c d
+--R +
+--R 2 5 3 6
+--R 24a b c d - 8b c
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R Type: Expression(Integer)
+--E 646
+
+--S 647 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 2 2 3 +-----+ +-----+
+--R (8b c d x + 16b c d x + 8b c )\|- c d \|- a b
+--R *
+--R +-----+ 2
+--R 2x\|- a b + b x - a
+--R log(---------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (a d - 6a b c d - 3b c d )x + (2a c d - 12a b c d - 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R a c d - 6a b c d - 3b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((2a d + 4a b c d - 6b c d)x + (- 2a c d + 12a b c d - 10b c )x)
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (16a c d - 48a b c d + 48a b c d - 16b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2 3 3 3
+--R (32a c d - 96a b c d + 96a b c d - 32b c d)x + 16a c d
+--R +
+--R 2 4 2 2 5 3 6
+--R - 48a b c d + 48a b c d - 16b c
+--R *
+--R +-----+
+--R \|- c d
+--R ,
+--R
+--R +-----+ 2
+--R 2 4 2 2 3 +-----+ +---+ 2x\|- a b + b x - a
+--R (4b c d x + 8b c d x + 4b c )\|- a b \|c d log(---------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (a d - 6a b c d - 3b c d )x + (2a c d - 12a b c d - 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R a c d - 6a b c d - 3b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +---+
+--R ((a d + 2a b c d - 3b c d)x + (- a c d + 6a b c d - 5b c )x)\|c d
+--R /
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2 3 3 3
+--R (16a c d - 48a b c d + 48a b c d - 16b c d)x + 8a c d
+--R +
+--R 2 4 2 2 5 3 6
+--R - 24a b c d + 24a b c d - 8b c
+--R *
+--R +---+
+--R \|c d
+--R ,
+--R
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (a d - 6a b c d - 3b c d )x + (2a c d - 12a b c d - 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R a c d - 6a b c d - 3b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +---+
+--R 2 4 2 2 3 +-----+ +---+ \|a b
+--R (- 16b c d x - 32b c d x - 16b c )\|- c d \|a b atan(------)
+--R b x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((2a d + 4a b c d - 6b c d)x + (- 2a c d + 12a b c d - 10b c )x)
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (16a c d - 48a b c d + 48a b c d - 16b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2 3 3 3
+--R (32a c d - 96a b c d + 96a b c d - 32b c d)x + 16a c d
+--R +
+--R 2 4 2 2 5 3 6
+--R - 48a b c d + 48a b c d - 16b c
+--R *
+--R +-----+
+--R \|- c d
+--R ,
+--R
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (a d - 6a b c d - 3b c d )x + (2a c d - 12a b c d - 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R a c d - 6a b c d - 3b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R +---+
+--R 2 4 2 2 3 +---+ +---+ \|a b
+--R (- 8b c d x - 16b c d x - 8b c )\|a b \|c d atan(------)
+--R b x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +---+
+--R ((a d + 2a b c d - 3b c d)x + (- a c d + 6a b c d - 5b c )x)\|c d
+--R /
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2 3 3 3
+--R (16a c d - 48a b c d + 48a b c d - 16b c d)x + 8a c d
+--R +
+--R 2 4 2 2 5 3 6
+--R - 24a b c d + 24a b c d - 8b c
+--R *
+--R +---+
+--R \|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 647
+
+--S 648 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----+ 2
+--R +-----+ +-----+ +-+ +-+ 2x\|- a b + b x - a
+--R 8b c\|- c d \|- a b \|c \|d log(---------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d - 6a b c d - 3b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 2a d + 12a b c d + 6b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R +-----+ +-+ +-+ +-+ +-+ x\|b
+--R - 16b c\|- c d \|a \|b \|c \|d atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 3 2 2 2 2 3 3 4 +-----+ +-+ +-+
+--R (16a c d - 48a b c d + 48a b c d - 16b c )\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 648
+
+--S 649 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 649
+
+--S 650 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----+ 2
+--R +-----+ +-+ +-+ +---+ 2x\|- a b + b x - a
+--R 4b c\|- a b \|c \|d \|c d log(---------------------)
+--R 2
+--R b x + a
+--R +
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (a d - 6a b c d - 3b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- a d + 6a b c d + 3b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R +-+ +-+ +-+ +-+ +---+ x\|b
+--R - 8b c\|a \|b \|c \|d \|c d atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 3 2 2 2 2 3 3 4 +-+ +-+ +---+
+--R (8a c d - 24a b c d + 24a b c d - 8b c )\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 650
+
+--S 651 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 651
+
+)clear all
+
+--S 652 of 1475
+t0:=x/((a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R x
+--R -----------------------------------------------------------------------------
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 652
+
+--S 653 of 1475
+r0:=1/4/((b*c-a*d)*(c+d*x^2)^2)+1/2*b/((b*c-a*d)^2*(c+d*x^2))+_
+ 1/2*b^2*log(a+b*x^2)/(b*c-a*d)^3-1/2*b^2*log(c+d*x^2)/(b*c-a*d)^3
+--R
+--R
+--R (2)
+--R 2 2 4 2 2 2 2 2
+--R (2b d x + 4b c d x + 2b c )log(d x + c)
+--R +
+--R 2 2 4 2 2 2 2 2 2 2 2
+--R (- 2b d x - 4b c d x - 2b c )log(b x + a) + (2a b d - 2b c d)x
+--R +
+--R 2 2 2 2
+--R - a d + 4a b c d - 3b c
+--R /
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (4a d - 12a b c d + 12a b c d - 4b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3 2 3 2
+--R (8a c d - 24a b c d + 24a b c d - 8b c d)x + 4a c d - 12a b c d
+--R +
+--R 2 4 3 5
+--R 12a b c d - 4b c
+--R Type: Expression(Integer)
+--E 653
+
+--S 654 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 4 2 2 2 2 2
+--R (2b d x + 4b c d x + 2b c )log(d x + c)
+--R +
+--R 2 2 4 2 2 2 2 2 2 2 2
+--R (- 2b d x - 4b c d x - 2b c )log(b x + a) + (2a b d - 2b c d)x
+--R +
+--R 2 2 2 2
+--R - a d + 4a b c d - 3b c
+--R /
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (4a d - 12a b c d + 12a b c d - 4b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3 2 3 2
+--R (8a c d - 24a b c d + 24a b c d - 8b c d)x + 4a c d - 12a b c d
+--R +
+--R 2 4 3 5
+--R 12a b c d - 4b c
+--R Type: Union(Expression(Integer),...)
+--E 654
+
+--S 655 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 655
+
+--S 656 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 656
+
+)clear all
+
+--S 657 of 1475
+t0:=1/((a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R -----------------------------------------------------------------------------
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 657
+
+--S 658 of 1475
+r0:=-1/4*d*x/(c*(b*c-a*d)*(c+d*x^2)^2)-1/8*d*(7*b*c-3*a*d)*x/_
+ (c^2*(b*c-a*d)^2*(c+d*x^2))+b^(5/2)*atan(x*sqrt(b)/sqrt(a))/_
+ ((b*c-a*d)^3*sqrt(a))-1/8*(15*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*_
+ atan(x*sqrt(d)/sqrt(c))*sqrt(d)/(c^(5/2)*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (3a d - 10a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (6a c d - 20a b c d + 30b c d)x + 3a c d - 10a b c d + 15b c
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 4 2 3 2 2 4 +-+ +-+ x\|b
+--R (- 8b c d x - 16b c d x - 8b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R ((3a d - 10a b c d + 7b c d )x + (5a c d - 14a b c d + 9b c d)x)
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3 2 5 2
+--R (16a c d - 48a b c d + 48a b c d - 16b c d)x + 8a c d - 24a b c d
+--R +
+--R 2 6 3 7
+--R 24a b c d - 8b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 658
+
+--S 659 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 4
+--R (3a d - 10a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (6a c d - 20a b c d + 30b c d)x + 3a c d - 10a b c d + 15b c
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 4 2 3 2 2 4 | b \| a
+--R (8b c d x + 16b c d x + 8b c ) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R (6a d - 20a b c d + 14b c d )x + (10a c d - 28a b c d + 18b c d)x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (16a c d - 48a b c d + 48a b c d - 16b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3
+--R (32a c d - 96a b c d + 96a b c d - 32b c d)x + 16a c d
+--R +
+--R 2 5 2 2 6 3 7
+--R - 48a b c d + 48a b c d - 16b c
+--R ,
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 4 2 3 2 2 4 | b \| a
+--R (4b c d x + 8b c d x + 4b c ) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 3a d + 10a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 6a c d + 20a b c d - 30b c d)x - 3a c d + 10a b c d - 15b c
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R (3a d - 10a b c d + 7b c d )x + (5a c d - 14a b c d + 9b c d)x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3 2 5 2
+--R (16a c d - 48a b c d + 48a b c d - 16b c d)x + 8a c d - 24a b c d
+--R +
+--R 2 6 3 7
+--R 24a b c d - 8b c
+--R ,
+--R
+--R 2 4 3 2 2 2 4
+--R (3a d - 10a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (6a c d - 20a b c d + 30b c d)x + 3a c d - 10a b c d + 15b c
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 2 4 2 3 2 2 4 |b \|a
+--R (16b c d x + 32b c d x + 16b c ) |- atan(-----)
+--R \|a b x
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R (6a d - 20a b c d + 14b c d )x + (10a c d - 28a b c d + 18b c d)x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (16a c d - 48a b c d + 48a b c d - 16b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3
+--R (32a c d - 96a b c d + 96a b c d - 32b c d)x + 16a c d
+--R +
+--R 2 5 2 2 6 3 7
+--R - 48a b c d + 48a b c d - 16b c
+--R ,
+--R
+--R 2 4 3 2 2 2 4
+--R (- 3a d + 10a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 6a c d + 20a b c d - 30b c d)x - 3a c d + 10a b c d - 15b c
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 2 4 2 3 2 2 4 |b \|a
+--R (8b c d x + 16b c d x + 8b c ) |- atan(-----)
+--R \|a b x
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R (3a d - 10a b c d + 7b c d )x + (5a c d - 14a b c d + 9b c d)x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3 2 5 2
+--R (16a c d - 48a b c d + 48a b c d - 16b c d)x + 8a c d - 24a b c d
+--R +
+--R 2 6 3 7
+--R 24a b c d - 8b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 659
+
+--S 660 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 2 | d +-+ +-+ \| c
+--R (3a d - 10a b c d + 15b c ) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R 8b c |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|d
+--R (- 6a d + 20a b c d - 30b c )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R 16b c \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 2 3 2 3 2 2 4 3 5 +-+ +-+
+--R (16a c d - 48a b c d + 48a b c d - 16b c )\|a \|c
+--R Type: Expression(Integer)
+--E 660
+
+--S 661 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 661
+
+--S 662 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R 4b c |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|d
+--R (- 3a d + 10a b c d - 15b c )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 2 +-+ +-+ |d \|c
+--R (- 3a d + 10a b c d - 15b c )\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R 8b c \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 2 3 2 3 2 2 4 3 5 +-+ +-+
+--R (8a c d - 24a b c d + 24a b c d - 8b c )\|a \|c
+--R Type: Expression(Integer)
+--E 662
+
+--S 663 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 663
+
+)clear all
+
+--S 664 of 1475
+t0:=1/(x*(a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 9 3 2 7 2 2 5 2 3 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3
+--R a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 664
+
+--S 665 of 1475
+r0:=-1/4*d/(c*(b*c-a*d)*(c+d*x^2)^2)-1/2*d*(2*b*c-a*d)/(c^2*_
+ (b*c-a*d)^2*(c+d*x^2))+log(x)/(a*c^3)-1/2*b^3*log(a+b*x^2)/_
+ (a*(b*c-a*d)^3)+1/2*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*_
+ log(c+d*x^2)/(c^3*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 3 5 2 4 2 2 3 4
+--R (- 2a d + 6a b c d - 6a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 2 3 2 3 2 3 2
+--R (- 4a c d + 12a b c d - 12a b c d )x - 2a c d + 6a b c d
+--R +
+--R 2 4
+--R - 6a b c d
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 3 3 2 4 3 4 2 3 5 2
+--R (2b c d x + 4b c d x + 2b c )log(b x + a)
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (4a d - 12a b c d + 12a b c d - 4b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3 2 3 2
+--R (8a c d - 24a b c d + 24a b c d - 8b c d)x + 4a c d - 12a b c d
+--R +
+--R 2 4 3 5
+--R 12a b c d - 4b c
+--R *
+--R log(x)
+--R +
+--R 3 4 2 2 3 2 3 2 2 3 2 3 2 3 2 2 4
+--R (2a c d - 6a b c d + 4a b c d )x + 3a c d - 8a b c d + 5a b c d
+--R /
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2 4
+--R (4a c d - 12a b c d + 12a b c d - 4a b c d )x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7 2 4 5 3 3 6 2
+--R (8a c d - 24a b c d + 24a b c d - 8a b c d)x + 4a c d - 12a b c d
+--R +
+--R 2 2 7 3 8
+--R 12a b c d - 4a b c
+--R Type: Expression(Integer)
+--E 665
+
+--S 666 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 5 2 4 2 2 3 4
+--R (- 2a d + 6a b c d - 6a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 2 3 2 3 2 3 2
+--R (- 4a c d + 12a b c d - 12a b c d )x - 2a c d + 6a b c d
+--R +
+--R 2 4
+--R - 6a b c d
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 3 3 2 4 3 4 2 3 5 2
+--R (2b c d x + 4b c d x + 2b c )log(b x + a)
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (4a d - 12a b c d + 12a b c d - 4b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3 2 3 2
+--R (8a c d - 24a b c d + 24a b c d - 8b c d)x + 4a c d - 12a b c d
+--R +
+--R 2 4 3 5
+--R 12a b c d - 4b c
+--R *
+--R log(x)
+--R +
+--R 3 4 2 2 3 2 3 2 2 3 2 3 2 3 2 2 4
+--R (2a c d - 6a b c d + 4a b c d )x + 3a c d - 8a b c d + 5a b c d
+--R /
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2 4
+--R (4a c d - 12a b c d + 12a b c d - 4a b c d )x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7 2 4 5 3 3 6 2
+--R (8a c d - 24a b c d + 24a b c d - 8a b c d)x + 4a c d - 12a b c d
+--R +
+--R 2 2 7 3 8
+--R 12a b c d - 4a b c
+--R Type: Union(Expression(Integer),...)
+--E 666
+
+--S 667 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 667
+
+--S 668 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 668
+
+)clear all
+
+--S 669 of 1475
+t0:=1/(x^2*(a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 10 3 2 8 2 2 6 2 3 4
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3 2
+--R a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 669
+
+--S 670 of 1475
+r0:=1/8*(-8*b^2*c^2+27*a*b*c*d-15*a^2*d^2)/(a*c^3*(b*c-a*d)^2*x)-_
+ 1/4*d/(c*(b*c-a*d)*x*(c+d*x^2)^2)-1/8*d*(9*b*c-5*a*d)/_
+ (c^2*(b*c-a*d)^2*x*(c+d*x^2))-b^(7/2)*atan(x*sqrt(b)/sqrt(a))/_
+ (a^(3/2)*(b*c-a*d)^3)+1/8*d^(3/2)*(35*b^2*c^2-42*a*b*c*d+_
+ 15*a^2*d^2)*atan(x*sqrt(d)/sqrt(c))/(c^(7/2)*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 3 5 2 4 2 2 3 5
+--R (- 15a d + 42a b c d - 35a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3
+--R (- 30a c d + 84a b c d - 70a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4
+--R (- 15a c d + 42a b c d - 35a b c d)x
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 3 3 2 5 3 4 3 3 5 +-+ +-+ x\|b
+--R (8b c d x + 16b c d x + 8b c x)\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 15a d + 42a b c d - 35a b c d + 8b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 25a c d + 70a b c d - 61a b c d + 16b c d)x - 8a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 24a b c d - 24a b c d + 8b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2 5
+--R (8a c d - 24a b c d + 24a b c d - 8a b c d )x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7 3
+--R (16a c d - 48a b c d + 48a b c d - 16a b c d)x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8
+--R (8a c d - 24a b c d + 24a b c d - 8a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 670
+
+--S 671 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 2 5 3 4 3 3 5 | b \| a
+--R (8b c d x + 16b c d x + 8b c x) |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 5 2 4 2 2 3 5
+--R (15a d - 42a b c d + 35a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3
+--R (30a c d - 84a b c d + 70a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4
+--R (15a c d - 42a b c d + 35a b c d)x
+--R *
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 30a d + 84a b c d - 70a b c d + 16b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 50a c d + 140a b c d - 122a b c d + 32b c d)x - 16a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 48a b c d - 48a b c d + 16b c
+--R /
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2 5
+--R (16a c d - 48a b c d + 48a b c d - 16a b c d )x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7 3
+--R (32a c d - 96a b c d + 96a b c d - 32a b c d)x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8
+--R (16a c d - 48a b c d + 48a b c d - 16a b c )x
+--R ,
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 2 5 3 4 3 3 5 | b \| a
+--R (4b c d x + 8b c d x + 4b c x) |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 5 2 4 2 2 3 5
+--R (15a d - 42a b c d + 35a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3
+--R (30a c d - 84a b c d + 70a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4
+--R (15a c d - 42a b c d + 35a b c d)x
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 15a d + 42a b c d - 35a b c d + 8b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 25a c d + 70a b c d - 61a b c d + 16b c d)x - 8a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 24a b c d - 24a b c d + 8b c
+--R /
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2 5
+--R (8a c d - 24a b c d + 24a b c d - 8a b c d )x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7 3
+--R (16a c d - 48a b c d + 48a b c d - 16a b c d)x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8
+--R (8a c d - 24a b c d + 24a b c d - 8a b c )x
+--R ,
+--R
+--R 3 5 2 4 2 2 3 5
+--R (15a d - 42a b c d + 35a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3
+--R (30a c d - 84a b c d + 70a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4
+--R (15a c d - 42a b c d + 35a b c d)x
+--R *
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 3 2 5 3 4 3 3 5 |b \|a
+--R (- 16b c d x - 32b c d x - 16b c x) |- atan(-----)
+--R \|a b x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 30a d + 84a b c d - 70a b c d + 16b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 50a c d + 140a b c d - 122a b c d + 32b c d)x - 16a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 48a b c d - 48a b c d + 16b c
+--R /
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2 5
+--R (16a c d - 48a b c d + 48a b c d - 16a b c d )x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7 3
+--R (32a c d - 96a b c d + 96a b c d - 32a b c d)x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8
+--R (16a c d - 48a b c d + 48a b c d - 16a b c )x
+--R ,
+--R
+--R 3 5 2 4 2 2 3 5
+--R (15a d - 42a b c d + 35a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3
+--R (30a c d - 84a b c d + 70a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4
+--R (15a c d - 42a b c d + 35a b c d)x
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 3 2 5 3 4 3 3 5 |b \|a
+--R (- 8b c d x - 16b c d x - 8b c x) |- atan(-----)
+--R \|a b x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 15a d + 42a b c d - 35a b c d + 8b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 25a c d + 70a b c d - 61a b c d + 16b c d)x - 8a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 24a b c d - 24a b c d + 8b c
+--R /
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2 5
+--R (8a c d - 24a b c d + 24a b c d - 8a b c d )x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7 3
+--R (16a c d - 48a b c d + 48a b c d - 16a b c d)x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8
+--R (8a c d - 24a b c d + 24a b c d - 8a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 671
+
+--S 672 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 | b +-+ +-+ \| a
+--R 8b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R 3 3 2 2 2 2 | d +-+ +-+
+--R (15a d - 42a b c d + 35a b c d) |- - \|a \|c
+--R \| c
+--R *
+--R +---+
+--R | d 2
+--R - 2c x |- - + d x - c
+--R \| c
+--R log(-----------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 +-+ +-+ x\|d
+--R (30a d - 84a b c d + 70a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 3 3 +-+ +-+ x\|b
+--R - 16b c \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 3 3 3 4 2 2 2 5 3 6 +-+ +-+
+--R (16a c d - 48a b c d + 48a b c d - 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 672
+
+--S 673 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 673
+
+--S 674 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 | b +-+ +-+ \| a
+--R 4b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 +-+ +-+ x\|d
+--R (15a d - 42a b c d + 35a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 3 3 2 2 2 2 +-+ +-+ |d \|c
+--R (15a d - 42a b c d + 35a b c d)\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 3 3 +-+ +-+ x\|b
+--R - 8b c \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 3 3 3 4 2 2 2 5 3 6 +-+ +-+
+--R (8a c d - 24a b c d + 24a b c d - 8a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 674
+
+--S 675 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 675
+
+)clear all
+
+--S 676 of 1475
+t0:=1/(x^3*(a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 11 3 2 9 2 2 7 2 3 5
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3 3
+--R a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 676
+
+--S 677 of 1475
+r0:=(-1/2)/(a*c^3*x^2)+1/4*d^2/(c^2*(b*c-a*d)*(c+d*x^2)^2)+1/2*d^2*_
+ (3*b*c-2*a*d)/(c^3*(b*c-a*d)^2*(c+d*x^2))-(b*c+3*a*d)*log(x)/_
+ (a^2*c^4)+1/2*b^4*log(a+b*x^2)/(a^2*(b*c-a*d)^3)-_
+ 1/2*d^2*(6*b^2*c^2-8*a*b*c*d+3*a^2*d^2)*log(c+d*x^2)/(c^4*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 4 6 3 5 2 2 2 4 6
+--R (6a d - 16a b c d + 12a b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 4
+--R (12a c d - 32a b c d + 24a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 2
+--R (6a c d - 16a b c d + 12a b c d )x
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 4 4 2 6 4 5 4 4 6 2 2
+--R (- 2b c d x - 4b c d x - 2b c x )log(b x + a)
+--R +
+--R 4 6 3 5 2 2 2 4 4 4 2 6
+--R (- 12a d + 32a b c d - 24a b c d + 4b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 4 5 4
+--R (- 24a c d + 64a b c d - 48a b c d + 8b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 4 6 2
+--R (- 12a c d + 32a b c d - 24a b c d + 4b c )x
+--R *
+--R log(x)
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4
+--R (- 6a c d + 16a b c d - 12a b c d + 2a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 2 4 3 3 3 4 2
+--R (- 9a c d + 24a b c d - 19a b c d + 4a b c d)x - 2a c d + 6a b c d
+--R +
+--R 2 2 5 3 6
+--R - 6a b c d + 2a b c
+--R /
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 6
+--R (4a c d - 12a b c d + 12a b c d - 4a b c d )x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8 4
+--R (8a c d - 24a b c d + 24a b c d - 8a b c d)x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9 2
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )x
+--R Type: Expression(Integer)
+--E 677
+
+--S 678 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 6 3 5 2 2 2 4 6
+--R (6a d - 16a b c d + 12a b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 4
+--R (12a c d - 32a b c d + 24a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 2
+--R (6a c d - 16a b c d + 12a b c d )x
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 4 4 2 6 4 5 4 4 6 2 2
+--R (- 2b c d x - 4b c d x - 2b c x )log(b x + a)
+--R +
+--R 4 6 3 5 2 2 2 4 4 4 2 6
+--R (- 12a d + 32a b c d - 24a b c d + 4b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 4 5 4
+--R (- 24a c d + 64a b c d - 48a b c d + 8b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 4 6 2
+--R (- 12a c d + 32a b c d - 24a b c d + 4b c )x
+--R *
+--R log(x)
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4
+--R (- 6a c d + 16a b c d - 12a b c d + 2a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 2 4 3 3 3 4 2
+--R (- 9a c d + 24a b c d - 19a b c d + 4a b c d)x - 2a c d + 6a b c d
+--R +
+--R 2 2 5 3 6
+--R - 6a b c d + 2a b c
+--R /
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 6
+--R (4a c d - 12a b c d + 12a b c d - 4a b c d )x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8 4
+--R (8a c d - 24a b c d + 24a b c d - 8a b c d)x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9 2
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )x
+--R Type: Union(Expression(Integer),...)
+--E 678
+
+--S 679 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 679
+
+--S 680 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 680
+
+)clear all
+
+--S 681 of 1475
+t0:=1/(x^4*(a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 12 3 2 10 2 2 8 2 3 6
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3 4
+--R a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 681
+
+--S 682 of 1475
+r0:=1/24*(-8*b^2*c^2+55*a*b*c*d-35*a^2*d^2)/(a*c^3*(b*c-a*d)^2*x^3)+_
+ 1/8*(8*b^3*c^3+8*a*b^2*c^2*d-55*a^2*b*c*d^2+35*a^3*d^3)/(a^2*_
+ c^4*(b*c-a*d)^2*x)-1/4*d/(c*(b*c-a*d)*x^3*(c+d*x^2)^2)-1/8*d*_
+ (11*b*c-7*a*d)/(c^2*(b*c-a*d)^2*x^3*(c+d*x^2))+b^(9/2)*atan(x*_
+ sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-a*d)^3)-1/8*d^(5/2)*(63*b^2*c^2-_
+ 90*a*b*c*d+35*a^2*d^2)*atan(x*sqrt(d)/sqrt(c))/(c^(9/2)*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 4 6 3 5 2 2 2 4 7
+--R (105a d - 270a b c d + 189a b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 5
+--R (210a c d - 540a b c d + 378a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3
+--R (105a c d - 270a b c d + 189a b c d )x
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 4 4 2 7 4 5 5 4 6 3 +-+ +-+ x\|b
+--R (- 24b c d x - 48b c d x - 24b c x )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 6 3 5 2 2 2 4 4 4 2 6
+--R (105a d - 270a b c d + 189a b c d - 24b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 4
+--R (175a c d - 450a b c d + 315a b c d + 8a b c d - 48b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 2
+--R (56a c d - 144a b c d + 96a b c d + 16a b c d - 24b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6
+--R - 8a c d + 24a b c d - 24a b c d + 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 7
+--R (24a c d - 72a b c d + 72a b c d - 24a b c d )x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8 5
+--R (48a c d - 144a b c d + 144a b c d - 48a b c d)x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9 3
+--R (24a c d - 72a b c d + 72a b c d - 24a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 682
+
+--S 683 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 6 3 5 2 2 2 4 7
+--R (105a d - 270a b c d + 189a b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 5
+--R (210a c d - 540a b c d + 378a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3
+--R (105a c d - 270a b c d + 189a b c d )x
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 4 4 2 7 4 5 5 4 6 3 | b \| a
+--R (24b c d x + 48b c d x + 24b c x ) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 4 6 3 5 2 2 2 4 4 4 2 6
+--R (210a d - 540a b c d + 378a b c d - 48b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 4
+--R (350a c d - 900a b c d + 630a b c d + 16a b c d - 96b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 2
+--R (112a c d - 288a b c d + 192a b c d + 32a b c d - 48b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6
+--R - 16a c d + 48a b c d - 48a b c d + 16a b c
+--R /
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 7
+--R (48a c d - 144a b c d + 144a b c d - 48a b c d )x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8 5
+--R (96a c d - 288a b c d + 288a b c d - 96a b c d)x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9 3
+--R (48a c d - 144a b c d + 144a b c d - 48a b c )x
+--R ,
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 4 4 2 7 4 5 5 4 6 3 | b \| a
+--R (12b c d x + 24b c d x + 12b c x ) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 4 6 3 5 2 2 2 4 7
+--R (- 105a d + 270a b c d - 189a b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 5
+--R (- 210a c d + 540a b c d - 378a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3
+--R (- 105a c d + 270a b c d - 189a b c d )x
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 4 6 3 5 2 2 2 4 4 4 2 6
+--R (105a d - 270a b c d + 189a b c d - 24b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 4
+--R (175a c d - 450a b c d + 315a b c d + 8a b c d - 48b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 2 4 3 3
+--R (56a c d - 144a b c d + 96a b c d + 16a b c d - 24b c )x - 8a c d
+--R +
+--R 3 4 2 2 2 5 3 6
+--R 24a b c d - 24a b c d + 8a b c
+--R /
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 7
+--R (24a c d - 72a b c d + 72a b c d - 24a b c d )x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8 5
+--R (48a c d - 144a b c d + 144a b c d - 48a b c d)x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9 3
+--R (24a c d - 72a b c d + 72a b c d - 24a b c )x
+--R ,
+--R
+--R 4 6 3 5 2 2 2 4 7
+--R (105a d - 270a b c d + 189a b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 5
+--R (210a c d - 540a b c d + 378a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3
+--R (105a c d - 270a b c d + 189a b c d )x
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 4 4 2 7 4 5 5 4 6 3 |b \|a
+--R (48b c d x + 96b c d x + 48b c x ) |- atan(-----)
+--R \|a b x
+--R +
+--R 4 6 3 5 2 2 2 4 4 4 2 6
+--R (210a d - 540a b c d + 378a b c d - 48b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 4
+--R (350a c d - 900a b c d + 630a b c d + 16a b c d - 96b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 2
+--R (112a c d - 288a b c d + 192a b c d + 32a b c d - 48b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6
+--R - 16a c d + 48a b c d - 48a b c d + 16a b c
+--R /
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 7
+--R (48a c d - 144a b c d + 144a b c d - 48a b c d )x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8 5
+--R (96a c d - 288a b c d + 288a b c d - 96a b c d)x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9 3
+--R (48a c d - 144a b c d + 144a b c d - 48a b c )x
+--R ,
+--R
+--R 4 6 3 5 2 2 2 4 7
+--R (- 105a d + 270a b c d - 189a b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 5
+--R (- 210a c d + 540a b c d - 378a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3
+--R (- 105a c d + 270a b c d - 189a b c d )x
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 4 4 2 7 4 5 5 4 6 3 |b \|a
+--R (24b c d x + 48b c d x + 24b c x ) |- atan(-----)
+--R \|a b x
+--R +
+--R 4 6 3 5 2 2 2 4 4 4 2 6
+--R (105a d - 270a b c d + 189a b c d - 24b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 4
+--R (175a c d - 450a b c d + 315a b c d + 8a b c d - 48b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 2 4 3 3
+--R (56a c d - 144a b c d + 96a b c d + 16a b c d - 24b c )x - 8a c d
+--R +
+--R 3 4 2 2 2 5 3 6
+--R 24a b c d - 24a b c d + 8a b c
+--R /
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 7
+--R (24a c d - 72a b c d + 72a b c d - 24a b c d )x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8 5
+--R (48a c d - 144a b c d + 144a b c d - 48a b c d)x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9 3
+--R (24a c d - 72a b c d + 72a b c d - 24a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 683
+
+--S 684 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R 4 4 3 3 2 2 2 2 | d +-+ +-+
+--R (35a d - 90a b c d + 63a b c d ) |- - \|a \|c
+--R \| c
+--R *
+--R +---+
+--R | d 2
+--R 2c x |- - + d x - c
+--R \| c
+--R log(---------------------)
+--R 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 4 4 | b +-+ +-+ \| a
+--R 8b c |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 4 4 3 3 2 2 2 2 +-+ +-+ x\|d
+--R (- 70a d + 180a b c d - 126a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 4 4 +-+ +-+ x\|b
+--R 16b c \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 4 3 4 5 2 3 2 6 2 3 7 +-+ +-+
+--R (16a c d - 48a b c d + 48a b c d - 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 684
+
+--S 685 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 685
+
+--S 686 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 4 4 | b +-+ +-+ \| a
+--R 4b c |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 4 4 3 3 2 2 2 2 +-+ +-+ x\|d
+--R (- 35a d + 90a b c d - 63a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 4 4 3 3 2 2 2 2 +-+ +-+ |d \|c
+--R (- 35a d + 90a b c d - 63a b c d )\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 4 4 +-+ +-+ x\|b
+--R 8b c \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 4 3 4 5 2 3 2 6 2 3 7 +-+ +-+
+--R (8a c d - 24a b c d + 24a b c d - 8a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 686
+
+--S 687 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 687
+
+)clear all
+
+--S 688 of 1475
+t0:=x/((1+x^2)*(4+x^2))
+--R
+--R
+--R x
+--R (1) ------------
+--R 4 2
+--R x + 5x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 688
+
+--S 689 of 1475
+r0:=1/6*log(1+x^2)-1/6*log(4+x^2)
+--R
+--R
+--R 2 2
+--R - log(x + 4) + log(x + 1)
+--R (2) ---------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 689
+
+--S 690 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R - log(x + 4) + log(x + 1)
+--R (3) ---------------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 690
+
+--S 691 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 691
+
+--S 692 of 1475
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 692
+
+)clear all
+
+--S 693 of 1475
+t0:=x^4*sqrt(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 4 | 2
+--R x \|d x + c
+--R (1) -------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 693
+
+--S 694 of 1475
+r0:=-1/8*(b^2*c^2+4*a*b*c*d-8*a^2*d^2)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/_
+ (b^3*d^(3/2))+a^(3/2)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*_
+ sqrt(c+d*x^2)))*sqrt(b*c-a*d)/b^3+1/8*(b*c-4*a*d)*x*_
+ sqrt(c+d*x^2)/(b^2*d)+1/4*x^3*sqrt(c+d*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 x\|d
+--R (8a d - 4a b c d - b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ +-+ +-+ x\|- a d + b c
+--R 8a d\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 3 2 +-+ | 2
+--R (2b d x + (- 4a b d + b c)x)\|d \|d x + c
+--R /
+--R 3 +-+
+--R 8b d\|d
+--R Type: Expression(Integer)
+--E 694
+
+--S 695 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+ +--------+
+--R 2 2 +-+ +-+ | 2 | 2
+--R (16a d x + 32a c d)\|c \|d \|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 3 4 2 2 2 +-+ | 2
+--R (- 4a d x - 32a c d x - 32a c d)\|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (2d x + 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (- 4d x - 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((32a d - 16a b c d - 4b c d)x + 64a c d - 32a b c d - 8b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 8a d + 4a b c d + b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 64a c d + 32a b c d + 8b c d)x - 64a c d + 32a b c d + 8b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R - 2b d x + (4a b d - 17b c d )x + (32a b c d - 24b c d)x
+--R +
+--R 2 2 3
+--R (32a b c d - 8b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 8b d x + (- 16a b d + 28b c d )x + (- 48a b c d + 28b c d)x
+--R +
+--R 2 2 3
+--R (- 32a b c d + 8b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 3 2 2 3 +-+ +-+ | 2
+--R (32b d x + 64b c d)\|c \|d \|d x + c
+--R +
+--R 3 3 4 3 2 2 3 2 +-+
+--R (- 8b d x - 64b c d x - 64b c d)\|d
+--R ,
+--R
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((32a d - 16a b c d - 4b c d)x + 64a c d - 32a b c d - 8b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 8a d + 4a b c d + b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 64a c d + 32a b c d + 8b c d)x - 64a c d + 32a b c d + 8b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-------------+ +--------+
+--R 2 2 | 2 +-+ +-+ | 2
+--R (- 32a d x - 64a c d)\|- a d + a b c \|c \|d \|d x + c
+--R +
+--R +-------------+
+--R 3 4 2 2 2 | 2 +-+
+--R (8a d x + 64a c d x + 64a c d)\|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+ +--------+
+--R 2 2 | 2 +-+ +-+ | 2
+--R (32a d x + 64a c d)\|- a d + a b c \|c \|d \|d x + c
+--R +
+--R +-------------+
+--R 3 4 2 2 2 | 2 +-+
+--R (- 8a d x - 64a c d x - 64a c d)\|- a d + a b c \|d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R - 2b d x + (4a b d - 17b c d )x + (32a b c d - 24b c d)x
+--R +
+--R 2 2 3
+--R (32a b c d - 8b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 8b d x + (- 16a b d + 28b c d )x + (- 48a b c d + 28b c d)x
+--R +
+--R 2 2 3
+--R (- 32a b c d + 8b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 3 2 2 3 +-+ +-+ | 2
+--R (32b d x + 64b c d)\|c \|d \|d x + c
+--R +
+--R 3 3 4 3 2 2 3 2 +-+
+--R (- 8b d x - 64b c d x - 64b c d)\|d
+--R ,
+--R
+--R +-----------+ +--------+
+--R 2 2 +---+ +-+ | 2 | 2
+--R (16a d x + 32a c d)\|- d \|c \|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 3 4 2 2 2 +---+ | 2
+--R (- 4a d x - 32a c d x - 32a c d)\|- d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (2d x + 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (- 4d x - 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (64a d - 32a b c d - 8b c d)x + 128a c d - 64a b c d
+--R +
+--R 2 3
+--R - 16b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 16a d + 8a b c d + 2b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 128a c d + 64a b c d + 16b c d)x - 128a c d + 64a b c d
+--R +
+--R 2 4
+--R 16b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R - 2b d x + (4a b d - 17b c d )x + (32a b c d - 24b c d)x
+--R +
+--R 2 2 3
+--R (32a b c d - 8b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 8b d x + (- 16a b d + 28b c d )x + (- 48a b c d + 28b c d)x
+--R +
+--R 2 2 3
+--R (- 32a b c d + 8b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 3 2 2 3 +---+ +-+ | 2
+--R (32b d x + 64b c d)\|- d \|c \|d x + c
+--R +
+--R 3 3 4 3 2 2 3 2 +---+
+--R (- 8b d x - 64b c d x - 64b c d)\|- d
+--R ,
+--R
+--R 2 3 2 2 2 2 2 2 2
+--R (64a d - 32a b c d - 8b c d)x + 128a c d - 64a b c d
+--R +
+--R 2 3
+--R - 16b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 16a d + 8a b c d + 2b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 128a c d + 64a b c d + 16b c d)x - 128a c d + 64a b c d
+--R +
+--R 2 4
+--R 16b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R +-------------+ +--------+
+--R 2 2 | 2 +---+ +-+ | 2
+--R (- 32a d x - 64a c d)\|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R +-------------+
+--R 3 4 2 2 2 | 2 +---+
+--R (8a d x + 64a c d x + 64a c d)\|- a d + a b c \|- d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+ +--------+
+--R 2 2 | 2 +---+ +-+ | 2
+--R (32a d x + 64a c d)\|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R +-------------+
+--R 3 4 2 2 2 | 2 +---+
+--R (- 8a d x - 64a c d x - 64a c d)\|- a d + a b c \|- d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R - 2b d x + (4a b d - 17b c d )x + (32a b c d - 24b c d)x
+--R +
+--R 2 2 3
+--R (32a b c d - 8b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 8b d x + (- 16a b d + 28b c d )x + (- 48a b c d + 28b c d)x
+--R +
+--R 2 2 3
+--R (- 32a b c d + 8b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 3 2 2 3 +---+ +-+ | 2
+--R (32b d x + 64b c d)\|- d \|c \|d x + c
+--R +
+--R 3 3 4 3 2 2 3 2 +---+
+--R (- 8b d x - 64b c d x - 64b c d)\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 695
+
+--S 696 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R +-+ | 2
+--R 4a d\|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2 2 +-+
+--R ((2d x + 4c x)\|a d - a b c + ((4a d - 2b c)x + 2a c)\|c )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (- 4d x - 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 2 2
+--R (8a d - 4a b c d - b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 x\|d
+--R (- 8a d + 4a b c d + b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ +-+ +-+ x\|- a d + b c
+--R - 8a d\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 8b d\|d
+--R Type: Expression(Integer)
+--E 696
+
+--S 697 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 697
+
+--S 698 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 2 2 2
+--R (8a d - 4a b c d - b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 x\|d
+--R (- 8a d + 4a b c d + b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R -
+--R +-------------+
+--R | 2 +-+
+--R 8a d\|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+ +-+
+--R | 2 +-+ a\|c
+--R 8a d\|- a d + a b c \|d atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R +-----------+
+--R +-----------+ +-+ +-+ x\|- a d + b c
+--R - 8a d\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 8b d\|d
+--R Type: Expression(Integer)
+--E 698
+
+--S 699 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 699
+
+)clear all
+
+--S 700 of 1475
+t0:=x^3*sqrt(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 3 | 2
+--R x \|d x + c
+--R (1) -------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 700
+
+--S 701 of 1475
+r0:=1/3*(c+d*x^2)^(3/2)/(b*d)+a*atanh(sqrt(b)*sqrt(c+d*x^2)/_
+ sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(5/2)-a*sqrt(c+d*x^2)/b^2
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R +-----------+ \|b \|d x + c
+--R 3a d\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R (b d x - 3a d + b c)\|b \|d x + c
+--R /
+--R 2 +-+
+--R 3b d\|b
+--R Type: Expression(Integer)
+--E 701
+
+--S 702 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+ +--------+
+--R 2 |- a d + b c +-+ | 2
+--R (3a d x + 12a c) |----------- \|c \|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 2 |- a d + b c
+--R (- 9a c d x - 12a c ) |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+
+--R ((2a b d + 4b c)x + 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (- 2b c d x + (- 6a b c d - 4b c )x - 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 4 2 2 | 2
+--R (- 6b c d x + (12a c d - 12b c )x )\|d x + c
+--R +
+--R 2 6 2 4 2 2 +-+
+--R (2b d x + (- 6a d + 12b c d)x + (- 12a c d + 12b c )x )\|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ | 2 2 2 2 2
+--R (6b d x + 24b c)\|c \|d x + c - 18b c d x - 24b c
+--R ,
+--R
+--R +---------+ +--------+
+--R 2 +-+ |a d - b c | 2
+--R (- 3a d x - 12a c)\|c |--------- \|d x + c
+--R \| b
+--R +
+--R +---------+
+--R 2 2 |a d - b c
+--R (9a c d x + 12a c ) |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R +--------+
+--R 4 2 2 | 2
+--R (- 3b c d x + (6a c d - 6b c )x )\|d x + c
+--R +
+--R 2 6 2 4 2 2 +-+
+--R (b d x + (- 3a d + 6b c d)x + (- 6a c d + 6b c )x )\|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ | 2 2 2 2 2
+--R (3b d x + 12b c)\|c \|d x + c - 9b c d x - 12b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 702
+
+--S 703 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +--------+
+--R 2 2 |- a d + b c +-+ +-+ | 2
+--R (3a d x + 12a c d) |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c +-+
+--R (- 9a c d x - 12a c d) |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 2 4
+--R ((2a b d + 4b c)x + 8a b c x ) |----------- \|c + 4b c x
+--R \| b
+--R +
+--R 2 2 2 2 2
+--R (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (- 2b c d x + (- 6a b c d - 4b c )x - 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 +-----------+ +-+ | 2
+--R (- 6a d x - 24a c d)\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+
+--R (18a c d x + 24a c d)\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((- 6a c d + 2b c d)x - 24a c d + 8b c )\|b \|d x + c
+--R +
+--R 2 2 2 2 3 +-+ +-+
+--R ((18a c d - 6b c d)x + 24a c d - 8b c )\|b \|c
+--R /
+--R +--------+
+--R 2 2 2 2 +-+ +-+ | 2 2 2 2 2 2 +-+
+--R (6b d x + 24b c d)\|b \|c \|d x + c + (- 18b c d x - 24b c d)\|b
+--R Type: Expression(Integer)
+--E 703
+
+--S 704 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 704
+
+--S 705 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 2 +-----------+ +-+ | 2
+--R (- 3a d x - 12a c d)\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+
+--R (9a c d x + 12a c d)\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +---------+ +--------+
+--R 2 2 +-+ +-+ |a d - b c | 2
+--R (- 3a d x - 12a c d)\|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R +---------+
+--R 2 2 2 +-+ |a d - b c
+--R (9a c d x + 12a c d)\|b |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((- 3a c d + b c d)x - 12a c d + 4b c )\|b \|d x + c
+--R +
+--R 2 2 2 2 3 +-+ +-+
+--R ((9a c d - 3b c d)x + 12a c d - 4b c )\|b \|c
+--R /
+--R +--------+
+--R 2 2 2 2 +-+ +-+ | 2 2 2 2 2 2 +-+
+--R (3b d x + 12b c d)\|b \|c \|d x + c + (- 9b c d x - 12b c d)\|b
+--R Type: Expression(Integer)
+--E 705
+
+--S 706 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 706
+
+)clear all
+
+--S 707 of 1475
+t0:=x^2*sqrt(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R x \|d x + c
+--R (1) -------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 707
+
+--S 708 of 1475
+r0:=1/2*(b*c-2*a*d)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/(b^2*sqrt(d))-_
+ atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*sqrt(a)*_
+ sqrt(b*c-a*d)/b^2+1/2*x*sqrt(c+d*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R x\|d
+--R (- 2a d + b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+ +--------+
+--R +-----------+ +-+ +-+ x\|- a d + b c +-+ | 2
+--R - 2\|- a d + b c \|a \|d atan(---------------) + b x\|d \|d x + c
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2b \|d
+--R Type: Expression(Integer)
+--E 708
+
+--S 709 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2 2
+--R ((4a d - 2b c)\|c \|d x + c + (- 2a d + b c d)x - 4a c d + 2b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-----------+ +--------+
+--R +-+ +-+ | 2 | 2
+--R 2\|c \|d \|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 2 +-+ | 2
+--R (- d x - 2c)\|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (- 2d x - 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (4d x + 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (- b d x - 2b c x)\|d \|d x + c + (2b d x + 2b c x)\|c \|d
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 2 2 +-+
+--R 4b \|c \|d \|d x + c + (- 2b d x - 4b c)\|d
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2 2
+--R ((4a d - 2b c)\|c \|d x + c + (- 2a d + b c d)x - 4a c d + 2b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-+ +-+ | 2
+--R 4\|- a d + a b c \|c \|d \|d x + c
+--R +
+--R +-------------+
+--R 2 | 2 +-+
+--R (- 2d x - 4c)\|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-+ +-+ | 2
+--R - 4\|- a d + a b c \|c \|d \|d x + c
+--R +
+--R +-------------+
+--R 2 | 2 +-+
+--R (2d x + 4c)\|- a d + a b c \|d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (- b d x - 2b c x)\|d \|d x + c + (2b d x + 2b c x)\|c \|d
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 2 2 +-+
+--R 4b \|c \|d \|d x + c + (- 2b d x - 4b c)\|d
+--R ,
+--R
+--R +-----------+ +--------+
+--R +---+ +-+ | 2 | 2
+--R 2\|- d \|c \|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 2 +---+ | 2
+--R (- d x - 2c)\|- d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (- 2d x - 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (4d x + 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ | 2 2 2
+--R (- 8a d + 4b c)\|c \|d x + c + (4a d - 2b c d)x + 8a c d
+--R +
+--R 2
+--R - 4b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R +--------+
+--R 3 +---+ | 2 3 +---+ +-+
+--R (- b d x - 2b c x)\|- d \|d x + c + (2b d x + 2b c x)\|- d \|c
+--R /
+--R +--------+
+--R 2 +---+ +-+ | 2 2 2 2 +---+
+--R 4b \|- d \|c \|d x + c + (- 2b d x - 4b c)\|- d
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2
+--R (- 8a d + 4b c)\|c \|d x + c + (4a d - 2b c d)x + 8a c d
+--R +
+--R 2
+--R - 4b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R +-------------+ +--------+
+--R | 2 +---+ +-+ | 2
+--R 4\|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 | 2 +---+
+--R (- 2d x - 4c)\|- a d + a b c \|- d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+ +--------+
+--R | 2 +---+ +-+ | 2
+--R - 4\|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 | 2 +---+
+--R (2d x + 4c)\|- a d + a b c \|- d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R +--------+
+--R 3 +---+ | 2 3 +---+ +-+
+--R (- b d x - 2b c x)\|- d \|d x + c + (2b d x + 2b c x)\|- d \|c
+--R /
+--R +--------+
+--R 2 +---+ +-+ | 2 2 2 2 +---+
+--R 4b \|- d \|c \|d x + c + (- 2b d x - 4b c)\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 709
+
+--S 710 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R (2a d - b c)log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-----------+
+--R +-+ | 2
+--R \|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (- 2d x - 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (4d x + 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-+
+--R x\|d
+--R (2a d - b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ +-+ +-+ x\|- a d + b c
+--R 2\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2b \|d
+--R Type: Expression(Integer)
+--E 710
+
+--S 711 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 711
+
+--S 712 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R (2a d - b c)log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R x\|d
+--R (2a d - b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 2\|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+ +-+
+--R | 2 +-+ a\|c
+--R - 2\|- a d + a b c \|d atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R +-----------+
+--R +-----------+ +-+ +-+ x\|- a d + b c
+--R 2\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2b \|d
+--R Type: Expression(Integer)
+--E 712
+
+--S 713 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 713
+
+)clear all
+
+--S 714 of 1475
+t0:=x*sqrt(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R x\|d x + c
+--R (1) ------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 714
+
+--S 715 of 1475
+r0:=-atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(3/2)+_
+ sqrt(c+d*x^2)/b
+--R
+--R
+--R +--------+
+--R +-+ | 2 +--------+
+--R +-----------+ \|b \|d x + c +-+ | 2
+--R - \|- a d + b c atanh(---------------) + \|b \|d x + c
+--R +-----------+
+--R \|- a d + b c
+--R (2) --------------------------------------------------------
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 715
+
+--S 716 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+ +--------+ +-----------+
+--R |- a d + b c +-+ | 2 |- a d + b c
+--R ( |----------- \|c \|d x + c - c |----------- )
+--R \| b \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+
+--R ((- 2a b d - 4b c)x - 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (2b c d x + (6a b c d + 4b c )x + 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 +-+
+--R 2d x \|c
+--R /
+--R +--------+
+--R +-+ | 2
+--R 2b\|c \|d x + c - 2b c
+--R ,
+--R
+--R +---------+ +--------+ +---------+
+--R +-+ |a d - b c | 2 |a d - b c
+--R (\|c |--------- \|d x + c - c |--------- )
+--R \| b \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R 2 +-+
+--R d x \|c
+--R /
+--R +--------+
+--R +-+ | 2
+--R b\|c \|d x + c - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 716
+
+--S 717 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +--------+ +-----------+
+--R |- a d + b c +-+ +-+ | 2 |- a d + b c +-+
+--R ( |----------- \|b \|c \|d x + c - c |----------- \|b )
+--R \| b \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+
+--R ((- 2a b d - 4b c)x - 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (2b c d x + (6a b c d + 4b c )x + 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +--------+ +-+ | 2
+--R +-----------+ +-+ | 2 +-----------+ \|b \|d x + c
+--R (2\|- a d + b c \|c \|d x + c - 2c\|- a d + b c )atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R 2c\|b \|d x + c - 2c\|b \|c
+--R /
+--R +--------+
+--R +-+ +-+ | 2 +-+
+--R 2b\|b \|c \|d x + c - 2b c\|b
+--R Type: Expression(Integer)
+--E 717
+
+--S 718 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 718
+
+--S 719 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +--------+ +-+ | 2
+--R +-----------+ +-+ | 2 +-----------+ \|b \|d x + c
+--R (\|- a d + b c \|c \|d x + c - c\|- a d + b c )atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +---------+ +--------+ +---------+
+--R +-+ +-+ |a d - b c | 2 +-+ |a d - b c
+--R (\|b \|c |--------- \|d x + c - c\|b |--------- )
+--R \| b \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R c\|b \|d x + c - c\|b \|c
+--R /
+--R +--------+
+--R +-+ +-+ | 2 +-+
+--R b\|b \|c \|d x + c - b c\|b
+--R Type: Expression(Integer)
+--E 719
+
+--S 720 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 720
+
+)clear all
+
+--S 721 of 1475
+t0:=sqrt(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 721
+
+--S 722 of 1475
+r0:=atanh(x*sqrt(d)/sqrt(c+d*x^2))*sqrt(d)/b+atan(x*sqrt(b*c-a*d)/_
+ (sqrt(a)*sqrt(c+d*x^2)))*sqrt(b*c-a*d)/(b*sqrt(a))
+--R
+--R
+--R +-+ +-----------+
+--R +-+ +-+ x\|d +-----------+ x\|- a d + b c
+--R \|a \|d atanh(-----------) + \|- a d + b c atan(---------------)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|d x + c \|a \|d x + c
+--R (2) ----------------------------------------------------------------
+--R +-+
+--R b\|a
+--R Type: Expression(Integer)
+--E 722
+
+--S 723 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R 2\|d log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R /
+--R 2b
+--R ,
+--R
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R \|d log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R -
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c \|c
+--R |----------- atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R /
+--R b
+--R ,
+--R
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R | 2 +-+
+--R +---+ \|d x + c - \|c
+--R 4\|- d atan(------------------)
+--R +---+
+--R x\|- d
+--R /
+--R 2b
+--R ,
+--R
+--R +--------+
+--R | 2 +-+
+--R +---+ \|d x + c - \|c
+--R 2\|- d atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R -
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c \|c
+--R |----------- atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R /
+--R b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 723
+
+--S 724 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-+ |a d - b c
+--R \|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R 2\|a \|d log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+ +-----------+
+--R +-+ +-+ x\|d +-----------+ x\|- a d + b c
+--R - 2\|a \|d atanh(-----------) - 2\|- a d + b c atan(---------------)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|d x + c \|a \|d x + c
+--R /
+--R +-+
+--R 2b\|a
+--R Type: Expression(Integer)
+--E 724
+
+--S 725 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 725
+
+--S 726 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R \|a \|d log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R +-+ +-+ x\|d
+--R - \|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R -
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c +-+ \|c
+--R |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R - \|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-+
+--R b\|a
+--R Type: Expression(Integer)
+--E 726
+
+--S 727 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 727
+
+)clear all
+
+--S 728 of 1475
+t0:=sqrt(c+d*x^2)/(x*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) -----------
+--R 3
+--R b x + a x
+--R Type: Expression(Integer)
+--E 728
+
+--S 729 of 1475
+r0:=-atanh(sqrt(c+d*x^2)/sqrt(c))*sqrt(c)/a+atanh(sqrt(b)*_
+ sqrt(c+d*x^2)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/(a*sqrt(b))
+--R
+--R
+--R +--------+ +--------+
+--R +-+ | 2 | 2
+--R +-----------+ \|b \|d x + c +-+ +-+ \|d x + c
+--R \|- a d + b c atanh(---------------) - \|b \|c atanh(-----------)
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R (2) -----------------------------------------------------------------
+--R +-+
+--R a\|b
+--R Type: Expression(Integer)
+--E 729
+
+--S 730 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R | 2 +-+
+--R +-+ \|d x + c - \|c
+--R 2\|c log(------------------)
+--R x
+--R +
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R /
+--R 2a
+--R ,
+--R
+--R +--------+
+--R | 2 +-+
+--R +-+ \|d x + c - \|c
+--R \|c log(------------------)
+--R x
+--R +
+--R +--------+
+--R +---------+ +-+ | 2 2
+--R |a d - b c a\|c \|d x + c - b c x - a c
+--R - |--------- atan(-------------------------------)
+--R \| b +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R /
+--R a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 730
+
+--S 731 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R +-+ +-+ \|d x + c - \|c
+--R 2\|b \|c log(------------------)
+--R x
+--R +
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+ +--------+
+--R +-+ | 2 | 2
+--R +-----------+ \|b \|d x + c +-+ +-+ \|d x + c
+--R - 2\|- a d + b c atanh(---------------) + 2\|b \|c atanh(-----------)
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R +-+
+--R 2a\|b
+--R Type: Expression(Integer)
+--E 731
+
+--S 732 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 732
+
+--S 733 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+ +--------+
+--R | 2 +-+ +-+ | 2
+--R +-+ +-+ \|d x + c - \|c +-----------+ \|b \|d x + c
+--R \|b \|c log(------------------) - \|- a d + b c atanh(---------------)
+--R x +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R +-+ +-+ \|d x + c
+--R \|b \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +---------+ +-+ | 2 2
+--R +-+ |a d - b c a\|c \|d x + c - b c x - a c
+--R - \|b |--------- atan(-------------------------------)
+--R \| b +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R /
+--R +-+
+--R a\|b
+--R Type: Expression(Integer)
+--E 733
+
+--S 734 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 734
+
+)clear all
+
+--S 735 of 1475
+t0:=sqrt(c+d*x^2)/(x^2*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) -----------
+--R 4 2
+--R b x + a x
+--R Type: Expression(Integer)
+--E 735
+
+--S 736 of 1475
+r0:=-atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*_
+ sqrt(b*c-a*d)/a^(3/2)-sqrt(c+d*x^2)/(a*x)
+--R
+--R
+--R +-----------+ +--------+
+--R +-----------+ x\|- a d + b c +-+ | 2
+--R - x\|- a d + b c atan(---------------) - \|a \|d x + c
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R (2) --------------------------------------------------------
+--R +-+
+--R a x\|a
+--R Type: Expression(Integer)
+--E 736
+
+--S 737 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+ +--------+ +---------+
+--R |a d - b c | 2 +-+ |a d - b c
+--R (x |--------- \|d x + c - x\|c |--------- )
+--R \| a \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ | 2 2
+--R 2\|c \|d x + c - 2d x - 2c
+--R /
+--R +--------+
+--R | 2 +-+
+--R 2a x\|d x + c - 2a x\|c
+--R ,
+--R
+--R +-----------+ +--------+ +-----------+
+--R |- a d + b c | 2 |- a d + b c +-+
+--R (x |----------- \|d x + c - x |----------- \|c )
+--R \| a \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +--------+ +-----------+
+--R |- a d + b c | 2 |- a d + b c +-+
+--R (- x |----------- \|d x + c + x |----------- \|c )
+--R \| a \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R +-+ | 2 2
+--R \|c \|d x + c - d x - c
+--R /
+--R +--------+
+--R | 2 +-+
+--R a x\|d x + c - a x\|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 737
+
+--S 738 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-+ |a d - b c
+--R \|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R 2\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-+
+--R 2a\|a
+--R Type: Expression(Integer)
+--E 738
+
+--S 739 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 739
+
+--S 740 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c +-+ \|c
+--R - |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R \|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-+
+--R a\|a
+--R Type: Expression(Integer)
+--E 740
+
+--S 741 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 741
+
+)clear all
+
+--S 742 of 1475
+t0:=sqrt(c+d*x^2)/(x^3*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) -----------
+--R 5 3
+--R b x + a x
+--R Type: Expression(Integer)
+--E 742
+
+--S 743 of 1475
+r0:=1/2*(2*b*c-a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))/(a^2*sqrt(c))-_
+ atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))*sqrt(b)*_
+ sqrt(b*c-a*d)/a^2-1/2*sqrt(c+d*x^2)/(a*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 +-----------+ +-+ +-+ \|b \|d x + c
+--R - 2x \|- a d + b c \|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 \|d x + c +-+ | 2
+--R (- a d + 2b c)x atanh(-----------) - a\|c \|d x + c
+--R +-+
+--R \|c
+--R /
+--R 2 2 +-+
+--R 2a x \|c
+--R Type: Expression(Integer)
+--E 743
+
+--S 744 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 | 2
+--R (2a c d - 4b c )x \|d x + c
+--R +
+--R 2 4 2 2 +-+
+--R ((- a d + 2b c d)x + (- 2a c d + 4b c )x )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-------------+ +--------+
+--R 2 | 2 +-+ | 2
+--R 2c x \|- a b d + b c \|c \|d x + c
+--R +
+--R +-------------+
+--R 4 2 2 | 2
+--R (- c d x - 2c x )\|- a b d + b c
+--R *
+--R log
+--R +-------------+ +--------+
+--R 2 2 +-+ 2 | 2 | 2
+--R ((2a b x + 2a )\|c - 2a x \|- a b d + b c )\|d x + c
+--R +
+--R +-------------+
+--R 4 2 | 2 +-+ 2 4
+--R (2b x + 2a x )\|- a b d + b c \|c + (a b d - 2b c)x
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R (a c d x + 2a c )\|d x + c + (- 2a c d x - 2a c )\|c
+--R /
+--R +--------+
+--R 2 2 +-+ | 2 2 4 2 2 2
+--R 4a c x \|c \|d x + c - 2a c d x - 4a c x
+--R ,
+--R
+--R +--------+
+--R 2 2 | 2
+--R (2a c d - 4b c )x \|d x + c
+--R +
+--R 2 4 2 2 +-+
+--R ((- a d + 2b c d)x + (- 2a c d + 4b c )x )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R 2 +-+ | 2 | 2
+--R 4c x \|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 4 2 2 | 2
+--R (- 2c d x - 4c x )\|a b d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +-----------+
+--R 2 +-+ | 2
+--R x \|c \|a b d - b c
+--R +
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R (a c d x + 2a c )\|d x + c + (- 2a c d x - 2a c )\|c
+--R /
+--R +--------+
+--R 2 2 +-+ | 2 2 4 2 2 2
+--R 4a c x \|c \|d x + c - 2a c d x - 4a c x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 744
+
+--S 745 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R (a d - 2b c)log(------------------)
+--R x
+--R +
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R *
+--R log
+--R +-------------+ +--------+
+--R 2 2 +-+ 2 | 2 | 2
+--R ((2a b x + 2a )\|c - 2a x \|- a b d + b c )\|d x + c
+--R +
+--R +-------------+
+--R 4 2 | 2 +-+ 2 4
+--R (2b x + 2a x )\|- a b d + b c \|c + (a b d - 2b c)x
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ | 2
+--R +-----------+ +-+ +-+ \|b \|d x + c
+--R 2\|- a d + b c \|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (a d - 2b c)atanh(-----------)
+--R +-+
+--R \|c
+--R /
+--R 2 +-+
+--R 2a \|c
+--R Type: Expression(Integer)
+--E 745
+
+--S 746 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 746
+
+--S 747 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R (a d - 2b c)log(------------------)
+--R x
+--R +
+--R +--------+
+--R +-+ | 2
+--R +-----------+ +-+ +-+ \|b \|d x + c
+--R 2\|- a d + b c \|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (a d - 2b c)atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2 2
+--R +-+ | 2 a\|c \|d x + c - b c x - a c
+--R 2\|c \|a b d - b c atan(-------------------------------)
+--R +-----------+
+--R 2 +-+ | 2
+--R x \|c \|a b d - b c
+--R /
+--R 2 +-+
+--R 2a \|c
+--R Type: Expression(Integer)
+--E 747
+
+--S 748 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 748
+
+)clear all
+
+--S 749 of 1475
+t0:=sqrt(c+d*x^2)/(x^4*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) -----------
+--R 6 4
+--R b x + a x
+--R Type: Expression(Integer)
+--E 749
+
+--S 750 of 1475
+r0:=b*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*sqrt(b*c-a*d)/_
+ a^(5/2)-1/3*sqrt(c+d*x^2)/(a*x^3)+1/3*(3*b*c-a*d)*sqrt(c+d*x^2)/(a^2*c*x)
+--R
+--R
+--R (2)
+--R +-----------+
+--R 3 +-----------+ x\|- a d + b c
+--R 3b c x \|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R ((- a d + 3b c)x - a c)\|a \|d x + c
+--R /
+--R 2 3 +-+
+--R 3a c x \|a
+--R Type: Expression(Integer)
+--E 750
+
+--S 751 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+ +--------+
+--R 5 2 3 |a d - b c | 2
+--R (3b c d x + 12b c x ) |--------- \|d x + c
+--R \| a
+--R +
+--R +---------+
+--R 5 2 3 +-+ |a d - b c
+--R (- 9b c d x - 12b c x )\|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R ((6a d - 18b c d)x + (14a c d - 24b c )x + 8a c )\|c \|d x + c
+--R +
+--R 3 2 6 2 2 4
+--R (- 2a d + 6b c d )x + (- 12a c d + 30b c d)x
+--R +
+--R 2 3 2 3
+--R (- 18a c d + 24b c )x - 8a c
+--R /
+--R +--------+
+--R 2 5 2 2 3 | 2 2 5 2 2 3 +-+
+--R (6a c d x + 24a c x )\|d x + c + (- 18a c d x - 24a c x )\|c
+--R ,
+--R
+--R +-----------+ +--------+
+--R 5 2 3 |- a d + b c | 2
+--R (- 3b c d x - 12b c x ) |----------- \|d x + c
+--R \| a
+--R +
+--R +-----------+
+--R 5 2 3 |- a d + b c +-+
+--R (9b c d x + 12b c x ) |----------- \|c
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +--------+
+--R 5 2 3 |- a d + b c | 2
+--R (3b c d x + 12b c x ) |----------- \|d x + c
+--R \| a
+--R +
+--R +-----------+
+--R 5 2 3 |- a d + b c +-+
+--R (- 9b c d x - 12b c x ) |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R ((3a d - 9b c d)x + (7a c d - 12b c )x + 4a c )\|c \|d x + c
+--R +
+--R 3 2 6 2 2 4 2 3 2
+--R (- a d + 3b c d )x + (- 6a c d + 15b c d)x + (- 9a c d + 12b c )x
+--R +
+--R 3
+--R - 4a c
+--R /
+--R +--------+
+--R 2 5 2 2 3 | 2 2 5 2 2 3 +-+
+--R (3a c d x + 12a c x )\|d x + c + (- 9a c d x - 12a c x )\|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 751
+
+--S 752 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-+ |a d - b c
+--R b\|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R - 2b\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 752
+
+--S 753 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 753
+
+--S 754 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R -
+--R +-----------+
+--R |- a d + b c +-+
+--R b |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c +-+ \|c
+--R b |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R - b\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 754
+
+--S 755 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 755
+
+)clear all
+
+--S 756 of 1475
+t0:=x^4*(c+d*x^2)^(3/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 6 4 | 2
+--R (d x + c x )\|d x + c
+--R (1) ------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 756
+
+--S 757 of 1475
+r0:=a^(3/2)*(b*c-a*d)^(3/2)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*_
+ sqrt(c+d*x^2)))/b^4-1/16*(b*c-2*a*d)*(b^2*c^2+8*a*b*c*d-_
+ 8*a^2*d^2)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/(b^4*d^(3/2))+_
+ 1/16*(b^2*c^2-10*a*b*c*d+8*a^2*d^2)*x*sqrt(c+d*x^2)/(b^3*d)+_
+ 1/24*(7*b*c-6*a*d)*x^3*sqrt(c+d*x^2)/b^2+1/6*d*x^5*sqrt(c+d*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|d
+--R (- 48a d + 72a b c d - 18a b c d - 3b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 +-----------+ +-+ +-+ x\|- a d + b c
+--R (- 48a d + 48a b c d)\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 3 2 5 2 2 3 3 2 2 2 3 2
+--R (8b d x + (- 12a b d + 14b c d)x + (24a b d - 30a b c d + 3b c )x)
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R 4 +-+
+--R 48b d\|d
+--R Type: Expression(Integer)
+--E 757
+
+--S 758 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (288a d - 432a b c d + 108a b c d + 18b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2
+--R (1536a c d - 2304a b c d + 576a b c d + 96b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5
+--R 1536a c d - 2304a b c d + 576a b c d + 96b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 6
+--R (- 48a d + 72a b c d - 18a b c d - 3b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (- 864a c d + 1296a b c d - 324a b c d - 54b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2
+--R (- 2304a c d + 3456a b c d - 864a b c d - 144b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6
+--R - 1536a c d + 2304a b c d - 576a b c d - 96b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 4 3 4 2 3 2 2 2
+--R (144a d - 144a b c d )x + (768a c d - 768a b c d )x
+--R +
+--R 2 2 2 3
+--R 768a c d - 768a b c d
+--R *
+--R +-----------+ +--------+
+--R +-+ +-+ | 2 | 2
+--R \|c \|d \|a d - a b c \|d x + c
+--R +
+--R 2 5 4 6 2 4 2 3 4
+--R (- 24a d + 24a b c d )x + (- 432a c d + 432a b c d )x
+--R +
+--R 2 2 3 3 2 2 2 3 2 4
+--R (- 1152a c d + 1152a b c d )x - 768a c d + 768a b c d
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (- 2d x - 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (4d x + 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R - 8b d x + (12a b d - 158b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (- 24a b d + 246a b c d - 639b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (- 432a b c d + 1116a b c d - 982b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (- 1152a b c d + 1824a b c d - 592b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (- 768a b c d + 960a b c d - 96b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R 48b d x + (- 72a b d + 388b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (144a b d - 636a b c d + 1062b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (912a b c d - 1908a b c d + 1266b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (1536a b c d - 2304a b c d + 640b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (768a b c d - 960a b c d + 96b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 4 3 4 4 2 2 4 2 +-+ +-+ | 2
+--R (288b d x + 1536b c d x + 1536b c d)\|c \|d \|d x + c
+--R +
+--R 4 4 6 4 3 4 4 2 2 2 4 3 +-+
+--R (- 48b d x - 864b c d x - 2304b c d x - 1536b c d)\|d
+--R ,
+--R
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (288a d - 432a b c d + 108a b c d + 18b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2
+--R (1536a c d - 2304a b c d + 576a b c d + 96b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5
+--R 1536a c d - 2304a b c d + 576a b c d + 96b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 6
+--R (- 48a d + 72a b c d - 18a b c d - 3b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (- 864a c d + 1296a b c d - 324a b c d - 54b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2
+--R (- 2304a c d + 3456a b c d - 864a b c d - 144b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6
+--R - 1536a c d + 2304a b c d - 576a b c d - 96b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 4 3 4 2 3 2 2 2
+--R (288a d - 288a b c d )x + (1536a c d - 1536a b c d )x
+--R +
+--R 2 2 2 3
+--R 1536a c d - 1536a b c d
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ +-+ | 2
+--R \|- a d + a b c \|c \|d \|d x + c
+--R +
+--R 2 5 4 6 2 4 2 3 4
+--R (- 48a d + 48a b c d )x + (- 864a c d + 864a b c d )x
+--R +
+--R 2 2 3 3 2 2 2 3 2 4
+--R (- 2304a c d + 2304a b c d )x - 1536a c d + 1536a b c d
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 2 4 3 4 2 3 2 2 2
+--R (- 288a d + 288a b c d )x + (- 1536a c d + 1536a b c d )x
+--R +
+--R 2 2 2 3
+--R - 1536a c d + 1536a b c d
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ +-+ | 2
+--R \|- a d + a b c \|c \|d \|d x + c
+--R +
+--R 2 5 4 6 2 4 2 3 4
+--R (48a d - 48a b c d )x + (864a c d - 864a b c d )x
+--R +
+--R 2 2 3 3 2 2 2 3 2 4
+--R (2304a c d - 2304a b c d )x + 1536a c d - 1536a b c d
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R - 8b d x + (12a b d - 158b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (- 24a b d + 246a b c d - 639b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (- 432a b c d + 1116a b c d - 982b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (- 1152a b c d + 1824a b c d - 592b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (- 768a b c d + 960a b c d - 96b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R 48b d x + (- 72a b d + 388b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (144a b d - 636a b c d + 1062b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (912a b c d - 1908a b c d + 1266b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (1536a b c d - 2304a b c d + 640b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (768a b c d - 960a b c d + 96b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 4 3 4 4 2 2 4 2 +-+ +-+ | 2
+--R (288b d x + 1536b c d x + 1536b c d)\|c \|d \|d x + c
+--R +
+--R 4 4 6 4 3 4 4 2 2 2 4 3 +-+
+--R (- 48b d x - 864b c d x - 2304b c d x - 1536b c d)\|d
+--R ,
+--R
+--R 2 4 3 4 2 3 2 2 2
+--R (144a d - 144a b c d )x + (768a c d - 768a b c d )x
+--R +
+--R 2 2 2 3
+--R 768a c d - 768a b c d
+--R *
+--R +-----------+ +--------+
+--R +---+ +-+ | 2 | 2
+--R \|- d \|c \|a d - a b c \|d x + c
+--R +
+--R 2 5 4 6 2 4 2 3 4
+--R (- 24a d + 24a b c d )x + (- 432a c d + 432a b c d )x
+--R +
+--R 2 2 3 3 2 2 2 3 2 4
+--R (- 1152a c d + 1152a b c d )x - 768a c d + 768a b c d
+--R *
+--R +-----------+
+--R +---+ | 2
+--R \|- d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (- 2d x - 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (4d x + 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 576a d + 864a b c d - 216a b c d - 36b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2
+--R (- 3072a c d + 4608a b c d - 1152a b c d - 192b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5
+--R - 3072a c d + 4608a b c d - 1152a b c d - 192b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 6
+--R (96a d - 144a b c d + 36a b c d + 6b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (1728a c d - 2592a b c d + 648a b c d + 108b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2
+--R (4608a c d - 6912a b c d + 1728a b c d + 288b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6
+--R 3072a c d - 4608a b c d + 1152a b c d + 192b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 3 5 11 2 5 3 4 9
+--R - 8b d x + (12a b d - 158b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (- 24a b d + 246a b c d - 639b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (- 432a b c d + 1116a b c d - 982b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (- 1152a b c d + 1824a b c d - 592b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (- 768a b c d + 960a b c d - 96b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R 48b d x + (- 72a b d + 388b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (144a b d - 636a b c d + 1062b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (912a b c d - 1908a b c d + 1266b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (1536a b c d - 2304a b c d + 640b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (768a b c d - 960a b c d + 96b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 4 3 4 4 2 2 4 2 +---+ +-+ | 2
+--R (288b d x + 1536b c d x + 1536b c d)\|- d \|c \|d x + c
+--R +
+--R 4 4 6 4 3 4 4 2 2 2 4 3 +---+
+--R (- 48b d x - 864b c d x - 2304b c d x - 1536b c d)\|- d
+--R ,
+--R
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 576a d + 864a b c d - 216a b c d - 36b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2
+--R (- 3072a c d + 4608a b c d - 1152a b c d - 192b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5
+--R - 3072a c d + 4608a b c d - 1152a b c d - 192b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 6
+--R (96a d - 144a b c d + 36a b c d + 6b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (1728a c d - 2592a b c d + 648a b c d + 108b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2
+--R (4608a c d - 6912a b c d + 1728a b c d + 288b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6
+--R 3072a c d - 4608a b c d + 1152a b c d + 192b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 4 3 4 2 3 2 2 2
+--R (288a d - 288a b c d )x + (1536a c d - 1536a b c d )x
+--R +
+--R 2 2 2 3
+--R 1536a c d - 1536a b c d
+--R *
+--R +-------------+ +--------+
+--R | 2 +---+ +-+ | 2
+--R \|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R 2 5 4 6 2 4 2 3 4
+--R (- 48a d + 48a b c d )x + (- 864a c d + 864a b c d )x
+--R +
+--R 2 2 3 3 2 2 2 3 2 4
+--R (- 2304a c d + 2304a b c d )x - 1536a c d + 1536a b c d
+--R *
+--R +-------------+
+--R | 2 +---+
+--R \|- a d + a b c \|- d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 2 4 3 4 2 3 2 2 2
+--R (- 288a d + 288a b c d )x + (- 1536a c d + 1536a b c d )x
+--R +
+--R 2 2 2 3
+--R - 1536a c d + 1536a b c d
+--R *
+--R +-------------+ +--------+
+--R | 2 +---+ +-+ | 2
+--R \|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R 2 5 4 6 2 4 2 3 4
+--R (48a d - 48a b c d )x + (864a c d - 864a b c d )x
+--R +
+--R 2 2 3 3 2 2 2 3 2 4
+--R (2304a c d - 2304a b c d )x + 1536a c d - 1536a b c d
+--R *
+--R +-------------+
+--R | 2 +---+
+--R \|- a d + a b c \|- d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R - 8b d x + (12a b d - 158b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (- 24a b d + 246a b c d - 639b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (- 432a b c d + 1116a b c d - 982b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (- 1152a b c d + 1824a b c d - 592b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (- 768a b c d + 960a b c d - 96b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R 48b d x + (- 72a b d + 388b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (144a b d - 636a b c d + 1062b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (912a b c d - 1908a b c d + 1266b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (1536a b c d - 2304a b c d + 640b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (768a b c d - 960a b c d + 96b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 4 3 4 4 2 2 4 2 +---+ +-+ | 2
+--R (288b d x + 1536b c d x + 1536b c d)\|- d \|c \|d x + c
+--R +
+--R 4 4 6 4 3 4 4 2 2 2 4 3 +---+
+--R (- 48b d x - 864b c d x - 2304b c d x - 1536b c d)\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 758
+
+--S 759 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (16a d - 24a b c d + 6a b c d + b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-----------+
+--R 2 2 +-+ | 2
+--R (8a d - 8a b c d)\|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (- 2d x - 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (4d x + 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|d
+--R (16a d - 24a b c d + 6a b c d + b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 +-----------+ +-+ +-+ x\|- a d + b c
+--R (16a d - 16a b c d)\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 4 +-+
+--R 16b d\|d
+--R Type: Expression(Integer)
+--E 759
+
+--S 760 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 760
+
+--S 761 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 3 3 2 2 2 2 3 3
+--R (16a d - 24a b c d + 6a b c d + b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|d
+--R (16a d - 24a b c d + 6a b c d + b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-------------+
+--R 2 2 | 2 +-+
+--R (16a d - 16a b c d)\|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+ +-+
+--R 2 2 | 2 +-+ a\|c
+--R (- 16a d + 16a b c d)\|- a d + a b c \|d atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R +-----------+
+--R 2 2 +-----------+ +-+ +-+ x\|- a d + b c
+--R (16a d - 16a b c d)\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 4 +-+
+--R 16b d\|d
+--R Type: Expression(Integer)
+--E 761
+
+--S 762 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 762
+
+)clear all
+
+--S 763 of 1475
+t0:=x^3*(c+d*x^2)^(3/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 5 3 | 2
+--R (d x + c x )\|d x + c
+--R (1) ------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 763
+
+--S 764 of 1475
+r0:=-1/3*a*(c+d*x^2)^(3/2)/b^2+1/5*(c+d*x^2)^(5/2)/(b*d)+a*_
+ (b*c-a*d)^(3/2)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/_
+ b^(7/2)-a*(b*c-a*d)*sqrt(c+d*x^2)/b^3
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 2 +-----------+ \|b \|d x + c
+--R (- 15a d + 15a b c d)\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2 +-+
+--R (3b d x + (- 5a b d + 6b c d)x + 15a d - 20a b c d + 3b c )\|b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 +-+
+--R 15b d\|b
+--R Type: Expression(Integer)
+--E 764
+
+--S 765 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 4 2 2 2 2 2 2
+--R (15a d - 15a b c d )x + (180a c d - 180a b c d)x + 240a c d
+--R +
+--R 3
+--R - 240a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 4 2 2 2 3 2
+--R (- 75a c d + 75a b c d )x + (- 300a c d + 300a b c d)x
+--R +
+--R 2 3 4
+--R - 240a c d + 240a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+
+--R ((- 2a b d - 4b c)x - 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (2b c d x + (6a b c d + 4b c )x + 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 3 8 3 2 2 2 6
+--R - 30b c d x + (50a b c d - 180b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 120a c d + 360a b c d - 360b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (- 240a c d + 480a b c d - 240b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 10 4 2 3 8
+--R 6b d x + (- 10a b d + 90b c d )x
+--R +
+--R 2 4 3 2 2 2 6
+--R (30a d - 170a b c d + 330b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (240a c d - 600a b c d + 480b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (240a c d - 480a b c d + 240b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 2 4 3 2 3 2 +-+ | 2 3 2 4
+--R (30b d x + 360b c d x + 480b c )\|c \|d x + c - 150b c d x
+--R +
+--R 3 2 2 3 3
+--R - 600b c d x - 480b c
+--R ,
+--R
+--R 2 3 2 4 2 2 2 2 2 2
+--R (15a d - 15a b c d )x + (180a c d - 180a b c d)x + 240a c d
+--R +
+--R 3
+--R - 240a b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 4 2 2 2 3 2
+--R (- 75a c d + 75a b c d )x + (- 300a c d + 300a b c d)x
+--R +
+--R 2 3 4
+--R - 240a c d + 240a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R 2 3 8 3 2 2 2 6
+--R - 15b c d x + (25a b c d - 90b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 60a c d + 180a b c d - 180b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (- 120a c d + 240a b c d - 120b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 10 4 2 3 8
+--R 3b d x + (- 5a b d + 45b c d )x
+--R +
+--R 2 4 3 2 2 2 6
+--R (15a d - 85a b c d + 165b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (120a c d - 300a b c d + 240b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (120a c d - 240a b c d + 120b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 2 4 3 2 3 2 +-+ | 2 3 2 4
+--R (15b d x + 180b c d x + 240b c )\|c \|d x + c - 75b c d x
+--R +
+--R 3 2 2 3 3
+--R - 300b c d x - 240b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 765
+
+--S 766 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 4 3 4 2 3 2 2 2 2 2 2
+--R (15a d - 15a b c d )x + (180a c d - 180a b c d )x + 240a c d
+--R +
+--R 3
+--R - 240a b c d
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ +-+ | 2
+--R |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R 2 4 2 3 4 2 2 3 3 2 2
+--R (- 75a c d + 75a b c d )x + (- 300a c d + 300a b c d )x
+--R +
+--R 2 3 2 4
+--R - 240a c d + 240a b c d
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+
+--R ((- 2a b d - 4b c)x - 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (2b c d x + (6a b c d + 4b c )x + 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 4 3 4 2 3 2 2 2 2 2 2
+--R (30a d - 30a b c d )x + (360a c d - 360a b c d )x + 480a c d
+--R +
+--R 3
+--R - 480a b c d
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 4 2 3 4 2 2 3 3 2 2
+--R (- 150a c d + 150a b c d )x + (- 600a c d + 600a b c d )x
+--R +
+--R 2 3 2 4
+--R - 480a c d + 480a b c d
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (30a c d - 40a b c d + 6b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (360a c d - 480a b c d + 72b c d)x + 480a c d - 640a b c d + 96b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 150a c d + 200a b c d - 30b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (- 600a c d + 800a b c d - 120b c d)x - 480a c d + 640a b c d
+--R +
+--R 2 5
+--R - 96b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 3 3 4 3 2 2 3 2 +-+ +-+ | 2
+--R (30b d x + 360b c d x + 480b c d)\|b \|c \|d x + c
+--R +
+--R 3 3 4 3 2 2 2 3 3 +-+
+--R (- 150b c d x - 600b c d x - 480b c d)\|b
+--R Type: Expression(Integer)
+--E 766
+
+--S 767 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 767
+
+--S 768 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 4 3 4 2 3 2 2 2 2 2 2
+--R (15a d - 15a b c d )x + (180a c d - 180a b c d )x + 240a c d
+--R +
+--R 3
+--R - 240a b c d
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 4 2 3 4 2 2 3 3 2 2
+--R (- 75a c d + 75a b c d )x + (- 300a c d + 300a b c d )x
+--R +
+--R 2 3 2 4
+--R - 240a c d + 240a b c d
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 4 3 4 2 3 2 2 2 2 2 2
+--R (15a d - 15a b c d )x + (180a c d - 180a b c d )x + 240a c d
+--R +
+--R 3
+--R - 240a b c d
+--R *
+--R +---------+ +--------+
+--R +-+ +-+ |a d - b c | 2
+--R \|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 4 2 3 4 2 2 3 3 2 2
+--R (- 75a c d + 75a b c d )x + (- 300a c d + 300a b c d )x
+--R +
+--R 2 3 2 4
+--R - 240a c d + 240a b c d
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|b |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (15a c d - 20a b c d + 3b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (180a c d - 240a b c d + 36b c d)x + 240a c d - 320a b c d + 48b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 75a c d + 100a b c d - 15b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (- 300a c d + 400a b c d - 60b c d)x - 240a c d + 320a b c d
+--R +
+--R 2 5
+--R - 48b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 3 3 4 3 2 2 3 2 +-+ +-+ | 2
+--R (15b d x + 180b c d x + 240b c d)\|b \|c \|d x + c
+--R +
+--R 3 3 4 3 2 2 2 3 3 +-+
+--R (- 75b c d x - 300b c d x - 240b c d)\|b
+--R Type: Expression(Integer)
+--E 768
+
+--S 769 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 769
+
+)clear all
+
+--S 770 of 1475
+t0:=x^2*(c+d*x^2)^(3/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (d x + c x )\|d x + c
+--R (1) ------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 770
+
+--S 771 of 1475
+r0:=-(b*c-a*d)^(3/2)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*_
+ sqrt(a)/b^3+1/8*(3*b^2*c^2-12*a*b*c*d+8*a^2*d^2)*atanh(x*_
+ sqrt(d)/sqrt(c+d*x^2))/(b^3*sqrt(d))+1/8*(5*b*c-4*a*d)*x*_
+ sqrt(c+d*x^2)/b^2+1/4*d*x^3*sqrt(c+d*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 x\|d
+--R (8a d - 12a b c d + 3b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ +-+ +-+ x\|- a d + b c
+--R (8a d - 8b c)\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 3 2 +-+ | 2
+--R (2b d x + (- 4a b d + 5b c)x)\|d \|d x + c
+--R /
+--R 3 +-+
+--R 8b \|d
+--R Type: Expression(Integer)
+--E 771
+
+--S 772 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+
+--R 2 2 2 +-+ +-+ | 2
+--R ((16a d - 16b c d)x + 32a c d - 32b c )\|c \|d \|a d - a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 4a d + 4b c d )x + (- 32a c d + 32b c d)x - 32a c d
+--R +
+--R 3
+--R 32b c
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (2d x + 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (- 4d x - 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (32a d - 48a b c d + 12b c d)x + 64a c d - 96a b c d
+--R +
+--R 2 3
+--R 24b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 8a d + 12a b c d - 3b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 64a c d + 96a b c d - 24b c d)x - 64a c d + 96a b c d - 24b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R - 2b d x + (4a b d - 21b c d )x + (32a b c d - 56b c d)x
+--R +
+--R 2 2 3
+--R (32a b c d - 40b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 8b d x + (- 16a b d + 44b c d )x + (- 48a b c d + 76b c d)x
+--R +
+--R 2 2 3
+--R (- 32a b c d + 40b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 3 2 3 +-+ +-+ | 2
+--R (32b d x + 64b c)\|c \|d \|d x + c
+--R +
+--R 3 2 4 3 2 3 2 +-+
+--R (- 8b d x - 64b c d x - 64b c )\|d
+--R ,
+--R
+--R 2 3 2 2 2 2 2 2 2
+--R (32a d - 48a b c d + 12b c d)x + 64a c d - 96a b c d
+--R +
+--R 2 3
+--R 24b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 8a d + 12a b c d - 3b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 64a c d + 96a b c d - 24b c d)x - 64a c d + 96a b c d - 24b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-------------+
+--R 2 2 2 | 2 +-+
+--R ((- 32a d + 32b c d)x - 64a c d + 64b c )\|- a d + a b c \|c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((8a d - 8b c d )x + (64a c d - 64b c d)x + 64a c d - 64b c )
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R 2 2 2 | 2 +-+ +-+
+--R ((32a d - 32b c d)x + 64a c d - 64b c )\|- a d + a b c \|c \|d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 8a d + 8b c d )x + (- 64a c d + 64b c d)x - 64a c d
+--R +
+--R 3
+--R 64b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R - 2b d x + (4a b d - 21b c d )x + (32a b c d - 56b c d)x
+--R +
+--R 2 2 3
+--R (32a b c d - 40b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 8b d x + (- 16a b d + 44b c d )x + (- 48a b c d + 76b c d)x
+--R +
+--R 2 2 3
+--R (- 32a b c d + 40b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 3 2 3 +-+ +-+ | 2
+--R (32b d x + 64b c)\|c \|d \|d x + c
+--R +
+--R 3 2 4 3 2 3 2 +-+
+--R (- 8b d x - 64b c d x - 64b c )\|d
+--R ,
+--R
+--R +-----------+
+--R 2 2 2 +---+ +-+ | 2
+--R ((16a d - 16b c d)x + 32a c d - 32b c )\|- d \|c \|a d - a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 4a d + 4b c d )x + (- 32a c d + 32b c d)x - 32a c d
+--R +
+--R 3
+--R 32b c
+--R *
+--R +-----------+
+--R +---+ | 2
+--R \|- d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (2d x + 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (- 4d x - 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (64a d - 96a b c d + 24b c d)x + 128a c d - 192a b c d
+--R +
+--R 2 3
+--R 48b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 16a d + 24a b c d - 6b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 128a c d + 192a b c d - 48b c d)x - 128a c d + 192a b c d
+--R +
+--R 2 4
+--R - 48b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R - 2b d x + (4a b d - 21b c d )x + (32a b c d - 56b c d)x
+--R +
+--R 2 2 3
+--R (32a b c d - 40b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 8b d x + (- 16a b d + 44b c d )x + (- 48a b c d + 76b c d)x
+--R +
+--R 2 2 3
+--R (- 32a b c d + 40b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 3 2 3 +---+ +-+ | 2
+--R (32b d x + 64b c)\|- d \|c \|d x + c
+--R +
+--R 3 2 4 3 2 3 2 +---+
+--R (- 8b d x - 64b c d x - 64b c )\|- d
+--R ,
+--R
+--R 2 3 2 2 2 2 2 2 2
+--R (64a d - 96a b c d + 24b c d)x + 128a c d - 192a b c d
+--R +
+--R 2 3
+--R 48b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 16a d + 24a b c d - 6b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 128a c d + 192a b c d - 48b c d)x - 128a c d + 192a b c d
+--R +
+--R 2 4
+--R - 48b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R +-------------+
+--R 2 2 2 | 2 +---+
+--R ((- 32a d + 32b c d)x - 64a c d + 64b c )\|- a d + a b c \|- d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((8a d - 8b c d )x + (64a c d - 64b c d)x + 64a c d - 64b c )
+--R *
+--R +-------------+
+--R | 2 +---+
+--R \|- a d + a b c \|- d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R 2 2 2 | 2 +---+
+--R ((32a d - 32b c d)x + 64a c d - 64b c )\|- a d + a b c \|- d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 8a d + 8b c d )x + (- 64a c d + 64b c d)x - 64a c d
+--R +
+--R 3
+--R 64b c
+--R *
+--R +-------------+
+--R | 2 +---+
+--R \|- a d + a b c \|- d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R - 2b d x + (4a b d - 21b c d )x + (32a b c d - 56b c d)x
+--R +
+--R 2 2 3
+--R (32a b c d - 40b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 8b d x + (- 16a b d + 44b c d )x + (- 48a b c d + 76b c d)x
+--R +
+--R 2 2 3
+--R (- 32a b c d + 40b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 3 2 3 +---+ +-+ | 2
+--R (32b d x + 64b c)\|- d \|c \|d x + c
+--R +
+--R 3 2 4 3 2 3 2 +---+
+--R (- 8b d x - 64b c d x - 64b c )\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 772
+
+--S 773 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R +-+ | 2
+--R (4a d - 4b c)\|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2 2 +-+
+--R ((2d x + 4c x)\|a d - a b c + ((4a d - 2b c)x + 2a c)\|c )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (- 4d x - 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 2 2
+--R (8a d - 12a b c d + 3b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 x\|d
+--R (- 8a d + 12a b c d - 3b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ +-+ +-+ x\|- a d + b c
+--R (- 8a d + 8b c)\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 8b \|d
+--R Type: Expression(Integer)
+--E 773
+
+--S 774 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 774
+
+--S 775 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 2 2 2
+--R (8a d - 12a b c d + 3b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 x\|d
+--R (- 8a d + 12a b c d - 3b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R (- 8a d + 8b c)\|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+ +-+
+--R | 2 +-+ a\|c
+--R (8a d - 8b c)\|- a d + a b c \|d atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R +-----------+
+--R +-----------+ +-+ +-+ x\|- a d + b c
+--R (- 8a d + 8b c)\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 8b \|d
+--R Type: Expression(Integer)
+--E 775
+
+--S 776 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 776
+
+)clear all
+
+--S 777 of 1475
+t0:=x*(c+d*x^2)^(3/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 3 | 2
+--R (d x + c x)\|d x + c
+--R (1) -----------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 777
+
+--S 778 of 1475
+r0:=1/3*(c+d*x^2)^(3/2)/b-(b*c-a*d)^(3/2)*atanh(sqrt(b)*_
+ sqrt(c+d*x^2)/sqrt(b*c-a*d))/b^(5/2)+(b*c-a*d)*sqrt(c+d*x^2)/b^2
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R +-----------+ \|b \|d x + c
+--R (3a d - 3b c)\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R (b d x - 3a d + 4b c)\|b \|d x + c
+--R /
+--R 2 +-+
+--R 3b \|b
+--R Type: Expression(Integer)
+--E 778
+
+--S 779 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+
+--R 2 2 2 |- a d + b c +-+
+--R ((3a d - 3b c d)x + 12a c d - 12b c ) |----------- \|c
+--R \| b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 3 |- a d + b c
+--R ((- 9a c d + 9b c d)x - 12a c d + 12b c ) |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+
+--R ((2a b d + 4b c)x + 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (- 2b c d x + (- 6a b c d - 4b c )x - 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 4 2 2 2 | 2
+--R (- 6b c d x + (12a c d - 24b c d)x )\|d x + c
+--R +
+--R 3 6 3 2 4 2 2 2 +-+
+--R (2b d x + (- 6a d + 18b c d )x + (- 12a c d + 24b c d)x )\|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ | 2 2 2 2 2
+--R (6b d x + 24b c)\|c \|d x + c - 18b c d x - 24b c
+--R ,
+--R
+--R +---------+
+--R 2 2 2 +-+ |a d - b c
+--R ((- 3a d + 3b c d)x - 12a c d + 12b c )\|c |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 2 2 2 3 |a d - b c
+--R ((9a c d - 9b c d)x + 12a c d - 12b c ) |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R +--------+
+--R 2 4 2 2 2 | 2
+--R (- 3b c d x + (6a c d - 12b c d)x )\|d x + c
+--R +
+--R 3 6 3 2 4 2 2 2 +-+
+--R (b d x + (- 3a d + 9b c d )x + (- 6a c d + 12b c d)x )\|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ | 2 2 2 2 2
+--R (3b d x + 12b c)\|c \|d x + c - 9b c d x - 12b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 779
+
+--S 780 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R 2 2 2 |- a d + b c +-+ +-+
+--R ((3a d - 3b c d)x + 12a c d - 12b c ) |----------- \|b \|c
+--R \| b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 3 |- a d + b c +-+
+--R ((- 9a c d + 9b c d)x - 12a c d + 12b c ) |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 2 4
+--R ((2a b d + 4b c)x + 8a b c x ) |----------- \|c + 4b c x
+--R \| b
+--R +
+--R 2 2 2 2 2
+--R (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (- 2b c d x + (- 6a b c d - 4b c )x - 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 +-----------+ +-+
+--R ((- 6a d + 6b c d)x - 24a c d + 24b c )\|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 2 3 +-----------+
+--R ((18a c d - 18b c d)x + 24a c d - 24b c )\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((- 6a c d + 8b c d)x - 24a c d + 32b c )\|b \|d x + c
+--R +
+--R 2 2 2 2 3 +-+ +-+
+--R ((18a c d - 24b c d)x + 24a c d - 32b c )\|b \|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ +-+ | 2 2 2 2 2 +-+
+--R (6b d x + 24b c)\|b \|c \|d x + c + (- 18b c d x - 24b c )\|b
+--R Type: Expression(Integer)
+--E 780
+
+--S 781 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 781
+
+--S 782 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 2 2 +-----------+ +-+
+--R ((- 3a d + 3b c d)x - 12a c d + 12b c )\|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 2 3 +-----------+
+--R ((9a c d - 9b c d)x + 12a c d - 12b c )\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +---------+
+--R 2 2 2 +-+ +-+ |a d - b c
+--R ((- 3a d + 3b c d)x - 12a c d + 12b c )\|b \|c |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 2 2 2 3 +-+ |a d - b c
+--R ((9a c d - 9b c d)x + 12a c d - 12b c )\|b |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((- 3a c d + 4b c d)x - 12a c d + 16b c )\|b \|d x + c
+--R +
+--R 2 2 2 2 3 +-+ +-+
+--R ((9a c d - 12b c d)x + 12a c d - 16b c )\|b \|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ +-+ | 2 2 2 2 2 +-+
+--R (3b d x + 12b c)\|b \|c \|d x + c + (- 9b c d x - 12b c )\|b
+--R Type: Expression(Integer)
+--E 782
+
+--S 783 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 783
+
+)clear all
+
+--S 784 of 1475
+t0:=(c+d*x^2)^(3/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 784
+
+--S 785 of 1475
+r0:=(b*c-a*d)^(3/2)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/_
+ (b^2*sqrt(a))+1/2*(3*b*c-2*a*d)*atanh(x*sqrt(d)/sqrt(c+d*x^2))*_
+ sqrt(d)/b^2+1/2*d*x*sqrt(c+d*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R +-+ +-+ x\|d
+--R (- 2a d + 3b c)\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+ +--------+
+--R +-----------+ x\|- a d + b c +-+ | 2
+--R (- 2a d + 2b c)\|- a d + b c atan(---------------) + b d x\|a \|d x + c
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2b \|a
+--R Type: Expression(Integer)
+--E 785
+
+--S 786 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ +-+ | 2
+--R (4a d - 6b c)\|c \|d \|d x + c
+--R +
+--R 2 2 2 +-+
+--R ((- 2a d + 3b c d)x - 4a c d + 6b c )\|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R (2a d - 2b c)\|c |--------- \|d x + c
+--R \| a
+--R +
+--R +---------+
+--R 2 2 2 |a d - b c
+--R ((- a d + b c d)x - 2a c d + 2b c ) |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 3 | 2 2 3 +-+
+--R (- b d x - 2b c d x)\|d x + c + (2b d x + 2b c d x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2
+--R 4b \|c \|d x + c - 2b d x - 4b c
+--R ,
+--R
+--R +--------+
+--R +-+ +-+ | 2
+--R (4a d - 6b c)\|c \|d \|d x + c
+--R +
+--R 2 2 2 +-+
+--R ((- 2a d + 3b c d)x - 4a c d + 6b c )\|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R (4a d - 4b c) |----------- \|c \|d x + c
+--R \| a
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c
+--R ((- 2a d + 2b c d)x - 4a c d + 4b c ) |-----------
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R (- 4a d + 4b c) |----------- \|c \|d x + c
+--R \| a
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c
+--R ((2a d - 2b c d)x + 4a c d - 4b c ) |-----------
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R 2 3 | 2 2 3 +-+
+--R (- b d x - 2b c d x)\|d x + c + (2b d x + 2b c d x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2
+--R 4b \|c \|d x + c - 2b d x - 4b c
+--R ,
+--R
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R (2a d - 2b c)\|c |--------- \|d x + c
+--R \| a
+--R +
+--R +---------+
+--R 2 2 2 |a d - b c
+--R ((- a d + b c d)x - 2a c d + 2b c ) |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +---+ +-+ | 2
+--R (- 8a d + 12b c)\|- d \|c \|d x + c
+--R +
+--R 2 2 2 +---+
+--R ((4a d - 6b c d)x + 8a c d - 12b c )\|- d
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R +--------+
+--R 2 3 | 2 2 3 +-+
+--R (- b d x - 2b c d x)\|d x + c + (2b d x + 2b c d x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2
+--R 4b \|c \|d x + c - 2b d x - 4b c
+--R ,
+--R
+--R +--------+
+--R +---+ +-+ | 2
+--R (- 8a d + 12b c)\|- d \|c \|d x + c
+--R +
+--R 2 2 2 +---+
+--R ((4a d - 6b c d)x + 8a c d - 12b c )\|- d
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R (4a d - 4b c) |----------- \|c \|d x + c
+--R \| a
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c
+--R ((- 2a d + 2b c d)x - 4a c d + 4b c ) |-----------
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R (- 4a d + 4b c) |----------- \|c \|d x + c
+--R \| a
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c
+--R ((2a d - 2b c d)x + 4a c d - 4b c ) |-----------
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R 2 3 | 2 2 3 +-+
+--R (- b d x - 2b c d x)\|d x + c + (2b d x + 2b c d x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2
+--R 4b \|c \|d x + c - 2b d x - 4b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 786
+
+--S 787 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-+ +-+
+--R (2a d - 3b c)\|a \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+
+--R +-+ |a d - b c
+--R (a d - b c)\|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-+
+--R +-+ +-+ x\|d
+--R (2a d - 3b c)\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (2a d - 2b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2b \|a
+--R Type: Expression(Integer)
+--E 787
+
+--S 788 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 788
+
+--S 789 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+ +-+
+--R (2a d - 3b c)\|a \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R +-+ +-+ x\|d
+--R (2a d - 3b c)\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R |- a d + b c +-+
+--R (2a d - 2b c) |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c +-+ \|c
+--R (- 2a d + 2b c) |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (2a d - 2b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2b \|a
+--R Type: Expression(Integer)
+--E 789
+
+--S 790 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 790
+
+)clear all
+
+--S 791 of 1475
+t0:=(c+d*x^2)^(3/2)/(x*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 3
+--R b x + a x
+--R Type: Expression(Integer)
+--E 791
+
+--S 792 of 1475
+r0:=-c^(3/2)*atanh(sqrt(c+d*x^2)/sqrt(c))/a+(b*c-a*d)^(3/2)*_
+ atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/(a*b^(3/2))+d*sqrt(c+d*x^2)/b
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R +-----------+ \|b \|d x + c
+--R (- a d + b c)\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2 +--------+
+--R +-+ +-+ \|d x + c +-+ | 2
+--R - b c\|b \|c atanh(-----------) + a d\|b \|d x + c
+--R +-+
+--R \|c
+--R /
+--R +-+
+--R a b\|b
+--R Type: Expression(Integer)
+--E 792
+
+--S 793 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +--------+ | 2 +-+
+--R 2 | 2 2 +-+ \|d x + c - \|c
+--R (2b c \|d x + c - 2b c \|c )log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R (a d - b c) |----------- \|c \|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 |- a d + b c
+--R (- a c d + b c ) |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c - 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (2b x + 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 +-+
+--R 2a d x \|c
+--R /
+--R +--------+
+--R +-+ | 2
+--R 2a b\|c \|d x + c - 2a b c
+--R ,
+--R
+--R +--------+
+--R +--------+ | 2 +-+
+--R 2 | 2 2 +-+ \|d x + c - \|c
+--R (b c \|d x + c - b c \|c )log(------------------)
+--R x
+--R +
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R (a d - b c)\|c |--------- \|d x + c
+--R \| b
+--R +
+--R +---------+
+--R 2 |a d - b c
+--R (- a c d + b c ) |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R 2 2 +-+
+--R a d x \|c
+--R /
+--R +--------+
+--R +-+ | 2
+--R a b\|c \|d x + c - a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 793
+
+--S 794 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +--------+ | 2 +-+
+--R 2 +-+ | 2 2 +-+ +-+ \|d x + c - \|c
+--R (2b c \|b \|d x + c - 2b c \|b \|c )log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R |- a d + b c +-+ +-+ | 2
+--R (a d - b c) |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 |- a d + b c +-+
+--R (- a c d + b c ) |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c - 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (2b x + 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R (2a d - 2b c)\|- a d + b c \|c \|d x + c
+--R +
+--R 2 +-----------+
+--R (- 2a c d + 2b c )\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +--------+ | 2
+--R 2 +-+ | 2 2 +-+ +-+ \|d x + c
+--R (2b c \|b \|d x + c - 2b c \|b \|c )atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R 2a c d\|b \|d x + c - 2a c d\|b \|c
+--R /
+--R +--------+
+--R +-+ +-+ | 2 +-+
+--R 2a b\|b \|c \|d x + c - 2a b c\|b
+--R Type: Expression(Integer)
+--E 794
+
+--S 795 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 795
+
+--S 796 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +--------+ | 2 +-+
+--R 2 +-+ | 2 2 +-+ +-+ \|d x + c - \|c
+--R (b c \|b \|d x + c - b c \|b \|c )log(------------------)
+--R x
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R (a d - b c)\|- a d + b c \|c \|d x + c
+--R +
+--R 2 +-----------+
+--R (- a c d + b c )\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +--------+ | 2
+--R 2 +-+ | 2 2 +-+ +-+ \|d x + c
+--R (b c \|b \|d x + c - b c \|b \|c )atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +---------+ +--------+
+--R +-+ +-+ |a d - b c | 2
+--R (a d - b c)\|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R +---------+
+--R 2 +-+ |a d - b c
+--R (- a c d + b c )\|b |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R a c d\|b \|d x + c - a c d\|b \|c
+--R /
+--R +--------+
+--R +-+ +-+ | 2 +-+
+--R a b\|b \|c \|d x + c - a b c\|b
+--R Type: Expression(Integer)
+--E 796
+
+--S 797 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 797
+
+)clear all
+
+--S 798 of 1475
+t0:=(c+d*x^2)^(3/2)/(x^2*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 4 2
+--R b x + a x
+--R Type: Expression(Integer)
+--E 798
+
+--S 799 of 1475
+r0:=-(b*c-a*d)^(3/2)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/_
+ (a^(3/2)*b)+d^(3/2)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/b-c*sqrt(c+d*x^2)/(a*x)
+--R
+--R
+--R (2)
+--R +-+
+--R +-+ +-+ x\|d
+--R a d x\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+ +--------+
+--R +-----------+ x\|- a d + b c +-+ | 2
+--R (a d - b c)x\|- a d + b c atan(---------------) - b c\|a \|d x + c
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-+
+--R a b x\|a
+--R Type: Expression(Integer)
+--E 799
+
+--S 800 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+ +--------+
+--R |a d - b c | 2
+--R (a d - b c)x |--------- \|d x + c
+--R \| a
+--R +
+--R +---------+
+--R +-+ |a d - b c
+--R (- a d + b c)x\|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R (2a d x\|d \|d x + c - 2a d x\|c \|d )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +--------+
+--R +-+ | 2 2 2
+--R 2b c\|c \|d x + c - 2b c d x - 2b c
+--R /
+--R +--------+
+--R | 2 +-+
+--R 2a b x\|d x + c - 2a b x\|c
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R (a d x\|d \|d x + c - a d x\|c \|d )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R (- a d + b c)x |----------- \|d x + c
+--R \| a
+--R +
+--R +-----------+
+--R |- a d + b c +-+
+--R (a d - b c)x |----------- \|c
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R (a d - b c)x |----------- \|d x + c
+--R \| a
+--R +
+--R +-----------+
+--R |- a d + b c +-+
+--R (- a d + b c)x |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R +-+ | 2 2 2
+--R b c\|c \|d x + c - b c d x - b c
+--R /
+--R +--------+
+--R | 2 +-+
+--R a b x\|d x + c - a b x\|c
+--R ,
+--R
+--R +---------+ +--------+
+--R |a d - b c | 2
+--R (a d - b c)x |--------- \|d x + c
+--R \| a
+--R +
+--R +---------+
+--R +-+ |a d - b c
+--R (- a d + b c)x\|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +--------+ | 2 +-+
+--R +---+ | 2 +---+ +-+ \|d x + c - \|c
+--R (4a d x\|- d \|d x + c - 4a d x\|- d \|c )atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R +--------+
+--R +-+ | 2 2 2
+--R 2b c\|c \|d x + c - 2b c d x - 2b c
+--R /
+--R +--------+
+--R | 2 +-+
+--R 2a b x\|d x + c - 2a b x\|c
+--R ,
+--R
+--R +--------+
+--R +--------+ | 2 +-+
+--R +---+ | 2 +---+ +-+ \|d x + c - \|c
+--R (2a d x\|- d \|d x + c - 2a d x\|- d \|c )atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R (- a d + b c)x |----------- \|d x + c
+--R \| a
+--R +
+--R +-----------+
+--R |- a d + b c +-+
+--R (a d - b c)x |----------- \|c
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R (a d - b c)x |----------- \|d x + c
+--R \| a
+--R +
+--R +-----------+
+--R |- a d + b c +-+
+--R (- a d + b c)x |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R +-+ | 2 2 2
+--R b c\|c \|d x + c - b c d x - b c
+--R /
+--R +--------+
+--R | 2 +-+
+--R a b x\|d x + c - a b x\|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 800
+
+--S 801 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-+ |a d - b c
+--R (a d - b c)\|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R 2a d\|a \|d log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R +-+ +-+ x\|d
+--R - 2a d\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (- 2a d + 2b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-+
+--R 2a b\|a
+--R Type: Expression(Integer)
+--E 801
+
+--S 802 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 802
+
+--S 803 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R a d\|a \|d log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R +-+ +-+ x\|d
+--R - a d\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R |- a d + b c +-+
+--R (- a d + b c) |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c +-+ \|c
+--R (a d - b c) |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (- a d + b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-+
+--R a b\|a
+--R Type: Expression(Integer)
+--E 803
+
+--S 804 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 804
+
+)clear all
+
+--S 805 of 1475
+t0:=(c+d*x^2)^(3/2)/(x^3*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 5 3
+--R b x + a x
+--R Type: Expression(Integer)
+--E 805
+
+--S 806 of 1475
+r0a:=-(b*c-a*d)^(3/2)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/_
+ (a^2*sqrt(b))+1/2*(2*b*c-3*a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))*_
+ sqrt(c)/a^2-1/2*c*sqrt(c+d*x^2)/(a*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 +-----------+ \|b \|d x + c
+--R (2a d - 2b c)x \|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 +-+ +-+ \|d x + c +-+ | 2
+--R (- 3a d + 2b c)x \|b \|c atanh(-----------) - a c\|b \|d x + c
+--R +-+
+--R \|c
+--R /
+--R 2 2 +-+
+--R 2a x \|b
+--R Type: Expression(Integer)
+--E 806
+
+--S 807 of 1475
+r0b:=-1/2*(c+d*x^2)^(3/2)/_
+ (a*x^2)-(b*c-a*d)^(3/2)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-_
+ a*d))/(a^2*sqrt(b))+1/2*(2*b*c-3*a*d)*atanh(sqrt(c+d*x^2)/_
+ sqrt(c))*sqrt(c)/a^2+1/2*d*sqrt(c+d*x^2)/a
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ | 2
+--R 2 +-----------+ \|b \|d x + c
+--R (2a d - 2b c)x \|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 +-+ +-+ \|d x + c +-+ | 2
+--R (- 3a d + 2b c)x \|b \|c atanh(-----------) - a c\|b \|d x + c
+--R +-+
+--R \|c
+--R /
+--R 2 2 +-+
+--R 2a x \|b
+--R Type: Expression(Integer)
+--E 807
+
+--S 808 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R +--------+
+--R 2 2 | 2
+--R (6a c d - 4b c )x \|d x + c
+--R +
+--R 2 4 2 2 +-+
+--R ((- 3a d + 2b c d)x + (- 6a c d + 4b c )x )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R 2 |- a d + b c +-+ | 2
+--R (2a d - 2b c)x |----------- \|c \|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 2 |- a d + b c
+--R ((- a d + b c d)x + (- 2a c d + 2b c )x ) |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R (a c d x + 2a c )\|d x + c + (- 2a c d x - 2a c )\|c
+--R /
+--R +--------+
+--R 2 2 +-+ | 2 2 4 2 2
+--R 4a x \|c \|d x + c - 2a d x - 4a c x
+--R ,
+--R
+--R +--------+
+--R 2 2 | 2
+--R (6a c d - 4b c )x \|d x + c
+--R +
+--R 2 4 2 2 +-+
+--R ((- 3a d + 2b c d)x + (- 6a c d + 4b c )x )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +---------+ +--------+
+--R 2 +-+ |a d - b c | 2
+--R (- 4a d + 4b c)x \|c |--------- \|d x + c
+--R \| b
+--R +
+--R +---------+
+--R 2 4 2 2 |a d - b c
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x ) |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R (a c d x + 2a c )\|d x + c + (- 2a c d x - 2a c )\|c
+--R /
+--R +--------+
+--R 2 2 +-+ | 2 2 4 2 2
+--R 4a x \|c \|d x + c - 2a d x - 4a c x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 808
+
+--S 809 of 1475
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +--------+
+--R 2 +-+ | 2
+--R (6a c d - 4b c )\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R ((- 3a d + 2b c d)x - 6a c d + 4b c )\|b \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R |- a d + b c +-+ +-+ | 2
+--R (2a d - 2b c) |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c +-+
+--R ((- a d + b c d)x - 2a c d + 2b c ) |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R (- 4a d + 4b c)\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+
+--R ((2a d - 2b c d)x + 4a c d - 4b c )\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R (6a c d - 4b c )\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R ((- 3a d + 2b c d)x - 6a c d + 4b c )\|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 2 2 +-+
+--R 4a \|b \|c \|d x + c + (- 2a d x - 4a c)\|b
+--R Type: Expression(Integer)
+--E 809
+
+--S 810 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 810
+
+--S 811 of 1475
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +--------+
+--R 2 +-+ | 2
+--R (6a c d - 4b c )\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R ((- 3a d + 2b c d)x - 6a c d + 4b c )\|b \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R (- 4a d + 4b c)\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+
+--R ((2a d - 2b c d)x + 4a c d - 4b c )\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R (6a c d - 4b c )\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R ((- 3a d + 2b c d)x - 6a c d + 4b c )\|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +---------+ +--------+
+--R +-+ +-+ |a d - b c | 2
+--R (- 4a d + 4b c)\|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R +---------+
+--R 2 2 2 +-+ |a d - b c
+--R ((2a d - 2b c d)x + 4a c d - 4b c )\|b |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 2 2 +-+
+--R 4a \|b \|c \|d x + c + (- 2a d x - 4a c)\|b
+--R Type: Expression(Integer)
+--E 811
+
+--S 812 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 812
+
+--S 813 of 1475
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +--------+
+--R 2 +-+ | 2
+--R (6a c d - 4b c )\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R ((- 3a d + 2b c d)x - 6a c d + 4b c )\|b \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R |- a d + b c +-+ +-+ | 2
+--R (2a d - 2b c) |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c +-+
+--R ((- a d + b c d)x - 2a c d + 2b c ) |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R (- 4a d + 4b c)\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+
+--R ((2a d - 2b c d)x + 4a c d - 4b c )\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R (6a c d - 4b c )\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R ((- 3a d + 2b c d)x - 6a c d + 4b c )\|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 2 2 +-+
+--R 4a \|b \|c \|d x + c + (- 2a d x - 4a c)\|b
+--R Type: Expression(Integer)
+--E 813
+
+--S 814 of 1475
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 814
+
+--S 815 of 1475
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +--------+
+--R 2 +-+ | 2
+--R (6a c d - 4b c )\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R ((- 3a d + 2b c d)x - 6a c d + 4b c )\|b \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R (- 4a d + 4b c)\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+
+--R ((2a d - 2b c d)x + 4a c d - 4b c )\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R (6a c d - 4b c )\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R ((- 3a d + 2b c d)x - 6a c d + 4b c )\|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +---------+ +--------+
+--R +-+ +-+ |a d - b c | 2
+--R (- 4a d + 4b c)\|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R +---------+
+--R 2 2 2 +-+ |a d - b c
+--R ((2a d - 2b c d)x + 4a c d - 4b c )\|b |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 2 2 +-+
+--R 4a \|b \|c \|d x + c + (- 2a d x - 4a c)\|b
+--R Type: Expression(Integer)
+--E 815
+
+--S 816 of 1475
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 816
+
+)clear all
+
+--S 817 of 1475
+t0:=(c+d*x^2)^(3/2)/(x^4*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 6 4
+--R b x + a x
+--R Type: Expression(Integer)
+--E 817
+
+--S 818 of 1475
+r0:=(b*c-a*d)^(3/2)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/_
+ a^(5/2)-1/3*c*sqrt(c+d*x^2)/(a*x^3)+1/3*(3*b*c-4*a*d)*sqrt(c+_
+ d*x^2)/(a^2*x)
+--R
+--R
+--R (2)
+--R +-----------+
+--R 3 +-----------+ x\|- a d + b c
+--R (- 3a d + 3b c)x \|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R ((- 4a d + 3b c)x - a c)\|a \|d x + c
+--R /
+--R 2 3 +-+
+--R 3a x \|a
+--R Type: Expression(Integer)
+--E 818
+
+--S 819 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+ +--------+
+--R 2 5 2 3 |a d - b c | 2
+--R ((3a d - 3b c d)x + (12a c d - 12b c )x ) |--------- \|d x + c
+--R \| a
+--R +
+--R +---------+
+--R 2 5 2 3 +-+ |a d - b c
+--R ((- 9a d + 9b c d)x + (- 12a c d + 12b c )x )\|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R ((24a d - 18b c d)x + (38a c d - 24b c )x + 8a c )\|c \|d x + c
+--R +
+--R 3 2 6 2 2 4
+--R (- 8a d + 6b c d )x + (- 42a c d + 30b c d)x
+--R +
+--R 2 3 2 3
+--R (- 42a c d + 24b c )x - 8a c
+--R /
+--R +--------+
+--R 2 5 2 3 | 2 2 5 2 3 +-+
+--R (6a d x + 24a c x )\|d x + c + (- 18a d x - 24a c x )\|c
+--R ,
+--R
+--R +-----------+
+--R 2 5 2 3 |- a d + b c
+--R ((3a d - 3b c d)x + (12a c d - 12b c )x ) |-----------
+--R \| a
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 5 2 3 |- a d + b c +-+
+--R ((- 9a d + 9b c d)x + (- 12a c d + 12b c )x ) |----------- \|c
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R 2 5 2 3 |- a d + b c
+--R ((- 3a d + 3b c d)x + (- 12a c d + 12b c )x ) |-----------
+--R \| a
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 5 2 3 |- a d + b c +-+
+--R ((9a d - 9b c d)x + (12a c d - 12b c )x ) |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R ((12a d - 9b c d)x + (19a c d - 12b c )x + 4a c )\|c \|d x + c
+--R +
+--R 3 2 6 2 2 4
+--R (- 4a d + 3b c d )x + (- 21a c d + 15b c d)x
+--R +
+--R 2 3 2 3
+--R (- 21a c d + 12b c )x - 4a c
+--R /
+--R +--------+
+--R 2 5 2 3 | 2 2 5 2 3 +-+
+--R (3a d x + 12a c x )\|d x + c + (- 9a d x - 12a c x )\|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 819
+
+--S 820 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-+ |a d - b c
+--R (a d - b c)\|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (2a d - 2b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 820
+
+--S 821 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 821
+
+--S 822 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R |- a d + b c +-+
+--R (a d - b c) |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c +-+ \|c
+--R (- a d + b c) |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (a d - b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 822
+
+--S 823 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 823
+
+)clear all
+
+--S 824 of 1475
+t0:=x^4*(c+d*x^2)^(5/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 8 6 2 4 | 2
+--R (d x + 2c d x + c x )\|d x + c
+--R (1) ----------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 824
+
+--S 825 of 1475
+r0:=1/8*d*x^5*(c+d*x^2)^(3/2)/b+a^(3/2)*(b*c-a*d)^(5/2)*atan(x*_
+ sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/b^5-1/128*(5*b^4*c^4+_
+ 40*a*b^3*c^3*d-240*a^2*b^2*c^2*d^2+320*a^3*b*c*d^3-128*a^4*d^4)*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))/(b^5*d^(3/2))+1/128*(5*b^3*c^3-_
+ 88*a*b^2*c^2*d+144*a^2*b*c*d^2-64*a^3*d^3)*x*sqrt(c+d*x^2)/_
+ (b^4*d)+1/192*(59*b^2*c^2-104*a*b*c*d+48*a^2*d^2)*x^3*sqrt(c+_
+ d*x^2)/b^3+1/48*d*(11*b*c-8*a*d)*x^5*sqrt(c+d*x^2)/b^2
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (384a d - 960a b c d + 720a b c d - 120a b c d - 15b c )
+--R *
+--R +-+
+--R x\|d
+--R atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 3 2 2 2 2 +-----------+ +-+ +-+
+--R (384a d - 768a b c d + 384a b c d)\|- a d + b c \|a \|d
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 4 3 7 3 3 4 2 5
+--R 48b d x + (- 64a b d + 136b c d )x
+--R +
+--R 2 2 3 3 2 4 2 3
+--R (96a b d - 208a b c d + 118b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3
+--R (- 192a b d + 432a b c d - 264a b c d + 15b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R 5 +-+
+--R 384b d\|d
+--R Type: Expression(Integer)
+--E 825
+
+--S 826 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 6 2 5 2 2 4 6
+--R (1536a d - 3072a b c d + 1536a b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 4
+--R (15360a c d - 30720a b c d + 15360a b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 2 3 3 3
+--R (36864a c d - 73728a b c d + 36864a b c d )x + 24576a c d
+--R +
+--R 2 4 2 2 5
+--R - 49152a b c d + 24576a b c d
+--R *
+--R +-----------+ +--------+
+--R +-+ +-+ | 2 | 2
+--R \|c \|d \|a d - a b c \|d x + c
+--R +
+--R 3 7 2 6 2 2 5 8
+--R (- 192a d + 384a b c d - 192a b c d )x
+--R +
+--R 3 6 2 2 5 2 3 4 6
+--R (- 6144a c d + 12288a b c d - 6144a b c d )x
+--R +
+--R 3 2 5 2 3 4 2 4 3 4
+--R (- 30720a c d + 61440a b c d - 30720a b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 2 3 4 3
+--R (- 49152a c d + 98304a b c d - 49152a b c d )x - 24576a c d
+--R +
+--R 2 5 2 2 6
+--R 49152a b c d - 24576a b c d
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (2d x + 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (- 4d x - 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R 3072a d - 7680a b c d + 5760a b c d - 960a b c d
+--R +
+--R 4 4 3
+--R - 120b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3
+--R 30720a c d - 76800a b c d + 57600a b c d - 9600a b c d
+--R +
+--R 4 5 2
+--R - 1200b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3
+--R 73728a c d - 184320a b c d + 138240a b c d
+--R +
+--R 3 5 2 4 6
+--R - 23040a b c d - 2880b c d
+--R *
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+--R 4 7
+--R - 1920b c
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+--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 8
+--R (- 384a d + 960a b c d - 720a b c d + 120a b c d + 15b c d )x
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+--R x
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+--R 4 2 6 3 3 5 2 2 4 4 3 5 3
+--R - 61440a c d + 153600a b c d - 115200a b c d + 19200a b c d
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+--R +
+--R 4 7 15 3 7 4 6 13
+--R - 48b d x + (64a b d - 1672b c d )x
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+--R 2 2 7 3 6 4 2 5 11
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+--R 3 7 2 2 6 3 2 5 4 3 4 9
+--R (192a b d - 3504a b c d + 17160a b c d - 37839b c d )x
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+--R (6144a b c d - 29184a b c d + 58112a b c d - 60320b c d )x
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+--R (30720a b c d - 93696a b c d + 103680a b c d - 50016b c d )x
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+--R (49152a b c d - 122880a b c d + 94208a b c d - 18944b c d)x
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+--R 3 4 3 2 2 5 2 3 6 4 7
+--R (24576a b c d - 55296a b c d + 33792a b c d - 1920b c )x
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+--R 4 7 15 3 7 4 6 13
+--R 384b d x + (- 512a b d + 5312b c d )x
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+--R 2 2 7 3 6 4 2 5 11
+--R (768a b d - 7296a b c d + 25968b c d )x
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+--R 3 7 2 2 6 3 2 5 4 3 4 9
+--R (- 1536a b d + 11904a b c d - 37824a b c d + 62856b c d )x
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+--R 3 6 2 2 2 5 3 3 4 4 4 3 7
+--R (- 16896a b c d + 64128a b c d - 100288a b c d + 83080b c d )x
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+--R 3 2 5 2 2 3 4 3 4 3 4 5 2 5
+--R (- 52224a b c d + 148224a b c d - 146560a b c d + 59248b c d )x
+--R +
+--R 3 3 4 2 2 4 3 3 5 2 4 6 3
+--R (- 61440a b c d + 150528a b c d - 111104a b c d + 19904b c d)x
+--R +
+--R 3 4 3 2 2 5 2 3 6 4 7
+--R (- 24576a b c d + 55296a b c d - 33792a b c d + 1920b c )x
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+--R (3072b d x + 30720b c d x + 73728b c d x + 49152b c d)\|c \|d
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+--R - 384b d x - 12288b c d x - 61440b c d x - 98304b c d x
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+--R 4 2 5 3 3 4 2 2 4 3
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+--R 49152a c d - 122880a b c d + 92160a b c d - 15360a b c d
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+--R - 1920b c
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+--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 8
+--R (- 384a d + 960a b c d - 720a b c d + 120a b c d + 15b c d )x
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+--R x
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+--R 4 2 6 3 3 5 2 2 4 4 3 5 3
+--R - 61440a c d + 153600a b c d - 115200a b c d + 19200a b c d
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+--R 4 3 5 3 4 4 2 2 5 3 3 6 2
+--R - 98304a c d + 245760a b c d - 184320a b c d + 30720a b c d
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+--R 4 4 4 3 5 3 2 2 6 2 3 7
+--R - 49152a c d + 122880a b c d - 92160a b c d + 15360a b c d
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+--R 3 6 2 5 2 2 4 6
+--R (- 3072a d + 6144a b c d - 3072a b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 4
+--R (- 30720a c d + 61440a b c d - 30720a b c d )x
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+--R - 49152a c d + 98304a b c d - 49152a b c d
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+--R (384a d - 768a b c d + 384a b c d )x
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+--R 3 3 4 2 4 3 2 5 2 2 3 4 3
+--R (98304a c d - 196608a b c d + 98304a b c d )x + 49152a c d
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+--R - 98304a b c d + 49152a b c d
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+--R (73728a c d - 147456a b c d + 73728a b c d )x + 49152a c d
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+--R - 98304a b c d + 49152a b c d
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+--R +
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+--R - 48b d x + (64a b d - 1672b c d )x
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+--R (6144a b c d - 29184a b c d + 58112a b c d - 60320b c d )x
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+--R (49152a b c d - 122880a b c d + 94208a b c d - 18944b c d)x
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+--R 3 4 3 2 2 5 2 3 6 4 7
+--R (24576a b c d - 55296a b c d + 33792a b c d - 1920b c )x
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+--R 384b d x + (- 512a b d + 5312b c d )x
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+--R 2 2 7 3 6 4 2 5 11
+--R (768a b d - 7296a b c d + 25968b c d )x
+--R +
+--R 3 7 2 2 6 3 2 5 4 3 4 9
+--R (- 1536a b d + 11904a b c d - 37824a b c d + 62856b c d )x
+--R +
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+--R (- 16896a b c d + 64128a b c d - 100288a b c d + 83080b c d )x
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+--R 3 2 5 2 2 3 4 3 4 3 4 5 2 5
+--R (- 52224a b c d + 148224a b c d - 146560a b c d + 59248b c d )x
+--R +
+--R 3 3 4 2 2 4 3 3 5 2 4 6 3
+--R (- 61440a b c d + 150528a b c d - 111104a b c d + 19904b c d)x
+--R +
+--R 3 4 3 2 2 5 2 3 6 4 7
+--R (- 24576a b c d + 55296a b c d - 33792a b c d + 1920b c )x
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+--R (3072b d x + 30720b c d x + 73728b c d x + 49152b c d)\|c \|d
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+--R - 384b d x - 12288b c d x - 61440b c d x - 98304b c d x
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+--R - 49152b c d
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+--R (36864a c d - 73728a b c d + 36864a b c d )x + 24576a c d
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+--R - 49152a b c d + 24576a b c d
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+--R (- 192a d + 384a b c d - 192a b c d )x
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+--R (- 6144a c d + 12288a b c d - 6144a b c d )x
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+--R 3 3 4 2 4 3 2 5 2 2 3 4 3
+--R (- 49152a c d + 98304a b c d - 49152a b c d )x - 24576a c d
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+--R 2 5 2 2 6
+--R 49152a b c d - 24576a b c d
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+--R ((4a d - 2b c)x + 2a c)\|c
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+--R (- 4d x - 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
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+--R 6144a d - 15360a b c d + 11520a b c d - 1920a b c d
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+--R - 240b c d
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+--R x
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+--R 4 6 3 2 5 2 2 3 4
+--R 61440a c d - 153600a b c d + 115200a b c d
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+--R 147456a c d - 368640a b c d + 276480a b c d
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+--R 98304a c d - 245760a b c d + 184320a b c d - 30720a b c d
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+--R - 3840b c
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+--R - 768a d + 1920a b c d - 1440a b c d + 240a b c d
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+--R x
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+--R - 24576a c d + 61440a b c d - 46080a b c d + 7680a b c d
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+--R 3840b c
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+--R - 48b d x + (64a b d - 1672b c d )x
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+--R (6144a b c d - 29184a b c d + 58112a b c d - 60320b c d )x
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+--R (30720a b c d - 93696a b c d + 103680a b c d - 50016b c d )x
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+--R 3 3 4 2 2 4 3 3 5 2 4 6 3
+--R (49152a b c d - 122880a b c d + 94208a b c d - 18944b c d)x
+--R +
+--R 3 4 3 2 2 5 2 3 6 4 7
+--R (24576a b c d - 55296a b c d + 33792a b c d - 1920b c )x
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+--R +
+--R 4 7 15 3 7 4 6 13
+--R 384b d x + (- 512a b d + 5312b c d )x
+--R +
+--R 2 2 7 3 6 4 2 5 11
+--R (768a b d - 7296a b c d + 25968b c d )x
+--R +
+--R 3 7 2 2 6 3 2 5 4 3 4 9
+--R (- 1536a b d + 11904a b c d - 37824a b c d + 62856b c d )x
+--R +
+--R 3 6 2 2 2 5 3 3 4 4 4 3 7
+--R (- 16896a b c d + 64128a b c d - 100288a b c d + 83080b c d )x
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+--R 3 2 5 2 2 3 4 3 4 3 4 5 2 5
+--R (- 52224a b c d + 148224a b c d - 146560a b c d + 59248b c d )x
+--R +
+--R 3 3 4 2 2 4 3 3 5 2 4 6 3
+--R (- 61440a b c d + 150528a b c d - 111104a b c d + 19904b c d)x
+--R +
+--R 3 4 3 2 2 5 2 3 6 4 7
+--R (- 24576a b c d + 55296a b c d - 33792a b c d + 1920b c )x
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+--R +--------+
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+--R - 384b d x - 12288b c d x - 61440b c d x - 98304b c d x
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+--R - 49152b c d
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+--R
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+--R 6144a d - 15360a b c d + 11520a b c d - 1920a b c d
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+--R x
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+--R 4 6 3 2 5 2 2 3 4
+--R 61440a c d - 153600a b c d + 115200a b c d
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+--R 3 4 3 4 5 2
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+--R 4
+--R x
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+--R 4 2 5 3 3 4 2 2 4 3
+--R 147456a c d - 368640a b c d + 276480a b c d
+--R +
+--R 3 5 2 4 6
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+--R 2
+--R x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6
+--R 98304a c d - 245760a b c d + 184320a b c d - 30720a b c d
+--R +
+--R 4 7
+--R - 3840b c
+--R *
+--R +--------+
+--R +-+ | 2
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+--R 4 8 3 7 2 2 2 6 3 3 5
+--R - 768a d + 1920a b c d - 1440a b c d + 240a b c d
+--R +
+--R 4 4 4
+--R 30b c d
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+--R 8
+--R x
+--R +
+--R 4 7 3 2 6 2 2 3 5 3 4 4
+--R - 24576a c d + 61440a b c d - 46080a b c d + 7680a b c d
+--R +
+--R 4 5 3
+--R 960b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 2 6 3 3 5 2 2 4 4
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+--R 3840b c
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+--R \|- d \|d x + c - \|- d \|c
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+--R d x
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+--R (- 73728a c d + 147456a b c d - 73728a b c d )x
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+--R - 49152a c d + 98304a b c d - 49152a b c d
+--R *
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+--R (384a d - 768a b c d + 384a b c d )x
+--R +
+--R 3 6 2 2 5 2 3 4 6
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+--R (61440a c d - 122880a b c d + 61440a b c d )x
+--R +
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+--R (98304a c d - 196608a b c d + 98304a b c d )x + 49152a c d
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+--R - 98304a b c d + 49152a b c d
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+--R *
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+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
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+--R (3072a d - 6144a b c d + 3072a b c d )x
+--R +
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+--R (6144a b c d - 29184a b c d + 58112a b c d - 60320b c d )x
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+--R (49152a b c d - 122880a b c d + 94208a b c d - 18944b c d)x
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+--R (24576a b c d - 55296a b c d + 33792a b c d - 1920b c )x
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+--R 384b d x + (- 512a b d + 5312b c d )x
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+--R (- 16896a b c d + 64128a b c d - 100288a b c d + 83080b c d )x
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+--R +
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+--R (- 61440a b c d + 150528a b c d - 111104a b c d + 19904b c d)x
+--R +
+--R 3 4 3 2 2 5 2 3 6 4 7
+--R (- 24576a b c d + 55296a b c d - 33792a b c d + 1920b c )x
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+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R 5 4 6 5 3 4 5 2 2 2 5 3 +---+ +-+
+--R (3072b d x + 30720b c d x + 73728b c d x + 49152b c d)\|- d \|c
+--R *
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+--R \|d x + c
+--R +
+--R 5 5 8 5 4 6 5 2 3 4 5 3 2 2
+--R - 384b d x - 12288b c d x - 61440b c d x - 98304b c d x
+--R +
+--R 5 4
+--R - 49152b c d
+--R *
+--R +---+
+--R \|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 826
+
+--S 827 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R 3 3 2 2 2 2 +-+ | 2
+--R (64a d - 128a b c d + 64a b c d)\|d \|a d - a b c
+--R *
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+--R +-----------+
+--R 3 | 2 2 +-+
+--R ((2d x + 4c x)\|a d - a b c + ((4a d - 2b c)x + 2a c)\|c )
+--R *
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+--R | 2
+--R \|d x + c
+--R +
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+--R 3 +-+ | 2 2 4
+--R (- 4d x - 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
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+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (128a d - 320a b c d + 240a b c d - 40a b c d - 5b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 128a d + 320a b c d - 240a b c d + 40a b c d + 5b c )
+--R *
+--R +-+
+--R x\|d
+--R atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 3 2 2 2 2 +-----------+ +-+ +-+
+--R (- 128a d + 256a b c d - 128a b c d)\|- a d + b c \|a \|d
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 5 +-+
+--R 128b d\|d
+--R Type: Expression(Integer)
+--E 827
+
+--S 828 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 828
+
+--S 829 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (128a d - 320a b c d + 240a b c d - 40a b c d - 5b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 128a d + 320a b c d - 240a b c d + 40a b c d + 5b c )
+--R *
+--R +-+
+--R x\|d
+--R atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-------------+
+--R 3 3 2 2 2 2 | 2 +-+
+--R (- 128a d + 256a b c d - 128a b c d)\|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R 3 3 2 2 2 2 | 2 +-+
+--R (128a d - 256a b c d + 128a b c d)\|- a d + a b c \|d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R 3 3 2 2 2 2 +-----------+ +-+ +-+
+--R (- 128a d + 256a b c d - 128a b c d)\|- a d + b c \|a \|d
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 5 +-+
+--R 128b d\|d
+--R Type: Expression(Integer)
+--E 829
+
+--S 830 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 830
+
+)clear all
+
+--S 831 of 1475
+t0:=x^3*(c+d*x^2)^(5/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (d x + 2c d x + c x )\|d x + c
+--R (1) ----------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 831
+
+--S 832 of 1475
+r0:=-1/3*a*(b*c-a*d)*(c+d*x^2)^(3/2)/b^3-1/5*a*(c+d*x^2)^(5/2)/b^2+_
+ 1/7*(c+d*x^2)^(7/2)/(b*d)+a*(b*c-a*d)^(5/2)*atanh(sqrt(b)*_
+ sqrt(c+d*x^2)/sqrt(b*c-a*d))/b^(9/2)-a*(b*c-a*d)^2*sqrt(c+d*x^2)/b^4
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 3 3 2 2 2 2 +-----------+ \|b \|d x + c
+--R (105a d - 210a b c d + 105a b c d)\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 3 3 6 2 3 3 2 4
+--R 15b d x + (- 21a b d + 45b c d )x
+--R +
+--R 2 3 2 2 3 2 2 3 3 2 2
+--R (35a b d - 77a b c d + 45b c d)x - 105a d + 245a b c d
+--R +
+--R 2 2 3 3
+--R - 161a b c d + 15b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R /
+--R 4 +-+
+--R 105b d\|b
+--R Type: Expression(Integer)
+--E 832
+
+--S 833 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 5 2 4 2 2 3 6
+--R (105a d - 210a b c d + 105a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 4
+--R (2520a c d - 5040a b c d + 2520a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4 2 3 3 2
+--R (8400a c d - 16800a b c d + 8400a b c d)x + 6720a c d
+--R +
+--R 2 4 2 5
+--R - 13440a b c d + 6720a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| b
+--R +
+--R 3 5 2 2 4 2 3 3 6
+--R (- 735a c d + 1470a b c d - 735a b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 4
+--R (- 5880a c d + 11760a b c d - 5880a b c d )x
+--R +
+--R 3 3 3 2 4 2 2 5 2 3 4 2
+--R (- 11760a c d + 23520a b c d - 11760a b c d)x - 6720a c d
+--R +
+--R 2 5 2 6
+--R 13440a b c d - 6720a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+
+--R ((2a b d + 4b c)x + 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
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+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (- 2b c d x + (- 6a b c d - 4b c )x - 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
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+--R \|c
+--R +
+--R 3 5 12 2 5 3 2 4 10
+--R - 210b c d x + (294a b c d - 2310b c d )x
+--R +
+--R 2 5 2 2 4 3 3 3 8
+--R (- 490a b c d + 3430a b c d - 9030b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (1260a c d - 6860a b c d + 15260a b c d - 17220b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (6720a c d - 23520a b c d + 30240a b c d - 16800b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (6720a c d - 20160a b c d + 20160a b c d - 6720b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 6 14 2 6 3 5 12
+--R 30b d x + (- 42a b d + 840b c d )x
+--R +
+--R 2 6 2 5 3 2 4 10
+--R (70a b d - 1204a b c d + 5460b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 8
+--R (- 210a d + 2240a b c d - 8540a b c d + 15960b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (- 3780a c d + 16100a b c d - 27860a b c d + 24780b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (- 10080a c d + 33600a b c d - 40320a b c d + 20160b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (- 6720a c d + 20160a b c d - 20160a b c d + 6720b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 3 6 4 2 4 4 2 2 4 3 +-+ | 2
+--R (210b d x + 5040b c d x + 16800b c d x + 13440b c )\|c \|d x + c
+--R +
+--R 4 3 6 4 2 2 4 4 3 2 4 4
+--R - 1470b c d x - 11760b c d x - 23520b c d x - 13440b c
+--R ,
+--R
+--R 3 5 2 4 2 2 3 6
+--R (- 105a d + 210a b c d - 105a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 4
+--R (- 2520a c d + 5040a b c d - 2520a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4 2 3 3 2
+--R (- 8400a c d + 16800a b c d - 8400a b c d)x - 6720a c d
+--R +
+--R 2 4 2 5
+--R 13440a b c d - 6720a b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 3 5 2 2 4 2 3 3 6
+--R (735a c d - 1470a b c d + 735a b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 4
+--R (5880a c d - 11760a b c d + 5880a b c d )x
+--R +
+--R 3 3 3 2 4 2 2 5 2 3 4 2
+--R (11760a c d - 23520a b c d + 11760a b c d)x + 6720a c d
+--R +
+--R 2 5 2 6
+--R - 13440a b c d + 6720a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R 3 5 12 2 5 3 2 4 10
+--R - 105b c d x + (147a b c d - 1155b c d )x
+--R +
+--R 2 5 2 2 4 3 3 3 8
+--R (- 245a b c d + 1715a b c d - 4515b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (630a c d - 3430a b c d + 7630a b c d - 8610b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (3360a c d - 11760a b c d + 15120a b c d - 8400b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (3360a c d - 10080a b c d + 10080a b c d - 3360b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 6 14 2 6 3 5 12
+--R 15b d x + (- 21a b d + 420b c d )x
+--R +
+--R 2 6 2 5 3 2 4 10
+--R (35a b d - 602a b c d + 2730b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 8
+--R (- 105a d + 1120a b c d - 4270a b c d + 7980b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (- 1890a c d + 8050a b c d - 13930a b c d + 12390b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (- 5040a c d + 16800a b c d - 20160a b c d + 10080b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (- 3360a c d + 10080a b c d - 10080a b c d + 3360b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 3 6 4 2 4 4 2 2 4 3 +-+ | 2
+--R (105b d x + 2520b c d x + 8400b c d x + 6720b c )\|c \|d x + c
+--R +
+--R 4 3 6 4 2 2 4 4 3 2 4 4
+--R - 735b c d x - 5880b c d x - 11760b c d x - 6720b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 833
+
+--S 834 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 6 2 5 2 2 4 6
+--R (105a d - 210a b c d + 105a b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 4
+--R (2520a c d - 5040a b c d + 2520a b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 2 3 3 3
+--R (8400a c d - 16800a b c d + 8400a b c d )x + 6720a c d
+--R +
+--R 2 4 2 2 5
+--R - 13440a b c d + 6720a b c d
+--R *
+--R +-----------+ +--------+
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+--R 13440a b c d - 6720a b c d
+--R *
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+--R |----------- \|b
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+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2
+--R (23520a c d - 54880a b c d + 36064a b c d - 3360b c d)x
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+--R 13440a c d - 31360a b c d + 20608a b c d - 1920b c
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+--R (210b d x + 5040b c d x + 16800b c d x + 13440b c d)\|b \|c
+--R *
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+--R +
+--R 4 4 6 4 2 3 4 4 3 2 2 4 4 +-+
+--R (- 1470b c d x - 11760b c d x - 23520b c d x - 13440b c d)\|b
+--R Type: Expression(Integer)
+--E 834
+
+--S 835 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 835
+
+--S 836 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 3 6 2 5 2 2 4 6
+--R (- 105a d + 210a b c d - 105a b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 4
+--R (- 2520a c d + 5040a b c d - 2520a b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 2 3 3 3
+--R (- 8400a c d + 16800a b c d - 8400a b c d )x - 6720a c d
+--R +
+--R 2 4 2 2 5
+--R 13440a b c d - 6720a b c d
+--R *
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+--R \|- a d + b c \|c \|d x + c
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+--R (735a c d - 1470a b c d + 735a b c d )x
+--R +
+--R 3 2 5 2 3 4 2 4 3 4
+--R (5880a c d - 11760a b c d + 5880a b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 2 3 4 3
+--R (11760a c d - 23520a b c d + 11760a b c d )x + 6720a c d
+--R +
+--R 2 5 2 2 6
+--R - 13440a b c d + 6720a b c d
+--R *
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+--R *
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+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
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+--R (- 105a d + 210a b c d - 105a b c d )x
+--R +
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+--R +
+--R 3 2 4 2 3 3 2 4 2 2 3 3 3
+--R (- 8400a c d + 16800a b c d - 8400a b c d )x - 6720a c d
+--R +
+--R 2 4 2 2 5
+--R 13440a b c d - 6720a b c d
+--R *
+--R +---------+ +--------+
+--R +-+ +-+ |a d - b c | 2
+--R \|b \|c |--------- \|d x + c
+--R \| b
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+--R +
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+--R (5880a c d - 11760a b c d + 5880a b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 2 3 4 3
+--R (11760a c d - 23520a b c d + 11760a b c d )x + 6720a c d
+--R +
+--R 2 5 2 2 6
+--R - 13440a b c d + 6720a b c d
+--R *
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+--R +-+ |a d - b c
+--R \|b |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R 3 6 2 2 5 2 3 4 3 4 3 6
+--R (- 105a c d + 245a b c d - 161a b c d + 15b c d )x
+--R +
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+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2
+--R (- 8400a c d + 19600a b c d - 12880a b c d + 1200b c d)x
+--R +
+--R 3 4 3 2 5 2 2 6 3 7
+--R - 6720a c d + 15680a b c d - 10304a b c d + 960b c
+--R *
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+--R +-+ | 2
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+--R +
+--R 3 6 2 2 5 2 3 4 3 4 3 6
+--R (735a c d - 1715a b c d + 1127a b c d - 105b c d )x
+--R +
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (5880a c d - 13720a b c d + 9016a b c d - 840b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2
+--R (11760a c d - 27440a b c d + 18032a b c d - 1680b c d)x
+--R +
+--R 3 4 3 2 5 2 2 6 3 7
+--R 6720a c d - 15680a b c d + 10304a b c d - 960b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 4 4 6 4 3 4 4 2 2 2 4 3 +-+ +-+ | 2
+--R (105b d x + 2520b c d x + 8400b c d x + 6720b c d)\|b \|c \|d x + c
+--R +
+--R 4 4 6 4 2 3 4 4 3 2 2 4 4 +-+
+--R (- 735b c d x - 5880b c d x - 11760b c d x - 6720b c d)\|b
+--R Type: Expression(Integer)
+--E 836
+
+--S 837 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 837
+
+)clear all
+
+--S 838 of 1475
+t0:=x^2*(c+d*x^2)^(5/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 6 4 2 2 | 2
+--R (d x + 2c d x + c x )\|d x + c
+--R (1) ----------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 838
+
+--S 839 of 1475
+r0:=1/6*d*x^3*(c+d*x^2)^(3/2)/b-(b*c-a*d)^(5/2)*atan(x*sqrt(b*c-a*d)/_
+ (sqrt(a)*sqrt(c+d*x^2)))*sqrt(a)/b^4+1/16*(5*b^3*c^3-30*a*b^2*_
+ c^2*d+40*a^2*b*c*d^2-16*a^3*d^3)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/_
+ (b^4*sqrt(d))+1/16*(11*b^2*c^2-18*a*b*c*d+8*a^2*d^2)*x*sqrt(c+_
+ d*x^2)/b^3+1/8*d*(3*b*c-2*a*d)*x^3*sqrt(c+d*x^2)/b^2
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|d
+--R (- 48a d + 120a b c d - 90a b c d + 15b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 2 +-----------+ +-+ +-+
+--R (- 48a d + 96a b c d - 48b c )\|- a d + b c \|a \|d
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 3 2 5 2 2 3 3 2 2 2 3 2
+--R (8b d x + (- 12a b d + 26b c d)x + (24a b d - 54a b c d + 33b c )x)
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R 4 +-+
+--R 48b \|d
+--R Type: Expression(Integer)
+--E 839
+
+--S 840 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (288a d - 720a b c d + 540a b c d - 90b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2
+--R (1536a c d - 3840a b c d + 2880a b c d - 480b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5
+--R 1536a c d - 3840a b c d + 2880a b c d - 480b c
+--R *
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+--R \|c \|d x + c
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 6
+--R (- 48a d + 120a b c d - 90a b c d + 15b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (- 864a c d + 2160a b c d - 1620a b c d + 270b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2
+--R (- 2304a c d + 5760a b c d - 4320a b c d + 720b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6
+--R - 1536a c d + 3840a b c d - 2880a b c d + 480b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 4 3 2 2 2 4
+--R (144a d - 288a b c d + 144b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2
+--R (768a c d - 1536a b c d + 768b c d)x + 768a c d
+--R +
+--R 3 2 4
+--R - 1536a b c d + 768b c
+--R *
+--R +-----------+ +--------+
+--R +-+ +-+ | 2 | 2
+--R \|c \|d \|a d - a b c \|d x + c
+--R +
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+--R (- 24a d + 48a b c d - 24b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
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+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (- 1152a c d + 2304a b c d - 1152b c d)x - 768a c d
+--R +
+--R 4 2 5
+--R 1536a b c d - 768b c
+--R *
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+--R +-+ | 2
+--R \|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (- 2d x - 4c x)\|a d - a b c
+--R +
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+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
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+--R +
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+--R 3 +-+ | 2 2 4
+--R (4d x + 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
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+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
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+--R - 8b d x + (12a b d - 170b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (- 24a b d + 270a b c d - 885b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (- 432a b c d + 1548a b c d - 2098b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (- 1152a b c d + 2976a b c d - 2416b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (- 768a b c d + 1728a b c d - 1056b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R 48b d x + (- 72a b d + 460b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (144a b d - 780a b c d + 1698b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (912a b c d - 2820a b c d + 3174b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (1536a b c d - 3840a b c d + 2944b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (768a b c d - 1728a b c d + 1056b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 4 2 4 4 2 4 2 +-+ +-+ | 2
+--R (288b d x + 1536b c d x + 1536b c )\|c \|d \|d x + c
+--R +
+--R 4 3 6 4 2 4 4 2 2 4 3 +-+
+--R (- 48b d x - 864b c d x - 2304b c d x - 1536b c )\|d
+--R ,
+--R
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (288a d - 720a b c d + 540a b c d - 90b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2
+--R (1536a c d - 3840a b c d + 2880a b c d - 480b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5
+--R 1536a c d - 3840a b c d + 2880a b c d - 480b c
+--R *
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+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 6
+--R (- 48a d + 120a b c d - 90a b c d + 15b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (- 864a c d + 2160a b c d - 1620a b c d + 270b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2
+--R (- 2304a c d + 5760a b c d - 4320a b c d + 720b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6
+--R - 1536a c d + 3840a b c d - 2880a b c d + 480b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 4 3 2 2 2 4
+--R (288a d - 576a b c d + 288b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2
+--R (1536a c d - 3072a b c d + 1536b c d)x + 1536a c d
+--R +
+--R 3 2 4
+--R - 3072a b c d + 1536b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ +-+ | 2
+--R \|- a d + a b c \|c \|d \|d x + c
+--R +
+--R 2 5 4 2 2 3 6
+--R (- 48a d + 96a b c d - 48b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 864a c d + 1728a b c d - 864b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (- 2304a c d + 4608a b c d - 2304b c d)x - 1536a c d
+--R +
+--R 4 2 5
+--R 3072a b c d - 1536b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 288a d + 576a b c d - 288b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2
+--R (- 1536a c d + 3072a b c d - 1536b c d)x - 1536a c d
+--R +
+--R 3 2 4
+--R 3072a b c d - 1536b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ +-+ | 2
+--R \|- a d + a b c \|c \|d \|d x + c
+--R +
+--R 2 5 4 2 2 3 6
+--R (48a d - 96a b c d + 48b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (864a c d - 1728a b c d + 864b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (2304a c d - 4608a b c d + 2304b c d)x + 1536a c d
+--R +
+--R 4 2 5
+--R - 3072a b c d + 1536b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R - 8b d x + (12a b d - 170b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (- 24a b d + 270a b c d - 885b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (- 432a b c d + 1548a b c d - 2098b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (- 1152a b c d + 2976a b c d - 2416b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (- 768a b c d + 1728a b c d - 1056b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R 48b d x + (- 72a b d + 460b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (144a b d - 780a b c d + 1698b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (912a b c d - 2820a b c d + 3174b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (1536a b c d - 3840a b c d + 2944b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (768a b c d - 1728a b c d + 1056b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 4 2 4 4 2 4 2 +-+ +-+ | 2
+--R (288b d x + 1536b c d x + 1536b c )\|c \|d \|d x + c
+--R +
+--R 4 3 6 4 2 4 4 2 2 4 3 +-+
+--R (- 48b d x - 864b c d x - 2304b c d x - 1536b c )\|d
+--R ,
+--R
+--R 2 4 3 2 2 2 4
+--R (144a d - 288a b c d + 144b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2
+--R (768a c d - 1536a b c d + 768b c d)x + 768a c d
+--R +
+--R 3 2 4
+--R - 1536a b c d + 768b c
+--R *
+--R +-----------+ +--------+
+--R +---+ +-+ | 2 | 2
+--R \|- d \|c \|a d - a b c \|d x + c
+--R +
+--R 2 5 4 2 2 3 6
+--R (- 24a d + 48a b c d - 24b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 432a c d + 864a b c d - 432b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (- 1152a c d + 2304a b c d - 1152b c d)x - 768a c d
+--R +
+--R 4 2 5
+--R 1536a b c d - 768b c
+--R *
+--R +-----------+
+--R +---+ | 2
+--R \|- d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (- 2d x - 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (4d x + 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 576a d + 1440a b c d - 1080a b c d + 180b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2
+--R (- 3072a c d + 7680a b c d - 5760a b c d + 960b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5
+--R - 3072a c d + 7680a b c d - 5760a b c d + 960b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 6
+--R (96a d - 240a b c d + 180a b c d - 30b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (1728a c d - 4320a b c d + 3240a b c d - 540b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2
+--R (4608a c d - 11520a b c d + 8640a b c d - 1440b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6
+--R 3072a c d - 7680a b c d + 5760a b c d - 960b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 3 5 11 2 5 3 4 9
+--R - 8b d x + (12a b d - 170b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (- 24a b d + 270a b c d - 885b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (- 432a b c d + 1548a b c d - 2098b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (- 1152a b c d + 2976a b c d - 2416b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (- 768a b c d + 1728a b c d - 1056b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R 48b d x + (- 72a b d + 460b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (144a b d - 780a b c d + 1698b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (912a b c d - 2820a b c d + 3174b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (1536a b c d - 3840a b c d + 2944b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (768a b c d - 1728a b c d + 1056b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 4 2 4 4 2 4 2 +---+ +-+ | 2
+--R (288b d x + 1536b c d x + 1536b c )\|- d \|c \|d x + c
+--R +
+--R 4 3 6 4 2 4 4 2 2 4 3 +---+
+--R (- 48b d x - 864b c d x - 2304b c d x - 1536b c )\|- d
+--R ,
+--R
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 576a d + 1440a b c d - 1080a b c d + 180b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2
+--R (- 3072a c d + 7680a b c d - 5760a b c d + 960b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5
+--R - 3072a c d + 7680a b c d - 5760a b c d + 960b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 6
+--R (96a d - 240a b c d + 180a b c d - 30b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (1728a c d - 4320a b c d + 3240a b c d - 540b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2
+--R (4608a c d - 11520a b c d + 8640a b c d - 1440b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6
+--R 3072a c d - 7680a b c d + 5760a b c d - 960b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 4 3 2 2 2 4
+--R (288a d - 576a b c d + 288b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2
+--R (1536a c d - 3072a b c d + 1536b c d)x + 1536a c d
+--R +
+--R 3 2 4
+--R - 3072a b c d + 1536b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +---+ +-+ | 2
+--R \|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R 2 5 4 2 2 3 6
+--R (- 48a d + 96a b c d - 48b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 864a c d + 1728a b c d - 864b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (- 2304a c d + 4608a b c d - 2304b c d)x - 1536a c d
+--R +
+--R 4 2 5
+--R 3072a b c d - 1536b c
+--R *
+--R +-------------+
+--R | 2 +---+
+--R \|- a d + a b c \|- d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 288a d + 576a b c d - 288b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2
+--R (- 1536a c d + 3072a b c d - 1536b c d)x - 1536a c d
+--R +
+--R 3 2 4
+--R 3072a b c d - 1536b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +---+ +-+ | 2
+--R \|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R 2 5 4 2 2 3 6
+--R (48a d - 96a b c d + 48b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (864a c d - 1728a b c d + 864b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (2304a c d - 4608a b c d + 2304b c d)x + 1536a c d
+--R +
+--R 4 2 5
+--R - 3072a b c d + 1536b c
+--R *
+--R +-------------+
+--R | 2 +---+
+--R \|- a d + a b c \|- d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R - 8b d x + (12a b d - 170b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (- 24a b d + 270a b c d - 885b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (- 432a b c d + 1548a b c d - 2098b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (- 1152a b c d + 2976a b c d - 2416b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (- 768a b c d + 1728a b c d - 1056b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R 48b d x + (- 72a b d + 460b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (144a b d - 780a b c d + 1698b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (912a b c d - 2820a b c d + 3174b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (1536a b c d - 3840a b c d + 2944b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (768a b c d - 1728a b c d + 1056b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 4 2 4 4 2 4 2 +---+ +-+ | 2
+--R (288b d x + 1536b c d x + 1536b c )\|- d \|c \|d x + c
+--R +
+--R 4 3 6 4 2 4 4 2 2 4 3 +---+
+--R (- 48b d x - 864b c d x - 2304b c d x - 1536b c )\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 840
+
+--S 841 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (16a d - 40a b c d + 30a b c d - 5b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-+ | 2
+--R (8a d - 16a b c d + 8b c )\|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (- 2d x - 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (4d x + 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|d
+--R (16a d - 40a b c d + 30a b c d - 5b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ +-+ +-+ x\|- a d + b c
+--R (16a d - 32a b c d + 16b c )\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 4 +-+
+--R 16b \|d
+--R Type: Expression(Integer)
+--E 841
+
+--S 842 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 842
+
+--S 843 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 3 3 2 2 2 2 3 3
+--R (16a d - 40a b c d + 30a b c d - 5b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|d
+--R (16a d - 40a b c d + 30a b c d - 5b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-------------+
+--R 2 2 2 2 | 2 +-+
+--R (16a d - 32a b c d + 16b c )\|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R 2 2 2 2 | 2 +-+
+--R (- 16a d + 32a b c d - 16b c )\|- a d + a b c \|d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ +-+ +-+ x\|- a d + b c
+--R (16a d - 32a b c d + 16b c )\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 4 +-+
+--R 16b \|d
+--R Type: Expression(Integer)
+--E 843
+
+--S 844 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 844
+
+)clear all
+
+--S 845 of 1475
+t0:=x*(c+d*x^2)^(5/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 5 3 2 | 2
+--R (d x + 2c d x + c x)\|d x + c
+--R (1) ---------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 845
+
+--S 846 of 1475
+r0:=1/3*(b*c-a*d)*(c+d*x^2)^(3/2)/b^2+1/5*(c+d*x^2)^(5/2)/b-_
+ (b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/_
+ b^(7/2)+(b*c-a*d)^2*sqrt(c+d*x^2)/b^3
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 2 2 2 +-----------+ \|b \|d x + c
+--R (- 15a d + 30a b c d - 15b c )\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2 +-+
+--R (3b d x + (- 5a b d + 11b c d)x + 15a d - 35a b c d + 23b c )\|b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 +-+
+--R 15b \|b
+--R Type: Expression(Integer)
+--E 846
+
+--S 847 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 4
+--R (15a d - 30a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (180a c d - 360a b c d + 180b c d)x + 240a c d - 480a b c d
+--R +
+--R 2 4
+--R 240b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| b
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 75a c d + 150a b c d - 75b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (- 300a c d + 600a b c d - 300b c d)x - 240a c d
+--R +
+--R 4 2 5
+--R 480a b c d - 240b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+
+--R ((- 2a b d - 4b c)x - 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (2b c d x + (6a b c d + 4b c )x + 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 4 8 4 2 2 3 6
+--R - 30b c d x + (50a b c d - 230b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 120a c d + 480a b c d - 720b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2
+--R (- 240a c d + 720a b c d - 720b c d)x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 10 5 2 4 8
+--R 6b d x + (- 10a b d + 100b c d )x
+--R +
+--R 2 5 4 2 2 3 6
+--R (30a d - 200a b c d + 500b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (240a c d - 840a b c d + 1080b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2
+--R (240a c d - 720a b c d + 720b c d)x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 2 4 3 2 3 2 +-+ | 2 3 2 4
+--R (30b d x + 360b c d x + 480b c )\|c \|d x + c - 150b c d x
+--R +
+--R 3 2 2 3 3
+--R - 600b c d x - 480b c
+--R ,
+--R
+--R 2 4 3 2 2 2 4
+--R (15a d - 30a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (180a c d - 360a b c d + 180b c d)x + 240a c d - 480a b c d
+--R +
+--R 2 4
+--R 240b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 75a c d + 150a b c d - 75b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (- 300a c d + 600a b c d - 300b c d)x - 240a c d
+--R +
+--R 4 2 5
+--R 480a b c d - 240b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R 2 4 8 4 2 2 3 6
+--R - 15b c d x + (25a b c d - 115b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 60a c d + 240a b c d - 360b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2
+--R (- 120a c d + 360a b c d - 360b c d)x
+--R *
+--R +--------+
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+--R +
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+--R +
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+--R 3 2 4 3 2 3 2 +-+ | 2 3 2 4
+--R (15b d x + 180b c d x + 240b c )\|c \|d x + c - 75b c d x
+--R +
+--R 3 2 2 3 3
+--R - 300b c d x - 240b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 847
+
+--S 848 of 1475
+m0a:=a0.1-r0
+--R
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+--R +
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+--R +
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+--R (360a c d - 840a b c d + 552b c d)x + 480a c d - 1120a b c d
+--R +
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+--R 736b c
+--R *
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+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (- 600a c d + 1400a b c d - 920b c d)x - 480a c d + 1120a b c d
+--R +
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+--R *
+--R +-+ +-+
+--R \|b \|c
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+--R (30b d x + 360b c d x + 480b c )\|b \|c \|d x + c
+--R +
+--R 3 2 4 3 2 2 3 3 +-+
+--R (- 150b c d x - 600b c d x - 480b c )\|b
+--R Type: Expression(Integer)
+--E 848
+
+--S 849 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 849
+
+--S 850 of 1475
+m0b:=a0.2-r0
+--R
+--R
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+--R 2 4 3 2 2 2 4
+--R (15a d - 30a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (180a c d - 360a b c d + 180b c d)x + 240a c d - 480a b c d
+--R +
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+--R *
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+--R 2 4 2 3 2 3 2 4
+--R (- 75a c d + 150a b c d - 75b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
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+--R +
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+--R *
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+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
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+--R 2 4 3 2 2 2 4
+--R (15a d - 30a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (180a c d - 360a b c d + 180b c d)x + 240a c d - 480a b c d
+--R +
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+--R 240b c
+--R *
+--R +---------+ +--------+
+--R +-+ +-+ |a d - b c | 2
+--R \|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 75a c d + 150a b c d - 75b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
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+--R +
+--R 2 5
+--R - 240b c
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|b |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (15a c d - 35a b c d + 23b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (180a c d - 420a b c d + 276b c d)x + 240a c d - 560a b c d
+--R +
+--R 2 5
+--R 368b c
+--R *
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+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 75a c d + 175a b c d - 115b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (- 300a c d + 700a b c d - 460b c d)x - 240a c d + 560a b c d
+--R +
+--R 2 5
+--R - 368b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 3 2 4 3 2 3 2 +-+ +-+ | 2
+--R (15b d x + 180b c d x + 240b c )\|b \|c \|d x + c
+--R +
+--R 3 2 4 3 2 2 3 3 +-+
+--R (- 75b c d x - 300b c d x - 240b c )\|b
+--R Type: Expression(Integer)
+--E 850
+
+--S 851 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 851
+
+)clear all
+
+--S 852 of 1475
+t0:=(c+d*x^2)^(5/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 852
+
+--S 853 of 1475
+r0:=1/4*d*x*(c+d*x^2)^(3/2)/b+(b*c-a*d)^(5/2)*atan(x*sqrt(b*c-a*d)/_
+ (sqrt(a)*sqrt(c+d*x^2)))/(b^3*sqrt(a))+1/8*(15*b^2*c^2-20*a*b*c*d+_
+ 8*a^2*d^2)*atanh(x*sqrt(d)/sqrt(c+d*x^2))*sqrt(d)/b^3+1/8*d*(7*b*c-_
+ 4*a*d)*x*sqrt(c+d*x^2)/b^2
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|d
+--R (8a d - 20a b c d + 15b c )\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (8a d - 16a b c d + 8b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 2 3 2 2 +-+ | 2
+--R (2b d x + (- 4a b d + 9b c d)x)\|a \|d x + c
+--R /
+--R 3 +-+
+--R 8b \|a
+--R Type: Expression(Integer)
+--E 853
+
+--S 854 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 2 2 2 2 2
+--R (16a d - 32a b c d + 16b c d)x + 32a c d - 64a b c d
+--R +
+--R 2 3
+--R 32b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
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+--R 2 4 3 2 2 2 4
+--R (- 4a d + 8a b c d - 4b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 32a c d + 64a b c d - 32b c d)x - 32a c d + 64a b c d
+--R +
+--R 2 4
+--R - 32b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (32a d - 80a b c d + 60b c d)x + 64a c d - 160a b c d
+--R +
+--R 2 3
+--R 120b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 8a d + 20a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 64a c d + 160a b c d - 120b c d)x - 64a c d + 160a b c d
+--R +
+--R 2 4
+--R - 120b c
+--R *
+--R +-+
+--R \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 4 7 4 2 3 5 3 2 2 2 3
+--R - 2b d x + (4a b d - 25b c d )x + (32a b c d - 88b c d )x
+--R +
+--R 2 2 2 3
+--R (32a b c d - 72b c d)x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 7 4 2 3 5 3 2 2 2 3
+--R 8b d x + (- 16a b d + 60b c d )x + (- 48a b c d + 124b c d )x
+--R +
+--R 2 2 2 3
+--R (- 32a b c d + 72b c d)x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 2 3 +-+ | 2 3 2 4 3 2 3 2
+--R (32b d x + 64b c)\|c \|d x + c - 8b d x - 64b c d x - 64b c
+--R ,
+--R
+--R 2 3 2 2 2 2 2 2 2
+--R (32a d - 80a b c d + 60b c d)x + 64a c d - 160a b c d
+--R +
+--R 2 3
+--R 120b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 8a d + 20a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 64a c d + 160a b c d - 120b c d)x - 64a c d + 160a b c d
+--R +
+--R 2 4
+--R - 120b c
+--R *
+--R +-+
+--R \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (- 32a d + 64a b c d - 32b c d)x - 64a c d + 128a b c d
+--R +
+--R 2 3
+--R - 64b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 2 4 3 2 2 2 4
+--R (8a d - 16a b c d + 8b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (64a c d - 128a b c d + 64b c d)x + 64a c d - 128a b c d
+--R +
+--R 2 4
+--R 64b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (32a d - 64a b c d + 32b c d)x + 64a c d - 128a b c d
+--R +
+--R 2 3
+--R 64b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 8a d + 16a b c d - 8b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 64a c d + 128a b c d - 64b c d)x - 64a c d + 128a b c d
+--R +
+--R 2 4
+--R - 64b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 4 7 4 2 3 5 3 2 2 2 3
+--R - 2b d x + (4a b d - 25b c d )x + (32a b c d - 88b c d )x
+--R +
+--R 2 2 2 3
+--R (32a b c d - 72b c d)x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 7 4 2 3 5 3 2 2 2 3
+--R 8b d x + (- 16a b d + 60b c d )x + (- 48a b c d + 124b c d )x
+--R +
+--R 2 2 2 3
+--R (- 32a b c d + 72b c d)x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 2 3 +-+ | 2 3 2 4 3 2 3 2
+--R (32b d x + 64b c)\|c \|d x + c - 8b d x - 64b c d x - 64b c
+--R ,
+--R
+--R 2 3 2 2 2 2 2 2 2
+--R (16a d - 32a b c d + 16b c d)x + 32a c d - 64a b c d
+--R +
+--R 2 3
+--R 32b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| a
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 4a d + 8a b c d - 4b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 32a c d + 64a b c d - 32b c d)x - 32a c d + 64a b c d
+--R +
+--R 2 4
+--R - 32b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (64a d - 160a b c d + 120b c d)x + 128a c d - 320a b c d
+--R +
+--R 2 3
+--R 240b c
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 16a d + 40a b c d - 30b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2
+--R (- 128a c d + 320a b c d - 240b c d)x - 128a c d
+--R +
+--R 3 2 4
+--R 320a b c d - 240b c
+--R *
+--R +---+
+--R \|- d
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 2 4 7 4 2 3 5 3 2 2 2 3
+--R - 2b d x + (4a b d - 25b c d )x + (32a b c d - 88b c d )x
+--R +
+--R 2 2 2 3
+--R (32a b c d - 72b c d)x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 7 4 2 3 5 3 2 2 2 3
+--R 8b d x + (- 16a b d + 60b c d )x + (- 48a b c d + 124b c d )x
+--R +
+--R 2 2 2 3
+--R (- 32a b c d + 72b c d)x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 2 3 +-+ | 2 3 2 4 3 2 3 2
+--R (32b d x + 64b c)\|c \|d x + c - 8b d x - 64b c d x - 64b c
+--R ,
+--R
+--R 2 3 2 2 2 2 2 2 2
+--R (64a d - 160a b c d + 120b c d)x + 128a c d - 320a b c d
+--R +
+--R 2 3
+--R 240b c
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 16a d + 40a b c d - 30b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2
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+--R +
+--R 3 2 4
+--R 320a b c d - 240b c
+--R *
+--R +---+
+--R \|- d
+--R *
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+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (- 32a d + 64a b c d - 32b c d)x - 64a c d + 128a b c d
+--R +
+--R 2 3
+--R - 64b c
+--R *
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+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 2 4 3 2 2 2 4
+--R (8a d - 16a b c d + 8b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (64a c d - 128a b c d + 64b c d)x + 64a c d - 128a b c d
+--R +
+--R 2 4
+--R 64b c
+--R *
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+--R |-----------
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+--R *
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+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
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+--R a d x |-----------
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+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (32a d - 64a b c d + 32b c d)x + 64a c d - 128a b c d
+--R +
+--R 2 3
+--R 64b c
+--R *
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+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
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+--R +
+--R 2 4 3 2 2 2 4
+--R (- 8a d + 16a b c d - 8b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 64a c d + 128a b c d - 64b c d)x - 64a c d + 128a b c d
+--R +
+--R 2 4
+--R - 64b c
+--R *
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+--R |- a d + b c
+--R |-----------
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+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 4 7 4 2 3 5 3 2 2 2 3
+--R - 2b d x + (4a b d - 25b c d )x + (32a b c d - 88b c d )x
+--R +
+--R 2 2 2 3
+--R (32a b c d - 72b c d)x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 7 4 2 3 5 3 2 2 2 3
+--R 8b d x + (- 16a b d + 60b c d )x + (- 48a b c d + 124b c d )x
+--R +
+--R 2 2 2 3
+--R (- 32a b c d + 72b c d)x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 2 3 +-+ | 2 3 2 4 3 2 3 2
+--R (32b d x + 64b c)\|c \|d x + c - 8b d x - 64b c d x - 64b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 854
+
+--S 855 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 2 2 2 2 +-+ |a d - b c
+--R (4a d - 8a b c d + 4b c )\|a |---------
+--R \| a
+--R *
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+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
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+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 2 2 +-+ +-+
+--R (8a d - 20a b c d + 15b c )\|a \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|d
+--R (- 8a d + 20a b c d - 15b c )\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (- 8a d + 16a b c d - 8b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 8b \|a
+--R Type: Expression(Integer)
+--E 855
+
+--S 856 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 856
+
+--S 857 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 2 2 2 +-+ +-+
+--R (8a d - 20a b c d + 15b c )\|a \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|d
+--R (- 8a d + 20a b c d - 15b c )\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 |- a d + b c +-+
+--R (- 8a d + 16a b c d - 8b c ) |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R 2 2 2 2 |- a d + b c +-+ \|c
+--R (8a d - 16a b c d + 8b c ) |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (- 8a d + 16a b c d - 8b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 8b \|a
+--R Type: Expression(Integer)
+--E 857
+
+--S 858 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 858
+
+)clear all
+
+--S 859 of 1475
+t0:=(c+d*x^2)^(5/2)/(x*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 3
+--R b x + a x
+--R Type: Expression(Integer)
+--E 859
+
+--S 860 of 1475
+r0:=1/3*d*(c+d*x^2)^(3/2)/b-c^(5/2)*atanh(sqrt(c+d*x^2)/sqrt(c))/a+_
+ (b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/_
+ (a*b^(5/2))+d*(2*b*c-a*d)*sqrt(c+d*x^2)/b^2
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 2 2 2 +-----------+ \|b \|d x + c
+--R (3a d - 6a b c d + 3b c )\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R 2 2 +-+ +-+ \|d x + c
+--R - 3b c \|b \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 2 2 +-+ | 2
+--R (a b d x - 3a d + 7a b c d)\|b \|d x + c
+--R /
+--R 2 +-+
+--R 3a b \|b
+--R Type: Expression(Integer)
+--E 860
+
+--S 861 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 3 2 2 4 | 2 2 3 2 2 4 +-+
+--R ((6b c d x + 24b c )\|d x + c + (- 18b c d x - 24b c )\|c )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d - 6a b c d + 3b c d)x + 12a c d - 24a b c d + 12b c )
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 9a c d + 18a b c d - 9b c d)x - 12a c d + 24a b c d
+--R +
+--R 2 4
+--R - 12b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 3 4 2 3 2 2 2 | 2
+--R (- 6a b c d x + (12a c d - 36a b c d )x )\|d x + c
+--R +
+--R 4 6 2 4 3 4 2 3 2 2 2 +-+
+--R (2a b d x + (- 6a d + 24a b c d )x + (- 12a c d + 36a b c d )x )\|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ | 2 2 2 2 2
+--R (6a b d x + 24a b c)\|c \|d x + c - 18a b c d x - 24a b c
+--R ,
+--R
+--R +--------+
+--R 2 3 2 2 4 | 2 2 3 2 2 4 +-+
+--R ((3b c d x + 12b c )\|d x + c + (- 9b c d x - 12b c )\|c )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (- 3a d + 6a b c d - 3b c d)x - 12a c d + 24a b c d
+--R +
+--R 2 3
+--R - 12b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (9a c d - 18a b c d + 9b c d)x + 12a c d - 24a b c d
+--R +
+--R 2 4
+--R 12b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R +--------+
+--R 3 4 2 3 2 2 2 | 2
+--R (- 3a b c d x + (6a c d - 18a b c d )x )\|d x + c
+--R +
+--R 4 6 2 4 3 4 2 3 2 2 2 +-+
+--R (a b d x + (- 3a d + 12a b c d )x + (- 6a c d + 18a b c d )x )\|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ | 2 2 2 2 2
+--R (3a b d x + 12a b c)\|c \|d x + c - 9a b c d x - 12a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 861
+
+--S 862 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 3 2 2 4 +-+ | 2 2 3 2 2 4 +-+ +-+
+--R ((6b c d x + 24b c )\|b \|d x + c + (- 18b c d x - 24b c )\|b \|c )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d - 6a b c d + 3b c d)x + 12a c d - 24a b c d + 12b c )
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ +-+ | 2
+--R |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 9a c d + 18a b c d - 9b c d)x - 12a c d + 24a b c d
+--R +
+--R 2 4
+--R - 12b c
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 6a d + 12a b c d - 6b c d)x - 24a c d + 48a b c d - 24b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (18a c d - 36a b c d + 18b c d)x + 24a c d - 48a b c d
+--R +
+--R 2 4
+--R 24b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 3 2 2 4 +-+ | 2 2 3 2 2 4 +-+ +-+
+--R ((6b c d x + 24b c )\|b \|d x + c + (- 18b c d x - 24b c )\|b \|c )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 3 2 2 2 2 2 2 3 +-+ | 2
+--R ((- 6a c d + 14a b c d )x - 24a c d + 56a b c d)\|b \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 3 +-+ +-+
+--R ((18a c d - 42a b c d )x + 24a c d - 56a b c d)\|b \|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ +-+ | 2 2 2 2 2 +-+
+--R (6a b d x + 24a b c)\|b \|c \|d x + c + (- 18a b c d x - 24a b c )\|b
+--R Type: Expression(Integer)
+--E 862
+
+--S 863 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 863
+
+--S 864 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 3 2 2 4 +-+ | 2 2 3 2 2 4 +-+ +-+
+--R ((3b c d x + 12b c )\|b \|d x + c + (- 9b c d x - 12b c )\|b \|c )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 3a d + 6a b c d - 3b c d)x - 12a c d + 24a b c d - 12b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((9a c d - 18a b c d + 9b c d)x + 12a c d - 24a b c d + 12b c )
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 3 2 2 4 +-+ | 2 2 3 2 2 4 +-+ +-+
+--R ((3b c d x + 12b c )\|b \|d x + c + (- 9b c d x - 12b c )\|b \|c )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 3a d + 6a b c d - 3b c d)x - 12a c d + 24a b c d - 12b c )
+--R *
+--R +---------+ +--------+
+--R +-+ +-+ |a d - b c | 2
+--R \|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((9a c d - 18a b c d + 9b c d)x + 12a c d - 24a b c d + 12b c )
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|b |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R +--------+
+--R 2 3 2 2 2 2 2 2 3 +-+ | 2
+--R ((- 3a c d + 7a b c d )x - 12a c d + 28a b c d)\|b \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 3 +-+ +-+
+--R ((9a c d - 21a b c d )x + 12a c d - 28a b c d)\|b \|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ +-+ | 2 2 2 2 2 +-+
+--R (3a b d x + 12a b c)\|b \|c \|d x + c + (- 9a b c d x - 12a b c )\|b
+--R Type: Expression(Integer)
+--E 864
+
+--S 865 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 865
+
+)clear all
+
+--S 866 of 1475
+t0:=(c+d*x^2)^(5/2)/(x^2*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 4 2
+--R b x + a x
+--R Type: Expression(Integer)
+--E 866
+
+--S 867 of 1475
+r0:=-c*(c+d*x^2)^(3/2)/(a*x)-(b*c-a*d)^(5/2)*atan(x*sqrt(b*c-a*d)/_
+ (sqrt(a)*sqrt(c+d*x^2)))/(a^(3/2)*b^2)+1/2*d^(3/2)*(5*b*c-2*a*d)*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))/b^2+1/2*d*(2*b*c+a*d)*_
+ x*sqrt(c+d*x^2)/(a*b)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (- 2a d + 5a b c d)x\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (- 2a d + 4a b c d - 2b c )x\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 2 2 2 +-+ | 2
+--R (a b d x - 2b c )\|a \|d x + c
+--R /
+--R 2 +-+
+--R 2a b x\|a
+--R Type: Expression(Integer)
+--E 867
+
+--S 868 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 3 2 3 2 2 2 +-+ | 2
+--R ((2a d - 5a b c d )x + (8a c d - 20a b c d)x)\|d \|d x + c
+--R +
+--R 2 3 2 3 2 2 2 +-+ +-+
+--R ((- 6a d + 15a b c d )x + (- 8a c d + 20a b c d)x)\|c \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((a d - 2a b c d + b c d)x + (4a c d - 8a b c d + 4b c )x)
+--R *
+--R +---------+ +--------+
+--R |a d - b c | 2
+--R |--------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 2 3
+--R (- 3a d + 6a b c d - 3b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 4a c d + 8a b c d - 4b c )x
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 3 4 2 2 2 2 2 3 +-+ | 2
+--R (- 3a b d x + (- 4a b c d + 6b c d)x + 8b c )\|c \|d x + c
+--R +
+--R 4 6 3 2 2 2 4 2 2 2 3 2 2 4
+--R a b d x + (5a b c d - 2b c d )x + (4a b c d - 10b c d)x - 8b c
+--R /
+--R +--------+
+--R 2 3 2 | 2 2 3 2 +-+
+--R (2a b d x + 8a b c x)\|d x + c + (- 6a b d x - 8a b c x)\|c
+--R ,
+--R
+--R +--------+
+--R 2 3 2 3 2 2 2 +-+ | 2
+--R ((2a d - 5a b c d )x + (8a c d - 20a b c d)x)\|d \|d x + c
+--R +
+--R 2 3 2 3 2 2 2 +-+ +-+
+--R ((- 6a d + 15a b c d )x + (- 8a c d + 20a b c d)x)\|c \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((2a d - 4a b c d + 2b c d)x + (8a c d - 16a b c d + 8b c )x)
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 2 3
+--R (- 6a d + 12a b c d - 6b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 8a c d + 16a b c d - 8b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 2 3 2 2 2 3
+--R (- 2a d + 4a b c d - 2b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 8a c d + 16a b c d - 8b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 2 3
+--R (6a d - 12a b c d + 6b c d)x
+--R +
+--R 2 2 2 2 3
+--R (8a c d - 16a b c d + 8b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R 3 4 2 2 2 2 2 3 +-+ | 2
+--R (- 3a b d x + (- 4a b c d + 6b c d)x + 8b c )\|c \|d x + c
+--R +
+--R 4 6 3 2 2 2 4 2 2 2 3 2 2 4
+--R a b d x + (5a b c d - 2b c d )x + (4a b c d - 10b c d)x - 8b c
+--R /
+--R +--------+
+--R 2 3 2 | 2 2 3 2 +-+
+--R (2a b d x + 8a b c x)\|d x + c + (- 6a b d x - 8a b c x)\|c
+--R ,
+--R
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((a d - 2a b c d + b c d)x + (4a c d - 8a b c d + 4b c )x)
+--R *
+--R +---------+ +--------+
+--R |a d - b c | 2
+--R |--------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 2 3
+--R (- 3a d + 6a b c d - 3b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 4a c d + 8a b c d - 4b c )x
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 3 2 2 2 +---+
+--R ((- 4a d + 10a b c d )x + (- 16a c d + 40a b c d)x)\|- d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 2 3 2 2 2 +---+ +-+
+--R ((12a d - 30a b c d )x + (16a c d - 40a b c d)x)\|- d \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R +--------+
+--R 3 4 2 2 2 2 2 3 +-+ | 2
+--R (- 3a b d x + (- 4a b c d + 6b c d)x + 8b c )\|c \|d x + c
+--R +
+--R 4 6 3 2 2 2 4 2 2 2 3 2 2 4
+--R a b d x + (5a b c d - 2b c d )x + (4a b c d - 10b c d)x - 8b c
+--R /
+--R +--------+
+--R 2 3 2 | 2 2 3 2 +-+
+--R (2a b d x + 8a b c x)\|d x + c + (- 6a b d x - 8a b c x)\|c
+--R ,
+--R
+--R 2 3 2 3 2 2 2 +---+
+--R ((- 4a d + 10a b c d )x + (- 16a c d + 40a b c d)x)\|- d
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 2 3 2 2 2 +---+ +-+
+--R ((12a d - 30a b c d )x + (16a c d - 40a b c d)x)\|- d \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((2a d - 4a b c d + 2b c d)x + (8a c d - 16a b c d + 8b c )x)
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 2 3
+--R (- 6a d + 12a b c d - 6b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 8a c d + 16a b c d - 8b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 2 3 2 2 2 3
+--R (- 2a d + 4a b c d - 2b c d)x
+--R +
+--R 2 2 2 2 3
+--R (- 8a c d + 16a b c d - 8b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 2 3
+--R (6a d - 12a b c d + 6b c d)x
+--R +
+--R 2 2 2 2 3
+--R (8a c d - 16a b c d + 8b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R 3 4 2 2 2 2 2 3 +-+ | 2
+--R (- 3a b d x + (- 4a b c d + 6b c d)x + 8b c )\|c \|d x + c
+--R +
+--R 4 6 3 2 2 2 4 2 2 2 3 2 2 4
+--R a b d x + (5a b c d - 2b c d )x + (4a b c d - 10b c d)x - 8b c
+--R /
+--R +--------+
+--R 2 3 2 | 2 2 3 2 +-+
+--R (2a b d x + 8a b c x)\|d x + c + (- 6a b d x - 8a b c x)\|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 868
+
+--S 869 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 +-+ +-+
+--R (2a d - 5a b c d)\|a \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+
+--R 2 2 2 2 +-+ |a d - b c
+--R (a d - 2a b c d + b c )\|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (2a d - 5a b c d)\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (2a d - 4a b c d + 2b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2a b \|a
+--R Type: Expression(Integer)
+--E 869
+
+--S 870 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 870
+
+--S 871 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 2 +-+ +-+
+--R (2a d - 5a b c d)\|a \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (2a d - 5a b c d)\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 |- a d + b c +-+
+--R (2a d - 4a b c d + 2b c ) |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R 2 2 2 2 |- a d + b c +-+ \|c
+--R (- 2a d + 4a b c d - 2b c ) |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (2a d - 4a b c d + 2b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2a b \|a
+--R Type: Expression(Integer)
+--E 871
+
+--S 872 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 872
+
+)clear all
+
+--S 873 of 1475
+t0:=(c+d*x^2)^(5/2)/(x^3*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 5 3
+--R b x + a x
+--R Type: Expression(Integer)
+--E 873
+
+--S 874 of 1475
+r0a:=-1/2*c*(c+d*x^2)^(3/2)/(a*x^2)+1/2*c^(3/2)*(2*b*c-5*a*d)*_
+ atanh(sqrt(c+d*x^2)/sqrt(c))/a^2-(b*c-a*d)^(5/2)*atanh(sqrt(b)*_
+ sqrt(c+d*x^2)/sqrt(b*c-a*d))/(a^2*b^(3/2))+1/2*d*(b*c+2*a*d)*_
+ sqrt(c+d*x^2)/(a*b)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 2 2 2 2 +-----------+ \|b \|d x + c
+--R (- 2a d + 4a b c d - 2b c )x \|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R 2 2 2 +-+ +-+ \|d x + c
+--R (- 5a b c d + 2b c )x \|b \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 2 2 +-+ | 2
+--R (2a d x - a b c )\|b \|d x + c
+--R /
+--R 2 2 +-+
+--R 2a b x \|b
+--R Type: Expression(Integer)
+--E 874
+
+--S 875 of 1475
+r0b:=1/2*d*(c+d*x^2)^(3/2)/a-1/2*(c+d*x^2)^(5/2)/_
+ (a*x^2)+1/2*c^(3/2)*(2*b*c-5*a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))/a^2-_
+ (b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/_
+ (a^2*b^(3/2))+1/2*d*(b*c+2*a*d)*sqrt(c+d*x^2)/(a*b)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ | 2
+--R 2 2 2 2 2 +-----------+ \|b \|d x + c
+--R (- 2a d + 4a b c d - 2b c )x \|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R 2 2 2 +-+ +-+ \|d x + c
+--R (- 5a b c d + 2b c )x \|b \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 2 2 +-+ | 2
+--R (2a d x - a b c )\|b \|d x + c
+--R /
+--R 2 2 +-+
+--R 2a b x \|b
+--R Type: Expression(Integer)
+--E 875
+
+--S 876 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R +--------+
+--R 2 2 2 3 4 3 2 4 2 | 2
+--R ((5a b c d - 2b c d)x + (20a b c d - 8b c )x )\|d x + c
+--R +
+--R 2 2 2 3 4 3 2 4 2 +-+
+--R ((- 15a b c d + 6b c d)x + (- 20a b c d + 8b c )x )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 4 2 2 2 2 3 2
+--R ((a d - 2a b c d + b c d)x + (4a c d - 8a b c d + 4b c )x )
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 3a c d + 6a b c d - 3b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (- 4a c d + 8a b c d - 4b c )x
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c - 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (2b x + 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 3 4 3 2 4 | 2
+--R (- 4a c d x + 3a b c d x + 4a b c )\|d x + c
+--R +
+--R 2 4 6 2 3 2 2 4 3 2 4 +-+
+--R (2a d x + (4a c d - a b c d )x - 5a b c d x - 4a b c )\|c
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 2
+--R (2a b d x + 8a b c x )\|c \|d x + c - 6a b c d x - 8a b c x
+--R ,
+--R
+--R +--------+
+--R 2 2 2 3 4 3 2 4 2 | 2
+--R ((5a b c d - 2b c d)x + (20a b c d - 8b c )x )\|d x + c
+--R +
+--R 2 2 2 3 4 3 2 4 2 +-+
+--R ((- 15a b c d + 6b c d)x + (- 20a b c d + 8b c )x )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 4
+--R (2a d - 4a b c d + 2b c d)x
+--R +
+--R 2 2 2 2 3 2
+--R (8a c d - 16a b c d + 8b c )x
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 6a c d + 12a b c d - 6b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (- 8a c d + 16a b c d - 8b c )x
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
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+--R +
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+--R 2 3 4 3 2 4 | 2
+--R (- 4a c d x + 3a b c d x + 4a b c )\|d x + c
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+--R 2 4 6 2 3 2 2 4 3 2 4 +-+
+--R (2a d x + (4a c d - a b c d )x - 5a b c d x - 4a b c )\|c
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 2
+--R (2a b d x + 8a b c x )\|c \|d x + c - 6a b c d x - 8a b c x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 876
+
+--S 877 of 1475
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((5a b c d - 2b c d)x + 20a b c d - 8b c )\|b \|d x + c
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+--R 2 2 2 3 2 3 2 4 +-+ +-+
+--R ((- 15a b c d + 6b c d)x - 20a b c d + 8b c )\|b \|c
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+--R \|d x + c - \|c
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+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((a d - 2a b c d + b c d)x + 4a c d - 8a b c d + 4b c )
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+--R |----------- \|b \|c \|d x + c
+--R \| b
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+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 3a c d + 6a b c d - 3b c d)x - 4a c d + 8a b c d - 4b c )
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+--R |----------- \|b
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+--R *
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+--R +-----------+ +--------+
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+--R ((2a b x + 2a )\|c - 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (2b x + 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
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+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((2a d - 4a b c d + 2b c d)x + 8a c d - 16a b c d + 8b c )
+--R *
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+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
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+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 6a c d + 12a b c d - 6b c d)x - 8a c d + 16a b c d - 8b c )
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+--R \|- a d + b c
+--R *
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+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
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+--R +
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+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((5a b c d - 2b c d)x + 20a b c d - 8b c )\|b \|d x + c
+--R +
+--R 2 2 2 3 2 3 2 4 +-+ +-+
+--R ((- 15a b c d + 6b c d)x - 20a b c d + 8b c )\|b \|c
+--R *
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+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
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+--R 2 3 2 2 2 2 +-+ | 2 2 3 2 2 2 2 +-+ +-+
+--R (2a c d x + 8a c d )\|b \|d x + c + (- 6a c d x - 8a c d )\|b \|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ +-+ | 2 2 2 2 2 +-+
+--R (2a b d x + 8a b c)\|b \|c \|d x + c + (- 6a b c d x - 8a b c )\|b
+--R Type: Expression(Integer)
+--E 877
+
+--S 878 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 878
+
+--S 879 of 1475
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((5a b c d - 2b c d)x + 20a b c d - 8b c )\|b \|d x + c
+--R +
+--R 2 2 2 3 2 3 2 4 +-+ +-+
+--R ((- 15a b c d + 6b c d)x - 20a b c d + 8b c )\|b \|c
+--R *
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+--R \|d x + c - \|c
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+--R x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((2a d - 4a b c d + 2b c d)x + 8a c d - 16a b c d + 8b c )
+--R *
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+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 6a c d + 12a b c d - 6b c d)x - 8a c d + 16a b c d - 8b c )
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
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+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
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+--R +
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+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((5a b c d - 2b c d)x + 20a b c d - 8b c )\|b \|d x + c
+--R +
+--R 2 2 2 3 2 3 2 4 +-+ +-+
+--R ((- 15a b c d + 6b c d)x - 20a b c d + 8b c )\|b \|c
+--R *
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+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((2a d - 4a b c d + 2b c d)x + 8a c d - 16a b c d + 8b c )\|b
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 6a c d + 12a b c d - 6b c d)x - 8a c d + 16a b c d - 8b c )
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|b |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R +--------+
+--R 2 3 2 2 2 2 +-+ | 2 2 3 2 2 2 2 +-+ +-+
+--R (2a c d x + 8a c d )\|b \|d x + c + (- 6a c d x - 8a c d )\|b \|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ +-+ | 2 2 2 2 2 +-+
+--R (2a b d x + 8a b c)\|b \|c \|d x + c + (- 6a b c d x - 8a b c )\|b
+--R Type: Expression(Integer)
+--E 879
+
+--S 880 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 880
+
+--S 881 of 1475
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((5a b c d - 2b c d)x + 20a b c d - 8b c )\|b \|d x + c
+--R +
+--R 2 2 2 3 2 3 2 4 +-+ +-+
+--R ((- 15a b c d + 6b c d)x - 20a b c d + 8b c )\|b \|c
+--R *
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+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((a d - 2a b c d + b c d)x + 4a c d - 8a b c d + 4b c )
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ +-+ | 2
+--R |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 3a c d + 6a b c d - 3b c d)x - 4a c d + 8a b c d - 4b c )
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c - 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (2b x + 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((2a d - 4a b c d + 2b c d)x + 8a c d - 16a b c d + 8b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 6a c d + 12a b c d - 6b c d)x - 8a c d + 16a b c d - 8b c )
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((5a b c d - 2b c d)x + 20a b c d - 8b c )\|b \|d x + c
+--R +
+--R 2 2 2 3 2 3 2 4 +-+ +-+
+--R ((- 15a b c d + 6b c d)x - 20a b c d + 8b c )\|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 3 2 2 2 2 +-+ | 2 2 3 2 2 2 2 +-+ +-+
+--R (2a c d x + 8a c d )\|b \|d x + c + (- 6a c d x - 8a c d )\|b \|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ +-+ | 2 2 2 2 2 +-+
+--R (2a b d x + 8a b c)\|b \|c \|d x + c + (- 6a b c d x - 8a b c )\|b
+--R Type: Expression(Integer)
+--E 881
+
+--S 882 of 1475
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 882
+
+--S 883 of 1475
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((5a b c d - 2b c d)x + 20a b c d - 8b c )\|b \|d x + c
+--R +
+--R 2 2 2 3 2 3 2 4 +-+ +-+
+--R ((- 15a b c d + 6b c d)x - 20a b c d + 8b c )\|b \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((2a d - 4a b c d + 2b c d)x + 8a c d - 16a b c d + 8b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 6a c d + 12a b c d - 6b c d)x - 8a c d + 16a b c d - 8b c )
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((5a b c d - 2b c d)x + 20a b c d - 8b c )\|b \|d x + c
+--R +
+--R 2 2 2 3 2 3 2 4 +-+ +-+
+--R ((- 15a b c d + 6b c d)x - 20a b c d + 8b c )\|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((2a d - 4a b c d + 2b c d)x + 8a c d - 16a b c d + 8b c )\|b
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 6a c d + 12a b c d - 6b c d)x - 8a c d + 16a b c d - 8b c )
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|b |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R +--------+
+--R 2 3 2 2 2 2 +-+ | 2 2 3 2 2 2 2 +-+ +-+
+--R (2a c d x + 8a c d )\|b \|d x + c + (- 6a c d x - 8a c d )\|b \|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ +-+ | 2 2 2 2 2 +-+
+--R (2a b d x + 8a b c)\|b \|c \|d x + c + (- 6a b c d x - 8a b c )\|b
+--R Type: Expression(Integer)
+--E 883
+
+--S 884 of 1475
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 884
+
+)clear all
+
+--S 885 of 1475
+t0:=(c+d*x^2)^(5/2)/(x^4*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 6 4
+--R b x + a x
+--R Type: Expression(Integer)
+--E 885
+
+--S 886 of 1475
+r0:=-1/3*c*(c+d*x^2)^(3/2)/(a*x^3)+(b*c-a*d)^(5/2)*atan(x*_
+ sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/(a^(5/2)*b)+d^(5/2)*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))/b+c*(b*c-2*a*d)*sqrt(c+d*x^2)/(a^2*x)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 3 +-+ +-+ x\|d
+--R 3a d x \|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 3 +-----------+ x\|- a d + b c
+--R (3a d - 6a b c d + 3b c )x \|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 2 2 2 +-+ | 2
+--R ((- 7a b c d + 3b c )x - a b c )\|a \|d x + c
+--R /
+--R 2 3 +-+
+--R 3a b x \|a
+--R Type: Expression(Integer)
+--E 886
+
+--S 887 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 2 5
+--R (3a d - 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 3
+--R (12a c d - 24a b c d + 12b c )x
+--R *
+--R +---------+ +--------+
+--R |a d - b c | 2
+--R |--------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 2 5
+--R (- 9a d + 18a b c d - 9b c d)x
+--R +
+--R 2 2 2 2 3 3
+--R (- 12a c d + 24a b c d - 12b c )x
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 3 5 2 2 3 +-+ | 2
+--R (6a d x + 24a c d x )\|d \|d x + c
+--R +
+--R 2 3 5 2 2 3 +-+ +-+
+--R (- 18a d x - 24a c d x )\|c \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 2 2 4 2 2 3 2 3 +-+
+--R ((42a b c d - 18b c d)x + (62a b c d - 24b c )x + 8a b c )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 2 6 2 2 2 3 4
+--R (- 14a b c d + 6b c d )x + (- 72a b c d + 30b c d)x
+--R +
+--R 3 2 4 2 4
+--R (- 66a b c d + 24b c )x - 8a b c
+--R /
+--R +--------+
+--R 2 5 2 3 | 2 2 5 2 3 +-+
+--R (6a b d x + 24a b c x )\|d x + c + (- 18a b d x - 24a b c x )\|c
+--R ,
+--R
+--R +--------+
+--R 2 3 5 2 2 3 +-+ | 2
+--R (3a d x + 12a c d x )\|d \|d x + c
+--R +
+--R 2 3 5 2 2 3 +-+ +-+
+--R (- 9a d x - 12a c d x )\|c \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 3 2 2 2 5
+--R (- 3a d + 6a b c d - 3b c d)x
+--R +
+--R 2 2 2 2 3 3
+--R (- 12a c d + 24a b c d - 12b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 2 5
+--R (9a d - 18a b c d + 9b c d)x
+--R +
+--R 2 2 2 2 3 3
+--R (12a c d - 24a b c d + 12b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 2 3 2 2 2 5
+--R (3a d - 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 3
+--R (12a c d - 24a b c d + 12b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 2 5
+--R (- 9a d + 18a b c d - 9b c d)x
+--R +
+--R 2 2 2 2 3 3
+--R (- 12a c d + 24a b c d - 12b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 2 2 4 2 2 3 2 3 +-+
+--R ((21a b c d - 9b c d)x + (31a b c d - 12b c )x + 4a b c )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 2 6 2 2 2 3 4
+--R (- 7a b c d + 3b c d )x + (- 36a b c d + 15b c d)x
+--R +
+--R 3 2 4 2 4
+--R (- 33a b c d + 12b c )x - 4a b c
+--R /
+--R +--------+
+--R 2 5 2 3 | 2 2 5 2 3 +-+
+--R (3a b d x + 12a b c x )\|d x + c + (- 9a b d x - 12a b c x )\|c
+--R ,
+--R
+--R 2 3 2 2 2 5
+--R (3a d - 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 3
+--R (12a c d - 24a b c d + 12b c )x
+--R *
+--R +---------+ +--------+
+--R |a d - b c | 2
+--R |--------- \|d x + c
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+--R +
+--R 2 3 2 2 2 5
+--R (- 9a d + 18a b c d - 9b c d)x
+--R +
+--R 2 2 2 2 3 3
+--R (- 12a c d + 24a b c d - 12b c )x
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
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+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
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+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 3 5 2 2 3 +---+ | 2
+--R (12a d x + 48a c d x )\|- d \|d x + c
+--R +
+--R 2 3 5 2 2 3 +---+ +-+
+--R (- 36a d x - 48a c d x )\|- d \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 2 2 2 4 2 2 3 2 3 +-+
+--R ((42a b c d - 18b c d)x + (62a b c d - 24b c )x + 8a b c )\|c
+--R *
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+--R \|d x + c
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+--R 3 2 2 2 6 2 2 2 3 4
+--R (- 14a b c d + 6b c d )x + (- 72a b c d + 30b c d)x
+--R +
+--R 3 2 4 2 4
+--R (- 66a b c d + 24b c )x - 8a b c
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+--R 2 5 2 3 | 2 2 5 2 3 +-+
+--R (6a b d x + 24a b c x )\|d x + c + (- 18a b d x - 24a b c x )\|c
+--R ,
+--R
+--R +--------+
+--R 2 3 5 2 2 3 +---+ | 2
+--R (6a d x + 24a c d x )\|- d \|d x + c
+--R +
+--R 2 3 5 2 2 3 +---+ +-+
+--R (- 18a d x - 24a c d x )\|- d \|c
+--R *
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+--R \|d x + c - \|c
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+--R +---+
+--R x\|- d
+--R +
+--R 2 3 2 2 2 5
+--R (- 3a d + 6a b c d - 3b c d)x
+--R +
+--R 2 2 2 2 3 3
+--R (- 12a c d + 24a b c d - 12b c )x
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+--R |----------- \|d x + c
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+--R +
+--R 2 3 2 2 2 5
+--R (9a d - 18a b c d + 9b c d)x
+--R +
+--R 2 2 2 2 3 3
+--R (12a c d - 24a b c d + 12b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
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+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 2 3 2 2 2 5
+--R (3a d - 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 3
+--R (12a c d - 24a b c d + 12b c )x
+--R *
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+--R |- a d + b c | 2
+--R |----------- \|d x + c
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+--R +
+--R 2 3 2 2 2 5
+--R (- 9a d + 18a b c d - 9b c d)x
+--R +
+--R 2 2 2 2 3 3
+--R (- 12a c d + 24a b c d - 12b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 2 2 4 2 2 3 2 3 +-+
+--R ((21a b c d - 9b c d)x + (31a b c d - 12b c )x + 4a b c )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 2 6 2 2 2 3 4
+--R (- 7a b c d + 3b c d )x + (- 36a b c d + 15b c d)x
+--R +
+--R 3 2 4 2 4
+--R (- 33a b c d + 12b c )x - 4a b c
+--R /
+--R +--------+
+--R 2 5 2 3 | 2 2 5 2 3 +-+
+--R (3a b d x + 12a b c x )\|d x + c + (- 9a b d x - 12a b c x )\|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 887
+
+--S 888 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 2 2 2 2 +-+ |a d - b c
+--R (a d - 2a b c d + b c )\|a |---------
+--R \| a
+--R *
+--R log
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+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R 2 2 +-+ +-+ (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R 2a d \|a \|d log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R - 2a d \|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (- 2a d + 4a b c d - 2b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2a b\|a
+--R Type: Expression(Integer)
+--E 888
+
+--S 889 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 889
+
+--S 890 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R 2 2 +-+ +-+ (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R a d \|a \|d log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R - a d \|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 |- a d + b c +-+
+--R (- a d + 2a b c d - b c ) |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R 2 2 2 2 |- a d + b c +-+ \|c
+--R (a d - 2a b c d + b c ) |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (- a d + 2a b c d - b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R a b\|a
+--R Type: Expression(Integer)
+--E 890
+
+--S 891 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 891
+
+)clear all
+
+--S 892 of 1475
+t0:=x^4/((a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 4
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 892
+
+--S 893 of 1475
+r0:=-1/2*(b*c+2*a*d)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/(b^2*d^(3/2))+_
+ a^(3/2)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/(b^2*_
+ sqrt(b*c-a*d))+1/2*x*sqrt(c+d*x^2)/(b*d)
+--R
+--R
+--R (2)
+--R +-+
+--R +-----------+ x\|d
+--R (- 2a d - b c)\|- a d + b c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+ +--------+
+--R +-+ +-+ x\|- a d + b c +-----------+ +-+ | 2
+--R 2a d\|a \|d atan(---------------) + b x\|- a d + b c \|d \|d x + c
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-----------+ +-+
+--R 2b d\|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 893
+
+--S 894 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2 2
+--R ((4a d + 2b c)\|c \|d x + c + (- 2a d - b c d)x - 4a c d - 2b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+ +--------+
+--R | a +-+ +-+ | 2
+--R 2a d |--------- \|c \|d \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 2 | a +-+
+--R (- a d x - 2a c d) |--------- \|d
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((- 2a d + 2b c d)x + (- 4a c d + 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((4a d - 4b c d)x + (4a c d - 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (- b d x - 2b c x)\|d \|d x + c + (2b d x + 2b c x)\|c \|d
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 2 2 2 +-+
+--R 4b d\|c \|d \|d x + c + (- 2b d x - 4b c d)\|d
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2 2
+--R ((4a d + 2b c)\|c \|d x + c + (- 2a d - b c d)x - 4a c d - 2b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-----------+ +--------+
+--R | a +-+ +-+ | 2
+--R 4a d |- --------- \|c \|d \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 | a +-+
+--R (- 2a d x - 4a c d) |- --------- \|d
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +--------+
+--R | a +-+ +-+ | 2
+--R - 4a d |- --------- \|c \|d \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 | a +-+
+--R (2a d x + 4a c d) |- --------- \|d
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (- b d x - 2b c x)\|d \|d x + c + (2b d x + 2b c x)\|c \|d
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 2 2 2 +-+
+--R 4b d\|c \|d \|d x + c + (- 2b d x - 4b c d)\|d
+--R ,
+--R
+--R +---------+ +--------+
+--R +---+ | a +-+ | 2
+--R 2a d\|- d |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 2 +---+ | a
+--R (- a d x - 2a c d)\|- d |---------
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((- 2a d + 2b c d)x + (- 4a c d + 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((4a d - 4b c d)x + (4a c d - 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ | 2 2 2
+--R (- 8a d - 4b c)\|c \|d x + c + (4a d + 2b c d)x + 8a c d
+--R +
+--R 2
+--R 4b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R +--------+
+--R 3 +---+ | 2 3 +---+ +-+
+--R (- b d x - 2b c x)\|- d \|d x + c + (2b d x + 2b c x)\|- d \|c
+--R /
+--R +--------+
+--R 2 +---+ +-+ | 2 2 2 2 2 +---+
+--R 4b d\|- d \|c \|d x + c + (- 2b d x - 4b c d)\|- d
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2
+--R (- 8a d - 4b c)\|c \|d x + c + (4a d + 2b c d)x + 8a c d
+--R +
+--R 2
+--R 4b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R +-----------+ +--------+
+--R +---+ | a +-+ | 2
+--R 4a d\|- d |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 +---+ | a
+--R (- 2a d x - 4a c d)\|- d |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +--------+
+--R +---+ | a +-+ | 2
+--R - 4a d\|- d |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 +---+ | a
+--R (2a d x + 4a c d)\|- d |- ---------
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +--------+
+--R 3 +---+ | 2 3 +---+ +-+
+--R (- b d x - 2b c x)\|- d \|d x + c + (2b d x + 2b c x)\|- d \|c
+--R /
+--R +--------+
+--R 2 +---+ +-+ | 2 2 2 2 2 +---+
+--R 4b d\|- d \|c \|d x + c + (- 2b d x - 4b c d)\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 894
+
+--S 895 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R (2a d + b c)\|- a d + b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+
+--R +-----------+ | a +-+
+--R a d\|- a d + b c |--------- \|d
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((- 2a d + 2b c d)x + (- 4a c d + 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((4a d - 4b c d)x + (4a c d - 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-+
+--R +-----------+ x\|d
+--R (2a d + b c)\|- a d + b c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-+ +-+ x\|- a d + b c
+--R - 2a d\|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-----------+ +-+
+--R 2b d\|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 895
+
+--S 896 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 896
+
+--S 897 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R (2a d + b c)\|- a d + b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R +-----------+ x\|d
+--R (2a d + b c)\|- a d + b c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ | a +-+
+--R 2a d\|- a d + b c |- --------- \|d
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +-+
+--R +-----------+ | a +-+ a\|c
+--R - 2a d\|- a d + b c |- --------- \|d atan(--------------------------)
+--R \| a d - b c +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-+ +-+ x\|- a d + b c
+--R - 2a d\|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-----------+ +-+
+--R 2b d\|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 897
+
+--S 898 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 898
+
+)clear all
+
+--S 899 of 1475
+t0:=x^3/((a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 3
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 899
+
+--S 900 of 1475
+r0:=a*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/(b^(3/2)*sqrt(b*c-a*d))+_
+ sqrt(c+d*x^2)/(b*d)
+--R
+--R
+--R +--------+
+--R +-+ | 2 +--------+
+--R \|b \|d x + c +-----------+ +-+ | 2
+--R a d atanh(---------------) + \|- a d + b c \|b \|d x + c
+--R +-----------+
+--R \|- a d + b c
+--R (2) ----------------------------------------------------------
+--R +-----------+ +-+
+--R b d\|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 900
+
+--S 901 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2
+--R (a\|c \|d x + c - a c)
+--R *
+--R log
+--R 2 2 2 3 2 4
+--R (- 2a b d - 2a b c d + 4b c )x
+--R +
+--R 2 2 2 2
+--R (- 8a b c d + 8a b c )x
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (2a b c d - 2b c d)x + (6a b c d - 2a b c d - 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (8a b c d - 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 | 2 +-+
+--R 2x \|- a b d + b c \|c
+--R /
+--R +-------------+ +--------+ +-------------+
+--R | 2 +-+ | 2 | 2
+--R 2b\|- a b d + b c \|c \|d x + c - 2b c\|- a b d + b c
+--R ,
+--R
+--R +--------+
+--R +-+ | 2
+--R (a\|c \|d x + c - a c)
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+
+--R 2 +-+ | 2
+--R x \|c \|a b d - b c
+--R /
+--R +-----------+ +--------+ +-----------+
+--R +-+ | 2 | 2 | 2
+--R b\|c \|a b d - b c \|d x + c - b c\|a b d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 901
+
+--S 902 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-----------+ +-+ +-+ | 2 +-----------+ +-+
+--R (a d\|- a d + b c \|b \|c \|d x + c - a c d\|- a d + b c \|b )
+--R *
+--R log
+--R 2 2 2 3 2 4
+--R (- 2a b d - 2a b c d + 4b c )x
+--R +
+--R 2 2 2 2
+--R (- 8a b c d + 8a b c )x
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (2a b c d - 2b c d)x + (6a b c d - 2a b c d - 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (8a b c d - 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+ +--------+ +-------------+
+--R | 2 +-+ | 2 | 2
+--R (- 2a d\|- a b d + b c \|c \|d x + c + 2a c d\|- a b d + b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-----------+ +-+ | 2
+--R 2c\|- a b d + b c \|- a d + b c \|b \|d x + c
+--R +
+--R +-------------+
+--R | 2 +-----------+ +-+ +-+
+--R - 2c\|- a b d + b c \|- a d + b c \|b \|c
+--R /
+--R +-------------+ +--------+
+--R | 2 +-----------+ +-+ +-+ | 2
+--R 2b d\|- a b d + b c \|- a d + b c \|b \|c \|d x + c
+--R +
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R - 2b c d\|- a b d + b c \|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 902
+
+--S 903 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 903
+
+--S 904 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +--------+ +-----------+
+--R +-+ | 2 | 2 | 2
+--R (- a d\|c \|a b d - b c \|d x + c + a c d\|a b d - b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +-----------+ +-+ +-+ | 2 +-----------+ +-+
+--R (a d\|- a d + b c \|b \|c \|d x + c - a c d\|- a d + b c \|b )
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+ +--------+
+--R +-----------+ +-+ | 2 | 2
+--R c\|- a d + b c \|b \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ +-+ +-+ | 2
+--R - c\|- a d + b c \|b \|c \|a b d - b c
+--R /
+--R +-----------+ +--------+
+--R +-----------+ +-+ +-+ | 2 | 2
+--R b d\|- a d + b c \|b \|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R - b c d\|- a d + b c \|b \|a b d - b c
+--R Type: Expression(Integer)
+--E 904
+
+--S 905 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 905
+
+)clear all
+
+--S 906 of 1475
+t0:=x^2/((a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 906
+
+--S 907 of 1475
+r0:=atanh(x*sqrt(d)/sqrt(c+d*x^2))/(b*sqrt(d))-atan(x*sqrt(b*c-a*d)/_
+ (sqrt(a)*sqrt(c+d*x^2)))*sqrt(a)/(b*sqrt(b*c-a*d))
+--R
+--R
+--R +-+ +-----------+
+--R +-----------+ x\|d +-+ +-+ x\|- a d + b c
+--R \|- a d + b c atanh(-----------) - \|a \|d atan(---------------)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|d x + c \|a \|d x + c
+--R (2) ----------------------------------------------------------------
+--R +-----------+ +-+
+--R b\|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 907
+
+--S 908 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R 2log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+
+--R | a +-+
+--R |--------- \|d
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((- 4a d + 4b c d)x + (- 4a c d + 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R /
+--R +-+
+--R 2b\|d
+--R ,
+--R
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R -
+--R +-----------+
+--R | a +-+
+--R |- --------- \|d
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +-+
+--R | a +-+ a\|c
+--R |- --------- \|d atan(--------------------------)
+--R \| a d - b c +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R /
+--R +-+
+--R b\|d
+--R ,
+--R
+--R +---------+
+--R +---+ | a
+--R \|- d |---------
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((- 4a d + 4b c d)x + (- 4a c d + 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R 4atan(------------------------------)
+--R d x
+--R /
+--R +---+
+--R 2b\|- d
+--R ,
+--R
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R 2atan(------------------------------)
+--R d x
+--R +
+--R -
+--R +-----------+
+--R +---+ | a
+--R \|- d |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +-+
+--R +---+ | a a\|c
+--R \|- d |- --------- atan(--------------------------)
+--R \| a d - b c +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R /
+--R +---+
+--R b\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 908
+
+--S 909 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R 2\|- a d + b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+
+--R +-----------+ | a +-+
+--R \|- a d + b c |--------- \|d
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((- 4a d + 4b c d)x + (- 4a c d + 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-+ +-----------+
+--R +-----------+ x\|d +-+ +-+ x\|- a d + b c
+--R - 2\|- a d + b c atanh(-----------) + 2\|a \|d atan(---------------)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|d x + c \|a \|d x + c
+--R /
+--R +-----------+ +-+
+--R 2b\|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 909
+
+--S 910 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 910
+
+--S 911 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R +-----------+ x\|d
+--R - \|- a d + b c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R -
+--R +-----------+
+--R +-----------+ | a +-+
+--R \|- a d + b c |- --------- \|d
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +-+
+--R +-----------+ | a +-+ a\|c
+--R \|- a d + b c |- --------- \|d atan(--------------------------)
+--R \| a d - b c +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-+ +-+ x\|- a d + b c
+--R \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+ +-+
+--R b\|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 911
+
+--S 912 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 912
+
+)clear all
+
+--S 913 of 1475
+t0:=x/((a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 913
+
+--S 914 of 1475
+r0:=-atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/(sqrt(b)*sqrt(b*c-a*d))
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R (2) - ----------------------
+--R +-----------+ +-+
+--R \|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 914
+
+--S 915 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R log
+--R 2 2 2 3 2 4 2 2 2 2 +-+
+--R ((2a b d + 2a b c d - 4b c )x + (8a b c d - 8a b c )x )\|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a b c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b c d + 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2 2 +-+
+--R (- b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x - 8a c )\|c
+--R /
+--R +-------------+
+--R | 2
+--R 2\|- a b d + b c
+--R ,
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R - -----------------------------------------------------------------]
+--R +-----------+
+--R | 2
+--R \|a b d - b c
+--R Type: Union(List(Expression(Integer)),...)
+--E 915
+
+--S 916 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R \|- a d + b c \|b
+--R *
+--R log
+--R 2 2 2 3 2 4 2 2 2 2
+--R ((2a b d + 2a b c d - 4b c )x + (8a b c d - 8a b c )x )
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a b c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b c d + 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +-------------+ +-+ | 2
+--R | 2 \|b \|d x + c
+--R 2\|- a b d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R /
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R 2\|- a b d + b c \|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 916
+
+--S 917 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 917
+
+--S 918 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-----------+ +-+ | 2
+--R | 2 \|b \|d x + c
+--R \|a b d - b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R -
+--R +-----------+ +-+
+--R \|- a d + b c \|b
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R /
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|b \|a b d - b c
+--R Type: Expression(Integer)
+--E 918
+
+--S 919 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 919
+
+)clear all
+
+--S 920 of 1475
+t0:=1/((a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 920
+
+--S 921 of 1475
+r0:=atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/(sqrt(a)*sqrt(b*c-a*d))
+--R
+--R
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R (2) ---------------------
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 921
+
+--S 922 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 2 | 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )\|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R /
+--R +-----------+
+--R | 2
+--R 2\|a d - a b c
+--R ,
+--R
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R - atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R - atan(--------------------)
+--R (a d - b c)x
+--R /
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 922
+
+--S 923 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - 2\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R 2\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 923
+
+--S 924 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 924
+
+--S 925 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R -
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R +-----------+ +-+ \|- a d + a b c \|c
+--R - \|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - \|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R \|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 925
+
+--S 926 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 926
+
+)clear all
+
+--S 927 of 1475
+t0:=1/(x*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +--------+
+--R 3 | 2
+--R (b x + a x)\|d x + c
+--R Type: Expression(Integer)
+--E 927
+
+--S 928 of 1475
+r0:=-atanh(sqrt(c+d*x^2)/sqrt(c))/(a*sqrt(c))+atanh(sqrt(b)*_
+ sqrt(c+d*x^2)/sqrt(b*c-a*d))*sqrt(b)/(a*sqrt(b*c-a*d))
+--R
+--R
+--R +--------+ +--------+
+--R +-+ | 2 | 2
+--R +-+ +-+ \|b \|d x + c +-----------+ \|d x + c
+--R \|b \|c atanh(---------------) - \|- a d + b c atanh(-----------)
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R (2) -----------------------------------------------------------------
+--R +-----------+ +-+
+--R a\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 928
+
+--S 929 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R | 2 +-+
+--R +-+ \|d x + c - \|c
+--R 2\|c log(------------------)
+--R x
+--R +
+--R +-----------+
+--R | b
+--R c |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (- 2a d + 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((2a b d - 2b c)x + (2a d - 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R /
+--R 2a c
+--R ,
+--R
+--R +--------+
+--R | 2 +-+
+--R +-+ \|d x + c - \|c
+--R \|c log(------------------)
+--R x
+--R +
+--R +--------+
+--R +---------+ +-+ | 2 2
+--R | b a\|c \|d x + c - b c x - a c
+--R c |--------- atan(-------------------------------)
+--R \|a d - b c +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R /
+--R a c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 929
+
+--S 930 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R +-----------+ \|d x + c - \|c
+--R 2\|- a d + b c log(------------------)
+--R x
+--R +
+--R +-----------+
+--R +-----------+ | b +-+
+--R \|- a d + b c |- --------- \|c
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (- 2a d + 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((2a b d - 2b c)x + (2a d - 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+ +--------+
+--R +-+ | 2 | 2
+--R +-+ +-+ \|b \|d x + c +-----------+ \|d x + c
+--R - 2\|b \|c atanh(---------------) + 2\|- a d + b c atanh(-----------)
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R +-----------+ +-+
+--R 2a\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 930
+
+--S 931 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 931
+
+--S 932 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+ +--------+
+--R | 2 +-+ +-+ | 2
+--R +-----------+ \|d x + c - \|c +-+ +-+ \|b \|d x + c
+--R \|- a d + b c log(------------------) - \|b \|c atanh(---------------)
+--R x +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R +-----------+ \|d x + c
+--R \|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +---------+ +-+ | 2 2
+--R +-----------+ | b +-+ a\|c \|d x + c - b c x - a c
+--R \|- a d + b c |--------- \|c atan(-------------------------------)
+--R \|a d - b c +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R /
+--R +-----------+ +-+
+--R a\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 932
+
+--S 933 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 933
+
+)clear all
+
+--S 934 of 1475
+t0:=1/(x^2*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 934
+
+--S 935 of 1475
+r0:=-b*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/(a^(3/2)*_
+ sqrt(b*c-a*d))-sqrt(c+d*x^2)/(a*c*x)
+--R
+--R
+--R +-----------+ +--------+
+--R x\|- a d + b c +-----------+ +-+ | 2
+--R - b c x atan(---------------) - \|- a d + b c \|a \|d x + c
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R (2) -------------------------------------------------------------
+--R +-----------+ +-+
+--R a c x\|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 935
+
+--S 936 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R | 2 +-+
+--R (b c x\|d x + c - b c x\|c )
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +--------+ +-----------+
+--R +-+ | 2 | 2 2 | 2
+--R 2\|c \|a d - a b c \|d x + c + (- 2d x - 2c)\|a d - a b c
+--R /
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 +-+ | 2
+--R 2a c x\|a d - a b c \|d x + c - 2a c x\|c \|a d - a b c
+--R ,
+--R
+--R +--------+
+--R | 2 +-+
+--R (b c x\|d x + c - b c x\|c )
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R +--------+ | 2 +-+
+--R | 2 +-+ \|- a d + a b c \|c
+--R (b c x\|d x + c - b c x\|c )atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +--------+ +-------------+
+--R | 2 +-+ | 2 2 | 2
+--R \|- a d + a b c \|c \|d x + c + (- d x - c)\|- a d + a b c
+--R /
+--R +-------------+ +--------+ +-------------+
+--R | 2 | 2 | 2 +-+
+--R a c x\|- a d + a b c \|d x + c - a c x\|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 936
+
+--S 937 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R b\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R | 2 x\|- a d + b c
+--R 2b\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R 2a\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 937
+
+--S 938 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 938
+
+--S 939 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +-+
+--R b\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R +-----------+ +-+ \|- a d + a b c \|c
+--R b\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R b\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R a\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 939
+
+--S 940 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 940
+
+)clear all
+
+--S 941 of 1475
+t0:=1/(x^3*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R 5 3 | 2
+--R (b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 941
+
+--S 942 of 1475
+r0:=1/2*(2*b*c+a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))/(a^2*c^(3/2))-_
+ b^(3/2)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/(a^2*_
+ sqrt(b*c-a*d))-1/2*sqrt(c+d*x^2)/(a*c*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 +-+ +-+ \|b \|d x + c
+--R - 2b c x \|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R 2 +-----------+ \|d x + c
+--R (a d + 2b c)x \|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R - a\|- a d + b c \|c \|d x + c
+--R /
+--R 2 2 +-----------+ +-+
+--R 2a c x \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 942
+
+--S 943 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 | 2
+--R (- 2a c d - 4b c )x \|d x + c
+--R +
+--R 2 4 2 2 +-+
+--R ((a d + 2b c d)x + (2a c d + 4b c )x )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R 2 2 | b +-+ | 2
+--R 2b c x |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 4 3 2 | b
+--R (- b c d x - 2b c x ) |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (2a d - 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((- 2a b d + 2b c)x + (- 2a d + 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R (a c d x + 2a c )\|d x + c + (- 2a c d x - 2a c )\|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ | 2 2 2 4 2 3 2
+--R 4a c x \|c \|d x + c - 2a c d x - 4a c x
+--R ,
+--R
+--R +--------+
+--R 2 2 | 2
+--R (- 2a c d - 4b c )x \|d x + c
+--R +
+--R 2 4 2 2 +-+
+--R ((a d + 2b c d)x + (2a c d + 4b c )x )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +---------+ +--------+
+--R 2 2 | b +-+ | 2
+--R - 4b c x |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 4 3 2 | b
+--R (2b c d x + 4b c x ) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R (a c d x + 2a c )\|d x + c + (- 2a c d x - 2a c )\|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ | 2 2 2 4 2 3 2
+--R 4a c x \|c \|d x + c - 2a c d x - 4a c x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 943
+
+--S 944 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R +-----------+ \|d x + c - \|c
+--R (- a d - 2b c)\|- a d + b c log(------------------)
+--R x
+--R +
+--R +-----------+
+--R +-----------+ | b +-+
+--R b c\|- a d + b c |- --------- \|c
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (2a d - 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((- 2a b d + 2b c)x + (- 2a d + 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ | 2
+--R +-+ +-+ \|b \|d x + c
+--R 2b c\|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R +-----------+ \|d x + c
+--R (- a d - 2b c)\|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R /
+--R 2 +-----------+ +-+
+--R 2a c\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 944
+
+--S 945 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 945
+
+--S 946 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 2 +-+
+--R +-----------+ \|d x + c - \|c
+--R (- a d - 2b c)\|- a d + b c log(------------------)
+--R x
+--R +
+--R +--------+
+--R +-+ | 2
+--R +-+ +-+ \|b \|d x + c
+--R 2b c\|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R +-----------+ \|d x + c
+--R (- a d - 2b c)\|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +---------+ +-+ | 2 2
+--R +-----------+ | b +-+ a\|c \|d x + c - b c x - a c
+--R - 2b c\|- a d + b c |--------- \|c atan(-------------------------------)
+--R \|a d - b c +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R /
+--R 2 +-----------+ +-+
+--R 2a c\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 946
+
+--S 947 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 947
+
+)clear all
+
+--S 948 of 1475
+t0:=1/(x^4*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R 6 4 | 2
+--R (b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 948
+
+--S 949 of 1475
+r0:=b^2*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/(a^(5/2)*_
+ sqrt(b*c-a*d))-1/3*sqrt(c+d*x^2)/(a*c*x^3)+1/3*(3*b*c+2*a*d)*_
+ sqrt(c+d*x^2)/(a^2*c^2*x)
+--R
+--R
+--R (2)
+--R +-----------+
+--R 2 2 3 x\|- a d + b c
+--R 3b c x atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 +-----------+ +-+ | 2
+--R ((2a d + 3b c)x - a c)\|- a d + b c \|a \|d x + c
+--R /
+--R 2 2 3 +-----------+ +-+
+--R 3a c x \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 949
+
+--S 950 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 5 2 3 3 | 2 2 2 5 2 3 3 +-+
+--R ((3b c d x + 12b c x )\|d x + c + (- 9b c d x - 12b c x )\|c )
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 4 2 2 2 +-+
+--R ((- 12a d - 18b c d)x + (- 10a c d - 24b c )x + 8a c )\|c
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 3 2 6 2 2 4 2 3 2
+--R (4a d + 6b c d )x + (18a c d + 30b c d)x + (6a c d + 24b c )x
+--R +
+--R 3
+--R - 8a c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R /
+--R +-----------+ +--------+
+--R 2 2 5 2 3 3 | 2 | 2
+--R (6a c d x + 24a c x )\|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 5 2 3 3 +-+ | 2
+--R (- 18a c d x - 24a c x )\|c \|a d - a b c
+--R ,
+--R
+--R +--------+
+--R 2 2 5 2 3 3 | 2 2 2 5 2 3 3 +-+
+--R ((- 3b c d x - 12b c x )\|d x + c + (9b c d x + 12b c x )\|c )
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +--------+
+--R 2 2 5 2 3 3 | 2 2 2 5 2 3 3 +-+
+--R ((- 3b c d x - 12b c x )\|d x + c + (9b c d x + 12b c x )\|c )
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 2 4 2 2 2
+--R ((- 6a d - 9b c d)x + (- 5a c d - 12b c )x + 4a c )
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 3 2 6 2 2 4 2 3 2
+--R (2a d + 3b c d )x + (9a c d + 15b c d)x + (3a c d + 12b c )x
+--R +
+--R 3
+--R - 4a c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R +-------------+ +--------+
+--R 2 2 5 2 3 3 | 2 | 2
+--R (3a c d x + 12a c x )\|- a d + a b c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 5 2 3 3 | 2 +-+
+--R (- 9a c d x - 12a c x )\|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 950
+
+--S 951 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----------+ +-+
+--R b \|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R - 2b \|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 2 +-----------+ +-+ | 2
+--R 2a \|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 951
+
+--S 952 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 952
+
+--S 953 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R -
+--R 2 +-----------+ +-+
+--R b \|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 2 +-----------+ +-+ \|- a d + a b c \|c
+--R - b \|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R - b \|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 2 | 2 +-----------+ +-+
+--R a \|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 953
+
+--S 954 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 954
+
+)clear all
+
+--S 955 of 1475
+t0:=x^4/((a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 4
+--R x
+--R (1) -----------------------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b d x + (a d + b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 955
+
+--S 956 of 1475
+r0:=a^(3/2)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/_
+ (b*(b*c-a*d)^(3/2))+atanh(x*sqrt(d)/sqrt(c+d*x^2))/(b*d^(3/2))-_
+ c*x/(d*(b*c-a*d)*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R +-----------+ | 2 x\|d
+--R (a d - b c)\|- a d + b c \|d x + c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +--------+ +-----------+
+--R +-+ +-+ | 2 x\|- a d + b c +-----------+ +-+
+--R - a d\|a \|d \|d x + c atan(---------------) + b c x\|- a d + b c \|d
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +--------+
+--R 2 2 +-----------+ +-+ | 2
+--R (a b d - b c d)\|- a d + b c \|d \|d x + c
+--R Type: Expression(Integer)
+--E 956
+
+--S 957 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2
+--R (2a d - 2b c)\|c \|d x + c + (- 2a d + 2b c d)x - 2a c d
+--R +
+--R 2
+--R 2b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+ +--------+
+--R | a +-+ +-+ | 2
+--R a d |--------- \|c \|d \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 2 | a +-+
+--R (- a d x - a c d) |--------- \|d
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((- 4a d + 4b c d)x + (- 4a c d + 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R - 2b c x\|d \|d x + c + 2b c x\|c \|d
+--R /
+--R +--------+
+--R 2 2 +-+ +-+ | 2
+--R (2a b d - 2b c d)\|c \|d \|d x + c
+--R +
+--R 3 2 2 2 2 2 2 +-+
+--R ((- 2a b d + 2b c d )x - 2a b c d + 2b c d)\|d
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2 2
+--R ((a d - b c)\|c \|d x + c + (- a d + b c d)x - a c d + b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-----------+ +--------+
+--R | a +-+ +-+ | 2
+--R - a d |- --------- \|c \|d \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 | a +-+
+--R (a d x + a c d) |- --------- \|d
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +--------+
+--R | a +-+ +-+ | 2
+--R a d |- --------- \|c \|d \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 | a +-+
+--R (- a d x - a c d) |- --------- \|d
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R - b c x\|d \|d x + c + b c x\|c \|d
+--R /
+--R +--------+
+--R 2 2 +-+ +-+ | 2
+--R (a b d - b c d)\|c \|d \|d x + c
+--R +
+--R 3 2 2 2 2 2 2 +-+
+--R ((- a b d + b c d )x - a b c d + b c d)\|d
+--R ,
+--R
+--R +---------+ +--------+
+--R +---+ | a +-+ | 2
+--R a d\|- d |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 2 +---+ | a
+--R (- a d x - a c d)\|- d |---------
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((- 4a d + 4b c d)x + (- 4a c d + 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ | 2 2 2
+--R (4a d - 4b c)\|c \|d x + c + (- 4a d + 4b c d)x - 4a c d
+--R +
+--R 2
+--R 4b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R - 2b c x\|- d \|d x + c + 2b c x\|- d \|c
+--R /
+--R +--------+
+--R 2 2 +---+ +-+ | 2
+--R (2a b d - 2b c d)\|- d \|c \|d x + c
+--R +
+--R 3 2 2 2 2 2 2 +---+
+--R ((- 2a b d + 2b c d )x - 2a b c d + 2b c d)\|- d
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2
+--R (2a d - 2b c)\|c \|d x + c + (- 2a d + 2b c d)x - 2a c d
+--R +
+--R 2
+--R 2b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R +-----------+ +--------+
+--R +---+ | a +-+ | 2
+--R - a d\|- d |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 +---+ | a
+--R (a d x + a c d)\|- d |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +--------+
+--R +---+ | a +-+ | 2
+--R a d\|- d |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 +---+ | a
+--R (- a d x - a c d)\|- d |- ---------
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R - b c x\|- d \|d x + c + b c x\|- d \|c
+--R /
+--R +--------+
+--R 2 2 +---+ +-+ | 2
+--R (a b d - b c d)\|- d \|c \|d x + c
+--R +
+--R 3 2 2 2 2 2 2 +---+
+--R ((- a b d + b c d )x - a b c d + b c d)\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 957
+
+--S 958 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R (2a d - 2b c)\|- a d + b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+
+--R +-----------+ | a +-+
+--R a d\|- a d + b c |--------- \|d
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((- 4a d + 4b c d)x + (- 4a c d + 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-+
+--R +-----------+ x\|d
+--R (- 2a d + 2b c)\|- a d + b c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-+ +-+ x\|- a d + b c
+--R 2a d\|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 2 +-----------+ +-+
+--R (2a b d - 2b c d)\|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 958
+
+--S 959 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 959
+
+--S 960 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R (a d - b c)\|- a d + b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R +-----------+ x\|d
+--R (- a d + b c)\|- a d + b c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R -
+--R +-----------+
+--R +-----------+ | a +-+
+--R a d\|- a d + b c |- --------- \|d
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +-+
+--R +-----------+ | a +-+ a\|c
+--R a d\|- a d + b c |- --------- \|d atan(--------------------------)
+--R \| a d - b c +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-+ +-+ x\|- a d + b c
+--R a d\|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 2 +-----------+ +-+
+--R (a b d - b c d)\|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 960
+
+--S 961 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 961
+
+)clear all
+
+--S 962 of 1475
+t0:=x^3/((a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 3
+--R x
+--R (1) -----------------------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b d x + (a d + b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 962
+
+--S 963 of 1475
+r0:=a*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/((b*c-a*d)^(3/2)*_
+ sqrt(b))-c/(d*(b*c-a*d)*sqrt(c+d*x^2))
+--R
+--R
+--R +--------+
+--R +--------+ +-+ | 2
+--R | 2 \|b \|d x + c +-----------+ +-+
+--R - a d\|d x + c atanh(---------------) + c\|- a d + b c \|b
+--R +-----------+
+--R \|- a d + b c
+--R (2) ------------------------------------------------------------
+--R +--------+
+--R 2 +-----------+ +-+ | 2
+--R (a d - b c d)\|- a d + b c \|b \|d x + c
+--R Type: Expression(Integer)
+--E 963
+
+--S 964 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2
+--R (a\|c \|d x + c - a d x - a c)
+--R *
+--R log
+--R 2 2 2 3 2 4
+--R (2a b d + 2a b c d - 4b c )x
+--R +
+--R 2 2 2 2
+--R (8a b c d - 8a b c )x
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a b c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b c d + 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 | 2 +-+
+--R - 2x \|- a b d + b c \|c
+--R /
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R (2a d - 2b c)\|- a b d + b c \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 2 | 2
+--R ((- 2a d + 2b c d)x - 2a c d + 2b c )\|- a b d + b c
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2
+--R (- a\|c \|d x + c + a d x + a c)
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+
+--R 2 +-+ | 2
+--R - x \|c \|a b d - b c
+--R /
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R (a d - b c)\|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 | 2
+--R ((- a d + b c d)x - a c d + b c )\|a b d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 964
+
+--S 965 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-----------+ +-+ | 2 +-----------+ +-+ +-+
+--R (a d\|- a d + b c \|b \|d x + c - a d\|- a d + b c \|b \|c )
+--R *
+--R log
+--R 2 2 2 3 2 4 2 2 2 2
+--R ((2a b d + 2a b c d - 4b c )x + (8a b c d - 8a b c )x )
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a b c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b c d + 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+ +--------+ +-------------+
+--R | 2 | 2 | 2 +-+
+--R (2a d\|- a b d + b c \|d x + c - 2a d\|- a b d + b c \|c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-----------+ +-+ +-+ | 2
+--R 2\|- a b d + b c \|- a d + b c \|b \|c \|d x + c
+--R +
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R - 2c\|- a b d + b c \|- a d + b c \|b
+--R /
+--R +-------------+ +--------+
+--R 2 | 2 +-----------+ +-+ | 2
+--R (2a d - 2b c d)\|- a b d + b c \|- a d + b c \|b \|d x + c
+--R +
+--R +-------------+
+--R 2 | 2 +-----------+ +-+ +-+
+--R (- 2a d + 2b c d)\|- a b d + b c \|- a d + b c \|b \|c
+--R Type: Expression(Integer)
+--E 965
+
+--S 966 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 966
+
+--S 967 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 +-+ | 2
+--R (a d\|a b d - b c \|d x + c - a d\|c \|a b d - b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2 +-----------+ +-+ +-+
+--R (- a d\|- a d + b c \|b \|d x + c + a d\|- a d + b c \|b \|c )
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+ +--------+
+--R +-----------+ +-+ +-+ | 2 | 2
+--R \|- a d + b c \|b \|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R - c\|- a d + b c \|b \|a b d - b c
+--R /
+--R +-----------+ +--------+
+--R 2 +-----------+ +-+ | 2 | 2
+--R (a d - b c d)\|- a d + b c \|b \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 +-----------+ +-+ +-+ | 2
+--R (- a d + b c d)\|- a d + b c \|b \|c \|a b d - b c
+--R Type: Expression(Integer)
+--E 967
+
+--S 968 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 968
+
+)clear all
+
+--S 969 of 1475
+t0:=x^2/((a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2
+--R x
+--R (1) -----------------------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b d x + (a d + b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 969
+
+--S 970 of 1475
+r0:=-atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*sqrt(a)/_
+ (b*c-a*d)^(3/2)+x/((b*c-a*d)*sqrt(c+d*x^2))
+--R
+--R
+--R +--------+ +-----------+
+--R +-+ | 2 x\|- a d + b c +-----------+
+--R \|a \|d x + c atan(---------------) - x\|- a d + b c
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R (2) ------------------------------------------------------
+--R +--------+
+--R +-----------+ | 2
+--R (a d - b c)\|- a d + b c \|d x + c
+--R Type: Expression(Integer)
+--E 970
+
+--S 971 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+ +--------+ +---------+
+--R | a +-+ | 2 2 | a
+--R ( |--------- \|c \|d x + c + (- d x - c) |--------- )
+--R \|a d - b c \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((- 2a d + 2b c d)x + (- 4a c d + 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((4a d - 4b c d)x + (4a c d - 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R | 2 +-+
+--R 2x\|d x + c - 2x\|c
+--R /
+--R +--------+
+--R +-+ | 2 2 2 2
+--R (2a d - 2b c)\|c \|d x + c + (- 2a d + 2b c d)x - 2a c d + 2b c
+--R ,
+--R
+--R +-----------+ +--------+ +-----------+
+--R | a +-+ | 2 2 | a
+--R ( |- --------- \|c \|d x + c + (- d x - c) |- --------- )
+--R \| a d - b c \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +--------+ +-----------+
+--R | a +-+ | 2 2 | a
+--R (- |- --------- \|c \|d x + c + (d x + c) |- --------- )
+--R \| a d - b c \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +--------+
+--R | 2 +-+
+--R x\|d x + c - x\|c
+--R /
+--R +--------+
+--R +-+ | 2 2 2 2
+--R (a d - b c)\|c \|d x + c + (- a d + b c d)x - a c d + b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 971
+
+--S 972 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-----------+ | a
+--R \|- a d + b c |---------
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((- 2a d + 2b c d)x + (- 4a c d + 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((4a d - 4b c d)x + (4a c d - 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+
+--R +-+ x\|- a d + b c
+--R - 2\|a atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R (2a d - 2b c)\|- a d + b c
+--R Type: Expression(Integer)
+--E 972
+
+--S 973 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 973
+
+--S 974 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R +-----------+ | a
+--R \|- a d + b c |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +-+
+--R +-----------+ | a a\|c
+--R - \|- a d + b c |- --------- atan(--------------------------)
+--R \| a d - b c +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-+ x\|- a d + b c
+--R - \|a atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R (a d - b c)\|- a d + b c
+--R Type: Expression(Integer)
+--E 974
+
+--S 975 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 975
+
+)clear all
+
+--S 976 of 1475
+t0:=x/((a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R x
+--R (1) -----------------------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b d x + (a d + b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 976
+
+--S 977 of 1475
+r0:=-atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))*sqrt(b)/(b*c-a*d)^(3/2)+_
+ 1/((b*c-a*d)*sqrt(c+d*x^2))
+--R
+--R
+--R +--------+
+--R +--------+ +-+ | 2
+--R +-+ | 2 \|b \|d x + c +-----------+
+--R \|b \|d x + c atanh(---------------) - \|- a d + b c
+--R +-----------+
+--R \|- a d + b c
+--R (2) ------------------------------------------------------
+--R +--------+
+--R +-----------+ | 2
+--R (a d - b c)\|- a d + b c \|d x + c
+--R Type: Expression(Integer)
+--E 977
+
+--S 978 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+ +--------+ +-----------+
+--R | b +-+ | 2 2 2 | b
+--R (c |- --------- \|c \|d x + c + (- c d x - c ) |- --------- )
+--R \| a d - b c \| a d - b c
+--R *
+--R log
+--R 2 2 2 2 4
+--R (- 2a d - 2a b c d + 4b c )x
+--R +
+--R 2 2 2
+--R (- 8a c d + 8a b c )x
+--R *
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (2a b c d - 2b c d)x + (6a c d - 2a b c d - 4b c )x
+--R +
+--R 2 2 3 2
+--R (8a c d - 8a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 +-+
+--R 2d x \|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2 2 3
+--R (2a c d - 2b c )\|c \|d x + c + (- 2a c d + 2b c d)x - 2a c d + 2b c
+--R ,
+--R
+--R +---------+ +--------+ +---------+
+--R | b +-+ | 2 2 2 | b
+--R (c |--------- \|c \|d x + c + (- c d x - c ) |--------- )
+--R \|a d - b c \|a d - b c
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b
+--R (a d - b c)x |---------
+--R \|a d - b c
+--R +
+--R 2 +-+
+--R d x \|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2 2 3
+--R (a c d - b c )\|c \|d x + c + (- a c d + b c d)x - a c d + b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 978
+
+--S 979 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +--------+
+--R +-----------+ | b | 2
+--R c\|- a d + b c |- --------- \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-----------+ | b +-+
+--R - c\|- a d + b c |- --------- \|c
+--R \| a d - b c
+--R *
+--R log
+--R 2 2 2 2 4 2 2 2
+--R ((- 2a d - 2a b c d + 4b c )x + (- 8a c d + 8a b c )x )
+--R *
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (2a b c d - 2b c d)x + (6a c d - 2a b c d - 4b c )x
+--R +
+--R 2 2 3 2
+--R (8a c d - 8a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +--------+ +-+ | 2
+--R +-+ | 2 +-+ +-+ \|b \|d x + c
+--R (- 2c\|b \|d x + c + 2c\|b \|c )atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2 +-----------+
+--R - 2\|- a d + b c \|c \|d x + c + 2c\|- a d + b c
+--R /
+--R +--------+
+--R 2 +-----------+ | 2
+--R (2a c d - 2b c )\|- a d + b c \|d x + c
+--R +
+--R 2 +-----------+ +-+
+--R (- 2a c d + 2b c )\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 979
+
+--S 980 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 980
+
+--S 981 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +--------+ +-+ | 2
+--R +-+ | 2 +-+ +-+ \|b \|d x + c
+--R (- c\|b \|d x + c + c\|b \|c )atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +---------+ +--------+
+--R +-----------+ | b | 2
+--R c\|- a d + b c |--------- \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R +-----------+ | b +-+
+--R - c\|- a d + b c |--------- \|c
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b
+--R (a d - b c)x |---------
+--R \|a d - b c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2 +-----------+
+--R - \|- a d + b c \|c \|d x + c + c\|- a d + b c
+--R /
+--R +--------+
+--R 2 +-----------+ | 2
+--R (a c d - b c )\|- a d + b c \|d x + c
+--R +
+--R 2 +-----------+ +-+
+--R (- a c d + b c )\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 981
+
+--S 982 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 982
+
+)clear all
+
+--S 983 of 1475
+t0:=1/((a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b d x + (a d + b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 983
+
+--S 984 of 1475
+r0:=b*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/((b*c-a*d)^(3/2)*_
+ sqrt(a))-d*x/(c*(b*c-a*d)*sqrt(c+d*x^2))
+--R
+--R
+--R +--------+ +-----------+
+--R | 2 x\|- a d + b c +-----------+ +-+
+--R - b c\|d x + c atan(---------------) + d x\|- a d + b c \|a
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R (2) -------------------------------------------------------------
+--R +--------+
+--R 2 +-----------+ +-+ | 2
+--R (a c d - b c )\|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 984
+
+--S 985 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2
+--R (b c\|c \|d x + c - b c d x - b c )
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 +-+ | 2
+--R - 2d x\|a d - a b c \|d x + c + 2d x\|c \|a d - a b c
+--R /
+--R +-----------+ +--------+
+--R 2 +-+ | 2 | 2
+--R (2a c d - 2b c )\|c \|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 3 | 2
+--R ((- 2a c d + 2b c d)x - 2a c d + 2b c )\|a d - a b c
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2
+--R (b c\|c \|d x + c - b c d x - b c )
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R +--------+ | 2 +-+
+--R +-+ | 2 2 2 \|- a d + a b c \|c
+--R (b c\|c \|d x + c - b c d x - b c )atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +--------+ +-------------+
+--R | 2 | 2 | 2 +-+
+--R - d x\|- a d + a b c \|d x + c + d x\|- a d + a b c \|c
+--R /
+--R +-------------+ +--------+
+--R 2 | 2 +-+ | 2
+--R (a c d - b c )\|- a d + a b c \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 2 2 3 | 2
+--R ((- a c d + b c d)x - a c d + b c )\|- a d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 985
+
+--S 986 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R b\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R | 2 x\|- a d + b c
+--R 2b\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R (2a d - 2b c)\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 986
+
+--S 987 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 987
+
+--S 988 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +-+
+--R b\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R +-----------+ +-+ \|- a d + a b c \|c
+--R b\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R b\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R (a d - b c)\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 988
+
+--S 989 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 989
+
+)clear all
+
+--S 990 of 1475
+t0:=1/(x*(a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------
+--R +--------+
+--R 5 3 | 2
+--R (b d x + (a d + b c)x + a c x)\|d x + c
+--R Type: Expression(Integer)
+--E 990
+
+--S 991 of 1475
+r0:=-atanh(sqrt(c+d*x^2)/sqrt(c))/(a*c^(3/2))+b^(3/2)*atanh(sqrt(b)*_
+ sqrt(c+d*x^2)/sqrt(b*c-a*d))/(a*(b*c-a*d)^(3/2))-d/(c*(b*c-a*d)*_
+ sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ +-+ | 2
+--R +-+ +-+ | 2 \|b \|d x + c
+--R - b c\|b \|c \|d x + c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +--------+ | 2
+--R +-----------+ | 2 \|d x + c
+--R (- a d + b c)\|- a d + b c \|d x + c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +-----------+ +-+
+--R a d\|- a d + b c \|c
+--R /
+--R +--------+
+--R 2 2 +-----------+ +-+ | 2
+--R (a c d - a b c )\|- a d + b c \|c \|d x + c
+--R Type: Expression(Integer)
+--E 991
+
+--S 992 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 | 2
+--R (2a c d - 2b c )\|d x + c
+--R +
+--R 2 2 2 +-+
+--R ((- 2a d + 2b c d)x - 2a c d + 2b c )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R 2 | b +-+ | 2
+--R b c |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 3 | b
+--R (- b c d x - b c ) |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (2a d - 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((- 2a b d + 2b c)x + (- 2a d + 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 +-+
+--R - 2a d x \|c
+--R /
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 2 3 2 2 3
+--R (2a c d - 2a b c )\|c \|d x + c + (- 2a c d + 2a b c d)x - 2a c d
+--R +
+--R 4
+--R 2a b c
+--R ,
+--R
+--R +--------+
+--R 2 | 2 2 2 2 +-+
+--R ((a c d - b c )\|d x + c + ((- a d + b c d)x - a c d + b c )\|c )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +---------+ +--------+ +---------+
+--R 2 | b +-+ | 2 2 2 3 | b
+--R (- b c |--------- \|c \|d x + c + (b c d x + b c ) |--------- )
+--R \|a d - b c \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 2 +-+
+--R - a d x \|c
+--R /
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 2 3 2 2 3 4
+--R (a c d - a b c )\|c \|d x + c + (- a c d + a b c d)x - a c d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 992
+
+--S 993 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-----------+ | 2
+--R (2a d - 2b c)\|- a d + b c \|d x + c
+--R +
+--R +-----------+ +-+
+--R (- 2a d + 2b c)\|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R +-----------+ | b +-+ | 2
+--R b c\|- a d + b c |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 +-----------+ | b
+--R - b c \|- a d + b c |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (2a d - 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((- 2a b d + 2b c)x + (- 2a d + 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +--------+ +-+ | 2
+--R +-+ +-+ | 2 2 +-+ \|b \|d x + c
+--R (2b c\|b \|c \|d x + c - 2b c \|b )atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +-----------+ | 2
+--R (2a d - 2b c)\|- a d + b c \|d x + c
+--R +
+--R +-----------+ +-+
+--R (- 2a d + 2b c)\|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +-----------+ | 2 +-----------+ +-+
+--R 2a d\|- a d + b c \|d x + c - 2a d\|- a d + b c \|c
+--R /
+--R +--------+
+--R 2 2 +-----------+ +-+ | 2
+--R (2a c d - 2a b c )\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 3 +-----------+
+--R (- 2a c d + 2a b c )\|- a d + b c
+--R Type: Expression(Integer)
+--E 993
+
+--S 994 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 994
+
+--S 995 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-----------+ | 2
+--R (a d - b c)\|- a d + b c \|d x + c
+--R +
+--R +-----------+ +-+
+--R (- a d + b c)\|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R +--------+ +-+ | 2
+--R +-+ +-+ | 2 2 +-+ \|b \|d x + c
+--R (b c\|b \|c \|d x + c - b c \|b )atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +-----------+ | 2
+--R (a d - b c)\|- a d + b c \|d x + c
+--R +
+--R +-----------+ +-+
+--R (- a d + b c)\|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +---------+ +--------+
+--R +-----------+ | b +-+ | 2
+--R - b c\|- a d + b c |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 +-----------+ | b
+--R b c \|- a d + b c |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R +--------+
+--R +-----------+ | 2 +-----------+ +-+
+--R a d\|- a d + b c \|d x + c - a d\|- a d + b c \|c
+--R /
+--R +--------+
+--R 2 2 +-----------+ +-+ | 2
+--R (a c d - a b c )\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 3 +-----------+
+--R (- a c d + a b c )\|- a d + b c
+--R Type: Expression(Integer)
+--E 995
+
+--S 996 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 996
+
+)clear all
+
+--S 997 of 1475
+t0:=1/(x^2*(a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------
+--R +--------+
+--R 6 4 2 | 2
+--R (b d x + (a d + b c)x + a c x )\|d x + c
+--R Type: Expression(Integer)
+--E 997
+
+--S 998 of 1475
+r0:=-b^2*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/(a^(3/2)*(b*c-_
+ a*d)^(3/2))-d/(c*(b*c-a*d)*x*sqrt(c+d*x^2))-(b*c-2*a*d)*sqrt(c+_
+ d*x^2)/(a*c^2*(b*c-a*d)*x)
+--R
+--R
+--R (2)
+--R +--------+ +-----------+
+--R 2 2 | 2 x\|- a d + b c
+--R b c x\|d x + c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 2 2 2 +-----------+ +-+
+--R ((- 2a d + b c d)x - a c d + b c )\|- a d + b c \|a
+--R /
+--R +--------+
+--R 2 2 3 +-----------+ +-+ | 2
+--R (a c d - a b c )x\|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 998
+
+--S 999 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 3 2 3 | 2 2 2 3 2 3 +-+
+--R ((b c d x + 2b c x)\|d x + c + (- 2b c d x - 2b c x)\|c )
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +--------+
+--R 2 2 2 +-+ | 2 | 2
+--R ((8a d - 4b c d)x + 4a c d - 4b c )\|c \|a d - a b c \|d x + c
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((- 4a d + 2b c d )x + (- 10a c d + 6b c d)x - 4a c d + 4b c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R /
+--R +-----------+ +--------+
+--R 2 2 2 3 3 2 3 4 | 2 | 2
+--R ((2a c d - 2a b c d)x + (4a c d - 4a b c )x)\|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 3 3 2 3 4 +-+ | 2
+--R ((- 4a c d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c \|a d - a b c
+--R ,
+--R
+--R +--------+
+--R 2 2 3 2 3 | 2 2 2 3 2 3 +-+
+--R ((- b c d x - 2b c x)\|d x + c + (2b c d x + 2b c x)\|c )
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +--------+
+--R 2 2 3 2 3 | 2 2 2 3 2 3 +-+
+--R ((- b c d x - 2b c x)\|d x + c + (2b c d x + 2b c x)\|c )
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +--------+
+--R 2 2 2 | 2 +-+ | 2
+--R ((4a d - 2b c d)x + 2a c d - 2b c )\|- a d + a b c \|c \|d x + c
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((- 2a d + b c d )x + (- 5a c d + 3b c d)x - 2a c d + 2b c )
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R +-------------+ +--------+
+--R 2 2 2 3 3 2 3 4 | 2 | 2
+--R ((a c d - a b c d)x + (2a c d - 2a b c )x)\|- a d + a b c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 2 3 3 2 3 4 | 2 +-+
+--R ((- 2a c d + 2a b c d)x + (- 2a c d + 2a b c )x)\|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 999
+
+--S 1000 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----------+ +-+
+--R b \|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R - 2b \|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 2 +-----------+ +-+ | 2
+--R (2a d - 2a b c)\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 1000
+
+--S 1001 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1001
+
+--S 1002 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R -
+--R 2 +-----------+ +-+
+--R b \|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 2 +-----------+ +-+ \|- a d + a b c \|c
+--R - b \|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R - b \|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 2 | 2 +-----------+ +-+
+--R (a d - a b c)\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 1002
+
+--S 1003 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1003
+
+)clear all
+
+--S 1004 of 1475
+t0:=1/(x^3*(a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------
+--R +--------+
+--R 7 5 3 | 2
+--R (b d x + (a d + b c)x + a c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1004
+
+--S 1005 of 1475
+r0:=1/2*(2*b*c+3*a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))/(a^2*c^(5/2))-b^(5/2)*_
+ atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/(a^2*(b*c-a*d)^(3/2))-_
+ 1/2*d*(b*c-3*a*d)/(a*c^2*(b*c-a*d)*sqrt(c+d*x^2))+(-1/2)/(a*c*_
+ x^2*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ +-+ | 2
+--R 2 2 2 +-+ +-+ | 2 \|b \|d x + c
+--R 2b c x \|b \|c \|d x + c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +--------+ | 2
+--R 2 2 2 2 2 +-----------+ | 2 \|d x + c
+--R (3a d - a b c d - 2b c )x \|- a d + b c \|d x + c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2 2 +-----------+ +-+
+--R ((- 3a d + a b c d)x - a c d + a b c )\|- a d + b c \|c
+--R /
+--R +--------+
+--R 3 2 2 3 2 +-----------+ +-+ | 2
+--R (2a c d - 2a b c )x \|- a d + b c \|c \|d x + c
+--R Type: Expression(Integer)
+--E 1005
+
+--S 1006 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 2 3 4
+--R (- 9a c d + 3a b c d + 6b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (- 12a c d + 4a b c d + 8b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 2 6
+--R (3a d - a b c d - 2b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (15a c d - 5a b c d - 10b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (12a c d - 4a b c d - 8b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R 2 3 4 2 4 2 | b +-+ | 2
+--R (3b c d x + 4b c x ) |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 3 2 6 2 4 4 2 5 2 | b
+--R (- b c d x - 5b c d x - 4b c x ) |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (- 2a d + 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((2a b d - 2b c)x + (2a d - 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 4 2 2 2 3 2 2 3
+--R (- 3a c d - a b c d )x + (5a c d - 5a b c d)x + 4a c d
+--R +
+--R 4
+--R - 4a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 6 2 3 2 2 4 2 2 2 3 2
+--R 2a d x + (a c d + 3a b c d )x + (- 7a c d + 7a b c d)x
+--R +
+--R 2 3 4
+--R - 4a c d + 4a b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 3 2 2 4 4 3 4 2 5 2 +-+ | 2
+--R ((6a c d - 6a b c d)x + (8a c d - 8a b c )x )\|c \|d x + c
+--R +
+--R 3 3 3 2 4 2 6 3 4 2 2 5 4
+--R (- 2a c d + 2a b c d )x + (- 10a c d + 10a b c d)x
+--R +
+--R 3 5 2 6 2
+--R (- 8a c d + 8a b c )x
+--R ,
+--R
+--R 2 3 2 2 2 3 4
+--R (- 9a c d + 3a b c d + 6b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (- 12a c d + 4a b c d + 8b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 2 6
+--R (3a d - a b c d - 2b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (15a c d - 5a b c d - 10b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (12a c d - 4a b c d - 8b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +---------+ +--------+
+--R 2 3 4 2 4 2 | b +-+ | 2
+--R (6b c d x + 8b c x ) |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 3 2 6 2 4 4 2 5 2 | b
+--R (- 2b c d x - 10b c d x - 8b c x ) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 3 2 2 4 2 2 2 3 2 2 3
+--R (- 3a c d - a b c d )x + (5a c d - 5a b c d)x + 4a c d
+--R +
+--R 4
+--R - 4a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 6 2 3 2 2 4 2 2 2 3 2
+--R 2a d x + (a c d + 3a b c d )x + (- 7a c d + 7a b c d)x
+--R +
+--R 2 3 4
+--R - 4a c d + 4a b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 3 2 2 4 4 3 4 2 5 2 +-+ | 2
+--R ((6a c d - 6a b c d)x + (8a c d - 8a b c )x )\|c \|d x + c
+--R +
+--R 3 3 3 2 4 2 6 3 4 2 2 5 4
+--R (- 2a c d + 2a b c d )x + (- 10a c d + 10a b c d)x
+--R +
+--R 3 5 2 6 2
+--R (- 8a c d + 8a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1006
+
+--S 1007 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 3a d + a b c d + 2b c d)x - 12a c d + 4a b c d + 8b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((9a d - 3a b c d - 6b c d)x + 12a c d - 4a b c d - 8b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R 2 2 2 2 3 +-----------+ | b +-+ | 2
+--R (b c d x + 4b c )\|- a d + b c |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 3 2 2 4 +-----------+ | b
+--R (- 3b c d x - 4b c )\|- a d + b c |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (- 2a d + 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((2a b d - 2b c)x + (2a d - 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ +-+ | 2 2 3 2 2 4 +-+
+--R ((- 2b c d x - 8b c )\|b \|c \|d x + c + (6b c d x + 8b c )\|b )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 3a d + a b c d + 2b c d)x - 12a c d + 4a b c d + 8b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((9a d - 3a b c d - 6b c d)x + 12a c d - 4a b c d - 8b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 3 2 2 2 +-----------+ | 2
+--R (- 2a d x - 8a c d )\|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 +-----------+ +-+
+--R (6a d x + 8a c d )\|- a d + b c \|c
+--R /
+--R +--------+
+--R 3 2 2 2 3 2 3 3 2 4 +-----------+ +-+ | 2
+--R ((2a c d - 2a b c d)x + 8a c d - 8a b c )\|- a d + b c \|c \|d x + c
+--R +
+--R 3 3 2 2 4 2 3 4 2 5 +-----------+
+--R ((- 6a c d + 6a b c d)x - 8a c d + 8a b c )\|- a d + b c
+--R Type: Expression(Integer)
+--E 1007
+
+--S 1008 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1008
+
+--S 1009 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 3a d + a b c d + 2b c d)x - 12a c d + 4a b c d + 8b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((9a d - 3a b c d - 6b c d)x + 12a c d - 4a b c d - 8b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ +-+ | 2 2 3 2 2 4 +-+
+--R ((- 2b c d x - 8b c )\|b \|c \|d x + c + (6b c d x + 8b c )\|b )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 3a d + a b c d + 2b c d)x - 12a c d + 4a b c d + 8b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((9a d - 3a b c d - 6b c d)x + 12a c d - 4a b c d - 8b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +---------+ +--------+
+--R 2 2 2 2 3 +-----------+ | b +-+ | 2
+--R (2b c d x + 8b c )\|- a d + b c |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 3 2 2 4 +-----------+ | b
+--R (- 6b c d x - 8b c )\|- a d + b c |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R +--------+
+--R 2 3 2 2 2 +-----------+ | 2
+--R (- 2a d x - 8a c d )\|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 +-----------+ +-+
+--R (6a d x + 8a c d )\|- a d + b c \|c
+--R /
+--R +--------+
+--R 3 2 2 2 3 2 3 3 2 4 +-----------+ +-+ | 2
+--R ((2a c d - 2a b c d)x + 8a c d - 8a b c )\|- a d + b c \|c \|d x + c
+--R +
+--R 3 3 2 2 4 2 3 4 2 5 +-----------+
+--R ((- 6a c d + 6a b c d)x - 8a c d + 8a b c )\|- a d + b c
+--R Type: Expression(Integer)
+--E 1009
+
+--S 1010 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1010
+
+)clear all
+
+--S 1011 of 1475
+t0:=1/(x^4*(a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------
+--R +--------+
+--R 8 6 4 | 2
+--R (b d x + (a d + b c)x + a c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1011
+
+--S 1012 of 1475
+r0:=b^3*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/(a^(5/2)*_
+ (b*c-a*d)^(3/2))-d/(c*(b*c-a*d)*x^3*sqrt(c+d*x^2))-1/3*(b*c-4*a*d)*_
+ sqrt(c+d*x^2)/(a*c^2*(b*c-a*d)*x^3)+1/3*(3*b*c-4*a*d)*(b*c+2*a*d)*_
+ sqrt(c+d*x^2)/(a^2*c^3*(b*c-a*d)*x)
+--R
+--R
+--R (2)
+--R +--------+ +-----------+
+--R 3 3 3 | 2 x\|- a d + b c
+--R - 3b c x \|d x + c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 2 3 2 2 2 4 2 2 2 2 3 2
+--R (8a d - 2a b c d - 3b c d)x + (4a c d - a b c d - 3b c )x
+--R +
+--R 2 2 3
+--R - a c d + a b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R /
+--R +--------+
+--R 3 3 2 4 3 +-----------+ +-+ | 2
+--R (3a c d - 3a b c )x \|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 1012
+
+--S 1013 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 3 2 7 3 4 5 3 5 3 | 2
+--R (3b c d x + 24b c d x + 24b c x )\|d x + c
+--R +
+--R 3 3 2 7 3 4 5 3 5 3 +-+
+--R (- 12b c d x - 36b c d x - 24b c x )\|c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 4 3 2 2 2 6
+--R (- 64a d + 16a b c d + 24b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 160a c d + 40a b c d + 72b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4
+--R (- 56a c d + 8a b c d + 48b c )x + 16a c d - 16a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a d - a b c \|d x + c
+--R +
+--R 2 5 4 2 2 3 8
+--R (16a d - 4a b c d - 6b c d )x
+--R +
+--R 2 4 2 3 2 3 2 6
+--R (136a c d - 34a b c d - 54b c d )x
+--R +
+--R 2 2 3 3 2 2 4 4 2 3 2 2 5 2
+--R (190a c d - 46a b c d - 96b c d)x + (48a c d - 48b c )x
+--R +
+--R 2 4 5
+--R - 16a c d + 16a b c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R /
+--R 3 3 3 2 4 2 7 3 4 2 2 5 5
+--R (6a c d - 6a b c d )x + (48a c d - 48a b c d)x
+--R +
+--R 3 5 2 6 3
+--R (48a c d - 48a b c )x
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 3 3 3 2 4 2 7 3 4 2 2 5 5
+--R (- 24a c d + 24a b c d )x + (- 72a c d + 72a b c d)x
+--R +
+--R 3 5 2 6 3
+--R (- 48a c d + 48a b c )x
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|c \|a d - a b c
+--R ,
+--R
+--R +--------+
+--R 3 3 2 7 3 4 5 3 5 3 | 2
+--R (3b c d x + 24b c d x + 24b c x )\|d x + c
+--R +
+--R 3 3 2 7 3 4 5 3 5 3 +-+
+--R (- 12b c d x - 36b c d x - 24b c x )\|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +--------+
+--R 3 3 2 7 3 4 5 3 5 3 | 2
+--R (3b c d x + 24b c d x + 24b c x )\|d x + c
+--R +
+--R 3 3 2 7 3 4 5 3 5 3 +-+
+--R (- 12b c d x - 36b c d x - 24b c x )\|c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 2 4 3 2 2 2 6
+--R (- 32a d + 8a b c d + 12b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 80a c d + 20a b c d + 36b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4
+--R (- 28a c d + 4a b c d + 24b c )x + 8a c d - 8a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 2 5 4 2 2 3 8
+--R (8a d - 2a b c d - 3b c d )x
+--R +
+--R 2 4 2 3 2 3 2 6
+--R (68a c d - 17a b c d - 27b c d )x
+--R +
+--R 2 2 3 3 2 2 4 4 2 3 2 2 5 2
+--R (95a c d - 23a b c d - 48b c d)x + (24a c d - 24b c )x
+--R +
+--R 2 4 5
+--R - 8a c d + 8a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R 3 3 3 2 4 2 7 3 4 2 2 5 5
+--R (3a c d - 3a b c d )x + (24a c d - 24a b c d)x
+--R +
+--R 3 5 2 6 3
+--R (24a c d - 24a b c )x
+--R *
+--R +-------------+ +--------+
+--R | 2 | 2
+--R \|- a d + a b c \|d x + c
+--R +
+--R 3 3 3 2 4 2 7 3 4 2 2 5 5
+--R (- 12a c d + 12a b c d )x + (- 36a c d + 36a b c d)x
+--R +
+--R 3 5 2 6 3
+--R (- 24a c d + 24a b c )x
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1013
+
+--S 1014 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 +-----------+ +-+
+--R b \|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 3 | 2 x\|- a d + b c
+--R 2b \|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 3 2 +-----------+ +-+ | 2
+--R (2a d - 2a b c)\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 1014
+
+--S 1015 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1015
+
+--S 1016 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 3 +-----------+ +-+
+--R b \|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 3 +-----------+ +-+ \|- a d + a b c \|c
+--R b \|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 3 | 2 x\|- a d + b c
+--R b \|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 3 2 | 2 +-----------+ +-+
+--R (a d - a b c)\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 1016
+
+--S 1017 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1017
+
+)clear all
+
+--S 1018 of 1475
+t0:=x^4/((a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R 4
+--R x
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|d x + c
+--R Type: Expression(Integer)
+--E 1018
+
+--S 1019 of 1475
+r0:=-1/3*c*x/(d*(b*c-a*d)*(c+d*x^2)^(3/2))+a^(3/2)*atan(x*sqrt(b*c-a*d)/_
+ (sqrt(a)*sqrt(c+d*x^2)))/(b*c-a*d)^(5/2)+1/3*(b*c-4*a*d)*x/(d*_
+ (b*c-a*d)^2*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+ +-----------+
+--R 2 +-+ | 2 x\|- a d + b c
+--R (3a d x + 3a c)\|a \|d x + c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 3 +-----------+
+--R ((- 4a d + b c)x - 3a c x)\|- a d + b c
+--R /
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d - 6a b c d + 3b c d)x + 3a c d - 6a b c d + 3b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R Type: Expression(Integer)
+--E 1019
+
+--S 1020 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+ +--------+
+--R 2 4 2 2 | a +-+ | 2
+--R (9a d x + 21a c d x + 12a c ) |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 3 6 2 4 2 2 3 | a
+--R (- 3a d x - 18a c d x - 27a c d x - 12a c ) |---------
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((- 2a d + 2b c d)x + (- 4a c d + 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((4a d - 4b c d)x + (4a c d - 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 5 2 3 2 | 2
+--R ((8a d - 2b c d)x + (38a c d - 8b c )x + 24a c x)\|d x + c
+--R +
+--R 2 5 2 3 2 +-+
+--R ((- 24a d + 6b c d)x + (- 50a c d + 8b c )x - 24a c x)\|c
+--R /
+--R 2 4 3 2 2 2 4
+--R (18a d - 36a b c d + 18b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (42a c d - 84a b c d + 42b c d)x + 24a c d - 48a b c d + 24b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 4 2 2 3 6
+--R (- 6a d + 12a b c d - 6b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 36a c d + 72a b c d - 36b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (- 54a c d + 108a b c d - 54b c d)x - 24a c d + 48a b c d - 24b c
+--R ,
+--R
+--R +-----------+ +--------+
+--R 2 4 2 2 | a +-+ | 2
+--R (9a d x + 21a c d x + 12a c ) |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 3 6 2 4 2 2 3 | a
+--R (- 3a d x - 18a c d x - 27a c d x - 12a c ) |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
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+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +--------+
+--R 2 4 2 2 | a +-+ | 2
+--R (- 9a d x - 21a c d x - 12a c ) |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 3 6 2 4 2 2 3 | a
+--R (3a d x + 18a c d x + 27a c d x + 12a c ) |- ---------
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +--------+
+--R 2 5 2 3 2 | 2
+--R ((4a d - b c d)x + (19a c d - 4b c )x + 12a c x)\|d x + c
+--R +
+--R 2 5 2 3 2 +-+
+--R ((- 12a d + 3b c d)x + (- 25a c d + 4b c )x - 12a c x)\|c
+--R /
+--R 2 4 3 2 2 2 4
+--R (9a d - 18a b c d + 9b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (21a c d - 42a b c d + 21b c d)x + 12a c d - 24a b c d + 12b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 4 2 2 3 6
+--R (- 3a d + 6a b c d - 3b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 18a c d + 36a b c d - 18b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (- 27a c d + 54a b c d - 27b c d)x - 12a c d + 24a b c d - 12b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1020
+
+--S 1021 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-----------+ | a
+--R a\|- a d + b c |---------
+--R \|a d - b c
+--R *
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+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((- 2a d + 2b c d)x + (- 4a c d + 4b c )x) |---------
+--R \|a d - b c
+--R *
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+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((4a d - 4b c d)x + (4a c d - 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+
+--R +-+ x\|- a d + b c
+--R - 2a\|a atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 2 2 2 +-----------+
+--R (2a d - 4a b c d + 2b c )\|- a d + b c
+--R Type: Expression(Integer)
+--E 1021
+
+--S 1022 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1022
+
+--S 1023 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R +-----------+ | a
+--R a\|- a d + b c |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +-+
+--R +-----------+ | a a\|c
+--R - a\|- a d + b c |- --------- atan(--------------------------)
+--R \| a d - b c +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-+ x\|- a d + b c
+--R - a\|a atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 2 2 2 +-----------+
+--R (a d - 2a b c d + b c )\|- a d + b c
+--R Type: Expression(Integer)
+--E 1023
+
+--S 1024 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1024
+
+)clear all
+
+--S 1025 of 1475
+t0:=x^3/((a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R 3
+--R x
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|d x + c
+--R Type: Expression(Integer)
+--E 1025
+
+--S 1026 of 1475
+r0:=-1/3*c/(d*(b*c-a*d)*(c+d*x^2)^(3/2))+a*atanh(sqrt(b)*sqrt(c+d*x^2)/_
+ sqrt(b*c-a*d))*sqrt(b)/(b*c-a*d)^(5/2)-a/((b*c-a*d)^2*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ +-+ | 2
+--R 2 2 +-+ | 2 \|b \|d x + c
+--R (3a d x + 3a c d)\|b \|d x + c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 2 2 +-----------+
+--R (- 3a d x - 2a c d - b c )\|- a d + b c
+--R /
+--R 2 4 3 2 2 2 2 2 3 2 2 2 3
+--R ((3a d - 6a b c d + 3b c d )x + 3a c d - 6a b c d + 3b c d)
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R Type: Expression(Integer)
+--E 1026
+
+--S 1027 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+ +--------+
+--R 2 4 2 2 3 | b +-+ | 2
+--R (9a c d x + 21a c d x + 12a c ) |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 3 6 2 2 4 3 2 4 | b
+--R (- 3a c d x - 18a c d x - 27a c d x - 12a c ) |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R 2 2 2 2 4
+--R (- 2a d - 2a b c d + 4b c )x
+--R +
+--R 2 2 2
+--R (- 8a c d + 8a b c )x
+--R *
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (2a b c d - 2b c d)x + (6a c d - 2a b c d - 4b c )x
+--R +
+--R 2 2 3 2
+--R (8a c d - 8a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 4 3 2 | 2
+--R ((- 6a c d - 6b c d)x - 12b c x )\|d x + c
+--R +
+--R 3 2 6 2 2 4 3 2 +-+
+--R ((4a d + 2b c d )x + (6a c d + 12b c d)x + 12b c x )\|c
+--R /
+--R 2 4 2 3 2 3 2 4
+--R (18a c d - 36a b c d + 18b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (42a c d - 84a b c d + 42b c d)x + 24a c d - 48a b c d + 24b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 6a c d + 12a b c d - 6b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 36a c d + 72a b c d - 36b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5 2 6
+--R (- 54a c d + 108a b c d - 54b c d)x - 24a c d + 48a b c d - 24b c
+--R ,
+--R
+--R +---------+ +--------+
+--R 2 4 2 2 3 | b +-+ | 2
+--R (9a c d x + 21a c d x + 12a c ) |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 3 6 2 2 4 3 2 4 | b
+--R (- 3a c d x - 18a c d x - 27a c d x - 12a c ) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b
+--R (a d - b c)x |---------
+--R \|a d - b c
+--R +
+--R +--------+
+--R 2 2 4 3 2 | 2
+--R ((- 3a c d - 3b c d)x - 6b c x )\|d x + c
+--R +
+--R 3 2 6 2 2 4 3 2 +-+
+--R ((2a d + b c d )x + (3a c d + 6b c d)x + 6b c x )\|c
+--R /
+--R 2 4 2 3 2 3 2 4
+--R (9a c d - 18a b c d + 9b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (21a c d - 42a b c d + 21b c d)x + 12a c d - 24a b c d + 12b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 3a c d + 6a b c d - 3b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 18a c d + 36a b c d - 18b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5 2 6
+--R (- 27a c d + 54a b c d - 27b c d)x - 12a c d + 24a b c d - 12b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1027
+
+--S 1028 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +--------+
+--R 2 2 2 +-----------+ | b | 2
+--R (3a c d x + 12a c d)\|- a d + b c |- --------- \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 2 +-----------+ | b +-+
+--R (- 9a c d x - 12a c d)\|- a d + b c |- --------- \|c
+--R \| a d - b c
+--R *
+--R log
+--R 2 2 2 2 4 2 2 2
+--R ((- 2a d - 2a b c d + 4b c )x + (- 8a c d + 8a b c )x )
+--R *
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (2a b c d - 2b c d)x + (6a c d - 2a b c d - 4b c )x
+--R +
+--R 2 2 3 2
+--R (8a c d - 8a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R (- 6a c d x - 24a c d)\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R (18a c d x + 24a c d)\|b \|c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 +-----------+ +-+ | 2
+--R ((- 4a d - 2b c d)x - 16a c d - 8b c )\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 2 3 +-----------+
+--R ((12a c d + 6b c d)x + 16a c d + 8b c )\|- a d + b c
+--R /
+--R 2 4 2 3 2 3 2 2 2 2 3 3 2 2 4
+--R ((6a c d - 12a b c d + 6b c d )x + 24a c d - 48a b c d + 24b c d)
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 2 4 2 3 2 3 2 2 2 2 3 3 2
+--R (- 18a c d + 36a b c d - 18b c d )x - 24a c d + 48a b c d
+--R +
+--R 2 4
+--R - 24b c d
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 1028
+
+--S 1029 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1029
+
+--S 1030 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R (- 3a c d x - 12a c d)\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R (9a c d x + 12a c d)\|b \|c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +---------+ +--------+
+--R 2 2 2 +-----------+ | b | 2
+--R (3a c d x + 12a c d)\|- a d + b c |--------- \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 2 2 +-----------+ | b +-+
+--R (- 9a c d x - 12a c d)\|- a d + b c |--------- \|c
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b
+--R (a d - b c)x |---------
+--R \|a d - b c
+--R +
+--R +--------+
+--R 2 2 2 +-----------+ +-+ | 2
+--R ((- 2a d - b c d)x - 8a c d - 4b c )\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 2 3 +-----------+
+--R ((6a c d + 3b c d)x + 8a c d + 4b c )\|- a d + b c
+--R /
+--R 2 4 2 3 2 3 2 2 2 2 3 3 2 2 4
+--R ((3a c d - 6a b c d + 3b c d )x + 12a c d - 24a b c d + 12b c d)
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 2 4 2 3 2 3 2 2 2 2 3 3 2
+--R (- 9a c d + 18a b c d - 9b c d )x - 12a c d + 24a b c d
+--R +
+--R 2 4
+--R - 12b c d
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 1030
+
+--S 1031 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1031
+
+)clear all
+
+--S 1032 of 1475
+t0:=x^2/((a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R 2
+--R x
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|d x + c
+--R Type: Expression(Integer)
+--E 1032
+
+--S 1033 of 1475
+r0:=1/3*x/((b*c-a*d)*(c+d*x^2)^(3/2))-b*atan(x*sqrt(b*c-a*d)/(sqrt(a)*_
+ sqrt(c+d*x^2)))*sqrt(a)/(b*c-a*d)^(5/2)+1/3*(2*b*c+a*d)*x/(c*_
+ (b*c-a*d)^2*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+ +-----------+
+--R 2 2 +-+ | 2 x\|- a d + b c
+--R (- 3b c d x - 3b c )\|a \|d x + c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 2 3 2 +-----------+
+--R ((a d + 2b c d)x + 3b c x)\|- a d + b c
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((3a c d - 6a b c d + 3b c d)x + 3a c d - 6a b c d + 3b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R Type: Expression(Integer)
+--E 1033
+
+--S 1034 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+ +--------+
+--R 2 4 2 2 3 | a +-+ | 2
+--R (9b c d x + 21b c d x + 12b c ) |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 3 6 2 2 4 3 2 4 | a
+--R (- 3b c d x - 18b c d x - 27b c d x - 12b c ) |---------
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((- 4a d + 4b c d)x + (- 4a c d + 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 3 2 5 2 2 3 3 | 2
+--R ((- 2a d - 4b c d )x + (- 8a c d - 22b c d)x - 24b c x)\|d x + c
+--R +
+--R 3 2 5 2 2 3 3 +-+
+--R ((6a d + 12b c d )x + (8a c d + 34b c d)x + 24b c x)\|c
+--R /
+--R 2 4 2 3 2 3 2 4
+--R (18a c d - 36a b c d + 18b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (42a c d - 84a b c d + 42b c d)x + 24a c d - 48a b c d + 24b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 6a c d + 12a b c d - 6b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 36a c d + 72a b c d - 36b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5 2 6
+--R (- 54a c d + 108a b c d - 54b c d)x - 24a c d + 48a b c d - 24b c
+--R ,
+--R
+--R +-----------+ +--------+
+--R 2 4 2 2 3 | a +-+ | 2
+--R (- 9b c d x - 21b c d x - 12b c ) |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 3 6 2 2 4 3 2 4 | a
+--R (3b c d x + 18b c d x + 27b c d x + 12b c ) |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
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+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +--------+
+--R 2 4 2 2 3 | a +-+ | 2
+--R (9b c d x + 21b c d x + 12b c ) |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 3 6 2 2 4 3 2 4 | a
+--R (- 3b c d x - 18b c d x - 27b c d x - 12b c ) |- ---------
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +--------+
+--R 3 2 5 2 2 3 3 | 2
+--R ((- a d - 2b c d )x + (- 4a c d - 11b c d)x - 12b c x)\|d x + c
+--R +
+--R 3 2 5 2 2 3 3 +-+
+--R ((3a d + 6b c d )x + (4a c d + 17b c d)x + 12b c x)\|c
+--R /
+--R 2 4 2 3 2 3 2 4
+--R (9a c d - 18a b c d + 9b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (21a c d - 42a b c d + 21b c d)x + 12a c d - 24a b c d + 12b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 3a c d + 6a b c d - 3b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 18a c d + 36a b c d - 18b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5 2 6
+--R (- 27a c d + 54a b c d - 27b c d)x - 12a c d + 24a b c d - 12b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1034
+
+--S 1035 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-----------+ | a
+--R b\|- a d + b c |---------
+--R \|a d - b c
+--R *
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+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((- 4a d + 4b c d)x + (- 4a c d + 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+
+--R +-+ x\|- a d + b c
+--R 2b\|a atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 2 2 2 +-----------+
+--R (2a d - 4a b c d + 2b c )\|- a d + b c
+--R Type: Expression(Integer)
+--E 1035
+
+--S 1036 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1036
+
+--S 1037 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R -
+--R +-----------+
+--R +-----------+ | a
+--R b\|- a d + b c |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +-+
+--R +-----------+ | a a\|c
+--R b\|- a d + b c |- --------- atan(--------------------------)
+--R \| a d - b c +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-+ x\|- a d + b c
+--R b\|a atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 2 2 2 +-----------+
+--R (a d - 2a b c d + b c )\|- a d + b c
+--R Type: Expression(Integer)
+--E 1037
+
+--S 1038 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1038
+
+)clear all
+
+--S 1039 of 1475
+t0:=x/((a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R x
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|d x + c
+--R Type: Expression(Integer)
+--E 1039
+
+--S 1040 of 1475
+r0:=1/3/((b*c-a*d)*(c+d*x^2)^(3/2))-b^(3/2)*atanh(sqrt(b)*sqrt(c+d*x^2)/_
+ sqrt(b*c-a*d))/(b*c-a*d)^(5/2)+b/((b*c-a*d)^2*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ +-+ | 2
+--R 2 +-+ | 2 \|b \|d x + c
+--R (- 3b d x - 3b c)\|b \|d x + c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 +-----------+
+--R (3b d x - a d + 4b c)\|- a d + b c
+--R /
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d - 6a b c d + 3b c d)x + 3a c d - 6a b c d + 3b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R Type: Expression(Integer)
+--E 1040
+
+--S 1041 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+ +--------+
+--R 2 2 4 3 2 4 | b +-+ | 2
+--R (9b c d x + 21b c d x + 12b c ) |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 3 6 3 2 4 4 2 5 | b
+--R (- 3b c d x - 18b c d x - 27b c d x - 12b c ) |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R 2 2 2 2 4 2 2 2
+--R ((2a d + 2a b c d - 4b c )x + (8a c d - 8a b c )x )
+--R *
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 6
+--R (- 2a b c d + 2b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (- 6a c d + 2a b c d + 4b c )x + (- 8a c d + 8a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
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+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 3 2 2 4 2 2 3 2 | 2
+--R ((- 6a c d + 18b c d )x + (- 12a c d + 24b c d)x )\|d x + c
+--R +
+--R 4 3 6 3 2 2 4
+--R (2a d - 8b c d )x + (12a c d - 30b c d )x
+--R +
+--R 2 2 3 2
+--R (12a c d - 24b c d)x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 2 2 4 3 3 2 4 2 4
+--R (18a c d - 36a b c d + 18b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5 2 6
+--R (42a c d - 84a b c d + 42b c d)x + 24a c d - 48a b c d + 24b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (- 6a c d + 12a b c d - 6b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (- 36a c d + 72a b c d - 36b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2 6 2 7
+--R (- 54a c d + 108a b c d - 54b c d)x - 24a c d + 48a b c d - 24b c
+--R ,
+--R
+--R +---------+ +--------+
+--R 2 2 4 3 2 4 | b +-+ | 2
+--R (- 9b c d x - 21b c d x - 12b c ) |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 3 6 3 2 4 4 2 5 | b
+--R (3b c d x + 18b c d x + 27b c d x + 12b c ) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b
+--R (a d - b c)x |---------
+--R \|a d - b c
+--R +
+--R +--------+
+--R 3 2 2 4 2 2 3 2 | 2
+--R ((- 3a c d + 9b c d )x + (- 6a c d + 12b c d)x )\|d x + c
+--R +
+--R 4 3 6 3 2 2 4 2 2 3 2 +-+
+--R ((a d - 4b c d )x + (6a c d - 15b c d )x + (6a c d - 12b c d)x )\|c
+--R /
+--R 2 2 4 3 3 2 4 2 4
+--R (9a c d - 18a b c d + 9b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5 2 6
+--R (21a c d - 42a b c d + 21b c d)x + 12a c d - 24a b c d + 12b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (- 3a c d + 6a b c d - 3b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (- 18a c d + 36a b c d - 18b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2 6 2 7
+--R (- 27a c d + 54a b c d - 27b c d)x - 12a c d + 24a b c d - 12b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1041
+
+--S 1042 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +--------+
+--R 2 2 3 +-----------+ | b | 2
+--R (3b c d x + 12b c )\|- a d + b c |- --------- \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 3 +-----------+ | b +-+
+--R (- 9b c d x - 12b c )\|- a d + b c |- --------- \|c
+--R \| a d - b c
+--R *
+--R log
+--R 2 2 2 2 4 2 2 2
+--R ((2a d + 2a b c d - 4b c )x + (8a c d - 8a b c )x )
+--R *
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 3 2
+--R (- 8a c d + 8a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 3 +-+ +-+
+--R ((6b c d x + 24b c )\|b \|d x + c + (- 18b c d x - 24b c )\|b \|c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 +-----------+ +-+ | 2
+--R ((- 2a d + 8b c d)x - 8a c d + 32b c )\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 2 3 +-----------+
+--R ((6a c d - 24b c d)x + 8a c d - 32b c )\|- a d + b c
+--R /
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R ((6a c d - 12a b c d + 6b c d)x + 24a c d - 48a b c d + 24b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R ((- 18a c d + 36a b c d - 18b c d)x - 24a c d + 48a b c d - 24b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 1042
+
+--S 1043 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1043
+
+--S 1044 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 3 +-+ +-+
+--R ((3b c d x + 12b c )\|b \|d x + c + (- 9b c d x - 12b c )\|b \|c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +---------+ +--------+
+--R 2 2 3 +-----------+ | b | 2
+--R (- 3b c d x - 12b c )\|- a d + b c |--------- \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 2 3 +-----------+ | b +-+
+--R (9b c d x + 12b c )\|- a d + b c |--------- \|c
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b
+--R (a d - b c)x |---------
+--R \|a d - b c
+--R +
+--R +--------+
+--R 2 2 2 +-----------+ +-+ | 2
+--R ((- a d + 4b c d)x - 4a c d + 16b c )\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 2 3 +-----------+
+--R ((3a c d - 12b c d)x + 4a c d - 16b c )\|- a d + b c
+--R /
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R ((3a c d - 6a b c d + 3b c d)x + 12a c d - 24a b c d + 12b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R ((- 9a c d + 18a b c d - 9b c d)x - 12a c d + 24a b c d - 12b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 1044
+
+--S 1045 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1045
+
+)clear all
+
+--S 1046 of 1475
+t0:=1/((a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|d x + c
+--R Type: Expression(Integer)
+--E 1046
+
+--S 1047 of 1475
+r0:=-1/3*d*x/(c*(b*c-a*d)*(c+d*x^2)^(3/2))+b^2*atan(x*sqrt(b*c-a*d)/_
+ (sqrt(a)*sqrt(c+d*x^2)))/((b*c-a*d)^(5/2)*sqrt(a))-1/3*d*(5*b*c-_
+ 2*a*d)*x/(c^2*(b*c-a*d)^2*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+ +-----------+
+--R 2 2 2 2 3 | 2 x\|- a d + b c
+--R (3b c d x + 3b c )\|d x + c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 3 2 3 2 2 +-----------+ +-+
+--R ((2a d - 5b c d )x + (3a c d - 6b c d)x)\|- a d + b c \|a
+--R /
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R ((3a c d - 6a b c d + 3b c d)x + 3a c d - 6a b c d + 3b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 1047
+
+--S 1048 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 4 2 3 2 2 4 +-+ | 2 2 2 3 6
+--R (9b c d x + 21b c d x + 12b c )\|c \|d x + c - 3b c d x
+--R +
+--R 2 3 2 4 2 4 2 2 5
+--R - 18b c d x - 27b c d x - 12b c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 4 3 5 3 2 2 3
+--R (- 4a d + 10b c d )x + (- 22a c d + 52b c d )x
+--R +
+--R 2 2 3
+--R (- 24a c d + 48b c d)x
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 4 3 5 3 2 2 3
+--R (12a d - 30b c d )x + (34a c d - 76b c d )x
+--R +
+--R 2 2 3
+--R (24a c d - 48b c d)x
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|c \|a d - a b c
+--R /
+--R 2 2 4 3 3 2 4 2 4
+--R (18a c d - 36a b c d + 18b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5 2 6
+--R (42a c d - 84a b c d + 42b c d)x + 24a c d - 48a b c d + 24b c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a d - a b c \|d x + c
+--R +
+--R 2 2 5 3 4 2 4 3 6
+--R (- 6a c d + 12a b c d - 6b c d )x
+--R +
+--R 2 3 4 4 3 2 5 2 4
+--R (- 36a c d + 72a b c d - 36b c d )x
+--R +
+--R 2 4 3 5 2 2 6 2 2 5 2 6
+--R (- 54a c d + 108a b c d - 54b c d)x - 24a c d + 48a b c d
+--R +
+--R 2 7
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+--R (21a c d - 42a b c d + 21b c d)x + 12a c d - 24a b c d + 12b c
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+--R (- 3a c d + 6a b c d - 3b c d )x
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+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R ]
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+--E 1048
+
+--S 1049 of 1475
+m0a:=a0.1-r0
+--R
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+--R +
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+--R (2a d - 4a b c d + 2b c )\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 1049
+
+--S 1050 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1050
+
+--S 1051 of 1475
+m0b:=a0.2-r0
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+--R +
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+--R (a d - b c)x
+--R +
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+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 2 2 2 2 | 2 +-----------+ +-+
+--R (a d - 2a b c d + b c )\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 1051
+
+--S 1052 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1052
+
+)clear all
+
+--S 1053 of 1475
+t0:=1/(x*(a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------------------
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+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x)\|d x + c
+--R Type: Expression(Integer)
+--E 1053
+
+--S 1054 of 1475
+r0:=-1/3*d/(c*(b*c-a*d)*(c+d*x^2)^(3/2))-atanh(sqrt(c+d*x^2)/sqrt(c))/_
+ (a*c^(5/2))+b^(5/2)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/_
+ (a*(b*c-a*d)^(5/2))-d*(2*b*c-a*d)/(c^2*(b*c-a*d)^2*sqrt(c+d*x^2))
+--R
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+--R ((- 3a d + 6a b c d - 3b c d)x - 3a c d + 6a b c d - 3b c )
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+--R +-----------+ | 2 \|d x + c
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+--R 2 3 2 2 2 2 2 +-----------+ +-+
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+--R ((3a c d - 6a b c d + 3a b c d)x + 3a c d - 6a b c d + 3a b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R Type: Expression(Integer)
+--E 1054
+
+--S 1055 of 1475
+a0:=integrate(t0,x)
+--R
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+--R 2 4 2 3 2 3 2 4
+--R (- 36a c d + 72a b c d - 36b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (- 54a c d + 108a b c d - 54b c d)x - 24a c d + 48a b c d
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+--R 2 3 2 4 2 4 2 2 5 | b +-+ | 2
+--R (9b c d x + 21b c d x + 12b c ) |- --------- \|c \|d x + c
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+--R +
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+--R 2 3 3 6 2 4 2 4 2 5 2 2 6 | b
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+--R /
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+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
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+--R 2 4 2 3 2 3 2 4
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+--R +
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+--R 2 3 2 4 2 4 2 2 5 | b +-+ | 2
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+--R +---------+
+--R 2 3 3 6 2 4 2 4 2 5 2 2 6 | b
+--R (- 3b c d x - 18b c d x - 27b c d x - 12b c ) |---------
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+--R a\|c \|d x + c - b c x - a c
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+--R +---------+
+--R 2 | b +-+
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+--R \|a d - b c
+--R +
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+--R 2 4 2 3 4 2 2 3 3 2 2 | 2
+--R ((9a c d - 15a b c d )x + (12a c d - 18a b c d )x )\|d x + c
+--R +
+--R 2 5 4 6 2 4 2 3 4
+--R (- 4a d + 7a b c d )x + (- 15a c d + 24a b c d )x
+--R +
+--R 2 2 3 3 2 2
+--R (- 12a c d + 18a b c d )x
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+--R 3 3 4 2 4 3 2 5 2 4
+--R (9a c d - 18a b c d + 9a b c d )x
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+--R 3 4 3 2 5 2 2 6 2 3 5 2 2 6
+--R (21a c d - 42a b c d + 21a b c d)x + 12a c d - 24a b c d
+--R +
+--R 2 7
+--R 12a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 3 5 2 4 4 2 5 3 6
+--R (- 3a c d + 6a b c d - 3a b c d )x
+--R +
+--R 3 4 4 2 5 3 2 6 2 4
+--R (- 18a c d + 36a b c d - 18a b c d )x
+--R +
+--R 3 5 3 2 6 2 2 7 2 3 6 2 2 7 2 8
+--R (- 27a c d + 54a b c d - 27a b c d)x - 12a c d + 24a b c d - 12a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1055
+
+--S 1056 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((6a d - 12a b c d + 6b c d)x + 24a c d - 48a b c d + 24b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
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+--R 2 3 2 2 2 2 2 2 2
+--R (- 18a d + 36a b c d - 18b c d)x - 24a c d + 48a b c d
+--R +
+--R 2 3
+--R - 24b c
+--R *
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+--R \|- a d + b c \|c
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+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
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+--R x
+--R +
+--R +-----------+ +--------+
+--R 2 2 2 2 3 +-----------+ | b +-+ | 2
+--R (3b c d x + 12b c )\|- a d + b c |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 3 2 2 4 +-----------+ | b
+--R (- 9b c d x - 12b c )\|- a d + b c |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (- 2a d + 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((2a b d - 2b c)x + (2a d - 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ +-+ | 2 2 3 2 2 4 +-+
+--R ((- 6b c d x - 24b c )\|b \|c \|d x + c + (18b c d x + 24b c )\|b )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((6a d - 12a b c d + 6b c d)x + 24a c d - 48a b c d + 24b c )
+--R *
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+--R 2 3 2 2 2 2 2 2 2
+--R (- 18a d + 36a b c d - 18b c d)x - 24a c d + 48a b c d
+--R +
+--R 2 3
+--R - 24b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 3 2 2 2 2 2 +-----------+ | 2
+--R ((8a d - 14a b c d )x + 32a c d - 56a b c d)\|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 +-----------+ +-+
+--R ((- 24a d + 42a b c d )x - 32a c d + 56a b c d)\|- a d + b c \|c
+--R /
+--R 3 2 3 2 3 2 2 4 2 3 3 2 2 4 2 5
+--R ((6a c d - 12a b c d + 6a b c d)x + 24a c d - 48a b c d + 24a b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 3 3 3 2 4 2 2 5 2 3 4 2 2 5
+--R (- 18a c d + 36a b c d - 18a b c d)x - 24a c d + 48a b c d
+--R +
+--R 2 6
+--R - 24a b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R Type: Expression(Integer)
+--E 1056
+
+--S 1057 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1057
+
+--S 1058 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d - 6a b c d + 3b c d)x + 12a c d - 24a b c d + 12b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 9a d + 18a b c d - 9b c d)x - 12a c d + 24a b c d - 12b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ +-+ | 2 2 3 2 2 4 +-+
+--R ((- 3b c d x - 12b c )\|b \|c \|d x + c + (9b c d x + 12b c )\|b )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d - 6a b c d + 3b c d)x + 12a c d - 24a b c d + 12b c )
+--R *
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+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
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+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 9a d + 18a b c d - 9b c d)x - 12a c d + 24a b c d - 12b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +---------+ +--------+
+--R 2 2 2 2 3 +-----------+ | b +-+ | 2
+--R (3b c d x + 12b c )\|- a d + b c |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 3 2 2 4 +-----------+ | b
+--R (- 9b c d x - 12b c )\|- a d + b c |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R +--------+
+--R 2 3 2 2 2 2 2 +-----------+ | 2
+--R ((4a d - 7a b c d )x + 16a c d - 28a b c d)\|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 +-----------+ +-+
+--R ((- 12a d + 21a b c d )x - 16a c d + 28a b c d)\|- a d + b c \|c
+--R /
+--R 3 2 3 2 3 2 2 4 2 3 3 2 2 4 2 5
+--R ((3a c d - 6a b c d + 3a b c d)x + 12a c d - 24a b c d + 12a b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 3 3 3 2 4 2 2 5 2 3 4 2 2 5
+--R (- 9a c d + 18a b c d - 9a b c d)x - 12a c d + 24a b c d
+--R +
+--R 2 6
+--R - 12a b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R Type: Expression(Integer)
+--E 1058
+
+--S 1059 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1059
+
+)clear all
+
+--S 1060 of 1475
+t0:=1/(x^2*(a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------------------------
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+--R 2 8 2 6 2 4 2 2 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1060
+
+--S 1061 of 1475
+r0:=-1/3*d/(c*(b*c-a*d)*x*(c+d*x^2)^(3/2))-b^3*atan(x*sqrt(b*c-a*d)/_
+ (sqrt(a)*sqrt(c+d*x^2)))/(a^(3/2)*(b*c-a*d)^(5/2))-1/3*d*(7*b*c-_
+ 4*a*d)/(c^2*(b*c-a*d)^2*x*sqrt(c+d*x^2))-1/3*(b*c-4*a*d)*(3*b*c-_
+ 2*a*d)*sqrt(c+d*x^2)/(a*c^3*(b*c-a*d)^2*x)
+--R
+--R
+--R (2)
+--R +--------+ +-----------+
+--R 3 3 3 3 4 | 2 x\|- a d + b c
+--R (- 3b c d x - 3b c x)\|d x + c atan(---------------)
+--R +--------+
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+--R \|a \|d x + c
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+--R (- 8a d + 14a b c d - 3b c d )x
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+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
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+--R *
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+--R /
+--R 3 3 3 2 4 2 2 5 3 3 4 2 2 5 2 6
+--R ((3a c d - 6a b c d + 3a b c d)x + (3a c d - 6a b c d + 3a b c )x)
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 1061
+
+--S 1062 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
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+--R 3 3 3 7 3 4 2 5 3 5 3 3 6 | 2
+--R (3b c d x + 27b c d x + 48b c d x + 24b c x)\|d x + c
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+--R +
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+--R 3 5 3 2 6 2 2 7 3
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+--R 3 6 2 2 7 2 8
+--R (- 48a c d + 96a b c d - 48a b c )x
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+--R
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+--R (3b c d x + 27b c d x + 48b c d x + 24b c x)\|d x + c
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+--R 3 3 3 7 3 4 2 5 3 5 3 3 6 +-+
+--R (- 12b c d x - 48b c d x - 60b c d x - 24b c x)\|c
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+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
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+--R (3b c d x + 27b c d x + 48b c d x + 24b c x)\|d x + c
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+--R 3 3 3 7 3 4 2 5 3 5 3 3 6 +-+
+--R (- 12b c d x - 48b c d x - 60b c d x - 24b c x)\|c
+--R *
+--R +-------------+
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+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 2 5 4 2 2 3 6
+--R (32a d - 56a b c d + 12b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (112a c d - 196a b c d + 48b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (108a c d - 192a b c d + 60b c d)x + 24a c d - 48a b c d + 24b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
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+--R +
+--R 2 6 5 2 2 4 8
+--R (- 8a d + 14a b c d - 3b c d )x
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 76a c d + 133a b c d - 30b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 163a c d + 286a b c d - 75b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5
+--R (- 120a c d + 216a b c d - 72b c d)x - 24a c d + 48a b c d
+--R +
+--R 2 6
+--R - 24b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R 3 3 5 2 4 4 2 5 3 7
+--R (3a c d - 6a b c d + 3a b c d )x
+--R +
+--R 3 4 4 2 5 3 2 6 2 5
+--R (27a c d - 54a b c d + 27a b c d )x
+--R +
+--R 3 5 3 2 6 2 2 7 3
+--R (48a c d - 96a b c d + 48a b c d)x
+--R +
+--R 3 6 2 2 7 2 8
+--R (24a c d - 48a b c d + 24a b c )x
+--R *
+--R +-------------+ +--------+
+--R | 2 | 2
+--R \|- a d + a b c \|d x + c
+--R +
+--R 3 3 5 2 4 4 2 5 3 7
+--R (- 12a c d + 24a b c d - 12a b c d )x
+--R +
+--R 3 4 4 2 5 3 2 6 2 5
+--R (- 48a c d + 96a b c d - 48a b c d )x
+--R +
+--R 3 5 3 2 6 2 2 7 3
+--R (- 60a c d + 120a b c d - 60a b c d)x
+--R +
+--R 3 6 2 2 7 2 8
+--R (- 24a c d + 48a b c d - 24a b c )x
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1062
+
+--S 1063 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 +-----------+ +-+
+--R b \|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 3 | 2 x\|- a d + b c
+--R 2b \|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 3 2 2 2 2 +-----------+ +-+ | 2
+--R (2a d - 4a b c d + 2a b c )\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 1063
+
+--S 1064 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1064
+
+--S 1065 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 3 +-----------+ +-+
+--R b \|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 3 +-----------+ +-+ \|- a d + a b c \|c
+--R b \|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 3 | 2 x\|- a d + b c
+--R b \|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 3 2 2 2 2 | 2 +-----------+ +-+
+--R (a d - 2a b c d + a b c )\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 1065
+
+--S 1066 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1066
+
+)clear all
+
+--S 1067 of 1475
+t0:=1/(x^3*(a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------------------------
+--R +--------+
+--R 2 9 2 7 2 5 2 3 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1067
+
+--S 1068 of 1475
+r0:=-1/6*d*(3*b*c-5*a*d)/(a*c^2*(b*c-a*d)*(c+d*x^2)^(3/2))+(-1/2)/_
+ (a*c*x^2*(c+d*x^2)^(3/2))+1/2*(2*b*c+5*a*d)*atanh(sqrt(c+d*x^2)/_
+ sqrt(c))/(a^2*c^(7/2))-b^(7/2)*atanh(sqrt(b)*sqrt(c+d*x^2)/_
+ sqrt(b*c-a*d))/(a^2*(b*c-a*d)^(5/2))-1/2*d*(b^2*c^2-8*a*b*c*d+_
+ 5*a^2*d^2)/(a*c^3*(b*c-a*d)^2*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ +-+ | 2
+--R 3 3 4 3 4 2 +-+ +-+ | 2 \|b \|d x + c
+--R (- 6b c d x - 6b c x )\|b \|c \|d x + c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (15a d - 24a b c d + 3a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2
+--R (15a c d - 24a b c d + 3a b c d + 6b c )x
+--R *
+--R +--------+
+--R +--------+ | 2
+--R +-----------+ | 2 \|d x + c
+--R \|- a d + b c \|d x + c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 3 4 2 3 2 2 2 4
+--R (- 15a d + 24a b c d - 3a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3 2 4
+--R (- 20a c d + 32a b c d - 6a b c d)x - 3a c d + 6a b c d - 3a b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R 4 3 3 3 4 2 2 2 5 4 4 4 2 3 5 2 2 6 2
+--R ((6a c d - 12a b c d + 6a b c d)x + (6a c d - 12a b c d + 6a b c )x )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R Type: Expression(Integer)
+--E 1068
+
+--S 1069 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 6 2 2 5 2 3 4 3 4 3 8
+--R (- 75a c d + 120a b c d - 15a b c d - 30b c d )x
+--R +
+--R 3 2 5 2 3 4 2 4 3 3 5 2 6
+--R (- 375a c d + 600a b c d - 75a b c d - 150b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 4
+--R (- 540a c d + 864a b c d - 108a b c d - 216b c d)x
+--R +
+--R 3 4 3 2 5 2 2 6 3 7 2
+--R (- 240a c d + 384a b c d - 48a b c d - 96b c )x
+--R *
+--R +--------+
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+--R \|d x + c
+--R +
+--R 3 7 2 6 2 2 5 3 3 4 10
+--R (15a d - 24a b c d + 3a b c d + 6b c d )x
+--R +
+--R 3 6 2 2 5 2 3 4 3 4 3 8
+--R (210a c d - 336a b c d + 42a b c d + 84b c d )x
+--R +
+--R 3 2 5 2 3 4 2 4 3 3 5 2 6
+--R (615a c d - 984a b c d + 123a b c d + 246b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 4
+--R (660a c d - 1056a b c d + 132a b c d + 264b c d)x
+--R +
+--R 3 4 3 2 5 2 2 6 3 7 2
+--R (240a c d - 384a b c d + 48a b c d + 96b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+
+--R 3 4 3 8 3 5 2 6 3 6 4 3 7 2 | b
+--R (15b c d x + 75b c d x + 108b c d x + 48b c x ) |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 4 4 10 3 5 3 8 3 6 2 6 3 7 4
+--R - 3b c d x - 42b c d x - 123b c d x - 132b c d x
+--R +
+--R 3 8 2
+--R - 48b c x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (2a d - 2a b c)x |- --------- )
+--R \| a d - b c
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+--R 2 4 2 2 | b +-+
+--R ((- 2a b d + 2b c)x + (- 2a d + 2a b c)x ) |- --------- \|c
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+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
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+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
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+--R 3 6 2 2 5 2 3 4 8
+--R (- 55a c d + 76a b c d + 3a b c d )x
+--R +
+--R 3 2 5 2 3 4 2 4 3 6
+--R (- 150a c d + 180a b c d + 42a b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 4
+--R (- 21a c d - 54a b c d + 123a b c d )x
+--R +
+--R 3 4 3 2 5 2 2 6 2 3 5 2 2 6
+--R (132a c d - 264a b c d + 132a b c d)x + 48a c d - 96a b c d
+--R +
+--R 2 7
+--R 48a b c
+--R *
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+--R \|d x + c
+--R +
+--R 3 7 2 6 10 3 6 2 2 5 2 3 4 8
+--R (14a d - 20a b c d )x + (121a c d - 160a b c d - 15a b c d )x
+--R +
+--R 3 2 5 2 3 4 2 4 3 6
+--R (174a c d - 180a b c d - 90a b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 4
+--R (- 39a c d + 174a b c d - 183a b c d )x
+--R +
+--R 3 4 3 2 5 2 2 6 2 3 5 2 2 6
+--R (- 156a c d + 312a b c d - 156a b c d)x - 48a c d + 96a b c d
+--R +
+--R 2 7
+--R - 48a b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 4 5 3 5 4 2 2 6 3 8
+--R (30a c d - 60a b c d + 30a b c d )x
+--R +
+--R 4 5 4 3 6 3 2 2 7 2 6
+--R (150a c d - 300a b c d + 150a b c d )x
+--R +
+--R 4 6 3 3 7 2 2 2 8 4
+--R (216a c d - 432a b c d + 216a b c d)x
+--R +
+--R 4 7 2 3 8 2 2 9 2
+--R (96a c d - 192a b c d + 96a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 4 4 6 3 5 5 2 2 6 4 10
+--R (- 6a c d + 12a b c d - 6a b c d )x
+--R +
+--R 4 5 5 3 6 4 2 2 7 3 8
+--R (- 84a c d + 168a b c d - 84a b c d )x
+--R +
+--R 4 6 4 3 7 3 2 2 8 2 6
+--R (- 246a c d + 492a b c d - 246a b c d )x
+--R +
+--R 4 7 3 3 8 2 2 2 9 4
+--R (- 264a c d + 528a b c d - 264a b c d)x
+--R +
+--R 4 8 2 3 9 2 2 10 2
+--R (- 96a c d + 192a b c d - 96a b c )x
+--R ,
+--R
+--R 3 6 2 2 5 2 3 4 3 4 3 8
+--R (- 75a c d + 120a b c d - 15a b c d - 30b c d )x
+--R +
+--R 3 2 5 2 3 4 2 4 3 3 5 2 6
+--R (- 375a c d + 600a b c d - 75a b c d - 150b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 4
+--R (- 540a c d + 864a b c d - 108a b c d - 216b c d)x
+--R +
+--R 3 4 3 2 5 2 2 6 3 7 2
+--R (- 240a c d + 384a b c d - 48a b c d - 96b c )x
+--R *
+--R +--------+
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+--R +
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+--R (615a c d - 984a b c d + 123a b c d + 246b c d )x
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+--R (660a c d - 1056a b c d + 132a b c d + 264b c d)x
+--R +
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+--R (240a c d - 384a b c d + 48a b c d + 96b c )x
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+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
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+--R \|a d - b c
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+--R 3 6 2 2 5 2 3 4 8
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+--R +
+--R 3 2 5 2 3 4 2 4 3 6
+--R (174a c d - 180a b c d - 90a b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 4
+--R (- 39a c d + 174a b c d - 183a b c d )x
+--R +
+--R 3 4 3 2 5 2 2 6 2 3 5 2 2 6
+--R (- 156a c d + 312a b c d - 156a b c d)x - 48a c d + 96a b c d
+--R +
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+--R 4 4 5 3 5 4 2 2 6 3 8
+--R (30a c d - 60a b c d + 30a b c d )x
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+--R (150a c d - 300a b c d + 150a b c d )x
+--R +
+--R 4 6 3 3 7 2 2 2 8 4
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+--R +
+--R 4 7 2 3 8 2 2 9 2
+--R (96a c d - 192a b c d + 96a b c )x
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+--R \|c \|d x + c
+--R +
+--R 4 4 6 3 5 5 2 2 6 4 10
+--R (- 6a c d + 12a b c d - 6a b c d )x
+--R +
+--R 4 5 5 3 6 4 2 2 7 3 8
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+--R +
+--R 4 6 4 3 7 3 2 2 8 2 6
+--R (- 246a c d + 492a b c d - 246a b c d )x
+--R +
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+--R +
+--R 4 8 2 3 9 2 2 10 2
+--R (- 96a c d + 192a b c d - 96a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1069
+
+--S 1070 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
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+--R (75a d - 120a b c d + 15a b c d + 30b c d )x
+--R +
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+--R (300a c d - 480a b c d + 60a b c d + 120b c d)x + 240a c d
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+--R - 384a b c d + 48a b c d + 96b c
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+--R \|d x + c - \|c
+--R log(------------------)
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+--R +
+--R +-----------+
+--R 3 3 2 4 3 4 2 3 5 +-----------+ | b +-+
+--R (3b c d x + 36b c d x + 48b c )\|- a d + b c |- --------- \|c
+--R \| a d - b c
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+--R \|d x + c
+--R +
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+--R 3 4 2 4 3 5 2 3 6 +-----------+ | b
+--R (- 15b c d x - 60b c d x - 48b c )\|- a d + b c |- ---------
+--R \| a d - b c
+--R *
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+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (2a d - 2a b c)x |- --------- )
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+--R 2 4 2 2 | b +-+
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+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
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+--R (6b c d x + 72b c d x + 96b c )\|b \|c \|d x + c
+--R +
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+--R (- 30b c d x - 120b c d x - 96b c )\|b
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+--R (6a c d - 12a b c d + 6a b c d )x
+--R +
+--R 4 4 3 3 5 2 2 2 6 2 4 5 2 3 6
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+--R +
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+--R (- 30a c d + 60a b c d - 30a b c d )x
+--R +
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+--R (- 120a c d + 240a b c d - 120a b c d)x - 96a c d + 192a b c d
+--R +
+--R 2 2 8
+--R - 96a b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R Type: Expression(Integer)
+--E 1070
+
+--S 1071 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1071
+
+--S 1072 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 15a d + 24a b c d - 3a b c d - 6b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 180a c d + 288a b c d - 36a b c d - 72b c d)x - 240a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 384a b c d - 48a b c d - 96b c
+--R *
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+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (75a d - 120a b c d + 15a b c d + 30b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (300a c d - 480a b c d + 60a b c d + 120b c d)x + 240a c d
+--R +
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+--R *
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+--R *
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+--R +
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+--R (6b c d x + 72b c d x + 96b c )\|b \|c \|d x + c
+--R +
+--R 3 4 2 4 3 5 2 3 6 +-+
+--R (- 30b c d x - 120b c d x - 96b c )\|b
+--R *
+--R +--------+
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+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
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+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 15a d + 24a b c d - 3a b c d - 6b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 180a c d + 288a b c d - 36a b c d - 72b c d)x - 240a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 384a b c d - 48a b c d - 96b c
+--R *
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+--R (75a d - 120a b c d + 15a b c d + 30b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (300a c d - 480a b c d + 60a b c d + 120b c d)x + 240a c d
+--R +
+--R 2 3 2 2 4 3 5
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+--R *
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+--R *
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+--R | 2
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+--R +-+
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+--R +
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+--R (- 6b c d x - 72b c d x - 96b c )\|- a d + b c |--------- \|c
+--R \|a d - b c
+--R *
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+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 4 2 4 3 5 2 3 6 +-----------+ | b
+--R (30b c d x + 120b c d x + 96b c )\|- a d + b c |---------
+--R \|a d - b c
+--R *
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+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
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+--R \|a d - b c
+--R +
+--R 3 5 2 4 4 3 4 2 2 3 2 3 2 3
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+--R +
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+--R 320a b c d
+--R *
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+--R \|- a d + b c \|d x + c
+--R +
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+--R (70a d - 100a b c d )x + (280a c d - 400a b c d )x + 224a c d
+--R +
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+--R - 320a b c d
+--R *
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+--R (6a c d - 12a b c d + 6a b c d )x
+--R +
+--R 4 4 3 3 5 2 2 2 6 2 4 5 2 3 6
+--R (72a c d - 144a b c d + 72a b c d)x + 96a c d - 192a b c d
+--R +
+--R 2 2 7
+--R 96a b c
+--R *
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+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 4
+--R (- 30a c d + 60a b c d - 30a b c d )x
+--R +
+--R 4 5 3 3 6 2 2 2 7 2 4 6 2 3 7
+--R (- 120a c d + 240a b c d - 120a b c d)x - 96a c d + 192a b c d
+--R +
+--R 2 2 8
+--R - 96a b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R Type: Expression(Integer)
+--E 1072
+
+--S 1073 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1073
+
+)clear all
+
+--S 1074 of 1475
+t0:=1/(x^4*(a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R 1
+--R (1) ---------------------------------------------------------------------
+--R +--------+
+--R 2 10 2 8 2 6 2 4 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|d x + c
+--R Type: Expression(Integer)
+--E 1074
+
+--S 1075 of 1475
+r0:=-1/3*d/(c*(b*c-a*d)*x^3*(c+d*x^2)^(3/2))+b^4*atan(x*sqrt(b*c-a*d)/_
+ (sqrt(a)*sqrt(c+d*x^2)))/(a^(5/2)*(b*c-a*d)^(5/2))-d*(3*b*c-_
+ 2*a*d)/(c^2*(b*c-a*d)^2*x^3*sqrt(c+d*x^2))-1/3*(b^2*c^2-12*a*b*_
+ c*d+8*a^2*d^2)*sqrt(c+d*x^2)/(a*c^3*(b*c-a*d)^2*x^3)+1/3*(b*c-_
+ 2*a*d)*(3*b^2*c^2+8*a*b*c*d-8*a^2*d^2)*sqrt(c+d*x^2)/(a^2*c^4*_
+ (b*c-a*d)^2*x)
+--R
+--R
+--R (2)
+--R +--------+ +-----------+
+--R 4 4 5 4 5 3 | 2 x\|- a d + b c
+--R (3b c d x + 3b c x )\|d x + c atan(---------------)
+--R +--------+
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+--R \|a \|d x + c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (16a d - 24a b c d + 2a b c d + 3b c d )x
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+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (24a c d - 36a b c d + 3a b c d + 6b c d)x
+--R +
+--R 3 2 3 2 3 2 3 5 2 3 3 2 2 4 2 5
+--R (6a c d - 9a b c d + 3b c )x - a c d + 2a b c d - a b c
+--R *
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+--R 4 4 3 3 5 2 2 2 6 5 4 5 2 3 6 2 2 7 3
+--R ((3a c d - 6a b c d + 3a b c d)x + (3a c d - 6a b c d + 3a b c )x )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 1075
+
+--S 1076 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 4 4 11 4 5 3 9 4 6 2 7 4 7 5 4 8 3
+--R (3b c d x + 57b c d x + 198b c d x + 240b c d x + 96b c x )
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+--R +
+--R 4 8 3
+--R - 96b c x
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+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
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+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
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+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
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+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
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+--R (- 192a d + 288a b c d - 24a b c d - 36b c d )x
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+--R 3 6 2 2 5 2 3 4 3 4 3 8
+--R (- 1312a c d + 1968a b c d - 164a b c d - 264b c d )x
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+--R 3 2 5 2 3 4 2 4 3 3 5 2 6
+--R (- 2632a c d + 3948a b c d - 320a b c d - 612b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 4
+--R (- 1908a c d + 2856a b c d - 180a b c d - 576b c d)x
+--R +
+--R 3 4 3 2 5 2 2 6 3 7 2 3 5 2
+--R (- 320a c d + 448a b c d + 64a b c d - 192b c )x + 64a c d
+--R +
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+--R - 128a b c d + 64a b c
+--R *
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+--R (32a d - 48a b c d + 4a b c d + 6b c d )x
+--R +
+--R 3 7 2 2 6 2 3 5 3 4 4 10
+--R (624a c d - 936a b c d + 78a b c d + 120b c d )x
+--R +
+--R 3 2 6 2 3 5 2 4 4 3 5 3 8
+--R (2412a c d - 3618a b c d + 300a b c d + 510b c d )x
+--R +
+--R 3 3 5 2 4 4 2 5 3 3 6 2 6
+--R (3542a c d - 5312a b c d + 414a b c d + 876b c d )x
+--R +
+--R 3 4 4 2 5 3 2 6 2 3 7 4
+--R (2076a c d - 3096a b c d + 156a b c d + 672b c d)x
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+--R 3 5 3 2 6 2 2 7 3 8 2 3 6 2
+--R (288a c d - 384a b c d - 96a b c d + 192b c )x - 64a c d
+--R +
+--R 2 7 2 8
+--R 128a b c d - 64a b c
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+--R \|a d - a b c
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+--R 4 4 6 3 5 5 2 2 6 4 11
+--R (6a c d - 12a b c d + 6a b c d )x
+--R +
+--R 4 5 5 3 6 4 2 2 7 3 9
+--R (114a c d - 228a b c d + 114a b c d )x
+--R +
+--R 4 6 4 3 7 3 2 2 8 2 7
+--R (396a c d - 792a b c d + 396a b c d )x
+--R +
+--R 4 7 3 3 8 2 2 2 9 5
+--R (480a c d - 960a b c d + 480a b c d)x
+--R +
+--R 4 8 2 3 9 2 2 10 3
+--R (192a c d - 384a b c d + 192a b c )x
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 4 4 6 3 5 5 2 2 6 4 11
+--R (- 36a c d + 72a b c d - 36a b c d )x
+--R +
+--R 4 5 5 3 6 4 2 2 7 3 9
+--R (- 264a c d + 528a b c d - 264a b c d )x
+--R +
+--R 4 6 4 3 7 3 2 2 8 2 7
+--R (- 612a c d + 1224a b c d - 612a b c d )x
+--R +
+--R 4 7 3 3 8 2 2 2 9 5
+--R (- 576a c d + 1152a b c d - 576a b c d)x
+--R +
+--R 4 8 2 3 9 2 2 10 3
+--R (- 192a c d + 384a b c d - 192a b c )x
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|c \|a d - a b c
+--R ,
+--R
+--R 4 4 4 11 4 5 3 9 4 6 2 7 4 7 5
+--R - 3b c d x - 57b c d x - 198b c d x - 240b c d x
+--R +
+--R 4 8 3
+--R - 96b c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 4 4 11 4 5 3 9 4 6 2 7 4 7 5
+--R 18b c d x + 132b c d x + 306b c d x + 288b c d x
+--R +
+--R 4 8 3
+--R 96b c x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 4 4 4 11 4 5 3 9 4 6 2 7 4 7 5
+--R - 3b c d x - 57b c d x - 198b c d x - 240b c d x
+--R +
+--R 4 8 3
+--R - 96b c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 4 4 11 4 5 3 9 4 6 2 7 4 7 5
+--R 18b c d x + 132b c d x + 306b c d x + 288b c d x
+--R +
+--R 4 8 3
+--R 96b c x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 3 7 2 6 2 2 5 3 3 4 10
+--R (- 96a d + 144a b c d - 12a b c d - 18b c d )x
+--R +
+--R 3 6 2 2 5 2 3 4 3 4 3 8
+--R (- 656a c d + 984a b c d - 82a b c d - 132b c d )x
+--R +
+--R 3 2 5 2 3 4 2 4 3 3 5 2 6
+--R (- 1316a c d + 1974a b c d - 160a b c d - 306b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 4
+--R (- 954a c d + 1428a b c d - 90a b c d - 288b c d)x
+--R +
+--R 3 4 3 2 5 2 2 6 3 7 2 3 5 2
+--R (- 160a c d + 224a b c d + 32a b c d - 96b c )x + 32a c d
+--R +
+--R 2 6 2 7
+--R - 64a b c d + 32a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 3 8 2 7 2 2 6 3 3 5 12
+--R (16a d - 24a b c d + 2a b c d + 3b c d )x
+--R +
+--R 3 7 2 2 6 2 3 5 3 4 4 10
+--R (312a c d - 468a b c d + 39a b c d + 60b c d )x
+--R +
+--R 3 2 6 2 3 5 2 4 4 3 5 3 8
+--R (1206a c d - 1809a b c d + 150a b c d + 255b c d )x
+--R +
+--R 3 3 5 2 4 4 2 5 3 3 6 2 6
+--R (1771a c d - 2656a b c d + 207a b c d + 438b c d )x
+--R +
+--R 3 4 4 2 5 3 2 6 2 3 7 4
+--R (1038a c d - 1548a b c d + 78a b c d + 336b c d)x
+--R +
+--R 3 5 3 2 6 2 2 7 3 8 2 3 6 2
+--R (144a c d - 192a b c d - 48a b c d + 96b c )x - 32a c d
+--R +
+--R 2 7 2 8
+--R 64a b c d - 32a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R 4 4 6 3 5 5 2 2 6 4 11
+--R (3a c d - 6a b c d + 3a b c d )x
+--R +
+--R 4 5 5 3 6 4 2 2 7 3 9
+--R (57a c d - 114a b c d + 57a b c d )x
+--R +
+--R 4 6 4 3 7 3 2 2 8 2 7
+--R (198a c d - 396a b c d + 198a b c d )x
+--R +
+--R 4 7 3 3 8 2 2 2 9 5
+--R (240a c d - 480a b c d + 240a b c d)x
+--R +
+--R 4 8 2 3 9 2 2 10 3
+--R (96a c d - 192a b c d + 96a b c )x
+--R *
+--R +-------------+ +--------+
+--R | 2 | 2
+--R \|- a d + a b c \|d x + c
+--R +
+--R 4 4 6 3 5 5 2 2 6 4 11
+--R (- 18a c d + 36a b c d - 18a b c d )x
+--R +
+--R 4 5 5 3 6 4 2 2 7 3 9
+--R (- 132a c d + 264a b c d - 132a b c d )x
+--R +
+--R 4 6 4 3 7 3 2 2 8 2 7
+--R (- 306a c d + 612a b c d - 306a b c d )x
+--R +
+--R 4 7 3 3 8 2 2 2 9 5
+--R (- 288a c d + 576a b c d - 288a b c d)x
+--R +
+--R 4 8 2 3 9 2 2 10 3
+--R (- 96a c d + 192a b c d - 96a b c )x
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1076
+
+--S 1077 of 1475
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 +-----------+ +-+
+--R b \|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 4 | 2 x\|- a d + b c
+--R - 2b \|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 4 2 3 2 2 2 +-----------+ +-+ | 2
+--R (2a d - 4a b c d + 2a b c )\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 1077
+
+--S 1078 of 1475
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1078
+
+--S 1079 of 1475
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R -
+--R 4 +-----------+ +-+
+--R b \|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 4 +-----------+ +-+ \|- a d + a b c \|c
+--R - b \|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 4 | 2 x\|- a d + b c
+--R - b \|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 4 2 3 2 2 2 | 2 +-----------+ +-+
+--R (a d - 2a b c d + a b c )\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 1079
+
+--S 1080 of 1475
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1080
+
+)clear all
+
+--S 1081 of 1475
+t0:=x^(7/2)*(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R 5 3 +-+
+--R (d x + c x )\|x
+--R (1) -----------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1081
+
+--S 1082 of 1475
+r0:=2/5*(b*c-a*d)*x^(5/2)/b^2+2/9*d*x^(9/2)/b-a^(5/4)*(b*c-a*d)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(13/4)*sqrt(2))+_
+ a^(5/4)*(b*c-a*d)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (b^(13/4)*sqrt(2))-1/2*a^(5/4)*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(13/4)*sqrt(2))+1/2*a^(5/4)*_
+ (b*c-a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (b^(13/4)*sqrt(2))-2*a*(b*c-a*d)*sqrt(x)/b^3
+--R
+--R
+--R (2)
+--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 45a d + 45a b c)\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (45a d - 45a b c)\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ \|2 \|b \|x + \|a
+--R (- 90a d + 90a b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ \|2 \|b \|x - \|a
+--R (- 90a d + 90a b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+4+-+ +-+
+--R (20b d x + (- 36a b d + 36b c)x + 180a d - 180a b c)\|2 \|b \|x
+--R /
+--R 3 +-+4+-+
+--R 90b \|2 \|b
+--R Type: Expression(Integer)
+--E 1082
+
+--S 1083 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +--------------------------------------------------+
+--R | 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R 3 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 45b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R *
+--R log
+--R 2 +-+
+--R (a d - a b c)\|x
+--R +
+--R +--------------------------------------------------+
+--R | 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R 3 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 2b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R +
+--R +--------------------------------------------------+
+--R | 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R 3 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 45b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R *
+--R log
+--R 2 +-+
+--R (a d - a b c)\|x
+--R +
+--R +--------------------------------------------------+
+--R | 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R 3 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R - 2b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R +
+--R +--------------------------------------------------+
+--R | 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R 3 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 90b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R *
+--R +--------------------------------------------------+
+--R | 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R 3 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 2b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R atan(--------------------------------------------------------)
+--R 2 +-+
+--R (a d - a b c)\|x
+--R +
+--R 2 4 2 2 2 +-+
+--R (10b d x + (- 18a b d + 18b c)x + 90a d - 90a b c)\|x
+--R /
+--R 3
+--R 45b
+--R Type: Union(Expression(Integer),...)
+--E 1083
+
+--S 1084 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - a b c)\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R 3 +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - a b c 4+-+
+--R 2b \|2 |-------------------------------------------------- \|b
+--R 4| 13
+--R \| 16b
+--R *
+--R log
+--R 2 +-+
+--R (a d - a b c)\|x
+--R +
+--R +--------------------------------------------------+
+--R | 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R 3 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 2b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R +
+--R +--------------------------------------------------+
+--R | 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R 3 +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - a b c 4+-+
+--R 2b \|2 |-------------------------------------------------- \|b
+--R 4| 13
+--R \| 16b
+--R *
+--R log
+--R 2 +-+
+--R (a d - a b c)\|x
+--R +
+--R +--------------------------------------------------+
+--R | 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R 3 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R - 2b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R +
+--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + a b c)\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ \|2 \|b \|x + \|a
+--R (2a d - 2a b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ \|2 \|b \|x - \|a
+--R (2a d - 2a b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------------------------------------------------+
+--R | 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R 3 +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - a b c 4+-+
+--R 4b \|2 |-------------------------------------------------- \|b
+--R 4| 13
+--R \| 16b
+--R *
+--R +--------------------------------------------------+
+--R | 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R 3 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 2b |--------------------------------------------------
+--R 4| 13
+--R \| 16b
+--R atan(--------------------------------------------------------)
+--R 2 +-+
+--R (a d - a b c)\|x
+--R /
+--R 3 +-+4+-+
+--R 2b \|2 \|b
+--R Type: Expression(Integer)
+--E 1084
+
+--S 1085 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1085
+
+)clear all
+
+--S 1086 of 1475
+t0:=x^(5/2)*(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R 4 2 +-+
+--R (d x + c x )\|x
+--R (1) -----------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1086
+
+--S 1087 of 1475
+r0:=2/3*(b*c-a*d)*x^(3/2)/b^2+2/7*d*x^(7/2)/b+a^(3/4)*(b*c-a*d)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(11/4)*sqrt(2))-_
+ a^(3/4)*(b*c-a*d)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (b^(11/4)*sqrt(2))-1/2*a^(3/4)*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(11/4)*sqrt(2))+1/2*a^(3/4)*_
+ (b*c-a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(b^(11/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 21a d + 21b c)\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (21a d - 21b c)\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 \|2 \|b \|x + \|a
+--R (42a d - 42b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 \|2 \|b \|x - \|a
+--R (42a d - 42b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+4+-+3 +-+
+--R (12b d x + (- 28a d + 28b c)x)\|2 \|b \|x
+--R /
+--R 2 +-+4+-+3
+--R 42b \|2 \|b
+--R Type: Expression(Integer)
+--E 1087
+
+--S 1088 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------------------------------------------+
+--R | 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 21b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R *
+--R log
+--R 5 3 4 2 3 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - a b c )\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R 8 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 8b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 21b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R *
+--R log
+--R 5 3 4 2 3 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - a b c )\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R 8 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R - 8b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R +
+--R +--------------------------------------------------+
+--R | 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 42b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R *
+--R +--------------------------------------------------+3
+--R | 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R 8 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 8b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R atan(---------------------------------------------------------)
+--R 5 3 4 2 3 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - a b c )\|x
+--R +
+--R 3 +-+
+--R (6b d x + (- 14a d + 14b c)x)\|x
+--R /
+--R 2
+--R 21b
+--R Type: Union(Expression(Integer),...)
+--E 1088
+
+--S 1089 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - b c)\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------------------------------------------------+
+--R | 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R 2 +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - a b c 4+-+3
+--R 2b \|2 |-------------------------------------------------- \|b
+--R 4| 11
+--R \| 16b
+--R *
+--R log
+--R 5 3 4 2 3 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - a b c )\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R 8 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 8b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R 2 +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - a b c 4+-+3
+--R 2b \|2 |-------------------------------------------------- \|b
+--R 4| 11
+--R \| 16b
+--R *
+--R log
+--R 5 3 4 2 3 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - a b c )\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R 8 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R - 8b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R +
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + b c)\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 \|2 \|b \|x + \|a
+--R (- 2a d + 2b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 \|2 \|b \|x - \|a
+--R (- 2a d + 2b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------------------------------------------------+
+--R | 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R 2 +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - a b c 4+-+3
+--R 4b \|2 |-------------------------------------------------- \|b
+--R 4| 11
+--R \| 16b
+--R *
+--R +--------------------------------------------------+3
+--R | 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R 8 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 8b |--------------------------------------------------
+--R 4| 11
+--R \| 16b
+--R atan(---------------------------------------------------------)
+--R 5 3 4 2 3 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - a b c )\|x
+--R /
+--R 2 +-+4+-+3
+--R 2b \|2 \|b
+--R Type: Expression(Integer)
+--E 1089
+
+--S 1090 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1090
+
+)clear all
+
+--S 1091 of 1475
+t0:=x^(3/2)*(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R 3 +-+
+--R (d x + c x)\|x
+--R (1) ----------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1091
+
+--S 1092 of 1475
+r0:=2/5*d*x^(5/2)/b+a^(1/4)*(b*c-a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(b^(9/4)*sqrt(2))-a^(1/4)*(b*c-a*d)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*sqrt(2))+1/2*a^(1/4)*(b*c-a*d)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(9/4)*_
+ sqrt(2))-1/2*a^(1/4)*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(b^(9/4)*sqrt(2))+2*(b*c-a*d)*sqrt(x)/b^2
+--R
+--R
+--R (2)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - 5b c)\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + 5b c)\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a
+--R (10a d - 10b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x - \|a
+--R (10a d - 10b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+ +-+
+--R (4b d x - 20a d + 20b c)\|2 \|b \|x
+--R /
+--R 2 +-+4+-+
+--R 10b \|2 \|b
+--R Type: Expression(Integer)
+--E 1092
+
+--S 1093 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 5b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R *
+--R log
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R +--------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 2b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 5b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R *
+--R log
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R +--------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R - 2b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 10b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R *
+--R +--------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 2b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R atan(--------------------------------------------------------)
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R 2 +-+
+--R (2b d x - 10a d + 10b c)\|x
+--R /
+--R 2
+--R 5b
+--R Type: Union(Expression(Integer),...)
+--E 1093
+
+--S 1094 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + b c)\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - a b c 4+-+
+--R 2b \|2 |-------------------------------------------------- \|b
+--R 4| 9
+--R \| 16b
+--R *
+--R log
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R +--------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 2b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - a b c 4+-+
+--R 2b \|2 |-------------------------------------------------- \|b
+--R 4| 9
+--R \| 16b
+--R *
+--R log
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R +--------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R - 2b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - b c)\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a
+--R (- 2a d + 2b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x - \|a
+--R (- 2a d + 2b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - a b c 4+-+
+--R 4b \|2 |-------------------------------------------------- \|b
+--R 4| 9
+--R \| 16b
+--R *
+--R +--------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - a b c
+--R 2b |--------------------------------------------------
+--R 4| 9
+--R \| 16b
+--R atan(--------------------------------------------------------)
+--R +-+
+--R (a d - b c)\|x
+--R /
+--R 2 +-+4+-+
+--R 2b \|2 \|b
+--R Type: Expression(Integer)
+--E 1094
+
+--S 1095 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1095
+
+)clear all
+
+--S 1096 of 1475
+t0:=(c+d*x^2)*sqrt(x)/(a+b*x^2)
+--R
+--R
+--R 2 +-+
+--R (d x + c)\|x
+--R (1) --------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1096
+
+--S 1097 of 1475
+r0:=2/3*d*x^(3/2)/b-(b*c-a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(1/4)*b^(7/4)*sqrt(2))+(b*c-a*d)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(1/4)*b^(7/4)*sqrt(2))+1/2*(b*c-a*d)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*_
+ b^(7/4)*sqrt(2))-1/2*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(7/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d - 3b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d + 3b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 6a d + 6b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a +-+4+-+4+-+3 +-+
+--R (- 6a d + 6b c)atan(-------------------) + 4d x\|2 \|a \|b \|x
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+4+-+3
+--R 6b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1097
+
+--S 1098 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 3b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 5 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 8a b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 3b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 5 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R - 8a b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 6b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R *
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 5 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 8a b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R atan(---------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R +-+
+--R 2d x\|x
+--R /
+--R 3b
+--R Type: Union(Expression(Integer),...)
+--E 1098
+
+--S 1099 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+4+-+3
+--R 2b\|2 |------------------------------------------------ \|a \|b
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 5 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 8a b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+4+-+3
+--R 2b\|2 |------------------------------------------------ \|a \|b
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 5 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R - 8a b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (2a d - 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (2a d - 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+4+-+3
+--R 4b\|2 |------------------------------------------------ \|a \|b
+--R 4| 7
+--R \| 16a b
+--R *
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 5 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 8a b |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R atan(---------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R /
+--R +-+4+-+4+-+3
+--R 2b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1099
+
+--S 1100 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1100
+
+)clear all
+
+--S 1101 of 1475
+t0:=(c+d*x^2)/((a+b*x^2)*sqrt(x))
+--R
+--R
+--R 2
+--R d x + c
+--R (1) --------------
+--R 2 +-+
+--R (b x + a)\|x
+--R Type: Expression(Integer)
+--E 1101
+
+--S 1102 of 1475
+r0:=-(b*c-a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(5/4)*_
+ sqrt(2))+(b*c-a*d)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(3/4)*b^(5/4)*sqrt(2))-1/2*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(5/4)*sqrt(2))+_
+ 1/2*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(3/4)*b^(5/4)*sqrt(2))+2*d*sqrt(x)/b
+--R
+--R
+--R (2)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 2a d + 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a +-+4+-+3 4+-+ +-+
+--R (- 2a d + 2b c)atan(-------------------) + 4d\|2 \|a \|b \|x
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+3 4+-+
+--R 2b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1102
+
+--S 1103 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 2a b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R - 2a b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 2b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R *
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 2a b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R atan(-------------------------------------------------------)
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R +-+
+--R 2d\|x
+--R /
+--R b
+--R Type: Union(Expression(Integer),...)
+--E 1103
+
+--S 1104 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+3 4+-+
+--R 2b\|2 |------------------------------------------------ \|a \|b
+--R 4| 3 5
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 2a b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+3 4+-+
+--R 2b\|2 |------------------------------------------------ \|a \|b
+--R 4| 3 5
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R - 2a b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (2a d - 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (2a d - 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+3 4+-+
+--R 4b\|2 |------------------------------------------------ \|a \|b
+--R 4| 3 5
+--R \| 16a b
+--R *
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 2a b |------------------------------------------------
+--R 4| 3 5
+--R \| 16a b
+--R atan(-------------------------------------------------------)
+--R +-+
+--R (a d - b c)\|x
+--R /
+--R +-+4+-+3 4+-+
+--R 2b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1104
+
+--S 1105 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1105
+
+)clear all
+
+--S 1106 of 1475
+t0:=(c+d*x^2)/(x^(3/2)*(a+b*x^2))
+--R
+--R
+--R 2
+--R d x + c
+--R (1) ----------------
+--R 3 +-+
+--R (b x + a x)\|x
+--R Type: Expression(Integer)
+--E 1106
+
+--S 1107 of 1475
+r0:=(b*c-a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(3/4)*_
+ sqrt(2))-(b*c-a*d)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(5/4)*b^(3/4)*sqrt(2))-1/2*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(3/4)*sqrt(2))+_
+ 1/2*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(5/4)*b^(3/4)*sqrt(2))-2*c/(a*sqrt(x))
+--R
+--R
+--R (2)
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + b c)\|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - b c)\|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x + \|a
+--R (2a d - 2b c)\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x - \|a +-+4+-+4+-+3
+--R (2a d - 2b c)\|x atan(-------------------) - 4c\|2 \|a \|b
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+4+-+3 +-+
+--R 2a\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1107
+
+--S 1108 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c +-+
+--R a |------------------------------------------------ \|x
+--R 4| 5 3
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 2 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 8a b |------------------------------------------------
+--R 4| 5 3
+--R \| 16a b
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c +-+
+--R a |------------------------------------------------ \|x
+--R 4| 5 3
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 2 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R - 8a b |------------------------------------------------
+--R 4| 5 3
+--R \| 16a b
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c +-+
+--R 2a |------------------------------------------------ \|x
+--R 4| 5 3
+--R \| 16a b
+--R *
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 2 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 8a b |------------------------------------------------
+--R 4| 5 3
+--R \| 16a b
+--R atan(---------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R - 2c
+--R /
+--R +-+
+--R a\|x
+--R Type: Union(Expression(Integer),...)
+--E 1108
+
+--S 1109 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+4+-+3
+--R 2a\|2 |------------------------------------------------ \|a \|b
+--R 4| 5 3
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 2 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 8a b |------------------------------------------------
+--R 4| 5 3
+--R \| 16a b
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+4+-+3
+--R 2a\|2 |------------------------------------------------ \|a \|b
+--R 4| 5 3
+--R \| 16a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 2 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R - 8a b |------------------------------------------------
+--R 4| 5 3
+--R \| 16a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 2a d + 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 2a d + 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+4+-+3
+--R 4a\|2 |------------------------------------------------ \|a \|b
+--R 4| 5 3
+--R \| 16a b
+--R *
+--R +------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 2 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 8a b |------------------------------------------------
+--R 4| 5 3
+--R \| 16a b
+--R atan(---------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R /
+--R +-+4+-+4+-+3
+--R 2a\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1109
+
+--S 1110 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1110
+
+)clear all
+
+--S 1111 of 1475
+t0:=(c+d*x^2)/(x^(5/2)*(a+b*x^2))
+--R
+--R
+--R 2
+--R d x + c
+--R (1) -----------------
+--R 4 2 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1111
+
+--S 1112 of 1475
+r0:=-2/3*c/(a*x^(3/2))+(b*c-a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(7/4)*b^(1/4)*sqrt(2))-(b*c-a*d)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(7/4)*b^(1/4)*sqrt(2))+1/2*(b*c-a*d)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(7/4)*b^(1/4)*sqrt(2))-1/2*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(1/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d - 3b c)x\|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d + 3b c)x\|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x + \|a
+--R (6a d - 6b c)x\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x - \|a +-+4+-+3 4+-+
+--R (6a d - 6b c)x\|x atan(-------------------) - 4c\|2 \|a \|b
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+3 4+-+ +-+
+--R 6a x\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1112
+
+--S 1113 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c +-+
+--R 3a x |------------------------------------------------ \|x
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 2a |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c +-+
+--R 3a x |------------------------------------------------ \|x
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R - 2a |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 4a b c d - 6a b c d + 4a b c d - b c +-+
+--R 6a x |------------------------------------------------ \|x
+--R 4| 7
+--R \| 16a b
+--R *
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 2a |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R atan(------------------------------------------------------)
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R - 2c
+--R /
+--R +-+
+--R 3a x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1113
+
+--S 1114 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+3 4+-+
+--R 2a\|2 |------------------------------------------------ \|a \|b
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 2a |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+3 4+-+
+--R 2a\|2 |------------------------------------------------ \|a \|b
+--R 4| 7
+--R \| 16a b
+--R *
+--R log
+--R +-+
+--R (a d - b c)\|x
+--R +
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R - 2a |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 2a d + 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 2a d + 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+3 4+-+
+--R 4a\|2 |------------------------------------------------ \|a \|b
+--R 4| 7
+--R \| 16a b
+--R *
+--R +------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 2a |------------------------------------------------
+--R 4| 7
+--R \| 16a b
+--R atan(------------------------------------------------------)
+--R +-+
+--R (a d - b c)\|x
+--R /
+--R +-+4+-+3 4+-+
+--R 2a\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1114
+
+--S 1115 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1115
+
+)clear all
+
+--S 1116 of 1475
+t0:=(c+d*x^2)/(x^(7/2)*(a+b*x^2))
+--R
+--R
+--R 2
+--R d x + c
+--R (1) -----------------
+--R 5 3 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1116
+
+--S 1117 of 1475
+r0:=-2/5*c/(a*x^(5/2))-b^(1/4)*(b*c-a*d)*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(9/4)*sqrt(2))+b^(1/4)*(b*c-a*d)*atan(1+_
+ b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*sqrt(2))+1/2*b^(1/4)*_
+ (b*c-a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(9/4)*sqrt(2))-1/2*b^(1/4)*(b*c-a*d)*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+_
+ 2*(b*c-a*d)/(a^2*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - 5b c)x \|b \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + 5b c)x \|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ +-+ \|2 \|b \|x + \|a
+--R (- 10a d + 10b c)x \|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ +-+ \|2 \|b \|x - \|a
+--R (- 10a d + 10b c)x \|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+
+--R ((- 20a d + 20b c)x - 4a c)\|2 \|a
+--R /
+--R 2 2 +-+4+-+ +-+
+--R 10a x \|2 \|a \|x
+--R Type: Expression(Integer)
+--E 1117
+
+--S 1118 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R 2 2 |- a b d + 4a b c d - 6a b c d + 4a b c d - b c +-+
+--R 5a x |-------------------------------------------------- \|x
+--R 4| 9
+--R \| 16a
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (a b d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R 7 |- a b d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 8a |--------------------------------------------------
+--R 4| 9
+--R \| 16a
+--R +
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R 2 2 |- a b d + 4a b c d - 6a b c d + 4a b c d - b c +-+
+--R 5a x |-------------------------------------------------- \|x
+--R 4| 9
+--R \| 16a
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (a b d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R 7 |- a b d + 4a b c d - 6a b c d + 4a b c d - b c
+--R - 8a |--------------------------------------------------
+--R 4| 9
+--R \| 16a
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R 2 2 |- a b d + 4a b c d - 6a b c d + 4a b c d - b c +-+
+--R 10a x |-------------------------------------------------- \|x
+--R 4| 9
+--R \| 16a
+--R *
+--R +--------------------------------------------------+3
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R 7 |- a b d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 8a |--------------------------------------------------
+--R 4| 9
+--R \| 16a
+--R atan(---------------------------------------------------------)
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (a b d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R 2
+--R (- 10a d + 10b c)x - 2a c
+--R /
+--R 2 2 +-+
+--R 5a x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1118
+
+--S 1119 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + b c)\|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R 2 +-+ |- a b d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+
+--R 2a \|2 |-------------------------------------------------- \|a
+--R 4| 9
+--R \| 16a
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (a b d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R 7 |- a b d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 8a |--------------------------------------------------
+--R 4| 9
+--R \| 16a
+--R +
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R 2 +-+ |- a b d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+
+--R 2a \|2 |-------------------------------------------------- \|a
+--R 4| 9
+--R \| 16a
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (a b d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R +--------------------------------------------------+3
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R 7 |- a b d + 4a b c d - 6a b c d + 4a b c d - b c
+--R - 8a |--------------------------------------------------
+--R 4| 9
+--R \| 16a
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - b c)\|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a
+--R (2a d - 2b c)\|b atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x - \|a
+--R (2a d - 2b c)\|b atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R +--------------------------------------------------+
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R 2 +-+ |- a b d + 4a b c d - 6a b c d + 4a b c d - b c 4+-+
+--R 4a \|2 |-------------------------------------------------- \|a
+--R 4| 9
+--R \| 16a
+--R *
+--R +--------------------------------------------------+3
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R 7 |- a b d + 4a b c d - 6a b c d + 4a b c d - b c
+--R 8a |--------------------------------------------------
+--R 4| 9
+--R \| 16a
+--R atan(---------------------------------------------------------)
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (a b d - 3a b c d + 3a b c d - b c )\|x
+--R /
+--R 2 +-+4+-+
+--R 2a \|2 \|a
+--R Type: Expression(Integer)
+--E 1119
+
+--S 1120 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1120
+
+)clear all
+
+--S 1121 of 1475
+t0:=x^(7/2)*(c+d*x^2)^2/(a+b*x^2)
+--R
+--R
+--R 2 7 5 2 3 +-+
+--R (d x + 2c d x + c x )\|x
+--R (1) ---------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1121
+
+--S 1122 of 1475
+r0:=2/5*(b*c-a*d)^2*x^(5/2)/b^3+2/9*d*(2*b*c-a*d)*x^(9/2)/b^2+2/13*_
+ d^2*x^(13/2)/b-a^(5/4)*(b*c-a*d)^2*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(b^(17/4)*sqrt(2))+a^(5/4)*(b*c-a*d)^2*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(17/4)*sqrt(2))-_
+ 1/2*a^(5/4)*(b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(b^(17/4)*sqrt(2))+1/2*a^(5/4)*(b*c-a*d)^2*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (b^(17/4)*sqrt(2))-2*a*(b*c-a*d)^2*sqrt(x)/b^4
+--R
+--R
+--R (2)
+--R 3 2 2 2 2 4+-+
+--R (585a d - 1170a b c d + 585a b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 2 2 2 4+-+
+--R (- 585a d + 1170a b c d - 585a b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 2 2 2 2 4+-+ \|2 \|b \|x + \|a
+--R (1170a d - 2340a b c d + 1170a b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 2 2 2 2 4+-+ \|2 \|b \|x - \|a
+--R (1170a d - 2340a b c d + 1170a b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 6 2 2 3 4
+--R 180b d x + (- 260a b d + 520b c d)x
+--R +
+--R 2 2 2 3 2 2 3 2 2
+--R (468a b d - 936a b c d + 468b c )x - 2340a d + 4680a b c d
+--R +
+--R 2 2
+--R - 2340a b c
+--R *
+--R +-+4+-+ +-+
+--R \|2 \|b \|x
+--R /
+--R 4 +-+4+-+
+--R 1170b \|2 \|b
+--R Type: Expression(Integer)
+--E 1122
+
+--S 1123 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4
+--R 585b
+--R *
+--R ROOT
+--R 13 8 12 7 11 2 2 6 10 3 3 5 9 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 8 5 5 3 7 6 6 2 6 7 7 5 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R *
+--R log
+--R 3 2 2 2 2 +-+
+--R (a d - 2a b c d + a b c )\|x
+--R +
+--R 4
+--R 2b
+--R *
+--R ROOT
+--R 13 8 12 7 11 2 2 6 10 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 9 4 4 4 8 5 5 3 7 6 6 2 6 7 7 5 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R +
+--R -
+--R 4
+--R 585b
+--R *
+--R ROOT
+--R 13 8 12 7 11 2 2 6 10 3 3 5 9 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 8 5 5 3 7 6 6 2 6 7 7 5 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R *
+--R log
+--R 3 2 2 2 2 +-+
+--R (a d - 2a b c d + a b c )\|x
+--R +
+--R -
+--R 4
+--R 2b
+--R *
+--R ROOT
+--R 13 8 12 7 11 2 2 6 10 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 9 4 4 4 8 5 5 3 7 6 6 2 6 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 5 8 8
+--R - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R +
+--R -
+--R 4
+--R 1170b
+--R *
+--R ROOT
+--R 13 8 12 7 11 2 2 6 10 3 3 5 9 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 8 5 5 3 7 6 6 2 6 7 7 5 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R *
+--R atan
+--R 4
+--R 2b
+--R *
+--R ROOT
+--R 13 8 12 7 11 2 2 6 10 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 9 4 4 4 8 5 5 3 7 6 6 2 6 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 5 8 8
+--R - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R /
+--R 3 2 2 2 2 +-+
+--R (a d - 2a b c d + a b c )\|x
+--R +
+--R 3 2 6 2 2 3 4
+--R 90b d x + (- 130a b d + 260b c d)x
+--R +
+--R 2 2 2 3 2 2 3 2 2
+--R (234a b d - 468a b c d + 234b c )x - 1170a d + 2340a b c d
+--R +
+--R 2 2
+--R - 1170a b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 4
+--R 585b
+--R Type: Union(Expression(Integer),...)
+--E 1123
+
+--S 1124 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - a b c )\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 13 8 12 7 11 2 2 6 10 3 3 5 9 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 8 5 5 3 7 6 6 2 6 7 7 5 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R 3 2 2 2 2 +-+
+--R (a d - 2a b c d + a b c )\|x
+--R +
+--R 4
+--R 2b
+--R *
+--R ROOT
+--R 13 8 12 7 11 2 2 6 10 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 9 4 4 4 8 5 5 3 7 6 6 2 6 7 7 5 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R +
+--R -
+--R 4 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 13 8 12 7 11 2 2 6 10 3 3 5 9 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 8 5 5 3 7 6 6 2 6 7 7 5 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R 3 2 2 2 2 +-+
+--R (a d - 2a b c d + a b c )\|x
+--R +
+--R -
+--R 4
+--R 2b
+--R *
+--R ROOT
+--R 13 8 12 7 11 2 2 6 10 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 9 4 4 4 8 5 5 3 7 6 6 2 6 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 5 8 8
+--R - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R +
+--R 3 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + a b c )\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 2 2 2 2 4+-+ \|2 \|b \|x + \|a
+--R (- 2a d + 4a b c d - 2a b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 2 2 2 2 4+-+ \|2 \|b \|x - \|a
+--R (- 2a d + 4a b c d - 2a b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 4 +-+
+--R 4b \|2
+--R *
+--R ROOT
+--R 13 8 12 7 11 2 2 6 10 3 3 5 9 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 8 5 5 3 7 6 6 2 6 7 7 5 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R atan
+--R 4
+--R 2b
+--R *
+--R ROOT
+--R 13 8 12 7 11 2 2 6 10 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 9 4 4 4 8 5 5 3 7 6 6 2 6 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 5 8 8
+--R - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R /
+--R 3 2 2 2 2 +-+
+--R (a d - 2a b c d + a b c )\|x
+--R /
+--R 4 +-+4+-+
+--R 2b \|2 \|b
+--R Type: Expression(Integer)
+--E 1124
+
+--S 1125 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1125
+
+)clear all
+
+--S 1126 of 1475
+t0:=x^(5/2)*(c+d*x^2)^2/(a+b*x^2)
+--R
+--R
+--R 2 6 4 2 2 +-+
+--R (d x + 2c d x + c x )\|x
+--R (1) ---------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1126
+
+--S 1127 of 1475
+r0:=2/3*(b*c-a*d)^2*x^(3/2)/b^3+2/7*d*(2*b*c-a*d)*x^(7/2)/b^2+_
+ 2/11*d^2*x^(11/2)/b+a^(3/4)*(b*c-a*d)^2*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(b^(15/4)*sqrt(2))-a^(3/4)*(b*c-a*d)^2*atan(1+_
+ b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(15/4)*sqrt(2))-1/2*a^(3/4)*_
+ (b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(b^(15/4)*sqrt(2))+1/2*a^(3/4)*(b*c-a*d)^2*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(15/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2 2 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (231a d - 462a b c d + 231b c )\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 4+-+3
+--R (- 231a d + 462a b c d - 231b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+3 \|2 \|b \|x + \|a
+--R (- 462a d + 924a b c d - 462b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+3 \|2 \|b \|x - \|a
+--R (- 462a d + 924a b c d - 462b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 5 2 2 3
+--R 84b d x + (- 132a b d + 264b c d)x
+--R +
+--R 2 2 2 2
+--R (308a d - 616a b c d + 308b c )x
+--R *
+--R +-+4+-+3 +-+
+--R \|2 \|b \|x
+--R /
+--R 3 +-+4+-+3
+--R 462b \|2 \|b
+--R Type: Expression(Integer)
+--E 1127
+
+--S 1128 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3
+--R 231b
+--R *
+--R ROOT
+--R 11 8 10 7 9 2 2 6 8 3 3 5 7 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 6 5 5 3 5 6 6 2 4 7 7 3 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 15
+--R 16b
+--R ,
+--R 4
+--R *
+--R log
+--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 3 5 5 2 6 6
+--R - 6a b c d + a b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 11
+--R 8b
+--R *
+--R ROOT
+--R 11 8 10 7 9 2 2 6 8 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 7 4 4 4 6 5 5 3 5 6 6 2 4 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 3 8 8
+--R - a b c
+--R /
+--R 15
+--R 16b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3
+--R 231b
+--R *
+--R ROOT
+--R 11 8 10 7 9 2 2 6 8 3 3 5 7 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 6 5 5 3 5 6 6 2 4 7 7 3 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 15
+--R 16b
+--R ,
+--R 4
+--R *
+--R log
+--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 3 5 5 2 6 6
+--R - 6a b c d + a b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 11
+--R 8b
+--R *
+--R ROOT
+--R 11 8 10 7 9 2 2 6 8 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 7 4 4 4 6 5 5 3 5 6 6 2 4 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 3 8 8
+--R - a b c
+--R /
+--R 15
+--R 16b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 3
+--R 462b
+--R *
+--R ROOT
+--R 11 8 10 7 9 2 2 6 8 3 3 5 7 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 6 5 5 3 5 6 6 2 4 7 7 3 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 15
+--R 16b
+--R ,
+--R 4
+--R *
+--R atan
+--R 11
+--R 8b
+--R *
+--R ROOT
+--R 11 8 10 7 9 2 2 6 8 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 7 4 4 4 6 5 5 3 5 6 6 2 4 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 3 8 8
+--R - a b c
+--R /
+--R 15
+--R 16b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 3 5 5 2 6 6
+--R - 6a b c d + a b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 5 2 2 3
+--R 42b d x + (- 66a b d + 132b c d)x
+--R +
+--R 2 2 2 2
+--R (154a d - 308a b c d + 154b c )x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3
+--R 231b
+--R Type: Union(Expression(Integer),...)
+--E 1128
+
+--S 1129 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 3 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 11 8 10 7 9 2 2 6 8 3 3 5 7 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 6 5 5 3 5 6 6 2 4 7 7 3 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 15
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R log
+--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 3 5 5 2 6 6
+--R - 6a b c d + a b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 11
+--R 8b
+--R *
+--R ROOT
+--R 11 8 10 7 9 2 2 6 8 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 7 4 4 4 6 5 5 3 5 6 6 2 4 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 3 8 8
+--R - a b c
+--R /
+--R 15
+--R 16b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 11 8 10 7 9 2 2 6 8 3 3 5 7 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 6 5 5 3 5 6 6 2 4 7 7 3 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 15
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R log
+--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 3 5 5 2 6 6
+--R - 6a b c d + a b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 11
+--R 8b
+--R *
+--R ROOT
+--R 11 8 10 7 9 2 2 6 8 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 7 4 4 4 6 5 5 3 5 6 6 2 4 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 3 8 8
+--R - a b c
+--R /
+--R 15
+--R 16b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+3 \|2 \|b \|x + \|a
+--R (2a d - 4a b c d + 2b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+3 \|2 \|b \|x - \|a
+--R (2a d - 4a b c d + 2b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 3 +-+
+--R 4b \|2
+--R *
+--R ROOT
+--R 11 8 10 7 9 2 2 6 8 3 3 5 7 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 6 5 5 3 5 6 6 2 4 7 7 3 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 15
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R atan
+--R 11
+--R 8b
+--R *
+--R ROOT
+--R 11 8 10 7 9 2 2 6 8 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 7 4 4 4 6 5 5 3 5 6 6 2 4 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 3 8 8
+--R - a b c
+--R /
+--R 15
+--R 16b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 3 5 5 2 6 6
+--R - 6a b c d + a b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3 +-+4+-+3
+--R 2b \|2 \|b
+--R Type: Expression(Integer)
+--E 1129
+
+--S 1130 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1130
+
+)clear all
+
+--S 1131 of 1475
+t0:=x^(3/2)*(c+d*x^2)^2/(a+b*x^2)
+--R
+--R
+--R 2 5 3 2 +-+
+--R (d x + 2c d x + c x)\|x
+--R (1) --------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1131
+
+--S 1132 of 1475
+r0:=2/5*d*(2*b*c-a*d)*x^(5/2)/b^2+2/9*d^2*x^(9/2)/b+a^(1/4)*(b*c-a*d)^2*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(13/4)*sqrt(2))-_
+ a^(1/4)*(b*c-a*d)^2*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (b^(13/4)*sqrt(2))+1/2*a^(1/4)*(b*c-a*d)^2*log(sqrt(a)+x*_
+ sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(13/4)*sqrt(2))-_
+ 1/2*a^(1/4)*(b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(b^(13/4)*sqrt(2))+2*(b*c-a*d)^2*sqrt(x)/b^3
+--R
+--R
+--R (2)
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 45a d + 90a b c d - 45b c )\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (45a d - 90a b c d + 45b c )\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|b \|x + \|a
+--R (- 90a d + 180a b c d - 90b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|b \|x - \|a
+--R (- 90a d + 180a b c d - 90b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R (20b d x + (- 36a b d + 72b c d)x + 180a d - 360a b c d + 180b c )
+--R *
+--R +-+4+-+ +-+
+--R \|2 \|b \|x
+--R /
+--R 3 +-+4+-+
+--R 90b \|2 \|b
+--R Type: Expression(Integer)
+--E 1132
+
+--S 1133 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3
+--R 45b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5 5 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 4 5 5 3 3 6 6 2 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 13
+--R 16b
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 3
+--R 2b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - a b c
+--R /
+--R 13
+--R 16b
+--R ,
+--R 4
+--R +
+--R 3
+--R 45b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5 5 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 4 5 5 3 3 6 6 2 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 13
+--R 16b
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 3
+--R 2b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - a b c
+--R /
+--R 13
+--R 16b
+--R ,
+--R 4
+--R +
+--R 3
+--R 90b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5 5 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 4 5 5 3 3 6 6 2 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 13
+--R 16b
+--R ,
+--R 4
+--R *
+--R atan
+--R 3
+--R 2b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5 5 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 4 5 5 3 3 6 6 2 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 13
+--R 16b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2 2 4 2 2 2 2 2 2 2 +-+
+--R (10b d x + (- 18a b d + 36b c d)x + 90a d - 180a b c d + 90b c )\|x
+--R /
+--R 3
+--R 45b
+--R Type: Union(Expression(Integer),...)
+--E 1133
+
+--S 1134 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 3 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5 5 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 4 5 5 3 3 6 6 2 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 13
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 3
+--R 2b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - a b c
+--R /
+--R 13
+--R 16b
+--R ,
+--R 4
+--R +
+--R 3 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5 5 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 4 5 5 3 3 6 6 2 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 13
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 3
+--R 2b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - a b c
+--R /
+--R 13
+--R 16b
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|b \|x + \|a
+--R (2a d - 4a b c d + 2b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|b \|x - \|a
+--R (2a d - 4a b c d + 2b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+
+--R 4b \|2
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5 5 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 4 5 5 3 3 6 6 2 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 13
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R atan
+--R 3
+--R 2b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5 5 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 4 5 5 3 3 6 6 2 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - a b c
+--R /
+--R 13
+--R 16b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R /
+--R 3 +-+4+-+
+--R 2b \|2 \|b
+--R Type: Expression(Integer)
+--E 1134
+
+--S 1135 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1135
+
+)clear all
+
+--S 1136 of 1475
+t0:=(c+d*x^2)^2*sqrt(x)/(a+b*x^2)
+--R
+--R
+--R 2 4 2 2 +-+
+--R (d x + 2c d x + c )\|x
+--R (1) -------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1136
+
+--S 1137 of 1475
+r0:=2/3*d*(2*b*c-a*d)*x^(3/2)/b^2+2/7*d^2*x^(7/2)/b-(b*c-a*d)^2*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(11/4)*_
+ sqrt(2))+(b*c-a*d)^2*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(1/4)*b^(11/4)*sqrt(2))+1/2*(b*c-a*d)^2*log(sqrt(a)+x*_
+ sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(11/4)*_
+ sqrt(2))-1/2*(b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(1/4)*b^(11/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 21a d + 42a b c d - 21b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (21a d - 42a b c d + 21b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (42a d - 84a b c d + 42b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (42a d - 84a b c d + 42b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 +-+4+-+4+-+3 +-+
+--R (12b d x + (- 28a d + 56b c d)x)\|2 \|a \|b \|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 42b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1137
+
+--S 1138 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R 21b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 8
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2
+--R 21b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 8
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2
+--R 42b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R atan
+--R 8
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 3 2 +-+
+--R (6b d x + (- 14a d + 28b c d)x)\|x
+--R /
+--R 2
+--R 21b
+--R Type: Union(Expression(Integer),...)
+--E 1138
+
+--S 1139 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 8
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 8
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+
+--R 4b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 8
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 2b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1139
+
+--S 1140 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1140
+
+)clear all
+
+--S 1141 of 1475
+t0:=(c+d*x^2)^2/((a+b*x^2)*sqrt(x))
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 2 +-+
+--R (b x + a)\|x
+--R Type: Expression(Integer)
+--E 1141
+
+--S 1142 of 1475
+r0:=2/5*d^2*x^(5/2)/b-(b*c-a*d)^2*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(3/4)*b^(9/4)*sqrt(2))+(b*c-a*d)^2*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(9/4)*sqrt(2))-1/2*(b*c-_
+ a*d)^2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(3/4)*b^(9/4)*sqrt(2))+1/2*(b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(9/4)*sqrt(2))+_
+ 2*d*(2*b*c-a*d)*sqrt(x)/b^2
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - 10a b c d + 5b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + 10a b c d - 5b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (10a d - 20a b c d + 10b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (10a d - 20a b c d + 10b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 +-+4+-+3 4+-+ +-+
+--R (4b d x - 20a d + 40b c d)\|2 \|a \|b \|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 10b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1142
+
+--S 1143 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R 5b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16a b
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2
+--R 2a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16a b
+--R ,
+--R 4
+--R +
+--R -
+--R 2
+--R 5b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16a b
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 2
+--R 2a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 3 9
+--R 16a b
+--R ,
+--R 4
+--R +
+--R -
+--R 2
+--R 10b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16a b
+--R ,
+--R 4
+--R *
+--R atan
+--R 2
+--R 2a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16a b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2 2 2 +-+
+--R (2b d x - 10a d + 20b c d)\|x
+--R /
+--R 2
+--R 5b
+--R Type: Union(Expression(Integer),...)
+--E 1143
+
+--S 1144 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2
+--R 2a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16a b
+--R ,
+--R 4
+--R +
+--R -
+--R 2 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 2
+--R 2a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 3 9
+--R 16a b
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 2 +-+
+--R 4b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 2
+--R 2a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 3 9
+--R 16a b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 2b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1144
+
+--S 1145 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1145
+
+)clear all
+
+--S 1146 of 1475
+t0:=(c+d*x^2)^2/(x^(3/2)*(a+b*x^2))
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 3 +-+
+--R (b x + a x)\|x
+--R Type: Expression(Integer)
+--E 1146
+
+--S 1147 of 1475
+r0:=2/3*d^2*x^(3/2)/b+(b*c-a*d)^2*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(5/4)*b^(7/4)*sqrt(2))-(b*c-a*d)^2*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(7/4)*sqrt(2))-1/2*(b*c-_
+ a*d)^2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(5/4)*b^(7/4)*sqrt(2))+1/2*(b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(7/4)*sqrt(2))-_
+ 2*c^2/(a*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d - 6a b c d + 3b c )\|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d + 6a b c d - 3b c )\|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 +-+ \|2 \|b \|x + \|a
+--R (- 6a d + 12a b c d - 6b c )\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 +-+ \|2 \|b \|x - \|a
+--R (- 6a d + 12a b c d - 6b c )\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 +-+4+-+4+-+3
+--R (4a d x - 12b c )\|2 \|a \|b
+--R /
+--R +-+4+-+4+-+3 +-+
+--R 6a b\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1147
+
+--S 1148 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 5 7
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 5
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 7
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 5 7
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 5
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 7
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 6a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 5 7
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 4 5
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 7
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 2
+--R 2a d x - 6b c
+--R /
+--R +-+
+--R 3a b\|x
+--R Type: Union(Expression(Integer),...)
+--E 1148
+
+--S 1149 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R +-+
+--R 2a b\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 5 7
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 5
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 7
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R +-+
+--R 2a b\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 5 7
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 5
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 7
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (2a d - 4a b c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (2a d - 4a b c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R +-+
+--R 4a b\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 5 7
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 4 5
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 7
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R +-+4+-+4+-+3
+--R 2a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1149
+
+--S 1150 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1150
+
+)clear all
+
+--S 1151 of 1475
+t0:=(c+d*x^2)^2/(x^(5/2)*(a+b*x^2))
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 4 2 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1151
+
+--S 1152 of 1475
+r0:=-2/3*c^2/(a*x^(3/2))+(b*c-a*d)^2*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(7/4)*b^(5/4)*sqrt(2))-(b*c-a*d)^2*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(5/4)*sqrt(2))+1/2*(b*c-_
+ a*d)^2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(7/4)*b^(5/4)*sqrt(2))-1/2*(b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(5/4)*sqrt(2))+_
+ 2*d^2*sqrt(x)/b
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d + 6a b c d - 3b c )x\|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d - 6a b c d + 3b c )x\|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 +-+ \|2 \|b \|x + \|a
+--R (- 6a d + 12a b c d - 6b c )x\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 +-+ \|2 \|b \|x - \|a
+--R (- 6a d + 12a b c d - 6b c )x\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 +-+4+-+3 4+-+
+--R (12a d x - 4b c )\|2 \|a \|b
+--R /
+--R +-+4+-+3 4+-+ +-+
+--R 6a b x\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1152
+
+--S 1153 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3a b x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2
+--R 2a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16a b
+--R ,
+--R 4
+--R +
+--R 3a b x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 2
+--R 2a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16a b
+--R ,
+--R 4
+--R +
+--R 6a b x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 2
+--R 2a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16a b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2 2 2
+--R 6a d x - 2b c
+--R /
+--R +-+
+--R 3a b x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1153
+
+--S 1154 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R +-+
+--R 2a b\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2
+--R 2a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16a b
+--R ,
+--R 4
+--R +
+--R +-+
+--R 2a b\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 2
+--R 2a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16a b
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (2a d - 4a b c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (2a d - 4a b c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+
+--R 4a b\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 2
+--R 2a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 7 5
+--R 16a b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R /
+--R +-+4+-+3 4+-+
+--R 2a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1154
+
+--S 1155 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1155
+
+)clear all
+
+--S 1156 of 1475
+t0:=(c+d*x^2)^2/(x^(7/2)*(a+b*x^2))
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 5 3 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1156
+
+--S 1157 of 1475
+r0:=-2/5*c^2/(a*x^(5/2))-(b*c-a*d)^2*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(9/4)*b^(3/4)*sqrt(2))+(b*c-a*d)^2*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*b^(3/4)*sqrt(2))+1/2*(b*c-_
+ a*d)^2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(9/4)*b^(3/4)*sqrt(2))-1/2*(b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*b^(3/4)*sqrt(2))+_
+ 2*c*(b*c-2*a*d)/(a^2*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + 10a b c d - 5b c )x \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 2 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - 10a b c d + 5b c )x \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 2 +-+ \|2 \|b \|x + \|a
+--R (10a d - 20a b c d + 10b c )x \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 2 +-+ \|2 \|b \|x - \|a
+--R (10a d - 20a b c d + 10b c )x \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 +-+4+-+4+-+3
+--R ((- 40a c d + 20b c )x - 4a c )\|2 \|a \|b
+--R /
+--R 2 2 +-+4+-+4+-+3 +-+
+--R 10a x \|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1157
+
+--S 1158 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R 5a x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 2
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2 2
+--R 5a x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 2
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 9 3
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2
+--R 10a x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 7 2
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 2
+--R (- 20a c d + 10b c )x - 2a c
+--R /
+--R 2 2 +-+
+--R 5a x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1158
+
+--S 1159 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 2a \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 2
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2 +-+
+--R 2a \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 2
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 9 3
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+
+--R 4a \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 7 2
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 9 3
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 5 5 6 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 2a \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1159
+
+--S 1160 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1160
+
+)clear all
+
+--S 1161 of 1475
+t0:=(c+d*x^2)^2/(x^(9/2)*(a+b*x^2))
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 6 4 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1161
+
+--S 1162 of 1475
+r0:=-2/7*c^2/(a*x^(7/2))+2/3*c*(b*c-2*a*d)/(a^2*x^(3/2))-(b*c-a*d)^2*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*b^(1/4)*_
+ sqrt(2))+(b*c-a*d)^2*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(11/4)*b^(1/4)*sqrt(2))-1/2*(b*c-a*d)^2*log(sqrt(a)+x*_
+ sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*b^(1/4)*_
+ sqrt(2))+1/2*(b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(11/4)*b^(1/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2 2 3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (21a d - 42a b c d + 21b c )x \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 3 +-+
+--R (- 21a d + 42a b c d - 21b c )x \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 3 +-+ \|2 \|b \|x + \|a
+--R (42a d - 84a b c d + 42b c )x \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 3 +-+ \|2 \|b \|x - \|a
+--R (42a d - 84a b c d + 42b c )x \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 +-+4+-+3 4+-+
+--R ((- 56a c d + 28b c )x - 12a c )\|2 \|a \|b
+--R /
+--R 2 3 +-+4+-+3 4+-+ +-+
+--R 42a x \|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1162
+
+--S 1163 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3
+--R 21a x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 3
+--R 2a
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R +
+--R -
+--R 2 3
+--R 21a x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 3
+--R 2a
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R +
+--R -
+--R 2 3
+--R 42a x
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 3
+--R 2a
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 2 2 2
+--R (- 28a c d + 14b c )x - 6a c
+--R /
+--R 2 3 +-+
+--R 21a x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1163
+
+--S 1164 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 2a \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R 3
+--R 2a
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R +
+--R -
+--R 2 +-+
+--R 2a \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R +
+--R -
+--R 3
+--R 2a
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (- 2a d + 4a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 2 +-+
+--R 4a \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 3
+--R 2a
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 11
+--R 16a b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d - 2a b c d + b c )\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 2a \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1164
+
+--S 1165 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1165
+
+)clear all
+
+--S 1166 of 1475
+t0:=(c+d*x^2)^2/(x^(11/2)*(a+b*x^2))
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 7 5 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1166
+
+--S 1167 of 1475
+r0:=-2/9*c^2/(a*x^(9/2))+2/5*c*(b*c-2*a*d)/(a^2*x^(5/2))+b^(1/4)*(b*c-_
+ a*d)^2*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*sqrt(2))-_
+ b^(1/4)*(b*c-a*d)^2*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(13/4)*sqrt(2))-1/2*b^(1/4)*(b*c-a*d)^2*log(sqrt(a)+x*_
+ sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))+_
+ 1/2*b^(1/4)*(b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))-2*(b*c-a*d)^2/(a^3*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 2 2 2 4 4+-+ +-+
+--R (45a d - 90a b c d + 45b c )x \|b \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 4 4+-+ +-+
+--R (- 45a d + 90a b c d - 45b c )x \|b \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4 4+-+ +-+ \|2 \|b \|x + \|a
+--R (- 90a d + 180a b c d - 90b c )x \|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4 4+-+ +-+ \|2 \|b \|x - \|a
+--R (- 90a d + 180a b c d - 90b c )x \|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 4 2 2 2
+--R (- 180a d + 360a b c d - 180b c )x + (- 72a c d + 36a b c )x
+--R +
+--R 2 2
+--R - 20a c
+--R *
+--R +-+4+-+
+--R \|2 \|a
+--R /
+--R 3 4 +-+4+-+ +-+
+--R 90a x \|2 \|a \|x
+--R Type: Expression(Integer)
+--E 1167
+
+--S 1168 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3 4
+--R 45a x
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5 4 5 4 4
+--R - a b d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 6 5 3 2 7 6 2 8 7 9 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16a
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2
+--R a b d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 6 5 7 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10
+--R 8a
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R - a b d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 9 8
+--R - b c
+--R /
+--R 13
+--R 16a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 4
+--R 45a x
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5 4 5 4 4
+--R - a b d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 6 5 3 2 7 6 2 8 7 9 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16a
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2
+--R a b d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 6 5 7 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 10
+--R 8a
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R - a b d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 9 8
+--R - b c
+--R /
+--R 13
+--R 16a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 3 4
+--R 90a x
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5 4 5 4 4
+--R - a b d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 6 5 3 2 7 6 2 8 7 9 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16a
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 10
+--R 8a
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R - a b d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 9 8
+--R - b c
+--R /
+--R 13
+--R 16a
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2
+--R a b d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 6 5 7 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R (- 90a d + 180a b c d - 90b c )x + (- 36a c d + 18a b c )x - 10a c
+--R /
+--R 3 4 +-+
+--R 45a x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1168
+
+--S 1169 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 2a b c d - b c )\|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 3 +-+
+--R 2a \|2
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5 4 5 4 4
+--R - a b d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 6 5 3 2 7 6 2 8 7 9 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16a
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|a
+--R *
+--R log
+--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2
+--R a b d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 6 5 7 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10
+--R 8a
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R - a b d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 9 8
+--R - b c
+--R /
+--R 13
+--R 16a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 +-+
+--R 2a \|2
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5 4 5 4 4
+--R - a b d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 6 5 3 2 7 6 2 8 7 9 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16a
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|a
+--R *
+--R log
+--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2
+--R a b d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 6 5 7 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 10
+--R 8a
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R - a b d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 9 8
+--R - b c
+--R /
+--R 13
+--R 16a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 2a b c d + b c )\|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|b \|x + \|a
+--R (2a d - 4a b c d + 2b c )\|b atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|b \|x - \|a
+--R (2a d - 4a b c d + 2b c )\|b atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 3 +-+
+--R 4a \|2
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5 4 5 4 4
+--R - a b d + 8a b c d - 28a b c d + 56a b c d - 70a b c d
+--R +
+--R 3 6 5 3 2 7 6 2 8 7 9 8
+--R 56a b c d - 28a b c d + 8a b c d - b c
+--R /
+--R 13
+--R 16a
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|a
+--R *
+--R atan
+--R 10
+--R 8a
+--R *
+--R ROOT
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R - a b d + 8a b c d - 28a b c d + 56a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7
+--R - 70a b c d + 56a b c d - 28a b c d + 8a b c d
+--R +
+--R 9 8
+--R - b c
+--R /
+--R 13
+--R 16a
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 2 5 4 3 2 4 3 4 3 3 2 5 4 2
+--R a b d - 6a b c d + 15a b c d - 20a b c d + 15a b c d
+--R +
+--R 6 5 7 6
+--R - 6a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3 +-+4+-+
+--R 2a \|2 \|a
+--R Type: Expression(Integer)
+--E 1169
+
+--S 1170 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1170
+
+)clear all
+
+--S 1171 of 1475
+t0:=x^(7/2)*(c+d*x^2)^3/(a+b*x^2)
+--R
+--R
+--R 3 9 2 7 2 5 3 3 +-+
+--R (d x + 3c d x + 3c d x + c x )\|x
+--R (1) -------------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1171
+
+--S 1172 of 1475
+r0:=2/5*(b*c-a*d)^3*x^(5/2)/b^4+2/1989*d*(393*b^2*c^2-582*a*b*c*d+221*_
+ a^2*d^2)*x^(9/2)/b^3+2/17*d*x^(9/2)*(c+d*x^2)^2/b+2/221*d*x^(9/2)*_
+ (c*(17*b*c-9*a*d)+d*(25*b*c-17*a*d)*x^2)/b^2-a^(5/4)*(b*c-a*d)^3*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(21/4)*sqrt(2))+_
+ a^(5/4)*(b*c-a*d)^3*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (b^(21/4)*sqrt(2))-1/2*a^(5/4)*(b*c-a*d)^3*log(sqrt(a)+x*_
+ sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(21/4)*sqrt(2))+_
+ 1/2*a^(5/4)*(b*c-a*d)^3*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(b^(21/4)*sqrt(2))-2*a*(b*c-a*d)^3*sqrt(x)/b^5
+--R
+--R
+--R (2)
+--R 4 3 3 2 2 2 2 3 3 4+-+
+--R (- 9945a d + 29835a b c d - 29835a b c d + 9945a b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 3 3 2 2 2 2 3 3 4+-+
+--R (9945a d - 29835a b c d + 29835a b c d - 9945a b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 3 3 2 2 2 2 3 3 4+-+
+--R (- 19890a d + 59670a b c d - 59670a b c d + 19890a b c )\|a
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 3 3 2 2 2 2 3 3 4+-+
+--R (- 19890a d + 59670a b c d - 59670a b c d + 19890a b c )\|a
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 3 8 3 3 4 2 6
+--R 2340b d x + (- 3060a b d + 9180b c d )x
+--R +
+--R 2 2 3 3 2 4 2 4
+--R (4420a b d - 13260a b c d + 13260b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 2
+--R (- 7956a b d + 23868a b c d - 23868a b c d + 7956b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R 39780a d - 119340a b c d + 119340a b c d - 39780a b c
+--R *
+--R +-+4+-+ +-+
+--R \|2 \|b \|x
+--R /
+--R 5 +-+4+-+
+--R 19890b \|2 \|b
+--R Type: Expression(Integer)
+--E 1172
+
+--S 1173 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 5
+--R 9945b
+--R *
+--R ROOT
+--R 17 12 16 11 15 2 2 10 14 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 13 4 4 8 12 5 5 7 11 6 6 6 10 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 9 8 8 4 8 9 9 3 7 10 10 2 6 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 5 12 12
+--R - a b c
+--R /
+--R 21
+--R 16b
+--R ,
+--R 4
+--R *
+--R log
+--R 4 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - a b c )\|x
+--R +
+--R 5
+--R 2b
+--R *
+--R ROOT
+--R 17 12 16 11 15 2 2 10 14 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 13 4 4 8 12 5 5 7 11 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 10 7 7 5 9 8 8 4 8 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 7 10 10 2 6 11 11 5 12 12
+--R - 66a b c d + 12a b c d - a b c
+--R /
+--R 21
+--R 16b
+--R ,
+--R 4
+--R +
+--R 5
+--R 9945b
+--R *
+--R ROOT
+--R 17 12 16 11 15 2 2 10 14 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 13 4 4 8 12 5 5 7 11 6 6 6 10 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 9 8 8 4 8 9 9 3 7 10 10 2 6 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 5 12 12
+--R - a b c
+--R /
+--R 21
+--R 16b
+--R ,
+--R 4
+--R *
+--R log
+--R 4 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - a b c )\|x
+--R +
+--R -
+--R 5
+--R 2b
+--R *
+--R ROOT
+--R 17 12 16 11 15 2 2 10 14 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 13 4 4 8 12 5 5 7 11 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 10 7 7 5 9 8 8 4 8 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 7 10 10 2 6 11 11 5 12 12
+--R - 66a b c d + 12a b c d - a b c
+--R /
+--R 21
+--R 16b
+--R ,
+--R 4
+--R +
+--R 5
+--R 19890b
+--R *
+--R ROOT
+--R 17 12 16 11 15 2 2 10 14 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 13 4 4 8 12 5 5 7 11 6 6 6 10 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 9 8 8 4 8 9 9 3 7 10 10 2 6 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 5 12 12
+--R - a b c
+--R /
+--R 21
+--R 16b
+--R ,
+--R 4
+--R *
+--R atan
+--R 5
+--R 2b
+--R *
+--R ROOT
+--R 17 12 16 11 15 2 2 10 14 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 13 4 4 8 12 5 5 7 11 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 10 7 7 5 9 8 8 4 8 9 9 3 7 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 6 11 11 5 12 12
+--R 12a b c d - a b c
+--R /
+--R 21
+--R 16b
+--R ,
+--R 4
+--R /
+--R 4 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - a b c )\|x
+--R +
+--R 4 3 8 3 3 4 2 6
+--R 1170b d x + (- 1530a b d + 4590b c d )x
+--R +
+--R 2 2 3 3 2 4 2 4
+--R (2210a b d - 6630a b c d + 6630b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 2
+--R (- 3978a b d + 11934a b c d - 11934a b c d + 3978b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R 19890a d - 59670a b c d + 59670a b c d - 19890a b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 5
+--R 9945b
+--R Type: Union(Expression(Integer),...)
+--E 1173
+
+--S 1174 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 3 3 2 2 2 2 3 3 4+-+
+--R (a d - 3a b c d + 3a b c d - a b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 5 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 17 12 16 11 15 2 2 10 14 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 13 4 4 8 12 5 5 7 11 6 6 6 10 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 9 8 8 4 8 9 9 3 7 10 10 2 6 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 5 12 12
+--R - a b c
+--R /
+--R 21
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R 4 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - a b c )\|x
+--R +
+--R 5
+--R 2b
+--R *
+--R ROOT
+--R 17 12 16 11 15 2 2 10 14 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 13 4 4 8 12 5 5 7 11 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 10 7 7 5 9 8 8 4 8 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 7 10 10 2 6 11 11 5 12 12
+--R - 66a b c d + 12a b c d - a b c
+--R /
+--R 21
+--R 16b
+--R ,
+--R 4
+--R +
+--R 5 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 17 12 16 11 15 2 2 10 14 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 13 4 4 8 12 5 5 7 11 6 6 6 10 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 9 8 8 4 8 9 9 3 7 10 10 2 6 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 5 12 12
+--R - a b c
+--R /
+--R 21
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R 4 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - a b c )\|x
+--R +
+--R -
+--R 5
+--R 2b
+--R *
+--R ROOT
+--R 17 12 16 11 15 2 2 10 14 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 13 4 4 8 12 5 5 7 11 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 10 7 7 5 9 8 8 4 8 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 7 10 10 2 6 11 11 5 12 12
+--R - 66a b c d + 12a b c d - a b c
+--R /
+--R 21
+--R 16b
+--R ,
+--R 4
+--R +
+--R 4 3 3 2 2 2 2 3 3 4+-+
+--R (- a d + 3a b c d - 3a b c d + a b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4 3 3 2 2 2 2 3 3 4+-+ \|2 \|b \|x + \|a
+--R (2a d - 6a b c d + 6a b c d - 2a b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4 3 3 2 2 2 2 3 3 4+-+ \|2 \|b \|x - \|a
+--R (2a d - 6a b c d + 6a b c d - 2a b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 5 +-+
+--R 4b \|2
+--R *
+--R ROOT
+--R 17 12 16 11 15 2 2 10 14 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 13 4 4 8 12 5 5 7 11 6 6 6 10 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 9 8 8 4 8 9 9 3 7 10 10 2 6 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 5 12 12
+--R - a b c
+--R /
+--R 21
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R atan
+--R 5
+--R 2b
+--R *
+--R ROOT
+--R 17 12 16 11 15 2 2 10 14 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 13 4 4 8 12 5 5 7 11 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 10 7 7 5 9 8 8 4 8 9 9 3 7 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 6 11 11 5 12 12
+--R 12a b c d - a b c
+--R /
+--R 21
+--R 16b
+--R ,
+--R 4
+--R /
+--R 4 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - a b c )\|x
+--R /
+--R 5 +-+4+-+
+--R 2b \|2 \|b
+--R Type: Expression(Integer)
+--E 1174
+
+--S 1175 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1175
+
+)clear all
+
+--S 1176 of 1475
+t0:=x^(5/2)*(c+d*x^2)^3/(a+b*x^2)
+--R
+--R
+--R 3 8 2 6 2 4 3 2 +-+
+--R (d x + 3c d x + 3c d x + c x )\|x
+--R (1) -------------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1176
+
+--S 1177 of 1475
+r0:=2/3*(b*c-a*d)^3*x^(3/2)/b^4+2/1155*d*(313*b^2*c^2-446*a*b*c*d+_
+ 165*a^2*d^2)*x^(7/2)/b^3+2/15*d*x^(7/2)*(c+d*x^2)^2/b+2/165*_
+ d*x^(7/2)*(c*(15*b*c-7*a*d)+d*(23*b*c-15*a*d)*x^2)/b^2+a^(3/4)*_
+ (b*c-a*d)^3*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(19/4)*_
+ sqrt(2))-a^(3/4)*(b*c-a*d)^3*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(b^(19/4)*sqrt(2))-1/2*a^(3/4)*(b*c-a*d)^3*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(19/4)*sqrt(2))+_
+ 1/2*a^(3/4)*(b*c-a*d)^3*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(b^(19/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 4+-+3
+--R (- 1155a d + 3465a b c d - 3465a b c d + 1155b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 4+-+3
+--R (1155a d - 3465a b c d + 3465a b c d - 1155b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 4+-+3
+--R (2310a d - 6930a b c d + 6930a b c d - 2310b c )\|a
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 2 3 3 4+-+3
+--R (2310a d - 6930a b c d + 6930a b c d - 2310b c )\|a
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 7 2 3 3 2 5
+--R 308b d x + (- 420a b d + 1260b c d )x
+--R +
+--R 2 3 2 2 3 2 3
+--R (660a b d - 1980a b c d + 1980b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 1540a d + 4620a b c d - 4620a b c d + 1540b c )x
+--R *
+--R +-+4+-+3 +-+
+--R \|2 \|b \|x
+--R /
+--R 4 +-+4+-+3
+--R 2310b \|2 \|b
+--R Type: Expression(Integer)
+--E 1177
+
+--S 1178 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4
+--R 1155b
+--R *
+--R ROOT
+--R 15 12 14 11 13 2 2 10 12 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 11 4 4 8 10 5 5 7 9 6 6 6 8 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 7 8 8 4 6 9 9 3 5 10 10 2 4 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 3 12 12
+--R - a b c
+--R /
+--R 19
+--R 16b
+--R ,
+--R 4
+--R *
+--R log
+--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - a b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14
+--R 8b
+--R *
+--R ROOT
+--R 15 12 14 11 13 2 2 10 12 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 11 4 4 8 10 5 5 7 9 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 8 7 7 5 7 8 8 4 6 9 9 3 5 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 4 11 11 3 12 12
+--R 12a b c d - a b c
+--R /
+--R 19
+--R 16b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 4
+--R 1155b
+--R *
+--R ROOT
+--R 15 12 14 11 13 2 2 10 12 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 11 4 4 8 10 5 5 7 9 6 6 6 8 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 7 8 8 4 6 9 9 3 5 10 10 2 4 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 3 12 12
+--R - a b c
+--R /
+--R 19
+--R 16b
+--R ,
+--R 4
+--R *
+--R log
+--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - a b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 14
+--R 8b
+--R *
+--R ROOT
+--R 15 12 14 11 13 2 2 10
+--R - a d + 12a b c d - 66a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R 220a b c d - 495a b c d + 792a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R - 924a b c d + 792a b c d - 495a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11 3 12 12
+--R 220a b c d - 66a b c d + 12a b c d - a b c
+--R /
+--R 19
+--R 16b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4
+--R 2310b
+--R *
+--R ROOT
+--R 15 12 14 11 13 2 2 10 12 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 11 4 4 8 10 5 5 7 9 6 6 6 8 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 7 8 8 4 6 9 9 3 5 10 10 2 4 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 3 12 12
+--R - a b c
+--R /
+--R 19
+--R 16b
+--R ,
+--R 4
+--R *
+--R atan
+--R 14
+--R 8b
+--R *
+--R ROOT
+--R 15 12 14 11 13 2 2 10 12 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 11 4 4 8 10 5 5 7 9 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 8 7 7 5 7 8 8 4 6 9 9 3 5 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 4 11 11 3 12 12
+--R 12a b c d - a b c
+--R /
+--R 19
+--R 16b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - a b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 3 3 7 2 3 3 2 5
+--R 154b d x + (- 210a b d + 630b c d )x
+--R +
+--R 2 3 2 2 3 2 3
+--R (330a b d - 990a b c d + 990b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 770a d + 2310a b c d - 2310a b c d + 770b c )x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 4
+--R 1155b
+--R Type: Union(Expression(Integer),...)
+--E 1178
+
+--S 1179 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 4+-+3
+--R (a d - 3a b c d + 3a b c d - b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 15 12 14 11 13 2 2 10 12 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 11 4 4 8 10 5 5 7 9 6 6 6 8 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 7 8 8 4 6 9 9 3 5 10 10 2 4 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 3 12 12
+--R - a b c
+--R /
+--R 19
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R log
+--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - a b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14
+--R 8b
+--R *
+--R ROOT
+--R 15 12 14 11 13 2 2 10 12 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 11 4 4 8 10 5 5 7 9 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 8 7 7 5 7 8 8 4 6 9 9 3 5 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 4 11 11 3 12 12
+--R 12a b c d - a b c
+--R /
+--R 19
+--R 16b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 4 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 15 12 14 11 13 2 2 10 12 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 11 4 4 8 10 5 5 7 9 6 6 6 8 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 7 8 8 4 6 9 9 3 5 10 10 2 4 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 3 12 12
+--R - a b c
+--R /
+--R 19
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R log
+--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - a b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 14
+--R 8b
+--R *
+--R ROOT
+--R 15 12 14 11 13 2 2 10
+--R - a d + 12a b c d - 66a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R 220a b c d - 495a b c d + 792a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R - 924a b c d + 792a b c d - 495a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11 3 12 12
+--R 220a b c d - 66a b c d + 12a b c d - a b c
+--R /
+--R 19
+--R 16b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 3 2 2 2 2 3 3 4+-+3
+--R (- a d + 3a b c d - 3a b c d + b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 4+-+3 \|2 \|b \|x + \|a
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 4+-+3 \|2 \|b \|x - \|a
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 +-+
+--R 4b \|2
+--R *
+--R ROOT
+--R 15 12 14 11 13 2 2 10 12 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 11 4 4 8 10 5 5 7 9 6 6 6 8 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 7 8 8 4 6 9 9 3 5 10 10 2 4 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 3 12 12
+--R - a b c
+--R /
+--R 19
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R atan
+--R 14
+--R 8b
+--R *
+--R ROOT
+--R 15 12 14 11 13 2 2 10 12 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 11 4 4 8 10 5 5 7 9 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 8 7 7 5 7 8 8 4 6 9 9 3 5 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 4 11 11 3 12 12
+--R 12a b c d - a b c
+--R /
+--R 19
+--R 16b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 11 9 10 8 9 2 2 7 8 3 3 6 7 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 6 5 5 4 5 6 6 3 4 7 7 2 3 8 8 2 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - a b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 4 +-+4+-+3
+--R 2b \|2 \|b
+--R Type: Expression(Integer)
+--E 1179
+
+--S 1180 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1180
+
+)clear all
+
+--S 1181 of 1475
+t0:=x^(3/2)*(c+d*x^2)^3/(a+b*x^2)
+--R
+--R
+--R 3 7 2 5 2 3 3 +-+
+--R (d x + 3c d x + 3c d x + c x)\|x
+--R (1) ------------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1181
+
+--S 1182 of 1475
+r0:=2/585*d*(241*b^2*c^2-326*a*b*c*d+117*a^2*d^2)*x^(5/2)/b^3+_
+ 2/13*d*x^(5/2)*(c+d*x^2)^2/b+2/117*d*x^(5/2)*(c*(13*b*c-5*a*d)+_
+ d*(21*b*c-13*a*d)*x^2)/b^2+a^(1/4)*(b*c-a*d)^3*atan(1-b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(b^(17/4)*sqrt(2))-a^(1/4)*(b*c-a*d)^3*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(17/4)*sqrt(2))+_
+ 1/2*a^(1/4)*(b*c-a*d)^3*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(b^(17/4)*sqrt(2))-1/2*a^(1/4)*(b*c-a*d)^3*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (b^(17/4)*sqrt(2))+2*(b*c-a*d)^3*sqrt(x)/b^4
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 4+-+
+--R (585a d - 1755a b c d + 1755a b c d - 585b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 4+-+
+--R (- 585a d + 1755a b c d - 1755a b c d + 585b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 4+-+
+--R (1170a d - 3510a b c d + 3510a b c d - 1170b c )\|a
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 2 3 3 4+-+
+--R (1170a d - 3510a b c d + 3510a b c d - 1170b c )\|a
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 6 2 3 3 2 4
+--R 180b d x + (- 260a b d + 780b c d )x
+--R +
+--R 2 3 2 2 3 2 2 3 3 2 2
+--R (468a b d - 1404a b c d + 1404b c d)x - 2340a d + 7020a b c d
+--R +
+--R 2 2 3 3
+--R - 7020a b c d + 2340b c
+--R *
+--R +-+4+-+ +-+
+--R \|2 \|b \|x
+--R /
+--R 4 +-+4+-+
+--R 1170b \|2 \|b
+--R Type: Expression(Integer)
+--E 1182
+
+--S 1183 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4
+--R 585b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10 10 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 9 4 4 8 8 5 5 7 7 6 6 6 6 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 5 8 8 4 4 9 9 3 3 10 10 2 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R 4
+--R 2b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10 10 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 9 4 4 8 8 5 5 7 7 6 6 6 6 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 5 8 8 4 4 9 9 3 3 10 10 2 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R +
+--R -
+--R 4
+--R 585b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10 10 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 9 4 4 8 8 5 5 7 7 6 6 6 6 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 5 8 8 4 4 9 9 3 3 10 10 2 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R -
+--R 4
+--R 2b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10
+--R - a d + 12a b c d - 66a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R 220a b c d - 495a b c d + 792a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R - 924a b c d + 792a b c d - 495a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11 12 12
+--R 220a b c d - 66a b c d + 12a b c d - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R +
+--R -
+--R 4
+--R 1170b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10 10 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 9 4 4 8 8 5 5 7 7 6 6 6 6 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 5 8 8 4 4 9 9 3 3 10 10 2 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R *
+--R atan
+--R 4
+--R 2b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10 10 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 9 4 4 8 8 5 5 7 7 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 6 7 7 5 5 8 8 4 4 9 9 3 3 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 2 11 11 12 12
+--R 12a b c d - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R 3 3 6 2 3 3 2 4
+--R 90b d x + (- 130a b d + 390b c d )x
+--R +
+--R 2 3 2 2 3 2 2 3 3 2 2
+--R (234a b d - 702a b c d + 702b c d)x - 1170a d + 3510a b c d
+--R +
+--R 2 2 3 3
+--R - 3510a b c d + 1170b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 4
+--R 585b
+--R Type: Union(Expression(Integer),...)
+--E 1183
+
+--S 1184 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 4+-+
+--R (- a d + 3a b c d - 3a b c d + b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10 10 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 9 4 4 8 8 5 5 7 7 6 6 6 6 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 5 8 8 4 4 9 9 3 3 10 10 2 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R 4
+--R 2b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10 10 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 9 4 4 8 8 5 5 7 7 6 6 6 6 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 5 8 8 4 4 9 9 3 3 10 10 2 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R +
+--R -
+--R 4 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10 10 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 9 4 4 8 8 5 5 7 7 6 6 6 6 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 5 8 8 4 4 9 9 3 3 10 10 2 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R -
+--R 4
+--R 2b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10
+--R - a d + 12a b c d - 66a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R 220a b c d - 495a b c d + 792a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R - 924a b c d + 792a b c d - 495a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11 12 12
+--R 220a b c d - 66a b c d + 12a b c d - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R +
+--R 3 3 2 2 2 2 3 3 4+-+
+--R (a d - 3a b c d + 3a b c d - b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 4+-+ \|2 \|b \|x + \|a
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 4+-+ \|2 \|b \|x - \|a
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 4 +-+
+--R 4b \|2
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10 10 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 9 4 4 8 8 5 5 7 7 6 6 6 6 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 5 8 8 4 4 9 9 3 3 10 10 2 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R atan
+--R 4
+--R 2b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10 10 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 9 4 4 8 8 5 5 7 7 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 6 7 7 5 5 8 8 4 4 9 9 3 3 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 2 11 11 12 12
+--R 12a b c d - a b c
+--R /
+--R 17
+--R 16b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R /
+--R 4 +-+4+-+
+--R 2b \|2 \|b
+--R Type: Expression(Integer)
+--E 1184
+
+--S 1185 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1185
+
+)clear all
+
+--S 1186 of 1475
+t0:=(c+d*x^2)^3*sqrt(x)/(a+b*x^2)
+--R
+--R
+--R 3 6 2 4 2 2 3 +-+
+--R (d x + 3c d x + 3c d x + c )\|x
+--R (1) -----------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1186
+
+--S 1187 of 1475
+r0:=2/231*d*(177*b^2*c^2-222*a*b*c*d+77*a^2*d^2)*x^(3/2)/b^3+_
+ 2/11*d*x^(3/2)*(c+d*x^2)^2/b+2/77*d*x^(3/2)*(c*(11*b*c-3*a*d)+_
+ d*(19*b*c-11*a*d)*x^2)/b^2-(b*c-a*d)^3*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(1/4)*b^(15/4)*sqrt(2))+(b*c-a*d)^3*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(15/4)*_
+ sqrt(2))+1/2*(b*c-a*d)^3*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(1/4)*b^(15/4)*sqrt(2))-1/2*(b*c-a*d)^3*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(1/4)*b^(15/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3
+--R (231a d - 693a b c d + 693a b c d - 231b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 231a d + 693a b c d - 693a b c d + 231b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 462a d + 1386a b c d - 1386a b c d + 462b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 462a d + 1386a b c d - 1386a b c d + 462b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 5 3 2 2 3
+--R 84b d x + (- 132a b d + 396b c d )x
+--R +
+--R 2 3 2 2 2
+--R (308a d - 924a b c d + 924b c d)x
+--R *
+--R +-+4+-+4+-+3 +-+
+--R \|2 \|a \|b \|x
+--R /
+--R 3 +-+4+-+4+-+3
+--R 462b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1187
+
+--S 1188 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3
+--R 231b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 15
+--R 16a b
+--R ,
+--R 4
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 11
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 66a b c d + 12a b c d - b c
+--R /
+--R 15
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3
+--R 231b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 15
+--R 16a b
+--R ,
+--R 4
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 11
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 66a b c d + 12a b c d - b c
+--R /
+--R 15
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 3
+--R 462b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 15
+--R 16a b
+--R ,
+--R 4
+--R *
+--R atan
+--R 11
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 66a b c d + 12a b c d - b c
+--R /
+--R 15
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 3 5 3 2 2 3
+--R 42b d x + (- 66a b d + 198b c d )x
+--R +
+--R 2 3 2 2 2
+--R (154a d - 462a b c d + 462b c d)x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3
+--R 231b
+--R Type: Union(Expression(Integer),...)
+--E 1188
+
+--S 1189 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (- a d + 3a b c d - 3a b c d + b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 3 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 15
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 11
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 66a b c d + 12a b c d - b c
+--R /
+--R 15
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 15
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 11
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 66a b c d + 12a b c d - b c
+--R /
+--R 15
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (a d - 3a b c d + 3a b c d - b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x + \|a
+--R (2a d - 6a b c d + 6a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x - \|a
+--R (2a d - 6a b c d + 6a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 3 +-+
+--R 4b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 15
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 11
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 66a b c d + 12a b c d - b c
+--R /
+--R 15
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3 +-+4+-+4+-+3
+--R 2b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1189
+
+--S 1190 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1190
+
+)clear all
+
+--S 1191 of 1475
+t0:=(c+d*x^2)^3/((a+b*x^2)*sqrt(x))
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 +-+
+--R (b x + a)\|x
+--R Type: Expression(Integer)
+--E 1191
+
+--S 1192 of 1475
+r0:=-(b*c-a*d)^3*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*_
+ b^(13/4)*sqrt(2))+(b*c-a*d)^3*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(3/4)*b^(13/4)*sqrt(2))-1/2*(b*c-a*d)^3*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(13/4)*_
+ sqrt(2))+1/2*(b*c-a*d)^3*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(3/4)*b^(13/4)*sqrt(2))+2/45*d*(121*b^2*c^2-_
+ 134*a*b*c*d+45*a^2*d^2)*sqrt(x)/b^3+2/9*d*(c+d*x^2)^2*sqrt(x)/_
+ b+2/45*d*(c*(9*b*c-a*d)+d*(17*b*c-9*a*d)*x^2)*sqrt(x)/b^2
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3
+--R (- 45a d + 135a b c d - 135a b c d + 45b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (45a d - 135a b c d + 135a b c d - 45b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x + \|a
+--R (- 90a d + 270a b c d - 270a b c d + 90b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x - \|a
+--R (- 90a d + 270a b c d - 270a b c d + 90b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 4 3 2 2 2 2 3 2
+--R 20b d x + (- 36a b d + 108b c d )x + 180a d - 540a b c d
+--R +
+--R 2 2
+--R 540b c d
+--R *
+--R +-+4+-+3 4+-+ +-+
+--R \|2 \|a \|b \|x
+--R /
+--R 3 +-+4+-+3 4+-+
+--R 90b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1192
+
+--S 1193 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3
+--R 45b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 3 13
+--R 16a b
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R 3
+--R 2a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3 2 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 11 11 12 12
+--R 12a b c d - b c
+--R /
+--R 3 13
+--R 16a b
+--R ,
+--R 4
+--R +
+--R 3
+--R 45b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 3 13
+--R 16a b
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R -
+--R 3
+--R 2a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3 2 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 11 11 12 12
+--R 12a b c d - b c
+--R /
+--R 3 13
+--R 16a b
+--R ,
+--R 4
+--R +
+--R 3
+--R 90b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 3 13
+--R 16a b
+--R ,
+--R 4
+--R *
+--R atan
+--R 3
+--R 2a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 3 13
+--R 16a b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R 2 3 4 3 2 2 2 2 3 2
+--R 10b d x + (- 18a b d + 54b c d )x + 90a d - 270a b c d
+--R +
+--R 2 2
+--R 270b c d
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3
+--R 45b
+--R Type: Union(Expression(Integer),...)
+--E 1193
+
+--S 1194 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 3a b c d + 3a b c d - b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 3 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 3 13
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R 3
+--R 2a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3 2 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 11 11 12 12
+--R 12a b c d - b c
+--R /
+--R 3 13
+--R 16a b
+--R ,
+--R 4
+--R +
+--R 3 +-+
+--R 2b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 3 13
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R -
+--R 3
+--R 2a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3 2 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 11 11 12 12
+--R 12a b c d - b c
+--R /
+--R 3 13
+--R 16a b
+--R ,
+--R 4
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- a d + 3a b c d - 3a b c d + b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x + \|a
+--R (2a d - 6a b c d + 6a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x - \|a
+--R (2a d - 6a b c d + 6a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+
+--R 4b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 3 13
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 3
+--R 2a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 3 13
+--R 16a b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R /
+--R 3 +-+4+-+3 4+-+
+--R 2b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1194
+
+--S 1195 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1195
+
+)clear all
+
+--S 1196 of 1475
+t0:=(c+d*x^2)^3/(x^(3/2)*(a+b*x^2))
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 3 +-+
+--R (b x + a x)\|x
+--R Type: Expression(Integer)
+--E 1196
+
+--S 1197 of 1475
+r0:=2/21*d*(15*b*c-7*a*d)*(3*b*c+a*d)*x^(3/2)/(a*b^2)-2/7*d*x^(3/2)*_
+ (c*(b*c-9*a*d)-d*(7*b*c+a*d)*x^2)/(a*b)+(b*c-a*d)^3*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(11/4)*_
+ sqrt(2))-(b*c-a*d)^3*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(5/4)*b^(11/4)*sqrt(2))-1/2*(b*c-a*d)^3*log(sqrt(a)+x*_
+ sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(11/4)*_
+ sqrt(2))+1/2*(b*c-a*d)^3*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(5/4)*b^(11/4)*sqrt(2))-2*c*(c+d*x^2)^2/(a*sqrt(x))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (- 21a d + 63a b c d - 63a b c d + 21b c )\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (21a d - 63a b c d + 63a b c d - 21b c )\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 +-+ \|2 \|b \|x + \|a
+--R (42a d - 126a b c d + 126a b c d - 42b c )\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 +-+ \|2 \|b \|x - \|a
+--R (42a d - 126a b c d + 126a b c d - 42b c )\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 4 2 3 2 2 2 3 +-+4+-+4+-+3
+--R (12a b d x + (- 28a d + 84a b c d )x - 84b c )\|2 \|a \|b
+--R /
+--R 2 +-+4+-+4+-+3 +-+
+--R 42a b \|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1197
+
+--S 1198 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R 21a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 5 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 8
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2
+--R - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 11 11 12 12
+--R 12a b c d - b c
+--R /
+--R 5 11
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2
+--R 21a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 5 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 8
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - a d + 12a b c d - 66a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 220a b c d - 495a b c d + 792a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 924a b c d + 792a b c d - 495a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 5 11
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2
+--R 42a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 5 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 4 8
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2
+--R - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 11 11 12 12
+--R 12a b c d - b c
+--R /
+--R 5 11
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 3 4 2 3 2 2 2 3
+--R 6a b d x + (- 14a d + 42a b c d )x - 42b c
+--R /
+--R 2 +-+
+--R 21a b \|x
+--R Type: Union(Expression(Integer),...)
+--E 1198
+
+--S 1199 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 3a b c d + 3a b c d - b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 2a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 5 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 8
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2
+--R - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 11 11 12 12
+--R 12a b c d - b c
+--R /
+--R 5 11
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2 +-+
+--R 2a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 5 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 8
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - a d + 12a b c d - 66a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 220a b c d - 495a b c d + 792a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 924a b c d + 792a b c d - 495a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 5 11
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- a d + 3a b c d - 3a b c d + b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x + \|a
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x - \|a
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+
+--R 4a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 5 11
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 4 8
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2
+--R - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 11 11 12 12
+--R 12a b c d - b c
+--R /
+--R 5 11
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 2a b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1199
+
+--S 1200 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1200
+
+)clear all
+
+--S 1201 of 1475
+t0:=(c+d*x^2)^3/(x^(5/2)*(a+b*x^2))
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 4 2 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1201
+
+--S 1202 of 1475
+r0:=-2/3*c*(c+d*x^2)^2/(a*x^(3/2))+(b*c-a*d)^3*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(7/4)*b^(9/4)*sqrt(2))-(b*c-a*d)^3*atan(1+_
+ b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(9/4)*sqrt(2))+_
+ 1/2*(b*c-a*d)^3*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(7/4)*b^(9/4)*sqrt(2))-1/2*(b*c-a*d)^3*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(9/4)*_
+ sqrt(2))+2/15*d*(13*b*c-5*a*d)*(b*c+3*a*d)*sqrt(x)/(a*b^2)-_
+ 2/15*d*(c*(3*b*c-11*a*d)-d*(5*b*c+3*a*d)*x^2)*sqrt(x)/(a*b)
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (15a d - 45a b c d + 45a b c d - 15b c )x\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (- 15a d + 45a b c d - 45a b c d + 15b c )x\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 +-+ \|2 \|b \|x + \|a
+--R (30a d - 90a b c d + 90a b c d - 30b c )x\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 +-+ \|2 \|b \|x - \|a
+--R (30a d - 90a b c d + 90a b c d - 30b c )x\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 4 2 3 2 2 2 3 +-+4+-+3 4+-+
+--R (12a b d x + (- 60a d + 180a b c d )x - 20b c )\|2 \|a \|b
+--R /
+--R 2 +-+4+-+3 4+-+ +-+
+--R 30a b x\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1202
+
+--S 1203 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R 15a b x
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 7 9
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R 2 2
+--R 2a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 7 9
+--R 16a b
+--R ,
+--R 4
+--R +
+--R -
+--R 2
+--R 15a b x
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 7 9
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R -
+--R 2 2
+--R 2a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - a d + 12a b c d - 66a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 220a b c d - 495a b c d + 792a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 924a b c d + 792a b c d - 495a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 7 9
+--R 16a b
+--R ,
+--R 4
+--R +
+--R -
+--R 2
+--R 30a b x
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 7 9
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 2 2
+--R 2a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3 2 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 11 11 12 12
+--R 12a b c d - b c
+--R /
+--R 7 9
+--R 16a b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R 3 4 2 3 2 2 2 3
+--R 6a b d x + (- 30a d + 90a b c d )x - 10b c
+--R /
+--R 2 +-+
+--R 15a b x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1203
+
+--S 1204 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (- a d + 3a b c d - 3a b c d + b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 2a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 7 9
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R 2 2
+--R 2a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 7 9
+--R 16a b
+--R ,
+--R 4
+--R +
+--R -
+--R 2 +-+
+--R 2a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 7 9
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R +
+--R -
+--R 2 2
+--R 2a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - a d + 12a b c d - 66a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 220a b c d - 495a b c d + 792a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 924a b c d + 792a b c d - 495a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 7 9
+--R 16a b
+--R ,
+--R 4
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (a d - 3a b c d + 3a b c d - b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x + \|a
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x - \|a
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 2 +-+
+--R 4a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 7 9
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 2 2
+--R 2a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3 2 10 10 2
+--R 792a b c d - 495a b c d + 220a b c d - 66a b c d
+--R +
+--R 11 11 12 12
+--R 12a b c d - b c
+--R /
+--R 7 9
+--R 16a b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 2a b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1204
+
+--S 1205 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1205
+
+)clear all
+
+--S 1206 of 1475
+t0:=(c+d*x^2)^3/(x^(7/2)*(a+b*x^2))
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 5 3 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1206
+
+--S 1207 of 1475
+r0:=2/15*d*(3*b*c+a*d)*(3*b*c+5*a*d)*x^(3/2)/(a^2*b)-2/5*c*(c+d*x^2)^2/_
+ (a*x^(5/2))-(b*c-a*d)^3*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(9/4)*b^(7/4)*sqrt(2))+(b*c-a*d)^3*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(9/4)*b^(7/4)*sqrt(2))+1/2*(b*c-a*d)^3*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*_
+ b^(7/4)*sqrt(2))-1/2*(b*c-a*d)^3*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*b^(7/4)*sqrt(2))+2/5*c*(c*_
+ (5*b*c-13*a*d)-d*(3*b*c+5*a*d)*x^2)/(a^2*sqrt(x))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 2 +-+
+--R (15a d - 45a b c d + 45a b c d - 15b c )x \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 2 +-+
+--R (- 15a d + 45a b c d - 45a b c d + 15b c )x \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 2 +-+
+--R (- 30a d + 90a b c d - 90a b c d + 30b c )x \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 2 3 3 2 +-+
+--R (- 30a d + 90a b c d - 90a b c d + 30b c )x \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 4 2 2 3 2 3 +-+4+-+4+-+3
+--R (20a d x + (- 180a b c d + 60b c )x - 12a b c )\|2 \|a \|b
+--R /
+--R 2 2 +-+4+-+4+-+3 +-+
+--R 30a b x \|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1207
+
+--S 1208 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 2 2
+--R 15a b x
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 9 7
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 5
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 66a b c d + 12a b c d - b c
+--R /
+--R 9 7
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2
+--R 15a b x
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 9 7
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 5
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 66a b c d + 12a b c d - b c
+--R /
+--R 9 7
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2 2
+--R 30a b x
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 9 7
+--R 16a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 7 5
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 66a b c d + 12a b c d - b c
+--R /
+--R 9 7
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 3 4 2 2 3 2 3
+--R 10a d x + (- 90a b c d + 30b c )x - 6a b c
+--R /
+--R 2 2 +-+
+--R 15a b x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1208
+
+--S 1209 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (- a d + 3a b c d - 3a b c d + b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 2 +-+
+--R 2a b\|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 9 7
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 5
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 66a b c d + 12a b c d - b c
+--R /
+--R 9 7
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 +-+
+--R 2a b\|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d - b c
+--R /
+--R 9 7
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 5
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 66a b c d + 12a b c d - b c
+--R /
+--R 9 7
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (a d - 3a b c d + 3a b c d - b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x + \|a
+--R (2a d - 6a b c d + 6a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x - \|a
+--R (2a d - 6a b c d + 6a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 2 +-+
+--R 4a b\|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 495a b c d + 792a b c d - 924a b c d + 792a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 495a b c d + 220a b c d - 66a b c d + 12a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 9 7
+--R 16a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 7 5
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - a d + 12a b c d - 66a b c d + 220a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 495a b c d + 792a b c d - 924a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R 792a b c d - 495a b c d + 220a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 66a b c d + 12a b c d - b c
+--R /
+--R 9 7
+--R 16a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R a d - 9a b c d + 36a b c d - 84a b c d + 126a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9
+--R - 126a b c d + 84a b c d - 36a b c d + 9a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 2a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1209
+
+--S 1210 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1210
+
+)clear all
+
+--S 1211 of 1475
+t0:=x^(7/2)/((a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) ----------------------------
+--R 4 2
+--R b d x + (a d + b c)x + a c
+--R Type: Expression(Integer)
+--E 1211
+
+--S 1212 of 1475
+r0:=-a^(5/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(5/4)*(b*c-a*d)*_
+ sqrt(2))+a^(5/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (b^(5/4)*(b*c-a*d)*sqrt(2))+c^(5/4)*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(d^(5/4)*(b*c-a*d)*sqrt(2))-c^(5/4)*atan(1+_
+ d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(d^(5/4)*(b*c-a*d)*sqrt(2))-_
+ 1/2*a^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(b^(5/4)*(b*c-a*d)*sqrt(2))+1/2*a^(5/4)*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(5/4)*(b*c-a*d)*_
+ sqrt(2))+1/2*c^(5/4)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(d^(5/4)*(b*c-a*d)*sqrt(2))-1/2*c^(5/4)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (d^(5/4)*(b*c-a*d)*sqrt(2))+2*sqrt(x)/(b*d)
+--R
+--R
+--R (2)
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R b c\|b \|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - a d\|a \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R a d\|a \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - b c\|b \|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R 2b c\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R 2b c\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a
+--R - 2a d\|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x - \|a +-+4+-+4+-+ +-+
+--R - 2a d\|a \|d atan(-------------------) + (4a d - 4b c)\|2 \|b \|d \|x
+--R 4+-+
+--R \|a
+--R /
+--R 2 2 +-+4+-+4+-+
+--R (2a b d - 2b c d)\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 1212
+
+--S 1213 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------------------------------------------------------+
+--R | 5
+--R | c
+--R b d |- --------------------------------------------------------
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R log
+--R +-+
+--R c\|x
+--R +
+--R 2
+--R (2a d - 2b c d)
+--R *
+--R +----------------------------------------------------------+
+--R | 5
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R +
+--R -
+--R +----------------------------------------------------------+
+--R | 5
+--R | c
+--R b d |- --------------------------------------------------------
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R log
+--R +-+
+--R c\|x
+--R +
+--R 2
+--R (- 2a d + 2b c d)
+--R *
+--R +----------------------------------------------------------+
+--R | 5
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R +
+--R -
+--R +---------------------------------------------------------+
+--R | 5
+--R | a
+--R b d |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R a\|x
+--R +
+--R 2
+--R (2a b d - 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R +---------------------------------------------------------+
+--R | 5
+--R | a
+--R b d |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R a\|x
+--R +
+--R 2
+--R (- 2a b d + 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R -
+--R +----------------------------------------------------------+
+--R | 5
+--R | c
+--R 2b d |- --------------------------------------------------------
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R atan
+--R 2
+--R (2a d - 2b c d)
+--R *
+--R +----------------------------------------------------------+
+--R | 5
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R /
+--R +-+
+--R c\|x
+--R +
+--R +---------------------------------------------------------+
+--R | 5
+--R | a
+--R 2b d |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R atan
+--R 2
+--R (2a b d - 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R +-+
+--R a\|x
+--R +
+--R +-+
+--R 2\|x
+--R /
+--R b d
+--R Type: Union(Expression(Integer),...)
+--E 1213
+
+--S 1214 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - b c\|b \|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R a d\|a \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 +-+
+--R (2a b d - 2b c d)\|2
+--R *
+--R +----------------------------------------------------------+
+--R | 5
+--R | c 4+-+4+-+
+--R |- -------------------------------------------------------- \|b \|d
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R log
+--R +-+
+--R c\|x
+--R +
+--R 2
+--R (2a d - 2b c d)
+--R *
+--R +----------------------------------------------------------+
+--R | 5
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R +
+--R 2 2 +-+
+--R (- 2a b d + 2b c d)\|2
+--R *
+--R +----------------------------------------------------------+
+--R | 5
+--R | c 4+-+4+-+
+--R |- -------------------------------------------------------- \|b \|d
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R log
+--R +-+
+--R c\|x
+--R +
+--R 2
+--R (- 2a d + 2b c d)
+--R *
+--R +----------------------------------------------------------+
+--R | 5
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R +
+--R 2 2 +-+
+--R (- 2a b d + 2b c d)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | a 4+-+4+-+
+--R |- ------------------------------------------------------- \|b \|d
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R a\|x
+--R +
+--R 2
+--R (2a b d - 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R 2 2 +-+
+--R (2a b d - 2b c d)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | a 4+-+4+-+
+--R |- ------------------------------------------------------- \|b \|d
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R a\|x
+--R +
+--R 2
+--R (- 2a b d + 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - a d\|a \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R b c\|b \|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R - 2b c\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R - 2b c\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a
+--R 2a d\|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x - \|a
+--R 2a d\|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 +-+
+--R (- 4a b d + 4b c d)\|2
+--R *
+--R +----------------------------------------------------------+
+--R | 5
+--R | c 4+-+4+-+
+--R |- -------------------------------------------------------- \|b \|d
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R atan
+--R 2
+--R (2a d - 2b c d)
+--R *
+--R +----------------------------------------------------------+
+--R | 5
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R /
+--R +-+
+--R c\|x
+--R +
+--R 2 2 +-+
+--R (4a b d - 4b c d)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | a 4+-+4+-+
+--R |- ------------------------------------------------------- \|b \|d
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R atan
+--R 2
+--R (2a b d - 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R +-+
+--R a\|x
+--R /
+--R 2 2 +-+4+-+4+-+
+--R (2a b d - 2b c d)\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 1214
+
+--S 1215 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1215
+
+)clear all
+
+--S 1216 of 1475
+t0:=x^(5/2)/((a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) ----------------------------
+--R 4 2
+--R b d x + (a d + b c)x + a c
+--R Type: Expression(Integer)
+--E 1216
+
+--S 1217 of 1475
+r0:=a^(3/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(3/4)*(b*c-a*d)*_
+ sqrt(2))-a^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(3/4)*_
+ (b*c-a*d)*sqrt(2))-c^(3/4)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/_
+ c^(1/4))/(d^(3/4)*(b*c-a*d)*sqrt(2))+c^(3/4)*atan(1+d^(1/4)*_
+ sqrt(2)*sqrt(x)/c^(1/4))/(d^(3/4)*(b*c-a*d)*sqrt(2))-_
+ 1/2*a^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(b^(3/4)*(b*c-a*d)*sqrt(2))+1/2*a^(3/4)*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(3/4)*(b*c-a*d)*_
+ sqrt(2))+1/2*c^(3/4)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(d^(3/4)*(b*c-a*d)*sqrt(2))-1/2*c^(3/4)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (d^(3/4)*(b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|a \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|b \|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x + \|c
+--R - 2\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x - \|c
+--R - 2\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x + \|a 4+-+3 4+-+3 \|2 \|b \|x - \|a
+--R 2\|a \|d atan(------------------- + 2\|a \|d atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R /
+--R +-+4+-+3 4+-+3
+--R (2a d - 2b c)\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 1217
+
+--S 1218 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +----------------------------------------------------------+
+--R | 3
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R log
+--R 2 +-+
+--R c \|x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2
+--R (8a d - 24a b c d + 24a b c d - 8b c d )
+--R *
+--R +----------------------------------------------------------+3
+--R | 3
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R +
+--R +----------------------------------------------------------+
+--R | 3
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R log
+--R 2 +-+
+--R c \|x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2
+--R (- 8a d + 24a b c d - 24a b c d + 8b c d )
+--R *
+--R +----------------------------------------------------------+3
+--R | 3
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R +
+--R +---------------------------------------------------------+
+--R | 3
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R 2 +-+
+--R a \|x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3
+--R (8a b d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 3
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R -
+--R +---------------------------------------------------------+
+--R | 3
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R 2 +-+
+--R a \|x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3
+--R (- 8a b d + 24a b c d - 24a b c d + 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 3
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R -
+--R +----------------------------------------------------------+
+--R | 3
+--R | c
+--R 2 |- --------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R atan
+--R 3 5 2 4 2 2 3 3 3 2
+--R (8a d - 24a b c d + 24a b c d - 8b c d )
+--R *
+--R +----------------------------------------------------------+3
+--R | 3
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R /
+--R 2 +-+
+--R c \|x
+--R +
+--R +---------------------------------------------------------+
+--R | 3
+--R | a
+--R 2 |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R atan
+--R 3 2 3 2 3 2 4 2 5 3
+--R (8a b d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 3
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R 2 +-+
+--R a \|x
+--R Type: Union(Expression(Integer),...)
+--E 1218
+
+--S 1219 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|b \|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+
+--R (- 2a d + 2b c)\|2
+--R *
+--R +----------------------------------------------------------+
+--R | 3
+--R | c 4+-+3 4+-+3
+--R |- -------------------------------------------------------- \|b \|d
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R log
+--R 2 +-+
+--R c \|x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2
+--R (8a d - 24a b c d + 24a b c d - 8b c d )
+--R *
+--R +----------------------------------------------------------+3
+--R | 3
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R +
+--R +-+
+--R (2a d - 2b c)\|2
+--R *
+--R +----------------------------------------------------------+
+--R | 3
+--R | c 4+-+3 4+-+3
+--R |- -------------------------------------------------------- \|b \|d
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R log
+--R 2 +-+
+--R c \|x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2
+--R (- 8a d + 24a b c d - 24a b c d + 8b c d )
+--R *
+--R +----------------------------------------------------------+3
+--R | 3
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R +
+--R +-+
+--R (2a d - 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | a 4+-+3 4+-+3
+--R |- ------------------------------------------------------- \|b \|d
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R 2 +-+
+--R a \|x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3
+--R (8a b d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 3
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R +-+
+--R (- 2a d + 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | a 4+-+3 4+-+3
+--R |- ------------------------------------------------------- \|b \|d
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R 2 +-+
+--R a \|x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3
+--R (- 8a b d + 24a b c d - 24a b c d + 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 3
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|a \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x + \|c
+--R 2\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x - \|c
+--R 2\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x + \|a
+--R - 2\|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x - \|a
+--R - 2\|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +----------------------------------------------------------+
+--R | 3
+--R | c 4+-+3 4+-+3
+--R |- -------------------------------------------------------- \|b \|d
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R atan
+--R 3 5 2 4 2 2 3 3 3 2
+--R (8a d - 24a b c d + 24a b c d - 8b c d )
+--R *
+--R +----------------------------------------------------------+3
+--R | 3
+--R | c
+--R |- --------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R /
+--R 2 +-+
+--R c \|x
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | a 4+-+3 4+-+3
+--R |- ------------------------------------------------------- \|b \|d
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R atan
+--R 3 2 3 2 3 2 4 2 5 3
+--R (8a b d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 3
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R 2 +-+
+--R a \|x
+--R /
+--R +-+4+-+3 4+-+3
+--R (2a d - 2b c)\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 1219
+
+--S 1220 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1220
+
+)clear all
+
+--S 1221 of 1475
+t0:=x^(3/2)/((a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) ----------------------------
+--R 4 2
+--R b d x + (a d + b c)x + a c
+--R Type: Expression(Integer)
+--E 1221
+
+--S 1222 of 1475
+r0:=a^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(1/4)*(b*c-a*d)*_
+ sqrt(2))-a^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (b^(1/4)*(b*c-a*d)*sqrt(2))-c^(1/4)*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(d^(1/4)*(b*c-a*d)*sqrt(2))+c^(1/4)*atan(1+_
+ d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(d^(1/4)*(b*c-a*d)*sqrt(2))+_
+ 1/2*a^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(b^(1/4)*(b*c-a*d)*sqrt(2))-1/2*a^(1/4)*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(1/4)*(b*c-a*d)*_
+ sqrt(2))-1/2*c^(1/4)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(d^(1/4)*(b*c-a*d)*sqrt(2))+1/2*c^(1/4)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(d^(1/4)*_
+ (b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|b \|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|a \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c 4+-+4+-+ \|2 \|d \|x - \|c
+--R - 2\|b \|c atan(-------------------) - 2\|b \|c atan(-------------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a 4+-+4+-+ \|2 \|b \|x - \|a
+--R 2\|a \|d atan(-------------------) + 2\|a \|d atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R /
+--R +-+4+-+4+-+
+--R (2a d - 2b c)\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 1222
+
+--S 1223 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +---------------------------------------------------------+
+--R | c
+--R |- -------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R log
+--R +-+
+--R \|x
+--R +
+--R (2a d - 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | c
+--R |- -------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R +
+--R +---------------------------------------------------------+
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R \|x
+--R +
+--R (2a d - 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R -
+--R +---------------------------------------------------------+
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R \|x
+--R +
+--R (- 2a d + 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R +---------------------------------------------------------+
+--R | c
+--R |- -------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R log
+--R +-+
+--R \|x
+--R +
+--R (- 2a d + 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | c
+--R |- -------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R +
+--R +---------------------------------------------------------+
+--R | c
+--R 2 |- -------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R atan
+--R (2a d - 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | c
+--R |- -------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R /
+--R +-+
+--R \|x
+--R +
+--R -
+--R +---------------------------------------------------------+
+--R | a
+--R 2 |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R atan
+--R (2a d - 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R +-+
+--R \|x
+--R Type: Union(Expression(Integer),...)
+--E 1223
+
+--S 1224 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|a \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+
+--R (- 2a d + 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | c 4+-+4+-+
+--R |- ------------------------------------------------------- \|b \|d
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R log
+--R +-+
+--R \|x
+--R +
+--R (2a d - 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | c
+--R |- -------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R +
+--R +-+
+--R (2a d - 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | a 4+-+4+-+
+--R |- ------------------------------------------------------- \|b \|d
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R \|x
+--R +
+--R (2a d - 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R +-+
+--R (- 2a d + 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | a 4+-+4+-+
+--R |- ------------------------------------------------------- \|b \|d
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R \|x
+--R +
+--R (- 2a d + 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R +-+
+--R (2a d - 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | c 4+-+4+-+
+--R |- ------------------------------------------------------- \|b \|d
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R log
+--R +-+
+--R \|x
+--R +
+--R (- 2a d + 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | c
+--R |- -------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|b \|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c 4+-+4+-+ \|2 \|d \|x - \|c
+--R 2\|b \|c atan(-------------------) + 2\|b \|c atan(-------------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a 4+-+4+-+ \|2 \|b \|x - \|a
+--R - 2\|a \|d atan(-------------------) - 2\|a \|d atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | c 4+-+4+-+
+--R |- ------------------------------------------------------- \|b \|d
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R *
+--R atan
+--R (2a d - 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | c
+--R |- -------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16b c d
+--R /
+--R +-+
+--R \|x
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | a 4+-+4+-+
+--R |- ------------------------------------------------------- \|b \|d
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R atan
+--R (2a d - 2b c)
+--R *
+--R +---------------------------------------------------------+
+--R | a
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R +-+
+--R \|x
+--R /
+--R +-+4+-+4+-+
+--R (2a d - 2b c)\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 1224
+
+--S 1225 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1225
+
+)clear all
+
+--S 1226 of 1475
+t0:=sqrt(x)/((a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R +-+
+--R \|x
+--R (1) ----------------------------
+--R 4 2
+--R b d x + (a d + b c)x + a c
+--R Type: Expression(Integer)
+--E 1226
+
+--S 1227 of 1475
+r0:=-b^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*_
+ (b*c-a*d)*sqrt(2))+b^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(1/4)*(b*c-a*d)*sqrt(2))+d^(1/4)*atan(1-d^(1/4)*_
+ sqrt(2)*sqrt(x)/c^(1/4))/(c^(1/4)*(b*c-a*d)*sqrt(2))-d^(1/4)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(1/4)*(b*c-a*d)*_
+ sqrt(2))+1/2*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(1/4)*(b*c-a*d)*sqrt(2))-1/2*b^(1/4)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*_
+ (b*c-a*d)*sqrt(2))-1/2*d^(1/4)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(1/4)*(b*c-a*d)*sqrt(2))+1/2*_
+ d^(1/4)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(1/4)*(b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c 4+-+4+-+ \|2 \|d \|x - \|c
+--R 2\|a \|d atan(-------------------) + 2\|a \|d atan(-------------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a 4+-+4+-+ \|2 \|b \|x - \|a
+--R - 2\|b \|c atan(-------------------) - 2\|b \|c atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R /
+--R +-+4+-+4+-+
+--R (2a d - 2b c)\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1227
+
+--S 1228 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------------------------------------------------------+
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R d\|x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R -
+--R +---------------------------------------------------------+
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R d\|x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 8a c d + 24a b c d - 24a b c d + 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R -
+--R +---------------------------------------------------------+
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R log
+--R +-+
+--R b\|x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R +---------------------------------------------------------+
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R log
+--R +-+
+--R b\|x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 8a d + 24a b c d - 24a b c d + 8a b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R -
+--R +---------------------------------------------------------+
+--R | b
+--R 2 |- -------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R atan
+--R 4 3 3 2 2 2 2 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R /
+--R +-+
+--R b\|x
+--R +
+--R +---------------------------------------------------------+
+--R | d
+--R 2 |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R atan
+--R 3 3 2 2 2 2 3 3 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R +-+
+--R d\|x
+--R Type: Union(Expression(Integer),...)
+--E 1228
+
+--S 1229 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+
+--R (2a d - 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | d 4+-+4+-+
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R d\|x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R +-+
+--R (- 2a d + 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | d 4+-+4+-+
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R d\|x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 8a c d + 24a b c d - 24a b c d + 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R +-+
+--R (- 2a d + 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | b 4+-+4+-+
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R log
+--R +-+
+--R b\|x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R +-+
+--R (2a d - 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | b 4+-+4+-+
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R log
+--R +-+
+--R b\|x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 8a d + 24a b c d - 24a b c d + 8a b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c 4+-+4+-+ \|2 \|d \|x - \|c
+--R - 2\|a \|d atan(-------------------) - 2\|a \|d atan(-------------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a 4+-+4+-+ \|2 \|b \|x - \|a
+--R 2\|b \|c atan(-------------------) + 2\|b \|c atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | b 4+-+4+-+
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R atan
+--R 4 3 3 2 2 2 2 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R /
+--R +-+
+--R b\|x
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | d 4+-+4+-+
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R atan
+--R 3 3 2 2 2 2 3 3 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R +-+
+--R d\|x
+--R /
+--R +-+4+-+4+-+
+--R (2a d - 2b c)\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1229
+
+--S 1230 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1230
+
+)clear all
+
+--S 1231 of 1475
+t0:=1/((a+b*x^2)*(c+d*x^2)*sqrt(x))
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R 4 2 +-+
+--R (b d x + (a d + b c)x + a c)\|x
+--R Type: Expression(Integer)
+--E 1231
+
+--S 1232 of 1475
+r0:=-b^(3/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*(b*c-a*d)*_
+ sqrt(2))+b^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*_
+ (b*c-a*d)*sqrt(2))+d^(3/4)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/_
+ c^(1/4))/(c^(3/4)*(b*c-a*d)*sqrt(2))-d^(3/4)*atan(1+d^(1/4)*_
+ sqrt(2)*sqrt(x)/c^(1/4))/(c^(3/4)*(b*c-a*d)*sqrt(2))-1/2*_
+ b^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(3/4)*(b*c-a*d)*sqrt(2))+1/2*b^(3/4)*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*(b*c-a*d)*sqrt(2))+_
+ 1/2*d^(3/4)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(3/4)*(b*c-a*d)*sqrt(2))-1/2*d^(3/4)*log(sqrt(c)+_
+ x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(3/4)*(b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x + \|c
+--R 2\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x - \|c
+--R 2\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x + \|a
+--R - 2\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x - \|a
+--R - 2\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+3 4+-+3
+--R (2a d - 2b c)\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1232
+
+--S 1233 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------------------------------------------------------+
+--R | 3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R d\|x
+--R +
+--R 2
+--R (2a c d - 2b c )
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R -
+--R +---------------------------------------------------------+
+--R | 3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R d\|x
+--R +
+--R 2
+--R (- 2a c d + 2b c )
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R -
+--R +---------------------------------------------------------+
+--R | 3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R log
+--R +-+
+--R b\|x
+--R +
+--R 2
+--R (2a d - 2a b c)
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R +---------------------------------------------------------+
+--R | 3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R log
+--R +-+
+--R b\|x
+--R +
+--R 2
+--R (- 2a d + 2a b c)
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R +---------------------------------------------------------+
+--R | 3
+--R | b
+--R 2 |- -------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R atan
+--R 2
+--R (2a d - 2a b c)
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R /
+--R +-+
+--R b\|x
+--R +
+--R -
+--R +---------------------------------------------------------+
+--R | 3
+--R | d
+--R 2 |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R atan
+--R 2
+--R (2a c d - 2b c )
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R +-+
+--R d\|x
+--R Type: Union(Expression(Integer),...)
+--E 1233
+
+--S 1234 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+
+--R (2a d - 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | d 4+-+3 4+-+3
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R d\|x
+--R +
+--R 2
+--R (2a c d - 2b c )
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R +-+
+--R (- 2a d + 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | d 4+-+3 4+-+3
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R +-+
+--R d\|x
+--R +
+--R 2
+--R (- 2a c d + 2b c )
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R +-+
+--R (- 2a d + 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | b 4+-+3 4+-+3
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R log
+--R +-+
+--R b\|x
+--R +
+--R 2
+--R (2a d - 2a b c)
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R +-+
+--R (2a d - 2b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | b 4+-+3 4+-+3
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R log
+--R +-+
+--R b\|x
+--R +
+--R 2
+--R (- 2a d + 2a b c)
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x + \|c
+--R - 2\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x - \|c
+--R - 2\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x + \|a
+--R 2\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x - \|a
+--R 2\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | b 4+-+3 4+-+3
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R atan
+--R 2
+--R (2a d - 2a b c)
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R /
+--R +-+
+--R b\|x
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | d 4+-+3 4+-+3
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R atan
+--R 2
+--R (2a c d - 2b c )
+--R *
+--R +---------------------------------------------------------+
+--R | 3
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R +-+
+--R d\|x
+--R /
+--R +-+4+-+3 4+-+3
+--R (2a d - 2b c)\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1234
+
+--S 1235 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1235
+
+)clear all
+
+--S 1236 of 1475
+t0:=1/(x^(3/2)*(a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ------------------------------------
+--R 5 3 +-+
+--R (b d x + (a d + b c)x + a c x)\|x
+--R Type: Expression(Integer)
+--E 1236
+
+--S 1237 of 1475
+r0:=b^(5/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*(b*c-a*d)*_
+ sqrt(2))-b^(5/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*_
+ (b*c-a*d)*sqrt(2))-d^(5/4)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(5/4)*(b*c-a*d)*sqrt(2))+d^(5/4)*atan(1+d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(5/4)*(b*c-a*d)*sqrt(2))-1/2*b^(5/4)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*_
+ (b*c-a*d)*sqrt(2))+1/2*b^(5/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*(b*c-a*d)*sqrt(2))+1/2*_
+ d^(5/4)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(5/4)*(b*c-a*d)*sqrt(2))-1/2*d^(5/4)*log(sqrt(c)+x*sqrt(d)+_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(5/4)*(b*c-a*d)*sqrt(2))+_
+ (-2)/(a*c*sqrt(x))
+--R
+--R
+--R (2)
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R a d\|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - b c\|b \|c \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R b c\|b \|c \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - a d\|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x + \|c
+--R - 2a d\|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x - \|c
+--R - 2a d\|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|b \|x + \|a
+--R 2b c\|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|b \|x - \|a +-+4+-+4+-+
+--R 2b c\|b \|c \|x atan(-------------------) + (- 4a d + 4b c)\|2 \|a \|c
+--R 4+-+
+--R \|a
+--R /
+--R 2 2 +-+4+-+4+-+ +-+
+--R (2a c d - 2a b c )\|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1237
+
+--S 1238 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +---------------------------------------------------------+
+--R | 5
+--R | d +-+
+--R a c |- ------------------------------------------------------- \|x
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R 4 +-+
+--R d \|x
+--R +
+--R 3 4 3 2 5 2 2 6 3 7
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 5
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R +---------------------------------------------------------+
+--R | 5
+--R | d +-+
+--R a c |- ------------------------------------------------------- \|x
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R 4 +-+
+--R d \|x
+--R +
+--R 3 4 3 2 5 2 2 6 3 7
+--R (- 8a c d + 24a b c d - 24a b c d + 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 5
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R +---------------------------------------------------------+
+--R | 5
+--R | b +-+
+--R a c |- ------------------------------------------------------- \|x
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R log
+--R 4 +-+
+--R b \|x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 5
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R -
+--R +---------------------------------------------------------+
+--R | 5
+--R | b +-+
+--R a c |- ------------------------------------------------------- \|x
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R log
+--R 4 +-+
+--R b \|x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (- 8a d + 24a b c d - 24a b c d + 8a b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 5
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R +---------------------------------------------------------+
+--R | 5
+--R | b +-+
+--R 2a c |- ------------------------------------------------------- \|x
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R atan
+--R 7 3 6 2 5 2 2 4 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 5
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R /
+--R 4 +-+
+--R b \|x
+--R +
+--R -
+--R +---------------------------------------------------------+
+--R | 5
+--R | d +-+
+--R 2a c |- ------------------------------------------------------- \|x
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R atan
+--R 3 4 3 2 5 2 2 6 3 7
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 5
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R 4 +-+
+--R d \|x
+--R +
+--R - 2
+--R /
+--R +-+
+--R a c\|x
+--R Type: Union(Expression(Integer),...)
+--E 1238
+
+--S 1239 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - a d\|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R b c\|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 +-+
+--R (- 2a c d + 2a b c )\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | d 4+-+4+-+
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R 4 +-+
+--R d \|x
+--R +
+--R 3 4 3 2 5 2 2 6 3 7
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 5
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R 2 2 +-+
+--R (2a c d - 2a b c )\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | d 4+-+4+-+
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R 4 +-+
+--R d \|x
+--R +
+--R 3 4 3 2 5 2 2 6 3 7
+--R (- 8a c d + 24a b c d - 24a b c d + 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 5
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R 2 2 +-+
+--R (2a c d - 2a b c )\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | b 4+-+4+-+
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R log
+--R 4 +-+
+--R b \|x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 5
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R 2 2 +-+
+--R (- 2a c d + 2a b c )\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | b 4+-+4+-+
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R log
+--R 4 +-+
+--R b \|x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (- 8a d + 24a b c d - 24a b c d + 8a b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 5
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - b c\|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R a d\|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R 2a d\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R 2a d\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a
+--R - 2b c\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x - \|a
+--R - 2b c\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | b 4+-+4+-+
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R atan
+--R 7 3 6 2 5 2 2 4 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 5
+--R | b
+--R |- -------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R /
+--R 4 +-+
+--R b \|x
+--R +
+--R 2 2 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R +---------------------------------------------------------+
+--R | 5
+--R | d 4+-+4+-+
+--R |- ------------------------------------------------------- \|a \|c
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R atan
+--R 3 4 3 2 5 2 2 6 3 7
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +---------------------------------------------------------+3
+--R | 5
+--R | d
+--R |- -------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R 4 +-+
+--R d \|x
+--R /
+--R 2 2 +-+4+-+4+-+
+--R (2a c d - 2a b c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1239
+
+--S 1240 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1240
+
+)clear all
+
+--S 1241 of 1475
+t0:=1/(x^(5/2)*(a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------
+--R 6 4 2 +-+
+--R (b d x + (a d + b c)x + a c x )\|x
+--R Type: Expression(Integer)
+--E 1241
+
+--S 1242 of 1475
+r0:=(-2/3)/(a*c*x^(3/2))+b^(7/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(7/4)*(b*c-a*d)*sqrt(2))-b^(7/4)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(7/4)*(b*c-a*d)*sqrt(2))-d^(7/4)*atan(1-_
+ d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(7/4)*(b*c-a*d)*sqrt(2))+_
+ d^(7/4)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(7/4)*(b*c-_
+ a*d)*sqrt(2))+1/2*b^(7/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(7/4)*(b*c-a*d)*sqrt(2))-1/2*b^(7/4)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*_
+ (b*c-a*d)*sqrt(2))-1/2*d^(7/4)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(7/4)*(b*c-a*d)*sqrt(2))+1/2*d^(7/4)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(7/4)*_
+ (b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 3a d x \|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 3b c x \|b \|c \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 3b c x \|b \|c \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 3a d x \|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|d \|x + \|c
+--R - 6a d x \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|d \|x - \|c
+--R - 6a d x \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|b \|x + \|a
+--R 6b c x \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|b \|x - \|a
+--R 6b c x \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+3 4+-+3
+--R (- 4a d + 4b c)\|2 \|a \|c
+--R /
+--R 2 2 +-+4+-+3 4+-+3 +-+
+--R (6a c d - 6a b c )x\|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1242
+
+--S 1243 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +-----------------------------------------------------------+
+--R | 7
+--R | d
+--R 3a c x |- ---------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 +-+
+--R d \|x
+--R +
+--R 2 3
+--R (2a c d - 2b c )
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | d
+--R |- ---------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R +-----------------------------------------------------------+
+--R | 7
+--R | d
+--R 3a c x |- ---------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 +-+
+--R d \|x
+--R +
+--R 2 3
+--R (- 2a c d + 2b c )
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | d
+--R |- ---------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R +-----------------------------------------------------------+
+--R | 7
+--R | b
+--R 3a c x |- ---------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 +-+
+--R b \|x
+--R +
+--R 3 2
+--R (2a d - 2a b c)
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | b
+--R |- ---------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R -
+--R +-----------------------------------------------------------+
+--R | 7
+--R | b
+--R 3a c x |- ---------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 +-+
+--R b \|x
+--R +
+--R 3 2
+--R (- 2a d + 2a b c)
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | b
+--R |- ---------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R -
+--R +-----------------------------------------------------------+
+--R | 7
+--R | b
+--R 6a c x |- ---------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 3 2
+--R (2a d - 2a b c)
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | b
+--R |- ---------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R /
+--R 2 +-+
+--R b \|x
+--R +
+--R +-----------------------------------------------------------+
+--R | 7
+--R | d
+--R 6a c x |- ---------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 2 3
+--R (2a c d - 2b c )
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | d
+--R |- ---------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R 2 +-+
+--R d \|x
+--R +
+--R - 2
+--R /
+--R +-+
+--R 3a c x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1243
+
+--S 1244 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R a d \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - b c \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 +-+
+--R (- 2a c d + 2a b c )\|2
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | d 4+-+3
+--R |- --------------------------------------------------------- \|a
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R 4+-+3
+--R \|c
+--R *
+--R log
+--R 2 +-+
+--R d \|x
+--R +
+--R 2 3
+--R (2a c d - 2b c )
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | d
+--R |- ---------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R 2 2 +-+
+--R (2a c d - 2a b c )\|2
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | d 4+-+3
+--R |- --------------------------------------------------------- \|a
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R 4+-+3
+--R \|c
+--R *
+--R log
+--R 2 +-+
+--R d \|x
+--R +
+--R 2 3
+--R (- 2a c d + 2b c )
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | d
+--R |- ---------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R 2 2 +-+
+--R (2a c d - 2a b c )\|2
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | b 4+-+3
+--R |- --------------------------------------------------------- \|a
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R 4+-+3
+--R \|c
+--R *
+--R log
+--R 2 +-+
+--R b \|x
+--R +
+--R 3 2
+--R (2a d - 2a b c)
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | b
+--R |- ---------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R 2 2 +-+
+--R (- 2a c d + 2a b c )\|2
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | b 4+-+3
+--R |- --------------------------------------------------------- \|a
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R 4+-+3
+--R \|c
+--R *
+--R log
+--R 2 +-+
+--R b \|x
+--R +
+--R 3 2
+--R (- 2a d + 2a b c)
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | b
+--R |- ---------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R b c \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - a d \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x + \|c
+--R 2a d \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x - \|c
+--R 2a d \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x + \|a
+--R - 2b c \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x - \|a
+--R - 2b c \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | b 4+-+3
+--R |- --------------------------------------------------------- \|a
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R 4+-+3
+--R \|c
+--R *
+--R atan
+--R 3 2
+--R (2a d - 2a b c)
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | b
+--R |- ---------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R /
+--R 2 +-+
+--R b \|x
+--R +
+--R 2 2 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | d 4+-+3
+--R |- --------------------------------------------------------- \|a
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R 4+-+3
+--R \|c
+--R *
+--R atan
+--R 2 3
+--R (2a c d - 2b c )
+--R *
+--R +-----------------------------------------------------------+
+--R | 7
+--R | d
+--R |- ---------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R 2 +-+
+--R d \|x
+--R /
+--R 2 2 +-+4+-+3 4+-+3
+--R (2a c d - 2a b c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1244
+
+--S 1245 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1245
+
+)clear all
+
+--S 1246 of 1475
+t0:=1/(x^(7/2)*(a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------
+--R 7 5 3 +-+
+--R (b d x + (a d + b c)x + a c x )\|x
+--R Type: Expression(Integer)
+--E 1246
+
+--S 1247 of 1475
+r0:=(-2/5)/(a*c*x^(5/2))-b^(9/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(9/4)*(b*c-a*d)*sqrt(2))+b^(9/4)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*(b*c-a*d)*sqrt(2))+d^(9/4)*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(9/4)*(b*c-a*d)*_
+ sqrt(2))-d^(9/4)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(9/4)*(b*c-a*d)*sqrt(2))+1/2*b^(9/4)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*(b*c-a*d)*sqrt(2))-_
+ 1/2*b^(9/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(9/4)*(b*c-a*d)*sqrt(2))-1/2*d^(9/4)*log(sqrt(c)+_
+ x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(9/4)*(b*c-a*d)*_
+ sqrt(2))+1/2*d^(9/4)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(c^(9/4)*(b*c-a*d)*sqrt(2))+2*(b*c+a*d)/(a^2*_
+ c^2*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 2 2 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 5a d x \|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 5b c x \|b \|c \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 5b c x \|b \|c \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 5a d x \|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+4+-+ +-+ \|2 \|d \|x + \|c
+--R 10a d x \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+4+-+ +-+ \|2 \|d \|x - \|c
+--R 10a d x \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+4+-+ +-+ \|2 \|b \|x + \|a
+--R - 10b c x \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+4+-+ +-+ \|2 \|b \|x - \|a
+--R - 10b c x \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 2 2 2 +-+4+-+4+-+
+--R ((20a d - 20b c )x - 4a c d + 4a b c )\|2 \|a \|c
+--R /
+--R 3 2 2 3 2 +-+4+-+4+-+ +-+
+--R (10a c d - 10a b c )x \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1247
+
+--S 1248 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------------------------------------------------------------+
+--R | 9
+--R 2 2 2 | d
+--R 5a c x |- -----------------------------------------------------------
+--R 4| 4 9 4 3 10 3 2 2 11 2 3 12 4 13
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 7 +-+
+--R d \|x
+--R +
+--R 3 7 3 2 8 2 2 9 3 10
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +-------------------------------------------------------------+3
+--R | 9
+--R | d
+--R |- -----------------------------------------------------------
+--R 4| 4 9 4 3 10 3 2 2 11 2 3 12 4 13
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R -
+--R 2 2 2
+--R 5a c x
+--R *
+--R +-------------------------------------------------------------+
+--R | 9
+--R | d +-+
+--R |- ----------------------------------------------------------- \|x
+--R 4| 4 9 4 3 10 3 2 2 11 2 3 12 4 13
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R log
+--R 7 +-+
+--R d \|x
+--R +
+--R 3 7 3 2 8 2 2 9 3 10
+--R (- 8a c d + 24a b c d - 24a b c d + 8b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2 3 12
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d
+--R +
+--R 4 13
+--R 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2 2 2
+--R 5a c x
+--R *
+--R +-------------------------------------------------------------+
+--R | 9
+--R | b +-+
+--R |- ----------------------------------------------------------- \|x
+--R 4| 13 4 12 3 11 2 2 2 10 3 3 9 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R log
+--R 7 +-+
+--R b \|x
+--R +
+--R 10 3 9 2 8 2 2 7 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2 10 3 3
+--R 16a d - 64a b c d + 96a b c d - 64a b c d
+--R +
+--R 9 4 4
+--R 16a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R +-------------------------------------------------------------+
+--R | 9
+--R 2 2 2 | b
+--R 5a c x |- -----------------------------------------------------------
+--R 4| 13 4 12 3 11 2 2 2 10 3 3 9 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 7 +-+
+--R b \|x
+--R +
+--R 10 3 9 2 8 2 2 7 3 3
+--R (- 8a d + 24a b c d - 24a b c d + 8a b c )
+--R *
+--R +-------------------------------------------------------------+3
+--R | 9
+--R | b
+--R |- -----------------------------------------------------------
+--R 4| 13 4 12 3 11 2 2 2 10 3 3 9 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R -
+--R 2 2 2
+--R 10a c x
+--R *
+--R +-------------------------------------------------------------+
+--R | 9
+--R | b +-+
+--R |- ----------------------------------------------------------- \|x
+--R 4| 13 4 12 3 11 2 2 2 10 3 3 9 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R atan
+--R 10 3 9 2 8 2 2 7 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2 10 3 3
+--R 16a d - 64a b c d + 96a b c d - 64a b c d
+--R +
+--R 9 4 4
+--R 16a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 7 +-+
+--R b \|x
+--R +
+--R 2 2 2
+--R 10a c x
+--R *
+--R +-------------------------------------------------------------+
+--R | 9
+--R | d +-+
+--R |- ----------------------------------------------------------- \|x
+--R 4| 4 9 4 3 10 3 2 2 11 2 3 12 4 13
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R atan
+--R 3 7 3 2 8 2 2 9 3 10
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +-------------------------------------------------------------+3
+--R | 9
+--R | d
+--R |- -----------------------------------------------------------
+--R 4| 4 9 4 3 10 3 2 2 11 2 3 12 4 13
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R 7 +-+
+--R d \|x
+--R +
+--R 2
+--R (10a d + 10b c)x - 2a c
+--R /
+--R 2 2 2 +-+
+--R 5a c x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1248
+
+--S 1249 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R a d \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - b c \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 2 3 +-+
+--R (2a c d - 2a b c )\|2
+--R *
+--R +-------------------------------------------------------------+
+--R | 9
+--R | d 4+-+
+--R |- ----------------------------------------------------------- \|a
+--R 4| 4 9 4 3 10 3 2 2 11 2 3 12 4 13
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R 4+-+
+--R \|c
+--R *
+--R log
+--R 7 +-+
+--R d \|x
+--R +
+--R 3 7 3 2 8 2 2 9 3 10
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +-------------------------------------------------------------+3
+--R | 9
+--R | d
+--R |- -----------------------------------------------------------
+--R 4| 4 9 4 3 10 3 2 2 11 2 3 12 4 13
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R 3 2 2 3 +-+
+--R (- 2a c d + 2a b c )\|2
+--R *
+--R +-------------------------------------------------------------+
+--R | 9
+--R | d 4+-+
+--R |- ----------------------------------------------------------- \|a
+--R 4| 4 9 4 3 10 3 2 2 11 2 3 12 4 13
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R 4+-+
+--R \|c
+--R *
+--R log
+--R 7 +-+
+--R d \|x
+--R +
+--R 3 7 3 2 8 2 2 9 3 10
+--R (- 8a c d + 24a b c d - 24a b c d + 8b c )
+--R *
+--R +-------------------------------------------------------------+3
+--R | 9
+--R | d
+--R |- -----------------------------------------------------------
+--R 4| 4 9 4 3 10 3 2 2 11 2 3 12 4 13
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R +
+--R 3 2 2 3 +-+
+--R (- 2a c d + 2a b c )\|2
+--R *
+--R +-------------------------------------------------------------+
+--R | 9
+--R | b 4+-+
+--R |- ----------------------------------------------------------- \|a
+--R 4| 13 4 12 3 11 2 2 2 10 3 3 9 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R 4+-+
+--R \|c
+--R *
+--R log
+--R 7 +-+
+--R b \|x
+--R +
+--R 10 3 9 2 8 2 2 7 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R +-------------------------------------------------------------+3
+--R | 9
+--R | b
+--R |- -----------------------------------------------------------
+--R 4| 13 4 12 3 11 2 2 2 10 3 3 9 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R 3 2 2 3 +-+
+--R (2a c d - 2a b c )\|2
+--R *
+--R +-------------------------------------------------------------+
+--R | 9
+--R | b 4+-+
+--R |- ----------------------------------------------------------- \|a
+--R 4| 13 4 12 3 11 2 2 2 10 3 3 9 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R 4+-+
+--R \|c
+--R *
+--R log
+--R 7 +-+
+--R b \|x
+--R +
+--R 10 3 9 2 8 2 2 7 3 3
+--R (- 8a d + 24a b c d - 24a b c d + 8a b c )
+--R *
+--R +-------------------------------------------------------------+3
+--R | 9
+--R | b
+--R |- -----------------------------------------------------------
+--R 4| 13 4 12 3 11 2 2 2 10 3 3 9 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R b c \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - a d \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|d \|x + \|c
+--R - 2a d \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|d \|x - \|c
+--R - 2a d \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|b \|x + \|a
+--R 2b c \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|b \|x - \|a
+--R 2b c \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 2 3 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R +-------------------------------------------------------------+
+--R | 9
+--R | b 4+-+
+--R |- ----------------------------------------------------------- \|a
+--R 4| 13 4 12 3 11 2 2 2 10 3 3 9 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R 4+-+
+--R \|c
+--R *
+--R atan
+--R 10 3 9 2 8 2 2 7 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R +-------------------------------------------------------------+3
+--R | 9
+--R | b
+--R |- -----------------------------------------------------------
+--R 4| 13 4 12 3 11 2 2 2 10 3 3 9 4 4
+--R \| 16a d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R /
+--R 7 +-+
+--R b \|x
+--R +
+--R 3 2 2 3 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R +-------------------------------------------------------------+
+--R | 9
+--R | d 4+-+
+--R |- ----------------------------------------------------------- \|a
+--R 4| 4 9 4 3 10 3 2 2 11 2 3 12 4 13
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R *
+--R 4+-+
+--R \|c
+--R *
+--R atan
+--R 3 7 3 2 8 2 2 9 3 10
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R +-------------------------------------------------------------+3
+--R | 9
+--R | d
+--R |- -----------------------------------------------------------
+--R 4| 4 9 4 3 10 3 2 2 11 2 3 12 4 13
+--R \| 16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c
+--R /
+--R 7 +-+
+--R d \|x
+--R /
+--R 3 2 2 3 +-+4+-+4+-+
+--R (2a c d - 2a b c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1249
+
+--S 1250 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1250
+
+)clear all
+
+--S 1251 of 1475
+t0:=x^(7/2)/((a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) -----------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Expression(Integer)
+--E 1251
+
+--S 1252 of 1475
+r0:=-a^(5/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(1/4)*(b*c-a*d)^2*_
+ sqrt(2))+a^(5/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(1/4)*_
+ (b*c-a*d)^2*sqrt(2))-1/4*c^(1/4)*(b*c-5*a*d)*atan(1-d^(1/4)*_
+ sqrt(2)*sqrt(x)/c^(1/4))/(d^(5/4)*(b*c-a*d)^2*sqrt(2))+1/4*_
+ c^(1/4)*(b*c-5*a*d)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (d^(5/4)*(b*c-a*d)^2*sqrt(2))-1/2*a^(5/4)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(1/4)*(b*c-a*d)^2*sqrt(2))+_
+ 1/2*a^(5/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(b^(1/4)*(b*c-a*d)^2*sqrt(2))-1/8*c^(1/4)*(b*c-5*a*d)*_
+ log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(d^(5/4)*_
+ (b*c-a*d)^2*sqrt(2))+1/8*c^(1/4)*(b*c-5*a*d)*log(sqrt(c)+_
+ x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(d^(5/4)*(b*c-a*d)^2*_
+ sqrt(2))-1/2*c*sqrt(x)/(d*(b*c-a*d)*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 2 2 4+-+4+-+
+--R ((- 5a d + b c d)x - 5a c d + b c )\|b \|c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (4a d x + 4a c d)\|a \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 4a d x - 4a c d)\|a \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 4+-+4+-+
+--R ((5a d - b c d)x + 5a c d - b c )\|b \|c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 4+-+4+-+
+--R ((- 10a d + 2b c d)x - 10a c d + 2b c )\|b \|c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 2 4+-+4+-+
+--R ((- 10a d + 2b c d)x - 10a c d + 2b c )\|b \|c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|b \|x + \|a
+--R (8a d x + 8a c d)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|b \|x - \|a
+--R (8a d x + 8a c d)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+4+-+ +-+
+--R (4a c d - 4b c )\|2 \|b \|d \|x
+--R /
+--R 2 4 3 2 2 2 2 2 3 2 2 2 3 +-+
+--R ((8a d - 16a b c d + 8b c d )x + 8a c d - 16a b c d + 8b c d)\|2
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R Type: Expression(Integer)
+--E 1252
+
+--S 1253 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2 2 2
+--R ((- 2a d + 2b c d )x - 2a c d + 2b c d)
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R - 625a c d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 8 13 7 12 6 2 2 11 5 3 3 10
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 4 9 3 5 5 8 2 6 6 7 7 7 6
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 8 8 5
+--R 4096b c d
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R (5a d - b c)\|x
+--R +
+--R 2 3 2 2 2
+--R (8a d - 16a b c d + 8b c d)
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R - 625a c d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 8 13 7 12 6 2 2 11
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 3 10 4 4 4 9 3 5 5 8
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 6 7 7 7 6 8 8 5
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R +
+--R 3 2 2 2 2
+--R ((2a d - 2b c d )x + 2a c d - 2b c d)
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R - 625a c d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 8 13 7 12 6 2 2 11 5 3 3 10
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 4 9 3 5 5 8 2 6 6 7 7 7 6
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 8 8 5
+--R 4096b c d
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R (5a d - b c)\|x
+--R +
+--R 2 3 2 2 2
+--R (- 8a d + 16a b c d - 8b c d)
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R - 625a c d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 8 13 7 12 6 2 2 11
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 3 10 4 4 4 9 3 5 5 8
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 6 7 7 7 6 8 8 5
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R +
+--R 3 2 2 2 2
+--R ((2a d - 2b c d )x + 2a c d - 2b c d)
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R 16a b d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7 9 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R a\|x
+--R +
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R 16a b d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 9 8
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 3 2 2 2 2
+--R ((- 2a d + 2b c d )x - 2a c d + 2b c d)
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R 16a b d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7 9 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R a\|x
+--R +
+--R 2 2 2 2
+--R (- 2a d + 4a b c d - 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R 16a b d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 9 8
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 3 2 2 2 2
+--R ((4a d - 4b c d )x + 4a c d - 4b c d)
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R - 625a c d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 8 13 7 12 6 2 2 11 5 3 3 10
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 4 9 3 5 5 8 2 6 6 7 7 7 6
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 8 8 5
+--R 4096b c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 2 3 2 2 2
+--R (8a d - 16a b c d + 8b c d)
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R - 625a c d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 8 13 7 12 6 2 2 11
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 3 10 4 4 4 9 3 5 5 8
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 6 7 7 7 6 8 8 5
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R /
+--R +-+
+--R (5a d - b c)\|x
+--R +
+--R 3 2 2 2 2
+--R ((- 4a d + 4b c d )x - 4a c d + 4b c d)
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R 16a b d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7 9 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R 16a b d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 9 8
+--R 16b c
+--R ,
+--R 4
+--R /
+--R +-+
+--R a\|x
+--R +
+--R +-+
+--R c\|x
+--R /
+--R 3 2 2 2 2
+--R (2a d - 2b c d )x + 2a c d - 2b c d
+--R Type: Union(Expression(Integer),...)
+--E 1253
+
+--S 1254 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - b c)\|b \|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 4a d\|a \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 3 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8b c d)\|2
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R - 625a c d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 8 13 7 12 6 2 2 11 5 3 3 10
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 4 9 3 5 5 8 2 6 6 7 7 7 6
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 8 8 5
+--R 4096b c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R +-+
+--R (5a d - b c)\|x
+--R +
+--R 2 3 2 2 2
+--R (8a d - 16a b c d + 8b c d)
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R - 625a c d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 8 13 7 12 6 2 2 11
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 3 10 4 4 4 9 3 5 5 8
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 6 7 7 7 6 8 8 5
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R +
+--R 2 3 2 2 2 +-+
+--R (8a d - 16a b c d + 8b c d)\|2
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R - 625a c d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 8 13 7 12 6 2 2 11 5 3 3 10
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 4 9 3 5 5 8 2 6 6 7 7 7 6
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 8 8 5
+--R 4096b c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R +-+
+--R (5a d - b c)\|x
+--R +
+--R 2 3 2 2 2
+--R (- 8a d + 16a b c d - 8b c d)
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R - 625a c d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 8 13 7 12 6 2 2 11
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 3 10 4 4 4 9 3 5 5 8
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 6 7 7 7 6 8 8 5
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R +
+--R 2 3 2 2 2 +-+
+--R (8a d - 16a b c d + 8b c d)\|2
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R 16a b d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7 9 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R +-+
+--R a\|x
+--R +
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R 16a b d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 9 8
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 2 3 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8b c d)\|2
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R 16a b d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7 9 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R +-+
+--R a\|x
+--R +
+--R 2 2 2 2
+--R (- 2a d + 4a b c d - 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R 16a b d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 9 8
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 4a d\|a \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + b c)\|b \|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R (10a d - 2b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R (10a d - 2b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a
+--R - 8a d\|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x - \|a
+--R - 8a d\|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 2 2 +-+
+--R (16a d - 32a b c d + 16b c d)\|2
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R - 625a c d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 8 13 7 12 6 2 2 11 5 3 3 10
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 4 9 3 5 5 8 2 6 6 7 7 7 6
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 8 8 5
+--R 4096b c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R atan
+--R 2 3 2 2 2
+--R (8a d - 16a b c d + 8b c d)
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R - 625a c d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 8 13 7 12 6 2 2 11
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 3 10 4 4 4 9 3 5 5 8
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 6 7 7 7 6 8 8 5
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R /
+--R +-+
+--R (5a d - b c)\|x
+--R +
+--R 2 3 2 2 2 +-+
+--R (- 16a d + 32a b c d - 16b c d)\|2
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R 16a b d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7 9 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R atan
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 8 8 7 2 7 6 3 2 6 5 4 3 5
+--R 16a b d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 5 4 4 3 6 5 3 2 7 6 2 8 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 9 8
+--R 16b c
+--R ,
+--R 4
+--R /
+--R +-+
+--R a\|x
+--R /
+--R 2 3 2 2 2 +-+4+-+4+-+
+--R (8a d - 16a b c d + 8b c d)\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 1254
+
+--S 1255 of 1475
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1255
+
+)clear all
+
+--S 1256 of 1475
+t0:=x^(5/2)/((a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) -----------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Expression(Integer)
+--E 1256
+
+--S 1257 of 1475
+r0:=1/2*x^(3/2)/((b*c-a*d)*(c+d*x^2))+a^(3/4)*b^(1/4)*atan(1-b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/((b*c-a*d)^2*sqrt(2))-a^(3/4)*b^(1/4)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/((b*c-a*d)^2*sqrt(2))-_
+ 1/4*(b*c+3*a*d)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(1/4)*d^(3/4)*(b*c-a*d)^2*sqrt(2))+1/4*(b*c+3*a*d)*atan(1+_
+ d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(1/4)*d^(3/4)*(b*c-a*d)^2*_
+ sqrt(2))-1/2*a^(3/4)*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/((b*c-a*d)^2*sqrt(2))+1/2*a^(3/4)*b^(1/4)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/((b*c-_
+ a*d)^2*sqrt(2))+1/8*(b*c+3*a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(1/4)*d^(3/4)*(b*c-a*d)^2*sqrt(2))-_
+ 1/8*(b*c+3*a*d)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(1/4)*d^(3/4)*(b*c-a*d)^2*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((- 3a d - b c d)x - 3a c d - b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4+-+3 4+-+4+-+4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (4d x + 4c)\|a \|b \|c \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4+-+3 4+-+4+-+4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 4d x - 4c)\|a \|b \|c \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((3a d + b c d)x + 3a c d + b c )log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|d \|x + \|c
+--R ((6a d + 2b c d)x + 6a c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|d \|x - \|c
+--R ((6a d + 2b c d)x + 6a c d + 2b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+3 4+-+4+-+4+-+3 \|2 \|b \|x + \|a
+--R (- 8d x - 8c)\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+3 4+-+4+-+4+-+3 \|2 \|b \|x - \|a
+--R (- 8d x - 8c)\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+4+-+3 +-+
+--R (- 4a d + 4b c)x\|2 \|c \|d \|x
+--R /
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+4+-+
+--R ((8a d - 16a b c d + 8b c d)x + 8a c d - 16a b c d + 8b c )\|2 \|c
+--R *
+--R 4+-+3
+--R \|d
+--R Type: Expression(Integer)
+--E 1257
+
+--S 1258 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2
+--R ((2a d - 2b c d)x + 2a c d - 2b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 8 11 7 2 10 6 2 3 9 5 3 4 8
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 5 7 3 5 6 6 2 6 7 5 7 8 4
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 8 9 3
+--R 4096b c d
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27a d + 27a b c d + 9a b c d + b c )\|x
+--R +
+--R 6 8 5 2 7 4 2 3 6 3 3 4 5
+--R 512a c d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 2 4 5 4 5 6 3 6 7 2
+--R 7680a b c d - 3072a b c d + 512b c d
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 8 11 7 2 10 6 2 3 9
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 4 8 4 4 5 7 3 5 6 6
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 7 5 7 8 4 8 9 3
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2
+--R ((- 2a d + 2b c d)x - 2a c d + 2b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 8 11 7 2 10 6 2 3 9 5 3 4 8
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 5 7 3 5 6 6 2 6 7 5 7 8 4
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 8 9 3
+--R 4096b c d
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27a d + 27a b c d + 9a b c d + b c )\|x
+--R +
+--R 6 8 5 2 7 4 2 3 6 3 3 4 5
+--R - 512a c d + 3072a b c d - 7680a b c d + 10240a b c d
+--R +
+--R 2 4 5 4 5 6 3 6 7 2
+--R - 7680a b c d + 3072a b c d - 512b c d
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 8 11 7 2 10 6 2 3 9
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 4 8 4 4 5 7 3 5 6 6
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 7 5 7 8 4 8 9 3
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2
+--R ((- 2a d + 2b c d)x - 2a c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R 2 +-+
+--R a b\|x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 8a d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 5 6 6
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 7 8 8
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2
+--R ((2a d - 2b c d)x + 2a c d - 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R 2 +-+
+--R a b\|x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R - 8a d + 48a b c d - 120a b c d + 160a b c d - 120a b c d
+--R +
+--R 5 5 6 6
+--R 48a b c d - 8b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 7 8 8
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2
+--R ((- 4a d + 4b c d)x - 4a c d + 4b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 8a d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 5 6 6
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 7 8 8
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 2 +-+
+--R a b\|x
+--R +
+--R 2 2 2
+--R ((4a d - 4b c d)x + 4a c d - 4b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 8 11 7 2 10 6 2 3 9 5 3 4 8
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 5 7 3 5 6 6 2 6 7 5 7 8 4
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 8 9 3
+--R 4096b c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 6 8 5 2 7 4 2 3 6 3 3 4 5
+--R 512a c d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 2 4 5 4 5 6 3 6 7 2
+--R 7680a b c d - 3072a b c d + 512b c d
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 8 11 7 2 10 6 2 3 9
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 4 8 4 4 5 7 3 5 6 6
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 7 5 7 8 4 8 9 3
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27a d + 27a b c d + 9a b c d + b c )\|x
+--R +
+--R +-+
+--R - x\|x
+--R /
+--R 2 2 2
+--R (2a d - 2b c d)x + 2a c d - 2b c
+--R Type: Union(Expression(Integer),...)
+--E 1258
+
+--S 1259 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d + b c)log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+3 4+-+4+-+4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - 4\|a \|b \|c \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 +-+
+--R (8a d - 16a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 8 11 7 2 10 6 2 3 9 5 3 4 8
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 5 7 3 5 6 6 2 6 7 5 7 8 4
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 8 9 3
+--R 4096b c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27a d + 27a b c d + 9a b c d + b c )\|x
+--R +
+--R 6 8 5 2 7 4 2 3 6 3 3 4 5
+--R 512a c d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 2 4 5 4 5 6 3 6 7 2
+--R 7680a b c d - 3072a b c d + 512b c d
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 8 11 7 2 10 6 2 3 9
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 4 8 4 4 5 7 3 5 6 6
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 7 5 7 8 4 8 9 3
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 8 11 7 2 10 6 2 3 9 5 3 4 8
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 5 7 3 5 6 6 2 6 7 5 7 8 4
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 8 9 3
+--R 4096b c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27a d + 27a b c d + 9a b c d + b c )\|x
+--R +
+--R 6 8 5 2 7 4 2 3 6 3 3 4 5
+--R - 512a c d + 3072a b c d - 7680a b c d + 10240a b c d
+--R +
+--R 2 4 5 4 5 6 3 6 7 2
+--R - 7680a b c d + 3072a b c d - 512b c d
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 8 11 7 2 10 6 2 3 9
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 4 8 4 4 5 7 3 5 6 6
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 7 5 7 8 4 8 9 3
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 2 +-+
+--R a b\|x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 8a d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 5 6 6
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 7 8 8
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+
+--R (8a d - 16a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R log
+--R 2 +-+
+--R a b\|x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R - 8a d + 48a b c d - 120a b c d + 160a b c d - 120a b c d
+--R +
+--R 5 5 6 6
+--R 48a b c d - 8b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 7 8 8
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4+-+3 4+-+4+-+4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R 4\|a \|b \|c \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d - b c)log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R (- 6a d - 2b c)atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R (- 6a d - 2b c)atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+4+-+4+-+3 \|2 \|b \|x + \|a
+--R 8\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+4+-+4+-+3 \|2 \|b \|x - \|a
+--R 8\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 +-+
+--R (- 16a d + 32a b c d - 16b c )\|2
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R atan
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 8a d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 5 6 6
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 7 8 8
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 2 +-+
+--R a b\|x
+--R +
+--R 2 2 2 2 +-+
+--R (16a d - 32a b c d + 16b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 8 11 7 2 10 6 2 3 9 5 3 4 8
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 5 7 3 5 6 6 2 6 7 5 7 8 4
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 8 9 3
+--R 4096b c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|c \|d
+--R *
+--R atan
+--R 6 8 5 2 7 4 2 3 6 3 3 4 5
+--R 512a c d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 2 4 5 4 5 6 3 6 7 2
+--R 7680a b c d - 3072a b c d + 512b c d
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 8 11 7 2 10 6 2 3 9
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 4 8 4 4 5 7 3 5 6 6
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 7 5 7 8 4 8 9 3
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27a d + 27a b c d + 9a b c d + b c )\|x
+--R /
+--R 2 2 2 2 +-+4+-+4+-+3
+--R (8a d - 16a b c d + 8b c )\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1259
+
+--S 1260 of 1475
+--d0:=D(m0,x)
+--E 1260
+
+)clear all
+
+--S 1261 of 1475
+t0:=x^(3/2)/((a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) -----------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Expression(Integer)
+--E 1261
+
+--S 1262 of 1475
+r0:=a^(1/4)*b^(3/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/((b*c-a*d)^2*_
+ sqrt(2))-a^(1/4)*b^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ ((b*c-a*d)^2*sqrt(2))-1/4*(3*b*c+a*d)*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(3/4)*d^(1/4)*(b*c-a*d)^2*sqrt(2))+1/4*(3*_
+ b*c+a*d)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(3/4)*_
+ d^(1/4)*(b*c-a*d)^2*sqrt(2))+1/2*a^(1/4)*b^(3/4)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/((b*c-a*d)^2*sqrt(2))-_
+ 1/2*a^(1/4)*b^(3/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/((b*c-a*d)^2*sqrt(2))-1/8*(3*b*c+a*d)*_
+ log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(3/4)*_
+ d^(1/4)*(b*c-a*d)^2*sqrt(2))+1/8*(3*b*c+a*d)*log(sqrt(c)+x*_
+ sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(3/4)*d^(1/4)*_
+ (b*c-a*d)^2*sqrt(2))+1/2*sqrt(x)/((b*c-a*d)*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((a d + 3b c d)x + a c d + 3b c )log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4+-+4+-+3 4+-+3 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 4d x - 4c)\|a \|b \|c \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4+-+4+-+3 4+-+3 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (4d x + 4c)\|a \|b \|c \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2
+--R ((- a d - 3b c d)x - a c d - 3b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|d \|x + \|c
+--R ((2a d + 6b c d)x + 2a c d + 6b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|d \|x - \|c
+--R ((2a d + 6b c d)x + 2a c d + 6b c )atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+4+-+3 4+-+3 4+-+ \|2 \|b \|x + \|a
+--R (- 8d x - 8c)\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+4+-+3 4+-+3 4+-+ \|2 \|b \|x - \|a
+--R (- 8d x - 8c)\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+3 4+-+ +-+
+--R (- 4a d + 4b c)\|2 \|c \|d \|x
+--R /
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+4+-+3
+--R ((8a d - 16a b c d + 8b c d)x + 8a c d - 16a b c d + 8b c )\|2 \|c
+--R *
+--R 4+-+
+--R \|d
+--R Type: Expression(Integer)
+--E 1262
+
+--S 1263 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2
+--R ((2a d - 2b c d)x + 2a c d - 2b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 8 3 9 7 4 8 6 2 5 7 5 3 6 6
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 7 5 3 5 8 4 2 6 9 3
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 7 10 2 8 11
+--R - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R (a d + 3b c)\|x
+--R +
+--R 2 2 2 2 3
+--R (8a c d - 16a b c d + 8b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 8 3 9 7 4 8 6 2 5 7
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 6 6 4 4 7 5 3 5 8 4
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 9 3 7 10 2 8 11
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R +
+--R 2 2 2
+--R ((- 2a d + 2b c d)x - 2a c d + 2b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 8 3 9 7 4 8 6 2 5 7 5 3 6 6
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 7 5 3 5 8 4 2 6 9 3
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 7 10 2 8 11
+--R - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R (a d + 3b c)\|x
+--R +
+--R 2 2 2 2 3
+--R (- 8a c d + 16a b c d - 8b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 8 3 9 7 4 8 6 2 5 7
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 6 6 4 4 7 5 3 5 8 4
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 9 3 7 10 2 8 11
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R +
+--R 2 2 2
+--R ((- 2a d + 2b c d)x - 2a c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R b\|x
+--R +
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 2 2 2
+--R ((2a d - 2b c d)x + 2a c d - 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R b\|x
+--R +
+--R 2 2 2 2
+--R (- 2a d + 4a b c d - 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 2 2 2
+--R ((4a d - 4b c d)x + 4a c d - 4b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c
+--R ,
+--R 4
+--R /
+--R +-+
+--R b\|x
+--R +
+--R 2 2 2
+--R ((- 4a d + 4b c d)x - 4a c d + 4b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 8 3 9 7 4 8 6 2 5 7 5 3 6 6
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 7 5 3 5 8 4 2 6 9 3
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 7 10 2 8 11
+--R - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 2 2 2 2 3
+--R (8a c d - 16a b c d + 8b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 8 3 9 7 4 8 6 2 5 7
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 6 6 4 4 7 5 3 5 8 4
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 9 3 7 10 2 8 11
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R /
+--R +-+
+--R (a d + 3b c)\|x
+--R +
+--R +-+
+--R - \|x
+--R /
+--R 2 2 2
+--R (2a d - 2b c d)x + 2a c d - 2b c
+--R Type: Union(Expression(Integer),...)
+--E 1263
+
+--S 1264 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d - 3b c)log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+3 4+-+3 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 4\|a \|b \|c \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 +-+
+--R (8a d - 16a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 8 3 9 7 4 8 6 2 5 7 5 3 6 6
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 7 5 3 5 8 4 2 6 9 3
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 7 10 2 8 11
+--R - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R +-+
+--R (a d + 3b c)\|x
+--R +
+--R 2 2 2 2 3
+--R (8a c d - 16a b c d + 8b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 8 3 9 7 4 8 6 2 5 7
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 6 6 4 4 7 5 3 5 8 4
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 9 3 7 10 2 8 11
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 8 3 9 7 4 8 6 2 5 7 5 3 6 6
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 7 5 3 5 8 4 2 6 9 3
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 7 10 2 8 11
+--R - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R +-+
+--R (a d + 3b c)\|x
+--R +
+--R 2 2 2 2 3
+--R (- 8a c d + 16a b c d - 8b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 8 3 9 7 4 8 6 2 5 7
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 6 6 4 4 7 5 3 5 8 4
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 9 3 7 10 2 8 11
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R +-+
+--R b\|x
+--R +
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+
+--R (8a d - 16a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R log
+--R +-+
+--R b\|x
+--R +
+--R 2 2 2 2
+--R (- 2a d + 4a b c d - 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 4+-+4+-+3 4+-+3 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 4\|a \|b \|c \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d + 3b c)log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R (- 2a d - 6b c)atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R (- 2a d - 6b c)atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+3 4+-+3 4+-+ \|2 \|b \|x + \|a
+--R 8\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+3 4+-+3 4+-+ \|2 \|b \|x - \|a
+--R 8\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 +-+
+--R (16a d - 32a b c d + 16b c )\|2
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R atan
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a b
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c
+--R ,
+--R 4
+--R /
+--R +-+
+--R b\|x
+--R +
+--R 2 2 2 2 +-+
+--R (- 16a d + 32a b c d - 16b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 8 3 9 7 4 8 6 2 5 7 5 3 6 6
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 7 5 3 5 8 4 2 6 9 3
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 7 10 2 8 11
+--R - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|c \|d
+--R *
+--R atan
+--R 2 2 2 2 3
+--R (8a c d - 16a b c d + 8b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 8 3 9 7 4 8 6 2 5 7
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 6 6 4 4 7 5 3 5 8 4
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 9 3 7 10 2 8 11
+--R 114688a b c d - 32768a b c d + 4096b c d
+--R ,
+--R 4
+--R /
+--R +-+
+--R (a d + 3b c)\|x
+--R /
+--R 2 2 2 2 +-+4+-+3 4+-+
+--R (8a d - 16a b c d + 8b c )\|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1264
+
+--S 1265 of 1475
+--d0:=D(m0,x)
+--E 1265
+
+)clear all
+
+--S 1266 of 1475
+t0:=sqrt(x)/((a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R +-+
+--R \|x
+--R (1) -----------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Expression(Integer)
+--E 1266
+
+--S 1267 of 1475
+r0:=-1/2*d*x^(3/2)/(c*(b*c-a*d)*(c+d*x^2))-b^(5/4)*atan(1-b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*(b*c-a*d)^2*sqrt(2))+b^(5/4)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*(b*c-a*d)^2*_
+ sqrt(2))+1/4*d^(1/4)*(5*b*c-a*d)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/_
+ c^(1/4))/(c^(5/4)*(b*c-a*d)^2*sqrt(2))-1/4*d^(1/4)*(5*b*c-a*d)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(5/4)*(b*c-a*d)^2*_
+ sqrt(2))+1/2*b^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(1/4)*(b*c-a*d)^2*sqrt(2))-1/2*b^(5/4)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*_
+ (b*c-a*d)^2*sqrt(2))-1/8*d^(1/4)*(5*b*c-a*d)*log(sqrt(c)+x*_
+ sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(5/4)*(b*c-a*d)^2*_
+ sqrt(2))+1/8*d^(1/4)*(5*b*c-a*d)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(5/4)*(b*c-a*d)^2*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2 4+-+4+-+
+--R ((- a d + 5b c d)x - a c d + 5b c )\|a \|d
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 4b c d x - 4b c )\|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (4b c d x + 4b c )\|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 4+-+4+-+
+--R ((a d - 5b c d)x + a c d - 5b c )\|a \|d
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+4+-+ \|2 \|d \|x + \|c
+--R ((2a d - 10b c d)x + 2a c d - 10b c )\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+4+-+ \|2 \|d \|x - \|c
+--R ((2a d - 10b c d)x + 2a c d - 10b c )\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|b \|x + \|a
+--R (8b c d x + 8b c )\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|b \|x - \|a
+--R (8b c d x + 8b c )\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+4+-+ +-+
+--R (4a d - 4b c d)x\|2 \|a \|c \|x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4 +-+4+-+
+--R ((8a c d - 16a b c d + 8b c d)x + 8a c d - 16a b c d + 8b c )\|2 \|a
+--R *
+--R 4+-+
+--R \|c
+--R Type: Expression(Integer)
+--E 1267
+
+--S 1268 of 1475
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 3
+--R ((2a c d - 2b c d)x + 2a c d - 2b c )
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625b c d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 7 12 8 13
+--R - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (a d - 15a b c d + 75a b c d - 125b c d)\|x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3
+--R 512a c d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 2 4 8 2 5 9 6 10
+--R 7680a b c d - 3072a b c d + 512b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R - a d + 20a b c d - 150a b c d + 500a b c d
+--R +
+--R 4 4
+--R - 625b c d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 8 5 4 4 9 4 3 5 10 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 11 2 7 12 8 13
+--R 114688a b c d - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 3
+--R ((- 2a c d + 2b c d)x - 2a c d + 2b c )
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625b c d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 7 12 8 13
+--R - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (a d - 15a b c d + 75a b c d - 125b c d)\|x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3
+--R - 512a c d + 3072a b c d - 7680a b c d + 10240a b c d
+--R +
+--R 2 4 8 2 5 9 6 10
+--R - 7680a b c d + 3072a b c d - 512b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R - a d + 20a b c d - 150a b c d + 500a b c d
+--R +
+--R 4 4
+--R - 625b c d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 8 5 4 4 9 4 3 5 10 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 11 2 7 12 8 13
+--R 114688a b c d - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 3
+--R ((2a c d - 2b c d)x + 2a c d - 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 4 +-+
+--R b \|x
+--R +
+--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2
+--R 8a d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 2 5 5 6 6
+--R - 48a b c d + 8a b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 2 7 7 8 8
+--R - 128a b c d + 16a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 3
+--R ((- 2a c d + 2b c d)x - 2a c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 4 +-+
+--R b \|x
+--R +
+--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2
+--R - 8a d + 48a b c d - 120a b c d + 160a b c d - 120a b c d
+--R +
+--R 2 5 5 6 6
+--R 48a b c d - 8a b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 2 7 7 8 8
+--R - 128a b c d + 16a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 3
+--R ((4a c d - 4b c d)x + 4a c d - 4b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16a b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2
+--R 8a d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 2 5 5 6 6
+--R - 48a b c d + 8a b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 2 7 7 8 8
+--R - 128a b c d + 16a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 4 +-+
+--R b \|x
+--R +
+--R 2 2 2 2 3
+--R ((4a c d - 4b c d)x + 4a c d - 4b c )
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625b c d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 7 12 8 13
+--R - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3
+--R 512a c d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 2 4 8 2 5 9 6 10
+--R 7680a b c d - 3072a b c d + 512b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R - a d + 20a b c d - 150a b c d + 500a b c d
+--R +
+--R 4 4
+--R - 625b c d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 8 5 4 4 9 4 3 5 10 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 11 2 7 12 8 13
+--R 114688a b c d - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (a d - 15a b c d + 75a b c d - 125b c d)\|x
+--R +
+--R +-+
+--R d x\|x
+--R /
+--R 2 2 2 2 3
+--R (2a c d - 2b c d)x + 2a c d - 2b c
+--R Type: Union(Expression(Integer),...)
+--E 1268
+
+--S 1269 of 1475
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 5b c)\|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 4b c\|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 3 +-+
+--R (8a c d - 16a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625b c d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 7 12 8 13
+--R - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (a d - 15a b c d + 75a b c d - 125b c d)\|x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3
+--R 512a c d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 2 4 8 2 5 9 6 10
+--R 7680a b c d - 3072a b c d + 512b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R - a d + 20a b c d - 150a b c d + 500a b c d
+--R +
+--R 4 4
+--R - 625b c d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 8 5 4 4 9 4 3 5 10 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 11 2 7 12 8 13
+--R 114688a b c d - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 3 +-+
+--R (- 8a c d + 16a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625b c d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 7 12 8 13
+--R - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (a d - 15a b c d + 75a b c d - 125b c d)\|x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3
+--R - 512a c d + 3072a b c d - 7680a b c d + 10240a b c d
+--R +
+--R 2 4 8 2 5 9 6 10
+--R - 7680a b c d + 3072a b c d - 512b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R - a d + 20a b c d - 150a b c d + 500a b c d
+--R +
+--R 4 4
+--R - 625b c d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 8 5 4 4 9 4 3 5 10 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 11 2 7 12 8 13
+--R 114688a b c d - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 3 +-+
+--R (8a c d - 16a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 4 +-+
+--R b \|x
+--R +
+--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2
+--R 8a d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 2 5 5 6 6
+--R - 48a b c d + 8a b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 2 7 7 8 8
+--R - 128a b c d + 16a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 3 +-+
+--R (- 8a c d + 16a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 4 +-+
+--R b \|x
+--R +
+--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2
+--R - 8a d + 48a b c d - 120a b c d + 160a b c d - 120a b c d
+--R +
+--R 2 5 5 6 6
+--R 48a b c d - 8a b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 2 7 7 8 8
+--R - 128a b c d + 16a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 4b c\|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 5b c)\|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R (- 2a d + 10b c)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R (- 2a d + 10b c)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a
+--R - 8b c\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x - \|a
+--R - 8b c\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 3 +-+
+--R (16a c d - 32a b c d + 16b c )\|2
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R atan
+--R 7 6 6 5 5 2 2 4 4 3 3 3 3 4 4 2
+--R 8a d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 2 5 5 6 6
+--R - 48a b c d + 8a b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 2 7 7 8 8
+--R - 128a b c d + 16a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 4 +-+
+--R b \|x
+--R +
+--R 2 2 2 2 3 +-+
+--R (16a c d - 32a b c d + 16b c )\|2
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625b c d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 4096a c d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 7 12 8 13
+--R - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R atan
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3
+--R 512a c d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 2 4 8 2 5 9 6 10
+--R 7680a b c d - 3072a b c d + 512b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R - a d + 20a b c d - 150a b c d + 500a b c d
+--R +
+--R 4 4
+--R - 625b c d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6
+--R 4096a c d - 32768a b c d + 114688a b c d
+--R +
+--R 5 3 8 5 4 4 9 4 3 5 10 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 6 11 2 7 12 8 13
+--R 114688a b c d - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (a d - 15a b c d + 75a b c d - 125b c d)\|x
+--R /
+--R 2 2 2 2 3 +-+4+-+4+-+
+--R (8a c d - 16a b c d + 8b c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1269
+
+--S 1270 of 1475
+--d0:=D(m0,x)
+--E 1270
+
+)clear all
+
+--S 1271 of 1475
+t0:=1/((a+b*x^2)*(c+d*x^2)^2*sqrt(x))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------------
+--R 2 6 2 4 2 2 2 +-+
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|x
+--R Type: Expression(Integer)
+--E 1271
+
+--S 1272 of 1475
+r0:=-b^(7/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*(b*c-_
+ a*d)^2*sqrt(2))+b^(7/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(3/4)*(b*c-a*d)^2*sqrt(2))+1/4*d^(3/4)*(7*b*c-3*a*d)*atan(1-_
+ d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(7/4)*(b*c-a*d)^2*sqrt(2))-_
+ 1/4*d^(3/4)*(7*b*c-3*a*d)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(7/4)*(b*c-a*d)^2*sqrt(2))-1/2*b^(7/4)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*(b*c-a*d)^2*sqrt(2))+_
+ 1/2*b^(7/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(3/4)*(b*c-a*d)^2*sqrt(2))+1/8*d^(3/4)*(7*b*c-_
+ 3*a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(7/4)*(b*c-a*d)^2*sqrt(2))-1/8*d^(3/4)*(7*b*c-3*a*d)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(7/4)*_
+ (b*c-a*d)^2*sqrt(2))-1/2*d*sqrt(x)/(c*(b*c-a*d)*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 2 2 4+-+3 4+-+3
+--R ((3a d - 7b c d)x + 3a c d - 7b c )\|a \|d
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (4b c d x + 4b c )\|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 4b c d x - 4b c )\|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 4+-+3 4+-+3
+--R ((- 3a d + 7b c d)x - 3a c d + 7b c )\|a \|d
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 4+-+3 4+-+3
+--R ((6a d - 14b c d)x + 6a c d - 14b c )\|a \|d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 2 4+-+3 4+-+3
+--R ((6a d - 14b c d)x + 6a c d - 14b c )\|a \|d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+3 4+-+3 \|2 \|b \|x + \|a
+--R (8b c d x + 8b c )\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+3 4+-+3 \|2 \|b \|x - \|a
+--R (8b c d x + 8b c )\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+3 4+-+3 +-+
+--R (4a d - 4b c d)\|2 \|a \|c \|x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4 +-+
+--R ((8a c d - 16a b c d + 8b c d)x + 8a c d - 16a b c d + 8b c )\|2
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 1272
+
+--S 1273 of 1475
+--a0:=integrate(t0,x)
+--E 1273
+
+--S 1274 of 1475
+--m0:=a0-r0
+--E 1274
+
+--S 1275 of 1475
+--d0:=D(m0,x)
+--E 1275
+
+)clear all
+
+--S 1276 of 1475
+t0:=1/(x^(3/2)*(a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------------------
+--R 2 7 2 5 2 3 2 +-+
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x)\|x
+--R Type: Expression(Integer)
+--E 1276
+
+--S 1277 of 1475
+r0:=b^(9/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*(b*c-_
+ a*d)^2*sqrt(2))-b^(9/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(5/4)*(b*c-a*d)^2*sqrt(2))-1/4*d^(5/4)*(9*b*c-5*a*d)*atan(1-_
+ d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(9/4)*(b*c-a*d)^2*sqrt(2))+_
+ 1/4*d^(5/4)*(9*b*c-5*a*d)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(9/4)*(b*c-a*d)^2*sqrt(2))-1/2*b^(9/4)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*(b*c-a*d)^2*sqrt(2))+_
+ 1/2*b^(9/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(5/4)*(b*c-a*d)^2*sqrt(2))+1/8*d^(5/4)*(9*b*c-_
+ 5*a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(9/4)*(b*c-a*d)^2*sqrt(2))-1/8*d^(5/4)*(9*b*c-5*a*d)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(9/4)*_
+ (b*c-a*d)^2*sqrt(2))+1/2*(-4*b*c+5*a*d)/(a*c^2*(b*c-a*d)*_
+ sqrt(x))-1/2*d/(c*(b*c-a*d)*(c+d*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 2 4+-+4+-+ +-+
+--R ((5a d - 9a b c d )x + 5a c d - 9a b c d)\|a \|d \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 2 3 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (4b c d x + 4b c )\|b \|c \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 3 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 4b c d x - 4b c )\|b \|c \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 3 2 2 2 2 2 4+-+4+-+ +-+
+--R ((- 5a d + 9a b c d )x - 5a c d + 9a b c d)\|a \|d \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 4+-+4+-+ +-+
+--R ((- 10a d + 18a b c d )x - 10a c d + 18a b c d)\|a \|d \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 4+-+4+-+ +-+
+--R ((- 10a d + 18a b c d )x - 10a c d + 18a b c d)\|a \|d \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 3 4+-+4+-+ +-+ \|2 \|b \|x + \|a
+--R (- 8b c d x - 8b c )\|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 3 4+-+4+-+ +-+ \|2 \|b \|x - \|a
+--R (- 8b c d x - 8b c )\|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 20a d + 36a b c d - 16b c d)x - 16a c d + 32a b c d - 16b c )
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R /
+--R 3 2 3 2 3 2 2 4 2 3 3 2 2 4 2 5 +-+
+--R ((8a c d - 16a b c d + 8a b c d)x + 8a c d - 16a b c d + 8a b c )\|2
+--R *
+--R 4+-+4+-+ +-+
+--R \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1277
+
+--S 1278 of 1475
+--a0:=integrate(t0,x)
+--E 1278
+
+--S 1279 of 1475
+--m0:=a0-r0
+--E 1279
+
+--S 1280 of 1475
+--d0:=D(m0,x)
+--E 1280
+
+)clear all
+
+--S 1281 of 1475
+t0:=1/(x^(5/2)*(a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------------
+--R 2 8 2 6 2 4 2 2 +-+
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|x
+--R Type: Expression(Integer)
+--E 1281
+
+--S 1282 of 1475
+r0:=1/6*(-4*b*c+7*a*d)/(a*c^2*(b*c-a*d)*x^(3/2))-1/2*d/(c*(b*c-a*d)*_
+ x^(3/2)*(c+d*x^2))+b^(11/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(7/4)*(b*c-a*d)^2*sqrt(2))-b^(11/4)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*(b*c-a*d)^2*sqrt(2))-1/4*_
+ d^(7/4)*(11*b*c-7*a*d)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(11/4)*(b*c-a*d)^2*sqrt(2))+1/4*d^(7/4)*(11*b*c-7*a*d)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(11/4)*(b*c-a*d)^2*_
+ sqrt(2))+1/2*b^(11/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(7/4)*(b*c-a*d)^2*sqrt(2))-1/2*b^(11/4)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*_
+ (b*c-a*d)^2*sqrt(2))-1/8*d^(7/4)*(11*b*c-7*a*d)*log(sqrt(c)+x*_
+ sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(11/4)*(b*c-a*d)^2*_
+ sqrt(2))+1/8*d^(7/4)*(11*b*c-7*a*d)*log(sqrt(c)+x*sqrt(d)+_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(11/4)*(b*c-a*d)^2*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 3 2 3 2 2 2 4+-+3 4+-+3 +-+
+--R ((- 21a d + 33a b c d )x + (- 21a c d + 33a b c d)x)\|a \|d \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 3 2 3 4+-+3 4+-+3 +-+
+--R (- 12b c d x - 12b c x)\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 3 2 3 4+-+3 4+-+3 +-+
+--R (12b c d x + 12b c x)\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 3 2 3 2 2 2 4+-+3 4+-+3 +-+
+--R ((21a d - 33a b c d )x + (21a c d - 33a b c d)x)\|a \|d \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 3 2 2 2 4+-+3 4+-+3 +-+
+--R ((- 42a d + 66a b c d )x + (- 42a c d + 66a b c d)x)\|a \|d \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 3 2 2 2 4+-+3 4+-+3 +-+
+--R ((- 42a d + 66a b c d )x + (- 42a c d + 66a b c d)x)\|a \|d \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 3 2 3 4+-+3 4+-+3 +-+ \|2 \|b \|x + \|a
+--R (- 24b c d x - 24b c x)\|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 3 2 3 4+-+3 4+-+3 +-+ \|2 \|b \|x - \|a
+--R (- 24b c d x - 24b c x)\|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 28a d + 44a b c d - 16b c d)x - 16a c d + 32a b c d - 16b c )
+--R *
+--R +-+4+-+3 4+-+3
+--R \|2 \|a \|c
+--R /
+--R 3 2 3 2 3 2 2 4 3
+--R (24a c d - 48a b c d + 24a b c d)x
+--R +
+--R 3 3 2 2 4 2 5
+--R (24a c d - 48a b c d + 24a b c )x
+--R *
+--R +-+4+-+3 4+-+3 +-+
+--R \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1282
+
+--S 1283 of 1475
+--a0:=integrate(t0,x)
+--E 1283
+
+--S 1284 of 1475
+--m0:=a0-r0
+--E 1284
+
+--S 1285 of 1475
+--d0:=D(m0,x)
+--E 1285
+
+)clear all
+
+--S 1286 of 1475
+t0:=1/(x^(7/2)*(a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------------
+--R 2 9 2 7 2 5 2 3 +-+
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|x
+--R Type: Expression(Integer)
+--E 1286
+
+--S 1287 of 1475
+r0:=1/10*(-4*b*c+9*a*d)/(a*c^2*(b*c-a*d)*x^(5/2))-1/2*d/(c*(b*c-a*d)*_
+ x^(5/2)*(c+d*x^2))-b^(13/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(9/4)*(b*c-a*d)^2*sqrt(2))+b^(13/4)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*(b*c-a*d)^2*sqrt(2))+1/4*_
+ d^(9/4)*(13*b*c-9*a*d)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(13/4)*(b*c-a*d)^2*sqrt(2))-1/4*d^(9/4)*(13*b*c-9*a*d)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(13/4)*(b*c-a*d)^2*_
+ sqrt(2))+1/2*b^(13/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(9/4)*(b*c-a*d)^2*sqrt(2))-1/2*b^(13/4)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*_
+ (b*c-a*d)^2*sqrt(2))-1/8*d^(9/4)*(13*b*c-9*a*d)*log(sqrt(c)+_
+ x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(13/4)*(b*c-_
+ a*d)^2*sqrt(2))+1/8*d^(9/4)*(13*b*c-9*a*d)*log(sqrt(c)+_
+ x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(13/4)*(b*c-a*d)^2*_
+ sqrt(2))+1/2*(4*b^2*c^2+4*a*b*c*d-9*a^2*d^2)/(a^2*c^3*_
+ (b*c-a*d)*sqrt(x))
+--R
+--R
+--R (2)
+--R 3 4 2 3 4 3 3 2 2 2 2 4+-+4+-+ +-+
+--R ((- 45a d + 65a b c d )x + (- 45a c d + 65a b c d )x )\|a \|d \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 3 4 3 4 2 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 20b c d x - 20b c x )\|b \|c \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 4 3 4 2 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (20b c d x + 20b c x )\|b \|c \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 4 2 3 4 3 3 2 2 2 2 4+-+4+-+ +-+
+--R ((45a d - 65a b c d )x + (45a c d - 65a b c d )x )\|a \|d \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 4 2 3 4 3 3 2 2 2 2 4+-+4+-+ +-+
+--R ((90a d - 130a b c d )x + (90a c d - 130a b c d )x )\|a \|d \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 4 2 3 4 3 3 2 2 2 2 4+-+4+-+ +-+
+--R ((90a d - 130a b c d )x + (90a c d - 130a b c d )x )\|a \|d \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 4 3 4 2 4+-+4+-+ +-+ \|2 \|b \|x + \|a
+--R (40b c d x + 40b c x )\|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 4 3 4 2 4+-+4+-+ +-+ \|2 \|b \|x - \|a
+--R (40b c d x + 40b c x )\|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 4 2 3 3 3 4
+--R (180a d - 260a b c d + 80b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (144a c d - 208a b c d - 16a b c d + 80b c )x - 16a c d
+--R +
+--R 2 3 2 4
+--R 32a b c d - 16a b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R /
+--R 4 3 3 3 4 2 2 2 5 4
+--R (40a c d - 80a b c d + 40a b c d)x
+--R +
+--R 4 4 2 3 5 2 2 6 2
+--R (40a c d - 80a b c d + 40a b c )x
+--R *
+--R +-+4+-+4+-+ +-+
+--R \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1287
+
+--S 1288 of 1475
+--a0:=integrate(t0,x)
+--E 1288
+
+--S 1289 of 1475
+--m0:=a0-r0
+--E 1289
+
+--S 1290 of 1475
+--d0:=D(m0,x)
+--E 1290
+
+)clear all
+
+--S 1291 of 1475
+t0:=x^(7/2)/((a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 3 +-+
+--R x \|x
+--R -----------------------------------------------------------------------------
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c
+--R Type: Expression(Integer)
+--E 1291
+
+--S 1292 of 1475
+r0:=-a^(5/4)*b^(3/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ ((b*c-a*d)^3*sqrt(2))+a^(5/4)*b^(3/4)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/((b*c-a*d)^3*sqrt(2))-1/32*(3*b^2*c^2-30*a*b*_
+ c*d-5*a^2*d^2)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(3/4)*_
+ d^(5/4)*(b*c-a*d)^3*sqrt(2))+1/32*(3*b^2*c^2-30*a*b*c*d-5*a^2*_
+ d^2)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(3/4)*d^(5/4)*_
+ (b*c-a*d)^3*sqrt(2))-1/2*a^(5/4)*b^(3/4)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/((b*c-a*d)^3*sqrt(2))+1/2*_
+ a^(5/4)*b^(3/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/((b*c-a*d)^3*sqrt(2))-1/64*(3*b^2*c^2-30*a*b*c*d-_
+ 5*a^2*d^2)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(3/4)*d^(5/4)*(b*c-a*d)^3*sqrt(2))+1/64*(3*b^2*c^2-_
+ 30*a*b*c*d-5*a^2*d^2)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(c^(3/4)*d^(5/4)*(b*c-a*d)^3*sqrt(2))-1/4*c*_
+ sqrt(x)/(d*(b*c-a*d)*(c+d*x^2)^2)+1/16*(b*c-9*a*d)*sqrt(x)/_
+ (d*(b*c-a*d)^2*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (5a d + 30a b c d - 3b c d )x + (10a c d + 60a b c d - 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 5a c d + 30a b c d - 3b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 4 2 2 2 4+-+4+-+3 4+-+3 4+-+
+--R (- 32a d x - 64a c d x - 32a c d)\|a \|b \|c \|d
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 4 2 2 2 4+-+4+-+3 4+-+3 4+-+
+--R (32a d x + 64a c d x + 32a c d)\|a \|b \|c \|d
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 5a d - 30a b c d + 3b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 10a c d - 60a b c d + 6b c d)x - 5a c d - 30a b c d + 3b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (10a d + 60a b c d - 6b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (20a c d + 120a b c d - 12b c d)x + 10a c d + 60a b c d - 6b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 4
+--R (10a d + 60a b c d - 6b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (20a c d + 120a b c d - 12b c d)x + 10a c d + 60a b c d - 6b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 4 2 2 2 4+-+4+-+3 4+-+3 4+-+
+--R (- 64a d x - 128a c d x - 64a c d)\|a \|b \|c \|d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 4 2 2 2 4+-+4+-+3 4+-+3 4+-+
+--R (- 64a d x - 128a c d x - 64a c d)\|a \|b \|c \|d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((- 36a d + 40a b c d - 4b c d)x - 20a c d + 8a b c d + 12b c )\|2
+--R *
+--R 4+-+3 4+-+ +-+
+--R \|c \|d \|x
+--R /
+--R 3 6 2 5 2 2 4 3 3 3 4
+--R (64a d - 192a b c d + 192a b c d - 64b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 2 3 2 4
+--R (128a c d - 384a b c d + 384a b c d - 128b c d )x + 64a c d
+--R +
+--R 2 3 3 2 4 2 3 5
+--R - 192a b c d + 192a b c d - 64b c d
+--R *
+--R +-+4+-+3 4+-+
+--R \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1292
+
+--S 1293 of 1475
+--a0:=integrate(t0,x)
+--E 1293
+
+--S 1294 of 1475
+--m0:=a0-r0
+--E 1294
+
+--S 1295 of 1475
+--d0:=D(m0,x)
+--E 1295
+
+)clear all
+
+--S 1296 of 1475
+t0:=x^(5/2)/((a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 2 +-+
+--R x \|x
+--R -----------------------------------------------------------------------------
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c
+--R Type: Expression(Integer)
+--E 1296
+
+--S 1297 of 1475
+r0:=1/4*x^(3/2)/((b*c-a*d)*(c+d*x^2)^2)+1/16*(5*b*c+3*a*d)*x^(3/2)/_
+ (c*(b*c-a*d)^2*(c+d*x^2))+a^(3/4)*b^(5/4)*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/((b*c-a*d)^3*sqrt(2))-a^(3/4)*b^(5/4)*atan(1+_
+ b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/((b*c-a*d)^3*sqrt(2))-1/32*(5*_
+ b^2*c^2+30*a*b*c*d-3*a^2*d^2)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/_
+ c^(1/4))/(c^(5/4)*d^(3/4)*(b*c-a*d)^3*sqrt(2))+1/32*(5*b^2*c^2+_
+ 30*a*b*c*d-3*a^2*d^2)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(5/4)*d^(3/4)*(b*c-a*d)^3*sqrt(2))-1/2*a^(3/4)*b^(5/4)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/((b*c-_
+ a*d)^3*sqrt(2))+1/2*a^(3/4)*b^(5/4)*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/((b*c-a*d)^3*sqrt(2))+1/64*_
+ (5*b^2*c^2+30*a*b*c*d-3*a^2*d^2)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(5/4)*d^(3/4)*(b*c-a*d)^3*sqrt(2))-_
+ 1/64*(5*b^2*c^2+30*a*b*c*d-3*a^2*d^2)*log(sqrt(c)+x*sqrt(d)+_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(5/4)*d^(3/4)*(b*c-a*d)^3*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (- 3a d + 30a b c d + 5b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 6a c d + 60a b c d + 10b c d)x - 3a c d + 30a b c d + 5b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 2 2 3 4+-+3 4+-+4+-+4+-+3
+--R (- 32b c d x - 64b c d x - 32b c )\|a \|b \|c \|d
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 2 3 4+-+3 4+-+4+-+4+-+3
+--R (32b c d x + 64b c d x + 32b c )\|a \|b \|c \|d
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d - 30a b c d - 5b c d )x + (6a c d - 60a b c d - 10b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d - 30a b c d - 5b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (6a d - 60a b c d - 10b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (12a c d - 120a b c d - 20b c d)x + 6a c d - 60a b c d - 10b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 4
+--R (6a d - 60a b c d - 10b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (12a c d - 120a b c d - 20b c d)x + 6a c d - 60a b c d - 10b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 2 2 3 4+-+3 4+-+4+-+4+-+3
+--R (64b c d x + 128b c d x + 64b c )\|a \|b \|c \|d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 3 4+-+3 4+-+4+-+4+-+3
+--R (64b c d x + 128b c d x + 64b c )\|a \|b \|c \|d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((12a d + 8a b c d - 20b c d)x + (- 4a c d + 40a b c d - 36b c )x)
+--R *
+--R +-+4+-+4+-+3 +-+
+--R \|2 \|c \|d \|x
+--R /
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (64a c d - 192a b c d + 192a b c d - 64b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2 3 3 3
+--R (128a c d - 384a b c d + 384a b c d - 128b c d)x + 64a c d
+--R +
+--R 2 4 2 2 5 3 6
+--R - 192a b c d + 192a b c d - 64b c
+--R *
+--R +-+4+-+4+-+3
+--R \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1297
+
+--S 1298 of 1475
+--a0:=integrate(t0,x)
+--E 1298
+
+--S 1299 of 1475
+--m0:=a0-r0
+--E 1299
+
+--S 1300 of 1475
+--d0:=D(m0,x)
+--E 1300
+
+)clear all
+
+--S 1301 of 1475
+t0:=x^(3/2)/((a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R +-+
+--R x\|x
+--R -----------------------------------------------------------------------------
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c
+--R Type: Expression(Integer)
+--E 1301
+
+--S 1302 of 1475
+r0:=a^(1/4)*b^(7/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/((b*c-a*d)^3*_
+ sqrt(2))-a^(1/4)*b^(7/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ ((b*c-a*d)^3*sqrt(2))-1/32*(21*b^2*c^2+14*a*b*c*d-3*a^2*d^2)*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(7/4)*d^(1/4)*(b*c-_
+ a*d)^3*sqrt(2))+1/32*(21*b^2*c^2+14*a*b*c*d-3*a^2*d^2)*atan(1+_
+ d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(7/4)*d^(1/4)*(b*c-a*d)^3*_
+ sqrt(2))+1/2*a^(1/4)*b^(7/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/((b*c-a*d)^3*sqrt(2))-1/2*a^(1/4)*_
+ b^(7/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ ((b*c-a*d)^3*sqrt(2))-1/64*(21*b^2*c^2+14*a*b*c*d-3*a^2*d^2)*_
+ log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(7/4)*_
+ d^(1/4)*(b*c-a*d)^3*sqrt(2))+1/64*(21*b^2*c^2+14*a*b*c*d-_
+ 3*a^2*d^2)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(7/4)*d^(1/4)*(b*c-a*d)^3*sqrt(2))+1/4*sqrt(x)/_
+ ((b*c-a*d)*(c+d*x^2)^2)+1/16*(7*b*c+a*d)*sqrt(x)/(c*(b*c-a*d)^2*_
+ (c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (3a d - 14a b c d - 21b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (6a c d - 28a b c d - 42b c d)x + 3a c d - 14a b c d - 21b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 2 2 3 4+-+4+-+3 4+-+3 4+-+
+--R (32b c d x + 64b c d x + 32b c )\|a \|b \|c \|d
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 2 3 4+-+4+-+3 4+-+3 4+-+
+--R (- 32b c d x - 64b c d x - 32b c )\|a \|b \|c \|d
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 3a d + 14a b c d + 21b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 6a c d + 28a b c d + 42b c d)x - 3a c d + 14a b c d + 21b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (6a d - 28a b c d - 42b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (12a c d - 56a b c d - 84b c d)x + 6a c d - 28a b c d - 42b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 4
+--R (6a d - 28a b c d - 42b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (12a c d - 56a b c d - 84b c d)x + 6a c d - 28a b c d - 42b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 2 2 3 4+-+4+-+3 4+-+3 4+-+
+--R (64b c d x + 128b c d x + 64b c )\|a \|b \|c \|d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 3 4+-+4+-+3 4+-+3 4+-+
+--R (64b c d x + 128b c d x + 64b c )\|a \|b \|c \|d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((4a d + 24a b c d - 28b c d)x - 12a c d + 56a b c d - 44b c )\|2
+--R *
+--R 4+-+3 4+-+ +-+
+--R \|c \|d \|x
+--R /
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (64a c d - 192a b c d + 192a b c d - 64b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2 3 3 3
+--R (128a c d - 384a b c d + 384a b c d - 128b c d)x + 64a c d
+--R +
+--R 2 4 2 2 5 3 6
+--R - 192a b c d + 192a b c d - 64b c
+--R *
+--R +-+4+-+3 4+-+
+--R \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1302
+
+--S 1303 of 1475
+--a0:=integrate(t0,x)
+--E 1303
+
+--S 1304 of 1475
+--m0:=a0-r0
+--E 1304
+
+--S 1305 of 1475
+--d0:=D(m0,x)
+--E 1305
+
+)clear all
+
+--S 1306 of 1475
+t0:=sqrt(x)/((a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R +-+
+--R \|x
+--R -----------------------------------------------------------------------------
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c
+--R Type: Expression(Integer)
+--E 1306
+
+--S 1307 of 1475
+r0:=-1/4*d*x^(3/2)/(c*(b*c-a*d)*(c+d*x^2)^2)-1/16*d*(13*b*c-5*a*d)*_
+ x^(3/2)/(c^2*(b*c-a*d)^2*(c+d*x^2))-b^(9/4)*atan(1-b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*(b*c-a*d)^3*sqrt(2))+b^(9/4)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*(b*c-a*d)^3*_
+ sqrt(2))+1/32*d^(1/4)*(45*b^2*c^2-18*a*b*c*d+5*a^2*d^2)*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(9/4)*(b*c-a*d)^3*_
+ sqrt(2))-1/32*d^(1/4)*(45*b^2*c^2-18*a*b*c*d+5*a^2*d^2)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(9/4)*(b*c-a*d)^3*_
+ sqrt(2))+1/2*b^(9/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(1/4)*(b*c-a*d)^3*sqrt(2))-1/2*b^(9/4)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*_
+ (b*c-a*d)^3*sqrt(2))-1/64*d^(1/4)*(45*b^2*c^2-18*a*b*c*d+5*_
+ a^2*d^2)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(9/4)*(b*c-a*d)^3*sqrt(2))+1/64*d^(1/4)*(45*b^2*c^2-18*a*_
+ b*c*d+5*a^2*d^2)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(9/4)*(b*c-a*d)^3*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (- 5a d + 18a b c d - 45b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 10a c d + 36a b c d - 90b c d)x - 5a c d + 18a b c d - 45b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 4 2 3 2 2 4 4+-+4+-+
+--R (32b c d x + 64b c d x + 32b c )\|b \|c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 4 2 3 2 2 4 4+-+4+-+
+--R (- 32b c d x - 64b c d x - 32b c )\|b \|c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 3 2 2 2 4
+--R (5a d - 18a b c d + 45b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (10a c d - 36a b c d + 90b c d)x + 5a c d - 18a b c d + 45b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (10a d - 36a b c d + 90b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (20a c d - 72a b c d + 180b c d)x + 10a c d - 36a b c d + 90b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 4
+--R (10a d - 36a b c d + 90b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (20a c d - 72a b c d + 180b c d)x + 10a c d - 36a b c d + 90b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4 2 3 2 2 4 4+-+4+-+ \|2 \|b \|x + \|a
+--R (- 64b c d x - 128b c d x - 64b c )\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4 2 3 2 2 4 4+-+4+-+ \|2 \|b \|x - \|a
+--R (- 64b c d x - 128b c d x - 64b c )\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 3 2 2 2 3
+--R (20a d - 72a b c d + 52b c d )x
+--R +
+--R 2 3 2 2 2 3
+--R (36a c d - 104a b c d + 68b c d)x
+--R *
+--R +-+4+-+4+-+ +-+
+--R \|2 \|a \|c \|x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (64a c d - 192a b c d + 192a b c d - 64b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3
+--R (128a c d - 384a b c d + 384a b c d - 128b c d)x + 64a c d
+--R +
+--R 2 5 2 2 6 3 7
+--R - 192a b c d + 192a b c d - 64b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1307
+
+--S 1308 of 1475
+--a0:=integrate(t0,x)
+--E 1308
+
+--S 1309 of 1475
+--m0:=a0-r0
+--E 1309
+
+--S 1310 of 1475
+--d0:=D(m0,x)
+--E 1310
+
+)clear all
+
+--S 1311 of 1475
+t0:=1/((a+b*x^2)*(c+d*x^2)^3*sqrt(x))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 8 3 2 6 2 2 4 2 3 2
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3
+--R a c
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1311
+
+--S 1312 of 1475
+r0:=-b^(11/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*_
+ (b*c-a*d)^3*sqrt(2))+b^(11/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(3/4)*(b*c-a*d)^3*sqrt(2))+1/32*d^(3/4)*(77*b^2*_
+ c^2-66*a*b*c*d+21*a^2*d^2)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/_
+ c^(1/4))/(c^(11/4)*(b*c-a*d)^3*sqrt(2))-1/32*d^(3/4)*(77*b^2*_
+ c^2-66*a*b*c*d+21*a^2*d^2)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/_
+ c^(1/4))/(c^(11/4)*(b*c-a*d)^3*sqrt(2))-1/2*b^(11/4)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*_
+ (b*c-a*d)^3*sqrt(2))+1/2*b^(11/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*(b*c-a*d)^3*sqrt(2))+1/64*_
+ d^(3/4)*(77*b^2*c^2-66*a*b*c*d+21*a^2*d^2)*log(sqrt(c)+x*_
+ sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(11/4)*(b*c-_
+ a*d)^3*sqrt(2))-1/64*d^(3/4)*(77*b^2*c^2-66*a*b*c*d+21*_
+ a^2*d^2)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(11/4)*(b*c-a*d)^3*sqrt(2))-1/4*d*sqrt(x)/_
+ (c*(b*c-a*d)*(c+d*x^2)^2)-1/16*d*(15*b*c-7*a*d)*sqrt(x)/_
+ (c^2*(b*c-a*d)^2*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (21a d - 66a b c d + 77b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (42a c d - 132a b c d + 154b c d)x + 21a c d - 66a b c d + 77b c
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 4 2 3 2 2 4 4+-+3 4+-+3
+--R (- 32b c d x - 64b c d x - 32b c )\|b \|c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 4 2 3 2 2 4 4+-+3 4+-+3
+--R (32b c d x + 64b c d x + 32b c )\|b \|c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 21a d + 66a b c d - 77b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 42a c d + 132a b c d - 154b c d)x - 21a c d + 66a b c d - 77b c
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 4
+--R (42a d - 132a b c d + 154b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (84a c d - 264a b c d + 308b c d)x + 42a c d - 132a b c d + 154b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x + \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 3 2 2 2 4
+--R (42a d - 132a b c d + 154b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (84a c d - 264a b c d + 308b c d)x + 42a c d - 132a b c d + 154b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x - \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4 2 3 2 2 4 4+-+3 4+-+3 \|2 \|b \|x + \|a
+--R (- 64b c d x - 128b c d x - 64b c )\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4 2 3 2 2 4 4+-+3 4+-+3 \|2 \|b \|x - \|a
+--R (- 64b c d x - 128b c d x - 64b c )\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 3 2 2 2 2 2 3 2 2 2 3
+--R ((28a d - 88a b c d + 60b c d )x + 44a c d - 120a b c d + 76b c d)
+--R *
+--R +-+4+-+3 4+-+3 +-+
+--R \|2 \|a \|c \|x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (64a c d - 192a b c d + 192a b c d - 64b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3
+--R (128a c d - 384a b c d + 384a b c d - 128b c d)x + 64a c d
+--R +
+--R 2 5 2 2 6 3 7
+--R - 192a b c d + 192a b c d - 64b c
+--R *
+--R +-+4+-+3 4+-+3
+--R \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1312
+
+--S 1313 of 1475
+--a0:=integrate(t0,x)
+--E 1313
+
+--S 1314 of 1475
+--m0:=a0-r0
+--E 1314
+
+--S 1315 of 1475
+--d0:=D(m0,x)
+--E 1315
+
+)clear all
+
+--S 1316 of 1475
+t0:=1/(x^(3/2)*(a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 9 3 2 7 2 2 5 2 3 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3
+--R a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1316
+
+--S 1317 of 1475
+r0:=b^(13/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*_
+ (b*c-a*d)^3*sqrt(2))-b^(13/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(5/4)*(b*c-a*d)^3*sqrt(2))-1/32*d^(5/4)*(117*b^2*_
+ c^2-130*a*b*c*d+45*a^2*d^2)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/_
+ c^(1/4))/(c^(13/4)*(b*c-a*d)^3*sqrt(2))+1/32*d^(5/4)*(117*b^2*_
+ c^2-130*a*b*c*d+45*a^2*d^2)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/_
+ c^(1/4))/(c^(13/4)*(b*c-a*d)^3*sqrt(2))-1/2*b^(13/4)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*_
+ (b*c-a*d)^3*sqrt(2))+1/2*b^(13/4)*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*(b*c-a*d)^3*sqrt(2))+_
+ 1/64*d^(5/4)*(117*b^2*c^2-130*a*b*c*d+45*a^2*d^2)*log(sqrt(c)+_
+ x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(13/4)*(b*c-_
+ a*d)^3*sqrt(2))-1/64*d^(5/4)*(117*b^2*c^2-130*a*b*c*d+45*_
+ a^2*d^2)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(13/4)*(b*c-a*d)^3*sqrt(2))+1/16*(-32*b^2*c^2+_
+ 85*a*b*c*d-45*a^2*d^2)/(a*c^3*(b*c-a*d)^2*sqrt(x))-_
+ 1/4*d/(c*(b*c-a*d)*(c+d*x^2)^2*sqrt(x))-1/16*d*(17*b*c-9*a*d)/_
+ (c^2*(b*c-a*d)^2*(c+d*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 3 5 2 4 2 2 3 4
+--R (45a d - 130a b c d + 117a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 2 3 2 3 2 3 2
+--R (90a c d - 260a b c d + 234a b c d )x + 45a c d - 130a b c d
+--R +
+--R 2 4
+--R 117a b c d
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 3 2 4 3 4 2 3 5 4+-+4+-+ +-+
+--R (- 32b c d x - 64b c d x - 32b c )\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 4 3 4 2 3 5 4+-+4+-+ +-+
+--R (32b c d x + 64b c d x + 32b c )\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 5 2 4 2 2 3 4
+--R (- 45a d + 130a b c d - 117a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 2 3 2 3 2 3 2
+--R (- 90a c d + 260a b c d - 234a b c d )x - 45a c d + 130a b c d
+--R +
+--R 2 4
+--R - 117a b c d
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 5 2 4 2 2 3 4
+--R (- 90a d + 260a b c d - 234a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 2 3 2 3 2 3 2
+--R (- 180a c d + 520a b c d - 468a b c d )x - 90a c d + 260a b c d
+--R +
+--R 2 4
+--R - 234a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x + \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 5 2 4 2 2 3 4
+--R (- 90a d + 260a b c d - 234a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 2 3 2 3 2 3 2
+--R (- 180a c d + 520a b c d - 468a b c d )x - 90a c d + 260a b c d
+--R +
+--R 2 4
+--R - 234a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x - \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 4 3 4 2 3 5 4+-+4+-+ +-+ \|2 \|b \|x + \|a
+--R (64b c d x + 128b c d x + 64b c )\|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 4 3 4 2 3 5 4+-+4+-+ +-+ \|2 \|b \|x - \|a
+--R (64b c d x + 128b c d x + 64b c )\|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 180a d + 520a b c d - 468a b c d + 128b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 324a c d + 936a b c d - 868a b c d + 256b c d)x - 128a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 384a b c d - 384a b c d + 128b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R /
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2 4
+--R (64a c d - 192a b c d + 192a b c d - 64a b c d )x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7 2 4 5 3
+--R (128a c d - 384a b c d + 384a b c d - 128a b c d)x + 64a c d
+--R +
+--R 3 6 2 2 2 7 3 8
+--R - 192a b c d + 192a b c d - 64a b c
+--R *
+--R +-+4+-+4+-+ +-+
+--R \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1317
+
+--S 1318 of 1475
+--a0:=integrate(t0,x)
+--E 1318
+
+--S 1319 of 1475
+--m0:=a0-r0
+--E 1319
+
+--S 1320 of 1475
+--d0:=D(m0,x)
+--E 1320
+
+)clear all
+
+--S 1321 of 1475
+t0:=1/(x^(5/2)*(a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 10 3 2 8 2 2 6 2 3 4
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3 2
+--R a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1321
+
+--S 1322 of 1475
+r0:=1/48*(-32*b^2*c^2+133*a*b*c*d-77*a^2*d^2)/(a*c^3*(b*c-a*d)^2*_
+ x^(3/2))-1/4*d/(c*(b*c-a*d)*x^(3/2)*(c+d*x^2)^2)-1/16*d*(19*b*_
+ c-11*a*d)/(c^2*(b*c-a*d)^2*x^(3/2)*(c+d*x^2))+b^(15/4)*atan(1-_
+ b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*(b*c-a*d)^3*sqrt(2))-_
+ b^(15/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*(b*c-_
+ a*d)^3*sqrt(2))-1/32*d^(7/4)*(165*b^2*c^2-210*a*b*c*d+77*_
+ a^2*d^2)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(15/4)*_
+ (b*c-a*d)^3*sqrt(2))+1/32*d^(7/4)*(165*b^2*c^2-210*a*b*c*d+77*_
+ a^2*d^2)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(15/4)*(b*_
+ c-a*d)^3*sqrt(2))+1/2*b^(15/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*(b*c-a*d)^3*sqrt(2))-1/2*_
+ b^(15/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(7/4)*(b*c-a*d)^3*sqrt(2))-1/64*d^(7/4)*(165*b^2*c^2-210*_
+ a*b*c*d+77*a^2*d^2)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(c^(15/4)*(b*c-a*d)^3*sqrt(2))+1/64*d^(7/4)*_
+ (165*b^2*c^2-210*a*b*c*d+77*a^2*d^2)*log(sqrt(c)+x*sqrt(d)+_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(15/4)*(b*c-a*d)^3*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 5 2 4 2 2 3 5
+--R (- 231a d + 630a b c d - 495a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3
+--R (- 462a c d + 1260a b c d - 990a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4
+--R (- 231a c d + 630a b c d - 495a b c d)x
+--R *
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 3 2 5 3 4 3 3 5 4+-+3 4+-+3 +-+
+--R (96b c d x + 192b c d x + 96b c x)\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 5 3 4 3 3 5 4+-+3 4+-+3 +-+
+--R (- 96b c d x - 192b c d x - 96b c x)\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 5 2 4 2 2 3 5
+--R (231a d - 630a b c d + 495a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3
+--R (462a c d - 1260a b c d + 990a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4
+--R (231a c d - 630a b c d + 495a b c d)x
+--R *
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 5 2 4 2 2 3 5
+--R (- 462a d + 1260a b c d - 990a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3
+--R (- 924a c d + 2520a b c d - 1980a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4
+--R (- 462a c d + 1260a b c d - 990a b c d)x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|d \|x + \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 5 2 4 2 2 3 5
+--R (- 462a d + 1260a b c d - 990a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3
+--R (- 924a c d + 2520a b c d - 1980a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4
+--R (- 462a c d + 1260a b c d - 990a b c d)x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|d \|x - \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 3 2 5 3 4 3 3 5 4+-+3 4+-+3 +-+
+--R (192b c d x + 384b c d x + 192b c x)\|b \|c \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 5 3 4 3 3 5 4+-+3 4+-+3 +-+
+--R (192b c d x + 384b c d x + 192b c x)\|b \|c \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 308a d + 840a b c d - 660a b c d + 128b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 484a c d + 1320a b c d - 1092a b c d + 256b c d)x - 128a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 384a b c d - 384a b c d + 128b c
+--R *
+--R +-+4+-+3 4+-+3
+--R \|2 \|a \|c
+--R /
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2 5
+--R (192a c d - 576a b c d + 576a b c d - 192a b c d )x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7 3
+--R (384a c d - 1152a b c d + 1152a b c d - 384a b c d)x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8
+--R (192a c d - 576a b c d + 576a b c d - 192a b c )x
+--R *
+--R +-+4+-+3 4+-+3 +-+
+--R \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1322
+
+--S 1323 of 1475
+--a0:=integrate(t0,x)
+--E 1323
+
+--S 1324 of 1475
+--m0:=a0-r0
+--E 1324
+
+--S 1325 of 1475
+--d0:=D(m0,x)
+--E 1325
+
+)clear all
+
+--S 1326 of 1475
+t0:=1/(x^(7/2)*(a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 11 3 2 9 2 2 7 2 3 5
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3 3
+--R a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1326
+
+--S 1327 of 1475
+r0:=1/80*(-32*b^2*c^2+189*a*b*c*d-117*a^2*d^2)/(a*c^3*(b*c-a*d)^2*_
+ x^(5/2))-1/4*d/(c*(b*c-a*d)*x^(5/2)*(c+d*x^2)^2)-1/16*d*(21*b*_
+ c-13*a*d)/(c^2*(b*c-a*d)^2*x^(5/2)*(c+d*x^2))-b^(17/4)*atan(1-_
+ b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*(b*c-a*d)^3*sqrt(2))+_
+ b^(17/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*(b*c-_
+ a*d)^3*sqrt(2))+1/32*d^(9/4)*(221*b^2*c^2-306*a*b*c*d+117*_
+ a^2*d^2)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(17/4)*_
+ (b*c-a*d)^3*sqrt(2))-1/32*d^(9/4)*(221*b^2*c^2-306*a*b*c*d+_
+ 117*a^2*d^2)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(17/4)*_
+ (b*c-a*d)^3*sqrt(2))+1/2*b^(17/4)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*(b*c-a*d)^3*sqrt(2))-_
+ 1/2*b^(17/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(9/4)*(b*c-a*d)^3*sqrt(2))-1/64*d^(9/4)*(221*b^2*_
+ c^2-306*a*b*c*d+117*a^2*d^2)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(17/4)*(b*c-a*d)^3*sqrt(2))+1/64*_
+ d^(9/4)*(221*b^2*c^2-306*a*b*c*d+117*a^2*d^2)*log(sqrt(c)+x*_
+ sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(17/4)*(b*c-a*d)^3*_
+ sqrt(2))+1/16*(32*b^3*c^3+32*a*b^2*c^2*d-189*a^2*b*c*d^2+117*_
+ a^3*d^3)/(a^2*c^4*(b*c-a*d)^2*sqrt(x))
+--R
+--R
+--R (2)
+--R 4 6 3 5 2 2 2 4 6
+--R (- 585a d + 1530a b c d - 1105a b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 4
+--R (- 1170a c d + 3060a b c d - 2210a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 2
+--R (- 585a c d + 1530a b c d - 1105a b c d )x
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4 4 2 6 4 5 4 4 6 2 4+-+4+-+ +-+
+--R (160b c d x + 320b c d x + 160b c x )\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 4 2 6 4 5 4 4 6 2 4+-+4+-+ +-+
+--R (- 160b c d x - 320b c d x - 160b c x )\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 6 3 5 2 2 2 4 6
+--R (585a d - 1530a b c d + 1105a b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 4
+--R (1170a c d - 3060a b c d + 2210a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 2
+--R (585a c d - 1530a b c d + 1105a b c d )x
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4 6 3 5 2 2 2 4 6
+--R (1170a d - 3060a b c d + 2210a b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 4
+--R (2340a c d - 6120a b c d + 4420a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 2
+--R (1170a c d - 3060a b c d + 2210a b c d )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x + \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 4 6 3 5 2 2 2 4 6
+--R (1170a d - 3060a b c d + 2210a b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 4
+--R (2340a c d - 6120a b c d + 4420a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 2
+--R (1170a c d - 3060a b c d + 2210a b c d )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x - \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 4 4 2 6 4 5 4 4 6 2 4+-+4+-+ +-+
+--R (- 320b c d x - 640b c d x - 320b c x )\|b \|c \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 4 2 6 4 5 4 4 6 2 4+-+4+-+ +-+
+--R (- 320b c d x - 640b c d x - 320b c x )\|b \|c \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 6 3 5 2 2 2 4 4 4 2 6
+--R (2340a d - 6120a b c d + 4420a b c d - 640b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2
+--R 4212a c d - 11016a b c d + 7956a b c d + 128a b c d
+--R +
+--R 4 5
+--R - 1280b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 2
+--R (1664a c d - 4352a b c d + 3072a b c d + 256a b c d - 640b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6
+--R - 128a c d + 384a b c d - 384a b c d + 128a b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R /
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 6
+--R (320a c d - 960a b c d + 960a b c d - 320a b c d )x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8 4
+--R (640a c d - 1920a b c d + 1920a b c d - 640a b c d)x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9 2
+--R (320a c d - 960a b c d + 960a b c d - 320a b c )x
+--R *
+--R +-+4+-+4+-+ +-+
+--R \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1327
+
+--S 1328 of 1475
+--a0:=integrate(t0,x)
+--E 1328
+
+--S 1329 of 1475
+--m0:=a0-r0
+--E 1329
+
+--S 1330 of 1475
+--d0:=D(m0,x)
+--E 1330
+
+)clear all
+
+--S 1331 of 1475
+t0:=x^(7/2)*sqrt(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 3 +-+ | 2
+--R x \|x \|d x + c
+--R (1) -----------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1331
+
+--S 1332 of 1475
+--r0:=2/7*x^(5/2)*sqrt(c+d*x^2)/b+2/21*(2*b*c-7*a*d)*sqrt(x)*_
+-- sqrt(c+d*x^2)/(b^2*d)+2/21*c^(1/4)*(2*b^2*c^2+14*a*b*c*d-21*_
+-- a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^3*(-d)^(5/4)*sqrt(c+d*x^2))+a*(b*c-a*d)*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^3*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+a*(b*c-a*d)*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^3*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1332
+
+--S 1333 of 1475
+--a0:=integrate(t0,x)
+--E 1333
+
+--S 1334 of 1475
+--m0:=a0-r0
+--E 1334
+
+--S 1335 of 1475
+--d0:=D(m0,x)
+--E 1335
+
+)clear all
+
+--S 1336 of 1475
+t0:=x^(5/2)*sqrt(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 +-+ | 2
+--R x \|x \|d x + c
+--R (1) -----------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1336
+
+--S 1337 of 1475
+--r0:=2/5*x^(3/2)*sqrt(c+d*x^2)/b+2/5*c^(3/4)*(2*b*c-5*a*d)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^2*(-d)^(3/4)*sqrt(c+d*x^2))-2/5*c^(3/4)*(2*b*c-5*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(b^2*(-d)^(3/4)*sqrt(c+d*x^2))-(b*c-a*d)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(-a)*sqrt((c+d*x^2)/c)/_
+-- (b^(5/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+(b*c-a*d)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(-a)*sqrt((c+d*x^2)/c)/_
+-- (b^(5/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1337
+
+--S 1338 of 1475
+--a0:=integrate(t0,x)
+--E 1338
+
+--S 1339 of 1475
+--m0:=a0-r0
+--E 1339
+
+--S 1340 of 1475
+--d0:=D(m0,x)
+--E 1340
+
+)clear all
+
+--S 1341 of 1475
+t0:=x^(3/2)*sqrt(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R x\|x \|d x + c
+--R (1) ----------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1341
+
+--S 1342 of 1475
+--r0:=2/3*sqrt(x)*sqrt(c+d*x^2)/b+2/3*c^(1/4)*(2*b*c-3*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(b^2*(-d)^(1/4)*sqrt(c+d*x^2))-(b*c-a*d)*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^2*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-(b*c-a*d)*elliptic_pi(sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^2*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 1342
+
+--S 1343 of 1475
+--a0:=integrate(t0,x)
+--E 1343
+
+--S 1344 of 1475
+--m0:=a0-r0
+--E 1344
+
+--S 1345 of 1475
+--d0:=D(m0,x)
+--E 1345
+
+)clear all
+
+--S 1346 of 1475
+t0:=sqrt(x)*sqrt(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R \|x \|d x + c
+--R (1) ---------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1346
+
+--S 1347 of 1475
+--r0:=-2*c^(3/4)*(-d)^(1/4)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/_
+-- c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(b*sqrt(c+d*x^2))+2*c^(3/4)*_
+-- (-d)^(1/4)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b*sqrt(c+d*x^2))-(b*c-a*d)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^(3/2)*_
+-- sqrt(-a)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+(b*c-a*d)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^(3/2)*_
+-- sqrt(-a)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1347
+
+--S 1348 of 1475
+--a0:=integrate(t0,x)
+--E 1348
+
+--S 1349 of 1475
+--m0:=a0-r0
+--E 1349
+
+--S 1350 of 1475
+--d0:=D(m0,x)
+--E 1350
+
+)clear all
+
+--S 1351 of 1475
+t0:=sqrt(c+d*x^2)/((a+b*x^2)*sqrt(x))
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) --------------
+--R 2 +-+
+--R (b x + a)\|x
+--R Type: Expression(Integer)
+--E 1351
+
+--S 1352 of 1475
+--r0:=-2*c^(1/4)*(-d)^(3/4)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/_
+-- c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(b*sqrt(c+d*x^2))+(b*c-a*d)*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*b*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+(b*c-a*d)*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (a*b*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1352
+
+--S 1353 of 1475
+--a0:=integrate(t0,x)
+--E 1353
+
+--S 1354 of 1475
+--m0:=a0-r0
+--E 1354
+
+--S 1355 of 1475
+--d0:=D(m0,x)
+--E 1355
+
+)clear all
+
+--S 1356 of 1475
+t0:=sqrt(c+d*x^2)/(x^(3/2)*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) ----------------
+--R 3 +-+
+--R (b x + a x)\|x
+--R Type: Expression(Integer)
+--E 1356
+
+--S 1357 of 1475
+--r0:=-2*sqrt(c+d*x^2)/(a*sqrt(x))-2*c^(3/4)*(-d)^(1/4)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(a*sqrt(c+d*x^2))+2*c^(3/4)*(-d)^(1/4)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(a*sqrt(c+d*x^2))-(b*c-a*d)*elliptic_pi(-sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(3/2)*sqrt(b)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+(b*c-a*d)*elliptic_pi(sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(3/2)*sqrt(b)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1357
+
+--S 1358 of 1475
+--a0:=integrate(t0,x)
+--E 1358
+
+--S 1359 of 1475
+--m0:=a0-r0
+--E 1359
+
+--S 1360 of 1475
+--d0:=D(m0,x)
+--E 1360
+
+)clear all
+
+--S 1361 of 1475
+t0:=sqrt(c+d*x^2)/(x^(5/2)*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) -----------------
+--R 4 2 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1361
+
+--S 1362 of 1475
+--r0:=-2/3*sqrt(c+d*x^2)/(a*x^(3/2))+2/3*c^(1/4)*(-d)^(3/4)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(a*sqrt(c+d*x^2))-(b*c-a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/_
+-- (sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- (b*c-a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (a^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1362
+
+--S 1363 of 1475
+--a0:=integrate(t0,x)
+--E 1363
+
+--S 1364 of 1475
+--m0:=a0-r0
+--E 1364
+
+--S 1365 of 1475
+--d0:=D(m0,x)
+--E 1365
+
+)clear all
+
+--S 1366 of 1475
+t0:=sqrt(c+d*x^2)/(x^(7/2)*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) -----------------
+--R 5 3 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1366
+
+--S 1367 of 1475
+--r0:=-2/5*sqrt(c+d*x^2)/(a*x^(5/2))+2/5*(5*b*c-2*a*d)*sqrt(c+d*x^2)/_
+-- (a^2*c*sqrt(x))+2/5*(-d)^(1/4)*(5*b*c-2*a*d)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(a^2*c^(1/4)*sqrt(c+d*x^2))-2/5*(-d)^(1/4)*(5*b*c-2*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(a^2*c^(1/4)*sqrt(c+d*x^2))-(b*c-a*d)*elliptic_pi(-sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt(b)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+(b*c-a*d)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(b)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(5/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1367
+
+--S 1368 of 1475
+--a0:=integrate(t0,x)
+--E 1368
+
+--S 1369 of 1475
+--m0:=a0-r0
+--E 1369
+
+--S 1370 of 1475
+--d0:=D(m0,x)
+--E 1370
+
+)clear all
+
+--S 1371 of 1475
+t0:=x^(7/2)*(c+d*x^2)^(3/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 5 3 +-+ | 2
+--R (d x + c x )\|x \|d x + c
+--R (1) ----------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1371
+
+--S 1372 of 1475
+--r0:=2/77*(13*b*c-11*a*d)*x^(5/2)*sqrt(c+d*x^2)/b^2+2/11*d*x^(9/2)*_
+-- sqrt(c+d*x^2)/b+2/231*(12*b^2*c^2-99*a*b*c*d+77*a^2*d^2)*sqrt(x)*_
+-- sqrt(c+d*x^2)/(b^3*d)+2/231*c^(1/4)*(12*b^3*c^3+132*a*b^2*c^2*d-_
+-- 385*a^2*b*c*d^2+231*a^3*d^3)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(b^4*(-d)^(5/4)*_
+-- sqrt(c+d*x^2))+a*(b*c-a*d)^2*elliptic_pi(-sqrt(-b)*sqrt(c)/_
+-- (sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^4*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+_
+-- a*(b*c-a*d)^2*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^4*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1372
+
+--S 1373 of 1475
+--a0:=integrate(t0,x)
+--E 1373
+
+--S 1374 of 1475
+--m0:=a0-r0
+--E 1374
+
+--S 1375 of 1475
+--d0:=D(m0,x)
+--E 1375
+
+)clear all
+
+--S 1376 of 1475
+t0:=x^(5/2)*(c+d*x^2)^(3/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 4 2 +-+ | 2
+--R (d x + c x )\|x \|d x + c
+--R (1) ----------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1376
+
+--S 1377 of 1475
+--r0:=2/45*(11*b*c-9*a*d)*x^(3/2)*sqrt(c+d*x^2)/b^2+2/9*d*x^(7/2)*_
+-- sqrt(c+d*x^2)/b+2/15*c^(3/4)*(4*b^2*c^2-21*a*b*c*d+15*a^2*d^2)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(b^3*(-d)^(3/4)*sqrt(c+d*x^2))-2/15*c^(3/4)*(4*b^2*c^2-21*a*_
+-- b*c*d+15*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^3*(-d)^(3/4)*sqrt(c+d*x^2))-(b*c-a*d)^2*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(-a)*sqrt((c+d*x^2)/c)/(b^(7/2)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+(b*c-a*d)^2*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(-a)*sqrt((c+d*x^2)/c)/(b^(7/2)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1377
+
+--S 1378 of 1475
+--a0:=integrate(t0,x)
+--E 1378
+
+--S 1379 of 1475
+--m0:=a0-r0
+--E 1379
+
+--S 1380 of 1475
+--d0:=D(m0,x)
+--E 1380
+
+)clear all
+
+--S 1381 of 1475
+t0:=x^(3/2)*(c+d*x^2)^(3/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 3 +-+ | 2
+--R (d x + c x)\|x \|d x + c
+--R (1) ---------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1381
+
+--S 1382 of 1475
+--r0:=2/7*d*x^(5/2)*sqrt(c+d*x^2)/b+2/21*(9*b*c-7*a*d)*sqrt(x)*_
+-- sqrt(c+d*x^2)/b^2+2/21*c^(1/4)*(12*b^2*c^2-35*a*b*c*d+21*a^2*_
+-- d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+_
+-- d*x^2)/c)/(b^3*(-d)^(1/4)*sqrt(c+d*x^2))-(b*c-a*d)^2*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^3*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-(b*c-a*d)^2*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^3*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1382
+
+--S 1383 of 1475
+--a0:=integrate(t0,x)
+--E 1383
+
+--S 1384 of 1475
+--m0:=a0-r0
+--E 1384
+
+--S 1385 of 1475
+--d0:=D(m0,x)
+--E 1385
+
+)clear all
+
+--S 1386 of 1475
+t0:=(c+d*x^2)^(3/2)*sqrt(x)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 +-+ | 2
+--R (d x + c)\|x \|d x + c
+--R (1) -------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1386
+
+--S 1387 of 1475
+--r0:=2/5*d*x^(3/2)*sqrt(c+d*x^2)/b-2/5*c^(3/4)*(-d)^(1/4)*(7*b*c-5*a*d)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(b^2*sqrt(c+d*x^2))+2/5*c^(3/4)*(-d)^(1/4)*(7*b*c-5*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(b^2*sqrt(c+d*x^2))-(b*c-a*d)^2*elliptic_pi(-sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^(5/2)*sqrt(-a)*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+(b*c-a*d)^2*elliptic_pi(sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^(5/2)*sqrt(-a)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 1387
+
+--S 1388 of 1475
+--a0:=integrate(t0,x)
+--E 1388
+
+--S 1389 of 1475
+--m0:=a0-r0
+--E 1389
+
+--S 1390 of 1475
+--d0:=D(m0,x)
+--E 1390
+
+)clear all
+
+--S 1391 of 1475
+t0:=(c+d*x^2)^(3/2)/((a+b*x^2)*sqrt(x))
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 2 +-+
+--R (b x + a)\|x
+--R Type: Expression(Integer)
+--E 1391
+
+--S 1392 of 1475
+--r0:=2/3*d*sqrt(x)*sqrt(c+d*x^2)/b-2/3*c^(1/4)*(-d)^(3/4)*(5*b*c-_
+-- 3*a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^2*sqrt(c+d*x^2))+(b*c-a*d)^2*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*b^2*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+(b*c-a*d)^2*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*b^2*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1392
+
+--S 1393 of 1475
+--a0:=integrate(t0,x)
+--E 1393
+
+--S 1394 of 1475
+--m0:=a0-r0
+--E 1394
+
+--S 1395 of 1475
+--d0:=D(m0,x)
+--E 1395
+
+)clear all
+
+--S 1396 of 1475
+t0:=(c+d*x^2)^(3/2)/(x^(3/2)*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 3 +-+
+--R (b x + a x)\|x
+--R Type: Expression(Integer)
+--E 1396
+
+--S 1397 of 1475
+--r0:=-2*c*sqrt(c+d*x^2)/(a*sqrt(x))-2*c^(3/4)*(-d)^(1/4)*(b*c+a*d)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (a*b*sqrt(c+d*x^2))+2*c^(3/4)*(-d)^(1/4)*(b*c+a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(a*b*sqrt(c+d*x^2))-(b*c-a*d)^2*elliptic_pi(-sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(3/2)*b^(3/2)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+(b*c-a*d)^2*elliptic_pi(sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(3/2)*b^(3/2)*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1397
+
+--S 1398 of 1475
+--a0:=integrate(t0,x)
+--E 1398
+
+--S 1399 of 1475
+--m0:=a0-r0
+--E 1399
+
+--S 1400 of 1475
+--d0:=D(m0,x)
+--E 1400
+
+)clear all
+
+--S 1401 of 1475
+t0:=(c+d*x^2)^(3/2)/(x^(5/2)*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 4 2 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1401
+
+--S 1402 of 1475
+--r0:=-2/3*c*sqrt(c+d*x^2)/(a*x^(3/2))+2/3*c^(1/4)*(-d)^(3/4)*_
+-- (b*c-3*a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a*b*sqrt(c+d*x^2))-(b*c-a*d)^2*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*b*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-(b*c-a*d)^2*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*b*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1402
+
+--S 1403 of 1475
+--a0:=integrate(t0,x)
+--E 1403
+
+--S 1404 of 1475
+--m0:=a0-r0
+--E 1404
+
+--S 1405 of 1475
+--d0:=D(m0,x)
+--E 1405
+
+)clear all
+
+--S 1406 of 1475
+t0:=(c+d*x^2)^(3/2)/(x^(7/2)*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 5 3 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1406
+
+--S 1407 of 1475
+--r0:=-2/5*c*sqrt(c+d*x^2)/(a*x^(5/2))+2/5*(5*b*c-7*a*d)*_
+-- sqrt(c+d*x^2)/(a^2*sqrt(x))+2/5*c^(3/4)*(-d)^(1/4)*(5*b*c-7*a*d)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(a^2*sqrt(c+d*x^2))-2/5*c^(3/4)*(-d)^(1/4)*(5*b*c-7*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(a^2*sqrt(c+d*x^2))-(b*c-a*d)^2*elliptic_pi(-sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),_
+-- -1)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*sqrt(b)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+(b*c-a*d)^2*elliptic_pi(sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*sqrt(b)*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1407
+
+--S 1408 of 1475
+--a0:=integrate(t0,x)
+--E 1408
+
+--S 1409 of 1475
+--m0:=a0-r0
+--E 1409
+
+--S 1410 of 1475
+--d0:=D(m0,x)
+--E 1410
+
+)clear all
+
+--S 1411 of 1475
+t0:=x^(7/2)*(c+d*x^2)^(5/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 7 5 2 3 +-+ | 2
+--R (d x + 2c d x + c x )\|x \|d x + c
+--R (1) --------------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1411
+
+--S 1412 of 1475
+--r0:=2/15*d*x^(9/2)*(c+d*x^2)^(3/2)/b+2/385*(69*b^2*c^2-120*a*b*c*d+_
+-- 55*a^2*d^2)*x^(5/2)*sqrt(c+d*x^2)/b^3+2/55*d*(7*b*c-5*a*d)*_
+-- x^(9/2)*sqrt(c+d*x^2)/b^2+2/231*(8*b^3*c^3-111*a*b^2*c^2*d+_
+-- 176*a^2*b*c*d^2-77*a^3*d^3)*sqrt(x)*sqrt(c+d*x^2)/(b^4*d)+_
+-- 2/231*c^(1/4)*(8*b^4*c^4+120*a*b^3*c^3*d-517*a^2*b^2*c^2*d^2+_
+-- 616*a^3*b*c*d^3-231*a^4*d^4)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(b^5*(-d)^(5/4)*_
+-- sqrt(c+d*x^2))+a*(b*c-a*d)^3*elliptic_pi(-sqrt(-b)*sqrt(c)/_
+-- (sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^5*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+_
+-- a*(b*c-a*d)^3*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^5*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1412
+
+--S 1413 of 1475
+--a0:=integrate(t0,x)
+--E 1413
+
+--S 1414 of 1475
+--m0:=a0-r0
+--E 1414
+
+--S 1415 of 1475
+--d0:=D(m0,x)
+--E 1415
+
+)clear all
+
+--S 1416 of 1475
+t0:=x^(5/2)*(c+d*x^2)^(5/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 6 4 2 2 +-+ | 2
+--R (d x + 2c d x + c x )\|x \|d x + c
+--R (1) --------------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1416
+
+--S 1417 of 1475
+--r0:=2/13*d*x^(7/2)*(c+d*x^2)^(3/2)/b+2/585*(155*b^2*c^2-260*a*b*c*d+_
+-- 117*a^2*d^2)*x^(3/2)*sqrt(c+d*x^2)/b^3+2/117*d*(19*b*c-13*a*d)*_
+-- x^(7/2)*sqrt(c+d*x^2)/b^2+2/195*c^(3/4)*(40*b^3*c^3-325*a*b^2*_
+-- c^2*d+468*a^2*b*c*d^2-195*a^3*d^3)*elliptic_e(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(b^4*(-d)^(3/4)*sqrt(c+_
+-- d*x^2))-2/195*c^(3/4)*(40*b^3*c^3-325*a*b^2*c^2*d+468*a^2*b*c*_
+-- d^2-195*a^3*d^3)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^4*(-d)^(3/4)*sqrt(c+d*x^2))-(b*c-a*d)^3*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(-a)*sqrt((c+d*x^2)/c)/(b^(9/2)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+(b*c-a*d)^3*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(-a)*sqrt((c+d*x^2)/c)/(b^(9/2)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1417
+
+--S 1418 of 1475
+--a0:=integrate(t0,x)
+--E 1418
+
+--S 1419 of 1475
+--m0:=a0-r0
+--E 1419
+
+--S 1420 of 1475
+--d0:=D(m0,x)
+--E 1420
+
+)clear all
+
+--S 1421 of 1475
+t0:=x^(3/2)*(c+d*x^2)^(5/2)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 5 3 2 +-+ | 2
+--R (d x + 2c d x + c x)\|x \|d x + c
+--R (1) -------------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1421
+
+--S 1422 of 1475
+--r0:=2/11*d*x^(5/2)*(c+d*x^2)^(3/2)/b+2/77*d*(17*b*c-11*a*d)*x^(5/2)*_
+-- sqrt(c+d*x^2)/b^2+2/231*(111*b^2*c^2-176*a*b*c*d+77*a^2*d^2)*_
+-- sqrt(x)*sqrt(c+d*x^2)/b^3+2/231*c^(1/4)*(120*b^3*c^3-517*a*b^2*_
+-- c^2*d+616*a^2*b*c*d^2-231*a^3*d^3)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(b^4*(-d)^(1/4)*sqrt(c+_
+-- d*x^2))-(b*c-a*d)^3*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*_
+-- x^2)/c)/(b^4*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-(b*c-a*d)^3*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^4*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 1422
+
+--S 1423 of 1475
+--a0:=integrate(t0,x)
+--E 1423
+
+--S 1424 of 1475
+--m0:=a0-r0
+--E 1424
+
+--S 1425 of 1475
+--d0:=D(m0,x)
+--E 1425
+
+)clear all
+
+--S 1426 of 1475
+t0:=(c+d*x^2)^(5/2)*sqrt(x)/(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 +-+ | 2
+--R (d x + 2c d x + c )\|x \|d x + c
+--R (1) ------------------------------------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 1426
+
+--S 1427 of 1475
+--r0:=2/9*d*x^(3/2)*(c+d*x^2)^(3/2)/b+2/15*d*(5*b*c-3*a*d)*x^(3/2)*_
+-- sqrt(c+d*x^2)/b^2-2/15*c^(3/4)*(-d)^(1/4)*(25*b^2*c^2-36*a*b*c*_
+-- d+15*a^2*d^2)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^3*sqrt(c+d*x^2))+2/15*c^(3/4)*(-d)^(1/4)*_
+-- (25*b^2*c^2-36*a*b*c*d+15*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(b^3*sqrt(c+d*x^2))-_
+-- (b*c-a*d)^3*elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^(7/2)*sqrt(-a)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+(b*c-_
+-- a*d)^3*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^(7/2)*sqrt(-a)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1427
+
+--S 1428 of 1475
+--a0:=integrate(t0,x)
+--E 1428
+
+--S 1429 of 1475
+--m0:=a0-r0
+--E 1429
+
+--S 1430 of 1475
+--d0:=D(m0,x)
+--E 1430
+
+)clear all
+
+--S 1431 of 1475
+t0:=(c+d*x^2)^(5/2)/((a+b*x^2)*sqrt(x))
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 2 +-+
+--R (b x + a)\|x
+--R Type: Expression(Integer)
+--E 1431
+
+--S 1432 of 1475
+--r0:=2/7*d*(c+d*x^2)^(3/2)*sqrt(x)/b+2/21*d*(13*b*c-7*a*d)*sqrt(x)*_
+-- sqrt(c+d*x^2)/b^2-2/21*c^(1/4)*(-d)^(3/4)*(47*b^2*c^2-56*a*b*c*d+_
+-- 21*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^3*sqrt(c+d*x^2))+(b*c-a*d)^3*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*b^3*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+(b*c-a*d)^3*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*b^3*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1432
+
+--S 1433 of 1475
+--a0:=integrate(t0,x)
+--E 1433
+
+--S 1434 of 1475
+--m0:=a0-r0
+--E 1434
+
+--S 1435 of 1475
+--d0:=D(m0,x)
+--E 1435
+
+)clear all
+
+--S 1436 of 1475
+t0:=(c+d*x^2)^(5/2)/(x^(3/2)*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 3 +-+
+--R (b x + a x)\|x
+--R Type: Expression(Integer)
+--E 1436
+
+--S 1437 of 1475
+--r0:=-2*c*(c+d*x^2)^(3/2)/(a*sqrt(x))+2/5*d*(5*b*c+a*d)*x^(3/2)*_
+-- sqrt(c+d*x^2)/(a*b)-2/5*c^(3/4)*(-d)^(1/4)*(5*b^2*c^2+12*a*b*c*d-_
+-- 5*a^2*d^2)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a*b^2*sqrt(c+d*x^2))+2/5*c^(3/4)*(-d)^(1/4)*_
+-- (5*b^2*c^2+12*a*b*c*d-5*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*b^2*sqrt(c+d*x^2))-_
+-- (b*c-a*d)^3*elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(3/2)*b^(5/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+_
+-- (b*c-a*d)^3*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(3/2)*b^(5/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1437
+
+--S 1438 of 1475
+--a0:=integrate(t0,x)
+--E 1438
+
+--S 1439 of 1475
+--m0:=a0-r0
+--E 1439
+
+--S 1440 of 1475
+--d0:=D(m0,x)
+--E 1440
+
+)clear all
+
+--S 1441 of 1475
+t0:=(c+d*x^2)^(5/2)/(x^(5/2)*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 4 2 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1441
+
+--S 1442 of 1475
+--r0:=-2/3*c*(c+d*x^2)^(3/2)/(a*x^(3/2))+2/3*d*(b*c+a*d)*sqrt(x)*_
+-- sqrt(c+d*x^2)/(a*b)+2/3*c^(1/4)*(-d)^(3/4)*(b^2*c^2-8*a*b*c*d+_
+-- 3*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a*b^2*sqrt(c+d*x^2))-(b*c-a*d)^3*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*b^2*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-(b*c-a*d)^3*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*b^2*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1442
+
+--S 1443 of 1475
+--a0:=integrate(t0,x)
+--E 1443
+
+--S 1444 of 1475
+--m0:=a0-r0
+--E 1444
+
+--S 1445 of 1475
+--d0:=D(m0,x)
+--E 1445
+
+)clear all
+
+--S 1446 of 1475
+t0:=(c+d*x^2)^(5/2)/(x^(7/2)*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 5 3 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1446
+
+--S 1447 of 1475
+--r0:=-2/5*c*(c+d*x^2)^(3/2)/(a*x^(5/2))+2/5*c*(5*b*c-11*a*d)*_
+-- sqrt(c+d*x^2)/(a^2*sqrt(x))+2/5*c^(3/4)*(-d)^(1/4)*(5*b^2*c^2-_
+-- 12*a*b*c*d-5*a^2*d^2)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/_
+-- c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a^2*b*sqrt(c+d*x^2))-2/5*_
+-- c^(3/4)*(-d)^(1/4)*(5*b^2*c^2-12*a*b*c*d-5*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(a^2*b*sqrt(c+d*x^2))-(b*c-a*d)^3*elliptic_pi(-sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*b^(3/2)*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+(b*c-a*d)^3*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*_
+-- b^(3/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1447
+
+--S 1448 of 1475
+--a0:=integrate(t0,x)
+--E 1448
+
+--S 1449 of 1475
+--m0:=a0-r0
+--E 1449
+
+--S 1450 of 1475
+--d0:=D(m0,x)
+--E 1450
+
+)clear all
+
+--S 1451 of 1475
+t0:=x^(7/2)/((a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 1451
+
+--S 1452 of 1475
+--r0:=2/3*sqrt(x)*sqrt(c+d*x^2)/(b*d)+2/3*c^(1/4)*(b*c+3*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(b^2*(-d)^(5/4)*sqrt(c+d*x^2))+a*elliptic_pi(-sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),_
+-- -1)*sqrt((c+d*x^2)/c)/(b^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+_
+-- a*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^2*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1452
+
+--S 1453 of 1475
+--a0:=integrate(t0,x)
+--E 1453
+
+--S 1454 of 1475
+--m0:=a0-r0
+--E 1454
+
+--S 1455 of 1475
+--d0:=D(m0,x)
+--E 1455
+
+)clear all
+
+--S 1456 of 1475
+t0:=x^(5/2)/((a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 1456
+
+--S 1457 of 1475
+--r0:=2*c^(3/4)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b*(-d)^(3/4)*sqrt(c+d*x^2))-2*c^(3/4)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/_
+-- c)/(b*(-d)^(3/4)*sqrt(c+d*x^2))-elliptic_pi(-sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt(-a)*sqrt((c+d*x^2)/c)/(b^(3/2)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(-a)*_
+-- sqrt((c+d*x^2)/c)/(b^(3/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1457
+
+--S 1458 of 1475
+--a0:=integrate(t0,x)
+--E 1458
+
+--S 1459 of 1475
+--m0:=a0-r0
+--E 1459
+
+--S 1460 of 1475
+--d0:=D(m0,x)
+--E 1460
+
+)clear all
+
+--S 1461 of 1475
+t0:=x^(3/2)/((a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 1461
+
+--S 1462 of 1475
+--r0:=2*c^(1/4)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b*(-d)^(1/4)*sqrt(c+d*x^2))-_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))-elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*_
+-- x^2)/c)/(b*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1462
+
+--S 1463 of 1475
+--a0:=integrate(t0,x)
+--E 1463
+
+--S 1464 of 1475
+--m0:=a0-r0
+--E 1464
+
+--S 1465 of 1475
+--d0:=D(m0,x)
+--E 1465
+
+)clear all
+
+--S 1466 of 1475
+t0:=sqrt(x)/((a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R +-+
+--R \|x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 1466
+
+--S 1467 of 1475
+--r0:=-elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(sqrt(-a)*_
+-- sqrt(b)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(sqrt(-a)*_
+-- sqrt(b)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1467
+
+--S 1468 of 1475
+--a0:=integrate(t0,x)
+--E 1468
+
+--S 1469 of 1475
+--m0:=a0-r0
+--E 1469
+
+--S 1470 of 1475
+--d0:=D(m0,x)
+--E 1470
+
+)clear all
+
+--S 1471 of 1475
+t0:=1/((a+b*x^2)*sqrt(x)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R +--------+
+--R 2 +-+ | 2
+--R (b x + a)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 1471
+
+--S 1472 of 1475
+--r0:=elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*_
+-- x^2)/c)/(a*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1472
+
+--S 1473 of 1475
+--a0:=integrate(t0,x)
+--E 1473
+
+--S 1474 of 1475
+--m0:=a0-r0
+--E 1474
+
+--S 1475 of 1475
+--d0:=D(m0,x)
+--E 1475
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich6c.input.pdf b/src/axiom-website/CATS/rich6c.input.pdf
new file mode 100644
index 0000000..d20e61f
Binary files /dev/null and b/src/axiom-website/CATS/rich6c.input.pdf differ
diff --git a/src/axiom-website/CATS/rich6d.input.pamphlet b/src/axiom-website/CATS/rich6d.input.pamphlet
new file mode 100644
index 0000000..02e32d4
--- /dev/null
+++ b/src/axiom-website/CATS/rich6d.input.pamphlet
@@ -0,0 +1,60948 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich6d.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p (c+d x^n)^q|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 297 supplied "optimal results".
+\item 256 matching answers.
+\item 1 case where Axiom answer differs from Rubi
+\item 100 cases where Axiom supplied 2 results.
+\item 35 cases that Axiom failed to integrate.
+\item 73 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich6d.output
+)spool rich6d.output
+)set message test on
+)set message auto off
+)clear all
+
+
+--S 1 of 1527
+t0:=1/(x^(3/2)*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------------
+--R +--------+
+--R 3 +-+ | 2
+--R (b x + a x)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 1527
+--r0:=-2*sqrt(c+d*x^2)/(a*c*sqrt(x))-2*(-d)^(1/4)*elliptic_e(_
+-- asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*_
+-- c^(1/4)*sqrt(c+d*x^2))+2*(-d)^(1/4)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*c^(1/4)*sqrt(c+d*x^2))-_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(b)*sqrt((c+d*x^2)/c)/((-a)^(3/2)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+elliptic_pi(sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt(b)*sqrt((c+d*x^2)/c)/((-a)^(3/2)*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 2
+
+--S 3 of 1527
+--a0:=integrate(t0,x)
+--E 3
+
+--S 4 of 1527
+--m0:=a0-r0
+--E 4
+
+--S 5 of 1527
+--d0:=D(m0,x)
+--E 5
+
+)clear all
+
+--S 6 of 1527
+t0:=1/(x^(5/2)*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R +--------+
+--R 4 2 +-+ | 2
+--R (b x + a x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 1527
+--r0:=-2/3*sqrt(c+d*x^2)/(a*c*x^(3/2))+2/3*(-d)^(3/4)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (a*c^(3/4)*sqrt(c+d*x^2))-b*elliptic_pi(-sqrt(-b)*sqrt(c)/_
+-- (sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-b*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 7
+
+--S 8 of 1527
+--a0:=integrate(t0,x)
+--E 8
+
+--S 9 of 1527
+--m0:=a0-r0
+--E 9
+
+--S 10 of 1527
+--d0:=D(m0,x)
+--E 10
+
+)clear all
+
+--S 11 of 1527
+t0:=1/(x^(7/2)*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R +--------+
+--R 5 3 +-+ | 2
+--R (b x + a x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 1527
+--r0:=-2/5*sqrt(c+d*x^2)/(a*c*x^(5/2))+2/5*(5*b*c+3*a*d)*_
+-- sqrt(c+d*x^2)/(a^2*c^2*sqrt(x))+2/5*(-d)^(1/4)*(5*b*c+3*a*d)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (a^2*c^(5/4)*sqrt(c+d*x^2))-2/5*(-d)^(1/4)*(5*b*c+3*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (a^2*c^(5/4)*sqrt(c+d*x^2))-b^(3/2)*elliptic_pi(-sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+b^(3/2)*elliptic_pi(sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(5/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 12
+
+--S 13 of 1527
+--a0:=integrate(t0,x)
+--E 13
+
+--S 14 of 1527
+--m0:=a0-r0
+--E 14
+
+--S 15 of 1527
+--d0:=D(m0,x)
+--E 15
+
+)clear all
+
+--S 16 of 1527
+t0:=x^(7/2)/((a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) -----------------------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b d x + (a d + b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 1527
+--r0:=-c*sqrt(x)/(d*(b*c-a*d)*sqrt(c+d*x^2))-c^(1/4)*(b*c-2*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (b*(-d)^(5/4)*(b*c-a*d)*sqrt(c+d*x^2))+a*elliptic_pi(-sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(b*(b*c-a*d)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/_
+-- sqrt(c)))+a*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (b*(b*c-a*d)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 17
+
+--S 18 of 1527
+--a0:=integrate(t0,x)
+--E 18
+
+--S 19 of 1527
+--m0:=a0-r0
+--E 19
+
+--S 20 of 1527
+--d0:=D(m0,x)
+--E 20
+
+)clear all
+
+--S 21 of 1527
+t0:=x^(5/2)/((a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) -----------------------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b d x + (a d + b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 1527
+--r0:=x^(3/2)/((b*c-a*d)*sqrt(c+d*x^2))-c^(3/4)*elliptic_e(_
+-- asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-d)^(3/4)*(b*c-a*d)*sqrt(c+d*x^2))+c^(3/4)*elliptic_f(_
+-- asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(3/4)*_
+-- (b*c-a*d)*sqrt(c+d*x^2))-elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(-a)*_
+-- sqrt((c+d*x^2)/c)/((b*c-a*d)*sqrt(b)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/_
+-- sqrt(c)))+elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(-a)*_
+-- sqrt((c+d*x^2)/c)/((b*c-a*d)*sqrt(b)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 22
+
+--S 23 of 1527
+--a0:=integrate(t0,x)
+--E 23
+
+--S 24 of 1527
+--m0:=a0-r0
+--E 24
+
+--S 25 of 1527
+--d0:=D(m0,x)
+--E 25
+
+)clear all
+
+--S 26 of 1527
+t0:=x^(3/2)/((a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) -----------------------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b d x + (a d + b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 1527
+--r0:=sqrt(x)/((b*c-a*d)*sqrt(c+d*x^2))+c^(1/4)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/((-d)^(1/4)*(b*c-a*d)*_
+-- sqrt(c+d*x^2))-elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((b*c-a*d)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-elliptic_pi(_
+-- sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((b*c-a*d)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 27
+
+--S 28 of 1527
+--a0:=integrate(t0,x)
+--E 28
+
+--S 29 of 1527
+--m0:=a0-r0
+--E 29
+
+--S 30 of 1527
+--d0:=D(m0,x)
+--E 30
+
+)clear all
+
+--S 31 of 1527
+t0:=sqrt(x)/((a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R +-+
+--R \|x
+--R (1) -----------------------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b d x + (a d + b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 1527
+--r0:=-d*x^(3/2)/(c*(b*c-a*d)*sqrt(c+d*x^2))-(-d)^(1/4)*elliptic_e(_
+-- asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(1/4)*_
+-- (b*c-a*d)*sqrt(c+d*x^2))+(-d)^(1/4)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(1/4)*(b*c-a*d)*_
+-- sqrt(c+d*x^2))-elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(b)*sqrt((c+d*x^2)/c)/_
+-- ((b*c-a*d)*sqrt(-a)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(b)*sqrt((c+d*x^2)/c)/((b*c-a*d)*_
+-- sqrt(-a)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 32
+
+--S 33 of 1527
+--a0:=integrate(t0,x)
+--E 33
+
+--S 34 of 1527
+--m0:=a0-r0
+--E 34
+
+--S 35 of 1527
+--d0:=D(m0,x)
+--E 35
+
+)clear all
+
+--S 36 of 1527
+t0:=1/((a+b*x^2)*(c+d*x^2)^(3/2)*sqrt(x))
+--R
+--R
+--R 1
+--R (1) ---------------------------------------------
+--R +--------+
+--R 4 2 +-+ | 2
+--R (b d x + (a d + b c)x + a c)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 1527
+--r0:=-d*sqrt(x)/(c*(b*c-a*d)*sqrt(c+d*x^2))+(-d)^(3/4)*elliptic_f(_
+-- asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(3/4)*_
+-- (b*c-a*d)*sqrt(c+d*x^2))+b*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+_
+-- d*x^2)/c)/(a*(b*c-a*d)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+_
+-- b*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 37
+
+--S 38 of 1527
+--a0:=integrate(t0,x)
+--E 38
+
+--S 39 of 1527
+--m0:=a0-r0
+--E 39
+
+--S 40 of 1527
+--d0:=D(m0,x)
+--E 40
+
+)clear all
+
+--S 41 of 1527
+t0:=1/(x^(3/2)*(a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------
+--R +--------+
+--R 5 3 +-+ | 2
+--R (b d x + (a d + b c)x + a c x)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 1527
+--r0:=-d/(c*(b*c-a*d)*sqrt(x)*sqrt(c+d*x^2))-(2*b*c-3*a*d)*sqrt(c+d*x^2)/_
+-- (a*c^2*(b*c-a*d)*sqrt(x))-(-d)^(1/4)*(2*b*c-3*a*d)*elliptic_e(_
+-- asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*c^(5/4)*_
+-- (b*c-a*d)*sqrt(c+d*x^2))+(-d)^(1/4)*(2*b*c-3*a*d)*elliptic_f(_
+-- asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*c^(5/4)*_
+-- (b*c-a*d)*sqrt(c+d*x^2))-b^(3/2)*elliptic_pi(-sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(3/2)*(b*c-a*d)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/_
+-- sqrt(c)))+b^(3/2)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(3/2)*(b*c-a*d)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 42
+
+--S 43 of 1527
+--a0:=integrate(t0,x)
+--E 43
+
+--S 44 of 1527
+--m0:=a0-r0
+--E 44
+
+--S 45 of 1527
+--d0:=D(m0,x)
+--E 45
+
+)clear all
+
+--S 46 of 1527
+t0:=1/(x^(5/2)*(a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------
+--R +--------+
+--R 6 4 2 +-+ | 2
+--R (b d x + (a d + b c)x + a c x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 1527
+--r0:=-d/(c*(b*c-a*d)*x^(3/2)*sqrt(c+d*x^2))-1/3*(2*b*c-5*a*d)*_
+-- sqrt(c+d*x^2)/(a*c^2*(b*c-a*d)*x^(3/2))+1/3*(-d)^(3/4)*(2*b*c-_
+-- 5*a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a*c^(7/4)*(b*c-a*d)*sqrt(c+d*x^2))-b^2*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-b^2*elliptic_pi(sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 47
+
+--S 48 of 1527
+--a0:=integrate(t0,x)
+--E 48
+
+--S 49 of 1527
+--m0:=a0-r0
+--E 49
+
+--S 50 of 1527
+--d0:=D(m0,x)
+--E 50
+
+)clear all
+
+--S 51 of 1527
+t0:=1/(x^(7/2)*(a+b*x^2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------
+--R +--------+
+--R 7 5 3 +-+ | 2
+--R (b d x + (a d + b c)x + a c x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 1527
+--r0:=-d/(c*(b*c-a*d)*x^(5/2)*sqrt(c+d*x^2))-1/5*(2*b*c-7*a*d)*_
+-- sqrt(c+d*x^2)/(a*c^2*(b*c-a*d)*x^(5/2))+1/5*(10*b^2*c^2+6*_
+-- a*b*c*d-21*a^2*d^2)*sqrt(c+d*x^2)/(a^2*c^3*(b*c-a*d)*sqrt(x))+_
+-- 1/5*(-d)^(1/4)*(10*b^2*c^2+6*a*b*c*d-21*a^2*d^2)*elliptic_e(_
+-- asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a^2*_
+-- c^(9/4)*(b*c-a*d)*sqrt(c+d*x^2))-1/5*(-d)^(1/4)*(10*b^2*c^2+_
+-- 6*a*b*c*d-21*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*c^(9/4)*(b*c-a*d)*sqrt(c+d*x^2))-b^(5/2)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*_
+-- (b*c-a*d)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+b^(5/2)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*_
+-- (b*c-a*d)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 52
+
+--S 53 of 1527
+--a0:=integrate(t0,x)
+--E 53
+
+--S 54 of 1527
+--m0:=a0-r0
+--E 54
+
+--S 55 of 1527
+--d0:=D(m0,x)
+--E 55
+
+)clear all
+
+--S 56 of 1527
+t0:=x^(7/2)/((a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|d x + c
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 1527
+--r0:=-1/3*c*sqrt(x)/(d*(b*c-a*d)*(c+d*x^2)^(3/2))+1/6*(b*c-7*a*d)*_
+-- sqrt(x)/(d*(b*c-a*d)^2*sqrt(c+d*x^2))-1/6*c^(1/4)*(b*c-7*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-d)^(5/4)*(b*c-a*d)^2*sqrt(c+d*x^2))+a*elliptic_pi(-sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((b*c-a*d)^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/_
+-- sqrt(c)))+a*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((b*c-a*d)^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 57
+
+--S 58 of 1527
+--a0:=integrate(t0,x)
+--E 58
+
+--S 59 of 1527
+--m0:=a0-r0
+--E 59
+
+--S 60 of 1527
+--d0:=D(m0,x)
+--E 60
+
+)clear all
+
+--S 61 of 1527
+t0:=x^(5/2)/((a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|d x + c
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 1527
+--r0:=1/3*x^(3/2)/((b*c-a*d)*(c+d*x^2)^(3/2))+1/2*(b*c+a*d)*x^(3/2)/_
+-- (c*(b*c-a*d)^2*sqrt(c+d*x^2))-1/2*(b*c+a*d)*elliptic_e(_
+-- asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(1/4)*_
+-- (-d)^(3/4)*(b*c-a*d)^2*sqrt(c+d*x^2))+1/2*(b*c+a*d)*elliptic_f(_
+-- asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(1/4)*_
+-- (-d)^(3/4)*(b*c-a*d)^2*sqrt(c+d*x^2))-elliptic_pi(-sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt(-a)*sqrt(b)*sqrt((c+d*x^2)/c)/((b*c-a*d)^2*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(-a)*_
+-- sqrt(b)*sqrt((c+d*x^2)/c)/((b*c-a*d)^2*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 62
+
+--S 63 of 1527
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 1527
+--m0:=a0-r0
+--E 64
+
+--S 65 of 1527
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 1527
+t0:=x^(3/2)/((a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|d x + c
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 1527
+--r0:=1/3*sqrt(x)/((b*c-a*d)*(c+d*x^2)^(3/2))+1/6*(5*b*c+a*d)*_
+-- sqrt(x)/(c*(b*c-a*d)^2*sqrt(c+d*x^2))+1/6*(5*b*c+a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (c^(3/4)*(-d)^(1/4)*(b*c-a*d)^2*sqrt(c+d*x^2))-_
+-- b*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((b*c-a*d)^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- b*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((b*c-a*d)^2*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 67
+
+--S 68 of 1527
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 1527
+--m0:=a0-r0
+--E 69
+
+--S 70 of 1527
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 1527
+t0:=sqrt(x)/((a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R +-+
+--R \|x
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|d x + c
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 1527
+--r0:=-1/3*d*x^(3/2)/(c*(b*c-a*d)*(c+d*x^2)^(3/2))-1/2*d*(3*b*c-a*d)*_
+-- x^(3/2)/(c^2*(b*c-a*d)^2*sqrt(c+d*x^2))-1/2*(-d)^(1/4)*(3*b*c-_
+-- a*d)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(5/4)*(b*c-a*d)^2*sqrt(c+d*x^2))+1/2*_
+-- (-d)^(1/4)*(3*b*c-a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/_
+-- c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(5/4)*(b*c-a*d)^2*sqrt(c+_
+-- d*x^2))-b^(3/2)*elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((b*c-a*d)^2*sqrt(-a)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+b^(3/2)*elliptic_pi(sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((b*c-a*d)^2*sqrt(-a)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 72
+
+--S 73 of 1527
+--a0:=integrate(t0,x)
+--E 73
+
+--S 74 of 1527
+--m0:=a0-r0
+--E 74
+
+--S 75 of 1527
+--d0:=D(m0,x)
+--E 75
+
+)clear all
+
+--S 76 of 1527
+t0:=1/((a+b*x^2)*(c+d*x^2)^(5/2)*sqrt(x))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 +-+ | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 1527
+--r0:=-1/3*d*sqrt(x)/(c*(b*c-a*d)*(c+d*x^2)^(3/2))-1/6*d*(11*b*c-5*a*d)*_
+-- sqrt(x)/(c^2*(b*c-a*d)^2*sqrt(c+d*x^2))+1/6*(-d)^(3/4)*(11*b*c-_
+-- 5*a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(7/4)*(b*c-a*d)^2*sqrt(c+d*x^2))+b^2*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)^2*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+b^2*elliptic_pi(sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)^2*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 77
+
+--S 78 of 1527
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 1527
+--m0:=a0-r0
+--E 79
+
+--S 80 of 1527
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 1527
+t0:=1/(x^(3/2)*(a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R -----------------------------------------------------------------------
+--R +--------+
+--R 2 7 2 5 2 3 2 +-+ | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 1527
+--r0:=-1/3*d/(c*(b*c-a*d)*(c+d*x^2)^(3/2)*sqrt(x))-1/6*d*(13*b*c-7*a*d)/_
+-- (c^2*(b*c-a*d)^2*sqrt(x)*sqrt(c+d*x^2))-1/2*(4*b^2*c^2-13*a*b*c*d+_
+-- 7*a^2*d^2)*sqrt(c+d*x^2)/(a*c^3*(b*c-a*d)^2*sqrt(x))-1/2*(-d)^(1/4)*_
+-- (4*b^2*c^2-13*a*b*c*d+7*a^2*d^2)*elliptic_e(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*c^(9/4)*(b*c-a*d)^2*_
+-- sqrt(c+d*x^2))+1/2*(-d)^(1/4)*(4*b^2*c^2-13*a*b*c*d+7*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (a*c^(9/4)*(b*c-a*d)^2*sqrt(c+d*x^2))-b^(5/2)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(3/2)*_
+-- (b*c-a*d)^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+b^(5/2)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(3/2)*_
+-- (b*c-a*d)^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 82
+
+--S 83 of 1527
+--a0:=integrate(t0,x)
+--E 83
+
+--S 84 of 1527
+--m0:=a0-r0
+--E 84
+
+--S 85 of 1527
+--d0:=D(m0,x)
+--E 85
+
+)clear all
+
+--S 86 of 1527
+t0:=1/(x^(5/2)*(a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R ------------------------------------------------------------------------
+--R +--------+
+--R 2 8 2 6 2 4 2 2 +-+ | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 1527
+--r0:=-1/3*d/(c*(b*c-a*d)*x^(3/2)*(c+d*x^2)^(3/2))-1/2*d*(5*b*c-3*a*d)/_
+-- (c^2*(b*c-a*d)^2*x^(3/2)*sqrt(c+d*x^2))-1/6*(4*b^2*c^2-25*a*b*c*d+_
+-- 15*a^2*d^2)*sqrt(c+d*x^2)/(a*c^3*(b*c-a*d)^2*x^(3/2))+1/6*_
+-- (-d)^(3/4)*(4*b^2*c^2-25*a*b*c*d+15*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a*c^(11/4)*(b*c-a*d)^2*sqrt(c+d*x^2))-_
+-- b^3*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)^2*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-b^3*elliptic_pi(sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)^2*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 87
+
+--S 88 of 1527
+--a0:=integrate(t0,x)
+--E 88
+
+--S 89 of 1527
+--m0:=a0-r0
+--E 89
+
+--S 90 of 1527
+--d0:=D(m0,x)
+--E 90
+
+)clear all
+
+--S 91 of 1527
+t0:=1/(x^(7/2)*(a+b*x^2)*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R ------------------------------------------------------------------------
+--R +--------+
+--R 2 9 2 7 2 5 2 3 +-+ | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 1527
+--r0:=-1/3*d/(c*(b*c-a*d)*x^(5/2)*(c+d*x^2)^(3/2))-1/6*d*(17*b*c-_
+-- 11*a*d)/(c^2*(b*c-a*d)^2*x^(5/2)*sqrt(c+d*x^2))-1/30*(12*b^2*c^2-_
+-- 119*a*b*c*d+77*a^2*d^2)*sqrt(c+d*x^2)/(a*c^3*(b*c-a*d)^2*x^(5/2))+_
+-- 1/10*(20*b^3*c^3+12*a*b^2*c^2*d-119*a^2*b*c*d^2+77*a^3*d^3)*_
+-- sqrt(c+d*x^2)/(a^2*c^4*(b*c-a*d)^2*sqrt(x))+1/10*(-d)^(1/4)*_
+-- (20*b^3*c^3+12*a*b^2*c^2*d-119*a^2*b*c*d^2+77*a^3*d^3)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+_
+-- d*x^2)/c)/(a^2*c^(13/4)*(b*c-a*d)^2*sqrt(c+d*x^2))-_
+-- 1/10*(-d)^(1/4)*(20*b^3*c^3+12*a*b^2*c^2*d-119*a^2*b*c*d^2+_
+-- 77*a^3*d^3)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*c^(13/4)*(b*c-a*d)^2*sqrt(c+d*x^2))-_
+-- b^(7/2)*elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(5/2)*(b*c-a*d)^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+_
+-- b^(7/2)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(5/2)*(b*c-a*d)^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 92
+
+--S 93 of 1527
+--a0:=integrate(t0,x)
+--E 93
+
+--S 94 of 1527
+--m0:=a0-r0
+--E 94
+
+--S 95 of 1527
+--d0:=D(m0,x)
+--E 95
+
+)clear all
+
+--S 96 of 1527
+t0:=x^m*(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 2 m
+--R (d x + c)x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 1527
+--r0:=1/2*(b*c-a*d)*x^(1+m)/(a*b*(a+b*x^2))+1/2*(a*d*(1+m)+b*(c-c*m))*_
+-- x^(1+m)*hypergeometric(1,1/2*(1+m),1/2*(3+m),-b*x^2/a)/(a^2*b*(1+m))
+--E 97
+
+--S 98 of 1527
+--a0:=integrate(t0,x)
+--E 98
+
+--S 99 of 1527
+--m0:=a0-r0
+--E 99
+
+--S 100 of 1527
+--d0:=D(m0,x)
+--E 100
+
+)clear all
+
+--S 101 of 1527
+t0:=x^4*(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 6 4
+--R d x + c x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 101
+
+--S 102 of 1527
+r0:=1/2*(3*b*c-5*a*d)*x/b^3-1/6*(3*b*c-5*a*d)*x^3/(a*b^2)+1/2*(b*c-a*d)*_
+ x^5/(a*b*(a+b*x^2))-1/2*(3*b*c-5*a*d)*atan(x*sqrt(b)/sqrt(a))*_
+ sqrt(a)/b^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 +-+ x\|b
+--R ((15a b d - 9b c)x + 15a d - 9a b c)\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 5 2 3 2 +-+
+--R (2b d x + (- 10a b d + 6b c)x + (- 15a d + 9a b c)x)\|b
+--R /
+--R 4 2 3 +-+
+--R (6b x + 6a b )\|b
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 2 2 | a \| b
+--R ((15a b d - 9b c)x + 15a d - 9a b c) |- - log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 2 5 2 3 2
+--R 4b d x + (- 20a b d + 12b c)x + (- 30a d + 18a b c)x
+--R /
+--R 4 2 3
+--R 12b x + 12a b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 2 |a \|b 2 5
+--R ((- 15a b d + 9b c)x - 15a d + 9a b c) |- atan(----) + 2b d x
+--R \|b x
+--R +
+--R 2 3 2
+--R (- 10a b d + 6b c)x + (- 15a d + 9a b c)x
+--R /
+--R 4 2 3
+--R 6b x + 6a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 103
+
+--S 104 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a +-+ \| b
+--R (5a d - 3b c) |- - \|b log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ x\|b
+--R (- 10a d + 6b c)\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+--S 106 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R (- 5a d + 3b c)\|a atan(-----) + (- 5a d + 3b c) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ------------------------------------------------------------------
+--R 3 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 107
+
+)clear all
+
+--S 108 of 1527
+t0:=x^3*(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 5 3
+--R d x + c x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 108
+
+--S 109 of 1527
+r0:=1/2*d*x^2/b^2+1/2*a*(b*c-a*d)/(b^3*(a+b*x^2))+1/2*(b*c-2*a*d)*_
+ log(a+b*x^2)/b^3
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 4 2
+--R ((- 2a b d + b c)x - 2a d + a b c)log(b x + a) + b d x + a b d x
+--R +
+--R 2
+--R - a d + a b c
+--R /
+--R 4 2 3
+--R 2b x + 2a b
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 4 2
+--R ((- 2a b d + b c)x - 2a d + a b c)log(b x + a) + b d x + a b d x
+--R +
+--R 2
+--R - a d + a b c
+--R /
+--R 4 2 3
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 110
+
+--S 111 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 112
+
+)clear all
+
+--S 113 of 1527
+t0:=x^2*(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 4 2
+--R d x + c x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 113
+
+--S 114 of 1527
+r0:=-1/2*(b*c-3*a*d)*x/(a*b^2)+1/2*(b*c-a*d)*x^3/(a*b*(a+b*x^2))+_
+ 1/2*(b*c-3*a*d)*atan(x*sqrt(b)/sqrt(a))/(b^(5/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 x\|b
+--R ((- 3a b d + b c)x - 3a d + a b c)atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 +-+ +-+
+--R (2b d x + (3a d - b c)x)\|a \|b
+--R /
+--R 3 2 2 +-+ +-+
+--R (2b x + 2a b )\|a \|b
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 (b x - a)\|- a b - 2a b x
+--R ((3a b d - b c)x + 3a d - a b c)log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 +-----+
+--R (4b d x + (6a d - 2b c)x)\|- a b
+--R /
+--R 3 2 2 +-----+
+--R (4b x + 4a b )\|- a b
+--R ,
+--R
+--R +---+
+--R 2 2 2 x\|a b
+--R ((- 3a b d + b c)x - 3a d + a b c)atan(-------)
+--R a
+--R +
+--R 3 +---+
+--R (2b d x + (3a d - b c)x)\|a b
+--R /
+--R 3 2 2 +---+
+--R (2b x + 2a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 115
+
+--S 116 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b - 2a b x
+--R (3a d - b c)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (6a d - 2b c)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (- 3a d + b c)\|a \|b atan(-------) + (3a d - b c)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 2b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 118
+
+--S 119 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 119
+
+)clear all
+
+--S 120 of 1527
+t0:=x*(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 3
+--R d x + c x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 120
+
+--S 121 of 1527
+r0:=1/2*(-b*c+a*d)/(b^2*(a+b*x^2))+1/2*d*log(a+b*x^2)/b^2
+--R
+--R
+--R 2 2
+--R (b d x + a d)log(b x + a) + a d - b c
+--R (2) ---------------------------------------
+--R 3 2 2
+--R 2b x + 2a b
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R (b d x + a d)log(b x + a) + a d - b c
+--R (3) ---------------------------------------
+--R 3 2 2
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 122
+
+--S 123 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 123
+
+--S 124 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 124
+
+)clear all
+
+--S 125 of 1527
+t0:=(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 2
+--R d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 125
+
+--S 126 of 1527
+r0:=1/2*(b*c-a*d)*x/(a*b*(a+b*x^2))+1/2*(b*c+a*d)*atan(x*sqrt(b)/_
+ sqrt(a))/(a^(3/2)*b^(3/2))
+--R
+--R
+--R +-+
+--R 2 2 2 x\|b +-+ +-+
+--R ((a b d + b c)x + a d + a b c)atan(-----) + (- a d + b c)x\|a \|b
+--R +-+
+--R \|a
+--R (2) -------------------------------------------------------------------
+--R 2 2 2 +-+ +-+
+--R (2a b x + 2a b)\|a \|b
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 (b x - a)\|- a b + 2a b x
+--R ((a b d + b c)x + a d + a b c)log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-----+
+--R (- 2a d + 2b c)x\|- a b
+--R /
+--R 2 2 2 +-----+
+--R (4a b x + 4a b)\|- a b
+--R ,
+--R +---+
+--R 2 2 2 x\|a b +---+
+--R ((a b d + b c)x + a d + a b c)atan(-------) + (- a d + b c)x\|a b
+--R a
+--R -------------------------------------------------------------------]
+--R 2 2 2 +---+
+--R (2a b x + 2a b)\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 127
+
+--S 128 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d + b c)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2a d - 2b c)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-----+ +-+ +-+
+--R 4a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 128
+
+--S 129 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (a d + b c)\|a \|b atan(-------) + (- a d - b c)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R 2a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 130
+
+--S 131 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 131
+
+)clear all
+
+--S 132 of 1527
+t0:=(c+d*x^2)/(x*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) --------------------
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 132
+
+--S 133 of 1527
+r0:=1/2*(b*c-a*d)/(a*b*(a+b*x^2))+c*log(x)/a^2-1/2*c*log(a+b*x^2)/a^2
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2
+--R (- b c x - a b c)log(b x + a) + (2b c x + 2a b c)log(x) - a d + a b c
+--R ------------------------------------------------------------------------
+--R 2 2 2 3
+--R 2a b x + 2a b
+--R Type: Expression(Integer)
+--E 133
+
+--S 134 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2
+--R (- b c x - a b c)log(b x + a) + (2b c x + 2a b c)log(x) - a d + a b c
+--R ------------------------------------------------------------------------
+--R 2 2 2 3
+--R 2a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 134
+
+--S 135 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 135
+
+--S 136 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 136
+
+)clear all
+
+--S 137 of 1527
+t0:=(c+d*x^2)/(x^2*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) ---------------------
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 137
+
+--S 138 of 1527
+r0:=1/2*(-3*b*c+a*d)/(a^2*b*x)+1/2*(b*c-a*d)/(a*b*x*(a+b*x^2))-_
+ 1/2*(3*b*c-a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*sqrt(b))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 2 x\|b
+--R ((a b d - 3b c)x + (a d - 3a b c)x)atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 +-+ +-+
+--R ((a d - 3b c)x - 2a c)\|a \|b
+--R /
+--R 2 3 3 +-+ +-+
+--R (2a b x + 2a x)\|a \|b
+--R Type: Expression(Integer)
+--E 138
+
+--S 139 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 3 2 (b x - a)\|- a b + 2a b x
+--R ((a b d - 3b c)x + (a d - 3a b c)x)log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 +-----+
+--R ((2a d - 6b c)x - 4a c)\|- a b
+--R /
+--R 2 3 3 +-----+
+--R (4a b x + 4a x)\|- a b
+--R ,
+--R
+--R +---+
+--R 2 3 2 x\|a b
+--R ((a b d - 3b c)x + (a d - 3a b c)x)atan(-------)
+--R a
+--R +
+--R 2 +---+
+--R ((a d - 3b c)x - 2a c)\|a b
+--R /
+--R 2 3 3 +---+
+--R (2a b x + 2a x)\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 139
+
+--S 140 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d - 3b c)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2a d + 6b c)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4a \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 140
+
+--S 141 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (a d - 3b c)\|a \|b atan(-------) + (- a d + 3b c)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 2a \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 143
+
+)clear all
+
+--S 144 of 1527
+t0:=(c+d*x^2)/(x^3*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) ---------------------
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 144
+
+--S 145 of 1527
+r0:=1/2*(-2*b*c+a*d)/(a^2*b*x^2)+1/2*(b*c-a*d)/(a*b*x^2*(a+b*x^2))-_
+ (2*b*c-a*d)*log(x)/a^3+1/2*(2*b*c-a*d)*log(a+b*x^2)/a^3
+--R
+--R
+--R (2)
+--R 2 4 2 2 2
+--R ((- a b d + 2b c)x + (- a d + 2a b c)x )log(b x + a)
+--R +
+--R 2 4 2 2 2 2 2
+--R ((2a b d - 4b c)x + (2a d - 4a b c)x )log(x) + (a d - 2a b c)x - a c
+--R /
+--R 3 4 4 2
+--R 2a b x + 2a x
+--R Type: Expression(Integer)
+--E 145
+
+--S 146 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 2
+--R ((- a b d + 2b c)x + (- a d + 2a b c)x )log(b x + a)
+--R +
+--R 2 4 2 2 2 2 2
+--R ((2a b d - 4b c)x + (2a d - 4a b c)x )log(x) + (a d - 2a b c)x - a c
+--R /
+--R 3 4 4 2
+--R 2a b x + 2a x
+--R Type: Union(Expression(Integer),...)
+--E 146
+
+--S 147 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 148
+
+)clear all
+
+--S 149 of 1527
+t0:=(c+d*x^2)/(x^4*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) ---------------------
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 149
+
+--S 150 of 1527
+r0:=1/6*(-5*b*c+3*a*d)/(a^2*b*x^3)+1/2*(5*b*c-3*a*d)/(a^3*x)+_
+ 1/2*(b*c-a*d)/(a*b*x^3*(a+b*x^2))+1/2*(5*b*c-3*a*d)*_
+ atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 5 2 3 +-+ x\|b
+--R ((- 9a b d + 15b c)x + (- 9a d + 15a b c)x )\|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+
+--R ((- 9a b d + 15b c)x + (- 6a d + 10a b c)x - 2a c)\|a
+--R /
+--R 3 5 4 3 +-+
+--R (6a b x + 6a x )\|a
+--R Type: Expression(Integer)
+--E 150
+
+--S 151 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 2 5 2 3 | b
+--R ((9a b d - 15b c)x + (9a d - 15a b c)x ) |- -
+--R \| a
+--R *
+--R +---+
+--R | b 2
+--R - 2a x |- - + b x - a
+--R \| a
+--R log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 4 2 2 2
+--R (- 18a b d + 30b c)x + (- 12a d + 20a b c)x - 4a c
+--R /
+--R 3 5 4 3
+--R 12a b x + 12a x
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 5 2 3 |b \|a
+--R ((9a b d - 15b c)x + (9a d - 15a b c)x ) |- atan(-----)
+--R \|a b x
+--R +
+--R 2 4 2 2 2
+--R (- 9a b d + 15b c)x + (- 6a d + 10a b c)x - 2a c
+--R /
+--R 3 5 4 3
+--R 6a b x + 6a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 151
+
+--S 152 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b +-+ \| a
+--R (3a d - 5b c) |- - \|a log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ x\|b
+--R (6a d - 10b c)\|b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 153
+
+--S 154 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R (3a d - 5b c)\|b atan(-----) + (3a d - 5b c)\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) ---------------------------------------------------------------
+--R 3 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 1527
+t0:=x^m*(c+d*x^2)^2/(a+b*x^2)^2
+--R
+--R
+--R 2 4 2 2 m
+--R (d x + 2c d x + c )x
+--R (1) -----------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 1527
+--r0:=d^2*x^(1+m)/(b^2*(1+m))+1/2*(b*c-a*d)^2*x^(1+m)/(a*b^2*(a+b*x^2))+_
+-- 1/2*(b*c-a*d)*(a*d*(3+m)+b*(c-c*m))*x^(1+m)*_
+-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-b*x^2/a)/(a^2*b^2*(1+m))
+--E 157
+
+--S 158 of 1527
+--a0:=integrate(t0,x)
+--E 158
+
+--S 159 of 1527
+--m0:=a0-r0
+--E 159
+
+--S 160 of 1527
+--d0:=D(m0,x)
+--E 160
+
+)clear all
+
+--S 161 of 1527
+t0:=x^4*(c+d*x^2)^2/(a+b*x^2)^2
+--R
+--R
+--R 2 8 6 2 4
+--R d x + 2c d x + c x
+--R (1) ---------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 161
+
+--S 162 of 1527
+r0a:=(b^2*c^2-4*a*b*c*d+3*a^2*d^2)*x/b^4+2/3*d*(b*c-a*d)*x^3/b^3+_
+ 1/5*d^2*x^5/b^2+1/2*a*(b*c-a*d)^2*x/(b^4*(a+b*x^2))-_
+ 1/2*(3*b^2*c^2-10*a*b*c*d+7*a^2*d^2)*atan(x*sqrt(b)/sqrt(a))*_
+ sqrt(a)/b^(9/2)
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2
+--R (- 105a b d + 150a b c d - 45b c )x - 105a d + 150a b c d
+--R +
+--R 2 2
+--R - 45a b c
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 2 7 2 2 3 5
+--R 6b d x + (- 14a b d + 20b c d)x
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R (70a b d - 100a b c d + 30b c )x + (105a d - 150a b c d + 45a b c )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 5 2 4 +-+
+--R (30b x + 30a b )\|b
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 1527
+r0b:=(b*c-3*a*d)*(b*c-a*d)*x/b^4+2/3*d*(b*c-a*d)*_
+ x^3/b^3+1/5*d^2*x^5/b^2+1/2*a*(b*c-a*d)^2*x/(b^4*(a+b*x^2))-_
+ 2*(b*c-2*a*d)*(b*c-a*d)*atan(x*sqrt(b)/sqrt(a))*_
+ sqrt(a)/b^(9/2)+1/2*(b*c-a*d)^2*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(9/2)
+--R
+--R
+--R (3)
+--R 2 2 2 3 2 2 3 2 2
+--R (- 105a b d + 150a b c d - 45b c )x - 105a d + 150a b c d
+--R +
+--R 2 2
+--R - 45a b c
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 2 7 2 2 3 5
+--R 6b d x + (- 14a b d + 20b c d)x
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R (70a b d - 100a b c d + 30b c )x + (105a d - 150a b c d + 45a b c )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 5 2 4 +-+
+--R (30b x + 30a b )\|b
+--R Type: Expression(Integer)
+--E 163
+
+--S 164 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 2 2 3 2 2 3 2 2
+--R (105a b d - 150a b c d + 45b c )x + 105a d - 150a b c d
+--R +
+--R 2 2
+--R 45a b c
+--R *
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R | a \| b
+--R |- - log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 3 2 7 2 2 3 5
+--R 12b d x + (- 28a b d + 40b c d)x
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R (140a b d - 200a b c d + 60b c )x + (210a d - 300a b c d + 90a b c )x
+--R /
+--R 5 2 4
+--R 60b x + 60a b
+--R ,
+--R
+--R 2 2 2 3 2 2 3 2 2
+--R (105a b d - 150a b c d + 45b c )x + 105a d - 150a b c d
+--R +
+--R 2 2
+--R 45a b c
+--R *
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b
+--R |- atan(----)
+--R \|b x
+--R +
+--R 3 2 7 2 2 3 5 2 2 2 3 2 3
+--R 6b d x + (- 14a b d + 20b c d)x + (70a b d - 100a b c d + 30b c )x
+--R +
+--R 3 2 2 2 2
+--R (105a d - 150a b c d + 45a b c )x
+--R /
+--R 5 2 4
+--R 30b x + 30a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 164
+
+--S 165 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 2 2 2 | a +-+ \| b
+--R (7a d - 10a b c d + 3b c ) |- - \|b log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-+ x\|b
+--R (14a d - 20a b c d + 6b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 165
+
+--S 166 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +-+
+--R 2 2 2 2 +-+ x\|b
+--R (7a d - 10a b c d + 3b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 2 2 |a +-+ \|b
+--R (7a d - 10a b c d + 3b c ) |- \|b atan(----)
+--R \|b x
+--R /
+--R 4 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 168
+
+--S 169 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 2 2 2 | a +-+ \| b
+--R (7a d - 10a b c d + 3b c ) |- - \|b log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-+ x\|b
+--R (14a d - 20a b c d + 6b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 170
+
+--S 171 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +-+
+--R 2 2 2 2 +-+ x\|b
+--R (7a d - 10a b c d + 3b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 2 2 |a +-+ \|b
+--R (7a d - 10a b c d + 3b c ) |- \|b atan(----)
+--R \|b x
+--R /
+--R 4 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 172
+
+)clear all
+
+--S 173 of 1527
+t0:=x^3*(c+d*x^2)^2/(a+b*x^2)^2
+--R
+--R
+--R 2 7 5 2 3
+--R d x + 2c d x + c x
+--R (1) ---------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 173
+
+--S 174 of 1527
+r0:=d*(b*c-a*d)*x^2/b^3+1/4*d^2*x^4/b^2+1/2*a*(b*c-a*d)^2/_
+ (b^4*(a+b*x^2))+1/2*(b*c-3*a*d)*(b*c-a*d)*log(a+b*x^2)/b^4
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((6a b d - 8a b c d + 2b c )x + 6a d - 8a b c d + 2a b c )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 3 2 6 2 2 3 4 2 2 2 2 3 2
+--R b d x + (- 3a b d + 4b c d)x + (- 4a b d + 4a b c d)x + 2a d
+--R +
+--R 2 2 2
+--R - 4a b c d + 2a b c
+--R /
+--R 5 2 4
+--R 4b x + 4a b
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((6a b d - 8a b c d + 2b c )x + 6a d - 8a b c d + 2a b c )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 3 2 6 2 2 3 4 2 2 2 2 3 2
+--R b d x + (- 3a b d + 4b c d)x + (- 4a b d + 4a b c d)x + 2a d
+--R +
+--R 2 2 2
+--R - 4a b c d + 2a b c
+--R /
+--R 5 2 4
+--R 4b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 175
+
+--S 176 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 177
+
+)clear all
+
+--S 178 of 1527
+t0:=x^2*(c+d*x^2)^2/(a+b*x^2)^2
+--R
+--R
+--R 2 6 4 2 2
+--R d x + 2c d x + c x
+--R (1) ---------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 178
+
+--S 179 of 1527
+r0a:=2*d*(b*c-a*d)*x/b^3+1/3*d^2*x^3/b^2-1/2*(b*c-a*d)^2*x/_
+ (b^3*(a+b*x^2))+1/2*(b^2*c^2-6*a*b*c*d+5*a^2*d^2)*_
+ atan(x*sqrt(b)/sqrt(a))/(b^(7/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((15a b d - 18a b c d + 3b c )x + 15a d - 18a b c d + 3a b c )
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 5 2 2 3 2 2 2 2
+--R (2b d x + (- 10a b d + 12b c d)x + (- 15a d + 18a b c d - 3b c )x)
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 4 2 3 +-+ +-+
+--R (6b x + 6a b )\|a \|b
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 1527
+r0b:=2*d*(b*c-a*d)*x/b^3+1/3*d^2*x^3/b^2-1/2*(b*c-a*d)^2*x/(b^3*(a+b*x^2))+_
+ (b*c-3*a*d)*(b*c-a*d)*atan(x*sqrt(b)/sqrt(a))/(b^(7/2)*_
+ sqrt(a))-1/2*(b*c-a*d)^2*atan(x*sqrt(b)/sqrt(a))/(b^(7/2)*sqrt(a))
+--R
+--R
+--R (3)
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((15a b d - 18a b c d + 3b c )x + 15a d - 18a b c d + 3a b c )
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 5 2 2 3 2 2 2 2
+--R (2b d x + (- 10a b d + 12b c d)x + (- 15a d + 18a b c d - 3b c )x)
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 4 2 3 +-+ +-+
+--R (6b x + 6a b )\|a \|b
+--R Type: Expression(Integer)
+--E 180
+
+--S 181 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((15a b d - 18a b c d + 3b c )x + 15a d - 18a b c d + 3a b c )
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 2 5 2 2 3
+--R 4b d x + (- 20a b d + 24b c d)x
+--R +
+--R 2 2 2 2
+--R (- 30a d + 36a b c d - 6b c )x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 4 2 3 +-----+
+--R (12b x + 12a b )\|- a b
+--R ,
+--R
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((15a b d - 18a b c d + 3b c )x + 15a d - 18a b c d + 3a b c )
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 2 5 2 2 3
+--R 2b d x + (- 10a b d + 12b c d)x
+--R +
+--R 2 2 2 2
+--R (- 15a d + 18a b c d - 3b c )x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 4 2 3 +---+
+--R (6b x + 6a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 181
+
+--S 182 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (5a d - 6a b c d + b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (- 10a d + 12a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 183
+
+--S 184 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (5a d - 6a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- 5a d + 6a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+ +-+ +---+
+--R 2b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 185
+
+--S 186 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (5a d - 6a b c d + b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (- 10a d + 12a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (5a d - 6a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- 5a d + 6a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+ +-+ +---+
+--R 2b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 188
+
+--S 189 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 189
+
+)clear all
+
+--S 190 of 1527
+t0:=x*(c+d*x^2)^2/(a+b*x^2)^2
+--R
+--R
+--R 2 5 3 2
+--R d x + 2c d x + c x
+--R (1) --------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 190
+
+--S 191 of 1527
+r0:=1/2*d^2*x^2/b^2-1/2*(b*c-a*d)^2/(b^3*(a+b*x^2))+d*(b*c-a*d)*_
+ log(a+b*x^2)/b^3
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2 2 2 4
+--R ((- 2a b d + 2b c d)x - 2a d + 2a b c d)log(b x + a) + b d x
+--R +
+--R 2 2 2 2 2 2
+--R a b d x - a d + 2a b c d - b c
+--R /
+--R 4 2 3
+--R 2b x + 2a b
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2 2 2 4
+--R ((- 2a b d + 2b c d)x - 2a d + 2a b c d)log(b x + a) + b d x
+--R +
+--R 2 2 2 2 2 2
+--R a b d x - a d + 2a b c d - b c
+--R /
+--R 4 2 3
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 192
+
+--S 193 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 193
+
+--S 194 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 194
+
+)clear all
+
+--S 195 of 1527
+t0:=(c+d*x^2)^2/(a+b*x^2)^2
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 195
+
+--S 196 of 1527
+r0:=d^2*x/b^2+1/2*(b*c-a*d)^2*x/(a*b^2*(a+b*x^2))+1/2*(b*c-a*d)*_
+ (b*c+3*a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(5/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 3 2 2 3 2 2 2 2 x\|b
+--R ((- 3a b d + 2a b c d + b c )x - 3a d + 2a b c d + a b c )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 2 2 2 +-+ +-+
+--R (2a b d x + (3a d - 2a b c d + b c )x)\|a \|b
+--R /
+--R 3 2 2 2 +-+ +-+
+--R (2a b x + 2a b )\|a \|b
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((3a b d - 2a b c d - b c )x + 3a d - 2a b c d - a b c )
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 2 2 2 2 +-----+
+--R (4a b d x + (6a d - 4a b c d + 2b c )x)\|- a b
+--R /
+--R 3 2 2 2 +-----+
+--R (4a b x + 4a b )\|- a b
+--R ,
+--R
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 3a b d + 2a b c d + b c )x - 3a d + 2a b c d + a b c )
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 3 2 2 2 2 +---+
+--R (2a b d x + (3a d - 2a b c d + b c )x)\|a b
+--R /
+--R 3 2 2 2 +---+
+--R (2a b x + 2a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 197
+
+--S 198 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b - 2a b x
+--R (3a d - 2a b c d - b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (6a d - 4a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 198
+
+--S 199 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (- 3a d + 2a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (3a d - 2a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+ +-+ +---+
+--R 2a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 200
+
+--S 201 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 201
+
+)clear all
+
+--S 202 of 1527
+t0:=(c+d*x^2)^2/(x*(a+b*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) --------------------
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 202
+
+--S 203 of 1527
+r0:=1/2*(b*c-a*d)^2/(a*b^2*(a+b*x^2))+c^2*log(x)/a^2-_
+ 1/2*(c^2/a^2-d^2/b^2)*log(a+b*x^2)
+--R
+--R
+--R (2)
+--R 2 2 3 2 2 3 2 2 2 2
+--R ((a b d - b c )x + a d - a b c )log(b x + a)
+--R +
+--R 3 2 2 2 2 3 2 2 2 2
+--R (2b c x + 2a b c )log(x) + a d - 2a b c d + a b c
+--R /
+--R 2 3 2 3 2
+--R 2a b x + 2a b
+--R Type: Expression(Integer)
+--E 203
+
+--S 204 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 3 2 2 3 2 2 2 2
+--R ((a b d - b c )x + a d - a b c )log(b x + a)
+--R +
+--R 3 2 2 2 2 3 2 2 2 2
+--R (2b c x + 2a b c )log(x) + a d - 2a b c d + a b c
+--R /
+--R 2 3 2 3 2
+--R 2a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 204
+
+--S 205 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 205
+
+--S 206 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 206
+
+)clear all
+
+--S 207 of 1527
+t0:=(c+d*x^2)^2/(x^2*(a+b*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) ---------------------
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 207
+
+--S 208 of 1527
+r0a:=-c^2/(a^2*x)-1/2*(b*c-a*d)^2*x/(a^2*b*(a+b*x^2))-_
+ 1/2*(3*b^2*c^2-2*a*b*c*d-a^2*d^2)*atan(x*sqrt(b)/sqrt(a))/_
+ (a^(5/2)*b^(3/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 3 2 3 3 2 2 2 2 x\|b
+--R ((a b d + 2a b c d - 3b c )x + (a d + 2a b c d - 3a b c )x)atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 2 2 2 +-+ +-+
+--R ((- a d + 2a b c d - 3b c )x - 2a b c )\|a \|b
+--R /
+--R 2 2 3 3 +-+ +-+
+--R (2a b x + 2a b x)\|a \|b
+--R Type: Expression(Integer)
+--E 208
+
+--S 209 of 1527
+r0b:=-c^2/(a^2*x)-1/2*(b*c-a*d)^2*x/_
+ (a^2*b*(a+b*x^2))-1/2*(b*c-a*d)^2*atan(x*sqrt(b)/sqrt(a))/_
+ (a^(5/2)*b^(3/2))-(b*c-a*d)*(b*c+a*d)*atan(x*sqrt(b)/sqrt(a))/_
+ (a^(5/2)*b^(3/2))
+--R
+--R
+--R (3)
+--R +-+
+--R 2 2 2 3 2 3 3 2 2 2 2 x\|b
+--R ((a b d + 2a b c d - 3b c )x + (a d + 2a b c d - 3a b c )x)atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 2 2 2 +-+ +-+
+--R ((- a d + 2a b c d - 3b c )x - 2a b c )\|a \|b
+--R /
+--R 2 2 3 3 +-+ +-+
+--R (2a b x + 2a b x)\|a \|b
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((a b d + 2a b c d - 3b c )x + (a d + 2a b c d - 3a b c )x)
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 2 2 2 2 2 +-----+
+--R ((- 2a d + 4a b c d - 6b c )x - 4a b c )\|- a b
+--R /
+--R 2 2 3 3 +-----+
+--R (4a b x + 4a b x)\|- a b
+--R ,
+--R
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((a b d + 2a b c d - 3b c )x + (a d + 2a b c d - 3a b c )x)
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 2 2 2 2 2 +---+
+--R ((- a d + 2a b c d - 3b c )x - 2a b c )\|a b
+--R /
+--R 2 2 3 3 +---+
+--R (2a b x + 2a b x)\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 210
+
+--S 211 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d + 2a b c d - 3b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (- 2a d - 4a b c d + 6b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (a d + 2a b c d - 3b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- a d - 2a b c d + 3b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+ +-+ +---+
+--R 2a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 213
+
+--S 214 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d + 2a b c d - 3b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (- 2a d - 4a b c d + 6b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 215
+
+--S 216 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (a d + 2a b c d - 3b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- a d - 2a b c d + 3b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+ +-+ +---+
+--R 2a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 218
+
+)clear all
+
+--S 219 of 1527
+t0:=(c+d*x^2)^2/(x^3*(a+b*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) ---------------------
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 219
+
+--S 220 of 1527
+r0:=-1/2*c^2/(a^2*x^2)-1/2*(b*c-a*d)^2/(a^2*b*(a+b*x^2))-_
+ 2*c*(b*c-a*d)*log(x)/a^3+c*(b*c-a*d)*log(a+b*x^2)/a^3
+--R
+--R
+--R (2)
+--R 2 3 2 4 2 2 2 2 2
+--R ((- 2a b c d + 2b c )x + (- 2a b c d + 2a b c )x )log(b x + a)
+--R +
+--R 2 3 2 4 2 2 2 2
+--R ((4a b c d - 4b c )x + (4a b c d - 4a b c )x )log(x)
+--R +
+--R 3 2 2 2 2 2 2 2
+--R (- a d + 2a b c d - 2a b c )x - a b c
+--R /
+--R 3 2 4 4 2
+--R 2a b x + 2a b x
+--R Type: Expression(Integer)
+--E 220
+
+--S 221 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 4 2 2 2 2 2
+--R ((- 2a b c d + 2b c )x + (- 2a b c d + 2a b c )x )log(b x + a)
+--R +
+--R 2 3 2 4 2 2 2 2
+--R ((4a b c d - 4b c )x + (4a b c d - 4a b c )x )log(x)
+--R +
+--R 3 2 2 2 2 2 2 2
+--R (- a d + 2a b c d - 2a b c )x - a b c
+--R /
+--R 3 2 4 4 2
+--R 2a b x + 2a b x
+--R Type: Union(Expression(Integer),...)
+--E 221
+
+--S 222 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 223
+
+)clear all
+
+--S 224 of 1527
+t0:=(c+d*x^2)^2/(x^4*(a+b*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) ---------------------
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 224
+
+--S 225 of 1527
+r0a:=-1/3*c^2/(a^2*x^3)+2*c*(b*c-a*d)/(a^3*x)+1/2*(b*c-a*d)^2*x/_
+ (a^3*(a+b*x^2))+1/2*(5*b^2*c^2-6*a*b*c*d+a^2*d^2)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(7/2)*sqrt(b))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 5 3 2 2 2 2 3
+--R ((3a b d - 18a b c d + 15b c )x + (3a d - 18a b c d + 15a b c )x )
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 2 4 2 2 2 2 2 +-+ +-+
+--R ((3a d - 18a b c d + 15b c )x + (- 12a c d + 10a b c )x - 2a c )\|a \|b
+--R /
+--R 3 5 4 3 +-+ +-+
+--R (6a b x + 6a x )\|a \|b
+--R Type: Expression(Integer)
+--E 225
+
+--S 226 of 1527
+r0b:=-1/3*c^2/(a^2*x^3)+_
+ 2*c*(b*c-a*d)/(a^3*x)+1/2*(b*c-a*d)^2*x/(a^3*(a+b*x^2))+_
+ 1/2*(b*c-a*d)^2*atan(x*sqrt(b)/sqrt(a))/(a^(7/2)*sqrt(b))+_
+ 2*c*(b*c-a*d)*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(7/2)
+--R
+--R
+--R (3)
+--R 2 2 2 3 2 5 3 2 2 2 2 3
+--R ((3a b d - 18a b c d + 15b c )x + (3a d - 18a b c d + 15a b c )x )
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 2 4 2 2 2 2 2 +-+ +-+
+--R ((3a d - 18a b c d + 15b c )x + (- 12a c d + 10a b c )x - 2a c )\|a \|b
+--R /
+--R 3 5 4 3 +-+ +-+
+--R (6a b x + 6a x )\|a \|b
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 2 2 3 2 5 3 2 2 2 2 3
+--R ((3a b d - 18a b c d + 15b c )x + (3a d - 18a b c d + 15a b c )x )
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R ((6a d - 36a b c d + 30b c )x + (- 24a c d + 20a b c )x - 4a c )
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 3 5 4 3 +-----+
+--R (12a b x + 12a x )\|- a b
+--R ,
+--R
+--R 2 2 2 3 2 5 3 2 2 2 2 3
+--R ((3a b d - 18a b c d + 15b c )x + (3a d - 18a b c d + 15a b c )x )
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 2 2 2 4 2 2 2 2 2 +---+
+--R ((3a d - 18a b c d + 15b c )x + (- 12a c d + 10a b c )x - 2a c )\|a b
+--R /
+--R 3 5 4 3 +---+
+--R (6a b x + 6a x )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 227
+
+--S 228 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d - 6a b c d + 5b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (- 2a d + 12a b c d - 10b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4a \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 228
+
+--S 229 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (a d - 6a b c d + 5b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- a d + 6a b c d - 5b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+ +-+ +---+
+--R 2a \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 230
+
+--S 231 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d - 6a b c d + 5b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (- 2a d + 12a b c d - 10b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4a \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 233
+
+--S 234 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (a d - 6a b c d + 5b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- a d + 6a b c d - 5b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+ +-+ +---+
+--R 2a \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 1527
+t0:=x^m*(c+d*x^2)^3/(a+b*x^2)^2
+--R
+--R
+--R 3 6 2 4 2 2 3 m
+--R (d x + 3c d x + 3c d x + c )x
+--R (1) ---------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 1527
+--r0:=1/2*d*(b*c*(1+m)-a*d*(3+m))*(a*d*(5+m)-b*c*(7+m))*x^(1+m)/_
+-- (a*b^3*(1+m)*(3+m))+1/2*(b*c-a*d)*x^(1+m)*(c+d*x^2)^2/(a*b*_
+-- (a+b*x^2))+1/2*d*x^(1+m)*(c*(a*d*(1+m)+b*(c-c*m))-d*(b*c*(3+m)-_
+-- a*d*(5+m))*x^2)/(a*b^2*(3+m))+1/2*(b*c-a*d)^2*(a*d*(5+m)+_
+-- b*(c-c*m))*x^(1+m)*hypergeometric(1,1/2*(1+m),1/2*(3+m),_
+-- -b*x^2/a)/(a^2*b^3*(1+m))
+--E 237
+
+--S 238 of 1527
+--a0:=integrate(t0,x)
+--E 238
+
+--S 239 of 1527
+--m0:=a0-r0
+--E 239
+
+--S 240 of 1527
+--d0:=D(m0,x)
+--E 240
+
+)clear all
+
+--S 241 of 1527
+t0:=x^4*(c+d*x^2)^3/(a+b*x^2)^2
+--R
+--R
+--R 3 10 2 8 2 6 3 4
+--R d x + 3c d x + 3c d x + c x
+--R (1) --------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 241
+
+--S 242 of 1527
+r0a:=(b*c-4*a*d)*(b*c-a*d)^2*x/b^5+d*(b*c-a*d)^2*x^3/b^4+_
+ 1/5*d^2*(3*b*c-2*a*d)*x^5/b^3+1/7*d^3*x^7/b^2+_
+ 1/2*a*(b*c-a*d)^3*x/(b^5*(a+b*x^2))+3/2*(b*c-a*d)^2*_
+ (-b*c+3*a*d)*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(11/2)
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (315a b d - 735a b c d + 525a b c d - 105b c )x + 315a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 735a b c d + 525a b c d - 105a b c
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 3 9 3 3 4 2 7
+--R 10b d x + (- 18a b d + 42b c d )x
+--R +
+--R 2 2 3 3 2 4 2 5
+--R (42a b d - 98a b c d + 70b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 210a b d + 490a b c d - 350a b c d + 70b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 315a d + 735a b c d - 525a b c d + 105a b c )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 6 2 5 +-+
+--R (70b x + 70a b )\|b
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 1527
+r0b:=(b*c-4*a*d)*(b*c-a*d)^2*x/b^5+d*(b*c-a*d)^2*x^3/b^4+_
+ 1/5*d^2*(3*b*c-2*a*d)*x^5/b^3+1/7*d^3*x^7/b^2+1/2*a*(b*c-a*d)^3*_
+ x/(b^5*(a+b*x^2))-(2*b*c-5*a*d)*(b*c-a*d)^2*atan(x*sqrt(b)/_
+ sqrt(a))*sqrt(a)/b^(11/2)+1/2*(b*c-a*d)^3*atan(x*sqrt(b)/_
+ sqrt(a))*sqrt(a)/b^(11/2)
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (315a b d - 735a b c d + 525a b c d - 105b c )x + 315a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 735a b c d + 525a b c d - 105a b c
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 3 9 3 3 4 2 7
+--R 10b d x + (- 18a b d + 42b c d )x
+--R +
+--R 2 2 3 3 2 4 2 5
+--R (42a b d - 98a b c d + 70b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 210a b d + 490a b c d - 350a b c d + 70b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 315a d + 735a b c d - 525a b c d + 105a b c )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 6 2 5 +-+
+--R (70b x + 70a b )\|b
+--R Type: Expression(Integer)
+--E 243
+
+--S 244 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (315a b d - 735a b c d + 525a b c d - 105b c )x + 315a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 735a b c d + 525a b c d - 105a b c
+--R *
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a \| b
+--R |- - log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 4 3 9 3 3 4 2 7
+--R 20b d x + (- 36a b d + 84b c d )x
+--R +
+--R 2 2 3 3 2 4 2 5
+--R (84a b d - 196a b c d + 140b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 420a b d + 980a b c d - 700a b c d + 140b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 630a d + 1470a b c d - 1050a b c d + 210a b c )x
+--R /
+--R 6 2 5
+--R 140b x + 140a b
+--R ,
+--R
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 315a b d + 735a b c d - 525a b c d + 105b c )x - 315a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 735a b c d - 525a b c d + 105a b c
+--R *
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b
+--R |- atan(----)
+--R \|b x
+--R +
+--R 4 3 9 3 3 4 2 7
+--R 10b d x + (- 18a b d + 42b c d )x
+--R +
+--R 2 2 3 3 2 4 2 5
+--R (42a b d - 98a b c d + 70b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 210a b d + 490a b c d - 350a b c d + 70b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 315a d + 735a b c d - 525a b c d + 105a b c )x
+--R /
+--R 6 2 5
+--R 70b x + 70a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 244
+
+--S 245 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R 3 3 2 2 2 2 3 3 | a +-+
+--R (9a d - 21a b c d + 15a b c d - 3b c ) |- - \|b
+--R \| b
+--R *
+--R +---+
+--R | a 2
+--R 2b x |- - + b x - a
+--R \| b
+--R log(---------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-+ x\|b
+--R (- 18a d + 42a b c d - 30a b c d + 6b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 245
+
+--S 246 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-+ x\|b
+--R (- 9a d + 21a b c d - 15a b c d + 3b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R 3 3 2 2 2 2 3 3 |a +-+ \|b
+--R (- 9a d + 21a b c d - 15a b c d + 3b c ) |- \|b atan(----)
+--R \|b x
+--R /
+--R 5 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 248
+
+--S 249 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +---+
+--R 3 3 2 2 2 2 3 3 | a +-+
+--R (9a d - 21a b c d + 15a b c d - 3b c ) |- - \|b
+--R \| b
+--R *
+--R +---+
+--R | a 2
+--R 2b x |- - + b x - a
+--R \| b
+--R log(---------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-+ x\|b
+--R (- 18a d + 42a b c d - 30a b c d + 6b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 250
+
+--S 251 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-+ x\|b
+--R (- 9a d + 21a b c d - 15a b c d + 3b c )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R 3 3 2 2 2 2 3 3 |a +-+ \|b
+--R (- 9a d + 21a b c d - 15a b c d + 3b c ) |- \|b atan(----)
+--R \|b x
+--R /
+--R 5 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 252
+
+)clear all
+
+--S 253 of 1527
+t0:=x^3*(c+d*x^2)^3/(a+b*x^2)^2
+--R
+--R
+--R 3 9 2 7 2 5 3 3
+--R d x + 3c d x + 3c d x + c x
+--R (1) -------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 253
+
+--S 254 of 1527
+r0:=3/2*d*(b*c-a*d)^2*x^2/b^4+1/4*d^2*(3*b*c-2*a*d)*x^4/b^3+_
+ 1/6*d^3*x^6/b^2+1/2*a*(b*c-a*d)^3/(b^5*(a+b*x^2))+_
+ 1/2*(b*c-4*a*d)*(b*c-a*d)^2*log(a+b*x^2)/b^5
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (- 24a b d + 54a b c d - 36a b c d + 6b c )x - 24a d + 54a b c d
+--R +
+--R 2 2 2 3 3
+--R - 36a b c d + 6a b c
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 4 3 8 3 3 4 2 6 2 2 3 3 2 4 2 4
+--R 2b d x + (- 4a b d + 9b c d )x + (12a b d - 27a b c d + 18b c d)x
+--R +
+--R 3 3 2 2 2 3 2 2 4 3 3 2 2 2 2
+--R (18a b d - 36a b c d + 18a b c d)x - 6a d + 18a b c d - 18a b c d
+--R +
+--R 3 3
+--R 6a b c
+--R /
+--R 6 2 5
+--R 12b x + 12a b
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (- 24a b d + 54a b c d - 36a b c d + 6b c )x - 24a d + 54a b c d
+--R +
+--R 2 2 2 3 3
+--R - 36a b c d + 6a b c
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 4 3 8 3 3 4 2 6 2 2 3 3 2 4 2 4
+--R 2b d x + (- 4a b d + 9b c d )x + (12a b d - 27a b c d + 18b c d)x
+--R +
+--R 3 3 2 2 2 3 2 2 4 3 3 2 2 2 2
+--R (18a b d - 36a b c d + 18a b c d)x - 6a d + 18a b c d - 18a b c d
+--R +
+--R 3 3
+--R 6a b c
+--R /
+--R 6 2 5
+--R 12b x + 12a b
+--R Type: Union(Expression(Integer),...)
+--E 255
+
+--S 256 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 257
+
+)clear all
+
+--S 258 of 1527
+t0:=x^2*(c+d*x^2)^3/(a+b*x^2)^2
+--R
+--R
+--R 3 8 2 6 2 4 3 2
+--R d x + 3c d x + 3c d x + c x
+--R (1) -------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 258
+
+--S 259 of 1527
+r0a:=3*d*(b*c-a*d)^2*x/b^4+1/3*d^2*(3*b*c-2*a*d)*x^3/b^3+1/5*d^3*x^5/b^2-_
+ 1/2*(b*c-a*d)^3*x/(b^4*(a+b*x^2))+1/2*(b*c-7*a*d)*(b*c-a*d)^2*_
+ atan(x*sqrt(b)/sqrt(a))/(b^(9/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 105a b d + 225a b c d - 135a b c d + 15b c )x - 105a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 225a b c d - 135a b c d + 15a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 3 7 2 3 3 2 5
+--R 6b d x + (- 14a b d + 30b c d )x
+--R +
+--R 2 3 2 2 3 2 3
+--R (70a b d - 150a b c d + 90b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (105a d - 225a b c d + 135a b c d - 15b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 5 2 4 +-+ +-+
+--R (30b x + 30a b )\|a \|b
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 1527
+r0b:=3*d*(b*c-a*d)^2*x/b^4+_
+ 1/3*d^2*(3*b*c-2*a*d)*x^3/b^3+1/5*d^3*x^5/b^2-1/2*(b*c-a*d)^3*x/_
+ (b^4*(a+b*x^2))+(b*c-4*a*d)*(b*c-a*d)^2*atan(x*sqrt(b)/sqrt(a))/_
+ (b^(9/2)*sqrt(a))-1/2*(b*c-a*d)^3*atan(x*sqrt(b)/sqrt(a))/_
+ (b^(9/2)*sqrt(a))
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 105a b d + 225a b c d - 135a b c d + 15b c )x - 105a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 225a b c d - 135a b c d + 15a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 3 7 2 3 3 2 5
+--R 6b d x + (- 14a b d + 30b c d )x
+--R +
+--R 2 3 2 2 3 2 3
+--R (70a b d - 150a b c d + 90b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (105a d - 225a b c d + 135a b c d - 15b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 5 2 4 +-+ +-+
+--R (30b x + 30a b )\|a \|b
+--R Type: Expression(Integer)
+--E 260
+
+--S 261 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (105a b d - 225a b c d + 135a b c d - 15b c )x + 105a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 225a b c d + 135a b c d - 15a b c
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 3 7 2 3 3 2 5
+--R 12b d x + (- 28a b d + 60b c d )x
+--R +
+--R 2 3 2 2 3 2 3
+--R (140a b d - 300a b c d + 180b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (210a d - 450a b c d + 270a b c d - 30b c )x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 5 2 4 +-----+
+--R (60b x + 60a b )\|- a b
+--R ,
+--R
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 105a b d + 225a b c d - 135a b c d + 15b c )x - 105a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 225a b c d - 135a b c d + 15a b c
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 3 3 7 2 3 3 2 5
+--R 6b d x + (- 14a b d + 30b c d )x
+--R +
+--R 2 3 2 2 3 2 3
+--R (70a b d - 150a b c d + 90b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (105a d - 225a b c d + 135a b c d - 15b c )x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 5 2 4 +---+
+--R (30b x + 30a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 261
+
+--S 262 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (7a d - 15a b c d + 9a b c d - b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (14a d - 30a b c d + 18a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-----+ +-+ +-+
+--R 4b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 263
+
+--S 264 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (- 7a d + 15a b c d - 9a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (7a d - 15a b c d + 9a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+ +-+ +---+
+--R 2b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 265
+
+--S 266 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (7a d - 15a b c d + 9a b c d - b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (14a d - 30a b c d + 18a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-----+ +-+ +-+
+--R 4b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (- 7a d + 15a b c d - 9a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (7a d - 15a b c d + 9a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+ +-+ +---+
+--R 2b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 268
+
+--S 269 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 269
+
+)clear all
+
+--S 270 of 1527
+t0:=x*(c+d*x^2)^3/(a+b*x^2)^2
+--R
+--R
+--R 3 7 2 5 2 3 3
+--R d x + 3c d x + 3c d x + c x
+--R (1) ------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 270
+
+--S 271 of 1527
+r0:=1/2*d^2*(3*b*c-2*a*d)*x^2/b^3+1/4*d^3*x^4/b^2-1/2*(b*c-a*d)^3/(b^4*_
+ (a+b*x^2))+3/2*d*(b*c-a*d)^2*log(a+b*x^2)/b^4
+--R
+--R
+--R (2)
+--R 2 3 2 2 3 2 2 3 3 2 2 2 2
+--R ((6a b d - 12a b c d + 6b c d)x + 6a d - 12a b c d + 6a b c d)
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 3 3 6 2 3 3 2 4 2 3 2 2 2 3 3
+--R b d x + (- 3a b d + 6b c d )x + (- 4a b d + 6a b c d )x + 2a d
+--R +
+--R 2 2 2 2 3 3
+--R - 6a b c d + 6a b c d - 2b c
+--R /
+--R 5 2 4
+--R 4b x + 4a b
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 3 2 2 3 3 2 2 2 2
+--R ((6a b d - 12a b c d + 6b c d)x + 6a d - 12a b c d + 6a b c d)
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 3 3 6 2 3 3 2 4 2 3 2 2 2 3 3
+--R b d x + (- 3a b d + 6b c d )x + (- 4a b d + 6a b c d )x + 2a d
+--R +
+--R 2 2 2 2 3 3
+--R - 6a b c d + 6a b c d - 2b c
+--R /
+--R 5 2 4
+--R 4b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 272
+
+--S 273 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 273
+
+--S 274 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 274
+
+)clear all
+
+--S 275 of 1527
+t0:=(c+d*x^2)^3/(a+b*x^2)^2
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 275
+
+--S 276 of 1527
+r0:=d^2*(3*b*c-2*a*d)*x/b^3+1/3*d^3*x^3/b^2+1/2*(b*c-a*d)^3*x/(a*b^3*_
+ (a+b*x^2))+1/2*(b*c-a*d)^2*(b*c+5*a*d)*atan(x*sqrt(b)/sqrt(a))/_
+ (a^(3/2)*b^(7/2))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (15a b d - 27a b c d + 9a b c d + 3b c )x + 15a d - 27a b c d
+--R +
+--R 2 2 2 3 3
+--R 9a b c d + 3a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 5 2 3 2 2 3
+--R 2a b d x + (- 10a b d + 18a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 15a d + 27a b c d - 9a b c d + 3b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 4 2 2 3 +-+ +-+
+--R (6a b x + 6a b )\|a \|b
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (15a b d - 27a b c d + 9a b c d + 3b c )x + 15a d - 27a b c d
+--R +
+--R 2 2 2 3 3
+--R 9a b c d + 3a b c
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 5 2 3 2 2 3
+--R 4a b d x + (- 20a b d + 36a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 30a d + 54a b c d - 18a b c d + 6b c )x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 4 2 2 3 +-----+
+--R (12a b x + 12a b )\|- a b
+--R ,
+--R
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (15a b d - 27a b c d + 9a b c d + 3b c )x + 15a d - 27a b c d
+--R +
+--R 2 2 2 3 3
+--R 9a b c d + 3a b c
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 3 5 2 3 2 2 3
+--R 2a b d x + (- 10a b d + 18a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 15a d + 27a b c d - 9a b c d + 3b c )x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 4 2 2 3 +---+
+--R (6a b x + 6a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 277
+
+--S 278 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (5a d - 9a b c d + 3a b c d + b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (- 10a d + 18a b c d - 6a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 278
+
+--S 279 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (5a d - 9a b c d + 3a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (- 5a d + 9a b c d - 3a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+ +-+ +---+
+--R 2a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 280
+
+--S 281 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 281
+
+)clear all
+
+--S 282 of 1527
+t0:=(c+d*x^2)^3/(x*(a+b*x^2)^2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 282
+
+--S 283 of 1527
+r0:=1/2*d^3*x^2/b^2+1/2*(b*c-a*d)^3/(a*b^3*(a+b*x^2))+c^3*log(x)/a^2-_
+ 1/2*(b*c-a*d)^2*(b*c+2*a*d)*log(a+b*x^2)/(a^2*b^3)
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 4 3 2 4 3 3 2 3 3
+--R ((- 2a b d + 3a b c d - b c )x - 2a d + 3a b c d - a b c )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 4 3 2 3 3 2 2 3 4 3 3 2 4 3 3 2
+--R (2b c x + 2a b c )log(x) + a b d x + a b d x - a d + 3a b c d
+--R +
+--R 2 2 2 3 3
+--R - 3a b c d + a b c
+--R /
+--R 2 4 2 3 3
+--R 2a b x + 2a b
+--R Type: Expression(Integer)
+--E 283
+
+--S 284 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 4 3 2 4 3 3 2 3 3
+--R ((- 2a b d + 3a b c d - b c )x - 2a d + 3a b c d - a b c )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 4 3 2 3 3 2 2 3 4 3 3 2 4 3 3 2
+--R (2b c x + 2a b c )log(x) + a b d x + a b d x - a d + 3a b c d
+--R +
+--R 2 2 2 3 3
+--R - 3a b c d + a b c
+--R /
+--R 2 4 2 3 3
+--R 2a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 284
+
+--S 285 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 285
+
+--S 286 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 286
+
+)clear all
+
+--S 287 of 1527
+t0:=(c+d*x^2)^3/(x^2*(a+b*x^2)^2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 287
+
+--S 288 of 1527
+r0a:=-c^3/(a^2*x)+d^3*x/b^2-1/2*(b*c-a*d)^3*x/(a^2*b^2*(a+b*x^2))-_
+ 3/2*(b*c-a*d)^2*(b*c+a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*_
+ b^(5/2))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 3a b d + 3a b c d + 3a b c d - 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 3a d + 3a b c d + 3a b c d - 3a b c )x
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 4 3 3 2 2 2 2 3 3 2 2 3 +-+ +-+
+--R (2a b d x + (3a d - 3a b c d + 3a b c d - 3b c )x - 2a b c )\|a \|b
+--R /
+--R 2 3 3 3 2 +-+ +-+
+--R (2a b x + 2a b x)\|a \|b
+--R Type: Expression(Integer)
+--E 288
+
+--S 289 of 1527
+r0b:=-c^3/(a^2*x)+d^3*x/b^2-1/2*(b*c-a*d)^3*x/(a^2*b^2*_
+ (a+b*x^2))-1/2*(b*c-a*d)^3*atan(x*sqrt(b)/sqrt(a))/_
+ (a^(5/2)*b^(5/2))-(b*c-a*d)^2*(b*c+2*a*d)*atan(x*sqrt(b)/_
+ sqrt(a))/(a^(5/2)*b^(5/2))
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 3a b d + 3a b c d + 3a b c d - 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 3a d + 3a b c d + 3a b c d - 3a b c )x
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 4 3 3 2 2 2 2 3 3 2 2 3 +-+ +-+
+--R (2a b d x + (3a d - 3a b c d + 3a b c d - 3b c )x - 2a b c )\|a \|b
+--R /
+--R 2 3 3 3 2 +-+ +-+
+--R (2a b x + 2a b x)\|a \|b
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 3 3 2 2 2 3 2 4 3 3
+--R (3a b d - 3a b c d - 3a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (3a d - 3a b c d - 3a b c d + 3a b c )x
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 4 3 3 2 2 2 2 3 3 2 2 3 +-----+
+--R (4a b d x + (6a d - 6a b c d + 6a b c d - 6b c )x - 4a b c )\|- a b
+--R /
+--R 2 3 3 3 2 +-----+
+--R (4a b x + 4a b x)\|- a b
+--R ,
+--R
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 3a b d + 3a b c d + 3a b c d - 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 3a d + 3a b c d + 3a b c d - 3a b c )x
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 3 4 3 3 2 2 2 2 3 3 2 2 3 +---+
+--R (2a b d x + (3a d - 3a b c d + 3a b c d - 3b c )x - 2a b c )\|a b
+--R /
+--R 2 3 3 3 2 +---+
+--R (2a b x + 2a b x)\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 290
+
+--S 291 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (3a d - 3a b c d - 3a b c d + 3b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (6a d - 6a b c d - 6a b c d + 6b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 +-----+ +-+ +-+
+--R 4a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (- 3a d + 3a b c d + 3a b c d - 3b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (3a d - 3a b c d - 3a b c d + 3b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 +-+ +-+ +---+
+--R 2a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 293
+
+--S 294 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (3a d - 3a b c d - 3a b c d + 3b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (6a d - 6a b c d - 6a b c d + 6b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 +-----+ +-+ +-+
+--R 4a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 295
+
+--S 296 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (- 3a d + 3a b c d + 3a b c d - 3b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (3a d - 3a b c d - 3a b c d + 3b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 +-+ +-+ +---+
+--R 2a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 298
+
+)clear all
+
+--S 299 of 1527
+t0:=(c+d*x^2)^3/(x^3*(a+b*x^2)^2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 299
+
+--S 300 of 1527
+r0:=-1/2*c^3/(a^2*x^2)-1/2*(b*c-a*d)^3/(a^2*b^2*(a+b*x^2))-_
+ c^2*(2*b*c-3*a*d)*log(x)/a^3+1/2*(b*c-a*d)^2*(2*b*c+a*d)*_
+ log(a+b*x^2)/(a^3*b^2)
+--R
+--R
+--R (2)
+--R 3 3 3 2 4 3 4 4 3 2 2 2 3 3 2
+--R ((a b d - 3a b c d + 2b c )x + (a d - 3a b c d + 2a b c )x )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 3 2 4 3 4 2 2 2 3 3 2
+--R ((6a b c d - 4b c )x + (6a b c d - 4a b c )x )log(x)
+--R +
+--R 4 3 3 2 2 2 2 3 3 2 2 2 3
+--R (a d - 3a b c d + 3a b c d - 2a b c )x - a b c
+--R /
+--R 3 3 4 4 2 2
+--R 2a b x + 2a b x
+--R Type: Expression(Integer)
+--E 300
+
+--S 301 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 3 2 4 3 4 4 3 2 2 2 3 3 2
+--R ((a b d - 3a b c d + 2b c )x + (a d - 3a b c d + 2a b c )x )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 3 2 4 3 4 2 2 2 3 3 2
+--R ((6a b c d - 4b c )x + (6a b c d - 4a b c )x )log(x)
+--R +
+--R 4 3 3 2 2 2 2 3 3 2 2 2 3
+--R (a d - 3a b c d + 3a b c d - 2a b c )x - a b c
+--R /
+--R 3 3 4 4 2 2
+--R 2a b x + 2a b x
+--R Type: Union(Expression(Integer),...)
+--E 301
+
+--S 302 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 303
+
+)clear all
+
+--S 304 of 1527
+t0:=(c+d*x^2)^3/(x^4*(a+b*x^2)^2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 304
+
+--S 305 of 1527
+r0a:=-1/3*c^3/(a^2*x^3)+c^2*(2*b*c-3*a*d)/(a^3*x)+1/2*(b*c-a*d)^3*_
+ x/(a^3*b*(a+b*x^2))+1/2*(b*c-a*d)^2*(5*b*c+a*d)*atan(x*_
+ sqrt(b)/sqrt(a))/(a^(7/2)*b^(3/2))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 5
+--R (3a b d + 9a b c d - 27a b c d + 15b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 3
+--R (3a d + 9a b c d - 27a b c d + 15a b c )x
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 3a d + 9a b c d - 27a b c d + 15b c )x
+--R +
+--R 2 2 2 3 2 2 3
+--R (- 18a b c d + 10a b c )x - 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 3 2 5 4 3 +-+ +-+
+--R (6a b x + 6a b x )\|a \|b
+--R Type: Expression(Integer)
+--E 305
+
+--S 306 of 1527
+r0b:=-1/3*c^3/(a^2*x^3)+_
+ c^2*(2*b*c-3*a*d)/(a^3*x)+1/2*(b*c-a*d)^3*x/(a^3*b*(a+b*x^2))+_
+ 1/2*(b*c-a*d)^3*atan(x*sqrt(b)/sqrt(a))/(a^(7/2)*b^(3/2))+_
+ (b*c-a*d)^2*(2*b*c+a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(7/2)*b^(3/2))
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 3 2 4 3 5
+--R (3a b d + 9a b c d - 27a b c d + 15b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 3
+--R (3a d + 9a b c d - 27a b c d + 15a b c )x
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 3a d + 9a b c d - 27a b c d + 15b c )x
+--R +
+--R 2 2 2 3 2 2 3
+--R (- 18a b c d + 10a b c )x - 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 3 2 5 4 3 +-+ +-+
+--R (6a b x + 6a b x )\|a \|b
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 3 3 2 2 2 3 2 4 3 5
+--R (3a b d + 9a b c d - 27a b c d + 15b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 3
+--R (3a d + 9a b c d - 27a b c d + 15a b c )x
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 6a d + 18a b c d - 54a b c d + 30b c )x
+--R +
+--R 2 2 2 3 2 2 3
+--R (- 36a b c d + 20a b c )x - 4a b c
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 3 2 5 4 3 +-----+
+--R (12a b x + 12a b x )\|- a b
+--R ,
+--R
+--R 3 3 2 2 2 3 2 4 3 5
+--R (3a b d + 9a b c d - 27a b c d + 15b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 3
+--R (3a d + 9a b c d - 27a b c d + 15a b c )x
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 3a d + 9a b c d - 27a b c d + 15b c )x
+--R +
+--R 2 2 2 3 2 2 3
+--R (- 18a b c d + 10a b c )x - 2a b c
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 3 2 5 4 3 +---+
+--R (6a b x + 6a b x )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 307
+
+--S 308 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (a d + 3a b c d - 9a b c d + 5b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (- 2a d - 6a b c d + 18a b c d - 10b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 308
+
+--S 309 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (a d + 3a b c d - 9a b c d + 5b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (- a d - 3a b c d + 9a b c d - 5b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+ +-+ +---+
+--R 2a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 310
+
+--S 311 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (a d + 3a b c d - 9a b c d + 5b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (- 2a d - 6a b c d + 18a b c d - 10b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 313
+
+--S 314 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (a d + 3a b c d - 9a b c d + 5b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (- a d - 3a b c d + 9a b c d - 5b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+ +-+ +---+
+--R 2a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 1527
+t0:=x^4/((a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 4
+--R x
+--R (1) --------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 316
+
+--S 317 of 1527
+r0a:=1/2*a*x/(b*(b*c-a*d)*(a+b*x^2))-1/2*(3*b*c-a*d)*atan(x*sqrt(b)/_
+ sqrt(a))*sqrt(a)/(b^(3/2)*(b*c-a*d)^2)+c^(3/2)*atan(x*sqrt(d)/_
+ sqrt(c))/((b*c-a*d)^2*sqrt(d))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (2b c x + 2a b c)\|b \|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 +-+ +-+ x\|b
+--R ((a b d - 3b c)x + a d - 3a b c)\|a \|d atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 +-+ +-+
+--R (- a d + a b c)x\|b \|d
+--R /
+--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +-+ +-+
+--R ((2a b d - 4a b c d + 2b c )x + 2a b d - 4a b c d + 2a b c )\|b \|d
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 1527
+r0b:=1/2*a*x/(b*(b*c-a*d)*(a+b*x^2))+_
+ 1/2*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/(b^(3/2)*(b*c-a*d))-_
+ (2*b*c-a*d)*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/(b^(3/2)*(b*c-a*d)^2)+_
+ c^(3/2)*atan(x*sqrt(d)/sqrt(c))/((b*c-a*d)^2*sqrt(d))
+--R
+--R
+--R (3)
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (2b c x + 2a b c)\|b \|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 +-+ +-+ x\|b
+--R ((a b d - 3b c)x + a d - 3a b c)\|a \|d atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 +-+ +-+
+--R (- a d + a b c)x\|b \|d
+--R /
+--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +-+ +-+
+--R ((2a b d - 4a b c d + 2b c )x + 2a b d - 4a b c d + 2a b c )\|b \|d
+--R Type: Expression(Integer)
+--E 318
+
+--S 319 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R +---+
+--R | c 2
+--R +---+ 2d x |- - + d x - c
+--R 2 2 | c \| d
+--R (2b c x + 2a b c) |- - log(---------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 2 2 | a \| b
+--R ((a b d - 3b c)x + a d - 3a b c) |- - log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 2
+--R (- 2a d + 2a b c)x
+--R /
+--R 2 2 2 3 4 2 2 3 2 2 2 3 2
+--R (4a b d - 8a b c d + 4b c )x + 4a b d - 8a b c d + 4a b c
+--R ,
+--R
+--R +---+
+--R | c 2
+--R +---+ 2d x |- - + d x - c
+--R 2 2 | c \| d
+--R (b c x + a b c) |- - log(---------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 2 |a \|b 2
+--R ((- a b d + 3b c)x - a d + 3a b c) |- atan(----) + (- a d + a b c)x
+--R \|b x
+--R /
+--R 2 2 2 3 4 2 2 3 2 2 2 3 2
+--R (2a b d - 4a b c d + 2b c )x + 2a b d - 4a b c d + 2a b c
+--R ,
+--R
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 2 2 | a \| b
+--R ((a b d - 3b c)x + a d - 3a b c) |- - log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R |c
+--R +-+ |-
+--R 2 2 |c \|d 2
+--R (- 4b c x - 4a b c) |- atan(----) + (- 2a d + 2a b c)x
+--R \|d x
+--R /
+--R 2 2 2 3 4 2 2 3 2 2 2 3 2
+--R (4a b d - 8a b c d + 4b c )x + 4a b d - 8a b c d + 4a b c
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 2 |a \|b
+--R ((- a b d + 3b c)x - a d + 3a b c) |- atan(----)
+--R \|b x
+--R +
+--R +-+
+--R |c
+--R +-+ |-
+--R 2 2 |c \|d 2
+--R (- 2b c x - 2a b c) |- atan(----) + (- a d + a b c)x
+--R \|d x
+--R /
+--R 2 2 2 3 4 2 2 3 2 2 2 3 2
+--R (2a b d - 4a b c d + 2b c )x + 2a b d - 4a b c d + 2a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 319
+
+--S 320 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R | c 2
+--R +---+ 2d x |- - + d x - c
+--R | c +-+ +-+ \| d
+--R 2b c |- - \|b \|d log(---------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a +-+ +-+ \| b
+--R (a d - 3b c) |- - \|b \|d log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R - 4b c\|b \|c atan(-----) + (- 2a d + 6b c)\|a \|d atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 2 2 2 3 2 +-+ +-+
+--R (4a b d - 8a b c d + 4b c )\|b \|d
+--R Type: Expression(Integer)
+--E 320
+
+--S 321 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R | c 2
+--R +---+ 2d x |- - + d x - c +-+
+--R | c +-+ +-+ \| d +-+ +-+ x\|d
+--R b c |- - \|b \|d log(---------------------) - 2b c\|b \|c atan(-----)
+--R \| d 2 +-+
+--R d x + c \|c
+--R +
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ +-+ x\|b |a +-+ +-+ \|b
+--R (- a d + 3b c)\|a \|d atan(-----) + (- a d + 3b c) |- \|b \|d atan(----)
+--R +-+ \|b x
+--R \|a
+--R /
+--R 2 2 2 3 2 +-+ +-+
+--R (2a b d - 4a b c d + 2b c )\|b \|d
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 323
+
+--S 324 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +---+
+--R | c 2
+--R +---+ 2d x |- - + d x - c
+--R | c +-+ +-+ \| d
+--R 2b c |- - \|b \|d log(---------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a +-+ +-+ \| b
+--R (a d - 3b c) |- - \|b \|d log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R - 4b c\|b \|c atan(-----) + (- 2a d + 6b c)\|a \|d atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 2 2 2 3 2 +-+ +-+
+--R (4a b d - 8a b c d + 4b c )\|b \|d
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 325
+
+--S 326 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R | c 2
+--R +---+ 2d x |- - + d x - c +-+
+--R | c +-+ +-+ \| d +-+ +-+ x\|d
+--R b c |- - \|b \|d log(---------------------) - 2b c\|b \|c atan(-----)
+--R \| d 2 +-+
+--R d x + c \|c
+--R +
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ +-+ x\|b |a +-+ +-+ \|b
+--R (- a d + 3b c)\|a \|d atan(-----) + (- a d + 3b c) |- \|b \|d atan(----)
+--R +-+ \|b x
+--R \|a
+--R /
+--R 2 2 2 3 2 +-+ +-+
+--R (2a b d - 4a b c d + 2b c )\|b \|d
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 327
+
+)clear all
+
+--S 328 of 1527
+t0:=x^3/((a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 3
+--R x
+--R (1) --------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 328
+
+--S 329 of 1527
+r0:=1/2*a/(b*(b*c-a*d)*(a+b*x^2))+1/2*c*log(a+b*x^2)/(b*c-a*d)^2-_
+ 1/2*c*log(c+d*x^2)/(b*c-a*d)^2
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2 2
+--R (- b c x - a b c)log(d x + c) + (b c x + a b c)log(b x + a) - a d + a b c
+--R -----------------------------------------------------------------------------
+--R 2 2 2 3 4 2 2 3 2 2 2 3 2
+--R (2a b d - 4a b c d + 2b c )x + 2a b d - 4a b c d + 2a b c
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2 2
+--R (- b c x - a b c)log(d x + c) + (b c x + a b c)log(b x + a) - a d + a b c
+--R -----------------------------------------------------------------------------
+--R 2 2 2 3 4 2 2 3 2 2 2 3 2
+--R (2a b d - 4a b c d + 2b c )x + 2a b d - 4a b c d + 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 330
+
+--S 331 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 332
+
+)clear all
+
+--S 333 of 1527
+t0:=x^2/((a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) --------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 333
+
+--S 334 of 1527
+r0a:=-1/2*x/((b*c-a*d)*(a+b*x^2))+1/2*(b*c+a*d)*atan(x*sqrt(b)/sqrt(a))/_
+ ((b*c-a*d)^2*sqrt(a)*sqrt(b))-atan(x*sqrt(d)/sqrt(c))*sqrt(c)*_
+ sqrt(d)/(b*c-a*d)^2
+--R
+--R
+--R (2)
+--R +-+
+--R 2 +-+ +-+ +-+ +-+ x\|d
+--R (- 2b x - 2a)\|a \|b \|c \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 x\|b +-+ +-+
+--R ((a b d + b c)x + a d + a b c)atan(-----) + (a d - b c)x\|a \|b
+--R +-+
+--R \|a
+--R /
+--R 2 2 2 3 2 2 3 2 2 2 2 +-+ +-+
+--R ((2a b d - 4a b c d + 2b c )x + 2a d - 4a b c d + 2a b c )\|a \|b
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 1527
+r0b:=-1/2*x/((b*c-a*d)*(a+b*x^2))-1/2*atan(x*_
+ sqrt(b)/sqrt(a))/((b*c-a*d)*sqrt(a)*sqrt(b))+c*atan(x*sqrt(b)/_
+ sqrt(a))*sqrt(b)/((b*c-a*d)^2*sqrt(a))-atan(x*sqrt(d)/sqrt(c))*_
+ sqrt(c)*sqrt(d)/(b*c-a*d)^2
+--R
+--R
+--R (3)
+--R +-+
+--R 2 +-+ +-+ +-+ +-+ x\|d
+--R (- 2b x - 2a)\|a \|b \|c \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 x\|b +-+ +-+
+--R ((a b d + b c)x + a d + a b c)atan(-----) + (a d - b c)x\|a \|b
+--R +-+
+--R \|a
+--R /
+--R 2 2 2 3 2 2 3 2 2 2 2 +-+ +-+
+--R ((2a b d - 4a b c d + 2b c )x + 2a d - 4a b c d + 2a b c )\|a \|b
+--R Type: Expression(Integer)
+--E 335
+
+--S 336 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 +-----+
+--R 2 2 2 (b x - a)\|- a b + 2a b x
+--R ((a b d + b c)x + a d + a b c)log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-----+ 2
+--R 2 +-----+ +-----+ - 2x\|- c d + d x - c
+--R (2b x + 2a)\|- c d \|- a b log(-----------------------)
+--R 2
+--R d x + c
+--R +
+--R +-----+
+--R (2a d - 2b c)x\|- a b
+--R /
+--R 2 2 2 3 2 2 3 2 2 2 2 +-----+
+--R ((4a b d - 8a b c d + 4b c )x + 4a d - 8a b c d + 4a b c )\|- a b
+--R ,
+--R
+--R +-----+ 2
+--R 2 +-----+ +---+ - 2x\|- c d + d x - c
+--R (b x + a)\|- c d \|a b log(-----------------------)
+--R 2
+--R d x + c
+--R +
+--R +---+
+--R 2 2 2 x\|a b +---+
+--R ((a b d + b c)x + a d + a b c)atan(-------) + (a d - b c)x\|a b
+--R a
+--R /
+--R 2 2 2 3 2 2 3 2 2 2 2 +---+
+--R ((2a b d - 4a b c d + 2b c )x + 2a d - 4a b c d + 2a b c )\|a b
+--R ,
+--R
+--R 2 +-----+
+--R 2 2 2 (b x - a)\|- a b + 2a b x
+--R ((a b d + b c)x + a d + a b c)log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +---+
+--R 2 +-----+ +---+ \|c d +-----+
+--R (4b x + 4a)\|- a b \|c d atan(------) + (2a d - 2b c)x\|- a b
+--R d x
+--R /
+--R 2 2 2 3 2 2 3 2 2 2 2 +-----+
+--R ((4a b d - 8a b c d + 4b c )x + 4a d - 8a b c d + 4a b c )\|- a b
+--R ,
+--R
+--R +---+
+--R 2 +---+ +---+ \|c d
+--R (2b x + 2a)\|a b \|c d atan(------)
+--R d x
+--R +
+--R +---+
+--R 2 2 2 x\|a b +---+
+--R ((a b d + b c)x + a d + a b c)atan(-------) + (a d - b c)x\|a b
+--R a
+--R /
+--R 2 2 2 3 2 2 3 2 2 2 2 +---+
+--R ((2a b d - 4a b c d + 2b c )x + 2a d - 4a b c d + 2a b c )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 336
+
+--S 337 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d + b c)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-----+ 2
+--R +-----+ +-----+ +-+ +-+ - 2x\|- c d + d x - c
+--R 2\|- c d \|- a b \|a \|b log(-----------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R +-----+ +-+ +-+ +-+ +-+ x\|d +-----+ x\|b
+--R 4\|- a b \|a \|b \|c \|d atan(-----) + (- 2a d - 2b c)\|- a b atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 2 2 2 2 +-----+ +-+ +-+
+--R (4a d - 8a b c d + 4b c )\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 338
+
+--S 339 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +-----+ 2
+--R +-----+ +-+ +-+ +---+ - 2x\|- c d + d x - c
+--R \|- c d \|a \|b \|a b log(-----------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+ +---+
+--R +-+ +-+ +---+ +-+ +-+ x\|d +-+ +-+ x\|a b
+--R 2\|a \|b \|a b \|c \|d atan(-----) + (a d + b c)\|a \|b atan(-------)
+--R +-+ a
+--R \|c
+--R +
+--R +-+
+--R +---+ x\|b
+--R (- a d - b c)\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 2 2 +-+ +-+ +---+
+--R (2a d - 4a b c d + 2b c )\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 340
+
+--S 341 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d + b c)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-----+ 2
+--R +-----+ +-----+ +-+ +-+ - 2x\|- c d + d x - c
+--R 2\|- c d \|- a b \|a \|b log(-----------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R +-----+ +-+ +-+ +-+ +-+ x\|d +-----+ x\|b
+--R 4\|- a b \|a \|b \|c \|d atan(-----) + (- 2a d - 2b c)\|- a b atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 2 2 2 2 +-----+ +-+ +-+
+--R (4a d - 8a b c d + 4b c )\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +-----+ 2
+--R +-----+ +-+ +-+ +---+ - 2x\|- c d + d x - c
+--R \|- c d \|a \|b \|a b log(-----------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+ +---+
+--R +-+ +-+ +---+ +-+ +-+ x\|d +-+ +-+ x\|a b
+--R 2\|a \|b \|a b \|c \|d atan(-----) + (a d + b c)\|a \|b atan(-------)
+--R +-+ a
+--R \|c
+--R +
+--R +-+
+--R +---+ x\|b
+--R (- a d - b c)\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 2 2 +-+ +-+ +---+
+--R (2a d - 4a b c d + 2b c )\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 343
+
+--S 344 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 344
+
+)clear all
+
+--S 345 of 1527
+t0:=x/((a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R x
+--R (1) --------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 345
+
+--S 346 of 1527
+r0:=(-1/2)/((b*c-a*d)*(a+b*x^2))-1/2*d*log(a+b*x^2)/(b*c-a*d)^2+_
+ 1/2*d*log(c+d*x^2)/(b*c-a*d)^2
+--R
+--R
+--R (2)
+--R 2 2 2 2
+--R (b d x + a d)log(d x + c) + (- b d x - a d)log(b x + a) + a d - b c
+--R -----------------------------------------------------------------------
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R (2a b d - 4a b c d + 2b c )x + 2a d - 4a b c d + 2a b c
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2
+--R (b d x + a d)log(d x + c) + (- b d x - a d)log(b x + a) + a d - b c
+--R -----------------------------------------------------------------------
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R (2a b d - 4a b c d + 2b c )x + 2a d - 4a b c d + 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 347
+
+--S 348 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 348
+
+--S 349 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 349
+
+)clear all
+
+--S 350 of 1527
+t0:=1/((a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 350
+
+--S 351 of 1527
+r0:=1/2*b*x/(a*(b*c-a*d)*(a+b*x^2))+1/2*(b*c-3*a*d)*atan(x*sqrt(b)/_
+ sqrt(a))*sqrt(b)/(a^(3/2)*(b*c-a*d)^2)+d^(3/2)*atan(x*sqrt(d)/_
+ sqrt(c))/((b*c-a*d)^2*sqrt(c))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (2a b d x + 2a d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 +-+ +-+ x\|b
+--R ((- 3a b d + b c)x - 3a d + a b c)\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 +-+ +-+
+--R (- a b d + b c)x\|a \|c
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2 +-+ +-+
+--R ((2a b d - 4a b c d + 2a b c )x + 2a d - 4a b c d + 2a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 | d \| c
+--R (2a b d x + 2a d) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 | b \| a
+--R ((3a b d - b c)x + 3a d - a b c) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2
+--R (- 2a b d + 2b c)x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (4a b d - 8a b c d + 4a b c )x + 4a d - 8a b c d + 4a b c
+--R ,
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 | b \| a
+--R ((3a b d - b c)x + 3a d - a b c) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 |d \|c 2
+--R (- 4a b d x - 4a d) |- atan(-----) + (- 2a b d + 2b c)x
+--R \|c d x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (4a b d - 8a b c d + 4a b c )x + 4a d - 8a b c d + 4a b c
+--R ,
+--R
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 | d \| c
+--R (a b d x + a d) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 2 |b \|a 2
+--R ((3a b d - b c)x + 3a d - a b c) |- atan(-----) + (- a b d + b c)x
+--R \|a b x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (2a b d - 4a b c d + 2a b c )x + 2a d - 4a b c d + 2a b c
+--R ,
+--R
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 |d \|c
+--R (- 2a b d x - 2a d) |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 2 |b \|a 2
+--R ((3a b d - b c)x + 3a d - a b c) |- atan(-----) + (- a b d + b c)x
+--R \|a b x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (2a b d - 4a b c d + 2a b c )x + 2a d - 4a b c d + 2a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 352
+
+--S 353 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d +-+ +-+ \| c
+--R 2a d |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R (3a d - b c) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R - 4a d\|a \|d atan(-----) + (6a d - 2b c)\|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 3 2 2 2 2 +-+ +-+
+--R (4a d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 353
+
+--S 354 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R (3a d - b c) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ +-+ c |-
+--R +-+ +-+ x\|d +-+ +-+ |d \|c
+--R - 4a d\|a \|d atan(-----) - 4a d\|a \|c |- atan(-----)
+--R +-+ \|c d x
+--R \|c
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R (6a d - 2b c)\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 2 2 2 2 +-+ +-+
+--R (4a d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 355
+
+--S 356 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 356
+
+)clear all
+
+--S 357 of 1527
+t0:=1/(x*(a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------
+--R 2 7 2 5 2 3 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 357
+
+--S 358 of 1527
+r0:=1/2*b/(a*(b*c-a*d)*(a+b*x^2))+log(x)/(a^2*c)-1/2*b*(b*c-2*a*d)*_
+ log(a+b*x^2)/(a^2*(b*c-a*d)^2)-1/2*d^2*log(c+d*x^2)/(c*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2
+--R (- a b d x - a d )log(d x + c)
+--R +
+--R 2 3 2 2 2 2 2 2
+--R ((2a b c d - b c )x + 2a b c d - a b c )log(b x + a)
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((2a b d - 4a b c d + 2b c )x + 2a d - 4a b c d + 2a b c )log(x)
+--R +
+--R 2 2 2
+--R - a b c d + a b c
+--R /
+--R 4 2 3 2 2 2 3 3 2 5 2 4 2 3 2 3
+--R (2a b c d - 4a b c d + 2a b c )x + 2a c d - 4a b c d + 2a b c
+--R Type: Expression(Integer)
+--E 358
+
+--S 359 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 3 2 2
+--R (- a b d x - a d )log(d x + c)
+--R +
+--R 2 3 2 2 2 2 2 2
+--R ((2a b c d - b c )x + 2a b c d - a b c )log(b x + a)
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((2a b d - 4a b c d + 2b c )x + 2a d - 4a b c d + 2a b c )log(x)
+--R +
+--R 2 2 2
+--R - a b c d + a b c
+--R /
+--R 4 2 3 2 2 2 3 3 2 5 2 4 2 3 2 3
+--R (2a b c d - 4a b c d + 2a b c )x + 2a c d - 4a b c d + 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 359
+
+--S 360 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 360
+
+--S 361 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 361
+
+)clear all
+
+--S 362 of 1527
+t0:=1/(x^2*(a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R 2 8 2 6 2 4 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 362
+
+--S 363 of 1527
+r0a:=(-1)/(a^2*c*x)-1/2*b^2*x/(a^2*(b*c-a*d)*(a+b*x^2))-1/2*b^(3/2)*_
+ (3*b*c-5*a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-a*d)^2)-_
+ d^(5/2)*atan(x*sqrt(d)/sqrt(c))/(c^(3/2)*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 3 3 2 +-+ +-+ x\|d
+--R (- 2a b d x - 2a d x)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 3 2 3 2 2 2 +-+ +-+ x\|b
+--R ((5a b c d - 3b c )x + (5a b c d - 3a b c )x)\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2 +-+ +-+
+--R ((- 2a b d + 5a b c d - 3b c )x - 2a d + 4a b c d - 2a b c )\|a \|c
+--R /
+--R 4 2 3 2 2 2 3 3 3 5 2 4 2 3 2 3
+--R ((2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x)
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 363
+
+--S 364 of 1527
+r0b:=(-1)/(a^2*c*x)-1/2*b^2*x/(a^2*(b*c-a*d)*(a+b*x^2))-b^(3/2)*(b*c-2*a*d)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-a*d)^2)-1/2*b^(3/2)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-a*d))-d^(5/2)*_
+ atan(x*sqrt(d)/sqrt(c))/(c^(3/2)*(b*c-a*d)^2)
+--R
+--R
+--R (3)
+--R +-+
+--R 2 2 3 3 2 +-+ +-+ x\|d
+--R (- 2a b d x - 2a d x)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 3 2 3 2 2 2 +-+ +-+ x\|b
+--R ((5a b c d - 3b c )x + (5a b c d - 3a b c )x)\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2 +-+ +-+
+--R ((- 2a b d + 5a b c d - 3b c )x - 2a d + 4a b c d - 2a b c )\|a \|c
+--R /
+--R 4 2 3 2 2 2 3 3 3 5 2 4 2 3 2 3
+--R ((2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x)
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R +---+
+--R 2 3 2 3 2 2 2 | b
+--R ((5a b c d - 3b c )x + (5a b c d - 3a b c )x) |- -
+--R \| a
+--R *
+--R +---+
+--R | b 2
+--R 2a x |- - + b x - a
+--R \| a
+--R log(---------------------)
+--R 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R 2 2 3 3 2 | d \| c
+--R (2a b d x + 2a d x) |- - log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R (- 4a b d + 10a b c d - 6b c )x - 4a d + 8a b c d - 4a b c
+--R /
+--R 4 2 3 2 2 2 3 3 3 5 2 4 2 3 2 3
+--R (4a b c d - 8a b c d + 4a b c )x + (4a c d - 8a b c d + 4a b c )x
+--R ,
+--R
+--R +---+
+--R 2 3 2 3 2 2 2 | b
+--R ((5a b c d - 3b c )x + (5a b c d - 3a b c )x) |- -
+--R \| a
+--R *
+--R +---+
+--R | b 2
+--R 2a x |- - + b x - a
+--R \| a
+--R log(---------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 3 3 2 |d \|c 2 2 2 3 2 2
+--R (4a b d x + 4a d x) |- atan(-----) + (- 4a b d + 10a b c d - 6b c )x
+--R \|c d x
+--R +
+--R 3 2 2 2 2
+--R - 4a d + 8a b c d - 4a b c
+--R /
+--R 4 2 3 2 2 2 3 3 3 5 2 4 2 3 2 3
+--R (4a b c d - 8a b c d + 4a b c )x + (4a c d - 8a b c d + 4a b c )x
+--R ,
+--R
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R 2 2 3 3 2 | d \| c
+--R (a b d x + a d x) |- - log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 3 2 3 2 2 2 |b \|a
+--R ((- 5a b c d + 3b c )x + (- 5a b c d + 3a b c )x) |- atan(-----)
+--R \|a b x
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R (- 2a b d + 5a b c d - 3b c )x - 2a d + 4a b c d - 2a b c
+--R /
+--R 4 2 3 2 2 2 3 3 3 5 2 4 2 3 2 3
+--R (2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x
+--R ,
+--R
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 3 3 2 |d \|c
+--R (2a b d x + 2a d x) |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 3 2 3 2 2 2 |b \|a
+--R ((- 5a b c d + 3b c )x + (- 5a b c d + 3a b c )x) |- atan(-----)
+--R \|a b x
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R (- 2a b d + 5a b c d - 3b c )x - 2a d + 4a b c d - 2a b c
+--R /
+--R 4 2 3 2 2 2 3 3 3 5 2 4 2 3 2 3
+--R (2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 365
+
+--S 366 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R (5a b c d - 3b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R 2 2 | d +-+ +-+ \| c
+--R 2a d |- - \|a \|c log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R 2 2 +-+ +-+ x\|d 2 2 +-+ +-+ x\|b
+--R 4a d \|a \|d atan(-----) + (- 10a b c d + 6b c )\|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 4 2 3 2 2 2 3 +-+ +-+
+--R (4a c d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R (5a b c d - 3b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ +-+ c |-
+--R 2 2 +-+ +-+ x\|d 2 2 +-+ +-+ |d \|c
+--R 4a d \|a \|d atan(-----) + 4a d \|a \|c |- atan(-----)
+--R +-+ \|c d x
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R (- 10a b c d + 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 2 3 2 2 2 3 +-+ +-+
+--R (4a c d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R (5a b c d - 3b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R 2 2 | d +-+ +-+ \| c
+--R 2a d |- - \|a \|c log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R 2 2 +-+ +-+ x\|d 2 2 +-+ +-+ x\|b
+--R 4a d \|a \|d atan(-----) + (- 10a b c d + 6b c )\|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 4 2 3 2 2 2 3 +-+ +-+
+--R (4a c d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 370
+
+--S 371 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R (5a b c d - 3b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ +-+ c |-
+--R 2 2 +-+ +-+ x\|d 2 2 +-+ +-+ |d \|c
+--R 4a d \|a \|d atan(-----) + 4a d \|a \|c |- atan(-----)
+--R +-+ \|c d x
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R (- 10a b c d + 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 2 3 2 2 2 3 +-+ +-+
+--R (4a c d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 373
+
+)clear all
+
+--S 374 of 1527
+t0:=1/(x^3*(a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R 2 9 2 7 2 5 2 3
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 374
+
+--S 375 of 1527
+r0:=(-1/2)/(a^2*c*x^2)-1/2*b^2/(a^2*(b*c-a*d)*(a+b*x^2))-(2*b*c+a*d)*_
+ log(x)/(a^3*c^2)+1/2*b^2*(2*b*c-3*a*d)*log(a+b*x^2)/(a^3*_
+ (b*c-a*d)^2)+1/2*d^3*log(c+d*x^2)/(c^2*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R 3 3 4 4 3 2 2
+--R (a b d x + a d x )log(d x + c)
+--R +
+--R 3 2 4 3 4 2 2 2 3 3 2 2
+--R ((- 3a b c d + 2b c )x + (- 3a b c d + 2a b c )x )log(b x + a)
+--R +
+--R 3 3 3 2 4 3 4 4 3 2 2 2 3 3 2
+--R ((- 2a b d + 6a b c d - 4b c )x + (- 2a d + 6a b c d - 4a b c )x )
+--R *
+--R log(x)
+--R +
+--R 3 2 2 2 2 3 3 2 4 2 3 2 2 2 3
+--R (- a b c d + 3a b c d - 2a b c )x - a c d + 2a b c d - a b c
+--R /
+--R 5 2 2 4 2 3 3 3 4 4 6 2 2 5 3 4 2 4 2
+--R (2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x
+--R Type: Expression(Integer)
+--E 375
+
+--S 376 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 4 4 3 2 2
+--R (a b d x + a d x )log(d x + c)
+--R +
+--R 3 2 4 3 4 2 2 2 3 3 2 2
+--R ((- 3a b c d + 2b c )x + (- 3a b c d + 2a b c )x )log(b x + a)
+--R +
+--R 3 3 3 2 4 3 4 4 3 2 2 2 3 3 2
+--R ((- 2a b d + 6a b c d - 4b c )x + (- 2a d + 6a b c d - 4a b c )x )
+--R *
+--R log(x)
+--R +
+--R 3 2 2 2 2 3 3 2 4 2 3 2 2 2 3
+--R (- a b c d + 3a b c d - 2a b c )x - a c d + 2a b c d - a b c
+--R /
+--R 5 2 2 4 2 3 3 3 4 4 6 2 2 5 3 4 2 4 2
+--R (2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x
+--R Type: Union(Expression(Integer),...)
+--E 376
+
+--S 377 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 378
+
+)clear all
+
+--S 379 of 1527
+t0:=1/(x^4*(a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------------
+--R 2 10 2 8 2 6 2 4
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 379
+
+--S 380 of 1527
+r0a:=(-1/3)/(a^2*c*x^3)+(2*b*c+a*d)/(a^3*c^2*x)+1/2*b^3*x/(a^3*(b*c-a*d)*_
+ (a+b*x^2))+1/2*b^(5/2)*(5*b*c-7*a*d)*atan(x*sqrt(b)/sqrt(a))/_
+ (a^(7/2)*(b*c-a*d)^2)+d^(7/2)*atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*_
+ (b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 5 4 3 3 +-+ +-+ x\|d
+--R (6a b d x + 6a d x )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 4 3 5 2 2 2 3 3 3 +-+ +-+
+--R ((- 21a b c d + 15b c )x + (- 21a b c d + 15a b c )x )\|b \|c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 3 3 2 4 3 4
+--R (6a b d - 21a b c d + 15b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 2 4 2 3 2
+--R (6a d - 2a b c d - 14a b c d + 10a b c )x - 2a c d + 4a b c d
+--R +
+--R 2 2 3
+--R - 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 5 2 2 4 2 3 3 3 4 5 6 2 2 5 3 4 2 4 3
+--R ((6a b c d - 12a b c d + 6a b c )x + (6a c d - 12a b c d + 6a b c )x )
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 380
+
+--S 381 of 1527
+r0b:=(-1/3)/(a^2*c*x^3)+(2*b*c+a*d)/(a^3*c^2*x)+_
+ 1/2*b^3*x/(a^3*(b*c-a*d)*(a+b*x^2))+b^(5/2)*(2*b*c-3*a*d)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(7/2)*(b*c-a*d)^2)+1/2*b^(5/2)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(7/2)*(b*c-a*d))+d^(7/2)*atan(x*_
+ sqrt(d)/sqrt(c))/(c^(5/2)*(b*c-a*d)^2)
+--R
+--R
+--R (3)
+--R +-+
+--R 3 3 5 4 3 3 +-+ +-+ x\|d
+--R (6a b d x + 6a d x )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 4 3 5 2 2 2 3 3 3 +-+ +-+
+--R ((- 21a b c d + 15b c )x + (- 21a b c d + 15a b c )x )\|b \|c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 3 3 2 4 3 4
+--R (6a b d - 21a b c d + 15b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 2 4 2 3 2
+--R (6a d - 2a b c d - 14a b c d + 10a b c )x - 2a c d + 4a b c d
+--R +
+--R 2 2 3
+--R - 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 5 2 2 4 2 3 3 3 4 5 6 2 2 5 3 4 2 4 3
+--R ((6a b c d - 12a b c d + 6a b c )x + (6a c d - 12a b c d + 6a b c )x )
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 3 3 5 4 3 3 | d \| c
+--R (6a b d x + 6a d x ) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R 3 2 4 3 5 2 2 2 3 3 3 | b
+--R ((21a b c d - 15b c )x + (21a b c d - 15a b c )x ) |- -
+--R \| a
+--R *
+--R +---+
+--R | b 2
+--R - 2a x |- - + b x - a
+--R \| a
+--R log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 3 3 2 4 3 4
+--R (12a b d - 42a b c d + 30b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 2 4 2 3 2
+--R (12a d - 4a b c d - 28a b c d + 20a b c )x - 4a c d + 8a b c d
+--R +
+--R 2 2 3
+--R - 4a b c
+--R /
+--R 5 2 2 4 2 3 3 3 4 5
+--R (12a b c d - 24a b c d + 12a b c )x
+--R +
+--R 6 2 2 5 3 4 2 4 3
+--R (12a c d - 24a b c d + 12a b c )x
+--R ,
+--R
+--R +---+
+--R 3 2 4 3 5 2 2 2 3 3 3 | b
+--R ((21a b c d - 15b c )x + (21a b c d - 15a b c )x ) |- -
+--R \| a
+--R *
+--R +---+
+--R | b 2
+--R - 2a x |- - + b x - a
+--R \| a
+--R log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 3 3 5 4 3 3 |d \|c
+--R (- 12a b d x - 12a d x ) |- atan(-----)
+--R \|c d x
+--R +
+--R 3 3 3 2 4 3 4
+--R (12a b d - 42a b c d + 30b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 2 4 2 3 2
+--R (12a d - 4a b c d - 28a b c d + 20a b c )x - 4a c d + 8a b c d
+--R +
+--R 2 2 3
+--R - 4a b c
+--R /
+--R 5 2 2 4 2 3 3 3 4 5
+--R (12a b c d - 24a b c d + 12a b c )x
+--R +
+--R 6 2 2 5 3 4 2 4 3
+--R (12a c d - 24a b c d + 12a b c )x
+--R ,
+--R
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 3 3 5 4 3 3 | d \| c
+--R (3a b d x + 3a d x ) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 2 4 3 5 2 2 2 3 3 3 |b \|a
+--R ((21a b c d - 15b c )x + (21a b c d - 15a b c )x ) |- atan(-----)
+--R \|a b x
+--R +
+--R 3 3 3 2 4 3 4
+--R (6a b d - 21a b c d + 15b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 2 4 2 3 2
+--R (6a d - 2a b c d - 14a b c d + 10a b c )x - 2a c d + 4a b c d
+--R +
+--R 2 2 3
+--R - 2a b c
+--R /
+--R 5 2 2 4 2 3 3 3 4 5 6 2 2 5 3 4 2 4 3
+--R (6a b c d - 12a b c d + 6a b c )x + (6a c d - 12a b c d + 6a b c )x
+--R ,
+--R
+--R +-+
+--R |d
+--R +-+ c |-
+--R 3 3 5 4 3 3 |d \|c
+--R (- 6a b d x - 6a d x ) |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 2 4 3 5 2 2 2 3 3 3 |b \|a
+--R ((21a b c d - 15b c )x + (21a b c d - 15a b c )x ) |- atan(-----)
+--R \|a b x
+--R +
+--R 3 3 3 2 4 3 4
+--R (6a b d - 21a b c d + 15b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 2 4 2 3 2
+--R (6a d - 2a b c d - 14a b c d + 10a b c )x - 2a c d + 4a b c d
+--R +
+--R 2 2 3
+--R - 2a b c
+--R /
+--R 5 2 2 4 2 3 3 3 4 5 6 2 2 5 3 4 2 4 3
+--R (6a b c d - 12a b c d + 6a b c )x + (6a c d - 12a b c d + 6a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 382
+
+--S 383 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 3 3 | d +-+ +-+ \| c
+--R 2a d |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (7a b c d - 5b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+ +-+
+--R 3 3 +-+ +-+ x\|d 2 2 3 3 +-+ +-+ x\|b
+--R - 4a d \|a \|d atan(-----) + (14a b c d - 10b c )\|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 5 2 2 4 3 3 2 4 +-+ +-+
+--R (4a c d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 383
+
+--S 384 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (7a b c d - 5b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ +-+ c |-
+--R 3 3 +-+ +-+ x\|d 3 3 +-+ +-+ |d \|c
+--R - 4a d \|a \|d atan(-----) - 4a d \|a \|c |- atan(-----)
+--R +-+ \|c d x
+--R \|c
+--R +
+--R +-+
+--R 2 2 3 3 +-+ +-+ x\|b
+--R (14a b c d - 10b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 2 2 4 3 3 2 4 +-+ +-+
+--R (4a c d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 385
+
+--S 386 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 3 3 | d +-+ +-+ \| c
+--R 2a d |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (7a b c d - 5b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+ +-+
+--R 3 3 +-+ +-+ x\|d 2 2 3 3 +-+ +-+ x\|b
+--R - 4a d \|a \|d atan(-----) + (14a b c d - 10b c )\|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 5 2 2 4 3 3 2 4 +-+ +-+
+--R (4a c d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 388
+
+--S 389 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (7a b c d - 5b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ +-+ c |-
+--R 3 3 +-+ +-+ x\|d 3 3 +-+ +-+ |d \|c
+--R - 4a d \|a \|d atan(-----) - 4a d \|a \|c |- atan(-----)
+--R +-+ \|c d x
+--R \|c
+--R +
+--R +-+
+--R 2 2 3 3 +-+ +-+ x\|b
+--R (14a b c d - 10b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 2 2 4 3 3 2 4 +-+ +-+
+--R (4a c d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 1527
+t0:=1/(x^5*(a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------------
+--R 2 11 2 9 2 7 2 5
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 391
+
+--S 392 of 1527
+r0:=(-1/4)/(a^2*c*x^4)+1/2*(2*b*c+a*d)/(a^3*c^2*x^2)+1/2*b^3/(a^3*(b*c-_
+ a*d)*(a+b*x^2))+(3*b^2*c^2+2*a*b*c*d+a^2*d^2)*log(x)/(a^4*c^3)-_
+ 1/2*b^3*(3*b*c-4*a*d)*log(a+b*x^2)/(a^4*(b*c-a*d)^2)-1/2*d^4*_
+ log(c+d*x^2)/(c^3*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R 4 4 6 5 4 4 2
+--R (- 2a b d x - 2a d x )log(d x + c)
+--R +
+--R 4 3 5 4 6 2 3 3 4 4 4 2
+--R ((8a b c d - 6b c )x + (8a b c d - 6a b c )x )log(b x + a)
+--R +
+--R 4 4 4 3 5 4 6 5 4 2 3 3 4 4 4
+--R ((4a b d - 16a b c d + 12b c )x + (4a d - 16a b c d + 12a b c )x )
+--R *
+--R log(x)
+--R +
+--R 4 3 2 3 3 4 4 4
+--R (2a b c d - 8a b c d + 6a b c )x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 2 5 2 2 4 3 3 2 4
+--R (2a c d - a b c d - 4a b c d + 3a b c )x - a c d + 2a b c d - a b c
+--R /
+--R 6 3 2 5 2 4 4 3 5 6 7 3 2 6 4 5 2 5 4
+--R (4a b c d - 8a b c d + 4a b c )x + (4a c d - 8a b c d + 4a b c )x
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 6 5 4 4 2
+--R (- 2a b d x - 2a d x )log(d x + c)
+--R +
+--R 4 3 5 4 6 2 3 3 4 4 4 2
+--R ((8a b c d - 6b c )x + (8a b c d - 6a b c )x )log(b x + a)
+--R +
+--R 4 4 4 3 5 4 6 5 4 2 3 3 4 4 4
+--R ((4a b d - 16a b c d + 12b c )x + (4a d - 16a b c d + 12a b c )x )
+--R *
+--R log(x)
+--R +
+--R 4 3 2 3 3 4 4 4
+--R (2a b c d - 8a b c d + 6a b c )x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 2 5 2 2 4 3 3 2 4
+--R (2a c d - a b c d - 4a b c d + 3a b c )x - a c d + 2a b c d - a b c
+--R /
+--R 6 3 2 5 2 4 4 3 5 6 7 3 2 6 4 5 2 5 4
+--R (4a b c d - 8a b c d + 4a b c )x + (4a c d - 8a b c d + 4a b c )x
+--R Type: Union(Expression(Integer),...)
+--E 393
+
+--S 394 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 395
+
+)clear all
+
+--S 396 of 1527
+t0:=1/(x^6*(a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------
+--R 2 12 2 10 2 8 2 6
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 396
+
+--S 397 of 1527
+r0a:=(-1/5)/(a^2*c*x^5)+1/3*(2*b*c+a*d)/(a^3*c^2*x^3)+(-3*b^2*c^2-_
+ 2*a*b*c*d-a^2*d^2)/(a^4*c^3*x)-1/2*b^4*x/(a^4*(b*c-a*d)*(a+b*x^2))-_
+ 1/2*b^(7/2)*(7*b*c-9*a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(9/2)*_
+ (b*c-a*d)^2)-d^(9/2)*atan(x*sqrt(d)/sqrt(c))/(c^(7/2)*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 4 4 7 5 4 5 +-+ +-+ x\|d
+--R (- 30a b d x - 30a d x )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 4 3 5 4 7 2 3 3 4 4 5 +-+ +-+
+--R ((135a b c d - 105b c )x + (135a b c d - 105a b c )x )\|b \|c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 4 4 3 5 4 6
+--R (- 30a b d + 135a b c d - 105b c )x
+--R +
+--R 5 4 4 3 2 3 3 4 4 4
+--R (- 30a d + 10a b c d + 90a b c d - 70a b c )x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 2 5 2 2 4 3
+--R (10a c d - 6a b c d - 18a b c d + 14a b c )x - 6a c d + 12a b c d
+--R +
+--R 3 2 4
+--R - 6a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 6 3 2 5 2 4 4 3 5 7
+--R (30a b c d - 60a b c d + 30a b c )x
+--R +
+--R 7 3 2 6 4 5 2 5 5
+--R (30a c d - 60a b c d + 30a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 1527
+r0b:=(-1/5)/(a^2*c*x^5)+1/3*(2*b*c+a*d)/(a^3*c^2*x^3)+_
+ (-3*b^2*c^2-2*a*b*c*d-a^2*d^2)/(a^4*c^3*x)-1/2*b^4*x/_
+ (a^4*(b*c-a*d)*(a+b*x^2))-b^(7/2)*(3*b*c-4*a*d)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(9/2)*(b*c-a*d)^2)-1/2*b^(7/2)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(9/2)*(b*c-a*d))-d^(9/2)*_
+ atan(x*sqrt(d)/sqrt(c))/(c^(7/2)*(b*c-a*d)^2)
+--R
+--R
+--R (3)
+--R +-+
+--R 4 4 7 5 4 5 +-+ +-+ x\|d
+--R (- 30a b d x - 30a d x )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 4 3 5 4 7 2 3 3 4 4 5 +-+ +-+
+--R ((135a b c d - 105b c )x + (135a b c d - 105a b c )x )\|b \|c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 4 4 3 5 4 6
+--R (- 30a b d + 135a b c d - 105b c )x
+--R +
+--R 5 4 4 3 2 3 3 4 4 4
+--R (- 30a d + 10a b c d + 90a b c d - 70a b c )x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 2 5 2 2 4 3
+--R (10a c d - 6a b c d - 18a b c d + 14a b c )x - 6a c d + 12a b c d
+--R +
+--R 3 2 4
+--R - 6a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 6 3 2 5 2 4 4 3 5 7
+--R (30a b c d - 60a b c d + 30a b c )x
+--R +
+--R 7 3 2 6 4 5 2 5 5
+--R (30a c d - 60a b c d + 30a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 398
+
+--S 399 of 1527
+--a0:=integrate(t0,x)
+--E 399
+
+--S 400 of 1527
+--m0:=a0-r0
+--E 400
+
+--S 401 of 1527
+--d0:=D(m0,x)
+--E 401
+
+)clear all
+
+--S 402 of 1527
+t0:=1/(x^7*(a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------
+--R 2 13 2 11 2 9 2 7
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 402
+
+--S 403 of 1527
+r0:=(-1/6)/(a^2*c*x^6)+1/4*(2*b*c+a*d)/(a^3*c^2*x^4)+_
+ 1/2*(-3*b^2*c^2-2*a*b*c*d-a^2*d^2)/(a^4*c^3*x^2)-_
+ 1/2*b^4/(a^4*(b*c-a*d)*(a+b*x^2))-(4*b^3*c^3+3*a*b^2*c^2*d+_
+ 2*a^2*b*c*d^2+a^3*d^3)*log(x)/(a^5*c^4)+1/2*b^4*(4*b*c-5*a*d)*_
+ log(a+b*x^2)/(a^5*(b*c-a*d)^2)+1/2*d^5*log(c+d*x^2)/(c^4*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R 5 5 8 6 5 6 2
+--R (6a b d x + 6a d x )log(d x + c)
+--R +
+--R 5 4 6 5 8 2 4 4 5 5 6 2
+--R ((- 30a b c d + 24b c )x + (- 30a b c d + 24a b c )x )log(b x + a)
+--R +
+--R 5 5 5 4 6 5 8
+--R (- 12a b d + 60a b c d - 48b c )x
+--R +
+--R 6 5 2 4 4 5 5 6
+--R (- 12a d + 60a b c d - 48a b c )x
+--R *
+--R log(x)
+--R +
+--R 5 4 2 4 4 5 5 6
+--R (- 6a b c d + 30a b c d - 24a b c )x
+--R +
+--R 6 4 5 2 3 3 3 4 2 4 5 4
+--R (- 6a c d + 3a b c d + 15a b c d - 12a b c )x
+--R +
+--R 6 2 3 5 3 2 4 2 4 3 3 5 2 6 3 2 5 4 4 2 5
+--R (3a c d - 2a b c d - 5a b c d + 4a b c )x - 2a c d + 4a b c d - 2a b c
+--R /
+--R 7 4 2 6 2 5 5 3 6 8 8 4 2 7 5 6 2 6 6
+--R (12a b c d - 24a b c d + 12a b c )x + (12a c d - 24a b c d + 12a b c )x
+--R Type: Expression(Integer)
+--E 403
+
+--S 404 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 5 8 6 5 6 2
+--R (6a b d x + 6a d x )log(d x + c)
+--R +
+--R 5 4 6 5 8 2 4 4 5 5 6 2
+--R ((- 30a b c d + 24b c )x + (- 30a b c d + 24a b c )x )log(b x + a)
+--R +
+--R 5 5 5 4 6 5 8
+--R (- 12a b d + 60a b c d - 48b c )x
+--R +
+--R 6 5 2 4 4 5 5 6
+--R (- 12a d + 60a b c d - 48a b c )x
+--R *
+--R log(x)
+--R +
+--R 5 4 2 4 4 5 5 6
+--R (- 6a b c d + 30a b c d - 24a b c )x
+--R +
+--R 6 4 5 2 3 3 3 4 2 4 5 4
+--R (- 6a c d + 3a b c d + 15a b c d - 12a b c )x
+--R +
+--R 6 2 3 5 3 2 4 2 4 3 3 5 2 6 3 2 5 4 4 2 5
+--R (3a c d - 2a b c d - 5a b c d + 4a b c )x - 2a c d + 4a b c d - 2a b c
+--R /
+--R 7 4 2 6 2 5 5 3 6 8 8 4 2 7 5 6 2 6 6
+--R (12a b c d - 24a b c d + 12a b c )x + (12a c d - 24a b c d + 12a b c )x
+--R Type: Union(Expression(Integer),...)
+--E 404
+
+--S 405 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 405
+
+--S 406 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 406
+
+)clear all
+
+--S 407 of 1527
+t0:=x^4/((a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 4
+--R x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 407
+
+--S 408 of 1527
+r0a:=1/2*a*x/((b*c-a*d)^2*(a+b*x^2))+1/2*c*x/((b*c-a*d)^2*(c+d*x^2))-_
+ 1/2*(3*b*c+a*d)*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/_
+ ((b*c-a*d)^3*sqrt(b))+1/2*(b*c+3*a*d)*atan(x*sqrt(d)/sqrt(c))*_
+ sqrt(c)/((b*c-a*d)^3*sqrt(d))
+--R
+--R
+--R (2)
+--R 2 2 4 2 2 2 2 2 2
+--R (- 3a b d - b c d)x + (- 3a d - 4a b c d - b c )x - 3a c d
+--R +
+--R 2
+--R - a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|b \|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((a b d + 3b c d)x + (a d + 4a b c d + 3b c )x + a c d + 3a b c )
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|a \|d atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 2 3 2 2 +-+ +-+
+--R ((a d - b c )x + (2a c d - 2a b c )x)\|b \|d
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (2a b d - 6a b c d + 6a b c d - 2b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (2a d - 4a b c d + 4a b c d - 2b c )x + 2a c d - 6a b c d
+--R +
+--R 2 2 3 3 4
+--R 6a b c d - 2a b c
+--R *
+--R +-+ +-+
+--R \|b \|d
+--R Type: Expression(Integer)
+--E 408
+
+--S 409 of 1527
+r0b:=1/2*a*x/((b*c-a*d)^2*(a+b*x^2))+_
+ 1/2*c*x/((b*c-a*d)^2*(c+d*x^2))+1/2*atan(x*sqrt(b)/sqrt(a))*_
+ sqrt(a)/((b*c-a*d)^2*sqrt(b))-2*c*atan(x*sqrt(b)/sqrt(a))*sqrt(a)*_
+ sqrt(b)/(b*c-a*d)^3+1/2*atan(x*sqrt(d)/sqrt(c))*sqrt(c)/_
+ ((b*c-a*d)^2*sqrt(d))+2*a*atan(x*sqrt(d)/sqrt(c))*sqrt(c)*_
+ sqrt(d)/(b*c-a*d)^3
+--R
+--R
+--R (3)
+--R 2 2 4 2 2 2 2 2 2
+--R (- 3a b d - b c d)x + (- 3a d - 4a b c d - b c )x - 3a c d
+--R +
+--R 2
+--R - a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|b \|c atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((a b d + 3b c d)x + (a d + 4a b c d + 3b c )x + a c d + 3a b c )
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|a \|d atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 2 3 2 2 +-+ +-+
+--R ((a d - b c )x + (2a c d - 2a b c )x)\|b \|d
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (2a b d - 6a b c d + 6a b c d - 2b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (2a d - 4a b c d + 4a b c d - 2b c )x + 2a c d - 6a b c d
+--R +
+--R 2 2 3 3 4
+--R 6a b c d - 2a b c
+--R *
+--R +-+ +-+
+--R \|b \|d
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((a b d + 3b c d)x + (a d + 4a b c d + 3b c )x + a c d + 3a b c )
+--R *
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a \| b
+--R |- - log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((3a b d + b c d)x + (3a d + 4a b c d + b c )x + 3a c d + a b c )
+--R *
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R | c \| d
+--R |- - log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R 2 2 2 2 3 2 2
+--R (2a d - 2b c )x + (4a c d - 4a b c )x
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (4a b d - 12a b c d + 12a b c d - 4b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (4a d - 8a b c d + 8a b c d - 4b c )x + 4a c d - 12a b c d
+--R +
+--R 2 2 3 3 4
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((3a b d + b c d)x + (3a d + 4a b c d + b c )x + 3a c d + a b c )
+--R *
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R | c \| d
+--R |- - log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d - 6b c d)x + (- 2a d - 8a b c d - 6b c )x - 2a c d
+--R +
+--R 2
+--R - 6a b c
+--R *
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b
+--R |- atan(----)
+--R \|b x
+--R +
+--R 2 2 2 2 3 2 2
+--R (2a d - 2b c )x + (4a c d - 4a b c )x
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (4a b d - 12a b c d + 12a b c d - 4b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (4a d - 8a b c d + 8a b c d - 4b c )x + 4a c d - 12a b c d
+--R +
+--R 2 2 3 3 4
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((a b d + 3b c d)x + (a d + 4a b c d + 3b c )x + a c d + 3a b c )
+--R *
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a \| b
+--R |- - log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (6a b d + 2b c d)x + (6a d + 8a b c d + 2b c )x + 6a c d
+--R +
+--R 2
+--R 2a b c
+--R *
+--R +-+
+--R |c
+--R +-+ |-
+--R |c \|d
+--R |- atan(----)
+--R \|d x
+--R +
+--R 2 2 2 2 3 2 2
+--R (2a d - 2b c )x + (4a c d - 4a b c )x
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (4a b d - 12a b c d + 12a b c d - 4b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (4a d - 8a b c d + 8a b c d - 4b c )x + 4a c d - 12a b c d
+--R +
+--R 2 2 3 3 4
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 3b c d)x + (- a d - 4a b c d - 3b c )x - a c d
+--R +
+--R 2
+--R - 3a b c
+--R *
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b
+--R |- atan(----)
+--R \|b x
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((3a b d + b c d)x + (3a d + 4a b c d + b c )x + 3a c d + a b c )
+--R *
+--R +-+
+--R |c
+--R +-+ |-
+--R |c \|d
+--R |- atan(----)
+--R \|d x
+--R +
+--R 2 2 2 2 3 2 2
+--R (a d - b c )x + (2a c d - 2a b c )x
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (2a b d - 6a b c d + 6a b c d - 2b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (2a d - 4a b c d + 4a b c d - 2b c )x + 2a c d - 6a b c d
+--R +
+--R 2 2 3 3 4
+--R 6a b c d - 2a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 410
+
+--S 411 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a +-+ +-+ \| b
+--R (a d + 3b c) |- - \|b \|d log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R | c +-+ +-+ \| d
+--R (3a d + b c) |- - \|b \|d log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R (6a d + 2b c)\|b \|c atan(-----) + (- 2a d - 6b c)\|a \|d atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (4a d - 12a b c d + 12a b c d - 4b c )\|b \|d
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R | c +-+ +-+ \| d
+--R (3a d + b c) |- - \|b \|d log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R (6a d + 2b c)\|b \|c atan(-----) + (- 2a d - 6b c)\|a \|d atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R |a +-+ +-+ \|b
+--R (- 2a d - 6b c) |- \|b \|d atan(----)
+--R \|b x
+--R /
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (4a d - 12a b c d + 12a b c d - 4b c )\|b \|d
+--R Type: Expression(Integer)
+--E 413
+
+--S 414 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a +-+ +-+ \| b
+--R (a d + 3b c) |- - \|b \|d log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R | c +-+ +-+ \| d
+--R (3a d + b c) |- - \|b \|d log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R (6a d + 2b c)\|b \|c atan(-----) + (- 2a d - 6b c)\|a \|d atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (4a d - 12a b c d + 12a b c d - 4b c )\|b \|d
+--R Type: Expression(Integer)
+--E 415
+
+--S 416 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R | c 2
+--R +---+ - 2d x |- - + d x - c
+--R | c +-+ +-+ \| d
+--R (3a d + b c) |- - \|b \|d log(-----------------------)
+--R \| d 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R (6a d + 2b c)\|b \|c atan(-----) + (- 2a d - 6b c)\|a \|d atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R +
+--R +-+
+--R |a
+--R +-+ |-
+--R |a +-+ +-+ \|b
+--R (- 2a d - 6b c) |- \|b \|d atan(----)
+--R \|b x
+--R /
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (4a d - 12a b c d + 12a b c d - 4b c )\|b \|d
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 418
+
+)clear all
+
+--S 419 of 1527
+t0:=x^3/((a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 3
+--R x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 419
+
+--S 420 of 1527
+r0:=1/2*a/((b*c-a*d)^2*(a+b*x^2))+1/2*c/((b*c-a*d)^2*(c+d*x^2))+_
+ 1/2*(b*c+a*d)*log(a+b*x^2)/(b*c-a*d)^3-1/2*(b*c+a*d)*_
+ log(c+d*x^2)/(b*c-a*d)^3
+--R
+--R
+--R (2)
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((a b d + b c d)x + (a d + 2a b c d + b c )x + a c d + a b c )
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((- a b d - b c d)x + (- a d - 2a b c d - b c )x - a c d - a b c )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 2 2 2 2 2 2 2
+--R (a d - b c )x + 2a c d - 2a b c
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (2a b d - 6a b c d + 6a b c d - 2b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2 2 2 3
+--R (2a d - 4a b c d + 4a b c d - 2b c )x + 2a c d - 6a b c d + 6a b c d
+--R +
+--R 3 4
+--R - 2a b c
+--R Type: Expression(Integer)
+--E 420
+
+--S 421 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((a b d + b c d)x + (a d + 2a b c d + b c )x + a c d + a b c )
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((- a b d - b c d)x + (- a d - 2a b c d - b c )x - a c d - a b c )
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 2 2 2 2 2 2 2
+--R (a d - b c )x + 2a c d - 2a b c
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (2a b d - 6a b c d + 6a b c d - 2b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2 2 2 3
+--R (2a d - 4a b c d + 4a b c d - 2b c )x + 2a c d - 6a b c d + 6a b c d
+--R +
+--R 3 4
+--R - 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 421
+
+--S 422 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 423
+
+)clear all
+
+--S 424 of 1527
+t0:=x^2/((a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 2
+--R x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 424
+
+--S 425 of 1527
+r0a:=-1/2*b*x/((b*c-a*d)^2*(a+b*x^2))-1/2*d*x/((b*c-a*d)^2*(c+d*x^2))+_
+ 1/2*(b*c+3*a*d)*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/((b*c-a*d)^3*_
+ sqrt(a))-1/2*(3*b*c+a*d)*atan(x*sqrt(d)/sqrt(c))*sqrt(d)/_
+ ((b*c-a*d)^3*sqrt(c))
+--R
+--R
+--R (2)
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((a b d + 3b c d)x + (a d + 4a b c d + 3b c )x + a c d + 3a b c )
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 3a b d - b c d)x + (- 3a d - 4a b c d - b c )x - 3a c d
+--R +
+--R 2
+--R - a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 3 2 2 2 2 +-+ +-+
+--R ((- 2a b d + 2b c d)x + (- a d + b c )x)\|a \|c
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (2a b d - 6a b c d + 6a b c d - 2b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (2a d - 4a b c d + 4a b c d - 2b c )x + 2a c d - 6a b c d
+--R +
+--R 2 2 3 3 4
+--R 6a b c d - 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 425
+
+--S 426 of 1527
+r0b:=-1/2*b*x/((b*c-a*d)^2*(a+b*x^2))-_
+ 1/2*d*x/((b*c-a*d)^2*(c+d*x^2))-1/2*atan(x*sqrt(b)/sqrt(a))*_
+ sqrt(b)/((b*c-a*d)^2*sqrt(a))+(b*c+a*d)*atan(x*sqrt(b)/sqrt(a))*_
+ sqrt(b)/((b*c-a*d)^3*sqrt(a))-1/2*atan(x*sqrt(d)/sqrt(c))*_
+ sqrt(d)/((b*c-a*d)^2*sqrt(c))-(b*c+a*d)*atan(x*sqrt(d)/sqrt(c))*_
+ sqrt(d)/((b*c-a*d)^3*sqrt(c))
+--R
+--R
+--R (3)
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((a b d + 3b c d)x + (a d + 4a b c d + 3b c )x + a c d + 3a b c )
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 3a b d - b c d)x + (- 3a d - 4a b c d - b c )x - 3a c d
+--R +
+--R 2
+--R - a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 3 2 2 2 2 +-+ +-+
+--R ((- 2a b d + 2b c d)x + (- a d + b c )x)\|a \|c
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (2a b d - 6a b c d + 6a b c d - 2b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (2a d - 4a b c d + 4a b c d - 2b c )x + 2a c d - 6a b c d
+--R +
+--R 2 2 3 3 4
+--R 6a b c d - 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((a b d + 3b c d)x + (a d + 4a b c d + 3b c )x + a c d + 3a b c )
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((3a b d + b c d)x + (3a d + 4a b c d + b c )x + 3a c d + a b c )
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 2 3 2 2 2 2
+--R (- 4a b d + 4b c d)x + (- 2a d + 2b c )x
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (4a b d - 12a b c d + 12a b c d - 4b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (4a d - 8a b c d + 8a b c d - 4b c )x + 4a c d - 12a b c d
+--R +
+--R 2 2 3 3 4
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((3a b d + b c d)x + (3a d + 4a b c d + b c )x + 3a c d + a b c )
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d - 6b c d)x + (- 2a d - 8a b c d - 6b c )x - 2a c d
+--R +
+--R 2
+--R - 6a b c
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 2 3 2 2 2 2
+--R (- 4a b d + 4b c d)x + (- 2a d + 2b c )x
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (4a b d - 12a b c d + 12a b c d - 4b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (4a d - 8a b c d + 8a b c d - 4b c )x + 4a c d - 12a b c d
+--R +
+--R 2 2 3 3 4
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((a b d + 3b c d)x + (a d + 4a b c d + 3b c )x + a c d + 3a b c )
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (6a b d + 2b c d)x + (6a d + 8a b c d + 2b c )x + 6a c d
+--R +
+--R 2
+--R 2a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 2 3 2 2 2 2
+--R (- 4a b d + 4b c d)x + (- 2a d + 2b c )x
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (4a b d - 12a b c d + 12a b c d - 4b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (4a d - 8a b c d + 8a b c d - 4b c )x + 4a c d - 12a b c d
+--R +
+--R 2 2 3 3 4
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 3b c d)x + (- a d - 4a b c d - 3b c )x - a c d
+--R +
+--R 2
+--R - 3a b c
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((3a b d + b c d)x + (3a d + 4a b c d + b c )x + 3a c d + a b c )
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 2 3 2 2 2 2
+--R (- 2a b d + 2b c d)x + (- a d + b c )x
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (2a b d - 6a b c d + 6a b c d - 2b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (2a d - 4a b c d + 4a b c d - 2b c )x + 2a c d - 6a b c d
+--R +
+--R 2 2 3 3 4
+--R 6a b c d - 2a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 427
+
+--S 428 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d +-+ +-+ \| c
+--R (a d + 3b c) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R (3a d + b c) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R (- 2a d - 6b c)\|a \|d atan(-----) + (6a d + 2b c)\|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (4a d - 12a b c d + 12a b c d - 4b c )\|a \|c
+--R Type: Expression(Integer)
+--E 428
+
+--S 429 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R (3a d + b c) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ +-+ x\|d
+--R (- 2a d - 6b c)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- +-+
+--R +-+ +-+ |d \|c +-+ +-+ x\|b
+--R (- 2a d - 6b c)\|a \|c |- atan(-----) + (6a d + 2b c)\|b \|c atan(-----)
+--R \|c d x +-+
+--R \|a
+--R /
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (4a d - 12a b c d + 12a b c d - 4b c )\|a \|c
+--R Type: Expression(Integer)
+--E 430
+
+--S 431 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d +-+ +-+ \| c
+--R (a d + 3b c) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R (3a d + b c) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R (- 2a d - 6b c)\|a \|d atan(-----) + (6a d + 2b c)\|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (4a d - 12a b c d + 12a b c d - 4b c )\|a \|c
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 433
+
+--S 434 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R (3a d + b c) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ +-+ x\|d
+--R (- 2a d - 6b c)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- +-+
+--R +-+ +-+ |d \|c +-+ +-+ x\|b
+--R (- 2a d - 6b c)\|a \|c |- atan(-----) + (6a d + 2b c)\|b \|c atan(-----)
+--R \|c d x +-+
+--R \|a
+--R /
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (4a d - 12a b c d + 12a b c d - 4b c )\|a \|c
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 435
+
+)clear all
+
+--S 436 of 1527
+t0:=x/((a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 436
+
+--S 437 of 1527
+r0:=-1/2*b/((b*c-a*d)^2*(a+b*x^2))-1/2*d/((b*c-a*d)^2*(c+d*x^2))-_
+ b*d*log(a+b*x^2)/(b*c-a*d)^3+b*d*log(c+d*x^2)/(b*c-a*d)^3
+--R
+--R
+--R (2)
+--R 2 2 4 2 2 2 2
+--R (- 2b d x + (- 2a b d - 2b c d)x - 2a b c d)log(d x + c)
+--R +
+--R 2 2 4 2 2 2 2
+--R (2b d x + (2a b d + 2b c d)x + 2a b c d)log(b x + a)
+--R +
+--R 2 2 2 2 2 2 2
+--R (- 2a b d + 2b c d)x - a d + b c
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (2a b d - 6a b c d + 6a b c d - 2b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2 2 2 3
+--R (2a d - 4a b c d + 4a b c d - 2b c )x + 2a c d - 6a b c d + 6a b c d
+--R +
+--R 3 4
+--R - 2a b c
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 4 2 2 2 2
+--R (- 2b d x + (- 2a b d - 2b c d)x - 2a b c d)log(d x + c)
+--R +
+--R 2 2 4 2 2 2 2
+--R (2b d x + (2a b d + 2b c d)x + 2a b c d)log(b x + a)
+--R +
+--R 2 2 2 2 2 2 2
+--R (- 2a b d + 2b c d)x - a d + b c
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (2a b d - 6a b c d + 6a b c d - 2b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2 2 2 3
+--R (2a d - 4a b c d + 4a b c d - 2b c )x + 2a c d - 6a b c d + 6a b c d
+--R +
+--R 3 4
+--R - 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 438
+
+--S 439 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 1527
+t0:=1/((a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 441
+
+--S 442 of 1527
+r0:=1/2*d*(b*c+a*d)*x/(a*c*(b*c-a*d)^2*(c+d*x^2))+1/2*b*x/(a*(b*c-a*d)*_
+ (a+b*x^2)*(c+d*x^2))+1/2*b^(3/2)*(b*c-5*a*d)*atan(x*sqrt(b)/_
+ sqrt(a))/(a^(3/2)*(b*c-a*d)^3)+1/2*d^(3/2)*(5*b*c-a*d)*_
+ atan(x*sqrt(d)/sqrt(c))/(c^(3/2)*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 2 3 2 2 4 3 3 2 2 2 2 2 3 2
+--R (a b d - 5a b c d )x + (a d - 4a b c d - 5a b c d)x + a c d
+--R +
+--R 2 2
+--R - 5a b c d
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2 2 2
+--R (5a b c d - b c d)x + (5a b c d + 4a b c d - b c )x + 5a b c d
+--R +
+--R 2 3
+--R - a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3 +-+ +-+
+--R ((a b d - b c d)x + (a d - a b c d + a b c d - b c )x)\|a \|c
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (2a c d - 4a b c d + 4a b c d - 2a b c )x + 2a c d - 6a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 6a b c d - 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 3 2 4 2 2 2 2 3 3 2 2 2
+--R (5a b c d - b c d)x + (5a b c d + 4a b c d - b c )x + 5a b c d
+--R +
+--R 2 3
+--R - a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2 3 2
+--R (a b d - 5a b c d )x + (a d - 4a b c d - 5a b c d)x + a c d
+--R +
+--R 2 2
+--R - 5a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3
+--R (2a b d - 2b c d)x + (2a d - 2a b c d + 2a b c d - 2b c )x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (4a b c d - 12a b c d + 12a b c d - 4a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (4a c d - 8a b c d + 8a b c d - 4a b c )x + 4a c d - 12a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 2 3 2 4 2 2 2 2 3 3 2 2 2
+--R (5a b c d - b c d)x + (5a b c d + 4a b c d - b c )x + 5a b c d
+--R +
+--R 2 3
+--R - a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (- 2a b d + 10a b c d )x + (- 2a d + 8a b c d + 10a b c d)x
+--R +
+--R 3 2 2 2
+--R - 2a c d + 10a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3
+--R (2a b d - 2b c d)x + (2a d - 2a b c d + 2a b c d - 2b c )x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (4a b c d - 12a b c d + 12a b c d - 4a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (4a c d - 8a b c d + 8a b c d - 4a b c )x + 4a c d - 12a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 3 2 2 4 3 3 2 2 2 2 2 3 2
+--R (a b d - 5a b c d )x + (a d - 4a b c d - 5a b c d)x + a c d
+--R +
+--R 2 2
+--R - 5a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (- 10a b c d + 2b c d)x + (- 10a b c d - 8a b c d + 2b c )x
+--R +
+--R 2 2 2 3
+--R - 10a b c d + 2a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3
+--R (2a b d - 2b c d)x + (2a d - 2a b c d + 2a b c d - 2b c )x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (4a b c d - 12a b c d + 12a b c d - 4a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (4a c d - 8a b c d + 8a b c d - 4a b c )x + 4a c d - 12a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (- a b d + 5a b c d )x + (- a d + 4a b c d + 5a b c d)x
+--R +
+--R 3 2 2 2
+--R - a c d + 5a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (- 5a b c d + b c d)x + (- 5a b c d - 4a b c d + b c )x
+--R +
+--R 2 2 2 3
+--R - 5a b c d + a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3
+--R (a b d - b c d)x + (a d - a b c d + a b c d - b c )x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (2a c d - 4a b c d + 4a b c d - 2a b c )x + 2a c d - 6a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 6a b c d - 2a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 443
+
+--S 444 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R (5a b c d - b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 | d +-+ +-+ \| c
+--R (a d - 5a b c d) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (- 2a d + 10a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R (- 10a b c d + 2b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 3 3 2 2 2 2 3 3 4 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+--S 446 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R (5a b c d - b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (- 2a d + 10a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 +-+ +-+ |d \|c
+--R (- 2a d + 10a b c d)\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R (- 10a b c d + 2b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 3 3 2 2 2 2 3 3 4 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 447
+
+)clear all
+
+--S 448 of 1527
+t0:=1/(x*(a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 9 2 2 7 2 2 2 2 5
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 3 2 2
+--R (2a c d + 2a b c )x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 448
+
+--S 449 of 1527
+r0:=1/2*b^2/(a*(b*c-a*d)^2*(a+b*x^2))+1/2*d^2/(c*(b*c-a*d)^2*(c+d*x^2))+_
+ log(x)/(a^2*c^2)-1/2*b^2*(b*c-3*a*d)*log(a+b*x^2)/(a^2*(b*c-a*d)^3)-_
+ 1/2*d^2*(3*b*c-a*d)*log(c+d*x^2)/(c^2*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 3 4 2 2 3 4 4 4 3 3 2 2 2 2 2
+--R (- a b d + 3a b c d )x + (- a d + 2a b c d + 3a b c d )x
+--R +
+--R 4 3 3 2 2
+--R - a c d + 3a b c d
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 3 2 2 4 3 4 2 2 2 2 3 3 4 4 2
+--R (- 3a b c d + b c d)x + (- 3a b c d - 2a b c d + b c )x
+--R +
+--R 2 2 3 3 4
+--R - 3a b c d + a b c
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (2a b d - 6a b c d + 6a b c d - 2b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (2a d - 4a b c d + 4a b c d - 2b c )x + 2a c d - 6a b c d
+--R +
+--R 2 2 3 3 4
+--R 6a b c d - 2a b c
+--R *
+--R log(x)
+--R +
+--R 3 3 3 3 2 4 3 3 2 2 2 2 3 3 4
+--R (a b c d - a b c d)x + a c d - a b c d + a b c d - a b c
+--R /
+--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 4
+--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x
+--R +
+--R 6 2 4 5 3 3 3 3 5 2 4 6 2 6 3 3 5 4 2
+--R (2a c d - 4a b c d + 4a b c d - 2a b c )x + 2a c d - 6a b c d
+--R +
+--R 4 2 5 3 3 6
+--R 6a b c d - 2a b c
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 4 2 2 3 4 4 4 3 3 2 2 2 2 2
+--R (- a b d + 3a b c d )x + (- a d + 2a b c d + 3a b c d )x
+--R +
+--R 4 3 3 2 2
+--R - a c d + 3a b c d
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 3 2 2 4 3 4 2 2 2 2 3 3 4 4 2
+--R (- 3a b c d + b c d)x + (- 3a b c d - 2a b c d + b c )x
+--R +
+--R 2 2 3 3 4
+--R - 3a b c d + a b c
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (2a b d - 6a b c d + 6a b c d - 2b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (2a d - 4a b c d + 4a b c d - 2b c )x + 2a c d - 6a b c d
+--R +
+--R 2 2 3 3 4
+--R 6a b c d - 2a b c
+--R *
+--R log(x)
+--R +
+--R 3 3 3 3 2 4 3 3 2 2 2 2 3 3 4
+--R (a b c d - a b c d)x + a c d - a b c d + a b c d - a b c
+--R /
+--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 4
+--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x
+--R +
+--R 6 2 4 5 3 3 3 3 5 2 4 6 2 6 3 3 5 4 2
+--R (2a c d - 4a b c d + 4a b c d - 2a b c )x + 2a c d - 6a b c d
+--R +
+--R 4 2 5 3 3 6
+--R 6a b c d - 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 450
+
+--S 451 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 452
+
+)clear all
+
+--S 453 of 1527
+t0:=1/(x^2*(a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 10 2 2 8 2 2 2 2 6
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 4 2 2 2
+--R (2a c d + 2a b c )x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 453
+
+--S 454 of 1527
+r0a:=(-1)/(a^2*c^2*x)-1/2*b^3*x/(a^2*(b*c-a*d)^2*(a+b*x^2))-_
+ 1/2*d^3*x/(c^2*(b*c-a*d)^2*(c+d*x^2))-1/2*b^(5/2)*(3*b*c-7*a*d)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-a*d)^3)-1/2*d^(5/2)*_
+ (7*b*c-3*a*d)*atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 3 4 2 2 3 5 4 4 3 3 2 2 2 2 3
+--R (- 3a b d + 7a b c d )x + (- 3a d + 4a b c d + 7a b c d )x
+--R +
+--R 4 3 3 2 2
+--R (- 3a c d + 7a b c d )x
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 2 4 3 5 2 2 2 2 3 3 4 4 3
+--R (- 7a b c d + 3b c d)x + (- 7a b c d - 4a b c d + 3b c )x
+--R +
+--R 2 2 3 3 4
+--R (- 7a b c d + 3a b c )x
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (- 3a b d + 7a b c d - 7a b c d + 3b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (- 3a d + 5a b c d - 5a b c d + 3b c )x - 2a c d + 6a b c d
+--R +
+--R 2 2 3 3 4
+--R - 6a b c d + 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5
+--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x
+--R +
+--R 6 2 4 5 3 3 3 3 5 2 4 6 3
+--R (2a c d - 4a b c d + 4a b c d - 2a b c )x
+--R +
+--R 6 3 3 5 4 2 4 2 5 3 3 6
+--R (2a c d - 6a b c d + 6a b c d - 2a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 1527
+r0b:=(-1)/(a^2*c^2*x)-1/2*b^3*x/(a^2*(b*c-a*d)^2*(a+b*x^2))-1/2*_
+ d^3*x/(c^2*(b*c-a*d)^2*(c+d*x^2))-b^(5/2)*(b*c-3*a*d)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-a*d)^3)-1/2*b^(5/2)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-a*d)^2)-1/2*d^(5/2)*_
+ atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*(b*c-a*d)^2)-d^(5/2)*_
+ (3*b*c-a*d)*atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*(b*c-a*d)^3)
+--R
+--R
+--R (3)
+--R 3 4 2 2 3 5 4 4 3 3 2 2 2 2 3
+--R (- 3a b d + 7a b c d )x + (- 3a d + 4a b c d + 7a b c d )x
+--R +
+--R 4 3 3 2 2
+--R (- 3a c d + 7a b c d )x
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 2 4 3 5 2 2 2 2 3 3 4 4 3
+--R (- 7a b c d + 3b c d)x + (- 7a b c d - 4a b c d + 3b c )x
+--R +
+--R 2 2 3 3 4
+--R (- 7a b c d + 3a b c )x
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (- 3a b d + 7a b c d - 7a b c d + 3b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (- 3a d + 5a b c d - 5a b c d + 3b c )x - 2a c d + 6a b c d
+--R +
+--R 2 2 3 3 4
+--R - 6a b c d + 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5
+--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x
+--R +
+--R 6 2 4 5 3 3 3 3 5 2 4 6 3
+--R (2a c d - 4a b c d + 4a b c d - 2a b c )x
+--R +
+--R 6 3 3 5 4 2 4 2 5 3 3 6
+--R (2a c d - 6a b c d + 6a b c d - 2a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 455
+
+--S 456 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 3 4 2 2 3 5 4 4 3 3 2 2 2 2 3
+--R (3a b d - 7a b c d )x + (3a d - 4a b c d - 7a b c d )x
+--R +
+--R 4 3 3 2 2
+--R (3a c d - 7a b c d )x
+--R *
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 3 2 2 4 3 5 2 2 2 2 3 3 4 4 3
+--R (7a b c d - 3b c d)x + (7a b c d + 4a b c d - 3b c )x
+--R +
+--R 2 2 3 3 4
+--R (7a b c d - 3a b c )x
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (- 6a b d + 14a b c d - 14a b c d + 6b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (- 6a d + 10a b c d - 10a b c d + 6b c )x - 4a c d + 12a b c d
+--R +
+--R 2 2 3 3 4
+--R - 12a b c d + 4a b c
+--R /
+--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5
+--R (4a b c d - 12a b c d + 12a b c d - 4a b c d)x
+--R +
+--R 6 2 4 5 3 3 3 3 5 2 4 6 3
+--R (4a c d - 8a b c d + 8a b c d - 4a b c )x
+--R +
+--R 6 3 3 5 4 2 4 2 5 3 3 6
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )x
+--R ,
+--R
+--R 3 2 2 4 3 5 2 2 2 2 3 3 4 4 3
+--R (7a b c d - 3b c d)x + (7a b c d + 4a b c d - 3b c )x
+--R +
+--R 2 2 3 3 4
+--R (7a b c d - 3a b c )x
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 4 2 2 3 5 4 4 3 3 2 2 2 2 3
+--R (6a b d - 14a b c d )x + (6a d - 8a b c d - 14a b c d )x
+--R +
+--R 4 3 3 2 2
+--R (6a c d - 14a b c d )x
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (- 6a b d + 14a b c d - 14a b c d + 6b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (- 6a d + 10a b c d - 10a b c d + 6b c )x - 4a c d + 12a b c d
+--R +
+--R 2 2 3 3 4
+--R - 12a b c d + 4a b c
+--R /
+--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5
+--R (4a b c d - 12a b c d + 12a b c d - 4a b c d)x
+--R +
+--R 6 2 4 5 3 3 3 3 5 2 4 6 3
+--R (4a c d - 8a b c d + 8a b c d - 4a b c )x
+--R +
+--R 6 3 3 5 4 2 4 2 5 3 3 6
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )x
+--R ,
+--R
+--R 3 4 2 2 3 5 4 4 3 3 2 2 2 2 3
+--R (3a b d - 7a b c d )x + (3a d - 4a b c d - 7a b c d )x
+--R +
+--R 4 3 3 2 2
+--R (3a c d - 7a b c d )x
+--R *
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 3 2 2 4 3 5 2 2 2 2 3 3 4 4 3
+--R (14a b c d - 6b c d)x + (14a b c d + 8a b c d - 6b c )x
+--R +
+--R 2 2 3 3 4
+--R (14a b c d - 6a b c )x
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (- 6a b d + 14a b c d - 14a b c d + 6b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (- 6a d + 10a b c d - 10a b c d + 6b c )x - 4a c d + 12a b c d
+--R +
+--R 2 2 3 3 4
+--R - 12a b c d + 4a b c
+--R /
+--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5
+--R (4a b c d - 12a b c d + 12a b c d - 4a b c d)x
+--R +
+--R 6 2 4 5 3 3 3 3 5 2 4 6 3
+--R (4a c d - 8a b c d + 8a b c d - 4a b c )x
+--R +
+--R 6 3 3 5 4 2 4 2 5 3 3 6
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )x
+--R ,
+--R
+--R 3 4 2 2 3 5 4 4 3 3 2 2 2 2 3
+--R (3a b d - 7a b c d )x + (3a d - 4a b c d - 7a b c d )x
+--R +
+--R 4 3 3 2 2
+--R (3a c d - 7a b c d )x
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 3 2 2 4 3 5 2 2 2 2 3 3 4 4 3
+--R (7a b c d - 3b c d)x + (7a b c d + 4a b c d - 3b c )x
+--R +
+--R 2 2 3 3 4
+--R (7a b c d - 3a b c )x
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (- 3a b d + 7a b c d - 7a b c d + 3b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (- 3a d + 5a b c d - 5a b c d + 3b c )x - 2a c d + 6a b c d
+--R +
+--R 2 2 3 3 4
+--R - 6a b c d + 2a b c
+--R /
+--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5
+--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x
+--R +
+--R 6 2 4 5 3 3 3 3 5 2 4 6 3
+--R (2a c d - 4a b c d + 4a b c d - 2a b c )x
+--R +
+--R 6 3 3 5 4 2 4 2 5 3 3 6
+--R (2a c d - 6a b c d + 6a b c d - 2a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 456
+
+--S 457 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R 3 3 2 2 | d +-+ +-+ \| c
+--R (3a d - 7a b c d ) |- - \|a \|c log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (7a b c d - 3b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 +-+ +-+ x\|d
+--R (6a d - 14a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 3 3 +-+ +-+ x\|b
+--R (14a b c d - 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 2 3 4 3 2 3 2 4 2 3 5 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 458
+
+--S 459 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (7a b c d - 3b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 +-+ +-+ x\|d
+--R (6a d - 14a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 3 3 2 2 +-+ +-+ |d \|c
+--R (6a d - 14a b c d )\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 3 3 +-+ +-+ x\|b
+--R (14a b c d - 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 2 3 4 3 2 3 2 4 2 3 5 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 460
+
+--S 461 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R 3 3 2 2 | d +-+ +-+ \| c
+--R (3a d - 7a b c d ) |- - \|a \|c log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (7a b c d - 3b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 +-+ +-+ x\|d
+--R (6a d - 14a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 3 3 +-+ +-+ x\|b
+--R (14a b c d - 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 2 3 4 3 2 3 2 4 2 3 5 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (7a b c d - 3b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 +-+ +-+ x\|d
+--R (6a d - 14a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 3 3 2 2 +-+ +-+ |d \|c
+--R (6a d - 14a b c d )\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 3 3 +-+ +-+ x\|b
+--R (14a b c d - 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 2 3 4 3 2 3 2 4 2 3 5 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 463
+
+--S 464 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 464
+
+)clear all
+
+--S 465 of 1527
+t0:=1/(x^3*(a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 11 2 2 9 2 2 2 2 7
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 5 2 2 3
+--R (2a c d + 2a b c )x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 465
+
+--S 466 of 1527
+r0:=(-1/2)/(a^2*c^2*x^2)-1/2*b^3/(a^2*(b*c-a*d)^2*(a+b*x^2))-_
+ 1/2*d^3/(c^2*(b*c-a*d)^2*(c+d*x^2))-2*(b*c+a*d)*log(x)/(a^3*c^3)+_
+ b^3*(b*c-2*a*d)*log(a+b*x^2)/(a^3*(b*c-a*d)^3)+d^3*(2*b*c-a*d)*_
+ log(c+d*x^2)/(c^3*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 4 5 3 2 4 6 5 5 4 4 3 2 2 3 4
+--R (2a b d - 4a b c d )x + (2a d - 2a b c d - 4a b c d )x
+--R +
+--R 5 4 4 2 3 2
+--R (2a c d - 4a b c d )x
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 4 3 2 5 4 6 2 3 3 2 4 4 5 5 4
+--R (4a b c d - 2b c d)x + (4a b c d + 2a b c d - 2b c )x
+--R +
+--R 2 3 4 4 5 2
+--R (4a b c d - 2a b c )x
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 4 5 3 2 4 4 3 2 5 4 6
+--R (- 4a b d + 8a b c d - 8a b c d + 4b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 4
+--R (- 4a d + 4a b c d + 8a b c d - 8a b c d - 4a b c d + 4b c )x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2
+--R (- 4a c d + 8a b c d - 8a b c d + 4a b c )x
+--R *
+--R log(x)
+--R +
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (- 2a b c d + 4a b c d - 4a b c d + 2a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (- 2a c d + 3a b c d - 3a b c d + 2a b c )x - a c d + 3a b c d
+--R +
+--R 3 2 4 2 3 5
+--R - 3a b c d + a b c
+--R /
+--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 6
+--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x
+--R +
+--R 7 3 4 6 4 3 4 3 6 3 4 7 4
+--R (2a c d - 4a b c d + 4a b c d - 2a b c )x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7 2
+--R (2a c d - 6a b c d + 6a b c d - 2a b c )x
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 5 3 2 4 6 5 5 4 4 3 2 2 3 4
+--R (2a b d - 4a b c d )x + (2a d - 2a b c d - 4a b c d )x
+--R +
+--R 5 4 4 2 3 2
+--R (2a c d - 4a b c d )x
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 4 3 2 5 4 6 2 3 3 2 4 4 5 5 4
+--R (4a b c d - 2b c d)x + (4a b c d + 2a b c d - 2b c )x
+--R +
+--R 2 3 4 4 5 2
+--R (4a b c d - 2a b c )x
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 4 5 3 2 4 4 3 2 5 4 6
+--R (- 4a b d + 8a b c d - 8a b c d + 4b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 4
+--R (- 4a d + 4a b c d + 8a b c d - 8a b c d - 4a b c d + 4b c )x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2
+--R (- 4a c d + 8a b c d - 8a b c d + 4a b c )x
+--R *
+--R log(x)
+--R +
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (- 2a b c d + 4a b c d - 4a b c d + 2a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (- 2a c d + 3a b c d - 3a b c d + 2a b c )x - a c d + 3a b c d
+--R +
+--R 3 2 4 2 3 5
+--R - 3a b c d + a b c
+--R /
+--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 6
+--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x
+--R +
+--R 7 3 4 6 4 3 4 3 6 3 4 7 4
+--R (2a c d - 4a b c d + 4a b c d - 2a b c )x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7 2
+--R (2a c d - 6a b c d + 6a b c d - 2a b c )x
+--R Type: Union(Expression(Integer),...)
+--E 467
+
+--S 468 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 468
+
+--S 469 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 469
+
+)clear all
+
+--S 470 of 1527
+t0:=1/(x^4*(a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 12 2 2 10 2 2 2 2 8
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 6 2 2 4
+--R (2a c d + 2a b c )x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 470
+
+--S 471 of 1527
+r0a:=(-1/3)/(a^2*c^2*x^3)+2*(b*c+a*d)/(a^3*c^3*x)+1/2*b^4*x/(a^3*(b*c-_
+ a*d)^2*(a+b*x^2))+1/2*d^4*x/(c^3*(b*c-a*d)^2*(c+d*x^2))+_
+ 1/2*b^(7/2)*(5*b*c-9*a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(7/2)*(b*c-_
+ a*d)^3)+1/2*d^(7/2)*(9*b*c-5*a*d)*atan(x*sqrt(d)/sqrt(c))/(c^(7/2)*_
+ (b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 4 5 3 2 4 7 5 5 4 4 3 2 2 3 5
+--R (15a b d - 27a b c d )x + (15a d - 12a b c d - 27a b c d )x
+--R +
+--R 5 4 4 2 3 3
+--R (15a c d - 27a b c d )x
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 4 3 2 5 4 7 2 3 3 2 4 4 5 5 5
+--R (27a b c d - 15b c d)x + (27a b c d + 12a b c d - 15b c )x
+--R +
+--R 2 3 4 4 5 3
+--R (27a b c d - 15a b c )x
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 5 3 2 4 4 3 2 5 4 6
+--R (15a b d - 27a b c d + 27a b c d - 15b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R 15a d - 17a b c d - 18a b c d + 18a b c d + 17a b c d
+--R +
+--R 5 5
+--R - 15b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3
+--R (10a c d - 20a b c d + 20a b c d - 10a b c )x - 2a c d
+--R +
+--R 4 3 2 3 2 4 2 3 5
+--R 6a b c d - 6a b c d + 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 7
+--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x
+--R +
+--R 7 3 4 6 4 3 4 3 6 3 4 7 5
+--R (6a c d - 12a b c d + 12a b c d - 6a b c )x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7 3
+--R (6a c d - 18a b c d + 18a b c d - 6a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 1527
+r0b:=(-1/3)/(a^2*c^2*x^3)+2*(b*c+a*d)/(a^3*c^3*x)+_
+ 1/2*b^4*x/(a^3*(b*c-a*d)^2*(a+b*x^2))+1/2*d^4*x/(c^3*(b*c-a*d)^2*_
+ (c+d*x^2))+2*b^(7/2)*(b*c-2*a*d)*atan(x*sqrt(b)/sqrt(a))/_
+ (a^(7/2)*(b*c-a*d)^3)+1/2*b^(7/2)*atan(x*sqrt(b)/sqrt(a))/_
+ (a^(7/2)*(b*c-a*d)^2)+1/2*d^(7/2)*atan(x*sqrt(d)/sqrt(c))/_
+ (c^(7/2)*(b*c-a*d)^2)+2*d^(7/2)*(2*b*c-a*d)*atan(x*sqrt(d)/_
+ sqrt(c))/(c^(7/2)*(b*c-a*d)^3)
+--R
+--R
+--R (3)
+--R 4 5 3 2 4 7 5 5 4 4 3 2 2 3 5
+--R (15a b d - 27a b c d )x + (15a d - 12a b c d - 27a b c d )x
+--R +
+--R 5 4 4 2 3 3
+--R (15a c d - 27a b c d )x
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 4 3 2 5 4 7 2 3 3 2 4 4 5 5 5
+--R (27a b c d - 15b c d)x + (27a b c d + 12a b c d - 15b c )x
+--R +
+--R 2 3 4 4 5 3
+--R (27a b c d - 15a b c )x
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 5 3 2 4 4 3 2 5 4 6
+--R (15a b d - 27a b c d + 27a b c d - 15b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R 15a d - 17a b c d - 18a b c d + 18a b c d + 17a b c d
+--R +
+--R 5 5
+--R - 15b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3
+--R (10a c d - 20a b c d + 20a b c d - 10a b c )x - 2a c d
+--R +
+--R 4 3 2 3 2 4 2 3 5
+--R 6a b c d - 6a b c d + 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 7
+--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x
+--R +
+--R 7 3 4 6 4 3 4 3 6 3 4 7 5
+--R (6a c d - 12a b c d + 12a b c d - 6a b c )x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7 3
+--R (6a c d - 18a b c d + 18a b c d - 6a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 4 3 2 5 4 7 2 3 3 2 4 4 5 5 5
+--R (27a b c d - 15b c d)x + (27a b c d + 12a b c d - 15b c )x
+--R +
+--R 2 3 4 4 5 3
+--R (27a b c d - 15a b c )x
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 4 5 3 2 4 7 5 5 4 4 3 2 2 3 5
+--R (15a b d - 27a b c d )x + (15a d - 12a b c d - 27a b c d )x
+--R +
+--R 5 4 4 2 3 3
+--R (15a c d - 27a b c d )x
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 4 5 3 2 4 4 3 2 5 4 6
+--R (30a b d - 54a b c d + 54a b c d - 30b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 4
+--R (30a d - 34a b c d - 36a b c d + 36a b c d + 34a b c d - 30b c )x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (20a c d - 40a b c d + 40a b c d - 20a b c )x - 4a c d + 12a b c d
+--R +
+--R 3 2 4 2 3 5
+--R - 12a b c d + 4a b c
+--R /
+--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 7
+--R (12a b c d - 36a b c d + 36a b c d - 12a b c d)x
+--R +
+--R 7 3 4 6 4 3 4 3 6 3 4 7 5
+--R (12a c d - 24a b c d + 24a b c d - 12a b c )x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7 3
+--R (12a c d - 36a b c d + 36a b c d - 12a b c )x
+--R ,
+--R
+--R 4 3 2 5 4 7 2 3 3 2 4 4 5 5 5
+--R (27a b c d - 15b c d)x + (27a b c d + 12a b c d - 15b c )x
+--R +
+--R 2 3 4 4 5 3
+--R (27a b c d - 15a b c )x
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 4 5 3 2 4 7
+--R (- 30a b d + 54a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 5 5 4 4 2 3 3
+--R (- 30a d + 24a b c d + 54a b c d )x + (- 30a c d + 54a b c d )x
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 4 5 3 2 4 4 3 2 5 4 6
+--R (30a b d - 54a b c d + 54a b c d - 30b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 4
+--R (30a d - 34a b c d - 36a b c d + 36a b c d + 34a b c d - 30b c )x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (20a c d - 40a b c d + 40a b c d - 20a b c )x - 4a c d + 12a b c d
+--R +
+--R 3 2 4 2 3 5
+--R - 12a b c d + 4a b c
+--R /
+--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 7
+--R (12a b c d - 36a b c d + 36a b c d - 12a b c d)x
+--R +
+--R 7 3 4 6 4 3 4 3 6 3 4 7 5
+--R (12a c d - 24a b c d + 24a b c d - 12a b c )x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7 3
+--R (12a c d - 36a b c d + 36a b c d - 12a b c )x
+--R ,
+--R
+--R 4 5 3 2 4 7 5 5 4 4 3 2 2 3 5
+--R (15a b d - 27a b c d )x + (15a d - 12a b c d - 27a b c d )x
+--R +
+--R 5 4 4 2 3 3
+--R (15a c d - 27a b c d )x
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 4 3 2 5 4 7 2 3 3 2 4 4 5 5 5
+--R (- 54a b c d + 30b c d)x + (- 54a b c d - 24a b c d + 30b c )x
+--R +
+--R 2 3 4 4 5 3
+--R (- 54a b c d + 30a b c )x
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 4 5 3 2 4 4 3 2 5 4 6
+--R (30a b d - 54a b c d + 54a b c d - 30b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 4
+--R (30a d - 34a b c d - 36a b c d + 36a b c d + 34a b c d - 30b c )x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (20a c d - 40a b c d + 40a b c d - 20a b c )x - 4a c d + 12a b c d
+--R +
+--R 3 2 4 2 3 5
+--R - 12a b c d + 4a b c
+--R /
+--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 7
+--R (12a b c d - 36a b c d + 36a b c d - 12a b c d)x
+--R +
+--R 7 3 4 6 4 3 4 3 6 3 4 7 5
+--R (12a c d - 24a b c d + 24a b c d - 12a b c )x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7 3
+--R (12a c d - 36a b c d + 36a b c d - 12a b c )x
+--R ,
+--R
+--R 4 5 3 2 4 7
+--R (- 15a b d + 27a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 5 5 4 4 2 3 3
+--R (- 15a d + 12a b c d + 27a b c d )x + (- 15a c d + 27a b c d )x
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 4 3 2 5 4 7 2 3 3 2 4 4 5 5 5
+--R (- 27a b c d + 15b c d)x + (- 27a b c d - 12a b c d + 15b c )x
+--R +
+--R 2 3 4 4 5 3
+--R (- 27a b c d + 15a b c )x
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 4 5 3 2 4 4 3 2 5 4 6
+--R (15a b d - 27a b c d + 27a b c d - 15b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 4
+--R (15a d - 17a b c d - 18a b c d + 18a b c d + 17a b c d - 15b c )x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (10a c d - 20a b c d + 20a b c d - 10a b c )x - 2a c d + 6a b c d
+--R +
+--R 3 2 4 2 3 5
+--R - 6a b c d + 2a b c
+--R /
+--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 7
+--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x
+--R +
+--R 7 3 4 6 4 3 4 3 6 3 4 7 5
+--R (6a c d - 12a b c d + 12a b c d - 6a b c )x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7 3
+--R (6a c d - 18a b c d + 18a b c d - 6a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 473
+
+--S 474 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 4 4 | b +-+ +-+ \| a
+--R (9a b c d - 5b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 4 4 3 3 | d +-+ +-+ \| c
+--R (5a d - 9a b c d ) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R 4 4 3 3 +-+ +-+ x\|d
+--R (- 10a d + 18a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 3 3 4 4 +-+ +-+ x\|b
+--R (- 18a b c d + 10b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 6 3 3 5 4 2 4 2 5 3 3 6 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 475
+
+--S 476 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 4 4 | b +-+ +-+ \| a
+--R (9a b c d - 5b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 4 4 3 3 +-+ +-+ x\|d
+--R (- 10a d + 18a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 4 4 3 3 +-+ +-+ |d \|c
+--R (- 10a d + 18a b c d )\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 3 3 4 4 +-+ +-+ x\|b
+--R (- 18a b c d + 10b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 6 3 3 5 4 2 4 2 5 3 3 6 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 4 4 | b +-+ +-+ \| a
+--R (9a b c d - 5b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 4 4 3 3 | d +-+ +-+ \| c
+--R (5a d - 9a b c d ) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R 4 4 3 3 +-+ +-+ x\|d
+--R (- 10a d + 18a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 3 3 4 4 +-+ +-+ x\|b
+--R (- 18a b c d + 10b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 6 3 3 5 4 2 4 2 5 3 3 6 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 478
+
+--S 479 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 4 4 | b +-+ +-+ \| a
+--R (9a b c d - 5b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 4 4 3 3 +-+ +-+ x\|d
+--R (- 10a d + 18a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 4 4 3 3 +-+ +-+ |d \|c
+--R (- 10a d + 18a b c d )\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 3 3 4 4 +-+ +-+ x\|b
+--R (- 18a b c d + 10b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 6 3 3 5 4 2 4 2 5 3 3 6 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 480
+
+--S 481 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 481
+
+)clear all
+
+--S 482 of 1527
+t0:=x^4/((a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 4
+--R x
+--R /
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 482
+
+--S 483 of 1527
+r0:=1/4*(b*c+2*a*d)*x/(b*(b*c-a*d)^2*(c+d*x^2)^2)+1/2*a*x/(b*(b*c-a*d)*_
+ (a+b*x^2)*(c+d*x^2)^2)+3/8*(b*c+3*a*d)*x/((b*c-a*d)^3*(c+d*x^2))-_
+ 3/2*(b*c+a*d)*atan(x*sqrt(b)/sqrt(a))*sqrt(a)*sqrt(b)/(b*c-a*d)^4+_
+ 3/8*(b^2*c^2+6*a*b*c*d+a^2*d^2)*atan(x*sqrt(d)/sqrt(c))/_
+ ((b*c-a*d)^4*sqrt(c)*sqrt(d))
+--R
+--R
+--R (2)
+--R 2 4 2 3 3 2 2 6
+--R (3a b d + 18a b c d + 3b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (3a d + 24a b c d + 39a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (6a c d + 39a b c d + 24a b c d + 3b c )x + 3a c d + 18a b c d
+--R +
+--R 2 4
+--R 3a b c
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 12a b d - 12b c d )x + (- 12a d - 36a b c d - 24b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 24a c d - 36a b c d - 12b c )x - 12a c d - 12a b c
+--R *
+--R +-+
+--R +-+ +-+ +-+ +-+ x\|b
+--R \|a \|b \|c \|d atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 2 3 2 5
+--R (- 9a b d + 6a b c d + 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 5a d - 9a b c d + 9a b c d + 5b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (- 3a c d - 6a b c d + 9a b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (8a b d - 32a b c d + 48a b c d - 32a b c d + 8b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 4
+--R (8a d - 16a b c d - 16a b c d + 64a b c d - 56a b c d + 16b c d)x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 2
+--R (16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d + 8b c )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R Type: Expression(Integer)
+--E 483
+
+--S 484 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 2 3 3 2 2 6
+--R (3a b d + 18a b c d + 3b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (3a d + 24a b c d + 39a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (6a c d + 39a b c d + 24a b c d + 3b c )x + 3a c d + 18a b c d
+--R +
+--R 2 4
+--R 3a b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (12a b d + 12b c d )x + (12a d + 36a b c d + 24b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (24a c d + 36a b c d + 12b c )x + 12a c d + 12a b c
+--R *
+--R +-----+ 2
+--R +-----+ +-----+ - 2x\|- a b + b x - a
+--R \|- c d \|- a b log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 2 2 3 2 5
+--R (- 18a b d + 12a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 10a d - 18a b c d + 18a b c d + 10b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (- 6a c d - 12a b c d + 18a b c )x
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R 16a d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 5 5
+--R 32b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5
+--R 32a c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 5 6
+--R 16b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R +-----+
+--R \|- c d
+--R ,
+--R
+--R 3 2 2 6 2 3 2 2 2 4
+--R (6a b d + 6b c d )x + (6a d + 18a b c d + 12b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (12a c d + 18a b c d + 6b c )x + 6a c d + 6a b c
+--R *
+--R +-----+ 2
+--R +-----+ +---+ - 2x\|- a b + b x - a
+--R \|- a b \|c d log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (3a b d + 18a b c d + 3b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (3a d + 24a b c d + 39a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (6a c d + 39a b c d + 24a b c d + 3b c )x + 3a c d + 18a b c d
+--R +
+--R 2 4
+--R 3a b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 2 2 3 2 5
+--R (- 9a b d + 6a b c d + 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 5a d - 9a b c d + 9a b c d + 5b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (- 3a c d - 6a b c d + 9a b c )x
+--R *
+--R +---+
+--R \|c d
+--R /
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (8a b d - 32a b c d + 48a b c d - 32a b c d + 8b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R 8a d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 5
+--R 16b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 5 6
+--R 8b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R *
+--R +---+
+--R \|c d
+--R ,
+--R
+--R 2 4 2 3 3 2 2 6
+--R (3a b d + 18a b c d + 3b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (3a d + 24a b c d + 39a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (6a c d + 39a b c d + 24a b c d + 3b c )x + 3a c d + 18a b c d
+--R +
+--R 2 4
+--R 3a b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (24a b d + 24b c d )x + (24a d + 72a b c d + 48b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (48a c d + 72a b c d + 24b c )x + 24a c d + 24a b c
+--R *
+--R +---+
+--R +-----+ +---+ \|a b
+--R \|- c d \|a b atan(------)
+--R b x
+--R +
+--R 2 3 2 2 3 2 5
+--R (- 18a b d + 12a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 10a d - 18a b c d + 18a b c d + 10b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (- 6a c d - 12a b c d + 18a b c )x
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (16a b d - 64a b c d + 96a b c d - 64a b c d + 16b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R 16a d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 5 5
+--R 32b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5
+--R 32a c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 5 6
+--R 16b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R *
+--R +-----+
+--R \|- c d
+--R ,
+--R
+--R 2 4 2 3 3 2 2 6
+--R (3a b d + 18a b c d + 3b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (3a d + 24a b c d + 39a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (6a c d + 39a b c d + 24a b c d + 3b c )x + 3a c d + 18a b c d
+--R +
+--R 2 4
+--R 3a b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (12a b d + 12b c d )x + (12a d + 36a b c d + 24b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (24a c d + 36a b c d + 12b c )x + 12a c d + 12a b c
+--R *
+--R +---+
+--R +---+ +---+ \|a b
+--R \|a b \|c d atan(------)
+--R b x
+--R +
+--R 2 3 2 2 3 2 5
+--R (- 9a b d + 6a b c d + 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 5a d - 9a b c d + 9a b c d + 5b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (- 3a c d - 6a b c d + 9a b c )x
+--R *
+--R +---+
+--R \|c d
+--R /
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (8a b d - 32a b c d + 48a b c d - 32a b c d + 8b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R 8a d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 5
+--R 16b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 5 6
+--R 8b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R *
+--R +---+
+--R \|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 484
+
+--S 485 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (3a d + 18a b c d + 3b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-----+ 2
+--R +-----+ +-----+ +-+ +-+ - 2x\|- a b + b x - a
+--R (12a d + 12b c)\|- c d \|- a b \|c \|d log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 6a d - 36a b c d - 6b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R +-----+ +-+ +-+ +-+ +-+ x\|b
+--R (24a d + 24b c)\|- c d \|a \|b \|c \|d atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----+ +-+ +-+
+--R (16a d - 64a b c d + 96a b c d - 64a b c d + 16b c )\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 485
+
+--S 486 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----+ 2
+--R +-----+ +-+ +-+ +---+ - 2x\|- a b + b x - a
+--R (6a d + 6b c)\|- a b \|c \|d \|c d log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (3a d + 18a b c d + 3b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 3a d - 18a b c d - 3b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R +-+ +-+ +-+ +-+ +---+ x\|b
+--R (12a d + 12b c)\|a \|b \|c \|d \|c d atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+ +-+ +---+
+--R (8a d - 32a b c d + 48a b c d - 32a b c d + 8b c )\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 488
+
+)clear all
+
+--S 489 of 1527
+t0:=x^3/((a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 3
+--R x
+--R /
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 489
+
+--S 490 of 1527
+r0:=1/2*a*b/((b*c-a*d)^3*(a+b*x^2))+1/4*c/((b*c-a*d)^2*(c+d*x^2)^2)+_
+ 1/2*(b*c+a*d)/((b*c-a*d)^3*(c+d*x^2))+1/2*b*(b*c+2*a*d)*_
+ log(a+b*x^2)/(b*c-a*d)^4-1/2*b*(b*c+2*a*d)*log(c+d*x^2)/(b*c-a*d)^4
+--R
+--R
+--R (2)
+--R 2 3 3 2 6 2 3 2 2 3 2 4
+--R (- 4a b d - 2b c d )x + (- 4a b d - 10a b c d - 4b c d)x
+--R +
+--R 2 2 2 2 3 3 2 2 2 2 3
+--R (- 8a b c d - 8a b c d - 2b c )x - 4a b c d - 2a b c
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 2 3 3 2 6 2 3 2 2 3 2 4
+--R (4a b d + 2b c d )x + (4a b d + 10a b c d + 4b c d)x
+--R +
+--R 2 2 2 2 3 3 2 2 2 2 3
+--R (8a b c d + 8a b c d + 2b c )x + 4a b c d + 2a b c
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 2 3 2 2 3 2 4
+--R (- 4a b d + 2a b c d + 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2 2 3
+--R (- 2a d - 5a b c d + 4a b c d + 3b c )x - a c d - 4a b c d + 5a b c
+--R /
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (4a b d - 16a b c d + 24a b c d - 16a b c d + 4b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 4
+--R (4a d - 8a b c d - 8a b c d + 32a b c d - 28a b c d + 8b c d)x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 2
+--R (8a c d - 28a b c d + 32a b c d - 8a b c d - 8a b c d + 4b c )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R 4a c d - 16a b c d + 24a b c d - 16a b c d + 4a b c
+--R Type: Expression(Integer)
+--E 490
+
+--S 491 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 3 2 6 2 3 2 2 3 2 4
+--R (- 4a b d - 2b c d )x + (- 4a b d - 10a b c d - 4b c d)x
+--R +
+--R 2 2 2 2 3 3 2 2 2 2 3
+--R (- 8a b c d - 8a b c d - 2b c )x - 4a b c d - 2a b c
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 2 3 3 2 6 2 3 2 2 3 2 4
+--R (4a b d + 2b c d )x + (4a b d + 10a b c d + 4b c d)x
+--R +
+--R 2 2 2 2 3 3 2 2 2 2 3
+--R (8a b c d + 8a b c d + 2b c )x + 4a b c d + 2a b c
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 2 3 2 2 3 2 4
+--R (- 4a b d + 2a b c d + 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2 2 3
+--R (- 2a d - 5a b c d + 4a b c d + 3b c )x - a c d - 4a b c d + 5a b c
+--R /
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (4a b d - 16a b c d + 24a b c d - 16a b c d + 4b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 4
+--R (4a d - 8a b c d - 8a b c d + 32a b c d - 28a b c d + 8b c d)x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 2
+--R (8a c d - 28a b c d + 32a b c d - 8a b c d - 8a b c d + 4b c )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R 4a c d - 16a b c d + 24a b c d - 16a b c d + 4a b c
+--R Type: Union(Expression(Integer),...)
+--E 491
+
+--S 492 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 493
+
+)clear all
+
+--S 494 of 1527
+t0:=x^2/((a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 2
+--R x
+--R /
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 494
+
+--S 495 of 1527
+r0:=-3/4*d*x/((b*c-a*d)^2*(c+d*x^2)^2)-1/2*x/((b*c-a*d)*(a+b*x^2)*_
+ (c+d*x^2)^2)-1/8*d*(11*b*c+a*d)*x/(c*(b*c-a*d)^3*(c+d*x^2))+_
+ 1/2*b^(3/2)*(b*c+5*a*d)*atan(x*sqrt(b)/sqrt(a))/((b*c-a*d)^4*_
+ sqrt(a))-1/8*(15*b^2*c^2+10*a*b*c*d-a^2*d^2)*atan(x*sqrt(d)/_
+ sqrt(c))*sqrt(d)/(c^(3/2)*(b*c-a*d)^4)
+--R
+--R
+--R (2)
+--R 2 4 2 3 3 2 2 6
+--R (a b d - 10a b c d - 15b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (a d - 8a b c d - 35a b c d - 30b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (2a c d - 19a b c d - 40a b c d - 15b c )x + a c d - 10a b c d
+--R +
+--R 2 4
+--R - 15a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (20a b c d + 4b c d )x + (20a b c d + 44a b c d + 8b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (40a b c d + 28a b c d + 4b c )x + 20a b c d + 4a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 4 2 3 3 2 2 5
+--R (a b d + 10a b c d - 11b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 3
+--R (a d + 5a b c d + 11a b c d - 17b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- a c d + 10a b c d - 5a b c d - 4b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8b c d )x
+--R +
+--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 6
+--R 16b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 5 7 2
+--R (16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d + 8b c )x
+--R +
+--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 495
+
+--S 496 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (20a b c d + 4b c d )x + (20a b c d + 44a b c d + 8b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (40a b c d + 28a b c d + 4b c )x + 20a b c d + 4a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (a b d - 10a b c d - 15b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (a d - 8a b c d - 35a b c d - 30b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (2a c d - 19a b c d - 40a b c d - 15b c )x + a c d - 10a b c d
+--R +
+--R 2 4
+--R - 15a b c
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 4 2 3 3 2 2 5
+--R (2a b d + 20a b c d - 22b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 3
+--R (2a d + 10a b c d + 22a b c d - 34b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 2a c d + 20a b c d - 10a b c d - 8b c )x
+--R /
+--R 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 6
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16b c d )x
+--R +
+--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 5 6
+--R 32b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6
+--R 32a c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 5 7
+--R 16b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R ,
+--R
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (10a b c d + 2b c d )x + (10a b c d + 22a b c d + 4b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (20a b c d + 14a b c d + 2b c )x + 10a b c d + 2a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- a b d + 10a b c d + 15b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- a d + 8a b c d + 35a b c d + 30b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 2a c d + 19a b c d + 40a b c d + 15b c )x - a c d
+--R +
+--R 2 3 2 4
+--R 10a b c d + 15a b c
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 4 2 3 3 2 2 5
+--R (a b d + 10a b c d - 11b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 3
+--R (a d + 5a b c d + 11a b c d - 17b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- a c d + 10a b c d - 5a b c d - 4b c )x
+--R /
+--R 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8b c d )x
+--R +
+--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 6
+--R 16b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 5 7 2
+--R (16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d + 8b c )x
+--R +
+--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R ,
+--R
+--R 2 4 2 3 3 2 2 6
+--R (a b d - 10a b c d - 15b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (a d - 8a b c d - 35a b c d - 30b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (2a c d - 19a b c d - 40a b c d - 15b c )x + a c d - 10a b c d
+--R +
+--R 2 4
+--R - 15a b c
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 3 3 2 2 6
+--R (- 40a b c d - 8b c d )x
+--R +
+--R 2 3 2 2 2 3 3 4
+--R (- 40a b c d - 88a b c d - 16b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (- 80a b c d - 56a b c d - 8b c )x - 40a b c d - 8a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 4 2 3 3 2 2 5
+--R (2a b d + 20a b c d - 22b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 3
+--R (2a d + 10a b c d + 22a b c d - 34b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 2a c d + 20a b c d - 10a b c d - 8b c )x
+--R /
+--R 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 6
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16b c d )x
+--R +
+--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 5 6
+--R 32b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6
+--R 32a c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 5 7
+--R 16b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R ,
+--R
+--R 2 4 2 3 3 2 2 6
+--R (- a b d + 10a b c d + 15b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- a d + 8a b c d + 35a b c d + 30b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 2a c d + 19a b c d + 40a b c d + 15b c )x - a c d
+--R +
+--R 2 3 2 4
+--R 10a b c d + 15a b c
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (- 20a b c d - 4b c d )x + (- 20a b c d - 44a b c d - 8b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (- 40a b c d - 28a b c d - 4b c )x - 20a b c d - 4a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 4 2 3 3 2 2 5
+--R (a b d + 10a b c d - 11b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 3
+--R (a d + 5a b c d + 11a b c d - 17b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- a c d + 10a b c d - 5a b c d - 4b c )x
+--R /
+--R 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8b c d )x
+--R +
+--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 6
+--R 16b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 5 7 2
+--R (16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d + 8b c )x
+--R +
+--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 496
+
+--S 497 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R (20a b c d + 4b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 2 | d +-+ +-+ \| c
+--R (a d - 10a b c d - 15b c ) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|d
+--R (- 2a d + 20a b c d + 30b c )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R (- 40a b c d - 8b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +-+ +-+
+--R (16a c d - 64a b c d + 96a b c d - 64a b c d + 16b c )\|a \|c
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 498
+
+--S 499 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R (10a b c d + 2b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|d
+--R (- a d + 10a b c d + 15b c )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 2 +-+ +-+ |d \|c
+--R (- a d + 10a b c d + 15b c )\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R (- 20a b c d - 4b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +-+ +-+
+--R (8a c d - 32a b c d + 48a b c d - 32a b c d + 8b c )\|a \|c
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 500
+
+)clear all
+
+--S 501 of 1527
+t0:=x/((a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R x
+--R /
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 501
+
+--S 502 of 1527
+r0:=-1/2*b^2/((b*c-a*d)^3*(a+b*x^2))-1/4*d/((b*c-a*d)^2*(c+d*x^2)^2)-_
+ b*d/((b*c-a*d)^3*(c+d*x^2))-3/2*b^2*d*log(a+b*x^2)/(b*c-a*d)^4+_
+ 3/2*b^2*d*log(c+d*x^2)/(b*c-a*d)^4
+--R
+--R
+--R (2)
+--R 3 3 6 2 3 3 2 4 2 2 3 2 2 2 2
+--R (6b d x + (6a b d + 12b c d )x + (12a b c d + 6b c d)x + 6a b c d)
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 3 3 6 2 3 3 2 4 2 2 3 2 2
+--R - 6b d x + (- 6a b d - 12b c d )x + (- 12a b c d - 6b c d)x
+--R +
+--R 2 2
+--R - 6a b c d
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 2 3 3 2 4 2 3 2 2 3 2 2 3 3
+--R (6a b d - 6b c d )x + (3a b d + 6a b c d - 9b c d)x - a d
+--R +
+--R 2 2 2 2 3 3
+--R 6a b c d - 3a b c d - 2b c
+--R /
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (4a b d - 16a b c d + 24a b c d - 16a b c d + 4b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 4
+--R (4a d - 8a b c d - 8a b c d + 32a b c d - 28a b c d + 8b c d)x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 2
+--R (8a c d - 28a b c d + 32a b c d - 8a b c d - 8a b c d + 4b c )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R 4a c d - 16a b c d + 24a b c d - 16a b c d + 4a b c
+--R Type: Expression(Integer)
+--E 502
+
+--S 503 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 6 2 3 3 2 4 2 2 3 2 2 2 2
+--R (6b d x + (6a b d + 12b c d )x + (12a b c d + 6b c d)x + 6a b c d)
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 3 3 6 2 3 3 2 4 2 2 3 2 2
+--R - 6b d x + (- 6a b d - 12b c d )x + (- 12a b c d - 6b c d)x
+--R +
+--R 2 2
+--R - 6a b c d
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 2 3 3 2 4 2 3 2 2 3 2 2 3 3
+--R (6a b d - 6b c d )x + (3a b d + 6a b c d - 9b c d)x - a d
+--R +
+--R 2 2 2 2 3 3
+--R 6a b c d - 3a b c d - 2b c
+--R /
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (4a b d - 16a b c d + 24a b c d - 16a b c d + 4b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 4
+--R (4a d - 8a b c d - 8a b c d + 32a b c d - 28a b c d + 8b c d)x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 2
+--R (8a c d - 28a b c d + 32a b c d - 8a b c d - 8a b c d + 4b c )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R 4a c d - 16a b c d + 24a b c d - 16a b c d + 4a b c
+--R Type: Union(Expression(Integer),...)
+--E 503
+
+--S 504 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 504
+
+--S 505 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 505
+
+)clear all
+
+--S 506 of 1527
+t0:=1/((a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 506
+
+--S 507 of 1527
+r0:=1/4*d*(2*b*c+a*d)*x/(a*c*(b*c-a*d)^2*(c+d*x^2)^2)+1/2*b*x/(a*(b*c-_
+ a*d)*(a+b*x^2)*(c+d*x^2)^2)+1/8*d*(4*b*c-a*d)*(b*c+3*a*d)*x/_
+ (a*c^2*(b*c-a*d)^3*(c+d*x^2))+1/2*b^(5/2)*(b*c-7*a*d)*atan(x*_
+ sqrt(b)/sqrt(a))/(a^(3/2)*(b*c-a*d)^4)+1/8*d^(3/2)*(35*b^2*c^2-_
+ 14*a*b*c*d+3*a^2*d^2)*atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*(b*c-a*d)^4)
+--R
+--R
+--R (2)
+--R 3 5 2 2 4 3 2 3 6
+--R (3a b d - 14a b c d + 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (3a d - 8a b c d + 7a b c d + 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (6a c d - 25a b c d + 56a b c d + 35a b c d)x + 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 14a b c d + 35a b c d
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (- 28a b c d + 4b c d )x + (- 28a b c d - 52a b c d + 8b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (- 56a b c d - 20a b c d + 4b c )x - 28a b c d + 4a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (3a b d - 14a b c d + 7a b c d + 4b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (3a d - 9a b c d - 7a b c d + 5a b c d + 8b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (5a c d - 18a b c d + 13a b c d - 4a b c d + 4b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 7
+--R 16a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 5 8
+--R 8a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 507
+
+--S 508 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 5 2 2 4 3 2 3 6
+--R (3a b d - 14a b c d + 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (3a d - 8a b c d + 7a b c d + 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (6a c d - 25a b c d + 56a b c d + 35a b c d)x + 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 14a b c d + 35a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (28a b c d - 4b c d )x + (28a b c d + 52a b c d - 8b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (56a b c d + 20a b c d - 4b c )x + 28a b c d - 4a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (6a b d - 28a b c d + 14a b c d + 8b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (6a d - 18a b c d - 14a b c d + 10a b c d + 16b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (10a c d - 36a b c d + 26a b c d - 8a b c d + 8b c )x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 5 7
+--R 32a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 32a c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 5 8
+--R 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R ,
+--R
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (14a b c d - 2b c d )x + (14a b c d + 26a b c d - 4b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (28a b c d + 10a b c d - 2b c )x + 14a b c d - 2a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 5 2 2 4 3 2 3 6
+--R (- 3a b d + 14a b c d - 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (- 3a d + 8a b c d - 7a b c d - 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (- 6a c d + 25a b c d - 56a b c d - 35a b c d)x - 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R 14a b c d - 35a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (3a b d - 14a b c d + 7a b c d + 4b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (3a d - 9a b c d - 7a b c d + 5a b c d + 8b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (5a c d - 18a b c d + 13a b c d - 4a b c d + 4b c )x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 7
+--R 16a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 5 8
+--R 8a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R ,
+--R
+--R 3 5 2 2 4 3 2 3 6
+--R (3a b d - 14a b c d + 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (3a d - 8a b c d + 7a b c d + 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (6a c d - 25a b c d + 56a b c d + 35a b c d)x + 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 14a b c d + 35a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (56a b c d - 8b c d )x + (56a b c d + 104a b c d - 16b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (112a b c d + 40a b c d - 8b c )x + 56a b c d - 8a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (6a b d - 28a b c d + 14a b c d + 8b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (6a d - 18a b c d - 14a b c d + 10a b c d + 16b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (10a c d - 36a b c d + 26a b c d - 8a b c d + 8b c )x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 5 7
+--R 32a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 32a c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 5 8
+--R 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R ,
+--R
+--R 3 5 2 2 4 3 2 3 6
+--R (- 3a b d + 14a b c d - 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (- 3a d + 8a b c d - 7a b c d - 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (- 6a c d + 25a b c d - 56a b c d - 35a b c d)x - 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R 14a b c d - 35a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (28a b c d - 4b c d )x + (28a b c d + 52a b c d - 8b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (56a b c d + 20a b c d - 4b c )x + 28a b c d - 4a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (3a b d - 14a b c d + 7a b c d + 4b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (3a d - 9a b c d - 7a b c d + 5a b c d + 8b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (5a c d - 18a b c d + 13a b c d - 4a b c d + 4b c )x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 7
+--R 16a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 5 8
+--R 8a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 508
+
+--S 509 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 3 3 2 2 2 2 | d +-+ +-+ \| c
+--R (3a d - 14a b c d + 35a b c d) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (28a b c d - 4b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 +-+ +-+ x\|d
+--R (- 6a d + 28a b c d - 70a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 3 3 +-+ +-+ x\|b
+--R (56a b c d - 8b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +-+ +-+
+--R (16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 509
+
+--S 510 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 510
+
+--S 511 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (14a b c d - 2b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 +-+ +-+ x\|d
+--R (- 3a d + 14a b c d - 35a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 3 3 2 2 2 2 +-+ +-+ |d \|c
+--R (- 3a d + 14a b c d - 35a b c d)\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 3 3 +-+ +-+ x\|b
+--R (28a b c d - 4b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +-+ +-+
+--R (8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 511
+
+--S 512 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 512
+
+)clear all
+
+--S 513 of 1527
+t0:=1/(x*(a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 3 11 3 2 2 9 2 3 2 2 2 7
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 5 2 2 3 3 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 513
+
+--S 514 of 1527
+r0:=1/2*b^3/(a*(b*c-a*d)^3*(a+b*x^2))+1/4*d^2/(c*(b*c-a*d)^2*(c+d*x^2)^2)+_
+ 1/2*d^2*(3*b*c-a*d)/(c^2*(b*c-a*d)^3*(c+d*x^2))+log(x)/(a^2*c^3)-_
+ 1/2*b^3*(b*c-4*a*d)*log(a+b*x^2)/(a^2*(b*c-a*d)^4)-_
+ 1/2*d^2*(6*b^2*c^2-4*a*b*c*d+a^2*d^2)*log(c+d*x^2)/(c^3*(b*c-a*d)^4)
+--R
+--R
+--R (2)
+--R 4 6 3 2 5 2 3 2 4 6
+--R (- 2a b d + 8a b c d - 12a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4
+--R (- 2a d + 4a b c d + 4a b c d - 24a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 2 5 2 4
+--R (- 4a c d + 14a b c d - 16a b c d - 12a b c d )x - 2a c d
+--R +
+--R 4 3 3 3 2 4 2
+--R 8a b c d - 12a b c d
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 4 3 3 5 4 2 6 2 3 3 3 4 4 2 5 5 4
+--R (8a b c d - 2b c d )x + (8a b c d + 14a b c d - 4b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 2 2 3 5 4 6
+--R (16a b c d + 4a b c d - 2b c )x + 8a b c d - 2a b c
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (4a b d - 16a b c d + 24a b c d - 16a b c d + 4b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 4
+--R (4a d - 8a b c d - 8a b c d + 32a b c d - 28a b c d + 8b c d)x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 2
+--R (8a c d - 28a b c d + 32a b c d - 8a b c d - 8a b c d + 4b c )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R 4a c d - 16a b c d + 24a b c d - 16a b c d + 4a b c
+--R *
+--R log(x)
+--R +
+--R 4 5 3 2 2 4 2 3 3 3 4 4 2 4
+--R (2a b c d - 8a b c d + 4a b c d + 2a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 2 5 2 4
+--R (2a c d - 5a b c d - 4a b c d + 3a b c d + 4a b c d)x + 3a c d
+--R +
+--R 4 3 3 3 2 4 2 2 3 5 4 6
+--R - 10a b c d + 7a b c d - 2a b c d + 2a b c
+--R /
+--R 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 2 5 7 2 6
+--R (4a b c d - 16a b c d + 24a b c d - 16a b c d + 4a b c d )x
+--R +
+--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2 2 5 8 4
+--R (4a c d - 8a b c d - 8a b c d + 32a b c d - 28a b c d + 8a b c d)x
+--R +
+--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8 2 5 9 2
+--R (8a c d - 28a b c d + 32a b c d - 8a b c d - 8a b c d + 4a b c )x
+--R +
+--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9
+--R 4a c d - 16a b c d + 24a b c d - 16a b c d + 4a b c
+--R Type: Expression(Integer)
+--E 514
+
+--S 515 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 6 3 2 5 2 3 2 4 6
+--R (- 2a b d + 8a b c d - 12a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4
+--R (- 2a d + 4a b c d + 4a b c d - 24a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 2 5 2 4
+--R (- 4a c d + 14a b c d - 16a b c d - 12a b c d )x - 2a c d
+--R +
+--R 4 3 3 3 2 4 2
+--R 8a b c d - 12a b c d
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 4 3 3 5 4 2 6 2 3 3 3 4 4 2 5 5 4
+--R (8a b c d - 2b c d )x + (8a b c d + 14a b c d - 4b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 2 2 3 5 4 6
+--R (16a b c d + 4a b c d - 2b c )x + 8a b c d - 2a b c
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (4a b d - 16a b c d + 24a b c d - 16a b c d + 4b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 4
+--R (4a d - 8a b c d - 8a b c d + 32a b c d - 28a b c d + 8b c d)x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 2
+--R (8a c d - 28a b c d + 32a b c d - 8a b c d - 8a b c d + 4b c )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R 4a c d - 16a b c d + 24a b c d - 16a b c d + 4a b c
+--R *
+--R log(x)
+--R +
+--R 4 5 3 2 2 4 2 3 3 3 4 4 2 4
+--R (2a b c d - 8a b c d + 4a b c d + 2a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 2 5 2 4
+--R (2a c d - 5a b c d - 4a b c d + 3a b c d + 4a b c d)x + 3a c d
+--R +
+--R 4 3 3 3 2 4 2 2 3 5 4 6
+--R - 10a b c d + 7a b c d - 2a b c d + 2a b c
+--R /
+--R 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 2 5 7 2 6
+--R (4a b c d - 16a b c d + 24a b c d - 16a b c d + 4a b c d )x
+--R +
+--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2 2 5 8 4
+--R (4a c d - 8a b c d - 8a b c d + 32a b c d - 28a b c d + 8a b c d)x
+--R +
+--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8 2 5 9 2
+--R (8a c d - 28a b c d + 32a b c d - 8a b c d - 8a b c d + 4a b c )x
+--R +
+--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9
+--R 4a c d - 16a b c d + 24a b c d - 16a b c d + 4a b c
+--R Type: Union(Expression(Integer),...)
+--E 515
+
+--S 516 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 516
+
+--S 517 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 517
+
+)clear all
+
+--S 518 of 1527
+t0:=1/(x^2*(a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 3 12 3 2 2 10 2 3 2 2 2 8
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 6 2 2 3 4 2 3 2
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 518
+
+--S 519 of 1527
+r0:=-3/8*(2*b*c-a*d)*(2*b^2*c^2-3*a*b*c*d+5*a^2*d^2)/(a^2*c^3*_
+ (b*c-a*d)^3*x)+1/4*d*(2*b*c+a*d)/(a*c*(b*c-a*d)^2*x*(c+d*x^2)^2)+_
+ 1/2*b/(a*(b*c-a*d)*x*(a+b*x^2)*(c+d*x^2)^2)+1/8*d*(4*b^2*c^2+_
+ 13*a*b*c*d-5*a^2*d^2)/(a*c^2*(b*c-a*d)^3*x*(c+d*x^2))-_
+ 3/2*b^(7/2)*(b*c-3*a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*_
+ (b*c-a*d)^4)-3/8*d^(5/2)*(21*b^2*c^2-18*a*b*c*d+5*a^2*d^2)*_
+ atan(x*sqrt(d)/sqrt(c))/(c^(7/2)*(b*c-a*d)^4)
+--R
+--R
+--R (2)
+--R 4 6 3 2 5 2 3 2 4 7
+--R (- 15a b d + 54a b c d - 63a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 5
+--R (- 15a d + 24a b c d + 45a b c d - 126a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 3
+--R (- 30a c d + 93a b c d - 72a b c d - 63a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2
+--R (- 15a c d + 54a b c d - 63a b c d )x
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 4 3 3 5 4 2 7 2 3 3 3 4 4 2 5 5 5
+--R (36a b c d - 12b c d )x + (36a b c d + 60a b c d - 24b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 3 2 3 5 4 6
+--R (72a b c d + 12a b c d - 12b c )x + (36a b c d - 12a b c )x
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (- 15a b d + 54a b c d - 63a b c d + 36a b c d - 12b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R - 15a d + 29a b c d + 27a b c d - 81a b c d + 64a b c d
+--R +
+--R 5 5
+--R - 24b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5
+--R - 25a c d + 82a b c d - 81a b c d + 16a b c d + 20a b c d
+--R +
+--R 5 6
+--R - 12b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R - 8a c d + 32a b c d - 48a b c d + 32a b c d - 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 2 5 7 2 7
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d )x
+--R +
+--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 2 5 8
+--R 16a b c d
+--R *
+--R 5
+--R x
+--R +
+--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 2 5 9
+--R 8a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9
+--R (8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 519
+
+--S 520 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 3 3 5 4 2 7 2 3 3 3 4 4 2 5 5 5
+--R (36a b c d - 12b c d )x + (36a b c d + 60a b c d - 24b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 3 2 3 5 4 6
+--R (72a b c d + 12a b c d - 12b c )x + (36a b c d - 12a b c )x
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 4 6 3 2 5 2 3 2 4 7
+--R (15a b d - 54a b c d + 63a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 5
+--R (15a d - 24a b c d - 45a b c d + 126a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 3
+--R (30a c d - 93a b c d + 72a b c d + 63a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2
+--R (15a c d - 54a b c d + 63a b c d )x
+--R *
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (- 30a b d + 108a b c d - 126a b c d + 72a b c d - 24b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R - 30a d + 58a b c d + 54a b c d - 162a b c d + 128a b c d
+--R +
+--R 5 5
+--R - 48b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5
+--R - 50a c d + 164a b c d - 162a b c d + 32a b c d + 40a b c d
+--R +
+--R 5 6
+--R - 24b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R - 16a c d + 64a b c d - 96a b c d + 64a b c d - 16a b c
+--R /
+--R 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 2 5 7 2 7
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16a b c d )x
+--R +
+--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 2 5 8
+--R 32a b c d
+--R *
+--R 5
+--R x
+--R +
+--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8
+--R 32a c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 2 5 9
+--R 16a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9
+--R (16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c )x
+--R ,
+--R
+--R 4 3 3 5 4 2 7 2 3 3 3 4 4 2 5 5 5
+--R (18a b c d - 6b c d )x + (18a b c d + 30a b c d - 12b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 3 2 3 5 4 6
+--R (36a b c d + 6a b c d - 6b c )x + (18a b c d - 6a b c )x
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 4 6 3 2 5 2 3 2 4 7
+--R (15a b d - 54a b c d + 63a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 5
+--R (15a d - 24a b c d - 45a b c d + 126a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 3
+--R (30a c d - 93a b c d + 72a b c d + 63a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2
+--R (15a c d - 54a b c d + 63a b c d )x
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (- 15a b d + 54a b c d - 63a b c d + 36a b c d - 12b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R - 15a d + 29a b c d + 27a b c d - 81a b c d + 64a b c d
+--R +
+--R 5 5
+--R - 24b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5
+--R - 25a c d + 82a b c d - 81a b c d + 16a b c d + 20a b c d
+--R +
+--R 5 6
+--R - 12b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R - 8a c d + 32a b c d - 48a b c d + 32a b c d - 8a b c
+--R /
+--R 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 2 5 7 2 7
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d )x
+--R +
+--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 2 5 8
+--R 16a b c d
+--R *
+--R 5
+--R x
+--R +
+--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 2 5 9
+--R 8a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9
+--R (8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c )x
+--R ,
+--R
+--R 4 6 3 2 5 2 3 2 4 7
+--R (15a b d - 54a b c d + 63a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 5
+--R (15a d - 24a b c d - 45a b c d + 126a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 3
+--R (30a c d - 93a b c d + 72a b c d + 63a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2
+--R (15a c d - 54a b c d + 63a b c d )x
+--R *
+--R +---+
+--R | d 2
+--R +---+ - 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(-----------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 4 3 3 5 4 2 7
+--R (- 72a b c d + 24b c d )x
+--R +
+--R 2 3 3 3 4 4 2 5 5 5
+--R (- 72a b c d - 120a b c d + 48b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 3 2 3 5 4 6
+--R (- 144a b c d - 24a b c d + 24b c )x + (- 72a b c d + 24a b c )x
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (- 30a b d + 108a b c d - 126a b c d + 72a b c d - 24b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R - 30a d + 58a b c d + 54a b c d - 162a b c d + 128a b c d
+--R +
+--R 5 5
+--R - 48b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5
+--R - 50a c d + 164a b c d - 162a b c d + 32a b c d + 40a b c d
+--R +
+--R 5 6
+--R - 24b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R - 16a c d + 64a b c d - 96a b c d + 64a b c d - 16a b c
+--R /
+--R 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 2 5 7 2 7
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16a b c d )x
+--R +
+--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 2 5 8
+--R 32a b c d
+--R *
+--R 5
+--R x
+--R +
+--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8
+--R 32a c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 2 5 9
+--R 16a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9
+--R (16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c )x
+--R ,
+--R
+--R 4 6 3 2 5 2 3 2 4 7
+--R (15a b d - 54a b c d + 63a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 5
+--R (15a d - 24a b c d - 45a b c d + 126a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 3
+--R (30a c d - 93a b c d + 72a b c d + 63a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2
+--R (15a c d - 54a b c d + 63a b c d )x
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 4 3 3 5 4 2 7
+--R (- 36a b c d + 12b c d )x
+--R +
+--R 2 3 3 3 4 4 2 5 5 5
+--R (- 36a b c d - 60a b c d + 24b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 3 2 3 5 4 6
+--R (- 72a b c d - 12a b c d + 12b c )x + (- 36a b c d + 12a b c )x
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (- 15a b d + 54a b c d - 63a b c d + 36a b c d - 12b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R - 15a d + 29a b c d + 27a b c d - 81a b c d + 64a b c d
+--R +
+--R 5 5
+--R - 24b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5
+--R - 25a c d + 82a b c d - 81a b c d + 16a b c d + 20a b c d
+--R +
+--R 5 6
+--R - 12b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R - 8a c d + 32a b c d - 48a b c d + 32a b c d - 8a b c
+--R /
+--R 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 2 5 7 2 7
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d )x
+--R +
+--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 2 5 8
+--R 16a b c d
+--R *
+--R 5
+--R x
+--R +
+--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 2 5 9
+--R 8a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9
+--R (8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 520
+
+--S 521 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 4 4 | b +-+ +-+ \| a
+--R (36a b c d - 12b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R 4 4 3 3 2 2 2 2 | d +-+ +-+
+--R (15a d - 54a b c d + 63a b c d ) |- - \|a \|c
+--R \| c
+--R *
+--R +---+
+--R | d 2
+--R - 2c x |- - + d x - c
+--R \| c
+--R log(-----------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 4 4 3 3 2 2 2 2 +-+ +-+ x\|d
+--R (30a d - 108a b c d + 126a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 3 3 4 4 +-+ +-+ x\|b
+--R (- 72a b c d + 24b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +-+ +-+
+--R (16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 521
+
+--S 522 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 522
+
+--S 523 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 3 4 4 | b +-+ +-+ \| a
+--R (18a b c d - 6b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 4 4 3 3 2 2 2 2 +-+ +-+ x\|d
+--R (15a d - 54a b c d + 63a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 4 4 3 3 2 2 2 2 +-+ +-+ |d \|c
+--R (15a d - 54a b c d + 63a b c d )\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 3 3 4 4 +-+ +-+ x\|b
+--R (- 36a b c d + 12b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +-+ +-+
+--R (8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 523
+
+--S 524 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 524
+
+)clear all
+
+--S 525 of 1527
+t0:=1/(x^3*(a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 3 13 3 2 2 11 2 3 2 2 2 9
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 7 2 2 3 5 2 3 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 525
+
+--S 526 of 1527
+r0:=(-1/2)/(a^2*c^3*x^2)-1/2*b^4/(a^2*(b*c-a*d)^3*(a+b*x^2))-_
+ 1/4*d^3/(c^2*(b*c-a*d)^2*(c+d*x^2)^2)-d^3*(2*b*c-a*d)/(c^3*(b*c-_
+ a*d)^3*(c+d*x^2))-(2*b*c+3*a*d)*log(x)/(a^3*c^4)+1/2*b^4*(2*b*c-_
+ 5*a*d)*log(a+b*x^2)/(a^3*(b*c-a*d)^4)+1/2*d^3*(10*b^2*c^2-_
+ 10*a*b*c*d+3*a^2*d^2)*log(c+d*x^2)/(c^4*(b*c-a*d)^4)
+--R
+--R
+--R (2)
+--R 5 7 4 2 6 3 3 2 5 8
+--R (6a b d - 20a b c d + 20a b c d )x
+--R +
+--R 6 7 5 6 4 2 2 5 3 3 3 4 6
+--R (6a d - 8a b c d - 20a b c d + 40a b c d )x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3 4
+--R (12a c d - 34a b c d + 20a b c d + 20a b c d )x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 2
+--R (6a c d - 20a b c d + 20a b c d )x
+--R *
+--R 2
+--R log(d x + c)
+--R +
+--R 5 4 3 6 5 2 8 2 4 4 3 5 5 2 6 6 6
+--R (- 10a b c d + 4b c d )x + (- 10a b c d - 16a b c d + 8b c d)x
+--R +
+--R 2 4 5 2 5 6 6 7 4 2 4 6 5 7 2
+--R (- 20a b c d - 2a b c d + 4b c )x + (- 10a b c d + 4a b c )x
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 5 7 4 2 6 3 3 2 5 5 4 3 6 5 2 8
+--R (- 12a b d + 40a b c d - 40a b c d + 20a b c d - 8b c d )x
+--R +
+--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3
+--R - 12a d + 16a b c d + 40a b c d - 80a b c d + 20a b c d
+--R +
+--R 5 5 2 6 6
+--R 32a b c d - 16b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2
+--R - 24a c d + 68a b c d - 40a b c d - 40a b c d + 40a b c d
+--R +
+--R 5 6 6 7
+--R 4a b c d - 8b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 2 4 6 5 7 2
+--R (- 12a c d + 40a b c d - 40a b c d + 20a b c d - 8a b c )x
+--R *
+--R log(x)
+--R +
+--R 5 6 4 2 2 5 3 3 3 4 2 4 4 3 5 5 2 6
+--R (- 6a b c d + 20a b c d - 20a b c d + 10a b c d - 4a b c d )x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2
+--R - 6a c d + 11a b c d + 10a b c d - 25a b c d + 18a b c d
+--R +
+--R 5 6
+--R - 8a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7 2
+--R (- 9a c d + 28a b c d - 25a b c d + 4a b c d + 6a b c d - 4a b c )x
+--R +
+--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7
+--R - 2a c d + 8a b c d - 12a b c d + 8a b c d - 2a b c
+--R /
+--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 8
+--R (4a b c d - 16a b c d + 24a b c d - 16a b c d + 4a b c d )x
+--R +
+--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 3 5 9 6
+--R (4a c d - 8a b c d - 8a b c d + 32a b c d - 28a b c d + 8a b c d)x
+--R +
+--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 3 5 10 4
+--R (8a c d - 28a b c d + 32a b c d - 8a b c d - 8a b c d + 4a b c )x
+--R +
+--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 2
+--R (4a c d - 16a b c d + 24a b c d - 16a b c d + 4a b c )x
+--R Type: Expression(Integer)
+--E 526
+
+--S 527 of 1527
+--a0:=integrate(t0,x)
+--E 527
+
+--S 528 of 1527
+--m0:=a0-r0
+--E 528
+
+--S 529 of 1527
+--d0:=D(m0,x)
+--E 529
+
+)clear all
+
+--S 530 of 1527
+t0:=1/(x^4*(a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 3 14 3 2 2 12 2 3 2 2 2 10
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 8 2 2 3 6 2 3 4
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 530
+
+--S 531 of 1527
+r0:=1/24*(-20*b^3*c^3+24*a*b^2*c^2*d-75*a^2*b*c*d^2+35*a^3*d^3)/(a^2*_
+ c^3*(b*c-a*d)^3*x^3)+1/8*(20*b^4*c^4-24*a*b^3*c^3*d-24*a^2*b^2*_
+ c^2*d^2+75*a^3*b*c*d^3-35*a^4*d^4)/(a^3*c^4*(b*c-a*d)^3*x)+_
+ 1/4*d*(2*b*c+a*d)/(a*c*(b*c-a*d)^2*x^3*(c+d*x^2)^2)+_
+ 1/2*b/(a*(b*c-a*d)*x^3*(a+b*x^2)*(c+d*x^2)^2)+1/8*d*(4*b^2*c^2+_
+ 15*a*b*c*d-7*a^2*d^2)/(a*c^2*(b*c-a*d)^3*x^3*(c+d*x^2))+_
+ 1/2*b^(9/2)*(5*b*c-11*a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(7/2)*_
+ (b*c-a*d)^4)+1/8*d^(7/2)*(99*b^2*c^2-110*a*b*c*d+35*a^2*d^2)*_
+ atan(x*sqrt(d)/sqrt(c))/(c^(9/2)*(b*c-a*d)^4)
+--R
+--R
+--R (2)
+--R 5 7 4 2 6 3 3 2 5 9
+--R (105a b d - 330a b c d + 297a b c d )x
+--R +
+--R 6 7 5 6 4 2 2 5 3 3 3 4 7
+--R (105a d - 120a b c d - 363a b c d + 594a b c d )x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3 5
+--R (210a c d - 555a b c d + 264a b c d + 297a b c d )x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 3
+--R (105a c d - 330a b c d + 297a b c d )x
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 5 4 3 6 5 2 9
+--R (- 132a b c d + 60b c d )x
+--R +
+--R 2 4 4 3 5 5 2 6 6 7
+--R (- 132a b c d - 204a b c d + 120b c d)x
+--R +
+--R 2 4 5 2 5 6 6 7 5 2 4 6 5 7 3
+--R (- 264a b c d - 12a b c d + 60b c )x + (- 132a b c d + 60a b c )x
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 5 7 4 2 6 3 3 2 5 5 4 3 6 5 2 8
+--R (105a b d - 330a b c d + 297a b c d - 132a b c d + 60b c d )x
+--R +
+--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3
+--R 105a d - 155a b c d - 253a b c d + 495a b c d - 88a b c d
+--R +
+--R 5 5 2 6 6
+--R - 224a b c d + 120b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2
+--R 175a c d - 494a b c d + 319a b c d + 176a b c d - 184a b c d
+--R +
+--R 5 6 6 7
+--R - 52a b c d + 60b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6
+--R 56a c d - 184a b c d + 176a b c d + 16a b c d - 104a b c d
+--R +
+--R 5 7
+--R 40a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7
+--R - 8a c d + 32a b c d - 48a b c d + 32a b c d - 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 9
+--R (24a b c d - 96a b c d + 144a b c d - 96a b c d + 24a b c d )x
+--R +
+--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2
+--R 24a c d - 48a b c d - 48a b c d + 192a b c d - 168a b c d
+--R +
+--R 3 5 9
+--R 48a b c d
+--R *
+--R 7
+--R x
+--R +
+--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9
+--R 48a c d - 168a b c d + 192a b c d - 48a b c d - 48a b c d
+--R +
+--R 3 5 10
+--R 24a b c
+--R *
+--R 5
+--R x
+--R +
+--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 3
+--R (24a c d - 96a b c d + 144a b c d - 96a b c d + 24a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 531
+
+--S 532 of 1527
+--a0:=integrate(t0,x)
+--E 532
+
+--S 533 of 1527
+--m0:=a0-r0
+--E 533
+
+--S 534 of 1527
+--d0:=D(m0,x)
+--E 534
+
+)clear all
+
+--S 535 of 1527
+t0:=x^4*sqrt(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 4 | 2
+--R x \|d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 535
+
+--S 536 of 1527
+r0:=1/2*(b*c-4*a*d)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/(b^3*sqrt(d))-_
+ 1/2*(3*b*c-4*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*_
+ sqrt(a)/(b^3*sqrt(b*c-a*d))+x*sqrt(c+d*x^2)/b^2-_
+ 1/2*x^3*sqrt(c+d*x^2)/(b*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 +-----------+ x\|d
+--R ((- 4a b d + b c)x - 4a d + a b c)\|- a d + b c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 +-+ +-+ x\|- a d + b c
+--R ((4a b d - 3b c)x + 4a d - 3a b c)\|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 3 +-----------+ +-+ | 2
+--R (b x + 2a b x)\|- a d + b c \|d \|d x + c
+--R /
+--R 4 2 3 +-----------+ +-+
+--R (2b x + 2a b )\|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 536
+
+--S 537 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 4 2 2 2 2 2
+--R (32a b d - 8b c d)x + (32a d + 56a b c d - 16b c )x
+--R +
+--R 2 2
+--R 64a c d - 16a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 8a b d + 2b c d )x + (- 8a d - 62a b c d + 16b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 64a c d - 48a b c d + 16b c )x - 64a c d + 16a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (16a b d - 12b c d)x + (16a d + 20a b c d - 24b c )x
+--R +
+--R 2 2
+--R 32a c d - 24a b c
+--R *
+--R +---------+ +--------+
+--R | a +-+ +-+ | 2
+--R |--------- \|c \|d \|d x + c
+--R \|a d - b c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 4a b d + 3b c d )x + (- 4a d - 29a b c d + 24b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 32a c d - 8a b c d + 24b c )x - 32a c d + 24a b c
+--R *
+--R +---------+
+--R | a +-+
+--R |--------- \|d
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((- 2a d + 2b c d)x + (- 4a c d + 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((4a d - 4b c d)x + (4a c d - 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 7 2 2 5 2 2 3
+--R - 2b d x + (- 4a b d - 16b c d)x + (- 32a b c d - 16b c )x
+--R +
+--R 2
+--R - 32a b c x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 2 7 2 2 5 2 2 3
+--R 8b d x + (16a b d + 24b c d)x + (48a b c d + 16b c )x
+--R +
+--R 2
+--R 32a b c x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 4 4 3 4 2 3 +-+ +-+ | 2
+--R (16b d x + (16a b d + 32b c)x + 32a b c)\|c \|d \|d x + c
+--R +
+--R 4 2 6 3 2 4 4 3 4 2 2
+--R - 4b d x + (- 4a b d - 32b c d)x + (- 32a b c d - 32b c )x
+--R +
+--R 3 2
+--R - 32a b c
+--R *
+--R +-+
+--R \|d
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2
+--R (16a b d - 4b c d)x + (16a d + 28a b c d - 8b c )x
+--R +
+--R 2 2
+--R 32a c d - 8a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 4a b d + b c d )x + (- 4a d - 31a b c d + 8b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 32a c d - 24a b c d + 8b c )x - 32a c d + 8a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (16a b d - 12b c d)x + (16a d + 20a b c d - 24b c )x
+--R +
+--R 2 2
+--R 32a c d - 24a b c
+--R *
+--R +-----------+ +--------+
+--R | a +-+ +-+ | 2
+--R |- --------- \|c \|d \|d x + c
+--R \| a d - b c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 4a b d + 3b c d )x + (- 4a d - 29a b c d + 24b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 32a c d - 8a b c d + 24b c )x - 32a c d + 24a b c
+--R *
+--R +-----------+
+--R | a +-+
+--R |- --------- \|d
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (- 16a b d + 12b c d)x + (- 16a d - 20a b c d + 24b c )x
+--R +
+--R 2 2
+--R - 32a c d + 24a b c
+--R *
+--R +-----------+ +--------+
+--R | a +-+ +-+ | 2
+--R |- --------- \|c \|d \|d x + c
+--R \| a d - b c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (4a b d - 3b c d )x + (4a d + 29a b c d - 24b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (32a c d + 8a b c d - 24b c )x + 32a c d - 24a b c
+--R *
+--R +-----------+
+--R | a +-+
+--R |- --------- \|d
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R 2 2 7 2 2 5 2 2 3
+--R - b d x + (- 2a b d - 8b c d)x + (- 16a b c d - 8b c )x
+--R +
+--R 2
+--R - 16a b c x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 2 2 7 2 2 5 2 2 3 2
+--R (4b d x + (8a b d + 12b c d)x + (24a b c d + 8b c )x + 16a b c x)
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R +--------+
+--R 4 4 3 4 2 3 +-+ +-+ | 2
+--R (8b d x + (8a b d + 16b c)x + 16a b c)\|c \|d \|d x + c
+--R +
+--R 4 2 6 3 2 4 4 3 4 2 2
+--R - 2b d x + (- 2a b d - 16b c d)x + (- 16a b c d - 16b c )x
+--R +
+--R 3 2
+--R - 16a b c
+--R *
+--R +-+
+--R \|d
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2
+--R (16a b d - 12b c d)x + (16a d + 20a b c d - 24b c )x
+--R +
+--R 2 2
+--R 32a c d - 24a b c
+--R *
+--R +---------+ +--------+
+--R +---+ | a +-+ | 2
+--R \|- d |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 4a b d + 3b c d )x + (- 4a d - 29a b c d + 24b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 32a c d - 8a b c d + 24b c )x - 32a c d + 24a b c
+--R *
+--R +---------+
+--R +---+ | a
+--R \|- d |---------
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((- 2a d + 2b c d)x + (- 4a c d + 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((4a d - 4b c d)x + (4a c d - 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (- 64a b d + 16b c d)x + (- 64a d - 112a b c d + 32b c )x
+--R +
+--R 2 2
+--R - 128a c d + 32a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (16a b d - 4b c d )x + (16a d + 124a b c d - 32b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (128a c d + 96a b c d - 32b c )x + 128a c d - 32a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 2 7 2 2 5 2 2 3
+--R - 2b d x + (- 4a b d - 16b c d)x + (- 32a b c d - 16b c )x
+--R +
+--R 2
+--R - 32a b c x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 2 7 2 2 5 2 2 3
+--R 8b d x + (16a b d + 24b c d)x + (48a b c d + 16b c )x
+--R +
+--R 2
+--R 32a b c x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 4 4 3 4 2 3 +---+ +-+ | 2
+--R (16b d x + (16a b d + 32b c)x + 32a b c)\|- d \|c \|d x + c
+--R +
+--R 4 2 6 3 2 4 4 3 4 2 2
+--R - 4b d x + (- 4a b d - 32b c d)x + (- 32a b c d - 32b c )x
+--R +
+--R 3 2
+--R - 32a b c
+--R *
+--R +---+
+--R \|- d
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2
+--R (- 32a b d + 8b c d)x + (- 32a d - 56a b c d + 16b c )x
+--R +
+--R 2 2
+--R - 64a c d + 16a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (8a b d - 2b c d )x + (8a d + 62a b c d - 16b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (64a c d + 48a b c d - 16b c )x + 64a c d - 16a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (16a b d - 12b c d)x + (16a d + 20a b c d - 24b c )x
+--R +
+--R 2 2
+--R 32a c d - 24a b c
+--R *
+--R +-----------+ +--------+
+--R +---+ | a +-+ | 2
+--R \|- d |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 4a b d + 3b c d )x + (- 4a d - 29a b c d + 24b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 32a c d - 8a b c d + 24b c )x - 32a c d + 24a b c
+--R *
+--R +-----------+
+--R +---+ | a
+--R \|- d |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (- 16a b d + 12b c d)x + (- 16a d - 20a b c d + 24b c )x
+--R +
+--R 2 2
+--R - 32a c d + 24a b c
+--R *
+--R +-----------+ +--------+
+--R +---+ | a +-+ | 2
+--R \|- d |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (4a b d - 3b c d )x + (4a d + 29a b c d - 24b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (32a c d + 8a b c d - 24b c )x + 32a c d - 24a b c
+--R *
+--R +-----------+
+--R +---+ | a
+--R \|- d |- ---------
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R 2 2 7 2 2 5 2 2 3
+--R - b d x + (- 2a b d - 8b c d)x + (- 16a b c d - 8b c )x
+--R +
+--R 2
+--R - 16a b c x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 2 2 7 2 2 5 2 2 3 2
+--R (4b d x + (8a b d + 12b c d)x + (24a b c d + 8b c )x + 16a b c x)
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R +--------+
+--R 4 4 3 4 2 3 +---+ +-+ | 2
+--R (8b d x + (8a b d + 16b c)x + 16a b c)\|- d \|c \|d x + c
+--R +
+--R 4 2 6 3 2 4 4 3 4 2 2
+--R - 2b d x + (- 2a b d - 16b c d)x + (- 16a b c d - 16b c )x
+--R +
+--R 3 2
+--R - 16a b c
+--R *
+--R +---+
+--R \|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 537
+
+--S 538 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R (8a d - 2b c)\|- a d + b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+
+--R +-----------+ | a +-+
+--R (4a d - 3b c)\|- a d + b c |--------- \|d
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((- 2a d + 2b c d)x + (- 4a c d + 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((4a d - 4b c d)x + (4a c d - 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-+
+--R +-----------+ x\|d
+--R (8a d - 2b c)\|- a d + b c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-+ +-+ x\|- a d + b c
+--R (- 8a d + 6b c)\|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-----------+ +-+
+--R 4b \|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 538
+
+--S 539 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 539
+
+--S 540 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R (4a d - b c)\|- a d + b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R +-----------+ x\|d
+--R (4a d - b c)\|- a d + b c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ | a +-+
+--R (4a d - 3b c)\|- a d + b c |- --------- \|d
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-----------+ | a +-+
+--R (- 4a d + 3b c)\|- a d + b c |- --------- \|d
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-+ +-+ x\|- a d + b c
+--R (- 4a d + 3b c)\|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-----------+ +-+
+--R 2b \|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 540
+
+--S 541 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 541
+
+)clear all
+
+--S 542 of 1527
+t0:=x^3*sqrt(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 3 | 2
+--R x \|d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 542
+
+--S 543 of 1527
+r0:=1/2*a*(c+d*x^2)^(3/2)/(b*(b*c-a*d)*(a+b*x^2))-1/2*(2*b*c-3*a*d)*_
+ atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/(b^(5/2)*_
+ sqrt(b*c-a*d))+1/2*(2*b*c-3*a*d)*sqrt(c+d*x^2)/(b^2*(b*c-a*d))
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 2 2 \|b \|d x + c
+--R ((3a b d - 2b c)x + 3a d - 2a b c)atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 +-----------+ +-+ | 2
+--R (2b x + 3a)\|- a d + b c \|b \|d x + c
+--R /
+--R 3 2 2 +-----------+ +-+
+--R (2b x + 2a b )\|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 543
+
+--S 544 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 4 2 2 2 2 2 2
+--R (3a b d - 2b c d)x + (3a d + 10a b c d - 8b c )x + 12a c d
+--R +
+--R 2
+--R - 8a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 2 2 4 2 2 2 2 3 2
+--R (- 9a b c d + 6b c d)x + (- 9a c d - 6a b c d + 8b c )x
+--R +
+--R 2 2 3
+--R - 12a c d + 8a b c
+--R *
+--R log
+--R 2 2 2 3 2 4
+--R (- 2a b d - 2a b c d + 4b c )x
+--R +
+--R 2 2 2 2
+--R (- 8a b c d + 8a b c )x
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (2a b c d - 2b c d)x + (6a b c d - 2a b c d - 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (8a b c d - 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+ +--------+
+--R 4 2 2 | 2 | 2
+--R (- 6b c d x + (- 12a c d + 8b c )x )\|- a b d + b c \|d x + c
+--R +
+--R +-------------+
+--R 2 6 2 4 2 2 | 2 +-+
+--R (4b d x + (6a d + 2b c d)x + (12a c d - 8b c )x )\|- a b d + b c \|c
+--R /
+--R +-------------+ +--------+
+--R 3 4 2 3 2 2 | 2 +-+ | 2
+--R (4b d x + (4a b d + 16b c)x + 16a b c)\|- a b d + b c \|c \|d x + c
+--R +
+--R +-------------+
+--R 3 4 2 3 2 2 2 2 | 2
+--R (- 12b c d x + (- 12a b c d - 16b c )x - 16a b c )\|- a b d + b c
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2 2
+--R (3a b d - 2b c d)x + (3a d + 10a b c d - 8b c )x + 12a c d
+--R +
+--R 2
+--R - 8a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 2 2 4 2 2 2 2 3 2
+--R (- 9a b c d + 6b c d)x + (- 9a c d - 6a b c d + 8b c )x
+--R +
+--R 2 2 3
+--R - 12a c d + 8a b c
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+ +--------+
+--R 4 2 2 | 2 | 2
+--R (- 3b c d x + (- 6a c d + 4b c )x )\|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 6 2 4 2 2 +-+ | 2
+--R (2b d x + (3a d + b c d)x + (6a c d - 4b c )x )\|c \|a b d - b c
+--R /
+--R +-----------+ +--------+
+--R 3 4 2 3 2 2 +-+ | 2 | 2
+--R (2b d x + (2a b d + 8b c)x + 8a b c)\|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 3 4 2 3 2 2 2 2 | 2
+--R (- 6b c d x + (- 6a b c d - 8b c )x - 8a b c )\|a b d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 544
+
+--S 545 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 +-----------+ +-+ +-+
+--R ((3a d - 2b c d)x + 12a c d - 8b c )\|- a d + b c \|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 2 3 +-----------+ +-+
+--R ((- 9a c d + 6b c d)x - 12a c d + 8b c )\|- a d + b c \|b
+--R *
+--R log
+--R 2 2 2 3 2 4
+--R (- 2a b d - 2a b c d + 4b c )x
+--R +
+--R 2 2 2 2
+--R (- 8a b c d + 8a b c )x
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (2a b c d - 2b c d)x + (6a b c d - 2a b c d - 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (8a b c d - 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 2 | 2 +-+
+--R ((- 6a d + 4b c d)x - 24a c d + 16b c )\|- a b d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-------------+
+--R 2 2 2 2 3 | 2
+--R ((18a c d - 12b c d)x + 24a c d - 16b c )\|- a b d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +-------------+ +--------+
+--R 2 2 | 2 +-----------+ +-+ | 2
+--R (6c d x + 24c )\|- a b d + b c \|- a d + b c \|b \|d x + c
+--R +
+--R +-------------+
+--R 2 2 | 2 +-----------+ +-+ +-+
+--R (- 18c d x - 24c )\|- a b d + b c \|- a d + b c \|b \|c
+--R /
+--R +-------------+ +--------+
+--R 2 2 2 | 2 +-----------+ +-+ +-+ | 2
+--R (4b d x + 16b c)\|- a b d + b c \|- a d + b c \|b \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 2 2 | 2 +-----------+ +-+
+--R (- 12b c d x - 16b c )\|- a b d + b c \|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 545
+
+--S 546 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 546
+
+--S 547 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +--------+
+--R 2 2 2 +-+ | 2 | 2
+--R ((- 3a d + 2b c d)x - 12a c d + 8b c )\|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 3 | 2
+--R ((9a c d - 6b c d)x + 12a c d - 8b c )\|a b d - b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 2 2 +-----------+ +-+ +-+
+--R ((3a d - 2b c d)x + 12a c d - 8b c )\|- a d + b c \|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 2 3 +-----------+ +-+
+--R ((- 9a c d + 6b c d)x - 12a c d + 8b c )\|- a d + b c \|b
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+ +--------+
+--R 2 2 +-----------+ +-+ | 2 | 2
+--R (3c d x + 12c )\|- a d + b c \|b \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 +-----------+ +-+ +-+ | 2
+--R (- 9c d x - 12c )\|- a d + b c \|b \|c \|a b d - b c
+--R /
+--R +-----------+ +--------+
+--R 2 2 2 +-----------+ +-+ +-+ | 2 | 2
+--R (2b d x + 8b c)\|- a d + b c \|b \|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ +-+ | 2
+--R (- 6b c d x - 8b c )\|- a d + b c \|b \|a b d - b c
+--R Type: Expression(Integer)
+--E 547
+
+--S 548 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 548
+
+)clear all
+
+--S 549 of 1527
+t0:=x^2*sqrt(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R x \|d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 549
+
+--S 550 of 1527
+r0:=atanh(x*sqrt(d)/sqrt(c+d*x^2))*sqrt(d)/b^2+1/2*(b*c-2*a*d)*_
+ atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/(b^2*sqrt(a)*_
+ sqrt(b*c-a*d))-1/2*x*sqrt(c+d*x^2)/(b*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 +-----------+ +-+ +-+ x\|d
+--R (2b x + 2a)\|- a d + b c \|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 x\|- a d + b c
+--R ((- 2a b d + b c)x - 2a d + a b c)atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R - b x\|- a d + b c \|a \|d x + c
+--R /
+--R 3 2 2 +-----------+ +-+
+--R (2b x + 2a b )\|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 550
+
+--S 551 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((4a b d - 2b c)x + 4a d - 2a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d + b c d)x + (- 2a d - 3a b c d + 2b c )x - 4a c d
+--R +
+--R 2
+--R 2a b c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +--------+
+--R 2 +-+ +-+ | 2 | 2
+--R (8b x + 8a)\|c \|d \|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 4 2 +-+ | 2
+--R (- 4b d x + (- 4a d - 8b c)x - 8a c)\|d \|a d - a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-----------+ +--------+
+--R 3 | 2 | 2
+--R (2b d x + 4b c x)\|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2
+--R (- 4b d x - 4b c x)\|c \|a d - a b c
+--R /
+--R +-----------+ +--------+
+--R 3 2 2 +-+ | 2 | 2
+--R (8b x + 8a b )\|c \|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 3 4 2 3 2 2 | 2
+--R (- 4b d x + (- 4a b d - 8b c)x - 8a b c)\|a d - a b c
+--R ,
+--R
+--R +-------------+ +--------+
+--R 2 | 2 +-+ +-+ | 2
+--R (4b x + 4a)\|- a d + a b c \|c \|d \|d x + c
+--R +
+--R +-------------+
+--R 4 2 | 2 +-+
+--R (- 2b d x + (- 2a d - 4b c)x - 4a c)\|- a d + a b c \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((4a b d - 2b c)x + 4a d - 2a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d + b c d)x + (- 2a d - 3a b c d + 2b c )x - 4a c d
+--R +
+--R 2
+--R 2a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((4a b d - 2b c)x + 4a d - 2a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d + b c d)x + (- 2a d - 3a b c d + 2b c )x - 4a c d
+--R +
+--R 2
+--R 2a b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +--------+
+--R 3 | 2 | 2
+--R (b d x + 2b c x)\|- a d + a b c \|d x + c
+--R +
+--R +-------------+
+--R 3 | 2 +-+
+--R (- 2b d x - 2b c x)\|- a d + a b c \|c
+--R /
+--R +-------------+ +--------+
+--R 3 2 2 | 2 +-+ | 2
+--R (4b x + 4a b )\|- a d + a b c \|c \|d x + c
+--R +
+--R +-------------+
+--R 3 4 2 3 2 2 | 2
+--R (- 2b d x + (- 2a b d - 4b c)x - 4a b c)\|- a d + a b c
+--R ,
+--R
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((4a b d - 2b c)x + 4a d - 2a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d + b c d)x + (- 2a d - 3a b c d + 2b c )x - 4a c d
+--R +
+--R 2
+--R 2a b c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +--------+
+--R 2 +---+ +-+ | 2 | 2
+--R (16b x + 16a)\|- d \|c \|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 4 2 +---+ | 2
+--R (- 8b d x + (- 8a d - 16b c)x - 16a c)\|- d \|a d - a b c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R +-----------+ +--------+
+--R 3 | 2 | 2
+--R (2b d x + 4b c x)\|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2
+--R (- 4b d x - 4b c x)\|c \|a d - a b c
+--R /
+--R +-----------+ +--------+
+--R 3 2 2 +-+ | 2 | 2
+--R (8b x + 8a b )\|c \|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 3 4 2 3 2 2 | 2
+--R (- 4b d x + (- 4a b d - 8b c)x - 8a b c)\|a d - a b c
+--R ,
+--R
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((4a b d - 2b c)x + 4a d - 2a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d + b c d)x + (- 2a d - 3a b c d + 2b c )x - 4a c d
+--R +
+--R 2
+--R 2a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+ +--------+
+--R 2 | 2 +---+ +-+ | 2
+--R (8b x + 8a)\|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R +-------------+
+--R 4 2 | 2 +---+
+--R (- 4b d x + (- 4a d - 8b c)x - 8a c)\|- a d + a b c \|- d
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((4a b d - 2b c)x + 4a d - 2a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d + b c d)x + (- 2a d - 3a b c d + 2b c )x - 4a c d
+--R +
+--R 2
+--R 2a b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +--------+
+--R 3 | 2 | 2
+--R (b d x + 2b c x)\|- a d + a b c \|d x + c
+--R +
+--R +-------------+
+--R 3 | 2 +-+
+--R (- 2b d x - 2b c x)\|- a d + a b c \|c
+--R /
+--R +-------------+ +--------+
+--R 3 2 2 | 2 +-+ | 2
+--R (4b x + 4a b )\|- a d + a b c \|c \|d x + c
+--R +
+--R +-------------+
+--R 3 4 2 3 2 2 | 2
+--R (- 2b d x + (- 2a b d - 4b c)x - 4a b c)\|- a d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 551
+
+--S 552 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R (2a d - b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+
+--R +-----------+ +-+ +-+ | 2
+--R 4\|- a d + b c \|a \|d \|a d - a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-----------+ +-+
+--R +-----------+ +-+ +-+ | 2 x\|d
+--R - 4\|- a d + b c \|a \|d \|a d - a b c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+ +-----------+
+--R | 2 x\|- a d + b c
+--R (4a d - 2b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 2 +-----------+ +-+ | 2
+--R 4b \|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 552
+
+--S 553 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 553
+
+--S 554 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-------------+
+--R | 2 +-----------+ +-+ +-+
+--R 2\|- a d + a b c \|- a d + b c \|a \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-------------+ +-+
+--R | 2 +-----------+ +-+ +-+ x\|d
+--R - 2\|- a d + a b c \|- a d + b c \|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+ +-+
+--R (2a d - b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R +-----------+ +-+ \|- a d + a b c \|c
+--R (2a d - b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R (2a d - b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 2 | 2 +-----------+ +-+
+--R 2b \|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 554
+
+--S 555 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 555
+
+)clear all
+
+--S 556 of 1527
+t0:=x*sqrt(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R | 2
+--R x\|d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 556
+
+--S 557 of 1527
+r0:=-1/2*d*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/(b^(3/2)*_
+ sqrt(b*c-a*d))-1/2*sqrt(c+d*x^2)/(b*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R +-+ | 2 +--------+
+--R 2 \|b \|d x + c +-----------+ +-+ | 2
+--R (- b d x - a d)atanh(---------------) - \|- a d + b c \|b \|d x + c
+--R +-----------+
+--R \|- a d + b c
+--R (2) ----------------------------------------------------------------------
+--R 2 2 +-----------+ +-+
+--R (2b x + 2a b)\|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 557
+
+--S 558 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 +-+ | 2 2 4
+--R (2a b d x + 2a d)\|c \|d x + c - a b d x
+--R +
+--R 2 2 2 2
+--R (- a d - 2a b c d)x - 2a c d
+--R *
+--R log
+--R 2 2 2 3 2 4
+--R (2a b d + 2a b c d - 4b c )x
+--R +
+--R 2 2 2 2
+--R (8a b c d - 8a b c )x
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a b c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b c d + 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+ +--------+
+--R 2 | 2 | 2
+--R (2a d - 4b c)x \|- a b d + b c \|d x + c
+--R +
+--R +-------------+
+--R 4 2 | 2 +-+
+--R (2b d x + (- 2a d + 4b c)x )\|- a b d + b c \|c
+--R /
+--R +-------------+ +--------+
+--R 2 2 2 | 2 +-+ | 2
+--R (8a b x + 8a b)\|- a b d + b c \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 4 2 2 2 2 | 2
+--R (- 4a b d x + (- 4a b d - 8a b c)x - 8a b c)\|- a b d + b c
+--R ,
+--R
+--R +--------+
+--R 2 2 +-+ | 2 2 4
+--R (- 2a b d x - 2a d)\|c \|d x + c + a b d x
+--R +
+--R 2 2 2 2
+--R (a d + 2a b c d)x + 2a c d
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+ +--------+
+--R 2 | 2 | 2
+--R (a d - 2b c)x \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 4 2 +-+ | 2
+--R (b d x + (- a d + 2b c)x )\|c \|a b d - b c
+--R /
+--R +-----------+ +--------+
+--R 2 2 2 +-+ | 2 | 2
+--R (4a b x + 4a b)\|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 2 2 | 2
+--R (- 2a b d x + (- 2a b d - 4a b c)x - 4a b c)\|a b d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 558
+
+--S 559 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-----------+ +-+ +-+ | 2
+--R 2a d\|- a d + b c \|b \|c \|d x + c
+--R +
+--R 2 2 +-----------+ +-+
+--R (- a d x - 2a c d)\|- a d + b c \|b
+--R *
+--R log
+--R 2 2 2 3 2 4 2 2 2 2
+--R ((2a b d + 2a b c d - 4b c )x + (8a b c d - 8a b c )x )
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a b c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b c d + 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R 4a d\|- a b d + b c \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 | 2
+--R (- 2a d x - 4a c d)\|- a b d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-----------+ +-+ | 2
+--R - 4c\|- a b d + b c \|- a d + b c \|b \|d x + c
+--R +
+--R +-------------+
+--R 2 | 2 +-----------+ +-+ +-+
+--R (2d x + 4c)\|- a b d + b c \|- a d + b c \|b \|c
+--R /
+--R +-------------+ +--------+
+--R | 2 +-----------+ +-+ +-+ | 2
+--R 8a b\|- a b d + b c \|- a d + b c \|b \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 | 2 +-----------+ +-+
+--R (- 4a b d x - 8a b c)\|- a b d + b c \|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 559
+
+--S 560 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 560
+
+--S 561 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +--------+ +-----------+
+--R +-+ | 2 | 2 2 2 | 2
+--R (2a d\|c \|a b d - b c \|d x + c + (- a d x - 2a c d)\|a b d - b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +-----------+ +-+ +-+ | 2
+--R - 2a d\|- a d + b c \|b \|c \|d x + c
+--R +
+--R 2 2 +-----------+ +-+
+--R (a d x + 2a c d)\|- a d + b c \|b
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+ +--------+
+--R +-----------+ +-+ | 2 | 2
+--R - 2c\|- a d + b c \|b \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 +-----------+ +-+ +-+ | 2
+--R (d x + 2c)\|- a d + b c \|b \|c \|a b d - b c
+--R /
+--R +-----------+ +--------+
+--R +-----------+ +-+ +-+ | 2 | 2
+--R 4a b\|- a d + b c \|b \|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 +-----------+ +-+ | 2
+--R (- 2a b d x - 4a b c)\|- a d + b c \|b \|a b d - b c
+--R Type: Expression(Integer)
+--E 561
+
+--S 562 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 562
+
+)clear all
+
+--S 563 of 1527
+t0:=sqrt(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 563
+
+--S 564 of 1527
+r0:=1/2*c*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/(a^(3/2)*_
+ sqrt(b*c-a*d))+1/2*x*sqrt(c+d*x^2)/(a*(a+b*x^2))
+--R
+--R
+--R +-----------+ +--------+
+--R 2 x\|- a d + b c +-----------+ +-+ | 2
+--R (b c x + a c)atan(---------------) + x\|- a d + b c \|a \|d x + c
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R (2) --------------------------------------------------------------------
+--R 2 2 +-----------+ +-+
+--R (2a b x + 2a )\|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 564
+
+--S 565 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R (2b c x + 2a c)\|c \|d x + c - b c d x + (- a c d - 2b c )x
+--R +
+--R 2
+--R - 2a c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +--------+
+--R 3 | 2 | 2
+--R (- 2d x - 4c x)\|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2
+--R (4d x + 4c x)\|c \|a d - a b c
+--R /
+--R +-----------+ +--------+
+--R 2 2 +-+ | 2 | 2
+--R (8a b x + 8a )\|c \|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 4 2 2 2 | 2
+--R (- 4a b d x + (- 4a d - 8a b c)x - 8a c)\|a d - a b c
+--R ,
+--R
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R (- 2b c x - 2a c)\|c \|d x + c + b c d x + (a c d + 2b c )x
+--R +
+--R 2
+--R 2a c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R (- 2b c x - 2a c)\|c \|d x + c + b c d x + (a c d + 2b c )x
+--R +
+--R 2
+--R 2a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +--------+
+--R 3 | 2 | 2
+--R (- d x - 2c x)\|- a d + a b c \|d x + c
+--R +
+--R +-------------+
+--R 3 | 2 +-+
+--R (2d x + 2c x)\|- a d + a b c \|c
+--R /
+--R +-------------+ +--------+
+--R 2 2 | 2 +-+ | 2
+--R (4a b x + 4a )\|- a d + a b c \|c \|d x + c
+--R +
+--R +-------------+
+--R 4 2 2 2 | 2
+--R (- 2a b d x + (- 2a d - 4a b c)x - 4a c)\|- a d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 565
+
+--S 566 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R c\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - 2c\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R 4a\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 566
+
+--S 567 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 567
+
+--S 568 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R -
+--R +-----------+ +-+
+--R c\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R +-----------+ +-+ \|- a d + a b c \|c
+--R - c\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - c\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R 2a\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 568
+
+--S 569 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 569
+
+)clear all
+
+--S 570 of 1527
+t0:=sqrt(c+d*x^2)/(x*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) --------------------
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R Type: Expression(Integer)
+--E 570
+
+--S 571 of 1527
+r0:=-atanh(sqrt(c+d*x^2)/sqrt(c))*sqrt(c)/a^2+1/2*(2*b*c-a*d)*_
+ atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/(a^2*sqrt(b)*_
+ sqrt(b*c-a*d))+1/2*sqrt(c+d*x^2)/(a*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 2 2 \|b \|d x + c
+--R ((- a b d + 2b c)x - a d + 2a b c)atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R 2 +-----------+ +-+ +-+ \|d x + c
+--R (- 2b x - 2a)\|- a d + b c \|b \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R a\|- a d + b c \|b \|d x + c
+--R /
+--R 2 2 3 +-----------+ +-+
+--R (2a b x + 2a )\|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 571
+
+--S 572 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------------+ +--------+
+--R 2 | 2 | 2
+--R (8b c x + 8a c)\|- a b d + b c \|d x + c
+--R +
+--R +-------------+
+--R 4 2 | 2 +-+
+--R (- 4b d x + (- 4a d - 8b c)x - 8a c)\|- a b d + b c \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((2a b d - 4b c)x + 2a d - 4a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R (- a b d + 2b c d)x + (- a d + 4b c )x - 2a c d + 4a b c
+--R *
+--R log
+--R +-------------+
+--R 2 2 | 2 +-+ 2 2 2
+--R ((2a b x + 2a )\|- a b d + b c \|c + (2a b d - 2a b c)x )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 4 2 2 2 +-+
+--R ((- 2a b d + 2b c)x + (- 2a b d + 2a b c)x )\|c
+--R +
+--R +-------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (- a d - 2a b c)x - 2a c)\|- a b d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-------------+ +--------+
+--R 2 | 2 | 2
+--R (- 2a d + 4b c)x \|- a b d + b c \|d x + c
+--R +
+--R +-------------+
+--R 4 2 | 2 +-+
+--R (- 2b d x + (2a d - 4b c)x )\|- a b d + b c \|c
+--R /
+--R +-------------+ +--------+
+--R 2 2 3 | 2 +-+ | 2
+--R (8a b x + 8a )\|- a b d + b c \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 4 3 2 2 3 | 2
+--R (- 4a b d x + (- 4a d - 8a b c)x - 8a c)\|- a b d + b c
+--R ,
+--R
+--R +-----------+ +--------+
+--R 2 | 2 | 2
+--R (4b c x + 4a c)\|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 4 2 +-+ | 2
+--R (- 2b d x + (- 2a d - 4b c)x - 4a c)\|c \|a b d - b c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((- 2a b d + 4b c)x - 2a d + 4a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R (a b d - 2b c d)x + (a d - 4b c )x + 2a c d - 4a b c
+--R *
+--R +-----------+ +--------+ +-----------+
+--R +-+ | 2 | 2 2 | 2
+--R a\|c \|a b d - b c \|d x + c + (- b c x - a c)\|a b d - b c
+--R atan(---------------------------------------------------------------)
+--R 2 2 +-+
+--R (a b d - b c)x \|c
+--R +
+--R +-----------+ +--------+
+--R 2 | 2 | 2
+--R (- a d + 2b c)x \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 4 2 +-+ | 2
+--R (- b d x + (a d - 2b c)x )\|c \|a b d - b c
+--R /
+--R +-----------+ +--------+
+--R 2 2 3 +-+ | 2 | 2
+--R (4a b x + 4a )\|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 4 3 2 2 3 | 2
+--R (- 2a b d x + (- 2a d - 4a b c)x - 4a c)\|a b d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 572
+
+--S 573 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-------------+ +--------+
+--R | 2 +-----------+ +-+ | 2
+--R 8c\|- a b d + b c \|- a d + b c \|b \|d x + c
+--R +
+--R +-------------+
+--R 2 | 2 +-----------+ +-+ +-+
+--R (- 4d x - 8c)\|- a b d + b c \|- a d + b c \|b \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R +-----------+ +-+ +-+ | 2
+--R (2a d - 4b c)\|- a d + b c \|b \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+ +-+
+--R ((- a d + 2b c d)x - 2a c d + 4b c )\|- a d + b c \|b
+--R *
+--R log
+--R +-------------+
+--R 2 2 | 2 +-+ 2 2 2
+--R ((2a b x + 2a )\|- a b d + b c \|c + (2a b d - 2a b c)x )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 4 2 2 2 +-+
+--R ((- 2a b d + 2b c)x + (- 2a b d + 2a b c)x )\|c
+--R +
+--R +-------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (- a d - 2a b c)x - 2a c)\|- a b d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R (4a d - 8b c)\|- a b d + b c \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 2 | 2
+--R ((- 2a d + 4b c d)x - 4a c d + 8b c )\|- a b d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-----------+ +-+ | 2
+--R 8c\|- a b d + b c \|- a d + b c \|b \|d x + c
+--R +
+--R +-------------+
+--R 2 | 2 +-----------+ +-+ +-+
+--R (- 4d x - 8c)\|- a b d + b c \|- a d + b c \|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-----------+ +-+ | 2
+--R 4c\|- a b d + b c \|- a d + b c \|b \|d x + c
+--R +
+--R +-------------+
+--R 2 | 2 +-----------+ +-+ +-+
+--R (- 2d x - 4c)\|- a b d + b c \|- a d + b c \|b \|c
+--R /
+--R +-------------+ +--------+
+--R 2 | 2 +-----------+ +-+ +-+ | 2
+--R 8a \|- a b d + b c \|- a d + b c \|b \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 2 | 2 +-----------+ +-+
+--R (- 4a d x - 8a c)\|- a b d + b c \|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 573
+
+--S 574 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 574
+
+--S 575 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +--------+
+--R +-----------+ +-+ | 2 | 2
+--R 4c\|- a d + b c \|b \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 +-----------+ +-+ +-+ | 2
+--R (- 2d x - 4c)\|- a d + b c \|b \|c \|a b d - b c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R (2a d - 4b c)\|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 | 2
+--R ((- a d + 2b c d)x - 2a c d + 4b c )\|a b d - b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +-----------+ +--------+
+--R +-----------+ +-+ | 2 | 2
+--R 4c\|- a d + b c \|b \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 +-----------+ +-+ +-+ | 2
+--R (- 2d x - 4c)\|- a d + b c \|b \|c \|a b d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +-----------+ +-+ +-+ | 2
+--R (- 2a d + 4b c)\|- a d + b c \|b \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+ +-+
+--R ((a d - 2b c d)x + 2a c d - 4b c )\|- a d + b c \|b
+--R *
+--R +-----------+ +--------+ +-----------+
+--R +-+ | 2 | 2 2 | 2
+--R a\|c \|a b d - b c \|d x + c + (- b c x - a c)\|a b d - b c
+--R atan(---------------------------------------------------------------)
+--R 2 2 +-+
+--R (a b d - b c)x \|c
+--R +
+--R +-----------+ +--------+
+--R +-----------+ +-+ | 2 | 2
+--R 2c\|- a d + b c \|b \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 +-----------+ +-+ +-+ | 2
+--R (- d x - 2c)\|- a d + b c \|b \|c \|a b d - b c
+--R /
+--R +-----------+ +--------+
+--R 2 +-----------+ +-+ +-+ | 2 | 2
+--R 4a \|- a d + b c \|b \|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 +-----------+ +-+ | 2
+--R (- 2a d x - 4a c)\|- a d + b c \|b \|a b d - b c
+--R Type: Expression(Integer)
+--E 575
+
+--S 576 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 576
+
+)clear all
+
+--S 577 of 1527
+t0:=sqrt(c+d*x^2)/(x^2*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) ---------------------
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R Type: Expression(Integer)
+--E 577
+
+--S 578 of 1527
+r0:=-1/2*(3*b*c-2*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/_
+ (a^(5/2)*sqrt(b*c-a*d))-3/2*sqrt(c+d*x^2)/(a^2*x)+_
+ 1/2*sqrt(c+d*x^2)/(a*x*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +-----------+
+--R 2 3 2 x\|- a d + b c
+--R ((2a b d - 3b c)x + (2a d - 3a b c)x)atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 +-----------+ +-+ | 2
+--R (- 3b x - 2a)\|- a d + b c \|a \|d x + c
+--R /
+--R 2 3 3 +-----------+ +-+
+--R (2a b x + 2a x)\|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 578
+
+--S 579 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 5 2 2 2 2 3
+--R (2a b d - 3b c d)x + (2a d + 5a b c d - 12b c )x
+--R +
+--R 2 2
+--R (8a c d - 12a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 5 2 2 2 2 3
+--R (- 6a b d + 9b c d)x + (- 6a d + a b c d + 12b c )x
+--R +
+--R 2 2
+--R (- 8a c d + 12a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +--------+
+--R 4 2 +-+ | 2 | 2
+--R (18b d x + (12a d + 24b c)x + 16a c)\|c \|a d - a b c \|d x + c
+--R +
+--R 2 6 2 4 2 2 2
+--R (- 6b d x + (- 4a d - 30b c d)x + (- 20a c d - 24b c )x - 16a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R /
+--R +-----------+ +--------+
+--R 2 5 3 2 3 3 | 2 | 2
+--R (4a b d x + (4a d + 16a b c)x + 16a c x)\|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 2 5 3 2 3 3 +-+ | 2
+--R (- 12a b d x + (- 12a d - 16a b c)x - 16a c x)\|c \|a d - a b c
+--R ,
+--R
+--R 2 2 5 2 2 2 2 3
+--R (- 2a b d + 3b c d)x + (- 2a d - 5a b c d + 12b c )x
+--R +
+--R 2 2
+--R (- 8a c d + 12a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 5 2 2 2 2 3
+--R (6a b d - 9b c d)x + (6a d - a b c d - 12b c )x
+--R +
+--R 2 2
+--R (8a c d - 12a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 2 2 5 2 2 2 2 3
+--R (- 2a b d + 3b c d)x + (- 2a d - 5a b c d + 12b c )x
+--R +
+--R 2 2
+--R (- 8a c d + 12a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 5 2 2 2 2 3
+--R (6a b d - 9b c d)x + (6a d - a b c d - 12b c )x
+--R +
+--R 2 2
+--R (8a c d - 12a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +--------+
+--R 4 2 | 2 +-+ | 2
+--R (9b d x + (6a d + 12b c)x + 8a c)\|- a d + a b c \|c \|d x + c
+--R +
+--R 2 6 2 4 2 2 2
+--R (- 3b d x + (- 2a d - 15b c d)x + (- 10a c d - 12b c )x - 8a c )
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R +-------------+ +--------+
+--R 2 5 3 2 3 3 | 2 | 2
+--R (2a b d x + (2a d + 8a b c)x + 8a c x)\|- a d + a b c \|d x + c
+--R +
+--R +-------------+
+--R 2 5 3 2 3 3 | 2 +-+
+--R (- 6a b d x + (- 6a d - 8a b c)x - 8a c x)\|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 579
+
+--S 580 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R (2a d - 3b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R | 2 x\|- a d + b c
+--R (- 4a d + 6b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 2 +-----------+ +-+ | 2
+--R 4a \|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 580
+
+--S 581 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 581
+
+--S 582 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +-+
+--R (- 2a d + 3b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R +-----------+ +-+ \|- a d + a b c \|c
+--R (- 2a d + 3b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R (- 2a d + 3b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 2 | 2 +-----------+ +-+
+--R 2a \|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 582
+
+--S 583 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 583
+
+)clear all
+
+--S 584 of 1527
+t0:=sqrt(c+d*x^2)/(x^3*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) ---------------------
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R Type: Expression(Integer)
+--E 584
+
+--S 585 of 1527
+r0:=1/2*(4*b*c-a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))/(a^3*sqrt(c))-_
+ 1/2*(4*b*c-3*a*d)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))*_
+ sqrt(b)/(a^3*sqrt(b*c-a*d))-b*sqrt(c+d*x^2)/(a^2*(a+b*x^2))-_
+ 1/2*sqrt(c+d*x^2)/(a*x^2*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 4 2 2 +-+ +-+ \|b \|d x + c
+--R ((3a b d - 4b c)x + (3a d - 4a b c)x )\|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 +-----------+ \|d x + c
+--R ((- a b d + 4b c)x + (- a d + 4a b c)x )\|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 +-----------+ +-+ | 2
+--R (- 2a b x - a )\|- a d + b c \|c \|d x + c
+--R /
+--R 3 4 4 2 +-----------+ +-+
+--R (2a b x + 2a x )\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 585
+
+--S 586 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 2 6 2 2 2 2 3 4
+--R (8a b c d - 32b c d)x + (8a c d - 16a b c d - 64b c )x
+--R +
+--R 2 2 3 2
+--R (16a c d - 64a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 8 2 3 2 2 2 6
+--R (- 2a b d + 8b c d )x + (- 2a d - 8a b c d + 64b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (- 16a c d + 48a b c d + 64b c )x + (- 16a c d + 64a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (12a b c d - 16b c d)x + (12a c d + 8a b c d - 32b c )x
+--R +
+--R 2 2 3 2
+--R (24a c d - 32a b c )x
+--R *
+--R +-----------+ +--------+
+--R | b +-+ | 2
+--R |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 3 2 2 2 8
+--R (- 3a b c d + 4b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (- 3a c d - 20a b c d + 32b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (- 24a c d + 8a b c d + 32b c )x + (- 24a c d + 32a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (- 2a d + 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((2a b d - 2b c)x + (2a d - 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (4a b c d - 8b c d)x + (2a c d + 24a b c d - 16b c )x
+--R +
+--R 2 2 3 2 2 3
+--R (16a c d + 16a b c )x + 16a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 8 2 2 2 6
+--R 2b c d x + (- 14a b c d + 16b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (- 8a c d - 32a b c d + 16b c )x + (- 24a c d - 16a b c )x
+--R +
+--R 2 3
+--R - 16a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 6 4 3 2 4 4 2 2 +-+ | 2
+--R (16a b c d x + (16a c d + 32a b c )x + 32a c x )\|c \|d x + c
+--R +
+--R 3 2 8 4 2 3 2 6 4 2 3 3 4
+--R - 4a b c d x + (- 4a c d - 32a b c d)x + (- 32a c d - 32a b c )x
+--R +
+--R 4 3 2
+--R - 32a c x
+--R ,
+--R
+--R 2 2 2 6 2 2 2 2 3 4
+--R (4a b c d - 16b c d)x + (4a c d - 8a b c d - 32b c )x
+--R +
+--R 2 2 3 2
+--R (8a c d - 32a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 8 2 3 2 2 2 6
+--R (- a b d + 4b c d )x + (- a d - 4a b c d + 32b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (- 8a c d + 24a b c d + 32b c )x + (- 8a c d + 32a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (12a b c d - 16b c d)x + (12a c d + 8a b c d - 32b c )x
+--R +
+--R 2 2 3 2
+--R (24a c d - 32a b c )x
+--R *
+--R +---------+ +--------+
+--R | b +-+ | 2
+--R |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R 3 2 2 2 8
+--R (- 3a b c d + 4b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (- 3a c d - 20a b c d + 32b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (- 24a c d + 8a b c d + 32b c )x + (- 24a c d + 32a b c )x
+--R *
+--R +---------+
+--R | b
+--R |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (2a b c d - 4b c d)x + (a c d + 12a b c d - 8b c )x
+--R +
+--R 2 2 3 2 2 3
+--R (8a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 8 2 2 2 6
+--R b c d x + (- 7a b c d + 8b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (- 4a c d - 16a b c d + 8b c )x + (- 12a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 6 4 3 2 4 4 2 2 +-+ | 2
+--R (8a b c d x + (8a c d + 16a b c )x + 16a c x )\|c \|d x + c
+--R +
+--R 3 2 8 4 2 3 2 6 4 2 3 3 4
+--R - 2a b c d x + (- 2a c d - 16a b c d)x + (- 16a c d - 16a b c )x
+--R +
+--R 4 3 2
+--R - 16a c x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 586
+
+--S 587 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R +-----------+ \|d x + c - \|c
+--R (2a d - 8b c)\|- a d + b c log(------------------)
+--R x
+--R +
+--R +-----------+
+--R +-----------+ | b +-+
+--R (3a d - 4b c)\|- a d + b c |- --------- \|c
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (- 2a d + 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((2a b d - 2b c)x + (2a d - 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ | 2
+--R +-+ +-+ \|b \|d x + c
+--R (- 6a d + 8b c)\|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R +-----------+ \|d x + c +-----------+
+--R (2a d - 8b c)\|- a d + b c atanh(-----------) - 2b c\|- a d + b c
+--R +-+
+--R \|c
+--R /
+--R 3 +-----------+ +-+
+--R 4a \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 587
+
+--S 588 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 588
+
+--S 589 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 2 +-+
+--R +-----------+ \|d x + c - \|c
+--R (a d - 4b c)\|- a d + b c log(------------------)
+--R x
+--R +
+--R +--------+
+--R +-+ | 2
+--R +-+ +-+ \|b \|d x + c
+--R (- 3a d + 4b c)\|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R +-----------+ \|d x + c
+--R (a d - 4b c)\|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +---------+
+--R +-----------+ | b +-+
+--R (3a d - 4b c)\|- a d + b c |--------- \|c
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R +-----------+
+--R - b c\|- a d + b c
+--R /
+--R 3 +-----------+ +-+
+--R 2a \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 589
+
+--S 590 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 590
+
+)clear all
+
+--S 591 of 1527
+t0:=sqrt(c+d*x^2)/(x^4*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) ---------------------
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R Type: Expression(Integer)
+--E 591
+
+--S 592 of 1527
+r0:=1/2*b*(5*b*c-4*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/_
+ (a^(7/2)*sqrt(b*c-a*d))-5/6*sqrt(c+d*x^2)/(a^2*x^3)+1/6*(15*b*c-_
+ 2*a*d)*sqrt(c+d*x^2)/(a^3*c*x)+1/2*sqrt(c+d*x^2)/(a*x^3*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 3 2 5 2 2 2 3
+--R ((- 12a b c d + 15b c )x + (- 12a b c d + 15a b c )x )
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 2 4 2 2 2 +-----------+ +-+
+--R ((- 2a b d + 15b c)x + (- 2a d + 10a b c)x - 2a c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 5 4 3 +-----------+ +-+
+--R (6a b c x + 6a c x )\|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 592
+
+--S 593 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 3 2 2 9
+--R (12a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 3 7
+--R (12a b c d + 129a b c d - 180b c d)x
+--R +
+--R 2 2 2 2 3 3 4 5
+--R (144a b c d + 12a b c d - 240b c )x
+--R +
+--R 2 3 2 4 3
+--R (192a b c d - 240a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 3 2 2 9
+--R (- 60a b c d + 75b c d )x
+--R +
+--R 2 3 2 2 2 3 3 7
+--R (- 60a b c d - 165a b c d + 300b c d)x
+--R +
+--R 2 2 2 2 3 3 4 5
+--R (- 240a b c d + 108a b c d + 240b c )x
+--R +
+--R 2 3 2 4 3
+--R (- 192a b c d + 240a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 3 2 2 8 2 3 2 2 2 6
+--R (20a b d - 150b c d )x + (20a d - 20a b c d - 600b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (100a c d - 336a b c d - 480b c )x + (144a c d - 320a b c )x
+--R +
+--R 2 3
+--R 64a c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a d - a b c \|d x + c
+--R +
+--R 4 2 3 10 2 4 3 2 2 2 8
+--R (- 4a b d + 30b c d )x + (- 4a d - 32a b c d + 390b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (- 56a c d + 148a b c d + 840b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (- 164a c d + 496a b c d + 480b c )x + (- 176a c d + 320a b c )x
+--R +
+--R 2 4
+--R - 64a c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R /
+--R 3 2 9 4 2 3 2 7 4 2 3 3 5
+--R 12a b c d x + (12a c d + 144a b c d)x + (144a c d + 192a b c )x
+--R +
+--R 4 3 3
+--R 192a c x
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 3 2 9 4 2 3 2 7
+--R - 60a b c d x + (- 60a c d - 240a b c d)x
+--R +
+--R 4 2 3 3 5 4 3 3
+--R (- 240a c d - 192a b c )x - 192a c x
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|c \|a d - a b c
+--R ,
+--R
+--R 2 3 3 2 2 9
+--R (12a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 3 7
+--R (12a b c d + 129a b c d - 180b c d)x
+--R +
+--R 2 2 2 2 3 3 4 5
+--R (144a b c d + 12a b c d - 240b c )x
+--R +
+--R 2 3 2 4 3
+--R (192a b c d - 240a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 3 2 2 9
+--R (- 60a b c d + 75b c d )x
+--R +
+--R 2 3 2 2 2 3 3 7
+--R (- 60a b c d - 165a b c d + 300b c d)x
+--R +
+--R 2 2 2 2 3 3 4 5
+--R (- 240a b c d + 108a b c d + 240b c )x
+--R +
+--R 2 3 2 4 3
+--R (- 192a b c d + 240a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 2 3 3 2 2 9
+--R (12a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 3 7
+--R (12a b c d + 129a b c d - 180b c d)x
+--R +
+--R 2 2 2 2 3 3 4 5
+--R (144a b c d + 12a b c d - 240b c )x
+--R +
+--R 2 3 2 4 3
+--R (192a b c d - 240a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 3 2 2 9
+--R (- 60a b c d + 75b c d )x
+--R +
+--R 2 3 2 2 2 3 3 7
+--R (- 60a b c d - 165a b c d + 300b c d)x
+--R +
+--R 2 2 2 2 3 3 4 5
+--R (- 240a b c d + 108a b c d + 240b c )x
+--R +
+--R 2 3 2 4 3
+--R (- 192a b c d + 240a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 3 2 2 8 2 3 2 2 2 6
+--R (10a b d - 75b c d )x + (10a d - 10a b c d - 300b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (50a c d - 168a b c d - 240b c )x + (72a c d - 160a b c )x
+--R +
+--R 2 3
+--R 32a c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 4 2 3 10 2 4 3 2 2 2 8
+--R (- 2a b d + 15b c d )x + (- 2a d - 16a b c d + 195b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (- 28a c d + 74a b c d + 420b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (- 82a c d + 248a b c d + 240b c )x + (- 88a c d + 160a b c )x
+--R +
+--R 2 4
+--R - 32a c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R 3 2 9 4 2 3 2 7 4 2 3 3 5
+--R 6a b c d x + (6a c d + 72a b c d)x + (72a c d + 96a b c )x
+--R +
+--R 4 3 3
+--R 96a c x
+--R *
+--R +-------------+ +--------+
+--R | 2 | 2
+--R \|- a d + a b c \|d x + c
+--R +
+--R 3 2 9 4 2 3 2 7
+--R - 30a b c d x + (- 30a c d - 120a b c d)x
+--R +
+--R 4 2 3 3 5 4 3 3
+--R (- 120a c d - 96a b c )x - 96a c x
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 593
+
+--S 594 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----------+ +-+
+--R (4a b d - 5b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (8a b d - 10b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 3 +-----------+ +-+ | 2
+--R 4a \|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 594
+
+--S 595 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 595
+
+--S 596 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 +-----------+ +-+
+--R (4a b d - 5b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 2 +-----------+ +-+ \|- a d + a b c \|c
+--R (4a b d - 5b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (4a b d - 5b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 3 | 2 +-----------+ +-+
+--R 2a \|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 596
+
+--S 597 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 597
+
+)clear all
+
+--S 598 of 1527
+t0:=x^4*(c+d*x^2)^(3/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 6 4 | 2
+--R (d x + c x )\|d x + c
+--R (1) ------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 598
+
+--S 599 of 1527
+r0:=-1/2*x^3*(c+d*x^2)^(3/2)/(b*(a+b*x^2))+3/8*(b^2*c^2-8*a*b*c*d+_
+ 8*a^2*d^2)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/(b^4*sqrt(d))-_
+ 3/2*(b*c-2*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*_
+ sqrt(a)*sqrt(b*c-a*d)/b^4+3/8*(3*b*c-4*a*d)*x*sqrt(c+d*x^2)/b^3+_
+ 3/4*d*x^3*sqrt(c+d*x^2)/b^2
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((24a b d - 24a b c d + 3b c )x + 24a d - 24a b c d + 3a b c )
+--R *
+--R +-+
+--R x\|d
+--R atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 +-----------+ +-+ +-+
+--R ((24a b d - 12b c)x + 24a d - 12a b c)\|- a d + b c \|a \|d
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 3 5 2 3 3 2 2 +-+ | 2
+--R (2b d x + (- 6a b d + 5b c)x + (- 12a b d + 9a b c)x)\|d \|d x + c
+--R /
+--R 5 2 4 +-+
+--R (8b x + 8a b )\|d
+--R Type: Expression(Integer)
+--E 599
+
+--S 600 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 2 6 2 3 2 2 2 4
+--R (72a b d - 36b c d )x + (72a d + 348a b c d - 192b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (384a c d + 192a b c d - 192b c )x + 384a c d - 192a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ +-+ | 2 | 2
+--R \|c \|d \|a d - a b c \|d x + c
+--R +
+--R 4 2 3 8
+--R (- 12a b d + 6b c d )x
+--R +
+--R 2 4 3 2 2 2 6
+--R (- 12a d - 210a b c d + 108b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 216a c d - 468a b c d + 288b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4
+--R (- 576a c d - 96a b c d + 192b c )x - 384a c d + 192a b c
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (2d x + 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (- 4d x - 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (144a b d - 144a b c d + 18b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (144a d + 624a b c d - 750a b c d + 96b c d)x
+--R +
+--R 3 3 2 3 3 4 2 3 2 2 2 3
+--R (768a c d - 672a b c d + 96b c )x + 768a c d - 768a b c d
+--R +
+--R 2 4
+--R 96a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 24a b d + 24a b c d - 3b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 24a d - 408a b c d + 429a b c d - 54b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 432a c d - 720a b c d + 1098a b c d - 144b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2 3 3 2
+--R (- 1152a c d + 384a b c d + 624a b c d - 96b c )x - 768a c d
+--R +
+--R 2 4 2 5
+--R 768a b c d - 96a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 3 4 11 2 4 3 3 9
+--R - 2b d x + (6a b d - 41b c d )x
+--R +
+--R 2 4 2 3 3 2 2 7
+--R (12a b d + 99a b c d - 186b c d )x
+--R +
+--R 2 3 2 2 2 3 3 5
+--R (216a b c d + 126a b c d - 304b c d)x
+--R +
+--R 2 2 2 2 3 3 4 3 2 3 2 4
+--R (576a b c d - 240a b c d - 160b c )x + (384a b c d - 288a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 3 4 11 2 4 3 3 9
+--R 12b d x + (- 36a b d + 106b c d )x
+--R +
+--R 2 4 2 3 3 2 2 7
+--R (- 72a b d - 174a b c d + 318b c d )x
+--R +
+--R 2 3 2 2 2 3 3 5
+--R (- 456a b c d - 42a b c d + 384b c d)x
+--R +
+--R 2 2 2 2 3 3 4 3
+--R (- 768a b c d + 384a b c d + 160b c )x
+--R +
+--R 2 3 2 4
+--R (- 384a b c d + 288a b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 5 2 6 4 2 5 4 4 5 2 2
+--R 48b d x + (48a b d + 256b c d)x + (256a b c d + 256b c )x
+--R +
+--R 4 2
+--R 256a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 5 3 8 4 3 5 2 6
+--R - 8b d x + (- 8a b d - 144b c d )x
+--R +
+--R 4 2 5 2 4 4 2 5 3 2 4 3
+--R (- 144a b c d - 384b c d)x + (- 384a b c d - 256b c )x - 256a b c
+--R *
+--R +-+
+--R \|d
+--R ,
+--R
+--R 2 4 2 3 3 2 2 6
+--R (144a b d - 144a b c d + 18b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (144a d + 624a b c d - 750a b c d + 96b c d)x
+--R +
+--R 3 3 2 3 3 4 2 3 2 2 2 3
+--R (768a c d - 672a b c d + 96b c )x + 768a c d - 768a b c d
+--R +
+--R 2 4
+--R 96a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 24a b d + 24a b c d - 3b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 24a d - 408a b c d + 429a b c d - 54b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 432a c d - 720a b c d + 1098a b c d - 144b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2 3 3 2
+--R (- 1152a c d + 384a b c d + 624a b c d - 96b c )x - 768a c d
+--R +
+--R 2 4 2 5
+--R 768a b c d - 96a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 3 2 2 6
+--R (- 144a b d + 72b c d )x
+--R +
+--R 2 3 2 2 2 4
+--R (- 144a d - 696a b c d + 384b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 768a c d - 384a b c d + 384b c )x - 768a c d + 384a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ +-+ | 2
+--R \|- a d + a b c \|c \|d \|d x + c
+--R +
+--R 4 2 3 8 2 4 3 2 2 2 6
+--R (24a b d - 12b c d )x + (24a d + 420a b c d - 216b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (432a c d + 936a b c d - 576b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4
+--R (1152a c d + 192a b c d - 384b c )x + 768a c d - 384a b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (144a b d - 72b c d )x + (144a d + 696a b c d - 384b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (768a c d + 384a b c d - 384b c )x + 768a c d - 384a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ +-+ | 2
+--R \|- a d + a b c \|c \|d \|d x + c
+--R +
+--R 4 2 3 8
+--R (- 24a b d + 12b c d )x
+--R +
+--R 2 4 3 2 2 2 6
+--R (- 24a d - 420a b c d + 216b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 432a c d - 936a b c d + 576b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4
+--R (- 1152a c d - 192a b c d + 384b c )x - 768a c d + 384a b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R 3 4 11 2 4 3 3 9
+--R - 2b d x + (6a b d - 41b c d )x
+--R +
+--R 2 4 2 3 3 2 2 7
+--R (12a b d + 99a b c d - 186b c d )x
+--R +
+--R 2 3 2 2 2 3 3 5
+--R (216a b c d + 126a b c d - 304b c d)x
+--R +
+--R 2 2 2 2 3 3 4 3 2 3 2 4
+--R (576a b c d - 240a b c d - 160b c )x + (384a b c d - 288a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 3 4 11 2 4 3 3 9
+--R 12b d x + (- 36a b d + 106b c d )x
+--R +
+--R 2 4 2 3 3 2 2 7
+--R (- 72a b d - 174a b c d + 318b c d )x
+--R +
+--R 2 3 2 2 2 3 3 5
+--R (- 456a b c d - 42a b c d + 384b c d)x
+--R +
+--R 2 2 2 2 3 3 4 3
+--R (- 768a b c d + 384a b c d + 160b c )x
+--R +
+--R 2 3 2 4
+--R (- 384a b c d + 288a b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 5 2 6 4 2 5 4 4 5 2 2
+--R 48b d x + (48a b d + 256b c d)x + (256a b c d + 256b c )x
+--R +
+--R 4 2
+--R 256a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 5 3 8 4 3 5 2 6
+--R - 8b d x + (- 8a b d - 144b c d )x
+--R +
+--R 4 2 5 2 4 4 2 5 3 2 4 3
+--R (- 144a b c d - 384b c d)x + (- 384a b c d - 256b c )x - 256a b c
+--R *
+--R +-+
+--R \|d
+--R ,
+--R
+--R 3 2 2 6 2 3 2 2 2 4
+--R (72a b d - 36b c d )x + (72a d + 348a b c d - 192b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (384a c d + 192a b c d - 192b c )x + 384a c d - 192a b c
+--R *
+--R +-----------+ +--------+
+--R +---+ +-+ | 2 | 2
+--R \|- d \|c \|a d - a b c \|d x + c
+--R +
+--R 4 2 3 8
+--R (- 12a b d + 6b c d )x
+--R +
+--R 2 4 3 2 2 2 6
+--R (- 12a d - 210a b c d + 108b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 216a c d - 468a b c d + 288b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4
+--R (- 576a c d - 96a b c d + 192b c )x - 384a c d + 192a b c
+--R *
+--R +-----------+
+--R +---+ | 2
+--R \|- d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (2d x + 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (- 4d x - 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (288a b d - 288a b c d + 36b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (288a d + 1248a b c d - 1500a b c d + 192b c d)x
+--R +
+--R 3 3 2 3 3 4 2 3 2 2
+--R (1536a c d - 1344a b c d + 192b c )x + 1536a c d
+--R +
+--R 2 3 2 4
+--R - 1536a b c d + 192a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 48a b d + 48a b c d - 6b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 48a d - 816a b c d + 858a b c d - 108b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 864a c d - 1440a b c d + 2196a b c d - 288b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2 3 3 2
+--R (- 2304a c d + 768a b c d + 1248a b c d - 192b c )x - 1536a c d
+--R +
+--R 2 4 2 5
+--R 1536a b c d - 192a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 3 4 11 2 4 3 3 9
+--R - 2b d x + (6a b d - 41b c d )x
+--R +
+--R 2 4 2 3 3 2 2 7
+--R (12a b d + 99a b c d - 186b c d )x
+--R +
+--R 2 3 2 2 2 3 3 5
+--R (216a b c d + 126a b c d - 304b c d)x
+--R +
+--R 2 2 2 2 3 3 4 3 2 3 2 4
+--R (576a b c d - 240a b c d - 160b c )x + (384a b c d - 288a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 3 4 11 2 4 3 3 9
+--R 12b d x + (- 36a b d + 106b c d )x
+--R +
+--R 2 4 2 3 3 2 2 7
+--R (- 72a b d - 174a b c d + 318b c d )x
+--R +
+--R 2 3 2 2 2 3 3 5
+--R (- 456a b c d - 42a b c d + 384b c d)x
+--R +
+--R 2 2 2 2 3 3 4 3
+--R (- 768a b c d + 384a b c d + 160b c )x
+--R +
+--R 2 3 2 4
+--R (- 384a b c d + 288a b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R 5 2 6 4 2 5 4 4 5 2 2
+--R 48b d x + (48a b d + 256b c d)x + (256a b c d + 256b c )x
+--R +
+--R 4 2
+--R 256a b c
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 5 3 8 4 3 5 2 6
+--R - 8b d x + (- 8a b d - 144b c d )x
+--R +
+--R 4 2 5 2 4 4 2 5 3 2 4 3
+--R (- 144a b c d - 384b c d)x + (- 384a b c d - 256b c )x - 256a b c
+--R *
+--R +---+
+--R \|- d
+--R ,
+--R
+--R 2 4 2 3 3 2 2 6
+--R (288a b d - 288a b c d + 36b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (288a d + 1248a b c d - 1500a b c d + 192b c d)x
+--R +
+--R 3 3 2 3 3 4 2 3 2 2
+--R (1536a c d - 1344a b c d + 192b c )x + 1536a c d
+--R +
+--R 2 3 2 4
+--R - 1536a b c d + 192a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 48a b d + 48a b c d - 6b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 48a d - 816a b c d + 858a b c d - 108b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 864a c d - 1440a b c d + 2196a b c d - 288b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2 3 3 2
+--R (- 2304a c d + 768a b c d + 1248a b c d - 192b c )x - 1536a c d
+--R +
+--R 2 4 2 5
+--R 1536a b c d - 192a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 3 2 2 6
+--R (- 144a b d + 72b c d )x
+--R +
+--R 2 3 2 2 2 4
+--R (- 144a d - 696a b c d + 384b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 768a c d - 384a b c d + 384b c )x - 768a c d + 384a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +---+ +-+ | 2
+--R \|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R 4 2 3 8 2 4 3 2 2 2 6
+--R (24a b d - 12b c d )x + (24a d + 420a b c d - 216b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (432a c d + 936a b c d - 576b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4
+--R (1152a c d + 192a b c d - 384b c )x + 768a c d - 384a b c
+--R *
+--R +-------------+
+--R | 2 +---+
+--R \|- a d + a b c \|- d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (144a b d - 72b c d )x + (144a d + 696a b c d - 384b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (768a c d + 384a b c d - 384b c )x + 768a c d - 384a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +---+ +-+ | 2
+--R \|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R 4 2 3 8
+--R (- 24a b d + 12b c d )x
+--R +
+--R 2 4 3 2 2 2 6
+--R (- 24a d - 420a b c d + 216b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 432a c d - 936a b c d + 576b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4
+--R (- 1152a c d - 192a b c d + 384b c )x - 768a c d + 384a b c
+--R *
+--R +-------------+
+--R | 2 +---+
+--R \|- a d + a b c \|- d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R 3 4 11 2 4 3 3 9
+--R - 2b d x + (6a b d - 41b c d )x
+--R +
+--R 2 4 2 3 3 2 2 7
+--R (12a b d + 99a b c d - 186b c d )x
+--R +
+--R 2 3 2 2 2 3 3 5
+--R (216a b c d + 126a b c d - 304b c d)x
+--R +
+--R 2 2 2 2 3 3 4 3 2 3 2 4
+--R (576a b c d - 240a b c d - 160b c )x + (384a b c d - 288a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 3 4 11 2 4 3 3 9
+--R 12b d x + (- 36a b d + 106b c d )x
+--R +
+--R 2 4 2 3 3 2 2 7
+--R (- 72a b d - 174a b c d + 318b c d )x
+--R +
+--R 2 3 2 2 2 3 3 5
+--R (- 456a b c d - 42a b c d + 384b c d)x
+--R +
+--R 2 2 2 2 3 3 4 3
+--R (- 768a b c d + 384a b c d + 160b c )x
+--R +
+--R 2 3 2 4
+--R (- 384a b c d + 288a b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R 5 2 6 4 2 5 4 4 5 2 2
+--R 48b d x + (48a b d + 256b c d)x + (256a b c d + 256b c )x
+--R +
+--R 4 2
+--R 256a b c
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 5 3 8 4 3 5 2 6
+--R - 8b d x + (- 8a b d - 144b c d )x
+--R +
+--R 4 2 5 2 4 4 2 5 3 2 4 3
+--R (- 144a b c d - 384b c d)x + (- 384a b c d - 256b c )x - 256a b c
+--R *
+--R +---+
+--R \|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 600
+
+--S 601 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R +-+ | 2
+--R (12a d - 6b c)\|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2 2 +-+
+--R ((2d x + 4c x)\|a d - a b c + ((4a d - 2b c)x + 2a c)\|c )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (- 4d x - 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 2 2
+--R (24a d - 24a b c d + 3b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 x\|d
+--R (- 24a d + 24a b c d - 3b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ +-+ +-+ x\|- a d + b c
+--R (- 24a d + 12b c)\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 4 +-+
+--R 8b \|d
+--R Type: Expression(Integer)
+--E 601
+
+--S 602 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 602
+
+--S 603 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 2 2 2
+--R (24a d - 24a b c d + 3b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 x\|d
+--R (- 24a d + 24a b c d - 3b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R (- 24a d + 12b c)\|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+ +-+
+--R | 2 +-+ a\|c
+--R (24a d - 12b c)\|- a d + a b c \|d atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R +-----------+
+--R +-----------+ +-+ +-+ x\|- a d + b c
+--R (- 24a d + 12b c)\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 4 +-+
+--R 8b \|d
+--R Type: Expression(Integer)
+--E 603
+
+--S 604 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 604
+
+)clear all
+
+--S 605 of 1527
+t0:=x^3*(c+d*x^2)^(3/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 5 3 | 2
+--R (d x + c x )\|d x + c
+--R (1) ------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 605
+
+--S 606 of 1527
+r0:=1/6*(2*b*c-5*a*d)*(c+d*x^2)^(3/2)/(b^2*(b*c-a*d))+1/2*a*_
+ (c+d*x^2)^(5/2)/(b*(b*c-a*d)*(a+b*x^2))-1/2*(2*b*c-5*a*d)*_
+ atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/_
+ b^(7/2)+1/2*(2*b*c-5*a*d)*sqrt(c+d*x^2)/b^3
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 2 2 +-----------+ \|b \|d x + c
+--R ((15a b d - 6b c)x + 15a d - 6a b c)\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R (2b d x + (- 10a b d + 8b c)x - 15a d + 11a b c)\|b \|d x + c
+--R /
+--R 4 2 3 +-+
+--R (6b x + 6a b )\|b
+--R Type: Expression(Integer)
+--E 606
+
+--S 607 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 2 6 2 3 2 2 2 4
+--R (15a b d - 6b c d )x + (15a d + 174a b c d - 72b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (180a c d + 168a b c d - 96b c )x + 240a c d - 96a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| b
+--R +
+--R 3 2 2 2 6
+--R (- 75a b c d + 30b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 75a c d - 270a b c d + 120b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4
+--R (- 300a c d - 120a b c d + 96b c )x - 240a c d + 96a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+
+--R ((2a b d + 4b c)x + 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (- 2b c d x + (- 6a b c d - 4b c )x - 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 3 8 3 2 2 2 6
+--R - 20b c d x + (70a b c d - 138b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (120a c d - 48a b c d - 120b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (240a c d - 336a b c d + 96b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 10 4 2 3 8
+--R 4b d x + (- 20a b d + 68b c d )x
+--R +
+--R 2 4 3 2 2 2 6
+--R (- 30a d - 88a b c d + 210b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 240a c d + 216a b c d + 72b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (- 240a c d + 336a b c d - 96b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 2 6 3 2 4 4 3 4 2 2
+--R 12b d x + (12a b d + 144b c d)x + (144a b c d + 192b c )x
+--R +
+--R 3 2
+--R 192a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 4 2 6 3 2 4 2 4 3 2 4 3 2
+--R - 60b c d x + (- 60a b c d - 240b c d)x + (- 240a b c d - 192b c )x
+--R +
+--R 3 3
+--R - 192a b c
+--R ,
+--R
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 15a b d + 6b c d )x + (- 15a d - 174a b c d + 72b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 180a c d - 168a b c d + 96b c )x - 240a c d + 96a b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 3 2 2 2 6
+--R (75a b c d - 30b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (75a c d + 270a b c d - 120b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4
+--R (300a c d + 120a b c d - 96b c )x + 240a c d - 96a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R 2 3 8 3 2 2 2 6
+--R - 10b c d x + (35a b c d - 69b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (60a c d - 24a b c d - 60b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (120a c d - 168a b c d + 48b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 10 4 2 3 8
+--R 2b d x + (- 10a b d + 34b c d )x
+--R +
+--R 2 4 3 2 2 2 6
+--R (- 15a d - 44a b c d + 105b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 120a c d + 108a b c d + 36b c d)x
+--R +
+--R 2 2 2 3 2 4 2
+--R (- 120a c d + 168a b c d - 48b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 2 6 3 2 4 4 3 4 2 2 3 2
+--R (6b d x + (6a b d + 72b c d)x + (72a b c d + 96b c )x + 96a b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 4 2 6 3 2 4 2 4 3 2 4 3 2
+--R - 30b c d x + (- 30a b c d - 120b c d)x + (- 120a b c d - 96b c )x
+--R +
+--R 3 3
+--R - 96a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 607
+
+--S 608 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 2 4 2 2 2 2
+--R (15a d - 6b c d )x + (180a c d - 72b c d)x + 240a c d
+--R +
+--R 3
+--R - 96b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ +-+ | 2
+--R |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (- 75a c d + 30b c d )x + (- 300a c d + 120b c d)x - 240a c d
+--R +
+--R 4
+--R 96b c
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 2 4
+--R ((2a b d + 4b c)x + 8a b c x ) |----------- \|c + 4b c x
+--R \| b
+--R +
+--R 2 2 2 2 2
+--R (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (- 2b c d x + (- 6a b c d - 4b c )x - 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 30a d + 12b c d )x + (- 360a c d + 144b c d)x - 480a c d
+--R +
+--R 3
+--R 192b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (150a c d - 60b c d )x + (600a c d - 240b c d)x + 480a c d
+--R +
+--R 4
+--R - 192b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (- 30a c d + 22b c d )x + (- 360a c d + 264b c d)x - 480a c d
+--R +
+--R 4
+--R 352b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (150a c d - 110b c d )x + (600a c d - 440b c d)x + 480a c d
+--R +
+--R 4
+--R - 352b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 3 2 4 3 2 3 2 +-+ +-+ | 2
+--R (12b d x + 144b c d x + 192b c )\|b \|c \|d x + c
+--R +
+--R 3 2 4 3 2 2 3 3 +-+
+--R (- 60b c d x - 240b c d x - 192b c )\|b
+--R Type: Expression(Integer)
+--E 608
+
+--S 609 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 609
+
+--S 610 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 3 2 4 2 2 2 2
+--R (- 15a d + 6b c d )x + (- 180a c d + 72b c d)x - 240a c d
+--R +
+--R 3
+--R 96b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (75a c d - 30b c d )x + (300a c d - 120b c d)x + 240a c d
+--R +
+--R 4
+--R - 96b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 15a d + 6b c d )x + (- 180a c d + 72b c d)x - 240a c d
+--R +
+--R 3
+--R 96b c
+--R *
+--R +---------+ +--------+
+--R +-+ +-+ |a d - b c | 2
+--R \|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (75a c d - 30b c d )x + (300a c d - 120b c d)x + 240a c d
+--R +
+--R 4
+--R - 96b c
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|b |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (- 15a c d + 11b c d )x + (- 180a c d + 132b c d)x - 240a c d
+--R +
+--R 4
+--R 176b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (75a c d - 55b c d )x + (300a c d - 220b c d)x + 240a c d
+--R +
+--R 4
+--R - 176b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 3 2 4 3 2 3 2 +-+ +-+ | 2
+--R (6b d x + 72b c d x + 96b c )\|b \|c \|d x + c
+--R +
+--R 3 2 4 3 2 2 3 3 +-+
+--R (- 30b c d x - 120b c d x - 96b c )\|b
+--R Type: Expression(Integer)
+--E 610
+
+--S 611 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 611
+
+)clear all
+
+--S 612 of 1527
+t0:=x^2*(c+d*x^2)^(3/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (d x + c x )\|d x + c
+--R (1) ------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 612
+
+--S 613 of 1527
+r0:=-1/2*x*(c+d*x^2)^(3/2)/(b*(a+b*x^2))+1/2*(3*b*c-4*a*d)*_
+ atanh(x*sqrt(d)/sqrt(c+d*x^2))*sqrt(d)/b^3+1/2*(b*c-4*a*d)*_
+ atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*sqrt(b*c-a*d)/_
+ (b^3*sqrt(a))+d*x*sqrt(c+d*x^2)/b^2
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 +-+ +-+ x\|d
+--R ((- 4a b d + 3b c)x - 4a d + 3a b c)\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 +-----------+ x\|- a d + b c
+--R ((- 4a b d + b c)x - 4a d + a b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 3 2 +-+ | 2
+--R (b d x + (2a b d - b c)x)\|a \|d x + c
+--R /
+--R 4 2 3 +-+
+--R (2b x + 2a b )\|a
+--R Type: Expression(Integer)
+--E 613
+
+--S 614 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 4 2 2 2 2 2
+--R (32a b d - 24b c d)x + (32a d + 40a b c d - 48b c )x
+--R +
+--R 2 2
+--R 64a c d - 48a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 8a b d + 6b c d )x + (- 8a d - 58a b c d + 48b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 64a c d - 16a b c d + 48b c )x - 64a c d + 48a b c
+--R *
+--R +-+
+--R \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (16a b d - 4b c d)x + (16a d + 28a b c d - 8b c )x
+--R +
+--R 2 2
+--R 32a c d - 8a b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| a
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 4a b d + b c d )x + (- 4a d - 31a b c d + 8b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 32a c d - 24a b c d + 8b c )x - 32a c d + 8a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 7 3 2 2 5 2 3
+--R - 2b d x + (- 4a b d - 14b c d )x - 32a b c d x
+--R +
+--R 2 2 3
+--R (- 32a b c d + 16b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 8b d x + (16a b d + 16b c d )x + (48a b c d - 8b c d)x
+--R +
+--R 2 2 3
+--R (32a b c d - 16b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 4 3 4 2 3 +-+ | 2 4 2 6
+--R (16b d x + (16a b d + 32b c)x + 32a b c)\|c \|d x + c - 4b d x
+--R +
+--R 3 2 4 4 3 4 2 2 3 2
+--R (- 4a b d - 32b c d)x + (- 32a b c d - 32b c )x - 32a b c
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2
+--R (16a b d - 12b c d)x + (16a d + 20a b c d - 24b c )x
+--R +
+--R 2 2
+--R 32a c d - 24a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 4a b d + 3b c d )x + (- 4a d - 29a b c d + 24b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 32a c d - 8a b c d + 24b c )x - 32a c d + 24a b c
+--R *
+--R +-+
+--R \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (16a b d - 4b c d)x + (16a d + 28a b c d - 8b c )x
+--R +
+--R 2 2
+--R 32a c d - 8a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 4a b d + b c d )x + (- 4a d - 31a b c d + 8b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 32a c d - 24a b c d + 8b c )x - 32a c d + 8a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (- 16a b d + 4b c d)x + (- 16a d - 28a b c d + 8b c )x
+--R +
+--R 2 2
+--R - 32a c d + 8a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (4a b d - b c d )x + (4a d + 31a b c d - 8b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (32a c d + 24a b c d - 8b c )x + 32a c d - 8a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 3 7 3 2 2 5 2 3
+--R - b d x + (- 2a b d - 7b c d )x - 16a b c d x
+--R +
+--R 2 2 3
+--R (- 16a b c d + 8b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 4b d x + (8a b d + 8b c d )x + (24a b c d - 4b c d)x
+--R +
+--R 2 2 3
+--R (16a b c d - 8b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 4 3 4 2 3 +-+ | 2 4 2 6
+--R (8b d x + (8a b d + 16b c)x + 16a b c)\|c \|d x + c - 2b d x
+--R +
+--R 3 2 4 4 3 4 2 2 3 2
+--R (- 2a b d - 16b c d)x + (- 16a b c d - 16b c )x - 16a b c
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2
+--R (16a b d - 4b c d)x + (16a d + 28a b c d - 8b c )x
+--R +
+--R 2 2
+--R 32a c d - 8a b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| a
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 4a b d + b c d )x + (- 4a d - 31a b c d + 8b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 32a c d - 24a b c d + 8b c )x - 32a c d + 8a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (- 64a b d + 48b c d)x + (- 64a d - 80a b c d + 96b c )x
+--R +
+--R 2 2
+--R - 128a c d + 96a b c
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (16a b d - 12b c d )x + (16a d + 116a b c d - 96b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (128a c d + 32a b c d - 96b c )x + 128a c d - 96a b c
+--R *
+--R +---+
+--R \|- d
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 2 3 7 3 2 2 5 2 3
+--R - 2b d x + (- 4a b d - 14b c d )x - 32a b c d x
+--R +
+--R 2 2 3
+--R (- 32a b c d + 16b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 8b d x + (16a b d + 16b c d )x + (48a b c d - 8b c d)x
+--R +
+--R 2 2 3
+--R (32a b c d - 16b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 4 3 4 2 3 +-+ | 2 4 2 6
+--R (16b d x + (16a b d + 32b c)x + 32a b c)\|c \|d x + c - 4b d x
+--R +
+--R 3 2 4 4 3 4 2 2 3 2
+--R (- 4a b d - 32b c d)x + (- 32a b c d - 32b c )x - 32a b c
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2
+--R (- 32a b d + 24b c d)x + (- 32a d - 40a b c d + 48b c )x
+--R +
+--R 2 2
+--R - 64a c d + 48a b c
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (8a b d - 6b c d )x + (8a d + 58a b c d - 48b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (64a c d + 16a b c d - 48b c )x + 64a c d - 48a b c
+--R *
+--R +---+
+--R \|- d
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (16a b d - 4b c d)x + (16a d + 28a b c d - 8b c )x
+--R +
+--R 2 2
+--R 32a c d - 8a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 4a b d + b c d )x + (- 4a d - 31a b c d + 8b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 32a c d - 24a b c d + 8b c )x - 32a c d + 8a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (- 16a b d + 4b c d)x + (- 16a d - 28a b c d + 8b c )x
+--R +
+--R 2 2
+--R - 32a c d + 8a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (4a b d - b c d )x + (4a d + 31a b c d - 8b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (32a c d + 24a b c d - 8b c )x + 32a c d - 8a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 3 7 3 2 2 5 2 3
+--R - b d x + (- 2a b d - 7b c d )x - 16a b c d x
+--R +
+--R 2 2 3
+--R (- 16a b c d + 8b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 7 3 2 2 5 2 2 2 3
+--R 4b d x + (8a b d + 8b c d )x + (24a b c d - 4b c d)x
+--R +
+--R 2 2 3
+--R (16a b c d - 8b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 4 3 4 2 3 +-+ | 2 4 2 6
+--R (8b d x + (8a b d + 16b c)x + 16a b c)\|c \|d x + c - 2b d x
+--R +
+--R 3 2 4 4 3 4 2 2 3 2
+--R (- 2a b d - 16b c d)x + (- 16a b c d - 16b c )x - 16a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 614
+
+--S 615 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-+ +-+
+--R (8a d - 6b c)\|a \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+
+--R +-+ |a d - b c
+--R (4a d - b c)\|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-+
+--R +-+ +-+ x\|d
+--R (8a d - 6b c)\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (8a d - 2b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 4b \|a
+--R Type: Expression(Integer)
+--E 615
+
+--S 616 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 616
+
+--S 617 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+ +-+
+--R (4a d - 3b c)\|a \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R +-+ +-+ x\|d
+--R (4a d - 3b c)\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R |- a d + b c +-+
+--R (4a d - b c) |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c +-+ \|c
+--R (- 4a d + b c) |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (4a d - b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 2b \|a
+--R Type: Expression(Integer)
+--E 617
+
+--S 618 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 618
+
+)clear all
+
+--S 619 of 1527
+t0:=x*(c+d*x^2)^(3/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 3 | 2
+--R (d x + c x)\|d x + c
+--R (1) -----------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 619
+
+--S 620 of 1527
+r0:=-1/2*(c+d*x^2)^(3/2)/(b*(a+b*x^2))-3/2*d*atanh(sqrt(b)*_
+ sqrt(c+d*x^2)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(5/2)+3/2*d*_
+ sqrt(c+d*x^2)/b^2
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 +-----------+ \|b \|d x + c
+--R (- 3b d x - 3a d)\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R (2b d x + 3a d - b c)\|b \|d x + c
+--R /
+--R 3 2 2 +-+
+--R (2b x + 2a b )\|b
+--R Type: Expression(Integer)
+--E 620
+
+--S 621 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+
+--R 2 4 2 2 2 2 |- a d + b c +-+
+--R (3a b d x + (3a d + 12a b c d)x + 12a c d) |----------- \|c
+--R \| b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 2 2 2 2 |- a d + b c
+--R (- 9a b c d x + (- 9a c d - 12a b c d)x - 12a c d) |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+
+--R ((- 2a b d - 4b c)x - 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (2b c d x + (6a b c d + 4b c )x + 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 4 2 2 2 2 3 2
+--R ((- 6a b c d - 2b c d)x + (- 12a c d + 12a b c d - 8b c )x )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 6 2 3 2 2 4 2 2 2 2 3 2 +-+
+--R (4a b d x + (6a d + 6b c d)x + (12a c d - 12a b c d + 8b c )x )\|c
+--R /
+--R +--------+
+--R 3 4 2 2 3 2 2 2 +-+ | 2
+--R (4a b d x + (4a b d + 16a b c)x + 16a b c)\|c \|d x + c
+--R +
+--R 3 4 2 2 3 2 2 2 2 2
+--R - 12a b c d x + (- 12a b c d - 16a b c )x - 16a b c
+--R ,
+--R
+--R +---------+
+--R 2 4 2 2 2 2 +-+ |a d - b c
+--R (3a b d x + (3a d + 12a b c d)x + 12a c d)\|c |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 4 2 2 2 2 2 2 |a d - b c
+--R (- 9a b c d x + (- 9a c d - 12a b c d)x - 12a c d) |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R +--------+
+--R 2 2 2 4 2 2 2 2 3 2 | 2
+--R ((- 3a b c d - b c d)x + (- 6a c d + 6a b c d - 4b c )x )\|d x + c
+--R +
+--R 3 6 2 3 2 2 4 2 2 2 2 3 2 +-+
+--R (2a b d x + (3a d + 3b c d)x + (6a c d - 6a b c d + 4b c )x )\|c
+--R /
+--R +--------+
+--R 3 4 2 2 3 2 2 2 +-+ | 2 3 4
+--R (2a b d x + (2a b d + 8a b c)x + 8a b c)\|c \|d x + c - 6a b c d x
+--R +
+--R 2 2 3 2 2 2 2 2
+--R (- 6a b c d - 8a b c )x - 8a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 621
+
+--S 622 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +--------+
+--R 2 2 |- a d + b c +-+ +-+ | 2
+--R (3a d x + 12a c d) |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c +-+
+--R (- 9a c d x - 12a c d) |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+
+--R ((- 2a b d - 4b c)x - 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (2b c d x + (6a b c d + 4b c )x + 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 +-----------+ +-+ | 2
+--R (6a d x + 24a c d)\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+
+--R (- 18a c d x - 24a c d)\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((6a c d - 2b c d)x + 24a c d - 8b c )\|b \|d x + c
+--R +
+--R 2 2 2 2 3 +-+ +-+
+--R ((- 18a c d + 6b c d)x - 24a c d + 8b c )\|b \|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ +-+ | 2 2 2 2 2 +-+
+--R (4a b d x + 16a b c)\|b \|c \|d x + c + (- 12a b c d x - 16a b c )\|b
+--R Type: Expression(Integer)
+--E 622
+
+--S 623 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 623
+
+--S 624 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 2 +-----------+ +-+ | 2
+--R (3a d x + 12a c d)\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+
+--R (- 9a c d x - 12a c d)\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +---------+ +--------+
+--R 2 2 +-+ +-+ |a d - b c | 2
+--R (3a d x + 12a c d)\|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R +---------+
+--R 2 2 2 +-+ |a d - b c
+--R (- 9a c d x - 12a c d)\|b |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((3a c d - b c d)x + 12a c d - 4b c )\|b \|d x + c
+--R +
+--R 2 2 2 2 3 +-+ +-+
+--R ((- 9a c d + 3b c d)x - 12a c d + 4b c )\|b \|c
+--R /
+--R +--------+
+--R 2 2 2 +-+ +-+ | 2 2 2 2 2 +-+
+--R (2a b d x + 8a b c)\|b \|c \|d x + c + (- 6a b c d x - 8a b c )\|b
+--R Type: Expression(Integer)
+--E 624
+
+--S 625 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 625
+
+)clear all
+
+--S 626 of 1527
+t0:=(c+d*x^2)^(3/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 626
+
+--S 627 of 1527
+r0:=d^(3/2)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/b^2+1/2*(b*c+2*a*d)*_
+ atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*sqrt(b*c-a*d)/_
+ (a^(3/2)*b^2)+1/2*(b*c-a*d)*x*sqrt(c+d*x^2)/(a*b*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (2a b d x + 2a d)\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 +-----------+ x\|- a d + b c
+--R ((2a b d + b c)x + 2a d + a b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R (- a b d + b c)x\|a \|d x + c
+--R /
+--R 3 2 2 2 +-+
+--R (2a b x + 2a b )\|a
+--R Type: Expression(Integer)
+--E 627
+
+--S 628 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+ +--------+
+--R 2 2 2 +-+ |a d - b c | 2
+--R ((4a b d + 2b c)x + 4a d + 2a b c)\|c |--------- \|d x + c
+--R \| a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d - b c d)x + (- 2a d - 5a b c d - 2b c )x - 4a c d
+--R +
+--R 2
+--R - 2a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 +-+ +-+ | 2
+--R (8a b d x + 8a d)\|c \|d \|d x + c
+--R +
+--R 2 4 2 2 2 2 +-+
+--R (- 4a b d x + (- 4a d - 8a b c d)x - 8a c d)\|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +--------+
+--R 2 2 3 2 2 | 2
+--R ((2a b d - 2b c d)x + (4a b c d - 4b c )x)\|d x + c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b d + 4b c d)x + (- 4a b c d + 4b c )x)\|c
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ | 2 3 4 2 2 3 2
+--R (8a b x + 8a b )\|c \|d x + c - 4a b d x + (- 4a b d - 8a b c)x
+--R +
+--R 2 2
+--R - 8a b c
+--R ,
+--R
+--R +--------+
+--R 2 2 +-+ +-+ | 2
+--R (4a b d x + 4a d)\|c \|d \|d x + c
+--R +
+--R 2 4 2 2 2 2 +-+
+--R (- 2a b d x + (- 2a d - 4a b c d)x - 4a c d)\|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-----------+ +--------+
+--R 2 2 2 |- a d + b c +-+ | 2
+--R ((- 4a b d - 2b c)x - 4a d - 2a b c) |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (2a b d + b c d)x + (2a d + 5a b c d + 2b c )x + 4a c d
+--R +
+--R 2
+--R 2a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +--------+
+--R 2 2 2 |- a d + b c +-+ | 2
+--R ((4a b d + 2b c)x + 4a d + 2a b c) |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d - b c d)x + (- 2a d - 5a b c d - 2b c )x - 4a c d
+--R +
+--R 2
+--R - 2a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R 2 2 3 2 2 | 2
+--R ((a b d - b c d)x + (2a b c d - 2b c )x)\|d x + c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 2a b d + 2b c d)x + (- 2a b c d + 2b c )x)\|c
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ | 2 3 4 2 2 3 2
+--R (4a b x + 4a b )\|c \|d x + c - 2a b d x + (- 2a b d - 4a b c)x
+--R +
+--R 2 2
+--R - 4a b c
+--R ,
+--R
+--R +---------+ +--------+
+--R 2 2 2 +-+ |a d - b c | 2
+--R ((4a b d + 2b c)x + 4a d + 2a b c)\|c |--------- \|d x + c
+--R \| a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d - b c d)x + (- 2a d - 5a b c d - 2b c )x - 4a c d
+--R +
+--R 2
+--R - 2a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 +---+ +-+ | 2
+--R (16a b d x + 16a d)\|- d \|c \|d x + c
+--R +
+--R 2 4 2 2 2 2 +---+
+--R (- 8a b d x + (- 8a d - 16a b c d)x - 16a c d)\|- d
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R +--------+
+--R 2 2 3 2 2 | 2
+--R ((2a b d - 2b c d)x + (4a b c d - 4b c )x)\|d x + c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b d + 4b c d)x + (- 4a b c d + 4b c )x)\|c
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ | 2 3 4 2 2 3 2
+--R (8a b x + 8a b )\|c \|d x + c - 4a b d x + (- 4a b d - 8a b c)x
+--R +
+--R 2 2
+--R - 8a b c
+--R ,
+--R
+--R +--------+
+--R 2 2 +---+ +-+ | 2
+--R (8a b d x + 8a d)\|- d \|c \|d x + c
+--R +
+--R 2 4 2 2 2 2 +---+
+--R (- 4a b d x + (- 4a d - 8a b c d)x - 8a c d)\|- d
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R +-----------+ +--------+
+--R 2 2 2 |- a d + b c +-+ | 2
+--R ((- 4a b d - 2b c)x - 4a d - 2a b c) |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (2a b d + b c d)x + (2a d + 5a b c d + 2b c )x + 4a c d
+--R +
+--R 2
+--R 2a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +--------+
+--R 2 2 2 |- a d + b c +-+ | 2
+--R ((4a b d + 2b c)x + 4a d + 2a b c) |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d - b c d)x + (- 2a d - 5a b c d - 2b c )x - 4a c d
+--R +
+--R 2
+--R - 2a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R 2 2 3 2 2 | 2
+--R ((a b d - b c d)x + (2a b c d - 2b c )x)\|d x + c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 2a b d + 2b c d)x + (- 2a b c d + 2b c )x)\|c
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ | 2 3 4 2 2 3 2
+--R (4a b x + 4a b )\|c \|d x + c - 2a b d x + (- 2a b d - 4a b c)x
+--R +
+--R 2 2
+--R - 4a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 628
+
+--S 629 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-+ |a d - b c
+--R (2a d + b c)\|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R 4a d\|a \|d log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R +-+ +-+ x\|d
+--R - 4a d\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (- 4a d - 2b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 4a b \|a
+--R Type: Expression(Integer)
+--E 629
+
+--S 630 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 630
+
+--S 631 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R 2a d\|a \|d log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R +-+ +-+ x\|d
+--R - 2a d\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R |- a d + b c +-+
+--R (- 2a d - b c) |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c +-+ \|c
+--R (2a d + b c) |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (- 2a d - b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2a b \|a
+--R Type: Expression(Integer)
+--E 631
+
+--S 632 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 632
+
+)clear all
+
+--S 633 of 1527
+t0:=(c+d*x^2)^(3/2)/(x*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R Type: Expression(Integer)
+--E 633
+
+--S 634 of 1527
+r0:=-c^(3/2)*atanh(sqrt(c+d*x^2)/sqrt(c))/a^2+1/2*(2*b*c+a*d)*_
+ atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/_
+ (a^2*b^(3/2))+1/2*(b*c-a*d)*sqrt(c+d*x^2)/(a*b*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 2 2 +-----------+ \|b \|d x + c
+--R ((a b d + 2b c)x + a d + 2a b c)\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R 2 2 +-+ +-+ \|d x + c
+--R (- 2b c x - 2a b c)\|b \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R (- a d + a b c)\|b \|d x + c
+--R /
+--R 2 2 2 3 +-+
+--R (2a b x + 2a b)\|b
+--R Type: Expression(Integer)
+--E 634
+
+--S 635 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 2 | 2
+--R (8b c x + 8a b c )\|d x + c
+--R +
+--R 2 4 2 2 2 2 +-+
+--R (- 4b c d x + (- 4a b c d - 8b c )x - 8a b c )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R 2 2 2 |- a d + b c +-+ | 2
+--R ((2a b d + 4b c)x + 2a d + 4a b c) |----------- \|c \|d x + c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x - 2a c d
+--R +
+--R 2
+--R - 4a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 2 2 2 | 2
+--R (2a d - 6a b c d + 4b c )x \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 +-+
+--R ((2a b d - 2b c d)x + (- 2a d + 6a b c d - 4b c )x )\|c
+--R /
+--R +--------+
+--R 2 2 2 3 +-+ | 2 2 2 4 3 2 2 2
+--R (8a b x + 8a b)\|c \|d x + c - 4a b d x + (- 4a b d - 8a b c)x
+--R +
+--R 3
+--R - 8a b c
+--R ,
+--R
+--R +--------+
+--R 2 2 2 2 | 2
+--R (4b c x + 4a b c )\|d x + c
+--R +
+--R 2 4 2 2 2 2 +-+
+--R (- 2b c d x + (- 2a b c d - 4b c )x - 4a b c )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +---------+ +--------+
+--R 2 2 2 +-+ |a d - b c | 2
+--R ((- 2a b d - 4b c)x - 2a d - 4a b c)\|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (a b d + 2b c d)x + (a d + 4a b c d + 4b c )x + 2a c d
+--R +
+--R 2
+--R 4a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R +--------+
+--R 2 2 2 2 2 | 2
+--R (a d - 3a b c d + 2b c )x \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 +-+
+--R ((a b d - b c d)x + (- a d + 3a b c d - 2b c )x )\|c
+--R /
+--R +--------+
+--R 2 2 2 3 +-+ | 2 2 2 4 3 2 2 2
+--R (4a b x + 4a b)\|c \|d x + c - 2a b d x + (- 2a b d - 4a b c)x
+--R +
+--R 3
+--R - 4a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 635
+
+--S 636 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 +-+ | 2 2 2 +-+ +-+
+--R (8b c \|b \|d x + c + (- 4b c d x - 8b c )\|b \|c )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+ +--------+
+--R |- a d + b c +-+ +-+ | 2
+--R (2a d + 4b c) |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c +-+
+--R ((- a d - 2b c d)x - 2a c d - 4b c ) |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R (- 4a d - 8b c)\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+
+--R ((2a d + 4b c d)x + 4a c d + 8b c )\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +--------+ | 2
+--R 2 +-+ | 2 2 2 +-+ +-+ \|d x + c
+--R (8b c \|b \|d x + c + (- 4b c d x - 8b c )\|b \|c )atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R (- 4a c d + 4b c )\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R ((2a d - 2b c d)x + 4a c d - 4b c )\|b \|c
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 2 2 +-+
+--R 8a b\|b \|c \|d x + c + (- 4a b d x - 8a b c)\|b
+--R Type: Expression(Integer)
+--E 636
+
+--S 637 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 637
+
+--S 638 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 +-+ | 2 2 2 +-+ +-+
+--R (4b c \|b \|d x + c + (- 2b c d x - 4b c )\|b \|c )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R (- 2a d - 4b c)\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+
+--R ((a d + 2b c d)x + 2a c d + 4b c )\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +--------+ | 2
+--R 2 +-+ | 2 2 2 +-+ +-+ \|d x + c
+--R (4b c \|b \|d x + c + (- 2b c d x - 4b c )\|b \|c )atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +---------+ +--------+
+--R +-+ +-+ |a d - b c | 2
+--R (- 2a d - 4b c)\|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R +---------+
+--R 2 2 2 +-+ |a d - b c
+--R ((a d + 2b c d)x + 2a c d + 4b c )\|b |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R (- 2a c d + 2b c )\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R ((a d - b c d)x + 2a c d - 2b c )\|b \|c
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 2 2 +-+
+--R 4a b\|b \|c \|d x + c + (- 2a b d x - 4a b c)\|b
+--R Type: Expression(Integer)
+--E 638
+
+--S 639 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 639
+
+)clear all
+
+--S 640 of 1527
+t0:=(c+d*x^2)^(3/2)/(x^2*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R Type: Expression(Integer)
+--E 640
+
+--S 641 of 1527
+r0:=-3/2*c*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*sqrt(b*c-a*d)/_
+ a^(5/2)-1/2*(3*b*c-a*d)*sqrt(c+d*x^2)/(a^2*b*x)+1/2*(b*c-a*d)*_
+ sqrt(c+d*x^2)/(a*b*x*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +-----------+
+--R 3 +-----------+ x\|- a d + b c
+--R (- 3b c x - 3a c x)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R ((a d - 3b c)x - 2a c)\|a \|d x + c
+--R /
+--R 2 3 3 +-+
+--R (2a b x + 2a x)\|a
+--R Type: Expression(Integer)
+--E 641
+
+--S 642 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+ +--------+
+--R 5 2 3 2 |a d - b c | 2
+--R (3b c d x + (3a c d + 12b c )x + 12a c x) |--------- \|d x + c
+--R \| a
+--R +
+--R +---------+
+--R 5 2 3 2 +-+ |a d - b c
+--R (- 9b c d x + (- 9a c d - 12b c )x - 12a c x)\|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R ((- 6a d + 18b c d)x + (4a c d + 24b c )x + 16a c )\|c \|d x + c
+--R +
+--R 3 2 6 2 2 4 2 3 2
+--R (2a d - 6b c d )x + (6a c d - 30b c d)x + (- 12a c d - 24b c )x
+--R +
+--R 3
+--R - 16a c
+--R /
+--R +--------+
+--R 2 5 3 2 3 3 | 2
+--R (4a b d x + (4a d + 16a b c)x + 16a c x)\|d x + c
+--R +
+--R 2 5 3 2 3 3 +-+
+--R (- 12a b d x + (- 12a d - 16a b c)x - 16a c x)\|c
+--R ,
+--R
+--R +-----------+
+--R 5 2 3 2 |- a d + b c
+--R (3b c d x + (3a c d + 12b c )x + 12a c x) |-----------
+--R \| a
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 5 2 3 2 |- a d + b c +-+
+--R (- 9b c d x + (- 9a c d - 12b c )x - 12a c x) |----------- \|c
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R 5 2 3 2 |- a d + b c
+--R (- 3b c d x + (- 3a c d - 12b c )x - 12a c x) |-----------
+--R \| a
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 5 2 3 2 |- a d + b c +-+
+--R (9b c d x + (9a c d + 12b c )x + 12a c x) |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R ((- 3a d + 9b c d)x + (2a c d + 12b c )x + 8a c )\|c \|d x + c
+--R +
+--R 3 2 6 2 2 4 2 3 2
+--R (a d - 3b c d )x + (3a c d - 15b c d)x + (- 6a c d - 12b c )x
+--R +
+--R 3
+--R - 8a c
+--R /
+--R +--------+
+--R 2 5 3 2 3 3 | 2
+--R (2a b d x + (2a d + 8a b c)x + 8a c x)\|d x + c
+--R +
+--R 2 5 3 2 3 3 +-+
+--R (- 6a b d x + (- 6a d - 8a b c)x - 8a c x)\|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 642
+
+--S 643 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-+ |a d - b c
+--R 3c\|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R 6c\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 643
+
+--S 644 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 644
+
+--S 645 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R |- a d + b c +-+
+--R 3c |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c +-+ \|c
+--R - 3c |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R 3c\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 645
+
+--S 646 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 646
+
+)clear all
+
+--S 647 of 1527
+t0:=(c+d*x^2)^(3/2)/(x^3*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R Type: Expression(Integer)
+--E 647
+
+--S 648 of 1527
+r0:=-1/2*(c+d*x^2)^(3/2)/(a*x^2*(a+b*x^2))+1/2*(4*b*c-3*a*d)*_
+ atanh(sqrt(c+d*x^2)/sqrt(c))*sqrt(c)/a^3-1/2*(4*b*c-a*d)*_
+ atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/_
+ (a^3*sqrt(b))-(b*c-a*d)*sqrt(c+d*x^2)/(a^2*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 4 2 2 +-----------+ \|b \|d x + c
+--R ((a b d - 4b c)x + (a d - 4a b c)x )\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 +-+ +-+ \|d x + c
+--R ((- 3a b d + 4b c)x + (- 3a d + 4a b c)x )\|b \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((a d - 2a b c)x - a c)\|b \|d x + c
+--R /
+--R 3 4 4 2 +-+
+--R (2a b x + 2a x )\|b
+--R Type: Expression(Integer)
+--E 648
+
+--S 649 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 2 6 2 2 2 2 3 4
+--R (24a b c d - 32b c d)x + (24a c d + 16a b c d - 64b c )x
+--R +
+--R 2 2 3 2
+--R (48a c d - 64a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 8 2 3 2 2 2 6
+--R (- 6a b d + 8b c d )x + (- 6a d - 40a b c d + 64b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (- 48a c d + 16a b c d + 64b c )x + (- 48a c d + 64a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (4a b d - 16b c d)x + (4a d - 8a b c d - 32b c )x
+--R +
+--R 2 2 2
+--R (8a c d - 32a b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| b
+--R +
+--R 3 2 2 8 2 3 2 2 2 6
+--R (- a b d + 4b c d )x + (- a d - 4a b c d + 32b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (- 8a c d + 24a b c d + 32b c )x + (- 8a c d + 32a b c )x
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 6
+--R (- 2a d + 12a b c d - 8b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (- 6a c d + 40a b c d - 16b c )x + (16a c d + 16a b c )x + 16a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 8 2 3 2 2 2 6
+--R (- 2a b d + 2b c d )x + (6a d - 30a b c d + 16b c d)x
+--R +
+--R 2 2 3 4 2 2 3 2 2 3
+--R (- 48a b c d + 16b c )x + (- 24a c d - 16a b c )x - 16a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 6 4 3 4 4 2 +-+ | 2
+--R (16a b d x + (16a d + 32a b c)x + 32a c x )\|c \|d x + c
+--R +
+--R 3 2 8 4 2 3 6 4 3 2 4
+--R - 4a b d x + (- 4a d - 32a b c d)x + (- 32a c d - 32a b c )x
+--R +
+--R 4 2 2
+--R - 32a c x
+--R ,
+--R
+--R 2 2 2 6 2 2 2 2 3 4
+--R (12a b c d - 16b c d)x + (12a c d + 8a b c d - 32b c )x
+--R +
+--R 2 2 3 2
+--R (24a c d - 32a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 8 2 3 2 2 2 6
+--R (- 3a b d + 4b c d )x + (- 3a d - 20a b c d + 32b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (- 24a c d + 8a b c d + 32b c )x + (- 24a c d + 32a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (- 4a b d + 16b c d)x + (- 4a d + 8a b c d + 32b c )x
+--R +
+--R 2 2 2
+--R (- 8a c d + 32a b c )x
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 3 2 2 8 2 3 2 2 2 6
+--R (a b d - 4b c d )x + (a d + 4a b c d - 32b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (8a c d - 24a b c d - 32b c )x + (8a c d - 32a b c )x
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R 2 3 2 2 2 6 2 2 2 2 3 4
+--R (- a d + 6a b c d - 4b c d)x + (- 3a c d + 20a b c d - 8b c )x
+--R +
+--R 2 2 3 2 2 3
+--R (8a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 8 2 3 2 2 2 6
+--R (- a b d + b c d )x + (3a d - 15a b c d + 8b c d)x
+--R +
+--R 2 2 3 4 2 2 3 2 2 3
+--R (- 24a b c d + 8b c )x + (- 12a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 6 4 3 4 4 2 +-+ | 2 3 2 8
+--R (8a b d x + (8a d + 16a b c)x + 16a c x )\|c \|d x + c - 2a b d x
+--R +
+--R 4 2 3 6 4 3 2 4 4 2 2
+--R (- 2a d - 16a b c d)x + (- 16a c d - 16a b c )x - 16a c x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 649
+
+--S 650 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((24a c d - 32b c d)x + 48a c d - 64b c )\|b \|d x + c
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 6a d + 8b c d )x + (- 48a c d + 64b c d)x - 48a c d
+--R +
+--R 3
+--R 64b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c +-+ +-+
+--R ((4a d - 16b c d)x + 8a c d - 32b c ) |----------- \|b \|c
+--R \| b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((- a d + 4b c d )x + (- 8a c d + 32b c d)x - 8a c d + 32b c )
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 2 +-----------+ +-+
+--R ((- 8a d + 32b c d)x - 16a c d + 64b c )\|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((2a d - 8b c d )x + (16a c d - 64b c d)x + 16a c d - 64b c )
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((24a c d - 32b c d)x + 48a c d - 64b c )\|b \|d x + c
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 6a d + 8b c d )x + (- 48a c d + 64b c d)x - 48a c d
+--R +
+--R 3
+--R 64b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((8a c d - 8b c d)x + 16a c d - 16b c )\|b \|d x + c
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((- 2a d + 2b c d )x + (- 16a c d + 16b c d)x - 16a c d + 16b c )
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 3 2 3 +-+ +-+ | 2
+--R (16a d x + 32a c)\|b \|c \|d x + c
+--R +
+--R 3 2 4 3 2 3 2 +-+
+--R (- 4a d x - 32a c d x - 32a c )\|b
+--R Type: Expression(Integer)
+--E 650
+
+--S 651 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 651
+
+--S 652 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((12a c d - 16b c d)x + 24a c d - 32b c )\|b \|d x + c
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 3a d + 4b c d )x + (- 24a c d + 32b c d)x - 24a c d
+--R +
+--R 3
+--R 32b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 2 +-----------+ +-+
+--R ((- 4a d + 16b c d)x - 8a c d + 32b c )\|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 4 2 2 2 2 3
+--R ((a d - 4b c d )x + (8a c d - 32b c d)x + 8a c d - 32b c )
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((12a c d - 16b c d)x + 24a c d - 32b c )\|b \|d x + c
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 3a d + 4b c d )x + (- 24a c d + 32b c d)x - 24a c d
+--R +
+--R 3
+--R 32b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +---------+
+--R 2 2 2 +-+ +-+ |a d - b c
+--R ((- 4a d + 16b c d)x - 8a c d + 32b c )\|b \|c |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 4 2 2 2 2 3 +-+
+--R ((a d - 4b c d )x + (8a c d - 32b c d)x + 8a c d - 32b c )\|b
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R +--------+
+--R 2 2 2 2 3 +-+ | 2
+--R ((4a c d - 4b c d)x + 8a c d - 8b c )\|b \|d x + c
+--R +
+--R 3 2 4 2 2 2 2 3 +-+ +-+
+--R ((- a d + b c d )x + (- 8a c d + 8b c d)x - 8a c d + 8b c )\|b \|c
+--R /
+--R +--------+
+--R 3 2 3 +-+ +-+ | 2
+--R (8a d x + 16a c)\|b \|c \|d x + c
+--R +
+--R 3 2 4 3 2 3 2 +-+
+--R (- 2a d x - 16a c d x - 16a c )\|b
+--R Type: Expression(Integer)
+--E 652
+
+--S 653 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 653
+
+)clear all
+
+--S 654 of 1527
+t0:=(c+d*x^2)^(3/2)/(x^4*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R Type: Expression(Integer)
+--E 654
+
+--S 655 of 1527
+r0:=1/2*(5*b*c-2*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*_
+ sqrt(b*c-a*d)/a^(7/2)-1/6*(5*b*c-3*a*d)*sqrt(c+d*x^2)/(a^2*b*x^3)+_
+ 1/6*(15*b*c-11*a*d)*sqrt(c+d*x^2)/(a^3*x)+1/2*(b*c-a*d)*_
+ sqrt(c+d*x^2)/(a*b*x^3*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 5 2 3 +-----------+
+--R ((- 6a b d + 15b c)x + (- 6a d + 15a b c)x )\|- a d + b c
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 4 2 2 2 +-+ | 2
+--R ((- 11a b d + 15b c)x + (- 8a d + 10a b c)x - 2a c)\|a \|d x + c
+--R /
+--R 3 5 4 3 +-+
+--R (6a b x + 6a x )\|a
+--R Type: Expression(Integer)
+--E 655
+
+--S 656 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 2 9 2 3 2 2 2 7
+--R (6a b d - 15b c d )x + (6a d + 57a b c d - 180b c d)x
+--R +
+--R 2 2 2 2 3 5 2 2 3 3
+--R (72a c d - 84a b c d - 240b c )x + (96a c d - 240a b c )x
+--R *
+--R +---------+ +--------+
+--R |a d - b c | 2
+--R |--------- \|d x + c
+--R \| a
+--R +
+--R 3 2 2 9
+--R (- 30a b d + 75b c d )x
+--R +
+--R 2 3 2 2 2 7
+--R (- 30a d - 45a b c d + 300b c d)x
+--R +
+--R 2 2 2 2 3 5
+--R (- 120a c d + 204a b c d + 240b c )x
+--R +
+--R 2 2 3 3
+--R (- 96a c d + 240a b c )x
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 3 2 2 8 2 3 2 2 2 6
+--R (110a b d - 150b c d )x + (80a d + 340a b c d - 600b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (340a c d - 48a b c d - 480b c )x + (336a c d - 320a b c )x
+--R +
+--R 2 3
+--R 64a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 4 2 3 10 2 4 3 2 2 2 8
+--R (- 22a b d + 30b c d )x + (- 16a d - 266a b c d + 390b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (- 212a c d - 356a b c d + 840b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (- 500a c d + 208a b c d + 480b c )x + (- 368a c d + 320a b c )x
+--R +
+--R 2 4
+--R - 64a c
+--R /
+--R 3 2 9 4 2 3 7 4 3 2 5
+--R 12a b d x + (12a d + 144a b c d)x + (144a c d + 192a b c )x
+--R +
+--R 4 2 3
+--R 192a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 9 4 2 3 7
+--R - 60a b d x + (- 60a d - 240a b c d)x
+--R +
+--R 4 3 2 5 4 2 3
+--R (- 240a c d - 192a b c )x - 192a c x
+--R *
+--R +-+
+--R \|c
+--R ,
+--R
+--R 3 2 2 9 2 3 2 2 2 7
+--R (6a b d - 15b c d )x + (6a d + 57a b c d - 180b c d)x
+--R +
+--R 2 2 2 2 3 5 2 2 3 3
+--R (72a c d - 84a b c d - 240b c )x + (96a c d - 240a b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 3 2 2 9
+--R (- 30a b d + 75b c d )x
+--R +
+--R 2 3 2 2 2 7
+--R (- 30a d - 45a b c d + 300b c d)x
+--R +
+--R 2 2 2 2 3 5
+--R (- 120a c d + 204a b c d + 240b c )x
+--R +
+--R 2 2 3 3
+--R (- 96a c d + 240a b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 3 2 2 9 2 3 2 2 2 7
+--R (- 6a b d + 15b c d )x + (- 6a d - 57a b c d + 180b c d)x
+--R +
+--R 2 2 2 2 3 5 2 2 3 3
+--R (- 72a c d + 84a b c d + 240b c )x + (- 96a c d + 240a b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 3 2 2 9 2 3 2 2 2 7
+--R (30a b d - 75b c d )x + (30a d + 45a b c d - 300b c d)x
+--R +
+--R 2 2 2 2 3 5 2 2 3 3
+--R (120a c d - 204a b c d - 240b c )x + (96a c d - 240a b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 3 2 2 8 2 3 2 2 2 6
+--R (55a b d - 75b c d )x + (40a d + 170a b c d - 300b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (170a c d - 24a b c d - 240b c )x + (168a c d - 160a b c )x
+--R +
+--R 2 3
+--R 32a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 4 2 3 10 2 4 3 2 2 2 8
+--R (- 11a b d + 15b c d )x + (- 8a d - 133a b c d + 195b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (- 106a c d - 178a b c d + 420b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (- 250a c d + 104a b c d + 240b c )x + (- 184a c d + 160a b c )x
+--R +
+--R 2 4
+--R - 32a c
+--R /
+--R 3 2 9 4 2 3 7 4 3 2 5
+--R 6a b d x + (6a d + 72a b c d)x + (72a c d + 96a b c )x
+--R +
+--R 4 2 3
+--R 96a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 9 4 2 3 7
+--R - 30a b d x + (- 30a d - 120a b c d)x
+--R +
+--R 4 3 2 5 4 2 3
+--R (- 120a c d - 96a b c )x - 96a c x
+--R *
+--R +-+
+--R \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 656
+
+--S 657 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-+ |a d - b c
+--R (2a d - 5b c)\|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (4a d - 10b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 657
+
+--S 658 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 658
+
+--S 659 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R |- a d + b c +-+
+--R (2a d - 5b c) |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c +-+ \|c
+--R (- 2a d + 5b c) |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (2a d - 5b c)\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 659
+
+--S 660 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 660
+
+)clear all
+
+--S 661 of 1527
+t0:=x^4*(c+d*x^2)^(5/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 8 6 2 4 | 2
+--R (d x + 2c d x + c x )\|d x + c
+--R (1) ----------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 661
+
+--S 662 of 1527
+r0:=2/3*d*x^3*(c+d*x^2)^(3/2)/b^2-1/2*x^3*(c+d*x^2)^(5/2)/(b*(a+b*x^2))-_
+ 1/2*(3*b*c-8*a*d)*(b*c-a*d)^(3/2)*atan(x*sqrt(b*c-a*d)/_
+ (sqrt(a)*sqrt(c+d*x^2)))*sqrt(a)/b^5+1/16*(5*b^3*c^3-_
+ 60*a*b^2*c^2*d+120*a^2*b*c*d^2-64*a^3*d^3)*atanh(x*sqrt(d)/_
+ sqrt(c+d*x^2))/(b^5*sqrt(d))+1/16*(19*b^2*c^2-52*a*b*c*d+_
+ 32*a^2*d^2)*x*sqrt(c+d*x^2)/b^4+1/8*d*(7*b*c-8*a*d)*x^3*sqrt(c+d*x^2)/b^3
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 192a b d + 360a b c d - 180a b c d + 15b c )x - 192a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 360a b c d - 180a b c d + 15a b c
+--R *
+--R +-+
+--R x\|d
+--R atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 3 2 2 3 2 2
+--R (- 192a b d + 264a b c d - 72b c )x - 192a d + 264a b c d
+--R +
+--R 2 2
+--R - 72a b c
+--R *
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+--R +-----------+ +-+ +-+ x\|- a d + b c
+--R \|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 4 2 7 3 2 4 5
+--R 8b d x + (- 16a b d + 26b c d)x
+--R +
+--R 2 2 2 3 4 2 3 3 2 2 2 3 2
+--R (48a b d - 82a b c d + 33b c )x + (96a b d - 156a b c d + 57a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R /
+--R 6 2 5 +-+
+--R (48b x + 48a b )\|d
+--R Type: Expression(Integer)
+--E 662
+
+--S 663 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 6 2 2 5 3 2 4 4 3 3 8
+--R (1536a b d - 2880a b c d + 1440a b c d - 120b c d )x
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+--R 1536a d + 12480a b c d - 27360a b c d + 14280a b c d
+--R +
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+--R - 1200b c d
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+--R x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2
+--R 15360a c d + 8064a b c d - 54720a b c d + 33360a b c d
+--R +
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+--R *
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+--R x
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+--R 4 2 4 3 3 3 2 2 4 2 3 5
+--R 36864a c d - 44544a b c d - 11520a b c d + 20160a b c d
+--R +
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+--R - 1920b c
+--R *
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+--R x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6
+--R 24576a c d - 46080a b c d + 23040a b c d - 1920a b c
+--R *
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+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 7 2 2 6 3 2 5 4 3 4 10
+--R (- 192a b d + 360a b c d - 180a b c d + 15b c d )x
+--R +
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+--R +
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+--R +
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+--R 2400b c d
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+--R +
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+--R x
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+--R 4 3 4 3 4 3 3 6 4 7 2
+--R (- 49152a c d + 67584a b c d - 19200a b c d + 1920b c )x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R - 24576a c d + 46080a b c d - 23040a b c d + 1920a b c
+--R *
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+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
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+--R \|c \|d x + c - c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (768a b d - 1056a b c d + 288b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (768a d + 6624a b c d - 10272a b c d + 2880b c d )x
+--R +
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+--R (7680a c d + 7872a b c d - 22464a b c d + 6912b c d)x
+--R +
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+--R (18432a c d - 13056a b c d - 9984a b c d + 4608b c )x
+--R +
+--R 3 3 2 2 4 2 5
+--R 12288a c d - 16896a b c d + 4608a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ +-+ | 2 | 2
+--R \|c \|d \|a d - a b c \|d x + c
+--R +
+--R 2 6 2 5 3 2 4 10
+--R (- 96a b d + 132a b c d - 36b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 8
+--R (- 96a d - 2940a b c d + 4188a b c d - 1152b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (- 3072a c d - 11136a b c d + 19968a b c d - 5760b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (- 15360a c d - 3456a b c d + 28032a b c d - 9216b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (- 24576a c d + 21504a b c d + 7680a b c d - 4608b c )x
+--R +
+--R 3 4 2 2 5 2 6
+--R - 12288a c d + 16896a b c d - 4608a b c
+--R *
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+--R +-+ | 2
+--R \|d \|a d - a b c
+--R *
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+--R 3 | 2
+--R (- 2d x - 4c x)\|a d - a b c
+--R +
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+--R ((4a d - 2b c)x + 2a c)\|c
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+--R \|d x + c
+--R +
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+--R 3 +-+ | 2 2 4
+--R (4d x + 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
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+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 4 6 15 3 6 4 5 13
+--R - 8b d x + (16a b d - 282b c d )x
+--R +
+--R 2 2 6 3 5 4 2 4 11
+--R (- 48a b d + 594a b c d - 2145b c d )x
+--R +
+--R 3 6 2 2 5 3 2 4 4 3 3 9
+--R (- 96a b d - 1380a b c d + 5127a b c d - 7264b c d )x
+--R +
+--R 3 5 2 2 2 4 3 3 3 4 4 2 7
+--R (- 3072a b c d - 2688a b c d + 15392a b c d - 12960b c d )x
+--R +
+--R 3 2 4 2 2 3 3 3 4 2 4 5 5
+--R (- 15360a b c d + 12672a b c d + 13920a b c d - 11776b c d)x
+--R +
+--R 3 3 3 2 2 4 2 3 5 4 6 3
+--R (- 24576a b c d + 33792a b c d - 4096a b c d - 4224b c )x
+--R +
+--R 3 4 2 2 2 5 3 6
+--R (- 12288a b c d + 19968a b c d - 7296a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 4 6 15 3 6 4 5 13
+--R 64b d x + (- 128a b d + 912b c d )x
+--R +
+--R 2 2 6 3 5 4 2 4 11
+--R (384a b d - 2064a b c d + 4728b c d )x
+--R +
+--R 3 6 2 2 5 3 2 4 4 3 3 9
+--R (768a b d + 2976a b c d - 11112a b c d + 12536b c d )x
+--R +
+--R 3 5 2 2 2 4 3 3 3 4 4 2 7
+--R (8448a b c d - 672a b c d - 22408a b c d + 18320b c d )x
+--R +
+--R 3 2 4 2 2 3 3 3 4 2 4 5 5
+--R (26112a b c d - 27072a b c d - 12784a b c d + 13888b c d)x
+--R +
+--R 3 3 3 2 2 4 2 3 5 4 6 3
+--R (30720a b c d - 43776a b c d + 7744a b c d + 4224b c )x
+--R +
+--R 3 4 2 2 2 5 3 6
+--R (12288a b c d - 19968a b c d + 7296a b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
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+--R 6 3 8 5 3 6 2 6
+--R 384b d x + (384a b d + 3840b c d )x
+--R +
+--R 5 2 6 2 4 5 2 6 3 2
+--R (3840a b c d + 9216b c d)x + (9216a b c d + 6144b c )x
+--R +
+--R 5 3
+--R 6144a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 6 4 10 5 4 6 3 8
+--R - 48b d x + (- 48a b d - 1536b c d )x
+--R +
+--R 5 3 6 2 2 6 5 2 2 6 3 4
+--R (- 1536a b c d - 7680b c d )x + (- 7680a b c d - 12288b c d)x
+--R +
+--R 5 3 6 4 2 5 4
+--R (- 12288a b c d - 6144b c )x - 6144a b c
+--R *
+--R +-+
+--R \|d
+--R ,
+--R
+--R 3 6 2 2 5 3 2 4 4 3 3 8
+--R (1536a b d - 2880a b c d + 1440a b c d - 120b c d )x
+--R +
+--R 4 6 3 5 2 2 2 4 3 3 3
+--R 1536a d + 12480a b c d - 27360a b c d + 14280a b c d
+--R +
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+--R - 1200b c d
+--R *
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+--R x
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+--R 4 5 3 2 4 2 2 3 3 3 4 2
+--R 15360a c d + 8064a b c d - 54720a b c d + 33360a b c d
+--R +
+--R 4 5
+--R - 2880b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5
+--R 36864a c d - 44544a b c d - 11520a b c d + 20160a b c d
+--R +
+--R 4 6
+--R - 1920b c
+--R *
+--R 2
+--R x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6
+--R 24576a c d - 46080a b c d + 23040a b c d - 1920a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 7 2 2 6 3 2 5 4 3 4 10
+--R (- 192a b d + 360a b c d - 180a b c d + 15b c d )x
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R - 192a d - 5784a b c d + 11340a b c d - 5745a b c d
+--R +
+--R 4 4 3
+--R 480b c d
+--R *
+--R 8
+--R x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3
+--R - 6144a c d - 19200a b c d + 51840a b c d - 28320a b c d
+--R +
+--R 4 5 2
+--R 2400b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R - 30720a c d + 8448a b c d + 63360a b c d - 43680a b c d
+--R +
+--R 4 6
+--R 3840b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 3 4 3 4 3 3 6 4 7 2
+--R (- 49152a c d + 67584a b c d - 19200a b c d + 1920b c )x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R - 24576a c d + 46080a b c d - 23040a b c d + 1920a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (1536a b d - 2112a b c d + 576b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (1536a d + 13248a b c d - 20544a b c d + 5760b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (15360a c d + 15744a b c d - 44928a b c d + 13824b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (36864a c d - 26112a b c d - 19968a b c d + 9216b c )x
+--R +
+--R 3 3 2 2 4 2 5
+--R 24576a c d - 33792a b c d + 9216a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ +-+ | 2
+--R \|- a d + a b c \|c \|d \|d x + c
+--R +
+--R 2 6 2 5 3 2 4 10
+--R (- 192a b d + 264a b c d - 72b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 8
+--R (- 192a d - 5880a b c d + 8376a b c d - 2304b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (- 6144a c d - 22272a b c d + 39936a b c d - 11520b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (- 30720a c d - 6912a b c d + 56064a b c d - 18432b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (- 49152a c d + 43008a b c d + 15360a b c d - 9216b c )x
+--R +
+--R 3 4 2 2 5 2 6
+--R - 24576a c d + 33792a b c d - 9216a b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 1536a b d + 2112a b c d - 576b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 1536a d - 13248a b c d + 20544a b c d - 5760b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 15360a c d - 15744a b c d + 44928a b c d - 13824b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (- 36864a c d + 26112a b c d + 19968a b c d - 9216b c )x
+--R +
+--R 3 3 2 2 4 2 5
+--R - 24576a c d + 33792a b c d - 9216a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ +-+ | 2
+--R \|- a d + a b c \|c \|d \|d x + c
+--R +
+--R 2 6 2 5 3 2 4 10
+--R (192a b d - 264a b c d + 72b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 8
+--R (192a d + 5880a b c d - 8376a b c d + 2304b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (6144a c d + 22272a b c d - 39936a b c d + 11520b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (30720a c d + 6912a b c d - 56064a b c d + 18432b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (49152a c d - 43008a b c d - 15360a b c d + 9216b c )x
+--R +
+--R 3 4 2 2 5 2 6
+--R 24576a c d - 33792a b c d + 9216a b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R 4 6 15 3 6 4 5 13
+--R - 8b d x + (16a b d - 282b c d )x
+--R +
+--R 2 2 6 3 5 4 2 4 11
+--R (- 48a b d + 594a b c d - 2145b c d )x
+--R +
+--R 3 6 2 2 5 3 2 4 4 3 3 9
+--R (- 96a b d - 1380a b c d + 5127a b c d - 7264b c d )x
+--R +
+--R 3 5 2 2 2 4 3 3 3 4 4 2 7
+--R (- 3072a b c d - 2688a b c d + 15392a b c d - 12960b c d )x
+--R +
+--R 3 2 4 2 2 3 3 3 4 2 4 5 5
+--R (- 15360a b c d + 12672a b c d + 13920a b c d - 11776b c d)x
+--R +
+--R 3 3 3 2 2 4 2 3 5 4 6 3
+--R (- 24576a b c d + 33792a b c d - 4096a b c d - 4224b c )x
+--R +
+--R 3 4 2 2 2 5 3 6
+--R (- 12288a b c d + 19968a b c d - 7296a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|d x + c
+--R +
+--R 4 6 15 3 6 4 5 13
+--R 64b d x + (- 128a b d + 912b c d )x
+--R +
+--R 2 2 6 3 5 4 2 4 11
+--R (384a b d - 2064a b c d + 4728b c d )x
+--R +
+--R 3 6 2 2 5 3 2 4 4 3 3 9
+--R (768a b d + 2976a b c d - 11112a b c d + 12536b c d )x
+--R +
+--R 3 5 2 2 2 4 3 3 3 4 4 2 7
+--R (8448a b c d - 672a b c d - 22408a b c d + 18320b c d )x
+--R +
+--R 3 2 4 2 2 3 3 3 4 2 4 5 5
+--R (26112a b c d - 27072a b c d - 12784a b c d + 13888b c d)x
+--R +
+--R 3 3 3 2 2 4 2 3 5 4 6 3
+--R (30720a b c d - 43776a b c d + 7744a b c d + 4224b c )x
+--R +
+--R 3 4 2 2 2 5 3 6
+--R (12288a b c d - 19968a b c d + 7296a b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 6 3 8 5 3 6 2 6
+--R 384b d x + (384a b d + 3840b c d )x
+--R +
+--R 5 2 6 2 4 5 2 6 3 2
+--R (3840a b c d + 9216b c d)x + (9216a b c d + 6144b c )x
+--R +
+--R 5 3
+--R 6144a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 6 4 10 5 4 6 3 8
+--R - 48b d x + (- 48a b d - 1536b c d )x
+--R +
+--R 5 3 6 2 2 6 5 2 2 6 3 4
+--R (- 1536a b c d - 7680b c d )x + (- 7680a b c d - 12288b c d)x
+--R +
+--R 5 3 6 4 2 5 4
+--R (- 12288a b c d - 6144b c )x - 6144a b c
+--R *
+--R +-+
+--R \|d
+--R ,
+--R
+--R 2 5 2 4 3 2 3 8
+--R (768a b d - 1056a b c d + 288b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (768a d + 6624a b c d - 10272a b c d + 2880b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (7680a c d + 7872a b c d - 22464a b c d + 6912b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (18432a c d - 13056a b c d - 9984a b c d + 4608b c )x
+--R +
+--R 3 3 2 2 4 2 5
+--R 12288a c d - 16896a b c d + 4608a b c
+--R *
+--R +-----------+ +--------+
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+--R \|- d \|c \|a d - a b c \|d x + c
+--R +
+--R 2 6 2 5 3 2 4 10
+--R (- 96a b d + 132a b c d - 36b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 8
+--R (- 96a d - 2940a b c d + 4188a b c d - 1152b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (- 3072a c d - 11136a b c d + 19968a b c d - 5760b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (- 15360a c d - 3456a b c d + 28032a b c d - 9216b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (- 24576a c d + 21504a b c d + 7680a b c d - 4608b c )x
+--R +
+--R 3 4 2 2 5 2 6
+--R - 12288a c d + 16896a b c d - 4608a b c
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+--R \|- d \|a d - a b c
+--R *
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+--R (- 2d x - 4c x)\|a d - a b c
+--R +
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+--R ((4a d - 2b c)x + 2a c)\|c
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+--R \|d x + c
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+--R 3 +-+ | 2 2 4
+--R (4d x + 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
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+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 3 6 2 2 5 3 2 4 4 3 3 8
+--R (- 3072a b d + 5760a b c d - 2880a b c d + 240b c d )x
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+--R 2400b c d
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+--R 4 5 3 2 4 2 2 3 3
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+--R 3 4 2 4 5
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+--R 4 2 4 3 3 3 2 2 4 2
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+--R - 40320a b c d + 3840b c
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+--R 4 3 3 3 4 2 2 2 5 3 6
+--R - 49152a c d + 92160a b c d - 46080a b c d + 3840a b c
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+--R (384a b d - 720a b c d + 360a b c d - 30b c d )x
+--R +
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+--R 384a d + 11568a b c d - 22680a b c d + 11490a b c d
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+--R x
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+--R 4 6 3 2 5 2 2 3 4 3 4 3
+--R 12288a c d + 38400a b c d - 103680a b c d + 56640a b c d
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+--R - 4800b c d
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+--R x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R 61440a c d - 16896a b c d - 126720a b c d + 87360a b c d
+--R +
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+--R 4 3 4 3 4 3 3 6 4 7 2
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+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R 49152a c d - 92160a b c d + 46080a b c d - 3840a b c
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+--R +---+ | 2 +---+ +-+
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+--R d x
+--R +
+--R 4 6 15 3 6 4 5 13
+--R - 8b d x + (16a b d - 282b c d )x
+--R +
+--R 2 2 6 3 5 4 2 4 11
+--R (- 48a b d + 594a b c d - 2145b c d )x
+--R +
+--R 3 6 2 2 5 3 2 4 4 3 3 9
+--R (- 96a b d - 1380a b c d + 5127a b c d - 7264b c d )x
+--R +
+--R 3 5 2 2 2 4 3 3 3 4 4 2 7
+--R (- 3072a b c d - 2688a b c d + 15392a b c d - 12960b c d )x
+--R +
+--R 3 2 4 2 2 3 3 3 4 2 4 5 5
+--R (- 15360a b c d + 12672a b c d + 13920a b c d - 11776b c d)x
+--R +
+--R 3 3 3 2 2 4 2 3 5 4 6 3
+--R (- 24576a b c d + 33792a b c d - 4096a b c d - 4224b c )x
+--R +
+--R 3 4 2 2 2 5 3 6
+--R (- 12288a b c d + 19968a b c d - 7296a b c )x
+--R *
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+--R +---+ | 2
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+--R +
+--R 4 6 15 3 6 4 5 13
+--R 64b d x + (- 128a b d + 912b c d )x
+--R +
+--R 2 2 6 3 5 4 2 4 11
+--R (384a b d - 2064a b c d + 4728b c d )x
+--R +
+--R 3 6 2 2 5 3 2 4 4 3 3 9
+--R (768a b d + 2976a b c d - 11112a b c d + 12536b c d )x
+--R +
+--R 3 5 2 2 2 4 3 3 3 4 4 2 7
+--R (8448a b c d - 672a b c d - 22408a b c d + 18320b c d )x
+--R +
+--R 3 2 4 2 2 3 3 3 4 2 4 5 5
+--R (26112a b c d - 27072a b c d - 12784a b c d + 13888b c d)x
+--R +
+--R 3 3 3 2 2 4 2 3 5 4 6 3
+--R (30720a b c d - 43776a b c d + 7744a b c d + 4224b c )x
+--R +
+--R 3 4 2 2 2 5 3 6
+--R (12288a b c d - 19968a b c d + 7296a b c )x
+--R *
+--R +---+ +-+
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+--R /
+--R 6 3 8 5 3 6 2 6
+--R 384b d x + (384a b d + 3840b c d )x
+--R +
+--R 5 2 6 2 4 5 2 6 3 2
+--R (3840a b c d + 9216b c d)x + (9216a b c d + 6144b c )x
+--R +
+--R 5 3
+--R 6144a b c
+--R *
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+--R +---+ +-+ | 2
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+--R +
+--R 6 4 10 5 4 6 3 8
+--R - 48b d x + (- 48a b d - 1536b c d )x
+--R +
+--R 5 3 6 2 2 6 5 2 2 6 3 4
+--R (- 1536a b c d - 7680b c d )x + (- 7680a b c d - 12288b c d)x
+--R +
+--R 5 3 6 4 2 5 4
+--R (- 12288a b c d - 6144b c )x - 6144a b c
+--R *
+--R +---+
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+--R ,
+--R
+--R 3 6 2 2 5 3 2 4 4 3 3 8
+--R (- 3072a b d + 5760a b c d - 2880a b c d + 240b c d )x
+--R +
+--R 4 6 3 5 2 2 2 4 3 3 3
+--R - 3072a d - 24960a b c d + 54720a b c d - 28560a b c d
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+--R x
+--R +
+--R 4 5 3 2 4 2 2 3 3
+--R - 30720a c d - 16128a b c d + 109440a b c d
+--R +
+--R 3 4 2 4 5
+--R - 66720a b c d + 5760b c d
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+--R x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2
+--R - 73728a c d + 89088a b c d + 23040a b c d
+--R +
+--R 3 5 4 6
+--R - 40320a b c d + 3840b c
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+--R x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6
+--R - 49152a c d + 92160a b c d - 46080a b c d + 3840a b c
+--R *
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+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 7 2 2 6 3 2 5 4 3 4 10
+--R (384a b d - 720a b c d + 360a b c d - 30b c d )x
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R 384a d + 11568a b c d - 22680a b c d + 11490a b c d
+--R +
+--R 4 4 3
+--R - 960b c d
+--R *
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+--R x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3
+--R 12288a c d + 38400a b c d - 103680a b c d + 56640a b c d
+--R +
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+--R - 4800b c d
+--R *
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+--R x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R 61440a c d - 16896a b c d - 126720a b c d + 87360a b c d
+--R +
+--R 4 6
+--R - 7680b c d
+--R *
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+--R x
+--R +
+--R 4 3 4 3 4 3 3 6 4 7 2
+--R (98304a c d - 135168a b c d + 38400a b c d - 3840b c )x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R 49152a c d - 92160a b c d + 46080a b c d - 3840a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (1536a b d - 2112a b c d + 576b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
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+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (15360a c d + 15744a b c d - 44928a b c d + 13824b c d)x
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+--R +
+--R 3 3 2 2 4 2 5
+--R 24576a c d - 33792a b c d + 9216a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +---+ +-+ | 2
+--R \|- a d + a b c \|- d \|c \|d x + c
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+--R 2 6 2 5 3 2 4 10
+--R (- 192a b d + 264a b c d - 72b c d )x
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+--R 3 6 2 5 2 2 4 3 3 3 8
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+--R 3 5 2 2 4 2 3 3 3 4 2 6
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+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (- 30720a c d - 6912a b c d + 56064a b c d - 18432b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (- 49152a c d + 43008a b c d + 15360a b c d - 9216b c )x
+--R +
+--R 3 4 2 2 5 2 6
+--R - 24576a c d + 33792a b c d - 9216a b c
+--R *
+--R +-------------+
+--R | 2 +---+
+--R \|- a d + a b c \|- d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 1536a b d + 2112a b c d - 576b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 1536a d - 13248a b c d + 20544a b c d - 5760b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 15360a c d - 15744a b c d + 44928a b c d - 13824b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (- 36864a c d + 26112a b c d + 19968a b c d - 9216b c )x
+--R +
+--R 3 3 2 2 4 2 5
+--R - 24576a c d + 33792a b c d - 9216a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +---+ +-+ | 2
+--R \|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R 2 6 2 5 3 2 4 10
+--R (192a b d - 264a b c d + 72b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 8
+--R (192a d + 5880a b c d - 8376a b c d + 2304b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (6144a c d + 22272a b c d - 39936a b c d + 11520b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (30720a c d + 6912a b c d - 56064a b c d + 18432b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (49152a c d - 43008a b c d - 15360a b c d + 9216b c )x
+--R +
+--R 3 4 2 2 5 2 6
+--R 24576a c d - 33792a b c d + 9216a b c
+--R *
+--R +-------------+
+--R | 2 +---+
+--R \|- a d + a b c \|- d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
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+--R +
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+--R - 8b d x + (16a b d - 282b c d )x
+--R +
+--R 2 2 6 3 5 4 2 4 11
+--R (- 48a b d + 594a b c d - 2145b c d )x
+--R +
+--R 3 6 2 2 5 3 2 4 4 3 3 9
+--R (- 96a b d - 1380a b c d + 5127a b c d - 7264b c d )x
+--R +
+--R 3 5 2 2 2 4 3 3 3 4 4 2 7
+--R (- 3072a b c d - 2688a b c d + 15392a b c d - 12960b c d )x
+--R +
+--R 3 2 4 2 2 3 3 3 4 2 4 5 5
+--R (- 15360a b c d + 12672a b c d + 13920a b c d - 11776b c d)x
+--R +
+--R 3 3 3 2 2 4 2 3 5 4 6 3
+--R (- 24576a b c d + 33792a b c d - 4096a b c d - 4224b c )x
+--R +
+--R 3 4 2 2 2 5 3 6
+--R (- 12288a b c d + 19968a b c d - 7296a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- d \|d x + c
+--R +
+--R 4 6 15 3 6 4 5 13
+--R 64b d x + (- 128a b d + 912b c d )x
+--R +
+--R 2 2 6 3 5 4 2 4 11
+--R (384a b d - 2064a b c d + 4728b c d )x
+--R +
+--R 3 6 2 2 5 3 2 4 4 3 3 9
+--R (768a b d + 2976a b c d - 11112a b c d + 12536b c d )x
+--R +
+--R 3 5 2 2 2 4 3 3 3 4 4 2 7
+--R (8448a b c d - 672a b c d - 22408a b c d + 18320b c d )x
+--R +
+--R 3 2 4 2 2 3 3 3 4 2 4 5 5
+--R (26112a b c d - 27072a b c d - 12784a b c d + 13888b c d)x
+--R +
+--R 3 3 3 2 2 4 2 3 5 4 6 3
+--R (30720a b c d - 43776a b c d + 7744a b c d + 4224b c )x
+--R +
+--R 3 4 2 2 2 5 3 6
+--R (12288a b c d - 19968a b c d + 7296a b c )x
+--R *
+--R +---+ +-+
+--R \|- d \|c
+--R /
+--R 6 3 8 5 3 6 2 6
+--R 384b d x + (384a b d + 3840b c d )x
+--R +
+--R 5 2 6 2 4 5 2 6 3 2
+--R (3840a b c d + 9216b c d)x + (9216a b c d + 6144b c )x
+--R +
+--R 5 3
+--R 6144a b c
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 6 4 10 5 4 6 3 8
+--R - 48b d x + (- 48a b d - 1536b c d )x
+--R +
+--R 5 3 6 2 2 6 5 2 2 6 3 4
+--R (- 1536a b c d - 7680b c d )x + (- 7680a b c d - 12288b c d)x
+--R +
+--R 5 3 6 4 2 5 4
+--R (- 12288a b c d - 6144b c )x - 6144a b c
+--R *
+--R +---+
+--R \|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 663
+
+--S 664 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (64a d - 120a b c d + 60a b c d - 5b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-+ | 2
+--R (32a d - 44a b c d + 12b c )\|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 3 | 2
+--R (- 2d x - 4c x)\|a d - a b c
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2 2 4
+--R (4d x + 4c x)\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|d
+--R (64a d - 120a b c d + 60a b c d - 5b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ +-+ +-+ x\|- a d + b c
+--R (64a d - 88a b c d + 24b c )\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 5 +-+
+--R 16b \|d
+--R Type: Expression(Integer)
+--E 664
+
+--S 665 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 665
+
+--S 666 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 3 3 2 2 2 2 3 3
+--R (64a d - 120a b c d + 60a b c d - 5b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d + d x)\|d x + c + (- d x - c)\|d - d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|d
+--R (64a d - 120a b c d + 60a b c d - 5b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-------------+
+--R 2 2 2 2 | 2 +-+
+--R (64a d - 88a b c d + 24b c )\|- a d + a b c \|d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R 2 2 2 2 | 2 +-+
+--R (- 64a d + 88a b c d - 24b c )\|- a d + a b c \|d
+--R *
+--R +-+
+--R a\|c
+--R atan(-----------------)
+--R +-------------+
+--R | 2
+--R x\|- a d + a b c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ +-+ +-+ x\|- a d + b c
+--R (64a d - 88a b c d + 24b c )\|- a d + b c \|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 5 +-+
+--R 16b \|d
+--R Type: Expression(Integer)
+--E 666
+
+--S 667 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 667
+
+)clear all
+
+--S 668 of 1527
+t0:=x^3*(c+d*x^2)^(5/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (d x + 2c d x + c x )\|d x + c
+--R (1) ----------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 668
+
+--S 669 of 1527
+r0:=1/6*(2*b*c-7*a*d)*(c+d*x^2)^(3/2)/b^3+1/10*(2*b*c-7*a*d)*_
+ (c+d*x^2)^(5/2)/(b^2*(b*c-a*d))+1/2*a*(c+d*x^2)^(7/2)/_
+ (b*(b*c-a*d)*(a+b*x^2))-1/2*(2*b*c-7*a*d)*(b*c-a*d)^(3/2)*_
+ atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/b^(9/2)+_
+ 1/2*(2*b*c-7*a*d)*(b*c-a*d)*sqrt(c+d*x^2)/b^4
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2
+--R (- 105a b d + 135a b c d - 30b c )x - 105a d + 135a b c d
+--R +
+--R 2 2
+--R - 30a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R +-----------+ \|b \|d x + c
+--R \|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 3 2 6 2 2 3 4
+--R 6b d x + (- 14a b d + 22b c d)x
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R (70a b d - 118a b c d + 46b c )x + 105a d - 170a b c d + 61a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R /
+--R 5 2 4 +-+
+--R (30b x + 30a b )\|b
+--R Type: Expression(Integer)
+--E 669
+
+--S 670 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 5 2 4 3 2 3 8
+--R (105a b d - 135a b c d + 30b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (105a d + 2385a b c d - 3210a b c d + 720b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (2520a c d + 5160a b c d - 10080a b c d + 2400b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (8400a c d - 4080a b c d - 6240a b c d + 1920b c )x
+--R +
+--R 3 3 2 2 4 2 5
+--R 6720a c d - 8640a b c d + 1920a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| b
+--R +
+--R 2 5 2 2 4 3 3 3 8
+--R (- 735a b c d + 945a b c d - 210b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (- 735a c d - 4935a b c d + 7350a b c d - 1680b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (- 5880a c d - 4200a b c d + 13440a b c d - 3360b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (- 11760a c d + 8400a b c d + 5280a b c d - 1920b c )x
+--R +
+--R 3 4 2 2 5 2 6
+--R - 6720a c d + 8640a b c d - 1920a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+
+--R ((- 2a b d - 4b c)x - 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (2b c d x + (6a b c d + 4b c )x + 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 3 5 12 2 5 3 2 4 10
+--R - 84b c d x + (196a b c d - 980b c d )x
+--R +
+--R 2 5 2 2 4 3 3 3 8
+--R (- 770a b c d + 2880a b c d - 4330b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (- 1260a c d - 760a b c d + 7460a b c d - 7920b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (- 6720a c d + 12000a b c d - 2880a b c d - 3360b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (- 6720a c d + 15360a b c d - 10560a b c d + 1920b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 6 14 2 6 3 5 12
+--R 12b d x + (- 28a b d + 344b c d )x
+--R +
+--R 2 6 2 5 3 2 4 10
+--R (140a b d - 936a b c d + 2440b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 8
+--R (210a d + 1690a b c d - 6310a b c d + 7750b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (3780a c d - 3320a b c d - 7340a b c d + 9840b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (10080a c d - 19680a b c d + 8160a b c d + 2400b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (6720a c d - 15360a b c d + 10560a b c d - 1920b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 5 3 8 4 3 5 2 6 4 2 5 2 4
+--R 60b d x + (60a b d + 1440b c d )x + (1440a b c d + 4800b c d)x
+--R +
+--R 4 2 5 3 2 4 3
+--R (4800a b c d + 3840b c )x + 3840a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 5 3 8 4 3 5 2 2 6
+--R - 420b c d x + (- 420a b c d - 3360b c d )x
+--R +
+--R 4 2 2 5 3 4 4 3 5 4 2
+--R (- 3360a b c d - 6720b c d)x + (- 6720a b c d - 3840b c )x
+--R +
+--R 4 4
+--R - 3840a b c
+--R ,
+--R
+--R 2 5 2 4 3 2 3 8
+--R (105a b d - 135a b c d + 30b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (105a d + 2385a b c d - 3210a b c d + 720b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (2520a c d + 5160a b c d - 10080a b c d + 2400b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (8400a c d - 4080a b c d - 6240a b c d + 1920b c )x
+--R +
+--R 3 3 2 2 4 2 5
+--R 6720a c d - 8640a b c d + 1920a b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 5 2 2 4 3 3 3 8
+--R (- 735a b c d + 945a b c d - 210b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (- 735a c d - 4935a b c d + 7350a b c d - 1680b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (- 5880a c d - 4200a b c d + 13440a b c d - 3360b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (- 11760a c d + 8400a b c d + 5280a b c d - 1920b c )x
+--R +
+--R 3 4 2 2 5 2 6
+--R - 6720a c d + 8640a b c d - 1920a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R 3 5 12 2 5 3 2 4 10
+--R - 42b c d x + (98a b c d - 490b c d )x
+--R +
+--R 2 5 2 2 4 3 3 3 8
+--R (- 385a b c d + 1440a b c d - 2165b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (- 630a c d - 380a b c d + 3730a b c d - 3960b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (- 3360a c d + 6000a b c d - 1440a b c d - 1680b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (- 3360a c d + 7680a b c d - 5280a b c d + 960b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 6 14 2 6 3 5 12
+--R 6b d x + (- 14a b d + 172b c d )x
+--R +
+--R 2 6 2 5 3 2 4 10
+--R (70a b d - 468a b c d + 1220b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 8
+--R (105a d + 845a b c d - 3155a b c d + 3875b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (1890a c d - 1660a b c d - 3670a b c d + 4920b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (5040a c d - 9840a b c d + 4080a b c d + 1200b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (3360a c d - 7680a b c d + 5280a b c d - 960b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 5 3 8 4 3 5 2 6 4 2 5 2 4
+--R 30b d x + (30a b d + 720b c d )x + (720a b c d + 2400b c d)x
+--R +
+--R 4 2 5 3 2 4 3
+--R (2400a b c d + 1920b c )x + 1920a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 5 3 8 4 3 5 2 2 6
+--R - 210b c d x + (- 210a b c d - 1680b c d )x
+--R +
+--R 4 2 2 5 3 4 4 3 5 4 2
+--R (- 1680a b c d - 3360b c d)x + (- 3360a b c d - 1920b c )x
+--R +
+--R 4 4
+--R - 1920a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 670
+
+--S 671 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 5 4 2 2 3 6
+--R (105a d - 135a b c d + 30b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (2520a c d - 3240a b c d + 720b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (8400a c d - 10800a b c d + 2400b c d)x + 6720a c d
+--R +
+--R 4 2 5
+--R - 8640a b c d + 1920b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ +-+ | 2
+--R |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 735a c d + 945a b c d - 210b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 5880a c d + 7560a b c d - 1680b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (- 11760a c d + 15120a b c d - 3360b c d)x - 6720a c d
+--R +
+--R 5 2 6
+--R 8640a b c d - 1920b c
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+
+--R ((- 2a b d - 4b c)x - 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (2b c d x + (6a b c d + 4b c )x + 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 5 4 2 2 3 6
+--R (210a d - 270a b c d + 60b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (5040a c d - 6480a b c d + 1440b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (16800a c d - 21600a b c d + 4800b c d)x + 13440a c d
+--R +
+--R 4 2 5
+--R - 17280a b c d + 3840b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 1470a c d + 1890a b c d - 420b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 11760a c d + 15120a b c d - 3360b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (- 23520a c d + 30240a b c d - 6720b c d)x - 13440a c d
+--R +
+--R 5 2 6
+--R 17280a b c d - 3840b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (210a c d - 340a b c d + 122b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (5040a c d - 8160a b c d + 2928b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (16800a c d - 27200a b c d + 9760b c d)x + 13440a c d
+--R +
+--R 5 2 6
+--R - 21760a b c d + 7808b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 1470a c d + 2380a b c d - 854b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 11760a c d + 19040a b c d - 6832b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (- 23520a c d + 38080a b c d - 13664b c d)x - 13440a c d
+--R +
+--R 5 2 6
+--R 21760a b c d - 7808b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 4 3 6 4 2 4 4 2 2 4 3 +-+ +-+ | 2
+--R (60b d x + 1440b c d x + 4800b c d x + 3840b c )\|b \|c \|d x + c
+--R +
+--R 4 3 6 4 2 2 4 4 3 2 4 4 +-+
+--R (- 420b c d x - 3360b c d x - 6720b c d x - 3840b c )\|b
+--R Type: Expression(Integer)
+--E 671
+
+--S 672 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 672
+
+--S 673 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 5 4 2 2 3 6
+--R (105a d - 135a b c d + 30b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (2520a c d - 3240a b c d + 720b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (8400a c d - 10800a b c d + 2400b c d)x + 6720a c d
+--R +
+--R 4 2 5
+--R - 8640a b c d + 1920b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 735a c d + 945a b c d - 210b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 5880a c d + 7560a b c d - 1680b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (- 11760a c d + 15120a b c d - 3360b c d)x - 6720a c d
+--R +
+--R 5 2 6
+--R 8640a b c d - 1920b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 5 4 2 2 3 6
+--R (105a d - 135a b c d + 30b c d )x
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (2520a c d - 3240a b c d + 720b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2
+--R (8400a c d - 10800a b c d + 2400b c d)x + 6720a c d
+--R +
+--R 4 2 5
+--R - 8640a b c d + 1920b c
+--R *
+--R +---------+ +--------+
+--R +-+ +-+ |a d - b c | 2
+--R \|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 735a c d + 945a b c d - 210b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 5880a c d + 7560a b c d - 1680b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (- 11760a c d + 15120a b c d - 3360b c d)x - 6720a c d
+--R +
+--R 5 2 6
+--R 8640a b c d - 1920b c
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|b |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (105a c d - 170a b c d + 61b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (2520a c d - 4080a b c d + 1464b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (8400a c d - 13600a b c d + 4880b c d)x + 6720a c d
+--R +
+--R 5 2 6
+--R - 10880a b c d + 3904b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 2 5 2 4 2 3 3 6
+--R (- 735a c d + 1190a b c d - 427b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 4
+--R (- 5880a c d + 9520a b c d - 3416b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2
+--R (- 11760a c d + 19040a b c d - 6832b c d)x - 6720a c d
+--R +
+--R 5 2 6
+--R 10880a b c d - 3904b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 4 3 6 4 2 4 4 2 2 4 3 +-+ +-+ | 2
+--R (30b d x + 720b c d x + 2400b c d x + 1920b c )\|b \|c \|d x + c
+--R +
+--R 4 3 6 4 2 2 4 4 3 2 4 4 +-+
+--R (- 210b c d x - 1680b c d x - 3360b c d x - 1920b c )\|b
+--R Type: Expression(Integer)
+--E 673
+
+--S 674 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 674
+
+)clear all
+
+--S 675 of 1527
+t0:=x^2*(c+d*x^2)^(5/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 6 4 2 2 | 2
+--R (d x + 2c d x + c x )\|d x + c
+--R (1) ----------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 675
+
+--S 676 of 1527
+r0:=3/4*d*x*(c+d*x^2)^(3/2)/b^2-1/2*x*(c+d*x^2)^(5/2)/(b*(a+b*x^2))+_
+ 1/2*(b*c-6*a*d)*(b*c-a*d)^(3/2)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*_
+ sqrt(c+d*x^2)))/(b^4*sqrt(a))+1/8*(15*b^2*c^2-40*a*b*c*d+24*_
+ a^2*d^2)*atanh(x*sqrt(d)/sqrt(c+d*x^2))*sqrt(d)/b^4+1/8*d*_
+ (11*b*c-12*a*d)*x*sqrt(c+d*x^2)/b^3
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2 2 2 +-+
+--R ((24a b d - 40a b c d + 15b c )x + 24a d - 40a b c d + 15a b c )\|a
+--R *
+--R +-+
+--R +-+ x\|d
+--R \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((24a b d - 28a b c d + 4b c )x + 24a d - 28a b c d + 4a b c )
+--R *
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R \|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 3 2 5 2 2 3 3 2 2 2 3 2
+--R (2b d x + (- 6a b d + 9b c d)x + (- 12a b d + 17a b c d - 4b c )x)
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 5 2 4 +-+
+--R (8b x + 8a b )\|a
+--R Type: Expression(Integer)
+--E 676
+
+--S 677 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 2 3 3 2 2 6
+--R (72a b d - 84a b c d + 12b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (72a d + 300a b c d - 436a b c d + 64b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (384a c d - 64a b c d - 384a b c d + 64b c )x + 384a c d
+--R +
+--R 2 3 2 4
+--R - 448a b c d + 64a b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| a
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 12a b d + 14a b c d - 2b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 12a d - 202a b c d + 250a b c d - 36b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 216a c d - 324a b c d + 636a b c d - 96b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2 3 3 2
+--R (- 576a c d + 288a b c d + 352a b c d - 64b c )x - 384a c d
+--R +
+--R 2 4 2 5
+--R 448a b c d - 64a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (144a b d - 240a b c d + 90b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (144a d + 528a b c d - 1190a b c d + 480b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (768a c d - 512a b c d - 800a b c d + 480b c )x + 768a c d
+--R +
+--R 2 3 2 4
+--R - 1280a b c d + 480a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 24a b d + 40a b c d - 15b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 24a d - 392a b c d + 705a b c d - 270b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 432a c d - 432a b c d + 1650a b c d - 720b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (- 1152a c d + 1152a b c d + 560a b c d - 480b c )x
+--R +
+--R 3 3 2 2 4 2 5
+--R - 768a c d + 1280a b c d - 480a b c
+--R *
+--R +-+
+--R \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R - 2b d x + (6a b d - 45b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (12a b d + 91a b c d - 254b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (216a b c d - 18a b c d - 424b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (576a b c d - 624a b c d - 96b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (384a b c d - 544a b c d + 128b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R 12b d x + (- 36a b d + 130b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (- 72a b d - 126a b c d + 446b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (- 456a b c d + 262a b c d + 488b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (- 768a b c d + 896a b c d + 32b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (- 384a b c d + 544a b c d - 128b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 5 2 6 4 2 5 4 4 5 2 2
+--R 48b d x + (48a b d + 256b c d)x + (256a b c d + 256b c )x
+--R +
+--R 4 2
+--R 256a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 5 3 8 4 3 5 2 6 4 2 5 2 4
+--R - 8b d x + (- 8a b d - 144b c d )x + (- 144a b c d - 384b c d)x
+--R +
+--R 4 2 5 3 2 4 3
+--R (- 384a b c d - 256b c )x - 256a b c
+--R ,
+--R
+--R 2 4 2 3 3 2 2 6
+--R (144a b d - 240a b c d + 90b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (144a d + 528a b c d - 1190a b c d + 480b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (768a c d - 512a b c d - 800a b c d + 480b c )x + 768a c d
+--R +
+--R 2 3 2 4
+--R - 1280a b c d + 480a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 24a b d + 40a b c d - 15b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 24a d - 392a b c d + 705a b c d - 270b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 432a c d - 432a b c d + 1650a b c d - 720b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (- 1152a c d + 1152a b c d + 560a b c d - 480b c )x
+--R +
+--R 3 3 2 2 4 2 5
+--R - 768a c d + 1280a b c d - 480a b c
+--R *
+--R +-+
+--R \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 144a b d + 168a b c d - 24b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 144a d - 600a b c d + 872a b c d - 128b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2
+--R (- 768a c d + 128a b c d + 768a b c d - 128b c )x
+--R +
+--R 3 2 2 2 3 2 4
+--R - 768a c d + 896a b c d - 128a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (24a b d - 28a b c d + 4b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (24a d + 404a b c d - 500a b c d + 72b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (432a c d + 648a b c d - 1272a b c d + 192b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2 3 3 2
+--R (1152a c d - 576a b c d - 704a b c d + 128b c )x + 768a c d
+--R +
+--R 2 4 2 5
+--R - 896a b c d + 128a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (144a b d - 168a b c d + 24b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (144a d + 600a b c d - 872a b c d + 128b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (768a c d - 128a b c d - 768a b c d + 128b c )x + 768a c d
+--R +
+--R 2 3 2 4
+--R - 896a b c d + 128a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 24a b d + 28a b c d - 4b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 24a d - 404a b c d + 500a b c d - 72b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 432a c d - 648a b c d + 1272a b c d - 192b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (- 1152a c d + 576a b c d + 704a b c d - 128b c )x
+--R +
+--R 3 3 2 2 4 2 5
+--R - 768a c d + 896a b c d - 128a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 3 5 11 2 5 3 4 9
+--R - 2b d x + (6a b d - 45b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (12a b d + 91a b c d - 254b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (216a b c d - 18a b c d - 424b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (576a b c d - 624a b c d - 96b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (384a b c d - 544a b c d + 128b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R 12b d x + (- 36a b d + 130b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (- 72a b d - 126a b c d + 446b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (- 456a b c d + 262a b c d + 488b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (- 768a b c d + 896a b c d + 32b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (- 384a b c d + 544a b c d - 128b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 5 2 6 4 2 5 4 4 5 2 2
+--R 48b d x + (48a b d + 256b c d)x + (256a b c d + 256b c )x
+--R +
+--R 4 2
+--R 256a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 5 3 8 4 3 5 2 6 4 2 5 2 4
+--R - 8b d x + (- 8a b d - 144b c d )x + (- 144a b c d - 384b c d)x
+--R +
+--R 4 2 5 3 2 4 3
+--R (- 384a b c d - 256b c )x - 256a b c
+--R ,
+--R
+--R 2 4 2 3 3 2 2 6
+--R (72a b d - 84a b c d + 12b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (72a d + 300a b c d - 436a b c d + 64b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (384a c d - 64a b c d - 384a b c d + 64b c )x + 384a c d
+--R +
+--R 2 3 2 4
+--R - 448a b c d + 64a b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| a
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 12a b d + 14a b c d - 2b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 12a d - 202a b c d + 250a b c d - 36b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 216a c d - 324a b c d + 636a b c d - 96b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2 3 3 2
+--R (- 576a c d + 288a b c d + 352a b c d - 64b c )x - 384a c d
+--R +
+--R 2 4 2 5
+--R 448a b c d - 64a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (288a b d - 480a b c d + 180b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (288a d + 1056a b c d - 2380a b c d + 960b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2
+--R (1536a c d - 1024a b c d - 1600a b c d + 960b c )x
+--R +
+--R 3 2 2 2 3 2 4
+--R 1536a c d - 2560a b c d + 960a b c
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 48a b d + 80a b c d - 30b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 48a d - 784a b c d + 1410a b c d - 540b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 864a c d - 864a b c d + 3300a b c d - 1440b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (- 2304a c d + 2304a b c d + 1120a b c d - 960b c )x
+--R +
+--R 3 3 2 2 4 2 5
+--R - 1536a c d + 2560a b c d - 960a b c
+--R *
+--R +---+
+--R \|- d
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 3 5 11 2 5 3 4 9
+--R - 2b d x + (6a b d - 45b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (12a b d + 91a b c d - 254b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (216a b c d - 18a b c d - 424b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (576a b c d - 624a b c d - 96b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (384a b c d - 544a b c d + 128b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 5 11 2 5 3 4 9
+--R 12b d x + (- 36a b d + 130b c d )x
+--R +
+--R 2 5 2 4 3 2 3 7
+--R (- 72a b d - 126a b c d + 446b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 5
+--R (- 456a b c d + 262a b c d + 488b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 3
+--R (- 768a b c d + 896a b c d + 32b c d)x
+--R +
+--R 2 3 2 2 4 3 5
+--R (- 384a b c d + 544a b c d - 128b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 5 2 6 4 2 5 4 4 5 2 2
+--R 48b d x + (48a b d + 256b c d)x + (256a b c d + 256b c )x
+--R +
+--R 4 2
+--R 256a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 5 3 8 4 3 5 2 6 4 2 5 2 4
+--R - 8b d x + (- 8a b d - 144b c d )x + (- 144a b c d - 384b c d)x
+--R +
+--R 4 2 5 3 2 4 3
+--R (- 384a b c d - 256b c )x - 256a b c
+--R ,
+--R
+--R 2 4 2 3 3 2 2 6
+--R (288a b d - 480a b c d + 180b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (288a d + 1056a b c d - 2380a b c d + 960b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2
+--R (1536a c d - 1024a b c d - 1600a b c d + 960b c )x
+--R +
+--R 3 2 2 2 3 2 4
+--R 1536a c d - 2560a b c d + 960a b c
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 48a b d + 80a b c d - 30b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 48a d - 784a b c d + 1410a b c d - 540b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 864a c d - 864a b c d + 3300a b c d - 1440b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (- 2304a c d + 2304a b c d + 1120a b c d - 960b c )x
+--R +
+--R 3 3 2 2 4 2 5
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+--R +---+
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+--R (1152a c d - 576a b c d - 704a b c d + 128b c )x + 768a c d
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+--R (216a b c d - 18a b c d - 424b c d )x
+--R +
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+--R 12b d x + (- 36a b d + 130b c d )x
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+--R 2 5 2 4 3 2 3 7
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+--R (- 456a b c d + 262a b c d + 488b c d )x
+--R +
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+--R (- 768a b c d + 896a b c d + 32b c d)x
+--R +
+--R 2 3 2 2 4 3 5
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+--R \|c
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+--R 5 2 6 4 2 5 4 4 5 2 2
+--R 48b d x + (48a b d + 256b c d)x + (256a b c d + 256b c )x
+--R +
+--R 4 2
+--R 256a b c
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+--R \|c \|d x + c
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+--R 5 3 8 4 3 5 2 6 4 2 5 2 4
+--R - 8b d x + (- 8a b d - 144b c d )x + (- 144a b c d - 384b c d)x
+--R +
+--R 4 2 5 3 2 4 3
+--R (- 384a b c d - 256b c )x - 256a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 677
+
+--S 678 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 2 2 2 2 +-+ |a d - b c
+--R (12a d - 14a b c d + 2b c )\|a |---------
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+--R (2a d x + 4a c x) |---------
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+--R +
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+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
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+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
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+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 2 2 +-+ +-+
+--R (24a d - 40a b c d + 15b c )\|a \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|d
+--R (- 24a d + 40a b c d - 15b c )\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (- 24a d + 28a b c d - 4b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 4 +-+
+--R 8b \|a
+--R Type: Expression(Integer)
+--E 678
+
+--S 679 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 679
+
+--S 680 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 2 2 2 +-+ +-+
+--R (24a d - 40a b c d + 15b c )\|a \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|d
+--R (- 24a d + 40a b c d - 15b c )\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 |- a d + b c +-+
+--R (- 24a d + 28a b c d - 4b c ) |----------- \|a
+--R \| a
+--R *
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+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R 2 2 2 2 |- a d + b c +-+ \|c
+--R (24a d - 28a b c d + 4b c ) |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (- 24a d + 28a b c d - 4b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 4 +-+
+--R 8b \|a
+--R Type: Expression(Integer)
+--E 680
+
+--S 681 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 681
+
+)clear all
+
+--S 682 of 1527
+t0:=x*(c+d*x^2)^(5/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 5 3 2 | 2
+--R (d x + 2c d x + c x)\|d x + c
+--R (1) ---------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 682
+
+--S 683 of 1527
+r0:=5/6*d*(c+d*x^2)^(3/2)/b^2-1/2*(c+d*x^2)^(5/2)/(b*(a+b*x^2))-_
+ 5/2*d*(b*c-a*d)^(3/2)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/_
+ b^(7/2)+5/2*d*(b*c-a*d)*sqrt(c+d*x^2)/b^3
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 +-----------+
+--R ((15a b d - 15b c d)x + 15a d - 15a b c d)\|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2 +-+
+--R (2b d x + (- 10a b d + 14b c d)x - 15a d + 20a b c d - 3b c )\|b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4 2 3 +-+
+--R (6b x + 6a b )\|b
+--R Type: Expression(Integer)
+--E 683
+
+--S 684 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 2 3 6
+--R (15a b d - 15a b c d )x
+--R +
+--R 3 4 2 3 2 2 2 4
+--R (15a d + 165a b c d - 180a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3
+--R (180a c d + 60a b c d - 240a b c d)x + 240a c d - 240a b c d
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| b
+--R +
+--R 2 4 2 2 3 6
+--R (- 75a b c d + 75a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 4
+--R (- 75a c d - 225a b c d + 300a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4 2 3 3 2
+--R (- 300a c d + 60a b c d + 240a b c d)x - 240a c d
+--R +
+--R 2 4
+--R 240a b c d
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| b
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+--R log
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+--R 2 4 2 |- a d + b c +-+
+--R ((2a b d + 4b c)x + 8a b c x ) |----------- \|c
+--R \| b
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
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+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (- 2b c d x + (- 6a b c d - 4b c )x - 8a b c x ) |-----------
+--R \| b
+--R /
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+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
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+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
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+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 4 8 2 4 2 2 3 3 3 2 6
+--R - 20a b c d x + (70a b c d - 180a b c d - 6b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (120a c d - 120a b c d - 120a b c d - 72b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (240a c d - 480a b c d + 240a b c d - 96b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 10 2 5 2 4 8
+--R 4a b d x + (- 20a b d + 80a b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 30a d - 70a b c d + 270a b c d + 30b c d )x
+--R +
+--R 3 4 2 2 3 3 4 4
+--R (- 240a c d + 360a b c d + 120b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (- 240a c d + 480a b c d - 240a b c d + 96b c )x
+--R *
+--R +-+
+--R \|c
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+--R 4 2 6 2 3 2 4 4 2 3 4 2 2
+--R 12a b d x + (12a b d + 144a b c d)x + (144a b c d + 192a b c )x
+--R +
+--R 2 3 2
+--R 192a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 4 2 6 2 3 2 4 2 4
+--R - 60a b c d x + (- 60a b c d - 240a b c d)x
+--R +
+--R 2 3 2 4 3 2 2 3 3
+--R (- 240a b c d - 192a b c )x - 192a b c
+--R ,
+--R
+--R 2 4 2 3 6
+--R (- 15a b d + 15a b c d )x
+--R +
+--R 3 4 2 3 2 2 2 4
+--R (- 15a d - 165a b c d + 180a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 2 3 2 2
+--R (- 180a c d - 60a b c d + 240a b c d)x - 240a c d
+--R +
+--R 2 3
+--R 240a b c d
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 4 2 2 3 6
+--R (75a b c d - 75a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 4
+--R (75a c d + 225a b c d - 300a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4 2 3 3 2 2 4
+--R (300a c d - 60a b c d - 240a b c d)x + 240a c d - 240a b c d
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R 2 4 8 2 4 2 2 3 3 3 2 6
+--R - 10a b c d x + (35a b c d - 90a b c d - 3b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (60a c d - 60a b c d - 60a b c d - 36b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (120a c d - 240a b c d + 120a b c d - 48b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 10 2 5 2 4 8
+--R 2a b d x + (- 10a b d + 40a b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 15a d - 35a b c d + 135a b c d + 15b c d )x
+--R +
+--R 3 4 2 2 3 3 4 4
+--R (- 120a c d + 180a b c d + 60b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 2
+--R (- 120a c d + 240a b c d - 120a b c d + 48b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 2 6 2 3 2 4 4 2 3 4 2 2
+--R 6a b d x + (6a b d + 72a b c d)x + (72a b c d + 96a b c )x
+--R +
+--R 2 3 2
+--R 96a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 4 2 6 2 3 2 4 2 4
+--R - 30a b c d x + (- 30a b c d - 120a b c d)x
+--R +
+--R 2 3 2 4 3 2 2 3 3
+--R (- 120a b c d - 96a b c )x - 96a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 684
+
+--S 685 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 4 3 4 2 3 2 2 2 2 2 2
+--R (15a d - 15a b c d )x + (180a c d - 180a b c d )x + 240a c d
+--R +
+--R 3
+--R - 240a b c d
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ +-+ | 2
+--R |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R 2 4 2 3 4 2 2 3 3 2 2
+--R (- 75a c d + 75a b c d )x + (- 300a c d + 300a b c d )x
+--R +
+--R 2 3 2 4
+--R - 240a c d + 240a b c d
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 2 4
+--R ((2a b d + 4b c)x + 8a b c x ) |----------- \|c + 4b c x
+--R \| b
+--R +
+--R 2 2 2 2 2
+--R (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-----------+
+--R 2 6 2 2 4 2 2 |- a d + b c
+--R (- 2b c d x + (- 6a b c d - 4b c )x - 8a b c x ) |-----------
+--R \| b
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 4 3 4 2 3 2 2 2
+--R (- 30a d + 30a b c d )x + (- 360a c d + 360a b c d )x
+--R +
+--R 2 2 2 3
+--R - 480a c d + 480a b c d
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 4 2 3 4 2 2 3 3 2 2
+--R (150a c d - 150a b c d )x + (600a c d - 600a b c d )x
+--R +
+--R 2 3 2 4
+--R 480a c d - 480a b c d
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 30a c d + 40a b c d - 6b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (- 360a c d + 480a b c d - 72b c d)x - 480a c d + 640a b c d
+--R +
+--R 2 5
+--R - 96b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (150a c d - 200a b c d + 30b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (600a c d - 800a b c d + 120b c d)x + 480a c d - 640a b c d
+--R +
+--R 2 5
+--R 96b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 3 2 4 3 2 3 2 +-+ +-+ | 2
+--R (12a b d x + 144a b c d x + 192a b c )\|b \|c \|d x + c
+--R +
+--R 3 2 4 3 2 2 3 3 +-+
+--R (- 60a b c d x - 240a b c d x - 192a b c )\|b
+--R Type: Expression(Integer)
+--E 685
+
+--S 686 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 686
+
+--S 687 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 4 3 4 2 3 2 2 2
+--R (- 15a d + 15a b c d )x + (- 180a c d + 180a b c d )x
+--R +
+--R 2 2 2 3
+--R - 240a c d + 240a b c d
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 4 2 3 4 2 2 3 3 2 2
+--R (75a c d - 75a b c d )x + (300a c d - 300a b c d )x
+--R +
+--R 2 3 2 4
+--R 240a c d - 240a b c d
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 4 3 4 2 3 2 2 2
+--R (- 15a d + 15a b c d )x + (- 180a c d + 180a b c d )x
+--R +
+--R 2 2 2 3
+--R - 240a c d + 240a b c d
+--R *
+--R +---------+ +--------+
+--R +-+ +-+ |a d - b c | 2
+--R \|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 4 2 3 4 2 2 3 3 2 2
+--R (75a c d - 75a b c d )x + (300a c d - 300a b c d )x
+--R +
+--R 2 3 2 4
+--R 240a c d - 240a b c d
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|b |---------
+--R \| b
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 |a d - b c
+--R b x |---------
+--R \| b
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (- 15a c d + 20a b c d - 3b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4
+--R (- 180a c d + 240a b c d - 36b c d)x - 240a c d + 320a b c d
+--R +
+--R 2 5
+--R - 48b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (75a c d - 100a b c d + 15b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (300a c d - 400a b c d + 60b c d)x + 240a c d - 320a b c d + 48b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 3 2 4 3 2 3 2 +-+ +-+ | 2
+--R (6a b d x + 72a b c d x + 96a b c )\|b \|c \|d x + c
+--R +
+--R 3 2 4 3 2 2 3 3 +-+
+--R (- 30a b c d x - 120a b c d x - 96a b c )\|b
+--R Type: Expression(Integer)
+--E 687
+
+--S 688 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 688
+
+)clear all
+
+--S 689 of 1527
+t0:=(c+d*x^2)^(5/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 689
+
+--S 690 of 1527
+r0:=1/2*(b*c-a*d)*x*(c+d*x^2)^(3/2)/(a*b*(a+b*x^2))+1/2*(b*c-a*d)^(3/2)*_
+ (b*c+4*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/_
+ (a^(3/2)*b^3)+1/2*d^(3/2)*(5*b*c-4*a*d)*atanh(x*sqrt(d)/_
+ sqrt(c+d*x^2))/b^3-1/2*d*(b*c-2*a*d)*x*sqrt(c+d*x^2)/(a*b^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 3 2 2 +-+ +-+ x\|d
+--R ((- 4a b d + 5a b c d)x - 4a d + 5a b c d)\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 4a b d + 3a b c d + b c )x - 4a d + 3a b c d + a b c )
+--R *
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R \|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 2 3 2 2 2 3 2 +-+ | 2
+--R (a b d x + (2a b d - 2a b c d + b c )x)\|a \|d x + c
+--R /
+--R 4 2 2 3 +-+
+--R (2a b x + 2a b )\|a
+--R Type: Expression(Integer)
+--E 690
+
+--S 691 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (32a b d - 40a b c d )x + (32a d + 24a b c d - 80a b c d)x
+--R +
+--R 3 2 2 2
+--R 64a c d - 80a b c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 2 4 2 3 6
+--R (- 8a b d + 10a b c d )x
+--R +
+--R 3 4 2 3 2 2 2 4
+--R (- 8a d - 54a b c d + 80a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3
+--R (- 64a c d + 16a b c d + 80a b c d)x - 64a c d + 80a b c d
+--R *
+--R +-+
+--R \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 3 2 2 3 2 4
+--R (16a b d - 12a b c d - 4b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2
+--R (16a d + 20a b c d - 28a b c d - 8b c )x + 32a c d
+--R +
+--R 2 2 2 3
+--R - 24a b c d - 8a b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| a
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 4a b d + 3a b c d + b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 4a d - 29a b c d + 25a b c d + 8b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 32a c d - 8a b c d + 32a b c d + 8b c )x - 32a c d
+--R +
+--R 2 3 2 4
+--R 24a b c d + 8a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 4 7 2 4 2 3 3 2 2 5
+--R - 2a b d x + (- 4a b d - 12a b c d - 2b c d )x
+--R +
+--R 2 3 2 2 2 3 3 3
+--R (- 32a b c d + 16a b c d - 16b c d)x
+--R +
+--R 2 2 2 2 3 3 4
+--R (- 32a b c d + 32a b c d - 16b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 7 2 4 2 3 3 2 2 5
+--R 8a b d x + (16a b d + 8a b c d + 8b c d )x
+--R +
+--R 2 3 2 2 2 3 3 3
+--R (48a b c d - 32a b c d + 24b c d)x
+--R +
+--R 2 2 2 2 3 3 4
+--R (32a b c d - 32a b c d + 16b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 4 2 3 4 2 2 3 +-+ | 2
+--R (16a b d x + (16a b d + 32a b c)x + 32a b c)\|c \|d x + c
+--R +
+--R 4 2 6 2 3 2 4 4 2 3 4 2 2
+--R - 4a b d x + (- 4a b d - 32a b c d)x + (- 32a b c d - 32a b c )x
+--R +
+--R 2 3 2
+--R - 32a b c
+--R ,
+--R
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (16a b d - 20a b c d )x + (16a d + 12a b c d - 40a b c d)x
+--R +
+--R 3 2 2 2
+--R 32a c d - 40a b c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|c \|d \|d x + c
+--R +
+--R 2 4 2 3 6
+--R (- 4a b d + 5a b c d )x
+--R +
+--R 3 4 2 3 2 2 2 4
+--R (- 4a d - 27a b c d + 40a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3
+--R (- 32a c d + 8a b c d + 40a b c d)x - 32a c d + 40a b c d
+--R *
+--R +-+
+--R \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 3 2 2 3 2 4
+--R (16a b d - 12a b c d - 4b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2
+--R (16a d + 20a b c d - 28a b c d - 8b c )x + 32a c d
+--R +
+--R 2 2 2 3
+--R - 24a b c d - 8a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 4a b d + 3a b c d + b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 4a d - 29a b c d + 25a b c d + 8b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 32a c d - 8a b c d + 32a b c d + 8b c )x - 32a c d
+--R +
+--R 2 3 2 4
+--R 24a b c d + 8a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 2 3 2 2 3 2 4
+--R (- 16a b d + 12a b c d + 4b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2
+--R (- 16a d - 20a b c d + 28a b c d + 8b c )x - 32a c d
+--R +
+--R 2 2 2 3
+--R 24a b c d + 8a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (4a b d - 3a b c d - b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (4a d + 29a b c d - 25a b c d - 8b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (32a c d + 8a b c d - 32a b c d - 8b c )x + 32a c d
+--R +
+--R 2 3 2 4
+--R - 24a b c d - 8a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 4 7 2 4 2 3 3 2 2 5
+--R - a b d x + (- 2a b d - 6a b c d - b c d )x
+--R +
+--R 2 3 2 2 2 3 3 3
+--R (- 16a b c d + 8a b c d - 8b c d)x
+--R +
+--R 2 2 2 2 3 3 4
+--R (- 16a b c d + 16a b c d - 8b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 7 2 4 2 3 3 2 2 5
+--R 4a b d x + (8a b d + 4a b c d + 4b c d )x
+--R +
+--R 2 3 2 2 2 3 3 3
+--R (24a b c d - 16a b c d + 12b c d)x
+--R +
+--R 2 2 2 2 3 3 4
+--R (16a b c d - 16a b c d + 8b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 4 2 3 4 2 2 3 +-+ | 2 4 2 6
+--R (8a b d x + (8a b d + 16a b c)x + 16a b c)\|c \|d x + c - 2a b d x
+--R +
+--R 2 3 2 4 4 2 3 4 2 2 2 3 2
+--R (- 2a b d - 16a b c d)x + (- 16a b c d - 16a b c )x - 16a b c
+--R ,
+--R
+--R 2 3 2 2 3 2 4
+--R (16a b d - 12a b c d - 4b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2
+--R (16a d + 20a b c d - 28a b c d - 8b c )x + 32a c d
+--R +
+--R 2 2 2 3
+--R - 24a b c d - 8a b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| a
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 4a b d + 3a b c d + b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 4a d - 29a b c d + 25a b c d + 8b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 32a c d - 8a b c d + 32a b c d + 8b c )x - 32a c d
+--R +
+--R 2 3 2 4
+--R 24a b c d + 8a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 4
+--R (- 64a b d + 80a b c d )x
+--R +
+--R 3 3 2 2 2 2 2 3 2 2 2
+--R (- 64a d - 48a b c d + 160a b c d)x - 128a c d + 160a b c d
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 2 4 2 3 6
+--R (16a b d - 20a b c d )x
+--R +
+--R 3 4 2 3 2 2 2 4
+--R (16a d + 108a b c d - 160a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3
+--R (128a c d - 32a b c d - 160a b c d)x + 128a c d - 160a b c d
+--R *
+--R +---+
+--R \|- d
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 2 4 7 2 4 2 3 3 2 2 5
+--R - 2a b d x + (- 4a b d - 12a b c d - 2b c d )x
+--R +
+--R 2 3 2 2 2 3 3 3
+--R (- 32a b c d + 16a b c d - 16b c d)x
+--R +
+--R 2 2 2 2 3 3 4
+--R (- 32a b c d + 32a b c d - 16b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 7 2 4 2 3 3 2 2 5
+--R 8a b d x + (16a b d + 8a b c d + 8b c d )x
+--R +
+--R 2 3 2 2 2 3 3 3
+--R (48a b c d - 32a b c d + 24b c d)x
+--R +
+--R 2 2 2 2 3 3 4
+--R (32a b c d - 32a b c d + 16b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 4 2 3 4 2 2 3 +-+ | 2
+--R (16a b d x + (16a b d + 32a b c)x + 32a b c)\|c \|d x + c
+--R +
+--R 4 2 6 2 3 2 4 4 2 3 4 2 2
+--R - 4a b d x + (- 4a b d - 32a b c d)x + (- 32a b c d - 32a b c )x
+--R +
+--R 2 3 2
+--R - 32a b c
+--R ,
+--R
+--R 2 3 2 2 4
+--R (- 32a b d + 40a b c d )x
+--R +
+--R 3 3 2 2 2 2 2 3 2 2 2
+--R (- 32a d - 24a b c d + 80a b c d)x - 64a c d + 80a b c d
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- d \|c \|d x + c
+--R +
+--R 2 4 2 3 6 3 4 2 3 2 2 2 4
+--R (8a b d - 10a b c d )x + (8a d + 54a b c d - 80a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3
+--R (64a c d - 16a b c d - 80a b c d)x + 64a c d - 80a b c d
+--R *
+--R +---+
+--R \|- d
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 2 3 2 2 3 2 4
+--R (16a b d - 12a b c d - 4b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2
+--R (16a d + 20a b c d - 28a b c d - 8b c )x + 32a c d
+--R +
+--R 2 2 2 3
+--R - 24a b c d - 8a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 4a b d + 3a b c d + b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 4a d - 29a b c d + 25a b c d + 8b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 32a c d - 8a b c d + 32a b c d + 8b c )x - 32a c d
+--R +
+--R 2 3 2 4
+--R 24a b c d + 8a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 2 3 2 2 3 2 4
+--R (- 16a b d + 12a b c d + 4b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2
+--R (- 16a d - 20a b c d + 28a b c d + 8b c )x - 32a c d
+--R +
+--R 2 2 2 3
+--R 24a b c d + 8a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| a
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (4a b d - 3a b c d - b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (4a d + 29a b c d - 25a b c d - 8b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (32a c d + 8a b c d - 32a b c d - 8b c )x + 32a c d
+--R +
+--R 2 3 2 4
+--R - 24a b c d - 8a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 4 7 2 4 2 3 3 2 2 5
+--R - a b d x + (- 2a b d - 6a b c d - b c d )x
+--R +
+--R 2 3 2 2 2 3 3 3
+--R (- 16a b c d + 8a b c d - 8b c d)x
+--R +
+--R 2 2 2 2 3 3 4
+--R (- 16a b c d + 16a b c d - 8b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 7 2 4 2 3 3 2 2 5
+--R 4a b d x + (8a b d + 4a b c d + 4b c d )x
+--R +
+--R 2 3 2 2 2 3 3 3
+--R (24a b c d - 16a b c d + 12b c d)x
+--R +
+--R 2 2 2 2 3 3 4
+--R (16a b c d - 16a b c d + 8b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 4 2 3 4 2 2 3 +-+ | 2 4 2 6
+--R (8a b d x + (8a b d + 16a b c)x + 16a b c)\|c \|d x + c - 2a b d x
+--R +
+--R 2 3 2 4 4 2 3 4 2 2 2 3 2
+--R (- 2a b d - 16a b c d)x + (- 16a b c d - 16a b c )x - 16a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 691
+
+--S 692 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 +-+ +-+
+--R (8a d - 10a b c d)\|a \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+
+--R 2 2 2 2 +-+ |a d - b c
+--R (4a d - 3a b c d - b c )\|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (8a d - 10a b c d)\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (8a d - 6a b c d - 2b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 4a b \|a
+--R Type: Expression(Integer)
+--E 692
+
+--S 693 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 693
+
+--S 694 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 2 +-+ +-+
+--R (4a d - 5a b c d)\|a \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (x\|d + \|c )\|d x + c - x\|c \|d - d x - c
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (4a d - 5a b c d)\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 |- a d + b c +-+
+--R (4a d - 3a b c d - b c ) |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R 2 2 2 2 |- a d + b c +-+ \|c
+--R (- 4a d + 3a b c d + b c ) |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (4a d - 3a b c d - b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 2a b \|a
+--R Type: Expression(Integer)
+--E 694
+
+--S 695 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 695
+
+)clear all
+
+--S 696 of 1527
+t0:=(c+d*x^2)^(5/2)/(x*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R Type: Expression(Integer)
+--E 696
+
+--S 697 of 1527
+r0:=1/2*(b*c-a*d)*(c+d*x^2)^(3/2)/(a*b*(a+b*x^2))-c^(5/2)*_
+ atanh(sqrt(c+d*x^2)/sqrt(c))/a^2+1/2*(b*c-a*d)^(3/2)*(2*b*c+3*a*d)*_
+ atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/(a^2*b^(5/2))-_
+ 1/2*d*(b*c-3*a*d)*sqrt(c+d*x^2)/(a*b^2)
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 3a b d + a b c d + 2b c )x - 3a d + a b c d + 2a b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R +-----------+ \|b \|d x + c
+--R \|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R 3 2 2 2 2 +-+ +-+ \|d x + c
+--R (- 2b c x - 2a b c )\|b \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 2 3 2 2 2 2 +-+ | 2
+--R (2a b d x + 3a d - 2a b c d + a b c )\|b \|d x + c
+--R /
+--R 2 3 2 3 2 +-+
+--R (2a b x + 2a b )\|b
+--R Type: Expression(Integer)
+--E 697
+
+--S 698 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 3 4 2 3 3 4 2 2 4 | 2
+--R (4b c d x + (4a b c d + 16b c )x + 16a b c )\|d x + c
+--R +
+--R 3 3 4 2 3 3 4 2 2 4 +-+
+--R (- 12b c d x + (- 12a b c d - 16b c )x - 16a b c )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 3 2 4
+--R (3a b d - a b c d - 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (3a d + 11a b c d - 6a b c d - 8b c )x + 12a c d - 4a b c d
+--R +
+--R 2 3
+--R - 8a b c
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 2 3 3 4
+--R (- 9a b c d + 3a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 9a c d - 9a b c d + 10a b c d + 8b c )x - 12a c d
+--R +
+--R 2 3 2 4
+--R 4a b c d + 8a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c - 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (2b x + 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 3 3 4
+--R (- 6a b c d - 4a b c d + 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2
+--R (- 12a c d + 16a b c d - 20a b c d + 8b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 6 3 4 2 3 2 2 2 3 3 4
+--R 4a b d x + (6a d - 2a b c d + 14a b c d - 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2
+--R (12a c d - 16a b c d + 20a b c d - 8b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 2 3 4 3 2 2 3 2 3 2 +-+ | 2
+--R (4a b d x + (4a b d + 16a b c)x + 16a b c)\|c \|d x + c
+--R +
+--R 2 3 4 3 2 2 3 2 2 3 2 2
+--R - 12a b c d x + (- 12a b c d - 16a b c )x - 16a b c
+--R ,
+--R
+--R +--------+
+--R 3 3 4 2 3 3 4 2 2 4 | 2
+--R (2b c d x + (2a b c d + 8b c )x + 8a b c )\|d x + c
+--R +
+--R 3 3 4 2 3 3 4 2 2 4 +-+
+--R (- 6b c d x + (- 6a b c d - 8b c )x - 8a b c )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 3 2 4
+--R (3a b d - a b c d - 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (3a d + 11a b c d - 6a b c d - 8b c )x + 12a c d - 4a b c d
+--R +
+--R 2 3
+--R - 8a b c
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 2 3 3 4
+--R (- 9a b c d + 3a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 9a c d - 9a b c d + 10a b c d + 8b c )x - 12a c d
+--R +
+--R 2 3 2 4
+--R 4a b c d + 8a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R 2 3 2 2 2 3 3 4
+--R (- 3a b c d - 2a b c d + b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2
+--R (- 6a c d + 8a b c d - 10a b c d + 4b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 6 3 4 2 3 2 2 2 3 3 4
+--R 2a b d x + (3a d - a b c d + 7a b c d - 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2
+--R (6a c d - 8a b c d + 10a b c d - 4b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 2 3 4 3 2 2 3 2 3 2 +-+ | 2 2 3 4
+--R (2a b d x + (2a b d + 8a b c)x + 8a b c)\|c \|d x + c - 6a b c d x
+--R +
+--R 3 2 2 3 2 2 3 2 2
+--R (- 6a b c d - 8a b c )x - 8a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 698
+
+--S 699 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 3 2 2 4 +-+ | 2 2 3 2 2 4 +-+ +-+
+--R ((4b c d x + 16b c )\|b \|d x + c + (- 12b c d x - 16b c )\|b \|c )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d - a b c d - 2b c d)x + 12a c d - 4a b c d - 8b c )
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ +-+ | 2
+--R |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 9a c d + 3a b c d + 6b c d)x - 12a c d + 4a b c d + 8b c )
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c - 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (2b x + 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((6a d - 2a b c d - 4b c d)x + 24a c d - 8a b c d - 16b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R (- 18a c d + 6a b c d + 12b c d)x - 24a c d + 8a b c d
+--R +
+--R 2 4
+--R 16b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 3 2 2 4 +-+ | 2 2 3 2 2 4 +-+ +-+
+--R ((4b c d x + 16b c )\|b \|d x + c + (- 12b c d x - 16b c )\|b \|c )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4 +-+
+--R ((6a c d - 4a b c d + 2b c d)x + 24a c d - 16a b c d + 8b c )\|b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 18a c d + 12a b c d - 6b c d)x - 24a c d + 16a b c d - 8b c )
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 2 2 2 2 2 +-+ +-+ | 2 2 2 2 2 2 2 +-+
+--R (4a b d x + 16a b c)\|b \|c \|d x + c + (- 12a b c d x - 16a b c )\|b
+--R Type: Expression(Integer)
+--E 699
+
+--S 700 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 700
+
+--S 701 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 3 2 2 4 +-+ | 2 2 3 2 2 4 +-+ +-+
+--R ((2b c d x + 8b c )\|b \|d x + c + (- 6b c d x - 8b c )\|b \|c )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((3a d - a b c d - 2b c d)x + 12a c d - 4a b c d - 8b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 9a c d + 3a b c d + 6b c d)x - 12a c d + 4a b c d + 8b c )
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 3 2 2 4 +-+ | 2 2 3 2 2 4 +-+ +-+
+--R ((2b c d x + 8b c )\|b \|d x + c + (- 6b c d x - 8b c )\|b \|c )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3 +-+
+--R ((3a d - a b c d - 2b c d)x + 12a c d - 4a b c d - 8b c )\|b
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 9a c d + 3a b c d + 6b c d)x - 12a c d + 4a b c d + 8b c )
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|b |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4 +-+
+--R ((3a c d - 2a b c d + b c d)x + 12a c d - 8a b c d + 4b c )\|b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4 +-+ +-+
+--R ((- 9a c d + 6a b c d - 3b c d)x - 12a c d + 8a b c d - 4b c )\|b \|c
+--R /
+--R +--------+
+--R 2 2 2 2 2 +-+ +-+ | 2 2 2 2 2 2 2 +-+
+--R (2a b d x + 8a b c)\|b \|c \|d x + c + (- 6a b c d x - 8a b c )\|b
+--R Type: Expression(Integer)
+--E 701
+
+--S 702 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 702
+
+)clear all
+
+--S 703 of 1527
+t0:=(c+d*x^2)^(5/2)/(x^2*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R Type: Expression(Integer)
+--E 703
+
+--S 704 of 1527
+r0:=1/2*(b*c-a*d)*(c+d*x^2)^(3/2)/(a*b*x*(a+b*x^2))-1/2*(b*c-a*d)^(3/2)*_
+ (3*b*c+2*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/_
+ (a^(5/2)*b^2)+d^(5/2)*atanh(x*sqrt(d)/sqrt(c+d*x^2))/b^2-_
+ 1/2*c*(3*b*c-a*d)*sqrt(c+d*x^2)/(a^2*b*x)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 3 3 2 +-+ +-+ x\|d
+--R (2a b d x + 2a d x)\|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((2a b d + a b c d - 3b c )x + (2a d + a b c d - 3a b c )x)
+--R *
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R \|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 2 2 3 2 2 2 2 +-+ | 2
+--R ((- a b d + 2a b c d - 3b c )x - 2a b c )\|a \|d x + c
+--R /
+--R 2 3 3 3 2 +-+
+--R (2a b x + 2a b x)\|a
+--R Type: Expression(Integer)
+--E 704
+
+--S 705 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 3 2 5
+--R (2a b d + a b c d - 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (2a d + 9a b c d + a b c d - 12b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (8a c d + 4a b c d - 12a b c )x
+--R *
+--R +---------+ +--------+
+--R |a d - b c | 2
+--R |--------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 3 2 5
+--R (- 6a b d - 3a b c d + 9b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 6a d - 11a b c d + 5a b c d + 12b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (- 8a c d - 4a b c d + 12a b c )x
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 3 5 3 3 2 2 3 3 2 +-+ | 2
+--R (4a b d x + (4a d + 16a b c d )x + 16a c d x)\|d \|d x + c
+--R +
+--R 2 3 5 3 3 2 2 3 3 2 +-+ +-+
+--R (- 12a b d x + (- 12a d - 16a b c d )x - 16a c d x)\|c \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 3 2 2 3 2 4
+--R (6a b d - 12a b c d + 18b c d)x
+--R +
+--R 2 2 2 2 3 3 2 2 3
+--R (8a b c d - 4a b c d + 24b c )x + 16a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 2a b d + 4a b c d - 6b c d )x
+--R +
+--R 2 3 2 2 2 3 3 4
+--R (- 10a b c d + 16a b c d - 30b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 4
+--R (- 8a b c d - 4a b c d - 24b c )x - 16a b c
+--R /
+--R +--------+
+--R 2 3 5 3 2 2 3 3 3 2 | 2
+--R (4a b d x + (4a b d + 16a b c)x + 16a b c x)\|d x + c
+--R +
+--R 2 3 5 3 2 2 3 3 3 2 +-+
+--R (- 12a b d x + (- 12a b d - 16a b c)x - 16a b c x)\|c
+--R ,
+--R
+--R +--------+
+--R 2 3 5 3 3 2 2 3 3 2 +-+ | 2
+--R (2a b d x + (2a d + 8a b c d )x + 8a c d x)\|d \|d x + c
+--R +
+--R 2 3 5 3 3 2 2 3 3 2 +-+ +-+
+--R (- 6a b d x + (- 6a d - 8a b c d )x - 8a c d x)\|c \|d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R 2 3 2 2 3 2 5
+--R (- 2a b d - a b c d + 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 2a d - 9a b c d - a b c d + 12b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (- 8a c d - 4a b c d + 12a b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 3 2 5
+--R (6a b d + 3a b c d - 9b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (6a d + 11a b c d - 5a b c d - 12b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (8a c d + 4a b c d - 12a b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 2 3 2 2 3 2 5
+--R (2a b d + a b c d - 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (2a d + 9a b c d + a b c d - 12b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (8a c d + 4a b c d - 12a b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 3 2 5
+--R (- 6a b d - 3a b c d + 9b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 6a d - 11a b c d + 5a b c d + 12b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (- 8a c d - 4a b c d + 12a b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 3 2 2 3 2 4
+--R (3a b d - 6a b c d + 9b c d)x
+--R +
+--R 2 2 2 2 3 3 2 2 3
+--R (4a b c d - 2a b c d + 12b c )x + 8a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- a b d + 2a b c d - 3b c d )x
+--R +
+--R 2 3 2 2 2 3 3 4
+--R (- 5a b c d + 8a b c d - 15b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 4
+--R (- 4a b c d - 2a b c d - 12b c )x - 8a b c
+--R /
+--R +--------+
+--R 2 3 5 3 2 2 3 3 3 2 | 2
+--R (2a b d x + (2a b d + 8a b c)x + 8a b c x)\|d x + c
+--R +
+--R 2 3 5 3 2 2 3 3 3 2 +-+
+--R (- 6a b d x + (- 6a b d - 8a b c)x - 8a b c x)\|c
+--R ,
+--R
+--R 2 3 2 2 3 2 5
+--R (2a b d + a b c d - 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (2a d + 9a b c d + a b c d - 12b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (8a c d + 4a b c d - 12a b c )x
+--R *
+--R +---------+ +--------+
+--R |a d - b c | 2
+--R |--------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 3 2 5
+--R (- 6a b d - 3a b c d + 9b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 6a d - 11a b c d + 5a b c d + 12b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (- 8a c d - 4a b c d + 12a b c )x
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 3 5 3 3 2 2 3 3 2 +---+ | 2
+--R (8a b d x + (8a d + 32a b c d )x + 32a c d x)\|- d \|d x + c
+--R +
+--R 2 3 5 3 3 2 2 3 3 2 +---+ +-+
+--R (- 24a b d x + (- 24a d - 32a b c d )x - 32a c d x)\|- d \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 2 3 2 2 3 2 4
+--R (6a b d - 12a b c d + 18b c d)x
+--R +
+--R 2 2 2 2 3 3 2 2 3
+--R (8a b c d - 4a b c d + 24b c )x + 16a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 2a b d + 4a b c d - 6b c d )x
+--R +
+--R 2 3 2 2 2 3 3 4
+--R (- 10a b c d + 16a b c d - 30b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 4
+--R (- 8a b c d - 4a b c d - 24b c )x - 16a b c
+--R /
+--R +--------+
+--R 2 3 5 3 2 2 3 3 3 2 | 2
+--R (4a b d x + (4a b d + 16a b c)x + 16a b c x)\|d x + c
+--R +
+--R 2 3 5 3 2 2 3 3 3 2 +-+
+--R (- 12a b d x + (- 12a b d - 16a b c)x - 16a b c x)\|c
+--R ,
+--R
+--R +--------+
+--R 2 3 5 3 3 2 2 3 3 2 +---+ | 2
+--R (4a b d x + (4a d + 16a b c d )x + 16a c d x)\|- d \|d x + c
+--R +
+--R 2 3 5 3 3 2 2 3 3 2 +---+ +-+
+--R (- 12a b d x + (- 12a d - 16a b c d )x - 16a c d x)\|- d \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R atan(------------------)
+--R +---+
+--R x\|- d
+--R +
+--R 2 3 2 2 3 2 5
+--R (- 2a b d - a b c d + 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 2a d - 9a b c d - a b c d + 12b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (- 8a c d - 4a b c d + 12a b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 3 2 5
+--R (6a b d + 3a b c d - 9b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (6a d + 11a b c d - 5a b c d - 12b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (8a c d + 4a b c d - 12a b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 2 3 2 2 3 2 5
+--R (2a b d + a b c d - 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (2a d + 9a b c d + a b c d - 12b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (8a c d + 4a b c d - 12a b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 2 3 2 2 3 2 5
+--R (- 6a b d - 3a b c d + 9b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 6a d - 11a b c d + 5a b c d + 12b c )x
+--R +
+--R 3 2 2 2 2 3
+--R (- 8a c d - 4a b c d + 12a b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 3 2 2 3 2 4
+--R (3a b d - 6a b c d + 9b c d)x
+--R +
+--R 2 2 2 2 3 3 2 2 3
+--R (4a b c d - 2a b c d + 12b c )x + 8a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- a b d + 2a b c d - 3b c d )x
+--R +
+--R 2 3 2 2 2 3 3 4
+--R (- 5a b c d + 8a b c d - 15b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 4
+--R (- 4a b c d - 2a b c d - 12b c )x - 8a b c
+--R /
+--R +--------+
+--R 2 3 5 3 2 2 3 3 3 2 | 2
+--R (2a b d x + (2a b d + 8a b c)x + 8a b c x)\|d x + c
+--R +
+--R 2 3 5 3 2 2 3 3 3 2 +-+
+--R (- 6a b d x + (- 6a b d - 8a b c)x - 8a b c x)\|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 705
+
+--S 706 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 2 2 2 2 +-+ |a d - b c
+--R (2a d + a b c d - 3b c )\|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (2a d x + 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (- 4a d x - 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R 2 2 +-+ +-+ (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R 4a d \|a \|d log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R - 4a d \|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (- 4a d - 2a b c d + 6b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 2 +-+
+--R 4a b \|a
+--R Type: Expression(Integer)
+--E 706
+
+--S 707 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 707
+
+--S 708 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R 2 2 +-+ +-+ (- x\|d + \|c )\|d x + c + x\|c \|d - d x - c
+--R 2a d \|a \|d log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R - 2a d \|a \|d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 |- a d + b c +-+
+--R (- 2a d - a b c d + 3b c ) |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R 2 2 2 2 |- a d + b c +-+ \|c
+--R (2a d + a b c d - 3b c ) |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R 2 2 2 2 +-----------+ x\|- a d + b c
+--R (- 2a d - a b c d + 3b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 2 +-+
+--R 2a b \|a
+--R Type: Expression(Integer)
+--E 708
+
+--S 709 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 709
+
+)clear all
+
+--S 710 of 1527
+t0:=(c+d*x^2)^(5/2)/(x^3*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R Type: Expression(Integer)
+--E 710
+
+--S 711 of 1527
+r0a:=1/2*c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))/a^3-_
+ 1/2*(b*c-a*d)^(3/2)*(4*b*c+a*d)*atanh(sqrt(b)*sqrt(c+d*x^2)/_
+ sqrt(b*c-a*d))/(a^3*b^(3/2))-1/2*c^2*sqrt(c+d*x^2)/(a^2*x^2)-_
+ 1/2*(b*c-a*d)^2*sqrt(c+d*x^2)/(a^2*b*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 4 3 2 2 2 2 2
+--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x )
+--R *
+--R +--------+
+--R +-+ | 2
+--R +-----------+ \|b \|d x + c
+--R \|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 3 2 4 2 2 2 2 +-+ +-+
+--R ((- 5a b c d + 4b c )x + (- 5a b c d + 4a b c )x )\|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 3 2 2 2 2 2 2 2 +-+ | 2
+--R ((- a d + 2a b c d - 2a b c )x - a b c )\|b \|d x + c
+--R /
+--R 3 2 4 4 2 +-+
+--R (2a b x + 2a b x )\|b
+--R Type: Expression(Integer)
+--E 711
+
+--S 712 of 1527
+r0b:=-(b*c-a*d)*_
+ (c+d*x^2)^(3/2)/(a^2*(a+b*x^2))-1/2*(c+d*x^2)^(5/2)/(a*x^2*(a+_
+ b*x^2))+1/2*c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))/a^3-_
+ 1/2*(b*c-a*d)^(3/2)*(4*b*c+a*d)*atanh(sqrt(b)*sqrt(c+d*x^2)/_
+ sqrt(b*c-a*d))/(a^3*b^(3/2))+1/2*d*(2*b*c-a*d)*sqrt(c+d*x^2)/(a^2*b)
+--R
+--R
+--R (3)
+--R 2 2 2 3 2 4 3 2 2 2 2 2
+--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x )
+--R *
+--R +--------+
+--R +-+ | 2
+--R +-----------+ \|b \|d x + c
+--R \|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 3 2 4 2 2 2 2 +-+ +-+
+--R ((- 5a b c d + 4b c )x + (- 5a b c d + 4a b c )x )\|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 3 2 2 2 2 2 2 2 +-+ | 2
+--R ((- a d + 2a b c d - 2a b c )x - a b c )\|b \|d x + c
+--R /
+--R 3 2 4 4 2 +-+
+--R (2a b x + 2a b x )\|b
+--R Type: Expression(Integer)
+--E 712
+
+--S 713 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R 2 2 2 3 3 6 2 2 2 2 3 3 4 4
+--R (40a b c d - 32b c d)x + (40a b c d + 48a b c d - 64b c )x
+--R +
+--R 2 3 2 4 2
+--R (80a b c d - 64a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 3 2 2 8
+--R (- 10a b c d + 8b c d )x
+--R +
+--R 2 3 2 2 2 3 3 6
+--R (- 10a b c d - 72a b c d + 64b c d)x
+--R +
+--R 2 2 2 2 3 3 4 4
+--R (- 80a b c d - 16a b c d + 64b c )x
+--R +
+--R 2 3 2 4 2
+--R (- 80a b c d + 64a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 3 2 6
+--R (4a b d + 12a b c d - 16b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (4a d + 20a b c d + 8a b c d - 32b c )x
+--R +
+--R 3 2 2 2 2 3 2
+--R (8a c d + 24a b c d - 32a b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R |----------- \|c \|d x + c
+--R \| b
+--R +
+--R 2 4 2 3 3 2 2 8
+--R (- a b d - 3a b c d + 4b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 6
+--R (- a d - 11a b c d - 20a b c d + 32b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (- 8a c d - 32a b c d + 8a b c d + 32b c )x
+--R +
+--R 3 2 2 2 3 2 4 2
+--R (- 8a c d - 24a b c d + 32a b c )x
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 3 4 2 3 2 2 2 3 3 6
+--R (2a d - 12a b c d + 20a b c d - 8b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (8a c d - 30a b c d + 56a b c d - 16b c )x
+--R +
+--R 2 3 2 4 2 2 4
+--R (16a b c d + 16a b c )x + 16a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 8
+--R (2a b d - 4a b c d + 2b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 6
+--R (- 6a d + 28a b c d - 46a b c d + 16b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (- 8a c d + 24a b c d - 64a b c d + 16b c )x
+--R +
+--R 2 3 2 4 2 2 4
+--R (- 24a b c d - 16a b c )x - 16a b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 2 6 4 3 2 4 4 2 +-+ | 2
+--R (16a b d x + (16a b d + 32a b c)x + 32a b c x )\|c \|d x + c
+--R +
+--R 3 2 2 8 4 2 3 2 6 4 3 2 2 4
+--R - 4a b d x + (- 4a b d - 32a b c d)x + (- 32a b c d - 32a b c )x
+--R +
+--R 4 2 2
+--R - 32a b c x
+--R ,
+--R
+--R 2 2 2 3 3 6 2 2 2 2 3 3 4 4
+--R (20a b c d - 16b c d)x + (20a b c d + 24a b c d - 32b c )x
+--R +
+--R 2 3 2 4 2
+--R (40a b c d - 32a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 3 3 2 2 8
+--R (- 5a b c d + 4b c d )x
+--R +
+--R 2 3 2 2 2 3 3 6
+--R (- 5a b c d - 36a b c d + 32b c d)x
+--R +
+--R 2 2 2 2 3 3 4 4 2 3 2 4 2
+--R (- 40a b c d - 8a b c d + 32b c )x + (- 40a b c d + 32a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 3 2 6
+--R (- 4a b d - 12a b c d + 16b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 4a d - 20a b c d - 8a b c d + 32b c )x
+--R +
+--R 3 2 2 2 2 3 2
+--R (- 8a c d - 24a b c d + 32a b c )x
+--R *
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 4 2 3 3 2 2 8
+--R (a b d + 3a b c d - 4b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 6
+--R (a d + 11a b c d + 20a b c d - 32b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (8a c d + 32a b c d - 8a b c d - 32b c )x
+--R +
+--R 3 2 2 2 3 2 4 2
+--R (8a c d + 24a b c d - 32a b c )x
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R 3 4 2 3 2 2 2 3 3 6
+--R (a d - 6a b c d + 10a b c d - 4b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (4a c d - 15a b c d + 28a b c d - 8b c )x
+--R +
+--R 2 3 2 4 2 2 4
+--R (8a b c d + 8a b c )x + 8a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 8
+--R (a b d - 2a b c d + b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 6
+--R (- 3a d + 14a b c d - 23a b c d + 8b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (- 4a c d + 12a b c d - 32a b c d + 8b c )x
+--R +
+--R 2 3 2 4 2 2 4
+--R (- 12a b c d - 8a b c )x - 8a b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 3 2 6 4 3 2 4 4 2 +-+ | 2
+--R (8a b d x + (8a b d + 16a b c)x + 16a b c x )\|c \|d x + c
+--R +
+--R 3 2 2 8 4 2 3 2 6 4 3 2 2 4
+--R - 2a b d x + (- 2a b d - 16a b c d)x + (- 16a b c d - 16a b c )x
+--R +
+--R 4 2 2
+--R - 16a b c x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 713
+
+--S 714 of 1527
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((40a b c d - 32b c d)x + 80a b c d - 64b c )\|b \|d x + c
+--R +
+--R 3 2 2 2 4 2 2 2 3 2
+--R (- 10a b c d + 8b c d )x + (- 80a b c d + 64b c d)x
+--R +
+--R 3 2 4
+--R - 80a b c d + 64b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((4a d + 12a b c d - 16b c d)x + 8a c d + 24a b c d - 32b c )
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ +-+ | 2
+--R |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R 2 4 3 2 2 2 4
+--R (- a d - 3a b c d + 4b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 8a c d - 24a b c d + 32b c d)x - 8a c d - 24a b c d + 32b c
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (- 8a d - 24a b c d + 32b c d)x - 16a c d - 48a b c d
+--R +
+--R 2 3
+--R 64b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (2a d + 6a b c d - 8b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (16a c d + 48a b c d - 64b c d)x + 16a c d + 48a b c d - 64b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((40a b c d - 32b c d)x + 80a b c d - 64b c )\|b \|d x + c
+--R +
+--R 3 2 2 2 4 2 2 2 3 2
+--R (- 10a b c d + 8b c d )x + (- 80a b c d + 64b c d)x
+--R +
+--R 3 2 4
+--R - 80a b c d + 64b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 8a c d + 16a b c d - 8b c d)x - 16a c d + 32a b c d - 16b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (2a d - 4a b c d + 2b c d )x + (16a c d - 32a b c d + 16b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 16a c d - 32a b c d + 16b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 3 2 3 +-+ +-+ | 2
+--R (16a b d x + 32a b c)\|b \|c \|d x + c
+--R +
+--R 3 2 4 3 2 3 2 +-+
+--R (- 4a b d x - 32a b c d x - 32a b c )\|b
+--R Type: Expression(Integer)
+--E 714
+
+--S 715 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 715
+
+--S 716 of 1527
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((20a b c d - 16b c d)x + 40a b c d - 32b c )\|b \|d x + c
+--R +
+--R 3 2 2 2 4 2 2 2 3 2
+--R (- 5a b c d + 4b c d )x + (- 40a b c d + 32b c d)x
+--R +
+--R 3 2 4
+--R - 40a b c d + 32b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 4a d - 12a b c d + 16b c d)x - 8a c d - 24a b c d + 32b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (a d + 3a b c d - 4b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (8a c d + 24a b c d - 32b c d)x + 8a c d + 24a b c d - 32b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((20a b c d - 16b c d)x + 40a b c d - 32b c )\|b \|d x + c
+--R +
+--R 3 2 2 2 4 2 2 2 3 2
+--R (- 5a b c d + 4b c d )x + (- 40a b c d + 32b c d)x
+--R +
+--R 3 2 4
+--R - 40a b c d + 32b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 4a d - 12a b c d + 16b c d)x - 8a c d - 24a b c d + 32b c )
+--R *
+--R +---------+ +--------+
+--R +-+ +-+ |a d - b c | 2
+--R \|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 4 3 2 2 2 4
+--R (a d + 3a b c d - 4b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (8a c d + 24a b c d - 32b c d)x + 8a c d + 24a b c d - 32b c
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|b |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4 +-+
+--R ((- 4a c d + 8a b c d - 4b c d)x - 8a c d + 16a b c d - 8b c )\|b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (a d - 2a b c d + b c d )x + (8a c d - 16a b c d + 8b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 8a c d - 16a b c d + 8b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 3 2 3 +-+ +-+ | 2
+--R (8a b d x + 16a b c)\|b \|c \|d x + c
+--R +
+--R 3 2 4 3 2 3 2 +-+
+--R (- 2a b d x - 16a b c d x - 16a b c )\|b
+--R Type: Expression(Integer)
+--E 716
+
+--S 717 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 717
+
+--S 718 of 1527
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((40a b c d - 32b c d)x + 80a b c d - 64b c )\|b \|d x + c
+--R +
+--R 3 2 2 2 4 2 2 2 3 2
+--R (- 10a b c d + 8b c d )x + (- 80a b c d + 64b c d)x
+--R +
+--R 3 2 4
+--R - 80a b c d + 64b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((4a d + 12a b c d - 16b c d)x + 8a c d + 24a b c d - 32b c )
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c +-+ +-+ | 2
+--R |----------- \|b \|c \|d x + c
+--R \| b
+--R +
+--R 2 4 3 2 2 2 4
+--R (- a d - 3a b c d + 4b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 8a c d - 24a b c d + 32b c d)x - 8a c d - 24a b c d + 32b c
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|b
+--R \| b
+--R *
+--R log
+--R +-----------+ +--------+
+--R 2 2 +-+ 2 |- a d + b c | 2
+--R ((2a b x + 2a )\|c + 2a b x |----------- )\|d x + c
+--R \| b
+--R +
+--R +-----------+
+--R 2 4 2 |- a d + b c +-+ 2 4
+--R (- 2b x - 2a b x ) |----------- \|c + (a b d - 2b c)x
+--R \| b
+--R +
+--R 2 2 2
+--R (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (- 8a d - 24a b c d + 32b c d)x - 16a c d - 48a b c d
+--R +
+--R 2 3
+--R 64b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (2a d + 6a b c d - 8b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (16a c d + 48a b c d - 64b c d)x + 16a c d + 48a b c d - 64b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((40a b c d - 32b c d)x + 80a b c d - 64b c )\|b \|d x + c
+--R +
+--R 3 2 2 2 4 2 2 2 3 2
+--R (- 10a b c d + 8b c d )x + (- 80a b c d + 64b c d)x
+--R +
+--R 3 2 4
+--R - 80a b c d + 64b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R ((- 8a c d + 16a b c d - 8b c d)x - 16a c d + 32a b c d - 16b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (2a d - 4a b c d + 2b c d )x + (16a c d - 32a b c d + 16b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 16a c d - 32a b c d + 16b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 3 2 3 +-+ +-+ | 2
+--R (16a b d x + 32a b c)\|b \|c \|d x + c
+--R +
+--R 3 2 4 3 2 3 2 +-+
+--R (- 4a b d x - 32a b c d x - 32a b c )\|b
+--R Type: Expression(Integer)
+--E 718
+
+--S 719 of 1527
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 719
+
+--S 720 of 1527
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((20a b c d - 16b c d)x + 40a b c d - 32b c )\|b \|d x + c
+--R +
+--R 3 2 2 2 4 2 2 2 3 2
+--R (- 5a b c d + 4b c d )x + (- 40a b c d + 32b c d)x
+--R +
+--R 3 2 4
+--R - 40a b c d + 32b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 4a d - 12a b c d + 16b c d)x - 8a c d - 24a b c d + 32b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 4 3 2 2 2 4
+--R (a d + 3a b c d - 4b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (8a c d + 24a b c d - 32b c d)x + 8a c d + 24a b c d - 32b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 3 2 3 2 4 +-+ | 2
+--R ((20a b c d - 16b c d)x + 40a b c d - 32b c )\|b \|d x + c
+--R +
+--R 3 2 2 2 4 2 2 2 3 2
+--R (- 5a b c d + 4b c d )x + (- 40a b c d + 32b c d)x
+--R +
+--R 3 2 4
+--R - 40a b c d + 32b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 4a d - 12a b c d + 16b c d)x - 8a c d - 24a b c d + 32b c )
+--R *
+--R +---------+ +--------+
+--R +-+ +-+ |a d - b c | 2
+--R \|b \|c |--------- \|d x + c
+--R \| b
+--R +
+--R 2 4 3 2 2 2 4
+--R (a d + 3a b c d - 4b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (8a c d + 24a b c d - 32b c d)x + 8a c d + 24a b c d - 32b c
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|b |---------
+--R \| b
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R b x \|c |---------
+--R \| b
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4 +-+
+--R ((- 4a c d + 8a b c d - 4b c d)x - 8a c d + 16a b c d - 8b c )\|b
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (a d - 2a b c d + b c d )x + (8a c d - 16a b c d + 8b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 8a c d - 16a b c d + 8b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R /
+--R +--------+
+--R 3 2 3 +-+ +-+ | 2
+--R (8a b d x + 16a b c)\|b \|c \|d x + c
+--R +
+--R 3 2 4 3 2 3 2 +-+
+--R (- 2a b d x - 16a b c d x - 16a b c )\|b
+--R Type: Expression(Integer)
+--E 720
+
+--S 721 of 1527
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 721
+
+)clear all
+
+--S 722 of 1527
+t0:=(c+d*x^2)^(5/2)/(x^4*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R Type: Expression(Integer)
+--E 722
+
+--S 723 of 1527
+r0:=1/2*(b*c-a*d)*(c+d*x^2)^(3/2)/(a*b*x^3*(a+b*x^2))+5/2*c*(b*c-_
+ a*d)^(3/2)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/a^(7/2)-_
+ 1/6*c*(5*b*c-3*a*d)*sqrt(c+d*x^2)/(a^2*b*x^3)+1/6*(15*b^2*c^2-_
+ 20*a*b*c*d+3*a^2*d^2)*sqrt(c+d*x^2)/(a^3*b*x)
+--R
+--R
+--R (2)
+--R 2 2 5 2 2 3 +-----------+
+--R ((- 15a b c d + 15b c )x + (- 15a c d + 15a b c )x )\|- a d + b c
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 2 2 2 2 4 2 2 2 2 2 +-+
+--R ((3a d - 20a b c d + 15b c )x + (- 14a c d + 10a b c )x - 2a c )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 5 4 3 +-+
+--R (6a b x + 6a x )\|a
+--R Type: Expression(Integer)
+--E 723
+
+--S 724 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 2 2 9
+--R (15a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 7
+--R (15a c d + 165a b c d - 180b c d)x
+--R +
+--R 2 2 2 3 2 4 5 2 3 4 3
+--R (180a c d + 60a b c d - 240b c )x + (240a c d - 240a b c )x
+--R *
+--R +---------+ +--------+
+--R |a d - b c | 2
+--R |--------- \|d x + c
+--R \| a
+--R +
+--R 3 2 2 2 9
+--R (- 75a b c d + 75b c d )x
+--R +
+--R 2 3 2 2 2 3 7
+--R (- 75a c d - 225a b c d + 300b c d)x
+--R +
+--R 2 2 2 3 2 4 5
+--R (- 300a c d + 60a b c d + 240b c )x
+--R +
+--R 2 3 4 3
+--R (- 240a c d + 240a b c )x
+--R *
+--R +---------+
+--R +-+ |a d - b c
+--R \|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 4 3 2 2 2 8
+--R (- 30a d + 200a b c d - 150b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (20a c d + 700a b c d - 600b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (484a c d + 240a b c d - 480b c )x + (528a c d - 320a b c )x
+--R +
+--R 2 4
+--R 64a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 4 2 2 3 10
+--R (6a d - 40a b c d + 30b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (50a c d - 500a b c d + 390b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (- 200a c d - 860a b c d + 840b c d)x
+--R +
+--R 2 3 2 4 2 5 4 2 4 5 2
+--R (- 740a c d - 80a b c d + 480b c )x + (- 560a c d + 320a b c )x
+--R +
+--R 2 5
+--R - 64a c
+--R /
+--R 3 2 9 4 2 3 7 4 3 2 5
+--R 12a b d x + (12a d + 144a b c d)x + (144a c d + 192a b c )x
+--R +
+--R 4 2 3
+--R 192a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 9 4 2 3 7
+--R - 60a b d x + (- 60a d - 240a b c d)x
+--R +
+--R 4 3 2 5 4 2 3
+--R (- 240a c d - 192a b c )x - 192a c x
+--R *
+--R +-+
+--R \|c
+--R ,
+--R
+--R 3 2 2 2 9
+--R (15a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 7
+--R (15a c d + 165a b c d - 180b c d)x
+--R +
+--R 2 2 2 3 2 4 5 2 3 4 3
+--R (180a c d + 60a b c d - 240b c )x + (240a c d - 240a b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 3 2 2 2 9
+--R (- 75a b c d + 75b c d )x
+--R +
+--R 2 3 2 2 2 3 7
+--R (- 75a c d - 225a b c d + 300b c d)x
+--R +
+--R 2 2 2 3 2 4 5
+--R (- 300a c d + 60a b c d + 240b c )x
+--R +
+--R 2 3 4 3
+--R (- 240a c d + 240a b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R 3 2 2 2 9
+--R (- 15a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 7
+--R (- 15a c d - 165a b c d + 180b c d)x
+--R +
+--R 2 2 2 3 2 4 5
+--R (- 180a c d - 60a b c d + 240b c )x
+--R +
+--R 2 3 4 3
+--R (- 240a c d + 240a b c )x
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 2
+--R |----------- \|d x + c
+--R \| a
+--R +
+--R 3 2 2 2 9
+--R (75a b c d - 75b c d )x
+--R +
+--R 2 3 2 2 2 3 7
+--R (75a c d + 225a b c d - 300b c d)x
+--R +
+--R 2 2 2 3 2 4 5 2 3 4 3
+--R (300a c d - 60a b c d - 240b c )x + (240a c d - 240a b c )x
+--R *
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(---------------)
+--R +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 4 3 2 2 2 8
+--R (- 15a d + 100a b c d - 75b c d )x
+--R +
+--R 2 3 2 2 2 3 6
+--R (10a c d + 350a b c d - 300b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (242a c d + 120a b c d - 240b c )x + (264a c d - 160a b c )x
+--R +
+--R 2 4
+--R 32a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 4 2 2 3 10
+--R (3a d - 20a b c d + 15b c d )x
+--R +
+--R 2 4 2 3 2 3 2 8
+--R (25a c d - 250a b c d + 195b c d )x
+--R +
+--R 2 2 3 3 2 2 4 6
+--R (- 100a c d - 430a b c d + 420b c d)x
+--R +
+--R 2 3 2 4 2 5 4 2 4 5 2
+--R (- 370a c d - 40a b c d + 240b c )x + (- 280a c d + 160a b c )x
+--R +
+--R 2 5
+--R - 32a c
+--R /
+--R 3 2 9 4 2 3 7 4 3 2 5
+--R 6a b d x + (6a d + 72a b c d)x + (72a c d + 96a b c )x
+--R +
+--R 4 2 3
+--R 96a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 9 4 2 3 7
+--R - 30a b d x + (- 30a d - 120a b c d)x
+--R +
+--R 4 3 2 5 4 2 3
+--R (- 120a c d - 96a b c )x - 96a c x
+--R *
+--R +-+
+--R \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 724
+
+--S 725 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 2 +-+ |a d - b c
+--R (5a c d - 5b c )\|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 3 |a d - b c
+--R (- 2a d x - 4a c x) |---------
+--R \| a
+--R +
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 3 +-+ |a d - b c 2 4
+--R (4a d x + 4a c x)\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 2 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+
+--R 2 +-----------+ x\|- a d + b c
+--R (10a c d - 10b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 725
+
+--S 726 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 726
+
+--S 727 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R 2 |- a d + b c +-+
+--R (5a c d - 5b c ) |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 3 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R 2 |- a d + b c +-+ \|c
+--R (- 5a c d + 5b c ) |----------- \|a atan(---------------)
+--R \| a +-----------+
+--R |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +-----------+
+--R 2 +-----------+ x\|- a d + b c
+--R (5a c d - 5b c )\|- a d + b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 727
+
+--S 728 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 728
+
+)clear all
+
+--S 729 of 1527
+t0:=x^4/((a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R 4
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R Type: Expression(Integer)
+--E 729
+
+--S 730 of 1527
+r0:=-1/2*(3*b*c-2*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*_
+ sqrt(a)/(b^2*(b*c-a*d)^(3/2))+atanh(x*sqrt(d)/sqrt(c+d*x^2))/(b^2*_
+ sqrt(d))+1/2*a*x*sqrt(c+d*x^2)/(b*(b*c-a*d)*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 +-----------+ x\|d
+--R ((2a b d - 2b c)x + 2a d - 2a b c)\|- a d + b c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 +-+ +-+ x\|- a d + b c
+--R ((- 2a b d + 3b c)x - 2a d + 3a b c)\|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R - a b x\|- a d + b c \|d \|d x + c
+--R /
+--R 3 4 2 2 2 3 +-----------+ +-+
+--R ((2a b d - 2b c)x + 2a b d - 2a b c)\|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 730
+
+--S 731 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((8a b d - 8b c)x + 8a d - 8a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 4a b d + 4b c d)x + (- 4a d - 4a b c d + 8b c )x - 8a c d
+--R +
+--R 2
+--R 8a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+ +--------+
+--R 2 2 2 | a +-+ +-+ | 2
+--R ((4a b d - 6b c)x + 4a d - 6a b c) |--------- \|c \|d \|d x + c
+--R \|a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d + 3b c d)x + (- 2a d - a b c d + 6b c )x - 4a c d
+--R +
+--R 2
+--R 6a b c
+--R *
+--R +---------+
+--R | a +-+
+--R |--------- \|d
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((- 4a d + 4b c d)x + (- 4a c d + 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (2a b d x + 4a b c x)\|d \|d x + c + (- 4a b d x - 4a b c x)\|c \|d
+--R /
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+--R 3 4 2 2 2 3 +-+ +-+ | 2
+--R ((8a b d - 8b c)x + 8a b d - 8a b c)\|c \|d \|d x + c
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+--R 3 2 4 4 2 2 2 3 4 2 2
+--R (- 4a b d + 4b c d)x + (- 4a b d - 4a b c d + 8b c )x
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+--R
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+--R 2 2 2 +-+ | 2
+--R ((4a b d - 4b c)x + 4a d - 4a b c)\|c \|d x + c
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+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d + 2b c d)x + (- 2a d - 2a b c d + 4b c )x - 4a c d
+--R +
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+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-----------+
+--R 2 2 2 | a +-+ +-+
+--R ((- 4a b d + 6b c)x - 4a d + 6a b c) |- --------- \|c \|d
+--R \| a d - b c
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+--R \|d x + c
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+--R 2 2 4 2 2 2 2 2 2
+--R (2a b d - 3b c d)x + (2a d + a b c d - 6b c )x + 4a c d
+--R +
+--R 2
+--R - 6a b c
+--R *
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+--R |- --------- \|d
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+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 2 | a +-+ +-+
+--R ((4a b d - 6b c)x + 4a d - 6a b c) |- --------- \|c \|d
+--R \| a d - b c
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+--R \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d + 3b c d)x + (- 2a d - a b c d + 6b c )x - 4a c d
+--R +
+--R 2
+--R 6a b c
+--R *
+--R +-----------+
+--R | a +-+
+--R |- --------- \|d
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (a b d x + 2a b c x)\|d \|d x + c + (- 2a b d x - 2a b c x)\|c \|d
+--R /
+--R +--------+
+--R 3 4 2 2 2 3 +-+ +-+ | 2
+--R ((4a b d - 4b c)x + 4a b d - 4a b c)\|c \|d \|d x + c
+--R +
+--R 3 2 4 4 2 2 2 3 4 2 2
+--R (- 2a b d + 2b c d)x + (- 2a b d - 2a b c d + 4b c )x
+--R +
+--R 2 2 3 2
+--R - 4a b c d + 4a b c
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+--R +-+
+--R \|d
+--R ,
+--R
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+--R 2 2 2 +---+ | a +-+
+--R ((4a b d - 6b c)x + 4a d - 6a b c)\|- d |--------- \|c
+--R \|a d - b c
+--R *
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+--R | 2
+--R \|d x + c
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+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d + 3b c d)x + (- 2a d - a b c d + 6b c )x - 4a c d
+--R +
+--R 2
+--R 6a b c
+--R *
+--R +---------+
+--R +---+ | a
+--R \|- d |---------
+--R \|a d - b c
+--R *
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+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((- 4a d + 4b c d)x + (- 4a c d + 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((16a b d - 16b c)x + 16a d - 16a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 8a b d + 8b c d)x + (- 8a d - 8a b c d + 16b c )x - 16a c d
+--R +
+--R 2
+--R 16a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R +--------+
+--R 3 +---+ | 2
+--R (2a b d x + 4a b c x)\|- d \|d x + c
+--R +
+--R 3 +---+ +-+
+--R (- 4a b d x - 4a b c x)\|- d \|c
+--R /
+--R +--------+
+--R 3 4 2 2 2 3 +---+ +-+ | 2
+--R ((8a b d - 8b c)x + 8a b d - 8a b c)\|- d \|c \|d x + c
+--R +
+--R 3 2 4 4 2 2 2 3 4 2 2
+--R (- 4a b d + 4b c d)x + (- 4a b d - 4a b c d + 8b c )x
+--R +
+--R 2 2 3 2
+--R - 8a b c d + 8a b c
+--R *
+--R +---+
+--R \|- d
+--R ,
+--R
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((8a b d - 8b c)x + 8a d - 8a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 4a b d + 4b c d)x + (- 4a d - 4a b c d + 8b c )x - 8a c d
+--R +
+--R 2
+--R 8a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R d x
+--R +
+--R +-----------+
+--R 2 2 2 +---+ | a +-+
+--R ((- 4a b d + 6b c)x - 4a d + 6a b c)\|- d |- --------- \|c
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (2a b d - 3b c d)x + (2a d + a b c d - 6b c )x + 4a c d
+--R +
+--R 2
+--R - 6a b c
+--R *
+--R +-----------+
+--R +---+ | a
+--R \|- d |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 2 +---+ | a +-+
+--R ((4a b d - 6b c)x + 4a d - 6a b c)\|- d |- --------- \|c
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d + 3b c d)x + (- 2a d - a b c d + 6b c )x - 4a c d
+--R +
+--R 2
+--R 6a b c
+--R *
+--R +-----------+
+--R +---+ | a
+--R \|- d |- ---------
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +--------+
+--R 3 +---+ | 2
+--R (a b d x + 2a b c x)\|- d \|d x + c
+--R +
+--R 3 +---+ +-+
+--R (- 2a b d x - 2a b c x)\|- d \|c
+--R /
+--R +--------+
+--R 3 4 2 2 2 3 +---+ +-+ | 2
+--R ((4a b d - 4b c)x + 4a b d - 4a b c)\|- d \|c \|d x + c
+--R +
+--R 3 2 4 4 2 2 2 3 4 2 2
+--R (- 2a b d + 2b c d)x + (- 2a b d - 2a b c d + 4b c )x
+--R +
+--R 2 2 3 2
+--R - 4a b c d + 4a b c
+--R *
+--R +---+
+--R \|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 731
+
+--S 732 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R (4a d - 4b c)\|- a d + b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +---------+
+--R +-----------+ | a +-+
+--R (2a d - 3b c)\|- a d + b c |--------- \|d
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((- 4a d + 4b c d)x + (- 4a c d + 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-+
+--R +-----------+ x\|d
+--R (- 4a d + 4b c)\|- a d + b c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-+ +-+ x\|- a d + b c
+--R (4a d - 6b c)\|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 3 +-----------+ +-+
+--R (4a b d - 4b c)\|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 732
+
+--S 733 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 733
+
+--S 734 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R (2a d - 2b c)\|- a d + b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|c \|d - d x)\|d x + c + (- d x - c)\|d + d x\|c
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c - c
+--R +
+--R +-+
+--R +-----------+ x\|d
+--R (- 2a d + 2b c)\|- a d + b c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R +-----------+ | a +-+
+--R (- 2a d + 3b c)\|- a d + b c |- --------- \|d
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-----------+ | a +-+
+--R (2a d - 3b c)\|- a d + b c |- --------- \|d
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-+ +-+ x\|- a d + b c
+--R (2a d - 3b c)\|a \|d atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 3 +-----------+ +-+
+--R (2a b d - 2b c)\|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 734
+
+--S 735 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 735
+
+)clear all
+
+--S 736 of 1527
+t0:=x^3/((a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R 3
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R Type: Expression(Integer)
+--E 736
+
+--S 737 of 1527
+r0:=-1/2*(2*b*c-a*d)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/(b^(3/2)*_
+ (b*c-a*d)^(3/2))+1/2*a*sqrt(c+d*x^2)/(b*(b*c-a*d)*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 2 2 \|b \|d x + c
+--R ((- a b d + 2b c)x - a d + 2a b c)atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R - a\|- a d + b c \|b \|d x + c
+--R /
+--R 2 3 2 2 2 +-----------+ +-+
+--R ((2a b d - 2b c)x + 2a b d - 2a b c)\|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 737
+
+--S 738 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((2a b d - 4b c)x + 2a d - 4a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R (- a b d + 2b c d)x + (- a d + 4b c )x - 2a c d + 4a b c
+--R *
+--R log
+--R 2 2 2 3 2 4
+--R (2a b d + 2a b c d - 4b c )x
+--R +
+--R 2 2 2 2
+--R (8a b c d - 8a b c )x
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a b c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b c d + 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+ +--------+
+--R 2 | 2 | 2
+--R (2a d - 4b c)x \|- a b d + b c \|d x + c
+--R +
+--R +-------------+
+--R 4 2 | 2 +-+
+--R (2b d x + (- 2a d + 4b c)x )\|- a b d + b c \|c
+--R /
+--R +-------------+ +--------+
+--R 2 3 2 2 2 | 2 +-+ | 2
+--R ((8a b d - 8b c)x + 8a b d - 8a b c)\|- a b d + b c \|c \|d x + c
+--R +
+--R 2 2 3 4 2 2 2 3 2 2
+--R (- 4a b d + 4b c d)x + (- 4a b d - 4a b c d + 8b c )x
+--R +
+--R 2 2 2
+--R - 8a b c d + 8a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a b d + b c
+--R ,
+--R
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((- 2a b d + 4b c)x - 2a d + 4a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R (a b d - 2b c d)x + (a d - 4b c )x + 2a c d - 4a b c
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+ +--------+
+--R 2 | 2 | 2
+--R (a d - 2b c)x \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 4 2 +-+ | 2
+--R (b d x + (- a d + 2b c)x )\|c \|a b d - b c
+--R /
+--R +-----------+ +--------+
+--R 2 3 2 2 2 +-+ | 2 | 2
+--R ((4a b d - 4b c)x + 4a b d - 4a b c)\|c \|a b d - b c \|d x + c
+--R +
+--R 2 2 3 4 2 2 2 3 2 2
+--R (- 2a b d + 2b c d)x + (- 2a b d - 2a b c d + 4b c )x
+--R +
+--R 2 2 2
+--R - 4a b c d + 4a b c
+--R *
+--R +-----------+
+--R | 2
+--R \|a b d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 738
+
+--S 739 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-----------+ +-+ +-+ | 2
+--R (2a d - 4b c)\|- a d + b c \|b \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+ +-+
+--R ((- a d + 2b c d)x - 2a c d + 4b c )\|- a d + b c \|b
+--R *
+--R log
+--R 2 2 2 3 2 4 2 2 2 2
+--R ((2a b d + 2a b c d - 4b c )x + (8a b c d - 8a b c )x )
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a b c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b c d + 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R (4a d - 8b c)\|- a b d + b c \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 2 | 2
+--R ((- 2a d + 4b c d)x - 4a c d + 8b c )\|- a b d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-----------+ +-+ | 2
+--R - 4c\|- a b d + b c \|- a d + b c \|b \|d x + c
+--R +
+--R +-------------+
+--R 2 | 2 +-----------+ +-+ +-+
+--R (2d x + 4c)\|- a b d + b c \|- a d + b c \|b \|c
+--R /
+--R +-------------+ +--------+
+--R 2 | 2 +-----------+ +-+ +-+ | 2
+--R (8a b d - 8b c)\|- a b d + b c \|- a d + b c \|b \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 2 2 2 | 2
+--R ((- 4a b d + 4b c d)x - 8a b c d + 8b c )\|- a b d + b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 739
+
+--S 740 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 740
+
+--S 741 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R (2a d - 4b c)\|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 | 2
+--R ((- a d + 2b c d)x - 2a c d + 4b c )\|a b d - b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +-----------+ +-+ +-+ | 2
+--R (- 2a d + 4b c)\|- a d + b c \|b \|c \|d x + c
+--R +
+--R 2 2 2 +-----------+ +-+
+--R ((a d - 2b c d)x + 2a c d - 4b c )\|- a d + b c \|b
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+ +--------+
+--R +-----------+ +-+ | 2 | 2
+--R - 2c\|- a d + b c \|b \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 +-----------+ +-+ +-+ | 2
+--R (d x + 2c)\|- a d + b c \|b \|c \|a b d - b c
+--R /
+--R +-----------+ +--------+
+--R 2 +-----------+ +-+ +-+ | 2 | 2
+--R (4a b d - 4b c)\|- a d + b c \|b \|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 2 +-----------+ +-+ | 2
+--R ((- 2a b d + 2b c d)x - 4a b c d + 4b c )\|- a d + b c \|b \|a b d - b c
+--R Type: Expression(Integer)
+--E 741
+
+--S 742 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 742
+
+)clear all
+
+--S 743 of 1527
+t0:=x^2/((a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R Type: Expression(Integer)
+--E 743
+
+--S 744 of 1527
+r0:=1/2*c*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/((b*c-a*d)^(3/2)*_
+ sqrt(a))-1/2*x*sqrt(c+d*x^2)/((b*c-a*d)*(a+b*x^2))
+--R
+--R
+--R +-----------+ +--------+
+--R 2 x\|- a d + b c +-----------+ +-+ | 2
+--R (- b c x - a c)atan(---------------) + x\|- a d + b c \|a \|d x + c
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R (2) ----------------------------------------------------------------------
+--R 2 2 2 +-----------+ +-+
+--R ((2a b d - 2b c)x + 2a d - 2a b c)\|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 744
+
+--S 745 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R (2b c x + 2a c)\|c \|d x + c - b c d x + (- a c d - 2b c )x
+--R +
+--R 2
+--R - 2a c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +--------+
+--R 3 | 2 | 2
+--R (- 2d x - 4c x)\|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2
+--R (4d x + 4c x)\|c \|a d - a b c
+--R /
+--R +-----------+ +--------+
+--R 2 2 2 +-+ | 2 | 2
+--R ((8a b d - 8b c)x + 8a d - 8a b c)\|c \|a d - a b c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 4a b d + 4b c d)x + (- 4a d - 4a b c d + 8b c )x - 8a c d
+--R +
+--R 2
+--R 8a b c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R ,
+--R
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R (2b c x + 2a c)\|c \|d x + c - b c d x + (- a c d - 2b c )x
+--R +
+--R 2
+--R - 2a c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R (2b c x + 2a c)\|c \|d x + c - b c d x + (- a c d - 2b c )x
+--R +
+--R 2
+--R - 2a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +--------+
+--R 3 | 2 | 2
+--R (- d x - 2c x)\|- a d + a b c \|d x + c
+--R +
+--R +-------------+
+--R 3 | 2 +-+
+--R (2d x + 2c x)\|- a d + a b c \|c
+--R /
+--R +-------------+ +--------+
+--R 2 2 2 | 2 +-+ | 2
+--R ((4a b d - 4b c)x + 4a d - 4a b c)\|- a d + a b c \|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d + 2b c d)x + (- 2a d - 2a b c d + 4b c )x - 4a c d
+--R +
+--R 2
+--R 4a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 745
+
+--S 746 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R c\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R | 2 x\|- a d + b c
+--R 2c\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R (4a d - 4b c)\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 746
+
+--S 747 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 747
+
+--S 748 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +-+
+--R c\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R +-----------+ +-+ \|- a d + a b c \|c
+--R c\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R c\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R (2a d - 2b c)\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 748
+
+--S 749 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 749
+
+)clear all
+
+--S 750 of 1527
+t0:=x/((a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R Type: Expression(Integer)
+--E 750
+
+--S 751 of 1527
+r0:=1/2*d*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/((b*c-a*d)^(3/2)*_
+ sqrt(b))-1/2*sqrt(c+d*x^2)/((b*c-a*d)*(a+b*x^2))
+--R
+--R
+--R +--------+
+--R +-+ | 2 +--------+
+--R 2 \|b \|d x + c +-----------+ +-+ | 2
+--R (- b d x - a d)atanh(---------------) + \|- a d + b c \|b \|d x + c
+--R +-----------+
+--R \|- a d + b c
+--R (2) ----------------------------------------------------------------------
+--R 2 2 2 +-----------+ +-+
+--R ((2a b d - 2b c)x + 2a d - 2a b c)\|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 751
+
+--S 752 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 +-+ | 2 2 4
+--R (2a b d x + 2a d)\|c \|d x + c - a b d x
+--R +
+--R 2 2 2 2
+--R (- a d - 2a b c d)x - 2a c d
+--R *
+--R log
+--R 2 2 2 3 2 4
+--R (2a b d + 2a b c d - 4b c )x
+--R +
+--R 2 2 2 2
+--R (8a b c d - 8a b c )x
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a b c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b c d + 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+ +--------+
+--R 2 | 2 | 2
+--R (- 2a d + 4b c)x \|- a b d + b c \|d x + c
+--R +
+--R +-------------+
+--R 4 2 | 2 +-+
+--R (- 2b d x + (2a d - 4b c)x )\|- a b d + b c \|c
+--R /
+--R +-------------+ +--------+
+--R 2 2 2 3 2 | 2 +-+ | 2
+--R ((8a b d - 8a b c)x + 8a d - 8a b c)\|- a b d + b c \|c \|d x + c
+--R +
+--R 2 2 2 4 3 2 2 2 2 2
+--R (- 4a b d + 4a b c d)x + (- 4a d - 4a b c d + 8a b c )x
+--R +
+--R 3 2 2
+--R - 8a c d + 8a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a b d + b c
+--R ,
+--R
+--R +--------+
+--R 2 2 +-+ | 2 2 4
+--R (- 2a b d x - 2a d)\|c \|d x + c + a b d x
+--R +
+--R 2 2 2 2
+--R (a d + 2a b c d)x + 2a c d
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+ +--------+
+--R 2 | 2 | 2
+--R (- a d + 2b c)x \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 4 2 +-+ | 2
+--R (- b d x + (a d - 2b c)x )\|c \|a b d - b c
+--R /
+--R +-----------+ +--------+
+--R 2 2 2 3 2 +-+ | 2 | 2
+--R ((4a b d - 4a b c)x + 4a d - 4a b c)\|c \|a b d - b c \|d x + c
+--R +
+--R 2 2 2 4 3 2 2 2 2 2
+--R (- 2a b d + 2a b c d)x + (- 2a d - 2a b c d + 4a b c )x
+--R +
+--R 3 2 2
+--R - 4a c d + 4a b c
+--R *
+--R +-----------+
+--R | 2
+--R \|a b d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 752
+
+--S 753 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-----------+ +-+ +-+ | 2
+--R 2a d\|- a d + b c \|b \|c \|d x + c
+--R +
+--R 2 2 +-----------+ +-+
+--R (- a d x - 2a c d)\|- a d + b c \|b
+--R *
+--R log
+--R 2 2 2 3 2 4 2 2 2 2
+--R ((2a b d + 2a b c d - 4b c )x + (8a b c d - 8a b c )x )
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a b c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b c d + 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R 4a d\|- a b d + b c \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 | 2
+--R (- 2a d x - 4a c d)\|- a b d + b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-----------+ +-+ | 2
+--R 4c\|- a b d + b c \|- a d + b c \|b \|d x + c
+--R +
+--R +-------------+
+--R 2 | 2 +-----------+ +-+ +-+
+--R (- 2d x - 4c)\|- a b d + b c \|- a d + b c \|b \|c
+--R /
+--R +-------------+ +--------+
+--R 2 | 2 +-----------+ +-+ +-+ | 2
+--R (8a d - 8a b c)\|- a b d + b c \|- a d + b c \|b \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 2 2 2 | 2
+--R ((- 4a d + 4a b c d)x - 8a c d + 8a b c )\|- a b d + b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 753
+
+--S 754 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 754
+
+--S 755 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +--------+ +-----------+
+--R +-+ | 2 | 2 2 2 | 2
+--R (2a d\|c \|a b d - b c \|d x + c + (- a d x - 2a c d)\|a b d - b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R +-----------+ +-+ +-+ | 2
+--R - 2a d\|- a d + b c \|b \|c \|d x + c
+--R +
+--R 2 2 +-----------+ +-+
+--R (a d x + 2a c d)\|- a d + b c \|b
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+ +--------+
+--R +-----------+ +-+ | 2 | 2
+--R 2c\|- a d + b c \|b \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 +-----------+ +-+ +-+ | 2
+--R (- d x - 2c)\|- a d + b c \|b \|c \|a b d - b c
+--R /
+--R +-----------+ +--------+
+--R 2 +-----------+ +-+ +-+ | 2 | 2
+--R (4a d - 4a b c)\|- a d + b c \|b \|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 2 2 +-----------+ +-+ | 2
+--R ((- 2a d + 2a b c d)x - 4a c d + 4a b c )\|- a d + b c \|b \|a b d - b c
+--R Type: Expression(Integer)
+--E 755
+
+--S 756 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 756
+
+)clear all
+
+--S 757 of 1527
+t0:=1/((a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R Type: Expression(Integer)
+--E 757
+
+--S 758 of 1527
+r0:=1/2*(b*c-2*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/_
+ (a^(3/2)*(b*c-a*d)^(3/2))+1/2*b*x*sqrt(c+d*x^2)/(a*(b*c-a*d)*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +-----------+
+--R 2 2 2 x\|- a d + b c
+--R ((2a b d - b c)x + 2a d - a b c)atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R - b x\|- a d + b c \|a \|d x + c
+--R /
+--R 2 2 2 3 2 +-----------+ +-+
+--R ((2a b d - 2a b c)x + 2a d - 2a b c)\|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 758
+
+--S 759 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((4a b d - 2b c)x + 4a d - 2a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 2a b d + b c d)x + (- 2a d - 3a b c d + 2b c )x - 4a c d
+--R +
+--R 2
+--R 2a b c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +--------+
+--R 3 | 2 | 2
+--R (2b d x + 4b c x)\|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 3 +-+ | 2
+--R (- 4b d x - 4b c x)\|c \|a d - a b c
+--R /
+--R +-----------+ +--------+
+--R 2 2 2 3 2 +-+ | 2 | 2
+--R ((8a b d - 8a b c)x + 8a d - 8a b c)\|c \|a d - a b c \|d x + c
+--R +
+--R 2 2 2 4 3 2 2 2 2 2
+--R (- 4a b d + 4a b c d)x + (- 4a d - 4a b c d + 8a b c )x
+--R +
+--R 3 2 2
+--R - 8a c d + 8a b c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R ,
+--R
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((- 4a b d + 2b c)x - 4a d + 2a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R (2a b d - b c d)x + (2a d + 3a b c d - 2b c )x + 4a c d - 2a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((- 4a b d + 2b c)x - 4a d + 2a b c)\|c \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R (2a b d - b c d)x + (2a d + 3a b c d - 2b c )x + 4a c d - 2a b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +--------+
+--R 3 | 2 | 2
+--R (b d x + 2b c x)\|- a d + a b c \|d x + c
+--R +
+--R +-------------+
+--R 3 | 2 +-+
+--R (- 2b d x - 2b c x)\|- a d + a b c \|c
+--R /
+--R +-------------+ +--------+
+--R 2 2 2 3 2 | 2 +-+ | 2
+--R ((4a b d - 4a b c)x + 4a d - 4a b c)\|- a d + a b c \|c \|d x + c
+--R +
+--R 2 2 2 4 3 2 2 2 2 2
+--R (- 2a b d + 2a b c d)x + (- 2a d - 2a b c d + 4a b c )x
+--R +
+--R 3 2 2
+--R - 4a c d + 4a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 759
+
+--S 760 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R (2a d - b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R | 2 x\|- a d + b c
+--R (- 4a d + 2b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 2 +-----------+ +-+ | 2
+--R (4a d - 4a b c)\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 760
+
+--S 761 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 761
+
+--S 762 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +-+
+--R (- 2a d + b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R +-----------+ +-+ \|- a d + a b c \|c
+--R (- 2a d + b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R (- 2a d + b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 2 | 2 +-----------+ +-+
+--R (2a d - 2a b c)\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 762
+
+--S 763 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 763
+
+)clear all
+
+--S 764 of 1527
+t0:=1/(x*(a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R +--------+
+--R 2 5 3 2 | 2
+--R (b x + 2a b x + a x)\|d x + c
+--R Type: Expression(Integer)
+--E 764
+
+--S 765 of 1527
+r0:=1/2*(2*b*c-3*a*d)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))*_
+ sqrt(b)/(a^2*(b*c-a*d)^(3/2))-atanh(sqrt(c+d*x^2)/sqrt(c))/_
+ (a^2*sqrt(c))+1/2*b*sqrt(c+d*x^2)/(a*(b*c-a*d)*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 2 2 +-+ +-+ \|b \|d x + c
+--R ((3a b d - 2b c)x + 3a d - 2a b c)\|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R 2 2 2 +-----------+ \|d x + c
+--R ((- 2a b d + 2b c)x - 2a d + 2a b c)\|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R - a b\|- a d + b c \|c \|d x + c
+--R /
+--R 3 2 2 2 4 3 +-----------+ +-+
+--R ((2a b d - 2a b c)x + 2a d - 2a b c)\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 765
+
+--S 766 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 2 2 | 2
+--R ((8a b c d - 8b c )x + 8a c d - 8a b c )\|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (- 4a b d + 4b c d)x + (- 4a d - 4a b c d + 8b c )x
+--R +
+--R 2 2
+--R - 8a c d + 8a b c
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +-----------+
+--R 2 2 2 2 2 | b +-+
+--R ((6a b c d - 4b c )x + 6a c d - 4a b c ) |- --------- \|c
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 4 2 2 2 2 3 2
+--R (- 3a b c d + 2b c d)x + (- 3a c d - 4a b c d + 4b c )x
+--R +
+--R 2 2 3
+--R - 6a c d + 4a b c
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (- 2a d + 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((2a b d - 2b c)x + (2a d - 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 2 | 2
+--R (2a b c d - 4b c )x \|d x + c
+--R +
+--R 2 4 2 2 2 +-+
+--R (2b c d x + (- 2a b c d + 4b c )x )\|c
+--R /
+--R +--------+
+--R 3 2 2 2 2 4 3 2 +-+ | 2
+--R ((8a b c d - 8a b c )x + 8a c d - 8a b c )\|c \|d x + c
+--R +
+--R 3 2 2 2 2 4 4 2 3 2 2 2 3 2
+--R (- 4a b c d + 4a b c d)x + (- 4a c d - 4a b c d + 8a b c )x
+--R +
+--R 4 2 3 3
+--R - 8a c d + 8a b c
+--R ,
+--R
+--R +--------+
+--R 2 2 2 2 2 | 2
+--R ((4a b c d - 4b c )x + 4a c d - 4a b c )\|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (- 2a b d + 2b c d)x + (- 2a d - 2a b c d + 4b c )x
+--R +
+--R 2 2
+--R - 4a c d + 4a b c
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +---------+
+--R 2 2 2 2 2 | b +-+
+--R ((6a b c d - 4b c )x + 6a c d - 4a b c ) |--------- \|c
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 2 4 2 2 2 2 3 2
+--R (- 3a b c d + 2b c d)x + (- 3a c d - 4a b c d + 4b c )x
+--R +
+--R 2 2 3
+--R - 6a c d + 4a b c
+--R *
+--R +---------+
+--R | b
+--R |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R +--------+
+--R 2 2 2 | 2 2 4 2 2 2 +-+
+--R (a b c d - 2b c )x \|d x + c + (b c d x + (- a b c d + 2b c )x )\|c
+--R /
+--R +--------+
+--R 3 2 2 2 2 4 3 2 +-+ | 2
+--R ((4a b c d - 4a b c )x + 4a c d - 4a b c )\|c \|d x + c
+--R +
+--R 3 2 2 2 2 4 4 2 3 2 2 2 3 2
+--R (- 2a b c d + 2a b c d)x + (- 2a c d - 2a b c d + 4a b c )x
+--R +
+--R 4 2 3 3
+--R - 4a c d + 4a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 766
+
+--S 767 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R +-----------+ \|d x + c - \|c
+--R (4a d - 4b c)\|- a d + b c log(------------------)
+--R x
+--R +
+--R +-----------+
+--R +-----------+ | b +-+
+--R (3a d - 2b c)\|- a d + b c |- --------- \|c
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (- 2a d + 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((2a b d - 2b c)x + (2a d - 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ | 2
+--R +-+ +-+ \|b \|d x + c
+--R (- 6a d + 4b c)\|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R +-----------+ \|d x + c +-----------+
+--R (4a d - 4b c)\|- a d + b c atanh(-----------) - 2b c\|- a d + b c
+--R +-+
+--R \|c
+--R /
+--R 3 2 +-----------+ +-+
+--R (4a d - 4a b c)\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 767
+
+--S 768 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 768
+
+--S 769 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 2 +-+
+--R +-----------+ \|d x + c - \|c
+--R (2a d - 2b c)\|- a d + b c log(------------------)
+--R x
+--R +
+--R +--------+
+--R +-+ | 2
+--R +-+ +-+ \|b \|d x + c
+--R (- 3a d + 2b c)\|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R +-----------+ \|d x + c
+--R (2a d - 2b c)\|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +---------+
+--R +-----------+ | b +-+
+--R (3a d - 2b c)\|- a d + b c |--------- \|c
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R +-----------+
+--R - b c\|- a d + b c
+--R /
+--R 3 2 +-----------+ +-+
+--R (2a d - 2a b c)\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 769
+
+--S 770 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 770
+
+)clear all
+
+--S 771 of 1527
+t0:=1/(x^2*(a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R +--------+
+--R 2 6 4 2 2 | 2
+--R (b x + 2a b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 771
+
+--S 772 of 1527
+r0:=-1/2*b*(3*b*c-4*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+_
+ d*x^2)))/(a^(5/2)*(b*c-a*d)^(3/2))-1/2*(3*b*c-2*a*d)*_
+ sqrt(c+d*x^2)/(a^2*c*(b*c-a*d)*x)+1/2*b*sqrt(c+d*x^2)/_
+ (a*(b*c-a*d)*x*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +-----------+
+--R 2 3 2 3 2 2 2 x\|- a d + b c
+--R ((- 4a b c d + 3b c )x + (- 4a b c d + 3a b c )x)atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 2 2 2 +-----------+ +-+ | 2
+--R ((- 2a b d + 3b c)x - 2a d + 2a b c)\|- a d + b c \|a \|d x + c
+--R /
+--R 3 2 2 2 3 4 3 2 +-----------+ +-+
+--R ((2a b c d - 2a b c )x + (2a c d - 2a b c )x)\|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 772
+
+--S 773 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 3 2 5 2 2 2 2 3 3 3
+--R (4a b c d - 3b c d)x + (4a b c d + 13a b c d - 12b c )x
+--R +
+--R 2 2 2 3
+--R (16a b c d - 12a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 3 2 5
+--R (- 12a b c d + 9b c d)x
+--R +
+--R 2 2 2 2 3 3 3 2 2 2 3
+--R (- 12a b c d - 7a b c d + 12b c )x + (- 16a b c d + 12a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (12a b d - 18b c d)x + (12a d + 4a b c d - 24b c )x + 16a c d
+--R +
+--R 2
+--R - 16a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a d - a b c \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 4a b d + 6b c d )x + (- 4a d - 16a b c d + 30b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 20a c d + 4a b c d + 24b c )x - 16a c d + 16a b c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R /
+--R 3 2 2 2 2 5 4 2 3 2 2 2 3 3
+--R (4a b c d - 4a b c d)x + (4a c d + 12a b c d - 16a b c )x
+--R +
+--R 4 2 3 3
+--R (16a c d - 16a b c )x
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 3 2 2 2 2 5 4 2 3 2 2 2 3 3
+--R (- 12a b c d + 12a b c d)x + (- 12a c d - 4a b c d + 16a b c )x
+--R +
+--R 4 2 3 3
+--R (- 16a c d + 16a b c )x
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|c \|a d - a b c
+--R ,
+--R
+--R 2 2 3 2 5 2 2 2 2 3 3 3
+--R (4a b c d - 3b c d)x + (4a b c d + 13a b c d - 12b c )x
+--R +
+--R 2 2 2 3
+--R (16a b c d - 12a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 3 2 5
+--R (- 12a b c d + 9b c d)x
+--R +
+--R 2 2 2 2 3 3 3 2 2 2 3
+--R (- 12a b c d - 7a b c d + 12b c )x + (- 16a b c d + 12a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 2 2 3 2 5 2 2 2 2 3 3 3
+--R (4a b c d - 3b c d)x + (4a b c d + 13a b c d - 12b c )x
+--R +
+--R 2 2 2 3
+--R (16a b c d - 12a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 3 2 5
+--R (- 12a b c d + 9b c d)x
+--R +
+--R 2 2 2 2 3 3 3 2 2 2 3
+--R (- 12a b c d - 7a b c d + 12b c )x + (- 16a b c d + 12a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (6a b d - 9b c d)x + (6a d + 2a b c d - 12b c )x + 8a c d
+--R +
+--R 2
+--R - 8a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 2a b d + 3b c d )x + (- 2a d - 8a b c d + 15b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 10a c d + 2a b c d + 12b c )x - 8a c d + 8a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R 3 2 2 2 2 5 4 2 3 2 2 2 3 3
+--R (2a b c d - 2a b c d)x + (2a c d + 6a b c d - 8a b c )x
+--R +
+--R 4 2 3 3
+--R (8a c d - 8a b c )x
+--R *
+--R +-------------+ +--------+
+--R | 2 | 2
+--R \|- a d + a b c \|d x + c
+--R +
+--R 3 2 2 2 2 5 4 2 3 2 2 2 3 3
+--R (- 6a b c d + 6a b c d)x + (- 6a c d - 2a b c d + 8a b c )x
+--R +
+--R 4 2 3 3
+--R (- 8a c d + 8a b c )x
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 773
+
+--S 774 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----------+ +-+
+--R (4a b d - 3b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (8a b d - 6b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 3 2 +-----------+ +-+ | 2
+--R (4a d - 4a b c)\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 774
+
+--S 775 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 775
+
+--S 776 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 +-----------+ +-+
+--R (4a b d - 3b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 2 +-----------+ +-+ \|- a d + a b c \|c
+--R (4a b d - 3b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (4a b d - 3b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 3 2 | 2 +-----------+ +-+
+--R (2a d - 2a b c)\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 776
+
+--S 777 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 777
+
+)clear all
+
+--S 778 of 1527
+t0:=1/(x^3*(a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (b x + 2a b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 778
+
+--S 779 of 1527
+r0:=1/2*(4*b*c+a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))/(a^3*c^(3/2))-_
+ 1/2*b^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(b)*sqrt(c+d*x^2)/_
+ sqrt(b*c-a*d))/(a^3*(b*c-a*d)^(3/2))-1/2*b*(2*b*c-a*d)*_
+ sqrt(c+d*x^2)/(a^2*c*(b*c-a*d)*(a+b*x^2))-1/2*sqrt(c+d*x^2)/_
+ (a*c*x^2*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 3 2 4 2 2 2 2 +-+ +-+
+--R ((- 5a b c d + 4b c )x + (- 5a b c d + 4a b c )x )\|b \|c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 2 2 3 2 4 3 2 2 2 2 2
+--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x )
+--R *
+--R +--------+
+--R | 2
+--R +-----------+ \|d x + c
+--R \|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 2 3 2 +-----------+ +-+ | 2
+--R ((- a b d + 2a b c)x - a d + a b c)\|- a d + b c \|c \|d x + c
+--R /
+--R 4 3 2 2 4 5 4 2 2 +-----------+ +-+
+--R ((2a b c d - 2a b c )x + (2a c d - 2a b c )x )\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 779
+
+--S 780 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 2 3 3 6
+--R (- 8a b c d - 24a b c d + 32b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (- 8a c d - 40a b c d - 16a b c d + 64b c )x
+--R +
+--R 3 2 2 2 3 2 4 2
+--R (- 16a c d - 48a b c d + 64a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 8
+--R (2a b d + 6a b c d - 8b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 6
+--R (2a d + 22a b c d + 40a b c d - 64b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (16a c d + 64a b c d - 16a b c d - 64b c )x
+--R +
+--R 3 2 2 2 3 2 4 2
+--R (16a c d + 48a b c d - 64a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 2 3 3 6 2 2 2 2 3 3 4 4
+--R (20a b c d - 16b c d)x + (20a b c d + 24a b c d - 32b c )x
+--R +
+--R 2 3 2 4 2
+--R (40a b c d - 32a b c )x
+--R *
+--R +-----------+ +--------+
+--R | b +-+ | 2
+--R |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 2 2 3 3 3 2 8
+--R (- 5a b c d + 4b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 6
+--R (- 5a b c d - 36a b c d + 32b c d)x
+--R +
+--R 2 3 2 2 4 3 5 4 2 4 2 5 2
+--R (- 40a b c d - 8a b c d + 32b c )x + (- 40a b c d + 32a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (2a d - 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((- 2a b d + 2b c)x + (- 2a d + 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 3 3 6
+--R (2a b c d - 4a b c d + 8b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (2a c d + 14a b c d - 24a b c d + 16b c )x
+--R +
+--R 3 2 2 2 4 2 3 3 2 4
+--R (16a c d - 16a b c )x + 16a c d - 16a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 8 2 3 2 2 2 3 3 6
+--R - 2b c d x + (- 8a b c d + 14a b c d - 16b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (- 8a c d - 16a b c d + 32a b c d - 16b c )x
+--R +
+--R 3 2 2 2 3 2 4 2 3 3 2 4
+--R (- 24a c d + 8a b c d + 16a b c )x - 16a c d + 16a b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 2 2 3 2 3 6 5 2 2 4 3 3 2 4 4
+--R (16a b c d - 16a b c d)x + (16a c d + 16a b c d - 32a b c )x
+--R +
+--R 5 3 4 4 2
+--R (32a c d - 32a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 4 2 3 3 2 3 2 8 5 2 3 4 3 2 3 2 4 6
+--R (- 4a b c d + 4a b c d )x + (- 4a c d - 28a b c d + 32a b c d)x
+--R +
+--R 5 3 2 3 2 5 4 5 4 4 5 2
+--R (- 32a c d + 32a b c )x + (- 32a c d + 32a b c )x
+--R ,
+--R
+--R 2 3 2 2 2 3 3 6
+--R (- 4a b c d - 12a b c d + 16b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (- 4a c d - 20a b c d - 8a b c d + 32b c )x
+--R +
+--R 3 2 2 2 3 2 4 2
+--R (- 8a c d - 24a b c d + 32a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 8
+--R (a b d + 3a b c d - 4b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 6
+--R (a d + 11a b c d + 20a b c d - 32b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (8a c d + 32a b c d - 8a b c d - 32b c )x
+--R +
+--R 3 2 2 2 3 2 4 2
+--R (8a c d + 24a b c d - 32a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 2 3 3 6
+--R (- 20a b c d + 16b c d)x
+--R +
+--R 2 2 2 2 3 3 4 4
+--R (- 20a b c d - 24a b c d + 32b c )x
+--R +
+--R 2 3 2 4 2
+--R (- 40a b c d + 32a b c )x
+--R *
+--R +---------+ +--------+
+--R | b +-+ | 2
+--R |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R 2 2 3 3 3 2 8 2 2 3 2 3 2 3 4 6
+--R (5a b c d - 4b c d )x + (5a b c d + 36a b c d - 32b c d)x
+--R +
+--R 2 3 2 2 4 3 5 4 2 4 2 5 2
+--R (40a b c d + 8a b c d - 32b c )x + (40a b c d - 32a b c )x
+--R *
+--R +---------+
+--R | b
+--R |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 3 2 2 2 3 3 6
+--R (a b c d - 2a b c d + 4b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4 3 2 2 2 4 2
+--R (a c d + 7a b c d - 12a b c d + 8b c )x + (8a c d - 8a b c )x
+--R +
+--R 3 3 2 4
+--R 8a c d - 8a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 8 2 3 2 2 2 3 3 6
+--R - b c d x + (- 4a b c d + 7a b c d - 8b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (- 4a c d - 8a b c d + 16a b c d - 8b c )x
+--R +
+--R 3 2 2 2 3 2 4 2 3 3 2 4
+--R (- 12a c d + 4a b c d + 8a b c )x - 8a c d + 8a b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 2 2 3 2 3 6 5 2 2 4 3 3 2 4 4
+--R (8a b c d - 8a b c d)x + (8a c d + 8a b c d - 16a b c )x
+--R +
+--R 5 3 4 4 2
+--R (16a c d - 16a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 4 2 3 3 2 3 2 8 5 2 3 4 3 2 3 2 4 6
+--R (- 2a b c d + 2a b c d )x + (- 2a c d - 14a b c d + 16a b c d)x
+--R +
+--R 5 3 2 3 2 5 4 5 4 4 5 2
+--R (- 16a c d + 16a b c )x + (- 16a c d + 16a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 780
+
+--S 781 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +-+
+--R 2 2 2 2 +-----------+ \|d x + c - \|c
+--R (- 2a d - 6a b c d + 8b c )\|- a d + b c log(------------------)
+--R x
+--R +
+--R +-----------+
+--R 2 2 +-----------+ | b +-+
+--R (5a b c d - 4b c )\|- a d + b c |- --------- \|c
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (2a d - 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((- 2a b d + 2b c)x + (- 2a d + 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ | 2
+--R 2 2 +-+ +-+ \|b \|d x + c
+--R (10a b c d - 8b c )\|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R 2 2 2 2 +-----------+ \|d x + c
+--R (- 2a d - 6a b c d + 8b c )\|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 +-----------+
+--R 2b c \|- a d + b c
+--R /
+--R 4 3 2 +-----------+ +-+
+--R (4a c d - 4a b c )\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 781
+
+--S 782 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 782
+
+--S 783 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 2 +-+
+--R 2 2 2 2 +-----------+ \|d x + c - \|c
+--R (- a d - 3a b c d + 4b c )\|- a d + b c log(------------------)
+--R x
+--R +
+--R +--------+
+--R +-+ | 2
+--R 2 2 +-+ +-+ \|b \|d x + c
+--R (5a b c d - 4b c )\|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 2
+--R 2 2 2 2 +-----------+ \|d x + c
+--R (- a d - 3a b c d + 4b c )\|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +---------+
+--R 2 2 +-----------+ | b +-+
+--R (- 5a b c d + 4b c )\|- a d + b c |--------- \|c
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 2 +-----------+
+--R b c \|- a d + b c
+--R /
+--R 4 3 2 +-----------+ +-+
+--R (2a c d - 2a b c )\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 783
+
+--S 784 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 784
+
+)clear all
+
+--S 785 of 1527
+t0:=1/(x^4*(a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R +--------+
+--R 2 8 6 2 4 | 2
+--R (b x + 2a b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 785
+
+--S 786 of 1527
+r0:=1/2*b^2*(5*b*c-6*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+_
+ d*x^2)))/(a^(7/2)*(b*c-a*d)^(3/2))-1/6*(5*b*c-2*a*d)*_
+ sqrt(c+d*x^2)/(a^2*c*(b*c-a*d)*x^3)+1/6*(15*b^2*c^2-8*a*b*c*d-_
+ 4*a^2*d^2)*sqrt(c+d*x^2)/(a^3*c^2*(b*c-a*d)*x)+1/2*b*_
+ sqrt(c+d*x^2)/(a*(b*c-a*d)*x^3*(a+b*x^2))
+--R
+--R
+--R (2)
+--R +-----------+
+--R 3 2 4 3 5 2 2 2 3 3 3 x\|- a d + b c
+--R ((18a b c d - 15b c )x + (18a b c d - 15a b c )x )atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 2 2 2 3 2 4 3 2 2 2 2 2
+--R (4a b d + 8a b c d - 15b c )x + (4a d + 6a b c d - 10a b c )x
+--R +
+--R 3 2 2
+--R - 2a c d + 2a b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|a \|d x + c
+--R /
+--R 4 2 3 2 3 5 5 2 4 3 3 +-----------+ +-+
+--R ((6a b c d - 6a b c )x + (6a c d - 6a b c )x )\|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 786
+
+--S 787 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 3 4 3 2 9
+--R (18a b c d - 15b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 7
+--R (18a b c d + 201a b c d - 180b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 5
+--R (216a b c d + 108a b c d - 240b c )x
+--R +
+--R 2 2 4 3 5 3
+--R (288a b c d - 240a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 3 4 3 2 9
+--R (- 90a b c d + 75b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 7
+--R (- 90a b c d - 285a b c d + 300b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 5
+--R (- 360a b c d + 12a b c d + 240b c )x
+--R +
+--R 2 2 4 3 5 3
+--R (- 288a b c d + 240a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 4 2 3 3 2 2 8
+--R (- 40a b d - 80a b c d + 150b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 6
+--R (- 40a d - 220a b c d - 220a b c d + 600b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (- 140a c d - 388a b c d + 144a b c d + 480b c )x
+--R +
+--R 3 2 2 2 3 2 4 2 3 3 2 4
+--R (- 48a c d - 272a b c d + 320a b c )x + 64a c d - 64a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a d - a b c \|d x + c
+--R +
+--R 2 5 2 4 3 2 3 10
+--R (8a b d + 16a b c d - 30b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 8
+--R (8a d + 116a b c d + 188a b c d - 390b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 6
+--R (100a c d + 384a b c d + 188a b c d - 840b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4
+--R (172a c d + 516a b c d - 304a b c d - 480b c )x
+--R +
+--R 3 3 2 2 4 2 5 2 3 4 2 5
+--R (16a c d + 304a b c d - 320a b c )x - 64a c d + 64a b c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R /
+--R 4 2 3 3 2 3 2 9
+--R (12a b c d - 12a b c d )x
+--R +
+--R 5 2 3 4 3 2 3 2 4 7
+--R (12a c d + 132a b c d - 144a b c d)x
+--R +
+--R 5 3 2 4 4 3 2 5 5 5 4 4 5 3
+--R (144a c d + 48a b c d - 192a b c )x + (192a c d - 192a b c )x
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 4 2 3 3 2 3 2 9
+--R (- 60a b c d + 60a b c d )x
+--R +
+--R 5 2 3 4 3 2 3 2 4 7
+--R (- 60a c d - 180a b c d + 240a b c d)x
+--R +
+--R 5 3 2 4 4 3 2 5 5 5 4 4 5 3
+--R (- 240a c d + 48a b c d + 192a b c )x + (- 192a c d + 192a b c )x
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|c \|a d - a b c
+--R ,
+--R
+--R 3 2 3 4 3 2 9
+--R (- 18a b c d + 15b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 7
+--R (- 18a b c d - 201a b c d + 180b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 5
+--R (- 216a b c d - 108a b c d + 240b c )x
+--R +
+--R 2 2 4 3 5 3
+--R (- 288a b c d + 240a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 3 4 3 2 9
+--R (90a b c d - 75b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 7
+--R (90a b c d + 285a b c d - 300b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 5
+--R (360a b c d - 12a b c d - 240b c )x
+--R +
+--R 2 2 4 3 5 3
+--R (288a b c d - 240a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 3 2 3 4 3 2 9
+--R (- 18a b c d + 15b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 7
+--R (- 18a b c d - 201a b c d + 180b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 5
+--R (- 216a b c d - 108a b c d + 240b c )x
+--R +
+--R 2 2 4 3 5 3
+--R (- 288a b c d + 240a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 3 4 3 2 9
+--R (90a b c d - 75b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 7
+--R (90a b c d + 285a b c d - 300b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 5
+--R (360a b c d - 12a b c d - 240b c )x
+--R +
+--R 2 2 4 3 5 3
+--R (288a b c d - 240a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 2 4 2 3 3 2 2 8
+--R (- 20a b d - 40a b c d + 75b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 6
+--R (- 20a d - 110a b c d - 110a b c d + 300b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R (- 70a c d - 194a b c d + 72a b c d + 240b c )x
+--R +
+--R 3 2 2 2 3 2 4 2 3 3 2 4
+--R (- 24a c d - 136a b c d + 160a b c )x + 32a c d - 32a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 2 5 2 4 3 2 3 10
+--R (4a b d + 8a b c d - 15b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 8
+--R (4a d + 58a b c d + 94a b c d - 195b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 6
+--R (50a c d + 192a b c d + 94a b c d - 420b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4
+--R (86a c d + 258a b c d - 152a b c d - 240b c )x
+--R +
+--R 3 3 2 2 4 2 5 2 3 4 2 5
+--R (8a c d + 152a b c d - 160a b c )x - 32a c d + 32a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R 4 2 3 3 2 3 2 9 5 2 3 4 3 2 3 2 4 7
+--R (6a b c d - 6a b c d )x + (6a c d + 66a b c d - 72a b c d)x
+--R +
+--R 5 3 2 4 4 3 2 5 5 5 4 4 5 3
+--R (72a c d + 24a b c d - 96a b c )x + (96a c d - 96a b c )x
+--R *
+--R +-------------+ +--------+
+--R | 2 | 2
+--R \|- a d + a b c \|d x + c
+--R +
+--R 4 2 3 3 2 3 2 9
+--R (- 30a b c d + 30a b c d )x
+--R +
+--R 5 2 3 4 3 2 3 2 4 7
+--R (- 30a c d - 90a b c d + 120a b c d)x
+--R +
+--R 5 3 2 4 4 3 2 5 5 5 4 4 5 3
+--R (- 120a c d + 24a b c d + 96a b c )x + (- 96a c d + 96a b c )x
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 787
+
+--S 788 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 +-----------+ +-+
+--R (6a b d - 5b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 2 3 | 2 x\|- a d + b c
+--R (- 12a b d + 10b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 4 3 +-----------+ +-+ | 2
+--R (4a d - 4a b c)\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 788
+
+--S 789 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 789
+
+--S 790 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 3 +-----------+ +-+
+--R (- 6a b d + 5b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 2 3 +-----------+ +-+ \|- a d + a b c \|c
+--R (- 6a b d + 5b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 2 3 | 2 x\|- a d + b c
+--R (- 6a b d + 5b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 4 3 | 2 +-----------+ +-+
+--R (2a d - 2a b c)\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 790
+
+--S 791 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 791
+
+)clear all
+
+--S 792 of 1527
+t0:=x^4/((a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 4
+--R x
+--R (1) ---------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 792
+
+--S 793 of 1527
+r0:=-3/2*c*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*sqrt(a)/_
+ (b*c-a*d)^(5/2)+1/2*(2*b*c+a*d)*x/(b*(b*c-a*d)^2*sqrt(c+d*x^2))+_
+ 1/2*a*x/(b*(b*c-a*d)*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+ +-----------+
+--R 2 +-+ | 2 x\|- a d + b c
+--R (- 3b c x - 3a c)\|a \|d x + c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 3 +-----------+
+--R ((a d + 2b c)x + 3a c x)\|- a d + b c
+--R /
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((2a b d - 4a b c d + 2b c )x + 2a d - 4a b c d + 2a b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R Type: Expression(Integer)
+--E 793
+
+--S 794 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+
+--R 4 2 2 2 | a +-+
+--R (9b c d x + (9a c d + 12b c )x + 12a c ) |--------- \|c
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 2 2 4 2 3 2
+--R - 3b c d x + (- 3a c d - 15b c d)x + (- 15a c d - 12b c )x
+--R +
+--R 3
+--R - 12a c
+--R *
+--R +---------+
+--R | a
+--R |---------
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((- 4a d + 4b c d)x + (- 4a c d + 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 5 2 3 2 | 2
+--R ((- 2a d - 4b c d)x + (- 14a c d - 16b c )x - 24a c x)\|d x + c
+--R +
+--R 2 5 2 3 2 +-+
+--R ((6a d + 12b c d)x + (26a c d + 16b c )x + 24a c x)\|c
+--R /
+--R 2 3 2 2 3 2 4
+--R (12a b d - 24a b c d + 12b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (12a d - 8a b c d - 20a b c d + 16b c )x + 16a c d - 32a b c d
+--R +
+--R 2 3
+--R 16a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 4a b d + 8a b c d - 4b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 4a d - 12a b c d + 36a b c d - 20b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (- 20a c d + 24a b c d + 12a b c d - 16b c )x - 16a c d + 32a b c d
+--R +
+--R 2 4
+--R - 16a b c
+--R ,
+--R
+--R +-----------+
+--R 4 2 2 2 | a +-+
+--R (- 9b c d x + (- 9a c d - 12b c )x - 12a c ) |- --------- \|c
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 2 2 4 2 3 2
+--R 3b c d x + (3a c d + 15b c d)x + (15a c d + 12b c )x
+--R +
+--R 3
+--R 12a c
+--R *
+--R +-----------+
+--R | a
+--R |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 4 2 2 2 | a +-+
+--R (9b c d x + (9a c d + 12b c )x + 12a c ) |- --------- \|c
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 2 2 4 2 3 2
+--R - 3b c d x + (- 3a c d - 15b c d)x + (- 15a c d - 12b c )x
+--R +
+--R 3
+--R - 12a c
+--R *
+--R +-----------+
+--R | a
+--R |- ---------
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +--------+
+--R 2 5 2 3 2 | 2
+--R ((- a d - 2b c d)x + (- 7a c d - 8b c )x - 12a c x)\|d x + c
+--R +
+--R 2 5 2 3 2 +-+
+--R ((3a d + 6b c d)x + (13a c d + 8b c )x + 12a c x)\|c
+--R /
+--R 2 3 2 2 3 2 4
+--R (6a b d - 12a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (6a d - 4a b c d - 10a b c d + 8b c )x + 8a c d - 16a b c d
+--R +
+--R 2 3
+--R 8a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 2a b d + 4a b c d - 2b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 2a d - 6a b c d + 18a b c d - 10b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (- 10a c d + 12a b c d + 6a b c d - 8b c )x - 8a c d + 16a b c d
+--R +
+--R 2 4
+--R - 8a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 794
+
+--S 795 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-----------+ | a
+--R 3c\|- a d + b c |---------
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((2a d - 2b c d)x + (4a c d - 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((- 4a d + 4b c d)x + (- 4a c d + 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+
+--R +-+ x\|- a d + b c
+--R 6c\|a atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 2 2 2 +-----------+
+--R (4a d - 8a b c d + 4b c )\|- a d + b c
+--R Type: Expression(Integer)
+--E 795
+
+--S 796 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 796
+
+--S 797 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R -
+--R +-----------+
+--R +-----------+ | a
+--R 3c\|- a d + b c |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+ +-+
+--R +-----------+ | a a\|c
+--R 3c\|- a d + b c |- --------- atan(--------------------------)
+--R \| a d - b c +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-+ x\|- a d + b c
+--R 3c\|a atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 2 2 2 2 +-----------+
+--R (2a d - 4a b c d + 2b c )\|- a d + b c
+--R Type: Expression(Integer)
+--E 797
+
+--S 798 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 798
+
+)clear all
+
+--S 799 of 1527
+t0:=x^3/((a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 3
+--R x
+--R (1) ---------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 799
+
+--S 800 of 1527
+r0:=-1/2*(2*b*c+a*d)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/_
+ ((b*c-a*d)^(5/2)*sqrt(b))+1/2*(2*b*c+a*d)/(b*(b*c-a*d)^2*_
+ sqrt(c+d*x^2))+1/2*a/(b*(b*c-a*d)*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ +-+ | 2
+--R 2 2 2 | 2 \|b \|d x + c
+--R ((- a b d - 2b c)x - a d - 2a b c)\|d x + c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 +-----------+ +-+
+--R ((a d + 2b c)x + 3a c)\|- a d + b c \|b
+--R /
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((2a b d - 4a b c d + 2b c )x + 2a d - 4a b c d + 2a b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|b \|d x + c
+--R Type: Expression(Integer)
+--E 800
+
+--S 801 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 4 2 2 2 2 2 2
+--R (3a b d + 6b c d)x + (3a d + 10a b c d + 8b c )x + 4a c d
+--R +
+--R 2
+--R 8a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- a b d - 2b c d )x + (- a d - 7a b c d - 10b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 5a c d - 14a b c d - 8b c )x - 4a c d - 8a b c
+--R *
+--R log
+--R 2 2 2 3 2 4
+--R (2a b d + 2a b c d - 4b c )x
+--R +
+--R 2 2 2 2
+--R (8a b c d - 8a b c )x
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a b c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b c d + 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+ +--------+
+--R 2 4 2 2 | 2 | 2
+--R ((- 2a d + 14b c d)x + (4a c d + 8b c )x )\|- a b d + b c \|d x + c
+--R +
+--R +-------------+
+--R 2 6 4 2 2 | 2 +-+
+--R (- 6b d x - 18b c d x + (- 4a c d - 8b c )x )\|- a b d + b c \|c
+--R /
+--R 2 3 2 2 3 2 4
+--R (12a b d - 24a b c d + 12b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (12a d - 8a b c d - 20a b c d + 16b c )x + 16a c d - 32a b c d
+--R +
+--R 2 3
+--R 16a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a b d + b c \|c \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 4a b d + 8a b c d - 4b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 4a d - 12a b c d + 36a b c d - 20b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 20a c d + 24a b c d + 12a b c d - 16b c )x - 16a c d
+--R +
+--R 2 3 2 4
+--R 32a b c d - 16a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a b d + b c
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2
+--R (- 3a b d - 6b c d)x + (- 3a d - 10a b c d - 8b c )x
+--R +
+--R 2 2
+--R - 4a c d - 8a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (a b d + 2b c d )x + (a d + 7a b c d + 10b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (5a c d + 14a b c d + 8b c )x + 4a c d + 8a b c
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+ +--------+
+--R 2 4 2 2 | 2 | 2
+--R ((- a d + 7b c d)x + (2a c d + 4b c )x )\|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 6 4 2 2 +-+ | 2
+--R (- 3b d x - 9b c d x + (- 2a c d - 4b c )x )\|c \|a b d - b c
+--R /
+--R 2 3 2 2 3 2 4
+--R (6a b d - 12a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (6a d - 4a b c d - 10a b c d + 8b c )x + 8a c d - 16a b c d
+--R +
+--R 2 3
+--R 8a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a b d - b c \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 2a b d + 4a b c d - 2b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 2a d - 6a b c d + 18a b c d - 10b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 10a c d + 12a b c d + 6a b c d - 8b c )x - 8a c d
+--R +
+--R 2 3 2 4
+--R 16a b c d - 8a b c
+--R *
+--R +-----------+
+--R | 2
+--R \|a b d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 801
+
+--S 802 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 2 +-----------+ +-+ | 2
+--R ((a d + 2b c d)x + 4a c d + 8b c )\|- a d + b c \|b \|d x + c
+--R +
+--R 2 2 2 +-----------+ +-+ +-+
+--R ((- 3a d - 6b c d)x - 4a c d - 8b c )\|- a d + b c \|b \|c
+--R *
+--R log
+--R 2 2 2 3 2 4 2 2 2 2
+--R ((2a b d + 2a b c d - 4b c )x + (8a b c d - 8a b c )x )
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+
+--R 2 2 4 2 2 2 2 2 | 2
+--R (4b c x + (4a c d + 8a b c )x + 8a c )\|- a b d + b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a b d + b c \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a b c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b c d + 8a b c )x
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +-------------+ +--------+
+--R 2 2 2 | 2 | 2
+--R ((2a d + 4b c d)x + 8a c d + 16b c )\|- a b d + b c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 2 | 2 +-+
+--R ((- 6a d - 12b c d)x - 8a c d - 16b c )\|- a b d + b c \|c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +-------------+ +--------+
+--R 2 | 2 +-----------+ +-+ +-+ | 2
+--R (6d x + 24c)\|- a b d + b c \|- a d + b c \|b \|c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 | 2 +-----------+ +-+
+--R (- 18c d x - 24c )\|- a b d + b c \|- a d + b c \|b
+--R /
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((4a d - 8a b c d + 4b c d)x + 16a c d - 32a b c d + 16b c )
+--R *
+--R +-------------+ +--------+
+--R | 2 +-----------+ +-+ | 2
+--R \|- a b d + b c \|- a d + b c \|b \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 12a d + 24a b c d - 12b c d)x - 16a c d + 32a b c d - 16b c )
+--R *
+--R +-------------+
+--R | 2 +-----------+ +-+ +-+
+--R \|- a b d + b c \|- a d + b c \|b \|c
+--R Type: Expression(Integer)
+--E 802
+
+--S 803 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 803
+
+--S 804 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +--------+
+--R 2 2 2 | 2 | 2
+--R ((a d + 2b c d)x + 4a c d + 8b c )\|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 2 +-+ | 2
+--R ((- 3a d - 6b c d)x - 4a c d - 8b c )\|c \|a b d - b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 +-----------+ +-+ | 2
+--R ((- a d - 2b c d)x - 4a c d - 8b c )\|- a d + b c \|b \|d x + c
+--R +
+--R 2 2 2 +-----------+ +-+ +-+
+--R ((3a d + 6b c d)x + 4a c d + 8b c )\|- a d + b c \|b \|c
+--R *
+--R +-----------+ +--------+ +-----------+
+--R | 2 | 2 2 +-+ | 2
+--R a\|a b d - b c \|d x + c + (- b x - a)\|c \|a b d - b c
+--R atan(-----------------------------------------------------------)
+--R 2 2
+--R (a b d - b c)x
+--R +
+--R +-----------+ +--------+
+--R 2 +-----------+ +-+ +-+ | 2 | 2
+--R (3d x + 12c)\|- a d + b c \|b \|c \|a b d - b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 +-----------+ +-+ | 2
+--R (- 9c d x - 12c )\|- a d + b c \|b \|a b d - b c
+--R /
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((2a d - 4a b c d + 2b c d)x + 8a c d - 16a b c d + 8b c )
+--R *
+--R +-----------+ +--------+
+--R +-----------+ +-+ | 2 | 2
+--R \|- a d + b c \|b \|a b d - b c \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 6a d + 12a b c d - 6b c d)x - 8a c d + 16a b c d - 8b c )
+--R *
+--R +-----------+
+--R +-----------+ +-+ +-+ | 2
+--R \|- a d + b c \|b \|c \|a b d - b c
+--R Type: Expression(Integer)
+--E 804
+
+--S 805 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 805
+
+)clear all
+
+--S 806 of 1527
+t0:=x^2/((a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 806
+
+--S 807 of 1527
+r0:=1/2*(b*c+2*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/_
+ ((b*c-a*d)^(5/2)*sqrt(a))-3/2*d*x/((b*c-a*d)^2*sqrt(c+d*x^2))-_
+ 1/2*x/((b*c-a*d)*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+ +-----------+
+--R 2 2 2 | 2 x\|- a d + b c
+--R ((2a b d + b c)x + 2a d + a b c)\|d x + c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 3 +-----------+ +-+
+--R (- 3b d x + (- 2a d - b c)x)\|- a d + b c \|a
+--R /
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((2a b d - 4a b c d + 2b c )x + 2a d - 4a b c d + 2a b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 807
+
+--S 808 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 4 2 2 2 2 2 2
+--R (6a b d + 3b c d)x + (6a d + 11a b c d + 4b c )x + 8a c d
+--R +
+--R 2
+--R 4a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 2a b d - b c d )x + (- 2a d - 11a b c d - 5b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 10a c d - 13a b c d - 4b c )x - 8a c d - 4a b c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+
+--R 2 5 2 3 2 | 2
+--R (6b d x + (4a d + 26b c d)x + (16a c d + 8b c )x)\|a d - a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 2 3 2 +-+
+--R (- 18b d x + (- 12a d - 30b c d)x + (- 16a c d - 8b c )x)\|c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R /
+--R 2 3 2 2 3 2 4
+--R (12a b d - 24a b c d + 12b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (12a d - 8a b c d - 20a b c d + 16b c )x + 16a c d - 32a b c d
+--R +
+--R 2 3
+--R 16a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a d - a b c \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 4a b d + 8a b c d - 4b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 4a d - 12a b c d + 36a b c d - 20b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 20a c d + 24a b c d + 12a b c d - 16b c )x - 16a c d
+--R +
+--R 2 3 2 4
+--R 32a b c d - 16a b c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R ,
+--R
+--R 2 2 4 2 2 2 2 2
+--R (- 6a b d - 3b c d)x + (- 6a d - 11a b c d - 4b c )x
+--R +
+--R 2 2
+--R - 8a c d - 4a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (2a b d + b c d )x + (2a d + 11a b c d + 5b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (10a c d + 13a b c d + 4b c )x + 8a c d + 4a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R (- 6a b d - 3b c d)x + (- 6a d - 11a b c d - 4b c )x
+--R +
+--R 2 2
+--R - 8a c d - 4a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (2a b d + b c d )x + (2a d + 11a b c d + 5b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (10a c d + 13a b c d + 4b c )x + 8a c d + 4a b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+
+--R 2 5 2 3 2 | 2
+--R (3b d x + (2a d + 13b c d)x + (8a c d + 4b c )x)\|- a d + a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 5 2 3 2
+--R (- 9b d x + (- 6a d - 15b c d)x + (- 8a c d - 4b c )x)
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R /
+--R 2 3 2 2 3 2 4
+--R (6a b d - 12a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (6a d - 4a b c d - 10a b c d + 8b c )x + 8a c d - 16a b c d
+--R +
+--R 2 3
+--R 8a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 2a b d + 4a b c d - 2b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 2a d - 6a b c d + 18a b c d - 10b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 10a c d + 12a b c d + 6a b c d - 8b c )x - 8a c d
+--R +
+--R 2 3 2 4
+--R 16a b c d - 8a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 808
+
+--S 809 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R (2a d + b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R | 2 x\|- a d + b c
+--R (- 4a d - 2b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 2 2 2 2 +-----------+ +-+ | 2
+--R (4a d - 8a b c d + 4b c )\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 809
+
+--S 810 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 810
+
+--S 811 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +-+
+--R (- 2a d - b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R +-----------+ +-+ \|- a d + a b c \|c
+--R (- 2a d - b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R (- 2a d - b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 2 2 2 2 | 2 +-----------+ +-+
+--R (2a d - 4a b c d + 2b c )\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 811
+
+--S 812 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 812
+
+)clear all
+
+--S 813 of 1527
+t0:=x/((a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R x
+--R (1) ---------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 813
+
+--S 814 of 1527
+r0:=3/2*d*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))*sqrt(b)/_
+ (b*c-a*d)^(5/2)-3/2*d/((b*c-a*d)^2*sqrt(c+d*x^2))+(-1/2)/_
+ ((b*c-a*d)*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ +-+ | 2
+--R 2 +-+ | 2 \|b \|d x + c
+--R (3b d x + 3a d)\|b \|d x + c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 +-----------+
+--R (- 3b d x - 2a d - b c)\|- a d + b c
+--R /
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((2a b d - 4a b c d + 2b c )x + 2a d - 4a b c d + 2a b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R Type: Expression(Integer)
+--E 814
+
+--S 815 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+
+--R 2 4 2 2 2 2 2 2 | b
+--R (9a b c d x + (9a c d + 12a b c d)x + 12a c d) |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 6 2 3 2 2 4
+--R - 3a b c d x + (- 3a c d - 15a b c d )x
+--R +
+--R 2 2 2 3 2 2 3
+--R (- 15a c d - 12a b c d)x - 12a c d
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R 2 2 2 2 4
+--R (- 2a d - 2a b c d + 4b c )x
+--R +
+--R 2 2 2
+--R (- 8a c d + 8a b c )x
+--R *
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (2a b c d - 2b c d)x + (6a c d - 2a b c d - 4b c )x
+--R +
+--R 2 2 3 2
+--R (8a c d - 8a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 4 2 2 2 2 3 2
+--R ((- 6a b c d - 6b c d)x + (- 8a c d + 4a b c d - 8b c )x )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (4a b d + 2b c d )x + (4a d + 4a b c d + 10b c d)x
+--R +
+--R 2 2 2 2 3 2
+--R (8a c d - 4a b c d + 8b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 3 3 2 2 2 2 3 3 4
+--R (12a b c d - 24a b c d + 12a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2
+--R (12a c d - 8a b c d - 20a b c d + 16a b c )x + 16a c d
+--R +
+--R 3 3 2 2 4
+--R - 32a b c d + 16a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 4 2 2 2 3 3 3 2 6
+--R (- 4a b c d + 8a b c d - 4a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4
+--R (- 4a c d - 12a b c d + 36a b c d - 20a b c d)x
+--R +
+--R 4 2 3 3 3 2 2 2 4 3 5 2 4 3 2
+--R (- 20a c d + 24a b c d + 12a b c d - 16a b c )x - 16a c d
+--R +
+--R 3 4 2 2 5
+--R 32a b c d - 16a b c
+--R ,
+--R
+--R +---------+
+--R 2 4 2 2 2 2 2 2 | b +-+
+--R (9a b c d x + (9a c d + 12a b c d)x + 12a c d) |--------- \|c
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 6 2 3 2 2 4
+--R - 3a b c d x + (- 3a c d - 15a b c d )x
+--R +
+--R 2 2 2 3 2 2 3
+--R (- 15a c d - 12a b c d)x - 12a c d
+--R *
+--R +---------+
+--R | b
+--R |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b
+--R (a d - b c)x |---------
+--R \|a d - b c
+--R +
+--R 2 2 2 4 2 2 2 2 3 2
+--R ((- 3a b c d - 3b c d)x + (- 4a c d + 2a b c d - 4b c )x )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (2a b d + b c d )x + (2a d + 2a b c d + 5b c d)x
+--R +
+--R 2 2 2 2 3 2
+--R (4a c d - 2a b c d + 4b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 3 3 2 2 2 2 3 3 4
+--R (6a b c d - 12a b c d + 6a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2 3 3
+--R (6a c d - 4a b c d - 10a b c d + 8a b c )x + 8a c d - 16a b c d
+--R +
+--R 2 2 4
+--R 8a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 4 2 2 2 3 3 3 2 6
+--R (- 2a b c d + 4a b c d - 2a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4
+--R (- 2a c d - 6a b c d + 18a b c d - 10a b c d)x
+--R +
+--R 4 2 3 3 3 2 2 2 4 3 5 2 4 3 2 3 4
+--R (- 10a c d + 12a b c d + 6a b c d - 8a b c )x - 8a c d + 16a b c d
+--R +
+--R 2 2 5
+--R - 8a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 815
+
+--S 816 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +--------+
+--R 2 2 2 +-----------+ | b | 2
+--R (3a c d x + 12a c d)\|- a d + b c |- --------- \|d x + c
+--R \| a d - b c
+--R +
+--R +-----------+
+--R 2 2 2 +-----------+ | b +-+
+--R (- 9a c d x - 12a c d)\|- a d + b c |- --------- \|c
+--R \| a d - b c
+--R *
+--R log
+--R 2 2 2 2 4 2 2 2
+--R ((- 2a d - 2a b c d + 4b c )x + (- 8a c d + 8a b c )x )
+--R *
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (2a b c d - 2b c d)x + (6a c d - 2a b c d - 4b c )x
+--R +
+--R 2 2 3 2
+--R (8a c d - 8a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R (- 6a c d x - 24a c d)\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R (18a c d x + 24a c d)\|b \|c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 2 2 2 +-----------+ +-+ | 2
+--R ((- 4a d - 2b c d)x - 16a c d - 8b c )\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 2 3 +-----------+
+--R ((12a c d + 6b c d)x + 16a c d + 8b c )\|- a d + b c
+--R /
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3 2 4
+--R ((4a c d - 8a b c d + 4a b c d)x + 16a c d - 32a b c d + 16a b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3
+--R (- 12a c d + 24a b c d - 12a b c d)x - 16a c d + 32a b c d
+--R +
+--R 2 4
+--R - 16a b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 816
+
+--S 817 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 817
+
+--S 818 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R (- 3a c d x - 12a c d)\|b \|d x + c
+--R +
+--R 2 2 2 +-+ +-+
+--R (9a c d x + 12a c d)\|b \|c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +---------+ +--------+
+--R 2 2 2 +-----------+ | b | 2
+--R (3a c d x + 12a c d)\|- a d + b c |--------- \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 2 2 +-----------+ | b +-+
+--R (- 9a c d x - 12a c d)\|- a d + b c |--------- \|c
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b
+--R (a d - b c)x |---------
+--R \|a d - b c
+--R +
+--R +--------+
+--R 2 2 2 +-----------+ +-+ | 2
+--R ((- 2a d - b c d)x - 8a c d - 4b c )\|- a d + b c \|c \|d x + c
+--R +
+--R 2 2 2 2 3 +-----------+
+--R ((6a c d + 3b c d)x + 8a c d + 4b c )\|- a d + b c
+--R /
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3 2 4
+--R ((2a c d - 4a b c d + 2a b c d)x + 8a c d - 16a b c d + 8a b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3 2 4
+--R ((- 6a c d + 12a b c d - 6a b c d)x - 8a c d + 16a b c d - 8a b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 818
+
+--S 819 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 819
+
+)clear all
+
+--S 820 of 1527
+t0:=1/((a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ---------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 820
+
+--S 821 of 1527
+r0:=1/2*b*(b*c-4*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/_
+ (a^(3/2)*(b*c-a*d)^(5/2))+1/2*d*(b*c+2*a*d)*x/(a*c*(b*c-a*d)^2*_
+ sqrt(c+d*x^2))+1/2*b*x/(a*(b*c-a*d)*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R 2 3 2 2 2 2 2 | 2
+--R ((- 4a b c d + b c )x - 4a b c d + a b c )\|d x + c
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 2 2 3 2 2 2 2 +-----------+ +-+
+--R ((2a b d + b c d)x + (2a d + b c )x)\|- a d + b c \|a
+--R /
+--R 3 2 2 2 2 3 3 2 4 2 3 2 2 2 3
+--R ((2a b c d - 4a b c d + 2a b c )x + 2a c d - 4a b c d + 2a b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 821
+
+--S 822 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (12a b c d - 3b c d)x + (12a b c d + 13a b c d - 4b c )x
+--R +
+--R 2 2 2 3
+--R 16a b c d - 4a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (- 4a b c d + b c d )x + (- 4a b c d - 19a b c d + 5b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (- 20a b c d - 11a b c d + 4b c )x - 16a b c d + 4a b c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 3 2 2 5 2 3 2 2 2 3
+--R (- 4a b d - 2b c d )x + (- 4a d - 16a b c d - 10b c d)x
+--R +
+--R 2 2 2 3
+--R (- 16a c d - 8b c )x
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 3 2 2 5 2 3 2 2 2 3
+--R (12a b d + 6b c d )x + (12a d + 16a b c d + 14b c d)x
+--R +
+--R 2 2 2 3
+--R (16a c d + 8b c )x
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|c \|a d - a b c
+--R /
+--R 3 3 2 2 2 2 3 3 4
+--R (12a b c d - 24a b c d + 12a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2
+--R (12a c d - 8a b c d - 20a b c d + 16a b c )x + 16a c d
+--R +
+--R 3 3 2 2 4
+--R - 32a b c d + 16a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a d - a b c \|d x + c
+--R +
+--R 3 4 2 2 2 3 3 3 2 6
+--R (- 4a b c d + 8a b c d - 4a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4
+--R (- 4a c d - 12a b c d + 36a b c d - 20a b c d)x
+--R +
+--R 4 2 3 3 3 2 2 2 4 3 5 2 4 3 2
+--R (- 20a c d + 24a b c d + 12a b c d - 16a b c )x - 16a c d
+--R +
+--R 3 4 2 2 5
+--R 32a b c d - 16a b c
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+--R | 2
+--R \|a d - a b c
+--R ,
+--R
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (12a b c d - 3b c d)x + (12a b c d + 13a b c d - 4b c )x
+--R +
+--R 2 2 2 3
+--R 16a b c d - 4a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (- 4a b c d + b c d )x + (- 4a b c d - 19a b c d + 5b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (- 20a b c d - 11a b c d + 4b c )x - 16a b c d + 4a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (12a b c d - 3b c d)x + (12a b c d + 13a b c d - 4b c )x
+--R +
+--R 2 2 2 3
+--R 16a b c d - 4a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (- 4a b c d + b c d )x + (- 4a b c d - 19a b c d + 5b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (- 20a b c d - 11a b c d + 4b c )x - 16a b c d + 4a b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 3 2 2 5 2 3 2 2 2 3
+--R (- 2a b d - b c d )x + (- 2a d - 8a b c d - 5b c d)x
+--R +
+--R 2 2 2 3
+--R (- 8a c d - 4b c )x
+--R *
+--R +-------------+ +--------+
+--R | 2 | 2
+--R \|- a d + a b c \|d x + c
+--R +
+--R 3 2 2 5 2 3 2 2 2 3
+--R (6a b d + 3b c d )x + (6a d + 8a b c d + 7b c d)x
+--R +
+--R 2 2 2 3
+--R (8a c d + 4b c )x
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R /
+--R 3 3 2 2 2 2 3 3 4
+--R (6a b c d - 12a b c d + 6a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2 3 3
+--R (6a c d - 4a b c d - 10a b c d + 8a b c )x + 8a c d - 16a b c d
+--R +
+--R 2 2 4
+--R 8a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 3 4 2 2 2 3 3 3 2 6
+--R (- 2a b c d + 4a b c d - 2a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4
+--R (- 2a c d - 6a b c d + 18a b c d - 10a b c d)x
+--R +
+--R 4 2 3 3 3 2 2 2 4 3 5 2 4 3 2
+--R (- 10a c d + 12a b c d + 6a b c d - 8a b c )x - 8a c d
+--R +
+--R 3 4 2 2 5
+--R 16a b c d - 8a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 822
+
+--S 823 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----------+ +-+
+--R (4a b d - b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (8a b d - 2b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 3 2 2 2 2 +-----------+ +-+ | 2
+--R (4a d - 8a b c d + 4a b c )\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 823
+
+--S 824 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 824
+
+--S 825 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 +-----------+ +-+
+--R (4a b d - b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 2 +-----------+ +-+ \|- a d + a b c \|c
+--R (4a b d - b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (4a b d - b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 3 2 2 2 2 | 2 +-----------+ +-+
+--R (2a d - 4a b c d + 2a b c )\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 825
+
+--S 826 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 826
+
+)clear all
+
+--S 827 of 1527
+t0:=1/(x*(a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------------------
+--R +--------+
+--R 2 7 2 5 2 3 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x)\|d x + c
+--R Type: Expression(Integer)
+--E 827
+
+--S 828 of 1527
+r0:=-atanh(sqrt(c+d*x^2)/sqrt(c))/(a^2*c^(3/2))+1/2*b^(3/2)*_
+ (2*b*c-5*a*d)*atanh(sqrt(b)*sqrt(c+d*x^2)/sqrt(b*c-a*d))/_
+ (a^2*(b*c-a*d)^(5/2))+1/2*d*(b*c+2*a*d)/(a*c*(b*c-a*d)^2*_
+ sqrt(c+d*x^2))+1/2*b/(a*(b*c-a*d)*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R 2 3 2 2 2 2 2 +-+ +-+ | 2
+--R ((- 5a b c d + 2b c )x - 5a b c d + 2a b c )\|b \|c \|d x + c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 2a b d + 4a b c d - 2b c )x - 2a d + 4a b c d - 2a b c )
+--R *
+--R +--------+
+--R +--------+ | 2
+--R +-----------+ | 2 \|d x + c
+--R \|- a d + b c \|d x + c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2 3 2 2 2 +-----------+ +-+
+--R ((2a b d + a b c d)x + 2a d + a b c )\|- a d + b c \|c
+--R /
+--R 4 2 3 2 2 2 3 3 2 5 2 4 2 3 2 3
+--R ((2a b c d - 4a b c d + 2a b c )x + 2a c d - 4a b c d + 2a b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R Type: Expression(Integer)
+--E 828
+
+--S 829 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 2 3 3 4
+--R (12a b c d - 24a b c d + 12b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (12a c d - 8a b c d - 20a b c d + 16b c )x + 16a c d
+--R +
+--R 2 3 2 4
+--R - 32a b c d + 16a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 4a b d + 8a b c d - 4b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 4a d - 12a b c d + 36a b c d - 20b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 20a c d + 24a b c d + 12a b c d - 16b c )x - 16a c d
+--R +
+--R 2 3 2 4
+--R 32a b c d - 16a b c
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 2 3 3 4 2 2 2 2 3 3 4 2
+--R (15a b c d - 6b c d)x + (15a b c d + 14a b c d - 8b c )x
+--R +
+--R 2 3 2 4
+--R 20a b c d - 8a b c
+--R *
+--R +-----------+ +--------+
+--R | b +-+ | 2
+--R |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 2 2 3 3 3 2 6
+--R (- 5a b c d + 2b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 4
+--R (- 5a b c d - 23a b c d + 10b c d)x
+--R +
+--R 2 3 2 2 4 3 5 2 2 4 2 5
+--R (- 25a b c d - 10a b c d + 8b c )x - 20a b c d + 8a b c
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (2a d - 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((- 2a b d + 2b c)x + (- 2a d + 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 3 2 2 2 3 3 4 3 3 2 3 3 4 2
+--R ((8a b c d - 2a b c d + 6b c d)x + (8a c d - 4a b c d + 8b c )x )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 6
+--R (- 4a b d - 2b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 4a d - 8a b c d + 4a b c d - 10b c d)x
+--R +
+--R 3 3 2 3 3 4 2
+--R (- 8a c d + 4a b c d - 8b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 2 3 3 2 3 2 2 3 4 4
+--R (12a b c d - 24a b c d + 12a b c d)x
+--R +
+--R 5 2 3 4 3 2 3 2 4 2 3 5 2 5 3 2
+--R (12a c d - 8a b c d - 20a b c d + 16a b c )x + 16a c d
+--R +
+--R 4 4 3 2 5
+--R - 32a b c d + 16a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 4 2 4 3 2 3 3 2 3 4 2 6
+--R (- 4a b c d + 8a b c d - 4a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4
+--R (- 4a c d - 12a b c d + 36a b c d - 20a b c d)x
+--R +
+--R 5 3 3 4 4 2 3 2 5 2 3 6 2 5 4 2
+--R (- 20a c d + 24a b c d + 12a b c d - 16a b c )x - 16a c d
+--R +
+--R 4 5 3 2 6
+--R 32a b c d - 16a b c
+--R ,
+--R
+--R 2 3 2 2 2 3 3 4
+--R (6a b c d - 12a b c d + 6b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (6a c d - 4a b c d - 10a b c d + 8b c )x + 8a c d
+--R +
+--R 2 3 2 4
+--R - 16a b c d + 8a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 2a b d + 4a b c d - 2b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 2a d - 6a b c d + 18a b c d - 10b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 10a c d + 12a b c d + 6a b c d - 8b c )x - 8a c d
+--R +
+--R 2 3 2 4
+--R 16a b c d - 8a b c
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 2 3 3 4
+--R (- 15a b c d + 6b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (- 15a b c d - 14a b c d + 8b c )x - 20a b c d + 8a b c
+--R *
+--R +---------+ +--------+
+--R | b +-+ | 2
+--R |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R 2 2 3 3 3 2 6 2 2 3 2 3 2 3 4 4
+--R (5a b c d - 2b c d )x + (5a b c d + 23a b c d - 10b c d)x
+--R +
+--R 2 3 2 2 4 3 5 2 2 4 2 5
+--R (25a b c d + 10a b c d - 8b c )x + 20a b c d - 8a b c
+--R *
+--R +---------+
+--R | b
+--R |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 3 2 2 2 3 3 4 3 3 2 3 3 4 2
+--R ((4a b c d - a b c d + 3b c d)x + (4a c d - 2a b c d + 4b c )x )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 3 2 2 6
+--R (- 2a b d - b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 2a d - 4a b c d + 2a b c d - 5b c d)x
+--R +
+--R 3 3 2 3 3 4 2
+--R (- 4a c d + 2a b c d - 4b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 2 3 3 2 3 2 2 3 4 4
+--R (6a b c d - 12a b c d + 6a b c d)x
+--R +
+--R 5 2 3 4 3 2 3 2 4 2 3 5 2 5 3 2 4 4
+--R (6a c d - 4a b c d - 10a b c d + 8a b c )x + 8a c d - 16a b c d
+--R +
+--R 3 2 5
+--R 8a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 4 2 4 3 2 3 3 2 3 4 2 6
+--R (- 2a b c d + 4a b c d - 2a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4
+--R (- 2a c d - 6a b c d + 18a b c d - 10a b c d)x
+--R +
+--R 5 3 3 4 4 2 3 2 5 2 3 6 2 5 4 2 4 5
+--R (- 10a c d + 12a b c d + 6a b c d - 8a b c )x - 8a c d + 16a b c d
+--R +
+--R 3 2 6
+--R - 8a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 829
+
+--S 830 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((4a d - 8a b c d + 4b c d)x + 16a c d - 32a b c d + 16b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2
+--R (- 12a d + 24a b c d - 12b c d)x - 16a c d + 32a b c d
+--R +
+--R 2 3
+--R - 16b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 2 2 2 2 3 +-----------+
+--R ((5a b c d - 2b c d)x + 20a b c d - 8b c )\|- a d + b c
+--R *
+--R +-----------+ +--------+
+--R | b +-+ | 2
+--R |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 2 2 2 3 2 3 2 4 +-----------+
+--R ((- 15a b c d + 6b c d)x - 20a b c d + 8b c )\|- a d + b c
+--R *
+--R +-----------+
+--R | b
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+--R *
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+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (2a d - 2a b c)x |- --------- )
+--R \| a d - b c
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+--R \|d x + c
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+--R 2 4 2 2 | b +-+
+--R ((- 2a b d + 2b c)x + (- 2a d + 2a b c)x ) |- --------- \|c
+--R \| a d - b c
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+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
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+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 2 2 2 2 3 +-+ +-+ | 2
+--R ((10a b c d - 4b c d)x + 40a b c d - 16b c )\|b \|c \|d x + c
+--R +
+--R 2 2 2 3 2 3 2 4 +-+
+--R ((- 30a b c d + 12b c d)x - 40a b c d + 16b c )\|b
+--R *
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+--R \|b \|d x + c
+--R atanh(---------------)
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+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((4a d - 8a b c d + 4b c d)x + 16a c d - 32a b c d + 16b c )
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+--R 2 3 2 2 2 2 2 2 2
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+--R +
+--R 2 3
+--R - 16b c
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+--R | 2
+--R \|d x + c
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+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 3 2 2 2 2 2 2 3 +-----------+ | 2
+--R ((4a d + 2b c d)x + 16a c d + 8b c )\|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 3 +-----------+ +-+
+--R ((- 12a d - 6b c d)x - 16a c d - 8b c )\|- a d + b c \|c
+--R /
+--R 4 3 3 2 2 2 2 3 2 4 2 2 3 3 2 2 4
+--R ((4a c d - 8a b c d + 4a b c d)x + 16a c d - 32a b c d + 16a b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 4 2 3 3 3 2 2 2 4 2 4 3 2 3 4
+--R (- 12a c d + 24a b c d - 12a b c d)x - 16a c d + 32a b c d
+--R +
+--R 2 2 5
+--R - 16a b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R Type: Expression(Integer)
+--E 830
+
+--S 831 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 831
+
+--S 832 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((2a d - 4a b c d + 2b c d)x + 8a c d - 16a b c d + 8b c )
+--R *
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+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 6a d + 12a b c d - 6b c d)x - 8a c d + 16a b c d - 8b c )
+--R *
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+--R \|- a d + b c \|c
+--R *
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+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 2 2 2 2 3 +-+ +-+ | 2
+--R ((5a b c d - 2b c d)x + 20a b c d - 8b c )\|b \|c \|d x + c
+--R +
+--R 2 2 2 3 2 3 2 4 +-+
+--R ((- 15a b c d + 6b c d)x - 20a b c d + 8b c )\|b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((2a d - 4a b c d + 2b c d)x + 8a c d - 16a b c d + 8b c )
+--R *
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+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((- 6a d + 12a b c d - 6b c d)x - 8a c d + 16a b c d - 8b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2 2 2 3 +-----------+
+--R ((- 5a b c d + 2b c d)x - 20a b c d + 8b c )\|- a d + b c
+--R *
+--R +---------+ +--------+
+--R | b +-+ | 2
+--R |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R +---------+
+--R 2 2 2 3 2 3 2 4 +-----------+ | b
+--R ((15a b c d - 6b c d)x + 20a b c d - 8b c )\|- a d + b c |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R +--------+
+--R 2 3 2 2 2 2 2 2 3 +-----------+ | 2
+--R ((2a d + b c d)x + 8a c d + 4b c )\|- a d + b c \|d x + c
+--R +
+--R 2 3 2 2 2 2 2 2 3 +-----------+ +-+
+--R ((- 6a d - 3b c d)x - 8a c d - 4b c )\|- a d + b c \|c
+--R /
+--R 4 3 3 2 2 2 2 3 2 4 2 2 3 3 2 2 4
+--R ((2a c d - 4a b c d + 2a b c d)x + 8a c d - 16a b c d + 8a b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 4 2 3 3 3 2 2 2 4 2 4 3 2 3 4 2 2 5
+--R ((- 6a c d + 12a b c d - 6a b c d)x - 8a c d + 16a b c d - 8a b c )
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R Type: Expression(Integer)
+--E 832
+
+--S 833 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 833
+
+)clear all
+
+--S 834 of 1527
+t0:=1/(x^2*(a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R 2 8 2 6 2 4 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|d x + c
+--R Type: Expression(Integer)
+--E 834
+
+--S 835 of 1527
+r0:=-3/2*b^2*(b*c-2*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/_
+ (a^(5/2)*(b*c-a*d)^(5/2))+1/2*d*(b*c+2*a*d)/(a*c*(b*c-a*d)^2*x*_
+ sqrt(c+d*x^2))+1/2*b/(a*(b*c-a*d)*x*(a+b*x^2)*sqrt(c+d*x^2))-_
+ 1/2*(3*b^2*c^2-4*a*b*c*d+4*a^2*d^2)*sqrt(c+d*x^2)/(a^2*c^2*(b*c-a*d)^2*x)
+--R
+--R
+--R (2)
+--R +--------+
+--R 3 2 4 3 3 2 2 2 3 3 | 2
+--R ((6a b c d - 3b c )x + (6a b c d - 3a b c )x)\|d x + c
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 2 3 2 2 3 2 4
+--R (- 4a b d + 4a b c d - 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (- 4a d + 2a b c d + 2a b c d - 3b c )x - 2a c d + 4a b c d
+--R +
+--R 2 3
+--R - 2a b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R /
+--R 4 2 2 3 2 3 2 3 4 3 5 2 2 4 3 3 2 4
+--R ((2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x)
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 835
+
+--S 836 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 3 4 3 2 7 2 2 2 3 3 3 2 4 4 5
+--R (6a b c d - 3b c d )x + (6a b c d + 45a b c d - 24b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 3 2 2 4 3 5
+--R (48a b c d + 24a b c d - 24b c )x + (48a b c d - 24a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 3 4 3 2 7
+--R (- 24a b c d + 12b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 5
+--R (- 24a b c d - 60a b c d + 36b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 3 2 2 4 3 5
+--R (- 72a b c d - 12a b c d + 24b c )x + (- 48a b c d + 24a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (32a b d - 32a b c d + 24b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (32a d + 48a b c d - 80a b c d + 72b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (80a c d - 64a b c d - 16a b c d + 48b c )x + 32a c d
+--R +
+--R 2 3 2 4
+--R - 64a b c d + 32a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a d - a b c \|d x + c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 8a b d + 8a b c d - 6b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 8a d - 60a b c d + 68a b c d - 54b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 68a c d - 24a b c d + 92a b c d - 96b c d)x
+--R +
+--R 3 2 3 2 3 2 3 5 2 3 3 2 2 4
+--R (- 96a c d + 96a b c d - 48b c )x - 32a c d + 64a b c d
+--R +
+--R 2 5
+--R - 32a b c
+--R *
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+--R \|a d - a b c
+--R /
+--R 4 2 4 3 2 3 3 2 3 4 2 7
+--R (4a b c d - 8a b c d + 4a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 5
+--R (4a c d + 24a b c d - 60a b c d + 32a b c d)x
+--R +
+--R 5 3 3 4 4 2 3 2 5 2 3 6 3
+--R (32a c d - 32a b c d - 32a b c d + 32a b c )x
+--R +
+--R 5 4 2 4 5 3 2 6
+--R (32a c d - 64a b c d + 32a b c )x
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 4 2 4 3 2 3 3 2 3 4 2 7
+--R (- 16a b c d + 32a b c d - 16a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 5
+--R (- 16a c d - 16a b c d + 80a b c d - 48a b c d)x
+--R +
+--R 5 3 3 4 4 2 3 2 5 2 3 6 3
+--R (- 48a c d + 64a b c d + 16a b c d - 32a b c )x
+--R +
+--R 5 4 2 4 5 3 2 6
+--R (- 32a c d + 64a b c d - 32a b c )x
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|c \|a d - a b c
+--R ,
+--R
+--R 3 2 3 4 3 2 7
+--R (- 6a b c d + 3b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 5
+--R (- 6a b c d - 45a b c d + 24b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 3 2 2 4 3 5
+--R (- 48a b c d - 24a b c d + 24b c )x + (- 48a b c d + 24a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 3 4 3 2 7
+--R (24a b c d - 12b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 5
+--R (24a b c d + 60a b c d - 36b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 3 2 2 4 3 5
+--R (72a b c d + 12a b c d - 24b c )x + (48a b c d - 24a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 3 2 3 4 3 2 7
+--R (- 6a b c d + 3b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 5
+--R (- 6a b c d - 45a b c d + 24b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 3 2 2 4 3 5
+--R (- 48a b c d - 24a b c d + 24b c )x + (- 48a b c d + 24a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 2 3 4 3 2 7
+--R (24a b c d - 12b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 5
+--R (24a b c d + 60a b c d - 36b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 3 2 2 4 3 5
+--R (72a b c d + 12a b c d - 24b c )x + (48a b c d - 24a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (16a b d - 16a b c d + 12b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (16a d + 24a b c d - 40a b c d + 36b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (40a c d - 32a b c d - 8a b c d + 24b c )x + 16a c d
+--R +
+--R 2 3 2 4
+--R - 32a b c d + 16a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 2 5 2 4 3 2 3 8
+--R (- 4a b d + 4a b c d - 3b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 6
+--R (- 4a d - 30a b c d + 34a b c d - 27b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 4
+--R (- 34a c d - 12a b c d + 46a b c d - 48b c d)x
+--R +
+--R 3 2 3 2 3 2 3 5 2 3 3 2 2 4
+--R (- 48a c d + 48a b c d - 24b c )x - 16a c d + 32a b c d
+--R +
+--R 2 5
+--R - 16a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R 4 2 4 3 2 3 3 2 3 4 2 7
+--R (2a b c d - 4a b c d + 2a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 5
+--R (2a c d + 12a b c d - 30a b c d + 16a b c d)x
+--R +
+--R 5 3 3 4 4 2 3 2 5 2 3 6 3
+--R (16a c d - 16a b c d - 16a b c d + 16a b c )x
+--R +
+--R 5 4 2 4 5 3 2 6
+--R (16a c d - 32a b c d + 16a b c )x
+--R *
+--R +-------------+ +--------+
+--R | 2 | 2
+--R \|- a d + a b c \|d x + c
+--R +
+--R 4 2 4 3 2 3 3 2 3 4 2 7
+--R (- 8a b c d + 16a b c d - 8a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 5
+--R (- 8a c d - 8a b c d + 40a b c d - 24a b c d)x
+--R +
+--R 5 3 3 4 4 2 3 2 5 2 3 6 3
+--R (- 24a c d + 32a b c d + 8a b c d - 16a b c )x
+--R +
+--R 5 4 2 4 5 3 2 6
+--R (- 16a c d + 32a b c d - 16a b c )x
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 836
+
+--S 837 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 +-----------+ +-+
+--R (6a b d - 3b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 2 3 | 2 x\|- a d + b c
+--R (- 12a b d + 6b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 4 2 3 2 2 2 +-----------+ +-+ | 2
+--R (4a d - 8a b c d + 4a b c )\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 837
+
+--S 838 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 838
+
+--S 839 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 3 +-----------+ +-+
+--R (- 6a b d + 3b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 2 3 +-----------+ +-+ \|- a d + a b c \|c
+--R (- 6a b d + 3b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 2 3 | 2 x\|- a d + b c
+--R (- 6a b d + 3b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 4 2 3 2 2 2 | 2 +-----------+ +-+
+--R (2a d - 4a b c d + 2a b c )\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 839
+
+--S 840 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 840
+
+)clear all
+
+--S 841 of 1527
+t0:=1/(x^3*(a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R 2 9 2 7 2 5 2 3 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|d x + c
+--R Type: Expression(Integer)
+--E 841
+
+--S 842 of 1527
+r0:=1/2*(4*b*c+3*a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))/(a^3*c^(5/2))-_
+ 1/2*b^(5/2)*(4*b*c-7*a*d)*atanh(sqrt(b)*sqrt(c+d*x^2)/_
+ sqrt(b*c-a*d))/(a^3*(b*c-a*d)^(5/2))-1/2*d*(2*b^2*c^2-2*a*b*c*d+_
+ 3*a^2*d^2)/(a^2*c^2*(b*c-a*d)^2*sqrt(c+d*x^2))-1/2*b*(2*b*c-a*d)/_
+ (a^2*c*(b*c-a*d)*(a+b*x^2)*sqrt(c+d*x^2))+(-1/2)/_
+ (a*c*x^2*(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R 3 2 4 3 4 2 2 2 3 3 2 +-+ +-+ | 2
+--R ((7a b c d - 4b c )x + (7a b c d - 4a b c )x )\|b \|c \|d x + c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 3 3 2 2 2 3 2 4 3 4
+--R (3a b d - 2a b c d - 5a b c d + 4b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 2
+--R (3a d - 2a b c d - 5a b c d + 4a b c )x
+--R *
+--R +--------+
+--R +--------+ | 2
+--R +-----------+ | 2 \|d x + c
+--R \|- a d + b c \|d x + c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 3 3 2 2 2 3 2 4
+--R (- 3a b d + 2a b c d - 2a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 2 4 2 3 2 2 2 3
+--R (- 3a d + a b c d + a b c d - 2a b c )x - a c d + 2a b c d - a b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R 5 2 2 4 2 3 3 3 4 4 6 2 2 5 3 4 2 4 2
+--R ((2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R Type: Expression(Integer)
+--E 842
+
+--S 843 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 5 2 2 2 4 3 3 3 4 4 2 8
+--R (- 30a b c d + 20a b c d + 50a b c d - 40b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2
+--R - 30a c d - 100a b c d + 130a b c d + 160a b c d
+--R +
+--R 4 5
+--R - 160b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 4 6 4
+--R (- 120a c d - 16a b c d + 264a b c d - 128b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6 2
+--R (- 96a c d + 64a b c d + 160a b c d - 128a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 6 2 2 5 3 2 4 4 3 3 10
+--R (6a b d - 4a b c d - 10a b c d + 8b c d )x
+--R +
+--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 8
+--R (6a d + 74a b c d - 62a b c d - 122a b c d + 104b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2
+--R 78a c d + 116a b c d - 242a b c d - 176a b c d
+--R +
+--R 4 5
+--R 224b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 4
+--R (168a c d - 16a b c d - 344a b c d + 64a b c d + 128b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6 2
+--R (96a c d - 64a b c d - 160a b c d + 128a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 3 3 3 4 4 2 8
+--R (35a b c d - 20b c d )x
+--R +
+--R 2 2 3 3 3 4 2 4 5 6
+--R (35a b c d + 120a b c d - 80b c d)x
+--R +
+--R 2 2 4 2 3 5 4 6 4 2 2 5 3 6 2
+--R (140a b c d + 32a b c d - 64b c )x + (112a b c d - 64a b c )x
+--R *
+--R +-----------+ +--------+
+--R | b +-+ | 2
+--R |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 3 3 4 4 4 3 10
+--R (- 7a b c d + 4b c d )x
+--R +
+--R 2 2 3 4 3 4 3 4 5 2 8
+--R (- 7a b c d - 87a b c d + 52b c d )x
+--R +
+--R 2 2 4 3 3 5 2 4 6 6
+--R (- 91a b c d - 144a b c d + 112b c d)x
+--R +
+--R 2 2 5 2 4 7 4 2 2 6 3 7 2
+--R (- 196a b c d + 64b c )x + (- 112a b c d + 64a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (- 2a d + 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((2a b d - 2b c)x + (2a d - 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 3 5 2 2 2 4 3 3 3 4 4 2 8
+--R (- 14a b c d - 4a b c d + 4a b c d - 10b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 6
+--R (- 14a c d - 10a b c d - 50a b c d + 42a b c d - 40b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 4
+--R (- 6a c d + 4a b c d - 86a b c d + 72a b c d - 32b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6 2 4 4 2
+--R (56a c d - 80a b c d - 8a b c d + 32a b c )x + 32a c d
+--R +
+--R 3 5 2 2 6
+--R - 64a b c d + 32a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 6 4 3 3 10
+--R (4a b d + 2b c d )x
+--R +
+--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 8
+--R (4a d + 22a b c d + 20a b c d - 18a b c d + 26b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 6
+--R (22a c d + 2a b c d + 90a b c d - 74a b c d + 56b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 4
+--R (- 18a c d + 28a b c d + 94a b c d - 88a b c d + 32b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6 2 4 4 2
+--R (- 72a c d + 112a b c d - 8a b c d - 32a b c )x - 32a c d
+--R +
+--R 3 5 2 2 6
+--R 64a b c d - 32a b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 5 3 4 4 2 4 3 3 3 5 2 8
+--R (20a b c d - 40a b c d + 20a b c d )x
+--R +
+--R 6 3 4 5 4 3 4 2 5 2 3 3 6 6
+--R (20a c d + 40a b c d - 140a b c d + 80a b c d)x
+--R +
+--R 6 4 3 5 5 2 4 2 6 3 3 7 4
+--R (80a c d - 96a b c d - 48a b c d + 64a b c )x
+--R +
+--R 6 5 2 5 6 4 2 7 2
+--R (64a c d - 128a b c d + 64a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 5 3 5 4 2 4 4 3 3 5 3 10
+--R (- 4a b c d + 8a b c d - 4a b c d )x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 8
+--R (- 4a c d - 44a b c d + 100a b c d - 52a b c d )x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 6
+--R (- 52a c d - 8a b c d + 172a b c d - 112a b c d)x
+--R +
+--R 6 5 3 5 6 2 4 2 7 3 3 8 4
+--R (- 112a c d + 160a b c d + 16a b c d - 64a b c )x
+--R +
+--R 6 6 2 5 7 4 2 8 2
+--R (- 64a c d + 128a b c d - 64a b c )x
+--R ,
+--R
+--R 3 5 2 2 2 4 3 3 3 4 4 2 8
+--R (- 15a b c d + 10a b c d + 25a b c d - 20b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 6
+--R (- 15a c d - 50a b c d + 65a b c d + 80a b c d - 80b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 4 6 4
+--R (- 60a c d - 8a b c d + 132a b c d - 64b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6 2
+--R (- 48a c d + 32a b c d + 80a b c d - 64a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 6 2 2 5 3 2 4 4 3 3 10
+--R (3a b d - 2a b c d - 5a b c d + 4b c d )x
+--R +
+--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 8
+--R (3a d + 37a b c d - 31a b c d - 61a b c d + 52b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 6
+--R (39a c d + 58a b c d - 121a b c d - 88a b c d + 112b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 4
+--R (84a c d - 8a b c d - 172a b c d + 32a b c d + 64b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6 2
+--R (48a c d - 32a b c d - 80a b c d + 64a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 3 3 3 4 4 2 8
+--R (35a b c d - 20b c d )x
+--R +
+--R 2 2 3 3 3 4 2 4 5 6
+--R (35a b c d + 120a b c d - 80b c d)x
+--R +
+--R 2 2 4 2 3 5 4 6 4 2 2 5 3 6 2
+--R (140a b c d + 32a b c d - 64b c )x + (112a b c d - 64a b c )x
+--R *
+--R +---------+ +--------+
+--R | b +-+ | 2
+--R |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R 3 3 4 4 4 3 10
+--R (- 7a b c d + 4b c d )x
+--R +
+--R 2 2 3 4 3 4 3 4 5 2 8
+--R (- 7a b c d - 87a b c d + 52b c d )x
+--R +
+--R 2 2 4 3 3 5 2 4 6 6
+--R (- 91a b c d - 144a b c d + 112b c d)x
+--R +
+--R 2 2 5 2 4 7 4 2 2 6 3 7 2
+--R (- 196a b c d + 64b c )x + (- 112a b c d + 64a b c )x
+--R *
+--R +---------+
+--R | b
+--R |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R 3 5 2 2 2 4 3 3 3 4 4 2 8
+--R (- 7a b c d - 2a b c d + 2a b c d - 5b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 6
+--R (- 7a c d - 5a b c d - 25a b c d + 21a b c d - 20b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 4
+--R (- 3a c d + 2a b c d - 43a b c d + 36a b c d - 16b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6 2 4 4 2
+--R (28a c d - 40a b c d - 4a b c d + 16a b c )x + 16a c d
+--R +
+--R 3 5 2 2 6
+--R - 32a b c d + 16a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 6 4 3 3 10
+--R (2a b d + b c d )x
+--R +
+--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 8
+--R (2a d + 11a b c d + 10a b c d - 9a b c d + 13b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 6
+--R (11a c d + a b c d + 45a b c d - 37a b c d + 28b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 4
+--R (- 9a c d + 14a b c d + 47a b c d - 44a b c d + 16b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6 2 4 4 2
+--R (- 36a c d + 56a b c d - 4a b c d - 16a b c )x - 16a c d
+--R +
+--R 3 5 2 2 6
+--R 32a b c d - 16a b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 5 3 4 4 2 4 3 3 3 5 2 8
+--R (10a b c d - 20a b c d + 10a b c d )x
+--R +
+--R 6 3 4 5 4 3 4 2 5 2 3 3 6 6
+--R (10a c d + 20a b c d - 70a b c d + 40a b c d)x
+--R +
+--R 6 4 3 5 5 2 4 2 6 3 3 7 4
+--R (40a c d - 48a b c d - 24a b c d + 32a b c )x
+--R +
+--R 6 5 2 5 6 4 2 7 2
+--R (32a c d - 64a b c d + 32a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 5 3 5 4 2 4 4 3 3 5 3 10
+--R (- 2a b c d + 4a b c d - 2a b c d )x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 8
+--R (- 2a c d - 22a b c d + 50a b c d - 26a b c d )x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 6
+--R (- 26a c d - 4a b c d + 86a b c d - 56a b c d)x
+--R +
+--R 6 5 3 5 6 2 4 2 7 3 3 8 4
+--R (- 56a c d + 80a b c d + 8a b c d - 32a b c )x
+--R +
+--R 6 6 2 5 7 4 2 8 2
+--R (- 32a c d + 64a b c d - 32a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 843
+
+--S 844 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 6a d + 4a b c d + 10a b c d - 8b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 72a c d + 48a b c d + 120a b c d - 96b c d)x - 96a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 64a b c d + 160a b c d - 128b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (30a d - 20a b c d - 50a b c d + 40b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (120a c d - 80a b c d - 200a b c d + 160b c d)x + 96a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R - 64a b c d - 160a b c d + 128b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 3 3 3 2 4 2 3 2 3 4 2 2 4
+--R (7a b c d - 4b c d )x + (84a b c d - 48b c d)x + 112a b c d
+--R +
+--R 3 5
+--R - 64b c
+--R *
+--R +-----------+ +--------+
+--R +-----------+ | b +-+ | 2
+--R \|- a d + b c |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 2 3 3 3 4 2 4 2 4 2 3 5 2
+--R (- 35a b c d + 20b c d )x + (- 140a b c d + 80b c d)x
+--R +
+--R 2 5 3 6
+--R - 112a b c d + 64b c
+--R *
+--R +-----------+
+--R +-----------+ | b
+--R \|- a d + b c |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (- 2a d + 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((2a b d - 2b c)x + (2a d - 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 3 3 3 2 4 2 3 2 3 4 2
+--R (- 14a b c d + 8b c d )x + (- 168a b c d + 96b c d)x
+--R +
+--R 2 4 3 5
+--R - 224a b c d + 128b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|b \|c \|d x + c
+--R +
+--R 2 3 3 3 4 2 4 2 4 2 3 5 2
+--R (70a b c d - 40b c d )x + (280a b c d - 160b c d)x
+--R +
+--R 2 5 3 6
+--R 224a b c d - 128b c
+--R *
+--R +-+
+--R \|b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 6a d + 4a b c d + 10a b c d - 8b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 72a c d + 48a b c d + 120a b c d - 96b c d)x - 96a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 64a b c d + 160a b c d - 128b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (30a d - 20a b c d - 50a b c d + 40b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (120a c d - 80a b c d - 200a b c d + 160b c d)x + 96a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R - 64a b c d - 160a b c d + 128b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 3 5 3 3 2 4 3 4 3 4 2 3 2 3 3 5
+--R ((- 4a d - 2b c d )x + (- 48a c d - 24b c d)x - 64a c d - 32b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 3 3 2 4 3 4 3 4 2 3 2 3 3 5
+--R ((20a d + 10b c d )x + (80a c d + 40b c d)x + 64a c d + 32b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R 5 2 4 4 3 3 3 2 4 2 4
+--R (4a c d - 8a b c d + 4a b c d )x
+--R +
+--R 5 3 3 4 4 2 3 2 5 2 5 4 2 4 5
+--R (48a c d - 96a b c d + 48a b c d)x + 64a c d - 128a b c d
+--R +
+--R 3 2 6
+--R 64a b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 5 3 4 4 4 3 3 2 5 2 4
+--R (- 20a c d + 40a b c d - 20a b c d )x
+--R +
+--R 5 4 3 4 5 2 3 2 6 2 5 5 2 4 6
+--R (- 80a c d + 160a b c d - 80a b c d)x - 64a c d + 128a b c d
+--R +
+--R 3 2 7
+--R - 64a b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R Type: Expression(Integer)
+--E 844
+
+--S 845 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 845
+
+--S 846 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 3a d + 2a b c d + 5a b c d - 4b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 36a c d + 24a b c d + 60a b c d - 48b c d)x - 48a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 32a b c d + 80a b c d - 64b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (15a d - 10a b c d - 25a b c d + 20b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (60a c d - 40a b c d - 100a b c d + 80b c d)x + 48a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R - 32a b c d - 80a b c d + 64b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 3 3 3 2 4 2 3 2 3 4 2
+--R (- 7a b c d + 4b c d )x + (- 84a b c d + 48b c d)x
+--R +
+--R 2 4 3 5
+--R - 112a b c d + 64b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|b \|c \|d x + c
+--R +
+--R 2 3 3 3 4 2 4 2 4 2 3 5 2
+--R (35a b c d - 20b c d )x + (140a b c d - 80b c d)x
+--R +
+--R 2 5 3 6
+--R 112a b c d - 64b c
+--R *
+--R +-+
+--R \|b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 3a d + 2a b c d + 5a b c d - 4b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 36a c d + 24a b c d + 60a b c d - 48b c d)x - 48a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 32a b c d + 80a b c d - 64b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (15a d - 10a b c d - 25a b c d + 20b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (60a c d - 40a b c d - 100a b c d + 80b c d)x + 48a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R - 32a b c d - 80a b c d + 64b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 3 3 3 2 4 2 3 2 3 4 2 2 4
+--R (7a b c d - 4b c d )x + (84a b c d - 48b c d)x + 112a b c d
+--R +
+--R 3 5
+--R - 64b c
+--R *
+--R +---------+ +--------+
+--R +-----------+ | b +-+ | 2
+--R \|- a d + b c |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R 2 3 3 3 4 2 4 2 4 2 3 5 2
+--R (- 35a b c d + 20b c d )x + (- 140a b c d + 80b c d)x
+--R +
+--R 2 5 3 6
+--R - 112a b c d + 64b c
+--R *
+--R +---------+
+--R +-----------+ | b
+--R \|- a d + b c |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R 3 5 3 3 2 4 3 4 3 4 2 3 2 3 3 5
+--R ((- 2a d - b c d )x + (- 24a c d - 12b c d)x - 32a c d - 16b c )
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 3 3 2 4 3 4 3 4 2 3 2 3 3 5
+--R ((10a d + 5b c d )x + (40a c d + 20b c d)x + 32a c d + 16b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R 5 2 4 4 3 3 3 2 4 2 4
+--R (2a c d - 4a b c d + 2a b c d )x
+--R +
+--R 5 3 3 4 4 2 3 2 5 2 5 4 2 4 5 3 2 6
+--R (24a c d - 48a b c d + 24a b c d)x + 32a c d - 64a b c d + 32a b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 5 3 4 4 4 3 3 2 5 2 4
+--R (- 10a c d + 20a b c d - 10a b c d )x
+--R +
+--R 5 4 3 4 5 2 3 2 6 2 5 5 2 4 6
+--R (- 40a c d + 80a b c d - 40a b c d)x - 32a c d + 64a b c d
+--R +
+--R 3 2 7
+--R - 32a b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R Type: Expression(Integer)
+--E 846
+
+--S 847 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 847
+
+)clear all
+
+--S 848 of 1527
+t0:=1/(x^4*(a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------------------
+--R +--------+
+--R 2 10 2 8 2 6 2 4 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|d x + c
+--R Type: Expression(Integer)
+--E 848
+
+--S 849 of 1527
+r0:=1/2*b^3*(5*b*c-8*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/_
+ (a^(7/2)*(b*c-a*d)^(5/2))+1/2*d*(b*c+2*a*d)/(a*c*(b*c-a*d)^2*_
+ x^3*sqrt(c+d*x^2))+1/2*b/(a*(b*c-a*d)*x^3*(a+b*x^2)*sqrt(c+d*x^2))-_
+ 1/6*(5*b^2*c^2-4*a*b*c*d+8*a^2*d^2)*sqrt(c+d*x^2)/(a^2*c^2*_
+ (b*c-a*d)^2*x^3)+1/6*(15*b^3*c^3-14*a*b^2*c^2*d-8*a^2*b*c*d^2+_
+ 16*a^3*d^3)*sqrt(c+d*x^2)/(a^3*c^3*(b*c-a*d)^2*x)
+--R
+--R
+--R (2)
+--R +--------+
+--R 4 3 5 4 5 2 3 3 4 4 3 | 2
+--R ((- 24a b c d + 15b c )x + (- 24a b c d + 15a b c )x )\|d x + c
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 6
+--R (16a b d - 8a b c d - 14a b c d + 15b c d)x
+--R +
+--R 4 4 2 2 2 2 3 3 4 4 4
+--R (16a d - 18a b c d - 4a b c d + 15b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2 3 3
+--R (8a c d - 6a b c d - 12a b c d + 10a b c )x - 2a c d + 4a b c d
+--R +
+--R 2 2 4
+--R - 2a b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R /
+--R 5 3 2 4 2 4 3 3 5 5 6 3 2 5 4 4 2 5 3
+--R ((6a b c d - 12a b c d + 6a b c )x + (6a c d - 12a b c d + 6a b c )x )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 849
+
+--S 850 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 3 4 5 4 3 11
+--R (24a b c d - 15b c d )x
+--R +
+--R 2 3 3 4 4 4 3 5 5 2 9
+--R (24a b c d + 417a b c d - 270b c d )x
+--R +
+--R 2 3 4 3 4 5 2 5 6 7
+--R (432a b c d + 882a b c d - 720b c d)x
+--R +
+--R 2 3 5 2 4 6 5 7 5
+--R (1152a b c d + 48a b c d - 480b c )x
+--R +
+--R 2 3 6 4 7 3
+--R (768a b c d - 480a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 3 4 5 4 3 11
+--R (- 144a b c d + 90b c d )x
+--R +
+--R 2 3 3 4 4 4 3 5 5 2 9
+--R (- 144a b c d - 822a b c d + 570b c d )x
+--R +
+--R 2 3 4 3 4 5 2 5 6 7
+--R (- 912a b c d - 966a b c d + 960b c d)x
+--R +
+--R 2 3 5 2 4 6 5 7 5
+--R (- 1536a b c d + 192a b c d + 480b c )x
+--R +
+--R 2 3 6 4 7 3
+--R (- 768a b c d + 480a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 3 6 2 2 5 3 2 4 4 3 3 10
+--R (- 192a b d + 96a b c d + 168a b c d - 180b c d )x
+--R +
+--R 4 6 3 5 2 2 2 4 3 3 3
+--R - 192a d - 1024a b c d + 728a b c d + 944a b c d
+--R +
+--R 4 4 2
+--R - 1140b c d
+--R *
+--R 8
+--R x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2
+--R - 1120a c d - 952a b c d + 1808a b c d + 1032a b c d
+--R +
+--R 4 5
+--R - 1920b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5
+--R - 1512a c d + 336a b c d + 1944a b c d - 384a b c d
+--R +
+--R 4 6
+--R - 960b c
+--R *
+--R 4
+--R x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6 2 4 4 2
+--R (- 384a c d + 128a b c d + 896a b c d - 640a b c )x + 128a c d
+--R +
+--R 3 5 2 2 6
+--R - 256a b c d + 128a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a d - a b c \|d x + c
+--R +
+--R 3 7 2 2 6 3 2 5 4 3 4 12
+--R (32a b d - 16a b c d - 28a b c d + 30b c d )x
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 10
+--R (32a d + 576a b c d - 324a b c d - 512a b c d + 570b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3
+--R 592a c d + 1524a b c d - 1440a b c d - 1468a b c d
+--R +
+--R 4 5 2
+--R 1980b c d
+--R *
+--R 8
+--R x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R 1820a c d + 816a b c d - 2676a b c d - 920a b c d
+--R +
+--R 4 6
+--R 2400b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 4
+--R (1720a c d - 432a b c d - 2376a b c d + 704a b c d + 960b c )x
+--R +
+--R 4 4 3 2 2 6 3 7 2 4 5 2 3 6
+--R (320a c d - 960a b c d + 640a b c )x - 128a c d + 256a b c d
+--R +
+--R 2 2 7
+--R - 128a b c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R /
+--R 5 3 5 4 2 4 4 3 3 5 3 11
+--R (12a b c d - 24a b c d + 12a b c d )x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 9
+--R (12a c d + 192a b c d - 420a b c d + 216a b c d )x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 7
+--R (216a c d + 144a b c d - 936a b c d + 576a b c d)x
+--R +
+--R 6 5 3 5 6 2 4 2 7 3 3 8 5
+--R (576a c d - 768a b c d - 192a b c d + 384a b c )x
+--R +
+--R 6 6 2 5 7 4 2 8 3
+--R (384a c d - 768a b c d + 384a b c )x
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 5 3 5 4 2 4 4 3 3 5 3 11
+--R (- 72a b c d + 144a b c d - 72a b c d )x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 9
+--R (- 72a c d - 312a b c d + 840a b c d - 456a b c d )x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 7
+--R (- 456a c d + 144a b c d + 1080a b c d - 768a b c d)x
+--R +
+--R 6 5 3 5 6 2 3 3 8 5
+--R (- 768a c d + 1152a b c d - 384a b c )x
+--R +
+--R 6 6 2 5 7 4 2 8 3
+--R (- 384a c d + 768a b c d - 384a b c )x
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|c \|a d - a b c
+--R ,
+--R
+--R 4 3 4 5 4 3 11
+--R (24a b c d - 15b c d )x
+--R +
+--R 2 3 3 4 4 4 3 5 5 2 9
+--R (24a b c d + 417a b c d - 270b c d )x
+--R +
+--R 2 3 4 3 4 5 2 5 6 7
+--R (432a b c d + 882a b c d - 720b c d)x
+--R +
+--R 2 3 5 2 4 6 5 7 5
+--R (1152a b c d + 48a b c d - 480b c )x
+--R +
+--R 2 3 6 4 7 3
+--R (768a b c d - 480a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 3 4 5 4 3 11
+--R (- 144a b c d + 90b c d )x
+--R +
+--R 2 3 3 4 4 4 3 5 5 2 9
+--R (- 144a b c d - 822a b c d + 570b c d )x
+--R +
+--R 2 3 4 3 4 5 2 5 6 7
+--R (- 912a b c d - 966a b c d + 960b c d)x
+--R +
+--R 2 3 5 2 4 6 5 7 5
+--R (- 1536a b c d + 192a b c d + 480b c )x
+--R +
+--R 2 3 6 4 7 3
+--R (- 768a b c d + 480a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 4 3 4 5 4 3 11
+--R (24a b c d - 15b c d )x
+--R +
+--R 2 3 3 4 4 4 3 5 5 2 9
+--R (24a b c d + 417a b c d - 270b c d )x
+--R +
+--R 2 3 4 3 4 5 2 5 6 7
+--R (432a b c d + 882a b c d - 720b c d)x
+--R +
+--R 2 3 5 2 4 6 5 7 5
+--R (1152a b c d + 48a b c d - 480b c )x
+--R +
+--R 2 3 6 4 7 3
+--R (768a b c d - 480a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 3 4 5 4 3 11
+--R (- 144a b c d + 90b c d )x
+--R +
+--R 2 3 3 4 4 4 3 5 5 2 9
+--R (- 144a b c d - 822a b c d + 570b c d )x
+--R +
+--R 2 3 4 3 4 5 2 5 6 7
+--R (- 912a b c d - 966a b c d + 960b c d)x
+--R +
+--R 2 3 5 2 4 6 5 7 5
+--R (- 1536a b c d + 192a b c d + 480b c )x
+--R +
+--R 2 3 6 4 7 3
+--R (- 768a b c d + 480a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 3 6 2 2 5 3 2 4 4 3 3 10
+--R (- 96a b d + 48a b c d + 84a b c d - 90b c d )x
+--R +
+--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 8
+--R (- 96a d - 512a b c d + 364a b c d + 472a b c d - 570b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2
+--R - 560a c d - 476a b c d + 904a b c d + 516a b c d
+--R +
+--R 4 5
+--R - 960b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 4
+--R (- 756a c d + 168a b c d + 972a b c d - 192a b c d - 480b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6 2 4 4 2
+--R (- 192a c d + 64a b c d + 448a b c d - 320a b c )x + 64a c d
+--R +
+--R 3 5 2 2 6
+--R - 128a b c d + 64a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 3 7 2 2 6 3 2 5 4 3 4 12
+--R (16a b d - 8a b c d - 14a b c d + 15b c d )x
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 10
+--R (16a d + 288a b c d - 162a b c d - 256a b c d + 285b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 8
+--R (296a c d + 762a b c d - 720a b c d - 734a b c d + 990b c d )x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R 910a c d + 408a b c d - 1338a b c d - 460a b c d
+--R +
+--R 4 6
+--R 1200b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 4
+--R (860a c d - 216a b c d - 1188a b c d + 352a b c d + 480b c )x
+--R +
+--R 4 4 3 2 2 6 3 7 2 4 5 2 3 6
+--R (160a c d - 480a b c d + 320a b c )x - 64a c d + 128a b c d
+--R +
+--R 2 2 7
+--R - 64a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R 5 3 5 4 2 4 4 3 3 5 3 11
+--R (6a b c d - 12a b c d + 6a b c d )x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 9
+--R (6a c d + 96a b c d - 210a b c d + 108a b c d )x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 7
+--R (108a c d + 72a b c d - 468a b c d + 288a b c d)x
+--R +
+--R 6 5 3 5 6 2 4 2 7 3 3 8 5
+--R (288a c d - 384a b c d - 96a b c d + 192a b c )x
+--R +
+--R 6 6 2 5 7 4 2 8 3
+--R (192a c d - 384a b c d + 192a b c )x
+--R *
+--R +-------------+ +--------+
+--R | 2 | 2
+--R \|- a d + a b c \|d x + c
+--R +
+--R 5 3 5 4 2 4 4 3 3 5 3 11
+--R (- 36a b c d + 72a b c d - 36a b c d )x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 9
+--R (- 36a c d - 156a b c d + 420a b c d - 228a b c d )x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 7
+--R (- 228a c d + 72a b c d + 540a b c d - 384a b c d)x
+--R +
+--R 6 5 3 5 6 2 3 3 8 5
+--R (- 384a c d + 576a b c d - 192a b c )x
+--R +
+--R 6 6 2 5 7 4 2 8 3
+--R (- 192a c d + 384a b c d - 192a b c )x
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 850
+
+--S 851 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 4 +-----------+ +-+
+--R (8a b d - 5b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 3 4 | 2 x\|- a d + b c
+--R (16a b d - 10b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 5 2 4 3 2 2 +-----------+ +-+ | 2
+--R (4a d - 8a b c d + 4a b c )\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 851
+
+--S 852 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 852
+
+--S 853 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 3 4 +-----------+ +-+
+--R (8a b d - 5b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 3 4 +-----------+ +-+ \|- a d + a b c \|c
+--R (8a b d - 5b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 3 4 | 2 x\|- a d + b c
+--R (8a b d - 5b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 5 2 4 3 2 2 | 2 +-----------+ +-+
+--R (2a d - 4a b c d + 2a b c )\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 853
+
+--S 854 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 854
+
+)clear all
+
+--S 855 of 1527
+t0:=x^4/((a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 4
+--R x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 855
+
+--S 856 of 1527
+r0:=1/6*(2*b*c+3*a*d)*x/(b*(b*c-a*d)^2*(c+d*x^2)^(3/2))+1/2*a*x/_
+ (b*(b*c-a*d)*(a+b*x^2)*(c+d*x^2)^(3/2))-1/2*(3*b*c+2*a*d)*_
+ atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))*sqrt(a)/(b*c-_
+ a*d)^(7/2)+1/6*(4*b*c+11*a*d)*x/((b*c-a*d)^3*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 2 4 2 2 2 2 2 2
+--R (6a b d + 9b c d)x + (6a d + 15a b c d + 9b c )x + 6a c d
+--R +
+--R 2
+--R 9a b c
+--R *
+--R +--------+ +-----------+
+--R +-+ | 2 x\|- a d + b c
+--R \|a \|d x + c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 2 2 5 2 2 2 2 3
+--R (- 11a b d - 4b c d)x + (- 8a d - 16a b c d - 6b c )x
+--R +
+--R 2 2
+--R (- 6a c d - 9a b c )x
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (6a b d - 18a b c d + 18a b c d - 6b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (6a d - 12a b c d + 12a b c d - 6b c )x + 6a c d - 18a b c d
+--R +
+--R 2 2 3 3 4
+--R 18a b c d - 6a b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R Type: Expression(Integer)
+--E 856
+
+--S 857 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 2 3 8 2 4 3 2 2 2 6
+--R (30a b d + 45b c d )x + (30a d + 195a b c d + 225b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (150a c d + 441a b c d + 324b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4
+--R (216a c d + 420a b c d + 144b c )x + 96a c d + 144a b c
+--R *
+--R +---------+ +--------+
+--R | a +-+ | 2
+--R |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R 5 2 4 10 2 5 4 2 2 3 8
+--R (- 6a b d - 9b c d )x + (- 6a d - 93a b c d - 126b c d )x
+--R +
+--R 2 4 2 3 2 3 2 6
+--R (- 84a c d - 372a b c d - 369b c d )x
+--R +
+--R 2 2 3 3 2 2 4 4
+--R (- 246a c d - 633a b c d - 396b c d)x
+--R +
+--R 2 3 2 4 2 5 2 2 4 5
+--R (- 264a c d - 492a b c d - 144b c )x - 96a c d - 144a b c
+--R *
+--R +---------+
+--R | a
+--R |---------
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((- 2a d + 2b c d)x + (- 4a c d + 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((4a d - 4b c d)x + (4a c d - 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 4 2 3 9 2 4 3 2 2 2 7
+--R (22a b d + 8b c d )x + (16a d + 296a b c d + 108b c d )x
+--R +
+--R 2 3 2 2 2 3 5
+--R (204a c d + 754a b c d + 272b c d)x
+--R +
+--R 2 2 2 3 2 4 3 2 3 4
+--R (400a c d + 728a b c d + 192b c )x + (192a c d + 288a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 2 3 9 2 4 3 2 2 2 7
+--R (- 110a b d - 40b c d )x + (- 80a d - 600a b c d - 220b c d )x
+--R +
+--R 2 3 2 2 2 3 5
+--R (- 380a c d - 1082a b c d - 368b c d)x
+--R +
+--R 2 2 2 3 2 4 3 2 3 4
+--R (- 496a c d - 872a b c d - 192b c )x + (- 192a c d - 288a b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 3 6 2 2 5 3 2 4 4 3 3 8
+--R (60a b d - 180a b c d + 180a b c d - 60b c d )x
+--R +
+--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 6
+--R (60a d + 120a b c d - 720a b c d + 840a b c d - 300b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 4
+--R (300a c d - 468a b c d - 396a b c d + 996a b c d - 432b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 2
+--R (432a c d - 1104a b c d + 720a b c d + 144a b c d - 192b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6
+--R 192a c d - 576a b c d + 576a b c d - 192a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 7 2 2 6 3 2 5 4 3 4 10
+--R (- 12a b d + 36a b c d - 36a b c d + 12b c d )x
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (- 12a d - 132a b c d + 468a b c d - 492a b c d + 168b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 6
+--R (- 168a c d + 12a b c d + 972a b c d - 1308a b c d + 492b c d )x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4
+--R (- 492a c d + 948a b c d + 108a b c d - 1092a b c d + 528b c d)x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 2
+--R (- 528a c d + 1392a b c d - 1008a b c d - 48a b c d + 192b c )x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R - 192a c d + 576a b c d - 576a b c d + 192a b c
+--R ,
+--R
+--R 4 2 3 8 2 4 3 2 2 2 6
+--R (30a b d + 45b c d )x + (30a d + 195a b c d + 225b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (150a c d + 441a b c d + 324b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4
+--R (216a c d + 420a b c d + 144b c )x + 96a c d + 144a b c
+--R *
+--R +-----------+ +--------+
+--R | a +-+ | 2
+--R |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 5 2 4 10 2 5 4 2 2 3 8
+--R (- 6a b d - 9b c d )x + (- 6a d - 93a b c d - 126b c d )x
+--R +
+--R 2 4 2 3 2 3 2 6
+--R (- 84a c d - 372a b c d - 369b c d )x
+--R +
+--R 2 2 3 3 2 2 4 4
+--R (- 246a c d - 633a b c d - 396b c d)x
+--R +
+--R 2 3 2 4 2 5 2 2 4 5
+--R (- 264a c d - 492a b c d - 144b c )x - 96a c d - 144a b c
+--R *
+--R +-----------+
+--R | a
+--R |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R 4 2 3 8
+--R (- 30a b d - 45b c d )x
+--R +
+--R 2 4 3 2 2 2 6
+--R (- 30a d - 195a b c d - 225b c d )x
+--R +
+--R 2 3 2 2 2 3 4
+--R (- 150a c d - 441a b c d - 324b c d)x
+--R +
+--R 2 2 2 3 2 4 2 2 3 4
+--R (- 216a c d - 420a b c d - 144b c )x - 96a c d - 144a b c
+--R *
+--R +-----------+ +--------+
+--R | a +-+ | 2
+--R |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 5 2 4 10 2 5 4 2 2 3 8
+--R (6a b d + 9b c d )x + (6a d + 93a b c d + 126b c d )x
+--R +
+--R 2 4 2 3 2 3 2 6
+--R (84a c d + 372a b c d + 369b c d )x
+--R +
+--R 2 2 3 3 2 2 4 4
+--R (246a c d + 633a b c d + 396b c d)x
+--R +
+--R 2 3 2 4 2 5 2 2 4 5
+--R (264a c d + 492a b c d + 144b c )x + 96a c d + 144a b c
+--R *
+--R +-----------+
+--R | a
+--R |- ---------
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R 4 2 3 9 2 4 3 2 2 2 7
+--R (11a b d + 4b c d )x + (8a d + 148a b c d + 54b c d )x
+--R +
+--R 2 3 2 2 2 3 5
+--R (102a c d + 377a b c d + 136b c d)x
+--R +
+--R 2 2 2 3 2 4 3 2 3 4
+--R (200a c d + 364a b c d + 96b c )x + (96a c d + 144a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 2 3 9 2 4 3 2 2 2 7
+--R (- 55a b d - 20b c d )x + (- 40a d - 300a b c d - 110b c d )x
+--R +
+--R 2 3 2 2 2 3 5
+--R (- 190a c d - 541a b c d - 184b c d)x
+--R +
+--R 2 2 2 3 2 4 3 2 3 4
+--R (- 248a c d - 436a b c d - 96b c )x + (- 96a c d - 144a b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 3 6 2 2 5 3 2 4 4 3 3 8
+--R (30a b d - 90a b c d + 90a b c d - 30b c d )x
+--R +
+--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 6
+--R (30a d + 60a b c d - 360a b c d + 420a b c d - 150b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 4
+--R (150a c d - 234a b c d - 198a b c d + 498a b c d - 216b c d)x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 2
+--R (216a c d - 552a b c d + 360a b c d + 72a b c d - 96b c )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 3 6
+--R 96a c d - 288a b c d + 288a b c d - 96a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 7 2 2 6 3 2 5 4 3 4 10
+--R (- 6a b d + 18a b c d - 18a b c d + 6b c d )x
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (- 6a d - 66a b c d + 234a b c d - 246a b c d + 84b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 6
+--R (- 84a c d + 6a b c d + 486a b c d - 654a b c d + 246b c d )x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4
+--R (- 246a c d + 474a b c d + 54a b c d - 546a b c d + 264b c d)x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 2
+--R (- 264a c d + 696a b c d - 504a b c d - 24a b c d + 96b c )x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R - 96a c d + 288a b c d - 288a b c d + 96a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 857
+
+--S 858 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-----------+ | a
+--R (2a d + 3b c)\|- a d + b c |---------
+--R \|a d - b c
+--R *
+--R log
+--R 2 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R +
+--R +---------+
+--R 2 3 2 | a
+--R ((- 2a d + 2b c d)x + (- 4a c d + 4b c )x) |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +---------+
+--R 2 3 2 | a +-+
+--R ((4a d - 4b c d)x + (4a c d - 4b c )x) |--------- \|c
+--R \|a d - b c
+--R +
+--R 2 4 2 2 2
+--R (- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+
+--R +-+ x\|- a d + b c
+--R (- 4a d - 6b c)\|a atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 3 2 2 2 2 3 3 +-----------+
+--R (4a d - 12a b c d + 12a b c d - 4b c )\|- a d + b c
+--R Type: Expression(Integer)
+--E 858
+
+--S 859 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 859
+
+--S 860 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R +-----------+ | a
+--R (2a d + 3b c)\|- a d + b c |- ---------
+--R \| a d - b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 2 3 | a
+--R (a d - b c d)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-----------+ | a
+--R (- 2a d - 3b c)\|- a d + b c |- ---------
+--R \| a d - b c
+--R *
+--R +-+
+--R a\|c
+--R atan(--------------------------)
+--R +-----------+
+--R | a
+--R (a d - b c)x |- ---------
+--R \| a d - b c
+--R +
+--R +-----------+
+--R +-+ x\|- a d + b c
+--R (- 2a d - 3b c)\|a atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R 3 3 2 2 2 2 3 3 +-----------+
+--R (2a d - 6a b c d + 6a b c d - 2b c )\|- a d + b c
+--R Type: Expression(Integer)
+--E 860
+
+--S 861 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 861
+
+)clear all
+
+--S 862 of 1527
+t0:=x^3/((a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 3
+--R x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 862
+
+--S 863 of 1527
+r0:=1/6*(2*b*c+3*a*d)/(b*(b*c-a*d)^2*(c+d*x^2)^(3/2))+1/2*a/(b*(b*c-_
+ a*d)*(a+b*x^2)*(c+d*x^2)^(3/2))-1/2*(2*b*c+3*a*d)*atanh(sqrt(b)*_
+ sqrt(c+d*x^2)/sqrt(b*c-a*d))*sqrt(b)/(b*c-a*d)^(7/2)+1/2*(2*b*c+_
+ 3*a*d)/((b*c-a*d)^3*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 2 4 2 2 2 2 2 2
+--R (9a b d + 6b c d)x + (9a d + 15a b c d + 6b c )x + 9a c d
+--R +
+--R 2
+--R 6a b c
+--R *
+--R +--------+
+--R +--------+ +-+ | 2
+--R +-+ | 2 \|b \|d x + c
+--R \|b \|d x + c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 9a b d - 6b c d)x + (- 6a d - 16a b c d - 8b c )x - 4a c d
+--R +
+--R 2
+--R - 11a b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (6a b d - 18a b c d + 18a b c d - 6b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (6a d - 12a b c d + 12a b c d - 6b c )x + 6a c d - 18a b c d
+--R +
+--R 2 2 3 3 4
+--R 18a b c d - 6a b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R Type: Expression(Integer)
+--E 863
+
+--S 864 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 2 2 3 8
+--R (45a b c d + 30b c d )x
+--R +
+--R 2 4 2 3 2 3 2 6
+--R (45a c d + 255a b c d + 150b c d )x
+--R +
+--R 2 2 3 3 2 2 4 4
+--R (225a c d + 474a b c d + 216b c d)x
+--R +
+--R 2 3 2 4 2 5 2 2 4 5
+--R (324a c d + 360a b c d + 96b c )x + 144a c d + 96a b c
+--R *
+--R +-----------+ +--------+
+--R | b +-+ | 2
+--R |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 5 2 2 4 10
+--R (- 9a b c d - 6b c d )x
+--R +
+--R 2 5 2 4 2 3 3 8
+--R (- 9a c d - 132a b c d - 84b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 6
+--R (- 126a c d - 453a b c d - 246b c d )x
+--R +
+--R 2 3 3 4 2 2 5 4
+--R (- 369a c d - 642a b c d - 264b c d)x
+--R +
+--R 2 4 2 5 2 6 2 2 5 6
+--R (- 396a c d - 408a b c d - 96b c )x - 144a c d - 96a b c
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R 2 2 2 2 4
+--R (- 2a d - 2a b c d + 4b c )x
+--R +
+--R 2 2 2
+--R (- 8a c d + 8a b c )x
+--R *
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (2a b c d - 2b c d)x + (6a c d - 2a b c d - 4b c )x
+--R +
+--R 2 2 3 2
+--R (8a c d - 8a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 4 2 2 3 8
+--R (- 22a b c d - 98b c d )x
+--R +
+--R 2 4 2 3 2 3 2 6
+--R (- 28a c d - 62a b c d - 390b c d )x
+--R +
+--R 2 2 3 3 2 2 4 4 4 2 5 2
+--R (- 48a c d - 144a b c d - 408b c d)x + (- 144a b c d - 96b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 5 2 4 10 2 5 4 2 2 3 8
+--R (8a b d + 22b c d )x + (8a d + 44a b c d + 248b c d )x
+--R +
+--R 2 4 2 3 2 3 2 6
+--R (52a c d + 116a b c d + 582b c d )x
+--R +
+--R 2 2 3 3 2 2 4 4 4 2 5 2
+--R (48a c d + 216a b c d + 456b c d)x + (144a b c d + 96b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (60a b c d - 180a b c d + 180a b c d - 60b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 6
+--R (60a c d + 120a b c d - 720a b c d + 840a b c d - 300b c d )x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4
+--R (300a c d - 468a b c d - 396a b c d + 996a b c d - 432b c d)x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 2
+--R (432a c d - 1104a b c d + 720a b c d + 144a b c d - 192b c )x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R 192a c d - 576a b c d + 576a b c d - 192a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 7 2 2 2 6 3 3 5 4 4 4 10
+--R (- 12a b c d + 36a b c d - 36a b c d + 12b c d )x
+--R +
+--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 8
+--R (- 12a c d - 132a b c d + 468a b c d - 492a b c d + 168b c d )x
+--R +
+--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 6
+--R (- 168a c d + 12a b c d + 972a b c d - 1308a b c d + 492b c d )x
+--R +
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2 4 7 4
+--R (- 492a c d + 948a b c d + 108a b c d - 1092a b c d + 528b c d)x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7 4 8 2
+--R (- 528a c d + 1392a b c d - 1008a b c d - 48a b c d + 192b c )x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8
+--R - 192a c d + 576a b c d - 576a b c d + 192a b c
+--R ,
+--R
+--R 4 2 2 3 8
+--R (45a b c d + 30b c d )x
+--R +
+--R 2 4 2 3 2 3 2 6
+--R (45a c d + 255a b c d + 150b c d )x
+--R +
+--R 2 2 3 3 2 2 4 4
+--R (225a c d + 474a b c d + 216b c d)x
+--R +
+--R 2 3 2 4 2 5 2 2 4 5
+--R (324a c d + 360a b c d + 96b c )x + 144a c d + 96a b c
+--R *
+--R +---------+ +--------+
+--R | b +-+ | 2
+--R |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R 5 2 2 4 10
+--R (- 9a b c d - 6b c d )x
+--R +
+--R 2 5 2 4 2 3 3 8
+--R (- 9a c d - 132a b c d - 84b c d )x
+--R +
+--R 2 2 4 3 3 2 4 2 6
+--R (- 126a c d - 453a b c d - 246b c d )x
+--R +
+--R 2 3 3 4 2 2 5 4
+--R (- 369a c d - 642a b c d - 264b c d)x
+--R +
+--R 2 4 2 5 2 6 2 2 5 6
+--R (- 396a c d - 408a b c d - 96b c )x - 144a c d - 96a b c
+--R *
+--R +---------+
+--R | b
+--R |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b
+--R (a d - b c)x |---------
+--R \|a d - b c
+--R +
+--R 4 2 2 3 8
+--R (- 11a b c d - 49b c d )x
+--R +
+--R 2 4 2 3 2 3 2 6
+--R (- 14a c d - 31a b c d - 195b c d )x
+--R +
+--R 2 2 3 3 2 2 4 4 4 2 5 2
+--R (- 24a c d - 72a b c d - 204b c d)x + (- 72a b c d - 48b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 5 2 4 10 2 5 4 2 2 3 8
+--R (4a b d + 11b c d )x + (4a d + 22a b c d + 124b c d )x
+--R +
+--R 2 4 2 3 2 3 2 6
+--R (26a c d + 58a b c d + 291b c d )x
+--R +
+--R 2 2 3 3 2 2 4 4 4 2 5 2
+--R (24a c d + 108a b c d + 228b c d)x + (72a b c d + 48b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (30a b c d - 90a b c d + 90a b c d - 30b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 6
+--R (30a c d + 60a b c d - 360a b c d + 420a b c d - 150b c d )x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4
+--R (150a c d - 234a b c d - 198a b c d + 498a b c d - 216b c d)x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 2
+--R (216a c d - 552a b c d + 360a b c d + 72a b c d - 96b c )x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R 96a c d - 288a b c d + 288a b c d - 96a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 7 2 2 2 6 3 3 5 4 4 4 10
+--R (- 6a b c d + 18a b c d - 18a b c d + 6b c d )x
+--R +
+--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 8
+--R (- 6a c d - 66a b c d + 234a b c d - 246a b c d + 84b c d )x
+--R +
+--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 6
+--R (- 84a c d + 6a b c d + 486a b c d - 654a b c d + 246b c d )x
+--R +
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2 4 7 4
+--R (- 246a c d + 474a b c d + 54a b c d - 546a b c d + 264b c d)x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7 4 8 2
+--R (- 264a c d + 696a b c d - 504a b c d - 24a b c d + 96b c )x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8
+--R - 96a c d + 288a b c d - 288a b c d + 96a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 864
+
+--S 865 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 2 2 4 2 2 3 2 3
+--R (9a c d + 6b c d )x + (108a c d + 72b c d)x + 144a c d
+--R +
+--R 4
+--R 96b c
+--R *
+--R +-----------+ +--------+
+--R +-----------+ | b | 2
+--R \|- a d + b c |- --------- \|d x + c
+--R \| a d - b c
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (- 45a c d - 30b c d )x + (- 180a c d - 120b c d)x - 144a c d
+--R +
+--R 4
+--R - 96b c
+--R *
+--R +-----------+
+--R +-----------+ | b +-+
+--R \|- a d + b c |- --------- \|c
+--R \| a d - b c
+--R *
+--R log
+--R 2 2 2 2 4 2 2 2
+--R ((- 2a d - 2a b c d + 4b c )x + (- 8a c d + 8a b c )x )
+--R *
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (2a b c d - 2b c d)x + (6a c d - 2a b c d - 4b c )x
+--R +
+--R 2 2 3 2
+--R (8a c d - 8a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (- 18a c d - 12b c d )x + (- 216a c d - 144b c d)x - 288a c d
+--R +
+--R 4
+--R - 192b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (90a c d + 60b c d )x + (360a c d + 240b c d)x + 288a c d
+--R +
+--R 4
+--R 192b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 8a d - 22b c d )x + (- 96a c d - 264b c d)x - 128a c d
+--R +
+--R 3
+--R - 352b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (40a c d + 110b c d )x + (160a c d + 440b c d)x + 128a c d
+--R +
+--R 4
+--R 352b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R /
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (12a c d - 36a b c d + 36a b c d - 12b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2 3 3 3
+--R (144a c d - 432a b c d + 432a b c d - 144b c d)x + 192a c d
+--R +
+--R 2 4 2 2 5 3 6
+--R - 576a b c d + 576a b c d - 192b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (- 60a c d + 180a b c d - 180a b c d + 60b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2 3 3 3
+--R (- 240a c d + 720a b c d - 720a b c d + 240b c d)x - 192a c d
+--R +
+--R 2 4 2 2 5 3 6
+--R 576a b c d - 576a b c d + 192b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 865
+
+--S 866 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 866
+
+--S 867 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 3 2 2 4 2 2 3 2 3
+--R (- 9a c d - 6b c d )x + (- 108a c d - 72b c d)x - 144a c d
+--R +
+--R 4
+--R - 96b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (45a c d + 30b c d )x + (180a c d + 120b c d)x + 144a c d
+--R +
+--R 4
+--R 96b c
+--R *
+--R +-+ +-+
+--R \|b \|c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (9a c d + 6b c d )x + (108a c d + 72b c d)x + 144a c d
+--R +
+--R 4
+--R 96b c
+--R *
+--R +---------+ +--------+
+--R +-----------+ | b | 2
+--R \|- a d + b c |--------- \|d x + c
+--R \|a d - b c
+--R +
+--R 3 2 2 4 2 2 3 2 3
+--R (- 45a c d - 30b c d )x + (- 180a c d - 120b c d)x - 144a c d
+--R +
+--R 4
+--R - 96b c
+--R *
+--R +---------+
+--R +-----------+ | b +-+
+--R \|- a d + b c |--------- \|c
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b
+--R (a d - b c)x |---------
+--R \|a d - b c
+--R +
+--R 3 2 4 2 2 2 2
+--R (- 4a d - 11b c d )x + (- 48a c d - 132b c d)x - 64a c d
+--R +
+--R 3
+--R - 176b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 3 2 2 4 2 2 3 2 3 4
+--R ((20a c d + 55b c d )x + (80a c d + 220b c d)x + 64a c d + 176b c )
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R /
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (6a c d - 18a b c d + 18a b c d - 6b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2 3 3 3
+--R (72a c d - 216a b c d + 216a b c d - 72b c d)x + 96a c d
+--R +
+--R 2 4 2 2 5 3 6
+--R - 288a b c d + 288a b c d - 96b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 4
+--R (- 30a c d + 90a b c d - 90a b c d + 30b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 2 3 3 3
+--R (- 120a c d + 360a b c d - 360a b c d + 120b c d)x - 96a c d
+--R +
+--R 2 4 2 2 5 3 6
+--R 288a b c d - 288a b c d + 96b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 867
+
+--S 868 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 868
+
+)clear all
+
+--S 869 of 1527
+t0:=x^2/((a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 2
+--R x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 869
+
+--S 870 of 1527
+r0:=-5/6*d*x/((b*c-a*d)^2*(c+d*x^2)^(3/2))-1/2*x/((b*c-a*d)*(a+b*x^2)*_
+ (c+d*x^2)^(3/2))+1/2*b*(b*c+4*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*_
+ sqrt(c+d*x^2)))/((b*c-a*d)^(7/2)*sqrt(a))-1/6*d*(13*b*c+2*a*d)*_
+ x/(c*(b*c-a*d)^3*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (- 12a b c d - 3b c d)x + (- 12a b c d - 15a b c d - 3b c )x
+--R +
+--R 2 2 2 3
+--R - 12a b c d - 3a b c
+--R *
+--R +--------+ +-----------+
+--R | 2 x\|- a d + b c
+--R \|d x + c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 3 2 2 5 2 3 2 2 2 3
+--R (2a b d + 13b c d )x + (2a d + 10a b c d + 18b c d)x
+--R +
+--R 2 2 3
+--R (12a b c d + 3b c )x
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R /
+--R 3 4 2 2 2 3 3 3 2 4 4 4
+--R (6a b c d - 18a b c d + 18a b c d - 6b c d)x
+--R +
+--R 4 4 3 2 3 3 4 4 5 2 4 2 3 3 3 2
+--R (6a c d - 12a b c d + 12a b c d - 6b c )x + 6a c d - 18a b c d
+--R +
+--R 2 2 4 3 5
+--R 18a b c d - 6a b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 870
+
+--S 871 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 3 8
+--R (60a b c d + 15b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 6
+--R (60a b c d + 315a b c d + 75b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 4
+--R (300a b c d + 507a b c d + 108b c d)x
+--R +
+--R 2 3 2 2 4 3 5 2 2 4 2 5
+--R (432a b c d + 300a b c d + 48b c )x + 192a b c d + 48a b c
+--R *
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+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 3 2 4 10
+--R (- 12a b c d - 3b c d )x
+--R +
+--R 2 5 2 2 4 3 3 3 8
+--R (- 12a b c d - 171a b c d - 42b c d )x
+--R +
+--R 2 2 4 2 3 3 3 4 2 6
+--R (- 168a b c d - 534a b c d - 123b c d )x
+--R +
+--R 2 3 3 2 4 2 3 5 4
+--R (- 492a b c d - 651a b c d - 132b c d)x
+--R +
+--R 2 4 2 2 5 3 6 2 2 5 2 6
+--R (- 528a b c d - 324a b c d - 48b c )x - 192a b c d - 48a b c
+--R *
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+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
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+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
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+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
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+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 5 2 4 9 2 5 4 2 2 3 7
+--R (- 4a b d - 26b c d )x + (- 4a d - 68a b c d - 348b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (- 48a c d - 328a b c d - 854b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3 4 2 5
+--R (- 64a c d - 608a b c d - 648b c d)x + (- 384a b c d - 96b c )x
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 5 2 4 9 2 5 4 2 2 3 7
+--R (20a b d + 130b c d )x + (20a d + 180a b c d + 700b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (80a c d + 584a b c d + 1166b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3 4 2 5
+--R (64a c d + 800a b c d + 696b c d)x + (384a b c d + 96b c )x
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|c \|a d - a b c
+--R /
+--R 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (60a b c d - 180a b c d + 180a b c d - 60b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 6
+--R (60a c d + 120a b c d - 720a b c d + 840a b c d - 300b c d )x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4
+--R (300a c d - 468a b c d - 396a b c d + 996a b c d - 432b c d)x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 2
+--R (432a c d - 1104a b c d + 720a b c d + 144a b c d - 192b c )x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R 192a c d - 576a b c d + 576a b c d - 192a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a d - a b c \|d x + c
+--R +
+--R 3 7 2 2 2 6 3 3 5 4 4 4 10
+--R (- 12a b c d + 36a b c d - 36a b c d + 12b c d )x
+--R +
+--R 4 7 3 2 6 2 2 3 5 3 4 4
+--R - 12a c d - 132a b c d + 468a b c d - 492a b c d
+--R +
+--R 4 5 3
+--R 168b c d
+--R *
+--R 8
+--R x
+--R +
+--R 4 2 6 3 3 5 2 2 4 4 3 5 3
+--R - 168a c d + 12a b c d + 972a b c d - 1308a b c d
+--R +
+--R 4 6 2
+--R 492b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2
+--R - 492a c d + 948a b c d + 108a b c d - 1092a b c d
+--R +
+--R 4 7
+--R 528b c d
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+--R 4
+--R x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7 4 8 2
+--R (- 528a c d + 1392a b c d - 1008a b c d - 48a b c d + 192b c )x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8
+--R - 192a c d + 576a b c d - 576a b c d + 192a b c
+--R *
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+--R | 2
+--R \|a d - a b c
+--R ,
+--R
+--R 2 4 3 2 3 8
+--R (60a b c d + 15b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 6
+--R (60a b c d + 315a b c d + 75b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 4
+--R (300a b c d + 507a b c d + 108b c d)x
+--R +
+--R 2 3 2 2 4 3 5 2 2 4 2 5
+--R (432a b c d + 300a b c d + 48b c )x + 192a b c d + 48a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 3 2 4 10
+--R (- 12a b c d - 3b c d )x
+--R +
+--R 2 5 2 2 4 3 3 3 8
+--R (- 12a b c d - 171a b c d - 42b c d )x
+--R +
+--R 2 2 4 2 3 3 3 4 2 6
+--R (- 168a b c d - 534a b c d - 123b c d )x
+--R +
+--R 2 3 3 2 4 2 3 5 4
+--R (- 492a b c d - 651a b c d - 132b c d)x
+--R +
+--R 2 4 2 2 5 3 6 2 2 5 2 6
+--R (- 528a b c d - 324a b c d - 48b c )x - 192a b c d - 48a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 2 4 3 2 3 8
+--R (60a b c d + 15b c d )x
+--R +
+--R 2 4 2 2 3 3 3 2 6
+--R (60a b c d + 315a b c d + 75b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 4
+--R (300a b c d + 507a b c d + 108b c d)x
+--R +
+--R 2 3 2 2 4 3 5 2 2 4 2 5
+--R (432a b c d + 300a b c d + 48b c )x + 192a b c d + 48a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 2 5 3 2 4 10
+--R (- 12a b c d - 3b c d )x
+--R +
+--R 2 5 2 2 4 3 3 3 8
+--R (- 12a b c d - 171a b c d - 42b c d )x
+--R +
+--R 2 2 4 2 3 3 3 4 2 6
+--R (- 168a b c d - 534a b c d - 123b c d )x
+--R +
+--R 2 3 3 2 4 2 3 5 4
+--R (- 492a b c d - 651a b c d - 132b c d)x
+--R +
+--R 2 4 2 2 5 3 6 2 2 5 2 6
+--R (- 528a b c d - 324a b c d - 48b c )x - 192a b c d - 48a b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 5 2 4 9 2 5 4 2 2 3 7
+--R (- 2a b d - 13b c d )x + (- 2a d - 34a b c d - 174b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (- 24a c d - 164a b c d - 427b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3 4 2 5
+--R (- 32a c d - 304a b c d - 324b c d)x + (- 192a b c d - 48b c )x
+--R *
+--R +-------------+ +--------+
+--R | 2 | 2
+--R \|- a d + a b c \|d x + c
+--R +
+--R 5 2 4 9 2 5 4 2 2 3 7
+--R (10a b d + 65b c d )x + (10a d + 90a b c d + 350b c d )x
+--R +
+--R 2 4 2 3 2 3 2 5
+--R (40a c d + 292a b c d + 583b c d )x
+--R +
+--R 2 2 3 3 2 2 4 3 4 2 5
+--R (32a c d + 400a b c d + 348b c d)x + (192a b c d + 48b c )x
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R /
+--R 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (30a b c d - 90a b c d + 90a b c d - 30b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 6
+--R (30a c d + 60a b c d - 360a b c d + 420a b c d - 150b c d )x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4
+--R (150a c d - 234a b c d - 198a b c d + 498a b c d - 216b c d)x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 2
+--R (216a c d - 552a b c d + 360a b c d + 72a b c d - 96b c )x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R 96a c d - 288a b c d + 288a b c d - 96a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 3 7 2 2 2 6 3 3 5 4 4 4 10
+--R (- 6a b c d + 18a b c d - 18a b c d + 6b c d )x
+--R +
+--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 8
+--R (- 6a c d - 66a b c d + 234a b c d - 246a b c d + 84b c d )x
+--R +
+--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 6
+--R (- 84a c d + 6a b c d + 486a b c d - 654a b c d + 246b c d )x
+--R +
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2 4 7 4
+--R (- 246a c d + 474a b c d + 54a b c d - 546a b c d + 264b c d)x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7 4 8 2
+--R (- 264a c d + 696a b c d - 504a b c d - 24a b c d + 96b c )x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8
+--R - 96a c d + 288a b c d - 288a b c d + 96a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 871
+
+--S 872 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----------+ +-+
+--R (4a b d + b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (8a b d + 2b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 3 3 2 2 2 2 3 3 +-----------+ +-+ | 2
+--R (4a d - 12a b c d + 12a b c d - 4b c )\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 872
+
+--S 873 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 873
+
+--S 874 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 +-----------+ +-+
+--R (4a b d + b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 2 +-----------+ +-+ \|- a d + a b c \|c
+--R (4a b d + b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (4a b d + b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 3 3 2 2 2 2 3 3 | 2 +-----------+ +-+
+--R (2a d - 6a b c d + 6a b c d - 2b c )\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 874
+
+--S 875 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 875
+
+)clear all
+
+--S 876 of 1527
+t0:=x/((a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 876
+
+--S 877 of 1527
+r0:=-5/6*d/((b*c-a*d)^2*(c+d*x^2)^(3/2))+(-1/2)/((b*c-a*d)*(a+b*x^2)*_
+ (c+d*x^2)^(3/2))+5/2*b^(3/2)*d*atanh(sqrt(b)*sqrt(c+d*x^2)/_
+ sqrt(b*c-a*d))/(b*c-a*d)^(7/2)-5/2*b*d/((b*c-a*d)^3*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R 2 2 4 2 2 2 +-+ | 2
+--R (- 15b d x + (- 15a b d - 15b c d)x - 15a b c d)\|b \|d x + c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R (15b d x + (10a b d + 20b c d)x - 2a d + 14a b c d + 3b c )
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (6a b d - 18a b c d + 18a b c d - 6b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (6a d - 12a b c d + 12a b c d - 6b c )x + 6a c d - 18a b c d
+--R +
+--R 2 2 3 3 4
+--R 18a b c d - 6a b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R Type: Expression(Integer)
+--E 877
+
+--S 878 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 4 8 2 2 4 2 3 3 6
+--R 75a b c d x + (75a b c d + 375a b c d )x
+--R +
+--R 2 3 3 2 4 2 4 2 4 2 2 5 2
+--R (375a b c d + 540a b c d )x + (540a b c d + 240a b c d)x
+--R +
+--R 2 5
+--R 240a b c d
+--R *
+--R +-----------+ +--------+
+--R | b +-+ | 2
+--R |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 2 2 5 10 2 2 5 2 3 4 8
+--R - 15a b c d x + (- 15a b c d - 210a b c d )x
+--R +
+--R 2 3 4 2 4 3 6
+--R (- 210a b c d - 615a b c d )x
+--R +
+--R 2 4 3 2 5 2 4
+--R (- 615a b c d - 660a b c d )x
+--R +
+--R 2 5 2 2 6 2 2 6
+--R (- 660a b c d - 240a b c d)x - 240a b c d
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R 2 2 2 2 4 2 2 2
+--R ((2a d + 2a b c d - 4b c )x + (8a c d - 8a b c )x )
+--R *
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 6
+--R (- 2a b c d + 2b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2
+--R (- 6a c d + 2a b c d + 4b c )x + (- 8a c d + 8a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 5 2 2 4 3 3 3 8
+--R (- 20a b c d + 110a b c d + 30b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (- 20a c d + 20a b c d + 330a b c d + 150b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (- 96a c d + 288a b c d + 192a b c d + 216b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (- 96a c d + 288a b c d - 48a b c d + 96b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 2 5 3 2 4 10
+--R (4a b d - 28a b c d - 6b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 8
+--R (4a d + 28a b c d - 248a b c d - 84b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (56a c d - 128a b c d - 432a b c d - 246b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (144a c d - 432a b c d - 168a b c d - 264b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (96a c d - 288a b c d + 48a b c d - 96b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 2 6 3 2 3 5 2 3 4 4 4 5 3 8
+--R (60a b c d - 180a b c d + 180a b c d - 60a b c d )x
+--R +
+--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3
+--R 60a c d + 120a b c d - 720a b c d + 840a b c d
+--R +
+--R 4 6 2
+--R - 300a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2
+--R 300a c d - 468a b c d - 396a b c d + 996a b c d
+--R +
+--R 4 7
+--R - 432a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 4 4 4 5 3 3 2 6 2 2 3 7 4 8 2
+--R (432a c d - 1104a b c d + 720a b c d + 144a b c d - 192a b c )x
+--R +
+--R 5 5 3 4 6 2 3 2 7 2 3 8
+--R 192a c d - 576a b c d + 576a b c d - 192a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 4 2 7 3 2 3 6 2 3 4 5 4 5 4 10
+--R (- 12a b c d + 36a b c d - 36a b c d + 12a b c d )x
+--R +
+--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 4 6 3 8
+--R (- 12a c d - 132a b c d + 468a b c d - 492a b c d + 168a b c d )x
+--R +
+--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 4 7 2 6
+--R (- 168a c d + 12a b c d + 972a b c d - 1308a b c d + 492a b c d )x
+--R +
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 4 8 4
+--R (- 492a c d + 948a b c d + 108a b c d - 1092a b c d + 528a b c d)x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8 4 9 2
+--R (- 528a c d + 1392a b c d - 1008a b c d - 48a b c d + 192a b c )x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9
+--R - 192a c d + 576a b c d - 576a b c d + 192a b c
+--R ,
+--R
+--R 2 2 4 8 2 2 4 2 3 3 6
+--R - 75a b c d x + (- 75a b c d - 375a b c d )x
+--R +
+--R 2 3 3 2 4 2 4
+--R (- 375a b c d - 540a b c d )x
+--R +
+--R 2 4 2 2 5 2 2 5
+--R (- 540a b c d - 240a b c d)x - 240a b c d
+--R *
+--R +---------+ +--------+
+--R | b +-+ | 2
+--R |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R 2 2 5 10 2 2 5 2 3 4 8
+--R 15a b c d x + (15a b c d + 210a b c d )x
+--R +
+--R 2 3 4 2 4 3 6 2 4 3 2 5 2 4
+--R (210a b c d + 615a b c d )x + (615a b c d + 660a b c d )x
+--R +
+--R 2 5 2 2 6 2 2 6
+--R (660a b c d + 240a b c d)x + 240a b c d
+--R *
+--R +---------+
+--R | b
+--R |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b
+--R (a d - b c)x |---------
+--R \|a d - b c
+--R +
+--R 2 5 2 2 4 3 3 3 8
+--R (- 10a b c d + 55a b c d + 15b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (- 10a c d + 10a b c d + 165a b c d + 75b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (- 48a c d + 144a b c d + 96a b c d + 108b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (- 48a c d + 144a b c d - 24a b c d + 48b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 6 2 5 3 2 4 10
+--R (2a b d - 14a b c d - 3b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 8
+--R (2a d + 14a b c d - 124a b c d - 42b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 6
+--R (28a c d - 64a b c d - 216a b c d - 123b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (72a c d - 216a b c d - 84a b c d - 132b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2
+--R (48a c d - 144a b c d + 24a b c d - 48b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 4 2 6 3 2 3 5 2 3 4 4 4 5 3 8
+--R (30a b c d - 90a b c d + 90a b c d - 30a b c d )x
+--R +
+--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 4 6 2 6
+--R (30a c d + 60a b c d - 360a b c d + 420a b c d - 150a b c d )x
+--R +
+--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2
+--R 150a c d - 234a b c d - 198a b c d + 498a b c d
+--R +
+--R 4 7
+--R - 216a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 4 4 4 5 3 3 2 6 2 2 3 7 4 8 2
+--R (216a c d - 552a b c d + 360a b c d + 72a b c d - 96a b c )x
+--R +
+--R 5 5 3 4 6 2 3 2 7 2 3 8
+--R 96a c d - 288a b c d + 288a b c d - 96a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 4 2 7 3 2 3 6 2 3 4 5 4 5 4 10
+--R (- 6a b c d + 18a b c d - 18a b c d + 6a b c d )x
+--R +
+--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 4 6 3 8
+--R (- 6a c d - 66a b c d + 234a b c d - 246a b c d + 84a b c d )x
+--R +
+--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 4 7 2 6
+--R (- 84a c d + 6a b c d + 486a b c d - 654a b c d + 246a b c d )x
+--R +
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 4 8 4
+--R (- 246a c d + 474a b c d + 54a b c d - 546a b c d + 264a b c d)x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8 4 9 2
+--R (- 264a c d + 696a b c d - 504a b c d - 24a b c d + 96a b c )x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9
+--R - 96a c d + 288a b c d - 288a b c d + 96a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 878
+
+--S 879 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 4 3 2 2 4 +-----------+
+--R (15a b c d x + 180a b c d x + 240a b c d)\|- a d + b c
+--R *
+--R +-----------+ +--------+
+--R | b | 2
+--R |- --------- \|d x + c
+--R \| a d - b c
+--R +
+--R 2 3 4 3 2 2 4 +-----------+
+--R (- 75a b c d x - 300a b c d x - 240a b c d)\|- a d + b c
+--R *
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R *
+--R log
+--R 2 2 2 2 4 2 2 2
+--R ((2a d + 2a b c d - 4b c )x + (8a c d - 8a b c )x )
+--R *
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 2 4 2 2 2 2 2
+--R 4b c x + (4a c d + 8a b c )x + 8a c
+--R *
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+--R \|d x + c
+--R +
+--R 2 2 6 2 2 2 2 4
+--R (a b d - 2b c d)x + (- a d - 4a b c d - 4b c )x
+--R +
+--R 2 2 2 2 2
+--R (- 8a c d - 8a b c )x - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 6 2 2 2 2 3 4
+--R (- 2a b c d + 2b c d)x + (- 6a c d + 2a b c d + 4b c )x
+--R +
+--R 2 2 3 2
+--R (- 8a c d + 8a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R /
+--R +--------+
+--R 4 2 2 2 | 2
+--R (4b c d x + (4a c d + 8b c )x + 8a c )\|d x + c
+--R +
+--R 2 6 2 4 2 2
+--R - b d x + (- a d - 8b c d)x + (- 8a c d - 8b c )x
+--R +
+--R 2
+--R - 8a c
+--R *
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R 2 3 4 3 2 2 4 +-+ | 2
+--R (30a b c d x + 360a b c d x + 480a b c d)\|b \|d x + c
+--R +
+--R 2 3 4 3 2 2 4 +-+ +-+
+--R (- 150a b c d x - 600a b c d x - 480a b c d)\|b \|c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 4a d + 28a b c d + 6b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 48a c d + 336a b c d + 72b c d)x - 64a c d + 448a b c d + 96b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (20a c d - 140a b c d - 30b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (80a c d - 560a b c d - 120b c d)x + 64a c d - 448a b c d - 96b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R /
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4
+--R (12a c d - 36a b c d + 36a b c d - 12a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 2 4 4 3
+--R (144a c d - 432a b c d + 432a b c d - 144a b c d)x + 192a c d
+--R +
+--R 3 5 2 2 2 6 3 7
+--R - 576a b c d + 576a b c d - 192a b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4
+--R (- 60a c d + 180a b c d - 180a b c d + 60a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 2 4 4 3
+--R (- 240a c d + 720a b c d - 720a b c d + 240a b c d)x - 192a c d
+--R +
+--R 3 5 2 2 2 6 3 7
+--R 576a b c d - 576a b c d + 192a b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 879
+
+--S 880 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 880
+
+--S 881 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 3 4 3 2 2 4 +-+ | 2
+--R (15a b c d x + 180a b c d x + 240a b c d)\|b \|d x + c
+--R +
+--R 2 3 4 3 2 2 4 +-+ +-+
+--R (- 75a b c d x - 300a b c d x - 240a b c d)\|b \|c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 2 3 4 3 2 2 4 +-----------+
+--R (- 15a b c d x - 180a b c d x - 240a b c d)\|- a d + b c
+--R *
+--R +---------+ +--------+
+--R | b | 2
+--R |--------- \|d x + c
+--R \|a d - b c
+--R +
+--R 2 3 4 3 2 2 4 +-----------+
+--R (75a b c d x + 300a b c d x + 240a b c d)\|- a d + b c
+--R *
+--R +---------+
+--R | b +-+
+--R |--------- \|c
+--R \|a d - b c
+--R *
+--R +--------+
+--R | 2 2 +-+
+--R a\|d x + c + (- b x - a)\|c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b
+--R (a d - b c)x |---------
+--R \|a d - b c
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 2a d + 14a b c d + 3b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 24a c d + 168a b c d + 36b c d)x - 32a c d + 224a b c d + 48b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 2 4 2 3 2 3 2 4
+--R (10a c d - 70a b c d - 15b c d )x
+--R +
+--R 2 2 3 3 2 2 4 2 2 3 2 4 2 5
+--R (40a c d - 280a b c d - 60b c d)x + 32a c d - 224a b c d - 48b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R /
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4
+--R (6a c d - 18a b c d + 18a b c d - 6a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 2 4 4 3
+--R (72a c d - 216a b c d + 216a b c d - 72a b c d)x + 96a c d
+--R +
+--R 3 5 2 2 2 6 3 7
+--R - 288a b c d + 288a b c d - 96a b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4
+--R (- 30a c d + 90a b c d - 90a b c d + 30a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 2 4 4 3
+--R (- 120a c d + 360a b c d - 360a b c d + 120a b c d)x - 96a c d
+--R +
+--R 3 5 2 2 2 6 3 7
+--R 288a b c d - 288a b c d + 96a b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 881
+
+--S 882 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 882
+
+)clear all
+
+--S 883 of 1527
+t0:=1/((a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 883
+
+--S 884 of 1527
+r0:=1/6*d*(3*b*c+2*a*d)*x/(a*c*(b*c-a*d)^2*(c+d*x^2)^(3/2))+1/2*b*x/_
+ (a*(b*c-a*d)*(a+b*x^2)*(c+d*x^2)^(3/2))+1/2*b^2*(b*c-6*a*d)*_
+ atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/(a^(3/2)*_
+ (b*c-a*d)^(7/2))+1/6*d*(3*b^2*c^2+16*a*b*c*d-4*a^2*d^2)*x/_
+ (a*c^2*(b*c-a*d)^3*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R 3 2 2 4 3 4 2 2 2 2 3 3 4 4 2
+--R (18a b c d - 3b c d)x + (18a b c d + 15a b c d - 3b c )x
+--R +
+--R 2 2 3 3 4
+--R 18a b c d - 3a b c
+--R *
+--R +--------+ +-----------+
+--R | 2 x\|- a d + b c
+--R \|d x + c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 2 4 2 3 3 2 2 5
+--R (4a b d - 16a b c d - 3b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 3
+--R (4a d - 10a b c d - 18a b c d - 6b c d)x
+--R +
+--R 3 3 2 2 2 3 4
+--R (6a c d - 18a b c d - 3b c )x
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R /
+--R 4 2 4 3 2 3 3 2 3 4 2 4 5 4
+--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x
+--R +
+--R 5 2 4 4 3 3 2 3 5 4 6 2 5 3 3 4 4 2
+--R (6a c d - 12a b c d + 12a b c d - 6a b c )x + 6a c d - 18a b c d
+--R +
+--R 3 2 5 2 3 6
+--R 18a b c d - 6a b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 884
+
+--S 885 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 4 4 3 3 8
+--R (90a b c d - 15b c d )x
+--R +
+--R 2 2 2 4 3 3 3 4 4 2 6
+--R (90a b c d + 435a b c d - 75b c d )x
+--R +
+--R 2 2 3 3 3 4 2 4 5 4
+--R (450a b c d + 573a b c d - 108b c d)x
+--R +
+--R 2 2 4 2 3 5 4 6 2 2 2 5 3 6
+--R (648a b c d + 180a b c d - 48b c )x + 288a b c d - 48a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 5 4 3 4 10
+--R (- 18a b c d + 3b c d )x
+--R +
+--R 2 2 2 5 3 3 4 4 4 3 8
+--R (- 18a b c d - 249a b c d + 42b c d )x
+--R +
+--R 2 2 3 4 3 4 3 4 5 2 6
+--R (- 252a b c d - 696a b c d + 123b c d )x
+--R +
+--R 2 2 4 3 3 5 2 4 6 4
+--R (- 738a b c d - 669a b c d + 132b c d)x
+--R +
+--R 2 2 5 2 3 6 4 7 2 2 2 6 3 7
+--R (- 792a b c d - 156a b c d + 48b c )x - 288a b c d + 48a b c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 6 2 5 3 2 4 9
+--R (- 8a b d + 32a b c d + 6b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 7
+--R (- 8a d - 76a b c d + 420a b c d + 84b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 5
+--R (- 108a c d + 148a b c d + 944a b c d + 246b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 3
+--R (- 272a c d + 752a b c d + 576a b c d + 264b c d)x
+--R +
+--R 3 3 3 2 4 2 3 6
+--R (- 192a c d + 576a b c d + 96b c )x
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 2 6 2 5 3 2 4 9
+--R (40a b d - 160a b c d - 30b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 7
+--R (40a d + 60a b c d - 820a b c d - 180b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 5
+--R (220a c d - 452a b c d - 1232a b c d - 366b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 3
+--R (368a c d - 1040a b c d - 576a b c d - 312b c d)x
+--R +
+--R 3 3 3 2 4 2 3 6
+--R (192a c d - 576a b c d - 96b c )x
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|c \|a d - a b c
+--R /
+--R 4 2 6 3 2 3 5 2 3 4 4 4 5 3 8
+--R (60a b c d - 180a b c d + 180a b c d - 60a b c d )x
+--R +
+--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3
+--R 60a c d + 120a b c d - 720a b c d + 840a b c d
+--R +
+--R 4 6 2
+--R - 300a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2
+--R 300a c d - 468a b c d - 396a b c d + 996a b c d
+--R +
+--R 4 7
+--R - 432a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 4 4 4 5 3 3 2 6 2 2 3 7 4 8 2
+--R (432a c d - 1104a b c d + 720a b c d + 144a b c d - 192a b c )x
+--R +
+--R 5 5 3 4 6 2 3 2 7 2 3 8
+--R 192a c d - 576a b c d + 576a b c d - 192a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a d - a b c \|d x + c
+--R +
+--R 4 2 7 3 2 3 6 2 3 4 5 4 5 4 10
+--R (- 12a b c d + 36a b c d - 36a b c d + 12a b c d )x
+--R +
+--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4
+--R - 12a c d - 132a b c d + 468a b c d - 492a b c d
+--R +
+--R 4 6 3
+--R 168a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3
+--R - 168a c d + 12a b c d + 972a b c d - 1308a b c d
+--R +
+--R 4 7 2
+--R 492a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2
+--R - 492a c d + 948a b c d + 108a b c d - 1092a b c d
+--R +
+--R 4 8
+--R 528a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8
+--R - 528a c d + 1392a b c d - 1008a b c d - 48a b c d
+--R +
+--R 4 9
+--R 192a b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9
+--R - 192a c d + 576a b c d - 576a b c d + 192a b c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R ,
+--R
+--R 3 2 4 4 3 3 8
+--R (- 90a b c d + 15b c d )x
+--R +
+--R 2 2 2 4 3 3 3 4 4 2 6
+--R (- 90a b c d - 435a b c d + 75b c d )x
+--R +
+--R 2 2 3 3 3 4 2 4 5 4
+--R (- 450a b c d - 573a b c d + 108b c d)x
+--R +
+--R 2 2 4 2 3 5 4 6 2 2 2 5 3 6
+--R (- 648a b c d - 180a b c d + 48b c )x - 288a b c d + 48a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 5 4 3 4 10 2 2 2 5 3 3 4 4 4 3 8
+--R (18a b c d - 3b c d )x + (18a b c d + 249a b c d - 42b c d )x
+--R +
+--R 2 2 3 4 3 4 3 4 5 2 6
+--R (252a b c d + 696a b c d - 123b c d )x
+--R +
+--R 2 2 4 3 3 5 2 4 6 4
+--R (738a b c d + 669a b c d - 132b c d)x
+--R +
+--R 2 2 5 2 3 6 4 7 2 2 2 6 3 7
+--R (792a b c d + 156a b c d - 48b c )x + 288a b c d - 48a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 3 2 4 4 3 3 8
+--R (- 90a b c d + 15b c d )x
+--R +
+--R 2 2 2 4 3 3 3 4 4 2 6
+--R (- 90a b c d - 435a b c d + 75b c d )x
+--R +
+--R 2 2 3 3 3 4 2 4 5 4
+--R (- 450a b c d - 573a b c d + 108b c d)x
+--R +
+--R 2 2 4 2 3 5 4 6 2 2 2 5 3 6
+--R (- 648a b c d - 180a b c d + 48b c )x - 288a b c d + 48a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 3 2 5 4 3 4 10 2 2 2 5 3 3 4 4 4 3 8
+--R (18a b c d - 3b c d )x + (18a b c d + 249a b c d - 42b c d )x
+--R +
+--R 2 2 3 4 3 4 3 4 5 2 6
+--R (252a b c d + 696a b c d - 123b c d )x
+--R +
+--R 2 2 4 3 3 5 2 4 6 4
+--R (738a b c d + 669a b c d - 132b c d)x
+--R +
+--R 2 2 5 2 3 6 4 7 2 2 2 6 3 7
+--R (792a b c d + 156a b c d - 48b c )x + 288a b c d - 48a b c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 2 6 2 5 3 2 4 9
+--R (- 4a b d + 16a b c d + 3b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 7
+--R (- 4a d - 38a b c d + 210a b c d + 42b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 5
+--R (- 54a c d + 74a b c d + 472a b c d + 123b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 3
+--R (- 136a c d + 376a b c d + 288a b c d + 132b c d)x
+--R +
+--R 3 3 3 2 4 2 3 6
+--R (- 96a c d + 288a b c d + 48b c )x
+--R *
+--R +-------------+ +--------+
+--R | 2 | 2
+--R \|- a d + a b c \|d x + c
+--R +
+--R 2 6 2 5 3 2 4 9
+--R (20a b d - 80a b c d - 15b c d )x
+--R +
+--R 3 6 2 5 2 2 4 3 3 3 7
+--R (20a d + 30a b c d - 410a b c d - 90b c d )x
+--R +
+--R 3 5 2 2 4 2 3 3 3 4 2 5
+--R (110a c d - 226a b c d - 616a b c d - 183b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 3
+--R (184a c d - 520a b c d - 288a b c d - 156b c d)x
+--R +
+--R 3 3 3 2 4 2 3 6
+--R (96a c d - 288a b c d - 48b c )x
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R /
+--R 4 2 6 3 2 3 5 2 3 4 4 4 5 3 8
+--R (30a b c d - 90a b c d + 90a b c d - 30a b c d )x
+--R +
+--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 4 6 2 6
+--R (30a c d + 60a b c d - 360a b c d + 420a b c d - 150a b c d )x
+--R +
+--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2
+--R 150a c d - 234a b c d - 198a b c d + 498a b c d
+--R +
+--R 4 7
+--R - 216a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 4 4 4 5 3 3 2 6 2 2 3 7 4 8 2
+--R (216a c d - 552a b c d + 360a b c d + 72a b c d - 96a b c )x
+--R +
+--R 5 5 3 4 6 2 3 2 7 2 3 8
+--R 96a c d - 288a b c d + 288a b c d - 96a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 4 2 7 3 2 3 6 2 3 4 5 4 5 4 10
+--R (- 6a b c d + 18a b c d - 18a b c d + 6a b c d )x
+--R +
+--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 4 6 3 8
+--R (- 6a c d - 66a b c d + 234a b c d - 246a b c d + 84a b c d )x
+--R +
+--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3
+--R - 84a c d + 6a b c d + 486a b c d - 654a b c d
+--R +
+--R 4 7 2
+--R 246a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2
+--R - 246a c d + 474a b c d + 54a b c d - 546a b c d
+--R +
+--R 4 8
+--R 264a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8 4 9 2
+--R (- 264a c d + 696a b c d - 504a b c d - 24a b c d + 96a b c )x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9
+--R - 96a c d + 288a b c d - 288a b c d + 96a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 885
+
+--S 886 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 +-----------+ +-+
+--R (6a b d - b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 2 3 | 2 x\|- a d + b c
+--R (- 12a b d + 2b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 4 3 3 2 2 2 2 3 3 +-----------+ +-+ | 2
+--R (4a d - 12a b c d + 12a b c d - 4a b c )\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 886
+
+--S 887 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 887
+
+--S 888 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 2 3 +-----------+ +-+
+--R (- 6a b d + b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 2 3 +-----------+ +-+ \|- a d + a b c \|c
+--R (- 6a b d + b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 2 3 | 2 x\|- a d + b c
+--R (- 6a b d + b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 4 3 3 2 2 2 2 3 3 | 2 +-----------+ +-+
+--R (2a d - 6a b c d + 6a b c d - 2a b c )\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 888
+
+--S 889 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 889
+
+)clear all
+
+--S 890 of 1527
+t0:=1/(x*(a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 9 2 2 7 2 2 2 2 5
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 3 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 890
+
+--S 891 of 1527
+r0:=1/6*d*(3*b*c+2*a*d)/(a*c*(b*c-a*d)^2*(c+d*x^2)^(3/2))+_
+ 1/2*b/(a*(b*c-a*d)*(a+b*x^2)*(c+d*x^2)^(3/2))-atanh(sqrt(c+d*x^2)/_
+ sqrt(c))/(a^2*c^(5/2))+1/2*b^(5/2)*(2*b*c-7*a*d)*atanh(sqrt(b)*_
+ sqrt(c+d*x^2)/sqrt(b*c-a*d))/(a^2*(b*c-a*d)^(7/2))+1/2*d*(b^2*c^2+_
+ 6*a*b*c*d-2*a^2*d^2)/(a*c^2*(b*c-a*d)^3*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R 3 2 2 4 3 4 2 2 2 2 3 3 4 4 2
+--R (21a b c d - 6b c d)x + (21a b c d + 15a b c d - 6b c )x
+--R +
+--R 2 2 3 3 4
+--R 21a b c d - 6a b c
+--R *
+--R +--------+
+--R +--------+ +-+ | 2
+--R +-+ +-+ | 2 \|b \|d x + c
+--R \|b \|c \|d x + c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (- 6a b d + 18a b c d - 18a b c d + 6b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (- 6a d + 12a b c d - 12a b c d + 6b c )x - 6a c d + 18a b c d
+--R +
+--R 2 2 3 3 4
+--R - 18a b c d + 6a b c
+--R *
+--R +--------+
+--R +--------+ | 2
+--R +-----------+ | 2 \|d x + c
+--R \|- a d + b c \|d x + c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 3 4 2 2 3 3 2 2 4
+--R (6a b d - 18a b c d - 3a b c d )x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 2 4 3 3 2 2
+--R (6a d - 10a b c d - 20a b c d - 6a b c d)x + 8a c d - 20a b c d
+--R +
+--R 3 4
+--R - 3a b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 4
+--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x
+--R +
+--R 6 2 4 5 3 3 3 3 5 2 4 6 2 6 3 3 5 4 2
+--R (6a c d - 12a b c d + 12a b c d - 6a b c )x + 6a c d - 18a b c d
+--R +
+--R 4 2 5 3 3 6
+--R 18a b c d - 6a b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R Type: Expression(Integer)
+--E 891
+
+--S 892 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (60a b c d - 180a b c d + 180a b c d - 60b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3
+--R 60a c d + 120a b c d - 720a b c d + 840a b c d
+--R +
+--R 4 5 2
+--R - 300b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R 300a c d - 468a b c d - 396a b c d + 996a b c d
+--R +
+--R 4 6
+--R - 432b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6
+--R 432a c d - 1104a b c d + 720a b c d + 144a b c d
+--R +
+--R 4 7
+--R - 192b c
+--R *
+--R 2
+--R x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R 192a c d - 576a b c d + 576a b c d - 192a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 7 2 2 6 3 2 5 4 3 4 10
+--R (- 12a b d + 36a b c d - 36a b c d + 12b c d )x
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R - 12a d - 132a b c d + 468a b c d - 492a b c d
+--R +
+--R 4 4 3
+--R 168b c d
+--R *
+--R 8
+--R x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3
+--R - 168a c d + 12a b c d + 972a b c d - 1308a b c d
+--R +
+--R 4 5 2
+--R 492b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R - 492a c d + 948a b c d + 108a b c d - 1092a b c d
+--R +
+--R 4 6
+--R 528b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6
+--R - 528a c d + 1392a b c d - 1008a b c d - 48a b c d
+--R +
+--R 4 7
+--R 192b c
+--R *
+--R 2
+--R x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R - 192a c d + 576a b c d - 576a b c d + 192a b c
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 3 3 4 4 4 3 8
+--R (105a b c d - 30b c d )x
+--R +
+--R 2 2 3 4 3 4 3 4 5 2 6
+--R (105a b c d + 495a b c d - 150b c d )x
+--R +
+--R 2 2 4 3 3 5 2 4 6 4
+--R (525a b c d + 606a b c d - 216b c d)x
+--R +
+--R 2 2 5 2 3 6 4 7 2 2 2 6 3 7
+--R (756a b c d + 120a b c d - 96b c )x + 336a b c d - 96a b c
+--R *
+--R +-----------+ +--------+
+--R | b +-+ | 2
+--R |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 3 3 5 4 4 4 10
+--R (- 21a b c d + 6b c d )x
+--R +
+--R 2 2 3 5 3 4 4 4 5 3 8
+--R (- 21a b c d - 288a b c d + 84b c d )x
+--R +
+--R 2 2 4 4 3 5 3 4 6 2 6
+--R (- 294a b c d - 777a b c d + 246b c d )x
+--R +
+--R 2 2 5 3 3 6 2 4 7 4
+--R (- 861a b c d - 678a b c d + 264b c d)x
+--R +
+--R 2 2 6 2 3 7 4 8 2 2 2 7 3 8
+--R (- 924a b c d - 72a b c d + 96b c )x - 336a b c d + 96a b c
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (- 2a d + 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((2a b d - 2b c)x + (2a d - 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (68a b c d - 164a b c d + 6a b c d - 30b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 6
+--R (68a c d + 76a b c d - 528a b c d + 54a b c d - 150b c d )x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4
+--R (240a c d - 336a b c d - 384a b c d + 96a b c d - 216b c d)x
+--R +
+--R 4 3 4 3 4 3 3 6 4 7 2
+--R (192a c d - 384a b c d + 48a b c d - 96b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 7 2 2 6 4 3 4 10
+--R (- 16a b d + 40a b c d + 6b c d )x
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (- 16a d - 124a b c d + 380a b c d - 24a b c d + 84b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 6
+--R (- 164a c d + 44a b c d + 720a b c d - 96a b c d + 246b c d )x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R - 336a c d + 528a b c d + 384a b c d - 120a b c d
+--R +
+--R 4 6
+--R 264b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 3 4 3 4 3 3 6 4 7 2
+--R (- 192a c d + 384a b c d - 48a b c d + 96b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 5 3 6 4 2 4 5 3 3 5 4 2 4 6 3 8
+--R (60a b c d - 180a b c d + 180a b c d - 60a b c d )x
+--R +
+--R 6 3 6 5 4 5 4 2 5 4 3 3 6 3
+--R 60a c d + 120a b c d - 720a b c d + 840a b c d
+--R +
+--R 2 4 7 2
+--R - 300a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 4 5 5 5 4 4 2 6 3 3 3 7 2
+--R 300a c d - 468a b c d - 396a b c d + 996a b c d
+--R +
+--R 2 4 8
+--R - 432a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 5 4 5 6 3 4 2 7 2 3 3 8 2 4 9 2
+--R (432a c d - 1104a b c d + 720a b c d + 144a b c d - 192a b c )x
+--R +
+--R 6 6 3 5 7 2 4 2 8 3 3 9
+--R 192a c d - 576a b c d + 576a b c d - 192a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 5 3 7 4 2 4 6 3 3 5 5 2 4 6 4 10
+--R (- 12a b c d + 36a b c d - 36a b c d + 12a b c d )x
+--R +
+--R 6 3 7 5 4 6 4 2 5 5 3 3 6 4 2 4 7 3 8
+--R (- 12a c d - 132a b c d + 468a b c d - 492a b c d + 168a b c d )x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3 2 4 8 2 6
+--R (- 168a c d + 12a b c d + 972a b c d - 1308a b c d + 492a b c d )x
+--R +
+--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2 2 4 9 4
+--R (- 492a c d + 948a b c d + 108a b c d - 1092a b c d + 528a b c d)x
+--R +
+--R 6 6 4 5 7 3 4 2 8 2 3 3 9 2 4 10 2
+--R (- 528a c d + 1392a b c d - 1008a b c d - 48a b c d + 192a b c )x
+--R +
+--R 6 7 3 5 8 2 4 2 9 3 3 10
+--R - 192a c d + 576a b c d - 576a b c d + 192a b c
+--R ,
+--R
+--R 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (30a b c d - 90a b c d + 90a b c d - 30b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3
+--R 30a c d + 60a b c d - 360a b c d + 420a b c d
+--R +
+--R 4 5 2
+--R - 150b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R 150a c d - 234a b c d - 198a b c d + 498a b c d
+--R +
+--R 4 6
+--R - 216b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 2
+--R (216a c d - 552a b c d + 360a b c d + 72a b c d - 96b c )x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R 96a c d - 288a b c d + 288a b c d - 96a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 7 2 2 6 3 2 5 4 3 4 10
+--R (- 6a b d + 18a b c d - 18a b c d + 6b c d )x
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (- 6a d - 66a b c d + 234a b c d - 246a b c d + 84b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3
+--R - 84a c d + 6a b c d + 486a b c d - 654a b c d
+--R +
+--R 4 5 2
+--R 246b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R - 246a c d + 474a b c d + 54a b c d - 546a b c d
+--R +
+--R 4 6
+--R 264b c d
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+--R 4
+--R x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6
+--R - 264a c d + 696a b c d - 504a b c d - 24a b c d
+--R +
+--R 4 7
+--R 96b c
+--R *
+--R 2
+--R x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7
+--R - 96a c d + 288a b c d - 288a b c d + 96a b c
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 3 3 4 4 4 3 8
+--R (105a b c d - 30b c d )x
+--R +
+--R 2 2 3 4 3 4 3 4 5 2 6
+--R (105a b c d + 495a b c d - 150b c d )x
+--R +
+--R 2 2 4 3 3 5 2 4 6 4
+--R (525a b c d + 606a b c d - 216b c d)x
+--R +
+--R 2 2 5 2 3 6 4 7 2 2 2 6 3 7
+--R (756a b c d + 120a b c d - 96b c )x + 336a b c d - 96a b c
+--R *
+--R +---------+ +--------+
+--R | b +-+ | 2
+--R |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R 3 3 5 4 4 4 10
+--R (- 21a b c d + 6b c d )x
+--R +
+--R 2 2 3 5 3 4 4 4 5 3 8
+--R (- 21a b c d - 288a b c d + 84b c d )x
+--R +
+--R 2 2 4 4 3 5 3 4 6 2 6
+--R (- 294a b c d - 777a b c d + 246b c d )x
+--R +
+--R 2 2 5 3 3 6 2 4 7 4
+--R (- 861a b c d - 678a b c d + 264b c d)x
+--R +
+--R 2 2 6 2 3 7 4 8 2 2 2 7 3 8
+--R (- 924a b c d - 72a b c d + 96b c )x - 336a b c d + 96a b c
+--R *
+--R +---------+
+--R | b
+--R |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (34a b c d - 82a b c d + 3a b c d - 15b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 6
+--R (34a c d + 38a b c d - 264a b c d + 27a b c d - 75b c d )x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4
+--R (120a c d - 168a b c d - 192a b c d + 48a b c d - 108b c d)x
+--R +
+--R 4 3 4 3 4 3 3 6 4 7 2
+--R (96a c d - 192a b c d + 24a b c d - 48b c )x
+--R *
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+--R \|d x + c
+--R +
+--R 3 7 2 2 6 4 3 4 10
+--R (- 8a b d + 20a b c d + 3b c d )x
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (- 8a d - 62a b c d + 190a b c d - 12a b c d + 42b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 6
+--R (- 82a c d + 22a b c d + 360a b c d - 48a b c d + 123b c d )x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 4
+--R (- 168a c d + 264a b c d + 192a b c d - 60a b c d + 132b c d)x
+--R +
+--R 4 3 4 3 4 3 3 6 4 7 2
+--R (- 96a c d + 192a b c d - 24a b c d + 48b c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R 5 3 6 4 2 4 5 3 3 5 4 2 4 6 3 8
+--R (30a b c d - 90a b c d + 90a b c d - 30a b c d )x
+--R +
+--R 6 3 6 5 4 5 4 2 5 4 3 3 6 3 2 4 7 2 6
+--R (30a c d + 60a b c d - 360a b c d + 420a b c d - 150a b c d )x
+--R +
+--R 6 4 5 5 5 4 4 2 6 3 3 3 7 2
+--R 150a c d - 234a b c d - 198a b c d + 498a b c d
+--R +
+--R 2 4 8
+--R - 216a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 5 4 5 6 3 4 2 7 2 3 3 8 2 4 9 2
+--R (216a c d - 552a b c d + 360a b c d + 72a b c d - 96a b c )x
+--R +
+--R 6 6 3 5 7 2 4 2 8 3 3 9
+--R 96a c d - 288a b c d + 288a b c d - 96a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 5 3 7 4 2 4 6 3 3 5 5 2 4 6 4 10
+--R (- 6a b c d + 18a b c d - 18a b c d + 6a b c d )x
+--R +
+--R 6 3 7 5 4 6 4 2 5 5 3 3 6 4 2 4 7 3 8
+--R (- 6a c d - 66a b c d + 234a b c d - 246a b c d + 84a b c d )x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3 2 4 8 2 6
+--R (- 84a c d + 6a b c d + 486a b c d - 654a b c d + 246a b c d )x
+--R +
+--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2 2 4 9 4
+--R (- 246a c d + 474a b c d + 54a b c d - 546a b c d + 264a b c d)x
+--R +
+--R 6 6 4 5 7 3 4 2 8 2 3 3 9 2 4 10 2
+--R (- 264a c d + 696a b c d - 504a b c d - 24a b c d + 96a b c )x
+--R +
+--R 6 7 3 5 8 2 4 2 9 3 3 10
+--R - 96a c d + 288a b c d - 288a b c d + 96a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 892
+
+--S 893 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (12a d - 36a b c d + 36a b c d - 12b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (144a c d - 432a b c d + 432a b c d - 144b c d)x + 192a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R - 576a b c d + 576a b c d - 192b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 60a d + 180a b c d - 180a b c d + 60b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2
+--R (- 240a c d + 720a b c d - 720a b c d + 240b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5
+--R - 192a c d + 576a b c d - 576a b c d + 192b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 3 3 3 2 4 2 3 2 3 4 2 2 4
+--R (21a b c d - 6b c d )x + (252a b c d - 72b c d)x + 336a b c d
+--R +
+--R 3 5
+--R - 96b c
+--R *
+--R +-----------+ +--------+
+--R +-----------+ | b +-+ | 2
+--R \|- a d + b c |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 2 3 3 3 4 2 4 2 4 2 3 5 2
+--R (- 105a b c d + 30b c d )x + (- 420a b c d + 120b c d)x
+--R +
+--R 2 5 3 6
+--R - 336a b c d + 96b c
+--R *
+--R +-----------+
+--R +-----------+ | b
+--R \|- a d + b c |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (- 2a d + 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((2a b d - 2b c)x + (2a d - 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 2 3 3 3 2 4 2 3 2 3 4 2
+--R (- 42a b c d + 12b c d )x + (- 504a b c d + 144b c d)x
+--R +
+--R 2 4 3 5
+--R - 672a b c d + 192b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|b \|c \|d x + c
+--R +
+--R 2 3 3 3 4 2 4 2 4 2 3 5 2
+--R (210a b c d - 60b c d )x + (840a b c d - 240b c d)x
+--R +
+--R 2 5 3 6
+--R 672a b c d - 192b c
+--R *
+--R +-+
+--R \|b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (12a d - 36a b c d + 36a b c d - 12b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (144a c d - 432a b c d + 432a b c d - 144b c d)x + 192a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R - 576a b c d + 576a b c d - 192b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 60a d + 180a b c d - 180a b c d + 60b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2
+--R (- 240a c d + 720a b c d - 720a b c d + 240b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5
+--R - 192a c d + 576a b c d - 576a b c d + 192b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 3 5 2 4 3 3 2 4
+--R (16a d - 40a b c d - 6b c d )x
+--R +
+--R 3 4 2 2 3 3 4 2 3 2 3 2 3 2
+--R (192a c d - 480a b c d - 72b c d)x + 256a c d - 640a b c d
+--R +
+--R 3 5
+--R - 96b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 2 4 3 3 2 4
+--R (- 80a d + 200a b c d + 30b c d )x
+--R +
+--R 3 4 2 2 3 3 4 2 3 2 3 2 3 2
+--R (- 320a c d + 800a b c d + 120b c d)x - 256a c d + 640a b c d
+--R +
+--R 3 5
+--R 96b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4
+--R (12a c d - 36a b c d + 36a b c d - 12a b c d )x
+--R +
+--R 5 3 4 4 4 3 3 2 5 2 2 3 6 2 5 4 3
+--R (144a c d - 432a b c d + 432a b c d - 144a b c d)x + 192a c d
+--R +
+--R 4 5 2 3 2 6 2 3 7
+--R - 576a b c d + 576a b c d - 192a b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 4
+--R (- 60a c d + 180a b c d - 180a b c d + 60a b c d )x
+--R +
+--R 5 4 4 4 5 3 3 2 6 2 2 3 7 2 5 5 3
+--R (- 240a c d + 720a b c d - 720a b c d + 240a b c d)x - 192a c d
+--R +
+--R 4 6 2 3 2 7 2 3 8
+--R 576a b c d - 576a b c d + 192a b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R Type: Expression(Integer)
+--E 893
+
+--S 894 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 894
+
+--S 895 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (6a d - 18a b c d + 18a b c d - 6b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (72a c d - 216a b c d + 216a b c d - 72b c d)x + 96a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R - 288a b c d + 288a b c d - 96b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 30a d + 90a b c d - 90a b c d + 30b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 120a c d + 360a b c d - 360a b c d + 120b c d)x - 96a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 288a b c d - 288a b c d + 96b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 2 3 3 3 2 4 2 3 2 3 4 2
+--R (- 21a b c d + 6b c d )x + (- 252a b c d + 72b c d)x
+--R +
+--R 2 4 3 5
+--R - 336a b c d + 96b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|b \|c \|d x + c
+--R +
+--R 2 3 3 3 4 2 4 2 4 2 3 5 2
+--R (105a b c d - 30b c d )x + (420a b c d - 120b c d)x
+--R +
+--R 2 5 3 6
+--R 336a b c d - 96b c
+--R *
+--R +-+
+--R \|b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (6a d - 18a b c d + 18a b c d - 6b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (72a c d - 216a b c d + 216a b c d - 72b c d)x + 96a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R - 288a b c d + 288a b c d - 96b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (- 30a d + 90a b c d - 90a b c d + 30b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (- 120a c d + 360a b c d - 360a b c d + 120b c d)x - 96a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 288a b c d - 288a b c d + 96b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 3 3 3 2 4 2 3 2 3 4 2 2 4
+--R (21a b c d - 6b c d )x + (252a b c d - 72b c d)x + 336a b c d
+--R +
+--R 3 5
+--R - 96b c
+--R *
+--R +---------+ +--------+
+--R +-----------+ | b +-+ | 2
+--R \|- a d + b c |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R 2 3 3 3 4 2 4 2 4 2 3 5 2
+--R (- 105a b c d + 30b c d )x + (- 420a b c d + 120b c d)x
+--R +
+--R 2 5 3 6
+--R - 336a b c d + 96b c
+--R *
+--R +---------+
+--R +-----------+ | b
+--R \|- a d + b c |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R 3 5 2 4 3 3 2 4
+--R (8a d - 20a b c d - 3b c d )x
+--R +
+--R 3 4 2 2 3 3 4 2 3 2 3 2 3 2 3 5
+--R (96a c d - 240a b c d - 36b c d)x + 128a c d - 320a b c d - 48b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 3 5 2 4 3 3 2 4
+--R (- 40a d + 100a b c d + 15b c d )x
+--R +
+--R 3 4 2 2 3 3 4 2 3 2 3 2 3 2
+--R (- 160a c d + 400a b c d + 60b c d)x - 128a c d + 320a b c d
+--R +
+--R 3 5
+--R 48b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4
+--R (6a c d - 18a b c d + 18a b c d - 6a b c d )x
+--R +
+--R 5 3 4 4 4 3 3 2 5 2 2 3 6 2 5 4 3
+--R (72a c d - 216a b c d + 216a b c d - 72a b c d)x + 96a c d
+--R +
+--R 4 5 2 3 2 6 2 3 7
+--R - 288a b c d + 288a b c d - 96a b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 4
+--R (- 30a c d + 90a b c d - 90a b c d + 30a b c d )x
+--R +
+--R 5 4 4 4 5 3 3 2 6 2 2 3 7 2 5 5 3
+--R (- 120a c d + 360a b c d - 360a b c d + 120a b c d)x - 96a c d
+--R +
+--R 4 6 2 3 2 7 2 3 8
+--R 288a b c d - 288a b c d + 96a b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R Type: Expression(Integer)
+--E 895
+
+--S 896 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 896
+
+)clear all
+
+--S 897 of 1527
+t0:=1/(x^2*(a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 10 2 2 8 2 2 2 2 6
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 4 2 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 897
+
+--S 898 of 1527
+r0:=1/6*d*(3*b*c+2*a*d)/(a*c*(b*c-a*d)^2*x*(c+d*x^2)^(3/2))+_
+ 1/2*b/(a*(b*c-a*d)*x*(a+b*x^2)*(c+d*x^2)^(3/2))-_
+ 1/2*b^3*(3*b*c-8*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*_
+ sqrt(c+d*x^2)))/(a^(5/2)*(b*c-a*d)^(7/2))+1/6*d*(3*b^2*c^2+_
+ 20*a*b*c*d-8*a^2*d^2)/(a*c^2*(b*c-a*d)^3*x*sqrt(c+d*x^2))-_
+ 1/6*(9*b^3*c^3-18*a*b^2*c^2*d+40*a^2*b*c*d^2-16*a^3*d^3)*_
+ sqrt(c+d*x^2)/(a^2*c^3*(b*c-a*d)^3*x)
+--R
+--R
+--R (2)
+--R 4 3 2 5 4 5 2 3 3 2 4 4 5 5 3
+--R (- 24a b c d + 9b c d)x + (- 24a b c d - 15a b c d + 9b c )x
+--R +
+--R 2 3 4 4 5
+--R (- 24a b c d + 9a b c )x
+--R *
+--R +--------+ +-----------+
+--R | 2 x\|- a d + b c
+--R \|d x + c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 6
+--R (- 16a b d + 40a b c d - 18a b c d + 9b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4
+--R (- 16a d + 16a b c d + 42a b c d - 30a b c d + 18b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5 2 4 2 3
+--R (- 24a c d + 54a b c d - 18a b c d - 6a b c d + 9b c )x - 6a c d
+--R +
+--R 3 3 2 2 2 4 3 5
+--R 18a b c d - 18a b c d + 6a b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R /
+--R 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5
+--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x
+--R +
+--R 6 3 4 5 4 3 3 3 6 2 4 7 3
+--R (6a c d - 12a b c d + 12a b c d - 6a b c )x
+--R +
+--R 6 4 3 5 5 2 4 2 6 3 3 7
+--R (6a c d - 18a b c d + 18a b c d - 6a b c )x
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 898
+
+--S 899 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 3 5 5 4 4 11
+--R (24a b c d - 9b c d )x
+--R +
+--R 2 3 3 5 4 4 4 5 5 3 9
+--R (24a b c d + 447a b c d - 171b c d )x
+--R +
+--R 2 3 4 4 4 5 3 5 6 2 7
+--R (456a b c d + 1413a b c d - 594b c d )x
+--R +
+--R 2 3 5 3 4 6 2 5 7 5
+--R (1584a b c d + 1326a b c d - 720b c d)x
+--R +
+--R 2 3 6 2 4 7 5 8 3
+--R (1920a b c d + 48a b c d - 288b c )x
+--R +
+--R 2 3 7 4 8
+--R (768a b c d - 288a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 3 5 5 4 4 11
+--R (- 144a b c d + 54b c d )x
+--R +
+--R 2 3 3 5 4 4 4 5 5 3 9
+--R (- 144a b c d - 1002a b c d + 396b c d )x
+--R +
+--R 2 3 4 4 4 5 3 5 6 2 7
+--R (- 1056a b c d - 2052a b c d + 918b c d )x
+--R +
+--R 2 3 5 3 4 6 2 5 7 5
+--R (- 2448a b c d - 1386a b c d + 864b c d)x
+--R +
+--R 2 3 6 2 4 7 5 8 3
+--R (- 2304a b c d + 96a b c d + 288b c )x
+--R +
+--R 2 3 7 4 8
+--R (- 768a b c d + 288a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 3 7 2 2 6 3 2 5 4 3 4 10
+--R (192a b d - 480a b c d + 216a b c d - 108b c d )x
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (192a d + 832a b c d - 3064a b c d + 1512a b c d - 792b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3
+--R 1312a c d - 648a b c d - 5032a b c d + 3144a b c d
+--R +
+--R 4 5 2
+--R - 1836b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R 2632a c d - 4696a b c d - 1320a b c d + 2232a b c d
+--R +
+--R 4 6
+--R - 1728b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 4 7 2 4 4 3
+--R (1920a c d - 4608a b c d + 2304a b c d - 576b c )x + 384a c d
+--R +
+--R 3 5 2 2 2 6 3 7
+--R - 1152a b c d + 1152a b c d - 384a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a d - a b c \|d x + c
+--R +
+--R 3 8 2 2 7 3 2 6 4 3 5 12
+--R (- 32a b d + 80a b c d - 36a b c d + 18b c d )x
+--R +
+--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4
+--R (- 32a d - 544a b c d + 1524a b c d - 708a b c d + 360b c d )
+--R *
+--R 10
+--R x
+--R +
+--R 4 7 3 2 6 2 2 3 5 3 4 4
+--R - 624a c d - 852a b c d + 5316a b c d - 2820a b c d
+--R +
+--R 4 5 3
+--R 1530b c d
+--R *
+--R 8
+--R x
+--R +
+--R 4 2 6 3 3 5 2 2 4 4 3 5 3
+--R - 2412a c d + 2492a b c d + 5908a b c d - 4236a b c d
+--R +
+--R 4 6 2
+--R 2628b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2
+--R - 3544a c d + 6856a b c d + 312a b c d - 2280a b c d
+--R +
+--R 4 7
+--R 2016b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7
+--R - 2112a c d + 5184a b c d - 2880a b c d + 192a b c d
+--R +
+--R 4 8
+--R 576b c
+--R *
+--R 2
+--R x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8
+--R - 384a c d + 1152a b c d - 1152a b c d + 384a b c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R /
+--R 5 3 7 4 2 4 6 3 3 5 5 2 4 6 4 11
+--R (12a b c d - 36a b c d + 36a b c d - 12a b c d )x
+--R +
+--R 6 3 7 5 4 6 4 2 5 5 3 3 6 4
+--R 12a c d + 192a b c d - 648a b c d + 672a b c d
+--R +
+--R 2 4 7 3
+--R - 228a b c d
+--R *
+--R 9
+--R x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3
+--R 228a c d + 108a b c d - 1692a b c d + 2148a b c d
+--R +
+--R 2 4 8 2
+--R - 792a b c d
+--R *
+--R 7
+--R x
+--R +
+--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2
+--R 792a c d - 1416a b c d - 504a b c d + 2088a b c d
+--R +
+--R 2 4 9
+--R - 960a b c d
+--R *
+--R 5
+--R x
+--R +
+--R 6 6 4 5 7 3 4 2 8 2 3 3 9
+--R 960a c d - 2496a b c d + 1728a b c d + 192a b c d
+--R +
+--R 2 4 10
+--R - 384a b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 7 3 5 8 2 4 2 9 3 3 10
+--R (384a c d - 1152a b c d + 1152a b c d - 384a b c )x
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 5 3 7 4 2 4 6 3 3 5 5 2 4 6 4 11
+--R (- 72a b c d + 216a b c d - 216a b c d + 72a b c d )x
+--R +
+--R 6 3 7 5 4 6 4 2 5 5 3 3 6 4
+--R - 72a c d - 312a b c d + 1368a b c d - 1512a b c d
+--R +
+--R 2 4 7 3
+--R 528a b c d
+--R *
+--R 9
+--R x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3
+--R - 528a c d + 360a b c d + 2088a b c d - 3144a b c d
+--R +
+--R 2 4 8 2
+--R 1224a b c d
+--R *
+--R 7
+--R x
+--R +
+--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2
+--R - 1224a c d + 2520a b c d - 216a b c d - 2232a b c d
+--R +
+--R 2 4 9
+--R 1152a b c d
+--R *
+--R 5
+--R x
+--R +
+--R 6 6 4 5 7 3 4 2 8 2 2 4 10 3
+--R (- 1152a c d + 3072a b c d - 2304a b c d + 384a b c )x
+--R +
+--R 6 7 3 5 8 2 4 2 9 3 3 10
+--R (- 384a c d + 1152a b c d - 1152a b c d + 384a b c )x
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|c \|a d - a b c
+--R ,
+--R
+--R 4 3 5 5 4 4 11
+--R (24a b c d - 9b c d )x
+--R +
+--R 2 3 3 5 4 4 4 5 5 3 9
+--R (24a b c d + 447a b c d - 171b c d )x
+--R +
+--R 2 3 4 4 4 5 3 5 6 2 7
+--R (456a b c d + 1413a b c d - 594b c d )x
+--R +
+--R 2 3 5 3 4 6 2 5 7 5
+--R (1584a b c d + 1326a b c d - 720b c d)x
+--R +
+--R 2 3 6 2 4 7 5 8 3
+--R (1920a b c d + 48a b c d - 288b c )x
+--R +
+--R 2 3 7 4 8
+--R (768a b c d - 288a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 3 5 5 4 4 11
+--R (- 144a b c d + 54b c d )x
+--R +
+--R 2 3 3 5 4 4 4 5 5 3 9
+--R (- 144a b c d - 1002a b c d + 396b c d )x
+--R +
+--R 2 3 4 4 4 5 3 5 6 2 7
+--R (- 1056a b c d - 2052a b c d + 918b c d )x
+--R +
+--R 2 3 5 3 4 6 2 5 7 5
+--R (- 2448a b c d - 1386a b c d + 864b c d)x
+--R +
+--R 2 3 6 2 4 7 5 8 3
+--R (- 2304a b c d + 96a b c d + 288b c )x
+--R +
+--R 2 3 7 4 8
+--R (- 768a b c d + 288a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 4 3 5 5 4 4 11
+--R (24a b c d - 9b c d )x
+--R +
+--R 2 3 3 5 4 4 4 5 5 3 9
+--R (24a b c d + 447a b c d - 171b c d )x
+--R +
+--R 2 3 4 4 4 5 3 5 6 2 7
+--R (456a b c d + 1413a b c d - 594b c d )x
+--R +
+--R 2 3 5 3 4 6 2 5 7 5
+--R (1584a b c d + 1326a b c d - 720b c d)x
+--R +
+--R 2 3 6 2 4 7 5 8 3
+--R (1920a b c d + 48a b c d - 288b c )x
+--R +
+--R 2 3 7 4 8
+--R (768a b c d - 288a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 3 5 5 4 4 11
+--R (- 144a b c d + 54b c d )x
+--R +
+--R 2 3 3 5 4 4 4 5 5 3 9
+--R (- 144a b c d - 1002a b c d + 396b c d )x
+--R +
+--R 2 3 4 4 4 5 3 5 6 2 7
+--R (- 1056a b c d - 2052a b c d + 918b c d )x
+--R +
+--R 2 3 5 3 4 6 2 5 7 5
+--R (- 2448a b c d - 1386a b c d + 864b c d)x
+--R +
+--R 2 3 6 2 4 7 5 8 3
+--R (- 2304a b c d + 96a b c d + 288b c )x
+--R +
+--R 2 3 7 4 8
+--R (- 768a b c d + 288a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 3 7 2 2 6 3 2 5 4 3 4 10
+--R (96a b d - 240a b c d + 108a b c d - 54b c d )x
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 8
+--R (96a d + 416a b c d - 1532a b c d + 756a b c d - 396b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3
+--R 656a c d - 324a b c d - 2516a b c d + 1572a b c d
+--R +
+--R 4 5 2
+--R - 918b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R 1316a c d - 2348a b c d - 660a b c d + 1116a b c d
+--R +
+--R 4 6
+--R - 864b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 4 7 2 4 4 3
+--R (960a c d - 2304a b c d + 1152a b c d - 288b c )x + 192a c d
+--R +
+--R 3 5 2 2 2 6 3 7
+--R - 576a b c d + 576a b c d - 192a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 3 8 2 2 7 3 2 6 4 3 5 12
+--R (- 16a b d + 40a b c d - 18a b c d + 9b c d )x
+--R +
+--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 10
+--R (- 16a d - 272a b c d + 762a b c d - 354a b c d + 180b c d )x
+--R +
+--R 4 7 3 2 6 2 2 3 5 3 4 4
+--R - 312a c d - 426a b c d + 2658a b c d - 1410a b c d
+--R +
+--R 4 5 3
+--R 765b c d
+--R *
+--R 8
+--R x
+--R +
+--R 4 2 6 3 3 5 2 2 4 4 3 5 3
+--R - 1206a c d + 1246a b c d + 2954a b c d - 2118a b c d
+--R +
+--R 4 6 2
+--R 1314b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2
+--R - 1772a c d + 3428a b c d + 156a b c d - 1140a b c d
+--R +
+--R 4 7
+--R 1008b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7
+--R - 1056a c d + 2592a b c d - 1440a b c d + 96a b c d
+--R +
+--R 4 8
+--R 288b c
+--R *
+--R 2
+--R x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8
+--R - 192a c d + 576a b c d - 576a b c d + 192a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R 5 3 7 4 2 4 6 3 3 5 5 2 4 6 4 11
+--R (6a b c d - 18a b c d + 18a b c d - 6a b c d )x
+--R +
+--R 6 3 7 5 4 6 4 2 5 5 3 3 6 4 2 4 7 3 9
+--R (6a c d + 96a b c d - 324a b c d + 336a b c d - 114a b c d )x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3
+--R 114a c d + 54a b c d - 846a b c d + 1074a b c d
+--R +
+--R 2 4 8 2
+--R - 396a b c d
+--R *
+--R 7
+--R x
+--R +
+--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2
+--R 396a c d - 708a b c d - 252a b c d + 1044a b c d
+--R +
+--R 2 4 9
+--R - 480a b c d
+--R *
+--R 5
+--R x
+--R +
+--R 6 6 4 5 7 3 4 2 8 2 3 3 9 2 4 10 3
+--R (480a c d - 1248a b c d + 864a b c d + 96a b c d - 192a b c )x
+--R +
+--R 6 7 3 5 8 2 4 2 9 3 3 10
+--R (192a c d - 576a b c d + 576a b c d - 192a b c )x
+--R *
+--R +-------------+ +--------+
+--R | 2 | 2
+--R \|- a d + a b c \|d x + c
+--R +
+--R 5 3 7 4 2 4 6 3 3 5 5 2 4 6 4 11
+--R (- 36a b c d + 108a b c d - 108a b c d + 36a b c d )x
+--R +
+--R 6 3 7 5 4 6 4 2 5 5 3 3 6 4
+--R - 36a c d - 156a b c d + 684a b c d - 756a b c d
+--R +
+--R 2 4 7 3
+--R 264a b c d
+--R *
+--R 9
+--R x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3
+--R - 264a c d + 180a b c d + 1044a b c d - 1572a b c d
+--R +
+--R 2 4 8 2
+--R 612a b c d
+--R *
+--R 7
+--R x
+--R +
+--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2
+--R - 612a c d + 1260a b c d - 108a b c d - 1116a b c d
+--R +
+--R 2 4 9
+--R 576a b c d
+--R *
+--R 5
+--R x
+--R +
+--R 6 6 4 5 7 3 4 2 8 2 2 4 10 3
+--R (- 576a c d + 1536a b c d - 1152a b c d + 192a b c )x
+--R +
+--R 6 7 3 5 8 2 4 2 9 3 3 10
+--R (- 192a c d + 576a b c d - 576a b c d + 192a b c )x
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 899
+
+--S 900 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 4 +-----------+ +-+
+--R (8a b d - 3b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 3 4 | 2 x\|- a d + b c
+--R (16a b d - 6b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 5 3 4 2 3 2 2 2 3 3 +-----------+ +-+ | 2
+--R (4a d - 12a b c d + 12a b c d - 4a b c )\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 900
+
+--S 901 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 901
+
+--S 902 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 3 4 +-----------+ +-+
+--R (8a b d - 3b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 3 4 +-----------+ +-+ \|- a d + a b c \|c
+--R (8a b d - 3b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 3 4 | 2 x\|- a d + b c
+--R (8a b d - 3b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 5 3 4 2 3 2 2 2 3 3 | 2 +-----------+ +-+
+--R (2a d - 6a b c d + 6a b c d - 2a b c )\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 902
+
+--S 903 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 903
+
+)clear all
+
+--S 904 of 1527
+t0:=1/(x^3*(a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 11 2 2 9 2 2 2 2 7
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 5 2 2 3
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 904
+
+--S 905 of 1527
+r0:=-1/6*d*(6*b^2*c^2-6*a*b*c*d+5*a^2*d^2)/(a^2*c^2*(b*c-a*d)^2*_
+ (c+d*x^2)^(3/2))-1/2*b*(2*b*c-a*d)/(a^2*c*(b*c-a*d)*(a+b*x^2)*_
+ (c+d*x^2)^(3/2))+(-1/2)/(a*c*x^2*(a+b*x^2)*(c+d*x^2)^(3/2))+_
+ 1/2*(4*b*c+5*a*d)*atanh(sqrt(c+d*x^2)/sqrt(c))/(a^3*c^(7/2))-_
+ 1/2*b^(7/2)*(4*b*c-9*a*d)*atanh(sqrt(b)*sqrt(c+d*x^2)/_
+ sqrt(b*c-a*d))/(a^3*(b*c-a*d)^(7/2))-1/2*d*(2*b*c-a*d)*(b^2*c^2-_
+ a*b*c*d+5*a^2*d^2)/(a^2*c^3*(b*c-a*d)^3*sqrt(c+d*x^2))
+--R
+--R
+--R (2)
+--R 4 3 2 5 4 6 2 3 3 2 4 4 5 5 4
+--R (- 27a b c d + 12b c d)x + (- 27a b c d - 15a b c d + 12b c )x
+--R +
+--R 2 3 4 4 5 2
+--R (- 27a b c d + 12a b c )x
+--R *
+--R +--------+
+--R +--------+ +-+ | 2
+--R +-+ +-+ | 2 \|b \|d x + c
+--R \|b \|c \|d x + c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
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+--R (15a b d - 33a b c d + 9a b c d + 21a b c d - 12b c d)x
+--R +
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+--R (15a d - 18a b c d - 24a b c d + 30a b c d + 9a b c d - 12b c )x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 2
+--R (15a c d - 33a b c d + 9a b c d + 21a b c d - 12a b c )x
+--R *
+--R +--------+
+--R +--------+ | 2
+--R +-----------+ | 2 \|d x + c
+--R \|- a d + b c \|d x + c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 6
+--R (- 15a b d + 33a b c d - 9a b c d + 6a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (- 15a d + 13a b c d + 35a b c d - 15a b c d + 12a b c d)x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 2
+--R (- 20a c d + 41a b c d - 9a b c d - 3a b c d + 6a b c )x
+--R +
+--R 5 2 3 4 3 2 3 2 4 2 3 5
+--R - 3a c d + 9a b c d - 9a b c d + 3a b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 6
+--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x
+--R +
+--R 7 3 4 6 4 3 4 3 6 3 4 7 4
+--R (6a c d - 12a b c d + 12a b c d - 6a b c )x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7 2
+--R (6a c d - 18a b c d + 18a b c d - 6a b c )x
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R Type: Expression(Integer)
+--E 905
+
+--S 906 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 8 3 2 2 7 2 3 3 6 4 4 5
+--R - 210a b c d + 462a b c d - 126a b c d - 294a b c d
+--R +
+--R 5 5 4
+--R 168b c d
+--R *
+--R 12
+--R x
+--R +
+--R 5 8 4 2 7 3 2 3 6 2 3 4 5
+--R - 210a c d - 1428a b c d + 4032a b c d - 1428a b c d
+--R +
+--R 4 5 4 5 6 3
+--R - 2478a b c d + 1512b c d
+--R *
+--R 10
+--R x
+--R +
+--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4
+--R - 1890a c d - 882a b c d + 9954a b c d - 5670a b c d
+--R +
+--R 4 6 3 5 7 2
+--R - 5544a b c d + 4032b c d
+--R *
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+--R x
+--R +
+--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3
+--R - 5040a c d + 5808a b c d + 8592a b c d - 10224a b c d
+--R +
+--R 4 7 2 5 8
+--R - 3360a b c d + 4224b c d
+--R *
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+--R x
+--R +
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2
+--R - 5280a c d + 9696a b c d + 1056a b c d - 8544a b c d
+--R +
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+--R 1536a b c d + 1536b c
+--R *
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+--R x
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+--R - 1920a c d + 4224a b c d - 1152a b c d - 2688a b c d
+--R +
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+--R 1536a b c
+--R *
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+--R x
+--R *
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+--R +
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+--R (30a b d - 66a b c d + 18a b c d + 42a b c d - 24b c d )x
+--R +
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+--R 30a d + 714a b c d - 1698a b c d + 510a b c d
+--R +
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+--R 1068a b c d - 624b c d
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+--R x
+--R +
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+--R 780a c d + 2154a b c d - 8046a b c d + 3414a b c d
+--R +
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+--R 4794a b c d - 3096b c d
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+--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4
+--R 3870a c d - 1074a b c d - 14046a b c d + 9882a b c d
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+--R x
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+--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3
+--R 7440a c d - 10128a b c d - 9264a b c d + 14160a b c d
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+--R *
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+--R x
+--R +
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2
+--R 6240a c d - 11808a b c d - 480a b c d + 9888a b c d
+--R +
+--R 4 8 5 9
+--R - 2304a b c d - 1536b c
+--R *
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+--R x
+--R +
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+--R 1920a c d - 4224a b c d + 1152a b c d + 2688a b c d
+--R +
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+--R - 1536a b c
+--R *
+--R 2
+--R x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 4 4 5 5 5 4 12
+--R (189a b c d - 84b c d )x
+--R +
+--R 2 3 4 5 4 5 4 5 6 3 10
+--R (189a b c d + 1617a b c d - 756b c d )x
+--R +
+--R 2 3 5 4 4 6 3 5 7 2 8
+--R (1701a b c d + 3780a b c d - 2016b c d )x
+--R +
+--R 2 3 6 3 4 7 2 5 8 6
+--R (4536a b c d + 2736a b c d - 2112b c d)x
+--R +
+--R 2 3 7 2 4 8 5 9 4
+--R (4752a b c d - 384a b c d - 768b c )x
+--R +
+--R 2 3 8 4 9 2
+--R (1728a b c d - 768a b c )x
+--R *
+--R +-----------+ +--------+
+--R | b +-+ | 2
+--R |- --------- \|c \|d x + c
+--R \| a d - b c
+--R +
+--R 4 4 6 5 5 5 14
+--R (- 27a b c d + 12b c d )x
+--R +
+--R 2 3 4 6 4 5 5 5 6 4 12
+--R (- 27a b c d - 690a b c d + 312b c d )x
+--R +
+--R 2 3 5 5 4 6 4 5 7 3 10
+--R (- 702a b c d - 3171a b c d + 1548b c d )x
+--R +
+--R 2 3 6 4 4 7 3 5 8 2 8
+--R (- 3483a b c d - 5148a b c d + 2976b c d )x
+--R +
+--R 2 3 7 3 4 8 2 5 9 6
+--R (- 6696a b c d - 2640a b c d + 2496b c d)x
+--R +
+--R 2 3 8 2 4 9 5 10 4
+--R (- 5616a b c d + 768a b c d + 768b c )x
+--R +
+--R 2 3 9 4 10 2
+--R (- 1728a b c d + 768a b c )x
+--R *
+--R +-----------+
+--R | b
+--R |- ---------
+--R \| a d - b c
+--R *
+--R log
+--R +-----------+
+--R 2 2 +-+ 2 2 | b
+--R ((2a b x + 2a )\|c + (2a d - 2a b c)x |- --------- )
+--R \| a d - b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 | b +-+
+--R ((- 2a b d + 2b c)x + (- 2a d + 2a b c)x ) |- --------- \|c
+--R \| a d - b c
+--R +
+--R 2 4 2 2 2
+--R (a b d - 2b c)x + (- a d - 2a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 4 8 3 2 2 7 2 3 3 6 4 4 5
+--R - 166a b c d + 298a b c d + 18a b c d - 12a b c d
+--R +
+--R 5 5 4
+--R 42b c d
+--R *
+--R 12
+--R x
+--R +
+--R 5 8 4 2 7 3 2 3 6 2 3 4 5
+--R - 166a c d - 706a b c d + 1622a b c d + 462a b c d
+--R +
+--R 4 5 4 5 6 3
+--R - 270a b c d + 378b c d
+--R *
+--R 10
+--R x
+--R +
+--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4
+--R - 1004a c d + 266a b c d + 1794a b c d + 2166a b c d
+--R +
+--R 4 6 3 5 7 2
+--R - 1170a b c d + 1008b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3
+--R - 1338a c d + 1662a b c d - 222a b c d + 3690a b c d
+--R +
+--R 4 7 2 5 8
+--R - 1968a b c d + 1056b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2
+--R 336a c d - 1296a b c d + 720a b c d + 2256a b c d
+--R +
+--R 4 8 5 9
+--R - 1440a b c d + 384b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8
+--R 1248a c d - 3360a b c d + 2592a b c d - 96a b c d
+--R +
+--R 4 9
+--R - 384a b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9
+--R 384a c d - 1152a b c d + 1152a b c d - 384a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 9 3 2 8 5 4 5 14
+--R (28a b d - 52a b c d - 6b c d )x
+--R +
+--R 5 9 4 8 3 2 2 7 2 3 3 6 4 4 5
+--R 28a d + 466a b c d - 890a b c d - 126a b c d + 78a b c d
+--R +
+--R 5 5 4
+--R - 156b c d
+--R *
+--R 12
+--R x
+--R +
+--R 5 8 4 2 7 3 2 3 6 2 3 4 5
+--R 518a c d + 762a b c d - 2522a b c d - 1218a b c d
+--R +
+--R 4 5 4 5 6 3
+--R 684a b c d - 774b c d
+--R *
+--R 10
+--R x
+--R +
+--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4
+--R 1652a c d - 1094a b c d - 1710a b c d - 3738a b c d
+--R +
+--R 4 6 3 5 7 2
+--R 1998a b c d - 1488b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3
+--R 1302a c d - 1362a b c d + 114a b c d - 4806a b c d
+--R +
+--R 4 7 2 5 8
+--R 2640a b c d - 1248b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2
+--R - 912a c d + 2832a b c d - 1872a b c d - 2256a b c d
+--R +
+--R 4 8 5 9
+--R 1632a b c d - 384b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8
+--R - 1440a c d + 3936a b c d - 3168a b c d + 288a b c d
+--R +
+--R 4 9
+--R 384a b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9
+--R - 384a c d + 1152a b c d - 1152a b c d + 384a b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R 6 4 7 5 2 5 6 4 3 6 5 3 4 7 4 12
+--R (84a b c d - 252a b c d + 252a b c d - 84a b c d )x
+--R +
+--R 7 4 7 6 5 6 5 2 6 5 4 3 7 4
+--R 84a c d + 504a b c d - 2016a b c d + 2184a b c d
+--R +
+--R 3 4 8 3
+--R - 756a b c d
+--R *
+--R 10
+--R x
+--R +
+--R 7 5 6 6 6 5 5 2 7 4 4 3 8 3
+--R 756a c d - 252a b c d - 3780a b c d + 5292a b c d
+--R +
+--R 3 4 9 2
+--R - 2016a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 7 6 5 6 7 4 5 2 8 3 4 3 9 2
+--R 2016a c d - 3936a b c d - 288a b c d + 4320a b c d
+--R +
+--R 3 4 10
+--R - 2112a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 7 7 4 6 8 3 5 2 9 2 4 3 10
+--R 2112a c d - 5568a b c d + 4032a b c d + 192a b c d
+--R +
+--R 3 4 11
+--R - 768a b c
+--R *
+--R 4
+--R x
+--R +
+--R 7 8 3 6 9 2 5 2 10 4 3 11 2
+--R (768a c d - 2304a b c d + 2304a b c d - 768a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|c \|d x + c
+--R +
+--R 6 4 8 5 2 5 7 4 3 6 6 3 4 7 5 14
+--R (- 12a b c d + 36a b c d - 36a b c d + 12a b c d )x
+--R +
+--R 7 4 8 6 5 7 5 2 6 6 4 3 7 5 3 4 8 4 12
+--R (- 12a c d - 276a b c d + 900a b c d - 924a b c d + 312a b c d )x
+--R +
+--R 7 5 7 6 6 6 5 2 7 5 4 3 8 4
+--R - 312a c d - 612a b c d + 3708a b c d - 4332a b c d
+--R +
+--R 3 4 9 3
+--R 1548a b c d
+--R *
+--R 10
+--R x
+--R +
+--R 7 6 6 6 7 5 5 2 8 4 4 3 9 3
+--R - 1548a c d + 1668a b c d + 4284a b c d - 7380a b c d
+--R +
+--R 3 4 10 2
+--R 2976a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 7 7 5 6 8 4 5 2 9 3 4 3 10 2
+--R - 2976a c d + 6432a b c d - 1440a b c d - 4512a b c d
+--R +
+--R 3 4 11
+--R 2496a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 7 8 4 6 9 3 5 2 10 2 4 3 11
+--R - 2496a c d + 6720a b c d - 5184a b c d + 192a b c d
+--R +
+--R 3 4 12
+--R 768a b c
+--R *
+--R 4
+--R x
+--R +
+--R 7 9 3 6 10 2 5 2 11 4 3 12 2
+--R (- 768a c d + 2304a b c d - 2304a b c d + 768a b c )x
+--R ,
+--R
+--R 4 8 3 2 2 7 2 3 3 6 4 4 5
+--R - 105a b c d + 231a b c d - 63a b c d - 147a b c d
+--R +
+--R 5 5 4
+--R 84b c d
+--R *
+--R 12
+--R x
+--R +
+--R 5 8 4 2 7 3 2 3 6 2 3 4 5
+--R - 105a c d - 714a b c d + 2016a b c d - 714a b c d
+--R +
+--R 4 5 4 5 6 3
+--R - 1239a b c d + 756b c d
+--R *
+--R 10
+--R x
+--R +
+--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4
+--R - 945a c d - 441a b c d + 4977a b c d - 2835a b c d
+--R +
+--R 4 6 3 5 7 2
+--R - 2772a b c d + 2016b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3
+--R - 2520a c d + 2904a b c d + 4296a b c d - 5112a b c d
+--R +
+--R 4 7 2 5 8
+--R - 1680a b c d + 2112b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2
+--R - 2640a c d + 4848a b c d + 528a b c d - 4272a b c d
+--R +
+--R 4 8 5 9
+--R 768a b c d + 768b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8
+--R - 960a c d + 2112a b c d - 576a b c d - 1344a b c d
+--R +
+--R 4 9
+--R 768a b c
+--R *
+--R 2
+--R x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 9 3 2 8 2 3 2 7 4 3 6 5 4 5 14
+--R (15a b d - 33a b c d + 9a b c d + 21a b c d - 12b c d )x
+--R +
+--R 5 9 4 8 3 2 2 7 2 3 3 6
+--R 15a d + 357a b c d - 849a b c d + 255a b c d
+--R +
+--R 4 4 5 5 5 4
+--R 534a b c d - 312b c d
+--R *
+--R 12
+--R x
+--R +
+--R 5 8 4 2 7 3 2 3 6 2 3 4 5
+--R 390a c d + 1077a b c d - 4023a b c d + 1707a b c d
+--R +
+--R 4 5 4 5 6 3
+--R 2397a b c d - 1548b c d
+--R *
+--R 10
+--R x
+--R +
+--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4
+--R 1935a c d - 537a b c d - 7023a b c d + 4941a b c d
+--R +
+--R 4 6 3 5 7 2
+--R 3660a b c d - 2976b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3
+--R 3720a c d - 5064a b c d - 4632a b c d + 7080a b c d
+--R +
+--R 4 7 2 5 8
+--R 1392a b c d - 2496b c d
+--R *
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+--R x
+--R +
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2
+--R 3120a c d - 5904a b c d - 240a b c d + 4944a b c d
+--R +
+--R 4 8 5 9
+--R - 1152a b c d - 768b c
+--R *
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+--R 7 9 3 6 10 2 5 2 11 4 3 12 2
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+--E 906
+
+--S 907 of 1527
+m0a:=a0.1-r0
+--R
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+--R (- 1344a c d + 4032a b c d - 4032a b c d + 1344a b c d)x
+--R +
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+--R - 768a c d + 2304a b c d - 2304a b c d + 768a b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R Type: Expression(Integer)
+--E 907
+
+--S 908 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 908
+
+--S 909 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
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+--R (- 15a d + 33a b c d - 9a b c d - 21a b c d + 12b c d )x
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+--R (105a d - 231a b c d + 63a b c d + 147a b c d - 84b c d )x
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+--R (27a b c d - 12b c d )x + (648a b c d - 288b c d )x
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+--R (- 189a b c d + 84b c d )x + (- 1512a b c d + 672b c d )x
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+--R (- 3024a b c d + 1344b c d)x - 1728a b c d + 768b c
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+--R (- 15a d + 33a b c d - 9a b c d - 21a b c d + 12b c d )x
+--R +
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+--R - 360a c d + 792a b c d - 216a b c d - 504a b c d
+--R +
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+--R 288b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R - 1200a c d + 2640a b c d - 720a b c d - 1680a b c d
+--R +
+--R 4 6
+--R 960b c d
+--R *
+--R 2
+--R x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R - 960a c d + 2112a b c d - 576a b c d - 1344a b c d + 768b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 6
+--R (105a d - 231a b c d + 63a b c d + 147a b c d - 84b c d )x
+--R +
+--R 4 6 3 2 5 2 2 3 4 3 4 3
+--R 840a c d - 1848a b c d + 504a b c d + 1176a b c d
+--R +
+--R 4 5 2
+--R - 672b c d
+--R *
+--R 4
+--R x
+--R +
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2
+--R 1680a c d - 3696a b c d + 1008a b c d + 2352a b c d
+--R +
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+--R - 1344b c d
+--R *
+--R 2
+--R x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R 960a c d - 2112a b c d + 576a b c d + 1344a b c d - 768b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 3 3 4 4 4 3 6 3 4 3 4 5 2 4
+--R (- 27a b c d + 12b c d )x + (- 648a b c d + 288b c d )x
+--R +
+--R 3 5 2 4 6 2 3 6 4 7
+--R (- 2160a b c d + 960b c d)x - 1728a b c d + 768b c
+--R *
+--R +---------+ +--------+
+--R +-----------+ | b +-+ | 2
+--R \|- a d + b c |--------- \|c \|d x + c
+--R \|a d - b c
+--R +
+--R 3 4 4 4 5 3 6 3 5 3 4 6 2 4
+--R (189a b c d - 84b c d )x + (1512a b c d - 672b c d )x
+--R +
+--R 3 6 2 4 7 2 3 7 4 8
+--R (3024a b c d - 1344b c d)x + 1728a b c d - 768b c
+--R *
+--R +---------+
+--R +-----------+ | b
+--R \|- a d + b c |---------
+--R \|a d - b c
+--R *
+--R +--------+
+--R +-+ | 2 2
+--R a\|c \|d x + c - b c x - a c
+--R atan(-------------------------------)
+--R +---------+
+--R 2 | b +-+
+--R (a d - b c)x |--------- \|c
+--R \|a d - b c
+--R +
+--R 4 7 3 6 4 4 3 6
+--R (- 14a d + 26a b c d + 3b c d )x
+--R +
+--R 4 6 3 2 5 4 5 2 4
+--R (- 336a c d + 624a b c d + 72b c d )x
+--R +
+--R 4 2 5 3 3 4 4 6 2 4 3 4 3 4 3
+--R (- 1120a c d + 2080a b c d + 240b c d)x - 896a c d + 1664a b c d
+--R +
+--R 4 7
+--R 192b c
+--R *
+--R +--------+
+--R +-----------+ | 2
+--R \|- a d + b c \|d x + c
+--R +
+--R 4 7 3 6 4 4 3 6
+--R (98a d - 182a b c d - 21b c d )x
+--R +
+--R 4 6 3 2 5 4 5 2 4
+--R (784a c d - 1456a b c d - 168b c d )x
+--R +
+--R 4 2 5 3 3 4 4 6 2 4 3 4 3 4 3
+--R (1568a c d - 2912a b c d - 336b c d)x + 896a c d - 1664a b c d
+--R +
+--R 4 7
+--R - 192b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R 6 3 6 5 4 5 4 2 5 4 3 3 6 3 6
+--R (6a c d - 18a b c d + 18a b c d - 6a b c d )x
+--R +
+--R 6 4 5 5 5 4 4 2 6 3 3 3 7 2 4
+--R (144a c d - 432a b c d + 432a b c d - 144a b c d )x
+--R +
+--R 6 5 4 5 6 3 4 2 7 2 3 3 8 2 6 6 3
+--R (480a c d - 1440a b c d + 1440a b c d - 480a b c d)x + 384a c d
+--R +
+--R 5 7 2 4 2 8 3 3 9
+--R - 1152a b c d + 1152a b c d - 384a b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|d x + c
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3 6
+--R (- 42a c d + 126a b c d - 126a b c d + 42a b c d )x
+--R +
+--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2 4
+--R (- 336a c d + 1008a b c d - 1008a b c d + 336a b c d )x
+--R +
+--R 6 6 4 5 7 3 4 2 8 2 3 3 9 2
+--R (- 672a c d + 2016a b c d - 2016a b c d + 672a b c d)x
+--R +
+--R 6 7 3 5 8 2 4 2 9 3 3 10
+--R - 384a c d + 1152a b c d - 1152a b c d + 384a b c
+--R *
+--R +-----------+
+--R \|- a d + b c
+--R Type: Expression(Integer)
+--E 909
+
+--S 910 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 910
+
+)clear all
+
+--S 911 of 1527
+t0:=1/(x^4*(a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 12 2 2 10 2 2 2 2 8
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 6 2 2 4
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 911
+
+--S 912 of 1527
+r0:=1/6*d*(3*b*c+2*a*d)/(a*c*(b*c-a*d)^2*x^3*(c+d*x^2)^(3/2))+_
+ 1/2*b/(a*(b*c-a*d)*x^3*(a+b*x^2)*(c+d*x^2)^(3/2))+5/2*b^4*(b*c-_
+ 2*a*d)*atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/(a^(7/2)*_
+ (b*c-a*d)^(7/2))+1/2*d*(b^2*c^2+8*a*b*c*d-4*a^2*d^2)/(a*c^2*_
+ (b*c-a*d)^3*x^3*sqrt(c+d*x^2))-1/6*(5*b^3*c^3-6*a*b^2*c^2*d+_
+ 32*a^2*b*c*d^2-16*a^3*d^3)*sqrt(c+d*x^2)/(a^2*c^3*(b*c-a*d)^3*_
+ x^3)+1/6*(15*b^4*c^4-20*a*b^3*c^3*d-12*a^2*b^2*c^2*d^2+64*a^3*_
+ b*c*d^3-32*a^4*d^4)*sqrt(c+d*x^2)/(a^3*c^4*(b*c-a*d)^3*x)
+--R
+--R
+--R (2)
+--R 5 4 2 6 5 7 2 4 4 2 5 5 6 6 5
+--R (30a b c d - 15b c d)x + (30a b c d + 15a b c d - 15b c )x
+--R +
+--R 2 4 5 5 6 3
+--R (30a b c d - 15a b c )x
+--R *
+--R +--------+ +-----------+
+--R | 2 x\|- a d + b c
+--R \|d x + c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R +
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 8
+--R (32a b d - 64a b c d + 12a b c d + 20a b c d - 15b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R 32a d - 16a b c d - 84a b c d + 38a b c d + 30a b c d
+--R +
+--R 5 5
+--R - 30b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 5 6 4
+--R (48a c d - 84a b c d - 6a b c d + 42a b c d - 15b c )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 2
+--R (12a c d - 26a b c d + 6a b c d + 18a b c d - 10a b c )x
+--R +
+--R 5 3 3 4 4 2 3 2 5 2 3 6
+--R - 2a c d + 6a b c d - 6a b c d + 2a b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R /
+--R 6 4 4 5 2 5 3 4 3 6 2 3 4 7 7
+--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x
+--R +
+--R 7 4 4 6 5 3 4 3 7 3 4 8 5
+--R (6a c d - 12a b c d + 12a b c d - 6a b c )x
+--R +
+--R 7 5 3 6 6 2 5 2 7 4 3 8 3
+--R (6a c d - 18a b c d + 18a b c d - 6a b c )x
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|a \|d x + c
+--R Type: Expression(Integer)
+--E 912
+
+--S 913 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 5 4 6 6 5 5 15
+--R (30a b c d - 15b c d )x
+--R +
+--R 2 4 4 6 5 5 5 6 6 4 13
+--R (30a b c d + 975a b c d - 495b c d )x
+--R +
+--R 2 4 5 5 5 6 4 6 7 3 11
+--R (990a b c d + 5265a b c d - 2880b c d )x
+--R +
+--R 2 4 6 4 5 7 3 6 8 2 9
+--R (5760a b c d + 9600a b c d - 6240b c d )x
+--R +
+--R 2 4 7 3 5 8 2 6 9 7
+--R (12480a b c d + 5280a b c d - 5760b c d)x
+--R +
+--R 2 4 8 2 5 9 6 10 5
+--R (11520a b c d - 1920a b c d - 1920b c )x
+--R +
+--R 2 4 9 5 10 3
+--R (3840a b c d - 1920a b c )x
+--R *
+--R +--------+
+--R | 2
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+--R +
+--R 5 4 6 6 5 5 15
+--R (- 240a b c d + 120b c d )x
+--R +
+--R 2 4 4 6 5 5 5 6 6 4 13
+--R (- 240a b c d - 2760a b c d + 1440b c d )x
+--R +
+--R 2 4 5 5 5 6 4 6 7 3 11
+--R (- 2880a b c d - 9360a b c d + 5400b c d )x
+--R +
+--R 2 4 6 4 5 7 3 6 8 2 9
+--R (- 10800a b c d - 12360a b c d + 8880b c d )x
+--R +
+--R 2 4 7 3 5 8 2 6 9 7
+--R (- 17760a b c d - 4560a b c d + 6720b c d)x
+--R +
+--R 2 4 8 2 5 9 6 10 5
+--R (- 13440a b c d + 2880a b c d + 1920b c )x
+--R +
+--R 2 4 9 5 10 3
+--R (- 3840a b c d + 1920a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R log
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+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
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+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
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+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
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+--R - 512a b d + 1024a b c d - 192a b c d - 320a b c d
+--R +
+--R 5 4 5
+--R 240b c d
+--R *
+--R 14
+--R x
+--R +
+--R 5 9 4 8 3 2 2 7 2 3 3 6
+--R - 512a d - 4864a b c d + 11584a b c d - 2528a b c d
+--R +
+--R 4 4 5 5 5 4
+--R - 3680a b c d + 2880b c d
+--R *
+--R 12
+--R x
+--R +
+--R 5 8 4 2 7 3 2 3 6 2 3 4 5
+--R - 5888a c d - 8384a b c d + 38112a b c d - 11360a b c d
+--R +
+--R 4 5 4 5 6 3
+--R - 12480a b c d + 10800b c d
+--R *
+--R 10
+--R x
+--R +
+--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4
+--R - 20160a c d + 11808a b c d + 49504a b c d - 24672a b c d
+--R +
+--R 4 6 3 5 7 2
+--R - 16480a b c d + 17760b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3
+--R - 28512a c d + 40416a b c d + 22944a b c d - 28768a b c d
+--R +
+--R 4 7 2 5 8
+--R - 6080a b c d + 13440b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2
+--R - 16576a c d + 30528a b c d + 192a b c d - 17984a b c d
+--R +
+--R 4 8 5 9
+--R 3840a b c d + 3840b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8
+--R - 2304a c d + 4352a b c d + 768a b c d - 5376a b c d
+--R +
+--R 4 9
+--R 2560a b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9
+--R 512a c d - 1536a b c d + 1536a b c d - 512a b c
+--R *
+--R +-----------+ +--------+
+--R +-+ | 2 | 2
+--R \|c \|a d - a b c \|d x + c
+--R +
+--R 4 10 3 2 9 2 3 2 8 4 3 7 5 4 6 16
+--R (64a b d - 128a b c d + 24a b c d + 40a b c d - 30b c d )x
+--R +
+--R 5 10 4 9 3 2 2 8 2 3 3 7
+--R 64a d + 2016a b c d - 4264a b c d + 844a b c d
+--R +
+--R 4 4 6 5 5 5
+--R 1340a b c d - 1020b c d
+--R *
+--R 14
+--R x
+--R +
+--R 5 9 4 2 8 3 2 3 7 2 3 4 6
+--R 2144a c d + 9048a b c d - 25868a b c d + 6356a b c d
+--R +
+--R 4 5 5 5 6 4
+--R 8320a b c d - 6750b c d
+--R *
+--R 12
+--R x
+--R +
+--R 5 2 8 4 3 7 3 2 4 6 2 3 5 5
+--R 13336a c d + 5836a b c d - 60020a b c d + 21028a b c d
+--R +
+--R 4 6 4 5 7 3
+--R 19820a b c d - 18240b c d
+--R *
+--R 10
+--R x
+--R +
+--R 5 3 7 4 4 6 3 2 5 5 2 3 6 4
+--R 32508a c d - 28532a b c d - 60940a b c d + 37124a b c d
+--R +
+--R 4 7 3 5 8 2
+--R 19840a b c d - 24000b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 4 6 4 5 5 3 2 6 4 2 3 7 3
+--R 36480a c d - 55040a b c d - 23040a b c d + 37120a b c d
+--R +
+--R 4 8 2 5 9
+--R 4480a b c d - 15360b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 5 5 4 6 4 3 2 7 3 2 3 8 2
+--R 17792a c d - 32896a b c d - 384a b c d + 20608a b c d
+--R +
+--R 4 9 5 10
+--R - 5120a b c d - 3840b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 6 4 4 7 3 3 2 8 2 2 3 9
+--R 2048a c d - 3584a b c d - 1536a b c d + 5632a b c d
+--R +
+--R 4 10
+--R - 2560a b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 7 3 4 8 2 3 2 9 2 3 10
+--R - 512a c d + 1536a b c d - 1536a b c d + 512a b c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R /
+--R 6 4 8 5 2 5 7 4 3 6 6 3 4 7 5 15
+--R (12a b c d - 36a b c d + 36a b c d - 12a b c d )x
+--R +
+--R 7 4 8 6 5 7 5 2 6 6 4 3 7 5
+--R 12a c d + 360a b c d - 1152a b c d + 1176a b c d
+--R +
+--R 3 4 8 4
+--R - 396a b c d
+--R *
+--R 13
+--R x
+--R +
+--R 7 5 7 6 6 6 5 2 7 5 4 3 8 4
+--R 396a c d + 1116a b c d - 5724a b c d + 6516a b c d
+--R +
+--R 3 4 9 3
+--R - 2304a b c d
+--R *
+--R 11
+--R x
+--R +
+--R 7 6 6 6 7 5 5 2 8 4 4 3 9 3
+--R 2304a c d - 1920a b c d - 8064a b c d + 12672a b c d
+--R +
+--R 3 4 10 2
+--R - 4992a b c d
+--R *
+--R 9
+--R x
+--R +
+--R 7 7 5 6 8 4 5 2 9 3 4 3 10 2
+--R 4992a c d - 10368a b c d + 1152a b c d + 8832a b c d
+--R +
+--R 3 4 11
+--R - 4608a b c d
+--R *
+--R 7
+--R x
+--R +
+--R 7 8 4 6 9 3 5 2 10 2 3 4 12 5
+--R (4608a c d - 12288a b c d + 9216a b c d - 1536a b c )x
+--R +
+--R 7 9 3 6 10 2 5 2 11 4 3 12 3
+--R (1536a c d - 4608a b c d + 4608a b c d - 1536a b c )x
+--R *
+--R +-----------+ +--------+
+--R | 2 | 2
+--R \|a d - a b c \|d x + c
+--R +
+--R 6 4 8 5 2 5 7 4 3 6 6 3 4 7 5 15
+--R (- 96a b c d + 288a b c d - 288a b c d + 96a b c d )x
+--R +
+--R 7 4 8 6 5 7 5 2 6 6 4 3 7 5
+--R - 96a c d - 864a b c d + 3168a b c d - 3360a b c d
+--R +
+--R 3 4 8 4
+--R 1152a b c d
+--R *
+--R 13
+--R x
+--R +
+--R 7 5 7 6 6 6 5 2 7 5 4 3 8 4
+--R - 1152a c d - 864a b c d + 9504a b c d - 11808a b c d
+--R +
+--R 3 4 9 3
+--R 4320a b c d
+--R *
+--R 11
+--R x
+--R +
+--R 7 6 6 6 7 5 5 2 8 4 4 3 9 3
+--R - 4320a c d + 5856a b c d + 8352a b c d - 16992a b c d
+--R +
+--R 3 4 10 2
+--R 7104a b c d
+--R *
+--R 9
+--R x
+--R +
+--R 7 7 5 6 8 4 5 2 9 3 4 3 10 2
+--R - 7104a c d + 15936a b c d - 5184a b c d - 9024a b c d
+--R +
+--R 3 4 11
+--R 5376a b c d
+--R *
+--R 7
+--R x
+--R +
+--R 7 8 4 6 9 3 5 2 10 2 4 3 11
+--R - 5376a c d + 14592a b c d - 11520a b c d + 768a b c d
+--R +
+--R 3 4 12
+--R 1536a b c
+--R *
+--R 5
+--R x
+--R +
+--R 7 9 3 6 10 2 5 2 11 4 3 12 3
+--R (- 1536a c d + 4608a b c d - 4608a b c d + 1536a b c )x
+--R *
+--R +-----------+
+--R +-+ | 2
+--R \|c \|a d - a b c
+--R ,
+--R
+--R 5 4 6 6 5 5 15
+--R (- 30a b c d + 15b c d )x
+--R +
+--R 2 4 4 6 5 5 5 6 6 4 13
+--R (- 30a b c d - 975a b c d + 495b c d )x
+--R +
+--R 2 4 5 5 5 6 4 6 7 3 11
+--R (- 990a b c d - 5265a b c d + 2880b c d )x
+--R +
+--R 2 4 6 4 5 7 3 6 8 2 9
+--R (- 5760a b c d - 9600a b c d + 6240b c d )x
+--R +
+--R 2 4 7 3 5 8 2 6 9 7
+--R (- 12480a b c d - 5280a b c d + 5760b c d)x
+--R +
+--R 2 4 8 2 5 9 6 10 5
+--R (- 11520a b c d + 1920a b c d + 1920b c )x
+--R +
+--R 2 4 9 5 10 3
+--R (- 3840a b c d + 1920a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 5 4 6 6 5 5 15
+--R (240a b c d - 120b c d )x
+--R +
+--R 2 4 4 6 5 5 5 6 6 4 13
+--R (240a b c d + 2760a b c d - 1440b c d )x
+--R +
+--R 2 4 5 5 5 6 4 6 7 3 11
+--R (2880a b c d + 9360a b c d - 5400b c d )x
+--R +
+--R 2 4 6 4 5 7 3 6 8 2 9
+--R (10800a b c d + 12360a b c d - 8880b c d )x
+--R +
+--R 2 4 7 3 5 8 2 6 9 7
+--R (17760a b c d + 4560a b c d - 6720b c d)x
+--R +
+--R 2 4 8 2 5 9 6 10 5
+--R (13440a b c d - 2880a b c d - 1920b c )x
+--R +
+--R 2 4 9 5 10 3
+--R (3840a b c d - 1920a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R 5 4 6 6 5 5 15
+--R (- 30a b c d + 15b c d )x
+--R +
+--R 2 4 4 6 5 5 5 6 6 4 13
+--R (- 30a b c d - 975a b c d + 495b c d )x
+--R +
+--R 2 4 5 5 5 6 4 6 7 3 11
+--R (- 990a b c d - 5265a b c d + 2880b c d )x
+--R +
+--R 2 4 6 4 5 7 3 6 8 2 9
+--R (- 5760a b c d - 9600a b c d + 6240b c d )x
+--R +
+--R 2 4 7 3 5 8 2 6 9 7
+--R (- 12480a b c d - 5280a b c d + 5760b c d)x
+--R +
+--R 2 4 8 2 5 9 6 10 5
+--R (- 11520a b c d + 1920a b c d + 1920b c )x
+--R +
+--R 2 4 9 5 10 3
+--R (- 3840a b c d + 1920a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 5 4 6 6 5 5 15
+--R (240a b c d - 120b c d )x
+--R +
+--R 2 4 4 6 5 5 5 6 6 4 13
+--R (240a b c d + 2760a b c d - 1440b c d )x
+--R +
+--R 2 4 5 5 5 6 4 6 7 3 11
+--R (2880a b c d + 9360a b c d - 5400b c d )x
+--R +
+--R 2 4 6 4 5 7 3 6 8 2 9
+--R (10800a b c d + 12360a b c d - 8880b c d )x
+--R +
+--R 2 4 7 3 5 8 2 6 9 7
+--R (17760a b c d + 4560a b c d - 6720b c d)x
+--R +
+--R 2 4 8 2 5 9 6 10 5
+--R (13440a b c d - 2880a b c d - 1920b c )x
+--R +
+--R 2 4 9 5 10 3
+--R (3840a b c d - 1920a b c )x
+--R *
+--R +-+
+--R \|c
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R (a d - b c)x
+--R +
+--R 4 9 3 2 8 2 3 2 7 4 3 6
+--R - 256a b d + 512a b c d - 96a b c d - 160a b c d
+--R +
+--R 5 4 5
+--R 120b c d
+--R *
+--R 14
+--R x
+--R +
+--R 5 9 4 8 3 2 2 7 2 3 3 6
+--R - 256a d - 2432a b c d + 5792a b c d - 1264a b c d
+--R +
+--R 4 4 5 5 5 4
+--R - 1840a b c d + 1440b c d
+--R *
+--R 12
+--R x
+--R +
+--R 5 8 4 2 7 3 2 3 6 2 3 4 5
+--R - 2944a c d - 4192a b c d + 19056a b c d - 5680a b c d
+--R +
+--R 4 5 4 5 6 3
+--R - 6240a b c d + 5400b c d
+--R *
+--R 10
+--R x
+--R +
+--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4
+--R - 10080a c d + 5904a b c d + 24752a b c d - 12336a b c d
+--R +
+--R 4 6 3 5 7 2
+--R - 8240a b c d + 8880b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3
+--R - 14256a c d + 20208a b c d + 11472a b c d - 14384a b c d
+--R +
+--R 4 7 2 5 8
+--R - 3040a b c d + 6720b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2
+--R - 8288a c d + 15264a b c d + 96a b c d - 8992a b c d
+--R +
+--R 4 8 5 9
+--R 1920a b c d + 1920b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 4 6 3 3 2 7 2 2 3 8
+--R - 1152a c d + 2176a b c d + 384a b c d - 2688a b c d
+--R +
+--R 4 9
+--R 1280a b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 6 3 4 7 2 3 2 8 2 3 9
+--R 256a c d - 768a b c d + 768a b c d - 256a b c
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 4 10 3 2 9 2 3 2 8 4 3 7 5 4 6 16
+--R (32a b d - 64a b c d + 12a b c d + 20a b c d - 15b c d )x
+--R +
+--R 5 10 4 9 3 2 2 8 2 3 3 7
+--R 32a d + 1008a b c d - 2132a b c d + 422a b c d
+--R +
+--R 4 4 6 5 5 5
+--R 670a b c d - 510b c d
+--R *
+--R 14
+--R x
+--R +
+--R 5 9 4 2 8 3 2 3 7 2 3 4 6
+--R 1072a c d + 4524a b c d - 12934a b c d + 3178a b c d
+--R +
+--R 4 5 5 5 6 4
+--R 4160a b c d - 3375b c d
+--R *
+--R 12
+--R x
+--R +
+--R 5 2 8 4 3 7 3 2 4 6 2 3 5 5
+--R 6668a c d + 2918a b c d - 30010a b c d + 10514a b c d
+--R +
+--R 4 6 4 5 7 3
+--R 9910a b c d - 9120b c d
+--R *
+--R 10
+--R x
+--R +
+--R 5 3 7 4 4 6 3 2 5 5 2 3 6 4
+--R 16254a c d - 14266a b c d - 30470a b c d + 18562a b c d
+--R +
+--R 4 7 3 5 8 2
+--R 9920a b c d - 12000b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 4 6 4 5 5 3 2 6 4 2 3 7 3
+--R 18240a c d - 27520a b c d - 11520a b c d + 18560a b c d
+--R +
+--R 4 8 2 5 9
+--R 2240a b c d - 7680b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 5 5 4 6 4 3 2 7 3 2 3 8 2
+--R 8896a c d - 16448a b c d - 192a b c d + 10304a b c d
+--R +
+--R 4 9 5 10
+--R - 2560a b c d - 1920b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 6 4 4 7 3 3 2 8 2 2 3 9
+--R 1024a c d - 1792a b c d - 768a b c d + 2816a b c d
+--R +
+--R 4 10
+--R - 1280a b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 7 3 4 8 2 3 2 9 2 3 10
+--R - 256a c d + 768a b c d - 768a b c d + 256a b c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R 6 4 8 5 2 5 7 4 3 6 6 3 4 7 5 15
+--R (6a b c d - 18a b c d + 18a b c d - 6a b c d )x
+--R +
+--R 7 4 8 6 5 7 5 2 6 6 4 3 7 5 3 4 8 4
+--R (6a c d + 180a b c d - 576a b c d + 588a b c d - 198a b c d )
+--R *
+--R 13
+--R x
+--R +
+--R 7 5 7 6 6 6 5 2 7 5 4 3 8 4
+--R 198a c d + 558a b c d - 2862a b c d + 3258a b c d
+--R +
+--R 3 4 9 3
+--R - 1152a b c d
+--R *
+--R 11
+--R x
+--R +
+--R 7 6 6 6 7 5 5 2 8 4 4 3 9 3
+--R 1152a c d - 960a b c d - 4032a b c d + 6336a b c d
+--R +
+--R 3 4 10 2
+--R - 2496a b c d
+--R *
+--R 9
+--R x
+--R +
+--R 7 7 5 6 8 4 5 2 9 3 4 3 10 2
+--R 2496a c d - 5184a b c d + 576a b c d + 4416a b c d
+--R +
+--R 3 4 11
+--R - 2304a b c d
+--R *
+--R 7
+--R x
+--R +
+--R 7 8 4 6 9 3 5 2 10 2 3 4 12 5
+--R (2304a c d - 6144a b c d + 4608a b c d - 768a b c )x
+--R +
+--R 7 9 3 6 10 2 5 2 11 4 3 12 3
+--R (768a c d - 2304a b c d + 2304a b c d - 768a b c )x
+--R *
+--R +-------------+ +--------+
+--R | 2 | 2
+--R \|- a d + a b c \|d x + c
+--R +
+--R 6 4 8 5 2 5 7 4 3 6 6 3 4 7 5 15
+--R (- 48a b c d + 144a b c d - 144a b c d + 48a b c d )x
+--R +
+--R 7 4 8 6 5 7 5 2 6 6 4 3 7 5
+--R - 48a c d - 432a b c d + 1584a b c d - 1680a b c d
+--R +
+--R 3 4 8 4
+--R 576a b c d
+--R *
+--R 13
+--R x
+--R +
+--R 7 5 7 6 6 6 5 2 7 5 4 3 8 4
+--R - 576a c d - 432a b c d + 4752a b c d - 5904a b c d
+--R +
+--R 3 4 9 3
+--R 2160a b c d
+--R *
+--R 11
+--R x
+--R +
+--R 7 6 6 6 7 5 5 2 8 4 4 3 9 3
+--R - 2160a c d + 2928a b c d + 4176a b c d - 8496a b c d
+--R +
+--R 3 4 10 2
+--R 3552a b c d
+--R *
+--R 9
+--R x
+--R +
+--R 7 7 5 6 8 4 5 2 9 3 4 3 10 2
+--R - 3552a c d + 7968a b c d - 2592a b c d - 4512a b c d
+--R +
+--R 3 4 11
+--R 2688a b c d
+--R *
+--R 7
+--R x
+--R +
+--R 7 8 4 6 9 3 5 2 10 2 4 3 11
+--R - 2688a c d + 7296a b c d - 5760a b c d + 384a b c d
+--R +
+--R 3 4 12
+--R 768a b c
+--R *
+--R 5
+--R x
+--R +
+--R 7 9 3 6 10 2 5 2 11 4 3 12 3
+--R (- 768a c d + 2304a b c d - 2304a b c d + 768a b c )x
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 913
+
+--S 914 of 1527
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 5 +-----------+ +-+
+--R (10a b d - 5b c)\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R 4 5 | 2 x\|- a d + b c
+--R (- 20a b d + 10b c)\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 6 3 5 2 4 2 2 3 3 3 +-----------+ +-+ | 2
+--R (4a d - 12a b c d + 12a b c d - 4a b c )\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 914
+
+--S 915 of 1527
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 915
+
+--S 916 of 1527
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 4 5 +-----------+ +-+
+--R (- 10a b d + 5b c)\|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 4 5 +-----------+ +-+ \|- a d + a b c \|c
+--R (- 10a b d + 5b c)\|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R 4 5 | 2 x\|- a d + b c
+--R (- 10a b d + 5b c)\|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 6 3 5 2 4 2 2 3 3 3 | 2 +-----------+ +-+
+--R (2a d - 6a b c d + 6a b c d - 2a b c )\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 916
+
+--S 917 of 1527
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 917
+
+)clear all
+
+--S 918 of 1527
+t0:=x^(7/2)*(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 5 3 +-+
+--R (d x + c x )\|x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 918
+
+--S 919 of 1527
+r0:=-1/10*(5*b*c-9*a*d)*x^(5/2)/(a*b^2)+1/2*(b*c-a*d)*x^(9/2)/_
+ (a*b*(a+b*x^2))+1/4*a^(1/4)*(5*b*c-9*a*d)*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(b^(13/4)*sqrt(2))-1/4*a^(1/4)*(5*b*c-9*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(13/4)*sqrt(2))+_
+ 1/8*a^(1/4)*(5*b*c-9*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(b^(13/4)*sqrt(2))-1/8*a^(1/4)*(5*b*c-9*a*d)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(13/4)*_
+ sqrt(2))+1/2*(5*b*c-9*a*d)*sqrt(x)/b^3
+--R
+--R
+--R (2)
+--R 2 2 2 4+-+
+--R ((45a b d - 25b c)x + 45a d - 25a b c)\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 4+-+
+--R ((- 45a b d + 25b c)x - 45a d + 25a b c)\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+ \|2 \|b \|x + \|a
+--R ((90a b d - 50b c)x + 90a d - 50a b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+ \|2 \|b \|x - \|a
+--R ((90a b d - 50b c)x + 90a d - 50a b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+4+-+ +-+
+--R (16b d x + (- 144a b d + 80b c)x - 180a d + 100a b c)\|2 \|b \|x
+--R /
+--R 4 2 3 +-+4+-+
+--R (40b x + 40a b )\|2 \|b
+--R Type: Expression(Integer)
+--E 919
+
+--S 920 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 3
+--R (10b x + 10a b )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 6561a d + 14580a b c d - 12150a b c d + 4500a b c d - 625a b c
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096b
+--R *
+--R log
+--R +-+
+--R (9a d - 5b c)\|x
+--R +
+--R 3
+--R 8b
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R - 6561a d + 14580a b c d - 12150a b c d + 4500a b c d
+--R +
+--R 4 4
+--R - 625a b c
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 4 2 3
+--R (- 10b x - 10a b )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 6561a d + 14580a b c d - 12150a b c d + 4500a b c d - 625a b c
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096b
+--R *
+--R log
+--R +-+
+--R (9a d - 5b c)\|x
+--R +
+--R -
+--R 3
+--R 8b
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2
+--R - 6561a d + 14580a b c d - 12150a b c d
+--R +
+--R 2 3 3 4 4
+--R 4500a b c d - 625a b c
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 4 2 3
+--R (- 20b x - 20a b )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 6561a d + 14580a b c d - 12150a b c d + 4500a b c d - 625a b c
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096b
+--R *
+--R atan
+--R 3
+--R 8b
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R - 6561a d + 14580a b c d - 12150a b c d + 4500a b c d
+--R +
+--R 4 4
+--R - 625a b c
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R /
+--R +-+
+--R (9a d - 5b c)\|x
+--R +
+--R 2 4 2 2 2 +-+
+--R (4b d x + (- 36a b d + 20b c)x - 45a d + 25a b c)\|x
+--R /
+--R 4 2 3
+--R 10b x + 10a b
+--R Type: Union(Expression(Integer),...)
+--E 920
+
+--S 921 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 9a d + 5b c)\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 +-+
+--R 8b \|2
+--R *
+--R +--------------------------------------------------------------------+
+--R | 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 6561a d + 14580a b c d - 12150a b c d + 4500a b c d - 625a b c
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096b
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R +-+
+--R (9a d - 5b c)\|x
+--R +
+--R 3
+--R 8b
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R - 6561a d + 14580a b c d - 12150a b c d + 4500a b c d
+--R +
+--R 4 4
+--R - 625a b c
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R +
+--R -
+--R 3 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R - 6561a d + 14580a b c d - 12150a b c d + 4500a b c d
+--R +
+--R 4 4
+--R - 625a b c
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R +-+
+--R (9a d - 5b c)\|x
+--R +
+--R -
+--R 3
+--R 8b
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2
+--R - 6561a d + 14580a b c d - 12150a b c d
+--R +
+--R 2 3 3 4 4
+--R 4500a b c d - 625a b c
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (9a d - 5b c)\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a
+--R (- 18a d + 10b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x - \|a
+--R (- 18a d + 10b c)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 3 +-+
+--R 16b \|2
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R - 6561a d + 14580a b c d - 12150a b c d + 4500a b c d
+--R +
+--R 4 4
+--R - 625a b c
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R atan
+--R 3
+--R 8b
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2
+--R - 6561a d + 14580a b c d - 12150a b c d
+--R +
+--R 2 3 3 4 4
+--R 4500a b c d - 625a b c
+--R /
+--R 13
+--R 4096b
+--R ,
+--R 4
+--R /
+--R +-+
+--R (9a d - 5b c)\|x
+--R /
+--R 3 +-+4+-+
+--R 8b \|2 \|b
+--R Type: Expression(Integer)
+--E 921
+
+--S 922 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 922
+
+)clear all
+
+--S 923 of 1527
+t0:=x^(5/2)*(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 4 2 +-+
+--R (d x + c x )\|x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 923
+
+--S 924 of 1527
+r0:=-1/6*(3*b*c-7*a*d)*x^(3/2)/(a*b^2)+1/2*(b*c-a*d)*x^(7/2)/(a*b*_
+ (a+b*x^2))-1/4*(3*b*c-7*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(1/4)*b^(11/4)*sqrt(2))+1/4*(3*b*c-7*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(11/4)*_
+ sqrt(2))+1/8*(3*b*c-7*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(1/4)*b^(11/4)*sqrt(2))-1/8*(3*b*c-7*a*d)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(1/4)*b^(11/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((21a b d - 9b c)x + 21a d - 9a b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2
+--R ((- 21a b d + 9b c)x - 21a d + 9a b c)
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x + \|a
+--R ((- 42a b d + 18b c)x - 42a d + 18a b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x - \|a
+--R ((- 42a b d + 18b c)x - 42a d + 18a b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+4+-+4+-+3 +-+
+--R (16b d x + (28a d - 12b c)x)\|2 \|a \|b \|x
+--R /
+--R 3 2 2 +-+4+-+4+-+3
+--R (24b x + 24a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 924
+
+--S 925 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2
+--R (- 6b x - 6a b )
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401a d + 4116a b c d - 2646a b c d + 756a b c d - 81b c
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (343a d - 441a b c d + 189a b c d - 27b c )\|x
+--R +
+--R 8
+--R 512a b
+--R *
+--R +--------------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401a d + 4116a b c d - 2646a b c d + 756a b c d - 81b c
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R +
+--R 3 2 2
+--R (6b x + 6a b )
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401a d + 4116a b c d - 2646a b c d + 756a b c d - 81b c
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (343a d - 441a b c d + 189a b c d - 27b c )\|x
+--R +
+--R -
+--R 8
+--R 512a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 2401a d + 4116a b c d - 2646a b c d
+--R +
+--R 3 3 4 4
+--R 756a b c d - 81b c
+--R /
+--R 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 2
+--R (- 12b x - 12a b )
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401a d + 4116a b c d - 2646a b c d + 756a b c d - 81b c
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R *
+--R atan
+--R 8
+--R 512a b
+--R *
+--R +--------------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401a d + 4116a b c d - 2646a b c d + 756a b c d - 81b c
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (343a d - 441a b c d + 189a b c d - 27b c )\|x
+--R +
+--R 3 +-+
+--R (4b d x + (7a d - 3b c)x)\|x
+--R /
+--R 3 2 2
+--R 6b x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 925
+
+--S 926 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 7a d + 3b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 2 +-+
+--R 8b \|2
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401a d + 4116a b c d - 2646a b c d + 756a b c d - 81b c
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (343a d - 441a b c d + 189a b c d - 27b c )\|x
+--R +
+--R 8
+--R 512a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 2401a d + 4116a b c d - 2646a b c d
+--R +
+--R 3 3 4 4
+--R 756a b c d - 81b c
+--R /
+--R 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 +-+
+--R 8b \|2
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401a d + 4116a b c d - 2646a b c d + 756a b c d - 81b c 4+-+
+--R |-------------------------------------------------------------- \|a
+--R 4| 11
+--R \| 4096a b
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (343a d - 441a b c d + 189a b c d - 27b c )\|x
+--R +
+--R -
+--R 8
+--R 512a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 2401a d + 4116a b c d - 2646a b c d
+--R +
+--R 3 3 4 4
+--R 756a b c d - 81b c
+--R /
+--R 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (7a d - 3b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (14a d - 6b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (14a d - 6b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 2 +-+
+--R 16b \|2
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 2401a d + 4116a b c d - 2646a b c d + 756a b c d - 81b c
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 8
+--R 512a b
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2
+--R - 2401a d + 4116a b c d - 2646a b c d
+--R +
+--R 3 3 4 4
+--R 756a b c d - 81b c
+--R /
+--R 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (343a d - 441a b c d + 189a b c d - 27b c )\|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 8b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 926
+
+--S 927 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 927
+
+)clear all
+
+--S 928 of 1527
+t0:=x^(3/2)*(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 3 +-+
+--R (d x + c x)\|x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 928
+
+--S 929 of 1527
+r0:=1/2*(b*c-a*d)*x^(5/2)/(a*b*(a+b*x^2))-1/4*(b*c-5*a*d)*atan(1-b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(9/4)*sqrt(2))+1/4*(b*c-5*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(9/4)*sqrt(2))-_
+ 1/8*(b*c-5*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(3/4)*b^(9/4)*sqrt(2))+1/8*(b*c-5*a*d)*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(9/4)*_
+ sqrt(2))-1/2*(b*c-5*a*d)*sqrt(x)/(a*b^2)
+--R
+--R
+--R (2)
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((- 5a b d + b c)x - 5a d + a b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((5a b d - b c)x + 5a d - a b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x + \|a
+--R ((- 10a b d + 2b c)x - 10a d + 2a b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x - \|a
+--R ((- 10a b d + 2b c)x - 10a d + 2a b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+3 4+-+ +-+
+--R (16b d x + 20a d - 4b c)\|2 \|a \|b \|x
+--R /
+--R 3 2 2 +-+4+-+3 4+-+
+--R (8b x + 8a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 929
+
+--S 930 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2
+--R (- 2b x - 2a b )
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625a d + 500a b c d - 150a b c d + 20a b c d - b c
+--R |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R *
+--R log
+--R +-+
+--R (5a d - b c)\|x
+--R +
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- 625a d + 500a b c d - 150a b c d + 20a b c d - b c
+--R 8a b |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R +
+--R 3 2 2
+--R (2b x + 2a b )
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625a d + 500a b c d - 150a b c d + 20a b c d - b c
+--R |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R *
+--R log
+--R +-+
+--R (5a d - b c)\|x
+--R +
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- 625a d + 500a b c d - 150a b c d + 20a b c d - b c
+--R - 8a b |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R +
+--R 3 2 2
+--R (4b x + 4a b )
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 625a d + 500a b c d - 150a b c d + 20a b c d - b c
+--R |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- 625a d + 500a b c d - 150a b c d + 20a b c d - b c
+--R 8a b |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R atan(----------------------------------------------------------------)
+--R +-+
+--R (5a d - b c)\|x
+--R +
+--R 2 +-+
+--R (4b d x + 5a d - b c)\|x
+--R /
+--R 3 2 2
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 930
+
+--S 931 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- 625a d + 500a b c d - 150a b c d + 20a b c d - b c
+--R 8b \|2 |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (5a d - b c)\|x
+--R +
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- 625a d + 500a b c d - 150a b c d + 20a b c d - b c
+--R 8a b |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R +
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- 625a d + 500a b c d - 150a b c d + 20a b c d - b c 4+-+3
+--R 8b \|2 |-------------------------------------------------------- \|a
+--R 4| 3 9
+--R \| 4096a b
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R +-+
+--R (5a d - b c)\|x
+--R +
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- 625a d + 500a b c d - 150a b c d + 20a b c d - b c
+--R - 8a b |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (10a d - 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (10a d - 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- 625a d + 500a b c d - 150a b c d + 20a b c d - b c
+--R 16b \|2 |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- 625a d + 500a b c d - 150a b c d + 20a b c d - b c
+--R 8a b |--------------------------------------------------------
+--R 4| 3 9
+--R \| 4096a b
+--R atan(----------------------------------------------------------------)
+--R +-+
+--R (5a d - b c)\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 8b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 931
+
+--S 932 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 932
+
+)clear all
+
+--S 933 of 1527
+t0:=(c+d*x^2)*sqrt(x)/(a+b*x^2)^2
+--R
+--R
+--R 2 +-+
+--R (d x + c)\|x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 933
+
+--S 934 of 1527
+r0:=1/2*(b*c-a*d)*x^(3/2)/(a*b*(a+b*x^2))-1/4*(b*c+3*a*d)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(7/4)*_
+ sqrt(2))+1/4*(b*c+3*a*d)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(5/4)*b^(7/4)*sqrt(2))+1/8*(b*c+3*a*d)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(7/4)*_
+ sqrt(2))-1/8*(b*c+3*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(5/4)*b^(7/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((- 3a b d - b c)x - 3a d - a b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((3a b d + b c)x + 3a d + a b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x + \|a
+--R ((6a b d + 2b c)x + 6a d + 2a b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x - \|a
+--R ((6a b d + 2b c)x + 6a d + 2a b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+4+-+3 +-+
+--R (- 4a d + 4b c)x\|2 \|a \|b \|x
+--R /
+--R 2 2 2 +-+4+-+4+-+3
+--R (8a b x + 8a b)\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 934
+
+--S 935 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2
+--R (2a b x + 2a b)
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27a d + 27a b c d + 9a b c d + b c )\|x
+--R +
+--R +------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 5 |- 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R 512a b |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R +
+--R 2 2 2
+--R (- 2a b x - 2a b)
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27a d + 27a b c d + 9a b c d + b c )\|x
+--R +
+--R +------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 5 |- 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R - 512a b |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R +
+--R 2 2 2
+--R (4a b x + 4a b)
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R *
+--R +------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 5 |- 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R 512a b |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R atan(-----------------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27a d + 27a b c d + 9a b c d + b c )\|x
+--R +
+--R +-+
+--R (- a d + b c)x\|x
+--R /
+--R 2 2 2
+--R 2a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 935
+
+--S 936 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d + b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- 81a d - 108a b c d - 54a b c d - 12a b c d - b c 4+-+
+--R 8a b\|2 |------------------------------------------------------ \|a
+--R 4| 5 7
+--R \| 4096a b
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27a d + 27a b c d + 9a b c d + b c )\|x
+--R +
+--R +------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 5 |- 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R 512a b |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R +
+--R -
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R 8a b\|2 |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27a d + 27a b c d + 9a b c d + b c )\|x
+--R +
+--R -
+--R 4 5
+--R 512a b
+--R *
+--R +------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d - b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 6a d - 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 6a d - 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- 81a d - 108a b c d - 54a b c d - 12a b c d - b c 4+-+
+--R 16a b\|2 |------------------------------------------------------ \|a
+--R 4| 5 7
+--R \| 4096a b
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R +------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 4 5 |- 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R 512a b |------------------------------------------------------
+--R 4| 5 7
+--R \| 4096a b
+--R atan(-----------------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (27a d + 27a b c d + 9a b c d + b c )\|x
+--R /
+--R +-+4+-+4+-+3
+--R 8a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 936
+
+--S 937 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 937
+
+)clear all
+
+--S 938 of 1527
+t0:=(c+d*x^2)/((a+b*x^2)^2*sqrt(x))
+--R
+--R
+--R 2
+--R d x + c
+--R (1) -------------------------
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R Type: Expression(Integer)
+--E 938
+
+--S 939 of 1527
+r0:=-1/4*(3*b*c+a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*_
+ b^(5/4)*sqrt(2))+1/4*(3*b*c+a*d)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(7/4)*b^(5/4)*sqrt(2))-1/8*(3*b*c+a*d)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(5/4)*_
+ sqrt(2))+1/8*(3*b*c+a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(7/4)*b^(5/4)*sqrt(2))+1/2*(b*c-a*d)*_
+ sqrt(x)/(a*b*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((a b d + 3b c)x + a d + 3a b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((- a b d - 3b c)x - a d - 3a b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x + \|a
+--R ((2a b d + 6b c)x + 2a d + 6a b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x - \|a
+--R ((2a b d + 6b c)x + 2a d + 6a b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+3 4+-+ +-+
+--R (- 4a d + 4b c)\|2 \|a \|b \|x
+--R /
+--R 2 2 2 +-+4+-+3 4+-+
+--R (8a b x + 8a b)\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 939
+
+--S 940 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2
+--R (2a b x + 2a b)
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R *
+--R log
+--R +-+
+--R (a d + 3b c)\|x
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R 8a b |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R +
+--R 2 2 2
+--R (- 2a b x - 2a b)
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R *
+--R log
+--R +-+
+--R (a d + 3b c)\|x
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R - 8a b |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R +
+--R 2 2 2
+--R (- 4a b x - 4a b)
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R 8a b |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R atan(-------------------------------------------------------------)
+--R +-+
+--R (a d + 3b c)\|x
+--R +
+--R +-+
+--R (- a d + b c)\|x
+--R /
+--R 2 2 2
+--R 2a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 940
+
+--S 941 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d - 3b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d - 12a b c d - 54a b c d - 108a b c d - 81b c 4+-+3
+--R 8a b\|2 |------------------------------------------------------ \|a
+--R 4| 7 5
+--R \| 4096a b
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R +-+
+--R (a d + 3b c)\|x
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R 8a b |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R +
+--R -
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R 8a b\|2 |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (a d + 3b c)\|x
+--R +
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R - 8a b |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d + 3b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 2a d - 6b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 2a d - 6b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R +-+ |- a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R 16a b\|2 |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R +------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 |- a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R 8a b |------------------------------------------------------
+--R 4| 7 5
+--R \| 4096a b
+--R atan(-------------------------------------------------------------)
+--R +-+
+--R (a d + 3b c)\|x
+--R /
+--R +-+4+-+3 4+-+
+--R 8a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 941
+
+--S 942 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 942
+
+)clear all
+
+--S 943 of 1527
+t0:=(c+d*x^2)/(x^(3/2)*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) --------------------------
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R Type: Expression(Integer)
+--E 943
+
+--S 944 of 1527
+r0:=1/4*(5*b*c-a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*_
+ b^(3/4)*sqrt(2))-1/4*(5*b*c-a*d)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(9/4)*b^(3/4)*sqrt(2))-1/8*(5*b*c-a*d)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*_
+ b^(3/4)*sqrt(2))+1/8*(5*b*c-a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*b^(3/4)*sqrt(2))+1/2*(-5*b*c+_
+ a*d)/(a^2*b*sqrt(x))+1/2*(b*c-a*d)/(a*b*(a+b*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 2 2 +-+
+--R ((- a b d + 5b c)x - a d + 5a b c)\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 +-+
+--R ((a b d - 5b c)x + a d - 5a b c)\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 +-+ \|2 \|b \|x + \|a
+--R ((2a b d - 10b c)x + 2a d - 10a b c)\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 +-+ \|2 \|b \|x - \|a
+--R ((2a b d - 10b c)x + 2a d - 10a b c)\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+4+-+3
+--R ((4a d - 20b c)x - 16a c)\|2 \|a \|b
+--R /
+--R 2 2 3 +-+4+-+4+-+3 +-+
+--R (8a b x + 8a )\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 944
+
+--S 945 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 3
+--R (2a b x + 2a )
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 20a b c d - 150a b c d + 500a b c d - 625b c +-+
+--R |-------------------------------------------------------- \|x
+--R 4| 9 3
+--R \| 4096a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 15a b c d + 75a b c d - 125b c )\|x
+--R +
+--R +--------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 7 2 |- a d + 20a b c d - 150a b c d + 500a b c d - 625b c
+--R 512a b |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R +
+--R 2 2 3
+--R (- 2a b x - 2a )
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 20a b c d - 150a b c d + 500a b c d - 625b c +-+
+--R |-------------------------------------------------------- \|x
+--R 4| 9 3
+--R \| 4096a b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 15a b c d + 75a b c d - 125b c )\|x
+--R +
+--R -
+--R 7 2
+--R 512a b
+--R *
+--R +--------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 20a b c d - 150a b c d + 500a b c d - 625b c
+--R |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R +
+--R 2 2 3
+--R (4a b x + 4a )
+--R *
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 20a b c d - 150a b c d + 500a b c d - 625b c +-+
+--R |-------------------------------------------------------- \|x
+--R 4| 9 3
+--R \| 4096a b
+--R *
+--R +--------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 7 2 |- a d + 20a b c d - 150a b c d + 500a b c d - 625b c
+--R 512a b |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R atan(-------------------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 15a b c d + 75a b c d - 125b c )\|x
+--R +
+--R 2
+--R (a d - 5b c)x - 4a c
+--R /
+--R 2 2 3 +-+
+--R (2a b x + 2a )\|x
+--R Type: Union(Expression(Integer),...)
+--E 945
+
+--S 946 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 5b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- a d + 20a b c d - 150a b c d + 500a b c d - 625b c 4+-+
+--R 8a \|2 |-------------------------------------------------------- \|a
+--R 4| 9 3
+--R \| 4096a b
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 15a b c d + 75a b c d - 125b c )\|x
+--R +
+--R +--------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 7 2 |- a d + 20a b c d - 150a b c d + 500a b c d - 625b c
+--R 512a b |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R +
+--R -
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- a d + 20a b c d - 150a b c d + 500a b c d - 625b c
+--R 8a \|2 |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 15a b c d + 75a b c d - 125b c )\|x
+--R +
+--R -
+--R 7 2
+--R 512a b
+--R *
+--R +--------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- a d + 20a b c d - 150a b c d + 500a b c d - 625b c
+--R |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 5b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 2a d + 10b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 2a d + 10b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 2 +-+ |- a d + 20a b c d - 150a b c d + 500a b c d - 625b c 4+-+
+--R 16a \|2 |-------------------------------------------------------- \|a
+--R 4| 9 3
+--R \| 4096a b
+--R *
+--R 4+-+3
+--R \|b
+--R *
+--R +--------------------------------------------------------+3
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 7 2 |- a d + 20a b c d - 150a b c d + 500a b c d - 625b c
+--R 512a b |--------------------------------------------------------
+--R 4| 9 3
+--R \| 4096a b
+--R atan(-------------------------------------------------------------------)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d - 15a b c d + 75a b c d - 125b c )\|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 8a \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 946
+
+--S 947 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 947
+
+)clear all
+
+--S 948 of 1527
+t0:=(c+d*x^2)/(x^(5/2)*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) ---------------------------
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 948
+
+--S 949 of 1527
+r0:=1/6*(-7*b*c+3*a*d)/(a^2*b*x^(3/2))+1/2*(b*c-a*d)/(a*b*x^(3/2)*_
+ (a+b*x^2))+1/4*(7*b*c-3*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(11/4)*b^(1/4)*sqrt(2))-1/4*(7*b*c-3*a*d)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*b^(1/4)*sqrt(2))+1/8*(7*b*c-_
+ 3*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(11/4)*b^(1/4)*sqrt(2))-1/8*(7*b*c-3*a*d)*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*b^(1/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 3 2 +-+
+--R ((9a b d - 21b c)x + (9a d - 21a b c)x)\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 3 2 +-+
+--R ((- 9a b d + 21b c)x + (- 9a d + 21a b c)x)\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 3 2 +-+ \|2 \|b \|x + \|a
+--R ((18a b d - 42b c)x + (18a d - 42a b c)x)\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 3 2 +-+ \|2 \|b \|x - \|a
+--R ((18a b d - 42b c)x + (18a d - 42a b c)x)\|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+3 4+-+
+--R ((12a d - 28b c)x - 16a c)\|2 \|a \|b
+--R /
+--R 2 3 3 +-+4+-+3 4+-+ +-+
+--R (24a b x + 24a x)\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 949
+
+--S 950 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 3
+--R (6a b x + 6a x)
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81a d + 756a b c d - 2646a b c d + 4116a b c d - 2401b c +-+
+--R |-------------------------------------------------------------- \|x
+--R 4| 11
+--R \| 4096a b
+--R *
+--R log
+--R +-+
+--R (3a d - 7b c)\|x
+--R +
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 3 |- 81a d + 756a b c d - 2646a b c d + 4116a b c d - 2401b c
+--R 8a |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R +
+--R 2 3 3
+--R (- 6a b x - 6a x)
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81a d + 756a b c d - 2646a b c d + 4116a b c d - 2401b c +-+
+--R |-------------------------------------------------------------- \|x
+--R 4| 11
+--R \| 4096a b
+--R *
+--R log
+--R +-+
+--R (3a d - 7b c)\|x
+--R +
+--R -
+--R 3
+--R 8a
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 81a d + 756a b c d - 2646a b c d + 4116a b c d
+--R +
+--R 4 4
+--R - 2401b c
+--R /
+--R 11
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 2 3 3
+--R (- 12a b x - 12a x)
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81a d + 756a b c d - 2646a b c d + 4116a b c d - 2401b c +-+
+--R |-------------------------------------------------------------- \|x
+--R 4| 11
+--R \| 4096a b
+--R *
+--R atan
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 3 |- 81a d + 756a b c d - 2646a b c d + 4116a b c d - 2401b c
+--R 8a |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R --------------------------------------------------------------------
+--R +-+
+--R (3a d - 7b c)\|x
+--R +
+--R 2
+--R (3a d - 7b c)x - 4a c
+--R /
+--R 2 3 3 +-+
+--R (6a b x + 6a x)\|x
+--R Type: Union(Expression(Integer),...)
+--E 950
+
+--S 951 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d + 7b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 8a \|2
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81a d + 756a b c d - 2646a b c d + 4116a b c d - 2401b c 4+-+3
+--R |-------------------------------------------------------------- \|a
+--R 4| 11
+--R \| 4096a b
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R +-+
+--R (3a d - 7b c)\|x
+--R +
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R 3 |- 81a d + 756a b c d - 2646a b c d + 4116a b c d - 2401b c
+--R 8a |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R +
+--R -
+--R 2 +-+
+--R 8a \|2
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81a d + 756a b c d - 2646a b c d + 4116a b c d - 2401b c
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (3a d - 7b c)\|x
+--R +
+--R -
+--R 3
+--R 8a
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 81a d + 756a b c d - 2646a b c d + 4116a b c d
+--R +
+--R 4 4
+--R - 2401b c
+--R /
+--R 11
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d - 7b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 6a d + 14b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 6a d + 14b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 2 +-+
+--R 16a \|2
+--R *
+--R +--------------------------------------------------------------+
+--R | 4 4 3 3 2 2 2 2 3 3 4 4
+--R |- 81a d + 756a b c d - 2646a b c d + 4116a b c d - 2401b c
+--R |--------------------------------------------------------------
+--R 4| 11
+--R \| 4096a b
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 3
+--R 8a
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3
+--R - 81a d + 756a b c d - 2646a b c d + 4116a b c d
+--R +
+--R 4 4
+--R - 2401b c
+--R /
+--R 11
+--R 4096a b
+--R ,
+--R 4
+--R /
+--R +-+
+--R (3a d - 7b c)\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 8a \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 951
+
+--S 952 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 952
+
+)clear all
+
+--S 953 of 1527
+t0:=(c+d*x^2)/(x^(7/2)*(a+b*x^2)^2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) ---------------------------
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 953
+
+--S 954 of 1527
+r0:=1/10*(-9*b*c+5*a*d)/(a^2*b*x^(5/2))+1/2*(b*c-a*d)/(a*b*x^(5/2)*_
+ (a+b*x^2))-1/4*b^(1/4)*(9*b*c-5*a*d)*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(13/4)*sqrt(2))+1/4*b^(1/4)*(9*b*c-5*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*sqrt(2))+_
+ 1/8*b^(1/4)*(9*b*c-5*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))-1/8*b^(1/4)*(9*b*c-5*a*d)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*_
+ sqrt(2))+1/2*(9*b*c-5*a*d)/(a^3*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 4 2 2 4+-+ +-+
+--R ((25a b d - 45b c)x + (25a d - 45a b c)x )\|b \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 2 4+-+ +-+
+--R ((- 25a b d + 45b c)x + (- 25a d + 45a b c)x )\|b \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 2 4+-+ +-+
+--R ((- 50a b d + 90b c)x + (- 50a d + 90a b c)x )\|b \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 4+-+ +-+
+--R ((- 50a b d + 90b c)x + (- 50a d + 90a b c)x )\|b \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+4+-+
+--R ((- 100a b d + 180b c)x + (- 80a d + 144a b c)x - 16a c)\|2 \|a
+--R /
+--R 3 4 4 2 +-+4+-+ +-+
+--R (40a b x + 40a x )\|2 \|a \|x
+--R Type: Expression(Integer)
+--E 954
+
+--S 955 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 4 4 2
+--R (- 10a b x - 10a x )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R |- 625a b d + 4500a b c d - 12150a b c d + 14580a b c d - 6561b c
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096a
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d - 675a b c d + 1215a b c d - 729b c )\|x
+--R +
+--R 10
+--R 512a
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2
+--R - 625a b d + 4500a b c d - 12150a b c d
+--R +
+--R 4 3 5 4
+--R 14580a b c d - 6561b c
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 4 4 2
+--R (10a b x + 10a x )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R |- 625a b d + 4500a b c d - 12150a b c d + 14580a b c d - 6561b c
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096a
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d - 675a b c d + 1215a b c d - 729b c )\|x
+--R +
+--R -
+--R 10
+--R 512a
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2
+--R - 625a b d + 4500a b c d - 12150a b c d
+--R +
+--R 4 3 5 4
+--R 14580a b c d - 6561b c
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 4 4 2
+--R (- 20a b x - 20a x )
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R |- 625a b d + 4500a b c d - 12150a b c d + 14580a b c d - 6561b c
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096a
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 10
+--R 512a
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2
+--R - 625a b d + 4500a b c d - 12150a b c d
+--R +
+--R 4 3 5 4
+--R 14580a b c d - 6561b c
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d - 675a b c d + 1215a b c d - 729b c )\|x
+--R +
+--R 2 4 2 2 2
+--R (- 25a b d + 45b c)x + (- 20a d + 36a b c)x - 4a c
+--R /
+--R 3 4 4 2 +-+
+--R (10a b x + 10a x )\|x
+--R Type: Union(Expression(Integer),...)
+--E 955
+
+--S 956 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + 9b c)\|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 3 +-+
+--R 8a \|2
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d + 4500a b c d - 12150a b c d + 14580a b c d
+--R +
+--R 5 4
+--R - 6561b c
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|a
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d - 675a b c d + 1215a b c d - 729b c )\|x
+--R +
+--R 10
+--R 512a
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2
+--R - 625a b d + 4500a b c d - 12150a b c d
+--R +
+--R 4 3 5 4
+--R 14580a b c d - 6561b c
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 +-+
+--R 8a \|2
+--R *
+--R +--------------------------------------------------------------------+
+--R | 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R |- 625a b d + 4500a b c d - 12150a b c d + 14580a b c d - 6561b c
+--R |--------------------------------------------------------------------
+--R 4| 13
+--R \| 4096a
+--R *
+--R 4+-+
+--R \|a
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d - 675a b c d + 1215a b c d - 729b c )\|x
+--R +
+--R -
+--R 10
+--R 512a
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2
+--R - 625a b d + 4500a b c d - 12150a b c d
+--R +
+--R 4 3 5 4
+--R 14580a b c d - 6561b c
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - 9b c)\|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a
+--R (10a d - 18b c)\|b atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x - \|a
+--R (10a d - 18b c)\|b atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 3 +-+
+--R 16a \|2
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d + 4500a b c d - 12150a b c d + 14580a b c d
+--R +
+--R 5 4
+--R - 6561b c
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|a
+--R *
+--R atan
+--R 10
+--R 512a
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2
+--R - 625a b d + 4500a b c d - 12150a b c d
+--R +
+--R 4 3 5 4
+--R 14580a b c d - 6561b c
+--R /
+--R 13
+--R 4096a
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d - 675a b c d + 1215a b c d - 729b c )\|x
+--R /
+--R 3 +-+4+-+
+--R 8a \|2 \|a
+--R Type: Expression(Integer)
+--E 956
+
+--S 957 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 957
+
+)clear all
+
+--S 958 of 1527
+t0:=x^(7/2)*(c+d*x^2)^2/(a+b*x^2)^2
+--R
+--R
+--R 2 7 5 2 3 +-+
+--R (d x + 2c d x + c x )\|x
+--R (1) ---------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 958
+
+--S 959 of 1527
+r0:=-1/10*(5*b*c-13*a*d)*(b*c-a*d)*x^(5/2)/(a*b^3)+2/9*d^2*x^(9/2)/b^2+_
+ 1/2*(b*c-a*d)^2*x^(9/2)/(a*b^2*(a+b*x^2))+1/4*a^(1/4)*(5*b*c-_
+ 13*a*d)*(b*c-a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (b^(17/4)*sqrt(2))-1/4*a^(1/4)*(5*b*c-13*a*d)*(b*c-a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(17/4)*sqrt(2))+_
+ 1/8*a^(1/4)*(5*b*c-13*a*d)*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(17/4)*sqrt(2))-1/8*a^(1/4)*_
+ (5*b*c-13*a*d)*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(b^(17/4)*sqrt(2))+1/2*(5*b*c-13*a*d)*_
+ (b*c-a*d)*sqrt(x)/b^4
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2
+--R (- 585a b d + 810a b c d - 225b c )x - 585a d + 810a b c d
+--R +
+--R 2 2
+--R - 225a b c
+--R *
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 2 3 2 2
+--R (585a b d - 810a b c d + 225b c )x + 585a d - 810a b c d
+--R +
+--R 2 2
+--R 225a b c
+--R *
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 2 3 2 2
+--R (- 1170a b d + 1620a b c d - 450b c )x - 1170a d + 1620a b c d
+--R +
+--R 2 2
+--R - 450a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a
+--R \|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 3 2 2 3 2 2
+--R (- 1170a b d + 1620a b c d - 450b c )x - 1170a d + 1620a b c d
+--R +
+--R 2 2
+--R - 450a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x - \|a
+--R \|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 6 2 2 3 4
+--R 80b d x + (- 208a b d + 288b c d)x
+--R +
+--R 2 2 2 3 2 2 3 2 2
+--R (1872a b d - 2592a b c d + 720b c )x + 2340a d - 3240a b c d
+--R +
+--R 2 2
+--R 900a b c
+--R *
+--R +-+4+-+ +-+
+--R \|2 \|b \|x
+--R /
+--R 5 2 4 +-+4+-+
+--R (360b x + 360a b )\|2 \|b
+--R Type: Expression(Integer)
+--E 959
+
+--S 960 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 2 4
+--R (- 90b x - 90a b )
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R - 28561a d + 158184a b c d - 372476a b c d + 485784a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R - 383046a b c d + 186840a b c d - 55100a b c d + 9000a b c d
+--R +
+--R 8 8
+--R - 625a b c
+--R /
+--R 17
+--R 4096b
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (13a d - 18a b c d + 5b c )\|x
+--R +
+--R 4
+--R 8b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6
+--R - 28561a d + 158184a b c d - 372476a b c d
+--R +
+--R 6 3 3 5 5 4 4 4 4 5 5 3
+--R 485784a b c d - 383046a b c d + 186840a b c d
+--R +
+--R 3 6 6 2 2 7 7 8 8
+--R - 55100a b c d + 9000a b c d - 625a b c
+--R /
+--R 17
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 5 2 4
+--R (90b x + 90a b )
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R - 28561a d + 158184a b c d - 372476a b c d + 485784a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R - 383046a b c d + 186840a b c d - 55100a b c d + 9000a b c d
+--R +
+--R 8 8
+--R - 625a b c
+--R /
+--R 17
+--R 4096b
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (13a d - 18a b c d + 5b c )\|x
+--R +
+--R -
+--R 4
+--R 8b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6
+--R - 28561a d + 158184a b c d - 372476a b c d
+--R +
+--R 6 3 3 5 5 4 4 4 4 5 5 3
+--R 485784a b c d - 383046a b c d + 186840a b c d
+--R +
+--R 3 6 6 2 2 7 7 8 8
+--R - 55100a b c d + 9000a b c d - 625a b c
+--R /
+--R 17
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 5 2 4
+--R (180b x + 180a b )
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R - 28561a d + 158184a b c d - 372476a b c d + 485784a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R - 383046a b c d + 186840a b c d - 55100a b c d + 9000a b c d
+--R +
+--R 8 8
+--R - 625a b c
+--R /
+--R 17
+--R 4096b
+--R ,
+--R 4
+--R *
+--R atan
+--R 4
+--R 8b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6
+--R - 28561a d + 158184a b c d - 372476a b c d
+--R +
+--R 6 3 3 5 5 4 4 4 4 5 5 3
+--R 485784a b c d - 383046a b c d + 186840a b c d
+--R +
+--R 3 6 6 2 2 7 7 8 8
+--R - 55100a b c d + 9000a b c d - 625a b c
+--R /
+--R 17
+--R 4096b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (13a d - 18a b c d + 5b c )\|x
+--R +
+--R 3 2 6 2 2 3 4
+--R 20b d x + (- 52a b d + 72b c d)x
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R (468a b d - 648a b c d + 180b c )x + 585a d - 810a b c d + 225a b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 5 2 4
+--R 90b x + 90a b
+--R Type: Union(Expression(Integer),...)
+--E 960
+
+--S 961 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (13a d - 18a b c d + 5b c )\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 4 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6
+--R - 28561a d + 158184a b c d - 372476a b c d
+--R +
+--R 6 3 3 5 5 4 4 4 4 5 5 3
+--R 485784a b c d - 383046a b c d + 186840a b c d
+--R +
+--R 3 6 6 2 2 7 7 8 8
+--R - 55100a b c d + 9000a b c d - 625a b c
+--R /
+--R 17
+--R 4096b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (13a d - 18a b c d + 5b c )\|x
+--R +
+--R 4
+--R 8b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6
+--R - 28561a d + 158184a b c d - 372476a b c d
+--R +
+--R 6 3 3 5 5 4 4 4 4 5 5 3
+--R 485784a b c d - 383046a b c d + 186840a b c d
+--R +
+--R 3 6 6 2 2 7 7 8 8
+--R - 55100a b c d + 9000a b c d - 625a b c
+--R /
+--R 17
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 4 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R - 28561a d + 158184a b c d - 372476a b c d + 485784a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R - 383046a b c d + 186840a b c d - 55100a b c d + 9000a b c d
+--R +
+--R 8 8
+--R - 625a b c
+--R /
+--R 17
+--R 4096b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (13a d - 18a b c d + 5b c )\|x
+--R +
+--R -
+--R 4
+--R 8b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6
+--R - 28561a d + 158184a b c d - 372476a b c d
+--R +
+--R 6 3 3 5 5 4 4 4 4 5 5 3
+--R 485784a b c d - 383046a b c d + 186840a b c d
+--R +
+--R 3 6 6 2 2 7 7 8 8
+--R - 55100a b c d + 9000a b c d - 625a b c
+--R /
+--R 17
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 13a d + 18a b c d - 5b c )\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|b \|x + \|a
+--R (26a d - 36a b c d + 10b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 4+-+ \|2 \|b \|x - \|a
+--R (26a d - 36a b c d + 10b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 +-+
+--R 16b \|2
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6 6 3 3 5
+--R - 28561a d + 158184a b c d - 372476a b c d + 485784a b c d
+--R +
+--R 5 4 4 4 4 5 5 3 3 6 6 2 2 7 7
+--R - 383046a b c d + 186840a b c d - 55100a b c d + 9000a b c d
+--R +
+--R 8 8
+--R - 625a b c
+--R /
+--R 17
+--R 4096b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R atan
+--R 4
+--R 8b
+--R *
+--R ROOT
+--R 9 8 8 7 7 2 2 6
+--R - 28561a d + 158184a b c d - 372476a b c d
+--R +
+--R 6 3 3 5 5 4 4 4 4 5 5 3
+--R 485784a b c d - 383046a b c d + 186840a b c d
+--R +
+--R 3 6 6 2 2 7 7 8 8
+--R - 55100a b c d + 9000a b c d - 625a b c
+--R /
+--R 17
+--R 4096b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (13a d - 18a b c d + 5b c )\|x
+--R /
+--R 4 +-+4+-+
+--R 8b \|2 \|b
+--R Type: Expression(Integer)
+--E 961
+
+--S 962 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 962
+
+)clear all
+
+--S 963 of 1527
+t0:=x^(5/2)*(c+d*x^2)^2/(a+b*x^2)^2
+--R
+--R
+--R 2 6 4 2 2 +-+
+--R (d x + 2c d x + c x )\|x
+--R (1) ---------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 963
+
+--S 964 of 1527
+r0:=-1/6*(3*b*c-11*a*d)*(b*c-a*d)*x^(3/2)/(a*b^3)+2/7*d^2*x^(7/2)/b^2+_
+ 1/2*(b*c-a*d)^2*x^(7/2)/(a*b^2*(a+b*x^2))-1/4*(3*b*c-11*a*d)*_
+ (b*c-a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*_
+ b^(15/4)*sqrt(2))+1/4*(3*b*c-11*a*d)*(b*c-a*d)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(15/4)*sqrt(2))+_
+ 1/8*(3*b*c-11*a*d)*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(15/4)*sqrt(2))-_
+ 1/8*(3*b*c-11*a*d)*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(15/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2
+--R (- 231a b d + 294a b c d - 63b c )x - 231a d + 294a b c d
+--R +
+--R 2 2
+--R - 63a b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((231a b d - 294a b c d + 63b c )x + 231a d - 294a b c d + 63a b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 2 3 2 2
+--R (462a b d - 588a b c d + 126b c )x + 462a d - 588a b c d
+--R +
+--R 2 2
+--R 126a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 3 2 2 3 2 2
+--R (462a b d - 588a b c d + 126b c )x + 462a d - 588a b c d
+--R +
+--R 2 2
+--R 126a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 5 2 2 3
+--R 48b d x + (- 176a b d + 224b c d)x
+--R +
+--R 2 2 2 2
+--R (- 308a d + 392a b c d - 84b c )x
+--R *
+--R +-+4+-+4+-+3 +-+
+--R \|2 \|a \|b \|x
+--R /
+--R 4 2 3 +-+4+-+4+-+3
+--R (168b x + 168a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 964
+
+--S 965 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 3
+--R (42b x + 42a b )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 14641a d + 74536a b c d - 158268a b c d + 181720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 122566a b c d + 49560a b c d - 11772a b c d + 1512a b c d
+--R +
+--R 8 8
+--R - 81b c
+--R /
+--R 15
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 1331a d - 5082a b c d + 7557a b c d - 5516a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 2061a b c d - 378a b c d + 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 11
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 14641a d + 74536a b c d - 158268a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 181720a b c d - 122566a b c d + 49560a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 11772a b c d + 1512a b c d - 81b c
+--R /
+--R 15
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 2 3
+--R (- 42b x - 42a b )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 14641a d + 74536a b c d - 158268a b c d + 181720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 122566a b c d + 49560a b c d - 11772a b c d + 1512a b c d
+--R +
+--R 8 8
+--R - 81b c
+--R /
+--R 15
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 1331a d - 5082a b c d + 7557a b c d - 5516a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 2061a b c d - 378a b c d + 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 11
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 14641a d + 74536a b c d - 158268a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 181720a b c d - 122566a b c d + 49560a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 11772a b c d + 1512a b c d - 81b c
+--R /
+--R 15
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 2 3
+--R (84b x + 84a b )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 14641a d + 74536a b c d - 158268a b c d + 181720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 122566a b c d + 49560a b c d - 11772a b c d + 1512a b c d
+--R +
+--R 8 8
+--R - 81b c
+--R /
+--R 15
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R atan
+--R 11
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 14641a d + 74536a b c d - 158268a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 181720a b c d - 122566a b c d + 49560a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 11772a b c d + 1512a b c d - 81b c
+--R /
+--R 15
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 1331a d - 5082a b c d + 7557a b c d - 5516a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 2061a b c d - 378a b c d + 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 5 2 2 3
+--R 12b d x + (- 44a b d + 56b c d)x
+--R +
+--R 2 2 2 2
+--R (- 77a d + 98a b c d - 21b c )x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 4 2 3
+--R 42b x + 42a b
+--R Type: Union(Expression(Integer),...)
+--E 965
+
+--S 966 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (11a d - 14a b c d + 3b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 14641a d + 74536a b c d - 158268a b c d + 181720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 122566a b c d + 49560a b c d - 11772a b c d + 1512a b c d
+--R +
+--R 8 8
+--R - 81b c
+--R /
+--R 15
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 1331a d - 5082a b c d + 7557a b c d - 5516a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 2061a b c d - 378a b c d + 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 11
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 14641a d + 74536a b c d - 158268a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 181720a b c d - 122566a b c d + 49560a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 11772a b c d + 1512a b c d - 81b c
+--R /
+--R 15
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 3 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 14641a d + 74536a b c d - 158268a b c d + 181720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 122566a b c d + 49560a b c d - 11772a b c d
+--R +
+--R 7 7 8 8
+--R 1512a b c d - 81b c
+--R /
+--R 15
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 1331a d - 5082a b c d + 7557a b c d - 5516a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 2061a b c d - 378a b c d + 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 11
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 14641a d + 74536a b c d - 158268a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 181720a b c d - 122566a b c d + 49560a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 11772a b c d + 1512a b c d - 81b c
+--R /
+--R 15
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 11a d + 14a b c d - 3b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (- 22a d + 28a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (- 22a d + 28a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+
+--R 16b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 14641a d + 74536a b c d - 158268a b c d + 181720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 122566a b c d + 49560a b c d - 11772a b c d + 1512a b c d
+--R +
+--R 8 8
+--R - 81b c
+--R /
+--R 15
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 11
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 14641a d + 74536a b c d - 158268a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 181720a b c d - 122566a b c d + 49560a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 11772a b c d + 1512a b c d - 81b c
+--R /
+--R 15
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 1331a d - 5082a b c d + 7557a b c d - 5516a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 2061a b c d - 378a b c d + 27b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3 +-+4+-+4+-+3
+--R 8b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 966
+
+--S 967 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 967
+
+)clear all
+
+--S 968 of 1527
+t0:=x^(3/2)*(c+d*x^2)^2/(a+b*x^2)^2
+--R
+--R
+--R 2 5 3 2 +-+
+--R (d x + 2c d x + c x)\|x
+--R (1) --------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 968
+
+--S 969 of 1527
+r0:=2/5*d^2*x^(5/2)/b^2+1/2*(b*c-a*d)^2*x^(5/2)/(a*b^2*(a+b*x^2))-_
+ 1/4*(b*c-9*a*d)*(b*c-a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(3/4)*b^(13/4)*sqrt(2))+1/4*(b*c-9*a*d)*(b*c-a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(13/4)*_
+ sqrt(2))-1/8*(b*c-9*a*d)*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(13/4)*sqrt(2))+_
+ 1/8*(b*c-9*a*d)*(b*c-a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(3/4)*b^(13/4)*sqrt(2))-1/2*(b*c-9*a*d)*_
+ (b*c-a*d)*sqrt(x)/(a*b^3)
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((45a b d - 50a b c d + 5b c )x + 45a d - 50a b c d + 5a b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 45a b d + 50a b c d - 5b c )x - 45a d + 50a b c d - 5a b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((90a b d - 100a b c d + 10b c )x + 90a d - 100a b c d + 10a b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((90a b d - 100a b c d + 10b c )x + 90a d - 100a b c d + 10a b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R (16b d x + (- 144a b d + 160b c d)x - 180a d + 200a b c d - 20b c )
+--R *
+--R +-+4+-+3 4+-+ +-+
+--R \|2 \|a \|b \|x
+--R /
+--R 4 2 3 +-+4+-+3 4+-+
+--R (40b x + 40a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 969
+
+--S 970 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 3
+--R (10b x + 10a b )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 6561a d + 29160a b c d - 51516a b c d + 45720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 21286a b c d + 5080a b c d - 636a b c d + 40a b c d - b c
+--R /
+--R 3 13
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (9a d - 10a b c d + b c )\|x
+--R +
+--R 3
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 6561a d + 29160a b c d - 51516a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 45720a b c d - 21286a b c d + 5080a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 636a b c d + 40a b c d - b c
+--R /
+--R 3 13
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 4 2 3
+--R (- 10b x - 10a b )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 6561a d + 29160a b c d - 51516a b c d + 45720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 21286a b c d + 5080a b c d - 636a b c d + 40a b c d - b c
+--R /
+--R 3 13
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (9a d - 10a b c d + b c )\|x
+--R +
+--R -
+--R 3
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 6561a d + 29160a b c d - 51516a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 45720a b c d - 21286a b c d + 5080a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 636a b c d + 40a b c d - b c
+--R /
+--R 3 13
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 4 2 3
+--R (- 20b x - 20a b )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 6561a d + 29160a b c d - 51516a b c d + 45720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 21286a b c d + 5080a b c d - 636a b c d + 40a b c d - b c
+--R /
+--R 3 13
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R atan
+--R 3
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 6561a d + 29160a b c d - 51516a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 45720a b c d - 21286a b c d + 5080a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 636a b c d + 40a b c d - b c
+--R /
+--R 3 13
+--R 4096a b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (9a d - 10a b c d + b c )\|x
+--R +
+--R 2 2 4 2 2 2 2 2 2 2 +-+
+--R (4b d x + (- 36a b d + 40b c d)x - 45a d + 50a b c d - 5b c )\|x
+--R /
+--R 4 2 3
+--R 10b x + 10a b
+--R Type: Union(Expression(Integer),...)
+--E 970
+
+--S 971 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 9a d + 10a b c d - b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 6561a d + 29160a b c d - 51516a b c d + 45720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 21286a b c d + 5080a b c d - 636a b c d + 40a b c d - b c
+--R /
+--R 3 13
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (9a d - 10a b c d + b c )\|x
+--R +
+--R 3
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 6561a d + 29160a b c d - 51516a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 45720a b c d - 21286a b c d + 5080a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 636a b c d + 40a b c d - b c
+--R /
+--R 3 13
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R -
+--R 3 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 6561a d + 29160a b c d - 51516a b c d + 45720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 21286a b c d + 5080a b c d - 636a b c d + 40a b c d - b c
+--R /
+--R 3 13
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (9a d - 10a b c d + b c )\|x
+--R +
+--R -
+--R 3
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 6561a d + 29160a b c d - 51516a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 45720a b c d - 21286a b c d + 5080a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 636a b c d + 40a b c d - b c
+--R /
+--R 3 13
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (9a d - 10a b c d + b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (- 18a d + 20a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (- 18a d + 20a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 3 +-+
+--R 16b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 6561a d + 29160a b c d - 51516a b c d + 45720a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 21286a b c d + 5080a b c d - 636a b c d + 40a b c d - b c
+--R /
+--R 3 13
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 3
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 6561a d + 29160a b c d - 51516a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 45720a b c d - 21286a b c d + 5080a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 636a b c d + 40a b c d - b c
+--R /
+--R 3 13
+--R 4096a b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (9a d - 10a b c d + b c )\|x
+--R /
+--R 3 +-+4+-+3 4+-+
+--R 8b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 971
+
+--S 972 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 972
+
+)clear all
+
+--S 973 of 1527
+t0:=(c+d*x^2)^2*sqrt(x)/(a+b*x^2)^2
+--R
+--R
+--R 2 4 2 2 +-+
+--R (d x + 2c d x + c )\|x
+--R (1) -------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 973
+
+--S 974 of 1527
+r0:=2/3*d^2*x^(3/2)/b^2+1/2*(b*c-a*d)^2*x^(3/2)/(a*b^2*(a+b*x^2))-_
+ 1/4*(b*c-a*d)*(b*c+7*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(5/4)*b^(11/4)*sqrt(2))+1/4*(b*c-a*d)*(b*c+7*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(11/4)*_
+ sqrt(2))+1/8*(b*c-a*d)*(b*c+7*a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(11/4)*sqrt(2))-_
+ 1/8*(b*c-a*d)*(b*c+7*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(5/4)*b^(11/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((21a b d - 18a b c d - 3b c )x + 21a d - 18a b c d - 3a b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 21a b d + 18a b c d + 3b c )x - 21a d + 18a b c d + 3a b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 42a b d + 36a b c d + 6b c )x - 42a d + 36a b c d + 6a b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 42a b d + 36a b c d + 6b c )x - 42a d + 36a b c d + 6a b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 2 2 2 +-+4+-+4+-+3 +-+
+--R (16a b d x + (28a d - 24a b c d + 12b c )x)\|2 \|a \|b \|x
+--R /
+--R 3 2 2 2 +-+4+-+4+-+3
+--R (24a b x + 24a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 974
+
+--S 975 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2 2
+--R (- 6a b x - 6a b )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 5 11
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 343a d - 882a b c d + 609a b c d + 36a b c d - 87a b c d
+--R +
+--R 5 5 6 6
+--R - 18a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 8
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 2 2
+--R (6a b x + 6a b )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 5 11
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 343a d - 882a b c d + 609a b c d + 36a b c d - 87a b c d
+--R +
+--R 5 5 6 6
+--R - 18a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 8
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 2401a d + 8232a b c d - 9212a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 2520a b c d + 1434a b c d - 360a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 188a b c d - 24a b c d - b c
+--R /
+--R 5 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 2 2
+--R (- 12a b x - 12a b )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 5 11
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R atan
+--R 4 8
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d
+--R +
+--R 8 8
+--R - b c
+--R /
+--R 5 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 343a d - 882a b c d + 609a b c d + 36a b c d - 87a b c d
+--R +
+--R 5 5 6 6
+--R - 18a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 3 2 2 2 2 +-+
+--R (4a b d x + (7a d - 6a b c d + 3b c )x)\|x
+--R /
+--R 3 2 2 2
+--R 6a b x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 975
+
+--S 976 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 7a d + 6a b c d + b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 2 +-+
+--R 8a b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 5 11
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 343a d - 882a b c d + 609a b c d + 36a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R - 87a b c d - 18a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 8
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 2401a d + 8232a b c d - 9212a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 2520a b c d + 1434a b c d - 360a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 188a b c d - 24a b c d - b c
+--R /
+--R 5 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 +-+
+--R 8a b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 5 11
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 343a d - 882a b c d + 609a b c d + 36a b c d - 87a b c d
+--R +
+--R 5 5 6 6
+--R - 18a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 8
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 2401a d + 8232a b c d - 9212a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 2520a b c d + 1434a b c d - 360a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 188a b c d - 24a b c d - b c
+--R /
+--R 5 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (7a d - 6a b c d - b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (14a d - 12a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (14a d - 12a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 2 +-+
+--R 16a b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 2401a d + 8232a b c d - 9212a b c d + 2520a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1434a b c d - 360a b c d - 188a b c d - 24a b c d - b c
+--R /
+--R 5 11
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 4 8
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 2401a d + 8232a b c d - 9212a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 2520a b c d + 1434a b c d - 360a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R - 188a b c d - 24a b c d - b c
+--R /
+--R 5 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 343a d - 882a b c d + 609a b c d + 36a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R - 87a b c d - 18a b c d - b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 8a b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 976
+
+--S 977 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 977
+
+)clear all
+
+--S 978 of 1527
+t0:=(c+d*x^2)^2/((a+b*x^2)^2*sqrt(x))
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------------
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R Type: Expression(Integer)
+--E 978
+
+--S 979 of 1527
+r0:=-1/4*(b*c-a*d)*(3*b*c+5*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(7/4)*b^(9/4)*sqrt(2))+1/4*(b*c-a*d)*(3*b*c+5*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(9/4)*sqrt(2))-_
+ 1/8*(b*c-a*d)*(3*b*c+5*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(7/4)*b^(9/4)*sqrt(2))+1/8*(b*c-a*d)*(3*b*c+_
+ 5*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(7/4)*b^(9/4)*sqrt(2))+2*d^2*sqrt(x)/b^2+1/2*(b*c-a*d)^2*_
+ sqrt(x)/(a*b^2*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 5a b d + 2a b c d + 3b c )x - 5a d + 2a b c d + 3a b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((5a b d - 2a b c d - 3b c )x + 5a d - 2a b c d - 3a b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 10a b d + 4a b c d + 6b c )x - 10a d + 4a b c d + 6a b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 10a b d + 4a b c d + 6b c )x - 10a d + 4a b c d + 6a b c )
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 2 2 +-+4+-+3 4+-+ +-+
+--R (16a b d x + 20a d - 8a b c d + 4b c )\|2 \|a \|b \|x
+--R /
+--R 3 2 2 2 +-+4+-+3 4+-+
+--R (8a b x + 8a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 979
+
+--S 980 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2 2
+--R (- 2a b x - 2a b )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d - 81b c
+--R /
+--R 7 9
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (5a d - 2a b c d - 3b c )\|x
+--R +
+--R 2 2
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d
+--R +
+--R 8 8
+--R - 81b c
+--R /
+--R 7 9
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 3 2 2 2
+--R (2a b x + 2a b )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d - 81b c
+--R /
+--R 7 9
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (5a d - 2a b c d - 3b c )\|x
+--R +
+--R -
+--R 2 2
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d
+--R +
+--R 8 8
+--R - 81b c
+--R /
+--R 7 9
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 3 2 2 2
+--R (4a b x + 4a b )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d - 81b c
+--R /
+--R 7 9
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R atan
+--R 2 2
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d
+--R +
+--R 8 8
+--R - 81b c
+--R /
+--R 7 9
+--R 4096a b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (5a d - 2a b c d - 3b c )\|x
+--R +
+--R 2 2 2 2 2 2 +-+
+--R (4a b d x + 5a d - 2a b c d + b c )\|x
+--R /
+--R 3 2 2 2
+--R 2a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 980
+
+--S 981 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - 2a b c d - 3b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 2 +-+
+--R 8a b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d - 81b c
+--R /
+--R 7 9
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (5a d - 2a b c d - 3b c )\|x
+--R +
+--R 2 2
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d
+--R +
+--R 8 8
+--R - 81b c
+--R /
+--R 7 9
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 2 +-+
+--R 8a b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d - 81b c
+--R /
+--R 7 9
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (5a d - 2a b c d - 3b c )\|x
+--R +
+--R -
+--R 2 2
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d
+--R +
+--R 8 8
+--R - 81b c
+--R /
+--R 7 9
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + 2a b c d + 3b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (10a d - 4a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (10a d - 4a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+
+--R 16a b \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d - 81b c
+--R /
+--R 7 9
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 2 2
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 625a d + 1000a b c d + 900a b c d - 1640a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d + 984a b c d + 324a b c d - 216a b c d
+--R +
+--R 8 8
+--R - 81b c
+--R /
+--R 7 9
+--R 4096a b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (5a d - 2a b c d - 3b c )\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 8a b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 981
+
+--S 982 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 982
+
+)clear all
+
+--S 983 of 1527
+t0:=(c+d*x^2)^2/(x^(3/2)*(a+b*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) --------------------------
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R Type: Expression(Integer)
+--E 983
+
+--S 984 of 1527
+r0:=-1/2*(5*b*c^2/a-2*c*d+a*d^2/b)*x^(3/2)/(a*(a+b*x^2))+1/4*(b*c-a*d)*_
+ (5*b*c+3*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*_
+ b^(7/4)*sqrt(2))-1/4*(b*c-a*d)*(5*b*c+3*a*d)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*b^(7/4)*sqrt(2))-1/8*(b*c-a*d)*_
+ (5*b*c+3*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(9/4)*b^(7/4)*sqrt(2))+1/8*(b*c-a*d)*(5*b*c+3*a*d)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*_
+ b^(7/4)*sqrt(2))-2*c^2/(a*(a+b*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2 2 2 +-+
+--R ((- 3a b d - 2a b c d + 5b c )x - 3a d - 2a b c d + 5a b c )\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2 +-+
+--R ((3a b d + 2a b c d - 5b c )x + 3a d + 2a b c d - 5a b c )\|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2 +-+
+--R ((6a b d + 4a b c d - 10b c )x + 6a d + 4a b c d - 10a b c )\|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2 +-+
+--R ((6a b d + 4a b c d - 10b c )x + 6a d + 4a b c d - 10a b c )\|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 2 2 +-+4+-+4+-+3
+--R ((- 4a d + 8a b c d - 20b c )x - 16a b c )\|2 \|a \|b
+--R /
+--R 2 2 2 3 +-+4+-+4+-+3 +-+
+--R (8a b x + 8a b)\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 984
+
+--S 985 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 3
+--R (2a b x + 2a b)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d - 646a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 1640a b c d + 900a b c d + 1000a b c d - 625b c
+--R /
+--R 9 7
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 27a d + 54a b c d - 99a b c d - 172a b c d + 165a b c d
+--R +
+--R 5 5 6 6
+--R 150a b c d - 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 5
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 646a b c d - 1640a b c d + 900a b c d
+--R +
+--R 7 7 8 8
+--R 1000a b c d - 625b c
+--R /
+--R 9 7
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 3
+--R (- 2a b x - 2a b)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d - 646a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 1640a b c d + 900a b c d + 1000a b c d - 625b c
+--R /
+--R 9 7
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 27a d + 54a b c d - 99a b c d - 172a b c d + 165a b c d
+--R +
+--R 5 5 6 6
+--R 150a b c d - 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 5
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 646a b c d - 1640a b c d + 900a b c d
+--R +
+--R 7 7 8 8
+--R 1000a b c d - 625b c
+--R /
+--R 9 7
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 3
+--R (4a b x + 4a b)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d - 646a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 1640a b c d + 900a b c d + 1000a b c d - 625b c
+--R /
+--R 9 7
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 7 5
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 646a b c d - 1640a b c d + 900a b c d
+--R +
+--R 7 7 8 8
+--R 1000a b c d - 625b c
+--R /
+--R 9 7
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 27a d + 54a b c d - 99a b c d - 172a b c d + 165a b c d
+--R +
+--R 5 5 6 6
+--R 150a b c d - 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 2 2 2 2
+--R (- a d + 2a b c d - 5b c )x - 4a b c
+--R /
+--R 2 2 2 3 +-+
+--R (2a b x + 2a b)\|x
+--R Type: Union(Expression(Integer),...)
+--E 985
+
+--S 986 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d + 2a b c d - 5b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 8a b\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d - 646a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 1640a b c d + 900a b c d + 1000a b c d - 625b c
+--R /
+--R 9 7
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 27a d + 54a b c d - 99a b c d - 172a b c d + 165a b c d
+--R +
+--R 5 5 6 6
+--R 150a b c d - 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 5
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 646a b c d - 1640a b c d + 900a b c d
+--R +
+--R 7 7 8 8
+--R 1000a b c d - 625b c
+--R /
+--R 9 7
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 2 +-+
+--R 8a b\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R - 646a b c d - 1640a b c d + 900a b c d + 1000a b c d
+--R +
+--R 8 8
+--R - 625b c
+--R /
+--R 9 7
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R 27a d + 54a b c d - 99a b c d - 172a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 165a b c d + 150a b c d - 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 5
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6
+--R - 81a d - 216a b c d + 324a b c d
+--R +
+--R 5 3 3 5 4 4 4 4 3 5 5 3
+--R 984a b c d - 646a b c d - 1640a b c d
+--R +
+--R 2 6 6 2 7 7 8 8
+--R 900a b c d + 1000a b c d - 625b c
+--R /
+--R 9 7
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d - 2a b c d + 5b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (- 6a d - 4a b c d + 10b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (- 6a d - 4a b c d + 10b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+
+--R 16a b\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d - 646a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R - 1640a b c d + 900a b c d + 1000a b c d - 625b c
+--R /
+--R 9 7
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 7 5
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - 81a d - 216a b c d + 324a b c d + 984a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 646a b c d - 1640a b c d + 900a b c d
+--R +
+--R 7 7 8 8
+--R 1000a b c d - 625b c
+--R /
+--R 9 7
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 27a d + 54a b c d - 99a b c d - 172a b c d + 165a b c d
+--R +
+--R 5 5 6 6
+--R 150a b c d - 125b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 8a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 986
+
+--S 987 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 987
+
+)clear all
+
+--S 988 of 1527
+t0:=(c+d*x^2)^2/(x^(5/2)*(a+b*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) ---------------------------
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 988
+
+--S 989 of 1527
+r0:=-2/3*c^2/(a*x^(3/2)*(a+b*x^2))+1/4*(b*c-a*d)*(7*b*c+a*d)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*b^(5/4)*_
+ sqrt(2))-1/4*(b*c-a*d)*(7*b*c+a*d)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(11/4)*b^(5/4)*sqrt(2))+1/8*(b*c-a*d)*_
+ (7*b*c+a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(11/4)*b^(5/4)*sqrt(2))-1/8*(b*c-a*d)*(7*b*c+a*d)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*_
+ b^(5/4)*sqrt(2))-1/6*(7*b*c^2/a-6*c*d+3*a*d^2/b)*sqrt(x)/(a*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((3a b d + 18a b c d - 21b c )x + (3a d + 18a b c d - 21a b c )x)
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 3
+--R (- 3a b d - 18a b c d + 21b c )x
+--R +
+--R 3 2 2 2 2
+--R (- 3a d - 18a b c d + 21a b c )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((6a b d + 36a b c d - 42b c )x + (6a d + 36a b c d - 42a b c )x)
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x + \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((6a b d + 36a b c d - 42b c )x + (6a d + 36a b c d - 42a b c )x)
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x - \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 2 2 +-+4+-+3 4+-+
+--R ((- 12a d + 24a b c d - 28b c )x - 16a b c )\|2 \|a \|b
+--R /
+--R 2 2 3 3 +-+4+-+3 4+-+ +-+
+--R (24a b x + 24a b x)\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 989
+
+--S 990 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 3 3
+--R (6a b x + 6a b x)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d - 24a b c d - 188a b c d - 360a b c d + 1434a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 2520a b c d - 9212a b c d + 8232a b c d - 2401b c
+--R /
+--R 11 5
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d + 6a b c d - 7b c )\|x
+--R +
+--R 3
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1434a b c d + 2520a b c d - 9212a b c d + 8232a b c d
+--R +
+--R 8 8
+--R - 2401b c
+--R /
+--R 11 5
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 2 2 3 3
+--R (- 6a b x - 6a b x)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d - 24a b c d - 188a b c d - 360a b c d + 1434a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 2520a b c d - 9212a b c d + 8232a b c d - 2401b c
+--R /
+--R 11 5
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d + 6a b c d - 7b c )\|x
+--R +
+--R -
+--R 3
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1434a b c d + 2520a b c d - 9212a b c d
+--R +
+--R 7 7 8 8
+--R 8232a b c d - 2401b c
+--R /
+--R 11 5
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 2 2 3 3
+--R (- 12a b x - 12a b x)
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d - 24a b c d - 188a b c d - 360a b c d + 1434a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 2520a b c d - 9212a b c d + 8232a b c d - 2401b c
+--R /
+--R 11 5
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 3
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1434a b c d + 2520a b c d - 9212a b c d + 8232a b c d
+--R +
+--R 8 8
+--R - 2401b c
+--R /
+--R 11 5
+--R 4096a b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d + 6a b c d - 7b c )\|x
+--R +
+--R 2 2 2 2 2 2
+--R (- 3a d + 6a b c d - 7b c )x - 4a b c
+--R /
+--R 2 2 3 3 +-+
+--R (6a b x + 6a b x)\|x
+--R Type: Union(Expression(Integer),...)
+--E 990
+
+--S 991 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d - 6a b c d + 7b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+
+--R 8a b\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d - 24a b c d - 188a b c d - 360a b c d + 1434a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 2520a b c d - 9212a b c d + 8232a b c d - 2401b c
+--R /
+--R 11 5
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d + 6a b c d - 7b c )\|x
+--R +
+--R 3
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1434a b c d + 2520a b c d - 9212a b c d + 8232a b c d
+--R +
+--R 8 8
+--R - 2401b c
+--R /
+--R 11 5
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R -
+--R 2 +-+
+--R 8a b\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1434a b c d + 2520a b c d - 9212a b c d + 8232a b c d
+--R +
+--R 8 8
+--R - 2401b c
+--R /
+--R 11 5
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 2 2 2 2 +-+
+--R (a d + 6a b c d - 7b c )\|x
+--R +
+--R -
+--R 3
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1434a b c d + 2520a b c d - 9212a b c d
+--R +
+--R 7 7 8 8
+--R 8232a b c d - 2401b c
+--R /
+--R 11 5
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d + 6a b c d - 7b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (- 2a d - 12a b c d + 14b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (- 2a d - 12a b c d + 14b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 2 +-+
+--R 16a b\|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1434a b c d + 2520a b c d - 9212a b c d + 8232a b c d
+--R +
+--R 8 8
+--R - 2401b c
+--R /
+--R 11 5
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 3
+--R 8a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d - 24a b c d - 188a b c d - 360a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1434a b c d + 2520a b c d - 9212a b c d
+--R +
+--R 7 7 8 8
+--R 8232a b c d - 2401b c
+--R /
+--R 11 5
+--R 4096a b
+--R ,
+--R 4
+--R /
+--R 2 2 2 2 +-+
+--R (a d + 6a b c d - 7b c )\|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 8a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 991
+
+--S 992 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 992
+
+)clear all
+
+--S 993 of 1527
+t0:=(c+d*x^2)^2/(x^(7/2)*(a+b*x^2)^2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) ---------------------------
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 993
+
+--S 994 of 1527
+r0:=-2/5*c^2/(a*x^(5/2)*(a+b*x^2))-1/4*(b*c-a*d)*(9*b*c-a*d)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*b^(3/4)*_
+ sqrt(2))+1/4*(b*c-a*d)*(9*b*c-a*d)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(13/4)*b^(3/4)*sqrt(2))+1/8*(b*c-a*d)*_
+ (9*b*c-a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(13/4)*b^(3/4)*sqrt(2))-1/8*(b*c-a*d)*(9*b*c-a*d)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*_
+ b^(3/4)*sqrt(2))+1/2*(b*c-a*d)*(9*b*c-a*d)/(a^3*b*sqrt(x))+_
+ 1/10*(-9*b*c^2/a+10*c*d-5*a*d^2/b)/(a*(a+b*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 4
+--R (- 5a b d + 50a b c d - 45b c )x
+--R +
+--R 3 2 2 2 2 2
+--R (- 5a d + 50a b c d - 45a b c )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 4 3 2 2 2 2 2
+--R ((5a b d - 50a b c d + 45b c )x + (5a d - 50a b c d + 45a b c )x )
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 4
+--R (10a b d - 100a b c d + 90b c )x
+--R +
+--R 3 2 2 2 2 2
+--R (10a d - 100a b c d + 90a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x + \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 3 2 4
+--R (10a b d - 100a b c d + 90b c )x
+--R +
+--R 3 2 2 2 2 2
+--R (10a d - 100a b c d + 90a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x - \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 4 2 2 2
+--R (20a d - 200a b c d + 180b c )x + (- 160a c d + 144a b c )x
+--R +
+--R 2 2
+--R - 16a c
+--R *
+--R +-+4+-+4+-+3
+--R \|2 \|a \|b
+--R /
+--R 3 4 4 2 +-+4+-+4+-+3 +-+
+--R (40a b x + 40a x )\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 994
+
+--S 995 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 4 4 2
+--R (10a b x + 10a x )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 40a b c d - 636a b c d + 5080a b c d - 21286a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 45720a b c d - 51516a b c d + 29160a b c d - 6561b c
+--R /
+--R 13 3
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 30a b c d + 327a b c d - 1540a b c d + 2943a b c d
+--R +
+--R 5 5 6 6
+--R - 2430a b c d + 729b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 2
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 13 3
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 4 4 2
+--R (- 10a b x - 10a x )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 40a b c d - 636a b c d + 5080a b c d - 21286a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 45720a b c d - 51516a b c d + 29160a b c d - 6561b c
+--R /
+--R 13 3
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 30a b c d + 327a b c d - 1540a b c d + 2943a b c d
+--R +
+--R 5 5 6 6
+--R - 2430a b c d + 729b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 10 2
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 13 3
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 4 4 2
+--R (20a b x + 20a x )
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 40a b c d - 636a b c d + 5080a b c d - 21286a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 45720a b c d - 51516a b c d + 29160a b c d - 6561b c
+--R /
+--R 13 3
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 10 2
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 13 3
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 30a b c d + 327a b c d - 1540a b c d + 2943a b c d
+--R +
+--R 5 5 6 6
+--R - 2430a b c d + 729b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 2 2 2 4 2 2 2 2 2
+--R (5a d - 50a b c d + 45b c )x + (- 40a c d + 36a b c )x - 4a c
+--R /
+--R 3 4 4 2 +-+
+--R (10a b x + 10a x )\|x
+--R Type: Union(Expression(Integer),...)
+--E 995
+
+--S 996 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 10a b c d + 9b c )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 +-+
+--R 8a \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 40a b c d - 636a b c d + 5080a b c d - 21286a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 45720a b c d - 51516a b c d + 29160a b c d - 6561b c
+--R /
+--R 13 3
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 30a b c d + 327a b c d - 1540a b c d + 2943a b c d
+--R +
+--R 5 5 6 6
+--R - 2430a b c d + 729b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 2
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 13 3
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 3 +-+
+--R 8a \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 13 3
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 6 6 5 5 4 2 2 4 3 3 3 3
+--R a d - 30a b c d + 327a b c d - 1540a b c d
+--R +
+--R 2 4 4 2 5 5 6 6
+--R 2943a b c d - 2430a b c d + 729b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 10 2
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 13 3
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 10a b c d - 9b c )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x + \|a
+--R (- 2a d + 20a b c d - 18b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 2 \|2 \|b \|x - \|a
+--R (- 2a d + 20a b c d - 18b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+
+--R 16a \|2
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4
+--R - a d + 40a b c d - 636a b c d + 5080a b c d - 21286a b c d
+--R +
+--R 3 5 5 3 2 6 6 2 7 7 8 8
+--R 45720a b c d - 51516a b c d + 29160a b c d - 6561b c
+--R /
+--R 13 3
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 10 2
+--R 512a b
+--R *
+--R ROOT
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R - a d + 40a b c d - 636a b c d + 5080a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R - 21286a b c d + 45720a b c d - 51516a b c d
+--R +
+--R 7 7 8 8
+--R 29160a b c d - 6561b c
+--R /
+--R 13 3
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R a d - 30a b c d + 327a b c d - 1540a b c d + 2943a b c d
+--R +
+--R 5 5 6 6
+--R - 2430a b c d + 729b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3 +-+4+-+4+-+3
+--R 8a \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 996
+
+--S 997 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 997
+
+)clear all
+
+--S 998 of 1527
+t0:=x^(7/2)*(c+d*x^2)^3/(a+b*x^2)^2
+--R
+--R
+--R 3 9 2 7 2 5 3 3 +-+
+--R (d x + 3c d x + 3c d x + c x )\|x
+--R (1) -------------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 998
+
+--S 999 of 1527
+r0:=1/1170*d*(2069*b^2*c^2-4138*a*b*c*d+1989*a^2*d^2)*x^(5/2)/b^4+_
+ 17/26*d*x^(5/2)*(c+d*x^2)^2/b^2-1/2*x^(5/2)*(c+d*x^2)^3/(b*(a+_
+ b*x^2))+1/234*d*x^(5/2)*(5*c*(13*b*c-17*a*d)+d*(201*b*c-221*a*d)*_
+ x^2)/b^3+1/4*a^(1/4)*(5*b*c-17*a*d)*(b*c-a*d)^2*atan(1-b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(b^(21/4)*sqrt(2))-1/4*a^(1/4)*(5*b*c-_
+ 17*a*d)*(b*c-a*d)^2*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (b^(21/4)*sqrt(2))+1/8*a^(1/4)*(5*b*c-17*a*d)*(b*c-a*d)^2*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(21/4)*_
+ sqrt(2))-1/8*a^(1/4)*(5*b*c-17*a*d)*(b*c-a*d)^2*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(21/4)*sqrt(2))+_
+ 1/2*(5*b*c-17*a*d)*(b*c-a*d)^2*sqrt(x)/b^5
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (9945a b d - 22815a b c d + 15795a b c d - 2925b c )x + 9945a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 22815a b c d + 15795a b c d - 2925a b c
+--R *
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 9945a b d + 22815a b c d - 15795a b c d + 2925b c )x - 9945a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 22815a b c d - 15795a b c d + 2925a b c
+--R *
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (19890a b d - 45630a b c d + 31590a b c d - 5850b c )x + 19890a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 45630a b c d + 31590a b c d - 5850a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a
+--R \|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (19890a b d - 45630a b c d + 31590a b c d - 5850b c )x + 19890a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 45630a b c d + 31590a b c d - 5850a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x - \|a
+--R \|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 3 8 3 3 4 2 6
+--R 720b d x + (- 1360a b d + 3120b c d )x
+--R +
+--R 2 2 3 3 2 4 2 4
+--R (3536a b d - 8112a b c d + 5616b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 2
+--R (- 31824a b d + 73008a b c d - 50544a b c d + 9360b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R - 39780a d + 91260a b c d - 63180a b c d + 11700a b c
+--R *
+--R +-+4+-+ +-+
+--R \|2 \|b \|x
+--R /
+--R 6 2 5 +-+4+-+
+--R (4680b x + 4680a b )\|2 \|b
+--R Type: Expression(Integer)
+--E 999
+
+--S 1000 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 2 5
+--R (1170b x + 1170a b )
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10
+--R - 83521a d + 766428a b c d - 3168018a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R 7783756a b c d - 12631455a b c d + 14225976a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R - 11369148a b c d + 6477048a b c d - 2603151a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11 12 12
+--R 718060a b c d - 128850a b c d + 13500a b c d - 625a b c
+--R /
+--R 21
+--R 4096b
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (17a d - 39a b c d + 27a b c d - 5b c )\|x
+--R +
+--R 5
+--R 8b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10
+--R - 83521a d + 766428a b c d - 3168018a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R 7783756a b c d - 12631455a b c d + 14225976a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R - 11369148a b c d + 6477048a b c d - 2603151a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R 718060a b c d - 128850a b c d + 13500a b c d
+--R +
+--R 12 12
+--R - 625a b c
+--R /
+--R 21
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 6 2 5
+--R (- 1170b x - 1170a b )
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10
+--R - 83521a d + 766428a b c d - 3168018a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R 7783756a b c d - 12631455a b c d + 14225976a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R - 11369148a b c d + 6477048a b c d - 2603151a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11 12 12
+--R 718060a b c d - 128850a b c d + 13500a b c d - 625a b c
+--R /
+--R 21
+--R 4096b
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (17a d - 39a b c d + 27a b c d - 5b c )\|x
+--R +
+--R -
+--R 5
+--R 8b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10
+--R - 83521a d + 766428a b c d - 3168018a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R 7783756a b c d - 12631455a b c d + 14225976a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R - 11369148a b c d + 6477048a b c d - 2603151a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R 718060a b c d - 128850a b c d + 13500a b c d
+--R +
+--R 12 12
+--R - 625a b c
+--R /
+--R 21
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 6 2 5
+--R (- 2340b x - 2340a b )
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10
+--R - 83521a d + 766428a b c d - 3168018a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R 7783756a b c d - 12631455a b c d + 14225976a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R - 11369148a b c d + 6477048a b c d - 2603151a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11 12 12
+--R 718060a b c d - 128850a b c d + 13500a b c d - 625a b c
+--R /
+--R 21
+--R 4096b
+--R ,
+--R 4
+--R *
+--R atan
+--R 5
+--R 8b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10
+--R - 83521a d + 766428a b c d - 3168018a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R 7783756a b c d - 12631455a b c d + 14225976a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R - 11369148a b c d + 6477048a b c d - 2603151a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R 718060a b c d - 128850a b c d + 13500a b c d
+--R +
+--R 12 12
+--R - 625a b c
+--R /
+--R 21
+--R 4096b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (17a d - 39a b c d + 27a b c d - 5b c )\|x
+--R +
+--R 4 3 8 3 3 4 2 6
+--R 180b d x + (- 340a b d + 780b c d )x
+--R +
+--R 2 2 3 3 2 4 2 4
+--R (884a b d - 2028a b c d + 1404b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 7956a b d + 18252a b c d - 12636a b c d + 2340b c )x - 9945a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 22815a b c d - 15795a b c d + 2925a b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 6 2 5
+--R 1170b x + 1170a b
+--R Type: Union(Expression(Integer),...)
+--E 1000
+
+--S 1001 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 4+-+
+--R (- 17a d + 39a b c d - 27a b c d + 5b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 5 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10
+--R - 83521a d + 766428a b c d - 3168018a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R 7783756a b c d - 12631455a b c d + 14225976a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R - 11369148a b c d + 6477048a b c d - 2603151a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11 12 12
+--R 718060a b c d - 128850a b c d + 13500a b c d - 625a b c
+--R /
+--R 21
+--R 4096b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (17a d - 39a b c d + 27a b c d - 5b c )\|x
+--R +
+--R 5
+--R 8b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10
+--R - 83521a d + 766428a b c d - 3168018a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R 7783756a b c d - 12631455a b c d + 14225976a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R - 11369148a b c d + 6477048a b c d - 2603151a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R 718060a b c d - 128850a b c d + 13500a b c d
+--R +
+--R 12 12
+--R - 625a b c
+--R /
+--R 21
+--R 4096b
+--R ,
+--R 4
+--R +
+--R -
+--R 5 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10
+--R - 83521a d + 766428a b c d - 3168018a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R 7783756a b c d - 12631455a b c d + 14225976a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R - 11369148a b c d + 6477048a b c d - 2603151a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R 718060a b c d - 128850a b c d + 13500a b c d
+--R +
+--R 12 12
+--R - 625a b c
+--R /
+--R 21
+--R 4096b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (17a d - 39a b c d + 27a b c d - 5b c )\|x
+--R +
+--R -
+--R 5
+--R 8b
+--R *
+--R ROOT
+--R 13 12 12 11
+--R - 83521a d + 766428a b c d
+--R +
+--R 11 2 2 10 10 3 3 9
+--R - 3168018a b c d + 7783756a b c d
+--R +
+--R 9 4 4 8 8 5 5 7
+--R - 12631455a b c d + 14225976a b c d
+--R +
+--R 7 6 6 6 6 7 7 5
+--R - 11369148a b c d + 6477048a b c d
+--R +
+--R 5 8 8 4 4 9 9 3
+--R - 2603151a b c d + 718060a b c d
+--R +
+--R 3 10 10 2 2 11 11 12 12
+--R - 128850a b c d + 13500a b c d - 625a b c
+--R /
+--R 21
+--R 4096b
+--R ,
+--R 4
+--R +
+--R 3 3 2 2 2 2 3 3 4+-+
+--R (17a d - 39a b c d + 27a b c d - 5b c )\|a
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 4+-+ \|2 \|b \|x + \|a
+--R (- 34a d + 78a b c d - 54a b c d + 10b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 4+-+ \|2 \|b \|x - \|a
+--R (- 34a d + 78a b c d - 54a b c d + 10b c )\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 5 +-+
+--R 16b \|2
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10
+--R - 83521a d + 766428a b c d - 3168018a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R 7783756a b c d - 12631455a b c d + 14225976a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R - 11369148a b c d + 6477048a b c d - 2603151a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R 718060a b c d - 128850a b c d + 13500a b c d
+--R +
+--R 12 12
+--R - 625a b c
+--R /
+--R 21
+--R 4096b
+--R ,
+--R 4
+--R *
+--R 4+-+
+--R \|b
+--R *
+--R atan
+--R 5
+--R 8b
+--R *
+--R ROOT
+--R 13 12 12 11 11 2 2 10
+--R - 83521a d + 766428a b c d - 3168018a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R 7783756a b c d - 12631455a b c d + 14225976a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R - 11369148a b c d + 6477048a b c d - 2603151a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R 718060a b c d - 128850a b c d + 13500a b c d
+--R +
+--R 12 12
+--R - 625a b c
+--R /
+--R 21
+--R 4096b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (17a d - 39a b c d + 27a b c d - 5b c )\|x
+--R /
+--R 5 +-+4+-+
+--R 8b \|2 \|b
+--R Type: Expression(Integer)
+--E 1001
+
+--S 1002 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1002
+
+)clear all
+
+--S 1003 of 1527
+t0:=x^(5/2)*(c+d*x^2)^3/(a+b*x^2)^2
+--R
+--R
+--R 3 8 2 6 2 4 3 2 +-+
+--R (d x + 3c d x + 3c d x + c x )\|x
+--R (1) -------------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1003
+
+--S 1004 of 1527
+r0:=1/154*d*(401*b^2*c^2-802*a*b*c*d+385*a^2*d^2)*x^(3/2)/b^4+15/22*d*_
+ x^(3/2)*(c+d*x^2)^2/b^2-1/2*x^(3/2)*(c+d*x^2)^3/(b*(a+b*x^2))+_
+ 3/154*d*x^(3/2)*(c*(11*b*c-15*a*d)+d*(51*b*c-55*a*d)*x^2)/b^3-_
+ 3/4*(b*c-5*a*d)*(b*c-a*d)^2*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(1/4)*b^(19/4)*sqrt(2))+3/4*(b*c-5*a*d)*(b*c-a*d)^2*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(19/4)*sqrt(2))+_
+ 3/8*(b*c-5*a*d)*(b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(1/4)*b^(19/4)*sqrt(2))-3/8*(b*c-5*a*d)*_
+ (b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(1/4)*b^(19/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (1155a b d - 2541a b c d + 1617a b c d - 231b c )x + 1155a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 2541a b c d + 1617a b c d - 231a b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 1155a b d + 2541a b c d - 1617a b c d + 231b c )x - 1155a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 2541a b c d - 1617a b c d + 231a b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 2310a b d + 5082a b c d - 3234a b c d + 462b c )x - 2310a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 5082a b c d - 3234a b c d + 462a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 2310a b d + 5082a b c d - 3234a b c d + 462b c )x - 2310a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 5082a b c d - 3234a b c d + 462a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 7 2 3 3 2 5
+--R 112b d x + (- 240a b d + 528b c d )x
+--R +
+--R 2 3 2 2 3 2 3
+--R (880a b d - 1936a b c d + 1232b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (1540a d - 3388a b c d + 2156a b c d - 308b c )x
+--R *
+--R +-+4+-+4+-+3 +-+
+--R \|2 \|a \|b \|x
+--R /
+--R 5 2 4 +-+4+-+4+-+3
+--R (616b x + 616a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1004
+
+--S 1005 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 2 4
+--R (- 154b x - 154a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 50625a d + 445500a b c d - 1753650a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 4067820a b c d - 6164991a b c d + 6396408a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 4628988a b c d + 2337336a b c d - 811215a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 187596a b c d - 27378a b c d + 2268a b c d - 81b c
+--R /
+--R 19
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 3375a d - 22275a b c d + 63180a b c d - 100332a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R 97362a b c d - 59130a b c d + 22140a b c d - 4860a b c d
+--R +
+--R 8 8 9 9
+--R 567a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 50625a d + 445500a b c d - 1753650a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 4067820a b c d - 6164991a b c d + 6396408a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 4628988a b c d + 2337336a b c d - 811215a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R 187596a b c d - 27378a b c d + 2268a b c d
+--R +
+--R 12 12
+--R - 81b c
+--R /
+--R 19
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 5 2 4
+--R (154b x + 154a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 50625a d + 445500a b c d - 1753650a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 4067820a b c d - 6164991a b c d + 6396408a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 4628988a b c d + 2337336a b c d - 811215a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 187596a b c d - 27378a b c d + 2268a b c d - 81b c
+--R /
+--R 19
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 3375a d - 22275a b c d + 63180a b c d - 100332a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R 97362a b c d - 59130a b c d + 22140a b c d - 4860a b c d
+--R +
+--R 8 8 9 9
+--R 567a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 14
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 50625a d + 445500a b c d - 1753650a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 4067820a b c d - 6164991a b c d + 6396408a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 4628988a b c d + 2337336a b c d - 811215a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R 187596a b c d - 27378a b c d + 2268a b c d
+--R +
+--R 12 12
+--R - 81b c
+--R /
+--R 19
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 5 2 4
+--R (- 308b x - 308a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 50625a d + 445500a b c d - 1753650a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 4067820a b c d - 6164991a b c d + 6396408a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 4628988a b c d + 2337336a b c d - 811215a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 187596a b c d - 27378a b c d + 2268a b c d - 81b c
+--R /
+--R 19
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R atan
+--R 14
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 50625a d + 445500a b c d - 1753650a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 4067820a b c d - 6164991a b c d + 6396408a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 4628988a b c d + 2337336a b c d - 811215a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R 187596a b c d - 27378a b c d + 2268a b c d
+--R +
+--R 12 12
+--R - 81b c
+--R /
+--R 19
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 3375a d - 22275a b c d + 63180a b c d - 100332a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R 97362a b c d - 59130a b c d + 22140a b c d - 4860a b c d
+--R +
+--R 8 8 9 9
+--R 567a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 3 3 7 2 3 3 2 5
+--R 28b d x + (- 60a b d + 132b c d )x
+--R +
+--R 2 3 2 2 3 2 3
+--R (220a b d - 484a b c d + 308b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (385a d - 847a b c d + 539a b c d - 77b c )x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 5 2 4
+--R 154b x + 154a b
+--R Type: Union(Expression(Integer),...)
+--E 1005
+
+--S 1006 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (- 15a d + 33a b c d - 21a b c d + 3b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 4 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 50625a d + 445500a b c d - 1753650a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 4067820a b c d - 6164991a b c d + 6396408a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 4628988a b c d + 2337336a b c d - 811215a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 187596a b c d - 27378a b c d + 2268a b c d - 81b c
+--R /
+--R 19
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 3375a d - 22275a b c d + 63180a b c d - 100332a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3
+--R 97362a b c d - 59130a b c d + 22140a b c d
+--R +
+--R 2 7 7 2 8 8 9 9
+--R - 4860a b c d + 567a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 50625a d + 445500a b c d - 1753650a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 4067820a b c d - 6164991a b c d + 6396408a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 4628988a b c d + 2337336a b c d - 811215a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R 187596a b c d - 27378a b c d + 2268a b c d
+--R +
+--R 12 12
+--R - 81b c
+--R /
+--R 19
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 50625a d + 445500a b c d - 1753650a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 4067820a b c d - 6164991a b c d + 6396408a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 4628988a b c d + 2337336a b c d - 811215a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 187596a b c d - 27378a b c d + 2268a b c d - 81b c
+--R /
+--R 19
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 3375a d - 22275a b c d + 63180a b c d - 100332a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R 97362a b c d - 59130a b c d + 22140a b c d - 4860a b c d
+--R +
+--R 8 8 9 9
+--R 567a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 14
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 50625a d + 445500a b c d - 1753650a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 4067820a b c d - 6164991a b c d + 6396408a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 4628988a b c d + 2337336a b c d - 811215a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R 187596a b c d - 27378a b c d + 2268a b c d
+--R +
+--R 12 12
+--R - 81b c
+--R /
+--R 19
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (15a d - 33a b c d + 21a b c d - 3b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x + \|a
+--R (30a d - 66a b c d + 42a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x - \|a
+--R (30a d - 66a b c d + 42a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 4 +-+
+--R 16b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 50625a d + 445500a b c d - 1753650a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 4067820a b c d - 6164991a b c d + 6396408a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 4628988a b c d + 2337336a b c d - 811215a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 187596a b c d - 27378a b c d + 2268a b c d - 81b c
+--R /
+--R 19
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 14
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 50625a d + 445500a b c d - 1753650a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 4067820a b c d - 6164991a b c d + 6396408a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 4628988a b c d + 2337336a b c d - 811215a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R 187596a b c d - 27378a b c d + 2268a b c d
+--R +
+--R 12 12
+--R - 81b c
+--R /
+--R 19
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 3375a d - 22275a b c d + 63180a b c d - 100332a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3
+--R 97362a b c d - 59130a b c d + 22140a b c d
+--R +
+--R 2 7 7 2 8 8 9 9
+--R - 4860a b c d + 567a b c d - 27b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 4 +-+4+-+4+-+3
+--R 8b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1006
+
+--S 1007 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1007
+
+)clear all
+
+--S 1008 of 1527
+t0:=x^(3/2)*(c+d*x^2)^3/(a+b*x^2)^2
+--R
+--R
+--R 3 7 2 5 2 3 3 +-+
+--R (d x + 3c d x + 3c d x + c x)\|x
+--R (1) ------------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1008
+
+--S 1009 of 1527
+r0:=-1/4*(b*c-13*a*d)*(b*c-a*d)^2*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(3/4)*b^(17/4)*sqrt(2))+1/4*(b*c-13*a*d)*(b*c-a*d)^2*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(17/4)*sqrt(2))-_
+ 1/8*(b*c-13*a*d)*(b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(17/4)*sqrt(2))+1/8*(b*c-_
+ 13*a*d)*(b*c-a*d)^2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(3/4)*b^(17/4)*sqrt(2))+1/90*d*(601*b^2*c^2-_
+ 1202*a*b*c*d+585*a^2*d^2)*sqrt(x)/b^4+13/18*d*(c+d*x^2)^2*_
+ sqrt(x)/b^2-1/2*(c+d*x^2)^3*sqrt(x)/(b*(a+b*x^2))+1/90*d*_
+ (c*(9*b*c-13*a*d)+d*(113*b*c-117*a*d)*x^2)*sqrt(x)/b^3
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 585a b d + 1215a b c d - 675a b c d + 45b c )x - 585a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 1215a b c d - 675a b c d + 45a b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (585a b d - 1215a b c d + 675a b c d - 45b c )x + 585a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 1215a b c d + 675a b c d - 45a b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 1170a b d + 2430a b c d - 1350a b c d + 90b c )x - 1170a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 2430a b c d - 1350a b c d + 90a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 1170a b d + 2430a b c d - 1350a b c d + 90b c )x - 1170a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 2430a b c d - 1350a b c d + 90a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 6 2 3 3 2 4
+--R 80b d x + (- 208a b d + 432b c d )x
+--R +
+--R 2 3 2 2 3 2 2 3 3 2 2
+--R (1872a b d - 3888a b c d + 2160b c d)x + 2340a d - 4860a b c d
+--R +
+--R 2 2 3 3
+--R 2700a b c d - 180b c
+--R *
+--R +-+4+-+3 4+-+ +-+
+--R \|2 \|a \|b \|x
+--R /
+--R 5 2 4 +-+4+-+3 4+-+
+--R (360b x + 360a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1009
+
+--S 1010 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 2 4
+--R (- 90b x - 90a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 28561a d + 237276a b c d - 871026a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 1853644a b c d - 2520207a b c d + 2272824a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 1365756a b c d + 535032a b c d - 130239a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 18412a b c d - 1458a b c d + 60a b c d - b c
+--R /
+--R 3 17
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (13a d - 27a b c d + 15a b c d - b c )\|x
+--R +
+--R 4
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 28561a d + 237276a b c d - 871026a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 1853644a b c d - 2520207a b c d + 2272824a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 1365756a b c d + 535032a b c d - 130239a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 18412a b c d - 1458a b c d + 60a b c d - b c
+--R /
+--R 3 17
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 5 2 4
+--R (90b x + 90a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 28561a d + 237276a b c d - 871026a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 1853644a b c d - 2520207a b c d + 2272824a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 1365756a b c d + 535032a b c d - 130239a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 18412a b c d - 1458a b c d + 60a b c d - b c
+--R /
+--R 3 17
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (13a d - 27a b c d + 15a b c d - b c )\|x
+--R +
+--R -
+--R 4
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 28561a d + 237276a b c d - 871026a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 1853644a b c d - 2520207a b c d + 2272824a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 1365756a b c d + 535032a b c d - 130239a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 18412a b c d - 1458a b c d + 60a b c d - b c
+--R /
+--R 3 17
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 5 2 4
+--R (180b x + 180a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 28561a d + 237276a b c d - 871026a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 1853644a b c d - 2520207a b c d + 2272824a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 1365756a b c d + 535032a b c d - 130239a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 18412a b c d - 1458a b c d + 60a b c d - b c
+--R /
+--R 3 17
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R atan
+--R 4
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 28561a d + 237276a b c d - 871026a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 1853644a b c d - 2520207a b c d + 2272824a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 1365756a b c d + 535032a b c d - 130239a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 18412a b c d - 1458a b c d + 60a b c d - b c
+--R /
+--R 3 17
+--R 4096a b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (13a d - 27a b c d + 15a b c d - b c )\|x
+--R +
+--R 3 3 6 2 3 3 2 4
+--R 20b d x + (- 52a b d + 108b c d )x
+--R +
+--R 2 3 2 2 3 2 2 3 3 2 2
+--R (468a b d - 972a b c d + 540b c d)x + 585a d - 1215a b c d
+--R +
+--R 2 2 3 3
+--R 675a b c d - 45b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 5 2 4
+--R 90b x + 90a b
+--R Type: Union(Expression(Integer),...)
+--E 1010
+
+--S 1011 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (13a d - 27a b c d + 15a b c d - b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 4 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 28561a d + 237276a b c d - 871026a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 1853644a b c d - 2520207a b c d + 2272824a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 1365756a b c d + 535032a b c d - 130239a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 18412a b c d - 1458a b c d + 60a b c d - b c
+--R /
+--R 3 17
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (13a d - 27a b c d + 15a b c d - b c )\|x
+--R +
+--R 4
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 28561a d + 237276a b c d - 871026a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 1853644a b c d - 2520207a b c d + 2272824a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 1365756a b c d + 535032a b c d - 130239a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 18412a b c d - 1458a b c d + 60a b c d - b c
+--R /
+--R 3 17
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 4 +-+
+--R 8b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 28561a d + 237276a b c d - 871026a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 1853644a b c d - 2520207a b c d + 2272824a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 1365756a b c d + 535032a b c d - 130239a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 18412a b c d - 1458a b c d + 60a b c d - b c
+--R /
+--R 3 17
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (13a d - 27a b c d + 15a b c d - b c )\|x
+--R +
+--R -
+--R 4
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 28561a d + 237276a b c d - 871026a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 1853644a b c d - 2520207a b c d + 2272824a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 1365756a b c d + 535032a b c d - 130239a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 18412a b c d - 1458a b c d + 60a b c d - b c
+--R /
+--R 3 17
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 13a d + 27a b c d - 15a b c d + b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x + \|a
+--R (26a d - 54a b c d + 30a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x - \|a
+--R (26a d - 54a b c d + 30a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 +-+
+--R 16b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 28561a d + 237276a b c d - 871026a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 1853644a b c d - 2520207a b c d + 2272824a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 1365756a b c d + 535032a b c d - 130239a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 18412a b c d - 1458a b c d + 60a b c d - b c
+--R /
+--R 3 17
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 4
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 28561a d + 237276a b c d - 871026a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 1853644a b c d - 2520207a b c d + 2272824a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 1365756a b c d + 535032a b c d - 130239a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 18412a b c d - 1458a b c d + 60a b c d - b c
+--R /
+--R 3 17
+--R 4096a b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (13a d - 27a b c d + 15a b c d - b c )\|x
+--R /
+--R 4 +-+4+-+3 4+-+
+--R 8b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1011
+
+--S 1012 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1012
+
+)clear all
+
+--S 1013 of 1527
+t0:=(c+d*x^2)^3*sqrt(x)/(a+b*x^2)^2
+--R
+--R
+--R 3 6 2 4 2 2 3 +-+
+--R (d x + 3c d x + 3c d x + c )\|x
+--R (1) -----------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1013
+
+--S 1014 of 1527
+r0:=-1/42*d*(15*b*c-11*a*d)*(3*b*c-7*a*d)*x^(3/2)/(a*b^3)+1/2*(b*c-a*d)*_
+ x^(3/2)*(c+d*x^2)^2/(a*b*(a+b*x^2))+1/14*d*x^(3/2)*(c*(b*c+3*a*d)-_
+ d*(7*b*c-11*a*d)*x^2)/(a*b^2)-1/4*(b*c-a*d)^2*(b*c+11*a*d)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(15/4)*sqrt(2))+_
+ 1/4*(b*c-a*d)^2*(b*c+11*a*d)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(5/4)*b^(15/4)*sqrt(2))+1/8*(b*c-a*d)^2*(b*c+11*a*d)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*_
+ b^(15/4)*sqrt(2))-1/8*(b*c-a*d)^2*(b*c+11*a*d)*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(15/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 231a b d + 441a b c d - 189a b c d - 21b c )x - 231a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 441a b c d - 189a b c d - 21a b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (231a b d - 441a b c d + 189a b c d + 21b c )x + 231a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 441a b c d + 189a b c d + 21a b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (462a b d - 882a b c d + 378a b c d + 42b c )x + 462a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 882a b c d + 378a b c d + 42a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (462a b d - 882a b c d + 378a b c d + 42b c )x + 462a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 882a b c d + 378a b c d + 42a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 5 2 3 2 2 3
+--R 48a b d x + (- 176a b d + 336a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 308a d + 588a b c d - 252a b c d + 84b c )x
+--R *
+--R +-+4+-+4+-+3 +-+
+--R \|2 \|a \|b \|x
+--R /
+--R 4 2 2 3 +-+4+-+4+-+3
+--R (168a b x + 168a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1014
+
+--S 1015 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 2 3
+--R (42a b x + 42a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 14641a d + 111804a b c d - 368082a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 676588a b c d - 746703a b c d + 486648a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4 3 9 9 3
+--R - 160188a b c d + 5688a b c d + 10017a b c d - 692a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 402a b c d - 36a b c d - b c
+--R /
+--R 5 15
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 1331a d - 7623a b c d + 17820a b c d - 21372a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R 13194a b c d - 3186a b c d - 372a b c d + 180a b c d
+--R +
+--R 8 8 9 9
+--R 27a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 11
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 14641a d + 111804a b c d - 368082a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 676588a b c d - 746703a b c d + 486648a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 160188a b c d + 5688a b c d + 10017a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 692a b c d - 402a b c d - 36a b c d - b c
+--R /
+--R 5 15
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 2 2 3
+--R (- 42a b x - 42a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 14641a d + 111804a b c d - 368082a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 676588a b c d - 746703a b c d + 486648a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4 3 9 9 3
+--R - 160188a b c d + 5688a b c d + 10017a b c d - 692a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 402a b c d - 36a b c d - b c
+--R /
+--R 5 15
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 1331a d - 7623a b c d + 17820a b c d - 21372a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R 13194a b c d - 3186a b c d - 372a b c d + 180a b c d
+--R +
+--R 8 8 9 9
+--R 27a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 11
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 14641a d + 111804a b c d - 368082a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 676588a b c d - 746703a b c d + 486648a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 160188a b c d + 5688a b c d + 10017a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 692a b c d - 402a b c d - 36a b c d - b c
+--R /
+--R 5 15
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 2 2 3
+--R (84a b x + 84a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 14641a d + 111804a b c d - 368082a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 676588a b c d - 746703a b c d + 486648a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4 3 9 9 3
+--R - 160188a b c d + 5688a b c d + 10017a b c d - 692a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 402a b c d - 36a b c d - b c
+--R /
+--R 5 15
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R atan
+--R 4 11
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 14641a d + 111804a b c d - 368082a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 676588a b c d - 746703a b c d + 486648a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 160188a b c d + 5688a b c d + 10017a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 692a b c d - 402a b c d - 36a b c d - b c
+--R /
+--R 5 15
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 1331a d - 7623a b c d + 17820a b c d - 21372a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R 13194a b c d - 3186a b c d - 372a b c d + 180a b c d
+--R +
+--R 8 8 9 9
+--R 27a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 3 5 2 3 2 2 3
+--R 12a b d x + (- 44a b d + 84a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 77a d + 147a b c d - 63a b c d + 21b c )x
+--R *
+--R +-+
+--R \|x
+--R /
+--R 4 2 2 3
+--R 42a b x + 42a b
+--R Type: Union(Expression(Integer),...)
+--E 1015
+
+--S 1016 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (11a d - 21a b c d + 9a b c d + b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 +-+
+--R 8a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 14641a d + 111804a b c d - 368082a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 676588a b c d - 746703a b c d + 486648a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4 3 9 9 3
+--R - 160188a b c d + 5688a b c d + 10017a b c d - 692a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 402a b c d - 36a b c d - b c
+--R /
+--R 5 15
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 1331a d - 7623a b c d + 17820a b c d - 21372a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R 13194a b c d - 3186a b c d - 372a b c d + 180a b c d
+--R +
+--R 8 8 9 9
+--R 27a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 11
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 14641a d + 111804a b c d - 368082a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 676588a b c d - 746703a b c d + 486648a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 160188a b c d + 5688a b c d + 10017a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 692a b c d - 402a b c d - 36a b c d - b c
+--R /
+--R 5 15
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 3 +-+
+--R 8a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 14641a d + 111804a b c d - 368082a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 676588a b c d - 746703a b c d + 486648a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4 3 9 9 3
+--R - 160188a b c d + 5688a b c d + 10017a b c d - 692a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 402a b c d - 36a b c d - b c
+--R /
+--R 5 15
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 1331a d - 7623a b c d + 17820a b c d - 21372a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R 13194a b c d - 3186a b c d - 372a b c d + 180a b c d
+--R +
+--R 8 8 9 9
+--R 27a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 4 11
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11
+--R - 14641a d + 111804a b c d
+--R +
+--R 10 2 2 10 9 3 3 9
+--R - 368082a b c d + 676588a b c d
+--R +
+--R 8 4 4 8 7 5 5 7
+--R - 746703a b c d + 486648a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 160188a b c d + 5688a b c d + 10017a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R - 692a b c d - 402a b c d - 36a b c d
+--R +
+--R 12 12
+--R - b c
+--R /
+--R 5 15
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 11a d + 21a b c d - 9a b c d - b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x + \|a
+--R (- 22a d + 42a b c d - 18a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x - \|a
+--R (- 22a d + 42a b c d - 18a b c d - 2b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+
+--R 16a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 14641a d + 111804a b c d - 368082a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 676588a b c d - 746703a b c d + 486648a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4 3 9 9 3
+--R - 160188a b c d + 5688a b c d + 10017a b c d - 692a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 402a b c d - 36a b c d - b c
+--R /
+--R 5 15
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 4 11
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 14641a d + 111804a b c d - 368082a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 676588a b c d - 746703a b c d + 486648a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 160188a b c d + 5688a b c d + 10017a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 692a b c d - 402a b c d - 36a b c d - b c
+--R /
+--R 5 15
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 1331a d - 7623a b c d + 17820a b c d - 21372a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R 13194a b c d - 3186a b c d - 372a b c d + 180a b c d
+--R +
+--R 8 8 9 9
+--R 27a b c d + b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3 +-+4+-+4+-+3
+--R 8a b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1016
+
+--S 1017 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1017
+
+)clear all
+
+--S 1018 of 1527
+t0:=(c+d*x^2)^3/((a+b*x^2)^2*sqrt(x))
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R Type: Expression(Integer)
+--E 1018
+
+--S 1019 of 1527
+r0:=-3/4*(b*c-a*d)^2*(b*c+3*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(7/4)*b^(13/4)*sqrt(2))+3/4*(b*c-a*d)^2*(b*c+3*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(13/4)*sqrt(2))-_
+ 3/8*(b*c-a*d)^2*(b*c+3*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(7/4)*b^(13/4)*sqrt(2))+3/8*(b*c-a*d)^2*_
+ (b*c+3*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(7/4)*b^(13/4)*sqrt(2))-1/10*d*(13*b*c-9*a*d)*_
+ (b*c-5*a*d)*sqrt(x)/(a*b^3)+1/2*(b*c-a*d)*(c+d*x^2)^2*_
+ sqrt(x)/(a*b*(a+b*x^2))+1/10*d*(c*(3*b*c+a*d)-d*(5*b*c-9*a*d)*_
+ x^2)*sqrt(x)/(a*b^2)
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (45a b d - 75a b c d + 15a b c d + 15b c )x + 45a d - 75a b c d
+--R +
+--R 2 2 2 3 3
+--R 15a b c d + 15a b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 45a b d + 75a b c d - 15a b c d - 15b c )x - 45a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 75a b c d - 15a b c d - 15a b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (90a b d - 150a b c d + 30a b c d + 30b c )x + 90a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 150a b c d + 30a b c d + 30a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (90a b d - 150a b c d + 30a b c d + 30b c )x + 90a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 150a b c d + 30a b c d + 30a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 4 2 3 2 2 2 3 3 2 2
+--R 16a b d x + (- 144a b d + 240a b c d )x - 180a d + 300a b c d
+--R +
+--R 2 2 3 3
+--R - 60a b c d + 20b c
+--R *
+--R +-+4+-+3 4+-+ +-+
+--R \|2 \|a \|b \|x
+--R /
+--R 4 2 2 3 +-+4+-+3 4+-+
+--R (40a b x + 40a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1019
+
+--S 1020 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 2 3
+--R (10a b x + 10a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 6561a d + 43740a b c d - 118098a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7 6 6 6 6
+--R 156492a b c d - 84159a b c d - 26568a b c d + 52164a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3 2 10 10 2
+--R - 11016a b c d - 10287a b c d + 3564a b c d + 1134a b c d
+--R +
+--R 11 11 12 12
+--R - 324a b c d - 81b c
+--R /
+--R 7 13
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (9a d - 15a b c d + 3a b c d + 3b c )\|x
+--R +
+--R 2 3
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 6561a d + 43740a b c d - 118098a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 156492a b c d - 84159a b c d - 26568a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R 52164a b c d - 11016a b c d - 10287a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 3564a b c d + 1134a b c d - 324a b c d - 81b c
+--R /
+--R 7 13
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 4 2 2 3
+--R (- 10a b x - 10a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 6561a d + 43740a b c d - 118098a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7 6 6 6 6
+--R 156492a b c d - 84159a b c d - 26568a b c d + 52164a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3 2 10 10 2
+--R - 11016a b c d - 10287a b c d + 3564a b c d + 1134a b c d
+--R +
+--R 11 11 12 12
+--R - 324a b c d - 81b c
+--R /
+--R 7 13
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (9a d - 15a b c d + 3a b c d + 3b c )\|x
+--R +
+--R -
+--R 2 3
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 6561a d + 43740a b c d - 118098a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 156492a b c d - 84159a b c d - 26568a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R 52164a b c d - 11016a b c d - 10287a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 3564a b c d + 1134a b c d - 324a b c d - 81b c
+--R /
+--R 7 13
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 4 2 2 3
+--R (- 20a b x - 20a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 6561a d + 43740a b c d - 118098a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7 6 6 6 6
+--R 156492a b c d - 84159a b c d - 26568a b c d + 52164a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3 2 10 10 2
+--R - 11016a b c d - 10287a b c d + 3564a b c d + 1134a b c d
+--R +
+--R 11 11 12 12
+--R - 324a b c d - 81b c
+--R /
+--R 7 13
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R atan
+--R 2 3
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 6561a d + 43740a b c d - 118098a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 156492a b c d - 84159a b c d - 26568a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R 52164a b c d - 11016a b c d - 10287a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 3564a b c d + 1134a b c d - 324a b c d - 81b c
+--R /
+--R 7 13
+--R 4096a b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (9a d - 15a b c d + 3a b c d + 3b c )\|x
+--R +
+--R 2 3 4 2 3 2 2 2 3 3 2 2
+--R 4a b d x + (- 36a b d + 60a b c d )x - 45a d + 75a b c d
+--R +
+--R 2 2 3 3
+--R - 15a b c d + 5b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 4 2 2 3
+--R 10a b x + 10a b
+--R Type: Union(Expression(Integer),...)
+--E 1020
+
+--S 1021 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (- 9a d + 15a b c d - 3a b c d - 3b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 +-+
+--R 8a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 6561a d + 43740a b c d - 118098a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7 6 6 6 6
+--R 156492a b c d - 84159a b c d - 26568a b c d + 52164a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3 2 10 10 2
+--R - 11016a b c d - 10287a b c d + 3564a b c d + 1134a b c d
+--R +
+--R 11 11 12 12
+--R - 324a b c d - 81b c
+--R /
+--R 7 13
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (9a d - 15a b c d + 3a b c d + 3b c )\|x
+--R +
+--R 2 3
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 6561a d + 43740a b c d - 118098a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 156492a b c d - 84159a b c d - 26568a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R 52164a b c d - 11016a b c d - 10287a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 3564a b c d + 1134a b c d - 324a b c d - 81b c
+--R /
+--R 7 13
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R -
+--R 3 +-+
+--R 8a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 6561a d + 43740a b c d - 118098a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 156492a b c d - 84159a b c d - 26568a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4 3 9 9 3
+--R 52164a b c d - 11016a b c d - 10287a b c d + 3564a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R 1134a b c d - 324a b c d - 81b c
+--R /
+--R 7 13
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (9a d - 15a b c d + 3a b c d + 3b c )\|x
+--R +
+--R -
+--R 2 3
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 6561a d + 43740a b c d - 118098a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 156492a b c d - 84159a b c d - 26568a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R 52164a b c d - 11016a b c d - 10287a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R 3564a b c d + 1134a b c d - 324a b c d
+--R +
+--R 12 12
+--R - 81b c
+--R /
+--R 7 13
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (9a d - 15a b c d + 3a b c d + 3b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x + \|a
+--R (- 18a d + 30a b c d - 6a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x - \|a
+--R (- 18a d + 30a b c d - 6a b c d - 6b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 3 +-+
+--R 16a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 6561a d + 43740a b c d - 118098a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 156492a b c d - 84159a b c d - 26568a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4 3 9 9 3
+--R 52164a b c d - 11016a b c d - 10287a b c d + 3564a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R 1134a b c d - 324a b c d - 81b c
+--R /
+--R 7 13
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 2 3
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 6561a d + 43740a b c d - 118098a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 156492a b c d - 84159a b c d - 26568a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R 52164a b c d - 11016a b c d - 10287a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R 3564a b c d + 1134a b c d - 324a b c d - 81b c
+--R /
+--R 7 13
+--R 4096a b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (9a d - 15a b c d + 3a b c d + 3b c )\|x
+--R /
+--R 3 +-+4+-+3 4+-+
+--R 8a b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1021
+
+--S 1022 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1022
+
+)clear all
+
+--S 1023 of 1527
+t0:=(c+d*x^2)^3/(x^(3/2)*(a+b*x^2)^2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R Type: Expression(Integer)
+--E 1023
+
+--S 1024 of 1527
+r0:=-1/6*d*(3*b*c-7*a*d)*(3*b*c+a*d)*x^(3/2)/(a^2*b^2)+1/4*(b*c-a*d)^2*_
+ (5*b*c+7*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*_
+ b^(11/4)*sqrt(2))-1/4*(b*c-a*d)^2*(5*b*c+7*a*d)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*b^(11/4)*sqrt(2))-_
+ 1/8*(b*c-a*d)^2*(5*b*c+7*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*b^(11/4)*sqrt(2))+_
+ 1/8*(b*c-a*d)^2*(5*b*c+7*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*b^(11/4)*sqrt(2))+_
+ 1/2*(b*c-a*d)*(c+d*x^2)^2/(a*b*(a+b*x^2)*sqrt(x))-_
+ 1/2*c*(c*(5*b*c-a*d)-d*(3*b*c-7*a*d)*x^2)/(a^2*b*sqrt(x))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (21a b d - 27a b c d - 9a b c d + 15b c )x + 21a d - 27a b c d
+--R +
+--R 2 2 2 3 3
+--R - 9a b c d + 15a b c
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (- 21a b d + 27a b c d + 9a b c d - 15b c )x - 21a d + 27a b c d
+--R +
+--R 2 2 2 3 3
+--R 9a b c d - 15a b c
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 42a b d + 54a b c d + 18a b c d - 30b c )x - 42a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 54a b c d + 18a b c d - 30a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x + \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 3 2 4 3 2 4 3
+--R (- 42a b d + 54a b c d + 18a b c d - 30b c )x - 42a d
+--R +
+--R 3 2 2 2 2 3 3
+--R 54a b c d + 18a b c d - 30a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x - \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 4 3 3 2 2 2 2 3 3 2 2 3
+--R (16a b d x + (28a d - 36a b c d + 36a b c d - 60b c )x - 48a b c )
+--R *
+--R +-+4+-+4+-+3
+--R \|2 \|a \|b
+--R /
+--R 2 3 2 3 2 +-+4+-+4+-+3 +-+
+--R (24a b x + 24a b )\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1024
+
+--S 1025 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 3 2
+--R (- 6a b x - 6a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 2401a d + 12348a b c d - 19698a b c d - 2324a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R 37665a b c d - 27144a b c d - 19068a b c d + 28728a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 1071a b c d - 11060a b c d + 3150a b c d + 1500a b c d
+--R +
+--R 12 12
+--R - 625b c
+--R /
+--R 9 11
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 343a d - 1323a b c d + 1260a b c d + 1140a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R - 2430a b c d + 342a b c d + 1308a b c d - 540a b c d
+--R +
+--R 8 8 9 9
+--R - 225a b c d + 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 8
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 2401a d + 12348a b c d - 19698a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 2324a b c d + 37665a b c d - 27144a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d + 28728a b c d - 1071a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R - 11060a b c d + 3150a b c d + 1500a b c d
+--R +
+--R 12 12
+--R - 625b c
+--R /
+--R 9 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 3 2 3 2
+--R (6a b x + 6a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 2401a d + 12348a b c d - 19698a b c d - 2324a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R 37665a b c d - 27144a b c d - 19068a b c d + 28728a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 1071a b c d - 11060a b c d + 3150a b c d + 1500a b c d
+--R +
+--R 12 12
+--R - 625b c
+--R /
+--R 9 11
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 343a d - 1323a b c d + 1260a b c d + 1140a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R - 2430a b c d + 342a b c d + 1308a b c d - 540a b c d
+--R +
+--R 8 8 9 9
+--R - 225a b c d + 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 8
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 2401a d + 12348a b c d - 19698a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 2324a b c d + 37665a b c d - 27144a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d + 28728a b c d - 1071a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R - 11060a b c d + 3150a b c d + 1500a b c d
+--R +
+--R 12 12
+--R - 625b c
+--R /
+--R 9 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 3 2 3 2
+--R (- 12a b x - 12a b )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 2401a d + 12348a b c d - 19698a b c d - 2324a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R 37665a b c d - 27144a b c d - 19068a b c d + 28728a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 1071a b c d - 11060a b c d + 3150a b c d + 1500a b c d
+--R +
+--R 12 12
+--R - 625b c
+--R /
+--R 9 11
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 7 8
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 2401a d + 12348a b c d - 19698a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 2324a b c d + 37665a b c d - 27144a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d + 28728a b c d - 1071a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R - 11060a b c d + 3150a b c d + 1500a b c d
+--R +
+--R 12 12
+--R - 625b c
+--R /
+--R 9 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 343a d - 1323a b c d + 1260a b c d + 1140a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R - 2430a b c d + 342a b c d + 1308a b c d - 540a b c d
+--R +
+--R 8 8 9 9
+--R - 225a b c d + 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 3 4 3 3 2 2 2 2 3 3 2 2 3
+--R 4a b d x + (7a d - 9a b c d + 9a b c d - 15b c )x - 12a b c
+--R /
+--R 2 3 2 3 2 +-+
+--R (6a b x + 6a b )\|x
+--R Type: Union(Expression(Integer),...)
+--E 1025
+
+--S 1026 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (- 7a d + 9a b c d + 3a b c d - 5b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 2 2 +-+
+--R 8a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 2401a d + 12348a b c d - 19698a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 2324a b c d + 37665a b c d - 27144a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d + 28728a b c d - 1071a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 11060a b c d + 3150a b c d + 1500a b c d - 625b c
+--R /
+--R 9 11
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 343a d - 1323a b c d + 1260a b c d + 1140a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R - 2430a b c d + 342a b c d + 1308a b c d - 540a b c d
+--R +
+--R 8 8 9 9
+--R - 225a b c d + 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 8
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 2401a d + 12348a b c d - 19698a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 2324a b c d + 37665a b c d - 27144a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d + 28728a b c d - 1071a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R - 11060a b c d + 3150a b c d + 1500a b c d
+--R +
+--R 12 12
+--R - 625b c
+--R /
+--R 9 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 +-+
+--R 8a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 2401a d + 12348a b c d - 19698a b c d - 2324a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R 37665a b c d - 27144a b c d - 19068a b c d + 28728a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R - 1071a b c d - 11060a b c d + 3150a b c d + 1500a b c d
+--R +
+--R 12 12
+--R - 625b c
+--R /
+--R 9 11
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 343a d - 1323a b c d + 1260a b c d + 1140a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R - 2430a b c d + 342a b c d + 1308a b c d - 540a b c d
+--R +
+--R 8 8 9 9
+--R - 225a b c d + 125b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 7 8
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 2401a d + 12348a b c d - 19698a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 2324a b c d + 37665a b c d - 27144a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d + 28728a b c d - 1071a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R - 11060a b c d + 3150a b c d + 1500a b c d
+--R +
+--R 12 12
+--R - 625b c
+--R /
+--R 9 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (7a d - 9a b c d - 3a b c d + 5b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x + \|a
+--R (14a d - 18a b c d - 6a b c d + 10b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x - \|a
+--R (14a d - 18a b c d - 6a b c d + 10b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R -
+--R 2 2 +-+
+--R 16a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 2401a d + 12348a b c d - 19698a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 2324a b c d + 37665a b c d - 27144a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d + 28728a b c d - 1071a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11 12 12
+--R - 11060a b c d + 3150a b c d + 1500a b c d - 625b c
+--R /
+--R 9 11
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 7 8
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 2401a d + 12348a b c d - 19698a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 2324a b c d + 37665a b c d - 27144a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d + 28728a b c d - 1071a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R - 11060a b c d + 3150a b c d + 1500a b c d
+--R +
+--R 12 12
+--R - 625b c
+--R /
+--R 9 11
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 343a d - 1323a b c d + 1260a b c d + 1140a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R - 2430a b c d + 342a b c d + 1308a b c d - 540a b c d
+--R +
+--R 8 8 9 9
+--R - 225a b c d + 125b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 2 2 +-+4+-+4+-+3
+--R 8a b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1026
+
+--S 1027 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1027
+
+)clear all
+
+--S 1028 of 1527
+t0:=(c+d*x^2)^3/(x^(5/2)*(a+b*x^2)^2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1028
+
+--S 1029 of 1527
+r0:=1/2*(b*c-a*d)*(c+d*x^2)^2/(a*b*x^(3/2)*(a+b*x^2))-1/6*c*(c*_
+ (7*b*c-3*a*d)-d*(b*c-5*a*d)*x^2)/(a^2*b*x^(3/2))+1/4*(b*c-a*d)^2*_
+ (7*b*c+5*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*_
+ b^(9/4)*sqrt(2))-1/4*(b*c-a*d)^2*(7*b*c+5*a*d)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*b^(9/4)*sqrt(2))+1/8*(b*c-_
+ a*d)^2*(7*b*c+5*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(11/4)*b^(9/4)*sqrt(2))-1/8*(b*c-a*d)^2*_
+ (7*b*c+5*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(11/4)*b^(9/4)*sqrt(2))-1/6*d*(b*c-5*a*d)*_
+ (b*c+3*a*d)*sqrt(x)/(a^2*b^2)
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 15a b d + 9a b c d + 27a b c d - 21b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 15a d + 9a b c d + 27a b c d - 21a b c )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 3
+--R (15a b d - 9a b c d - 27a b c d + 21b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (15a d - 9a b c d - 27a b c d + 21a b c )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 30a b d + 18a b c d + 54a b c d - 42b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 30a d + 18a b c d + 54a b c d - 42a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x + \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 30a b d + 18a b c d + 54a b c d - 42b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 30a d + 18a b c d + 54a b c d - 42a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x - \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 4 3 3 2 2 2 2 3 3 2 2 3
+--R (48a b d x + (60a d - 36a b c d + 36a b c d - 28b c )x - 16a b c )
+--R *
+--R +-+4+-+3 4+-+
+--R \|2 \|a \|b
+--R /
+--R 2 3 3 3 2 +-+4+-+3 4+-+ +-+
+--R (24a b x + 24a b x)\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1029
+
+--S 1030 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 3 3 2
+--R (- 6a b x - 6a b x)
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 625a d + 1500a b c d + 3150a b c d - 11060a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 1071a b c d + 28728a b c d - 19068a b c d - 27144a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R 37665a b c d - 2324a b c d - 19698a b c d + 12348a b c d
+--R +
+--R 12 12
+--R - 2401b c
+--R /
+--R 11 9
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (5a d - 3a b c d - 9a b c d + 7b c )\|x
+--R +
+--R 3 2
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 625a d + 1500a b c d + 3150a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 11060a b c d - 1071a b c d + 28728a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d - 27144a b c d + 37665a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R - 2324a b c d - 19698a b c d + 12348a b c d
+--R +
+--R 12 12
+--R - 2401b c
+--R /
+--R 11 9
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 2 3 3 3 2
+--R (6a b x + 6a b x)
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 625a d + 1500a b c d + 3150a b c d - 11060a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 1071a b c d + 28728a b c d - 19068a b c d - 27144a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R 37665a b c d - 2324a b c d - 19698a b c d + 12348a b c d
+--R +
+--R 12 12
+--R - 2401b c
+--R /
+--R 11 9
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (5a d - 3a b c d - 9a b c d + 7b c )\|x
+--R +
+--R -
+--R 3 2
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 625a d + 1500a b c d + 3150a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 11060a b c d - 1071a b c d + 28728a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d - 27144a b c d + 37665a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R - 2324a b c d - 19698a b c d + 12348a b c d
+--R +
+--R 12 12
+--R - 2401b c
+--R /
+--R 11 9
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 2 3 3 3 2
+--R (12a b x + 12a b x)
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 625a d + 1500a b c d + 3150a b c d - 11060a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 1071a b c d + 28728a b c d - 19068a b c d - 27144a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R 37665a b c d - 2324a b c d - 19698a b c d + 12348a b c d
+--R +
+--R 12 12
+--R - 2401b c
+--R /
+--R 11 9
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 3 2
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 625a d + 1500a b c d + 3150a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 11060a b c d - 1071a b c d + 28728a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d - 27144a b c d + 37665a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R - 2324a b c d - 19698a b c d + 12348a b c d
+--R +
+--R 12 12
+--R - 2401b c
+--R /
+--R 11 9
+--R 4096a b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (5a d - 3a b c d - 9a b c d + 7b c )\|x
+--R +
+--R 2 3 4 3 3 2 2 2 2 3 3 2 2 3
+--R 12a b d x + (15a d - 9a b c d + 9a b c d - 7b c )x - 4a b c
+--R /
+--R 2 3 3 3 2 +-+
+--R (6a b x + 6a b x)\|x
+--R Type: Union(Expression(Integer),...)
+--E 1030
+
+--S 1031 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (5a d - 3a b c d - 9a b c d + 7b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R 2 2 +-+
+--R 8a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 625a d + 1500a b c d + 3150a b c d - 11060a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 1071a b c d + 28728a b c d - 19068a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R - 27144a b c d + 37665a b c d - 2324a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 19698a b c d + 12348a b c d - 2401b c
+--R /
+--R 11 9
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (5a d - 3a b c d - 9a b c d + 7b c )\|x
+--R +
+--R 3 2
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 625a d + 1500a b c d + 3150a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 11060a b c d - 1071a b c d + 28728a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d - 27144a b c d + 37665a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R - 2324a b c d - 19698a b c d + 12348a b c d
+--R +
+--R 12 12
+--R - 2401b c
+--R /
+--R 11 9
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 2 2 +-+
+--R 8a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 625a d + 1500a b c d + 3150a b c d - 11060a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 1071a b c d + 28728a b c d - 19068a b c d - 27144a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R 37665a b c d - 2324a b c d - 19698a b c d + 12348a b c d
+--R +
+--R 12 12
+--R - 2401b c
+--R /
+--R 11 9
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (5a d - 3a b c d - 9a b c d + 7b c )\|x
+--R +
+--R -
+--R 3 2
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 625a d + 1500a b c d + 3150a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 11060a b c d - 1071a b c d + 28728a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d - 27144a b c d + 37665a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R - 2324a b c d - 19698a b c d + 12348a b c d
+--R +
+--R 12 12
+--R - 2401b c
+--R /
+--R 11 9
+--R 4096a b
+--R ,
+--R 4
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 5a d + 3a b c d + 9a b c d - 7b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x + \|a
+--R (10a d - 6a b c d - 18a b c d + 14b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x - \|a
+--R (10a d - 6a b c d - 18a b c d + 14b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 +-+
+--R 16a b \|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 625a d + 1500a b c d + 3150a b c d - 11060a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 1071a b c d + 28728a b c d - 19068a b c d - 27144a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2 11 11
+--R 37665a b c d - 2324a b c d - 19698a b c d + 12348a b c d
+--R +
+--R 12 12
+--R - 2401b c
+--R /
+--R 11 9
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 3 2
+--R 8a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 625a d + 1500a b c d + 3150a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R - 11060a b c d - 1071a b c d + 28728a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R - 19068a b c d - 27144a b c d + 37665a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R - 2324a b c d - 19698a b c d + 12348a b c d
+--R +
+--R 12 12
+--R - 2401b c
+--R /
+--R 11 9
+--R 4096a b
+--R ,
+--R 4
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (5a d - 3a b c d - 9a b c d + 7b c )\|x
+--R /
+--R 2 2 +-+4+-+3 4+-+
+--R 8a b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1031
+
+--S 1032 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1032
+
+)clear all
+
+--S 1033 of 1527
+t0:=(c+d*x^2)^3/(x^(7/2)*(a+b*x^2)^2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1033
+
+--S 1034 of 1527
+r0:=1/2*(b*c-a*d)*(c+d*x^2)^2/(a*b*x^(5/2)*(a+b*x^2))-1/10*c*(c*(9*b*c-_
+ 5*a*d)+d*(b*c+3*a*d)*x^2)/(a^2*b*x^(5/2))-3/4*(b*c-a*d)^2*(3*b*c+_
+ a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*b^(7/4)*_
+ sqrt(2))+3/4*(b*c-a*d)^2*(3*b*c+a*d)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(13/4)*b^(7/4)*sqrt(2))+3/8*(b*c-a*d)^2*_
+ (3*b*c+a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(13/4)*b^(7/4)*sqrt(2))-3/8*(b*c-a*d)^2*(3*b*c+_
+ a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(13/4)*b^(7/4)*sqrt(2))+1/10*c*(9*b*c-13*a*d)*(5*b*c-a*d)/_
+ (a^3*b*sqrt(x))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 4
+--R (- 15a b d - 15a b c d + 75a b c d - 45b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 2
+--R (- 15a d - 15a b c d + 75a b c d - 45a b c )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 4
+--R (15a b d + 15a b c d - 75a b c d + 45b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 2
+--R (15a d + 15a b c d - 75a b c d + 45a b c )x
+--R *
+--R +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 4
+--R (30a b d + 30a b c d - 150a b c d + 90b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 2
+--R (30a d + 30a b c d - 150a b c d + 90a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x + \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 3 2 4 3 4
+--R (30a b d + 30a b c d - 150a b c d + 90b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 2
+--R (30a d + 30a b c d - 150a b c d + 90a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R +-+ \|2 \|b \|x - \|a
+--R \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 20a d + 60a b c d - 300a b c d + 180b c )x
+--R +
+--R 2 2 2 3 2 2 3
+--R (- 240a b c d + 144a b c )x - 16a b c
+--R *
+--R +-+4+-+4+-+3
+--R \|2 \|a \|b
+--R /
+--R 3 2 4 4 2 +-+4+-+4+-+3 +-+
+--R (40a b x + 40a b x )\|2 \|a \|b \|x
+--R Type: Expression(Integer)
+--E 1034
+
+--S 1035 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 4 2
+--R (10a b x + 10a b x )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 81a d - 324a b c d + 1134a b c d + 3564a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 10287a b c d - 11016a b c d + 52164a b c d - 26568a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2
+--R - 84159a b c d + 156492a b c d - 118098a b c d
+--R +
+--R 11 11 12 12
+--R 43740a b c d - 6561b c
+--R /
+--R 13 7
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R 27a d + 81a b c d - 324a b c d - 540a b c d + 2106a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8
+--R - 162a b c d - 5076a b c d + 6804a b c d - 3645a b c d
+--R +
+--R 9 9
+--R 729b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 5
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 81a d - 324a b c d + 1134a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 3564a b c d - 10287a b c d - 11016a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R 52164a b c d - 26568a b c d - 84159a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R 156492a b c d - 118098a b c d + 43740a b c d
+--R +
+--R 12 12
+--R - 6561b c
+--R /
+--R 13 7
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 4 4 2
+--R (- 10a b x - 10a b x )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 81a d - 324a b c d + 1134a b c d + 3564a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 10287a b c d - 11016a b c d + 52164a b c d - 26568a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2
+--R - 84159a b c d + 156492a b c d - 118098a b c d
+--R +
+--R 11 11 12 12
+--R 43740a b c d - 6561b c
+--R /
+--R 13 7
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R 27a d + 81a b c d - 324a b c d - 540a b c d + 2106a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8
+--R - 162a b c d - 5076a b c d + 6804a b c d - 3645a b c d
+--R +
+--R 9 9
+--R 729b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 10 5
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 81a d - 324a b c d + 1134a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 3564a b c d - 10287a b c d - 11016a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R 52164a b c d - 26568a b c d - 84159a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R 156492a b c d - 118098a b c d + 43740a b c d
+--R +
+--R 12 12
+--R - 6561b c
+--R /
+--R 13 7
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 4 4 2
+--R (20a b x + 20a b x )
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 81a d - 324a b c d + 1134a b c d + 3564a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 10287a b c d - 11016a b c d + 52164a b c d - 26568a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2
+--R - 84159a b c d + 156492a b c d - 118098a b c d
+--R +
+--R 11 11 12 12
+--R 43740a b c d - 6561b c
+--R /
+--R 13 7
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 10 5
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 81a d - 324a b c d + 1134a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 3564a b c d - 10287a b c d - 11016a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R 52164a b c d - 26568a b c d - 84159a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R 156492a b c d - 118098a b c d + 43740a b c d
+--R +
+--R 12 12
+--R - 6561b c
+--R /
+--R 13 7
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R 27a d + 81a b c d - 324a b c d - 540a b c d + 2106a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8
+--R - 162a b c d - 5076a b c d + 6804a b c d - 3645a b c d
+--R +
+--R 9 9
+--R 729b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 5a d + 15a b c d - 75a b c d + 45b c )x
+--R +
+--R 2 2 2 3 2 2 3
+--R (- 60a b c d + 36a b c )x - 4a b c
+--R /
+--R 3 2 4 4 2 +-+
+--R (10a b x + 10a b x )\|x
+--R Type: Union(Expression(Integer),...)
+--E 1035
+
+--S 1036 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (3a d + 3a b c d - 15a b c d + 9b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 +-+
+--R 8a b\|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 81a d - 324a b c d + 1134a b c d + 3564a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 10287a b c d - 11016a b c d + 52164a b c d - 26568a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2
+--R - 84159a b c d + 156492a b c d - 118098a b c d
+--R +
+--R 11 11 12 12
+--R 43740a b c d - 6561b c
+--R /
+--R 13 7
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R 27a d + 81a b c d - 324a b c d - 540a b c d + 2106a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8
+--R - 162a b c d - 5076a b c d + 6804a b c d - 3645a b c d
+--R +
+--R 9 9
+--R 729b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 5
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 81a d - 324a b c d + 1134a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 3564a b c d - 10287a b c d - 11016a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R 52164a b c d - 26568a b c d - 84159a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R 156492a b c d - 118098a b c d + 43740a b c d
+--R +
+--R 12 12
+--R - 6561b c
+--R /
+--R 13 7
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R -
+--R 3 +-+
+--R 8a b\|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 81a d - 324a b c d + 1134a b c d + 3564a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6
+--R - 10287a b c d - 11016a b c d + 52164a b c d
+--R +
+--R 5 7 7 5 4 8 8 4 3 9 9 3
+--R - 26568a b c d - 84159a b c d + 156492a b c d
+--R +
+--R 2 10 10 2 11 11 12 12
+--R - 118098a b c d + 43740a b c d - 6561b c
+--R /
+--R 13 7
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 9 9 8 8 7 2 2 7 6 3 3 6
+--R 27a d + 81a b c d - 324a b c d - 540a b c d
+--R +
+--R 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
+--R 2106a b c d - 162a b c d - 5076a b c d + 6804a b c d
+--R +
+--R 8 8 9 9
+--R - 3645a b c d + 729b c
+--R *
+--R +-+
+--R \|x
+--R +
+--R -
+--R 10 5
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 81a d - 324a b c d + 1134a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 3564a b c d - 10287a b c d - 11016a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R 52164a b c d - 26568a b c d - 84159a b c d
+--R +
+--R 3 9 9 3 2 10 10 2
+--R 156492a b c d - 118098a b c d
+--R +
+--R 11 11 12 12
+--R 43740a b c d - 6561b c
+--R /
+--R 13 7
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 3a d - 3a b c d + 15a b c d - 9b c )
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x + \|a
+--R (- 6a d - 6a b c d + 30a b c d - 18b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 2 2 2 2 3 3 \|2 \|b \|x - \|a
+--R (- 6a d - 6a b c d + 30a b c d - 18b c )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+
+--R 16a b\|2
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10 9 3 3 9
+--R - 81a d - 324a b c d + 1134a b c d + 3564a b c d
+--R +
+--R 8 4 4 8 7 5 5 7 6 6 6 6 5 7 7 5
+--R - 10287a b c d - 11016a b c d + 52164a b c d - 26568a b c d
+--R +
+--R 4 8 8 4 3 9 9 3 2 10 10 2
+--R - 84159a b c d + 156492a b c d - 118098a b c d
+--R +
+--R 11 11 12 12
+--R 43740a b c d - 6561b c
+--R /
+--R 13 7
+--R 4096a b
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 10 5
+--R 512a b
+--R *
+--R ROOT
+--R 12 12 11 11 10 2 2 10
+--R - 81a d - 324a b c d + 1134a b c d
+--R +
+--R 9 3 3 9 8 4 4 8 7 5 5 7
+--R 3564a b c d - 10287a b c d - 11016a b c d
+--R +
+--R 6 6 6 6 5 7 7 5 4 8 8 4
+--R 52164a b c d - 26568a b c d - 84159a b c d
+--R +
+--R 3 9 9 3 2 10 10 2 11 11
+--R 156492a b c d - 118098a b c d + 43740a b c d
+--R +
+--R 12 12
+--R - 6561b c
+--R /
+--R 13 7
+--R 4096a b
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5
+--R 27a d + 81a b c d - 324a b c d - 540a b c d + 2106a b c d
+--R +
+--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8
+--R - 162a b c d - 5076a b c d + 6804a b c d - 3645a b c d
+--R +
+--R 9 9
+--R 729b c
+--R *
+--R +-+
+--R \|x
+--R /
+--R 3 +-+4+-+4+-+3
+--R 8a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1036
+
+--S 1037 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1037
+
+)clear all
+
+--S 1038 of 1527
+t0:=x^(7/2)/((a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) --------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Expression(Integer)
+--E 1038
+
+--S 1039 of 1527
+r0:=1/4*a^(1/4)*(5*b*c-a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (b^(5/4)*(b*c-a*d)^2*sqrt(2))-1/4*a^(1/4)*(5*b*c-a*d)*atan(1+_
+ b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(5/4)*(b*c-a*d)^2*sqrt(2))-_
+ c^(5/4)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(d^(1/4)*(b*c-_
+ a*d)^2*sqrt(2))+c^(5/4)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (d^(1/4)*(b*c-a*d)^2*sqrt(2))+1/8*a^(1/4)*(5*b*c-a*d)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(5/4)*_
+ (b*c-a*d)^2*sqrt(2))-1/8*a^(1/4)*(5*b*c-a*d)*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(5/4)*(b*c-a*d)^2*_
+ sqrt(2))-1/2*c^(5/4)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(d^(1/4)*(b*c-a*d)^2*sqrt(2))+1/2*c^(5/4)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (d^(1/4)*(b*c-a*d)^2*sqrt(2))+1/2*a*sqrt(x)/(b*(b*c-a*d)*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (4b c x + 4a b c)\|b \|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 4+-+4+-+
+--R ((a b d - 5b c)x + a d - 5a b c)\|a \|d
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 4+-+4+-+
+--R ((- a b d + 5b c)x - a d + 5a b c)\|a \|d
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 4b c x - 4a b c)\|b \|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|d \|x + \|c
+--R (8b c x + 8a b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|d \|x - \|c
+--R (8b c x + 8a b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+4+-+ \|2 \|b \|x + \|a
+--R ((2a b d - 10b c)x + 2a d - 10a b c)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+4+-+ \|2 \|b \|x - \|a
+--R ((2a b d - 10b c)x + 2a d - 10a b c)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+4+-+ +-+
+--R (- 4a d + 4a b c)\|2 \|b \|d \|x
+--R /
+--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +-+4+-+
+--R ((8a b d - 16a b c d + 8b c )x + 8a b d - 16a b c d + 8a b c )\|2 \|b
+--R *
+--R 4+-+
+--R \|d
+--R Type: Expression(Integer)
+--E 1039
+
+--S 1040 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2
+--R ((2a b d - 2b c)x + 2a b d - 2a b c)
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625a b c
+--R /
+--R 8 5 8 7 6 7 6 7 2 6 5 8 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 9 4 4 3 10 5 3 2 11 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 12 7 13 8
+--R - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R (a d - 5b c)\|x
+--R +
+--R 2 2 2 3 2
+--R (8a b d - 16a b c d + 8b c )
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625a b c
+--R /
+--R 8 5 8 7 6 7 6 7 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 5 8 3 5 4 9 4 4 3 10 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 11 6 2 12 7 13 8
+--R 114688a b c d - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R +
+--R 2 3 2 2 2
+--R ((- 2a b d + 2b c)x - 2a b d + 2a b c)
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625a b c
+--R /
+--R 8 5 8 7 6 7 6 7 2 6 5 8 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 9 4 4 3 10 5 3 2 11 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 12 7 13 8
+--R - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R (a d - 5b c)\|x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b d + 16a b c d - 8b c )
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625a b c
+--R /
+--R 8 5 8 7 6 7 6 7 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 5 8 3 5 4 9 4 4 3 10 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 11 6 2 12 7 13 8
+--R 114688a b c d - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R +
+--R 2 3 2 2 2
+--R ((2a b d - 2b c)x + 2a b d - 2a b c)
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 8 9 7 8 6 2 2 7 5 3 3 6
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 5 3 5 5 4 2 6 6 3 7 7 2
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c d
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R c\|x
+--R +
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 8 9 7 8 6 2 2 7 5 3 3 6
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 5 3 5 5 4 2 6 6 3 7 7 2
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c d
+--R ,
+--R 4
+--R +
+--R 2 3 2 2 2
+--R ((- 2a b d + 2b c)x - 2a b d + 2a b c)
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 8 9 7 8 6 2 2 7 5 3 3 6
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 5 3 5 5 4 2 6 6 3 7 7 2
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c d
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R c\|x
+--R +
+--R 2 2 2 2
+--R (- 2a d + 4a b c d - 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 8 9 7 8 6 2 2 7 5 3 3 6
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 5 3 5 5 4 2 6 6 3 7 7 2
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c d
+--R ,
+--R 4
+--R +
+--R 2 3 2 2 2
+--R ((- 4a b d + 4b c)x - 4a b d + 4a b c)
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 8 9 7 8 6 2 2 7 5 3 3 6
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 5 3 5 5 4 2 6 6 3 7 7 2
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 8 9 7 8 6 2 2 7 5 3 3 6
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 5 3 5 5 4 2 6 6 3 7 7 2
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c d
+--R ,
+--R 4
+--R /
+--R +-+
+--R c\|x
+--R +
+--R 2 3 2 2 2
+--R ((- 4a b d + 4b c)x - 4a b d + 4a b c)
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625a b c
+--R /
+--R 8 5 8 7 6 7 6 7 2 6 5 8 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 9 4 4 3 10 5 3 2 11 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 12 7 13 8
+--R - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 2 2 2 3 2
+--R (8a b d - 16a b c d + 8b c )
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625a b c
+--R /
+--R 8 5 8 7 6 7 6 7 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 5 8 3 5 4 9 4 4 3 10 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 11 6 2 12 7 13 8
+--R 114688a b c d - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R /
+--R +-+
+--R (a d - 5b c)\|x
+--R +
+--R +-+
+--R - a\|x
+--R /
+--R 2 3 2 2 2
+--R (2a b d - 2b c)x + 2a b d - 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 1040
+
+--S 1041 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 4b c\|b \|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d + 5b c)\|a \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 +-+
+--R (8a b d - 16a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625a b c
+--R /
+--R 8 5 8 7 6 7 6 7 2 6 5 8 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 9 4 4 3 10 5 3 2 11 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 12 7 13 8
+--R - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R +-+
+--R (a d - 5b c)\|x
+--R +
+--R 2 2 2 3 2
+--R (8a b d - 16a b c d + 8b c )
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625a b c
+--R /
+--R 8 5 8 7 6 7 6 7 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 5 8 3 5 4 9 4 4 3 10 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 11 6 2 12 7 13 8
+--R 114688a b c d - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R +
+--R 2 2 2 3 2 +-+
+--R (- 8a b d + 16a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625a b c
+--R /
+--R 8 5 8 7 6 7 6 7 2 6 5 8 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 9 4 4 3 10 5 3 2 11 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 12 7 13 8
+--R - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R +-+
+--R (a d - 5b c)\|x
+--R +
+--R 2 2 2 3 2
+--R (- 8a b d + 16a b c d - 8b c )
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625a b c
+--R /
+--R 8 5 8 7 6 7 6 7 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 5 8 3 5 4 9 4 4 3 10 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 11 6 2 12 7 13 8
+--R 114688a b c d - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R +
+--R 2 2 2 3 2 +-+
+--R (8a b d - 16a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 8 9 7 8 6 2 2 7 5 3 3 6
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 5 3 5 5 4 2 6 6 3 7 7 2
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R +-+
+--R c\|x
+--R +
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 8 9 7 8 6 2 2 7 5 3 3 6
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 5 3 5 5 4 2 6 6 3 7 7 2
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c d
+--R ,
+--R 4
+--R +
+--R 2 2 2 3 2 +-+
+--R (- 8a b d + 16a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 8 9 7 8 6 2 2 7 5 3 3 6
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 5 3 5 5 4 2 6 6 3 7 7 2
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R +-+
+--R c\|x
+--R +
+--R 2 2 2 2
+--R (- 2a d + 4a b c d - 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 8 9 7 8 6 2 2 7 5 3 3 6
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 5 3 5 5 4 2 6 6 3 7 7 2
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c d
+--R ,
+--R 4
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d - 5b c)\|a \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 4b c\|b \|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R - 8b c\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R - 8b c\|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a
+--R (- 2a d + 10b c)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x - \|a
+--R (- 2a d + 10b c)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 3 2 +-+
+--R (- 16a b d + 32a b c d - 16b c )\|2
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 8 9 7 8 6 2 2 7 5 3 3 6
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 5 3 5 5 4 2 6 6 3 7 7 2
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c d
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R atan
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 8 9 7 8 6 2 2 7 5 3 3 6
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 5 3 5 5 4 2 6 6 3 7 7 2
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c d
+--R ,
+--R 4
+--R /
+--R +-+
+--R c\|x
+--R +
+--R 2 2 2 3 2 +-+
+--R (- 16a b d + 32a b c d - 16b c )\|2
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625a b c
+--R /
+--R 8 5 8 7 6 7 6 7 2 6 5 8 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 4 9 4 4 3 10 5 3 2 11 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 12 7 13 8
+--R - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R atan
+--R 2 2 2 3 2
+--R (8a b d - 16a b c d + 8b c )
+--R *
+--R ROOT
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d + 20a b c d - 150a b c d + 500a b c d - 625a b c
+--R /
+--R 8 5 8 7 6 7 6 7 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 5 8 3 5 4 9 4 4 3 10 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 2 11 6 2 12 7 13 8
+--R 114688a b c d - 32768a b c d + 4096b c
+--R ,
+--R 4
+--R /
+--R +-+
+--R (a d - 5b c)\|x
+--R /
+--R 2 2 2 3 2 +-+4+-+4+-+
+--R (8a b d - 16a b c d + 8b c )\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 1041
+
+--S 1042 of 1527
+--d0:=D(m0,x)
+--E 1042
+
+)clear all
+
+--S 1043 of 1527
+t0:=x^(5/2)/((a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) --------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Expression(Integer)
+--E 1043
+
+--S 1044 of 1527
+r0:=-1/2*x^(3/2)/((b*c-a*d)*(a+b*x^2))-1/4*(3*b*c+a*d)*atan(1-b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(3/4)*(b*c-a*d)^2*sqrt(2))+_
+ 1/4*(3*b*c+a*d)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(1/4)*b^(3/4)*(b*c-a*d)^2*sqrt(2))+c^(3/4)*d^(1/4)*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/((b*c-a*d)^2*sqrt(2))-_
+ c^(3/4)*d^(1/4)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/((b*c-_
+ a*d)^2*sqrt(2))+1/8*(3*b*c+a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(3/4)*(b*c-a*d)^2*_
+ sqrt(2))-1/8*(3*b*c+a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(1/4)*b^(3/4)*(b*c-a*d)^2*sqrt(2))-_
+ 1/2*c^(3/4)*d^(1/4)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/((b*c-a*d)^2*sqrt(2))+1/2*c^(3/4)*d^(1/4)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ ((b*c-a*d)^2*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 4+-+4+-+3 4+-+3 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (4b x + 4a)\|a \|b \|c \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((- a b d - 3b c)x - a d - 3a b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((a b d + 3b c)x + a d + 3a b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4+-+4+-+3 4+-+3 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 4b x - 4a)\|a \|b \|c \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+4+-+3 4+-+3 4+-+ \|2 \|d \|x + \|c
+--R (- 8b x - 8a)\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+4+-+3 4+-+3 4+-+ \|2 \|d \|x - \|c
+--R (- 8b x - 8a)\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x + \|a
+--R ((2a b d + 6b c)x + 2a d + 6a b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x - \|a
+--R ((2a b d + 6b c)x + 2a d + 6a b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+4+-+3 +-+
+--R (4a d - 4b c)x\|2 \|a \|b \|x
+--R /
+--R 2 2 2 3 2 2 3 2 2 2 2 +-+4+-+
+--R ((8a b d - 16a b c d + 8b c )x + 8a d - 16a b c d + 8a b c )\|2 \|a
+--R *
+--R 4+-+3
+--R \|b
+--R Type: Expression(Integer)
+--E 1044
+
+--S 1045 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2
+--R ((2a b d - 2b c)x + 2a d - 2a b c)
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 11 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d + 9a b c d + 27a b c d + 27b c )\|x
+--R +
+--R 7 2 6 6 3 5 5 4 2 4 4 5 3 3
+--R 512a b d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 3 6 4 2 2 7 5 8 6
+--R 7680a b c d - 3072a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 9 3 8 8 4 7 7 5 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 6 6 3 5 5 7 4 4 4 8 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 3 9 6 2 2 10 7 11 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2
+--R ((- 2a b d + 2b c)x - 2a d + 2a b c)
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 11 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d + 9a b c d + 27a b c d + 27b c )\|x
+--R +
+--R 7 2 6 6 3 5 5 4 2 4 4 5 3 3
+--R - 512a b d + 3072a b c d - 7680a b c d + 10240a b c d
+--R +
+--R 3 6 4 2 2 7 5 8 6
+--R - 7680a b c d + 3072a b c d - 512a b c
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 9 3 8 8 4 7 7 5 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 6 6 3 5 5 7 4 4 4 8 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 3 9 6 2 2 10 7 11 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2
+--R ((- 2a b d + 2b c)x - 2a d + 2a b c)
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R 2 +-+
+--R c d\|x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 8a d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 5 6 6
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 7 8 8
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2
+--R ((2a b d - 2b c)x + 2a d - 2a b c)
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R 2 +-+
+--R c d\|x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R - 8a d + 48a b c d - 120a b c d + 160a b c d - 120a b c d
+--R +
+--R 5 5 6 6
+--R 48a b c d - 8b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 7 8 8
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2
+--R ((- 4a b d + 4b c)x - 4a d + 4a b c)
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 8a d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 5 6 6
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 7 8 8
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 2 +-+
+--R c d\|x
+--R +
+--R 2 2 2
+--R ((4a b d - 4b c)x + 4a d - 4a b c)
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 11 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 7 2 6 6 3 5 5 4 2 4 4 5 3 3
+--R 512a b d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 3 6 4 2 2 7 5 8 6
+--R 7680a b c d - 3072a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 9 3 8 8 4 7 7 5 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 6 6 3 5 5 7 4 4 4 8 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 3 9 6 2 2 10 7 11 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d + 9a b c d + 27a b c d + 27b c )\|x
+--R +
+--R +-+
+--R x\|x
+--R /
+--R 2 2 2
+--R (2a b d - 2b c)x + 2a d - 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 1045
+
+--S 1046 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+3 4+-+3 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 4\|a \|b \|c \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d + 3b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 +-+
+--R (8a d - 16a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 11 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d + 9a b c d + 27a b c d + 27b c )\|x
+--R +
+--R 7 2 6 6 3 5 5 4 2 4 4 5 3 3
+--R 512a b d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 3 6 4 2 2 7 5 8 6
+--R 7680a b c d - 3072a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 9 3 8 8 4 7 7 5 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 6 6 3 5 5 7 4 4 4 8 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 3 9 6 2 2 10 7 11 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 11 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d + 9a b c d + 27a b c d + 27b c )\|x
+--R +
+--R 7 2 6 6 3 5 5 4 2 4 4 5 3 3
+--R - 512a b d + 3072a b c d - 7680a b c d + 10240a b c d
+--R +
+--R 3 6 4 2 2 7 5 8 6
+--R - 7680a b c d + 3072a b c d - 512a b c
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 9 3 8 8 4 7 7 5 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 6 6 3 5 5 7 4 4 4 8 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 3 9 6 2 2 10 7 11 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 2 +-+
+--R c d\|x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 8a d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 5 6 6
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 7 8 8
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 2 +-+
+--R (8a d - 16a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R log
+--R 2 +-+
+--R c d\|x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R - 8a d + 48a b c d - 120a b c d + 160a b c d - 120a b c d
+--R +
+--R 5 5 6 6
+--R 48a b c d - 8b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 7 8 8
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d - 3b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+3 4+-+3 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 4\|a \|b \|c \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+3 4+-+3 4+-+ \|2 \|d \|x + \|c
+--R 8\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+3 4+-+3 4+-+ \|2 \|d \|x - \|c
+--R 8\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 2a d - 6b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 2a d - 6b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 +-+
+--R (- 16a d + 32a b c d - 16b c )\|2
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2
+--R 8a d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 5 6 6
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 7 8 8
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 2 +-+
+--R c d\|x
+--R +
+--R 2 2 2 2 +-+
+--R (16a d - 32a b c d + 16b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 9 3 8 8 4 7 7 5 2 6 6 6 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 5 7 4 4 4 8 5 3 3 9 6 2 2 10 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 11 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+3
+--R \|a \|b
+--R *
+--R atan
+--R 7 2 6 6 3 5 5 4 2 4 4 5 3 3
+--R 512a b d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 3 6 4 2 2 7 5 8 6
+--R 7680a b c d - 3072a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - a d - 12a b c d - 54a b c d - 108a b c d - 81b c
+--R /
+--R 9 3 8 8 4 7 7 5 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 6 6 3 5 5 7 4 4 4 8 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 3 9 6 2 2 10 7 11 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 2 3 3 +-+
+--R (a d + 9a b c d + 27a b c d + 27b c )\|x
+--R /
+--R 2 2 2 2 +-+4+-+4+-+3
+--R (8a d - 16a b c d + 8b c )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1046
+
+--S 1047 of 1527
+--d0:=D(m0,x)
+--E 1047
+
+)clear all
+
+--S 1048 of 1527
+t0:=x^(3/2)/((a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) --------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Expression(Integer)
+--E 1048
+
+--S 1049 of 1527
+r0:=-1/4*(b*c+3*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*_
+ b^(1/4)*(b*c-a*d)^2*sqrt(2))+1/4*(b*c+3*a*d)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(1/4)*(b*c-a*d)^2*sqrt(2))+_
+ c^(1/4)*d^(3/4)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/((b*c-_
+ a*d)^2*sqrt(2))-c^(1/4)*d^(3/4)*atan(1+d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/((b*c-a*d)^2*sqrt(2))-1/8*(b*c+3*a*d)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*_
+ b^(1/4)*(b*c-a*d)^2*sqrt(2))+1/8*(b*c+3*a*d)*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(1/4)*_
+ (b*c-a*d)^2*sqrt(2))+1/2*c^(1/4)*d^(3/4)*log(sqrt(c)+_
+ x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/((b*c-a*d)^2*_
+ sqrt(2))-1/2*c^(1/4)*d^(3/4)*log(sqrt(c)+x*sqrt(d)+_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/((b*c-a*d)^2*sqrt(2))-_
+ 1/2*sqrt(x)/((b*c-a*d)*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 4+-+3 4+-+4+-+4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 4b x - 4a)\|a \|b \|c \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((3a b d + b c)x + 3a d + a b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R ((- 3a b d - b c)x - 3a d - a b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4+-+3 4+-+4+-+4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (4b x + 4a)\|a \|b \|c \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+3 4+-+4+-+4+-+3 \|2 \|d \|x + \|c
+--R (- 8b x - 8a)\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+3 4+-+4+-+4+-+3 \|2 \|d \|x - \|c
+--R (- 8b x - 8a)\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x + \|a
+--R ((6a b d + 2b c)x + 6a d + 2a b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 \|2 \|b \|x - \|a
+--R ((6a b d + 2b c)x + 6a d + 2a b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+3 4+-+ +-+
+--R (4a d - 4b c)\|2 \|a \|b \|x
+--R /
+--R 2 2 2 3 2 2 3 2 2 2 2 +-+4+-+3
+--R ((8a b d - 16a b c d + 8b c )x + 8a d - 16a b c d + 8a b c )\|2 \|a
+--R *
+--R 4+-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1049
+
+--S 1050 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2
+--R ((2a b d - 2b c)x + 2a d - 2a b c)
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 11 8 10 2 7 9 3 2 6 8 4 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 7 5 4 4 6 6 5 3 5 7 6 2 4 8 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 3 9 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R (3a d + b c)\|x
+--R +
+--R 3 2 2 2 2
+--R (8a d - 16a b c d + 8a b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 11 8 10 2 7 9 3 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 8 4 3 5 7 5 4 4 6 6 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 5 7 6 2 4 8 7 3 9 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R +
+--R 2 2 2
+--R ((- 2a b d + 2b c)x - 2a d + 2a b c)
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 11 8 10 2 7 9 3 2 6 8 4 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 7 5 4 4 6 6 5 3 5 7 6 2 4 8 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 3 9 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R (3a d + b c)\|x
+--R +
+--R 3 2 2 2 2
+--R (- 8a d + 16a b c d - 8a b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 11 8 10 2 7 9 3 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 8 4 3 5 7 5 4 4 6 6 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 5 7 6 2 4 8 7 3 9 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R +
+--R 2 2 2
+--R ((- 2a b d + 2b c)x - 2a d + 2a b c)
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R d\|x
+--R +
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 2 2 2
+--R ((2a b d - 2b c)x + 2a d - 2a b c)
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R +-+
+--R d\|x
+--R +
+--R 2 2 2 2
+--R (- 2a d + 4a b c d - 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 2 2 2
+--R ((4a b d - 4b c)x + 4a d - 4a b c)
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c
+--R ,
+--R 4
+--R /
+--R +-+
+--R d\|x
+--R +
+--R 2 2 2
+--R ((- 4a b d + 4b c)x - 4a d + 4a b c)
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 11 8 10 2 7 9 3 2 6 8 4 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 7 5 4 4 6 6 5 3 5 7 6 2 4 8 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 3 9 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 3 2 2 2 2
+--R (8a d - 16a b c d + 8a b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 11 8 10 2 7 9 3 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 8 4 3 5 7 5 4 4 6 6 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 5 7 6 2 4 8 7 3 9 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R /
+--R +-+
+--R (3a d + b c)\|x
+--R +
+--R +-+
+--R \|x
+--R /
+--R 2 2 2
+--R (2a b d - 2b c)x + 2a d - 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 1050
+
+--S 1051 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 4+-+4+-+4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R 4\|a \|b \|c \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d - b c)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 2 +-+
+--R (8a d - 16a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 11 8 10 2 7 9 3 2 6 8 4 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 7 5 4 4 6 6 5 3 5 7 6 2 4 8 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 3 9 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (3a d + b c)\|x
+--R +
+--R 3 2 2 2 2
+--R (8a d - 16a b c d + 8a b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 11 8 10 2 7 9 3 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 8 4 3 5 7 5 4 4 6 6 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 5 7 6 2 4 8 7 3 9 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 11 8 10 2 7 9 3 2 6 8 4 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 7 5 4 4 6 6 5 3 5 7 6 2 4 8 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 3 9 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R (3a d + b c)\|x
+--R +
+--R 3 2 2 2 2
+--R (- 8a d + 16a b c d - 8a b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 11 8 10 2 7 9 3 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 8 4 3 5 7 5 4 4 6 6 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 5 7 6 2 4 8 7 3 9 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R d\|x
+--R +
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 2 2 2 2 +-+
+--R (8a d - 16a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R log
+--R +-+
+--R d\|x
+--R +
+--R 2 2 2 2
+--R (- 2a d + 4a b c d - 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c
+--R ,
+--R 4
+--R +
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d + b c)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 4+-+4+-+4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - 4\|a \|b \|c \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+4+-+4+-+3 \|2 \|d \|x + \|c
+--R 8\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+4+-+4+-+3 \|2 \|d \|x - \|c
+--R 8\|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R (- 6a d - 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R (- 6a d - 2b c)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 +-+
+--R (16a d - 32a b c d + 16b c )\|2
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7 8 8
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 2 2 2 2
+--R (2a d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R c d
+--R /
+--R 8 8 7 7 6 2 2 6 5 3 3 5
+--R 16a d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 4 4 3 5 5 3 2 6 6 2 7 7
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 8
+--R 16b c
+--R ,
+--R 4
+--R /
+--R +-+
+--R d\|x
+--R +
+--R 2 2 2 2 +-+
+--R (- 16a d + 32a b c d - 16b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 11 8 10 2 7 9 3 2 6 8 4 3 5
+--R 4096a b d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 7 5 4 4 6 6 5 3 5 7 6 2 4 8 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 3 9 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+
+--R \|a \|b
+--R *
+--R atan
+--R 3 2 2 2 2
+--R (8a d - 16a b c d + 8a b c )
+--R *
+--R ROOT
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 81a d - 108a b c d - 54a b c d - 12a b c d - b c
+--R /
+--R 11 8 10 2 7 9 3 2 6
+--R 4096a b d - 32768a b c d + 114688a b c d
+--R +
+--R 8 4 3 5 7 5 4 4 6 6 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 5 7 6 2 4 8 7 3 9 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R /
+--R +-+
+--R (3a d + b c)\|x
+--R /
+--R 2 2 2 2 +-+4+-+3 4+-+
+--R (8a d - 16a b c d + 8b c )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 1051
+
+--S 1052 of 1527
+--d0:=D(m0,x)
+--E 1052
+
+)clear all
+
+--S 1053 of 1527
+t0:=sqrt(x)/((a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R +-+
+--R \|x
+--R (1) --------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Expression(Integer)
+--E 1053
+
+--S 1054 of 1527
+r0:=1/2*b*x^(3/2)/(a*(b*c-a*d)*(a+b*x^2))-1/4*b^(1/4)*(b*c-5*a*d)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*(b*c-a*d)^2*_
+ sqrt(2))+1/4*b^(1/4)*(b*c-5*a*d)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(5/4)*(b*c-a*d)^2*sqrt(2))-d^(5/4)*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(1/4)*(b*c-a*d)^2*_
+ sqrt(2))+d^(5/4)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(1/4)*(b*c-a*d)^2*sqrt(2))+1/8*b^(1/4)*(b*c-5*a*d)*_
+ log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(5/4)*(b*c-a*d)^2*sqrt(2))-1/8*b^(1/4)*(b*c-5*a*d)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(5/4)*(b*c-a*d)^2*sqrt(2))+1/2*d^(5/4)*log(sqrt(c)+_
+ x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(1/4)*_
+ (b*c-a*d)^2*sqrt(2))-1/2*d^(5/4)*log(sqrt(c)+x*sqrt(d)+_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(1/4)*(b*c-a*d)^2*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 4a b d x - 4a d)\|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 4+-+4+-+
+--R ((5a b d - b c)x + 5a d - a b c)\|b \|c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 4+-+4+-+
+--R ((- 5a b d + b c)x - 5a d + a b c)\|b \|c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (4a b d x + 4a d)\|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|d \|x + \|c
+--R (8a b d x + 8a d)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|d \|x - \|c
+--R (8a b d x + 8a d)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+4+-+ \|2 \|b \|x + \|a
+--R ((- 10a b d + 2b c)x - 10a d + 2a b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 4+-+4+-+ \|2 \|b \|x - \|a
+--R ((- 10a b d + 2b c)x - 10a d + 2a b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+4+-+ +-+
+--R (- 4a b d + 4b c)x\|2 \|a \|c \|x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2 +-+4+-+
+--R ((8a b d - 16a b c d + 8a b c )x + 8a d - 16a b c d + 8a b c )\|2 \|a
+--R *
+--R 4+-+
+--R \|c
+--R Type: Expression(Integer)
+--E 1054
+
+--S 1055 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 3 2
+--R ((2a b d - 2a b c)x + 2a d - 2a b c)
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2 7 8 8 9
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R 4 +-+
+--R d \|x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2
+--R 8a c d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 6 6 7
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 8 8 9
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 3 2
+--R ((- 2a b d + 2a b c)x - 2a d + 2a b c)
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2 7 8 8 9
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R 4 +-+
+--R d \|x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3
+--R - 8a c d + 48a b c d - 120a b c d + 160a b c d
+--R +
+--R 2 4 5 2 5 6 6 7
+--R - 120a b c d + 48a b c d - 8b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 8 8 9
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 3 2
+--R ((- 2a b d + 2a b c)x - 2a d + 2a b c)
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R - 625a b d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 13 8 12 7 11 2 2 6 10 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 9 4 4 4 8 5 5 3 7 6 6 2 6 7 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 5 8 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d - 75a b c d + 15a b c d - b c )\|x
+--R +
+--R 10 6 9 5 8 2 2 4 7 3 3 3
+--R 512a d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 6 4 4 2 5 5 5 4 6 6
+--R 7680a b c d - 3072a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d + 500a b c d - 150a b c d + 20a b c d
+--R +
+--R 5 4
+--R - b c
+--R /
+--R 13 8 12 7 11 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 10 3 3 5 9 4 4 4 8 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 7 6 6 2 6 7 7 5 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 3 2
+--R ((2a b d - 2a b c)x + 2a d - 2a b c)
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R - 625a b d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 13 8 12 7 11 2 2 6 10 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 9 4 4 4 8 5 5 3 7 6 6 2 6 7 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 5 8 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d - 75a b c d + 15a b c d - b c )\|x
+--R +
+--R 10 6 9 5 8 2 2 4 7 3 3 3
+--R - 512a d + 3072a b c d - 7680a b c d + 10240a b c d
+--R +
+--R 6 4 4 2 5 5 5 4 6 6
+--R - 7680a b c d + 3072a b c d - 512a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d + 500a b c d - 150a b c d + 20a b c d
+--R +
+--R 5 4
+--R - b c
+--R /
+--R 13 8 12 7 11 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 10 3 3 5 9 4 4 4 8 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 7 6 6 2 6 7 7 5 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 2 3 2
+--R ((- 4a b d + 4a b c)x - 4a d + 4a b c)
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R - 625a b d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 13 8 12 7 11 2 2 6 10 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 9 4 4 4 8 5 5 3 7 6 6 2 6 7 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 5 8 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 10 6 9 5 8 2 2 4 7 3 3 3
+--R 512a d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 6 4 4 2 5 5 5 4 6 6
+--R 7680a b c d - 3072a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d + 500a b c d - 150a b c d + 20a b c d
+--R +
+--R 5 4
+--R - b c
+--R /
+--R 13 8 12 7 11 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 10 3 3 5 9 4 4 4 8 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 7 6 6 2 6 7 7 5 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d - 75a b c d + 15a b c d - b c )\|x
+--R +
+--R 2 2 2 3 2
+--R ((4a b d - 4a b c)x + 4a d - 4a b c)
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2 7 8 8 9
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2
+--R 8a c d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 6 6 7
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 8 8 9
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 4 +-+
+--R d \|x
+--R +
+--R +-+
+--R - b x\|x
+--R /
+--R 2 2 2 3 2
+--R (2a b d - 2a b c)x + 2a d - 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 1055
+
+--S 1056 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 4a d\|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d + b c)\|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 2 2 2 +-+
+--R (8a d - 16a b c d + 8a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2 7 8 8 9
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 4 +-+
+--R d \|x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2
+--R 8a c d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 6 6 7
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 8 8 9
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2 7 8 8 9
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 4 +-+
+--R d \|x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3
+--R - 8a c d + 48a b c d - 120a b c d + 160a b c d
+--R +
+--R 2 4 5 2 5 6 6 7
+--R - 120a b c d + 48a b c d - 8b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 8 8 9
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8a b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R - 625a b d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 13 8 12 7 11 2 2 6 10 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 9 4 4 4 8 5 5 3 7 6 6 2 6 7 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 5 8 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d - 75a b c d + 15a b c d - b c )\|x
+--R +
+--R 10 6 9 5 8 2 2 4 7 3 3 3
+--R 512a d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 6 4 4 2 5 5 5 4 6 6
+--R 7680a b c d - 3072a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d + 500a b c d - 150a b c d + 20a b c d
+--R +
+--R 5 4
+--R - b c
+--R /
+--R 13 8 12 7 11 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 10 3 3 5 9 4 4 4 8 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 7 6 6 2 6 7 7 5 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 2 2 2 +-+
+--R (8a d - 16a b c d + 8a b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R - 625a b d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 13 8 12 7 11 2 2 6 10 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 9 4 4 4 8 5 5 3 7 6 6 2 6 7 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 5 8 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d - 75a b c d + 15a b c d - b c )\|x
+--R +
+--R 10 6 9 5 8 2 2 4 7 3 3 3
+--R - 512a d + 3072a b c d - 7680a b c d + 10240a b c d
+--R +
+--R 6 4 4 2 5 5 5 4 6 6
+--R - 7680a b c d + 3072a b c d - 512a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d + 500a b c d - 150a b c d + 20a b c d
+--R +
+--R 5 4
+--R - b c
+--R /
+--R 13 8 12 7 11 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 10 3 3 5 9 4 4 4 8 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 7 6 6 2 6 7 7 5 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d - b c)\|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 4a d\|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R - 8a d\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R - 8a d\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a
+--R (10a d - 2b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x - \|a
+--R (10a d - 2b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 2 2 2 +-+
+--R (- 16a d + 32a b c d - 16a b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R - 625a b d + 500a b c d - 150a b c d + 20a b c d - b c
+--R /
+--R 13 8 12 7 11 2 2 6 10 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 9 4 4 4 8 5 5 3 7 6 6 2 6 7 7
+--R 286720a b c d - 229376a b c d + 114688a b c d - 32768a b c d
+--R +
+--R 5 8 8
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R atan
+--R 10 6 9 5 8 2 2 4 7 3 3 3
+--R 512a d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 6 4 4 2 5 5 5 4 6 6
+--R 7680a b c d - 3072a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d + 500a b c d - 150a b c d + 20a b c d
+--R +
+--R 5 4
+--R - b c
+--R /
+--R 13 8 12 7 11 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 10 3 3 5 9 4 4 4 8 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 7 6 6 2 6 7 7 5 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d - 75a b c d + 15a b c d - b c )\|x
+--R +
+--R 3 2 2 2 2 +-+
+--R (16a d - 32a b c d + 16a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2 7 8 8 9
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d + 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R atan
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2
+--R 8a c d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 6 6 7
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 8 8 7 2 7 6 2 3 6 5 3 4 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 5 4 3 5 6 3 2 6 7 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 8 8 9
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 4 +-+
+--R d \|x
+--R /
+--R 3 2 2 2 2 +-+4+-+4+-+
+--R (8a d - 16a b c d + 8a b c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1056
+
+--S 1057 of 1527
+--d0:=D(m0,x)
+--E 1057
+
+)clear all
+
+--S 1058 of 1527
+t0:=1/((a+b*x^2)^2*(c+d*x^2)*sqrt(x))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------------
+--R 2 6 2 4 2 2 2 +-+
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|x
+--R Type: Expression(Integer)
+--E 1058
+
+--S 1059 of 1527
+r0:=-1/4*b^(3/4)*(3*b*c-7*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(7/4)*(b*c-a*d)^2*sqrt(2))+1/4*b^(3/4)*(3*b*c-7*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*(b*c-a*d)^2*_
+ sqrt(2))-d^(7/4)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(3/4)*(b*c-a*d)^2*sqrt(2))+d^(7/4)*atan(1+d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(3/4)*(b*c-a*d)^2*sqrt(2))-1/8*b^(3/4)*_
+ (3*b*c-7*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(7/4)*(b*c-a*d)^2*sqrt(2))+1/8*b^(3/4)*(3*b*c-_
+ 7*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(7/4)*(b*c-a*d)^2*sqrt(2))-1/2*d^(7/4)*log(sqrt(c)+x*sqrt(d)-_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(3/4)*(b*c-a*d)^2*sqrt(2))+_
+ 1/2*d^(7/4)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(3/4)*(b*c-a*d)^2*sqrt(2))+1/2*b*sqrt(x)/_
+ (a*(b*c-a*d)*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 2 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (4a b d x + 4a d)\|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 2 4+-+3 4+-+3
+--R ((- 7a b d + 3b c)x - 7a d + 3a b c)\|b \|c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 4+-+3 4+-+3
+--R ((7a b d - 3b c)x + 7a d - 3a b c)\|b \|c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 4a b d x - 4a d)\|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+3 4+-+3 \|2 \|d \|x + \|c
+--R (8a b d x + 8a d)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+3 4+-+3 \|2 \|d \|x - \|c
+--R (8a b d x + 8a d)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 2 4+-+3 4+-+3
+--R ((- 14a b d + 6b c)x - 14a d + 6a b c)\|b \|c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 4+-+3 4+-+3
+--R ((- 14a b d + 6b c)x - 14a d + 6a b c)\|b \|c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+3 4+-+3 +-+
+--R (- 4a b d + 4b c)\|2 \|a \|c \|x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2 +-+
+--R ((8a b d - 16a b c d + 8a b c )x + 8a d - 16a b c d + 8a b c )\|2
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 1059
+
+--S 1060 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 3 2
+--R ((2a b d - 2a b c)x + 2a d - 2a b c)
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 11
+--R 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R 2 +-+
+--R d \|x
+--R +
+--R 2 2 2 2 3
+--R (2a c d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 11
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 2 2 2 3 2
+--R ((- 2a b d + 2a b c)x - 2a d + 2a b c)
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 11
+--R 16b c
+--R ,
+--R 4
+--R *
+--R log
+--R 2 +-+
+--R d \|x
+--R +
+--R 2 2 2 2 3
+--R (- 2a c d + 4a b c d - 2b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 11
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 2 2 2 3 2
+--R ((- 2a b d + 2a b c)x - 2a d + 2a b c)
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R - 2401a b d + 4116a b c d - 2646a b c d + 756a b c d - 81b c
+--R /
+--R 15 8 14 7 13 2 2 6 12 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 11 4 4 4 10 5 5 3 9 6 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 8 7 7 7 8 8
+--R - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 2 +-+
+--R (7a b d - 3b c)\|x
+--R +
+--R 4 2 3 2 2 2
+--R (8a d - 16a b c d + 8a b c )
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R - 2401a b d + 4116a b c d - 2646a b c d + 756a b c d
+--R +
+--R 7 4
+--R - 81b c
+--R /
+--R 15 8 14 7 13 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 12 3 3 5 11 4 4 4 10 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 9 6 6 2 8 7 7 7 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R +
+--R 2 2 2 3 2
+--R ((2a b d - 2a b c)x + 2a d - 2a b c)
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R - 2401a b d + 4116a b c d - 2646a b c d + 756a b c d - 81b c
+--R /
+--R 15 8 14 7 13 2 2 6 12 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 11 4 4 4 10 5 5 3 9 6 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 8 7 7 7 8 8
+--R - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 2 +-+
+--R (7a b d - 3b c)\|x
+--R +
+--R 4 2 3 2 2 2
+--R (- 8a d + 16a b c d - 8a b c )
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R - 2401a b d + 4116a b c d - 2646a b c d + 756a b c d
+--R +
+--R 7 4
+--R - 81b c
+--R /
+--R 15 8 14 7 13 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 12 3 3 5 11 4 4 4 10 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 9 6 6 2 8 7 7 7 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R +
+--R 2 2 2 3 2
+--R ((4a b d - 4a b c)x + 4a d - 4a b c)
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R - 2401a b d + 4116a b c d - 2646a b c d + 756a b c d - 81b c
+--R /
+--R 15 8 14 7 13 2 2 6 12 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 11 4 4 4 10 5 5 3 9 6 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 8 7 7 7 8 8
+--R - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 4 2 3 2 2 2
+--R (8a d - 16a b c d + 8a b c )
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R - 2401a b d + 4116a b c d - 2646a b c d + 756a b c d
+--R +
+--R 7 4
+--R - 81b c
+--R /
+--R 15 8 14 7 13 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 12 3 3 5 11 4 4 4 10 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 9 6 6 2 8 7 7 7 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R /
+--R 2 +-+
+--R (7a b d - 3b c)\|x
+--R +
+--R 2 2 2 3 2
+--R ((- 4a b d + 4a b c)x - 4a d + 4a b c)
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 11
+--R 16b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 2 2 2 2 3
+--R (2a c d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 11
+--R 16b c
+--R ,
+--R 4
+--R /
+--R 2 +-+
+--R d \|x
+--R +
+--R +-+
+--R - b\|x
+--R /
+--R 2 2 2 3 2
+--R (2a b d - 2a b c)x + 2a d - 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 1060
+
+--S 1061 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - 4a d \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (7a d - 3b c)\|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 2 2 2 +-+
+--R (8a d - 16a b c d + 8a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 11
+--R 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2 +-+
+--R d \|x
+--R +
+--R 2 2 2 2 3
+--R (2a c d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 11
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 3 2 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 11
+--R 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2 +-+
+--R d \|x
+--R +
+--R 2 2 2 2 3
+--R (- 2a c d + 4a b c d - 2b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 11
+--R 16b c
+--R ,
+--R 4
+--R +
+--R 3 2 2 2 2 +-+
+--R (- 8a d + 16a b c d - 8a b c )\|2
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R - 2401a b d + 4116a b c d - 2646a b c d + 756a b c d - 81b c
+--R /
+--R 15 8 14 7 13 2 2 6 12 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 11 4 4 4 10 5 5 3 9 6 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 8 7 7 7 8 8
+--R - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2 +-+
+--R (7a b d - 3b c)\|x
+--R +
+--R 4 2 3 2 2 2
+--R (8a d - 16a b c d + 8a b c )
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R - 2401a b d + 4116a b c d - 2646a b c d + 756a b c d
+--R +
+--R 7 4
+--R - 81b c
+--R /
+--R 15 8 14 7 13 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 12 3 3 5 11 4 4 4 10 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 9 6 6 2 8 7 7 7 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R +
+--R 3 2 2 2 2 +-+
+--R (8a d - 16a b c d + 8a b c )\|2
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R - 2401a b d + 4116a b c d - 2646a b c d + 756a b c d - 81b c
+--R /
+--R 15 8 14 7 13 2 2 6 12 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 11 4 4 4 10 5 5 3 9 6 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 8 7 7 7 8 8
+--R - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2 +-+
+--R (7a b d - 3b c)\|x
+--R +
+--R 4 2 3 2 2 2
+--R (- 8a d + 16a b c d - 8a b c )
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R - 2401a b d + 4116a b c d - 2646a b c d + 756a b c d
+--R +
+--R 7 4
+--R - 81b c
+--R /
+--R 15 8 14 7 13 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 12 3 3 5 11 4 4 4 10 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 9 6 6 2 8 7 7 7 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 7a d + 3b c)\|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R 4a d \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x + \|c
+--R - 8a d \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x - \|c
+--R - 8a d \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x + \|a
+--R (14a d - 6b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x - \|a
+--R (14a d - 6b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 2 2 2 +-+
+--R (16a d - 32a b c d + 16a b c )\|2
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R - 2401a b d + 4116a b c d - 2646a b c d + 756a b c d - 81b c
+--R /
+--R 15 8 14 7 13 2 2 6 12 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 11 4 4 4 10 5 5 3 9 6 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 8 7 7 7 8 8
+--R - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R atan
+--R 4 2 3 2 2 2
+--R (8a d - 16a b c d + 8a b c )
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R - 2401a b d + 4116a b c d - 2646a b c d + 756a b c d
+--R +
+--R 7 4
+--R - 81b c
+--R /
+--R 15 8 14 7 13 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 12 3 3 5 11 4 4 4 10 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 9 6 6 2 8 7 7 7 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R /
+--R 2 +-+
+--R (7a b d - 3b c)\|x
+--R +
+--R 3 2 2 2 2 +-+
+--R (- 16a d + 32a b c d - 16a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 11
+--R 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R atan
+--R 2 2 2 2 3
+--R (2a c d - 4a b c d + 2b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 8 3 8 7 4 7 6 2 5 6 5 3 6 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 7 4 3 5 8 3 2 6 9 2 7 10
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 11
+--R 16b c
+--R ,
+--R 4
+--R /
+--R 2 +-+
+--R d \|x
+--R /
+--R 3 2 2 2 2 +-+4+-+3 4+-+3
+--R (8a d - 16a b c d + 8a b c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1061
+
+--S 1062 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1062
+
+)clear all
+
+--S 1063 of 1527
+t0:=1/(x^(3/2)*(a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------------
+--R 2 7 2 5 2 3 2 +-+
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x)\|x
+--R Type: Expression(Integer)
+--E 1063
+
+--S 1064 of 1527
+r0:=1/4*b^(5/4)*(5*b*c-9*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(9/4)*(b*c-a*d)^2*sqrt(2))-1/4*b^(5/4)*(5*b*c-9*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*(b*c-a*d)^2*_
+ sqrt(2))+d^(9/4)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/_
+ (c^(5/4)*(b*c-a*d)^2*sqrt(2))-d^(9/4)*atan(1+d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(5/4)*(b*c-a*d)^2*sqrt(2))-1/8*b^(5/4)*_
+ (5*b*c-9*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(9/4)*(b*c-a*d)^2*sqrt(2))+1/8*b^(5/4)*(5*b*c-9*a*d)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*_
+ (b*c-a*d)^2*sqrt(2))-1/2*d^(9/4)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(5/4)*(b*c-a*d)^2*sqrt(2))+1/2*d^(9/4)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(5/4)*_
+ (b*c-a*d)^2*sqrt(2))+1/2*(-5*b*c+4*a*d)/(a^2*c*(b*c-a*d)*sqrt(x))+_
+ 1/2*b/(a*(b*c-a*d)*(a+b*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (4a b d x + 4a d )\|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 2 2 2 4+-+4+-+ +-+
+--R ((- 9a b c d + 5b c )x - 9a b c d + 5a b c )\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 3 2 2 2 2 2 4+-+4+-+ +-+
+--R ((9a b c d - 5b c )x + 9a b c d - 5a b c )\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 2 3 2 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 4a b d x - 4a d )\|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 3 2 4+-+4+-+ +-+ \|2 \|d \|x + \|c
+--R (- 8a b d x - 8a d )\|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 2 3 2 4+-+4+-+ +-+ \|2 \|d \|x - \|c
+--R (- 8a b d x - 8a d )\|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 2 4+-+4+-+ +-+
+--R ((18a b c d - 10b c )x + 18a b c d - 10a b c )\|b \|c \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 2 2 2 2 4+-+4+-+ +-+
+--R ((18a b c d - 10b c )x + 18a b c d - 10a b c )\|b \|c \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 16a b d + 36a b c d - 20b c )x - 16a d + 32a b c d - 16a b c )
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R /
+--R 4 2 3 2 2 2 3 3 2 5 2 4 2 3 2 3 +-+
+--R ((8a b c d - 16a b c d + 8a b c )x + 8a c d - 16a b c d + 8a b c )\|2
+--R *
+--R 4+-+4+-+ +-+
+--R \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1064
+
+--S 1065 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2 2 2 4 3 2
+--R ((- 2a b c d + 2a b c )x - 2a c d + 2a b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2 7 12
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 13
+--R 16b c
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 7 +-+
+--R d \|x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3 2 4 8 2
+--R 8a c d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 9 6 10
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 12 8 13
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 2 2 2 4 3 2
+--R ((2a b c d - 2a b c )x + 2a c d - 2a b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2 7 12
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 13
+--R 16b c
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 7 +-+
+--R d \|x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3
+--R - 8a c d + 48a b c d - 120a b c d + 160a b c d
+--R +
+--R 2 4 8 2 5 9 6 10
+--R - 120a b c d + 48a b c d - 8b c
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 12 8 13
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 2 2 2 4 3 2
+--R ((2a b c d - 2a b c )x + 2a c d - 2a b c )
+--R *
+--R ROOT
+--R 4 5 4 3 6 3 2 7 2 2 8 3
+--R - 6561a b d + 14580a b c d - 12150a b c d + 4500a b c d
+--R +
+--R 9 4
+--R - 625b c
+--R /
+--R 17 8 16 7 15 2 2 6 14 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 13 4 4 4 12 5 5 3 11 6 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 10 7 7 9 8 8
+--R - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 4 3 2 5 2 6 2 7 3 +-+
+--R (729a b d - 1215a b c d + 675a b c d - 125b c )\|x
+--R +
+--R 13 6 12 5 11 2 2 4 10 3 3 3
+--R 512a d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 9 4 4 2 8 5 5 7 6 6
+--R 7680a b c d - 3072a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 5 4 3 6 3 2 7 2 2
+--R - 6561a b d + 14580a b c d - 12150a b c d
+--R +
+--R 8 3 9 4
+--R 4500a b c d - 625b c
+--R /
+--R 17 8 16 7 15 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 14 3 3 5 13 4 4 4 12 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 11 6 6 2 10 7 7 9 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 2 2 2 4 3 2
+--R ((- 2a b c d + 2a b c )x - 2a c d + 2a b c )
+--R *
+--R ROOT
+--R 4 5 4 3 6 3 2 7 2 2 8 3
+--R - 6561a b d + 14580a b c d - 12150a b c d + 4500a b c d
+--R +
+--R 9 4
+--R - 625b c
+--R /
+--R 17 8 16 7 15 2 2 6 14 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 13 4 4 4 12 5 5 3 11 6 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 10 7 7 9 8 8
+--R - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R log
+--R 3 4 3 2 5 2 6 2 7 3 +-+
+--R (729a b d - 1215a b c d + 675a b c d - 125b c )\|x
+--R +
+--R 13 6 12 5 11 2 2 4 10 3 3 3
+--R - 512a d + 3072a b c d - 7680a b c d + 10240a b c d
+--R +
+--R 9 4 4 2 8 5 5 7 6 6
+--R - 7680a b c d + 3072a b c d - 512a b c
+--R *
+--R ROOT
+--R 4 5 4 3 6 3 2 7 2 2
+--R - 6561a b d + 14580a b c d - 12150a b c d
+--R +
+--R 8 3 9 4
+--R 4500a b c d - 625b c
+--R /
+--R 17 8 16 7 15 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 14 3 3 5 13 4 4 4 12 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 11 6 6 2 10 7 7 9 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 2 2 2 2 4 3 2
+--R ((4a b c d - 4a b c )x + 4a c d - 4a b c )
+--R *
+--R ROOT
+--R 4 5 4 3 6 3 2 7 2 2 8 3
+--R - 6561a b d + 14580a b c d - 12150a b c d + 4500a b c d
+--R +
+--R 9 4
+--R - 625b c
+--R /
+--R 17 8 16 7 15 2 2 6 14 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 13 4 4 4 12 5 5 3 11 6 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 10 7 7 9 8 8
+--R - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 13 6 12 5 11 2 2 4 10 3 3 3
+--R 512a d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 9 4 4 2 8 5 5 7 6 6
+--R 7680a b c d - 3072a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 5 4 3 6 3 2 7 2 2
+--R - 6561a b d + 14580a b c d - 12150a b c d
+--R +
+--R 8 3 9 4
+--R 4500a b c d - 625b c
+--R /
+--R 17 8 16 7 15 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 14 3 3 5 13 4 4 4 12 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 11 6 6 2 10 7 7 9 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 4 3 2 5 2 6 2 7 3 +-+
+--R (729a b d - 1215a b c d + 675a b c d - 125b c )\|x
+--R +
+--R 3 2 2 2 2 4 3 2
+--R ((- 4a b c d + 4a b c )x - 4a c d + 4a b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2 7 12
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 13
+--R 16b c
+--R ,
+--R 4
+--R *
+--R +-+
+--R \|x
+--R *
+--R atan
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3 2 4 8 2
+--R 8a c d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 9 6 10
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 12 8 13
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 7 +-+
+--R d \|x
+--R +
+--R 2 2 2
+--R (- 4a b d + 5b c)x - 4a d + 4a b c
+--R /
+--R 3 2 2 2 2 4 3 2 +-+
+--R ((2a b c d - 2a b c )x + 2a c d - 2a b c )\|x
+--R Type: Union(Expression(Integer),...)
+--E 1065
+
+--S 1066 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 4a d \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (9a b c d - 5b c )\|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 2 3 2 2 2 3 +-+
+--R (- 8a c d + 16a b c d - 8a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2 7 12
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 13
+--R 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 7 +-+
+--R d \|x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3 2 4 8 2
+--R 8a c d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 9 6 10
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 12 8 13
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 2 3 2 2 2 3 +-+
+--R (8a c d - 16a b c d + 8a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2 7 12
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 13
+--R 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 7 +-+
+--R d \|x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3
+--R - 8a c d + 48a b c d - 120a b c d + 160a b c d
+--R +
+--R 2 4 8 2 5 9 6 10
+--R - 120a b c d + 48a b c d - 8b c
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 12 8 13
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 2 3 2 2 2 3 +-+
+--R (8a c d - 16a b c d + 8a b c )\|2
+--R *
+--R ROOT
+--R 4 5 4 3 6 3 2 7 2 2 8 3
+--R - 6561a b d + 14580a b c d - 12150a b c d + 4500a b c d
+--R +
+--R 9 4
+--R - 625b c
+--R /
+--R 17 8 16 7 15 2 2 6 14 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 13 4 4 4 12 5 5 3 11 6 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 10 7 7 9 8 8
+--R - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 4 3 2 5 2 6 2 7 3 +-+
+--R (729a b d - 1215a b c d + 675a b c d - 125b c )\|x
+--R +
+--R 13 6 12 5 11 2 2 4 10 3 3 3
+--R 512a d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 9 4 4 2 8 5 5 7 6 6
+--R 7680a b c d - 3072a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 5 4 3 6 3 2 7 2 2
+--R - 6561a b d + 14580a b c d - 12150a b c d
+--R +
+--R 8 3 9 4
+--R 4500a b c d - 625b c
+--R /
+--R 17 8 16 7 15 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 14 3 3 5 13 4 4 4 12 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 11 6 6 2 10 7 7 9 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4 2 3 2 2 2 3 +-+
+--R (- 8a c d + 16a b c d - 8a b c )\|2
+--R *
+--R ROOT
+--R 4 5 4 3 6 3 2 7 2 2 8 3
+--R - 6561a b d + 14580a b c d - 12150a b c d + 4500a b c d
+--R +
+--R 9 4
+--R - 625b c
+--R /
+--R 17 8 16 7 15 2 2 6 14 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 13 4 4 4 12 5 5 3 11 6 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 10 7 7 9 8 8
+--R - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 4 3 2 5 2 6 2 7 3 +-+
+--R (729a b d - 1215a b c d + 675a b c d - 125b c )\|x
+--R +
+--R 13 6 12 5 11 2 2 4 10 3 3 3
+--R - 512a d + 3072a b c d - 7680a b c d + 10240a b c d
+--R +
+--R 9 4 4 2 8 5 5 7 6 6
+--R - 7680a b c d + 3072a b c d - 512a b c
+--R *
+--R ROOT
+--R 4 5 4 3 6 3 2 7 2 2
+--R - 6561a b d + 14580a b c d - 12150a b c d
+--R +
+--R 8 3 9 4
+--R 4500a b c d - 625b c
+--R /
+--R 17 8 16 7 15 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 14 3 3 5 13 4 4 4 12 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 11 6 6 2 10 7 7 9 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 9a b c d + 5b c )\|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 4a d \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|d \|x + \|c
+--R 8a d \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|d \|x - \|c
+--R 8a d \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|b \|x + \|a
+--R (- 18a b c d + 10b c )\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 4+-+4+-+ \|2 \|b \|x - \|a
+--R (- 18a b c d + 10b c )\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 2 3 2 2 2 3 +-+
+--R (16a c d - 32a b c d + 16a b c )\|2
+--R *
+--R ROOT
+--R 4 5 4 3 6 3 2 7 2 2 8 3
+--R - 6561a b d + 14580a b c d - 12150a b c d + 4500a b c d
+--R +
+--R 9 4
+--R - 625b c
+--R /
+--R 17 8 16 7 15 2 2 6 14 3 3 5
+--R 4096a d - 32768a b c d + 114688a b c d - 229376a b c d
+--R +
+--R 13 4 4 4 12 5 5 3 11 6 6 2
+--R 286720a b c d - 229376a b c d + 114688a b c d
+--R +
+--R 10 7 7 9 8 8
+--R - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R atan
+--R 13 6 12 5 11 2 2 4 10 3 3 3
+--R 512a d - 3072a b c d + 7680a b c d - 10240a b c d
+--R +
+--R 9 4 4 2 8 5 5 7 6 6
+--R 7680a b c d - 3072a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 5 4 3 6 3 2 7 2 2
+--R - 6561a b d + 14580a b c d - 12150a b c d
+--R +
+--R 8 3 9 4
+--R 4500a b c d - 625b c
+--R /
+--R 17 8 16 7 15 2 2 6
+--R 4096a d - 32768a b c d + 114688a b c d
+--R +
+--R 14 3 3 5 13 4 4 4 12 5 5 3
+--R - 229376a b c d + 286720a b c d - 229376a b c d
+--R +
+--R 11 6 6 2 10 7 7 9 8 8
+--R 114688a b c d - 32768a b c d + 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 4 3 2 5 2 6 2 7 3 +-+
+--R (729a b d - 1215a b c d + 675a b c d - 125b c )\|x
+--R +
+--R 4 2 3 2 2 2 3 +-+
+--R (- 16a c d + 32a b c d - 16a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2 7 12
+--R 1120a b c d - 896a b c d + 448a b c d - 128a b c d
+--R +
+--R 8 13
+--R 16b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R atan
+--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3 2 4 8 2
+--R 8a c d - 48a b c d + 120a b c d - 160a b c d + 120a b c d
+--R +
+--R 5 9 6 10
+--R - 48a b c d + 8b c
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 8 5 8 7 6 7 6 2 7 6 5 3 8 5
+--R 16a c d - 128a b c d + 448a b c d - 896a b c d
+--R +
+--R 4 4 9 4 3 5 10 3 2 6 11 2
+--R 1120a b c d - 896a b c d + 448a b c d
+--R +
+--R 7 12 8 13
+--R - 128a b c d + 16b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 7 +-+
+--R d \|x
+--R /
+--R 4 2 3 2 2 2 3 +-+4+-+4+-+
+--R (8a c d - 16a b c d + 8a b c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1066
+
+--S 1067 of 1527
+--d0:=D(m0,x)
+--E 1067
+
+)clear all
+
+--S 1068 of 1527
+t0:=1/(x^(5/2)*(a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------------
+--R 2 8 2 6 2 4 2 2 +-+
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|x
+--R Type: Expression(Integer)
+--E 1068
+
+--S 1069 of 1527
+r0:=1/6*(-7*b*c+4*a*d)/(a^2*c*(b*c-a*d)*x^(3/2))+1/2*b/(a*(b*c-a*d)*_
+ x^(3/2)*(a+b*x^2))+1/4*b^(7/4)*(7*b*c-11*a*d)*atan(1-b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*(b*c-a*d)^2*sqrt(2))-_
+ 1/4*b^(7/4)*(7*b*c-11*a*d)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(11/4)*(b*c-a*d)^2*sqrt(2))+d^(11/4)*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(7/4)*(b*c-a*d)^2*sqrt(2))-d^(11/4)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(7/4)*(b*c-a*d)^2*_
+ sqrt(2))+1/8*b^(7/4)*(7*b*c-11*a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*(b*c-a*d)^2*sqrt(2))-_
+ 1/8*b^(7/4)*(7*b*c-11*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*(b*c-a*d)^2*sqrt(2))+_
+ 1/2*d^(11/4)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(7/4)*(b*c-a*d)^2*sqrt(2))-1/2*d^(11/4)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(7/4)*(b*c-a*d)^2*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 3 3 2 4+-+3 4+-+3 +-+
+--R (- 12a b d x - 12a d x)\|a \|d \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 3 2 2 2 4+-+3 4+-+3 +-+
+--R ((33a b c d - 21b c )x + (33a b c d - 21a b c )x)\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 3 2 3 2 2 2 4+-+3 4+-+3 +-+
+--R ((- 33a b c d + 21b c )x + (- 33a b c d + 21a b c )x)\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 3 3 2 4+-+3 4+-+3 +-+
+--R (12a b d x + 12a d x)\|a \|d \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 3 3 2 4+-+3 4+-+3 +-+ \|2 \|d \|x + \|c
+--R (- 24a b d x - 24a d x)\|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 2 3 3 2 4+-+3 4+-+3 +-+ \|2 \|d \|x - \|c
+--R (- 24a b d x - 24a d x)\|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 3 2 2 2 4+-+3 4+-+3 +-+
+--R ((66a b c d - 42b c )x + (66a b c d - 42a b c )x)\|b \|c \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 3 2 2 2 4+-+3 4+-+3 +-+
+--R ((66a b c d - 42b c )x + (66a b c d - 42a b c )x)\|b \|c \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 16a b d + 44a b c d - 28b c )x - 16a d + 32a b c d - 16a b c )
+--R *
+--R +-+4+-+3 4+-+3
+--R \|2 \|a \|c
+--R /
+--R 4 2 3 2 2 2 3 3 3
+--R (24a b c d - 48a b c d + 24a b c )x
+--R +
+--R 5 2 4 2 3 2 3
+--R (24a c d - 48a b c d + 24a b c )x
+--R *
+--R +-+4+-+3 4+-+3 +-+
+--R \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1069
+
+--S 1070 of 1527
+--a0:=integrate(t0,x)
+--E 1070
+
+--S 1071 of 1527
+--m0:=a0-r0
+--E 1071
+
+--S 1072 of 1527
+--d0:=D(m0,x)
+--E 1072
+
+)clear all
+
+--S 1073 of 1527
+t0:=1/(x^(7/2)*(a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------------
+--R 2 9 2 7 2 5 2 3 +-+
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|x
+--R Type: Expression(Integer)
+--E 1073
+
+--S 1074 of 1527
+r0:=1/10*(-9*b*c+4*a*d)/(a^2*c*(b*c-a*d)*x^(5/2))+1/2*b/(a*(b*c-a*d)*_
+ x^(5/2)*(a+b*x^2))-1/4*b^(9/4)*(9*b*c-13*a*d)*atan(1-b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*(b*c-a*d)^2*sqrt(2))+_
+ 1/4*b^(9/4)*(9*b*c-13*a*d)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(13/4)*(b*c-a*d)^2*sqrt(2))-d^(13/4)*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(9/4)*(b*c-a*d)^2*sqrt(2))+d^(13/4)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(9/4)*(b*c-a*d)^2*_
+ sqrt(2))+1/8*b^(9/4)*(9*b*c-13*a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*(b*c-a*d)^2*sqrt(2))-_
+ 1/8*b^(9/4)*(9*b*c-13*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*(b*c-a*d)^2*sqrt(2))+_
+ 1/2*d^(13/4)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(9/4)*(b*c-a*d)^2*sqrt(2))-1/2*d^(13/4)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(9/4)*(b*c-a*d)^2*sqrt(2))+1/2*(9*b^2*c^2-4*a*b*c*d-_
+ 4*a^2*d^2)/(a^3*c^2*(b*c-a*d)*sqrt(x))
+--R
+--R
+--R (2)
+--R 3 3 4 4 3 2 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 20a b d x - 20a d x )\|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 2 4 3 4 2 2 2 3 3 2 4+-+4+-+ +-+
+--R ((65a b c d - 45b c )x + (65a b c d - 45a b c )x )\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 4 3 4 2 2 2 3 3 2 4+-+4+-+ +-+
+--R ((- 65a b c d + 45b c )x + (- 65a b c d + 45a b c )x )\|b \|c \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 4 4 3 2 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (20a b d x + 20a d x )\|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 4 4 3 2 4+-+4+-+ +-+ \|2 \|d \|x + \|c
+--R (40a b d x + 40a d x )\|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 3 4 4 3 2 4+-+4+-+ +-+ \|2 \|d \|x - \|c
+--R (40a b d x + 40a d x )\|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 2 4 3 4 2 2 2 3 3 2 4+-+4+-+ +-+
+--R ((- 130a b c d + 90b c )x + (- 130a b c d + 90a b c )x )\|b \|c \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x + \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 4 3 4 2 2 2 3 3 2 4+-+4+-+ +-+
+--R ((- 130a b c d + 90b c )x + (- 130a b c d + 90a b c )x )\|b \|c \|x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 3 2 4 3 4
+--R (80a b d - 260a b c d + 180b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 2 4 2
+--R (80a d - 16a b c d - 208a b c d + 144a b c )x - 16a c d
+--R +
+--R 3 2 2 2 3
+--R 32a b c d - 16a b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R /
+--R 5 2 2 4 2 3 3 3 4 4
+--R (40a b c d - 80a b c d + 40a b c )x
+--R +
+--R 6 2 2 5 3 4 2 4 2
+--R (40a c d - 80a b c d + 40a b c )x
+--R *
+--R +-+4+-+4+-+ +-+
+--R \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1074
+
+--S 1075 of 1527
+--a0:=integrate(t0,x)
+--E 1075
+
+--S 1076 of 1527
+--m0:=a0-r0
+--E 1076
+
+--S 1077 of 1527
+--d0:=D(m0,x)
+--E 1077
+
+)clear all
+
+--S 1078 of 1527
+t0:=x^(7/2)/((a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 3 +-+
+--R x \|x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Expression(Integer)
+--E 1078
+
+--S 1079 of 1527
+r0:=1/4*a^(1/4)*(5*b*c+3*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (b^(1/4)*(b*c-a*d)^3*sqrt(2))-1/4*a^(1/4)*(5*b*c+3*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(1/4)*(b*c-a*d)^3*_
+ sqrt(2))-1/4*c^(1/4)*(3*b*c+5*a*d)*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(d^(1/4)*(b*c-a*d)^3*sqrt(2))+1/4*c^(1/4)*_
+ (3*b*c+5*a*d)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(d^(1/4)*_
+ (b*c-a*d)^3*sqrt(2))+1/8*a^(1/4)*(5*b*c+3*a*d)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(1/4)*(b*c-a*d)^3*_
+ sqrt(2))-1/8*a^(1/4)*(5*b*c+3*a*d)*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(1/4)*(b*c-a*d)^3*sqrt(2))-_
+ 1/8*c^(1/4)*(3*b*c+5*a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(d^(1/4)*(b*c-a*d)^3*sqrt(2))+1/8*c^(1/4)*_
+ (3*b*c+5*a*d)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(d^(1/4)*(b*c-a*d)^3*sqrt(2))+1/2*(b*c+a*d)*_
+ sqrt(x)/(b*(b*c-a*d)^2*(c+d*x^2))+1/2*a*sqrt(x)/(b*(b*c-a*d)*_
+ (a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 2 4 2 2 2 2 2 2
+--R (- 5a b d - 3b c d)x + (- 5a d - 8a b c d - 3b c )x - 5a c d
+--R +
+--R 2
+--R - 3a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (3a b d + 5b c d)x + (3a d + 8a b c d + 5b c )x + 3a c d
+--R +
+--R 2
+--R 5a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 3a b d - 5b c d)x + (- 3a d - 8a b c d - 5b c )x - 3a c d
+--R +
+--R 2
+--R - 5a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (5a b d + 3b c d)x + (5a d + 8a b c d + 3b c )x + 5a c d
+--R +
+--R 2
+--R 3a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 10a b d - 6b c d)x + (- 10a d - 16a b c d - 6b c )x - 10a c d
+--R +
+--R 2
+--R - 6a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 10a b d - 6b c d)x + (- 10a d - 16a b c d - 6b c )x - 10a c d
+--R +
+--R 2
+--R - 6a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (6a b d + 10b c d)x + (6a d + 16a b c d + 10b c )x + 6a c d
+--R +
+--R 2
+--R 10a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (6a b d + 10b c d)x + (6a d + 16a b c d + 10b c )x + 6a c d
+--R +
+--R 2
+--R 10a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x - \|a
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 2 2 2 +-+4+-+4+-+ +-+
+--R ((4a d - 4b c )x + 8a c d - 8a b c )\|2 \|b \|d \|x
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (8a b d - 24a b c d + 24a b c d - 8b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (8a d - 16a b c d + 16a b c d - 8b c )x + 8a c d - 24a b c d
+--R +
+--R 2 2 3 3 4
+--R 24a b c d - 8a b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|b \|d
+--R Type: Expression(Integer)
+--E 1079
+
+--S 1080 of 1527
+--a0:=integrate(t0,x)
+--E 1080
+
+--S 1081 of 1527
+--m0:=a0-r0
+--E 1081
+
+--S 1082 of 1527
+--d0:=D(m0,x)
+--E 1082
+
+)clear all
+
+--S 1083 of 1527
+t0:=x^(5/2)/((a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 2 +-+
+--R x \|x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Expression(Integer)
+--E 1083
+
+--S 1084 of 1527
+r0:=-d*x^(3/2)/((b*c-a*d)^2*(c+d*x^2))-1/2*x^(3/2)/((b*c-a*d)*(a+b*x^2)*_
+ (c+d*x^2))-1/4*b^(1/4)*(3*b*c+5*a*d)*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(1/4)*(b*c-a*d)^3*sqrt(2))+1/4*b^(1/4)*_
+ (3*b*c+5*a*d)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*_
+ (b*c-a*d)^3*sqrt(2))+1/4*d^(1/4)*(5*b*c+3*a*d)*atan(1-d^(1/4)*_
+ sqrt(2)*sqrt(x)/c^(1/4))/(c^(1/4)*(b*c-a*d)^3*sqrt(2))-1/4*d^(1/4)*_
+ (5*b*c+3*a*d)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(1/4)*_
+ (b*c-a*d)^3*sqrt(2))+1/8*b^(1/4)*(3*b*c+5*a*d)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*(b*c-a*d)^3*_
+ sqrt(2))-1/8*b^(1/4)*(3*b*c+5*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*(b*c-a*d)^3*sqrt(2))-1/8*d^(1/4)*_
+ (5*b*c+3*a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(1/4)*(b*c-a*d)^3*sqrt(2))+1/8*d^(1/4)*(5*b*c+3*a*d)*log(sqrt(c)+_
+ x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(1/4)*(b*c-a*d)^3*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 4 2 2 2 2 2 2
+--R (- 3a b d - 5b c d)x + (- 3a d - 8a b c d - 5b c )x - 3a c d
+--R +
+--R 2
+--R - 5a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (5a b d + 3b c d)x + (5a d + 8a b c d + 3b c )x + 5a c d
+--R +
+--R 2
+--R 3a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 5a b d - 3b c d)x + (- 5a d - 8a b c d - 3b c )x - 5a c d
+--R +
+--R 2
+--R - 3a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (3a b d + 5b c d)x + (3a d + 8a b c d + 5b c )x + 3a c d
+--R +
+--R 2
+--R 5a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (6a b d + 10b c d)x + (6a d + 16a b c d + 10b c )x + 6a c d
+--R +
+--R 2
+--R 10a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (6a b d + 10b c d)x + (6a d + 16a b c d + 10b c )x + 6a c d
+--R +
+--R 2
+--R 10a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 10a b d - 6b c d)x + (- 10a d - 16a b c d - 6b c )x - 10a c d
+--R +
+--R 2
+--R - 6a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 10a b d - 6b c d)x + (- 10a d - 16a b c d - 6b c )x - 10a c d
+--R +
+--R 2
+--R - 6a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x - \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 3 2 2 2 2 +-+4+-+4+-+ +-+
+--R ((- 8a b d + 8b c d)x + (- 4a d + 4b c )x)\|2 \|a \|c \|x
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (8a b d - 24a b c d + 24a b c d - 8b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (8a d - 16a b c d + 16a b c d - 8b c )x + 8a c d - 24a b c d
+--R +
+--R 2 2 3 3 4
+--R 24a b c d - 8a b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1084
+
+--S 1085 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 3 2 4
+--R (2a b d - 4a b c d + 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2 2 3
+--R (2a d - 2a b c d - 2a b c d + 2b c )x + 2a c d - 4a b c d + 2a b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R - 81a d - 540a b c d - 1350a b c d - 1500a b c d - 625b c d
+--R /
+--R 12 12 11 2 11 10 2 3 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 4 9 8 4 5 8 7 5 6 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 7 6 5 7 8 5 4 8 9 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 10 3 2 10 11 2 11 12 12 13
+--R - 901120a b c d + 270336a b c d - 49152a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (27a d + 135a b c d + 225a b c d + 125b c d)\|x
+--R +
+--R 9 9 8 2 8 7 2 3 7 6 3 4 6
+--R 512a c d - 4608a b c d + 18432a b c d - 43008a b c d
+--R +
+--R 5 4 5 5 4 5 6 4 3 6 7 3 2 7 8 2
+--R 64512a b c d - 64512a b c d + 43008a b c d - 18432a b c d
+--R +
+--R 8 9 9 10
+--R 4608a b c d - 512b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R - 81a d - 540a b c d - 1350a b c d - 1500a b c d
+--R +
+--R 4 4
+--R - 625b c d
+--R /
+--R 12 12 11 2 11 10 2 3 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 4 9 8 4 5 8 7 5 6 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 7 6 5 7 8 5 4 8 9 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 10 3 2 10 11 2 11 12
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 13
+--R 4096b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 3 2 2 3 2 4
+--R (- 2a b d + 4a b c d - 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (- 2a d + 2a b c d + 2a b c d - 2b c )x - 2a c d + 4a b c d
+--R +
+--R 2 3
+--R - 2a b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R - 81a d - 540a b c d - 1350a b c d - 1500a b c d - 625b c d
+--R /
+--R 12 12 11 2 11 10 2 3 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 4 9 8 4 5 8 7 5 6 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 7 6 5 7 8 5 4 8 9 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 10 3 2 10 11 2 11 12 12 13
+--R - 901120a b c d + 270336a b c d - 49152a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (27a d + 135a b c d + 225a b c d + 125b c d)\|x
+--R +
+--R 9 9 8 2 8 7 2 3 7 6 3 4 6
+--R - 512a c d + 4608a b c d - 18432a b c d + 43008a b c d
+--R +
+--R 5 4 5 5 4 5 6 4 3 6 7 3
+--R - 64512a b c d + 64512a b c d - 43008a b c d
+--R +
+--R 2 7 8 2 8 9 9 10
+--R 18432a b c d - 4608a b c d + 512b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R - 81a d - 540a b c d - 1350a b c d - 1500a b c d
+--R +
+--R 4 4
+--R - 625b c d
+--R /
+--R 12 12 11 2 11 10 2 3 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 4 9 8 4 5 8 7 5 6 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 7 6 5 7 8 5 4 8 9 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 10 3 2 10 11 2 11 12
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 13
+--R 4096b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 3 2 2 3 2 4
+--R (- 2a b d + 4a b c d - 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (- 2a d + 2a b c d + 2a b c d - 2b c )x - 2a c d + 4a b c d
+--R +
+--R 2 3
+--R - 2a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R - 625a b d - 1500a b c d - 1350a b c d - 540a b c d - 81b c
+--R /
+--R 13 12 12 11 11 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d + 225a b c d + 135a b c d + 27b c )\|x
+--R +
+--R 10 9 9 8 8 2 2 7 7 3 3 6
+--R 512a d - 4608a b c d + 18432a b c d - 43008a b c d
+--R +
+--R 6 4 4 5 5 5 5 4 4 6 6 3 3 7 7 2
+--R 64512a b c d - 64512a b c d + 43008a b c d - 18432a b c d
+--R +
+--R 2 8 8 9 9
+--R 4608a b c d - 512a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d - 1500a b c d - 1350a b c d - 540a b c d
+--R +
+--R 5 4
+--R - 81b c
+--R /
+--R 13 12 12 11 11 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 3 2 2 3 2 4
+--R (2a b d - 4a b c d + 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2 2 3
+--R (2a d - 2a b c d - 2a b c d + 2b c )x + 2a c d - 4a b c d + 2a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R - 625a b d - 1500a b c d - 1350a b c d - 540a b c d - 81b c
+--R /
+--R 13 12 12 11 11 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d + 225a b c d + 135a b c d + 27b c )\|x
+--R +
+--R 10 9 9 8 8 2 2 7 7 3 3 6
+--R - 512a d + 4608a b c d - 18432a b c d + 43008a b c d
+--R +
+--R 6 4 4 5 5 5 5 4 4 6 6 3
+--R - 64512a b c d + 64512a b c d - 43008a b c d
+--R +
+--R 3 7 7 2 2 8 8 9 9
+--R 18432a b c d - 4608a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d - 1500a b c d - 1350a b c d - 540a b c d
+--R +
+--R 5 4
+--R - 81b c
+--R /
+--R 13 12 12 11 11 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2 3 2 2 3 2 4
+--R (- 4a b d + 8a b c d - 4b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (- 4a d + 4a b c d + 4a b c d - 4b c )x - 4a c d + 8a b c d
+--R +
+--R 2 3
+--R - 4a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R - 625a b d - 1500a b c d - 1350a b c d - 540a b c d - 81b c
+--R /
+--R 13 12 12 11 11 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 10 9 9 8 8 2 2 7 7 3 3 6
+--R 512a d - 4608a b c d + 18432a b c d - 43008a b c d
+--R +
+--R 6 4 4 5 5 5 5 4 4 6 6 3 3 7 7 2
+--R 64512a b c d - 64512a b c d + 43008a b c d - 18432a b c d
+--R +
+--R 2 8 8 9 9
+--R 4608a b c d - 512a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d - 1500a b c d - 1350a b c d - 540a b c d
+--R +
+--R 5 4
+--R - 81b c
+--R /
+--R 13 12 12 11 11 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d + 225a b c d + 135a b c d + 27b c )\|x
+--R +
+--R 2 3 2 2 3 2 4
+--R (4a b d - 8a b c d + 4b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2 2 3
+--R (4a d - 4a b c d - 4a b c d + 4b c )x + 4a c d - 8a b c d + 4a b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R - 81a d - 540a b c d - 1350a b c d - 1500a b c d - 625b c d
+--R /
+--R 12 12 11 2 11 10 2 3 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 4 9 8 4 5 8 7 5 6 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 7 6 5 7 8 5 4 8 9 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 10 3 2 10 11 2 11 12 12 13
+--R - 901120a b c d + 270336a b c d - 49152a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 9 9 8 2 8 7 2 3 7 6 3 4 6
+--R 512a c d - 4608a b c d + 18432a b c d - 43008a b c d
+--R +
+--R 5 4 5 5 4 5 6 4 3 6 7 3 2 7 8 2
+--R 64512a b c d - 64512a b c d + 43008a b c d - 18432a b c d
+--R +
+--R 8 9 9 10
+--R 4608a b c d - 512b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R - 81a d - 540a b c d - 1350a b c d - 1500a b c d
+--R +
+--R 4 4
+--R - 625b c d
+--R /
+--R 12 12 11 2 11 10 2 3 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 4 9 8 4 5 8 7 5 6 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 7 6 5 7 8 5 4 8 9 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 10 3 2 10 11 2 11 12
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 13
+--R 4096b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (27a d + 135a b c d + 225a b c d + 125b c d)\|x
+--R +
+--R 3 +-+
+--R (- 2b d x + (- a d - b c)x)\|x
+--R /
+--R 2 3 2 2 3 2 4
+--R (2a b d - 4a b c d + 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2 2 3
+--R (2a d - 2a b c d - 2a b c d + 2b c )x + 2a c d - 4a b c d + 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 1085
+
+--S 1086 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (3a d + 5b c)\|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5a d - 3b c)\|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (8a d - 24a b c d + 24a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R - 81a d - 540a b c d - 1350a b c d - 1500a b c d - 625b c d
+--R /
+--R 12 12 11 2 11 10 2 3 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 4 9 8 4 5 8 7 5 6 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 7 6 5 7 8 5 4 8 9 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 10 3 2 10 11 2 11 12 12 13
+--R - 901120a b c d + 270336a b c d - 49152a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (27a d + 135a b c d + 225a b c d + 125b c d)\|x
+--R +
+--R 9 9 8 2 8 7 2 3 7 6 3 4 6
+--R 512a c d - 4608a b c d + 18432a b c d - 43008a b c d
+--R +
+--R 5 4 5 5 4 5 6 4 3 6 7 3 2 7 8 2
+--R 64512a b c d - 64512a b c d + 43008a b c d - 18432a b c d
+--R +
+--R 8 9 9 10
+--R 4608a b c d - 512b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R - 81a d - 540a b c d - 1350a b c d - 1500a b c d
+--R +
+--R 4 4
+--R - 625b c d
+--R /
+--R 12 12 11 2 11 10 2 3 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 4 9 8 4 5 8 7 5 6 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 7 6 5 7 8 5 4 8 9 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 10 3 2 10 11 2 11 12
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 13
+--R 4096b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (- 8a d + 24a b c d - 24a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R - 81a d - 540a b c d - 1350a b c d - 1500a b c d - 625b c d
+--R /
+--R 12 12 11 2 11 10 2 3 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 4 9 8 4 5 8 7 5 6 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 7 6 5 7 8 5 4 8 9 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 10 3 2 10 11 2 11 12 12 13
+--R - 901120a b c d + 270336a b c d - 49152a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (27a d + 135a b c d + 225a b c d + 125b c d)\|x
+--R +
+--R 9 9 8 2 8 7 2 3 7 6 3 4 6
+--R - 512a c d + 4608a b c d - 18432a b c d + 43008a b c d
+--R +
+--R 5 4 5 5 4 5 6 4 3 6 7 3
+--R - 64512a b c d + 64512a b c d - 43008a b c d
+--R +
+--R 2 7 8 2 8 9 9 10
+--R 18432a b c d - 4608a b c d + 512b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R - 81a d - 540a b c d - 1350a b c d - 1500a b c d
+--R +
+--R 4 4
+--R - 625b c d
+--R /
+--R 12 12 11 2 11 10 2 3 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 4 9 8 4 5 8 7 5 6 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 7 6 5 7 8 5 4 8 9 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 10 3 2 10 11 2 11 12
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 13
+--R 4096b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (- 8a d + 24a b c d - 24a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R - 625a b d - 1500a b c d - 1350a b c d - 540a b c d - 81b c
+--R /
+--R 13 12 12 11 11 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d + 225a b c d + 135a b c d + 27b c )\|x
+--R +
+--R 10 9 9 8 8 2 2 7 7 3 3 6
+--R 512a d - 4608a b c d + 18432a b c d - 43008a b c d
+--R +
+--R 6 4 4 5 5 5 5 4 4 6 6 3 3 7 7 2
+--R 64512a b c d - 64512a b c d + 43008a b c d - 18432a b c d
+--R +
+--R 2 8 8 9 9
+--R 4608a b c d - 512a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d - 1500a b c d - 1350a b c d - 540a b c d
+--R +
+--R 5 4
+--R - 81b c
+--R /
+--R 13 12 12 11 11 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (8a d - 24a b c d + 24a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R - 625a b d - 1500a b c d - 1350a b c d - 540a b c d - 81b c
+--R /
+--R 13 12 12 11 11 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d + 225a b c d + 135a b c d + 27b c )\|x
+--R +
+--R 10 9 9 8 8 2 2 7 7 3 3 6
+--R - 512a d + 4608a b c d - 18432a b c d + 43008a b c d
+--R +
+--R 6 4 4 5 5 5 5 4 4 6 6 3
+--R - 64512a b c d + 64512a b c d - 43008a b c d
+--R +
+--R 3 7 7 2 2 8 8 9 9
+--R 18432a b c d - 4608a b c d + 512a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d - 1500a b c d - 1350a b c d - 540a b c d
+--R +
+--R 5 4
+--R - 81b c
+--R /
+--R 13 12 12 11 11 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5a d + 3b c)\|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3a d - 5b c)\|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R (- 6a d - 10b c)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R (- 6a d - 10b c)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a
+--R (10a d + 6b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x - \|a
+--R (10a d + 6b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (- 16a d + 48a b c d - 48a b c d + 16b c )\|2
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R - 625a b d - 1500a b c d - 1350a b c d - 540a b c d - 81b c
+--R /
+--R 13 12 12 11 11 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R atan
+--R 10 9 9 8 8 2 2 7 7 3 3 6
+--R 512a d - 4608a b c d + 18432a b c d - 43008a b c d
+--R +
+--R 6 4 4 5 5 5 5 4 4 6 6 3 3 7 7 2
+--R 64512a b c d - 64512a b c d + 43008a b c d - 18432a b c d
+--R +
+--R 2 8 8 9 9
+--R 4608a b c d - 512a b c
+--R *
+--R ROOT
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 625a b d - 1500a b c d - 1350a b c d - 540a b c d
+--R +
+--R 5 4
+--R - 81b c
+--R /
+--R 13 12 12 11 11 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 10 3 3 9 9 4 4 8 8 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 7 6 6 6 6 7 7 5 5 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 4 9 9 3 3 10 10 2 2 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 3 2 2 2 3 2 4 3 +-+
+--R (125a b d + 225a b c d + 135a b c d + 27b c )\|x
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (16a d - 48a b c d + 48a b c d - 16b c )\|2
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R - 81a d - 540a b c d - 1350a b c d - 1500a b c d - 625b c d
+--R /
+--R 12 12 11 2 11 10 2 3 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 4 9 8 4 5 8 7 5 6 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 7 6 5 7 8 5 4 8 9 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 10 3 2 10 11 2 11 12 12 13
+--R - 901120a b c d + 270336a b c d - 49152a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R atan
+--R 9 9 8 2 8 7 2 3 7 6 3 4 6
+--R 512a c d - 4608a b c d + 18432a b c d - 43008a b c d
+--R +
+--R 5 4 5 5 4 5 6 4 3 6 7 3 2 7 8 2
+--R 64512a b c d - 64512a b c d + 43008a b c d - 18432a b c d
+--R +
+--R 8 9 9 10
+--R 4608a b c d - 512b c
+--R *
+--R ROOT
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R - 81a d - 540a b c d - 1350a b c d - 1500a b c d
+--R +
+--R 4 4
+--R - 625b c d
+--R /
+--R 12 12 11 2 11 10 2 3 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 4 9 8 4 5 8 7 5 6 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 7 6 5 7 8 5 4 8 9 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 10 3 2 10 11 2 11 12
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 13
+--R 4096b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (27a d + 135a b c d + 225a b c d + 125b c d)\|x
+--R /
+--R 3 3 2 2 2 2 3 3 +-+4+-+4+-+
+--R (8a d - 24a b c d + 24a b c d - 8b c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1086
+
+--S 1087 of 1527
+--d0:=D(m0,x)
+--E 1087
+
+)clear all
+
+--S 1088 of 1527
+t0:=x^(3/2)/((a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R +-+
+--R x\|x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Expression(Integer)
+--E 1088
+
+--S 1089 of 1527
+r0:=-1/4*b^(3/4)*(b*c+7*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(3/4)*(b*c-a*d)^3*sqrt(2))+1/4*b^(3/4)*(b*c+7*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*(b*c-a*d)^3*_
+ sqrt(2))+1/4*d^(3/4)*(7*b*c+a*d)*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(3/4)*(b*c-a*d)^3*sqrt(2))-1/4*d^(3/4)*_
+ (7*b*c+a*d)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(3/4)*_
+ (b*c-a*d)^3*sqrt(2))-1/8*b^(3/4)*(b*c+7*a*d)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*(b*c-a*d)^3*_
+ sqrt(2))+1/8*b^(3/4)*(b*c+7*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*(b*c-a*d)^3*sqrt(2))+1/8*d^(3/4)*_
+ (7*b*c+a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(3/4)*(b*c-a*d)^3*sqrt(2))-1/8*d^(3/4)*(7*b*c+a*d)*log(sqrt(c)+_
+ x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(3/4)*(b*c-a*d)^3*_
+ sqrt(2))-d*sqrt(x)/((b*c-a*d)^2*(c+d*x^2))-1/2*sqrt(x)/_
+ ((b*c-a*d)*(a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((a b d + 7b c d)x + (a d + 8a b c d + 7b c )x + a c d + 7a b c )
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 7a b d - b c d)x + (- 7a d - 8a b c d - b c )x - 7a c d
+--R +
+--R 2
+--R - a b c
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4 2 2 2 2 2 2 2
+--R ((7a b d + b c d)x + (7a d + 8a b c d + b c )x + 7a c d + a b c )
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 7b c d)x + (- a d - 8a b c d - 7b c )x - a c d
+--R +
+--R 2
+--R - 7a b c
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (2a b d + 14b c d)x + (2a d + 16a b c d + 14b c )x + 2a c d
+--R +
+--R 2
+--R 14a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x + \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (2a b d + 14b c d)x + (2a d + 16a b c d + 14b c )x + 2a c d
+--R +
+--R 2
+--R 14a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x - \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 14a b d - 2b c d)x + (- 14a d - 16a b c d - 2b c )x - 14a c d
+--R +
+--R 2
+--R - 2a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x + \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- 14a b d - 2b c d)x + (- 14a d - 16a b c d - 2b c )x - 14a c d
+--R +
+--R 2
+--R - 2a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x - \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 2 2 2 +-+4+-+3 4+-+3 +-+
+--R ((- 8a b d + 8b c d)x - 4a d + 4b c )\|2 \|a \|c \|x
+--R /
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (8a b d - 24a b c d + 24a b c d - 8b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3 3 2 2
+--R (8a d - 16a b c d + 16a b c d - 8b c )x + 8a c d - 24a b c d
+--R +
+--R 2 2 3 3 4
+--R 24a b c d - 8a b c
+--R *
+--R +-+4+-+3 4+-+3
+--R \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1089
+
+--S 1090 of 1527
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 3 2 4
+--R (2a b d - 4a b c d + 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2 2 3
+--R (2a d - 2a b c d - 2a b c d + 2b c )x + 2a c d - 4a b c d + 2a b c
+--R *
+--R ROOT
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R - a d - 28a b c d - 294a b c d - 1372a b c d - 2401b c d
+--R /
+--R 12 3 12 11 4 11 10 2 5 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 6 9 8 4 7 8 7 5 8 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 9 6 5 7 10 5 4 8 11 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 12 3 2 10 13 2 11 14 12 15
+--R - 901120a b c d + 270336a b c d - 49152a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R log
+--R 2 +-+
+--R (a d + 7b c d)\|x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R ROOT
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R - a d - 28a b c d - 294a b c d - 1372a b c d
+--R +
+--R 4 4 3
+--R - 2401b c d
+--R /
+--R 12 3 12 11 4 11 10 2 5 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 6 9 8 4 7 8 7 5 8 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 9 6 5 7 10 5 4 8 11 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 12 3 2 10 13 2 11 14
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 15
+--R 4096b c
+--R ,
+--R 4
+--R +
+--R 2 3 2 2 3 2 4
+--R (- 2a b d + 4a b c d - 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (- 2a d + 2a b c d + 2a b c d - 2b c )x - 2a c d + 4a b c d
+--R +
+--R 2 3
+--R - 2a b c
+--R *
+--R ROOT
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R - a d - 28a b c d - 294a b c d - 1372a b c d - 2401b c d
+--R /
+--R 12 3 12 11 4 11 10 2 5 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 6 9 8 4 7 8 7 5 8 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 9 6 5 7 10 5 4 8 11 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 12 3 2 10 13 2 11 14 12 15
+--R - 901120a b c d + 270336a b c d - 49152a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R log
+--R 2 +-+
+--R (a d + 7b c d)\|x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 8a c d + 24a b c d - 24a b c d + 8b c )
+--R *
+--R ROOT
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R - a d - 28a b c d - 294a b c d - 1372a b c d
+--R +
+--R 4 4 3
+--R - 2401b c d
+--R /
+--R 12 3 12 11 4 11 10 2 5 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 6 9 8 4 7 8 7 5 8 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 9 6 5 7 10 5 4 8 11 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 12 3 2 10 13 2 11 14
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 15
+--R 4096b c
+--R ,
+--R 4
+--R +
+--R 2 3 2 2 3 2 4
+--R (- 2a b d + 4a b c d - 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (- 2a d + 2a b c d + 2a b c d - 2b c )x - 2a c d + 4a b c d
+--R +
+--R 2 3
+--R - 2a b c
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R - 2401a b d - 1372a b c d - 294a b c d - 28a b c d - b c
+--R /
+--R 15 12 14 11 13 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 3 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 2 +-+
+--R (7a b d + b c)\|x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R - 2401a b d - 1372a b c d - 294a b c d - 28a b c d
+--R +
+--R 7 4
+--R - b c
+--R /
+--R 15 12 14 11 13 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 3 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R +
+--R 2 3 2 2 3 2 4
+--R (2a b d - 4a b c d + 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2 2 3
+--R (2a d - 2a b c d - 2a b c d + 2b c )x + 2a c d - 4a b c d + 2a b c
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R - 2401a b d - 1372a b c d - 294a b c d - 28a b c d - b c
+--R /
+--R 15 12 14 11 13 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 3 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 2 +-+
+--R (7a b d + b c)\|x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 8a d + 24a b c d - 24a b c d + 8a b c )
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R - 2401a b d - 1372a b c d - 294a b c d - 28a b c d
+--R +
+--R 7 4
+--R - b c
+--R /
+--R 15 12 14 11 13 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 3 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R +
+--R 2 3 2 2 3 2 4
+--R (4a b d - 8a b c d + 4b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2 2 3
+--R (4a d - 4a b c d - 4a b c d + 4b c )x + 4a c d - 8a b c d + 4a b c
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R - 2401a b d - 1372a b c d - 294a b c d - 28a b c d - b c
+--R /
+--R 15 12 14 11 13 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 3 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 4 3 3 2 2 2 2 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R - 2401a b d - 1372a b c d - 294a b c d - 28a b c d
+--R +
+--R 7 4
+--R - b c
+--R /
+--R 15 12 14 11 13 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 3 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R /
+--R 2 +-+
+--R (7a b d + b c)\|x
+--R +
+--R 2 3 2 2 3 2 4
+--R (- 4a b d + 8a b c d - 4b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (- 4a d + 4a b c d + 4a b c d - 4b c )x - 4a c d + 8a b c d
+--R +
+--R 2 3
+--R - 4a b c
+--R *
+--R ROOT
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R - a d - 28a b c d - 294a b c d - 1372a b c d - 2401b c d
+--R /
+--R 12 3 12 11 4 11 10 2 5 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 6 9 8 4 7 8 7 5 8 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 9 6 5 7 10 5 4 8 11 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 12 3 2 10 13 2 11 14 12 15
+--R - 901120a b c d + 270336a b c d - 49152a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R atan
+--R 3 3 2 2 2 2 3 3 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R ROOT
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R - a d - 28a b c d - 294a b c d - 1372a b c d
+--R +
+--R 4 4 3
+--R - 2401b c d
+--R /
+--R 12 3 12 11 4 11 10 2 5 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 6 9 8 4 7 8 7 5 8 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 9 6 5 7 10 5 4 8 11 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 12 3 2 10 13 2 11 14
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 15
+--R 4096b c
+--R ,
+--R 4
+--R /
+--R 2 +-+
+--R (a d + 7b c d)\|x
+--R +
+--R 2 +-+
+--R (- 2b d x - a d - b c)\|x
+--R /
+--R 2 3 2 2 3 2 4
+--R (2a b d - 4a b c d + 2b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2 2 3
+--R (2a d - 2a b c d - 2a b c d + 2b c )x + 2a c d - 4a b c d + 2a b c
+--R Type: Union(Expression(Integer),...)
+--E 1090
+
+--S 1091 of 1527
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- a d - 7b c)\|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (7a d + b c)\|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (8a d - 24a b c d + 24a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R - a d - 28a b c d - 294a b c d - 1372a b c d - 2401b c d
+--R /
+--R 12 3 12 11 4 11 10 2 5 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 6 9 8 4 7 8 7 5 8 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 9 6 5 7 10 5 4 8 11 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 12 3 2 10 13 2 11 14 12 15
+--R - 901120a b c d + 270336a b c d - 49152a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2 +-+
+--R (a d + 7b c d)\|x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R ROOT
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R - a d - 28a b c d - 294a b c d - 1372a b c d
+--R +
+--R 4 4 3
+--R - 2401b c d
+--R /
+--R 12 3 12 11 4 11 10 2 5 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 6 9 8 4 7 8 7 5 8 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 9 6 5 7 10 5 4 8 11 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 12 3 2 10 13 2 11 14
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 15
+--R 4096b c
+--R ,
+--R 4
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (- 8a d + 24a b c d - 24a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R - a d - 28a b c d - 294a b c d - 1372a b c d - 2401b c d
+--R /
+--R 12 3 12 11 4 11 10 2 5 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 6 9 8 4 7 8 7 5 8 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 9 6 5 7 10 5 4 8 11 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 12 3 2 10 13 2 11 14 12 15
+--R - 901120a b c d + 270336a b c d - 49152a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2 +-+
+--R (a d + 7b c d)\|x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 8a c d + 24a b c d - 24a b c d + 8b c )
+--R *
+--R ROOT
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R - a d - 28a b c d - 294a b c d - 1372a b c d
+--R +
+--R 4 4 3
+--R - 2401b c d
+--R /
+--R 12 3 12 11 4 11 10 2 5 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 6 9 8 4 7 8 7 5 8 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 9 6 5 7 10 5 4 8 11 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 12 3 2 10 13 2 11 14
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 15
+--R 4096b c
+--R ,
+--R 4
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (- 8a d + 24a b c d - 24a b c d + 8b c )\|2
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R - 2401a b d - 1372a b c d - 294a b c d - 28a b c d - b c
+--R /
+--R 15 12 14 11 13 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 3 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2 +-+
+--R (7a b d + b c)\|x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R - 2401a b d - 1372a b c d - 294a b c d - 28a b c d
+--R +
+--R 7 4
+--R - b c
+--R /
+--R 15 12 14 11 13 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 3 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (8a d - 24a b c d + 24a b c d - 8b c )\|2
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R - 2401a b d - 1372a b c d - 294a b c d - 28a b c d - b c
+--R /
+--R 15 12 14 11 13 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 3 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2 +-+
+--R (7a b d + b c)\|x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (- 8a d + 24a b c d - 24a b c d + 8a b c )
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R - 2401a b d - 1372a b c d - 294a b c d - 28a b c d
+--R +
+--R 7 4
+--R - b c
+--R /
+--R 15 12 14 11 13 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 3 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 7a d - b c)\|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R (a d + 7b c)\|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x + \|c
+--R (- 2a d - 14b c)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x - \|c
+--R (- 2a d - 14b c)\|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x + \|a
+--R (14a d + 2b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x - \|a
+--R (14a d + 2b c)\|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (16a d - 48a b c d + 48a b c d - 16b c )\|2
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R - 2401a b d - 1372a b c d - 294a b c d - 28a b c d - b c
+--R /
+--R 15 12 14 11 13 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 3 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R atan
+--R 4 3 3 2 2 2 2 3 3
+--R (8a d - 24a b c d + 24a b c d - 8a b c )
+--R *
+--R ROOT
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R - 2401a b d - 1372a b c d - 294a b c d - 28a b c d
+--R +
+--R 7 4
+--R - b c
+--R /
+--R 15 12 14 11 13 2 2 10
+--R 4096a d - 49152a b c d + 270336a b c d
+--R +
+--R 12 3 3 9 11 4 4 8 10 5 5 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 9 6 6 6 8 7 7 5 7 8 8 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 6 9 9 3 5 10 10 2 4 11 11
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 3 12 12
+--R 4096a b c
+--R ,
+--R 4
+--R /
+--R 2 +-+
+--R (7a b d + b c)\|x
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (- 16a d + 48a b c d - 48a b c d + 16b c )\|2
+--R *
+--R ROOT
+--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R - a d - 28a b c d - 294a b c d - 1372a b c d - 2401b c d
+--R /
+--R 12 3 12 11 4 11 10 2 5 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 6 9 8 4 7 8 7 5 8 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 9 6 5 7 10 5 4 8 11 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 12 3 2 10 13 2 11 14 12 15
+--R - 901120a b c d + 270336a b c d - 49152a b c d + 4096b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R atan
+--R 3 3 2 2 2 2 3 3 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c )
+--R *
+--R ROOT
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R - a d - 28a b c d - 294a b c d - 1372a b c d
+--R +
+--R 4 4 3
+--R - 2401b c d
+--R /
+--R 12 3 12 11 4 11 10 2 5 10
+--R 4096a c d - 49152a b c d + 270336a b c d
+--R +
+--R 9 3 6 9 8 4 7 8 7 5 8 7
+--R - 901120a b c d + 2027520a b c d - 3244032a b c d
+--R +
+--R 6 6 9 6 5 7 10 5 4 8 11 4
+--R 3784704a b c d - 3244032a b c d + 2027520a b c d
+--R +
+--R 3 9 12 3 2 10 13 2 11 14
+--R - 901120a b c d + 270336a b c d - 49152a b c d
+--R +
+--R 12 15
+--R 4096b c
+--R ,
+--R 4
+--R /
+--R 2 +-+
+--R (a d + 7b c d)\|x
+--R /
+--R 3 3 2 2 2 2 3 3 +-+4+-+3 4+-+3
+--R (8a d - 24a b c d + 24a b c d - 8b c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1091
+
+--S 1092 of 1527
+--d0:=D(m0,x)
+--E 1092
+
+)clear all
+
+--S 1093 of 1527
+t0:=sqrt(x)/((a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R +-+
+--R \|x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Expression(Integer)
+--E 1093
+
+--S 1094 of 1527
+r0:=1/2*d*(b*c+a*d)*x^(3/2)/(a*c*(b*c-a*d)^2*(c+d*x^2))+1/2*b*x^(3/2)/_
+ (a*(b*c-a*d)*(a+b*x^2)*(c+d*x^2))-1/4*b^(5/4)*(b*c-9*a*d)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*(b*c-a*d)^3*_
+ sqrt(2))+1/4*b^(5/4)*(b*c-9*a*d)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(5/4)*(b*c-a*d)^3*sqrt(2))-1/4*d^(5/4)*_
+ (9*b*c-a*d)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(5/4)*_
+ (b*c-a*d)^3*sqrt(2))+1/4*d^(5/4)*(9*b*c-a*d)*atan(1+d^(1/4)*_
+ sqrt(2)*sqrt(x)/c^(1/4))/(c^(5/4)*(b*c-a*d)^3*sqrt(2))+_
+ 1/8*b^(5/4)*(b*c-9*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(5/4)*(b*c-a*d)^3*sqrt(2))-1/8*b^(5/4)*(b*c-_
+ 9*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(5/4)*(b*c-a*d)^3*sqrt(2))+1/8*d^(5/4)*(9*b*c-a*d)*log(sqrt(c)+_
+ x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(5/4)*(b*c-a*d)^3*_
+ sqrt(2))-1/8*d^(5/4)*(9*b*c-a*d)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(5/4)*(b*c-a*d)^3*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 3 2 2 4 3 3 2 2 2 2 2 3 2
+--R (- a b d + 9a b c d )x + (- a d + 8a b c d + 9a b c d)x - a c d
+--R +
+--R 2 2
+--R 9a b c d
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (- 9a b c d + b c d)x + (- 9a b c d - 8a b c d + b c )x
+--R +
+--R 2 2 2 3
+--R - 9a b c d + a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2 2 2
+--R (9a b c d - b c d)x + (9a b c d + 8a b c d - b c )x + 9a b c d
+--R +
+--R 2 3
+--R - a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2 3 2
+--R (a b d - 9a b c d )x + (a d - 8a b c d - 9a b c d)x + a c d
+--R +
+--R 2 2
+--R - 9a b c d
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (2a b d - 18a b c d )x + (2a d - 16a b c d - 18a b c d)x
+--R +
+--R 3 2 2 2
+--R 2a c d - 18a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (2a b d - 18a b c d )x + (2a d - 16a b c d - 18a b c d)x
+--R +
+--R 3 2 2 2
+--R 2a c d - 18a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (18a b c d - 2b c d)x + (18a b c d + 16a b c d - 2b c )x
+--R +
+--R 2 2 2 3
+--R 18a b c d - 2a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (18a b c d - 2b c d)x + (18a b c d + 16a b c d - 2b c )x
+--R +
+--R 2 2 2 3
+--R 18a b c d - 2a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x - \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3 +-+
+--R ((4a b d - 4b c d)x + (4a d - 4a b c d + 4a b c d - 4b c )x)\|2
+--R *
+--R 4+-+4+-+ +-+
+--R \|a \|c \|x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (8a b c d - 24a b c d + 24a b c d - 8a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (8a c d - 16a b c d + 16a b c d - 8a b c )x + 8a c d - 24a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 24a b c d - 8a b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1094
+
+--S 1095 of 1527
+--a0:=integrate(t0,x)
+--E 1095
+
+--S 1096 of 1527
+--m0:=a0-r0
+--E 1096
+
+--S 1097 of 1527
+--d0:=D(m0,x)
+--E 1097
+
+)clear all
+
+--S 1098 of 1527
+t0:=1/((a+b*x^2)^2*(c+d*x^2)^2*sqrt(x))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1098
+
+--S 1099 of 1527
+r0:=-1/4*b^(7/4)*(3*b*c-11*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(7/4)*(b*c-a*d)^3*sqrt(2))+1/4*b^(7/4)*(3*b*c-11*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*(b*c-a*d)^3*_
+ sqrt(2))-1/4*d^(7/4)*(11*b*c-3*a*d)*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(7/4)*(b*c-a*d)^3*sqrt(2))+1/4*d^(7/4)*_
+ (11*b*c-3*a*d)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(7/4)*_
+ (b*c-a*d)^3*sqrt(2))-1/8*b^(7/4)*(3*b*c-11*a*d)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*(b*c-a*d)^3*_
+ sqrt(2))+1/8*b^(7/4)*(3*b*c-11*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*(b*c-a*d)^3*sqrt(2))-1/8*d^(7/4)*_
+ (11*b*c-3*a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(7/4)*(b*c-a*d)^3*sqrt(2))+1/8*d^(7/4)*(11*b*c-3*a*d)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(7/4)*_
+ (b*c-a*d)^3*sqrt(2))+1/2*d*(b*c+a*d)*sqrt(x)/(a*c*(b*c-a*d)^2*_
+ (c+d*x^2))+1/2*b*sqrt(x)/(a*(b*c-a*d)*(a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (3a b d - 11a b c d )x + (3a d - 8a b c d - 11a b c d)x
+--R +
+--R 3 2 2 2
+--R 3a c d - 11a b c d
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (11a b c d - 3b c d)x + (11a b c d + 8a b c d - 3b c )x
+--R +
+--R 2 2 2 3
+--R 11a b c d - 3a b c
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (- 11a b c d + 3b c d)x + (- 11a b c d - 8a b c d + 3b c )x
+--R +
+--R 2 2 2 3
+--R - 11a b c d + 3a b c
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (- 3a b d + 11a b c d )x + (- 3a d + 8a b c d + 11a b c d)x
+--R +
+--R 3 2 2 2
+--R - 3a c d + 11a b c d
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (6a b d - 22a b c d )x + (6a d - 16a b c d - 22a b c d)x
+--R +
+--R 3 2 2 2
+--R 6a c d - 22a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x + \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (6a b d - 22a b c d )x + (6a d - 16a b c d - 22a b c d)x
+--R +
+--R 3 2 2 2
+--R 6a c d - 22a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x - \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (22a b c d - 6b c d)x + (22a b c d + 16a b c d - 6b c )x
+--R +
+--R 2 2 2 3
+--R 22a b c d - 6a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x + \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (22a b c d - 6b c d)x + (22a b c d + 16a b c d - 6b c )x
+--R +
+--R 2 2 2 3
+--R 22a b c d - 6a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x - \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 3 2 2 3 3 2 2 2 2 3 3 +-+4+-+3
+--R ((4a b d - 4b c d)x + 4a d - 4a b c d + 4a b c d - 4b c )\|2 \|a
+--R *
+--R 4+-+3 +-+
+--R \|c \|x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (8a b c d - 24a b c d + 24a b c d - 8a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (8a c d - 16a b c d + 16a b c d - 8a b c )x + 8a c d - 24a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 24a b c d - 8a b c
+--R *
+--R +-+4+-+3 4+-+3
+--R \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1099
+
+--S 1100 of 1527
+--a0:=integrate(t0,x)
+--E 1100
+
+--S 1101 of 1527
+--m0:=a0-r0
+--E 1101
+
+--S 1102 of 1527
+--d0:=D(m0,x)
+--E 1102
+
+)clear all
+
+--S 1103 of 1527
+t0:=1/(x^(3/2)*(a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 9 2 2 7 2 2 2 2 5
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 3 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1103
+
+--S 1104 of 1527
+r0:=1/4*b^(9/4)*(5*b*c-13*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(9/4)*(b*c-a*d)^3*sqrt(2))-1/4*b^(9/4)*(5*b*c-13*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*(b*c-a*d)^3*_
+ sqrt(2))+1/4*d^(9/4)*(13*b*c-5*a*d)*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(9/4)*(b*c-a*d)^3*sqrt(2))-1/4*d^(9/4)*_
+ (13*b*c-5*a*d)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(9/4)*_
+ (b*c-a*d)^3*sqrt(2))-1/8*b^(9/4)*(5*b*c-13*a*d)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*(b*c-a*d)^3*_
+ sqrt(2))+1/8*b^(9/4)*(5*b*c-13*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*(b*c-a*d)^3*sqrt(2))-1/8*d^(9/4)*_
+ (13*b*c-5*a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(9/4)*(b*c-a*d)^3*sqrt(2))+1/8*d^(9/4)*(13*b*c-5*a*d)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(9/4)*_
+ (b*c-a*d)^3*sqrt(2))+1/2*(-5*b^2*c^2+8*a*b*c*d-5*a^2*d^2)/(a^2*_
+ c^2*(b*c-a*d)^2*sqrt(x))+1/2*d*(b*c+a*d)/(a*c*(b*c-a*d)^2*_
+ (c+d*x^2)*sqrt(x))+1/2*b/(a*(b*c-a*d)*(a+b*x^2)*(c+d*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 3 4 2 2 3 4 4 4 3 3 2 2 2 2 2
+--R (5a b d - 13a b c d )x + (5a d - 8a b c d - 13a b c d )x
+--R +
+--R 4 3 3 2 2
+--R 5a c d - 13a b c d
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 2 2 4 3 4 2 2 2 2 3 3 4 4 2
+--R (13a b c d - 5b c d)x + (13a b c d + 8a b c d - 5b c )x
+--R +
+--R 2 2 3 3 4
+--R 13a b c d - 5a b c
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 2 4 3 4 2 2 2 2 3 3 4 4 2
+--R (- 13a b c d + 5b c d)x + (- 13a b c d - 8a b c d + 5b c )x
+--R +
+--R 2 2 3 3 4
+--R - 13a b c d + 5a b c
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 4 2 2 3 4 4 4 3 3 2 2 2 2 2
+--R (- 5a b d + 13a b c d )x + (- 5a d + 8a b c d + 13a b c d )x
+--R +
+--R 4 3 3 2 2
+--R - 5a c d + 13a b c d
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 4 2 2 3 4 4 4 3 3 2 2 2 2 2
+--R (- 10a b d + 26a b c d )x + (- 10a d + 16a b c d + 26a b c d )x
+--R +
+--R 4 3 3 2 2
+--R - 10a c d + 26a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x + \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 4 2 2 3 4 4 4 3 3 2 2 2 2 2
+--R (- 10a b d + 26a b c d )x + (- 10a d + 16a b c d + 26a b c d )x
+--R +
+--R 4 3 3 2 2
+--R - 10a c d + 26a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x - \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 2 2 4 3 4 2 2 2 2 3 3 4 4 2
+--R (- 26a b c d + 10b c d)x + (- 26a b c d - 16a b c d + 10b c )x
+--R +
+--R 2 2 3 3 4
+--R - 26a b c d + 10a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|b \|x + \|a
+--R \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 2 4 3 4 2 2 2 2 3 3 4 4 2
+--R (- 26a b c d + 10b c d)x + (- 26a b c d - 16a b c d + 10b c )x
+--R +
+--R 2 2 3 3 4
+--R - 26a b c d + 10a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|b \|x - \|a
+--R \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (- 20a b d + 52a b c d - 52a b c d + 20b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3
+--R (- 20a d + 36a b c d - 36a b c d + 20b c )x - 16a c d
+--R +
+--R 3 2 2 2 2 3 3 4
+--R 48a b c d - 48a b c d + 16a b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R /
+--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 4
+--R (8a b c d - 24a b c d + 24a b c d - 8a b c d)x
+--R +
+--R 6 2 4 5 3 3 3 3 5 2 4 6 2 6 3 3 5 4 2
+--R (8a c d - 16a b c d + 16a b c d - 8a b c )x + 8a c d - 24a b c d
+--R +
+--R 4 2 5 3 3 6
+--R 24a b c d - 8a b c
+--R *
+--R +-+4+-+4+-+ +-+
+--R \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1104
+
+--S 1105 of 1527
+--a0:=integrate(t0,x)
+--E 1105
+
+--S 1106 of 1527
+--m0:=a0-r0
+--E 1106
+
+--S 1107 of 1527
+--d0:=D(m0,x)
+--E 1107
+
+)clear all
+
+--S 1108 of 1527
+t0:=1/(x^(5/2)*(a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 10 2 2 8 2 2 2 2 6
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 4 2 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1108
+
+--S 1109 of 1527
+r0:=1/6*(-7*b^2*c^2+8*a*b*c*d-7*a^2*d^2)/(a^2*c^2*(b*c-a*d)^2*x^(3/2))+_
+ 1/2*d*(b*c+a*d)/(a*c*(b*c-a*d)^2*x^(3/2)*(c+d*x^2))+1/2*b/(a*(b*c-_
+ a*d)*x^(3/2)*(a+b*x^2)*(c+d*x^2))+1/4*b^(11/4)*(7*b*c-15*a*d)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*(b*c-a*d)^3*_
+ sqrt(2))-1/4*b^(11/4)*(7*b*c-15*a*d)*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(11/4)*(b*c-a*d)^3*sqrt(2))+1/4*d^(11/4)*_
+ (15*b*c-7*a*d)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(11/4)*_
+ (b*c-a*d)^3*sqrt(2))-1/4*d^(11/4)*(15*b*c-7*a*d)*atan(1+d^(1/4)*_
+ sqrt(2)*sqrt(x)/c^(1/4))/(c^(11/4)*(b*c-a*d)^3*sqrt(2))+_
+ 1/8*b^(11/4)*(7*b*c-15*a*d)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*(b*c-a*d)^3*sqrt(2))-_
+ 1/8*b^(11/4)*(7*b*c-15*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*(b*c-a*d)^3*sqrt(2))+_
+ 1/8*d^(11/4)*(15*b*c-7*a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(11/4)*(b*c-a*d)^3*sqrt(2))-_
+ 1/8*d^(11/4)*(15*b*c-7*a*d)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(11/4)*(b*c-a*d)^3*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 4 2 2 3 5 4 4 3 3 2 2 2 2 3
+--R (- 21a b d + 45a b c d )x + (- 21a d + 24a b c d + 45a b c d )x
+--R +
+--R 4 3 3 2 2
+--R (- 21a c d + 45a b c d )x
+--R *
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 2 2 4 3 5 2 2 2 2 3 3 4 4 3
+--R (- 45a b c d + 21b c d)x + (- 45a b c d - 24a b c d + 21b c )x
+--R +
+--R 2 2 3 3 4
+--R (- 45a b c d + 21a b c )x
+--R *
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 2 4 3 5 2 2 2 2 3 3 4 4 3
+--R (45a b c d - 21b c d)x + (45a b c d + 24a b c d - 21b c )x
+--R +
+--R 2 2 3 3 4
+--R (45a b c d - 21a b c )x
+--R *
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 4 2 2 3 5 4 4 3 3 2 2 2 2 3
+--R (21a b d - 45a b c d )x + (21a d - 24a b c d - 45a b c d )x
+--R +
+--R 4 3 3 2 2
+--R (21a c d - 45a b c d )x
+--R *
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 4 2 2 3 5 4 4 3 3 2 2 2 2 3
+--R (- 42a b d + 90a b c d )x + (- 42a d + 48a b c d + 90a b c d )x
+--R +
+--R 4 3 3 2 2
+--R (- 42a c d + 90a b c d )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|d \|x + \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 4 2 2 3 5 4 4 3 3 2 2 2 2 3
+--R (- 42a b d + 90a b c d )x + (- 42a d + 48a b c d + 90a b c d )x
+--R +
+--R 4 3 3 2 2
+--R (- 42a c d + 90a b c d )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|d \|x - \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 2 2 4 3 5 2 2 2 2 3 3 4 4 3
+--R (- 90a b c d + 42b c d)x + (- 90a b c d - 48a b c d + 42b c )x
+--R +
+--R 2 2 3 3 4
+--R (- 90a b c d + 42a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|b \|x + \|a
+--R \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 2 4 3 5 2 2 2 2 3 3 4 4 3
+--R (- 90a b c d + 42b c d)x + (- 90a b c d - 48a b c d + 42b c )x
+--R +
+--R 2 2 3 3 4
+--R (- 90a b c d + 42a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|b \|x - \|a
+--R \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 4
+--R (- 28a b d + 60a b c d - 60a b c d + 28b c d)x
+--R +
+--R 4 4 3 3 3 3 4 4 2 4 3
+--R (- 28a d + 44a b c d - 44a b c d + 28b c )x - 16a c d
+--R +
+--R 3 2 2 2 2 3 3 4
+--R 48a b c d - 48a b c d + 16a b c
+--R *
+--R +-+4+-+3 4+-+3
+--R \|2 \|a \|c
+--R /
+--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5
+--R (24a b c d - 72a b c d + 72a b c d - 24a b c d)x
+--R +
+--R 6 2 4 5 3 3 3 3 5 2 4 6 3
+--R (24a c d - 48a b c d + 48a b c d - 24a b c )x
+--R +
+--R 6 3 3 5 4 2 4 2 5 3 3 6
+--R (24a c d - 72a b c d + 72a b c d - 24a b c )x
+--R *
+--R +-+4+-+3 4+-+3 +-+
+--R \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1109
+
+--S 1110 of 1527
+--a0:=integrate(t0,x)
+--E 1110
+
+--S 1111 of 1527
+--m0:=a0-r0
+--E 1111
+
+--S 1112 of 1527
+--d0:=D(m0,x)
+--E 1112
+
+)clear all
+
+--S 1113 of 1527
+t0:=1/(x^(7/2)*(a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 11 2 2 9 2 2 2 2 7
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 5 2 2 3
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1113
+
+--S 1114 of 1527
+r0:=1/10*(-9*b^2*c^2+8*a*b*c*d-9*a^2*d^2)/(a^2*c^2*(b*c-a*d)^2*x^(5/2))+_
+ 1/2*d*(b*c+a*d)/(a*c*(b*c-a*d)^2*x^(5/2)*(c+d*x^2))+1/2*b/_
+ (a*(b*c-a*d)*x^(5/2)*(a+b*x^2)*(c+d*x^2))-1/4*b^(13/4)*_
+ (9*b*c-17*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*_
+ (b*c-a*d)^3*sqrt(2))+1/4*b^(13/4)*(9*b*c-17*a*d)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*(b*c-a*d)^3*sqrt(2))-_
+ 1/4*d^(13/4)*(17*b*c-9*a*d)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/_
+ c^(1/4))/(c^(13/4)*(b*c-a*d)^3*sqrt(2))+1/4*d^(13/4)*(17*b*c-_
+ 9*a*d)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(13/4)*(b*c-_
+ a*d)^3*sqrt(2))+1/8*b^(13/4)*(9*b*c-17*a*d)*log(sqrt(a)+x*_
+ sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*(b*c-a*d)^3*_
+ sqrt(2))-1/8*b^(13/4)*(9*b*c-17*a*d)*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*(b*c-a*d)^3*sqrt(2))+_
+ 1/8*d^(13/4)*(17*b*c-9*a*d)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(c^(13/4)*(b*c-a*d)^3*sqrt(2))-1/8*d^(13/4)*_
+ (17*b*c-9*a*d)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(13/4)*(b*c-a*d)^3*sqrt(2))+1/2*(b*c+a*d)*(9*b^2*c^2-_
+ 17*a*b*c*d+9*a^2*d^2)/(a^3*c^3*(b*c-a*d)^2*sqrt(x))
+--R
+--R
+--R (2)
+--R 4 5 3 2 4 6 5 5 4 4 3 2 2 3 4
+--R (- 45a b d + 85a b c d )x + (- 45a d + 40a b c d + 85a b c d )x
+--R +
+--R 5 4 4 2 3 2
+--R (- 45a c d + 85a b c d )x
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4 3 2 5 4 6 2 3 3 2 4 4 5 5 4
+--R (- 85a b c d + 45b c d)x + (- 85a b c d - 40a b c d + 45b c )x
+--R +
+--R 2 3 4 4 5 2
+--R (- 85a b c d + 45a b c )x
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 3 2 5 4 6 2 3 3 2 4 4 5 5 4
+--R (85a b c d - 45b c d)x + (85a b c d + 40a b c d - 45b c )x
+--R +
+--R 2 3 4 4 5 2
+--R (85a b c d - 45a b c )x
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 5 3 2 4 6 5 5 4 4 3 2 2 3 4
+--R (45a b d - 85a b c d )x + (45a d - 40a b c d - 85a b c d )x
+--R +
+--R 5 4 4 2 3 2
+--R (45a c d - 85a b c d )x
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4 5 3 2 4 6 5 5 4 4 3 2 2 3 4
+--R (90a b d - 170a b c d )x + (90a d - 80a b c d - 170a b c d )x
+--R +
+--R 5 4 4 2 3 2
+--R (90a c d - 170a b c d )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x + \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 4 5 3 2 4 6 5 5 4 4 3 2 2 3 4
+--R (90a b d - 170a b c d )x + (90a d - 80a b c d - 170a b c d )x
+--R +
+--R 5 4 4 2 3 2
+--R (90a c d - 170a b c d )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x - \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 4 3 2 5 4 6 2 3 3 2 4 4 5 5 4
+--R (170a b c d - 90b c d)x + (170a b c d + 80a b c d - 90b c )x
+--R +
+--R 2 3 4 4 5 2
+--R (170a b c d - 90a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|b \|x + \|a
+--R \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 3 2 5 4 6 2 3 3 2 4 4 5 5 4
+--R (170a b c d - 90b c d)x + (170a b c d + 80a b c d - 90b c )x
+--R +
+--R 2 3 4 4 5 2
+--R (170a b c d - 90a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|b \|x - \|a
+--R \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 5 3 2 4 4 3 2 5 4 6
+--R (180a b d - 340a b c d + 340a b c d - 180b c d)x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R 180a d - 196a b c d - 272a b c d + 272a b c d + 196a b c d
+--R +
+--R 5 5
+--R - 180b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3
+--R (144a c d - 288a b c d + 288a b c d - 144a b c )x - 16a c d
+--R +
+--R 4 3 2 3 2 4 2 3 5
+--R 48a b c d - 48a b c d + 16a b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R /
+--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 6
+--R (40a b c d - 120a b c d + 120a b c d - 40a b c d)x
+--R +
+--R 7 3 4 6 4 3 4 3 6 3 4 7 4
+--R (40a c d - 80a b c d + 80a b c d - 40a b c )x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7 2
+--R (40a c d - 120a b c d + 120a b c d - 40a b c )x
+--R *
+--R +-+4+-+4+-+ +-+
+--R \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1114
+
+--S 1115 of 1527
+--a0:=integrate(t0,x)
+--E 1115
+
+--S 1116 of 1527
+--m0:=a0-r0
+--E 1116
+
+--S 1117 of 1527
+--d0:=D(m0,x)
+--E 1117
+
+)clear all
+
+--S 1118 of 1527
+t0:=x^(7/2)/((a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 3 +-+
+--R x \|x
+--R /
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Expression(Integer)
+--E 1118
+
+--S 1119 of 1527
+r0:=1/4*a^(1/4)*b^(3/4)*(5*b*c+7*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/((b*c-a*d)^4*sqrt(2))-1/4*a^(1/4)*b^(3/4)*(5*b*c+7*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/((b*c-a*d)^4*sqrt(2))-_
+ 1/32*(21*b^2*c^2+70*a*b*c*d+5*a^2*d^2)*atan(1-d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(3/4)*d^(1/4)*(b*c-a*d)^4*sqrt(2))+_
+ 1/32*(21*b^2*c^2+70*a*b*c*d+5*a^2*d^2)*atan(1+d^(1/4)*sqrt(2)*_
+ sqrt(x)/c^(1/4))/(c^(3/4)*d^(1/4)*(b*c-a*d)^4*sqrt(2))+_
+ 1/8*a^(1/4)*b^(3/4)*(5*b*c+7*a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/((b*c-a*d)^4*sqrt(2))-_
+ 1/8*a^(1/4)*b^(3/4)*(5*b*c+7*a*d)*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/((b*c-a*d)^4*sqrt(2))-_
+ 1/64*(21*b^2*c^2+70*a*b*c*d+5*a^2*d^2)*log(sqrt(c)+x*sqrt(d)-_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(3/4)*d^(1/4)*(b*c-a*d)^4*_
+ sqrt(2))+1/64*(21*b^2*c^2+70*a*b*c*d+5*a^2*d^2)*log(sqrt(c)+_
+ x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(3/4)*d^(1/4)*_
+ (b*c-a*d)^4*sqrt(2))+1/4*(b*c+2*a*d)*sqrt(x)/(b*(b*c-a*d)^2*_
+ (c+d*x^2)^2)+1/2*a*sqrt(x)/(b*(b*c-a*d)*(a+b*x^2)*(c+d*x^2)^2)+_
+ 1/16*(7*b*c+17*a*d)*sqrt(x)/((b*c-a*d)^3*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 4 2 3 3 2 2 6
+--R (5a b d + 70a b c d + 21b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (5a d + 80a b c d + 161a b c d + 42b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (10a c d + 145a b c d + 112a b c d + 21b c )x + 5a c d
+--R +
+--R 2 3 2 4
+--R 70a b c d + 21a b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 56a b d - 40b c d )x + (- 56a d - 152a b c d - 80b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 112a c d - 136a b c d - 40b c )x - 56a c d - 40a b c
+--R *
+--R 4+-+4+-+3 4+-+3 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|b \|c \|d log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (56a b d + 40b c d )x + (56a d + 152a b c d + 80b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (112a c d + 136a b c d + 40b c )x + 56a c d + 40a b c
+--R *
+--R 4+-+4+-+3 4+-+3 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|b \|c \|d log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 5a b d - 70a b c d - 21b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 5a d - 80a b c d - 161a b c d - 42b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 10a c d - 145a b c d - 112a b c d - 21b c )x - 5a c d
+--R +
+--R 2 3 2 4
+--R - 70a b c d - 21a b c
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (10a b d + 140a b c d + 42b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (10a d + 160a b c d + 322a b c d + 84b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (20a c d + 290a b c d + 224a b c d + 42b c )x + 10a c d
+--R +
+--R 2 3 2 4
+--R 140a b c d + 42a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x + \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (10a b d + 140a b c d + 42b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (10a d + 160a b c d + 322a b c d + 84b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (20a c d + 290a b c d + 224a b c d + 42b c )x + 10a c d
+--R +
+--R 2 3 2 4
+--R 140a b c d + 42a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|d \|x - \|c
+--R atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 112a b d - 80b c d )x + (- 112a d - 304a b c d - 160b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 224a c d - 272a b c d - 80b c )x - 112a c d - 80a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+3 4+-+3 4+-+ \|2 \|b \|x + \|a
+--R \|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 2 6 2 3 2 2 2 4
+--R (- 112a b d - 80b c d )x + (- 112a d - 304a b c d - 160b c d)x
+--R +
+--R 2 2 2 2 3 2 2 2 3
+--R (- 224a c d - 272a b c d - 80b c )x - 112a c d - 80a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+3 4+-+3 4+-+ \|2 \|b \|x - \|a
+--R \|a \|b \|c \|d atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 2 2 3 2 4
+--R (- 68a b d + 40a b c d + 28b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 3 2 2 2
+--R (- 36a d - 76a b c d + 68a b c d + 44b c )x - 20a c d - 56a b c d
+--R +
+--R 2 3
+--R 76a b c
+--R *
+--R +-+4+-+3 4+-+ +-+
+--R \|2 \|c \|d \|x
+--R /
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (64a b d - 256a b c d + 384a b c d - 256a b c d + 64b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2
+--R 64a d - 128a b c d - 128a b c d + 512a b c d - 448a b c d
+--R +
+--R 5 5
+--R 128b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5
+--R 128a c d - 448a b c d + 512a b c d - 128a b c d - 128a b c d
+--R +
+--R 5 6
+--R 64b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R 64a c d - 256a b c d + 384a b c d - 256a b c d + 64a b c
+--R *
+--R +-+4+-+3 4+-+
+--R \|2 \|c \|d
+--R Type: Expression(Integer)
+--E 1119
+
+--S 1120 of 1527
+--a0:=integrate(t0,x)
+--E 1120
+
+--S 1121 of 1527
+--m0:=a0-r0
+--E 1121
+
+--S 1122 of 1527
+--d0:=D(m0,x)
+--E 1122
+
+)clear all
+
+--S 1123 of 1527
+t0:=x^(5/2)/((a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 2 +-+
+--R x \|x
+--R /
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Expression(Integer)
+--E 1123
+
+--S 1124 of 1527
+r0:=-3/4*d*x^(3/2)/((b*c-a*d)^2*(c+d*x^2)^2)-1/2*x^(3/2)/((b*c-a*d)*_
+ (a+b*x^2)*(c+d*x^2)^2)-3/16*d*(7*b*c+a*d)*x^(3/2)/(c*(b*c-a*d)^3*_
+ (c+d*x^2))-3/4*b^(5/4)*(b*c+3*a*d)*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(1/4)*(b*c-a*d)^4*sqrt(2))+3/4*b^(5/4)*_
+ (b*c+3*a*d)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*_
+ (b*c-a*d)^4*sqrt(2))+3/32*d^(1/4)*(15*b^2*c^2+18*a*b*c*d-a^2*d^2)*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(5/4)*(b*c-a*d)^4*_
+ sqrt(2))-3/32*d^(1/4)*(15*b^2*c^2+18*a*b*c*d-a^2*d^2)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(5/4)*(b*c-a*d)^4*_
+ sqrt(2))+3/8*b^(5/4)*(b*c+3*a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*(b*c-a*d)^4*sqrt(2))-_
+ 3/8*b^(5/4)*(b*c+3*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(1/4)*(b*c-a*d)^4*sqrt(2))-3/64*d^(1/4)*_
+ (15*b^2*c^2+18*a*b*c*d-a^2*d^2)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(5/4)*(b*c-a*d)^4*sqrt(2))+3/64*_
+ d^(1/4)*(15*b^2*c^2+18*a*b*c*d-a^2*d^2)*log(sqrt(c)+x*sqrt(d)+_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(5/4)*(b*c-a*d)^4*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 4 2 3 3 2 2 6
+--R (- 3a b d + 54a b c d + 45b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 3a d + 48a b c d + 153a b c d + 90b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 6a c d + 105a b c d + 144a b c d + 45b c )x - 3a c d
+--R +
+--R 2 3 2 4
+--R 54a b c d + 45a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 3 2 2 6
+--R (- 72a b c d - 24b c d )x
+--R +
+--R 2 3 2 2 2 3 3 4
+--R (- 72a b c d - 168a b c d - 48b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (- 144a b c d - 120a b c d - 24b c )x - 72a b c d - 24a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (72a b c d + 24b c d )x + (72a b c d + 168a b c d + 48b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (144a b c d + 120a b c d + 24b c )x + 72a b c d + 24a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (3a b d - 54a b c d - 45b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (3a d - 48a b c d - 153a b c d - 90b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (6a c d - 105a b c d - 144a b c d - 45b c )x + 3a c d - 54a b c d
+--R +
+--R 2 4
+--R - 45a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (6a b d - 108a b c d - 90b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (6a d - 96a b c d - 306a b c d - 180b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (12a c d - 210a b c d - 288a b c d - 90b c )x + 6a c d
+--R +
+--R 2 3 2 4
+--R - 108a b c d - 90a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (6a b d - 108a b c d - 90b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (6a d - 96a b c d - 306a b c d - 180b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (12a c d - 210a b c d - 288a b c d - 90b c )x + 6a c d
+--R +
+--R 2 3 2 4
+--R - 108a b c d - 90a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (144a b c d + 48b c d )x + (144a b c d + 336a b c d + 96b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (288a b c d + 240a b c d + 48b c )x + 144a b c d + 48a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (144a b c d + 48b c d )x + (144a b c d + 336a b c d + 96b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (288a b c d + 240a b c d + 48b c )x + 144a b c d + 48a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x - \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 3 3 2 2 5
+--R (12a b d + 72a b c d - 84b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 3
+--R (12a d + 36a b c d + 84a b c d - 132b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (- 4a c d + 72a b c d - 36a b c d - 32b c )x
+--R *
+--R +-+4+-+4+-+ +-+
+--R \|2 \|a \|c \|x
+--R /
+--R 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 6
+--R (64a b c d - 256a b c d + 384a b c d - 256a b c d + 64b c d )x
+--R +
+--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2
+--R 64a c d - 128a b c d - 128a b c d + 512a b c d - 448a b c d
+--R +
+--R 5 6
+--R 128b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6
+--R 128a c d - 448a b c d + 512a b c d - 128a b c d - 128a b c d
+--R +
+--R 5 7
+--R 64b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7
+--R 64a c d - 256a b c d + 384a b c d - 256a b c d + 64a b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1124
+
+--S 1125 of 1527
+--a0:=integrate(t0,x)
+--E 1125
+
+--S 1126 of 1527
+--m0:=a0-r0
+--E 1126
+
+--S 1127 of 1527
+--d0:=D(m0,x)
+--E 1127
+
+)clear all
+
+--S 1128 of 1527
+t0:=x^(3/2)/((a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R +-+
+--R x\|x
+--R /
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Expression(Integer)
+--E 1128
+
+--S 1129 of 1527
+r0:=-1/4*b^(7/4)*(b*c+11*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(3/4)*(b*c-a*d)^4*sqrt(2))+1/4*b^(7/4)*(b*c+11*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*(b*c-a*d)^4*_
+ sqrt(2))+1/32*d^(3/4)*(77*b^2*c^2+22*a*b*c*d-3*a^2*d^2)*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(7/4)*(b*c-a*d)^4*_
+ sqrt(2))-1/32*d^(3/4)*(77*b^2*c^2+22*a*b*c*d-3*a^2*d^2)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(7/4)*(b*c-a*d)^4*_
+ sqrt(2))-1/8*b^(7/4)*(b*c+11*a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*(b*c-a*d)^4*sqrt(2))+_
+ 1/8*b^(7/4)*(b*c+11*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(3/4)*(b*c-a*d)^4*sqrt(2))+1/64*d^(3/4)*_
+ (77*b^2*c^2+22*a*b*c*d-3*a^2*d^2)*log(sqrt(c)+x*sqrt(d)-_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(7/4)*(b*c-a*d)^4*sqrt(2))-_
+ 1/64*d^(3/4)*(77*b^2*c^2+22*a*b*c*d-3*a^2*d^2)*log(sqrt(c)+_
+ x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(7/4)*(b*c-a*d)^4*_
+ sqrt(2))-3/4*d*sqrt(x)/((b*c-a*d)^2*(c+d*x^2)^2)-1/2*sqrt(x)/_
+ ((b*c-a*d)*(a+b*x^2)*(c+d*x^2)^2)-1/16*d*(23*b*c+a*d)*sqrt(x)/_
+ (c*(b*c-a*d)^3*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 4 2 3 3 2 2 6
+--R (3a b d - 22a b c d - 77b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (3a d - 16a b c d - 121a b c d - 154b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3
+--R (6a c d - 41a b c d - 176a b c d - 77b c )x + 3a c d - 22a b c d
+--R +
+--R 2 4
+--R - 77a b c
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (88a b c d + 8b c d )x + (88a b c d + 184a b c d + 16b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (176a b c d + 104a b c d + 8b c )x + 88a b c d + 8a b c
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (- 88a b c d - 8b c d )x + (- 88a b c d - 184a b c d - 16b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (- 176a b c d - 104a b c d - 8b c )x - 88a b c d - 8a b c
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (- 3a b d + 22a b c d + 77b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (- 3a d + 16a b c d + 121a b c d + 154b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (- 6a c d + 41a b c d + 176a b c d + 77b c )x - 3a c d
+--R +
+--R 2 3 2 4
+--R 22a b c d + 77a b c
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (6a b d - 44a b c d - 154b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (6a d - 32a b c d - 242a b c d - 308b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (12a c d - 82a b c d - 352a b c d - 154b c )x + 6a c d
+--R +
+--R 2 3 2 4
+--R - 44a b c d - 154a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x + \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (6a b d - 44a b c d - 154b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 4
+--R (6a d - 32a b c d - 242a b c d - 308b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (12a c d - 82a b c d - 352a b c d - 154b c )x + 6a c d
+--R +
+--R 2 3 2 4
+--R - 44a b c d - 154a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x - \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (176a b c d + 16b c d )x + (176a b c d + 368a b c d + 32b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (352a b c d + 208a b c d + 16b c )x + 176a b c d + 16a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x + \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 3 3 2 2 6 2 3 2 2 2 3 3 4
+--R (176a b c d + 16b c d )x + (176a b c d + 368a b c d + 32b c d)x
+--R +
+--R 2 2 2 2 3 3 4 2 2 3 2 4
+--R (352a b c d + 208a b c d + 16b c )x + 176a b c d + 16a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x - \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 3 3 2 2 4
+--R (4a b d + 88a b c d - 92b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 2 3 3
+--R (4a d + 44a b c d + 92a b c d - 140b c d)x - 12a c d
+--R +
+--R 2 2 2 2 3 3 4
+--R 88a b c d - 44a b c d - 32b c
+--R *
+--R +-+4+-+3 4+-+3 +-+
+--R \|2 \|a \|c \|x
+--R /
+--R 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 6
+--R (64a b c d - 256a b c d + 384a b c d - 256a b c d + 64b c d )x
+--R +
+--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2
+--R 64a c d - 128a b c d - 128a b c d + 512a b c d - 448a b c d
+--R +
+--R 5 6
+--R 128b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6
+--R 128a c d - 448a b c d + 512a b c d - 128a b c d - 128a b c d
+--R +
+--R 5 7
+--R 64b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7
+--R 64a c d - 256a b c d + 384a b c d - 256a b c d + 64a b c
+--R *
+--R +-+4+-+3 4+-+3
+--R \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1129
+
+--S 1130 of 1527
+--a0:=integrate(t0,x)
+--E 1130
+
+--S 1131 of 1527
+--m0:=a0-r0
+--E 1131
+
+--S 1132 of 1527
+--d0:=D(m0,x)
+--E 1132
+
+)clear all
+
+--S 1133 of 1527
+t0:=sqrt(x)/((a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R +-+
+--R \|x
+--R /
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Expression(Integer)
+--E 1133
+
+--S 1134 of 1527
+r0:=1/4*d*(2*b*c+a*d)*x^(3/2)/(a*c*(b*c-a*d)^2*(c+d*x^2)^2)+_
+ 1/2*b*x^(3/2)/(a*(b*c-a*d)*(a+b*x^2)*(c+d*x^2)^2)+_
+ 1/16*d*(8*b^2*c^2+21*a*b*c*d-5*a^2*d^2)*x^(3/2)/(a*c^2*(b*c-a*d)^3*_
+ (c+d*x^2))-1/4*b^(9/4)*(b*c-13*a*d)*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(5/4)*(b*c-a*d)^4*sqrt(2))+1/4*b^(9/4)*_
+ (b*c-13*a*d)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*_
+ (b*c-a*d)^4*sqrt(2))-1/32*d^(5/4)*(117*b^2*c^2-26*a*b*c*d+_
+ 5*a^2*d^2)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(9/4)*_
+ (b*c-a*d)^4*sqrt(2))+1/32*d^(5/4)*(117*b^2*c^2-26*a*b*c*d+_
+ 5*a^2*d^2)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(9/4)*_
+ (b*c-a*d)^4*sqrt(2))+1/8*b^(9/4)*(b*c-13*a*d)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*(b*c-a*d)^4*_
+ sqrt(2))-1/8*b^(9/4)*(b*c-13*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*(b*c-a*d)^4*sqrt(2))+_
+ 1/64*d^(5/4)*(117*b^2*c^2-26*a*b*c*d+5*a^2*d^2)*log(sqrt(c)+_
+ x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(9/4)*(b*c-a*d)^4*_
+ sqrt(2))-1/64*d^(5/4)*(117*b^2*c^2-26*a*b*c*d+5*a^2*d^2)*_
+ log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(9/4)*(b*c-a*d)^4*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 5 2 2 4 3 2 3 6
+--R (- 5a b d + 26a b c d - 117a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (- 5a d + 16a b c d - 65a b c d - 234a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (- 10a c d + 47a b c d - 208a b c d - 117a b c d)x - 5a c d
+--R +
+--R 3 3 2 2 2 4
+--R 26a b c d - 117a b c d
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (104a b c d - 8b c d )x + (104a b c d + 200a b c d - 16b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (208a b c d + 88a b c d - 8b c )x + 104a b c d - 8a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 3 4 3 2 6
+--R (- 104a b c d + 8b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 4
+--R (- 104a b c d - 200a b c d + 16b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (- 208a b c d - 88a b c d + 8b c )x - 104a b c d + 8a b c
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 5 2 2 4 3 2 3 6
+--R (5a b d - 26a b c d + 117a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (5a d - 16a b c d + 65a b c d + 234a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (10a c d - 47a b c d + 208a b c d + 117a b c d)x + 5a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 26a b c d + 117a b c d
+--R *
+--R 4+-+4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 5 2 2 4 3 2 3 6
+--R (10a b d - 52a b c d + 234a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (10a d - 32a b c d + 130a b c d + 468a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (20a c d - 94a b c d + 416a b c d + 234a b c d)x + 10a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 52a b c d + 234a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x + \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 5 2 2 4 3 2 3 6
+--R (10a b d - 52a b c d + 234a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (10a d - 32a b c d + 130a b c d + 468a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (20a c d - 94a b c d + 416a b c d + 234a b c d)x + 10a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 52a b c d + 234a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|d \|x - \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 2 3 4 3 2 6
+--R (- 208a b c d + 16b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 4
+--R (- 208a b c d - 400a b c d + 32b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (- 416a b c d - 176a b c d + 16b c )x - 208a b c d + 16a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x + \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 3 4 3 2 6
+--R (- 208a b c d + 16b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 4
+--R (- 208a b c d - 400a b c d + 32b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (- 416a b c d - 176a b c d + 16b c )x - 208a b c d + 16a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ \|2 \|b \|x - \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (20a b d - 104a b c d + 52a b c d + 32b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (20a d - 68a b c d - 52a b c d + 36a b c d + 64b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (36a c d - 136a b c d + 100a b c d - 32a b c d + 32b c )x
+--R *
+--R +-+4+-+4+-+ +-+
+--R \|2 \|a \|c \|x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (64a b c d - 256a b c d + 384a b c d - 256a b c d + 64a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 64a c d - 128a b c d - 128a b c d + 512a b c d - 448a b c d
+--R +
+--R 5 7
+--R 128a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 128a c d - 448a b c d + 512a b c d - 128a b c d - 128a b c d
+--R +
+--R 5 8
+--R 64a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 64a c d - 256a b c d + 384a b c d - 256a b c d + 64a b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1134
+
+--S 1135 of 1527
+--a0:=integrate(t0,x)
+--E 1135
+
+--S 1136 of 1527
+--m0:=a0-r0
+--E 1136
+
+--S 1137 of 1527
+--d0:=D(m0,x)
+--E 1137
+
+)clear all
+
+--S 1138 of 1527
+t0:=1/((a+b*x^2)^2*(c+d*x^2)^3*sqrt(x))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1138
+
+--S 1139 of 1527
+r0:=-3/4*b^(11/4)*(b*c-5*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(7/4)*(b*c-a*d)^4*sqrt(2))+3/4*b^(11/4)*(b*c-5*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*(b*c-a*d)^4*_
+ sqrt(2))-3/32*d^(7/4)*(55*b^2*c^2-30*a*b*c*d+7*a^2*d^2)*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(11/4)*(b*c-a*d)^4*_
+ sqrt(2))+3/32*d^(7/4)*(55*b^2*c^2-30*a*b*c*d+7*a^2*d^2)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(11/4)*(b*c-a*d)^4*_
+ sqrt(2))-3/8*b^(11/4)*(b*c-5*a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*(b*c-a*d)^4*sqrt(2))+_
+ 3/8*b^(11/4)*(b*c-5*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(7/4)*(b*c-a*d)^4*sqrt(2))-3/64*d^(7/4)*_
+ (55*b^2*c^2-30*a*b*c*d+7*a^2*d^2)*log(sqrt(c)+x*sqrt(d)-_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(11/4)*(b*c-a*d)^4*sqrt(2))+_
+ 3/64*d^(7/4)*(55*b^2*c^2-30*a*b*c*d+7*a^2*d^2)*log(sqrt(c)+_
+ x*sqrt(d)+c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(11/4)*(b*c-a*d)^4*_
+ sqrt(2))+1/4*d*(2*b*c+a*d)*sqrt(x)/(a*c*(b*c-a*d)^2*(c+d*x^2)^2)+_
+ 1/2*b*sqrt(x)/(a*(b*c-a*d)*(a+b*x^2)*(c+d*x^2)^2)+_
+ 1/16*d*(8*b^2*c^2+23*a*b*c*d-7*a^2*d^2)*sqrt(x)/_
+ (a*c^2*(b*c-a*d)^3*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 3 5 2 2 4 3 2 3 6
+--R (21a b d - 90a b c d + 165a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (21a d - 48a b c d - 15a b c d + 330a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (42a c d - 159a b c d + 240a b c d + 165a b c d)x + 21a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 90a b c d + 165a b c d
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 2 3 4 3 2 6
+--R (- 120a b c d + 24b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 4
+--R (- 120a b c d - 216a b c d + 48b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (- 240a b c d - 72a b c d + 24b c )x - 120a b c d + 24a b c
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (120a b c d - 24b c d )x + (120a b c d + 216a b c d - 48b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (240a b c d + 72a b c d - 24b c )x + 120a b c d - 24a b c
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 5 2 2 4 3 2 3 6
+--R (- 21a b d + 90a b c d - 165a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (- 21a d + 48a b c d + 15a b c d - 330a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (- 42a c d + 159a b c d - 240a b c d - 165a b c d)x - 21a c d
+--R +
+--R 3 3 2 2 2 4
+--R 90a b c d - 165a b c d
+--R *
+--R 4+-+3 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 3 5 2 2 4 3 2 3 6
+--R (42a b d - 180a b c d + 330a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (42a d - 96a b c d - 30a b c d + 660a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (84a c d - 318a b c d + 480a b c d + 330a b c d)x + 42a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 180a b c d + 330a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x + \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 5 2 2 4 3 2 3 6
+--R (42a b d - 180a b c d + 330a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (42a d - 96a b c d - 30a b c d + 660a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (84a c d - 318a b c d + 480a b c d + 330a b c d)x + 42a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 180a b c d + 330a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|d \|x - \|c
+--R \|a \|d atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 3 2 3 4 3 2 6
+--R (- 240a b c d + 48b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 4
+--R (- 240a b c d - 432a b c d + 96b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (- 480a b c d - 144a b c d + 48b c )x - 240a b c d + 48a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x + \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 2 3 4 3 2 6
+--R (- 240a b c d + 48b c d )x
+--R +
+--R 2 2 2 3 3 3 2 4 4 4
+--R (- 240a b c d - 432a b c d + 96b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (- 480a b c d - 144a b c d + 48b c )x - 240a b c d + 48a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 \|2 \|b \|x - \|a
+--R \|b \|c atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 4
+--R (28a b d - 120a b c d + 60a b c d + 32b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2
+--R (28a d - 76a b c d - 60a b c d + 44a b c d + 64b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R 44a c d - 152a b c d + 108a b c d - 32a b c d + 32b c
+--R *
+--R +-+4+-+3 4+-+3 +-+
+--R \|2 \|a \|c \|x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (64a b c d - 256a b c d + 384a b c d - 256a b c d + 64a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 64a c d - 128a b c d - 128a b c d + 512a b c d - 448a b c d
+--R +
+--R 5 7
+--R 128a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 128a c d - 448a b c d + 512a b c d - 128a b c d - 128a b c d
+--R +
+--R 5 8
+--R 64a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 64a c d - 256a b c d + 384a b c d - 256a b c d + 64a b c
+--R *
+--R +-+4+-+3 4+-+3
+--R \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1139
+
+--S 1140 of 1527
+--a0:=integrate(t0,x)
+--E 1140
+
+--S 1141 of 1527
+--m0:=a0-r0
+--E 1141
+
+--S 1142 of 1527
+--d0:=D(m0,x)
+--E 1142
+
+)clear all
+
+--S 1143 of 1527
+t0:=1/(x^(3/2)*(a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 3 11 3 2 2 9 2 3 2 2 2 7
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 5 2 2 3 3 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1143
+
+--S 1144 of 1527
+r0:=1/4*b^(13/4)*(5*b*c-17*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(9/4)*(b*c-a*d)^4*sqrt(2))-1/4*b^(13/4)*(5*b*c-17*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*(b*c-a*d)^4*_
+ sqrt(2))+1/32*d^(9/4)*(221*b^2*c^2-170*a*b*c*d+45*a^2*d^2)*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(13/4)*(b*c-a*d)^4*_
+ sqrt(2))-1/32*d^(9/4)*(221*b^2*c^2-170*a*b*c*d+45*a^2*d^2)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(13/4)*(b*c-a*d)^4*_
+ sqrt(2))-1/8*b^(13/4)*(5*b*c-17*a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*(b*c-a*d)^4*sqrt(2))+_
+ 1/8*b^(13/4)*(5*b*c-17*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*(b*c-a*d)^4*sqrt(2))-_
+ 1/64*d^(9/4)*(221*b^2*c^2-170*a*b*c*d+45*a^2*d^2)*_
+ log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(13/4)*(b*c-a*d)^4*sqrt(2))+1/64*d^(9/4)*(221*b^2*c^2-_
+ 170*a*b*c*d+45*a^2*d^2)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*d^(1/4)*_
+ sqrt(2)*sqrt(x))/(c^(13/4)*(b*c-a*d)^4*sqrt(2))+_
+ 1/16*(-40*b^3*c^3+96*a*b^2*c^2*d-125*a^2*b*c*d^2+45*a^3*_
+ d^3)/(a^2*c^3*(b*c-a*d)^3*sqrt(x))+1/4*d*(2*b*c+a*d)/_
+ (a*c*(b*c-a*d)^2*(c+d*x^2)^2*sqrt(x))+1/2*b/(a*(b*c-a*d)*_
+ (a+b*x^2)*(c+d*x^2)^2*sqrt(x))+1/16*d*(8*b^2*c^2+25*a*b*c*d-_
+ 9*a^2*d^2)/(a*c^2*(b*c-a*d)^3*(c+d*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 4 6 3 2 5 2 3 2 4 6
+--R (45a b d - 170a b c d + 221a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4
+--R (45a d - 80a b c d - 119a b c d + 442a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 2 5 2 4
+--R (90a c d - 295a b c d + 272a b c d + 221a b c d )x + 45a c d
+--R +
+--R 4 3 3 3 2 4 2
+--R - 170a b c d + 221a b c d
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4 3 3 5 4 2 6
+--R (- 136a b c d + 40b c d )x
+--R +
+--R 2 3 3 3 4 4 2 5 5 4
+--R (- 136a b c d - 232a b c d + 80b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 2 2 3 5 4 6
+--R (- 272a b c d - 56a b c d + 40b c )x - 136a b c d + 40a b c
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 3 3 5 4 2 6 2 3 3 3 4 4 2 5 5 4
+--R (136a b c d - 40b c d )x + (136a b c d + 232a b c d - 80b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 2 2 3 5 4 6
+--R (272a b c d + 56a b c d - 40b c )x + 136a b c d - 40a b c
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 6 3 2 5 2 3 2 4 6
+--R (- 45a b d + 170a b c d - 221a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4
+--R (- 45a d + 80a b c d + 119a b c d - 442a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 2 5 2 4
+--R (- 90a c d + 295a b c d - 272a b c d - 221a b c d )x - 45a c d
+--R +
+--R 4 3 3 3 2 4 2
+--R 170a b c d - 221a b c d
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4 6 3 2 5 2 3 2 4 6
+--R (- 90a b d + 340a b c d - 442a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4
+--R (- 90a d + 160a b c d + 238a b c d - 884a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 2 5 2 4
+--R (- 180a c d + 590a b c d - 544a b c d - 442a b c d )x - 90a c d
+--R +
+--R 4 3 3 3 2 4 2
+--R 340a b c d - 442a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x + \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 4 6 3 2 5 2 3 2 4 6
+--R (- 90a b d + 340a b c d - 442a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 4
+--R (- 90a d + 160a b c d + 238a b c d - 884a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 2 5 2 4
+--R (- 180a c d + 590a b c d - 544a b c d - 442a b c d )x - 90a c d
+--R +
+--R 4 3 3 3 2 4 2
+--R 340a b c d - 442a b c d
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x - \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 4 3 3 5 4 2 6 2 3 3 3 4 4 2 5 5 4
+--R (272a b c d - 80b c d )x + (272a b c d + 464a b c d - 160b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 2 2 3 5 4 6
+--R (544a b c d + 112a b c d - 80b c )x + 272a b c d - 80a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|b \|x + \|a
+--R \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 3 3 5 4 2 6 2 3 3 3 4 4 2 5 5 4
+--R (272a b c d - 80b c d )x + (272a b c d + 464a b c d - 160b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 2 2 3 5 4 6
+--R (544a b c d + 112a b c d - 80b c )x + 272a b c d - 80a b c
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|b \|x - \|a
+--R \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 6
+--R (- 180a b d + 680a b c d - 884a b c d + 544a b c d - 160b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3
+--R - 180a d + 356a b c d + 340a b c d - 1156a b c d
+--R +
+--R 4 4 2 5 5
+--R 960a b c d - 320b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2
+--R - 324a c d + 1096a b c d - 1156a b c d + 256a b c d
+--R +
+--R 4 5 5 6
+--R 288a b c d - 160b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R - 128a c d + 512a b c d - 768a b c d + 512a b c d - 128a b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R /
+--R 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 2 5 7 2 6
+--R (64a b c d - 256a b c d + 384a b c d - 256a b c d + 64a b c d )x
+--R +
+--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2
+--R 64a c d - 128a b c d - 128a b c d + 512a b c d - 448a b c d
+--R +
+--R 2 5 8
+--R 128a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8
+--R 128a c d - 448a b c d + 512a b c d - 128a b c d - 128a b c d
+--R +
+--R 2 5 9
+--R 64a b c
+--R *
+--R 2
+--R x
+--R +
+--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9
+--R 64a c d - 256a b c d + 384a b c d - 256a b c d + 64a b c
+--R *
+--R +-+4+-+4+-+ +-+
+--R \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1144
+
+--S 1145 of 1527
+--a0:=integrate(t0,x)
+--E 1145
+
+--S 1146 of 1527
+--m0:=a0-r0
+--E 1146
+
+--S 1147 of 1527
+--d0:=D(m0,x)
+--E 1147
+
+)clear all
+
+--S 1148 of 1527
+t0:=1/(x^(5/2)*(a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 3 12 3 2 2 10 2 3 2 2 2 8
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 6 2 2 3 4 2 3 2
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1148
+
+--S 1149 of 1527
+r0:=1/48*(-56*b^3*c^3+96*a*b^2*c^2*d-189*a^2*b*c*d^2+77*a^3*d^3)/_
+ (a^2*c^3*(b*c-a*d)^3*x^(3/2))+1/4*d*(2*b*c+a*d)/(a*c*(b*c-_
+ a*d)^2*x^(3/2)*(c+d*x^2)^2)+1/2*b/(a*(b*c-a*d)*x^(3/2)*_
+ (a+b*x^2)*(c+d*x^2)^2)+1/16*d*(8*b^2*c^2+27*a*b*c*d-_
+ 11*a^2*d^2)/(a*c^2*(b*c-a*d)^3*x^(3/2)*(c+d*x^2))+1/4*b^(15/4)*_
+ (7*b*c-19*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(11/4)*(b*c-a*d)^4*sqrt(2))-1/4*b^(15/4)*(7*b*c-19*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*(b*c-a*d)^4*_
+ sqrt(2))+1/32*d^(11/4)*(285*b^2*c^2-266*a*b*c*d+77*a^2*d^2)*_
+ atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(15/4)*(b*c-a*d)^4*_
+ sqrt(2))-1/32*d^(11/4)*(285*b^2*c^2-266*a*b*c*d+77*a^2*d^2)*_
+ atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(15/4)*(b*c-a*d)^4*_
+ sqrt(2))+1/8*b^(15/4)*(7*b*c-19*a*d)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*(b*c-a*d)^4*sqrt(2))-_
+ 1/8*b^(15/4)*(7*b*c-19*a*d)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*(b*c-a*d)^4*sqrt(2))+_
+ 1/64*d^(11/4)*(285*b^2*c^2-266*a*b*c*d+77*a^2*d^2)*_
+ log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/_
+ (c^(15/4)*(b*c-a*d)^4*sqrt(2))-1/64*d^(11/4)*(285*b^2*c^2-_
+ 266*a*b*c*d+77*a^2*d^2)*log(sqrt(c)+x*sqrt(d)+c^(1/4)*_
+ d^(1/4)*sqrt(2)*sqrt(x))/(c^(15/4)*(b*c-a*d)^4*sqrt(2))
+--R
+--R
+--R (2)
+--R 4 6 3 2 5 2 3 2 4 7
+--R (- 231a b d + 798a b c d - 855a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 5
+--R (- 231a d + 336a b c d + 741a b c d - 1710a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 3
+--R (- 462a c d + 1365a b c d - 912a b c d - 855a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2
+--R (- 231a c d + 798a b c d - 855a b c d )x
+--R *
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4 3 3 5 4 2 7
+--R (456a b c d - 168b c d )x
+--R +
+--R 2 3 3 3 4 4 2 5 5 5
+--R (456a b c d + 744a b c d - 336b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 3 2 3 5 4 6
+--R (912a b c d + 120a b c d - 168b c )x + (456a b c d - 168a b c )x
+--R *
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 3 3 5 4 2 7
+--R (- 456a b c d + 168b c d )x
+--R +
+--R 2 3 3 3 4 4 2 5 5 5
+--R (- 456a b c d - 744a b c d + 336b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 3 2 3 5 4 6
+--R (- 912a b c d - 120a b c d + 168b c )x + (- 456a b c d + 168a b c )x
+--R *
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4 6 3 2 5 2 3 2 4 7
+--R (231a b d - 798a b c d + 855a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 5
+--R (231a d - 336a b c d - 741a b c d + 1710a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 3
+--R (462a c d - 1365a b c d + 912a b c d + 855a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2
+--R (231a c d - 798a b c d + 855a b c d )x
+--R *
+--R 4+-+3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 4 6 3 2 5 2 3 2 4 7
+--R (- 462a b d + 1596a b c d - 1710a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 5
+--R (- 462a d + 672a b c d + 1482a b c d - 3420a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 3
+--R (- 924a c d + 2730a b c d - 1824a b c d - 1710a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2
+--R (- 462a c d + 1596a b c d - 1710a b c d )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|d \|x + \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 4 6 3 2 5 2 3 2 4 7
+--R (- 462a b d + 1596a b c d - 1710a b c d )x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3 5
+--R (- 462a d + 672a b c d + 1482a b c d - 3420a b c d )x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2 3
+--R (- 924a c d + 2730a b c d - 1824a b c d - 1710a b c d )x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2
+--R (- 462a c d + 1596a b c d - 1710a b c d )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|d \|x - \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 4 3 3 5 4 2 7
+--R (912a b c d - 336b c d )x
+--R +
+--R 2 3 3 3 4 4 2 5 5 5
+--R (912a b c d + 1488a b c d - 672b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 3 2 3 5 4 6
+--R (1824a b c d + 240a b c d - 336b c )x + (912a b c d - 336a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|b \|x + \|a
+--R \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 3 3 5 4 2 7
+--R (912a b c d - 336b c d )x
+--R +
+--R 2 3 3 3 4 4 2 5 5 5
+--R (912a b c d + 1488a b c d - 672b c d)x
+--R +
+--R 2 3 4 2 4 5 5 6 3 2 3 5 4 6
+--R (1824a b c d + 240a b c d - 336b c )x + (912a b c d - 336a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 4+-+3 +-+ \|2 \|b \|x - \|a
+--R \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 4 6 3 2 5 2 3 2 4 4 3 3
+--R - 308a b d + 1064a b c d - 1140a b c d + 608a b c d
+--R +
+--R 5 4 2
+--R - 224b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 6 4 5 3 2 2 4 2 3 3 3
+--R - 308a d + 580a b c d + 532a b c d - 1444a b c d
+--R +
+--R 4 4 2 5 5
+--R 1088a b c d - 448b c d
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 4 2 4 3 2 3 3 2 3 4 2
+--R - 484a c d + 1544a b c d - 1444a b c d + 256a b c d
+--R +
+--R 4 5 5 6
+--R 352a b c d - 224b c
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
+--R - 128a c d + 512a b c d - 768a b c d + 512a b c d - 128a b c
+--R *
+--R +-+4+-+3 4+-+3
+--R \|2 \|a \|c
+--R /
+--R 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3
+--R 192a b c d - 768a b c d + 1152a b c d - 768a b c d
+--R +
+--R 2 5 7 2
+--R 192a b c d
+--R *
+--R 7
+--R x
+--R +
+--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2
+--R 192a c d - 384a b c d - 384a b c d + 1536a b c d - 1344a b c d
+--R +
+--R 2 5 8
+--R 384a b c d
+--R *
+--R 5
+--R x
+--R +
+--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8
+--R 384a c d - 1344a b c d + 1536a b c d - 384a b c d - 384a b c d
+--R +
+--R 2 5 9
+--R 192a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9
+--R (192a c d - 768a b c d + 1152a b c d - 768a b c d + 192a b c )x
+--R *
+--R +-+4+-+3 4+-+3 +-+
+--R \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1149
+
+--S 1150 of 1527
+--a0:=integrate(t0,x)
+--E 1150
+
+--S 1151 of 1527
+--m0:=a0-r0
+--E 1151
+
+--S 1152 of 1527
+--d0:=D(m0,x)
+--E 1152
+
+)clear all
+
+--S 1153 of 1527
+t0:=1/(x^(7/2)*(a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 3 13 3 2 2 11 2 3 2 2 2 9
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 7 2 2 3 5 2 3 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1153
+
+--S 1154 of 1527
+r0:=-3/80*(24*b^3*c^3-32*a*b^2*c^2*d+87*a^2*b*c*d^2-39*a^3*d^3)/_
+ (a^2*c^3*(b*c-a*d)^3*x^(5/2))+1/4*d*(2*b*c+a*d)/(a*c*(b*c-a*d)^2*_
+ x^(5/2)*(c+d*x^2)^2)+1/2*b/(a*(b*c-a*d)*x^(5/2)*(a+b*x^2)*_
+ (c+d*x^2)^2)+1/16*d*(8*b^2*c^2+29*a*b*c*d-13*a^2*d^2)/_
+ (a*c^2*(b*c-a*d)^3*x^(5/2)*(c+d*x^2))-3/4*b^(17/4)*_
+ (3*b*c-7*a*d)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(13/4)*(b*c-a*d)^4*sqrt(2))+3/4*b^(17/4)*(3*b*c-7*a*d)*_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*_
+ (b*c-a*d)^4*sqrt(2))-3/32*d^(13/4)*(119*b^2*c^2-126*a*b*c*d+_
+ 39*a^2*d^2)*atan(1-d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(17/4)*_
+ (b*c-a*d)^4*sqrt(2))+3/32*d^(13/4)*(119*b^2*c^2-126*a*b*c*d+_
+ 39*a^2*d^2)*atan(1+d^(1/4)*sqrt(2)*sqrt(x)/c^(1/4))/(c^(17/4)*_
+ (b*c-a*d)^4*sqrt(2))+3/8*b^(17/4)*(3*b*c-7*a*d)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*_
+ (b*c-a*d)^4*sqrt(2))-3/8*b^(17/4)*(3*b*c-7*a*d)*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*_
+ (b*c-a*d)^4*sqrt(2))+3/64*d^(13/4)*(119*b^2*c^2-126*a*b*c*d+_
+ 39*a^2*d^2)*log(sqrt(c)+x*sqrt(d)-c^(1/4)*d^(1/4)*sqrt(2)*_
+ sqrt(x))/(c^(17/4)*(b*c-a*d)^4*sqrt(2))-3/64*d^(13/4)*_
+ (119*b^2*c^2-126*a*b*c*d+39*a^2*d^2)*log(sqrt(c)+x*sqrt(d)+_
+ c^(1/4)*d^(1/4)*sqrt(2)*sqrt(x))/(c^(17/4)*(b*c-a*d)^4*sqrt(2))+_
+ 3/16*(24*b^4*c^4-32*a*b^3*c^3*d-32*a^2*b^2*c^2*d^2+87*a^3*b*c*d^3-_
+ 39*a^4*d^4)/(a^3*c^4*(b*c-a*d)^3*sqrt(x))
+--R
+--R
+--R (2)
+--R 5 7 4 2 6 3 3 2 5 8
+--R (- 585a b d + 1890a b c d - 1785a b c d )x
+--R +
+--R 6 7 5 6 4 2 2 5 3 3 3 4 6
+--R (- 585a d + 720a b c d + 1995a b c d - 3570a b c d )x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3 4
+--R (- 1170a c d + 3195a b c d - 1680a b c d - 1785a b c d )x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 2
+--R (- 585a c d + 1890a b c d - 1785a b c d )x
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(\|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 5 4 3 6 5 2 8
+--R (840a b c d - 360b c d )x
+--R +
+--R 2 4 4 3 5 5 2 6 6 6
+--R (840a b c d + 1320a b c d - 720b c d)x
+--R +
+--R 2 4 5 2 5 6 6 7 4 2 4 6 5 7 2
+--R (1680a b c d + 120a b c d - 360b c )x + (840a b c d - 360a b c )x
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 5 4 3 6 5 2 8
+--R (- 840a b c d + 360b c d )x
+--R +
+--R 2 4 4 3 5 5 2 6 6 6
+--R (- 840a b c d - 1320a b c d + 720b c d)x
+--R +
+--R 2 4 5 2 5 6 6 7 4
+--R (- 1680a b c d - 120a b c d + 360b c )x
+--R +
+--R 2 4 6 5 7 2
+--R (- 840a b c d + 360a b c )x
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|c \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 5 7 4 2 6 3 3 2 5 8
+--R (585a b d - 1890a b c d + 1785a b c d )x
+--R +
+--R 6 7 5 6 4 2 2 5 3 3 3 4 6
+--R (585a d - 720a b c d - 1995a b c d + 3570a b c d )x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3 4
+--R (1170a c d - 3195a b c d + 1680a b c d + 1785a b c d )x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 2
+--R (585a c d - 1890a b c d + 1785a b c d )x
+--R *
+--R 4+-+4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a \|d \|x log(- \|2 \|c \|d \|x + x\|d + \|c )
+--R +
+--R 5 7 4 2 6 3 3 2 5 8
+--R (1170a b d - 3780a b c d + 3570a b c d )x
+--R +
+--R 6 7 5 6 4 2 2 5 3 3 3 4 6
+--R (1170a d - 1440a b c d - 3990a b c d + 7140a b c d )x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3 4
+--R (2340a c d - 6390a b c d + 3360a b c d + 3570a b c d )x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 2
+--R (1170a c d - 3780a b c d + 3570a b c d )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x + \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 5 7 4 2 6 3 3 2 5 8
+--R (1170a b d - 3780a b c d + 3570a b c d )x
+--R +
+--R 6 7 5 6 4 2 2 5 3 3 3 4 6
+--R (1170a d - 1440a b c d - 3990a b c d + 7140a b c d )x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3 4
+--R (2340a c d - 6390a b c d + 3360a b c d + 3570a b c d )x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 2
+--R (1170a c d - 3780a b c d + 3570a b c d )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|d \|x - \|c
+--R \|a \|d \|x atan(-------------------)
+--R 4+-+
+--R \|c
+--R +
+--R 5 4 3 6 5 2 8
+--R (- 1680a b c d + 720b c d )x
+--R +
+--R 2 4 4 3 5 5 2 6 6 6
+--R (- 1680a b c d - 2640a b c d + 1440b c d)x
+--R +
+--R 2 4 5 2 5 6 6 7 4
+--R (- 3360a b c d - 240a b c d + 720b c )x
+--R +
+--R 2 4 6 5 7 2
+--R (- 1680a b c d + 720a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|b \|x + \|a
+--R \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 5 4 3 6 5 2 8
+--R (- 1680a b c d + 720b c d )x
+--R +
+--R 2 4 4 3 5 5 2 6 6 6
+--R (- 1680a b c d - 2640a b c d + 1440b c d)x
+--R +
+--R 2 4 5 2 5 6 6 7 4
+--R (- 3360a b c d - 240a b c d + 720b c )x
+--R +
+--R 2 4 6 5 7 2
+--R (- 1680a b c d + 720a b c )x
+--R *
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+4+-+ +-+ \|2 \|b \|x - \|a
+--R \|b \|c \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 5 7 4 2 6 3 3 2 5 5 4 3
+--R 2340a b d - 7560a b c d + 7140a b c d - 3360a b c d
+--R +
+--R 6 5 2
+--R 1440b c d
+--R *
+--R 8
+--R x
+--R +
+--R 6 7 5 6 4 2 2 5 3 3 3 4
+--R 2340a d - 3348a b c d - 6468a b c d + 12852a b c d
+--R +
+--R 2 4 4 3 5 5 2 6 6
+--R - 2688a b c d - 5568a b c d + 2880b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 6 5 2 5 4 2 3 4 3 3 4 3
+--R 4212a c d - 11944a b c d + 7476a b c d + 5376a b c d
+--R +
+--R 2 4 5 2 5 6 6 7
+--R - 5504a b c d - 1056a b c d + 1440b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2
+--R 1664a c d - 5504a b c d + 5376a b c d + 256a b c d
+--R +
+--R 2 4 6 5 7
+--R - 2944a b c d + 1152a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7
+--R - 128a c d + 512a b c d - 768a b c d + 512a b c d - 128a b c
+--R *
+--R +-+4+-+4+-+
+--R \|2 \|a \|c
+--R /
+--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3
+--R 320a b c d - 1280a b c d + 1920a b c d - 1280a b c d
+--R +
+--R 3 5 8 2
+--R 320a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2
+--R 320a c d - 640a b c d - 640a b c d + 2560a b c d - 2240a b c d
+--R +
+--R 3 5 9
+--R 640a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9
+--R 640a c d - 2240a b c d + 2560a b c d - 640a b c d - 640a b c d
+--R +
+--R 3 5 10
+--R 320a b c
+--R *
+--R 4
+--R x
+--R +
+--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 2
+--R (320a c d - 1280a b c d + 1920a b c d - 1280a b c d + 320a b c )x
+--R *
+--R +-+4+-+4+-+ +-+
+--R \|2 \|a \|c \|x
+--R Type: Expression(Integer)
+--E 1154
+
+--S 1155 of 1527
+--a0:=integrate(t0,x)
+--E 1155
+
+--S 1156 of 1527
+--m0:=a0-r0
+--E 1156
+
+--S 1157 of 1527
+--d0:=D(m0,x)
+--E 1157
+
+)clear all
+
+--S 1158 of 1527
+t0:=x^(7/2)*sqrt(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 3 +-+ | 2
+--R x \|x \|d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1158
+
+--S 1159 of 1527
+--r0:=-1/2*x^(5/2)*sqrt(c+d*x^2)/(b*(a+b*x^2))+7/6*sqrt(x)*sqrt(c+_
+-- d*x^2)/b^2+1/6*c^(1/4)*(8*b*c-21*a*d)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(b^3*(-d)^(1/4)*_
+-- sqrt(c+d*x^2))-1/4*(5*b*c-7*a*d)*elliptic_pi(-sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^3*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))-1/4*(5*b*c-7*a*d)*elliptic_pi(_
+-- sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^3*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1159
+
+--S 1160 of 1527
+--a0:=integrate(t0,x)
+--E 1160
+
+--S 1161 of 1527
+--m0:=a0-r0
+--E 1161
+
+--S 1162 of 1527
+--d0:=D(m0,x)
+--E 1162
+
+)clear all
+
+--S 1163 of 1527
+t0:=x^(5/2)*sqrt(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 +-+ | 2
+--R x \|x \|d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1163
+
+--S 1164 of 1527
+--r0:=-1/2*x^(3/2)*sqrt(c+d*x^2)/(b*(a+b*x^2))-5/2*c^(3/4)*(-d)^(1/4)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^2*sqrt(c+d*x^2))+5/2*c^(3/4)*(-d)^(1/4)*elliptic_f(_
+-- asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^2*sqrt(c+d*x^2))-1/4*(3*b*c-5*a*d)*elliptic_pi(-sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^(5/2)*sqrt(-a)*sqrt(c+_
+-- d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+1/4*(3*b*c-5*a*d)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^(5/2)*_
+-- sqrt(-a)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1164
+
+--S 1165 of 1527
+--a0:=integrate(t0,x)
+--E 1165
+
+--S 1166 of 1527
+--m0:=a0-r0
+--E 1166
+
+--S 1167 of 1527
+--d0:=D(m0,x)
+--E 1167
+
+)clear all
+
+--S 1168 of 1527
+t0:=x^(3/2)*sqrt(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R x\|x \|d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1168
+
+--S 1169 of 1527
+--r0:=-1/2*sqrt(x)*sqrt(c+d*x^2)/(b*(a+b*x^2))-3/2*c^(1/4)*(-d)^(3/4)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^2*sqrt(c+d*x^2))+1/4*(b*c-3*a*d)*elliptic_pi(-sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),_
+-- -1)*sqrt((c+d*x^2)/c)/(a*b^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/_
+-- sqrt(c)))+1/4*(b*c-3*a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/_
+-- (sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(a*b^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1169
+
+--S 1170 of 1527
+--a0:=integrate(t0,x)
+--E 1170
+
+--S 1171 of 1527
+--m0:=a0-r0
+--E 1171
+
+--S 1172 of 1527
+--d0:=D(m0,x)
+--E 1172
+
+)clear all
+
+--S 1173 of 1527
+t0:=sqrt(x)*sqrt(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R \|x \|d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1173
+
+--S 1174 of 1527
+--r0:=1/2*x^(3/2)*sqrt(c+d*x^2)/(a*(a+b*x^2))+1/2*c^(3/4)*(-d)^(1/4)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (a*b*sqrt(c+d*x^2))-1/2*c^(3/4)*(-d)^(1/4)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*_
+-- x^2)/c)/(a*b*sqrt(c+d*x^2))+1/4*(b*c+a*d)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(3/2)*b^(3/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 1/4*(b*c+a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(3/2)*b^(3/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1174
+
+--S 1175 of 1527
+--a0:=integrate(t0,x)
+--E 1175
+
+--S 1176 of 1527
+--m0:=a0-r0
+--E 1176
+
+--S 1177 of 1527
+--d0:=D(m0,x)
+--E 1177
+
+)clear all
+
+--S 1178 of 1527
+t0:=sqrt(c+d*x^2)/((a+b*x^2)^2*sqrt(x))
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) -------------------------
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R Type: Expression(Integer)
+--E 1178
+
+--S 1179 of 1527
+--r0:=1/2*sqrt(x)*sqrt(c+d*x^2)/(a*(a+b*x^2))-1/2*c^(1/4)*(-d)^(3/4)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+_
+-- d*x^2)/c)/(a*b*sqrt(c+d*x^2))+1/4*(3*b*c-a*d)*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (a^2*b*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+1/4*(3*b*c-a*d)*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*b*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1179
+
+--S 1180 of 1527
+--a0:=integrate(t0,x)
+--E 1180
+
+--S 1181 of 1527
+--m0:=a0-r0
+--E 1181
+
+--S 1182 of 1527
+--d0:=D(m0,x)
+--E 1182
+
+)clear all
+
+--S 1183 of 1527
+t0:=sqrt(c+d*x^2)/(x^(3/2)*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) --------------------------
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R Type: Expression(Integer)
+--E 1183
+
+--S 1184 of 1527
+--r0:=-5/2*sqrt(c+d*x^2)/(a^2*sqrt(x))+1/2*sqrt(c+d*x^2)/(a*(a+b*x^2)*_
+-- sqrt(x))-5/2*c^(3/4)*(-d)^(1/4)*elliptic_e(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a^2*sqrt(c+d*x^2))+_
+-- 5/2*c^(3/4)*(-d)^(1/4)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),_
+-- -1)*sqrt((c+d*x^2)/c)/(a^2*sqrt(c+d*x^2))+1/4*(5*b*c-3*a*d)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*_
+-- sqrt(b)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-1/4*(5*b*c-_
+-- 3*a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(5/2)*sqrt(b)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1184
+
+--S 1185 of 1527
+--a0:=integrate(t0,x)
+--E 1185
+
+--S 1186 of 1527
+--m0:=a0-r0
+--E 1186
+
+--S 1187 of 1527
+--d0:=D(m0,x)
+--E 1187
+
+)clear all
+
+--S 1188 of 1527
+t0:=sqrt(c+d*x^2)/(x^(5/2)*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) ---------------------------
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1188
+
+--S 1189 of 1527
+--r0:=-7/6*sqrt(c+d*x^2)/(a^2*x^(3/2))+1/2*sqrt(c+d*x^2)/(a*x^(3/2)*_
+-- (a+b*x^2))+7/6*c^(1/4)*(-d)^(3/4)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a^2*sqrt(c+d*x^2))-_
+-- 1/4*(7*b*c-5*a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^3*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 1/4*(7*b*c-5*a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^3*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1189
+
+--S 1190 of 1527
+--a0:=integrate(t0,x)
+--E 1190
+
+--S 1191 of 1527
+--m0:=a0-r0
+--E 1191
+
+--S 1192 of 1527
+--d0:=D(m0,x)
+--E 1192
+
+)clear all
+
+--S 1193 of 1527
+t0:=sqrt(c+d*x^2)/(x^(7/2)*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) ---------------------------
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1193
+
+--S 1194 of 1527
+--r0:=-9/10*sqrt(c+d*x^2)/(a^2*x^(5/2))+1/2*sqrt(c+d*x^2)/(a*x^(5/2)*_
+-- (a+b*x^2))+1/10*(45*b*c-8*a*d)*sqrt(c+d*x^2)/(a^3*c*sqrt(x))+_
+-- 1/10*(-d)^(1/4)*(45*b*c-8*a*d)*elliptic_e(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a^3*c^(1/4)*sqrt(c+_
+-- d*x^2))-1/10*(-d)^(1/4)*(45*b*c-8*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^3*c^(1/4)*sqrt(c+d*x^2))+1/4*(9*b*c-_
+-- 7*a*d)*elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(b)*sqrt((c+_
+-- d*x^2)/c)/((-a)^(7/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 1/4*(9*b*c-7*a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(b)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(7/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1194
+
+--S 1195 of 1527
+--a0:=integrate(t0,x)
+--E 1195
+
+--S 1196 of 1527
+--m0:=a0-r0
+--E 1196
+
+--S 1197 of 1527
+--d0:=D(m0,x)
+--E 1197
+
+)clear all
+
+--S 1198 of 1527
+t0:=x^(7/2)*(c+d*x^2)^(3/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 5 3 +-+ | 2
+--R (d x + c x )\|x \|d x + c
+--R (1) ----------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1198
+
+--S 1199 of 1527
+--r0:=-1/2*x^(5/2)*(c+d*x^2)^(3/2)/(b*(a+b*x^2))+11/14*d*x^(5/2)*_
+-- sqrt(c+d*x^2)/b^2+1/42*(57*b*c-77*a*d)*sqrt(x)*sqrt(c+d*x^2)/b^3+_
+-- 1/42*c^(1/4)*(48*b^2*c^2-259*a*b*c*d+231*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+_
+-- d*x^2)/c)/(b^4*(-d)^(1/4)*sqrt(c+d*x^2))-1/4*(5*b*c-11*a*d)*_
+-- (b*c-a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^4*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-1/4*(5*b*c-11*a*d)*_
+-- (b*c-a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^4*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1199
+
+--S 1200 of 1527
+--a0:=integrate(t0,x)
+--E 1200
+
+--S 1201 of 1527
+--m0:=a0-r0
+--E 1201
+
+--S 1202 of 1527
+--d0:=D(m0,x)
+--E 1202
+
+)clear all
+
+--S 1203 of 1527
+t0:=x^(5/2)*(c+d*x^2)^(3/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 4 2 +-+ | 2
+--R (d x + c x )\|x \|d x + c
+--R (1) ----------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1203
+
+--S 1204 of 1527
+--r0:=-1/2*x^(3/2)*(c+d*x^2)^(3/2)/(b*(a+b*x^2))+9/10*d*x^(3/2)*_
+-- sqrt(c+d*x^2)/b^2-3/10*c^(3/4)*(-d)^(1/4)*(11*b*c-15*a*d)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+_
+-- d*x^2)/c)/(b^3*sqrt(c+d*x^2))+3/10*c^(3/4)*(-d)^(1/4)*(11*b*c-_
+-- 15*a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^3*sqrt(c+d*x^2))-3/4*(b*c-3*a*d)*(b*c-_
+-- a*d)*elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^(7/2)*sqrt(-a)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+_
+-- 3/4*(b*c-3*a*d)*(b*c-a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^(7/2)*sqrt(-a)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 1204
+
+--S 1205 of 1527
+--a0:=integrate(t0,x)
+--E 1205
+
+--S 1206 of 1527
+--m0:=a0-r0
+--E 1206
+
+--S 1207 of 1527
+--d0:=D(m0,x)
+--E 1207
+
+)clear all
+
+--S 1208 of 1527
+t0:=x^(3/2)*(c+d*x^2)^(3/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 3 +-+ | 2
+--R (d x + c x)\|x \|d x + c
+--R (1) ---------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1208
+
+--S 1209 of 1527
+--r0:=-1/2*(c+d*x^2)^(3/2)*sqrt(x)/(b*(a+b*x^2))+7/6*d*sqrt(x)*_
+-- sqrt(c+d*x^2)/b^2-1/6*c^(1/4)*(-d)^(3/4)*(17*b*c-21*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+_
+-- d*x^2)/c)/(b^3*sqrt(c+d*x^2))+1/4*(b*c-7*a*d)*(b*c-a*d)*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*b^3*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+1/4*(b*c-7*a*d)*(b*c-a*d)*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*b^3*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1209
+
+--S 1210 of 1527
+--a0:=integrate(t0,x)
+--E 1210
+
+--S 1211 of 1527
+--m0:=a0-r0
+--E 1211
+
+--S 1212 of 1527
+--d0:=D(m0,x)
+--E 1212
+
+)clear all
+
+--S 1213 of 1527
+t0:=(c+d*x^2)^(3/2)*sqrt(x)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 +-+ | 2
+--R (d x + c)\|x \|d x + c
+--R (1) -------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1213
+
+--S 1214 of 1527
+--r0:=1/2*(b*c-a*d)*x^(3/2)*sqrt(c+d*x^2)/(a*b*(a+b*x^2))+1/2*c^(3/4)*_
+-- (-d)^(1/4)*(b*c-5*a*d)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/_
+-- c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*b^2*sqrt(c+d*x^2))-1/2*_
+-- c^(3/4)*(-d)^(1/4)*(b*c-5*a*d)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*b^2*sqrt(c+d*x^2))+_
+-- 1/4*(b*c-a*d)*(b*c+5*a*d)*elliptic_pi(-sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(3/2)*b^(5/2)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))-1/4*(b*c-a*d)*(b*c+5*a*d)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(3/2)*_
+-- b^(5/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1214
+
+--S 1215 of 1527
+--a0:=integrate(t0,x)
+--E 1215
+
+--S 1216 of 1527
+--m0:=a0-r0
+--E 1216
+
+--S 1217 of 1527
+--d0:=D(m0,x)
+--E 1217
+
+)clear all
+
+--S 1218 of 1527
+t0:=(c+d*x^2)^(3/2)/((a+b*x^2)^2*sqrt(x))
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) -------------------------
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R Type: Expression(Integer)
+--E 1218
+
+--S 1219 of 1527
+--r0:=1/2*(b*c-a*d)*sqrt(x)*sqrt(c+d*x^2)/(a*b*(a+b*x^2))-1/2*c^(1/4)*_
+-- (-d)^(3/4)*(b*c+3*a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/_
+-- c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*b^2*sqrt(c+d*x^2))+3/4*_
+-- (b*c-a*d)*(b*c+a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*b^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/_
+-- sqrt(c)))+3/4*(b*c-a*d)*(b*c+a*d)*elliptic_pi(sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*b^2*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 1219
+
+--S 1220 of 1527
+--a0:=integrate(t0,x)
+--E 1220
+
+--S 1221 of 1527
+--m0:=a0-r0
+--E 1221
+
+--S 1222 of 1527
+--d0:=D(m0,x)
+--E 1222
+
+)clear all
+
+--S 1223 of 1527
+t0:=(c+d*x^2)^(3/2)/(x^(3/2)*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) --------------------------
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R Type: Expression(Integer)
+--E 1223
+
+--S 1224 of 1527
+--r0:=-1/2*(5*b*c-a*d)*sqrt(c+d*x^2)/(a^2*b*sqrt(x))+1/2*(b*c-a*d)*_
+-- sqrt(c+d*x^2)/(a*b*(a+b*x^2)*sqrt(x))-1/2*c^(3/4)*(-d)^(1/4)*_
+-- (5*b*c-a*d)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*b*sqrt(c+d*x^2))+1/2*c^(3/4)*(-d)^(1/4)*_
+-- (5*b*c-a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*b*sqrt(c+d*x^2))+1/4*(b*c-a*d)*(5*b*c+_
+-- a*d)*elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(5/2)*b^(3/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 1/4*(b*c-a*d)*(5*b*c+a*d)*elliptic_pi(sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(5/2)*b^(3/2)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 1224
+
+--S 1225 of 1527
+--a0:=integrate(t0,x)
+--E 1225
+
+--S 1226 of 1527
+--m0:=a0-r0
+--E 1226
+
+--S 1227 of 1527
+--d0:=D(m0,x)
+--E 1227
+
+)clear all
+
+--S 1228 of 1527
+t0:=(c+d*x^2)^(3/2)/(x^(5/2)*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------------
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1228
+
+--S 1229 of 1527
+--r0:=-1/6*(7*b*c-3*a*d)*sqrt(c+d*x^2)/(a^2*b*x^(3/2))+1/2*(b*c-a*d)*_
+-- sqrt(c+d*x^2)/(a*b*x^(3/2)*(a+b*x^2))+1/6*c^(1/4)*(-d)^(3/4)*_
+-- (7*b*c-3*a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*b*sqrt(c+d*x^2))-1/4*(b*c-a*d)*(7*b*c-_
+-- a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (a^3*b*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-1/4*(b*c-a*d)*_
+-- (7*b*c-a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (a^3*b*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1229
+
+--S 1230 of 1527
+--a0:=integrate(t0,x)
+--E 1230
+
+--S 1231 of 1527
+--m0:=a0-r0
+--E 1231
+
+--S 1232 of 1527
+--d0:=D(m0,x)
+--E 1232
+
+)clear all
+
+--S 1233 of 1527
+t0:=(c+d*x^2)^(3/2)/(x^(7/2)*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------------
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1233
+
+--S 1234 of 1527
+--r0:=-1/10*(9*b*c-5*a*d)*sqrt(c+d*x^2)/(a^2*b*x^(5/2))+1/2*(b*c-a*d)*_
+-- sqrt(c+d*x^2)/(a*b*x^(5/2)*(a+b*x^2))+3/10*(15*b*c-11*a*d)*_
+-- sqrt(c+d*x^2)/(a^3*sqrt(x))+3/10*c^(3/4)*(-d)^(1/4)*(15*b*c-_
+-- 11*a*d)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^3*sqrt(c+d*x^2))-3/10*c^(3/4)*(-d)^(1/4)*_
+-- (15*b*c-11*a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^3*sqrt(c+d*x^2))+3/4*(b*c-a*d)*(3*b*c-a*d)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(7/2)*_
+-- sqrt(b)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-3/4*(b*c-a*d)*_
+-- (3*b*c-a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(7/2)*sqrt(b)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1234
+
+--S 1235 of 1527
+--a0:=integrate(t0,x)
+--E 1235
+
+--S 1236 of 1527
+--m0:=a0-r0
+--E 1236
+
+--S 1237 of 1527
+--d0:=D(m0,x)
+--E 1237
+
+)clear all
+
+--S 1238 of 1527
+t0:=x^(7/2)*(c+d*x^2)^(5/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 7 5 2 3 +-+ | 2
+--R (d x + 2c d x + c x )\|x \|d x + c
+--R (1) --------------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1238
+
+--S 1239 of 1527
+--r0:=15/22*d*x^(5/2)*(c+d*x^2)^(3/2)/b^2-1/2*x^(5/2)*(c+d*x^2)^(5/2)/_
+-- (b*(a+b*x^2))+5/154*d*(29*b*c-33*a*d)*x^(5/2)*sqrt(c+d*x^2)/b^3+_
+-- 5/462*(135*b^2*c^2-374*a*b*c*d+231*a^2*d^2)*sqrt(x)*sqrt(c+_
+-- d*x^2)/b^4+5/462*c^(1/4)*(96*b^3*c^3-781*a*b^2*c^2*d+1386*a^2*b*c*_
+-- d^2-693*a^3*d^3)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^5*(-d)^(1/4)*sqrt(c+d*x^2))-5/4*(b*c-_
+-- 3*a*d)*(b*c-a*d)^2*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^5*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 5/4*(b*c-3*a*d)*(b*c-a*d)^2*elliptic_pi(sqrt(-b)*sqrt(c)/_
+-- (sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^5*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1239
+
+--S 1240 of 1527
+--a0:=integrate(t0,x)
+--E 1240
+
+--S 1241 of 1527
+--m0:=a0-r0
+--E 1241
+
+--S 1242 of 1527
+--d0:=D(m0,x)
+--E 1242
+
+)clear all
+
+--S 1243 of 1527
+t0:=x^(5/2)*(c+d*x^2)^(5/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 6 4 2 2 +-+ | 2
+--R (d x + 2c d x + c x )\|x \|d x + c
+--R (1) --------------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1243
+
+--S 1244 of 1527
+--r0:=13/18*d*x^(3/2)*(c+d*x^2)^(3/2)/b^2-1/2*x^(3/2)*(c+d*x^2)^(5/2)/_
+-- (b*(a+b*x^2))+1/30*d*(35*b*c-39*a*d)*x^(3/2)*sqrt(c+d*x^2)/b^3-_
+-- 1/30*c^(3/4)*(-d)^(1/4)*(115*b^2*c^2-318*a*b*c*d+195*a^2*d^2)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^4*sqrt(c+d*x^2))+1/30*c^(3/4)*(-d)^(1/4)*(115*b^2*c^2-_
+-- 318*a*b*c*d+195*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/_
+-- c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(b^4*sqrt(c+d*x^2))-1/4*(3*b*c-_
+-- 13*a*d)*(b*c-a*d)^2*elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^(9/2)*sqrt(-a)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+1/4*(3*b*c-13*a*d)*(b*c-a*d)^2*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^(9/2)*_
+-- sqrt(-a)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1244
+
+--S 1245 of 1527
+--a0:=integrate(t0,x)
+--E 1245
+
+--S 1246 of 1527
+--m0:=a0-r0
+--E 1246
+
+--S 1247 of 1527
+--d0:=D(m0,x)
+--E 1247
+
+)clear all
+
+--S 1248 of 1527
+t0:=x^(3/2)*(c+d*x^2)^(5/2)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 5 3 2 +-+ | 2
+--R (d x + 2c d x + c x)\|x \|d x + c
+--R (1) -------------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1248
+
+--S 1249 of 1527
+--r0:=11/14*d*(c+d*x^2)^(3/2)*sqrt(x)/b^2-1/2*(c+d*x^2)^(5/2)*sqrt(x)/_
+-- (b*(a+b*x^2))+1/42*d*(73*b*c-77*a*d)*sqrt(x)*sqrt(c+d*x^2)/b^3-_
+-- 1/42*c^(1/4)*(-d)^(3/4)*(167*b^2*c^2-406*a*b*c*d+231*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^4*sqrt(c+d*x^2))+1/4*(b*c-11*a*d)*(b*c-a*d)^2*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (a*b^4*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+1/4*(b*c-_
+-- 11*a*d)*(b*c-a*d)^2*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(a*b^4*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1249
+
+--S 1250 of 1527
+--a0:=integrate(t0,x)
+--E 1250
+
+--S 1251 of 1527
+--m0:=a0-r0
+--E 1251
+
+--S 1252 of 1527
+--d0:=D(m0,x)
+--E 1252
+
+)clear all
+
+--S 1253 of 1527
+t0:=(c+d*x^2)^(5/2)*sqrt(x)/(a+b*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 4 2 2 +-+ | 2
+--R (d x + 2c d x + c )\|x \|d x + c
+--R (1) ------------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 1253
+
+--S 1254 of 1527
+--r0:=1/2*(b*c-a*d)*x^(3/2)*(c+d*x^2)^(3/2)/(a*b*(a+b*x^2))-1/10*d*_
+-- (5*b*c-9*a*d)*x^(3/2)*sqrt(c+d*x^2)/(a*b^2)+1/10*c^(3/4)*(-d)^(1/4)*_
+-- (5*b^2*c^2-58*a*b*c*d+45*a^2*d^2)*elliptic_e(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*b^3*sqrt(c+d*x^2))-_
+-- 1/10*c^(3/4)*(-d)^(1/4)*(5*b^2*c^2-58*a*b*c*d+45*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (a*b^3*sqrt(c+d*x^2))+1/4*(b*c-a*d)^2*(b*c+9*a*d)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(3/2)*_
+-- b^(7/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-1/4*(b*c-a*d)^2*_
+-- (b*c+9*a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(3/2)*b^(7/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1254
+
+--S 1255 of 1527
+--a0:=integrate(t0,x)
+--E 1255
+
+--S 1256 of 1527
+--m0:=a0-r0
+--E 1256
+
+--S 1257 of 1527
+--d0:=D(m0,x)
+--E 1257
+
+)clear all
+
+--S 1258 of 1527
+t0:=(c+d*x^2)^(5/2)/((a+b*x^2)^2*sqrt(x))
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R Type: Expression(Integer)
+--E 1258
+
+--S 1259 of 1527
+--r0:=1/2*(b*c-a*d)*(c+d*x^2)^(3/2)*sqrt(x)/(a*b*(a+b*x^2))-_
+-- 1/6*d*(3*b*c-7*a*d)*sqrt(x)*sqrt(c+d*x^2)/(a*b^2)-1/6*c^(1/4)*_
+-- (-d)^(3/4)*(3*b^2*c^2+26*a*b*c*d-21*a^2*d^2)*elliptic_f(_
+-- asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*_
+-- b^3*sqrt(c+d*x^2))+1/4*(b*c-a*d)^2*(3*b*c+7*a*d)*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*b^3*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+1/4*(b*c-a*d)^2*(3*_
+-- b*c+7*a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (a^2*b^3*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1259
+
+--S 1260 of 1527
+--a0:=integrate(t0,x)
+--E 1260
+
+--S 1261 of 1527
+--m0:=a0-r0
+--E 1261
+
+--S 1262 of 1527
+--d0:=D(m0,x)
+--E 1262
+
+)clear all
+
+--S 1263 of 1527
+t0:=(c+d*x^2)^(5/2)/(x^(3/2)*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R Type: Expression(Integer)
+--E 1263
+
+--S 1264 of 1527
+--r0:=1/2*(b*c-a*d)*(c+d*x^2)^(3/2)/(a*b*(a+b*x^2)*sqrt(x))-_
+-- 1/2*c*(5*b*c-a*d)*sqrt(c+d*x^2)/(a^2*b*sqrt(x))-1/2*c^(3/4)*_
+-- (-d)^(1/4)*(5*b^2*c^2-2*a*b*c*d+5*a^2*d^2)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*b^2*sqrt(c+d*x^2))+1/2*c^(3/4)*(-d)^(1/4)*_
+-- (5*b^2*c^2-2*a*b*c*d+5*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a^2*b^2*sqrt(c+d*x^2))+_
+-- 5/4*(b*c-a*d)^2*(b*c+a*d)*elliptic_pi(-sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(5/2)*b^(5/2)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))-5/4*(b*c-a*d)^2*(b*c+a*d)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*_
+-- b^(5/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1264
+
+--S 1265 of 1527
+--a0:=integrate(t0,x)
+--E 1265
+
+--S 1266 of 1527
+--m0:=a0-r0
+--E 1266
+
+--S 1267 of 1527
+--d0:=D(m0,x)
+--E 1267
+
+)clear all
+
+--S 1268 of 1527
+t0:=(c+d*x^2)^(5/2)/(x^(5/2)*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1268
+
+--S 1269 of 1527
+--r0:=1/2*(b*c-a*d)*(c+d*x^2)^(3/2)/(a*b*x^(3/2)*(a+b*x^2))-_
+-- 1/6*c*(7*b*c-3*a*d)*sqrt(c+d*x^2)/(a^2*b*x^(3/2))+1/6*c^(1/4)*_
+-- (-d)^(3/4)*(7*b^2*c^2-6*a*b*c*d-9*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (a^2*b^2*sqrt(c+d*x^2))-1/4*(b*c-a*d)^2*(7*b*c+3*a*d)*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^3*b^2*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-1/4*(b*c-a*d)^2*(7*b*c+_
+-- 3*a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (a^3*b^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1269
+
+--S 1270 of 1527
+--a0:=integrate(t0,x)
+--E 1270
+
+--S 1271 of 1527
+--m0:=a0-r0
+--E 1271
+
+--S 1272 of 1527
+--d0:=D(m0,x)
+--E 1272
+
+)clear all
+
+--S 1273 of 1527
+t0:=(c+d*x^2)^(5/2)/(x^(7/2)*(a+b*x^2)^2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|d x + c
+--R (1) --------------------------------
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 1273
+
+--S 1274 of 1527
+--r0:=1/2*(b*c-a*d)*(c+d*x^2)^(3/2)/(a*b*x^(5/2)*(a+b*x^2))-_
+-- 1/10*c*(9*b*c-5*a*d)*sqrt(c+d*x^2)/(a^2*b*x^(5/2))+_
+-- 1/10*(45*b^2*c^2-58*a*b*c*d+5*a^2*d^2)*sqrt(c+d*x^2)/(a^3*b*_
+-- sqrt(x))+1/10*c^(3/4)*(-d)^(1/4)*(45*b^2*c^2-58*a*b*c*d+_
+-- 5*a^2*d^2)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^3*b*sqrt(c+d*x^2))-1/10*c^(3/4)*(-d)^(1/4)*_
+-- (45*b^2*c^2-58*a*b*c*d+5*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a^3*b*sqrt(c+d*x^2))+_
+-- 1/4*(b*c-a*d)^2*(9*b*c+a*d)*elliptic_pi(-sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(7/2)*b^(3/2)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))-1/4*(b*c-a*d)^2*(9*b*c+a*d)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(7/2)*_
+-- b^(3/2)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1274
+
+--S 1275 of 1527
+--a0:=integrate(t0,x)
+--E 1275
+
+--S 1276 of 1527
+--m0:=a0-r0
+--E 1276
+
+--S 1277 of 1527
+--d0:=D(m0,x)
+--E 1277
+
+)clear all
+
+--S 1278 of 1527
+t0:=x^(7/2)/((a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R Type: Expression(Integer)
+--E 1278
+
+--S 1279 of 1527
+--r0:=1/2*a*sqrt(x)*sqrt(c+d*x^2)/(b*(b*c-a*d)*(a+b*x^2))+1/2*c^(1/4)*_
+-- (4*b*c-3*a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^2*(-d)^(1/4)*(b*c-a*d)*sqrt(c+d*x^2))-_
+-- 1/4*(5*b*c-3*a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(b^2*(b*c-a*d)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))-1/4*(5*b*c-3*a*d)*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^2*(b*c-a*d)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1279
+
+--S 1280 of 1527
+--a0:=integrate(t0,x)
+--E 1280
+
+--S 1281 of 1527
+--m0:=a0-r0
+--E 1281
+
+--S 1282 of 1527
+--d0:=D(m0,x)
+--E 1282
+
+)clear all
+
+--S 1283 of 1527
+t0:=x^(5/2)/((a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R Type: Expression(Integer)
+--E 1283
+
+--S 1284 of 1527
+--r0:=-1/2*x^(3/2)*sqrt(c+d*x^2)/((b*c-a*d)*(a+b*x^2))-1/2*c^(3/4)*_
+-- (-d)^(1/4)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b*(b*c-a*d)*sqrt(c+d*x^2))+1/2*c^(3/4)*_
+-- (-d)^(1/4)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b*(b*c-a*d)*sqrt(c+d*x^2))-1/4*(3*b*c-a*d)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(b^(3/2)*(b*c-_
+-- a*d)*sqrt(-a)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+1/4*_
+-- (3*b*c-a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (b^(3/2)*(b*c-a*d)*sqrt(-a)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1284
+
+--S 1285 of 1527
+--a0:=integrate(t0,x)
+--E 1285
+
+--S 1286 of 1527
+--m0:=a0-r0
+--E 1286
+
+--S 1287 of 1527
+--d0:=D(m0,x)
+--E 1287
+
+)clear all
+
+--S 1288 of 1527
+t0:=x^(3/2)/((a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R Type: Expression(Integer)
+--E 1288
+
+--S 1289 of 1527
+--r0:=-1/2*sqrt(x)*sqrt(c+d*x^2)/((b*c-a*d)*(a+b*x^2))+1/2*c^(1/4)*_
+-- (-d)^(3/4)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b*(b*c-a*d)*sqrt(c+d*x^2))+1/4*(b*c+a*d)*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*b*(b*c-a*d)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+1/4*(b*c+a*d)*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*b*(b*c-a*d)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1289
+
+--S 1290 of 1527
+--a0:=integrate(t0,x)
+--E 1290
+
+--S 1291 of 1527
+--m0:=a0-r0
+--E 1291
+
+--S 1292 of 1527
+--d0:=D(m0,x)
+--E 1292
+
+)clear all
+
+--S 1293 of 1527
+t0:=sqrt(x)/((a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R +-+
+--R \|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|d x + c
+--R Type: Expression(Integer)
+--E 1293
+
+--S 1294 of 1527
+--r0:=1/2*b*x^(3/2)*sqrt(c+d*x^2)/(a*(b*c-a*d)*(a+b*x^2))+1/2*c^(3/4)*_
+-- (-d)^(1/4)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a*(b*c-a*d)*sqrt(c+d*x^2))-1/2*c^(3/4)*_
+-- (-d)^(1/4)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a*(b*c-a*d)*sqrt(c+d*x^2))+1/4*(b*c-3*a*d)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(3/2)*_
+-- (b*c-a*d)*sqrt(b)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 1/4*(b*c-3*a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(3/2)*(b*c-a*d)*sqrt(b)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1294
+
+--S 1295 of 1527
+--a0:=integrate(t0,x)
+--E 1295
+
+--S 1296 of 1527
+--m0:=a0-r0
+--E 1296
+
+--S 1297 of 1527
+--d0:=D(m0,x)
+--E 1297
+
+)clear all
+
+--S 1298 of 1527
+t0:=1/((a+b*x^2)^2*sqrt(x)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ------------------------------------
+--R +--------+
+--R 2 4 2 2 +-+ | 2
+--R (b x + 2a b x + a )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 1298
+
+--S 1299 of 1527
+--r0:=1/2*b*sqrt(x)*sqrt(c+d*x^2)/(a*(b*c-a*d)*(a+b*x^2))-1/2*c^(1/4)*_
+-- (-d)^(3/4)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a*(b*c-a*d)*sqrt(c+d*x^2))+1/4*(3*b*c-5*a*d)*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+1/4*(3*b*c-5*a*d)*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1299
+
+--S 1300 of 1527
+--a0:=integrate(t0,x)
+--E 1300
+
+--S 1301 of 1527
+--m0:=a0-r0
+--E 1301
+
+--S 1302 of 1527
+--d0:=D(m0,x)
+--E 1302
+
+)clear all
+
+--S 1303 of 1527
+t0:=1/(x^(3/2)*(a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------
+--R +--------+
+--R 2 5 3 2 +-+ | 2
+--R (b x + 2a b x + a x)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 1303
+
+--S 1304 of 1527
+--r0:=-1/2*(5*b*c-4*a*d)*sqrt(c+d*x^2)/(a^2*c*(b*c-a*d)*sqrt(x))+_
+-- 1/2*b*sqrt(c+d*x^2)/(a*(b*c-a*d)*(a+b*x^2)*sqrt(x))-1/2*(-d)^(1/4)*_
+-- (5*b*c-4*a*d)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*c^(1/4)*(b*c-a*d)*sqrt(c+d*x^2))+_
+-- 1/2*(-d)^(1/4)*(5*b*c-4*a*d)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a^2*c^(1/4)*(b*c-a*d)*_
+-- sqrt(c+d*x^2))+1/4*(5*b*c-7*a*d)*elliptic_pi(-sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt(b)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*(b*c-a*d)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))-1/4*(5*b*c-7*a*d)*elliptic_pi(sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt(b)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*(b*c-a*d)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 1304
+
+--S 1305 of 1527
+--a0:=integrate(t0,x)
+--E 1305
+
+--S 1306 of 1527
+--m0:=a0-r0
+--E 1306
+
+--S 1307 of 1527
+--d0:=D(m0,x)
+--E 1307
+
+)clear all
+
+--S 1308 of 1527
+t0:=1/(x^(5/2)*(a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------
+--R +--------+
+--R 2 6 4 2 2 +-+ | 2
+--R (b x + 2a b x + a x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 1308
+
+--S 1309 of 1527
+--r0:=-1/6*(7*b*c-4*a*d)*sqrt(c+d*x^2)/(a^2*c*(b*c-a*d)*x^(3/2))+_
+-- 1/2*b*sqrt(c+d*x^2)/(a*(b*c-a*d)*x^(3/2)*(a+b*x^2))+1/6*(-d)^(3/4)*_
+-- (7*b*c-4*a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*c^(3/4)*(b*c-a*d)*sqrt(c+d*x^2))-1/4*b*_
+-- (7*b*c-9*a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (a^3*(b*c-a*d)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-1/4*b*_
+-- (7*b*c-9*a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- (a^3*(b*c-a*d)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1309
+
+--S 1310 of 1527
+--a0:=integrate(t0,x)
+--E 1310
+
+--S 1311 of 1527
+--m0:=a0-r0
+--E 1311
+
+--S 1312 of 1527
+--d0:=D(m0,x)
+--E 1312
+
+)clear all
+
+--S 1313 of 1527
+t0:=1/(x^(7/2)*(a+b*x^2)^2*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------
+--R +--------+
+--R 2 7 5 2 3 +-+ | 2
+--R (b x + 2a b x + a x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 1313
+
+--S 1314 of 1527
+--r0:=-1/10*(9*b*c-4*a*d)*sqrt(c+d*x^2)/(a^2*c*(b*c-a*d)*x^(5/2))+_
+-- 1/2*b*sqrt(c+d*x^2)/(a*(b*c-a*d)*x^(5/2)*(a+b*x^2))+1/10*(45*b^2*_
+-- c^2-28*a*b*c*d-12*a^2*d^2)*sqrt(c+d*x^2)/(a^3*c^2*(b*c-a*d)*_
+-- sqrt(x))+1/10*(-d)^(1/4)*(45*b^2*c^2-28*a*b*c*d-12*a^2*d^2)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (a^3*c^(5/4)*(b*c-a*d)*sqrt(c+d*x^2))-1/10*(-d)^(1/4)*(45*b^2*c^2-_
+-- 28*a*b*c*d-12*a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/_
+-- c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a^3*c^(5/4)*(b*c-a*d)*_
+-- sqrt(c+d*x^2))+1/4*b^(3/2)*(9*b*c-11*a*d)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(7/2)*_
+-- (b*c-a*d)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-1/4*b^(3/2)*_
+-- (9*b*c-11*a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(7/2)*(b*c-a*d)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1314
+
+--S 1315 of 1527
+--a0:=integrate(t0,x)
+--E 1315
+
+--S 1316 of 1527
+--m0:=a0-r0
+--E 1316
+
+--S 1317 of 1527
+--d0:=D(m0,x)
+--E 1317
+
+)clear all
+
+--S 1318 of 1527
+t0:=x^(7/2)/((a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) ---------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 1318
+
+--S 1319 of 1527
+--r0:=1/2*(2*b*c+a*d)*sqrt(x)/(b*(b*c-a*d)^2*sqrt(c+d*x^2))+1/2*a*_
+-- sqrt(x)/(b*(b*c-a*d)*(a+b*x^2)*sqrt(c+d*x^2))+1/2*c^(1/4)*_
+-- (2*b*c+a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(b*(-d)^(1/4)*(b*c-a*d)^2*sqrt(c+d*x^2))-_
+-- 1/4*(5*b*c+a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(b*(b*c-a*d)^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/_
+-- sqrt(c)))-1/4*(5*b*c+a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/_
+-- (sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(b*(b*c-a*d)^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1319
+
+--S 1320 of 1527
+--a0:=integrate(t0,x)
+--E 1320
+
+--S 1321 of 1527
+--m0:=a0-r0
+--E 1321
+
+--S 1322 of 1527
+--d0:=D(m0,x)
+--E 1322
+
+)clear all
+
+--S 1323 of 1527
+t0:=x^(5/2)/((a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) ---------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 1323
+
+--S 1324 of 1527
+--r0:=-3/2*d*x^(3/2)/((b*c-a*d)^2*sqrt(c+d*x^2))-1/2*x^(3/2)/((b*c-a*d)*_
+-- (a+b*x^2)*sqrt(c+d*x^2))-3/2*c^(3/4)*(-d)^(1/4)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((b*c-a*d)^2*sqrt(c+d*x^2))+3/2*c^(3/4)*_
+-- (-d)^(1/4)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((b*c-a*d)^2*sqrt(c+d*x^2))-3/4*(b*c+a*d)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((b*c-a*d)^2*_
+-- sqrt(-a)*sqrt(b)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+_
+-- 3/4*(b*c+a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((b*c-a*d)^2*sqrt(-a)*sqrt(b)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1324
+
+--S 1325 of 1527
+--a0:=integrate(t0,x)
+--E 1325
+
+--S 1326 of 1527
+--m0:=a0-r0
+--E 1326
+
+--S 1327 of 1527
+--d0:=D(m0,x)
+--E 1327
+
+)clear all
+
+--S 1328 of 1527
+t0:=x^(3/2)/((a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) ---------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 1328
+
+--S 1329 of 1527
+--r0:=-3/2*d*sqrt(x)/((b*c-a*d)^2*sqrt(c+d*x^2))-1/2*sqrt(x)/_
+-- ((b*c-a*d)*(a+b*x^2)*sqrt(c+d*x^2))+3/2*c^(1/4)*(-d)^(3/4)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+_
+-- d*x^2)/c)/((b*c-a*d)^2*sqrt(c+d*x^2))+1/4*(b*c+5*a*d)*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)^2*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+1/4*(b*c+5*a*d)*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)^2*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1329
+
+--S 1330 of 1527
+--a0:=integrate(t0,x)
+--E 1330
+
+--S 1331 of 1527
+--m0:=a0-r0
+--E 1331
+
+--S 1332 of 1527
+--d0:=D(m0,x)
+--E 1332
+
+)clear all
+
+--S 1333 of 1527
+t0:=sqrt(x)/((a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R +-+
+--R \|x
+--R (1) ---------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|d x + c
+--R Type: Expression(Integer)
+--E 1333
+
+--S 1334 of 1527
+--r0:=1/2*d*(b*c+2*a*d)*x^(3/2)/(a*c*(b*c-a*d)^2*sqrt(c+d*x^2))+_
+-- 1/2*b*x^(3/2)/(a*(b*c-a*d)*(a+b*x^2)*sqrt(c+d*x^2))+_
+-- 1/2*(-d)^(1/4)*(b*c+2*a*d)*elliptic_e(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*c^(1/4)*(b*c-a*d)^2*_
+-- sqrt(c+d*x^2))-1/2*(-d)^(1/4)*(b*c+2*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (a*c^(1/4)*(b*c-a*d)^2*sqrt(c+d*x^2))+1/4*(b*c-7*a*d)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(b)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(3/2)*(b*c-a*d)^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 1/4*(b*c-7*a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(b)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(3/2)*(b*c-a*d)^2*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 1334
+
+--S 1335 of 1527
+--a0:=integrate(t0,x)
+--E 1335
+
+--S 1336 of 1527
+--m0:=a0-r0
+--E 1336
+
+--S 1337 of 1527
+--d0:=D(m0,x)
+--E 1337
+
+)clear all
+
+--S 1338 of 1527
+t0:=1/((a+b*x^2)^2*(c+d*x^2)^(3/2)*sqrt(x))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 +-+ | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 1338
+
+--S 1339 of 1527
+--r0:=1/2*d*(b*c+2*a*d)*sqrt(x)/(a*c*(b*c-a*d)^2*sqrt(c+d*x^2))+_
+-- 1/2*b*sqrt(x)/(a*(b*c-a*d)*(a+b*x^2)*sqrt(c+d*x^2))-_
+-- 1/2*(-d)^(3/4)*(b*c+2*a*d)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*c^(3/4)*(b*c-a*d)^2*_
+-- sqrt(c+d*x^2))+3/4*b*(b*c-3*a*d)*elliptic_pi(-sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)^2*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+3/4*b*(b*c-3*a*d)*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)^2*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1339
+
+--S 1340 of 1527
+--a0:=integrate(t0,x)
+--E 1340
+
+--S 1341 of 1527
+--m0:=a0-r0
+--E 1341
+
+--S 1342 of 1527
+--d0:=D(m0,x)
+--E 1342
+
+)clear all
+
+--S 1343 of 1527
+t0:=1/(x^(3/2)*(a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ---------------------------------------------------------------------
+--R +--------+
+--R 2 7 2 5 2 3 2 +-+ | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x)\|x \|d x + c
+--R Type: Expression(Integer)
+--E 1343
+
+--S 1344 of 1527
+--r0:=1/2*d*(b*c+2*a*d)/(a*c*(b*c-a*d)^2*sqrt(x)*sqrt(c+d*x^2))+_
+-- 1/2*b/(a*(b*c-a*d)*(a+b*x^2)*sqrt(x)*sqrt(c+d*x^2))-_
+-- 1/2*(5*b^2*c^2-8*a*b*c*d+6*a^2*d^2)*sqrt(c+d*x^2)/(a^2*c^2*_
+-- (b*c-a*d)^2*sqrt(x))-1/2*(-d)^(1/4)*(5*b^2*c^2-8*a*b*c*d+_
+-- 6*a^2*d^2)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*c^(5/4)*(b*c-a*d)^2*sqrt(c+d*x^2))+_
+-- 1/2*(-d)^(1/4)*(5*b^2*c^2-8*a*b*c*d+6*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*c^(5/4)*(b*c-a*d)^2*sqrt(c+d*x^2))+_
+-- 1/4*b^(3/2)*(5*b*c-11*a*d)*elliptic_pi(-sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(5/2)*(b*c-a*d)^2*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))-1/4*b^(3/2)*(5*b*c-11*a*d)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*_
+-- (b*c-a*d)^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1344
+
+--S 1345 of 1527
+--a0:=integrate(t0,x)
+--E 1345
+
+--S 1346 of 1527
+--m0:=a0-r0
+--E 1346
+
+--S 1347 of 1527
+--d0:=D(m0,x)
+--E 1347
+
+)clear all
+
+--S 1348 of 1527
+t0:=1/(x^(5/2)*(a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------------------------
+--R +--------+
+--R 2 8 2 6 2 4 2 2 +-+ | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 1348
+
+--S 1349 of 1527
+--r0:=1/2*d*(b*c+2*a*d)/(a*c*(b*c-a*d)^2*x^(3/2)*sqrt(c+d*x^2))+_
+-- 1/2*b/(a*(b*c-a*d)*x^(3/2)*(a+b*x^2)*sqrt(c+d*x^2))-_
+-- 1/6*(7*b^2*c^2-8*a*b*c*d+10*a^2*d^2)*sqrt(c+d*x^2)/(a^2*c^2*_
+-- (b*c-a*d)^2*x^(3/2))+1/6*(-d)^(3/4)*(7*b^2*c^2-8*a*b*c*d+10*_
+-- a^2*d^2)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*c^(7/4)*(b*c-a*d)^2*sqrt(c+d*x^2))-_
+-- 1/4*b^2*(7*b*c-13*a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+_
+-- d*x^2)/c)/(a^3*(b*c-a*d)^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/_
+-- sqrt(c)))-1/4*b^2*(7*b*c-13*a*d)*elliptic_pi(sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^3*(b*c-a*d)^2*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 1349
+
+--S 1350 of 1527
+--a0:=integrate(t0,x)
+--E 1350
+
+--S 1351 of 1527
+--m0:=a0-r0
+--E 1351
+
+--S 1352 of 1527
+--d0:=D(m0,x)
+--E 1352
+
+)clear all
+
+--S 1353 of 1527
+t0:=1/(x^(7/2)*(a+b*x^2)^2*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------------------------
+--R +--------+
+--R 2 9 2 7 2 5 2 3 +-+ | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|x \|d x + c
+--R Type: Expression(Integer)
+--E 1353
+
+--S 1354 of 1527
+--r0:=1/2*d*(b*c+2*a*d)/(a*c*(b*c-a*d)^2*x^(5/2)*sqrt(c+d*x^2))+_
+-- 1/2*b/(a*(b*c-a*d)*x^(5/2)*(a+b*x^2)*sqrt(c+d*x^2))-_
+-- 1/10*(9*b^2*c^2-8*a*b*c*d+14*a^2*d^2)*sqrt(c+d*x^2)/(a^2*c^2*_
+-- (b*c-a*d)^2*x^(5/2))+3/10*(15*b^3*c^3-16*a*b^2*c^2*d-8*a^2*b*_
+-- c*d^2+14*a^3*d^3)*sqrt(c+d*x^2)/(a^3*c^3*(b*c-a*d)^2*sqrt(x))+_
+-- 3/10*(-d)^(1/4)*(15*b^3*c^3-16*a*b^2*c^2*d-8*a^2*b*c*d^2+14*_
+-- a^3*d^3)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^3*c^(9/4)*(b*c-a*d)^2*sqrt(c+d*x^2))-_
+-- 3/10*(-d)^(1/4)*(15*b^3*c^3-16*a*b^2*c^2*d-8*a^2*b*c*d^2+_
+-- 14*a^3*d^3)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^3*c^(9/4)*(b*c-a*d)^2*sqrt(c+d*x^2))+_
+-- 3/4*b^(5/2)*(3*b*c-5*a*d)*elliptic_pi(-sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(7/2)*(b*c-a*d)^2*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))-3/4*b^(5/2)*(3*b*c-5*a*d)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(7/2)*(b*c-a*d)^2*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1354
+
+--S 1355 of 1527
+--a0:=integrate(t0,x)
+--E 1355
+
+--S 1356 of 1527
+--m0:=a0-r0
+--E 1356
+
+--S 1357 of 1527
+--d0:=D(m0,x)
+--E 1357
+
+)clear all
+
+--S 1358 of 1527
+t0:=x^(7/2)/((a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 3 +-+
+--R x \|x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 1358
+
+--S 1359 of 1527
+--r0:=1/6*(2*b*c+3*a*d)*sqrt(x)/(b*(b*c-a*d)^2*(c+d*x^2)^(3/2))+_
+-- 1/2*a*sqrt(x)/(b*(b*c-a*d)*(a+b*x^2)*(c+d*x^2)^(3/2))+5/6*_
+-- (b*c+2*a*d)*sqrt(x)/((b*c-a*d)^3*sqrt(c+d*x^2))+5/6*c^(1/4)*_
+-- (b*c+2*a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(1/4)*(b*c-a*d)^3*sqrt(c+d*x^2))-_
+-- 5/4*(b*c+a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((b*c-a*d)^3*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 5/4*(b*c+a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((b*c-a*d)^3*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1359
+
+--S 1360 of 1527
+--a0:=integrate(t0,x)
+--E 1360
+
+--S 1361 of 1527
+--m0:=a0-r0
+--E 1361
+
+--S 1362 of 1527
+--d0:=D(m0,x)
+--E 1362
+
+)clear all
+
+--S 1363 of 1527
+t0:=x^(5/2)/((a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 2 +-+
+--R x \|x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 1363
+
+--S 1364 of 1527
+--r0:=-5/6*d*x^(3/2)/((b*c-a*d)^2*(c+d*x^2)^(3/2))-1/2*x^(3/2)/_
+-- ((b*c-a*d)*(a+b*x^2)*(c+d*x^2)^(3/2))-1/2*d*(4*b*c+a*d)*_
+-- x^(3/2)/(c*(b*c-a*d)^3*sqrt(c+d*x^2))-1/2*(-d)^(1/4)*(4*b*c+_
+-- a*d)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(1/4)*(b*c-a*d)^3*sqrt(c+d*x^2))+_
+-- 1/2*(-d)^(1/4)*(4*b*c+a*d)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(c^(1/4)*(b*c-a*d)^3*_
+-- sqrt(c+d*x^2))-1/4*(3*b*c+7*a*d)*elliptic_pi(-sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt(b)*sqrt((c+d*x^2)/c)/((b*c-a*d)^3*sqrt(-a)*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+1/4*(3*b*c+7*a*d)*elliptic_pi(sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt(b)*sqrt((c+d*x^2)/c)/((b*c-a*d)^3*_
+-- sqrt(-a)*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1364
+
+--S 1365 of 1527
+--a0:=integrate(t0,x)
+--E 1365
+
+--S 1366 of 1527
+--m0:=a0-r0
+--E 1366
+
+--S 1367 of 1527
+--d0:=D(m0,x)
+--E 1367
+
+)clear all
+
+--S 1368 of 1527
+t0:=x^(3/2)/((a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R +-+
+--R x\|x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 1368
+
+--S 1369 of 1527
+--r0:=-5/6*d*sqrt(x)/((b*c-a*d)^2*(c+d*x^2)^(3/2))-1/2*sqrt(x)/_
+-- ((b*c-a*d)*(a+b*x^2)*(c+d*x^2)^(3/2))-1/6*d*(14*b*c+a*d)*_
+-- sqrt(x)/(c*(b*c-a*d)^3*sqrt(c+d*x^2))+1/6*(-d)^(3/4)*(14*b*c+_
+-- a*d)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(c^(3/4)*(b*c-a*d)^3*sqrt(c+d*x^2))+_
+-- 1/4*b*(b*c+9*a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(a*(b*c-a*d)^3*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+1/4*b*(b*c+9*a*d)*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)^3*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1369
+
+--S 1370 of 1527
+--a0:=integrate(t0,x)
+--E 1370
+
+--S 1371 of 1527
+--m0:=a0-r0
+--E 1371
+
+--S 1372 of 1527
+--d0:=D(m0,x)
+--E 1372
+
+)clear all
+
+--S 1373 of 1527
+t0:=sqrt(x)/((a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R +-+
+--R \|x
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 1373
+
+--S 1374 of 1527
+--r0:=1/6*d*(3*b*c+2*a*d)*x^(3/2)/(a*c*(b*c-a*d)^2*(c+d*x^2)^(3/2))+_
+-- 1/2*b*x^(3/2)/(a*(b*c-a*d)*(a+b*x^2)*(c+d*x^2)^(3/2))+_
+-- 1/2*d*(b^2*c^2+5*a*b*c*d-a^2*d^2)*x^(3/2)/(a*c^2*(b*c-a*d)^3*_
+-- sqrt(c+d*x^2))+1/2*(-d)^(1/4)*(b^2*c^2+5*a*b*c*d-a^2*d^2)*_
+-- elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+_
+-- d*x^2)/c)/(a*c^(5/4)*(b*c-a*d)^3*sqrt(c+d*x^2))-1/2*(-d)^(1/4)*_
+-- (b^2*c^2+5*a*b*c*d-a^2*d^2)*elliptic_f(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a*c^(5/4)*(b*c-a*d)^3*_
+-- sqrt(c+d*x^2))+1/4*b^(3/2)*(b*c-11*a*d)*elliptic_pi(-sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/_
+-- sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(3/2)*(b*c-a*d)^3*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-1/4*b^(3/2)*(b*c-_
+-- 11*a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/_
+-- ((-a)^(3/2)*(b*c-a*d)^3*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1374
+
+--S 1375 of 1527
+--a0:=integrate(t0,x)
+--E 1375
+
+--S 1376 of 1527
+--m0:=a0-r0
+--E 1376
+
+--S 1377 of 1527
+--d0:=D(m0,x)
+--E 1377
+
+)clear all
+
+--S 1378 of 1527
+t0:=1/((a+b*x^2)^2*(c+d*x^2)^(5/2)*sqrt(x))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|x \|d x + c
+--R Type: Expression(Integer)
+--E 1378
+
+--S 1379 of 1527
+--r0:=1/6*d*(3*b*c+2*a*d)*sqrt(x)/(a*c*(b*c-a*d)^2*(c+d*x^2)^(3/2))+_
+-- 1/2*b*sqrt(x)/(a*(b*c-a*d)*(a+b*x^2)*(c+d*x^2)^(3/2))+_
+-- 1/6*d*(3*b^2*c^2+17*a*b*c*d-5*a^2*d^2)*sqrt(x)/(a*c^2*(b*c-a*d)^3*_
+-- sqrt(c+d*x^2))-1/6*(-d)^(3/4)*(3*b^2*c^2+17*a*b*c*d-5*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (a*c^(7/4)*(b*c-a*d)^3*sqrt(c+d*x^2))+1/4*b^2*(3*b*c-13*a*d)*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)^3*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))+1/4*b^2*(3*b*c-13*a*d)*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)^3*_
+-- sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1379
+
+--S 1380 of 1527
+--a0:=integrate(t0,x)
+--E 1380
+
+--S 1381 of 1527
+--m0:=a0-r0
+--E 1381
+
+--S 1382 of 1527
+--d0:=D(m0,x)
+--E 1382
+
+)clear all
+
+--S 1383 of 1527
+t0:=1/(x^(3/2)*(a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 9 2 2 7 2 2 2 2 5
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 3 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|x \|d x + c
+--R Type: Expression(Integer)
+--E 1383
+
+--S 1384 of 1527
+--r0:=1/6*d*(3*b*c+2*a*d)/(a*c*(b*c-a*d)^2*(c+d*x^2)^(3/2)*sqrt(x))+_
+-- 1/2*b/(a*(b*c-a*d)*(a+b*x^2)*(c+d*x^2)^(3/2)*sqrt(x))+_
+-- 1/6*d*(3*b^2*c^2+19*a*b*c*d-7*a^2*d^2)/(a*c^2*(b*c-a*d)^3*_
+-- sqrt(x)*sqrt(c+d*x^2))-1/2*(5*b^3*c^3-12*a*b^2*c^2*d+19*a^2*b*c*d^2-_
+-- 7*a^3*d^3)*sqrt(c+d*x^2)/(a^2*c^3*(b*c-a*d)^3*sqrt(x))-_
+-- 1/2*(-d)^(1/4)*(5*b^3*c^3-12*a*b^2*c^2*d+19*a^2*b*c*d^2-_
+-- 7*a^3*d^3)*elliptic_e(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*c^(9/4)*(b*c-a*d)^3*sqrt(c+d*x^2))+_
+-- 1/2*(-d)^(1/4)*(5*b^3*c^3-12*a*b^2*c^2*d+19*a^2*b*c*d^2-7*a^3*d^3)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/_
+-- (a^2*c^(9/4)*(b*c-a*d)^3*sqrt(c+d*x^2))+5/4*b^(5/2)*(b*c-3*a*d)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(5/2)*_
+-- (b*c-a*d)^3*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 5/4*b^(5/2)*(b*c-3*a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(5/2)*(b*c-a*d)^3*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 1384
+
+--S 1385 of 1527
+--a0:=integrate(t0,x)
+--E 1385
+
+--S 1386 of 1527
+--m0:=a0-r0
+--E 1386
+
+--S 1387 of 1527
+--d0:=D(m0,x)
+--E 1387
+
+)clear all
+
+--S 1388 of 1527
+t0:=1/(x^(5/2)*(a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 10 2 2 8 2 2 2 2 6
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 4 2 2 2
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|x \|d x + c
+--R Type: Expression(Integer)
+--E 1388
+
+--S 1389 of 1527
+--r0:=1/6*d*(3*b*c+2*a*d)/(a*c*(b*c-a*d)^2*x^(3/2)*(c+d*x^2)^(3/2))+_
+-- 1/2*b/(a*(b*c-a*d)*x^(3/2)*(a+b*x^2)*(c+d*x^2)^(3/2))+_
+-- 1/2*d*(b^2*c^2+7*a*b*c*d-3*a^2*d^2)/(a*c^2*(b*c-a*d)^3*x^(3/2)*_
+-- sqrt(c+d*x^2))-1/6*(7*b^3*c^3-12*a*b^2*c^2*d+35*a^2*b*c*d^2-_
+-- 15*a^3*d^3)*sqrt(c+d*x^2)/(a^2*c^3*(b*c-a*d)^3*x^(3/2))+_
+-- 1/6*(-d)^(3/4)*(7*b^3*c^3-12*a*b^2*c^2*d+35*a^2*b*c*d^2-_
+-- 15*a^3*d^3)*elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^2*c^(11/4)*(b*c-a*d)^3*sqrt(c+d*x^2))-_
+-- 1/4*b^3*(7*b*c-17*a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+_
+-- d*x^2)/c)/(a^3*(b*c-a*d)^3*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 1/4*b^3*(7*b*c-17*a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^3*(b*c-a*d)^3*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1389
+
+--S 1390 of 1527
+--a0:=integrate(t0,x)
+--E 1390
+
+--S 1391 of 1527
+--m0:=a0-r0
+--E 1391
+
+--S 1392 of 1527
+--d0:=D(m0,x)
+--E 1392
+
+)clear all
+
+--S 1393 of 1527
+t0:=1/(x^(7/2)*(a+b*x^2)^2*(c+d*x^2)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 11 2 2 9 2 2 2 2 7
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 5 2 2 3
+--R (2a c d + 2a b c )x + a c x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|x \|d x + c
+--R Type: Expression(Integer)
+--E 1393
+
+--S 1394 of 1527
+--r0:=1/6*d*(3*b*c+2*a*d)/(a*c*(b*c-a*d)^2*x^(5/2)*(c+d*x^2)^(3/2))+_
+-- 1/2*b/(a*(b*c-a*d)*x^(5/2)*(a+b*x^2)*(c+d*x^2)^(3/2))+_
+-- 1/6*d*(3*b^2*c^2+23*a*b*c*d-11*a^2*d^2)/(a*c^2*(b*c-a*d)^3*_
+-- x^(5/2)*sqrt(c+d*x^2))-1/30*(27*b^3*c^3-36*a*b^2*c^2*d+161*_
+-- a^2*b*c*d^2-77*a^3*d^3)*sqrt(c+d*x^2)/(a^2*c^3*(b*c-a*d)^3*_
+-- x^(5/2))+1/10*(45*b^4*c^4-68*a*b^3*c^3*d-36*a^2*b^2*c^2*d^2+_
+-- 161*a^3*b*c*d^3-77*a^4*d^4)*sqrt(c+d*x^2)/(a^3*c^4*(b*c-a*d)^3*_
+-- sqrt(x))+1/10*(-d)^(1/4)*(45*b^4*c^4-68*a*b^3*c^3*d-36*a^2*b^2*_
+-- c^2*d^2+161*a^3*b*c*d^3-77*a^4*d^4)*elliptic_e(asin((-d)^(1/4)*_
+-- sqrt(x)/c^(1/4)),-1)*sqrt((c+d*x^2)/c)/(a^3*c^(13/4)*(b*c-a*d)^3*_
+-- sqrt(c+d*x^2))-1/10*(-d)^(1/4)*(45*b^4*c^4-68*a*b^3*c^3*d-_
+-- 36*a^2*b^2*c^2*d^2+161*a^3*b*c*d^3-77*a^4*d^4)*_
+-- elliptic_f(asin((-d)^(1/4)*sqrt(x)/c^(1/4)),-1)*_
+-- sqrt((c+d*x^2)/c)/(a^3*c^(13/4)*(b*c-a*d)^3*sqrt(c+d*x^2))+_
+-- 1/4*b^(7/2)*(9*b*c-19*a*d)*elliptic_pi(-sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(sqrt(x)*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^2)/c)/((-a)^(7/2)*(b*c-a*d)^3*sqrt(c+d*x^2)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))-1/4*b^(7/2)*(9*b*c-19*a*d)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(sqrt(x)*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^2)/c)/((-a)^(7/2)*_
+-- (b*c-a*d)^3*sqrt(c+d*x^2)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 1394
+
+--S 1395 of 1527
+--a0:=integrate(t0,x)
+--E 1395
+
+--S 1396 of 1527
+--m0:=a0-r0
+--E 1396
+
+--S 1397 of 1527
+--d0:=D(m0,x)
+--E 1397
+
+)clear all
+
+--S 1398 of 1527
+t0:=x*(a+b*x^2)^(3/2)/sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 3 | 2
+--R (b x + a x)\|b x + a
+--R (1) -----------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 1398
+
+--S 1399 of 1527
+r0:=3/8*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x^2)/(sqrt(b)*_
+ sqrt(c+d*x^2)))/(d^(5/2)*sqrt(b))+1/4*(a+b*x^2)^(3/2)*_
+ sqrt(c+d*x^2)/d-3/8*(b*c-a*d)*sqrt(a+b*x^2)*sqrt(c+d*x^2)/d^2
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 2 2 2 \|d \|b x + a
+--R (3a d - 6a b c d + 3b c )atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R +--------+ +--------+
+--R 2 +-+ +-+ | 2 | 2
+--R (2b d x + 5a d - 3b c)\|b \|d \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 8d \|b \|d
+--R Type: Expression(Integer)
+--E 1399
+
+--S 1400 of 1527
+--a0:=integrate(t0,x)
+--E 1400
+
+--S 1401 of 1527
+--m0:=a0-r0
+--E 1401
+
+--S 1402 of 1527
+--d0:=D(m0,x)
+--E 1402
+
+)clear all
+
+--S 1403 of 1527
+t0:=x*(a+b*x^2)^(1/2)/sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R x\|b x + a
+--R (1) ------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 1403
+
+--S 1404 of 1527
+r0:=-1/2*(b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x^2)/(sqrt(b)*_
+ sqrt(c+d*x^2)))/(d^(3/2)*sqrt(b))+1/2*sqrt(a+b*x^2)*sqrt(c+d*x^2)/d
+--R
+--R
+--R +--------+
+--R +-+ | 2 +--------+ +--------+
+--R \|d \|b x + a +-+ +-+ | 2 | 2
+--R (a d - b c)atanh(---------------) + \|b \|d \|b x + a \|d x + c
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R (2) ------------------------------------------------------------------
+--R +-+ +-+
+--R 2d\|b \|d
+--R Type: Expression(Integer)
+--E 1404
+
+--S 1405 of 1527
+--a0:=integrate(t0,x)
+--E 1405
+
+--S 1406 of 1527
+--m0:=a0-r0
+--E 1406
+
+--S 1407 of 1527
+--d0:=D(m0,x)
+--E 1407
+
+)clear all
+
+--S 1408 of 1527
+t0:=x/((a+b*x^2)^(1/2)*sqrt(c+d*x^2))
+--R
+--R
+--R x
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1408
+
+--S 1409 of 1527
+r0:=atanh(sqrt(d)*sqrt(a+b*x^2)/(sqrt(b)*sqrt(c+d*x^2)))/(sqrt(b)*sqrt(d))
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R \|d \|b x + a
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R (2) ----------------------
+--R +-+ +-+
+--R \|b \|d
+--R Type: Expression(Integer)
+--E 1409
+
+--S 1410 of 1527
+--a0:=integrate(t0,x)
+--E 1410
+
+--S 1411 of 1527
+--m0:=a0-r0
+--E 1411
+
+--S 1412 of 1527
+--d0:=D(m0,x)
+--E 1412
+
+)clear all
+
+--S 1413 of 1527
+t0:=x/((a+b*x^2)^(3/2)*sqrt(c+d*x^2))
+--R
+--R
+--R x
+--R (1) --------------------------------
+--R +--------+ +--------+
+--R 2 | 2 | 2
+--R (b x + a)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1413
+
+--S 1414 of 1527
+r0:=-sqrt(c+d*x^2)/((b*c-a*d)*sqrt(a+b*x^2))
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (2) ----------------------
+--R +--------+
+--R | 2
+--R (a d - b c)\|b x + a
+--R Type: Expression(Integer)
+--E 1414
+
+--S 1415 of 1527 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--------+
+--R | 2 | 2 2 2
+--R 10a\|b x + a \|d x + c + (b c + 25a b)x + a c + 25a
+--R (3) --------------------------------------------------------
+--R 2 2 2 3 2
+--R (10a b d - 10a b c)x + 10a d - 10a b c
+--R Type: Union(Expression(Integer),...)
+--E 1415
+
+--S 1416 of 1527 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R c + 25a
+--R (4) ---------------
+--R 2
+--R 10a d - 10a b c
+--R Type: Expression(Integer)
+--E 1416
+
+--S 1417 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1417
+
+)clear all
+
+--S 1418 of 1527
+t0:=x/((a+b*x^2)^(5/2)*sqrt(c+d*x^2))
+--R
+--R
+--R x
+--R (1) -------------------------------------------
+--R +--------+ +--------+
+--R 2 4 2 2 | 2 | 2
+--R (b x + 2a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1418
+
+--S 1419 of 1527
+r0:=-1/3*sqrt(c+d*x^2)/((b*c-a*d)*(a+b*x^2)^(3/2))+_
+ 2/3*d*sqrt(c+d*x^2)/((b*c-a*d)^2*sqrt(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R 2 | 2
+--R (2b d x + 3a d - b c)\|d x + c
+--R ------------------------------------------------------------------------
+--R +--------+
+--R 2 2 2 3 2 2 3 2 2 2 2 | 2
+--R ((3a b d - 6a b c d + 3b c )x + 3a d - 6a b c d + 3a b c )\|b x + a
+--R Type: Expression(Integer)
+--E 1419
+
+--S 1420 of 1527 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--------+
+--R 2 2 3 2 | 2 | 2
+--R (20a b d x + 30a d - 10a b c)\|b x + a \|d x + c
+--R +
+--R 2 2 2 3 2 3 4
+--R ((3a b c + 75a b )d - b c - 25a b c)x
+--R +
+--R 2 3 2 2 2 2 2 3 4 2 2
+--R ((6a b c + 150a b)d - 2a b c - 50a b c)x + (3a c + 75a )d - a b c
+--R +
+--R 3
+--R - 25a b c
+--R /
+--R 4 2 2 3 3 2 4 2 4
+--R (30a b d - 60a b c d + 30a b c )x
+--R +
+--R 5 2 4 2 3 3 2 2 6 2 5 4 2 2
+--R (60a b d - 120a b c d + 60a b c )x + 30a d - 60a b c d + 30a b c
+--R Type: Union(Expression(Integer),...)
+--E 1420
+
+--S 1421 of 1527 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R (3a c + 75a )d - b c - 25a b c
+--R (4) -------------------------------
+--R 4 2 3 2 2 2
+--R 30a d - 60a b c d + 30a b c
+--R Type: Expression(Integer)
+--E 1421
+
+--S 1422 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1422
+
+)clear all
+
+--S 1423 of 1527
+t0:=x/((a+b*x^2)^(7/2)*sqrt(c+d*x^2))
+--R
+--R
+--R x
+--R (1) -----------------------------------------------------
+--R +--------+ +--------+
+--R 3 6 2 4 2 2 3 | 2 | 2
+--R (b x + 3a b x + 3a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1423
+
+--S 1424 of 1527
+r0:=-1/5*sqrt(c+d*x^2)/((b*c-a*d)*(a+b*x^2)^(5/2))+_
+ 4/15*d*sqrt(c+d*x^2)/((b*c-a*d)^2*(a+b*x^2)^(3/2))-_
+ 8/15*d^2*sqrt(c+d*x^2)/((b*c-a*d)^3*sqrt(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R 2 2 4 2 2 2 2 2 2 2 | 2
+--R (8b d x + (20a b d - 4b c d)x + 15a d - 10a b c d + 3b c )\|d x + c
+--R /
+--R 3 2 3 2 3 2 4 2 5 3 4
+--R (15a b d - 45a b c d + 45a b c d - 15b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 2 5 3 4 2
+--R (30a b d - 90a b c d + 90a b c d - 30a b c )x + 15a d - 45a b c d
+--R +
+--R 3 2 2 2 3 3
+--R 45a b c d - 15a b c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 1424
+
+--S 1425 of 1527 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2 4 4 2 3 2 2 5 2 4
+--R 64a b d x + (160a b d - 32a b c d)x + 120a d - 80a b c d
+--R +
+--R 3 2 2
+--R 24a b c
+--R *
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + a \|d x + c
+--R +
+--R 2 3 3 3 2 4 2 2 4 5 3 5 2 6
+--R ((- 15a b c - 240a b )d + (10a b c + 160a b c)d - 3b c - 48a b c )x
+--R +
+--R 3 2 4 2 2 2 3 2 3 3 4 3
+--R (- 45a b c - 720a b )d + (30a b c + 480a b c)d - 9a b c
+--R +
+--R 2 4 2
+--R - 144a b c
+--R *
+--R 4
+--R x
+--R +
+--R 4 5 2 3 2 2 4 2 2 3 3 3 3 2 2
+--R ((- 45a b c - 720a b)d + (30a b c + 480a b c)d - 9a b c - 144a b c )x
+--R +
+--R 5 6 2 4 2 5 3 2 3 4 2 2
+--R (- 15a c - 240a )d + (10a b c + 160a b c)d - 3a b c - 48a b c
+--R /
+--R 6 3 3 5 4 2 4 5 2 3 6 3 6
+--R (120a b d - 360a b c d + 360a b c d - 120a b c )x
+--R +
+--R 7 2 3 6 3 2 5 4 2 4 5 3 4
+--R (360a b d - 1080a b c d + 1080a b c d - 360a b c )x
+--R +
+--R 8 3 7 2 2 6 3 2 5 4 3 2 9 3
+--R (360a b d - 1080a b c d + 1080a b c d - 360a b c )x + 120a d
+--R +
+--R 8 2 7 2 2 6 3 3
+--R - 360a b c d + 360a b c d - 120a b c
+--R Type: Union(Expression(Integer),...)
+--E 1425
+
+--S 1426 of 1527 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2 3 2 2 2 2 3 2 2
+--R (- 15a c - 240a )d + (10a b c + 160a b c)d - 3b c - 48a b c
+--R (4) ---------------------------------------------------------------
+--R 6 3 5 2 4 2 2 3 3 3
+--R 120a d - 360a b c d + 360a b c d - 120a b c
+--R Type: Expression(Integer)
+--E 1426
+
+--S 1427 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1427
+
+)clear all
+
+--S 1428 of 1527
+t0:=x/(sqrt(a-b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R x
+--R (1) ------------------------
+--R +----------+ +--------+
+--R | 2 | 2
+--R \|- b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1428
+
+--S 1429 of 1527
+r0:=-atan(sqrt(d)*sqrt(a-b*x^2)/(sqrt(b)*sqrt(c+d*x^2)))/(sqrt(b)*sqrt(d))
+--R
+--R
+--R +----------+
+--R | 2 +-+
+--R \|- b x + a \|d
+--R atan(-----------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R (2) - -----------------------
+--R +-+ +-+
+--R \|b \|d
+--R Type: Expression(Integer)
+--E 1429
+
+--S 1430 of 1527
+--a0:=integrate(t0,x)
+--E 1430
+
+--S 1431 of 1527
+--m0:=a0-r0
+--E 1431
+
+--S 1432 of 1527
+--d0:=D(m0,x)
+--E 1432
+
+)clear all
+
+--S 1433 of 1527
+t0:=x/(sqrt(a-b*x^2)*sqrt(c-d*x^2))
+--R
+--R
+--R x
+--R (1) --------------------------
+--R +----------+ +----------+
+--R | 2 | 2
+--R \|- d x + c \|- b x + a
+--R Type: Expression(Integer)
+--E 1433
+
+--S 1434 of 1527
+r0:=-atanh(sqrt(d)*sqrt(a-b*x^2)/(sqrt(b)*sqrt(c-d*x^2)))/(sqrt(b)*sqrt(d))
+--R
+--R
+--R +----------+
+--R | 2 +-+
+--R \|- b x + a \|d
+--R atanh(-----------------)
+--R +----------+
+--R | 2 +-+
+--R \|- d x + c \|b
+--R (2) - ------------------------
+--R +-+ +-+
+--R \|b \|d
+--R Type: Expression(Integer)
+--E 1434
+
+--S 1435 of 1527
+--a0:=integrate(t0,x)
+--E 1435
+
+--S 1436 of 1527
+--m0:=a0-r0
+--E 1436
+
+--S 1437 of 1527
+--d0:=D(m0,x)
+--E 1437
+
+)clear all
+
+--S 1438 of 1527
+t0:=x*sqrt(-1+3*x^2)/sqrt(2-3*x^2)
+--R
+--R
+--R +-------+
+--R | 2
+--R x\|3x - 1
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 3x + 2
+--R Type: Expression(Integer)
+--E 1438
+
+--S 1439 of 1527
+r0:=-1/12*asin(3-6*x^2)-1/6*sqrt(2-3*x^2)*sqrt(-1+3*x^2)
+--R
+--R
+--R +---------+ +-------+
+--R | 2 | 2 2
+--R - 2\|- 3x + 2 \|3x - 1 + asin(6x - 3)
+--R (2) -----------------------------------------
+--R 12
+--R Type: Expression(Integer)
+--E 1439
+
+--S 1440 of 1527 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+ +---------+
+--R | 2 | 2 +---------+ +-------+
+--R 47\|3x - 1 + 52\|- 3x + 2 | 2 | 2
+--R - atan(-----------------------------) - \|- 3x + 2 \|3x - 1
+--R +-------+ +---------+
+--R | 2 | 2
+--R 52\|3x - 1 - 47\|- 3x + 2
+--R (3) --------------------------------------------------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 1440
+
+--S 1441 of 1527 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +-------+ +---------+
+--R | 2 | 2
+--R 47\|3x - 1 + 52\|- 3x + 2 2
+--R - 2atan(-----------------------------) - asin(6x - 3)
+--R +-------+ +---------+
+--R | 2 | 2
+--R 52\|3x - 1 - 47\|- 3x + 2
+--R (4) ------------------------------------------------------
+--R 12
+--R Type: Expression(Integer)
+--E 1441
+
+--S 1442 of 1527
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R +-----------------+ +---------+ +-------+
+--R | 4 2 3 | 2 | 2
+--R (- 4888x\|- 36x + 36x - 8 - 2970x - 3428x)\|- 3x + 2 \|3x - 1
+--R +
+--R +-----------------+
+--R 3 | 4 2 5 3
+--R (1485x + 1714x)\|- 36x + 36x - 8 - 87984x + 87984x - 19552x
+--R /
+--R +-----------------+ +---------+ +-------+
+--R 2 | 4 2 | 2 | 2
+--R (2970x + 3428)\|- 36x + 36x - 8 \|- 3x + 2 \|3x - 1
+--R +
+--R +-----------------+
+--R 4 2 | 4 2
+--R (87984x - 87984x + 19552)\|- 36x + 36x - 8
+--R Type: Expression(Integer)
+--E 1442
+
+)clear all
+
+--S 1443 of 1527
+t0:=x^3*(a+b*x^2)^(5/2)/sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (b x + 2a b x + a x )\|b x + a
+--R (1) ----------------------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 1443
+
+--S 1444 of 1527
+r0:=5/128*(b*c-a*d)^3*(7*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x^2)/_
+ (sqrt(b)*sqrt(c+d*x^2)))/(b^(3/2)*d^(9/2))+5/192*(b*c-a*d)*_
+ (7*b*c+a*d)*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/(b*d^3)-_
+ 1/48*(7*b*c+a*d)*(a+b*x^2)^(5/2)*sqrt(c+d*x^2)/(b*d^2)+_
+ 1/8*(a+b*x^2)^(7/2)*sqrt(c+d*x^2)/(b*d)-5/128*(b*c-a*d)^2*_
+ (7*b*c+a*d)*sqrt(a+b*x^2)*sqrt(c+d*x^2)/(b*d^4)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 15a d - 60a b c d + 270a b c d - 300a b c d + 105b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|b x + a
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 3 3 6 2 3 3 2 4
+--R 48b d x + (136a b d - 56b c d )x
+--R +
+--R 2 3 2 2 3 2 2 3 3 2 2
+--R (118a b d - 172a b c d + 70b c d)x + 15a d - 191a b c d
+--R +
+--R 2 2 3 3
+--R 265a b c d - 105b c
+--R *
+--R +--------+ +--------+
+--R +-+ +-+ | 2 | 2
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 4 +-+ +-+
+--R 384b d \|b \|d
+--R Type: Expression(Integer)
+--E 1444
+
+--S 1445 of 1527
+--a0:=integrate(t0,x)
+--E 1445
+
+--S 1446 of 1527
+--m0:=a0-r0
+--E 1446
+
+--S 1447 of 1527
+--d0:=D(m0,x)
+--E 1447
+
+)clear all
+
+--S 1448 of 1527
+t0:=x^3*(a+b*x^2)^(3/2)/sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 5 3 | 2
+--R (b x + a x )\|b x + a
+--R (1) ------------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 1448
+
+--S 1449 of 1527
+r0:=-1/16*(b*c-a*d)^2*(5*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x^2)/_
+ (sqrt(b)*sqrt(c+d*x^2)))/(b^(3/2)*d^(7/2))-_
+ 1/24*(5*b*c+a*d)*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/(b*d^2)+_
+ 1/6*(a+b*x^2)^(5/2)*sqrt(c+d*x^2)/(b*d)+1/16*(b*c-a*d)*_
+ (5*b*c+a*d)*sqrt(a+b*x^2)*sqrt(c+d*x^2)/(b*d^3)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (- 3a d - 9a b c d + 27a b c d - 15b c )atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2 +-+ +-+
+--R (8b d x + (14a b d - 10b c d)x + 3a d - 22a b c d + 15b c )\|b \|d
+--R *
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + a \|d x + c
+--R /
+--R 3 +-+ +-+
+--R 48b d \|b \|d
+--R Type: Expression(Integer)
+--E 1449
+
+--S 1450 of 1527
+--a0:=integrate(t0,x)
+--E 1450
+
+--S 1451 of 1527
+--m0:=a0-r0
+--E 1451
+
+--S 1452 of 1527
+--d0:=D(m0,x)
+--E 1452
+
+)clear all
+
+--S 1453 of 1527
+t0:=x^3*(a+b*x^2)^(1/2)/sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 3 | 2
+--R x \|b x + a
+--R (1) -------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 1453
+
+--S 1454 of 1527
+r0:=1/8*(b*c-a*d)*(3*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x^2)/_
+ (sqrt(b)*sqrt(c+d*x^2)))/(b^(3/2)*d^(5/2))+1/4*(a+b*x^2)^(3/2)*_
+ sqrt(c+d*x^2)/(b*d)-1/8*(3*b*c+a*d)*sqrt(a+b*x^2)*sqrt(c+d*x^2)/(b*d^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 2 2 2 \|d \|b x + a
+--R (- a d - 2a b c d + 3b c )atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R +--------+ +--------+
+--R 2 +-+ +-+ | 2 | 2
+--R (2b d x + a d - 3b c)\|b \|d \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 8b d \|b \|d
+--R Type: Expression(Integer)
+--E 1454
+
+--S 1455 of 1527
+--a0:=integrate(t0,x)
+--E 1455
+
+--S 1456 of 1527
+--m0:=a0-r0
+--E 1456
+
+--S 1457 of 1527
+--d0:=D(m0,x)
+--E 1457
+
+)clear all
+
+--S 1458 of 1527
+t0:=x^3/((a+b*x^2)^(1/2)*sqrt(c+d*x^2))
+--R
+--R
+--R 3
+--R x
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1458
+
+--S 1459 of 1527
+r0:=-1/2*(b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x^2)/(sqrt(b)*sqrt(c+d*x^2)))/_
+ (b^(3/2)*d^(3/2))+1/2*sqrt(a+b*x^2)*sqrt(c+d*x^2)/(b*d)
+--R
+--R
+--R +--------+
+--R +-+ | 2 +--------+ +--------+
+--R \|d \|b x + a +-+ +-+ | 2 | 2
+--R (- a d - b c)atanh(---------------) + \|b \|d \|b x + a \|d x + c
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R (2) --------------------------------------------------------------------
+--R +-+ +-+
+--R 2b d\|b \|d
+--R Type: Expression(Integer)
+--E 1459
+
+--S 1460 of 1527
+--a0:=integrate(t0,x)
+--E 1460
+
+--S 1461 of 1527
+--m0:=a0-r0
+--E 1461
+
+--S 1462 of 1527
+--d0:=D(m0,x)
+--E 1462
+
+)clear all
+
+--S 1463 of 1527
+t0:=x^3/((a+b*x^2)^(3/2)*sqrt(c+d*x^2))
+--R
+--R
+--R 3
+--R x
+--R (1) --------------------------------
+--R +--------+ +--------+
+--R 2 | 2 | 2
+--R (b x + a)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1463
+
+--S 1464 of 1527
+r0:=atanh(sqrt(d)*sqrt(a+b*x^2)/(sqrt(b)*sqrt(c+d*x^2)))/(b^(3/2)*_
+ sqrt(d))+a*sqrt(c+d*x^2)/(b*(b*c-a*d)*sqrt(a+b*x^2))
+--R
+--R
+--R +--------+
+--R +--------+ +-+ | 2 +--------+
+--R | 2 \|d \|b x + a +-+ +-+ | 2
+--R (a d - b c)\|b x + a atanh(---------------) - a\|b \|d \|d x + c
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R (2) -------------------------------------------------------------------
+--R +--------+
+--R 2 +-+ +-+ | 2
+--R (a b d - b c)\|b \|d \|b x + a
+--R Type: Expression(Integer)
+--E 1464
+
+--S 1465 of 1527
+--a0:=integrate(t0,x)
+--E 1465
+
+--S 1466 of 1527
+--m0:=a0-r0
+--E 1466
+
+--S 1467 of 1527
+--d0:=D(m0,x)
+--E 1467
+
+)clear all
+
+--S 1468 of 1527
+t0:=x^3/((a+b*x^2)^(5/2)*sqrt(c+d*x^2))
+--R
+--R
+--R 3
+--R x
+--R (1) -------------------------------------------
+--R +--------+ +--------+
+--R 2 4 2 2 | 2 | 2
+--R (b x + 2a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1468
+
+--S 1469 of 1527
+r0:=1/3*a*sqrt(c+d*x^2)/(b*(b*c-a*d)*(a+b*x^2)^(3/2))-_
+ 1/3*(3*b*c-a*d)*sqrt(c+d*x^2)/(b*(b*c-a*d)^2*sqrt(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R 2 | 2
+--R ((a d - 3b c)x - 2a c)\|d x + c
+--R ------------------------------------------------------------------------
+--R +--------+
+--R 2 2 2 3 2 2 3 2 2 2 2 | 2
+--R ((3a b d - 6a b c d + 3b c )x + 3a d - 6a b c d + 3a b c )\|b x + a
+--R Type: Expression(Integer)
+--E 1469
+
+--S 1470 of 1527 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--------+
+--R 2 2 2 | 2 | 2 2 2 2 4
+--R ((4a d - 12a b c)x - 8a c)\|b x + a \|d x + c + (- b c - 16a b c)x
+--R +
+--R 2 2 2 2 2 3
+--R (- 2a b c - 32a b c)x - a c - 16a c
+--R /
+--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 2
+--R (12a b d - 24a b c d + 12a b c )x + (24a b d - 48a b c d + 24a b c )x
+--R +
+--R 5 2 4 3 2 2
+--R 12a d - 24a b c d + 12a b c
+--R Type: Union(Expression(Integer),...)
+--E 1470
+
+--S 1471 of 1527 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2
+--R - c - 16a c
+--R (4) -----------------------------
+--R 3 2 2 2 2
+--R 12a d - 24a b c d + 12a b c
+--R Type: Expression(Integer)
+--E 1471
+
+--S 1472 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1472
+
+)clear all
+
+--S 1473 of 1527
+t0:=x^5*(a+b*x^2)^(5/2)/sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 9 7 2 5 | 2
+--R (b x + 2a b x + a x )\|b x + a
+--R (1) ----------------------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 1473
+
+--S 1474 of 1527
+r0:=-1/256*(b*c-a*d)^3*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*_
+ atanh(sqrt(d)*sqrt(a+b*x^2)/(sqrt(b)*sqrt(c+d*x^2)))/_
+ (b^(5/2)*d^(11/2))-1/384*(b*c-a*d)*(63*b^2*c^2+14*a*b*c*d+_
+ 3*a^2*d^2)*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/(b^2*d^4)+1/480*_
+ (63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*(a+b*x^2)^(5/2)*sqrt(c+d*x^2)/_
+ (b^2*d^3)-3/80*(3*b*c+a*d)*(a+b*x^2)^(7/2)*sqrt(c+d*x^2)/_
+ (b^2*d^2)+1/10*x^2*(a+b*x^2)^(7/2)*sqrt(c+d*x^2)/(b*d)+_
+ 1/256*(b*c-a*d)^2*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*_
+ sqrt(a+b*x^2)*sqrt(c+d*x^2)/(b^2*d^5)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R 45a d + 75a b c d + 450a b c d - 2250a b c d + 2625a b c d
+--R +
+--R 5 5
+--R - 945b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|b x + a
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 4 4 8 3 4 4 3 6
+--R 384b d x + (1008a b d - 432b c d )x
+--R +
+--R 2 2 4 3 3 4 2 2 4
+--R (744a b d - 1184a b c d + 504b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 2 4 4
+--R (30a b d - 962a b c d + 1498a b c d - 630b c d)x - 45a d
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R - 90a b c d + 1564a b c d - 2310a b c d + 945b c
+--R *
+--R +--------+ +--------+
+--R +-+ +-+ | 2 | 2
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 5 +-+ +-+
+--R 3840b d \|b \|d
+--R Type: Expression(Integer)
+--E 1474
+
+--S 1475 of 1527
+--a0:=integrate(t0,x)
+--E 1475
+
+--S 1476 of 1527
+--m0:=a0-r0
+--E 1476
+
+--S 1477 of 1527
+--d0:=D(m0,x)
+--E 1477
+
+)clear all
+
+--S 1478 of 1527
+t0:=x^5*(a+b*x^2)^(3/2)/sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 7 5 | 2
+--R (b x + a x )\|b x + a
+--R (1) ------------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 1478
+
+--S 1479 of 1527
+r0:=1/128*(b*c-a*d)^2*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*_
+ atanh(sqrt(d)*sqrt(a+b*x^2)/(sqrt(b)*sqrt(c+d*x^2)))/_
+ (b^(5/2)*d^(9/2))+1/192*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*_
+ (a+b*x^2)^(3/2)*sqrt(c+d*x^2)/(b^2*d^3)-1/48*(7*b*c+3*a*d)*_
+ (a+b*x^2)^(5/2)*sqrt(c+d*x^2)/(b^2*d^2)+1/8*x^2*(a+b*x^2)^(5/2)*_
+ sqrt(c+d*x^2)/(b*d)-1/128*(b*c-a*d)*(35*b^2*c^2+10*a*b*c*d+_
+ 3*a^2*d^2)*sqrt(a+b*x^2)*sqrt(c+d*x^2)/(b^2*d^4)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (9a d + 12a b c d + 54a b c d - 180a b c d + 105b c )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|d \|b x + a
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 3 3 6 2 3 3 2 4
+--R 48b d x + (72a b d - 56b c d )x
+--R +
+--R 2 3 2 2 3 2 2 3 3 2 2 2 2
+--R (6a b d - 92a b c d + 70b c d)x - 9a d - 15a b c d + 145a b c d
+--R +
+--R 3 3
+--R - 105b c
+--R *
+--R +--------+ +--------+
+--R +-+ +-+ | 2 | 2
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 4 +-+ +-+
+--R 384b d \|b \|d
+--R Type: Expression(Integer)
+--E 1479
+
+--S 1480 of 1527
+--a0:=integrate(t0,x)
+--E 1480
+
+--S 1481 of 1527
+--m0:=a0-r0
+--E 1481
+
+--S 1482 of 1527
+--d0:=D(m0,x)
+--E 1482
+
+)clear all
+
+--S 1483 of 1527
+t0:=x^5*(a+b*x^2)^(1/2)/sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 5 | 2
+--R x \|b x + a
+--R (1) -------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 1483
+
+--S 1484 of 1527
+r0:=-1/16*(b*c-a*d)*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x^2)/(sqrt(b)*sqrt(c+d*x^2)))/(b^(5/2)*d^(7/2))-_
+ 1/24*(5*b*c+3*a*d)*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/(b^2*d^2)+_
+ 1/6*x^2*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/(b*d)+_
+ 1/16*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*sqrt(a+b*x^2)*sqrt(c+d*x^2)/(b^2*d^3)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (3a d + 3a b c d + 9a b c d - 15b c )atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R 2 2 4 2 2 2 2 2 2 2 +-+ +-+
+--R (8b d x + (2a b d - 10b c d)x - 3a d - 4a b c d + 15b c )\|b \|d
+--R *
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + a \|d x + c
+--R /
+--R 2 3 +-+ +-+
+--R 48b d \|b \|d
+--R Type: Expression(Integer)
+--E 1484
+
+--S 1485 of 1527
+--a0:=integrate(t0,x)
+--E 1485
+
+--S 1486 of 1527
+--m0:=a0-r0
+--E 1486
+
+--S 1487 of 1527
+--d0:=D(m0,x)
+--E 1487
+
+)clear all
+
+--S 1488 of 1527
+t0:=x^5/((a+b*x^2)^(1/2)*sqrt(c+d*x^2))
+--R
+--R
+--R 5
+--R x
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1488
+
+--S 1489 of 1527
+r0:=-1/8*(4*a*b*c*d-3*(b*c+a*d)^2)*atanh(sqrt(d)*sqrt(a+b*x^2)/_
+ (sqrt(b)*sqrt(c+d*x^2)))/(b^(5/2)*d^(5/2))-3/8*(b*c+a*d)*_
+ sqrt(a+b*x^2)*sqrt(c+d*x^2)/(b^2*d^2)+1/4*x^2*_
+ sqrt(a+b*x^2)*sqrt(c+d*x^2)/(b*d)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 2 2 2 2 \|d \|b x + a
+--R (3a d + 2a b c d + 3b c )atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R +--------+ +--------+
+--R 2 +-+ +-+ | 2 | 2
+--R (2b d x - 3a d - 3b c)\|b \|d \|b x + a \|d x + c
+--R /
+--R 2 2 +-+ +-+
+--R 8b d \|b \|d
+--R Type: Expression(Integer)
+--E 1489
+
+--S 1490 of 1527
+--a0:=integrate(t0,x)
+--E 1490
+
+--S 1491 of 1527
+--m0:=a0-r0
+--E 1491
+
+--S 1492 of 1527
+--d0:=D(m0,x)
+--E 1492
+
+)clear all
+
+--S 1493 of 1527
+t0:=x^5/((a+b*x^2)^(3/2)*sqrt(c+d*x^2))
+--R
+--R
+--R 5
+--R x
+--R (1) --------------------------------
+--R +--------+ +--------+
+--R 2 | 2 | 2
+--R (b x + a)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1493
+
+--S 1494 of 1527
+r0:=-1/2*(b*c+3*a*d)*atanh(sqrt(d)*sqrt(a+b*x^2)/(sqrt(b)*_
+ sqrt(c+d*x^2)))/(b^(5/2)*d^(3/2))-a^2*sqrt(c+d*x^2)/_
+ (b^2*(b*c-a*d)*sqrt(a+b*x^2))+1/2*sqrt(a+b*x^2)*sqrt(c+d*x^2)/(b^2*d)
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ +-+ | 2
+--R 2 2 2 2 | 2 \|d \|b x + a
+--R (- 3a d + 2a b c d + b c )\|b x + a atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R +--------+
+--R 2 2 2 +-+ +-+ | 2
+--R ((a b d - b c)x + 3a d - a b c)\|b \|d \|d x + c
+--R /
+--R +--------+
+--R 2 2 3 +-+ +-+ | 2
+--R (2a b d - 2b c d)\|b \|d \|b x + a
+--R Type: Expression(Integer)
+--E 1494
+
+--S 1495 of 1527
+--a0:=integrate(t0,x)
+--E 1495
+
+--S 1496 of 1527
+--m0:=a0-r0
+--E 1496
+
+--S 1497 of 1527
+--d0:=D(m0,x)
+--E 1497
+
+)clear all
+
+--S 1498 of 1527
+t0:=x^5/((a+b*x^2)^(5/2)*sqrt(c+d*x^2))
+--R
+--R
+--R 5
+--R x
+--R (1) -------------------------------------------
+--R +--------+ +--------+
+--R 2 4 2 2 | 2 | 2
+--R (b x + 2a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1498
+
+--S 1499 of 1527
+r0:=atanh(sqrt(d)*sqrt(a+b*x^2)/(sqrt(b)*sqrt(c+d*x^2)))/(b^(5/2)*_
+ sqrt(d))-1/3*a^2*sqrt(c+d*x^2)/(b^2*(b*c-a*d)*(a+b*x^2)^(3/2))+_
+ 2/3*a*(3*b*c-2*a*d)*sqrt(c+d*x^2)/(b^2*(b*c-a*d)^2*sqrt(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((3a b d - 6a b c d + 3b c )x + 3a d - 6a b c d + 3a b c )
+--R *
+--R +--------+
+--R +--------+ +-+ | 2
+--R | 2 \|d \|b x + a
+--R \|b x + a atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|d x + c
+--R +
+--R +--------+
+--R 2 2 2 3 2 +-+ +-+ | 2
+--R ((- 4a b d + 6a b c)x - 3a d + 5a b c)\|b \|d \|d x + c
+--R /
+--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +-+ +-+
+--R ((3a b d - 6a b c d + 3b c )x + 3a b d - 6a b c d + 3a b c )\|b \|d
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 1499
+
+--S 1500 of 1527
+--a0:=integrate(t0,x)
+--E 1500
+
+--S 1501 of 1527
+--m0:=a0-r0
+--E 1501
+
+--S 1502 of 1527
+--d0:=D(m0,x)
+--E 1502
+
+)clear all
+
+--S 1503 of 1527
+t0:=x^5/((a+b*x^2)^(7/2)*sqrt(c+d*x^2))
+--R
+--R
+--R 5
+--R x
+--R (1) -----------------------------------------------------
+--R +--------+ +--------+
+--R 3 6 2 4 2 2 3 | 2 | 2
+--R (b x + 3a b x + 3a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1503
+
+--S 1504 of 1527
+r0:=-1/5*a^2*sqrt(c+d*x^2)/(b^2*(b*c-a*d)*(a+b*x^2)^(5/2))+_
+ 2/15*a*(5*b*c-3*a*d)*sqrt(c+d*x^2)/(b^2*(b*c-a*d)^2*_
+ (a+b*x^2)^(3/2))-1/15*(15*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*_
+ sqrt(c+d*x^2)/(b^2*(b*c-a*d)^3*sqrt(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 2 2 2 4 2 2 2 2 2
+--R ((3a d - 10a b c d + 15b c )x + (- 4a c d + 20a b c )x + 8a c )
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 3 2 3 2 3 2 4 2 5 3 4
+--R (15a b d - 45a b c d + 45a b c d - 15b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 2 5 3 4 2
+--R (30a b d - 90a b c d + 90a b c d - 30a b c )x + 15a d - 45a b c d
+--R +
+--R 3 2 2 2 3 3
+--R 45a b c d - 15a b c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 1504
+
+--S 1505 of 1527 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 2 2 2 4 3 2 2 2 3 2
+--R ((3a d - 10a b c d + 15a b c )x + (- 4a c d + 20a b c )x + 8a c )
+--R *
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + a \|d x + c
+--R +
+--R 3 3 3 2 6 2 3 2 2 2 4
+--R (- 2b c - 8a b c )x + (- 6a b c - 24a b c )x
+--R +
+--R 2 3 3 2 2 3 3 4 2
+--R (- 6a b c - 24a b c )x - 2a c - 8a c
+--R /
+--R 4 3 3 3 4 2 2 5 2 6 3 6
+--R (15a b d - 45a b c d + 45a b c d - 15a b c )x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (45a b d - 135a b c d + 135a b c d - 45a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2 7 3 6 2
+--R (45a b d - 135a b c d + 135a b c d - 45a b c )x + 15a d - 45a b c d
+--R +
+--R 5 2 2 4 3 3
+--R 45a b c d - 15a b c
+--R Type: Union(Expression(Integer),...)
+--E 1505
+
+--S 1506 of 1527 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 3 2
+--R - 2c - 8a c
+--R (4) ------------------------------------------
+--R 4 3 3 2 2 2 2 3 3
+--R 15a d - 45a b c d + 45a b c d - 15a b c
+--R Type: Expression(Integer)
+--E 1506
+
+--S 1507 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1507
+
+)clear all
+
+--S 1508 of 1527
+t0:=x^5/((a+b*x^2)^(9/2)*sqrt(c+d*x^2))
+--R
+--R
+--R 5
+--R x
+--R (1) ---------------------------------------------------------------
+--R +--------+ +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1508
+
+--S 1509 of 1527
+r0:=-1/7*a^2*sqrt(c+d*x^2)/(b^2*(b*c-a*d)*(a+b*x^2)^(7/2))+_
+ 2/35*a*(7*b*c-4*a*d)*sqrt(c+d*x^2)/(b^2*(b*c-a*d)^2*_
+ (a+b*x^2)^(5/2))-1/105*(35*b^2*c^2-14*a*b*c*d+3*a^2*d^2)*_
+ sqrt(c+d*x^2)/(b^2*(b*c-a*d)^3*(a+b*x^2)^(3/2))+_
+ 2/105*d*(35*b^2*c^2-14*a*b*c*d+3*a^2*d^2)*sqrt(c+d*x^2)/_
+ (b^2*(b*c-a*d)^4*sqrt(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 3 2 2 3 2 6
+--R (6a b d - 28a b c d + 70b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (21a d - 101a b c d + 259a b c d - 35b c )x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (- 28a c d + 200a b c d - 28a b c )x + 56a c d - 8a b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 6
+--R (105a b d - 420a b c d + 630a b c d - 420a b c d + 105b c )x
+--R +
+--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 4
+--R (315a b d - 1260a b c d + 1890a b c d - 1260a b c d + 315a b c )x
+--R +
+--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 2
+--R (315a b d - 1260a b c d + 1890a b c d - 1260a b c d + 315a b c )x
+--R +
+--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R 105a d - 420a b c d + 630a b c d - 420a b c d + 105a b c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 1509
+
+--S 1510 of 1527 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 3 2 2 2 3 2 6
+--R (6a b d - 28a b c d + 70a b c d)x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3 4
+--R (21a d - 101a b c d + 259a b c d - 35a b c )x
+--R +
+--R 5 2 4 2 3 2 3 2 5 2 4 3
+--R (- 28a c d + 200a b c d - 28a b c )x + 56a c d - 8a b c
+--R *
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + a \|d x + c
+--R +
+--R 4 3 2 4 2 5 4 5 3 8
+--R ((- 7a b c - 112a b c )d + b c + 16a b c )x
+--R +
+--R 2 3 3 3 3 2 4 4 2 4 3 6
+--R ((- 28a b c - 448a b c )d + 4a b c + 64a b c )x
+--R +
+--R 3 2 3 4 2 2 2 3 4 3 3 3 4
+--R ((- 42a b c - 672a b c )d + 6a b c + 96a b c )x
+--R +
+--R 4 3 5 2 3 2 4 4 2 3 2 5 3 6 2
+--R ((- 28a b c - 448a b c )d + 4a b c + 64a b c )x + (- 7a c - 112a c )d
+--R +
+--R 4 4 5 3
+--R a b c + 16a b c
+--R /
+--R 6 4 4 5 5 3 4 6 2 2 3 7 3 2 8 4 8
+--R (105a b d - 420a b c d + 630a b c d - 420a b c d + 105a b c )x
+--R +
+--R 7 3 4 6 4 3 5 5 2 2 4 6 3 3 7 4 6
+--R (420a b d - 1680a b c d + 2520a b c d - 1680a b c d + 420a b c )x
+--R +
+--R 8 2 4 7 3 3 6 4 2 2 5 5 3 4 6 4 4
+--R (630a b d - 2520a b c d + 3780a b c d - 2520a b c d + 630a b c )x
+--R +
+--R 9 4 8 2 3 7 3 2 2 6 4 3 5 5 4 2
+--R (420a b d - 1680a b c d + 2520a b c d - 1680a b c d + 420a b c )x
+--R +
+--R 10 4 9 3 8 2 2 2 7 3 3 6 4 4
+--R 105a d - 420a b c d + 630a b c d - 420a b c d + 105a b c
+--R Type: Union(Expression(Integer),...)
+--E 1510
+
+--S 1511 of 1527 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 3 2 2 4 3
+--R (- 7a c - 112a c )d + b c + 16a b c
+--R (4) ------------------------------------------------------------
+--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 105a d - 420a b c d + 630a b c d - 420a b c d + 105a b c
+--R Type: Expression(Integer)
+--E 1511
+
+--S 1512 of 1527
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1512
+
+)clear all
+
+--S 1513 of 1527
+t0:=x^2/(sqrt(2+b*x^2)*sqrt(3+d*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + 2 \|d x + 3
+--R Type: Expression(Integer)
+--E 1513
+
+--S 1514 of 1527
+--r0:=elliptic_e(asin(x*sqrt(-d)/sqrt(3)),3/2*b/d)*sqrt(2)/_
+-- (b*sqrt(-d))-elliptic_f(asin(x*sqrt(-d)/sqrt(3)),3/2*b/d)*_
+-- sqrt(2)/(b*sqrt(-d))
+--E 1514
+
+--S 1515 of 1527
+--a0:=integrate(t0,x)
+--E 1515
+
+--S 1516 of 1527
+--m0:=a0-r0
+--E 1516
+
+--S 1517 of 1527
+--d0:=D(m0,x)
+--E 1517
+
+)clear all
+
+--S 1518 of 1527
+t0:=x^2/(sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 1518
+
+--S 1519 of 1527
+--r0:=elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b*sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))-a*elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*_
+-- sqrt(c)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(b*sqrt(-d)*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 1519
+
+--S 1520 of 1527
+--a0:=integrate(t0,x)
+--E 1520
+
+--S 1521 of 1527
+--m0:=a0-r0
+--E 1521
+
+--S 1522 of 1527
+--d0:=D(m0,x)
+--E 1522
+
+)clear all
+
+--S 1523 of 1527
+t0:=x^2/(sqrt(4-x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|- x + 4 \|d x + c
+--R Type: Expression(Integer)
+--E 1523
+
+--S 1524 of 1527
+--r0:=elliptic_e(asin(1/2*x),-4*d/c)*sqrt(c+d*x^2)/_
+-- (d*sqrt((c+d*x^2)/c))-c*elliptic_f(asin(1/2*x),-4*d/c)*_
+-- sqrt((c+d*x^2)/c)/(d*sqrt(c+d*x^2))
+--E 1524
+
+--S 1525 of 1527
+--a0:=integrate(t0,x)
+--E 1525
+
+--S 1526 of 1527
+--m0:=a0-r0
+--E 1526
+
+--S 1527 of 1527
+--d0:=D(m0,x)
+--E 1527
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich6d.input.pdf b/src/axiom-website/CATS/rich6d.input.pdf
new file mode 100644
index 0000000..b9f232e
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diff --git a/src/axiom-website/CATS/rich6e.input.pamphlet b/src/axiom-website/CATS/rich6e.input.pamphlet
new file mode 100644
index 0000000..42c5c53
--- /dev/null
+++ b/src/axiom-website/CATS/rich6e.input.pamphlet
@@ -0,0 +1,30847 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich6e.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p (c+d x^n)^q|
+There are:
+\begin{itemize}
+\item 135 integrals in this file.
+\item 136 supplied "optimal results".
+\item 98 matching answers.
+\item 3 cases where Axiom answer differs from Rubi
+\item 19 cases where Axiom supplied 2 results.
+\item 13 cases that Axiom failed to integrate.
+\item 36 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich6e.output
+)spool rich6e.output
+)set message test on
+)set message auto off
+)clear all
+
+
+--S 1 of 716
+t0:=x^2/(sqrt(4+x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) --------------------
+--R +------+ +--------+
+--R | 2 | 2
+--R \|x + 4 \|d x + c
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 716
+--r0:=-%i*elliptic_e(%i*asinh(1/2*x),4*d/c)*sqrt(c+d*x^2)/_
+-- (d*sqrt((c+d*x^2)/c))+%i*c*elliptic_f(%i*asinh(1/2*x),4*d/c)*_
+-- sqrt((c+d*x^2)/c)/(d*sqrt(c+d*x^2))
+--E 2
+
+--S 3 of 716
+--a0:=integrate(t0,x)
+--E 3
+
+--S 4 of 716
+--m0:=a0-r0
+--E 4
+
+--S 5 of 716
+--d0:=D(m0,x)
+--E 5
+
+)clear all
+
+--S 6 of 716
+t0:=x^2/(sqrt(1-x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------
+--R +--------+ +-------+
+--R | 2 | 2
+--R \|- x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 716
+--r0:=1/3*elliptic_e(asin(x),-3/2)*sqrt(2)-1/3*elliptic_f(asin(x),-3/2)*sqrt(2)
+--E 7
+
+--S 8 of 716
+--a0:=integrate(t0,x)
+--E 8
+
+--S 9 of 716
+--m0:=a0-r0
+--E 9
+
+--S 10 of 716
+--d0:=D(m0,x)
+--E 10
+
+)clear all
+
+--S 11 of 716
+t0:=x^2/(sqrt(2-3*x^2)*sqrt(1-x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) -----------------------
+--R +---------+ +--------+
+--R | 2 | 2
+--R \|- 3x + 2 \|- x + 1
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 716
+--r0:=-1/3*elliptic_e(asin(x),3/2)*sqrt(2)+1/3*elliptic_f(asin(x),3/2)*sqrt(2)
+--E 12
+
+--S 13 of 716
+--a0:=integrate(t0,x)
+--E 13
+
+--S 14 of 716
+--m0:=a0-r0
+--E 14
+
+--S 15 of 716
+--d0:=D(m0,x)
+--E 15
+
+)clear all
+
+--S 16 of 716
+t0:=x^2/(sqrt(4-x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------
+--R +--------+ +-------+
+--R | 2 | 2
+--R \|- x + 4 \|3x + 2
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 716
+--r0:=1/3*elliptic_e(asin(1/2*x),-6)*sqrt(2)-_
+-- 1/3*elliptic_f(asin(1/2*x),-6)*sqrt(2)
+--E 17
+
+--S 18 of 716
+--a0:=integrate(t0,x)
+--E 18
+
+--S 19 of 716
+--m0:=a0-r0
+--E 19
+
+--S 20 of 716
+--d0:=D(m0,x)
+--E 20
+
+)clear all
+
+--S 21 of 716
+t0:=x^2/(sqrt(2-3*x^2)*sqrt(4-x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) -----------------------
+--R +---------+ +--------+
+--R | 2 | 2
+--R \|- 3x + 2 \|- x + 4
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 716
+--r0:=-1/3*elliptic_e(asin(1/2*x),6)*sqrt(2)+_
+-- 1/3*elliptic_f(asin(1/2*x),6)*sqrt(2)
+--E 22
+
+--S 23 of 716
+--a0:=integrate(t0,x)
+--E 23
+
+--S 24 of 716
+--m0:=a0-r0
+--E 24
+
+--S 25 of 716
+--d0:=D(m0,x)
+--E 25
+
+)clear all
+
+--S 26 of 716
+t0:=x^2/(sqrt(1-4*x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------
+--R +---------+ +-------+
+--R | 2 | 2
+--R \|- 4x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 716
+--r0:=1/3*elliptic_e(asin(2*x),-3/8)/sqrt(2)-_
+-- 1/3*elliptic_f(asin(2*x),-3/8)/sqrt(2)
+--E 27
+
+--S 28 of 716
+--a0:=integrate(t0,x)
+--E 28
+
+--S 29 of 716
+--m0:=a0-r0
+--E 29
+
+--S 30 of 716
+--d0:=D(m0,x)
+--E 30
+
+)clear all
+
+--S 31 of 716
+t0:=x^2/(sqrt(1-4*x^2)*sqrt(2-3*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) ------------------------
+--R +---------+ +---------+
+--R | 2 | 2
+--R \|- 4x + 1 \|- 3x + 2
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 716
+--r0:=-1/3*elliptic_e(asin(2*x),3/8)/sqrt(2)+_
+-- 1/3*elliptic_f(asin(2*x),3/8)/sqrt(2)
+--E 32
+
+--S 33 of 716
+--a0:=integrate(t0,x)
+--E 33
+
+--S 34 of 716
+--m0:=a0-r0
+--E 34
+
+--S 35 of 716
+--d0:=D(m0,x)
+--E 35
+
+)clear all
+
+--S 36 of 716
+t0:=x^2/(sqrt(1+x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) -------------------
+--R +------+ +-------+
+--R | 2 | 2
+--R \|x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 716
+--r0:=-1/3*%i*elliptic_e(%i*asinh(x),3/2)*sqrt(2)+_
+-- 1/3*%i*elliptic_f(%i*asinh(x),3/2)*sqrt(2)
+--E 37
+
+--S 38 of 716
+--a0:=integrate(t0,x)
+--E 38
+
+--S 39 of 716
+--m0:=a0-r0
+--E 39
+
+--S 40 of 716
+--d0:=D(m0,x)
+--E 40
+
+)clear all
+
+--S 41 of 716
+t0:=x^2/(sqrt(2-3*x^2)*sqrt(1+x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------
+--R +---------+ +------+
+--R | 2 | 2
+--R \|- 3x + 2 \|x + 1
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 716
+--r0:=elliptic_e(asin(x*sqrt(3/2)),-2/3)/sqrt(3)-_
+-- elliptic_f(asin(x*sqrt(3/2)),-2/3)/sqrt(3)
+--E 42
+
+--S 43 of 716
+--a0:=integrate(t0,x)
+--E 43
+
+--S 44 of 716
+--m0:=a0-r0
+--E 44
+
+--S 45 of 716
+--d0:=D(m0,x)
+--E 45
+
+)clear all
+
+--S 46 of 716
+t0:=x^2/(sqrt(4+x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) -------------------
+--R +------+ +-------+
+--R | 2 | 2
+--R \|x + 4 \|3x + 2
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 716
+--r0:=-1/3*%i*elliptic_e(%i*asinh(1/2*x),6)*sqrt(2)+_
+-- 1/3*%i*elliptic_f(%i*asinh(1/2*x),6)*sqrt(2)
+--E 47
+
+--S 48 of 716
+--a0:=integrate(t0,x)
+--E 48
+
+--S 49 of 716
+--m0:=a0-r0
+--E 49
+
+--S 50 of 716
+--d0:=D(m0,x)
+--E 50
+
+)clear all
+
+--S 51 of 716
+t0:=x^2/(sqrt(2-3*x^2)*sqrt(4+x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------
+--R +---------+ +------+
+--R | 2 | 2
+--R \|- 3x + 2 \|x + 4
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 716
+--r0:=2*elliptic_e(asin(x*sqrt(3/2)),-1/6)/sqrt(3)-_
+-- 2*elliptic_f(asin(x*sqrt(3/2)),-1/6)/sqrt(3)
+--E 52
+
+--S 53 of 716
+--a0:=integrate(t0,x)
+--E 53
+
+--S 54 of 716
+--m0:=a0-r0
+--E 54
+
+--S 55 of 716
+--d0:=D(m0,x)
+--E 55
+
+)clear all
+
+--S 56 of 716
+t0:=x^2/(sqrt(2+3*x^2)*sqrt(1+4*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) --------------------
+--R +-------+ +-------+
+--R | 2 | 2
+--R \|3x + 2 \|4x + 1
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 716
+--r0:=-1/3*%i*elliptic_e(%i*asinh(2*x),3/8)/sqrt(2)+_
+-- 1/3*%i*elliptic_f(%i*asinh(2*x),3/8)/sqrt(2)
+--E 57
+
+--S 58 of 716
+--a0:=integrate(t0,x)
+--E 58
+
+--S 59 of 716
+--m0:=a0-r0
+--E 59
+
+--S 60 of 716
+--d0:=D(m0,x)
+--E 60
+
+)clear all
+
+--S 61 of 716
+t0:=x^2/(sqrt(2-3*x^2)*sqrt(1+4*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------
+--R +---------+ +-------+
+--R | 2 | 2
+--R \|- 3x + 2 \|4x + 1
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 716
+--r0:=1/4*elliptic_e(asin(x*sqrt(3/2)),-8/3)/sqrt(3)-_
+-- 1/4*elliptic_f(asin(x*sqrt(3/2)),-8/3)/sqrt(3)
+--E 62
+
+--S 63 of 716
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 716
+--m0:=a0-r0
+--E 64
+
+--S 65 of 716
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 716
+t0:=x^2/(sqrt(1-x^2)*sqrt(-1+2*x^2))
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------
+--R +--------+ +-------+
+--R | 2 | 2
+--R \|- x + 1 \|2x - 1
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 716
+--r0:=1/2*elliptic_f(asin(x),2)*sqrt(1-2*x^2)/sqrt(-1+2*x^2)+_
+-- 1/2*elliptic_e(asin(x),2)*sqrt(-1+2*x^2)/sqrt(1-2*x^2)
+--E 67
+
+--S 68 of 716
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 716
+--m0:=a0-r0
+--E 69
+
+--S 70 of 716
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 716
+t0:=x*sqrt(-1+3*x^2)/sqrt(2-3*x^2)
+--R
+--R
+--R +-------+
+--R | 2
+--R x\|3x - 1
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 3x + 2
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 716
+r0:=-1/12*asin(3-6*x^2)-1/6*sqrt(2-3*x^2)*sqrt(-1+3*x^2)
+--R
+--R
+--R +---------+ +-------+
+--R | 2 | 2 2
+--R - 2\|- 3x + 2 \|3x - 1 + asin(6x - 3)
+--R (2) -----------------------------------------
+--R 12
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 716 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+ +---------+
+--R | 2 | 2 +---------+ +-------+
+--R 47\|3x - 1 - 52\|- 3x + 2 | 2 | 2
+--R atan(-----------------------------) - \|- 3x + 2 \|3x - 1
+--R +-------+ +---------+
+--R | 2 | 2
+--R 52\|3x - 1 + 47\|- 3x + 2
+--R (3) ------------------------------------------------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 716
+m0:=a0-r0 ok to fail, differs by a constant
+--R
+--R
+--R +-------+ +---------+
+--R | 2 | 2
+--R 47\|3x - 1 - 52\|- 3x + 2 2
+--R 2atan(-----------------------------) - asin(6x - 3)
+--R +-------+ +---------+
+--R | 2 | 2
+--R 52\|3x - 1 + 47\|- 3x + 2
+--R (4) ----------------------------------------------------
+--R 12
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +-----------------+ +---------+ +-------+
+--R | 4 2 3 | 2 | 2
+--R (4888x\|- 36x + 36x - 8 - 2970x - 3428x)\|- 3x + 2 \|3x - 1
+--R +
+--R +-----------------+
+--R 3 | 4 2 5 3
+--R (1485x + 1714x)\|- 36x + 36x - 8 + 87984x - 87984x + 19552x
+--R /
+--R +-----------------+ +---------+ +-------+
+--R 2 | 4 2 | 2 | 2
+--R (2970x + 3428)\|- 36x + 36x - 8 \|- 3x + 2 \|3x - 1
+--R +
+--R +-----------------+
+--R 4 2 | 4 2
+--R (- 87984x + 87984x - 19552)\|- 36x + 36x - 8
+--R Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 716
+t0:=x^2*sqrt(-1+3*x^2)/sqrt(2-3*x^2)
+--R
+--R
+--R +-------+
+--R 2 | 2
+--R x \|3x - 1
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 3x + 2
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 716
+--r0:=-1/3*elliptic_e(asin(x*sqrt(3)),1/2)*sqrt(2/3)*_
+-- sqrt(1-3*x^2)/sqrt(-1+3*x^2)+2/9*elliptic_f(asin(x*sqrt(3)),1/2)*_
+-- sqrt(2/3)*sqrt(1-3*x^2)/sqrt(-1+3*x^2)-1/9*x*sqrt(2-3*x^2)*sqrt(-1+3*x^2)
+--E 77
+
+--S 78 of 716
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 716
+--m0:=a0-r0
+--E 79
+
+--S 80 of 716
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 716
+t0:=x^3*sqrt(-1+3*x^2)/sqrt(2-3*x^2)
+--R
+--R
+--R +-------+
+--R 3 | 2
+--R x \|3x - 1
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 3x + 2
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 716
+r0:=-7/144*asin(3-6*x^2)-1/36*(-1+3*x^2)^(3/2)*sqrt(2-3*x^2)-_
+ 7/72*sqrt(2-3*x^2)*sqrt(-1+3*x^2)
+--R
+--R
+--R +---------+ +-------+
+--R 2 | 2 | 2 2
+--R (- 12x - 10)\|- 3x + 2 \|3x - 1 + 7asin(6x - 3)
+--R (2) ----------------------------------------------------
+--R 144
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 716 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +---------+
+--R | 2 | 2 +---------+ +-------+
+--R 47\|3x - 1 + 52\|- 3x + 2 2 | 2 | 2
+--R - 7atan(-----------------------------) + (- 6x - 5)\|- 3x + 2 \|3x - 1
+--R +-------+ +---------+
+--R | 2 | 2
+--R 52\|3x - 1 - 47\|- 3x + 2
+--R --------------------------------------------------------------------------
+--R 72
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 716 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R +-------+ +---------+
+--R | 2 | 2
+--R 47\|3x - 1 + 52\|- 3x + 2 2
+--R - 14atan(-----------------------------) - 7asin(6x - 3)
+--R +-------+ +---------+
+--R | 2 | 2
+--R 52\|3x - 1 - 47\|- 3x + 2
+--R (4) --------------------------------------------------------
+--R 144
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +-----------------+ +---------+ +-------+
+--R | 4 2 3 | 2 | 2
+--R (- 34216x\|- 36x + 36x - 8 - 20790x - 23996x)\|- 3x + 2 \|3x - 1
+--R +
+--R +-----------------+
+--R 3 | 4 2 5 3
+--R (10395x + 11998x)\|- 36x + 36x - 8 - 615888x + 615888x - 136864x
+--R /
+--R +-----------------+ +---------+ +-------+
+--R 2 | 4 2 | 2 | 2
+--R (35640x + 41136)\|- 36x + 36x - 8 \|- 3x + 2 \|3x - 1
+--R +
+--R +-----------------+
+--R 4 2 | 4 2
+--R (1055808x - 1055808x + 234624)\|- 36x + 36x - 8
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 716
+t0:=x^4*sqrt(-1+3*x^2)/sqrt(2-3*x^2)
+--R
+--R
+--R +-------+
+--R 4 | 2
+--R x \|3x - 1
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 3x + 2
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 716
+--r0:=-8/45*elliptic_e(asin(x*sqrt(3)),1/2)*sqrt(2/3)*_
+-- sqrt(1-3*x^2)/sqrt(-1+3*x^2)+17/135*elliptic_f(asin(x*sqrt(3)),1/2)*_
+-- sqrt(2/3)*sqrt(1-3*x^2)/sqrt(-1+3*x^2)-7/135*x*sqrt(2-3*x^2)*_
+-- sqrt(-1+3*x^2)-1/15*x^3*sqrt(2-3*x^2)*sqrt(-1+3*x^2)
+--E 87
+
+--S 88 of 716
+--a0:=integrate(t0,x)
+--E 88
+
+--S 89 of 716
+--m0:=a0-r0
+--E 89
+
+--S 90 of 716
+--d0:=D(m0,x)
+--E 90
+
+)clear all
+
+--S 91 of 716
+t0:=x^2*sqrt(2+b*x^2)/sqrt(3+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R x \|b x + 2
+--R (1) -------------
+--R +--------+
+--R | 2
+--R \|d x + 3
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 716
+--r0:=2/3*(3*b-d)*elliptic_e(asin(x*sqrt(-d)/sqrt(3)),3/2*b/d)*_
+-- sqrt(2)/(b*(-d)^(3/2))-1/3*(3*b-2*d)*_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(3)),3/2*b/d)*sqrt(2)/_
+-- (b*(-d)^(3/2))+1/3*x*sqrt(2+b*x^2)*sqrt(3+d*x^2)/d
+--E 92
+
+--S 93 of 716
+--a0:=integrate(t0,x)
+--E 93
+
+--S 94 of 716
+--m0:=a0-r0
+--E 94
+
+--S 95 of 716
+--d0:=D(m0,x)
+--E 95
+
+)clear all
+
+--S 96 of 716
+t0:=x^2*sqrt(a+b*x^2)/sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R x \|b x + a
+--R (1) -------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 716
+--r0:=1/3*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)/d+1/3*(2*b*c-a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b*(-d)^(3/2)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))-1/3*a*(b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/sqrt(c)),_
+-- b*c/(a*d))*sqrt(c)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/_
+-- (b*(-d)^(3/2)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 97
+
+--S 98 of 716
+--a0:=integrate(t0,x)
+--E 98
+
+--S 99 of 716
+--m0:=a0-r0
+--E 99
+
+--S 100 of 716
+--d0:=D(m0,x)
+--E 100
+
+)clear all
+
+--S 101 of 716
+t0:=x^2*(c+d*x)^2/(a+b*x^3)
+--R
+--R
+--R 2 4 3 2 2
+--R d x + 2c d x + c x
+--R (1) ---------------------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 101
+
+--S 102 of 716
+r0:=2*c*d*x/b+1/2*d^2*x^2/b-1/3*a^(1/3)*d*(2*b^(1/3)*c-a^(1/3)*d)*_
+ log(a^(1/3)+b^(1/3)*x)/b^(5/3)+1/6*a^(1/3)*d*(2*b^(1/3)*c-_
+ a^(1/3)*d)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(5/3)+_
+ 1/3*c^2*log(a+b*x^3)/b+a^(1/3)*d*(2*b^(1/3)*c+a^(1/3)*d)*_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(5/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+3+-+ 2 +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (2c d\|3 \|a \|b - d \|3 \|a )log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+3+-+ 2 +-+3+-+2 3+-+ 3+-+
+--R (- 4c d\|3 \|a \|b + 2d \|3 \|a )log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3+-+3+-+ 2 3+-+2 2x\|b - \|a
+--R (- 12c d\|a \|b - 6d \|a )atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 +-+ 3 2 2 +-+ 3+-+2
+--R (2c \|3 log(b x + a) + (3d x + 12c d x)\|3 )\|b
+--R /
+--R +-+3+-+2
+--R 6b\|3 \|b
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------------------+
+--R | 3 2 2 2 3 4
+--R |- 9b %%BG0 + 6b c %%BG0 - 8a c d - b c 2
+--R (- b |----------------------------------------- - b %%BG0 + c )
+--R | 3
+--R \| 3b
+--R *
+--R log
+--R +-----------------------------------------+
+--R | 3 2 2 2 3 4
+--R 3 2 2 |- 9b %%BG0 + 6b c %%BG0 - 8a c d - b c
+--R (9b %%BG0 + 9b c ) |-----------------------------------------
+--R | 3
+--R \| 3b
+--R +
+--R 3 2 2 2 4 3 3 4
+--R - 9b %%BG0 + 18b c %%BG0 + (2a d + 16b c d)x - 4a c d - 5b c
+--R +
+--R +-----------------------------------------+
+--R | 3 2 2 2 3 4
+--R |- 9b %%BG0 + 6b c %%BG0 - 8a c d - b c 2
+--R (b |----------------------------------------- - b %%BG0 + c )
+--R | 3
+--R \| 3b
+--R *
+--R log
+--R +-----------------------------------------+
+--R | 3 2 2 2 3 4
+--R 3 2 2 |- 9b %%BG0 + 6b c %%BG0 - 8a c d - b c
+--R (- 9b %%BG0 - 9b c ) |-----------------------------------------
+--R | 3
+--R \| 3b
+--R +
+--R 3 2 2 2 4 3 3 4
+--R - 9b %%BG0 + 18b c %%BG0 + (2a d + 16b c d)x - 4a c d - 5b c
+--R +
+--R 2b %%BG0
+--R *
+--R 3 2 2 2 4 3 3 4
+--R log(9b %%BG0 - 18b c %%BG0 + (a d + 8b c d)x + 4a c d + 5b c )
+--R +
+--R 2 2
+--R d x + 4c d x
+--R /
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----------------------------------------+
+--R | 3 2 2 2 3 4
+--R +-+3+-+2 |- 9b %%BG0 + 6b c %%BG0 - 8a c d - b c
+--R - 3b\|3 \|b |-----------------------------------------
+--R | 3
+--R \| 3b
+--R +
+--R +-+3+-+2 2 +-+3+-+2
+--R - 3b\|3 \|b %%BG0 + 3c \|3 \|b
+--R *
+--R log
+--R +-----------------------------------------+
+--R | 3 2 2 2 3 4
+--R 3 2 2 |- 9b %%BG0 + 6b c %%BG0 - 8a c d - b c
+--R (9b %%BG0 + 9b c ) |-----------------------------------------
+--R | 3
+--R \| 3b
+--R +
+--R 3 2 2 2 4 3 3 4
+--R - 9b %%BG0 + 18b c %%BG0 + (2a d + 16b c d)x - 4a c d - 5b c
+--R +
+--R +-----------------------------------------+
+--R | 3 2 2 2 3 4
+--R +-+3+-+2 |- 9b %%BG0 + 6b c %%BG0 - 8a c d - b c
+--R 3b\|3 \|b |-----------------------------------------
+--R | 3
+--R \| 3b
+--R +
+--R +-+3+-+2 2 +-+3+-+2
+--R - 3b\|3 \|b %%BG0 + 3c \|3 \|b
+--R *
+--R log
+--R +-----------------------------------------+
+--R | 3 2 2 2 3 4
+--R 3 2 2 |- 9b %%BG0 + 6b c %%BG0 - 8a c d - b c
+--R (- 9b %%BG0 - 9b c ) |-----------------------------------------
+--R | 3
+--R \| 3b
+--R +
+--R 3 2 2 2 4 3 3 4
+--R - 9b %%BG0 + 18b c %%BG0 + (2a d + 16b c d)x - 4a c d - 5b c
+--R +
+--R +-+3+-+2
+--R 6b\|3 \|b %%BG0
+--R *
+--R 3 2 2 2 4 3 3 4
+--R log(9b %%BG0 - 18b c %%BG0 + (a d + 8b c d)x + 4a c d + 5b c )
+--R +
+--R +-+3+-+3+-+ 2 +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 2c d\|3 \|a \|b + d \|3 \|a )log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+3+-+ 2 +-+3+-+2 3+-+ 3+-+
+--R (4c d\|3 \|a \|b - 2d \|3 \|a )log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3+-+3+-+ 2 3+-+2 2x\|b - \|a 2 +-+ 3 3+-+2
+--R (12c d\|a \|b + 6d \|a )atan(-------------) - 2c \|3 log(b x + a)\|b
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+2
+--R 6b\|3 \|b
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 716
+t0:=x^8/((a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 8
+--R x
+--R (1) ----------------------------
+--R 6 3
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 106
+
+--S 107 of 716
+r0:=1/3*x^3/(b*d)+1/3*a^2*log(a+b*x^3)/(b^2*(b*c-a*d))-_
+ 1/3*c^2*log(c+d*x^3)/(d^2*(b*c-a*d))
+--R
+--R
+--R 2 2 3 2 2 3 2 2 3
+--R b c log(d x + c) - a d log(b x + a) + (a b d - b c d)x
+--R (2) ----------------------------------------------------------
+--R 2 3 3 2
+--R 3a b d - 3b c d
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 3 2 2 3 2 2 3
+--R b c log(d x + c) - a d log(b x + a) + (a b d - b c d)x
+--R (3) ----------------------------------------------------------
+--R 2 3 3 2
+--R 3a b d - 3b c d
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 716
+t0:=x^7/((a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 7
+--R x
+--R (1) ----------------------------
+--R 6 3
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 111
+
+--S 112 of 716
+r0:=1/2*x^2/(b*d)-1/3*a^(5/3)*log(a^(1/3)+b^(1/3)*x)/(b^(5/3)*(b*c-a*d))+_
+ 1/3*c^(5/3)*log(c^(1/3)+d^(1/3)*x)/(d^(5/3)*(b*c-a*d))+_
+ 1/6*a^(5/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(5/3)*_
+ (b*c-a*d))-1/6*c^(5/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/_
+ (d^(5/3)*(b*c-a*d))-a^(5/3)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(b^(5/3)*(b*c-a*d)*sqrt(3))+c^(5/3)*_
+ atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(d^(5/3)*(b*c-a*d)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R b c\|3 \|b \|c log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R - 2b c\|3 \|b \|c log(x\|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - a d\|3 \|a \|d log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R +-+3+-+2 3+-+2 3+-+ 3+-+ 3+-+2 3+-+2 2x\|d - \|c
+--R 2a d\|3 \|a \|d log(x\|b + \|a + 6b c \|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|b - \|a 2 +-+3+-+2 3+-+2
+--R - 6a d \|a \|d atan(------------- + (3a d - 3b c)x \|3 \|b \|d
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R 2 2 +-+3+-+2 3+-+2
+--R (6a b d - 6b c d)\|3 \|b \|d
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--+2 +----+ +----+2
+--R | 2 | 2 | 2 | 2
+--R +-+ |a |a +-+ | c | c
+--R 2a d\|3 |-- log(b |-- + a x + 2b c\|3 |- -- log(d |- -- + c x)
+--R 3| 2 3| 2 3| 2 3| 2
+--R \|b \|b \| d \| d
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | c | c | c 2
+--R - b c\|3 |- -- log(- d x |- -- - c |- -- + c x )
+--R 3| 2 3| 2 3| 2
+--R \| d \| d \| d
+--R +
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+ |a |a |a 2
+--R - a d\|3 |-- log(- b x |-- + a |-- + a x )
+--R 3| 2 3| 2 3| 2
+--R \|b \|b \|b
+--R +
+--R +--+2
+--R | 2
+--R +-+ |a +-+
+--R +--+ b\|3 |-- - 2a x\|3
+--R | 2 3| 2
+--R |a \|b
+--R 6a d |-- atan(----------------------)
+--R 3| 2 +--+2
+--R \|b | 2
+--R |a
+--R 3b |--
+--R 3| 2
+--R \|b
+--R +
+--R +----+2
+--R | 2
+--R +-+ | c +-+
+--R +----+ d\|3 |- -- - 2c x\|3
+--R | 2 3| 2
+--R | c \| d 2 +-+
+--R 6b c |- -- atan(------------------------ + (3a d - 3b c)x \|3
+--R 3| 2 +----+2
+--R \| d | 2
+--R | c
+--R 3d |- --
+--R 3| 2
+--R \| d
+--R /
+--R 2 2 +-+
+--R (6a b d - 6b c d)\|3
+--R Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - b c\|3 \|b \|c log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R 2b c\|3 \|b \|c log(x\|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R a d\|3 \|a \|d log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R - 2a d\|3 \|a \|d log(x\|b + \|a )
+--R +
+--R +--+ +--+2
+--R | 2 | 2
+--R +-+ |a 3+-+2 3+-+2 |a
+--R 2a d\|3 |-- \|b \|d log(b |-- + a x)
+--R 3| 2 3| 2
+--R \|b \|b
+--R +
+--R +----+ +----+2
+--R | 2 | 2
+--R +-+ | c 3+-+2 3+-+2 | c
+--R 2b c\|3 |- -- \|b \|d log(d |- -- + c x)
+--R 3| 2 3| 2
+--R \| d \| d
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | c 3+-+2 3+-+2 | c | c 2
+--R - b c\|3 |- -- \|b \|d log(- d x |- -- - c |- -- + c x )
+--R 3| 2 3| 2 3| 2
+--R \| d \| d \| d
+--R +
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+ |a 3+-+2 3+-+2 |a |a 2
+--R - a d\|3 |-- \|b \|d log(- b x |-- + a |-- + a x )
+--R 3| 2 3| 2 3| 2
+--R \|b \|b \|b
+--R +
+--R 3+-+ 3+-+ 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|d - \|c 3+-+2 3+-+2 2x\|b - \|a
+--R - 6b c \|b \|c atan(------------- + 6a d \|a \|d atan(-------------)
+--R +-+3+-+ +-+3+-+
+--R \|3 \|c \|3 \|a
+--R +
+--R +--+2
+--R | 2
+--R +-+ |a +-+
+--R +--+ b\|3 |-- - 2a x\|3
+--R | 2 3| 2
+--R |a 3+-+2 3+-+2 \|b
+--R 6a d |-- \|b \|d atan(----------------------)
+--R 3| 2 +--+2
+--R \|b | 2
+--R |a
+--R 3b |--
+--R 3| 2
+--R \|b
+--R +
+--R +----+2
+--R | 2
+--R +-+ | c +-+
+--R +----+ d\|3 |- -- - 2c x\|3
+--R | 2 3| 2
+--R | c 3+-+2 3+-+2 \| d
+--R 6b c |- -- \|b \|d atan(------------------------)
+--R 3| 2 +----+2
+--R \| d | 2
+--R | c
+--R 3d |- --
+--R 3| 2
+--R \| d
+--R /
+--R 2 2 +-+3+-+2 3+-+2
+--R (6a b d - 6b c d)\|3 \|b \|d
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 716
+t0:=x^6/((a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 6
+--R x
+--R (1) ----------------------------
+--R 6 3
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 116
+
+--S 117 of 716
+r0:=x/(b*d)+1/3*a^(4/3)*log(a^(1/3)+b^(1/3)*x)/(b^(4/3)*(b*c-a*d))-_
+ 1/3*c^(4/3)*log(c^(1/3)+d^(1/3)*x)/(d^(4/3)*(b*c-a*d))-_
+ 1/6*a^(4/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(4/3)*_
+ (b*c-a*d))+1/6*c^(4/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/_
+ (d^(4/3)*(b*c-a*d))-a^(4/3)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*_
+ sqrt(3)))/(b^(4/3)*(b*c-a*d)*sqrt(3))+c^(4/3)*atan((c^(1/3)-_
+ 2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(d^(4/3)*(b*c-a*d)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - b c\|3 \|b \|c log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+3+-+ 3+-+ 3+-+
+--R 2b c\|3 \|b \|c log(x\|d + \|c )
+--R +
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R a d\|3 \|a \|d log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R +-+3+-+3+-+ 3+-+ 3+-+ 3+-+3+-+ 2x\|d - \|c
+--R - 2a d\|3 \|a \|d log(x\|b + \|a ) + 6b c\|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3+-+3+-+ 2x\|b - \|a +-+3+-+3+-+
+--R - 6a d\|a \|d atan(-------------) + (6a d - 6b c)x\|3 \|b \|d
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R 2 2 +-+3+-+3+-+
+--R (6a b d - 6b c d)\|3 \|b \|d
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+2 +-+ +-+ +-+
+--R +-+ |c |c |c 2 +-+ |c |c
+--R - b c\|3 3|- log(3|- - x 3|- + x + 2b c\|3 3|- log(3|- + x)
+--R \|d \|d \|d \|d \|d
+--R +
+--R +---+ +---+2 +---+
+--R +-+ | a | a | a 2
+--R - a d\|3 3|- - log(3|- - + x 3|- - + x )
+--R \| b \| b \| b
+--R +
+--R +---+
+--R +-+ | a +-+
+--R +---+ +---+ +---+ \|3 3|- - + 2x\|3
+--R +-+ | a | a | a \| b
+--R 2a d\|3 3|- - log(- 3|- - + x - 6a d 3|- - atan(-------------------)
+--R \| b \| b \| b +---+
+--R | a
+--R 3 3|- -
+--R \| b
+--R +
+--R +-+
+--R +-+ |c +-+
+--R +-+ \|3 3|- - 2x\|3
+--R |c \|d +-+
+--R - 6b c 3|- atan(----------------- + (6a d - 6b c)x\|3
+--R \|d +-+
+--R |c
+--R 3 3|-
+--R \|d
+--R /
+--R 2 2 +-+
+--R (6a b d - 6b c d)\|3
+--R Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R b c\|3 \|b \|c log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+3+-+ 3+-+ 3+-+
+--R - 2b c\|3 \|b \|c log(x\|d + \|c )
+--R +
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - a d\|3 \|a \|d log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+3+-+ 3+-+ 3+-+
+--R 2a d\|3 \|a \|d log(x\|b + \|a )
+--R +
+--R +-+ +-+2 +-+
+--R +-+ |c 3+-+3+-+ |c |c 2
+--R - b c\|3 3|- \|b \|d log(3|- - x 3|- + x )
+--R \|d \|d \|d
+--R +
+--R +-+ +-+
+--R +-+ |c 3+-+3+-+ |c
+--R 2b c\|3 3|- \|b \|d log(3|- + x)
+--R \|d \|d
+--R +
+--R +---+ +---+2 +---+
+--R +-+ | a 3+-+3+-+ | a | a 2
+--R - a d\|3 3|- - \|b \|d log(3|- - + x 3|- - + x )
+--R \| b \| b \| b
+--R +
+--R +---+ +---+ 3+-+ 3+-+
+--R +-+ | a 3+-+3+-+ | a 3+-+3+-+ 2x\|d - \|c
+--R 2a d\|3 3|- - \|b \|d log(- 3|- - + x - 6b c\|b \|c atan(-------------)
+--R \| b \| b +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3+-+3+-+ 2x\|b - \|a
+--R 6a d\|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +---+
+--R +-+ | a +-+
+--R +---+ \|3 3|- - + 2x\|3
+--R | a 3+-+3+-+ \| b
+--R - 6a d 3|- - \|b \|d atan(-------------------)
+--R \| b +---+
+--R | a
+--R 3 3|- -
+--R \| b
+--R +
+--R +-+
+--R +-+ |c +-+
+--R +-+ \|3 3|- - 2x\|3
+--R |c 3+-+3+-+ \|d
+--R - 6b c 3|- \|b \|d atan(-----------------)
+--R \|d +-+
+--R |c
+--R 3 3|-
+--R \|d
+--R /
+--R 2 2 +-+3+-+3+-+
+--R (6a b d - 6b c d)\|3 \|b \|d
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 716
+t0:=x^5/((a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 5
+--R x
+--R (1) ----------------------------
+--R 6 3
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 121
+
+--S 122 of 716
+r0:=-1/3*a*log(a+b*x^3)/(b*(b*c-a*d))+1/3*c*log(c+d*x^3)/(d*(b*c-a*d))
+--R
+--R
+--R 3 3
+--R - b c log(d x + c) + a d log(b x + a)
+--R (2) ---------------------------------------
+--R 2 2
+--R 3a b d - 3b c d
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3
+--R - b c log(d x + c) + a d log(b x + a)
+--R (3) ---------------------------------------
+--R 2 2
+--R 3a b d - 3b c d
+--R Type: Union(Expression(Integer),...)
+--E 123
+
+--S 124 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 716
+t0:=x^4/((a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 4
+--R x
+--R (1) ----------------------------
+--R 6 3
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 126
+
+--S 127 of 716
+r0:=1/3*a^(2/3)*log(a^(1/3)+b^(1/3)*x)/(b^(2/3)*(b*c-a*d))-_
+ 1/3*c^(2/3)*log(c^(1/3)+d^(1/3)*x)/(d^(2/3)*(b*c-a*d))-_
+ 1/6*a^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(2/3)*_
+ (b*c-a*d))+1/6*c^(2/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*_
+ x^2)/(d^(2/3)*(b*c-a*d))+a^(2/3)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(b^(2/3)*(b*c-a*d)*sqrt(3))-c^(2/3)*_
+ atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(d^(2/3)*(b*c-a*d)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|b \|c log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R 2\|3 \|b \|c log(x\|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|a \|d log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R +-+3+-+2 3+-+2 3+-+ 3+-+ 3+-+2 3+-+2 2x\|d - \|c
+--R - 2\|3 \|a \|d log(x\|b + \|a - 6\|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|b - \|a
+--R 6\|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+2 3+-+2
+--R (6a d - 6b c)\|3 \|b \|d
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--+2 +----+ +----+2
+--R | 2 | 2 | 2 | 2
+--R +-+ |c |c +-+ | a | a
+--R 2\|3 |-- log(d |-- + c x + 2\|3 |- -- log(b |- -- + a x)
+--R 3| 2 3| 2 3| 2 3| 2
+--R \|d \|d \| b \| b
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | a | a | a 2
+--R - \|3 |- -- log(- b x |- -- - a |- -- + a x )
+--R 3| 2 3| 2 3| 2
+--R \| b \| b \| b
+--R +
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+ |c |c |c 2
+--R - \|3 |-- log(- d x |-- + c |-- + c x )
+--R 3| 2 3| 2 3| 2
+--R \|d \|d \|d
+--R +
+--R +--+2 +----+2
+--R | 2 | 2
+--R +-+ |c +-+ +-+ | a +-+
+--R +--+ d\|3 |-- - 2c x\|3 +----+ b\|3 |- -- - 2a x\|3
+--R | 2 3| 2 | 2 3| 2
+--R |c \|d | a \| b
+--R 6 |-- atan(---------------------- + 6 |- -- atan(------------------------)
+--R 3| 2 +--+2 3| 2 +----+2
+--R \|d | 2 \| b | 2
+--R |c | a
+--R 3d |-- 3b |- --
+--R 3| 2 3| 2
+--R \|d \| b
+--R /
+--R +-+
+--R (6a d - 6b c)\|3
+--R Type: Union(Expression(Integer),...)
+--E 128
+
+--S 129 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|b \|c log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R - 2\|3 \|b \|c log(x\|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|a \|d log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R 2\|3 \|a \|d log(x\|b + \|a )
+--R +
+--R +--+ +--+2
+--R | 2 | 2
+--R +-+ |c 3+-+2 3+-+2 |c
+--R 2\|3 |-- \|b \|d log(d |-- + c x)
+--R 3| 2 3| 2
+--R \|d \|d
+--R +
+--R +----+ +----+2
+--R | 2 | 2
+--R +-+ | a 3+-+2 3+-+2 | a
+--R 2\|3 |- -- \|b \|d log(b |- -- + a x)
+--R 3| 2 3| 2
+--R \| b \| b
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | a 3+-+2 3+-+2 | a | a 2
+--R - \|3 |- -- \|b \|d log(- b x |- -- - a |- -- + a x )
+--R 3| 2 3| 2 3| 2
+--R \| b \| b \| b
+--R +
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+ |c 3+-+2 3+-+2 |c |c 2
+--R - \|3 |-- \|b \|d log(- d x |-- + c |-- + c x )
+--R 3| 2 3| 2 3| 2
+--R \|d \|d \|d
+--R +
+--R 3+-+ 3+-+ 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|d - \|c 3+-+2 3+-+2 2x\|b - \|a
+--R 6\|b \|c atan(------------- - 6\|a \|d atan(-------------)
+--R +-+3+-+ +-+3+-+
+--R \|3 \|c \|3 \|a
+--R +
+--R +--+2
+--R | 2
+--R +-+ |c +-+
+--R +--+ d\|3 |-- - 2c x\|3
+--R | 2 3| 2
+--R |c 3+-+2 3+-+2 \|d
+--R 6 |-- \|b \|d atan(----------------------)
+--R 3| 2 +--+2
+--R \|d | 2
+--R |c
+--R 3d |--
+--R 3| 2
+--R \|d
+--R +
+--R +----+2
+--R | 2
+--R +-+ | a +-+
+--R +----+ b\|3 |- -- - 2a x\|3
+--R | 2 3| 2
+--R | a 3+-+2 3+-+2 \| b
+--R 6 |- -- \|b \|d atan(------------------------)
+--R 3| 2 +----+2
+--R \| b | 2
+--R | a
+--R 3b |- --
+--R 3| 2
+--R \| b
+--R /
+--R +-+3+-+2 3+-+2
+--R (6a d - 6b c)\|3 \|b \|d
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 130
+
+)clear all
+
+--S 131 of 716
+t0:=x^3/((a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 3
+--R x
+--R (1) ----------------------------
+--R 6 3
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 131
+
+--S 132 of 716
+r0:=-1/3*a^(1/3)*log(a^(1/3)+b^(1/3)*x)/(b^(1/3)*(b*c-a*d))+_
+ 1/3*c^(1/3)*log(c^(1/3)+d^(1/3)*x)/(d^(1/3)*(b*c-a*d))+_
+ 1/6*a^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/_
+ (b^(1/3)*(b*c-a*d))-1/6*c^(1/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+_
+ d^(2/3)*x^2)/(d^(1/3)*(b*c-a*d))+a^(1/3)*atan((a^(1/3)-_
+ 2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(1/3)*(b*c-a*d)*sqrt(3))-_
+ c^(1/3)*atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/_
+ (d^(1/3)*(b*c-a*d)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|b \|c log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+3+-+ 3+-+ 3+-+
+--R - 2\|3 \|b \|c log(x\|d + \|c )
+--R +
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|a \|d log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R +-+3+-+3+-+ 3+-+ 3+-+ 3+-+3+-+ 2x\|d - \|c
+--R 2\|3 \|a \|d log(x\|b + \|a ) - 6\|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3+-+3+-+ 2x\|b - \|a
+--R 6\|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+3+-+
+--R (6a d - 6b c)\|3 \|b \|d
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+2 +-+ +-+ +-+
+--R +-+ |a |a |a 2 +-+ |a |a
+--R - \|3 3|- log(3|- - x 3|- + x + 2\|3 3|- log(3|- + x)
+--R \|b \|b \|b \|b \|b
+--R +
+--R +---+ +---+2 +---+ +---+ +---+
+--R +-+ | c | c | c 2 +-+ | c | c
+--R - \|3 3|- - log(3|- - + x 3|- - + x + 2\|3 3|- - log(- 3|- - + x)
+--R \| d \| d \| d \| d \| d
+--R +
+--R +---+ +-+
+--R +-+ | c +-+ +-+ |a +-+
+--R +---+ \|3 3|- - + 2x\|3 +-+ \|3 3|- - 2x\|3
+--R | c \| d |a \|b
+--R - 6 3|- - atan(------------------- - 6 3|- atan(-----------------)
+--R \| d +---+ \|b +-+
+--R | c |a
+--R 3 3|- - 3 3|-
+--R \| d \|b
+--R /
+--R +-+
+--R (6a d - 6b c)\|3
+--R Type: Union(Expression(Integer),...)
+--E 133
+
+--S 134 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|b \|c log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+3+-+ 3+-+ 3+-+
+--R 2\|3 \|b \|c log(x\|d + \|c )
+--R +
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|a \|d log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+3+-+ 3+-+ 3+-+
+--R - 2\|3 \|a \|d log(x\|b + \|a )
+--R +
+--R +-+ +-+2 +-+
+--R +-+ |a 3+-+3+-+ |a |a 2
+--R - \|3 3|- \|b \|d log(3|- - x 3|- + x )
+--R \|b \|b \|b
+--R +
+--R +-+ +-+
+--R +-+ |a 3+-+3+-+ |a
+--R 2\|3 3|- \|b \|d log(3|- + x)
+--R \|b \|b
+--R +
+--R +---+ +---+2 +---+
+--R +-+ | c 3+-+3+-+ | c | c 2
+--R - \|3 3|- - \|b \|d log(3|- - + x 3|- - + x )
+--R \| d \| d \| d
+--R +
+--R +---+ +---+ 3+-+ 3+-+
+--R +-+ | c 3+-+3+-+ | c 3+-+3+-+ 2x\|d - \|c
+--R 2\|3 3|- - \|b \|d log(- 3|- - + x + 6\|b \|c atan(-------------)
+--R \| d \| d +-+3+-+
+--R \|3 \|c
+--R +
+--R +---+
+--R +-+ | c +-+
+--R 3+-+ 3+-+ +---+ \|3 3|- - + 2x\|3
+--R 3+-+3+-+ 2x\|b - \|a | c 3+-+3+-+ \| d
+--R - 6\|a \|d atan(-------------) - 6 3|- - \|b \|d atan(-------------------)
+--R +-+3+-+ \| d +---+
+--R \|3 \|a | c
+--R 3 3|- -
+--R \| d
+--R +
+--R +-+
+--R +-+ |a +-+
+--R +-+ \|3 3|- - 2x\|3
+--R |a 3+-+3+-+ \|b
+--R - 6 3|- \|b \|d atan(-----------------)
+--R \|b +-+
+--R |a
+--R 3 3|-
+--R \|b
+--R /
+--R +-+3+-+3+-+
+--R (6a d - 6b c)\|3 \|b \|d
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 135
+
+)clear all
+
+--S 136 of 716
+t0:=x^2/((a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------------
+--R 6 3
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 136
+
+--S 137 of 716
+r0:=1/3*log(a+b*x^3)/(b*c-a*d)-1/3*log(c+d*x^3)/(b*c-a*d)
+--R
+--R
+--R 3 3
+--R log(d x + c) - log(b x + a)
+--R (2) -----------------------------
+--R 3a d - 3b c
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3
+--R log(d x + c) - log(b x + a)
+--R (3) -----------------------------
+--R 3a d - 3b c
+--R Type: Union(Expression(Integer),...)
+--E 138
+
+--S 139 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 140
+
+)clear all
+
+--S 141 of 716
+t0:=x/((a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R x
+--R (1) ----------------------------
+--R 6 3
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 141
+
+--S 142 of 716
+r0:=-1/3*b^(1/3)*log(a^(1/3)+b^(1/3)*x)/(a^(1/3)*(b*c-a*d))+_
+ 1/3*d^(1/3)*log(c^(1/3)+d^(1/3)*x)/(c^(1/3)*(b*c-a*d))+_
+ 1/6*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*_
+ (b*c-a*d))-1/6*d^(1/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*_
+ x^2)/(c^(1/3)*(b*c-a*d))-b^(1/3)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(1/3)*(b*c-a*d)*sqrt(3))+d^(1/3)*_
+ atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(1/3)*(b*c-a*d)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+3+-+ 3+-+ 3+-+
+--R - 2\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R +-+3+-+3+-+ 3+-+ 3+-+ 3+-+3+-+ 2x\|d - \|c
+--R 2\|3 \|b \|c log(x\|b + \|a ) + 6\|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3+-+3+-+ 2x\|b - \|a
+--R - 6\|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+3+-+
+--R (6a d - 6b c)\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+2 +---+ +---+2
+--R +-+ |b |b +-+ | d | d
+--R 2\|3 3|- log(a 3|- + b x + 2\|3 3|- - log(c 3|- - + d x)
+--R \|a \|a \| c \| c
+--R +
+--R +---+ +---+2 +---+
+--R +-+ | d | d | d 2
+--R - \|3 3|- - log(- c x 3|- - - c 3|- - + d x )
+--R \| c \| c \| c
+--R +
+--R +-+ +-+2 +-+
+--R +-+ |b |b |b 2
+--R - \|3 3|- log(- a x 3|- + a 3|- + b x )
+--R \|a \|a \|a
+--R +
+--R +-+2 +---+2
+--R +-+ |b +-+ +-+ | d +-+
+--R +-+ a\|3 3|- - 2b x\|3 +---+ c\|3 3|- - - 2d x\|3
+--R |b \|a | d \| c
+--R 6 3|- atan(--------------------- + 6 3|- - atan(-----------------------)
+--R \|a +-+2 \| c +---+2
+--R |b | d
+--R 3a 3|- 3c 3|- -
+--R \|a \| c
+--R /
+--R +-+
+--R (6a d - 6b c)\|3
+--R Type: Union(Expression(Integer),...)
+--E 143
+
+--S 144 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+3+-+ 3+-+ 3+-+
+--R 2\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+ +-+2
+--R +-+3+-+3+-+ 3+-+ 3+-+ +-+3+-+ |b 3+-+ |b
+--R - 2\|3 \|b \|c log(x\|b + \|a ) + 2\|3 \|a 3|- \|c log(a 3|- + b x)
+--R \|a \|a
+--R +
+--R +---+ +---+2
+--R +-+ | d 3+-+3+-+ | d
+--R 2\|3 3|- - \|a \|c log(c 3|- - + d x)
+--R \| c \| c
+--R +
+--R +---+ +---+2 +---+
+--R +-+ | d 3+-+3+-+ | d | d 2
+--R - \|3 3|- - \|a \|c log(- c x 3|- - - c 3|- - + d x )
+--R \| c \| c \| c
+--R +
+--R +-+ +-+2 +-+
+--R +-+3+-+ |b 3+-+ |b |b 2
+--R - \|3 \|a 3|- \|c log(- a x 3|- + a 3|- + b x )
+--R \|a \|a \|a
+--R +
+--R 3+-+ 3+-+ 3+-+ 3+-+
+--R 3+-+3+-+ 2x\|d - \|c 3+-+3+-+ 2x\|b - \|a
+--R - 6\|a \|d atan(-------------) + 6\|b \|c atan(-------------)
+--R +-+3+-+ +-+3+-+
+--R \|3 \|c \|3 \|a
+--R +
+--R +-+2
+--R +-+ |b +-+
+--R +-+ a\|3 3|- - 2b x\|3
+--R 3+-+ |b 3+-+ \|a
+--R 6\|a 3|- \|c atan(---------------------)
+--R \|a +-+2
+--R |b
+--R 3a 3|-
+--R \|a
+--R +
+--R +---+2
+--R +-+ | d +-+
+--R +---+ c\|3 3|- - - 2d x\|3
+--R | d 3+-+3+-+ \| c
+--R 6 3|- - \|a \|c atan(-----------------------)
+--R \| c +---+2
+--R | d
+--R 3c 3|- -
+--R \| c
+--R /
+--R +-+3+-+3+-+
+--R (6a d - 6b c)\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 145
+
+)clear all
+
+--S 146 of 716
+t0:=1/((a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R 6 3
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 146
+
+--S 147 of 716
+r0:=1/3*b^(2/3)*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*(b*c-a*d))-1/3*d^(2/3)*_
+ log(c^(1/3)+d^(1/3)*x)/(c^(2/3)*(b*c-a*d))-1/6*b^(2/3)*_
+ log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*(b*c-a*d))+_
+ 1/6*d^(2/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(2/3)*_
+ (b*c-a*d))-b^(2/3)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_
+ (a^(2/3)*(b*c-a*d)*sqrt(3))+d^(2/3)*atan((c^(1/3)-2*d^(1/3)*x)/_
+ (c^(1/3)*sqrt(3)))/(c^(2/3)*(b*c-a*d)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R 2\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R +-+3+-+2 3+-+2 3+-+ 3+-+ 3+-+2 3+-+2 2x\|d - \|c
+--R - 2\|3 \|b \|c log(x\|b + \|a + 6\|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|b - \|a
+--R - 6\|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+2 3+-+2
+--R (6a d - 6b c)\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+ |d 2 |d |d 2 2
+--R - \|3 |-- log(c |-- - c d x |-- + d x )
+--R 3| 2 3| 2 3| 2
+--R \|c \|c \|c
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R +-+ |d |d
+--R 2\|3 |-- log(c |-- + d x)
+--R 3| 2 3| 2
+--R \|c \|c
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b 2 | b | b 2 2
+--R - \|3 |- -- log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ +----+ +----+ a\|3 |- -- + 2b x\|3
+--R | 2 | 2 | 2 3| 2
+--R +-+ | b | b | b \| a
+--R 2\|3 |- -- log(- a |- -- + b x - 6 |- -- atan(-----------------------)
+--R 3| 2 3| 2 3| 2 +----+
+--R \| a \| a \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R +--+
+--R | 2
+--R +-+ |d +-+
+--R +--+ c\|3 |-- - 2d x\|3
+--R | 2 3| 2
+--R |d \|c
+--R - 6 |-- atan(---------------------)
+--R 3| 2 +--+
+--R \|c | 2
+--R |d
+--R 3c |--
+--R 3| 2
+--R \|c
+--R /
+--R +-+
+--R (6a d - 6b c)\|3
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+3+-+2 3+-+2 |d 2 |d |d 2 2
+--R - \|3 \|a \|c |-- log(c |-- - c d x |-- + d x )
+--R 3| 2 3| 2 3| 2
+--R \|c \|c \|c
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R +-+3+-+2 3+-+2 |d |d
+--R 2\|3 \|a \|c |-- log(c |-- + d x)
+--R 3| 2 3| 2
+--R \|c \|c
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R - 2\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R 2\|3 \|b \|c log(x\|b + \|a )
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b 3+-+2 3+-+2 2 | b | b 2 2
+--R - \|3 |- -- \|a \|c log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R +-+ | b 3+-+2 3+-+2 | b
+--R 2\|3 |- -- \|a \|c log(- a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R 3+-+ 3+-+ 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|d - \|c 3+-+2 3+-+2 2x\|b - \|a
+--R - 6\|a \|d atan(------------- + 6\|b \|c atan(-------------)
+--R +-+3+-+ +-+3+-+
+--R \|3 \|c \|3 \|a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- + 2b x\|3
+--R | 2 3| 2
+--R | b 3+-+2 3+-+2 \| a
+--R - 6 |- -- \|a \|c atan(-----------------------)
+--R 3| 2 +----+
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R +--+
+--R | 2
+--R +-+ |d +-+
+--R +--+ c\|3 |-- - 2d x\|3
+--R | 2 3| 2
+--R 3+-+2 3+-+2 |d \|c
+--R - 6\|a \|c |-- atan(---------------------)
+--R 3| 2 +--+
+--R \|c | 2
+--R |d
+--R 3c |--
+--R 3| 2
+--R \|c
+--R /
+--R +-+3+-+2 3+-+2
+--R (6a d - 6b c)\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 716
+t0:=1/(x*(a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 1
+--R (1) ------------------------------
+--R 7 4
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 151
+
+--S 152 of 716
+r0:=log(x)/(a*c)-1/3*b*log(a+b*x^3)/(a*(b*c-a*d))+_
+ 1/3*d*log(c+d*x^3)/(c*(b*c-a*d))
+--R
+--R
+--R 3 3
+--R - a d log(d x + c) + b c log(b x + a) + (3a d - 3b c)log(x)
+--R (2) -------------------------------------------------------------
+--R 2 2
+--R 3a c d - 3a b c
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3
+--R - a d log(d x + c) + b c log(b x + a) + (3a d - 3b c)log(x)
+--R (3) -------------------------------------------------------------
+--R 2 2
+--R 3a c d - 3a b c
+--R Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 716
+t0:=1/(x^2*(a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 8 5 2
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 156
+
+--S 157 of 716
+r0:=(-1)/(a*c*x)+1/3*b^(4/3)*log(a^(1/3)+b^(1/3)*x)/(a^(4/3)*(b*c-a*d))-_
+ 1/3*d^(4/3)*log(c^(1/3)+d^(1/3)*x)/(c^(4/3)*(b*c-a*d))-_
+ 1/6*b^(4/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(4/3)*_
+ (b*c-a*d))+1/6*d^(4/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*_
+ x^2)/(c^(4/3)*(b*c-a*d))+b^(4/3)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(4/3)*(b*c-a*d)*sqrt(3))-d^(4/3)*_
+ atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(4/3)*(b*c-a*d)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - a d x\|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+3+-+ 3+-+ 3+-+
+--R 2a d x\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R b c x\|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R +-+3+-+3+-+ 3+-+ 3+-+ 3+-+3+-+ 2x\|d - \|c
+--R - 2b c x\|3 \|b \|c log(x\|b + \|a ) - 6a d x\|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3+-+3+-+ 2x\|b - \|a +-+3+-+3+-+
+--R 6b c x\|b \|c atan(-------------) + (- 6a d + 6b c)\|3 \|a \|c
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R 2 2 +-+3+-+3+-+
+--R (6a c d - 6a b c )x\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+2 +---+ +---+2
+--R +-+ |d |d +-+ | b | b
+--R 2a d x\|3 3|- log(c 3|- + d x + 2b c x\|3 3|- - log(a 3|- - + b x)
+--R \|c \|c \| a \| a
+--R +
+--R +---+ +---+2 +---+
+--R +-+ | b | b | b 2
+--R - b c x\|3 3|- - log(- a x 3|- - - a 3|- - + b x )
+--R \| a \| a \| a
+--R +
+--R +-+ +-+2 +-+
+--R +-+ |d |d |d 2
+--R - a d x\|3 3|- log(- c x 3|- + c 3|- + d x )
+--R \|c \|c \|c
+--R +
+--R +-+2
+--R +-+ |d +-+
+--R +-+ c\|3 3|- - 2d x\|3
+--R |d \|c
+--R 6a d x 3|- atan(---------------------)
+--R \|c +-+2
+--R |d
+--R 3c 3|-
+--R \|c
+--R +
+--R +---+2
+--R +-+ | b +-+
+--R +---+ a\|3 3|- - - 2b x\|3
+--R | b \| a +-+
+--R 6b c x 3|- - atan(----------------------- + (- 6a d + 6b c)\|3
+--R \| a +---+2
+--R | b
+--R 3a 3|- -
+--R \| a
+--R /
+--R 2 2 +-+
+--R (6a c d - 6a b c )x\|3
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R a d\|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+3+-+ 3+-+ 3+-+
+--R - 2a d\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +-+ +-+2
+--R +-+3+-+3+-+ |d |d
+--R 2a d\|3 \|a \|c 3|- log(c 3|- + d x)
+--R \|c \|c
+--R +
+--R +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - b c\|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+3+-+ 3+-+ 3+-+
+--R 2b c\|3 \|b \|c log(x\|b + \|a )
+--R +
+--R +---+ +---+2
+--R +-+ | b 3+-+3+-+ | b
+--R 2b c\|3 3|- - \|a \|c log(a 3|- - + b x)
+--R \| a \| a
+--R +
+--R +---+ +---+2 +---+
+--R +-+ | b 3+-+3+-+ | b | b 2
+--R - b c\|3 3|- - \|a \|c log(- a x 3|- - - a 3|- - + b x )
+--R \| a \| a \| a
+--R +
+--R +-+ +-+2 +-+
+--R +-+3+-+3+-+ |d |d |d 2
+--R - a d\|3 \|a \|c 3|- log(- c x 3|- + c 3|- + d x )
+--R \|c \|c \|c
+--R +
+--R 3+-+ 3+-+ 3+-+ 3+-+
+--R 3+-+3+-+ 2x\|d - \|c 3+-+3+-+ 2x\|b - \|a
+--R 6a d\|a \|d atan(-------------) - 6b c\|b \|c atan(-------------)
+--R +-+3+-+ +-+3+-+
+--R \|3 \|c \|3 \|a
+--R +
+--R +-+2
+--R +-+ |d +-+
+--R +-+ c\|3 3|- - 2d x\|3
+--R 3+-+3+-+ |d \|c
+--R 6a d\|a \|c 3|- atan(---------------------)
+--R \|c +-+2
+--R |d
+--R 3c 3|-
+--R \|c
+--R +
+--R +---+2
+--R +-+ | b +-+
+--R +---+ a\|3 3|- - - 2b x\|3
+--R | b 3+-+3+-+ \| a
+--R 6b c 3|- - \|a \|c atan(-----------------------)
+--R \| a +---+2
+--R | b
+--R 3a 3|- -
+--R \| a
+--R /
+--R 2 2 +-+3+-+3+-+
+--R (6a c d - 6a b c )\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 716
+t0:=1/(x^3*(a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 9 6 3
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 161
+
+--S 162 of 716
+r0:=(-1/2)/(a*c*x^2)-1/3*b^(5/3)*log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*_
+ (b*c-a*d))+1/3*d^(5/3)*log(c^(1/3)+d^(1/3)*x)/(c^(5/3)*(b*c-a*d))+_
+ 1/6*b^(5/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*_
+ (b*c-a*d))-1/6*d^(5/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*_
+ x^2)/(c^(5/3)*(b*c-a*d))+b^(5/3)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(5/3)*(b*c-a*d)*sqrt(3))-d^(5/3)*_
+ atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(5/3)*(b*c-a*d)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R a d x \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R - 2a d x \|3 \|a \|d log(x\|d + \|c )
+--R +
+--R 2 +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - b c x \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R 2b c x \|3 \|b \|c log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 3+-+2 3+-+2 2x\|d - \|c
+--R - 6a d x \|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 2 3+-+2 3+-+2 2x\|b - \|a +-+3+-+2 3+-+2
+--R 6b c x \|b \|c atan(------------ + (- 3a d + 3b c)\|3 \|a \|c
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R 2 2 2 +-+3+-+2 3+-+2
+--R (6a c d - 6a b c )x \|3 \|a \|c
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R 2 +-+ |b 2 |b |b 2 2
+--R - b c x \|3 |-- log(a |-- - a b x |-- + b x )
+--R 3| 2 3| 2 3| 2
+--R \|a \|a \|a
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R 2 +-+ |b |b
+--R 2b c x \|3 |-- log(a |-- + b x)
+--R 3| 2 3| 2
+--R \|a \|a
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R 2 +-+ | d 2 | d | d 2 2
+--R - a d x \|3 |- -- log(c |- -- + c d x |- -- + d x )
+--R 3| 2 3| 2 3| 2
+--R \| c \| c \| c
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R 2 +-+ | d | d
+--R 2a d x \|3 |- -- log(- c |- -- + d x)
+--R 3| 2 3| 2
+--R \| c \| c
+--R +
+--R +----+
+--R | 2
+--R +-+ | d +-+
+--R +----+ c\|3 |- -- + 2d x\|3
+--R | 2 3| 2
+--R 2 | d \| c
+--R - 6a d x |- -- atan(-----------------------)
+--R 3| 2 +----+
+--R \| c | 2
+--R | d
+--R 3c |- --
+--R 3| 2
+--R \| c
+--R +
+--R +--+
+--R | 2
+--R +-+ |b +-+
+--R +--+ a\|3 |-- - 2b x\|3
+--R | 2 3| 2
+--R 2 |b \|a +-+
+--R - 6b c x |-- atan(--------------------- + (- 3a d + 3b c)\|3
+--R 3| 2 +--+
+--R \|a | 2
+--R |b
+--R 3a |--
+--R 3| 2
+--R \|a
+--R /
+--R 2 2 2 +-+
+--R (6a c d - 6a b c )x \|3
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - a d\|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R 2a d\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+3+-+2 |b 3+-+2 2 |b |b 2 2
+--R - b c\|3 \|a |-- \|c log(a |-- - a b x |-- + b x )
+--R 3| 2 3| 2 3| 2
+--R \|a \|a \|a
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R +-+3+-+2 |b 3+-+2 |b
+--R 2b c\|3 \|a |-- \|c log(a |-- + b x)
+--R 3| 2 3| 2
+--R \|a \|a
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R b c\|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R - 2b c\|3 \|b \|c log(x\|b + \|a )
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | d 3+-+2 3+-+2 2 | d | d 2 2
+--R - a d\|3 |- -- \|a \|c log(c |- -- + c d x |- -- + d x )
+--R 3| 2 3| 2 3| 2
+--R \| c \| c \| c
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R +-+ | d 3+-+2 3+-+2 | d
+--R 2a d\|3 |- -- \|a \|c log(- c |- -- + d x)
+--R 3| 2 3| 2
+--R \| c \| c
+--R +
+--R 3+-+ 3+-+ 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|d - \|c 3+-+2 3+-+2 2x\|b - \|a
+--R 6a d \|a \|d atan(------------- - 6b c \|b \|c atan(-------------)
+--R +-+3+-+ +-+3+-+
+--R \|3 \|c \|3 \|a
+--R +
+--R +----+
+--R | 2
+--R +-+ | d +-+
+--R +----+ c\|3 |- -- + 2d x\|3
+--R | 2 3| 2
+--R | d 3+-+2 3+-+2 \| c
+--R - 6a d |- -- \|a \|c atan(-----------------------)
+--R 3| 2 +----+
+--R \| c | 2
+--R | d
+--R 3c |- --
+--R 3| 2
+--R \| c
+--R +
+--R +--+
+--R | 2
+--R +-+ |b +-+
+--R +--+ a\|3 |-- - 2b x\|3
+--R | 2 3| 2
+--R 3+-+2 |b 3+-+2 \|a
+--R - 6b c \|a |-- \|c atan(---------------------)
+--R 3| 2 +--+
+--R \|a | 2
+--R |b
+--R 3a |--
+--R 3| 2
+--R \|a
+--R /
+--R 2 2 +-+3+-+2 3+-+2
+--R (6a c d - 6a b c )\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 716
+t0:=1/(x^4*(a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 10 7 4
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 166
+
+--S 167 of 716
+r0:=(-1/3)/(a*c*x^3)-(b*c+a*d)*log(x)/(a^2*c^2)+1/3*b^2*log(a+b*x^3)/_
+ (a^2*(b*c-a*d))-1/3*d^2*log(c+d*x^3)/(c^2*(b*c-a*d))
+--R
+--R
+--R (2)
+--R 2 2 3 3 2 2 3 3 2 2 2 2 3
+--R a d x log(d x + c) - b c x log(b x + a) + (- 3a d + 3b c )x log(x)
+--R +
+--R 2 2
+--R - a c d + a b c
+--R /
+--R 3 2 2 3 3
+--R (3a c d - 3a b c )x
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 3 3 2 2 3 3 2 2 2 2 3
+--R a d x log(d x + c) - b c x log(b x + a) + (- 3a d + 3b c )x log(x)
+--R +
+--R 2 2
+--R - a c d + a b c
+--R /
+--R 3 2 2 3 3
+--R (3a c d - 3a b c )x
+--R Type: Union(Expression(Integer),...)
+--E 168
+
+--S 169 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 170
+
+)clear all
+
+--S 171 of 716
+t0:=1/(x^5*(a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 11 8 5
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 171
+
+--S 172 of 716
+r0:=(-1/4)/(a*c*x^4)+(b*c+a*d)/(a^2*c^2*x)-1/3*b^(7/3)*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(7/3)*(b*c-a*d))+1/3*d^(7/3)*log(c^(1/3)+d^(1/3)*x)/_
+ (c^(7/3)*(b*c-a*d))+1/6*b^(7/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/(a^(7/3)*(b*c-a*d))-1/6*d^(7/3)*log(c^(2/3)-_
+ c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(7/3)*(b*c-a*d))-b^(7/3)*_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(7/3)*(b*c-a*d)*_
+ sqrt(3))+d^(7/3)*atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/_
+ (c^(7/3)*(b*c-a*d)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 2 4 +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R 2a d x \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 2 4 +-+3+-+3+-+ 3+-+ 3+-+
+--R - 4a d x \|3 \|a \|d log(x\|d + \|c )
+--R +
+--R 2 2 4 +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - 2b c x \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 2 4 +-+3+-+3+-+ 3+-+ 3+-+
+--R 4b c x \|3 \|b \|c log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+ 3+-+ 3+-+
+--R 2 2 4 3+-+3+-+ 2x\|d - \|c 2 2 4 3+-+3+-+ 2x\|b - \|a
+--R 12a d x \|a \|d atan(------------- - 12b c x \|b \|c atan(-------------)
+--R +-+3+-+ +-+3+-+
+--R \|3 \|c \|3 \|a
+--R +
+--R 2 2 2 2 3 2 2 +-+3+-+3+-+
+--R ((12a d - 12b c )x - 3a c d + 3a b c )\|3 \|a \|c
+--R /
+--R 3 2 2 3 4 +-+3+-+3+-+
+--R (12a c d - 12a b c )x \|3 \|a \|c
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+2 +---+ +---+2
+--R 2 2 4 +-+ |b |b 2 2 4 +-+ | d | d
+--R 4b c x \|3 3|- log(a 3|- + b x + 4a d x \|3 3|- - log(c 3|- - + d x)
+--R \|a \|a \| c \| c
+--R +
+--R +---+ +---+2 +---+
+--R 2 2 4 +-+ | d | d | d 2
+--R - 2a d x \|3 3|- - log(- c x 3|- - - c 3|- - + d x )
+--R \| c \| c \| c
+--R +
+--R +-+ +-+2 +-+
+--R 2 2 4 +-+ |b |b |b 2
+--R - 2b c x \|3 3|- log(- a x 3|- + a 3|- + b x )
+--R \|a \|a \|a
+--R +
+--R +-+2
+--R +-+ |b +-+
+--R +-+ a\|3 3|- - 2b x\|3
+--R 2 2 4 |b \|a
+--R 12b c x 3|- atan(---------------------)
+--R \|a +-+2
+--R |b
+--R 3a 3|-
+--R \|a
+--R +
+--R +---+2
+--R +-+ | d +-+
+--R +---+ c\|3 3|- - - 2d x\|3
+--R 2 2 4 | d \| c
+--R 12a d x 3|- - atan(-----------------------)
+--R \| c +---+2
+--R | d
+--R 3c 3|- -
+--R \| c
+--R +
+--R 2 2 2 2 3 2 2 +-+
+--R ((12a d - 12b c )x - 3a c d + 3a b c )\|3
+--R /
+--R 3 2 2 3 4 +-+
+--R (12a c d - 12a b c )x \|3
+--R Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - a d \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 2 +-+3+-+3+-+ 3+-+ 3+-+
+--R 2a d \|3 \|a \|d log(x\|d + \|c )
+--R +
+--R 2 2 +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R b c \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 2 +-+3+-+3+-+ 3+-+ 3+-+
+--R - 2b c \|3 \|b \|c log(x\|b + \|a )
+--R +
+--R +-+ +-+2
+--R 2 2 +-+3+-+ |b 3+-+ |b
+--R 2b c \|3 \|a 3|- \|c log(a 3|- + b x)
+--R \|a \|a
+--R +
+--R +---+ +---+2
+--R 2 2 +-+ | d 3+-+3+-+ | d
+--R 2a d \|3 3|- - \|a \|c log(c 3|- - + d x)
+--R \| c \| c
+--R +
+--R +---+ +---+2 +---+
+--R 2 2 +-+ | d 3+-+3+-+ | d | d 2
+--R - a d \|3 3|- - \|a \|c log(- c x 3|- - - c 3|- - + d x )
+--R \| c \| c \| c
+--R +
+--R +-+ +-+2 +-+
+--R 2 2 +-+3+-+ |b 3+-+ |b |b 2
+--R - b c \|3 \|a 3|- \|c log(- a x 3|- + a 3|- + b x )
+--R \|a \|a \|a
+--R +
+--R 3+-+ 3+-+ 3+-+ 3+-+
+--R 2 2 3+-+3+-+ 2x\|d - \|c 2 2 3+-+3+-+ 2x\|b - \|a
+--R - 6a d \|a \|d atan(------------- + 6b c \|b \|c atan(-------------)
+--R +-+3+-+ +-+3+-+
+--R \|3 \|c \|3 \|a
+--R +
+--R +-+2
+--R +-+ |b +-+
+--R +-+ a\|3 3|- - 2b x\|3
+--R 2 2 3+-+ |b 3+-+ \|a
+--R 6b c \|a 3|- \|c atan(---------------------)
+--R \|a +-+2
+--R |b
+--R 3a 3|-
+--R \|a
+--R +
+--R +---+2
+--R +-+ | d +-+
+--R +---+ c\|3 3|- - - 2d x\|3
+--R 2 2 | d 3+-+3+-+ \| c
+--R 6a d 3|- - \|a \|c atan(-----------------------)
+--R \| c +---+2
+--R | d
+--R 3c 3|- -
+--R \| c
+--R /
+--R 3 2 2 3 +-+3+-+3+-+
+--R (6a c d - 6a b c )\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 716
+t0:=1/(x^6*(a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 12 9 6
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 176
+
+--S 177 of 716
+r0:=(-1/5)/(a*c*x^5)+1/2*(b*c+a*d)/(a^2*c^2*x^2)+1/3*b^(8/3)*_
+ log(a^(1/3)+b^(1/3)*x)/(a^(8/3)*(b*c-a*d))-1/3*d^(8/3)*_
+ log(c^(1/3)+d^(1/3)*x)/(c^(8/3)*(b*c-a*d))-1/6*b^(8/3)*_
+ log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(8/3)*(b*c-a*d))+_
+ 1/6*d^(8/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(8/3)*_
+ (b*c-a*d))-b^(8/3)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_
+ (a^(8/3)*(b*c-a*d)*sqrt(3))+d^(8/3)*atan((c^(1/3)-2*d^(1/3)*x)/_
+ (c^(1/3)*sqrt(3)))/(c^(8/3)*(b*c-a*d)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 2 5 +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - 5a d x \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 2 5 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R 10a d x \|3 \|a \|d log(x\|d + \|c )
+--R +
+--R 2 2 5 +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R 5b c x \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 2 5 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R - 10b c x \|3 \|b \|c log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 2 5 3+-+2 3+-+2 2x\|d - \|c
+--R 30a d x \|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 2 2 5 3+-+2 3+-+2 2x\|b - \|a
+--R - 30b c x \|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 2 2 2 3 2 2 +-+3+-+2 3+-+2
+--R ((15a d - 15b c )x - 6a c d + 6a b c )\|3 \|a \|c
+--R /
+--R 3 2 2 3 5 +-+3+-+2 3+-+2
+--R (30a c d - 30a b c )x \|3 \|a \|c
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R 2 2 5 +-+ |d 2 |d |d 2 2
+--R - 5a d x \|3 |-- log(c |-- - c d x |-- + d x )
+--R 3| 2 3| 2 3| 2
+--R \|c \|c \|c
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R 2 2 5 +-+ |d |d
+--R 10a d x \|3 |-- log(c |-- + d x)
+--R 3| 2 3| 2
+--R \|c \|c
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R 2 2 5 +-+ | b 2 | b | b 2 2
+--R - 5b c x \|3 |- -- log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R 2 2 5 +-+ | b | b
+--R 10b c x \|3 |- -- log(- a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- + 2b x\|3
+--R | 2 3| 2
+--R 2 2 5 | b \| a
+--R - 30b c x |- -- atan(-----------------------)
+--R 3| 2 +----+
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R +--+
+--R | 2
+--R +-+ |d +-+
+--R +--+ c\|3 |-- - 2d x\|3
+--R | 2 3| 2
+--R 2 2 5 |d \|c
+--R - 30a d x |-- atan(---------------------)
+--R 3| 2 +--+
+--R \|c | 2
+--R |d
+--R 3c |--
+--R 3| 2
+--R \|c
+--R +
+--R 2 2 2 2 3 2 2 +-+
+--R ((15a d - 15b c )x - 6a c d + 6a b c )\|3
+--R /
+--R 3 2 2 3 5 +-+
+--R (30a c d - 30a b c )x \|3
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R 2 2 +-+3+-+2 3+-+2 |d 2 |d |d 2 2
+--R - a d \|3 \|a \|c |-- log(c |-- - c d x |-- + d x )
+--R 3| 2 3| 2 3| 2
+--R \|c \|c \|c
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R 2 2 +-+3+-+2 3+-+2 |d |d
+--R 2a d \|3 \|a \|c |-- log(c |-- + d x)
+--R 3| 2 3| 2
+--R \|c \|c
+--R +
+--R 2 2 +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R a d \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 2 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R - 2a d \|3 \|a \|d log(x\|d + \|c )
+--R +
+--R 2 2 +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - b c \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 2 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R 2b c \|3 \|b \|c log(x\|b + \|a )
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R 2 2 +-+ | b 3+-+2 3+-+2 2 | b | b 2 2
+--R - b c \|3 |- -- \|a \|c log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R 2 2 +-+ | b 3+-+2 3+-+2 | b
+--R 2b c \|3 |- -- \|a \|c log(- a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R 3+-+ 3+-+ 3+-+ 3+-+
+--R 2 2 3+-+2 3+-+2 2x\|d - \|c 2 2 3+-+2 3+-+2 2x\|b - \|a
+--R - 6a d \|a \|d atan(------------ + 6b c \|b \|c atan(-------------)
+--R +-+3+-+ +-+3+-+
+--R \|3 \|c \|3 \|a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- + 2b x\|3
+--R | 2 3| 2
+--R 2 2 | b 3+-+2 3+-+2 \| a
+--R - 6b c |- -- \|a \|c atan(-----------------------)
+--R 3| 2 +----+
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R +--+
+--R | 2
+--R +-+ |d +-+
+--R +--+ c\|3 |-- - 2d x\|3
+--R | 2 3| 2
+--R 2 2 3+-+2 3+-+2 |d \|c
+--R - 6a d \|a \|c |-- atan(---------------------)
+--R 3| 2 +--+
+--R \|c | 2
+--R |d
+--R 3c |--
+--R 3| 2
+--R \|c
+--R /
+--R 3 2 2 3 +-+3+-+2 3+-+2
+--R (6a c d - 6a b c )\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 716
+t0:=1/(x^7*(a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R 13 10 7
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 181
+
+--S 182 of 716
+r0:=(-1/6)/(a*c*x^6)+1/3*(b*c+a*d)/(a^2*c^2*x^3)+(b^2*c^2+a*b*c*d+_
+ a^2*d^2)*log(x)/(a^3*c^3)-1/3*b^3*log(a+b*x^3)/(a^3*(b*c-a*d))+_
+ 1/3*d^3*log(c+d*x^3)/(c^3*(b*c-a*d))
+--R
+--R
+--R (2)
+--R 3 3 6 3 3 3 6 3 3 3 3 3 6
+--R - 2a d x log(d x + c) + 2b c x log(b x + a) + (6a d - 6b c )x log(x)
+--R +
+--R 3 2 2 3 3 3 2 2 3
+--R (2a c d - 2a b c )x - a c d + a b c
+--R /
+--R 4 3 3 4 6
+--R (6a c d - 6a b c )x
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 6 3 3 3 6 3 3 3 3 3 6
+--R - 2a d x log(d x + c) + 2b c x log(b x + a) + (6a d - 6b c )x log(x)
+--R +
+--R 3 2 2 3 3 3 2 2 3
+--R (2a c d - 2a b c )x - a c d + a b c
+--R /
+--R 4 3 3 4 6
+--R (6a c d - 6a b c )x
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 716
+t0:=1/(x^8*(a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R 14 11 8
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 186
+
+--S 187 of 716
+r0:=(-1/7)/(a*c*x^7)+1/4*(b*c+a*d)/(a^2*c^2*x^4)+(-b^2*c^2-a*b*c*d-_
+ a^2*d^2)/(a^3*c^3*x)+1/3*b^(10/3)*log(a^(1/3)+b^(1/3)*x)/(a^(10/3)*_
+ (b*c-a*d))-1/3*d^(10/3)*log(c^(1/3)+d^(1/3)*x)/(c^(10/3)*(b*c-a*d))-_
+ 1/6*b^(10/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(10/3)*_
+ (b*c-a*d))+1/6*d^(10/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*_
+ x^2)/(c^(10/3)*(b*c-a*d))+b^(10/3)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(10/3)*(b*c-a*d)*sqrt(3))-d^(10/3)*_
+ atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(10/3)*(b*c-a*d)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 3 7 +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - 14a d x \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R 3 3 7 +-+3+-+3+-+ 3+-+ 3+-+
+--R 28a d x \|3 \|a \|d log(x\|d + \|c )
+--R +
+--R 3 3 7 +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R 14b c x \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3 3 7 +-+3+-+3+-+ 3+-+ 3+-+
+--R - 28b c x \|3 \|b \|c log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 3 7 3+-+3+-+ 2x\|d - \|c
+--R - 84a d x \|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3 3 7 3+-+3+-+ 2x\|b - \|a
+--R 84b c x \|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 3 3 3 3 6 3 2 2 3 3 3 2 2 3
+--R ((- 84a d + 84b c )x + (21a c d - 21a b c )x - 12a c d + 12a b c )
+--R *
+--R +-+3+-+3+-+
+--R \|3 \|a \|c
+--R /
+--R 4 3 3 4 7 +-+3+-+3+-+
+--R (84a c d - 84a b c )x \|3 \|a \|c
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+2
+--R 3 3 7 +-+ |d |d
+--R 28a d x \|3 3|- log(c 3|- + d x)
+--R \|c \|c
+--R +
+--R +---+ +---+2
+--R 3 3 7 +-+ | b | b
+--R 28b c x \|3 3|- - log(a 3|- - + b x)
+--R \| a \| a
+--R +
+--R +---+ +---+2 +---+
+--R 3 3 7 +-+ | b | b | b 2
+--R - 14b c x \|3 3|- - log(- a x 3|- - - a 3|- - + b x )
+--R \| a \| a \| a
+--R +
+--R +-+ +-+2 +-+
+--R 3 3 7 +-+ |d |d |d 2
+--R - 14a d x \|3 3|- log(- c x 3|- + c 3|- + d x )
+--R \|c \|c \|c
+--R +
+--R +-+2
+--R +-+ |d +-+
+--R +-+ c\|3 3|- - 2d x\|3
+--R 3 3 7 |d \|c
+--R 84a d x 3|- atan(---------------------)
+--R \|c +-+2
+--R |d
+--R 3c 3|-
+--R \|c
+--R +
+--R +---+2
+--R +-+ | b +-+
+--R +---+ a\|3 3|- - - 2b x\|3
+--R 3 3 7 | b \| a
+--R 84b c x 3|- - atan(-----------------------)
+--R \| a +---+2
+--R | b
+--R 3a 3|- -
+--R \| a
+--R +
+--R 3 3 3 3 6 3 2 2 3 3 3 2 2 3 +-+
+--R ((- 84a d + 84b c )x + (21a c d - 21a b c )x - 12a c d + 12a b c )\|3
+--R /
+--R 4 3 3 4 7 +-+
+--R (84a c d - 84a b c )x \|3
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R a d \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R 3 3 +-+3+-+3+-+ 3+-+ 3+-+
+--R - 2a d \|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +-+ +-+2
+--R 3 3 +-+3+-+3+-+ |d |d
+--R 2a d \|3 \|a \|c 3|- log(c 3|- + d x)
+--R \|c \|c
+--R +
+--R 3 3 +-+3+-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - b c \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3 3 +-+3+-+3+-+ 3+-+ 3+-+
+--R 2b c \|3 \|b \|c log(x\|b + \|a )
+--R +
+--R +---+ +---+2
+--R 3 3 +-+ | b 3+-+3+-+ | b
+--R 2b c \|3 3|- - \|a \|c log(a 3|- - + b x)
+--R \| a \| a
+--R +
+--R +---+ +---+2 +---+
+--R 3 3 +-+ | b 3+-+3+-+ | b | b 2
+--R - b c \|3 3|- - \|a \|c log(- a x 3|- - - a 3|- - + b x )
+--R \| a \| a \| a
+--R +
+--R +-+ +-+2 +-+
+--R 3 3 +-+3+-+3+-+ |d |d |d 2
+--R - a d \|3 \|a \|c 3|- log(- c x 3|- + c 3|- + d x )
+--R \|c \|c \|c
+--R +
+--R 3+-+ 3+-+ 3+-+ 3+-+
+--R 3 3 3+-+3+-+ 2x\|d - \|c 3 3 3+-+3+-+ 2x\|b - \|a
+--R 6a d \|a \|d atan(------------- - 6b c \|b \|c atan(-------------)
+--R +-+3+-+ +-+3+-+
+--R \|3 \|c \|3 \|a
+--R +
+--R +-+2
+--R +-+ |d +-+
+--R +-+ c\|3 3|- - 2d x\|3
+--R 3 3 3+-+3+-+ |d \|c
+--R 6a d \|a \|c 3|- atan(---------------------)
+--R \|c +-+2
+--R |d
+--R 3c 3|-
+--R \|c
+--R +
+--R +---+2
+--R +-+ | b +-+
+--R +---+ a\|3 3|- - - 2b x\|3
+--R 3 3 | b 3+-+3+-+ \| a
+--R 6b c 3|- - \|a \|c atan(-----------------------)
+--R \| a +---+2
+--R | b
+--R 3a 3|- -
+--R \| a
+--R /
+--R 4 3 3 4 +-+3+-+3+-+
+--R (6a c d - 6a b c )\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 716
+t0:=x^8/((a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 8
+--R x
+--R (1) ----------------------------
+--R 8 4
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 191
+
+--S 192 of 716
+r0:=x/(b*d)-1/2*a^(5/4)*atan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(b^(5/4)*_
+ (b*c-a*d)*sqrt(2))+1/2*a^(5/4)*atan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/_
+ (b^(5/4)*(b*c-a*d)*sqrt(2))+1/2*c^(5/4)*atan(1-d^(1/4)*x*sqrt(2)/_
+ c^(1/4))/(d^(5/4)*(b*c-a*d)*sqrt(2))-1/2*c^(5/4)*atan(1+d^(1/4)*x*_
+ sqrt(2)/c^(1/4))/(d^(5/4)*(b*c-a*d)*sqrt(2))-1/4*a^(5/4)*_
+ log(-a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(b^(5/4)*_
+ (b*c-a*d)*sqrt(2))+1/4*a^(5/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+_
+ sqrt(a)+x^2*sqrt(b))/(b^(5/4)*(b*c-a*d)*sqrt(2))+1/4*c^(5/4)*_
+ log(-c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(d^(5/4)*_
+ (b*c-a*d)*sqrt(2))-1/4*c^(5/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+_
+ sqrt(c)+x^2*sqrt(d))/(d^(5/4)*(b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R b c\|b \|c log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - a d\|a \|d log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R a d\|a \|d log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - b c\|b \|c log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|d + \|c 4+-+4+-+ x\|2 \|d - \|c
+--R 2b c\|b \|c atan(----------------) + 2b c\|b \|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|b + \|a 4+-+4+-+ x\|2 \|b - \|a
+--R - 2a d\|a \|d atan(----------------) - 2a d\|a \|d atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+4+-+4+-+
+--R (4a d - 4b c)x\|2 \|b \|d
+--R /
+--R 2 2 +-+4+-+4+-+
+--R (4a b d - 4b c d)\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R b d
+--R *
+--R +------------------------------------------------------------------+
+--R | 5
+--R | c
+--R |- ----------------------------------------------------------------
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R log
+--R 2
+--R (4a d - 4b c d)
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 4 9 3 8 2 2 2 7 3 3 6
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4 5
+--R 256b c d
+--R ,
+--R 4
+--R +
+--R c x
+--R +
+--R -
+--R b d
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 2
+--R (4a b d - 4b c)
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 4 5 4 3 6 3 2 7 2 2
+--R 256a b d - 1024a b c d + 1536a b c d
+--R +
+--R 8 3 9 4
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R +
+--R a x
+--R +
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | a
+--R b d |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 2
+--R (- 4a b d + 4b c)
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 4 5 4 3 6 3 2 7 2 2 8 3
+--R 256a b d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 9 4
+--R 256b c
+--R ,
+--R 4
+--R +
+--R a x
+--R +
+--R -
+--R b d
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 4 9 3 8 2 2 2 7 3 3 6
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4 5
+--R 256b c d
+--R ,
+--R 4
+--R *
+--R log
+--R 2
+--R (- 4a d + 4b c d)
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 4 9 3 8 2 2 2 7
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 3 3 6 4 4 5
+--R - 1024a b c d + 256b c d
+--R ,
+--R 4
+--R +
+--R c x
+--R +
+--R -
+--R 2b d
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 4 9 3 8 2 2 2 7 3 3 6
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4 5
+--R 256b c d
+--R ,
+--R 4
+--R *
+--R atan
+--R 2
+--R (4a d - 4b c d)
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 4 9 3 8 2 2 2 7
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 3 3 6 4 4 5
+--R - 1024a b c d + 256b c d
+--R ,
+--R 4
+--R /
+--R c x
+--R +
+--R 2b d
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R atan
+--R 2
+--R (4a b d - 4b c)
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 4 5 4 3 6 3 2 7 2 2 8 3
+--R 256a b d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 9 4
+--R 256b c
+--R ,
+--R 4
+--R /
+--R a x
+--R +
+--R x
+--R /
+--R b d
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - b c\|b \|c log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R a d\|a \|d log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 2 +-+
+--R (4a b d - 4b c d)\|2
+--R *
+--R +------------------------------------------------------------------+
+--R | 5
+--R | c
+--R |- ----------------------------------------------------------------
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R 2
+--R (4a d - 4b c d)
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 4 9 3 8 2 2 2 7 3 3 6
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4 5
+--R 256b c d
+--R ,
+--R 4
+--R +
+--R c x
+--R +
+--R 2 2 +-+
+--R (- 4a b d + 4b c d)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R 2
+--R (4a b d - 4b c)
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 4 5 4 3 6 3 2 7 2 2 8 3
+--R 256a b d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 9 4
+--R 256b c
+--R ,
+--R 4
+--R +
+--R a x
+--R +
+--R 2 2 +-+
+--R (4a b d - 4b c d)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R 2
+--R (- 4a b d + 4b c)
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 4 5 4 3 6 3 2 7 2 2 8 3
+--R 256a b d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 9 4
+--R 256b c
+--R ,
+--R 4
+--R +
+--R a x
+--R +
+--R 2 2 +-+
+--R (- 4a b d + 4b c d)\|2
+--R *
+--R +------------------------------------------------------------------+
+--R | 5
+--R | c
+--R |- ----------------------------------------------------------------
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R 2
+--R (- 4a d + 4b c d)
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 4 9 3 8 2 2 2 7 3 3 6
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4 5
+--R 256b c d
+--R ,
+--R 4
+--R +
+--R c x
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - a d\|a \|d log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R b c\|b \|c log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|d + \|c 4+-+4+-+ x\|2 \|d - \|c
+--R - 2b c\|b \|c atan(----------------) - 2b c\|b \|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|b + \|a 4+-+4+-+ x\|2 \|b - \|a
+--R 2a d\|a \|d atan(----------------) + 2a d\|a \|d atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R 2 2 +-+
+--R (- 8a b d + 8b c d)\|2
+--R *
+--R +------------------------------------------------------------------+
+--R | 5
+--R | c
+--R |- ----------------------------------------------------------------
+--R 4| 4 9 3 8 2 2 2 7 3 3 6 4 4 5
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R atan
+--R 2
+--R (4a d - 4b c d)
+--R *
+--R ROOT
+--R -
+--R 5
+--R c
+--R /
+--R 4 9 3 8 2 2 2 7 3 3 6
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4 5
+--R 256b c d
+--R ,
+--R 4
+--R /
+--R c x
+--R +
+--R 2 2 +-+
+--R (8a b d - 8b c d)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 7 2 2 8 3 9 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R atan
+--R 2
+--R (4a b d - 4b c)
+--R *
+--R ROOT
+--R -
+--R 5
+--R a
+--R /
+--R 4 5 4 3 6 3 2 7 2 2 8 3
+--R 256a b d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 9 4
+--R 256b c
+--R ,
+--R 4
+--R /
+--R a x
+--R /
+--R 2 2 +-+4+-+4+-+
+--R (4a b d - 4b c d)\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 716
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 716
+t0:=x^7/((a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 7
+--R x
+--R (1) ----------------------------
+--R 8 4
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 196
+
+--S 197 of 716
+r0:=-1/4*a*log(a+b*x^4)/(b*(b*c-a*d))+1/4*c*log(c+d*x^4)/(d*(b*c-a*d))
+--R
+--R
+--R 4 4
+--R - b c log(d x + c) + a d log(b x + a)
+--R (2) ---------------------------------------
+--R 2 2
+--R 4a b d - 4b c d
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 4
+--R - b c log(d x + c) + a d log(b x + a)
+--R (3) ---------------------------------------
+--R 2 2
+--R 4a b d - 4b c d
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 716
+t0:=x^6/((a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 6
+--R x
+--R (1) ----------------------------
+--R 8 4
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 201
+
+--S 202 of 716
+r0:=1/2*a^(3/4)*atan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(b^(3/4)*(b*c-a*d)*_
+ sqrt(2))-1/2*a^(3/4)*atan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(b^(3/4)*_
+ (b*c-a*d)*sqrt(2))-1/2*c^(3/4)*atan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/_
+ (d^(3/4)*(b*c-a*d)*sqrt(2))+1/2*c^(3/4)*atan(1+d^(1/4)*x*sqrt(2)/_
+ c^(1/4))/(d^(3/4)*(b*c-a*d)*sqrt(2))-1/4*a^(3/4)*log(-a^(1/4)*_
+ b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(b^(3/4)*(b*c-a*d)*sqrt(2))+_
+ 1/4*a^(3/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/_
+ (b^(3/4)*(b*c-a*d)*sqrt(2))+1/4*c^(3/4)*log(-c^(1/4)*d^(1/4)*x*_
+ sqrt(2)+sqrt(c)+x^2*sqrt(d))/(d^(3/4)*(b*c-a*d)*sqrt(2))-1/4*_
+ c^(3/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/_
+ (d^(3/4)*(b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R \|b \|c log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - \|a \|d log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R \|a \|d log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - \|b \|c log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+3 4+-+3 x\|2 \|d + \|c 4+-+3 4+-+3 x\|2 \|d - \|c
+--R - 2\|b \|c atan(---------------- - 2\|b \|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+3 4+-+3 x\|2 \|b + \|a 4+-+3 4+-+3 x\|2 \|b - \|a
+--R 2\|a \|d atan(---------------- + 2\|a \|d atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R /
+--R +-+4+-+3 4+-+3
+--R (4a d - 4b c)\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +------------------------------------------------------------------+
+--R | 3
+--R | c
+--R |- ----------------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R log
+--R 3 5 2 4 2 2 3 3 3 2
+--R (64a d - 192a b c d + 192a b c d - 64b c d )
+--R *
+--R ROOT
+--R -
+--R 3
+--R c
+--R /
+--R 4 7 3 6 2 2 2 5
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 3 3 4 4 4 3
+--R - 1024a b c d + 256b c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2
+--R c x
+--R +
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 3 2 3 2 3 2 4 2 5 3
+--R (64a b d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a
+--R /
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R 256a b d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 7 4
+--R 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2
+--R a x
+--R +
+--R -
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 3 2 3 2 3 2 4 2 5 3
+--R (- 64a b d + 192a b c d - 192a b c d + 64b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a
+--R /
+--R 4 3 4 3 4 3 2 5 2 2
+--R 256a b d - 1024a b c d + 1536a b c d
+--R +
+--R 6 3 7 4
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2
+--R a x
+--R +
+--R +------------------------------------------------------------------+
+--R | 3
+--R | c
+--R |- ----------------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R log
+--R 3 5 2 4 2 2 3 3 3 2
+--R (- 64a d + 192a b c d - 192a b c d + 64b c d )
+--R *
+--R ROOT
+--R -
+--R 3
+--R c
+--R /
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4 3
+--R 256b c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2
+--R c x
+--R +
+--R -
+--R +------------------------------------------------------------------+
+--R | 3
+--R | c
+--R 2 |- ----------------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R atan
+--R 3 5 2 4 2 2 3 3 3 2
+--R (64a d - 192a b c d + 192a b c d - 64b c d )
+--R *
+--R ROOT
+--R -
+--R 3
+--R c
+--R /
+--R 4 7 3 6 2 2 2 5
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 3 3 4 4 4 3
+--R - 1024a b c d + 256b c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 2
+--R c x
+--R +
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | a
+--R 2 |- ---------------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R atan
+--R 3 2 3 2 3 2 4 2 5 3
+--R (64a b d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a
+--R /
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R 256a b d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 7 4
+--R 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 2
+--R a x
+--R Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - \|b \|c log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R \|a \|d log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +------------------------------------------------------------------+
+--R | 3
+--R | c
+--R |- ----------------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R 4+-+3 4+-+3
+--R \|b \|d
+--R *
+--R log
+--R 3 5 2 4 2 2 3 3 3 2
+--R (64a d - 192a b c d + 192a b c d - 64b c d )
+--R *
+--R ROOT
+--R -
+--R 3
+--R c
+--R /
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4 3
+--R 256b c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2
+--R c x
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+3 4+-+3
+--R \|b \|d
+--R *
+--R log
+--R 3 2 3 2 3 2 4 2 5 3
+--R (64a b d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a
+--R /
+--R 4 3 4 3 4 3 2 5 2 2
+--R 256a b d - 1024a b c d + 1536a b c d
+--R +
+--R 6 3 7 4
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2
+--R a x
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+3 4+-+3
+--R \|b \|d
+--R *
+--R log
+--R 3 2 3 2 3 2 4 2 5 3
+--R (- 64a b d + 192a b c d - 192a b c d + 64b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a
+--R /
+--R 4 3 4 3 4 3 2 5 2 2
+--R 256a b d - 1024a b c d + 1536a b c d
+--R +
+--R 6 3 7 4
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2
+--R a x
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +------------------------------------------------------------------+
+--R | 3
+--R | c
+--R |- ----------------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R 4+-+3 4+-+3
+--R \|b \|d
+--R *
+--R log
+--R 3 5 2 4 2 2 3 3 3 2
+--R (- 64a d + 192a b c d - 192a b c d + 64b c d )
+--R *
+--R ROOT
+--R -
+--R 3
+--R c
+--R /
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4 3
+--R 256b c d
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 2
+--R c x
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - \|a \|d log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R \|b \|c log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+3 4+-+3 x\|2 \|d + \|c 4+-+3 4+-+3 x\|2 \|d - \|c
+--R 2\|b \|c atan(---------------- + 2\|b \|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+3 4+-+3 x\|2 \|b + \|a 4+-+3 4+-+3 x\|2 \|b - \|a
+--R - 2\|a \|d atan(---------------- - 2\|a \|d atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+
+--R (- 8a d + 8b c)\|2
+--R *
+--R +------------------------------------------------------------------+
+--R | 3
+--R | c
+--R |- ----------------------------------------------------------------
+--R 4| 4 7 3 6 2 2 2 5 3 3 4 4 4 3
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R 4+-+3 4+-+3
+--R \|b \|d
+--R *
+--R atan
+--R 3 5 2 4 2 2 3 3 3 2
+--R (64a d - 192a b c d + 192a b c d - 64b c d )
+--R *
+--R ROOT
+--R -
+--R 3
+--R c
+--R /
+--R 4 7 3 6 2 2 2 5 3 3 4
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4 3
+--R 256b c d
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 2
+--R c x
+--R +
+--R +-+
+--R (8a d - 8b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 5 2 2 6 3 7 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+3 4+-+3
+--R \|b \|d
+--R *
+--R atan
+--R 3 2 3 2 3 2 4 2 5 3
+--R (64a b d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R a
+--R /
+--R 4 3 4 3 4 3 2 5 2 2
+--R 256a b d - 1024a b c d + 1536a b c d
+--R +
+--R 6 3 7 4
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 2
+--R a x
+--R /
+--R +-+4+-+3 4+-+3
+--R (4a d - 4b c)\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 716
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 716
+t0:=x^5/((a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 5
+--R x
+--R (1) ----------------------------
+--R 8 4
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 206
+
+--S 207 of 716
+r0:=-1/2*atan(x^2*sqrt(b)/sqrt(a))*sqrt(a)/((b*c-a*d)*sqrt(b))+_
+ 1/2*atan(x^2*sqrt(d)/sqrt(c))*sqrt(c)/((b*c-a*d)*sqrt(d))
+--R
+--R
+--R 2 +-+ 2 +-+
+--R +-+ +-+ x \|d +-+ +-+ x \|b
+--R - \|b \|c atan(------) + \|a \|d atan(------)
+--R +-+ +-+
+--R \|c \|a
+--R (2) ---------------------------------------------
+--R +-+ +-+
+--R (2a d - 2b c)\|b \|d
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+
+--R 2 | a 4 2 | c 4
+--R +---+ 2b x |- - + b x - a +---+ - 2d x |- - + d x - c
+--R | a \| b | c \| d
+--R |- - log(----------------------) + |- - log(------------------------)
+--R \| b 4 \| d 4
+--R b x + a d x + c
+--R [-----------------------------------------------------------------------,
+--R 4a d - 4b c
+--R +---+ +-+
+--R 2 | c 4 |a
+--R +---+ - 2d x |- - + d x - c +-+ |-
+--R | c \| d |a \|b
+--R |- - log(------------------------) - 2 |- atan(----)
+--R \| d 4 \|b 2
+--R d x + c x
+--R -----------------------------------------------------,
+--R 4a d - 4b c
+--R +---+ +-+
+--R 2 | a 4 |c
+--R +---+ 2b x |- - + b x - a +-+ |-
+--R | a \| b |c \|d
+--R |- - log(----------------------) + 2 |- atan(----)
+--R \| b 4 \|d 2
+--R b x + a x
+--R ---------------------------------------------------,
+--R 4a d - 4b c
+--R +-+ +-+
+--R |a |c
+--R +-+ |- +-+ |-
+--R |a \|b |c \|d
+--R - |- atan(----) + |- atan(----)
+--R \|b 2 \|d 2
+--R x x
+--R ---------------------------------]
+--R 2a d - 2b c
+--R Type: Union(List(Expression(Integer)),...)
+--E 208
+
+--S 209 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R 2 | a 4
+--R +---+ 2b x |- - + b x - a
+--R | a +-+ +-+ \| b
+--R |- - \|b \|d log(----------------------)
+--R \| b 4
+--R b x + a
+--R +
+--R +---+
+--R 2 | c 4
+--R +---+ - 2d x |- - + d x - c 2 +-+
+--R | c +-+ +-+ \| d +-+ +-+ x \|d
+--R |- - \|b \|d log(------------------------) + 2\|b \|c atan(------)
+--R \| d 4 +-+
+--R d x + c \|c
+--R +
+--R 2 +-+
+--R +-+ +-+ x \|b
+--R - 2\|a \|d atan(------)
+--R +-+
+--R \|a
+--R /
+--R +-+ +-+
+--R (4a d - 4b c)\|b \|d
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 210
+
+--S 211 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 | c 4
+--R +---+ - 2d x |- - + d x - c 2 +-+
+--R | c +-+ +-+ \| d +-+ +-+ x \|d
+--R |- - \|b \|d log(------------------------) + 2\|b \|c atan(------)
+--R \| d 4 +-+
+--R d x + c \|c
+--R +
+--R +-+
+--R |a
+--R 2 +-+ +-+ |-
+--R +-+ +-+ x \|b |a +-+ +-+ \|b
+--R - 2\|a \|d atan(------) - 2 |- \|b \|d atan(----)
+--R +-+ \|b 2
+--R \|a x
+--R /
+--R +-+ +-+
+--R (4a d - 4b c)\|b \|d
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 212
+
+)clear all
+
+--S 213 of 716
+t0:=x^4/((a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 4
+--R x
+--R (1) ----------------------------
+--R 8 4
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 213
+
+--S 214 of 716
+r0:=1/2*a^(1/4)*atan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(b^(1/4)*(b*c-a*d)*_
+ sqrt(2))-1/2*a^(1/4)*atan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(b^(1/4)*_
+ (b*c-a*d)*sqrt(2))-1/2*c^(1/4)*atan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/_
+ (d^(1/4)*(b*c-a*d)*sqrt(2))+1/2*c^(1/4)*atan(1+d^(1/4)*x*sqrt(2)/_
+ c^(1/4))/(d^(1/4)*(b*c-a*d)*sqrt(2))+1/4*a^(1/4)*log(-a^(1/4)*_
+ b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(b^(1/4)*(b*c-a*d)*sqrt(2))-_
+ 1/4*a^(1/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/_
+ (b^(1/4)*(b*c-a*d)*sqrt(2))-1/4*c^(1/4)*log(-c^(1/4)*d^(1/4)*x*_
+ sqrt(2)+sqrt(c)+x^2*sqrt(d))/(d^(1/4)*(b*c-a*d)*sqrt(2))+1/4*_
+ c^(1/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/_
+ (d^(1/4)*(b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - \|b \|c log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R \|a \|d log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - \|a \|d log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R \|b \|c log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|d + \|c 4+-+4+-+ x\|2 \|d - \|c
+--R - 2\|b \|c atan(----------------) - 2\|b \|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|b + \|a 4+-+4+-+ x\|2 \|b - \|a
+--R 2\|a \|d atan(----------------) + 2\|a \|d atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R /
+--R +-+4+-+4+-+
+--R (4a d - 4b c)\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +-----------------------------------------------------------------+
+--R | c
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R log
+--R (4a d - 4b c)
+--R *
+--R ROOT
+--R -
+--R c
+--R /
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4
+--R 256b c d
+--R ,
+--R 4
+--R +
+--R x
+--R +
+--R +-----------------------------------------------------------------+
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R (4a d - 4b c)
+--R *
+--R +-----------------------------------------------------------------+
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R +
+--R x
+--R +
+--R -
+--R +-----------------------------------------------------------------+
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R (- 4a d + 4b c)
+--R *
+--R ROOT
+--R -
+--R a
+--R /
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R 256a b d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4
+--R 256b c
+--R ,
+--R 4
+--R +
+--R x
+--R +
+--R +-----------------------------------------------------------------+
+--R | c
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R log
+--R (- 4a d + 4b c)
+--R *
+--R +-----------------------------------------------------------------+
+--R | c
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R +
+--R x
+--R +
+--R +-----------------------------------------------------------------+
+--R | c
+--R 2 |- ---------------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R atan
+--R (4a d - 4b c)
+--R *
+--R +-----------------------------------------------------------------+
+--R | c
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R /
+--R x
+--R +
+--R -
+--R +-----------------------------------------------------------------+
+--R | a
+--R 2 |- ---------------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R atan
+--R (4a d - 4b c)
+--R *
+--R ROOT
+--R -
+--R a
+--R /
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R 256a b d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4
+--R 256b c
+--R ,
+--R 4
+--R /
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 215
+
+--S 216 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R \|b \|c log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - \|a \|d log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | c
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R (4a d - 4b c)
+--R *
+--R ROOT
+--R -
+--R c
+--R /
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4
+--R 256b c d
+--R ,
+--R 4
+--R +
+--R x
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R (4a d - 4b c)
+--R *
+--R ROOT
+--R -
+--R a
+--R /
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R 256a b d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4
+--R 256b c
+--R ,
+--R 4
+--R +
+--R x
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R (- 4a d + 4b c)
+--R *
+--R ROOT
+--R -
+--R a
+--R /
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R 256a b d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4
+--R 256b c
+--R ,
+--R 4
+--R +
+--R x
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | c
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R log
+--R (- 4a d + 4b c)
+--R *
+--R ROOT
+--R -
+--R c
+--R /
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4
+--R 256b c d
+--R ,
+--R 4
+--R +
+--R x
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R \|a \|d log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - \|b \|c log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|d + \|c 4+-+4+-+ x\|2 \|d - \|c
+--R 2\|b \|c atan(----------------) + 2\|b \|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|b + \|a 4+-+4+-+ x\|2 \|b - \|a
+--R - 2\|a \|d atan(----------------) - 2\|a \|d atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+
+--R (8a d - 8b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | c
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c d
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R atan
+--R (4a d - 4b c)
+--R *
+--R ROOT
+--R -
+--R c
+--R /
+--R 4 5 3 4 2 2 2 3 3 3 2
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4
+--R 256b c d
+--R ,
+--R 4
+--R /
+--R x
+--R +
+--R +-+
+--R (- 8a d + 8b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | a
+--R |- ---------------------------------------------------------------
+--R 4| 4 4 3 2 3 2 3 2 2 4 3 5 4
+--R \| 256a b d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+4+-+
+--R \|b \|d
+--R *
+--R atan
+--R (4a d - 4b c)
+--R *
+--R ROOT
+--R -
+--R a
+--R /
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R 256a b d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4
+--R 256b c
+--R ,
+--R 4
+--R /
+--R x
+--R /
+--R +-+4+-+4+-+
+--R (4a d - 4b c)\|2 \|b \|d
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 716
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 217
+
+)clear all
+
+--S 218 of 716
+t0:=x^3/((a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 3
+--R x
+--R (1) ----------------------------
+--R 8 4
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 218
+
+--S 219 of 716
+r0:=1/4*log(a+b*x^4)/(b*c-a*d)-1/4*log(c+d*x^4)/(b*c-a*d)
+--R
+--R
+--R 4 4
+--R log(d x + c) - log(b x + a)
+--R (2) -----------------------------
+--R 4a d - 4b c
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 4
+--R log(d x + c) - log(b x + a)
+--R (3) -----------------------------
+--R 4a d - 4b c
+--R Type: Union(Expression(Integer),...)
+--E 220
+
+--S 221 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 222
+
+)clear all
+
+--S 223 of 716
+t0:=x^2/((a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------------
+--R 8 4
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 223
+
+--S 224 of 716
+r0:=-1/2*b^(1/4)*atan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*(b*c-a*d)*_
+ sqrt(2))+1/2*b^(1/4)*atan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*_
+ (b*c-a*d)*sqrt(2))+1/2*d^(1/4)*atan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/_
+ (c^(1/4)*(b*c-a*d)*sqrt(2))-1/2*d^(1/4)*atan(1+d^(1/4)*x*sqrt(2)/_
+ c^(1/4))/(c^(1/4)*(b*c-a*d)*sqrt(2))+1/4*b^(1/4)*log(-a^(1/4)*_
+ b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(1/4)*(b*c-a*d)*sqrt(2))-_
+ 1/4*b^(1/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/_
+ (a^(1/4)*(b*c-a*d)*sqrt(2))-1/4*d^(1/4)*log(-c^(1/4)*d^(1/4)*x*_
+ sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(1/4)*(b*c-a*d)*sqrt(2))+1/4*_
+ d^(1/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/_
+ (c^(1/4)*(b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - \|a \|d log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R \|b \|c log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - \|b \|c log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R \|a \|d log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|d + \|c 4+-+4+-+ x\|2 \|d - \|c
+--R 2\|a \|d atan(----------------) + 2\|a \|d atan(----------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|b + \|a 4+-+4+-+ x\|2 \|b - \|a
+--R - 2\|b \|c atan(----------------) - 2\|b \|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R /
+--R +-+4+-+4+-+
+--R (4a d - 4b c)\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +-----------------------------------------------------------------+
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R log
+--R 4 3 3 2 2 2 2 3 3
+--R (64a d - 192a b c d + 192a b c d - 64a b c )
+--R *
+--R ROOT
+--R -
+--R b
+--R /
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R b x
+--R +
+--R +-----------------------------------------------------------------+
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 4
+--R (64a c d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R d
+--R /
+--R 4 4 3 2 3 2 2 3 2 3 4
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 5
+--R 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R d x
+--R +
+--R -
+--R +-----------------------------------------------------------------+
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 4
+--R (- 64a c d + 192a b c d - 192a b c d + 64b c )
+--R *
+--R ROOT
+--R -
+--R d
+--R /
+--R 4 4 3 2 3 2 2 3 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 4 4 5
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R d x
+--R +
+--R +-----------------------------------------------------------------+
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R log
+--R 4 3 3 2 2 2 2 3 3
+--R (- 64a d + 192a b c d - 192a b c d + 64a b c )
+--R *
+--R ROOT
+--R -
+--R b
+--R /
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R b x
+--R +
+--R +-----------------------------------------------------------------+
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R atan
+--R 4 3
+--R 64a d
+--R *
+--R ROOT
+--R -
+--R b
+--R /
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 2 2 2 2 3 3 4
+--R (192a b c d - 192a b c d + 64a b c )
+--R *
+--R ROOT
+--R -
+--R b
+--R /
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R - b x
+--R +
+--R -
+--R +-----------------------------------------------------------------+
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R atan
+--R 4 3
+--R 64a d
+--R *
+--R ROOT
+--R -
+--R b
+--R /
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 2 2 2 2 3 3 4
+--R (192a b c d - 192a b c d + 64a b c )
+--R *
+--R ROOT
+--R -
+--R b
+--R /
+--R 5 4 4 3 3 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 2 3 3 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R b x
+--R Type: Union(Expression(Integer),...)
+--E 225
+
+--S 226 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R \|a \|d log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - \|b \|c log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 4 3 3 2 2 2 2 3 3
+--R (64a d - 192a b c d + 192a b c d - 64a b c )
+--R *
+--R ROOT
+--R -
+--R b
+--R /
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R b x
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 4
+--R (64a c d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R d
+--R /
+--R 4 4 3 2 3 2 2 3 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 4 4 5
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R d x
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 3 2 2 2 2 3 3 4
+--R (- 64a c d + 192a b c d - 192a b c d + 64b c )
+--R *
+--R ROOT
+--R -
+--R d
+--R /
+--R 4 4 3 2 3 2 2 3 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 4 4 5
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R d x
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 4 3 3 2 2 2 2 3 3
+--R (- 64a d + 192a b c d - 192a b c d + 64a b c )
+--R *
+--R ROOT
+--R -
+--R b
+--R /
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R b x
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R \|b \|c log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - \|a \|d log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|d + \|c 4+-+4+-+ x\|2 \|d - \|c
+--R - 2\|a \|d atan(----------------) - 2\|a \|d atan(----------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|b + \|a 4+-+4+-+ x\|2 \|b - \|a
+--R 2\|b \|c atan(----------------) + 2\|b \|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R atan
+--R 4 3
+--R 64a d
+--R *
+--R ROOT
+--R -
+--R b
+--R /
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 2 2 2 2 3 3 4
+--R (192a b c d - 192a b c d + 64a b c )
+--R *
+--R ROOT
+--R -
+--R b
+--R /
+--R 5 4 4 3 3 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 2 3 3 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R - b x
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R atan
+--R 4 3
+--R 64a d
+--R *
+--R ROOT
+--R -
+--R b
+--R /
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R /
+--R 3 2 2 2 2 3 3 4
+--R (192a b c d - 192a b c d + 64a b c )
+--R *
+--R ROOT
+--R -
+--R b
+--R /
+--R 5 4 4 3 3 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 2 3 3 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R b x
+--R /
+--R +-+4+-+4+-+
+--R (4a d - 4b c)\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 716
+--d0:=D(m0,x)
+--E 227
+
+)clear all
+
+--S 228 of 716
+t0:=x/((a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R x
+--R (1) ----------------------------
+--R 8 4
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 228
+
+--S 229 of 716
+r0:=1/2*atan(x^2*sqrt(b)/sqrt(a))*sqrt(b)/((b*c-a*d)*sqrt(a))-_
+ 1/2*atan(x^2*sqrt(d)/sqrt(c))*sqrt(d)/((b*c-a*d)*sqrt(c))
+--R
+--R
+--R 2 +-+ 2 +-+
+--R +-+ +-+ x \|d +-+ +-+ x \|b
+--R \|a \|d atan(------) - \|b \|c atan(------)
+--R +-+ +-+
+--R \|c \|a
+--R (2) -------------------------------------------
+--R +-+ +-+
+--R (2a d - 2b c)\|a \|c
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+
+--R 2 | d 4 2 | b 4
+--R +---+ 2c x |- - + d x - c +---+ - 2a x |- - + b x - a
+--R | d \| c | b \| a
+--R |- - log(----------------------) + |- - log(------------------------)
+--R \| c 4 \| a 4
+--R d x + c b x + a
+--R [-----------------------------------------------------------------------,
+--R 4a d - 4b c
+--R +---+ +-+
+--R 2 | b 4 |d
+--R +---+ - 2a x |- - + b x - a +-+ c |-
+--R | b \| a |d \|c
+--R |- - log(------------------------) - 2 |- atan(-----)
+--R \| a 4 \|c 2
+--R b x + a d x
+--R ------------------------------------------------------,
+--R 4a d - 4b c
+--R +---+ +-+
+--R 2 | d 4 |b
+--R +---+ 2c x |- - + d x - c +-+ a |-
+--R | d \| c |b \|a
+--R |- - log(----------------------) + 2 |- atan(-----)
+--R \| c 4 \|a 2
+--R d x + c b x
+--R ----------------------------------------------------,
+--R 4a d - 4b c
+--R +-+ +-+
+--R |d |b
+--R +-+ c |- +-+ a |-
+--R |d \|c |b \|a
+--R - |- atan(-----) + |- atan(-----)
+--R \|c 2 \|a 2
+--R d x b x
+--R -----------------------------------]
+--R 2a d - 2b c
+--R Type: Union(List(Expression(Integer)),...)
+--E 230
+
+--S 231 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R 2 | d 4
+--R +---+ 2c x |- - + d x - c
+--R | d +-+ +-+ \| c
+--R |- - \|a \|c log(----------------------)
+--R \| c 4
+--R d x + c
+--R +
+--R +---+
+--R 2 | b 4
+--R +---+ - 2a x |- - + b x - a 2 +-+
+--R | b +-+ +-+ \| a +-+ +-+ x \|d
+--R |- - \|a \|c log(------------------------) - 2\|a \|d atan(------)
+--R \| a 4 +-+
+--R b x + a \|c
+--R +
+--R 2 +-+
+--R +-+ +-+ x \|b
+--R 2\|b \|c atan(------)
+--R +-+
+--R \|a
+--R /
+--R +-+ +-+
+--R (4a d - 4b c)\|a \|c
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 | b 4
+--R +---+ - 2a x |- - + b x - a 2 +-+
+--R | b +-+ +-+ \| a +-+ +-+ x \|d
+--R |- - \|a \|c log(------------------------) - 2\|a \|d atan(------)
+--R \| a 4 +-+
+--R b x + a \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- 2 +-+
+--R +-+ +-+ |d \|c +-+ +-+ x \|b
+--R - 2\|a \|c |- atan(-----) + 2\|b \|c atan(------)
+--R \|c 2 +-+
+--R d x \|a
+--R /
+--R +-+ +-+
+--R (4a d - 4b c)\|a \|c
+--R Type: Expression(Integer)
+--E 233
+
+--S 234 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 234
+
+)clear all
+
+--S 235 of 716
+t0:=1/((a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R 8 4
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 235
+
+--S 236 of 716
+r0:=-1/2*b^(3/4)*atan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*(b*c-a*d)*_
+ sqrt(2))+1/2*b^(3/4)*atan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*_
+ (b*c-a*d)*sqrt(2))+1/2*d^(3/4)*atan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/_
+ (c^(3/4)*(b*c-a*d)*sqrt(2))-1/2*d^(3/4)*atan(1+d^(1/4)*x*_
+ sqrt(2)/c^(1/4))/(c^(3/4)*(b*c-a*d)*sqrt(2))-1/4*b^(3/4)*_
+ log(-a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(3/4)*_
+ (b*c-a*d)*sqrt(2))+1/4*b^(3/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+_
+ sqrt(a)+x^2*sqrt(b))/(a^(3/4)*(b*c-a*d)*sqrt(2))+1/4*d^(3/4)*_
+ log(-c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(3/4)*_
+ (b*c-a*d)*sqrt(2))-1/4*d^(3/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+_
+ sqrt(c)+x^2*sqrt(d))/(c^(3/4)*(b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R \|a \|d log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - \|b \|c log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R \|b \|c log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - \|a \|d log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+3 4+-+3 x\|2 \|d + \|c 4+-+3 4+-+3 x\|2 \|d - \|c
+--R 2\|a \|d atan(---------------- + 2\|a \|d atan(----------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+3 4+-+3 x\|2 \|b + \|a 4+-+3 4+-+3 x\|2 \|b - \|a
+--R - 2\|b \|c atan(---------------- - 2\|b \|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R /
+--R +-+4+-+3 4+-+3
+--R (4a d - 4b c)\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R log
+--R 2
+--R (4a d - 4a b c)
+--R *
+--R ROOT
+--R -
+--R 3
+--R b
+--R /
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 3 4 4
+--R 256a b c
+--R ,
+--R 4
+--R +
+--R b x
+--R +
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 2
+--R (4a c d - 4b c )
+--R *
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R +
+--R d x
+--R +
+--R -
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 2
+--R (- 4a c d + 4b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R d
+--R /
+--R 4 3 4 3 4 3 2 2 5 2 3 6
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 7
+--R 256b c
+--R ,
+--R 4
+--R +
+--R d x
+--R +
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R log
+--R 2
+--R (- 4a d + 4a b c)
+--R *
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R +
+--R b x
+--R +
+--R -
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R atan
+--R 2
+--R 4a d
+--R *
+--R ROOT
+--R -
+--R 3
+--R b
+--R /
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 3 4 4
+--R 256a b c
+--R ,
+--R 4
+--R /
+--R 2
+--R 4a b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R b
+--R /
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 3 4 4
+--R 256a b c
+--R ,
+--R 4
+--R +
+--R - b x
+--R +
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R atan
+--R 2
+--R 4a d
+--R *
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R /
+--R 2
+--R 4a b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R b
+--R /
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 3 4 4
+--R 256a b c
+--R ,
+--R 4
+--R +
+--R b x
+--R Type: Union(Expression(Integer),...)
+--E 237
+
+--S 238 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - \|a \|d log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R \|b \|c log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2
+--R (4a d - 4a b c)
+--R *
+--R ROOT
+--R -
+--R 3
+--R b
+--R /
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 3 4 4
+--R 256a b c
+--R ,
+--R 4
+--R +
+--R b x
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2
+--R (4a c d - 4b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R d
+--R /
+--R 4 3 4 3 4 3 2 2 5 2 3 6
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 7
+--R 256b c
+--R ,
+--R 4
+--R +
+--R d x
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 3 4 3 4 3 2 2 5 2 3 6 4 7
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2
+--R (- 4a c d + 4b c )
+--R *
+--R ROOT
+--R -
+--R 3
+--R d
+--R /
+--R 4 3 4 3 4 3 2 2 5 2 3 6
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 7
+--R 256b c
+--R ,
+--R 4
+--R +
+--R d x
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2
+--R (- 4a d + 4a b c)
+--R *
+--R ROOT
+--R -
+--R 3
+--R b
+--R /
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 3 4 4
+--R 256a b c
+--R ,
+--R 4
+--R +
+--R b x
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - \|b \|c log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R \|a \|d log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+3 4+-+3 x\|2 \|d + \|c 4+-+3 4+-+3 x\|2 \|d - \|c
+--R - 2\|a \|d atan(---------------- - 2\|a \|d atan(----------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+3 4+-+3 x\|2 \|b + \|a 4+-+3 4+-+3 x\|2 \|b - \|a
+--R 2\|b \|c atan(---------------- + 2\|b \|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+
+--R (- 4a d + 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R atan
+--R 2
+--R 4a d
+--R *
+--R ROOT
+--R -
+--R 3
+--R b
+--R /
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 3 4 4
+--R 256a b c
+--R ,
+--R 4
+--R /
+--R 2
+--R 4a b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R b
+--R /
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 3 4 4
+--R 256a b c
+--R ,
+--R 4
+--R +
+--R - b x
+--R +
+--R +-+
+--R (4a d - 4b c)\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 3
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 7 4 6 3 5 2 2 2 4 3 3 3 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R atan
+--R 2
+--R 4a d
+--R *
+--R ROOT
+--R -
+--R 3
+--R b
+--R /
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 3 4 4
+--R 256a b c
+--R ,
+--R 4
+--R /
+--R 2
+--R 4a b c
+--R *
+--R ROOT
+--R -
+--R 3
+--R b
+--R /
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 3 4 4
+--R 256a b c
+--R ,
+--R 4
+--R +
+--R b x
+--R /
+--R +-+4+-+3 4+-+3
+--R (4a d - 4b c)\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 238
+
+--S 239 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 11 2 2 9 10 3 3 8
+--R 1024a b c d - 4096a b c d
+--R +
+--R 9 4 6 9 4 4 7
+--R (- 2048a b c + 2048a b c )d
+--R +
+--R 8 5 7 8 5 5 6
+--R (12288a b c + 16384a b c )d
+--R +
+--R 7 6 8 7 6 6 5
+--R (- 30720a b c - 40960a b c )d
+--R +
+--R 6 7 9 6 7 7 4
+--R (40960a b c + 45056a b c )d
+--R +
+--R 5 8 10 5 8 8 3
+--R (- 30720a b c - 26624a b c )d
+--R +
+--R 4 9 11 4 9 9 2
+--R (12288a b c + 8192a b c )d
+--R +
+--R 3 10 12 3 10 10
+--R (- 2048a b c - 1024a b c )d
+--R *
+--R 14
+--R x
+--R +
+--R 12 2 9 11 2 3 8 10 3 4 7
+--R 2048a b c d - 8192a b c d + 8192a b c d
+--R +
+--R 9 4 7 9 4 5 6
+--R (4096a b c + 12288a b c )d
+--R +
+--R 8 5 10 8 5 8 8 5 6 5
+--R (1024a b c - 18432a b c - 39936a b c )d
+--R +
+--R 7 6 11 7 6 9 7 6 7 4
+--R (- 4096a b c + 32768a b c + 45056a b c )d
+--R +
+--R 6 7 12 6 7 10 6 7 8 3
+--R (6144a b c - 28672a b c - 26624a b c )d
+--R +
+--R 5 8 13 5 8 11 5 8 9 2
+--R (- 4096a b c + 12288a b c + 8192a b c )d
+--R +
+--R 4 9 14 4 9 12 4 9 10
+--R (1024a b c - 2048a b c - 1024a b c )d
+--R *
+--R 10
+--R x
+--R +
+--R 13 2 9 12 3 8
+--R 1024a c d - 4096a b c d
+--R +
+--R 11 2 6 11 2 4 7
+--R (2048a b c + 6144a b c )d
+--R +
+--R 10 3 7 10 3 5 6
+--R (- 8192a b c - 4096a b c )d
+--R +
+--R 9 4 10 9 4 8 9 4 6 5
+--R (1024a b c + 12288a b c + 1024a b c )d
+--R +
+--R 8 5 11 8 5 9 4
+--R (- 4096a b c - 8192a b c )d
+--R +
+--R 7 6 12 7 6 10 3 6 7 13 2
+--R (6144a b c + 2048a b c )d - 4096a b c d
+--R +
+--R 5 8 14
+--R 1024a b c d
+--R *
+--R 6
+--R x
+--R *
+--R ROOT
+--R -
+--R 3
+--R d
+--R /
+--R 4 3 4 3 4 3 2 2 5 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 6 4 7
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 9 2 9 8 3 8 7 4 4 7 4 2 7
+--R - 64a b d + 128a b c d + (128a b c + 192a b c )d
+--R +
+--R 6 5 5 6 5 3 6
+--R (- 512a b c - 768a b c )d
+--R +
+--R 5 6 6 5 6 4 5
+--R (768a b c + 832a b c )d
+--R +
+--R 4 7 7 4 7 5 4 3 8 8 3 8 6 3
+--R (- 512a b c - 384a b c )d + (128a b c + 64a b c )d
+--R *
+--R 16
+--R x
+--R +
+--R 10 9 9 2 8 8 3 2 7
+--R - 128a b d + 256a b c d + 128a b c d
+--R +
+--R 7 4 5 7 4 3 6
+--R (- 256a b c - 768a b c )d
+--R +
+--R 6 5 8 6 5 6 6 5 4 5
+--R (- 64a b c + 640a b c + 832a b c )d
+--R +
+--R 5 6 9 5 6 7 5 6 5 4
+--R (128a b c - 512a b c - 384a b c )d
+--R +
+--R 4 7 10 4 7 8 4 7 6 3
+--R (- 64a b c + 128a b c + 64a b c )d
+--R *
+--R 12
+--R x
+--R +
+--R 11 9 10 8 9 2 4 9 2 2 7
+--R - 64a d + 128a b c d + (- 128a b c - 64a b c )d
+--R +
+--R 8 3 5 6 7 4 8 7 4 6 5
+--R 256a b c d + (- 64a b c - 128a b c )d
+--R +
+--R 6 5 9 4 5 6 10 3
+--R 128a b c d - 64a b c d
+--R *
+--R 8
+--R x
+--R *
+--R ROOT
+--R -
+--R 3
+--R b
+--R /
+--R 7 4 6 3 5 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 4 3 3 3 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 7 4 2 7 6 5 3 6 5 6 4 5 4 7 5 4
+--R 64a b c d - 384a b c d + 960a b c d - 1280a b c d
+--R +
+--R 3 8 6 3 2 9 7 2 10 8
+--R 960a b c d - 384a b c d + 64a b c d
+--R *
+--R 16
+--R x
+--R +
+--R 8 3 2 7 7 4 3 6
+--R 128a b c d - 768a b c d
+--R +
+--R 6 5 6 6 5 4 5
+--R (- 256a b c + 1664a b c )d
+--R +
+--R 5 6 7 5 6 5 4
+--R (768a b c - 1792a b c )d
+--R +
+--R 4 7 10 4 7 8 4 7 6 3
+--R (- 64a b c - 896a b c + 1088a b c )d
+--R +
+--R 3 8 11 3 8 9 3 8 7 2
+--R (128a b c + 512a b c - 384a b c )d
+--R +
+--R 2 9 12 2 9 10 2 9 8
+--R (- 64a b c - 128a b c + 64a b c )d
+--R *
+--R 12
+--R x
+--R +
+--R 9 2 2 7 8 3 3 6
+--R 64a b c d - 384a b c d
+--R +
+--R 7 4 6 7 4 4 5
+--R (- 256a b c + 704a b c )d
+--R +
+--R 6 5 7 6 5 5 4
+--R (768a b c - 512a b c )d
+--R +
+--R 5 6 10 5 6 8 5 6 6 3
+--R (- 64a b c - 896a b c + 128a b c )d
+--R +
+--R 4 7 11 4 7 9 2
+--R (128a b c + 512a b c )d
+--R +
+--R 3 8 12 3 8 10
+--R (- 64a b c - 128a b c )d
+--R *
+--R 8
+--R x
+--R *
+--R ROOT
+--R -
+--R 3
+--R d
+--R /
+--R 4 3 4 3 4 3 2 2 5 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 6 4 7
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 5 4 7 4 5 6 3 6 2 5 2 7 3 4
+--R - 4a b d + 16a b c d - 24a b c d + 16a b c d
+--R +
+--R 8 4 3
+--R - 4a b c d
+--R *
+--R 18
+--R x
+--R +
+--R 6 3 7 5 4 6 4 5 4 4 5 2 5
+--R - 8a b d + 32a b c d + (16a b c - 32a b c )d
+--R +
+--R 3 6 5 3 6 3 4 2 7 8 2 7 6 2 7 4 3
+--R (- 16a b c + 16a b c )d + (4a b c + 8a b c - 4a b c )d
+--R *
+--R 14
+--R x
+--R +
+--R 7 2 7 6 3 6 5 4 4 5 4 2 5
+--R - 4a b d + 16a b c d + (16a b c - 8a b c )d
+--R +
+--R 4 5 5 4 3 6 8 3 6 6 3
+--R - 16a b c d + (4a b c + 8a b c )d
+--R *
+--R 10
+--R x
+--R *
+--R 4+-+2
+--R \|b
+--R +
+--R 10 2 2 9 9 3 3 8
+--R - 1024a b c d + 4096a b c d
+--R +
+--R 8 4 6 8 4 4 7
+--R (2048a b c - 2048a b c )d
+--R +
+--R 7 5 7 7 5 5 6
+--R (- 12288a b c - 16384a b c )d
+--R +
+--R 6 6 8 6 6 6 5
+--R (30720a b c + 40960a b c )d
+--R +
+--R 5 7 9 5 7 7 4
+--R (- 40960a b c - 45056a b c )d
+--R +
+--R 4 8 10 4 8 8 3
+--R (30720a b c + 26624a b c )d
+--R +
+--R 3 9 11 3 9 9 2
+--R (- 12288a b c - 8192a b c )d
+--R +
+--R 2 10 12 2 10 10
+--R (2048a b c + 1024a b c )d
+--R *
+--R 14
+--R x
+--R +
+--R 11 2 9 10 2 3 8 9 3 4 7
+--R - 2048a b c d + 8192a b c d - 8192a b c d
+--R +
+--R 8 4 7 8 4 5 6
+--R (- 4096a b c - 12288a b c )d
+--R +
+--R 7 5 10 7 5 8 7 5 6 5
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+--R (4096a b c - 6144a b c - 512a b c )d
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+--R 10 4 10 10 4 8 10 4 6 7
+--R (512a b c + 3072a b c + 7680a b c )d
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+--R 9 5 11 9 5 9 9 5 7 6
+--R (- 512a b c - 3072a b c - 38400a b c )d
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+--R (12800a b c + 9216a b c + 13824a b c )d
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+--R (512a b c - 12288a b c - 8192a b c )d
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+--R 10 4 11 10 4 9 10 4 7 6
+--R (1024a b c + 17408a b c + 2048a b c )d
+--R +
+--R 9 5 12 9 5 10 9 5 8 5
+--R (- 4096a b c - 21504a b c - 24576a b c )d
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+--R (5120a b c + 25600a b c + 41984a b c )d
+--R +
+--R 7 7 12 7 7 10 3
+--R (- 27648a b c - 35840a b c )d
+--R +
+--R 6 8 15 6 8 13 6 8 11 2
+--R (- 5120a b c + 19456a b c + 17408a b c )d
+--R +
+--R 5 9 16 5 9 14 5 9 12
+--R (4096a b c - 7168a b c - 4608a b c )d
+--R +
+--R 4 10 17 4 10 15 4 10 13
+--R - 1024a b c + 1024a b c + 512a b c
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+--R +
+--R 14 4 9 13 5 8
+--R 512a c d - 2560a b c d
+--R +
+--R 12 2 8 12 2 6 7
+--R (1024a b c + 5120a b c )d
+--R +
+--R 11 3 9 11 3 7 6
+--R (- 5120a b c - 5120a b c )d
+--R +
+--R 10 4 12 10 4 10 10 4 8 5
+--R (512a b c + 10240a b c + 2560a b c )d
+--R +
+--R 9 5 13 9 5 11 9 5 9 4
+--R (- 2560a b c - 10240a b c - 512a b c )d
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+--R 8 6 14 8 6 12 3
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+--R 7 7 15 7 7 13 2 6 8 16 5 9 17
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+--R 4 3 4 3 4 3 2 2 5 2
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+--R - 1024a b c d + 256b c
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+--R - 32a b d + 96a b c d + (64a b c + 32a b c )d
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+--R (- 64a b c - 32a b c )d
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+--R x
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+--R - 96a b d + 224a b c d + (64a b c + 160a b c )d
+--R +
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+--R +
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+--R (- 32a b c + 448a b c + 640a b c )d
+--R +
+--R 5 7 9 5 7 7 5 7 5 6
+--R (96a b c + 64a b c + 384a b c )d
+--R +
+--R 4 8 10 4 8 8 4 8 6 5
+--R (- 96a b c - 640a b c - 768a b c )d
+--R +
+--R 3 9 11 3 9 9 3 9 7 4
+--R (32a b c + 512a b c + 384a b c )d
+--R +
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+--R x
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+--R - 96a b d + 96a b c d + (- 64a b c + 384a b c )d
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+--R +
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+--R (- 64a b c - 576a b c - 1024a b c )d
+--R +
+--R 6 6 9 6 6 7 6 6 5 6
+--R (128a b c + 1344a b c + 2112a b c )d
+--R +
+--R 5 7 8 5 7 6 5
+--R (- 1472a b c - 1408a b c )d
+--R +
+--R 4 8 11 4 8 9 4 8 7 4
+--R (- 128a b c + 576a b c + 256a b c )d
+--R +
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+--R (64a b c + 64a b c + 96a b c )d
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+--R (256a b c + 64a b c + 384a b c )d
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+--R (- 256a b c - 576a b c - 768a b c )d
+--R +
+--R 4 8 12 4 8 10 4 8 8 3
+--R (32a b c + 512a b c + 384a b c )d
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+--R (32a b c - 128a b c - 64a b c )d
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+--R 12 10 11 2 9 10 2 5 10 2 3 8
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+--R (320a b c - 96a b c )d
+--R +
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+--R (- 64a b c - 320a b c - 416a b c )d
+--R +
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+--R (128a b c + 384a b c + 800a b c )d
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+--R 6 6 9 6 6 7 4
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+--R +
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+--R +
+--R 4 8 13 4 8 11 4 8 9 2
+--R (64a b c - 64a b c - 32a b c )d
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+--R 12 2 9 11 3 8 10 2 6 10 2 4 7
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+--R **
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+--R +
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+--R 32a b c d - 224a b c d + 672a b c d - 1120a b c d
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+--R 3 9 6 5 2 10 7 4 11 8 3 12 9 2
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+--R x
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+--R 96a b c d - 608a b c d + (- 128a b c + 1440a b c )d
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+--R (512a b c - 1504a b c )d
+--R +
+--R 4 8 10 4 8 8 4 8 6 5
+--R (- 32a b c - 832a b c + 320a b c )d
+--R +
+--R 3 9 11 3 9 9 3 9 7 4
+--R (96a b c + 704a b c + 832a b c )d
+--R +
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+--R (- 96a b c - 320a b c - 896a b c )d
+--R +
+--R 11 13 11 11 11 9 2 12 10
+--R (32a b c + 64a b c + 384a b c )d - 64b c d
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+--R x
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+--R 96a b c d - 480a b c d + (- 256a b c + 448a b c )d
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+--R (768a b c + 1216a b c )d
+--R +
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+--R (- 64a b c - 640a b c - 3264a b c )d
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+--R (128a b c - 256a b c + 3200a b c )d
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+--R x
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+--R 32a b c d - 32a b c d + (- 128a b c - 704a b c )d
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+--R (256a b c + 1664a b c + 960a b c )d
+--R +
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+--R (- 256a b c - 512a b c - 960a b c )d
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+--R (32a b c - 64a b c + 384a b c )d + 32a b c
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+--R 64a b c - 64a b c
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+--R 10
+--R x
+--R +
+--R 10 2 3 8 9 3 4 7 8 4 7 8 4 5 6
+--R 64a b c d - 352a b c d + (- 256a b c + 416a b c )d
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+--R (768a b c + 544a b c )d
+--R +
+--R 6 6 11 6 6 9 6 6 7 4
+--R (- 64a b c - 640a b c - 1696a b c )d
+--R +
+--R 5 7 12 5 7 10 5 7 8 3
+--R (128a b c - 256a b c + 1632a b c )d
+--R +
+--R 4 8 11 4 8 9 2
+--R (768a b c - 800a b c )d
+--R +
+--R 3 9 14 3 9 12 3 9 10 2 10 15
+--R (- 128a b c - 512a b c + 224a b c )d + 64a b c
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+--R 128a b c - 32a b c
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+--R x
+--R +
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+--R 32a b c d - 224a b c d + (- 128a b c + 544a b c )d
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+--R 7 5 9 7 5 7 4
+--R (512a b c - 608a b c )d
+--R +
+--R 6 6 12 6 6 10 6 6 8 3
+--R (- 32a b c - 832a b c + 320a b c )d
+--R +
+--R 5 7 13 5 7 11 5 7 9 2
+--R (96a b c + 704a b c - 64a b c )d
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+--R x
+--R *
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+--R x
+--R +
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+--R - 6a b d + 26a b c d + (8a b c - 32a b c )d
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+--R (- 16a b c + 4a b c )d + (2a b c + 12a b c + 20a b c )d
+--R +
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+--R (- 2a b c - 4a b c - 16a b c )d + 4b c d
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+--R 20
+--R x
+--R +
+--R 7 3 9 6 4 8 5 5 4 5 5 2 7
+--R - 6a b d + 18a b c d + (16a b c + 14a b c )d
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+--R 2 8 7 2 8 5 4 9 10 9 8 9 6 3
+--R (16a b c - 18a b c )d + (- 4a b c - 8a b c - 2a b c )d
+--R +
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+--R x
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+--R - 2a b d - 2a b c d + (8a b c + 42a b c )d
+--R +
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+--R (16a b c - 54a b c )d + (2a b c - 44a b c + 4a b c )d
+--R +
+--R 3 7 9 3 7 7 3 7 5 4
+--R (6a b c + 28a b c + 24a b c )d
+--R +
+--R 2 8 10 2 8 8 2 8 6 3
+--R (- 6a b c - 4a b c - 16a b c )d
+--R +
+--R 9 11 9 9 9 7 2
+--R (- 2a b c - 4a b c + 4a b c )d
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+--R x
+--R +
+--R 8 2 8 7 3 2 7 6 4 5 6 4 3 6
+--R - 4a b c d + 14a b c d + (16a b c + 6a b c )d
+--R +
+--R 5 5 6 5 5 4 5 4 6 9 4 6 7 4 6 5 4
+--R (- 16a b c - 36a b c )d + (4a b c - 8a b c + 28a b c )d
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+--R x
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+--R 8 2 2 7 7 3 3 6 6 4 6 6 4 4 5
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+--R +
+--R 5 5 7 5 5 5 4 4 6 10 4 6 8 3
+--R (- 16a b c + 4a b c )d + (2a b c + 12a b c )d
+--R +
+--R 3 7 11 3 7 9 2
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+--R 4
+--R x
+--R *
+--R 4+-+2
+--R \|a
+--R *
+--R 4+-+2
+--R \|c
+--R Type: Expression(Integer)
+--E 239
+
+)clear all
+
+--S 240 of 716
+t0:=1/(x*(a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) ------------------------------
+--R 9 5
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 240
+
+--S 241 of 716
+r0:=log(x)/(a*c)-1/4*b*log(a+b*x^4)/(a*(b*c-a*d))+_
+ 1/4*d*log(c+d*x^4)/(c*(b*c-a*d))
+--R
+--R
+--R 4 4
+--R - a d log(d x + c) + b c log(b x + a) + (4a d - 4b c)log(x)
+--R (2) -------------------------------------------------------------
+--R 2 2
+--R 4a c d - 4a b c
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 4
+--R - a d log(d x + c) + b c log(b x + a) + (4a d - 4b c)log(x)
+--R (3) -------------------------------------------------------------
+--R 2 2
+--R 4a c d - 4a b c
+--R Type: Union(Expression(Integer),...)
+--E 242
+
+--S 243 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 243
+
+--S 244 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 244
+
+)clear all
+
+--S 245 of 716
+t0:=1/(x^2*(a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 10 6 2
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 245
+
+--S 246 of 716
+r0:=(-1)/(a*c*x)+1/2*b^(5/4)*atan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/_
+ (a^(5/4)*(b*c-a*d)*sqrt(2))-1/2*b^(5/4)*atan(1+b^(1/4)*x*_
+ sqrt(2)/a^(1/4))/(a^(5/4)*(b*c-a*d)*sqrt(2))-1/2*d^(5/4)*_
+ atan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(5/4)*(b*c-a*d)*sqrt(2))+_
+ 1/2*d^(5/4)*atan(1+d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(5/4)*(b*c-a*d)*_
+ sqrt(2))-1/4*b^(5/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(b))/(a^(5/4)*(b*c-a*d)*sqrt(2))+1/4*b^(5/4)*log(a^(1/4)*_
+ b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(5/4)*(b*c-a*d)*sqrt(2))+_
+ 1/4*d^(5/4)*log(-c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/_
+ (c^(5/4)*(b*c-a*d)*sqrt(2))-1/4*d^(5/4)*log(c^(1/4)*d^(1/4)*x*_
+ sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(5/4)*(b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R a d x\|a \|d log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - b c x\|b \|c log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R b c x\|b \|c log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - a d x\|a \|d log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|d + \|c
+--R - 2a d x\|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|d - \|c
+--R - 2a d x\|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|b + \|a
+--R 2b c x\|b \|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|b - \|a +-+4+-+4+-+
+--R 2b c x\|b \|c atan(----------------) + (- 4a d + 4b c)\|2 \|a \|c
+--R 4+-+
+--R \|a
+--R /
+--R 2 2 +-+4+-+4+-+
+--R (4a c d - 4a b c )x\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R a c x
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R log
+--R 10 2 6 9 3 5 8 2 4 4 7 3 5 3
+--R 384a c d - 1920a b c d + 3968a b c d - 4352a b c d
+--R +
+--R 6 4 6 2 5 5 7 4 6 8
+--R 2688a b c d - 896a b c d + 128a b c
+--R *
+--R x
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 4 8 3 7 2 2 2 6 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 9 6 7 2 4 4 6 3 5 3 5 4 6 2 4 5 7
+--R - 16a d - 144a b c d + 288a b c d - 240a b c d + 96a b c d
+--R +
+--R 3 6 8
+--R - 16a b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 4 8 3 7 2 2 2 6 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 2
+--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c )x
+--R +
+--R 2a c x
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R log
+--R 7 3 6 2 5 2 2 4 3 3
+--R (64a d - 192a b c d + 192a b c d - 64a b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 4 8 3 7 2 2 2 6 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4
+--R b x
+--R +
+--R 2
+--R 2a c x
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 3 5 3 2 6 2 2 7 3 8
+--R (64a c d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 4 5 4 3 6 3 2 2 7 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 8 4 9
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4
+--R d x
+--R +
+--R -
+--R 2a c x
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 3 4 3 2 5 2 2 6 3 7
+--R (64a c d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 4 5 4 3 6 3 2 2 7 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 8 4 9
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4
+--R d x
+--R +
+--R 2a c x
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 3 4 3 2 5 2 2 6 3 7
+--R (- 64a c d + 192a b c d - 192a b c d + 64b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 4 5 4 3 6 3 2 2 7 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 8 4 9
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4
+--R d x
+--R +
+--R -
+--R 2
+--R 2a c x
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 3 5 3 2 6 2 2 7 3 8
+--R (- 64a c d + 192a b c d - 192a b c d + 64b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 4 5 4 3 6 3 2 2 7 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 8 4 9
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4
+--R d x
+--R +
+--R -
+--R 2a c x
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R log
+--R 7 3 6 2 5 2 2 4 3 3
+--R (- 64a d + 192a b c d - 192a b c d + 64a b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 4 8 3 7 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 6 3 3 5 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4
+--R b x
+--R +
+--R -
+--R 2
+--R a c x
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R log
+--R 10 2 6 9 3 5 8 2 4 4 7 3 5 3
+--R - 384a c d + 1920a b c d - 3968a b c d + 4352a b c d
+--R +
+--R 6 4 6 2 5 5 7 4 6 8
+--R - 2688a b c d + 896a b c d - 128a b c
+--R *
+--R x
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 4 8 3 7 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 6 3 3 5 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 9 6 7 2 4 4 6 3 5 3 5 4 6 2
+--R - 16a d - 144a b c d + 288a b c d - 240a b c d
+--R +
+--R 4 5 7 3 6 8
+--R 96a b c d - 16a b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 4 8 3 7 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 6 3 3 5 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 2
+--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c )x
+--R +
+--R - 2
+--R /
+--R 2a c x
+--R Type: Union(Expression(Integer),...)
+--E 247
+
+--S 248 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - a d\|a \|d log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R b c\|b \|c log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 2 3 +-+
+--R (2a c d - 2a b c )\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 10 2 6 9 3 5 8 2 4 4 7 3 5 3
+--R 384a c d - 1920a b c d + 3968a b c d - 4352a b c d
+--R +
+--R 6 4 6 2 5 5 7 4 6 8
+--R 2688a b c d - 896a b c d + 128a b c
+--R *
+--R x
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 4 8 3 7 2 2 2 6 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 9 6 7 2 4 4 6 3 5 3 5 4 6 2 4 5 7
+--R - 16a d - 144a b c d + 288a b c d - 240a b c d + 96a b c d
+--R +
+--R 3 6 8
+--R - 16a b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 4 8 3 7 2 2 2 6 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 2
+--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c )x
+--R +
+--R 2 2 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 7 3 6 2 5 2 2 4 3 3
+--R (64a d - 192a b c d + 192a b c d - 64a b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 4 8 3 7 2 2 2 6 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4
+--R b x
+--R +
+--R 2 2 3 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 5 3 2 6 2 2 7 3 8
+--R (64a c d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 4 5 4 3 6 3 2 2 7 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 8 4 9
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4
+--R d x
+--R +
+--R 2 2 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 4 3 2 5 2 2 6 3 7
+--R (64a c d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 4 5 4 3 6 3 2 2 7 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 8 4 9
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4
+--R d x
+--R +
+--R 2 2 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 4 3 2 5 2 2 6 3 7
+--R (- 64a c d + 192a b c d - 192a b c d + 64b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 4 5 4 3 6 3 2 2 7 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 8 4 9
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4
+--R d x
+--R +
+--R 2 2 3 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | d
+--R |- ---------------------------------------------------------------
+--R 4| 4 5 4 3 6 3 2 2 7 2 3 8 4 9
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 5 3 2 6 2 2 7 3 8
+--R (- 64a c d + 192a b c d - 192a b c d + 64b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R d
+--R /
+--R 4 5 4 3 6 3 2 2 7 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 8 4 9
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4
+--R d x
+--R +
+--R 2 2 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 7 3 6 2 5 2 2 4 3 3
+--R (- 64a d + 192a b c d - 192a b c d + 64a b c )
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 4 8 3 7 2 2 2 6 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 4
+--R b x
+--R +
+--R 2 2 3 +-+
+--R (- 2a c d + 2a b c )\|2
+--R *
+--R +-----------------------------------------------------------------+
+--R | 5
+--R | b
+--R |- ---------------------------------------------------------------
+--R 4| 9 4 8 3 7 2 2 2 6 3 3 5 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 10 2 6 9 3 5 8 2 4 4 7 3 5 3
+--R - 384a c d + 1920a b c d - 3968a b c d + 4352a b c d
+--R +
+--R 6 4 6 2 5 5 7 4 6 8
+--R - 2688a b c d + 896a b c d - 128a b c
+--R *
+--R x
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 4 8 3 7 2 2 2 6 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 9 6 7 2 4 4 6 3 5 3 5 4 6 2 4 5 7
+--R - 16a d - 144a b c d + 288a b c d - 240a b c d + 96a b c d
+--R +
+--R 3 6 8
+--R - 16a b c
+--R *
+--R ROOT
+--R -
+--R 5
+--R b
+--R /
+--R 9 4 8 3 7 2 2 2 6 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 5 4 4
+--R 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 2
+--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c )x
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - b c\|b \|c log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R a d\|a \|d log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|d + \|c 4+-+4+-+ x\|2 \|d - \|c
+--R 2a d\|a \|d atan(----------------) + 2a d\|a \|d atan(----------------)
+--R 4+-+ 4+-+
+--R \|c \|c
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+4+-+ x\|2 \|b + \|a 4+-+4+-+ x\|2 \|b - \|a
+--R - 2b c\|b \|c atan(----------------) - 2b c\|b \|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R /
+--R 2 2 +-+4+-+4+-+
+--R (4a c d - 4a b c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 248
+
+--S 249 of 716
+--d0:=D(m0,x)
+--E 249
+
+)clear all
+
+--S 250 of 716
+t0:=1/(x^3*(a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 11 7 3
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 250
+
+--S 251 of 716
+r0:=(-1/2)/(a*c*x^2)-1/2*b^(3/2)*atan(x^2*sqrt(b)/sqrt(a))/(a^(3/2)*_
+ (b*c-a*d))+1/2*d^(3/2)*atan(x^2*sqrt(d)/sqrt(c))/(c^(3/2)*(b*c-a*d))
+--R
+--R
+--R (2)
+--R 2 +-+ 2 +-+
+--R 2 +-+ +-+ x \|d 2 +-+ +-+ x \|b
+--R - a d x \|a \|d atan(------) + b c x \|b \|c atan(------)
+--R +-+ +-+
+--R \|c \|a
+--R +
+--R +-+ +-+
+--R (- a d + b c)\|a \|c
+--R /
+--R 2 2 2 +-+ +-+
+--R (2a c d - 2a b c )x \|a \|c
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 2 | b 4
+--R +---+ 2a x |- - + b x - a
+--R 2 | b \| a
+--R b c x |- - log(----------------------)
+--R \| a 4
+--R b x + a
+--R +
+--R +---+
+--R 2 | d 4
+--R +---+ - 2c x |- - + d x - c
+--R 2 | d \| c
+--R a d x |- - log(------------------------) - 2a d + 2b c
+--R \| c 4
+--R d x + c
+--R /
+--R 2 2 2
+--R (4a c d - 4a b c )x
+--R ,
+--R
+--R +---+ +-+
+--R 2 | b 4 |d
+--R +---+ 2a x |- - + b x - a +-+ c |-
+--R 2 | b \| a 2 |d \|c
+--R b c x |- - log(----------------------) + 2a d x |- atan(-----) - 2a d
+--R \| a 4 \|c 2
+--R b x + a d x
+--R +
+--R 2b c
+--R /
+--R 2 2 2
+--R (4a c d - 4a b c )x
+--R ,
+--R
+--R +---+ +-+
+--R 2 | d 4 |b
+--R +---+ - 2c x |- - + d x - c +-+ a |-
+--R 2 | d \| c 2 |b \|a
+--R a d x |- - log(------------------------) - 2b c x |- atan(-----)
+--R \| c 4 \|a 2
+--R d x + c b x
+--R +
+--R - 2a d + 2b c
+--R /
+--R 2 2 2
+--R (4a c d - 4a b c )x
+--R ,
+--R +-+ +-+
+--R |d |b
+--R +-+ c |- +-+ a |-
+--R 2 |d \|c 2 |b \|a
+--R a d x |- atan(-----) - b c x |- atan(-----) - a d + b c
+--R \|c 2 \|a 2
+--R d x b x
+--R ---------------------------------------------------------]
+--R 2 2 2
+--R (2a c d - 2a b c )x
+--R Type: Union(List(Expression(Integer)),...)
+--E 252
+
+--S 253 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R 2 | b 4
+--R +---+ 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R b c |- - \|a \|c log(----------------------)
+--R \| a 4
+--R b x + a
+--R +
+--R +---+
+--R 2 | d 4
+--R +---+ - 2c x |- - + d x - c 2 +-+
+--R | d +-+ +-+ \| c +-+ +-+ x \|d
+--R a d |- - \|a \|c log(------------------------) + 2a d\|a \|d atan(------)
+--R \| c 4 +-+
+--R d x + c \|c
+--R +
+--R 2 +-+
+--R +-+ +-+ x \|b
+--R - 2b c\|b \|c atan(------)
+--R +-+
+--R \|a
+--R /
+--R 2 2 +-+ +-+
+--R (4a c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 253
+
+--S 254 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 | b 4
+--R +---+ 2a x |- - + b x - a 2 +-+
+--R | b +-+ +-+ \| a +-+ +-+ x \|d
+--R b c |- - \|a \|c log(----------------------) + 2a d\|a \|d atan(------)
+--R \| a 4 +-+
+--R b x + a \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- 2 +-+
+--R +-+ +-+ |d \|c +-+ +-+ x \|b
+--R 2a d\|a \|c |- atan(-----) - 2b c\|b \|c atan(------)
+--R \|c 2 +-+
+--R d x \|a
+--R /
+--R 2 2 +-+ +-+
+--R (4a c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 255
+
+--S 256 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 256
+
+)clear all
+
+--S 257 of 716
+t0:=1/(x^4*(a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 12 8 4
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 257
+
+--S 258 of 716
+r0:=(-1/3)/(a*c*x^3)+1/2*b^(7/4)*atan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/_
+ (a^(7/4)*(b*c-a*d)*sqrt(2))-1/2*b^(7/4)*atan(1+b^(1/4)*x*_
+ sqrt(2)/a^(1/4))/(a^(7/4)*(b*c-a*d)*sqrt(2))-1/2*d^(7/4)*_
+ atan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(7/4)*(b*c-a*d)*sqrt(2))+_
+ 1/2*d^(7/4)*atan(1+d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(7/4)*(b*c-a*d)*_
+ sqrt(2))+1/4*b^(7/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*_
+ sqrt(b))/(a^(7/4)*(b*c-a*d)*sqrt(2))-1/4*b^(7/4)*log(a^(1/4)*_
+ b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(7/4)*(b*c-a*d)*sqrt(2))-_
+ 1/4*d^(7/4)*log(-c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/_
+ (c^(7/4)*(b*c-a*d)*sqrt(2))+1/4*d^(7/4)*log(c^(1/4)*d^(1/4)*x*_
+ sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(7/4)*(b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - 3a d x \|a \|d log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 3 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R 3b c x \|b \|c log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 3 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - 3b c x \|b \|c log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 3 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R 3a d x \|a \|d log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+
+--R 3 4+-+3 4+-+3 x\|2 \|d + \|c
+--R - 6a d x \|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+
+--R 3 4+-+3 4+-+3 x\|2 \|d - \|c
+--R - 6a d x \|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+
+--R 3 4+-+3 4+-+3 x\|2 \|b + \|a
+--R 6b c x \|b \|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 3 4+-+3 4+-+3 x\|2 \|b - \|a +-+4+-+3 4+-+3
+--R 6b c x \|b \|c atan(--------------- + (- 4a d + 4b c)\|2 \|a \|c
+--R 4+-+
+--R \|a
+--R /
+--R 2 2 3 +-+4+-+3 4+-+3
+--R (12a c d - 12a b c )x \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 258
+
+--S 259 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 2 3
+--R 3a c x
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2 8 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 7 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 6 2 4 2 4
+--R (16a d + 16a b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 8 3 3 7 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 2 3 2
+--R 8a b c x
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 8 3 3 7 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R +
+--R 4 2
+--R b x
+--R +
+--R 2 3
+--R 3a c x
+--R *
+--R +-------------------------------------------------------------------+
+--R | 7
+--R | b
+--R |- -----------------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R log
+--R 6 2 4 2 4
+--R (16a d + 16a b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 8 3 3 7 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R -
+--R 2 3 2
+--R 8a b c x
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 8 3 3 7 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R +
+--R 4 2
+--R b x
+--R +
+--R 3
+--R 6a c x
+--R *
+--R +-------------------------------------------------------------------+
+--R | 7
+--R | b
+--R |- -----------------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R log
+--R 3 2
+--R (4a d - 4a b c)
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2 8 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 7 4 4
+--R 256a b c
+--R ,
+--R 4
+--R +
+--R 2
+--R b x
+--R +
+--R -
+--R 2 3
+--R 6a c x
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 4 7 4 3 8 3 2 2 9 2 3 10
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 11
+--R 256b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 4
+--R (4a c d - 4b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 4 7 4 3 8 3 2 2 9 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 10 4 11
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R +
+--R 2
+--R d x
+--R +
+--R -
+--R 3
+--R 6a c x
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 4 7 4 3 8 3 2 2 9 2 3 10
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 11
+--R 256b c
+--R ,
+--R 4
+--R *
+--R log
+--R 2 3
+--R (4a c d - 4b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 4 7 4 3 8 3 2 2 9 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 10 4 11
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R +
+--R 2
+--R d x
+--R +
+--R 3
+--R 6a c x
+--R *
+--R +-------------------------------------------------------------------+
+--R | 7
+--R | d
+--R |- -----------------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 2 3
+--R (- 4a c d + 4b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 4 7 4 3 8 3 2 2 9 2 3 10
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 11
+--R 256b c
+--R ,
+--R 4
+--R +
+--R 2
+--R d x
+--R +
+--R 2 3
+--R 6a c x
+--R *
+--R +-------------------------------------------------------------------+
+--R | 7
+--R | d
+--R |- -----------------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R log
+--R 3 4
+--R (- 4a c d + 4b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 4 7 4 3 8 3 2 2 9 2 3 10
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 11
+--R 256b c
+--R ,
+--R 4
+--R +
+--R 2
+--R d x
+--R +
+--R -
+--R 3
+--R 6a c x
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2 8 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 7 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 2
+--R (- 4a d + 4a b c)
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 8 3 3 7 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R +
+--R 2
+--R b x
+--R +
+--R - 2
+--R /
+--R 3
+--R 6a c x
+--R Type: Union(Expression(Integer),...)
+--E 259
+
+--S 260 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R a d \|a \|d log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - b c \|b \|c log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 2 3 +-+
+--R (- 2a c d + 2a b c )\|2
+--R *
+--R +-------------------------------------------------------------------+
+--R | 7
+--R | b
+--R |- -----------------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 6 2 4 2 4
+--R (16a d + 16a b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 8 3 3 7 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 2 3 2
+--R 8a b c x
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2 8 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 7 4 4
+--R 256a b c
+--R ,
+--R 4
+--R +
+--R 4 2
+--R b x
+--R +
+--R 2 2 3 +-+
+--R (2a c d - 2a b c )\|2
+--R *
+--R +-------------------------------------------------------------------+
+--R | 7
+--R | b
+--R |- -----------------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 6 2 4 2 4
+--R (16a d + 16a b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 8 3 3 7 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R -
+--R 2 3 2
+--R 8a b c x
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 8 3 3 7 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R +
+--R 4 2
+--R b x
+--R +
+--R 2 2 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R +-------------------------------------------------------------------+
+--R | 7
+--R | b
+--R |- -----------------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 3 2
+--R (4a d - 4a b c)
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2 8 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 7 4 4
+--R 256a b c
+--R ,
+--R 4
+--R +
+--R 2
+--R b x
+--R +
+--R 2 2 3 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R +-------------------------------------------------------------------+
+--R | 7
+--R | d
+--R |- -----------------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 3 4
+--R (4a c d - 4b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 4 7 4 3 8 3 2 2 9 2 3 10
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 11
+--R 256b c
+--R ,
+--R 4
+--R +
+--R 2
+--R d x
+--R +
+--R 2 2 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R +-------------------------------------------------------------------+
+--R | 7
+--R | d
+--R |- -----------------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2 3
+--R (4a c d - 4b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 4 7 4 3 8 3 2 2 9 2 3 10
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 11
+--R 256b c
+--R ,
+--R 4
+--R +
+--R 2
+--R d x
+--R +
+--R 2 2 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R +-------------------------------------------------------------------+
+--R | 7
+--R | d
+--R |- -----------------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 2 3
+--R (- 4a c d + 4b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 4 7 4 3 8 3 2 2 9 2 3 10
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 11
+--R 256b c
+--R ,
+--R 4
+--R +
+--R 2
+--R d x
+--R +
+--R 2 2 3 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R +-------------------------------------------------------------------+
+--R | 7
+--R | d
+--R |- -----------------------------------------------------------------
+--R 4| 4 7 4 3 8 3 2 2 9 2 3 10 4 11
+--R \| 256a c d - 1024a b c d + 1536a b c d - 1024a b c d + 256b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 3 4
+--R (- 4a c d + 4b c )
+--R *
+--R ROOT
+--R -
+--R 7
+--R d
+--R /
+--R 4 7 4 3 8 3 2 2 9 2 3 10
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 11
+--R 256b c
+--R ,
+--R 4
+--R +
+--R 2
+--R d x
+--R +
+--R 2 2 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R +-------------------------------------------------------------------+
+--R | 7
+--R | b
+--R |- -----------------------------------------------------------------
+--R 4| 11 4 10 3 9 2 2 2 8 3 3 7 4 4
+--R \| 256a d - 1024a b c d + 1536a b c d - 1024a b c d + 256a b c
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 3 2
+--R (- 4a d + 4a b c)
+--R *
+--R ROOT
+--R -
+--R 7
+--R b
+--R /
+--R 11 4 10 3 9 2 2 2 8 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 7 4 4
+--R 256a b c
+--R ,
+--R 4
+--R +
+--R 2
+--R b x
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R b c \|b \|c log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - a d \|a \|d log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+3 4+-+3 x\|2 \|d + \|c
+--R 2a d \|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+3 4+-+3 x\|2 \|d - \|c
+--R 2a d \|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+3 4+-+3 x\|2 \|b + \|a
+--R - 2b c \|b \|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+3 4+-+3 x\|2 \|b - \|a
+--R - 2b c \|b \|c atan(----------------)
+--R 4+-+
+--R \|a
+--R /
+--R 2 2 +-+4+-+3 4+-+3
+--R (4a c d - 4a b c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 260
+
+--S 261 of 716
+--d0:=D(m0,x)
+--E 261
+
+)clear all
+
+--S 262 of 716
+t0:=1/(x^5*(a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 13 9 5
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 262
+
+--S 263 of 716
+r0:=(-1/4)/(a*c*x^4)-(b*c+a*d)*log(x)/(a^2*c^2)+_
+ 1/4*b^2*log(a+b*x^4)/(a^2*(b*c-a*d))-1/4*d^2*log(c+d*x^4)/(c^2*(b*c-a*d))
+--R
+--R
+--R (2)
+--R 2 2 4 4 2 2 4 4 2 2 2 2 4
+--R a d x log(d x + c) - b c x log(b x + a) + (- 4a d + 4b c )x log(x)
+--R +
+--R 2 2
+--R - a c d + a b c
+--R /
+--R 3 2 2 3 4
+--R (4a c d - 4a b c )x
+--R Type: Expression(Integer)
+--E 263
+
+--S 264 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 4 4 2 2 4 4 2 2 2 2 4
+--R a d x log(d x + c) - b c x log(b x + a) + (- 4a d + 4b c )x log(x)
+--R +
+--R 2 2
+--R - a c d + a b c
+--R /
+--R 3 2 2 3 4
+--R (4a c d - 4a b c )x
+--R Type: Union(Expression(Integer),...)
+--E 264
+
+--S 265 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 265
+
+--S 266 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 266
+
+)clear all
+
+--S 267 of 716
+t0:=1/(x^6*(a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R 14 10 6
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 267
+
+--S 268 of 716
+r0:=(-1/5)/(a*c*x^5)+(b*c+a*d)/(a^2*c^2*x)-1/2*b^(9/4)*atan(1-b^(1/4)*x*_
+ sqrt(2)/a^(1/4))/(a^(9/4)*(b*c-a*d)*sqrt(2))+1/2*b^(9/4)*_
+ atan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(9/4)*(b*c-a*d)*sqrt(2))+_
+ 1/2*d^(9/4)*atan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(9/4)*(b*c-a*d)*_
+ sqrt(2))-1/2*d^(9/4)*atan(1+d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(9/4)*_
+ (b*c-a*d)*sqrt(2))+1/4*b^(9/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+_
+ sqrt(a)+x^2*sqrt(b))/(a^(9/4)*(b*c-a*d)*sqrt(2))-1/4*b^(9/4)*_
+ log(a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(9/4)*_
+ (b*c-a*d)*sqrt(2))-1/4*d^(9/4)*log(-c^(1/4)*d^(1/4)*x*sqrt(2)+_
+ sqrt(c)+x^2*sqrt(d))/(c^(9/4)*(b*c-a*d)*sqrt(2))+1/4*d^(9/4)*_
+ log(c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(9/4)*_
+ (b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 5 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - 5a d x \|a \|d log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 2 2 5 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R 5b c x \|b \|c log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 2 5 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - 5b c x \|b \|c log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 2 5 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R 5a d x \|a \|d log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 5 4+-+4+-+ x\|2 \|d + \|c
+--R 10a d x \|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 5 4+-+4+-+ x\|2 \|d - \|c
+--R 10a d x \|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 5 4+-+4+-+ x\|2 \|b + \|a
+--R - 10b c x \|b \|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 5 4+-+4+-+ x\|2 \|b - \|a
+--R - 10b c x \|b \|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 4 2 2 +-+4+-+4+-+
+--R ((20a d - 20b c )x - 4a c d + 4a b c )\|2 \|a \|c
+--R /
+--R 3 2 2 3 5 +-+4+-+4+-+
+--R (20a c d - 20a b c )x \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 268
+
+--S 269 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 2 3 5
+--R 5a c x
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2 10 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 9 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 13 2 6 12 3 5 11 2 4 4 10 3 5 3
+--R 384a c d - 1920a b c d + 3968a b c d - 4352a b c d
+--R +
+--R 9 4 6 2 8 5 7 7 6 8
+--R 2688a b c d - 896a b c d + 128a b c
+--R *
+--R x
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 10 3 3 9 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 11 6 9 3 4 4 8 4 5 3 7 5 6 2
+--R - 16a b d - 144a b c d + 288a b c d - 240a b c d
+--R +
+--R 6 6 7 5 7 8
+--R 96a b c d - 16a b c
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 10 3 3 9 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 4 6 4 3 7 3 2 8 2 2 9 3 10 4 2
+--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c )x
+--R +
+--R -
+--R 2 2 5
+--R 10a c x
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2 10 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 9 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 10 3 9 2 8 2 2 7 3 3
+--R (64a d - 192a b c d + 192a b c d - 64a b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 10 3 3 9 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 7
+--R b x
+--R +
+--R -
+--R 2 3 5
+--R 10a c x
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2 3 12
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 13
+--R 256b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 8 3 2 9 2 2 10 3 11
+--R (64a c d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 12 4 13
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 7
+--R d x
+--R +
+--R 2 2 5
+--R 10a c x
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2 3 12
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 13
+--R 256b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 7 3 2 8 2 2 9 3 10
+--R (64a c d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 12 4 13
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 7
+--R d x
+--R +
+--R -
+--R 2 2 5
+--R 10a c x
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2 3 12
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 13
+--R 256b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 7 3 2 8 2 2 9 3 10
+--R (- 64a c d + 192a b c d - 192a b c d + 64b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 12 4 13
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 7
+--R d x
+--R +
+--R 2 3 5
+--R 10a c x
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2 3 12
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 13
+--R 256b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 8 3 2 9 2 2 10 3 11
+--R (- 64a c d + 192a b c d - 192a b c d + 64b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 12 4 13
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 7
+--R d x
+--R +
+--R 2 2 5
+--R 10a c x
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2 10 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 9 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 10 3 9 2 8 2 2 7 3 3
+--R (- 64a d + 192a b c d - 192a b c d + 64a b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 10 3 3 9 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 7
+--R b x
+--R +
+--R 2 3 5
+--R 5a c x
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2 10 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 9 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 13 2 6 12 3 5 11 2 4 4 10 3 5 3
+--R - 384a c d + 1920a b c d - 3968a b c d + 4352a b c d
+--R +
+--R 9 4 6 2 8 5 7 7 6 8
+--R - 2688a b c d + 896a b c d - 128a b c
+--R *
+--R x
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 10 3 3 9 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 11 6 9 3 4 4 8 4 5 3 7 5 6 2
+--R - 16a b d - 144a b c d + 288a b c d - 240a b c d
+--R +
+--R 6 6 7 5 7 8
+--R 96a b c d - 16a b c
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 10 3 3 9 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 4 6 4 3 7 3 2 8 2 2 9 3 10 4 2
+--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c )x
+--R +
+--R 4
+--R (10a d + 10b c)x - 2a c
+--R /
+--R 2 2 5
+--R 10a c x
+--R Type: Union(Expression(Integer),...)
+--E 269
+
+--S 270 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R a d \|a \|d log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - b c \|b \|c log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 3 3 2 4 +-+
+--R (- 2a c d + 2a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2 10 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 9 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 13 2 6 12 3 5 11 2 4 4 10 3 5 3
+--R 384a c d - 1920a b c d + 3968a b c d - 4352a b c d
+--R +
+--R 9 4 6 2 8 5 7 7 6 8
+--R 2688a b c d - 896a b c d + 128a b c
+--R *
+--R x
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 10 3 3 9 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 11 6 9 3 4 4 8 4 5 3 7 5 6 2
+--R - 16a b d - 144a b c d + 288a b c d - 240a b c d
+--R +
+--R 6 6 7 5 7 8
+--R 96a b c d - 16a b c
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 10 3 3 9 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 4 6 4 3 7 3 2 8 2 2 9 3 10 4 2
+--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c )x
+--R +
+--R 3 2 2 3 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2 10 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 9 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 10 3 9 2 8 2 2 7 3 3
+--R (64a d - 192a b c d + 192a b c d - 64a b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 10 3 3 9 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 7
+--R b x
+--R +
+--R 3 3 2 4 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2 3 12
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 13
+--R 256b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 8 3 2 9 2 2 10 3 11
+--R (64a c d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 12 4 13
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 7
+--R d x
+--R +
+--R 3 2 2 3 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2 3 12
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 13
+--R 256b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 7 3 2 8 2 2 9 3 10
+--R (64a c d - 192a b c d + 192a b c d - 64b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 12 4 13
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 7
+--R d x
+--R +
+--R 3 2 2 3 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2 3 12
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 13
+--R 256b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 7 3 2 8 2 2 9 3 10
+--R (- 64a c d + 192a b c d - 192a b c d + 64b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 12 4 13
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 7
+--R d x
+--R +
+--R 3 3 2 4 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2 3 12
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 13
+--R 256b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 3 8 3 2 9 2 2 10 3 11
+--R (- 64a c d + 192a b c d - 192a b c d + 64b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R d
+--R /
+--R 4 9 4 3 10 3 2 2 11 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 12 4 13
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 7
+--R d x
+--R +
+--R 3 2 2 3 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2 10 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 9 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 10 3 9 2 8 2 2 7 3 3
+--R (- 64a d + 192a b c d - 192a b c d + 64a b c )
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 10 3 3 9 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 7
+--R b x
+--R +
+--R 3 3 2 4 +-+
+--R (2a c d - 2a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2 10 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 9 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R 4+-+4+-+
+--R \|a \|c
+--R *
+--R log
+--R 13 2 6 12 3 5 11 2 4 4 10 3 5 3
+--R - 384a c d + 1920a b c d - 3968a b c d + 4352a b c d
+--R +
+--R 9 4 6 2 8 5 7 7 6 8
+--R - 2688a b c d + 896a b c d - 128a b c
+--R *
+--R x
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 10 3 3 9 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 3
+--R +
+--R 11 6 9 3 4 4 8 4 5 3 7 5 6 2
+--R - 16a b d - 144a b c d + 288a b c d - 240a b c d
+--R +
+--R 6 6 7 5 7 8
+--R 96a b c d - 16a b c
+--R *
+--R ROOT
+--R -
+--R 9
+--R b
+--R /
+--R 13 4 12 3 11 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 10 3 3 9 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 4 6 4 3 7 3 2 8 2 2 9 3 10 4 2
+--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c )x
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R b c \|b \|c log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 2 4+-+4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - a d \|a \|d log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 4+-+4+-+ x\|2 \|d + \|c
+--R - 2a d \|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 4+-+4+-+ x\|2 \|d - \|c
+--R - 2a d \|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 2 2 4+-+4+-+ x\|2 \|b + \|a 2 2 4+-+4+-+ x\|2 \|b - \|a
+--R 2b c \|b \|c atan(---------------- + 2b c \|b \|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R /
+--R 3 2 2 3 +-+4+-+4+-+
+--R (4a c d - 4a b c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 270
+
+--S 271 of 716
+--d0:=D(m0,x)
+--E 271
+
+)clear all
+
+--S 272 of 716
+t0:=1/(x^7*(a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R 15 11 7
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 272
+
+--S 273 of 716
+r0:=(-1/6)/(a*c*x^6)+1/2*(b*c+a*d)/(a^2*c^2*x^2)+1/2*b^(5/2)*_
+ atan(x^2*sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-a*d))-1/2*d^(5/2)*_
+ atan(x^2*sqrt(d)/sqrt(c))/(c^(5/2)*(b*c-a*d))
+--R
+--R
+--R (2)
+--R 2 +-+ 2 +-+
+--R 2 2 6 +-+ +-+ x \|d 2 2 6 +-+ +-+ x \|b
+--R 3a d x \|a \|d atan(------) - 3b c x \|b \|c atan(------)
+--R +-+ +-+
+--R \|c \|a
+--R +
+--R 2 2 2 2 4 2 2 +-+ +-+
+--R ((3a d - 3b c )x - a c d + a b c )\|a \|c
+--R /
+--R 3 2 2 3 6 +-+ +-+
+--R (6a c d - 6a b c )x \|a \|c
+--R Type: Expression(Integer)
+--E 273
+
+--S 274 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 2 | d 4
+--R +---+ 2c x |- - + d x - c
+--R 2 2 6 | d \| c
+--R 3a d x |- - log(----------------------)
+--R \| c 4
+--R d x + c
+--R +
+--R +---+
+--R 2 | b 4
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 6 | b \| a 2 2 2 2 4 2
+--R 3b c x |- - log(------------------------) + (6a d - 6b c )x - 2a c d
+--R \| a 4
+--R b x + a
+--R +
+--R 2
+--R 2a b c
+--R /
+--R 3 2 2 3 6
+--R (12a c d - 12a b c )x
+--R ,
+--R
+--R +---+ +-+
+--R 2 | b 4 |d
+--R +---+ - 2a x |- - + b x - a +-+ c |-
+--R 2 2 6 | b \| a 2 2 6 |d \|c
+--R 3b c x |- - log(------------------------) - 6a d x |- atan(-----)
+--R \| a 4 \|c 2
+--R b x + a d x
+--R +
+--R 2 2 2 2 4 2 2
+--R (6a d - 6b c )x - 2a c d + 2a b c
+--R /
+--R 3 2 2 3 6
+--R (12a c d - 12a b c )x
+--R ,
+--R
+--R +---+ +-+
+--R 2 | d 4 |b
+--R +---+ 2c x |- - + d x - c +-+ a |-
+--R 2 2 6 | d \| c 2 2 6 |b \|a
+--R 3a d x |- - log(----------------------) + 6b c x |- atan(-----)
+--R \| c 4 \|a 2
+--R d x + c b x
+--R +
+--R 2 2 2 2 4 2 2
+--R (6a d - 6b c )x - 2a c d + 2a b c
+--R /
+--R 3 2 2 3 6
+--R (12a c d - 12a b c )x
+--R ,
+--R
+--R +-+ +-+
+--R |d |b
+--R +-+ c |- +-+ a |-
+--R 2 2 6 |d \|c 2 2 6 |b \|a 2 2 2 2 4
+--R - 3a d x |- atan(-----) + 3b c x |- atan(-----) + (3a d - 3b c )x
+--R \|c 2 \|a 2
+--R d x b x
+--R +
+--R 2 2
+--R - a c d + a b c
+--R /
+--R 3 2 2 3 6
+--R (6a c d - 6a b c )x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 274
+
+--S 275 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R 2 | d 4
+--R +---+ 2c x |- - + d x - c
+--R 2 2 | d +-+ +-+ \| c
+--R a d |- - \|a \|c log(----------------------)
+--R \| c 4
+--R d x + c
+--R +
+--R +---+
+--R 2 | b 4
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R b c |- - \|a \|c log(------------------------)
+--R \| a 4
+--R b x + a
+--R +
+--R 2 +-+ 2 +-+
+--R 2 2 +-+ +-+ x \|d 2 2 +-+ +-+ x \|b
+--R - 2a d \|a \|d atan(------) + 2b c \|b \|c atan(------)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 3 2 2 3 +-+ +-+
+--R (4a c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 275
+
+--S 276 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 | b 4
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R b c |- - \|a \|c log(------------------------)
+--R \| a 4
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R 2 +-+ +-+ c |-
+--R 2 2 +-+ +-+ x \|d 2 2 +-+ +-+ |d \|c
+--R - 2a d \|a \|d atan(------) - 2a d \|a \|c |- atan(-----)
+--R +-+ \|c 2
+--R \|c d x
+--R +
+--R 2 +-+
+--R 2 2 +-+ +-+ x \|b
+--R 2b c \|b \|c atan(------)
+--R +-+
+--R \|a
+--R /
+--R 3 2 2 3 +-+ +-+
+--R (4a c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 278
+
+)clear all
+
+--S 279 of 716
+t0:=1/(x^8*(a+b*x^4)*(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R 16 12 8
+--R b d x + (a d + b c)x + a c x
+--R Type: Fraction(Polynomial(Integer))
+--E 279
+
+--S 280 of 716
+r0:=(-1/7)/(a*c*x^7)+1/3*(b*c+a*d)/(a^2*c^2*x^3)-1/2*b^(11/4)*_
+ atan(1-b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*(b*c-a*d)*sqrt(2))+_
+ 1/2*b^(11/4)*atan(1+b^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*(b*c-a*d)*_
+ sqrt(2))+1/2*d^(11/4)*atan(1-d^(1/4)*x*sqrt(2)/c^(1/4))/(c^(11/4)*_
+ (b*c-a*d)*sqrt(2))-1/2*d^(11/4)*atan(1+d^(1/4)*x*sqrt(2)/c^(1/4))/_
+ (c^(11/4)*(b*c-a*d)*sqrt(2))-1/4*b^(11/4)*log(-a^(1/4)*b^(1/4)*x*_
+ sqrt(2)+sqrt(a)+x^2*sqrt(b))/(a^(11/4)*(b*c-a*d)*sqrt(2))+_
+ 1/4*b^(11/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(b))/_
+ (a^(11/4)*(b*c-a*d)*sqrt(2))+1/4*d^(11/4)*log(-c^(1/4)*d^(1/4)*x*_
+ sqrt(2)+sqrt(c)+x^2*sqrt(d))/(c^(11/4)*(b*c-a*d)*sqrt(2))-_
+ 1/4*d^(11/4)*log(c^(1/4)*d^(1/4)*x*sqrt(2)+sqrt(c)+x^2*sqrt(d))/_
+ (c^(11/4)*(b*c-a*d)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 2 7 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R 21a d x \|a \|d log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 2 2 7 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - 21b c x \|b \|c log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 2 7 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R 21b c x \|b \|c log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 2 7 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - 21a d x \|a \|d log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 7 4+-+3 4+-+3 x\|2 \|d + \|c
+--R 42a d x \|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 7 4+-+3 4+-+3 x\|2 \|d - \|c
+--R 42a d x \|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 7 4+-+3 4+-+3 x\|2 \|b + \|a
+--R - 42b c x \|b \|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 7 4+-+3 4+-+3 x\|2 \|b - \|a
+--R - 42b c x \|b \|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 2 2 2 4 2 2 +-+4+-+3 4+-+3
+--R ((28a d - 28b c )x - 12a c d + 12a b c )\|2 \|a \|c
+--R /
+--R 3 2 2 3 7 +-+4+-+3 4+-+3
+--R (84a c d - 84a b c )x \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 280
+
+--S 281 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 7
+--R 21a c x
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2 12 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 11 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 8 2 6 2 4
+--R (16a d + 16a b c )
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 12 3 3 11 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 3 4 2
+--R 8a b c x
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 12 3 3 11 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R +
+--R 6 2
+--R b x
+--R +
+--R -
+--R 2 3 7
+--R 21a c x
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2 12 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 11 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 8 2 6 2 4
+--R (16a d + 16a b c )
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 12 3 3 11 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R -
+--R 3 4 2
+--R 8a b c x
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 12 3 3 11 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R +
+--R 6 2
+--R b x
+--R +
+--R -
+--R 2 2 7
+--R 42a c x
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2 12 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 11 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 4 3
+--R (4a d - 4a b c)
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 12 3 3 11 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R +
+--R 3
+--R b x
+--R +
+--R 2 3 7
+--R 42a c x
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2 3 14
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 15
+--R 256b c
+--R ,
+--R 4
+--R *
+--R log
+--R 4 5
+--R (4a c d - 4b c )
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 14 4 15
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R +
+--R 3
+--R d x
+--R +
+--R 2 2 7
+--R 42a c x
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2 3 14
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 15
+--R 256b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 4
+--R (4a c d - 4b c )
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 14 4 15
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R +
+--R 3
+--R d x
+--R +
+--R -
+--R 2 2 7
+--R 42a c x
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2 3 14
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 15
+--R 256b c
+--R ,
+--R 4
+--R *
+--R log
+--R 3 4
+--R (- 4a c d + 4b c )
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 14 4 15
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R +
+--R 3
+--R d x
+--R +
+--R -
+--R 2 3 7
+--R 42a c x
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2 3 14
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 15
+--R 256b c
+--R ,
+--R 4
+--R *
+--R log
+--R 4 5
+--R (- 4a c d + 4b c )
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 14 4 15
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R +
+--R 3
+--R d x
+--R +
+--R 2 2 7
+--R 42a c x
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2 12 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 11 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R log
+--R 4 3
+--R (- 4a d + 4a b c)
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 12 3 3 11 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R +
+--R 3
+--R b x
+--R +
+--R 4
+--R (14a d + 14b c)x - 6a c
+--R /
+--R 2 2 7
+--R 42a c x
+--R Type: Union(Expression(Integer),...)
+--E 281
+
+--S 282 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - a d \|a \|d log(x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R 2 2 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R b c \|b \|c log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 3 3 2 4 +-+
+--R (2a c d - 2a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2 12 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 11 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 8 2 6 2 4
+--R (16a d + 16a b c )
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 12 3 3 11 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R 3 4 2
+--R 8a b c x
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 12 3 3 11 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R +
+--R 6 2
+--R b x
+--R +
+--R 3 3 2 4 +-+
+--R (- 2a c d + 2a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2 12 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 11 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 8 2 6 2 4
+--R (16a d + 16a b c )
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 12 3 3 11 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R **
+--R 2
+--R +
+--R -
+--R 3 4 2
+--R 8a b c x
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 12 3 3 11 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R +
+--R 6 2
+--R b x
+--R +
+--R 3 2 2 3 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2 12 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 11 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 4 3
+--R (4a d - 4a b c)
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 12 3 3 11 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R +
+--R 3
+--R b x
+--R +
+--R 3 3 2 4 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2 3 14
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 15
+--R 256b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 4 5
+--R (4a c d - 4b c )
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 14 4 15
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R +
+--R 3
+--R d x
+--R +
+--R 3 2 2 3 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2 3 14
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 15
+--R 256b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 3 4
+--R (4a c d - 4b c )
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 14 4 15
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R +
+--R 3
+--R d x
+--R +
+--R 3 2 2 3 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2 3 14
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 15
+--R 256b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 3 4
+--R (- 4a c d + 4b c )
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 14 4 15
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R +
+--R 3
+--R d x
+--R +
+--R 3 3 2 4 +-+
+--R (- 4a c d + 4a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2 3 14
+--R 256a c d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 4 15
+--R 256b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 4 5
+--R (- 4a c d + 4b c )
+--R *
+--R ROOT
+--R -
+--R 11
+--R d
+--R /
+--R 4 11 4 3 12 3 2 2 13 2
+--R 256a c d - 1024a b c d + 1536a b c d
+--R +
+--R 3 14 4 15
+--R - 1024a b c d + 256b c
+--R ,
+--R 4
+--R +
+--R 3
+--R d x
+--R +
+--R 3 2 2 3 +-+
+--R (4a c d - 4a b c )\|2
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2 12 3 3
+--R 256a d - 1024a b c d + 1536a b c d - 1024a b c d
+--R +
+--R 11 4 4
+--R 256a b c
+--R ,
+--R 4
+--R *
+--R 4+-+3 4+-+3
+--R \|a \|c
+--R *
+--R log
+--R 4 3
+--R (- 4a d + 4a b c)
+--R *
+--R ROOT
+--R -
+--R 11
+--R b
+--R /
+--R 15 4 14 3 13 2 2 2
+--R 256a d - 1024a b c d + 1536a b c d
+--R +
+--R 12 3 3 11 4 4
+--R - 1024a b c d + 256a b c
+--R ,
+--R 4
+--R +
+--R 3
+--R b x
+--R +
+--R 2 2 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - b c \|b \|c log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 2 4+-+3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R a d \|a \|d log(- x\|2 \|c \|d + x \|d + \|c )
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 4+-+3 4+-+3 x\|2 \|d + \|c
+--R - 2a d \|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 4+-+3 4+-+3 x\|2 \|d - \|c
+--R - 2a d \|a \|d atan(----------------)
+--R 4+-+
+--R \|c
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 4+-+3 4+-+3 x\|2 \|b + \|a
+--R 2b c \|b \|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 2 2 4+-+3 4+-+3 x\|2 \|b - \|a
+--R 2b c \|b \|c atan(----------------)
+--R 4+-+
+--R \|a
+--R /
+--R 3 2 2 3 +-+4+-+3 4+-+3
+--R (4a c d - 4a b c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 716
+--d0:=D(m0,x)
+--E 283
+
+)clear all
+
+--S 284 of 716
+t0:=x^8*sqrt(c+d*x^4)/(a+b*x^4)
+--R
+--R
+--R +--------+
+--R 8 | 4
+--R x \|d x + c
+--R (1) -------------
+--R 4
+--R b x + a
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 716
+--r0:=1/21*(2*b*c-7*a*d)*x*sqrt(c+d*x^4)/(b^2*d)+1/7*x^5*_
+-- sqrt(c+d*x^4)/b+1/21*c^(1/4)*(2*b^2*c^2+14*a*b*c*d-21*a^2*d^2)*_
+-- elliptic_f(asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/_
+-- (b^3*(-d)^(5/4)*sqrt(c+d*x^4))+1/2*a*(b*c-a*d)*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/(b^3*_
+-- sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))+1/2*a*(b*c-a*d)*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(x*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/(b^3*sqrt(c+_
+-- d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 285
+
+--S 286 of 716
+--a0:=integrate(t0,x)
+--E 286
+
+--S 287 of 716
+--m0:=a0-r0
+--E 287
+
+--S 288 of 716
+--d0:=D(m0,x)
+--E 288
+
+)clear all
+
+--S 289 of 716
+t0:=x^7*sqrt(c+d*x^4)/(a+b*x^4)
+--R
+--R
+--R +--------+
+--R 7 | 4
+--R x \|d x + c
+--R (1) -------------
+--R 4
+--R b x + a
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 716
+r0:=1/6*(c+d*x^4)^(3/2)/(b*d)+1/2*a*atanh(sqrt(b)*sqrt(c+d*x^4)/_
+ sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(5/2)-1/2*a*sqrt(c+d*x^4)/b^2
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 4
+--R +-----------+ \|b \|d x + c
+--R 3a d\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R 4 +-+ | 4
+--R (b d x - 3a d + b c)\|b \|d x + c
+--R /
+--R 2 +-+
+--R 6b d\|b
+--R Type: Expression(Integer)
+--E 290
+
+--S 291 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+
+--R |- a d + b c
+--R 3a d |-----------
+--R \| b
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 4 4
+--R 2b |----------- \|d x + c + b d x - a d + 2b c
+--R \| b
+--R log(-------------------------------------------------)
+--R 4
+--R b x + a
+--R +
+--R +--------+
+--R 4 | 4
+--R (2b d x - 6a d + 2b c)\|d x + c
+--R /
+--R 2
+--R 12b d
+--R ,
+--R +--------+
+--R +---------+ | 4 +--------+
+--R |a d - b c \|d x + c 4 | 4
+--R 3a d |--------- atan(------------) + (b d x - 3a d + b c)\|d x + c
+--R \| b +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R ---------------------------------------------------------------------]
+--R 2
+--R 6b d
+--R Type: Union(List(Expression(Integer)),...)
+--E 291
+
+--S 292 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +--------+
+--R |- a d + b c | 4 4
+--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c
+--R |- a d + b c +-+ \| b
+--R a |----------- \|b log(-------------------------------------------------)
+--R \| b 4
+--R b x + a
+--R +
+--R +--------+
+--R +-+ | 4
+--R +-----------+ \|b \|d x + c
+--R - 2a\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R /
+--R 2 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 293
+
+--S 294 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+ +--------+
+--R +-+ | 4 +---------+ | 4
+--R +-----------+ \|b \|d x + c +-+ |a d - b c \|d x + c
+--R - a\|- a d + b c atanh(---------------) + a\|b |--------- atan(------------)
+--R +-----------+ \| b +---------+
+--R \|- a d + b c |a d - b c
+--R |---------
+--R \| b
+--R -----------------------------------------------------------------------------
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 716
+t0:=x^6*sqrt(c+d*x^4)/(a+b*x^4)
+--R
+--R
+--R +--------+
+--R 6 | 4
+--R x \|d x + c
+--R (1) -------------
+--R 4
+--R b x + a
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 716
+--r0:=1/5*x^3*sqrt(c+d*x^4)/b+1/5*c^(3/4)*(2*b*c-5*a*d)*_
+-- elliptic_e(asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/_
+-- (b^2*(-d)^(3/4)*sqrt(c+d*x^4))-1/5*c^(3/4)*(2*b*c-5*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/_
+-- (b^2*(-d)^(3/4)*sqrt(c+d*x^4))-1/2*(b*c-a*d)*elliptic_pi(-sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt(-a)*sqrt((c+d*x^4)/c)/(b^(5/2)*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/_
+-- sqrt(c)))+1/2*(b*c-a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*_
+-- sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(-a)*_
+-- sqrt((c+d*x^4)/c)/(b^(5/2)*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 297
+
+--S 298 of 716
+--a0:=integrate(t0,x)
+--E 298
+
+--S 299 of 716
+--m0:=a0-r0
+--E 299
+
+--S 300 of 716
+--d0:=D(m0,x)
+--E 300
+
+)clear all
+
+--S 301 of 716
+t0:=x^5*sqrt(c+d*x^4)/(a+b*x^4)
+--R
+--R
+--R +--------+
+--R 5 | 4
+--R x \|d x + c
+--R (1) -------------
+--R 4
+--R b x + a
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 716
+r0:=1/4*(b*c-2*a*d)*atanh(x^2*sqrt(d)/sqrt(c+d*x^4))/(b^2*sqrt(d))-_
+ 1/2*atan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))*sqrt(a)*_
+ sqrt(b*c-a*d)/b^2+1/4*x^2*sqrt(c+d*x^4)/b
+--R
+--R
+--R (2)
+--R 2 +-+
+--R x \|d
+--R (- 2a d + b c)atanh(-----------)
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R 2 +-----------+ +--------+
+--R +-----------+ +-+ +-+ x \|- a d + b c 2 +-+ | 4
+--R - 2\|- a d + b c \|a \|d atan(----------------) + b x \|d \|d x + c
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 4b \|d
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 4 2 4 2
+--R ((4a d - 2b c)\|c \|d x + c + (- 2a d + b c d)x - 4a c d + 2b c )
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|c \|d + d x )\|d x + c + (- d x - c)\|d - d x \|c
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|c \|d x + c - c
+--R +
+--R +-----------+ +--------+
+--R +-+ +-+ | 2 | 4
+--R 2\|c \|d \|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 4 +-+ | 2
+--R (- d x - 2c)\|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 6 2 | 2
+--R (- 2d x - 4c x )\|a d - a b c
+--R +
+--R 4 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R +-----------+
+--R 6 2 +-+ | 2 2 8
+--R (4d x + 4c x )\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 4 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 6 2 +-+ | 4 6 2 +-+ +-+
+--R (- b d x - 2b c x )\|d \|d x + c + (2b d x + 2b c x )\|c \|d
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 4 2 4 2 +-+
+--R 8b \|c \|d \|d x + c + (- 4b d x - 8b c)\|d
+--R ,
+--R
+--R +--------+
+--R +-+ | 4 2 4 2
+--R ((4a d - 2b c)\|c \|d x + c + (- 2a d + b c d)x - 4a c d + 2b c )
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|c \|d + d x )\|d x + c + (- d x - c)\|d - d x \|c
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|c \|d x + c - c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-+ +-+ | 4
+--R 4\|- a d + a b c \|c \|d \|d x + c
+--R +
+--R +-------------+
+--R 4 | 2 +-+
+--R (- 2d x - 4c)\|- a d + a b c \|d
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 6 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+ +--------+
+--R | 2 +-+ +-+ | 4
+--R - 4\|- a d + a b c \|c \|d \|d x + c
+--R +
+--R +-------------+
+--R 4 | 2 +-+
+--R (2d x + 4c)\|- a d + a b c \|d
+--R *
+--R +-+
+--R a\|c
+--R atan(------------------)
+--R +-------------+
+--R 2 | 2
+--R x \|- a d + a b c
+--R +
+--R +--------+
+--R 6 2 +-+ | 4 6 2 +-+ +-+
+--R (- b d x - 2b c x )\|d \|d x + c + (2b d x + 2b c x )\|c \|d
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 4 2 4 2 +-+
+--R 8b \|c \|d \|d x + c + (- 4b d x - 8b c)\|d
+--R ,
+--R
+--R +-----------+ +--------+
+--R +---+ +-+ | 2 | 4
+--R 2\|- d \|c \|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 4 +---+ | 2
+--R (- d x - 2c)\|- d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 6 2 | 2
+--R (- 2d x - 4c x )\|a d - a b c
+--R +
+--R 4 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R +-----------+
+--R 6 2 +-+ | 2 2 8
+--R (4d x + 4c x )\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 4 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ | 4 2 4
+--R (- 8a d + 4b c)\|c \|d x + c + (4a d - 2b c d)x + 8a c d
+--R +
+--R 2
+--R - 4b c
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R 2
+--R d x
+--R +
+--R +--------+
+--R 6 2 +---+ | 4 6 2 +---+ +-+
+--R (- b d x - 2b c x )\|- d \|d x + c + (2b d x + 2b c x )\|- d \|c
+--R /
+--R +--------+
+--R 2 +---+ +-+ | 4 2 4 2 +---+
+--R 8b \|- d \|c \|d x + c + (- 4b d x - 8b c)\|- d
+--R ,
+--R
+--R +--------+
+--R +-+ | 4 2 4
+--R (- 8a d + 4b c)\|c \|d x + c + (4a d - 2b c d)x + 8a c d
+--R +
+--R 2
+--R - 4b c
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- d \|d x + c - \|- d \|c
+--R atan(------------------------------)
+--R 2
+--R d x
+--R +
+--R +-------------+ +--------+
+--R | 2 +---+ +-+ | 4
+--R 4\|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R +-------------+
+--R 4 | 2 +---+
+--R (- 2d x - 4c)\|- a d + a b c \|- d
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 6 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+ +--------+
+--R | 2 +---+ +-+ | 4
+--R - 4\|- a d + a b c \|- d \|c \|d x + c
+--R +
+--R +-------------+
+--R 4 | 2 +---+
+--R (2d x + 4c)\|- a d + a b c \|- d
+--R *
+--R +-+
+--R a\|c
+--R atan(------------------)
+--R +-------------+
+--R 2 | 2
+--R x \|- a d + a b c
+--R +
+--R +--------+
+--R 6 2 +---+ | 4 6 2 +---+ +-+
+--R (- b d x - 2b c x )\|- d \|d x + c + (2b d x + 2b c x )\|- d \|c
+--R /
+--R +--------+
+--R 2 +---+ +-+ | 4 2 4 2 +---+
+--R 8b \|- d \|c \|d x + c + (- 4b d x - 8b c)\|- d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 303
+
+--S 304 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R (2a d - b c)
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|c \|d + d x )\|d x + c + (- d x - c)\|d - d x \|c
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|c \|d x + c - c
+--R +
+--R +-----------+
+--R +-+ | 2
+--R \|d \|a d - a b c
+--R *
+--R log
+--R +-----------+
+--R 6 2 | 2
+--R (- 2d x - 4c x )\|a d - a b c
+--R +
+--R 4 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R +-----------+
+--R 6 2 +-+ | 2 2 8
+--R (4d x + 4c x )\|c \|a d - a b c + (- 2a d + b c d)x
+--R +
+--R 2 4 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 +-+
+--R x \|d
+--R (2a d - b c)atanh(-----------)
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R 2 +-----------+
+--R +-----------+ +-+ +-+ x \|- a d + b c
+--R 2\|- a d + b c \|a \|d atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 4b \|d
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 305
+
+--S 306 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R (2a d - b c)
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|c \|d + d x )\|d x + c + (- d x - c)\|d - d x \|c
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|c \|d x + c - c
+--R +
+--R 2 +-+
+--R x \|d
+--R (2a d - b c)atanh(-----------)
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 2\|- a d + a b c \|d
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 6 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+ +-+
+--R | 2 +-+ a\|c
+--R - 2\|- a d + a b c \|d atan(------------------)
+--R +-------------+
+--R 2 | 2
+--R x \|- a d + a b c
+--R +
+--R 2 +-----------+
+--R +-----------+ +-+ +-+ x \|- a d + b c
+--R 2\|- a d + b c \|a \|d atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 4b \|d
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 307
+
+)clear all
+
+--S 308 of 716
+t0:=x^4*sqrt(c+d*x^4)/(a+b*x^4)
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R x \|d x + c
+--R (1) -------------
+--R 4
+--R b x + a
+--R Type: Expression(Integer)
+--E 308
+
+--S 309 of 716
+--r0:=1/3*x*sqrt(c+d*x^4)/b+1/3*c^(1/4)*(2*b*c-3*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/_
+-- (b^2*(-d)^(1/4)*sqrt(c+d*x^4))-1/2*(b*c-a*d)*elliptic_pi(-sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^4)/c)/(b^2*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 1/2*(b*c-a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/(b^2*_
+-- sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 309
+
+--S 310 of 716
+--a0:=integrate(t0,x)
+--E 310
+
+--S 311 of 716
+--m0:=a0-r0
+--E 311
+
+--S 312 of 716
+--d0:=D(m0,x)
+--E 312
+
+)clear all
+
+--S 313 of 716
+t0:=x^3*sqrt(c+d*x^4)/(a+b*x^4)
+--R
+--R
+--R +--------+
+--R 3 | 4
+--R x \|d x + c
+--R (1) -------------
+--R 4
+--R b x + a
+--R Type: Expression(Integer)
+--E 313
+
+--S 314 of 716
+r0:=-1/2*atanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/b^(3/2)+_
+ 1/2*sqrt(c+d*x^4)/b
+--R
+--R
+--R +--------+
+--R +-+ | 4 +--------+
+--R +-----------+ \|b \|d x + c +-+ | 4
+--R - \|- a d + b c atanh(---------------) + \|b \|d x + c
+--R +-----------+
+--R \|- a d + b c
+--R (2) --------------------------------------------------------
+--R +-+
+--R 2b\|b
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+ +--------+
+--R |- a d + b c | 4 4
+--R +-----------+ - 2b |----------- \|d x + c + b d x - a d + 2b c
+--R |- a d + b c \| b
+--R |----------- log(---------------------------------------------------)
+--R \| b 4
+--R b x + a
+--R +
+--R +--------+
+--R | 4
+--R 2\|d x + c
+--R /
+--R 4b
+--R ,
+--R +--------+
+--R +---------+ | 4 +--------+
+--R |a d - b c \|d x + c | 4
+--R - |--------- atan(------------) + \|d x + c
+--R \| b +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R ----------------------------------------------]
+--R 2b
+--R Type: Union(List(Expression(Integer)),...)
+--E 315
+
+--S 316 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|b
+--R \| b
+--R *
+--R +-----------+ +--------+
+--R |- a d + b c | 4 4
+--R - 2b |----------- \|d x + c + b d x - a d + 2b c
+--R \| b
+--R log(---------------------------------------------------)
+--R 4
+--R b x + a
+--R +
+--R +--------+
+--R +-+ | 4
+--R +-----------+ \|b \|d x + c
+--R 2\|- a d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R /
+--R +-+
+--R 4b\|b
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+ +--------+
+--R +-+ | 4 +---------+ | 4
+--R +-----------+ \|b \|d x + c +-+ |a d - b c \|d x + c
+--R \|- a d + b c atanh(---------------) - \|b |--------- atan(------------)
+--R +-----------+ \| b +---------+
+--R \|- a d + b c |a d - b c
+--R |---------
+--R \| b
+--R -------------------------------------------------------------------------
+--R +-+
+--R 2b\|b
+--R Type: Expression(Integer)
+--E 318
+
+--S 319 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 319
+
+)clear all
+
+--S 320 of 716
+t0:=x^2*sqrt(c+d*x^4)/(a+b*x^4)
+--R
+--R
+--R +--------+
+--R 2 | 4
+--R x \|d x + c
+--R (1) -------------
+--R 4
+--R b x + a
+--R Type: Expression(Integer)
+--E 320
+
+--S 321 of 716
+--r0:=-c^(3/4)*(-d)^(1/4)*elliptic_e(asin((-d)^(1/4)*x/c^(1/4)),-1)*_
+-- sqrt((c+d*x^4)/c)/(b*sqrt(c+d*x^4))+c^(3/4)*(-d)^(1/4)*_
+-- elliptic_f(asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/_
+-- (b*sqrt(c+d*x^4))-1/2*(b*c-a*d)*elliptic_pi(-sqrt(b)*sqrt(c)/_
+-- (sqrt(-a)*sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^4)/c)/(b^(3/2)*sqrt(-a)*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/_
+-- sqrt(c)))+1/2*(b*c-a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*_
+-- sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/_
+-- (b^(3/2)*sqrt(-a)*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 321
+
+--S 322 of 716
+--a0:=integrate(t0,x)
+--E 322
+
+--S 323 of 716
+--m0:=a0-r0
+--E 323
+
+--S 324 of 716
+--d0:=D(m0,x)
+--E 324
+
+)clear all
+
+--S 325 of 716
+t0:=x*sqrt(c+d*x^4)/(a+b*x^4)
+--R
+--R
+--R +--------+
+--R | 4
+--R x\|d x + c
+--R (1) ------------
+--R 4
+--R b x + a
+--R Type: Expression(Integer)
+--E 325
+
+--S 326 of 716
+r0:=1/2*atanh(x^2*sqrt(d)/sqrt(c+d*x^4))*sqrt(d)/b+_
+ 1/2*atan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))*_
+ sqrt(b*c-a*d)/(b*sqrt(a))
+--R
+--R
+--R 2 +-+ 2 +-----------+
+--R +-+ +-+ x \|d +-----------+ x \|- a d + b c
+--R \|a \|d atanh(-----------) + \|- a d + b c atan(----------------)
+--R +--------+ +--------+
+--R | 4 +-+ | 4
+--R \|d x + c \|a \|d x + c
+--R (2) -----------------------------------------------------------------
+--R +-+
+--R 2b\|a
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 6 2 |a d - b c
+--R (2a d x + 4a c x ) |---------
+--R \| a
+--R +
+--R 4 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R +---------+
+--R 6 2 +-+ |a d - b c 2 8
+--R (- 4a d x - 4a c x )\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 4 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 +-+ +-+ | 4 2 +-+ +-+ 4
+--R +-+ (- x \|d + \|c )\|d x + c + x \|c \|d - d x - c
+--R 2\|d log(----------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|c \|d x + c - c
+--R /
+--R 4b
+--R ,
+--R
+--R +--------+
+--R 2 +-+ +-+ | 4 2 +-+ +-+ 4
+--R +-+ (- x \|d + \|c )\|d x + c + x \|c \|d - d x - c
+--R \|d log(----------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|c \|d x + c - c
+--R +
+--R -
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 6 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c \|c
+--R |----------- atan(----------------)
+--R \| a +-----------+
+--R 2 |- a d + b c
+--R x |-----------
+--R \| a
+--R /
+--R 2b
+--R ,
+--R
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 6 2 |a d - b c
+--R (2a d x + 4a c x ) |---------
+--R \| a
+--R +
+--R 4 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R +---------+
+--R 6 2 +-+ |a d - b c 2 8
+--R (- 4a d x - 4a c x )\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 4 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R | 4 +-+
+--R +---+ \|d x + c - \|c
+--R 4\|- d atan(------------------)
+--R 2 +---+
+--R x \|- d
+--R /
+--R 4b
+--R ,
+--R
+--R +--------+
+--R | 4 +-+
+--R +---+ \|d x + c - \|c
+--R 2\|- d atan(------------------)
+--R 2 +---+
+--R x \|- d
+--R +
+--R -
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| a
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 6 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c \|c
+--R |----------- atan(----------------)
+--R \| a +-----------+
+--R 2 |- a d + b c
+--R x |-----------
+--R \| a
+--R /
+--R 2b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 327
+
+--S 328 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-+ |a d - b c
+--R \|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 6 2 |a d - b c
+--R (2a d x + 4a c x ) |---------
+--R \| a
+--R +
+--R 4 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R +---------+
+--R 6 2 +-+ |a d - b c 2 8
+--R (- 4a d x - 4a c x )\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 4 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 +-+ +-+ | 4 2 +-+ +-+ 4
+--R +-+ +-+ (- x \|d + \|c )\|d x + c + x \|c \|d - d x - c
+--R 2\|a \|d log(----------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|c \|d x + c - c
+--R +
+--R 2 +-+ 2 +-----------+
+--R +-+ +-+ x \|d +-----------+ x \|- a d + b c
+--R - 2\|a \|d atanh(-----------) - 2\|- a d + b c atan(----------------)
+--R +--------+ +--------+
+--R | 4 +-+ | 4
+--R \|d x + c \|a \|d x + c
+--R /
+--R +-+
+--R 4b\|a
+--R Type: Expression(Integer)
+--E 328
+
+--S 329 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 +-+ +-+ | 4 2 +-+ +-+ 4
+--R +-+ +-+ (- x \|d + \|c )\|d x + c + x \|c \|d - d x - c
+--R \|a \|d log(----------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|c \|d x + c - c
+--R +
+--R 2 +-+
+--R +-+ +-+ x \|d
+--R - \|a \|d atanh(-----------)
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R -
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 6 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c +-+ \|c
+--R |----------- \|a atan(----------------)
+--R \| a +-----------+
+--R 2 |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 +-----------+
+--R +-----------+ x \|- a d + b c
+--R - \|- a d + b c atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R +-+
+--R 2b\|a
+--R Type: Expression(Integer)
+--E 330
+
+--S 331 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 331
+
+)clear all
+
+--S 332 of 716
+t0:=sqrt(c+d*x^4)/(a+b*x^4)
+--R
+--R
+--R +--------+
+--R | 4
+--R \|d x + c
+--R (1) -----------
+--R 4
+--R b x + a
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 716
+--r0:=-c^(1/4)*(-d)^(3/4)*elliptic_f(asin((-d)^(1/4)*x/c^(1/4)),-1)*_
+-- sqrt((c+d*x^4)/c)/(b*sqrt(c+d*x^4))+1/2*(b*c-a*d)*_
+-- elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(x*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/(a*b*sqrt(c+_
+-- d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))+1/2*(b*c-a*d)*elliptic_pi(sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^4)/c)/(a*b*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 333
+
+--S 334 of 716
+--a0:=integrate(t0,x)
+--E 334
+
+--S 335 of 716
+--m0:=a0-r0
+--E 335
+
+--S 336 of 716
+--d0:=D(m0,x)
+--E 336
+
+)clear all
+
+--S 337 of 716
+t0:=sqrt(c+d*x^4)/(x*(a+b*x^4))
+--R
+--R
+--R +--------+
+--R | 4
+--R \|d x + c
+--R (1) -----------
+--R 5
+--R b x + a x
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 716
+r0:=-1/2*atanh(sqrt(c+d*x^4)/sqrt(c))*sqrt(c)/a+1/2*atanh(sqrt(b)*_
+ sqrt(c+d*x^4)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/(a*sqrt(b))
+--R
+--R
+--R +--------+ +--------+
+--R +-+ | 4 | 4
+--R +-----------+ \|b \|d x + c +-+ +-+ \|d x + c
+--R \|- a d + b c atanh(---------------) - \|b \|c atanh(-----------)
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R (2) -----------------------------------------------------------------
+--R +-+
+--R 2a\|b
+--R Type: Expression(Integer)
+--E 338
+
+--S 339 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+ +--------+
+--R |- a d + b c | 4 4
+--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c
+--R |- a d + b c \| b
+--R |----------- log(-------------------------------------------------)
+--R \| b 4
+--R b x + a
+--R +
+--R +--------+
+--R +-+ | 4 4
+--R +-+ - 2\|c \|d x + c + d x + 2c
+--R \|c log(------------------------------)
+--R 4
+--R x
+--R /
+--R 4a
+--R ,
+--R +--------+ +--------+
+--R +-+ | 4 4 +---------+ | 4
+--R +-+ - 2\|c \|d x + c + d x + 2c |a d - b c \|d x + c
+--R \|c log(------------------------------) + 2 |--------- atan(------------)
+--R 4 \| b +---------+
+--R x |a d - b c
+--R |---------
+--R \| b
+--R -------------------------------------------------------------------------,
+--R 4a
+--R
+--R +-----------+ +--------+
+--R |- a d + b c | 4 4
+--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c
+--R |- a d + b c \| b
+--R |----------- log(-------------------------------------------------)
+--R \| b 4
+--R b x + a
+--R +
+--R +--------+
+--R | 4
+--R +---+ \|d x + c
+--R - 2\|- c atan(-----------)
+--R +---+
+--R \|- c
+--R /
+--R 4a
+--R ,
+--R +--------+ +--------+
+--R | 4 +---------+ | 4
+--R +---+ \|d x + c |a d - b c \|d x + c
+--R - \|- c atan(-----------) + |--------- atan(------------)
+--R +---+ \| b +---------+
+--R \|- c |a d - b c
+--R |---------
+--R \| b
+--R ----------------------------------------------------------]
+--R 2a
+--R Type: Union(List(Expression(Integer)),...)
+--E 339
+
+--S 340 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +--------+
+--R |- a d + b c | 4 4
+--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c
+--R |- a d + b c +-+ \| b
+--R |----------- \|b log(-------------------------------------------------)
+--R \| b 4
+--R b x + a
+--R +
+--R +--------+
+--R +-+ | 4 4
+--R +-+ +-+ - 2\|c \|d x + c + d x + 2c
+--R \|b \|c log(------------------------------)
+--R 4
+--R x
+--R +
+--R +--------+ +--------+
+--R +-+ | 4 | 4
+--R +-----------+ \|b \|d x + c +-+ +-+ \|d x + c
+--R - 2\|- a d + b c atanh(---------------) + 2\|b \|c atanh(-----------)
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R +-+
+--R 4a\|b
+--R Type: Expression(Integer)
+--E 340
+
+--S 341 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ | 4 4
+--R +-+ +-+ - 2\|c \|d x + c + d x + 2c
+--R \|b \|c log(------------------------------)
+--R 4
+--R x
+--R +
+--R +--------+ +--------+
+--R +-+ | 4 | 4
+--R +-----------+ \|b \|d x + c +-+ +-+ \|d x + c
+--R - 2\|- a d + b c atanh(---------------) + 2\|b \|c atanh(-----------)
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R +
+--R +--------+
+--R +---------+ | 4
+--R +-+ |a d - b c \|d x + c
+--R 2\|b |--------- atan(------------)
+--R \| b +---------+
+--R |a d - b c
+--R |---------
+--R \| b
+--R /
+--R +-+
+--R 4a\|b
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 343
+
+)clear all
+
+--S 344 of 716
+t0:=sqrt(c+d*x^4)/(x^2*(a+b*x^4))
+--R
+--R
+--R +--------+
+--R | 4
+--R \|d x + c
+--R (1) -----------
+--R 6 2
+--R b x + a x
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 716
+--r0:=-sqrt(c+d*x^4)/(a*x)-c^(3/4)*(-d)^(1/4)*elliptic_e(asin((-d)^(1/4)*_
+-- x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/(a*sqrt(c+d*x^4))+c^(3/4)*_
+-- (-d)^(1/4)*elliptic_f(asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+_
+-- d*x^4)/c)/(a*sqrt(c+d*x^4))-1/2*(b*c-a*d)*elliptic_pi(-sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^4)/c)/((-a)^(3/2)*sqrt(b)*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/_
+-- sqrt(c)))+1/2*(b*c-a*d)*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*_
+-- sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/_
+-- ((-a)^(3/2)*sqrt(b)*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 345
+
+--S 346 of 716
+--a0:=integrate(t0,x)
+--E 346
+
+--S 347 of 716
+--m0:=a0-r0
+--E 347
+
+--S 348 of 716
+--d0:=D(m0,x)
+--E 348
+
+)clear all
+
+--S 349 of 716
+t0:=sqrt(c+d*x^4)/(x^3*(a+b*x^4))
+--R
+--R
+--R +--------+
+--R | 4
+--R \|d x + c
+--R (1) -----------
+--R 7 3
+--R b x + a x
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 716
+r0:=-1/2*atan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))*_
+ sqrt(b*c-a*d)/a^(3/2)-1/2*sqrt(c+d*x^4)/(a*x^2)
+--R
+--R
+--R 2 +-----------+ +--------+
+--R 2 +-----------+ x \|- a d + b c +-+ | 4
+--R - x \|- a d + b c atan(----------------) - \|a \|d x + c
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R (2) ----------------------------------------------------------
+--R 2 +-+
+--R 2a x \|a
+--R Type: Expression(Integer)
+--E 350
+
+--S 351 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+ +--------+ +---------+
+--R 2 |a d - b c | 4 2 +-+ |a d - b c
+--R (x |--------- \|d x + c - x \|c |--------- )
+--R \| a \| a
+--R *
+--R log
+--R +---------+
+--R 6 2 |a d - b c
+--R (- 2a d x - 4a c x ) |---------
+--R \| a
+--R +
+--R 4 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R +---------+
+--R 6 2 +-+ |a d - b c 2 8
+--R (4a d x + 4a c x )\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 4 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ | 4 4
+--R 2\|c \|d x + c - 2d x - 2c
+--R /
+--R +--------+
+--R 2 | 4 2 +-+
+--R 4a x \|d x + c - 4a x \|c
+--R ,
+--R
+--R +-----------+ +--------+ +-----------+
+--R 2 |- a d + b c | 4 2 |- a d + b c +-+
+--R (x |----------- \|d x + c - x |----------- \|c )
+--R \| a \| a
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 6 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +--------+ +-----------+
+--R 2 |- a d + b c | 4 2 |- a d + b c +-+
+--R (- x |----------- \|d x + c + x |----------- \|c )
+--R \| a \| a
+--R *
+--R +-+
+--R \|c
+--R atan(----------------)
+--R +-----------+
+--R 2 |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R +-+ | 4 4
+--R \|c \|d x + c - d x - c
+--R /
+--R +--------+
+--R 2 | 4 2 +-+
+--R 2a x \|d x + c - 2a x \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 351
+
+--S 352 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-+ |a d - b c
+--R \|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 6 2 |a d - b c
+--R (- 2a d x - 4a c x ) |---------
+--R \| a
+--R +
+--R 4 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R +---------+
+--R 6 2 +-+ |a d - b c 2 8
+--R (4a d x + 4a c x )\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 4 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 +-----------+
+--R +-----------+ x \|- a d + b c
+--R 2\|- a d + b c atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R +-+
+--R 4a\|a
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 353
+
+--S 354 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 6 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c +-+ \|c
+--R - |----------- \|a atan(----------------)
+--R \| a +-----------+
+--R 2 |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 +-----------+
+--R +-----------+ x \|- a d + b c
+--R \|- a d + b c atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R +-+
+--R 2a\|a
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 716
+t0:=sqrt(c+d*x^4)/(x^4*(a+b*x^4))
+--R
+--R
+--R +--------+
+--R | 4
+--R \|d x + c
+--R (1) -----------
+--R 8 4
+--R b x + a x
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 716
+--r0:=-1/3*sqrt(c+d*x^4)/(a*x^3)+1/3*c^(1/4)*(-d)^(3/4)*_
+-- elliptic_f(asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/_
+-- (a*sqrt(c+d*x^4))-1/2*(b*c-a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/_
+-- (sqrt(a)*sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^4)/c)/(a^2*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 1/2*(b*c-a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/(a^2*_
+-- sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 357
+
+--S 358 of 716
+--a0:=integrate(t0,x)
+--E 358
+
+--S 359 of 716
+--m0:=a0-r0
+--E 359
+
+--S 360 of 716
+--d0:=D(m0,x)
+--E 360
+
+)clear all
+
+--S 361 of 716
+t0:=sqrt(c+d*x^4)/(x^5*(a+b*x^4))
+--R
+--R
+--R +--------+
+--R | 4
+--R \|d x + c
+--R (1) -----------
+--R 9 5
+--R b x + a x
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 716
+r0:=1/4*(2*b*c-a*d)*atanh(sqrt(c+d*x^4)/sqrt(c))/(a^2*sqrt(c))-_
+ 1/2*atanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))*sqrt(b)*_
+ sqrt(b*c-a*d)/a^2-1/4*sqrt(c+d*x^4)/(a*x^4)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 4
+--R 4 +-----------+ +-+ +-+ \|b \|d x + c
+--R - 2x \|- a d + b c \|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 4 +--------+
+--R 4 \|d x + c +-+ | 4
+--R (- a d + 2b c)x atanh(-----------) - a\|c \|d x + c
+--R +-+
+--R \|c
+--R /
+--R 2 4 +-+
+--R 4a x \|c
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R | 4 4 +-+
+--R 4 - 2c\|d x + c + (d x + 2c)\|c
+--R (a d - 2b c)x log(---------------------------------)
+--R 4
+--R x
+--R +
+--R +-------------+
+--R 4 | 2 +-+
+--R 2x \|- a b d + b c \|c
+--R *
+--R +-------------+ +--------+
+--R | 2 | 4 4
+--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c
+--R log(----------------------------------------------------)
+--R 4
+--R b x + a
+--R +
+--R +--------+
+--R +-+ | 4
+--R - 2a\|c \|d x + c
+--R /
+--R 2 4 +-+
+--R 8a x \|c
+--R ,
+--R
+--R +--------+
+--R | 4 4 +-+
+--R 4 - 2c\|d x + c + (d x + 2c)\|c
+--R (a d - 2b c)x log(---------------------------------)
+--R 4
+--R x
+--R +
+--R +--------+
+--R +-----------+ | 4 +--------+
+--R 4 +-+ | 2 b\|d x + c +-+ | 4
+--R - 4x \|c \|a b d - b c atan(--------------) - 2a\|c \|d x + c
+--R +-----------+
+--R | 2
+--R \|a b d - b c
+--R /
+--R 2 4 +-+
+--R 8a x \|c
+--R ,
+--R
+--R +-------------+
+--R 4 | 2 +---+
+--R x \|- a b d + b c \|- c
+--R *
+--R +-------------+ +--------+
+--R | 2 | 4 4
+--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c
+--R log(----------------------------------------------------)
+--R 4
+--R b x + a
+--R +
+--R +--------+
+--R +---+ | 4 +--------+
+--R 4 \|- c \|d x + c +---+ | 4
+--R (- a d + 2b c)x atan(-----------------) - a\|- c \|d x + c
+--R c
+--R /
+--R 2 4 +---+
+--R 4a x \|- c
+--R ,
+--R
+--R +--------+
+--R +---+ | 4
+--R 4 \|- c \|d x + c
+--R (- a d + 2b c)x atan(-----------------)
+--R c
+--R +
+--R +--------+
+--R +-----------+ | 4 +--------+
+--R 4 +---+ | 2 b\|d x + c +---+ | 4
+--R - 2x \|- c \|a b d - b c atan(--------------) - a\|- c \|d x + c
+--R +-----------+
+--R | 2
+--R \|a b d - b c
+--R /
+--R 2 4 +---+
+--R 4a x \|- c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 363
+
+--S 364 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 4 4 +-+
+--R - 2c\|d x + c + (d x + 2c)\|c
+--R (a d - 2b c)log(---------------------------------)
+--R 4
+--R x
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 2\|- a b d + b c \|c
+--R *
+--R +-------------+ +--------+
+--R | 2 | 4 4
+--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c
+--R log(----------------------------------------------------)
+--R 4
+--R b x + a
+--R +
+--R +--------+
+--R +-+ | 4
+--R +-----------+ +-+ +-+ \|b \|d x + c
+--R 4\|- a d + b c \|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 4
+--R \|d x + c
+--R (2a d - 4b c)atanh(-----------)
+--R +-+
+--R \|c
+--R /
+--R 2 +-+
+--R 8a \|c
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 365
+
+--S 366 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 4 4 +-+
+--R - 2c\|d x + c + (d x + 2c)\|c
+--R (a d - 2b c)log(---------------------------------)
+--R 4
+--R x
+--R +
+--R +--------+
+--R +-+ | 4
+--R +-----------+ +-+ +-+ \|b \|d x + c
+--R 4\|- a d + b c \|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+ +--------+
+--R | 4 +-----------+ | 4
+--R \|d x + c +-+ | 2 b\|d x + c
+--R (2a d - 4b c)atanh(-----------) - 4\|c \|a b d - b c atan(--------------)
+--R +-+ +-----------+
+--R \|c | 2
+--R \|a b d - b c
+--R /
+--R 2 +-+
+--R 8a \|c
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 367
+
+)clear all
+
+--S 368 of 716
+t0:=sqrt(c+d*x^4)/(x^6*(a+b*x^4))
+--R
+--R
+--R +--------+
+--R | 4
+--R \|d x + c
+--R (1) ------------
+--R 10 6
+--R b x + a x
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 716
+--r0:=-1/5*sqrt(c+d*x^4)/(a*x^5)+1/5*(5*b*c-2*a*d)*sqrt(c+d*x^4)/_
+-- (a^2*c*x)+1/5*(-d)^(1/4)*(5*b*c-2*a*d)*elliptic_e(asin((-d)^(1/4)*_
+-- x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/(a^2*c^(1/4)*sqrt(c+d*x^4))-_
+-- 1/5*(-d)^(1/4)*(5*b*c-2*a*d)*elliptic_f(asin((-d)^(1/4)*x/c^(1/4)),_
+-- -1)*sqrt((c+d*x^4)/c)/(a^2*c^(1/4)*sqrt(c+d*x^4))-1/2*(b*c-a*d)*_
+-- elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(x*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(b)*sqrt((c+d*x^4)/c)/((-a)^(5/2)*_
+-- sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))+1/2*(b*c-a*d)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(x*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(b)*sqrt((c+d*x^4)/c)/((-a)^(5/2)*_
+-- sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 369
+
+--S 370 of 716
+--a0:=integrate(t0,x)
+--E 370
+
+--S 371 of 716
+--m0:=a0-r0
+--E 371
+
+--S 372 of 716
+--d0:=D(m0,x)
+--E 372
+
+)clear all
+
+--S 373 of 716
+t0:=sqrt(c+d*x^4)/(x^7*(a+b*x^4))
+--R
+--R
+--R +--------+
+--R | 4
+--R \|d x + c
+--R (1) ------------
+--R 11 7
+--R b x + a x
+--R Type: Expression(Integer)
+--E 373
+
+--S 374 of 716
+r0:=1/2*b*atan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))*_
+ sqrt(b*c-a*d)/a^(5/2)-1/6*sqrt(c+d*x^4)/(a*x^6)+_
+ 1/6*(3*b*c-a*d)*sqrt(c+d*x^4)/(a^2*c*x^2)
+--R
+--R
+--R (2)
+--R 2 +-----------+
+--R 6 +-----------+ x \|- a d + b c
+--R 3b c x \|- a d + b c atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 4 +-+ | 4
+--R ((- a d + 3b c)x - a c)\|a \|d x + c
+--R /
+--R 2 6 +-+
+--R 6a c x \|a
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---------+ +--------+
+--R 10 2 6 |a d - b c | 4
+--R (3b c d x + 12b c x ) |--------- \|d x + c
+--R \| a
+--R +
+--R +---------+
+--R 10 2 6 +-+ |a d - b c
+--R (- 9b c d x - 12b c x )\|c |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 6 2 |a d - b c
+--R (2a d x + 4a c x ) |---------
+--R \| a
+--R +
+--R 4 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R +---------+
+--R 6 2 +-+ |a d - b c 2 8
+--R (- 4a d x - 4a c x )\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 4 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +--------+
+--R 2 8 2 4 2 +-+ | 4
+--R ((6a d - 18b c d)x + (14a c d - 24b c )x + 8a c )\|c \|d x + c
+--R +
+--R 3 2 12 2 2 8
+--R (- 2a d + 6b c d )x + (- 12a c d + 30b c d)x
+--R +
+--R 2 3 4 3
+--R (- 18a c d + 24b c )x - 8a c
+--R /
+--R +--------+
+--R 2 10 2 2 6 | 4 2 10 2 2 6 +-+
+--R (12a c d x + 48a c x )\|d x + c + (- 36a c d x - 48a c x )\|c
+--R ,
+--R
+--R +-----------+ +--------+
+--R 10 2 6 |- a d + b c | 4
+--R (- 3b c d x - 12b c x ) |----------- \|d x + c
+--R \| a
+--R +
+--R +-----------+
+--R 10 2 6 |- a d + b c +-+
+--R (9b c d x + 12b c x ) |----------- \|c
+--R \| a
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 6 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +--------+
+--R 10 2 6 |- a d + b c | 4
+--R (3b c d x + 12b c x ) |----------- \|d x + c
+--R \| a
+--R +
+--R +-----------+
+--R 10 2 6 |- a d + b c +-+
+--R (- 9b c d x - 12b c x ) |----------- \|c
+--R \| a
+--R *
+--R +-+
+--R \|c
+--R atan(----------------)
+--R +-----------+
+--R 2 |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R +--------+
+--R 2 8 2 4 2 +-+ | 4
+--R ((3a d - 9b c d)x + (7a c d - 12b c )x + 4a c )\|c \|d x + c
+--R +
+--R 3 2 12 2 2 8 2 3 4
+--R (- a d + 3b c d )x + (- 6a c d + 15b c d)x + (- 9a c d + 12b c )x
+--R +
+--R 3
+--R - 4a c
+--R /
+--R +--------+
+--R 2 10 2 2 6 | 4 2 10 2 2 6 +-+
+--R (6a c d x + 24a c x )\|d x + c + (- 18a c d x - 24a c x )\|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 375
+
+--S 376 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +-+ |a d - b c
+--R b\|a |---------
+--R \| a
+--R *
+--R log
+--R +---------+
+--R 6 2 |a d - b c
+--R (2a d x + 4a c x ) |---------
+--R \| a
+--R +
+--R 4 +-+
+--R ((4a d - 2b c)x + 2a c)\|c
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R +---------+
+--R 6 2 +-+ |a d - b c 2 8
+--R (- 4a d x - 4a c x )\|c |--------- + (- 2a d + b c d)x
+--R \| a
+--R +
+--R 2 4 2
+--R (- 5a c d + 2b c )x - 2a c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 +-----------+
+--R +-----------+ x \|- a d + b c
+--R - 2b\|- a d + b c atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R -
+--R +-----------+
+--R |- a d + b c +-+
+--R b |----------- \|a
+--R \| a
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-----------+
+--R 6 |- a d + b c
+--R a d x |-----------
+--R \| a
+--R +
+--R +-----------+ +-+
+--R |- a d + b c +-+ \|c
+--R b |----------- \|a atan(----------------)
+--R \| a +-----------+
+--R 2 |- a d + b c
+--R x |-----------
+--R \| a
+--R +
+--R 2 +-----------+
+--R +-----------+ x \|- a d + b c
+--R - b\|- a d + b c atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 378
+
+--S 379 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 379
+
+)clear all
+
+--S 380 of 716
+t0:=sqrt(c+d*x^4)/(x^8*(a+b*x^4))
+--R
+--R
+--R +--------+
+--R | 4
+--R \|d x + c
+--R (1) ------------
+--R 12 8
+--R b x + a x
+--R Type: Expression(Integer)
+--E 380
+
+--S 381 of 716
+--r0:=-1/7*sqrt(c+d*x^4)/(a*x^7)+1/21*(7*b*c-2*a*d)*sqrt(c+d*x^4)/_
+-- (a^2*c*x^3)-1/21*(-d)^(3/4)*(7*b*c-2*a*d)*elliptic_f(_
+-- asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/(a^2*c^(3/4)*_
+-- sqrt(c+d*x^4))+1/2*b*(b*c-a*d)*elliptic_pi(-sqrt(-b)*sqrt(c)/_
+-- (sqrt(a)*sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^4)/c)/(a^3*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))+_
+-- 1/2*b*(b*c-a*d)*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),_
+-- asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/(a^3*_
+-- sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 381
+
+--S 382 of 716
+--a0:=integrate(t0,x)
+--E 382
+
+--S 383 of 716
+--m0:=a0-r0
+--E 383
+
+--S 384 of 716
+--d0:=D(m0,x)
+--E 384
+
+)clear all
+
+--S 385 of 716
+t0:=x^8/((a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 8
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 385
+
+--S 386 of 716
+--r0:=1/3*x*sqrt(c+d*x^4)/(b*d)+1/3*c^(1/4)*(b*c+3*a*d)*_
+-- elliptic_f(asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/_
+-- (b^2*(-d)^(5/4)*sqrt(c+d*x^4))+1/2*a*elliptic_pi(-sqrt(-b)*_
+-- sqrt(c)/(sqrt(a)*sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^4)/c)/(b^2*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))+_
+-- 1/2*a*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(x*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/(b^2*sqrt(c+_
+-- d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 386
+
+--S 387 of 716
+--a0:=integrate(t0,x)
+--E 387
+
+--S 388 of 716
+--m0:=a0-r0
+--E 388
+
+--S 389 of 716
+--d0:=D(m0,x)
+--E 389
+
+)clear all
+
+--S 390 of 716
+t0:=x^7/((a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 7
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 390
+
+--S 391 of 716
+r0:=1/2*a*atanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))/(b^(3/2)*_
+ sqrt(b*c-a*d))+1/2*sqrt(c+d*x^4)/(b*d)
+--R
+--R
+--R +--------+
+--R +-+ | 4 +--------+
+--R \|b \|d x + c +-----------+ +-+ | 4
+--R a d atanh(---------------) + \|- a d + b c \|b \|d x + c
+--R +-----------+
+--R \|- a d + b c
+--R (2) ----------------------------------------------------------
+--R +-----------+ +-+
+--R 2b d\|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R a d
+--R *
+--R log
+--R +--------+
+--R 2 | 4
+--R (- 2a b d + 2b c)\|d x + c
+--R +
+--R +-------------+
+--R 4 | 2
+--R (b d x - a d + 2b c)\|- a b d + b c
+--R /
+--R 4
+--R b x + a
+--R +
+--R +-------------+ +--------+
+--R | 2 | 4
+--R 2\|- a b d + b c \|d x + c
+--R /
+--R +-------------+
+--R | 2
+--R 4b d\|- a b d + b c
+--R ,
+--R +-----------+ +--------+
+--R | 2 | 4 +-----------+ +--------+
+--R \|a b d - b c \|d x + c | 2 | 4
+--R - a d atan(-------------------------) + \|a b d - b c \|d x + c
+--R a d - b c
+--R -----------------------------------------------------------------]
+--R +-----------+
+--R | 2
+--R 2b d\|a b d - b c
+--R Type: Union(List(Expression(Integer)),...)
+--E 392
+
+--S 393 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R a\|- a d + b c \|b
+--R *
+--R +--------+ +-------------+
+--R 2 | 4 4 | 2
+--R (- 2a b d + 2b c)\|d x + c + (b d x - a d + 2b c)\|- a b d + b c
+--R log(--------------------------------------------------------------------)
+--R 4
+--R b x + a
+--R +
+--R +--------+
+--R +-------------+ +-+ | 4
+--R | 2 \|b \|d x + c
+--R - 2a\|- a b d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R /
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R 4b\|- a b d + b c \|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 393
+
+--S 394 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-----------+ +-+ | 4
+--R | 2 \|b \|d x + c
+--R - a\|a b d - b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +-----------+ +--------+
+--R | 2 | 4
+--R +-----------+ +-+ \|a b d - b c \|d x + c
+--R - a\|- a d + b c \|b atan(-------------------------)
+--R a d - b c
+--R /
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R 2b\|- a d + b c \|b \|a b d - b c
+--R Type: Expression(Integer)
+--E 395
+
+--S 396 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 396
+
+)clear all
+
+--S 397 of 716
+t0:=x^6/((a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 6
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 716
+--r0:=c^(3/4)*elliptic_e(asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/_
+-- (b*(-d)^(3/4)*sqrt(c+d*x^4))-c^(3/4)*elliptic_f(asin((-d)^(1/4)*_
+-- x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/(b*(-d)^(3/4)*sqrt(c+d*x^4))-_
+-- 1/2*elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(x*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(-a)*sqrt((c+d*x^4)/c)/(b^(3/2)*_
+-- sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))+1/2*elliptic_pi(sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt(-a)*sqrt((c+d*x^4)/c)/(b^(3/2)*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 398
+
+--S 399 of 716
+--a0:=integrate(t0,x)
+--E 399
+
+--S 400 of 716
+--m0:=a0-r0
+--E 400
+
+--S 401 of 716
+--d0:=D(m0,x)
+--E 401
+
+)clear all
+
+--S 402 of 716
+t0:=x^5/((a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 5
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 716
+r0:=1/2*atanh(x^2*sqrt(d)/sqrt(c+d*x^4))/(b*sqrt(d))-_
+ 1/2*atan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))*_
+ sqrt(a)/(b*sqrt(b*c-a*d))
+--R
+--R
+--R 2 +-+ 2 +-----------+
+--R +-----------+ x \|d +-+ +-+ x \|- a d + b c
+--R \|- a d + b c atanh(-----------) - \|a \|d atan(----------------)
+--R +--------+ +--------+
+--R | 4 +-+ | 4
+--R \|d x + c \|a \|d x + c
+--R (2) -----------------------------------------------------------------
+--R +-----------+ +-+
+--R 2b\|- a d + b c \|d
+--R Type: Expression(Integer)
+--E 403
+
+--S 404 of 716
+--a0:=integrate(t0,x)
+--E 404
+
+--S 405 of 716
+--m0:=a0-r0
+--E 405
+
+--S 406 of 716
+--d0:=D(m0,x)
+--E 406
+
+)clear all
+
+--S 407 of 716
+t0:=x^4/((a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 4
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 716
+--r0:=c^(1/4)*elliptic_f(asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/_
+-- (b*(-d)^(1/4)*sqrt(c+d*x^4))-1/2*elliptic_pi(-sqrt(-b)*sqrt(c)/_
+-- (sqrt(a)*sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+_
+-- d*x^4)/c)/(b*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 1/2*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(x*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/(b*sqrt(c+d*x^4)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 408
+
+--S 409 of 716
+--a0:=integrate(t0,x)
+--E 409
+
+--S 410 of 716
+--m0:=a0-r0
+--E 410
+
+--S 411 of 716
+--d0:=D(m0,x)
+--E 411
+
+)clear all
+
+--S 412 of 716
+t0:=x^3/((a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 3
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 716
+r0:=-1/2*atanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))/(sqrt(b)*sqrt(b*c-a*d))
+--R
+--R
+--R +--------+
+--R +-+ | 4
+--R \|b \|d x + c
+--R atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R (2) - ----------------------
+--R +-----------+ +-+
+--R 2\|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 413
+
+--S 414 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +-------------+
+--R 2 | 4 4 | 2
+--R (2a b d - 2b c)\|d x + c + (b d x - a d + 2b c)\|- a b d + b c
+--R log(------------------------------------------------------------------)
+--R 4
+--R b x + a
+--R [-----------------------------------------------------------------------,
+--R +-------------+
+--R | 2
+--R 4\|- a b d + b c
+--R +-----------+ +--------+
+--R | 2 | 4
+--R \|a b d - b c \|d x + c
+--R atan(-------------------------)
+--R a d - b c
+--R -------------------------------]
+--R +-----------+
+--R | 2
+--R 2\|a b d - b c
+--R Type: Union(List(Expression(Integer)),...)
+--E 414
+
+--S 415 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R \|- a d + b c \|b
+--R *
+--R +--------+ +-------------+
+--R 2 | 4 4 | 2
+--R (2a b d - 2b c)\|d x + c + (b d x - a d + 2b c)\|- a b d + b c
+--R log(------------------------------------------------------------------)
+--R 4
+--R b x + a
+--R +
+--R +--------+
+--R +-------------+ +-+ | 4
+--R | 2 \|b \|d x + c
+--R 2\|- a b d + b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R /
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R 4\|- a b d + b c \|- a d + b c \|b
+--R Type: Expression(Integer)
+--E 415
+
+--S 416 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-----------+ +-+ | 4
+--R | 2 \|b \|d x + c
+--R \|a b d - b c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +-----------+ +--------+
+--R | 2 | 4
+--R +-----------+ +-+ \|a b d - b c \|d x + c
+--R \|- a d + b c \|b atan(-------------------------)
+--R a d - b c
+--R /
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R 2\|- a d + b c \|b \|a b d - b c
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 418
+
+)clear all
+
+--S 419 of 716
+t0:=x^2/((a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 716
+--r0:=-1/2*elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(x*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/(sqrt(-a)*sqrt(b)*_
+-- sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))+1/2*elliptic_pi(sqrt(b)*_
+-- sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^4)/c)/(sqrt(-a)*sqrt(b)*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 420
+
+--S 421 of 716
+--a0:=integrate(t0,x)
+--E 421
+
+--S 422 of 716
+--m0:=a0-r0
+--E 422
+
+--S 423 of 716
+--d0:=D(m0,x)
+--E 423
+
+)clear all
+
+--S 424 of 716
+t0:=x/((a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 716
+r0:=1/2*atan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))/(sqrt(a)*sqrt(b*c-a*d))
+--R
+--R
+--R 2 +-----------+
+--R x \|- a d + b c
+--R atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R (2) ----------------------
+--R +-----------+ +-+
+--R 2\|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 425
+
+--S 426 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R log
+--R +-----------+
+--R 4 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 6 2 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 8 2 4 2 | 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )\|a d - a b c
+--R +
+--R 2 2 6 2 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x )\|c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R /
+--R +-----------+
+--R | 2
+--R 4\|a d - a b c
+--R ,
+--R
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R - atan(-----------------------------------------------------)
+--R +-------------+
+--R 6 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R - atan(--------------------)
+--R 2
+--R (a d - b c)x
+--R /
+--R +-------------+
+--R | 2
+--R 2\|- a d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 426
+
+--S 427 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 4 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 6 2 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R 2 8 2 4 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 6 2 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x )\|c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ 2 +-----------+
+--R | 2 x \|- a d + b c
+--R - 2\|a d - a b c atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R 4\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 428
+
+--S 429 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R -
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 6 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R +-----------+ +-+ \|- a d + a b c \|c
+--R - \|- a d + b c \|a atan(--------------------)
+--R 2
+--R (a d - b c)x
+--R +
+--R +-------------+ 2 +-----------+
+--R | 2 x \|- a d + b c
+--R - \|- a d + a b c atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R 2\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 430
+
+)clear all
+
+--S 431 of 716
+t0:=1/((a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 716
+--r0:=1/2*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(x*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/(a*sqrt(c+d*x^4)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))+1/2*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/_
+-- (a*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 432
+
+--S 433 of 716
+--a0:=integrate(t0,x)
+--E 433
+
+--S 434 of 716
+--m0:=a0-r0
+--E 434
+
+--S 435 of 716
+--d0:=D(m0,x)
+--E 435
+
+)clear all
+
+--S 436 of 716
+t0:=1/(x*(a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +--------+
+--R 5 | 4
+--R (b x + a x)\|d x + c
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 716
+r0:=-1/2*atanh(sqrt(c+d*x^4)/sqrt(c))/(a*sqrt(c))+_
+ 1/2*atanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))*sqrt(b)/(a*sqrt(b*c-a*d))
+--R
+--R
+--R +--------+ +--------+
+--R +-+ | 4 | 4
+--R +-+ +-+ \|b \|d x + c +-----------+ \|d x + c
+--R \|b \|c atanh(---------------) - \|- a d + b c atanh(-----------)
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R (2) -----------------------------------------------------------------
+--R +-----------+ +-+
+--R 2a\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R | 4 4 +-+
+--R - 2c\|d x + c + (d x + 2c)\|c
+--R log(---------------------------------)
+--R 4
+--R x
+--R +
+--R +-----------+
+--R | b +-+
+--R |- --------- \|c
+--R \| a d - b c
+--R *
+--R +-----------+ +--------+
+--R | b | 4 4
+--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c
+--R \| a d - b c
+--R log(--------------------------------------------------------------)
+--R 4
+--R b x + a
+--R /
+--R +-+
+--R 4a\|c
+--R ,
+--R
+--R +--------+
+--R | 4 4 +-+
+--R - 2c\|d x + c + (d x + 2c)\|c
+--R log(---------------------------------)
+--R 4
+--R x
+--R +
+--R +--------+
+--R +---------+ | 4
+--R | b +-+ b\|d x + c
+--R - 2 |--------- \|c atan(-----------------------)
+--R \|a d - b c +---------+
+--R | b
+--R (a d - b c) |---------
+--R \|a d - b c
+--R /
+--R +-+
+--R 4a\|c
+--R ,
+--R
+--R +-----------+
+--R +---+ | b
+--R \|- c |- ---------
+--R \| a d - b c
+--R *
+--R +-----------+ +--------+
+--R | b | 4 4
+--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c
+--R \| a d - b c
+--R log(--------------------------------------------------------------)
+--R 4
+--R b x + a
+--R +
+--R +--------+
+--R +---+ | 4
+--R \|- c \|d x + c
+--R - 2atan(-----------------)
+--R c
+--R /
+--R +---+
+--R 4a\|- c
+--R ,
+--R +--------+ +--------+
+--R +---+ | 4 +---------+ | 4
+--R \|- c \|d x + c +---+ | b b\|d x + c
+--R - atan(-----------------) - \|- c |--------- atan(-----------------------)
+--R c \|a d - b c +---------+
+--R | b
+--R (a d - b c) |---------
+--R \|a d - b c
+--R ---------------------------------------------------------------------------]
+--R +---+
+--R 2a\|- c
+--R Type: Union(List(Expression(Integer)),...)
+--E 438
+
+--S 439 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 4 4 +-+
+--R +-----------+ - 2c\|d x + c + (d x + 2c)\|c
+--R \|- a d + b c log(---------------------------------)
+--R 4
+--R x
+--R +
+--R +-----------+
+--R +-----------+ | b +-+
+--R \|- a d + b c |- --------- \|c
+--R \| a d - b c
+--R *
+--R +-----------+ +--------+
+--R | b | 4 4
+--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c
+--R \| a d - b c
+--R log(--------------------------------------------------------------)
+--R 4
+--R b x + a
+--R +
+--R +--------+ +--------+
+--R +-+ | 4 | 4
+--R +-+ +-+ \|b \|d x + c +-----------+ \|d x + c
+--R - 2\|b \|c atanh(---------------) + 2\|- a d + b c atanh(-----------)
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R +-----------+ +-+
+--R 4a\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 440
+
+--S 441 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 4 4 +-+
+--R +-----------+ - 2c\|d x + c + (d x + 2c)\|c
+--R \|- a d + b c log(---------------------------------)
+--R 4
+--R x
+--R +
+--R +--------+ +--------+
+--R +-+ | 4 | 4
+--R +-+ +-+ \|b \|d x + c +-----------+ \|d x + c
+--R - 2\|b \|c atanh(---------------) + 2\|- a d + b c atanh(-----------)
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R +
+--R +--------+
+--R +---------+ | 4
+--R +-----------+ | b +-+ b\|d x + c
+--R - 2\|- a d + b c |--------- \|c atan(-----------------------)
+--R \|a d - b c +---------+
+--R | b
+--R (a d - b c) |---------
+--R \|a d - b c
+--R /
+--R +-----------+ +-+
+--R 4a\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 442
+
+)clear all
+
+--S 443 of 716
+t0:=1/(x^2*(a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R 6 2 | 4
+--R (b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 443
+
+--S 444 of 716
+--r0:=-sqrt(c+d*x^4)/(a*c*x)-(-d)^(1/4)*elliptic_e(asin((-d)^(1/4)*_
+-- x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/(a*c^(1/4)*sqrt(c+d*x^4))+(-d)^(1/4)*_
+-- elliptic_f(asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/(a*c^(1/4)*_
+-- sqrt(c+d*x^4))-1/2*elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(b)*sqrt((c+d*x^4)/c)/_
+-- ((-a)^(3/2)*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))+_
+-- 1/2*elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(x*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt(b)*sqrt((c+d*x^4)/c)/((-a)^(3/2)*_
+-- sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 444
+
+--S 445 of 716
+--a0:=integrate(t0,x)
+--E 445
+
+--S 446 of 716
+--m0:=a0-r0
+--E 446
+
+--S 447 of 716
+--d0:=D(m0,x)
+--E 447
+
+)clear all
+
+--S 448 of 716
+t0:=1/(x^3*(a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R 7 3 | 4
+--R (b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 448
+
+--S 449 of 716
+r0:=-1/2*b*atan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))/_
+ (a^(3/2)*sqrt(b*c-a*d))-1/2*sqrt(c+d*x^4)/(a*c*x^2)
+--R
+--R
+--R 2 +-----------+ +--------+
+--R 2 x \|- a d + b c +-----------+ +-+ | 4
+--R - b c x atan(----------------) - \|- a d + b c \|a \|d x + c
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R (2) --------------------------------------------------------------
+--R 2 +-----------+ +-+
+--R 2a c x \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 | 4 2 +-+
+--R (b c x \|d x + c - b c x \|c )
+--R *
+--R log
+--R +-----------+
+--R 4 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 6 2 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R 2 8 2 4 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 6 2 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x )\|c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +--------+ +-----------+
+--R +-+ | 2 | 4 4 | 2
+--R 2\|c \|a d - a b c \|d x + c + (- 2d x - 2c)\|a d - a b c
+--R /
+--R +-----------+ +--------+ +-----------+
+--R 2 | 2 | 4 2 +-+ | 2
+--R 4a c x \|a d - a b c \|d x + c - 4a c x \|c \|a d - a b c
+--R ,
+--R
+--R +--------+
+--R 2 | 4 2 +-+
+--R (b c x \|d x + c - b c x \|c )
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 6 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R +--------+ | 2 +-+
+--R 2 | 4 2 +-+ \|- a d + a b c \|c
+--R (b c x \|d x + c - b c x \|c )atan(--------------------)
+--R 2
+--R (a d - b c)x
+--R +
+--R +-------------+ +--------+ +-------------+
+--R | 2 +-+ | 4 4 | 2
+--R \|- a d + a b c \|c \|d x + c + (- d x - c)\|- a d + a b c
+--R /
+--R +-------------+ +--------+ +-------------+
+--R 2 | 2 | 4 2 | 2 +-+
+--R 2a c x \|- a d + a b c \|d x + c - 2a c x \|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 450
+
+--S 451 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R b\|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 4 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 6 2 2 2
+--R (2a d - 2a b c d)x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R 2 8 2 4 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 6 2 2 2 +-+
+--R ((- 4a d + 4a b c d)x + (- 4a c d + 4a b c )x )\|c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ 2 +-----------+
+--R | 2 x \|- a d + b c
+--R 2b\|a d - a b c atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R 4a\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+ +-+
+--R b\|- a d + b c \|a
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 6 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R +-----------+ +-+ \|- a d + a b c \|c
+--R b\|- a d + b c \|a atan(--------------------)
+--R 2
+--R (a d - b c)x
+--R +
+--R +-------------+ 2 +-----------+
+--R | 2 x \|- a d + b c
+--R b\|- a d + a b c atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R 2a\|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 453
+
+--S 454 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 454
+
+)clear all
+
+--S 455 of 716
+t0:=1/(x^4*(a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R 8 4 | 4
+--R (b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 455
+
+--S 456 of 716
+--r0:=-1/3*sqrt(c+d*x^4)/(a*c*x^3)+1/3*(-d)^(3/4)*_
+-- elliptic_f(asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/_
+-- (a*c^(3/4)*sqrt(c+d*x^4))-1/2*b*elliptic_pi(-sqrt(-b)*sqrt(c)/_
+-- (sqrt(a)*sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*_
+-- sqrt((c+d*x^4)/c)/(a^2*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))-_
+-- 1/2*b*elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(x*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/(a^2*sqrt(c+d*x^4)*_
+-- sqrt(-sqrt(-d)/sqrt(c)))
+--E 456
+
+--S 457 of 716
+--a0:=integrate(t0,x)
+--E 457
+
+--S 458 of 716
+--m0:=a0-r0
+--E 458
+
+--S 459 of 716
+--d0:=D(m0,x)
+--E 459
+
+)clear all
+
+--S 460 of 716
+t0:=1/(x^5*(a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R 9 5 | 4
+--R (b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 460
+
+--S 461 of 716
+r0:=1/4*(2*b*c+a*d)*atanh(sqrt(c+d*x^4)/sqrt(c))/(a^2*c^(3/2))-_
+ 1/2*b^(3/2)*atanh(sqrt(b)*sqrt(c+d*x^4)/sqrt(b*c-a*d))/_
+ (a^2*sqrt(b*c-a*d))-1/4*sqrt(c+d*x^4)/(a*c*x^4)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 4
+--R 4 +-+ +-+ \|b \|d x + c
+--R - 2b c x \|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 4
+--R 4 +-----------+ \|d x + c
+--R (a d + 2b c)x \|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +-----------+ +-+ | 4
+--R - a\|- a d + b c \|c \|d x + c
+--R /
+--R 2 4 +-----------+ +-+
+--R 4a c x \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+
+--R 4 | b +-+
+--R 2b c x |- --------- \|c
+--R \| a d - b c
+--R *
+--R +-----------+ +--------+
+--R | b | 4 4
+--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c
+--R \| a d - b c
+--R log(------------------------------------------------------------)
+--R 4
+--R b x + a
+--R +
+--R +--------+
+--R | 4 4 +-+ +--------+
+--R 4 2c\|d x + c + (d x + 2c)\|c +-+ | 4
+--R (a d + 2b c)x log(-------------------------------) - 2a\|c \|d x + c
+--R 4
+--R x
+--R /
+--R 2 4 +-+
+--R 8a c x \|c
+--R ,
+--R
+--R +--------+
+--R | 4 4 +-+
+--R 4 2c\|d x + c + (d x + 2c)\|c
+--R (a d + 2b c)x log(-------------------------------)
+--R 4
+--R x
+--R +
+--R +--------+
+--R +---------+ | 4 +--------+
+--R 4 | b +-+ b\|d x + c +-+ | 4
+--R 4b c x |--------- \|c atan(-----------------------) - 2a\|c \|d x + c
+--R \|a d - b c +---------+
+--R | b
+--R (a d - b c) |---------
+--R \|a d - b c
+--R /
+--R 2 4 +-+
+--R 8a c x \|c
+--R ,
+--R
+--R +-----------+
+--R 4 +---+ | b
+--R b c x \|- c |- ---------
+--R \| a d - b c
+--R *
+--R +-----------+ +--------+
+--R | b | 4 4
+--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c
+--R \| a d - b c
+--R log(------------------------------------------------------------)
+--R 4
+--R b x + a
+--R +
+--R +--------+
+--R +---+ | 4 +--------+
+--R 4 \|- c \|d x + c +---+ | 4
+--R (a d + 2b c)x atan(-----------------) - a\|- c \|d x + c
+--R c
+--R /
+--R 2 4 +---+
+--R 4a c x \|- c
+--R ,
+--R
+--R +--------+
+--R +---+ | 4
+--R 4 \|- c \|d x + c
+--R (a d + 2b c)x atan(-----------------)
+--R c
+--R +
+--R +--------+
+--R +---------+ | 4
+--R 4 +---+ | b b\|d x + c
+--R 2b c x \|- c |--------- atan(-----------------------)
+--R \|a d - b c +---------+
+--R | b
+--R (a d - b c) |---------
+--R \|a d - b c
+--R +
+--R +--------+
+--R +---+ | 4
+--R - a\|- c \|d x + c
+--R /
+--R 2 4 +---+
+--R 4a c x \|- c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 462
+
+--S 463 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R +-----------+ | b +-+
+--R 2b c\|- a d + b c |- --------- \|c
+--R \| a d - b c
+--R *
+--R +-----------+ +--------+
+--R | b | 4 4
+--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c
+--R \| a d - b c
+--R log(------------------------------------------------------------)
+--R 4
+--R b x + a
+--R +
+--R +--------+
+--R | 4 4 +-+
+--R +-----------+ 2c\|d x + c + (d x + 2c)\|c
+--R (a d + 2b c)\|- a d + b c log(-------------------------------)
+--R 4
+--R x
+--R +
+--R +--------+
+--R +-+ | 4
+--R +-+ +-+ \|b \|d x + c
+--R 4b c\|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 4
+--R +-----------+ \|d x + c
+--R (- 2a d - 4b c)\|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R /
+--R 2 +-----------+ +-+
+--R 8a c\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 463
+
+--S 464 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 4 4 +-+
+--R +-----------+ 2c\|d x + c + (d x + 2c)\|c
+--R (a d + 2b c)\|- a d + b c log(-------------------------------)
+--R 4
+--R x
+--R +
+--R +--------+
+--R +-+ | 4
+--R +-+ +-+ \|b \|d x + c
+--R 4b c\|b \|c atanh(---------------)
+--R +-----------+
+--R \|- a d + b c
+--R +
+--R +--------+
+--R | 4
+--R +-----------+ \|d x + c
+--R (- 2a d - 4b c)\|- a d + b c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R +--------+
+--R +---------+ | 4
+--R +-----------+ | b +-+ b\|d x + c
+--R 4b c\|- a d + b c |--------- \|c atan(-----------------------)
+--R \|a d - b c +---------+
+--R | b
+--R (a d - b c) |---------
+--R \|a d - b c
+--R /
+--R 2 +-----------+ +-+
+--R 8a c\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 465
+
+--S 466 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 466
+
+)clear all
+
+--S 467 of 716
+t0:=1/(x^6*(a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R +--------+
+--R 10 6 | 4
+--R (b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 716
+--r0:=-1/5*sqrt(c+d*x^4)/(a*c*x^5)+1/5*(5*b*c+3*a*d)*sqrt(c+d*x^4)/_
+-- (a^2*c^2*x)+1/5*(-d)^(1/4)*(5*b*c+3*a*d)*elliptic_e(asin((-d)^(1/4)*_
+-- x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/(a^2*c^(5/4)*sqrt(c+d*x^4))-_
+-- 1/5*(-d)^(1/4)*(5*b*c+3*a*d)*elliptic_f(asin((-d)^(1/4)*_
+-- x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/(a^2*c^(5/4)*sqrt(c+d*x^4))-_
+-- 1/2*b^(3/2)*elliptic_pi(-sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),_
+-- asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/((-a)^(5/2)*_
+-- sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))+1/2*b^(3/2)*_
+-- elliptic_pi(sqrt(b)*sqrt(c)/(sqrt(-a)*sqrt(-d)),asin(x*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/((-a)^(5/2)*_
+-- sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 468
+
+--S 469 of 716
+--a0:=integrate(t0,x)
+--E 469
+
+--S 470 of 716
+--m0:=a0-r0
+--E 470
+
+--S 471 of 716
+--d0:=D(m0,x)
+--E 471
+
+)clear all
+
+--S 472 of 716
+t0:=1/(x^7*(a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R +--------+
+--R 11 7 | 4
+--R (b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 716
+r0:=1/2*b^2*atan(x^2*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^4)))/_
+ (a^(5/2)*sqrt(b*c-a*d))-1/6*sqrt(c+d*x^4)/(a*c*x^6)+_
+ 1/6*(3*b*c+2*a*d)*sqrt(c+d*x^4)/(a^2*c^2*x^2)
+--R
+--R
+--R (2)
+--R 2 +-----------+
+--R 2 2 6 x \|- a d + b c
+--R 3b c x atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R +
+--R +--------+
+--R 4 +-----------+ +-+ | 4
+--R ((2a d + 3b c)x - a c)\|- a d + b c \|a \|d x + c
+--R /
+--R 2 2 6 +-----------+ +-+
+--R 6a c x \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 473
+
+--S 474 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 10 2 3 6 | 4 2 2 10 2 3 6 +-+
+--R ((3b c d x + 12b c x )\|d x + c + (- 9b c d x - 12b c x )\|c )
+--R *
+--R log
+--R +-----------+
+--R 4 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 6 2 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R 2 8 2 4 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 6 2 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x )\|c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R 2 8 2 4 2 +-+
+--R ((- 12a d - 18b c d)x + (- 10a c d - 24b c )x + 8a c )\|c
+--R *
+--R +-----------+ +--------+
+--R | 2 | 4
+--R \|a d - a b c \|d x + c
+--R +
+--R 3 2 12 2 2 8 2 3 4
+--R (4a d + 6b c d )x + (18a c d + 30b c d)x + (6a c d + 24b c )x
+--R +
+--R 3
+--R - 8a c
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R /
+--R +-----------+ +--------+
+--R 2 2 10 2 3 6 | 2 | 4
+--R (12a c d x + 48a c x )\|a d - a b c \|d x + c
+--R +
+--R +-----------+
+--R 2 2 10 2 3 6 +-+ | 2
+--R (- 36a c d x - 48a c x )\|c \|a d - a b c
+--R ,
+--R
+--R +--------+
+--R 2 2 10 2 3 6 | 4 2 2 10 2 3 6 +-+
+--R ((- 3b c d x - 12b c x )\|d x + c + (9b c d x + 12b c x )\|c )
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 6 | 2
+--R d x \|- a d + a b c
+--R +
+--R +--------+
+--R 2 2 10 2 3 6 | 4 2 2 10 2 3 6 +-+
+--R ((- 3b c d x - 12b c x )\|d x + c + (9b c d x + 12b c x )\|c )
+--R *
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R atan(--------------------)
+--R 2
+--R (a d - b c)x
+--R +
+--R 2 8 2 4 2
+--R ((- 6a d - 9b c d)x + (- 5a c d - 12b c )x + 4a c )
+--R *
+--R +-------------+ +--------+
+--R | 2 +-+ | 4
+--R \|- a d + a b c \|c \|d x + c
+--R +
+--R 3 2 12 2 2 8 2 3 4
+--R (2a d + 3b c d )x + (9a c d + 15b c d)x + (3a c d + 12b c )x
+--R +
+--R 3
+--R - 4a c
+--R *
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R /
+--R +-------------+ +--------+
+--R 2 2 10 2 3 6 | 2 | 4
+--R (6a c d x + 24a c x )\|- a d + a b c \|d x + c
+--R +
+--R +-------------+
+--R 2 2 10 2 3 6 | 2 +-+
+--R (- 18a c d x - 24a c x )\|- a d + a b c \|c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 474
+
+--S 475 of 716
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----------+ +-+
+--R b \|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 4 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 6 2 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 4
+--R \|d x + c
+--R +
+--R 2 8 2 4 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 6 2 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x )\|c
+--R /
+--R +--------+
+--R 4 +-+ | 4 8 4
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ 2 +-----------+
+--R 2 | 2 x \|- a d + b c
+--R - 2b \|a d - a b c atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R 2 +-----------+ +-+ | 2
+--R 4a \|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 475
+
+--S 476 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 716
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R -
+--R 2 +-----------+ +-+
+--R b \|- a d + b c \|a
+--R *
+--R +--------+
+--R 4 | 4 4 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 6 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R 2 +-----------+ +-+ \|- a d + a b c \|c
+--R - b \|- a d + b c \|a atan(--------------------)
+--R 2
+--R (a d - b c)x
+--R +
+--R +-------------+ 2 +-----------+
+--R 2 | 2 x \|- a d + b c
+--R - b \|- a d + a b c atan(----------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R 2 | 2 +-----------+ +-+
+--R 2a \|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 478
+
+)clear all
+
+--S 479 of 716
+t0:=1/(x^8*(a+b*x^4)*sqrt(c+d*x^4))
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R +--------+
+--R 12 8 | 4
+--R (b x + a x )\|d x + c
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 716
+--r0:=-1/7*sqrt(c+d*x^4)/(a*c*x^7)+1/21*(7*b*c+5*a*d)*sqrt(c+d*x^4)/_
+-- (a^2*c^2*x^3)-1/21*(-d)^(3/4)*(7*b*c+5*a*d)*elliptic_f(_
+-- asin((-d)^(1/4)*x/c^(1/4)),-1)*sqrt((c+d*x^4)/c)/(a^2*c^(7/4)*_
+-- sqrt(c+d*x^4))+1/2*b^2*elliptic_pi(-sqrt(-b)*sqrt(c)/(sqrt(a)*_
+-- sqrt(-d)),asin(x*sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/_
+-- (a^3*sqrt(c+d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))+1/2*b^2*_
+-- elliptic_pi(sqrt(-b)*sqrt(c)/(sqrt(a)*sqrt(-d)),asin(x*_
+-- sqrt(-sqrt(-d)/sqrt(c))),-1)*sqrt((c+d*x^4)/c)/(a^3*sqrt(c+_
+-- d*x^4)*sqrt(-sqrt(-d)/sqrt(c)))
+--E 480
+
+--S 481 of 716
+--a0:=integrate(t0,x)
+--E 481
+
+--S 482 of 716
+--m0:=a0-r0
+--E 482
+
+--S 483 of 716
+--d0:=D(m0,x)
+--E 483
+
+)clear all
+
+--S 484 of 716
+t0:=x^(-1+2*n)*(a+b*x^n)^3/(c+d*x^n)
+--R
+--R
+--R 3 n 3 2 n 2 2 n 3 2n - 1
+--R (b (x ) + 3a b (x ) + 3a b x + a )x
+--R (1) --------------------------------------------
+--R n
+--R d x + c
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 716
+r0:=-(b*c-a*d)^3*x^n/(d^4*n)+1/2*b*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*_
+ x^(2*n)/(d^3*n)-1/3*b^2*(b*c-3*a*d)*x^(3*n)/(d^2*n)+_
+ 1/4*b^3*x^(4*n)/(d*n)+c*(b*c-a*d)^3*log(c+d*x^n)/(d^5*n)
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 4 n 3 4 4n
+--R (- 12a c d + 36a b c d - 36a b c d + 12b c )log(d x + c) + 3b d x
+--R +
+--R 2 4 3 3 3n 2 4 2 3 3 2 2 2n
+--R (12a b d - 4b c d )x + (18a b d - 18a b c d + 6b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 n
+--R (12a d - 36a b c d + 36a b c d - 12b c d)x
+--R /
+--R 5
+--R 12d n
+--R Type: Expression(Integer)
+--E 485
+
+--S 486 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 2 3 3 4 n log(x)
+--R (- 12a c d + 36a b c d - 36a b c d + 12b c )log(d %e + c)
+--R +
+--R 3 4 n log(x) 4 2 4 3 3 n log(x) 3
+--R 3b d (%e ) + (12a b d - 4b c d )(%e )
+--R +
+--R 2 4 2 3 3 2 2 n log(x) 2
+--R (18a b d - 18a b c d + 6b c d )(%e )
+--R +
+--R 3 4 2 3 2 2 2 3 3 n log(x)
+--R (12a d - 36a b c d + 36a b c d - 12b c d)%e
+--R /
+--R 5
+--R 12d n
+--R Type: Union(Expression(Integer),...)
+--E 486
+
+--S 487 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 4 n log(x)
+--R (- 12a c d + 36a b c d - 36a b c d + 12b c )log(d %e + c)
+--R +
+--R 3 3 2 2 2 2 3 3 4 n
+--R (12a c d - 36a b c d + 36a b c d - 12b c )log(d x + c)
+--R +
+--R 3 4 n log(x) 4 2 4 3 3 n log(x) 3
+--R 3b d (%e ) + (12a b d - 4b c d )(%e )
+--R +
+--R 2 4 2 3 3 2 2 n log(x) 2
+--R (18a b d - 18a b c d + 6b c d )(%e )
+--R +
+--R 3 4 2 3 2 2 2 3 3 n log(x) 3 4 4n
+--R (12a d - 36a b c d + 36a b c d - 12b c d)%e - 3b d x
+--R +
+--R 2 4 3 3 3n 2 4 2 3 3 2 2 2n
+--R (- 12a b d + 4b c d )x + (- 18a b d + 18a b c d - 6b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 n
+--R (- 12a d + 36a b c d - 36a b c d + 12b c d)x
+--R /
+--R 5
+--R 12d n
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 488
+
+)clear all
+
+--S 489 of 716
+t0:=x^(-1+2*n)*(a+b*x^n)^2/(c+d*x^n)
+--R
+--R
+--R 2 n 2 n 2 2n - 1
+--R (b (x ) + 2a b x + a )x
+--R (1) -------------------------------
+--R n
+--R d x + c
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 716
+r0:=(b*c-a*d)^2*x^n/(d^3*n)-1/2*b*(b*c-2*a*d)*x^(2*n)/(d^2*n)+_
+ 1/3*b^2*x^(3*n)/(d*n)-c*(b*c-a*d)^2*log(c+d*x^n)/(d^4*n)
+--R
+--R
+--R (2)
+--R 2 2 2 2 3 n 2 3 3n
+--R (- 6a c d + 12a b c d - 6b c )log(d x + c) + 2b d x
+--R +
+--R 3 2 2 2n 2 3 2 2 2 n
+--R (6a b d - 3b c d )x + (6a d - 12a b c d + 6b c d)x
+--R /
+--R 4
+--R 6d n
+--R Type: Expression(Integer)
+--E 490
+
+--S 491 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 3 n log(x) 2 3 n log(x) 3
+--R (- 6a c d + 12a b c d - 6b c )log(d %e + c) + 2b d (%e )
+--R +
+--R 3 2 2 n log(x) 2 2 3 2 2 2 n log(x)
+--R (6a b d - 3b c d )(%e ) + (6a d - 12a b c d + 6b c d)%e
+--R /
+--R 4
+--R 6d n
+--R Type: Union(Expression(Integer),...)
+--E 491
+
+--S 492 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 3 n log(x)
+--R (- 6a c d + 12a b c d - 6b c )log(d %e + c)
+--R +
+--R 2 2 2 2 3 n 2 3 n log(x) 3
+--R (6a c d - 12a b c d + 6b c )log(d x + c) + 2b d (%e )
+--R +
+--R 3 2 2 n log(x) 2
+--R (6a b d - 3b c d )(%e )
+--R +
+--R 2 3 2 2 2 n log(x) 2 3 3n
+--R (6a d - 12a b c d + 6b c d)%e - 2b d x
+--R +
+--R 3 2 2 2n 2 3 2 2 2 n
+--R (- 6a b d + 3b c d )x + (- 6a d + 12a b c d - 6b c d)x
+--R /
+--R 4
+--R 6d n
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 493
+
+)clear all
+
+--S 494 of 716
+t0:=x^(-1+2*n)*(a+b*x^n)/(c+d*x^n)
+--R
+--R
+--R n 2n - 1
+--R (b x + a)x
+--R (1) -----------------
+--R n
+--R d x + c
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 716
+r0:=-(b*c-a*d)*x^n/(d^2*n)+1/2*b*x^(2*n)/(d*n)+_
+ c*(b*c-a*d)*log(c+d*x^n)/(d^3*n)
+--R
+--R
+--R 2 n 2 2n 2 n
+--R (- 2a c d + 2b c )log(d x + c) + b d x + (2a d - 2b c d)x
+--R (2) --------------------------------------------------------------
+--R 3
+--R 2d n
+--R Type: Expression(Integer)
+--E 495
+
+--S 496 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 n log(x) 2 n log(x) 2
+--R (- 2a c d + 2b c )log(d %e + c) + b d (%e )
+--R +
+--R 2 n log(x)
+--R (2a d - 2b c d)%e
+--R /
+--R 3
+--R 2d n
+--R Type: Union(Expression(Integer),...)
+--E 496
+
+--S 497 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 n log(x) 2 n
+--R (- 2a c d + 2b c )log(d %e + c) + (2a c d - 2b c )log(d x + c)
+--R +
+--R 2 n log(x) 2 2 n log(x) 2 2n
+--R b d (%e ) + (2a d - 2b c d)%e - b d x
+--R +
+--R 2 n
+--R (- 2a d + 2b c d)x
+--R /
+--R 3
+--R 2d n
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 498
+
+)clear all
+
+--S 499 of 716
+t0:=x^(-1+2*n)/((a+b*x^n)*(c+d*x^n))
+--R
+--R
+--R 2n - 1
+--R x
+--R (1) -------------------------------
+--R n 2 n
+--R b d (x ) + (a d + b c)x + a c
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 716
+r0:=-a*log(a+b*x^n)/(b*(b*c-a*d)*n)+c*log(c+d*x^n)/(d*(b*c-a*d)*n)
+--R
+--R
+--R n n
+--R - b c log(d x + c) + a d log(b x + a)
+--R (2) ---------------------------------------
+--R 2 2
+--R (a b d - b c d)n
+--R Type: Expression(Integer)
+--E 500
+
+--S 501 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R n log(x) n log(x)
+--R - b c log(d %e + c) + a d log(b %e + a)
+--R (3) -------------------------------------------------------
+--R 2 2
+--R (a b d - b c d)n
+--R Type: Union(Expression(Integer),...)
+--E 501
+
+--S 502 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R n log(x) n log(x)
+--R - b c log(d %e + c) + a d log(b %e + a)
+--R +
+--R n n
+--R b c log(d x + c) - a d log(b x + a)
+--R /
+--R 2 2
+--R (a b d - b c d)n
+--R Type: Expression(Integer)
+--E 502
+
+--S 503 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 503
+
+)clear all
+
+--S 504 of 716
+t0:=x^(-1+2*n)/((a+b*x^n)^2*(c+d*x^n))
+--R
+--R
+--R 2n - 1
+--R x
+--R (1) --------------------------------------------------------
+--R 2 n 3 2 n 2 2 n 2
+--R b d (x ) + (2a b d + b c)(x ) + (a d + 2a b c)x + a c
+--R Type: Expression(Integer)
+--E 504
+
+--S 505 of 716
+r0:=a/(b*(b*c-a*d)*n*(a+b*x^n))+c*log(a+b*x^n)/((b*c-a*d)^2*n)-_
+ c*log(c+d*x^n)/((b*c-a*d)^2*n)
+--R
+--R
+--R (2)
+--R 2 n n 2 n n 2
+--R (- b c x - a b c)log(d x + c) + (b c x + a b c)log(b x + a) - a d + a b c
+--R -----------------------------------------------------------------------------
+--R 2 2 2 3 4 2 n 3 2 2 2 3 2
+--R (a b d - 2a b c d + b c )n x + (a b d - 2a b c d + a b c )n
+--R Type: Expression(Integer)
+--E 505
+
+--S 506 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 n log(x) n log(x)
+--R (- b c %e - a b c)log(d %e + c)
+--R +
+--R 2 n log(x) n log(x) 2
+--R (b c %e + a b c)log(b %e + a) - a d + a b c
+--R /
+--R 2 2 2 3 4 2 n log(x) 3 2 2 2 3 2
+--R (a b d - 2a b c d + b c )n %e + (a b d - 2a b c d + a b c )n
+--R Type: Union(Expression(Integer),...)
+--E 506
+
+--S 507 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 n n log(x) n 2 n log(x)
+--R ((- b c x - a b c)%e - a b c x - a c)log(d %e + c)
+--R +
+--R 2 n n log(x) n 2 n log(x)
+--R ((b c x + a b c)%e + a b c x + a c)log(b %e + a)
+--R +
+--R 2 n n log(x) n 2 n
+--R ((b c x + a b c)%e + a b c x + a c)log(d x + c)
+--R +
+--R 2 n n log(x) n 2 n
+--R ((- b c x - a b c)%e - a b c x - a c)log(b x + a)
+--R +
+--R 2 n log(x) 2 n
+--R (a d - a b c)%e + (- a d + a b c)x
+--R /
+--R 2 2 2 3 4 2 n 3 2 2 2 3 2
+--R ((a b d - 2a b c d + b c )n x + (a b d - 2a b c d + a b c )n)
+--R *
+--R n log(x)
+--R %e
+--R +
+--R 3 2 2 2 3 2 n 4 2 3 2 2 2
+--R (a b d - 2a b c d + a b c )n x + (a d - 2a b c d + a b c )n
+--R Type: Expression(Integer)
+--E 507
+
+--S 508 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 508
+
+)clear all
+
+--S 509 of 716
+t0:=x^(-1+2*n)/((a+b*x^n)^3*(c+d*x^n))
+--R
+--R
+--R (1)
+--R 2n - 1
+--R x
+--R /
+--R 3 n 4 2 3 n 3 2 2 n 2
+--R b d (x ) + (3a b d + b c)(x ) + (3a b d + 3a b c)(x )
+--R +
+--R 3 2 n 3
+--R (a d + 3a b c)x + a c
+--R Type: Expression(Integer)
+--E 509
+
+--S 510 of 716
+r0:=1/2*a/(b*(b*c-a*d)*n*(a+b*x^n)^2)-c/((b*c-a*d)^2*n*(a+b*x^n))-_
+ c*d*log(a+b*x^n)/((b*c-a*d)^3*n)+c*d*log(c+d*x^n)/((b*c-a*d)^3*n)
+--R
+--R
+--R (2)
+--R 3 n 2 2 n 2 n
+--R (- 2b c d (x ) - 4a b c d x - 2a b c d)log(d x + c)
+--R +
+--R 3 n 2 2 n 2 n
+--R (2b c d (x ) + 4a b c d x + 2a b c d)log(b x + a)
+--R +
+--R 2 3 2 n 3 2 2 2
+--R (- 2a b c d + 2b c )x - a d + a b c
+--R /
+--R 3 3 3 2 4 2 5 2 6 3 n 2
+--R (2a b d - 6a b c d + 6a b c d - 2b c )n (x )
+--R +
+--R 4 2 3 3 3 2 2 4 2 5 3 n
+--R (4a b d - 12a b c d + 12a b c d - 4a b c )n x
+--R +
+--R 5 3 4 2 2 3 3 2 2 4 3
+--R (2a b d - 6a b c d + 6a b c d - 2a b c )n
+--R Type: Expression(Integer)
+--E 510
+
+--S 511 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 n log(x) 2 2 n log(x) 2
+--R (- 2b c d (%e ) - 4a b c d %e - 2a b c d)
+--R *
+--R n log(x)
+--R log(d %e + c)
+--R +
+--R 3 n log(x) 2 2 n log(x) 2
+--R (2b c d (%e ) + 4a b c d %e + 2a b c d)
+--R *
+--R n log(x)
+--R log(b %e + a)
+--R +
+--R 2 3 2 n log(x) 3 2 2 2
+--R (- 2a b c d + 2b c )%e - a d + a b c
+--R /
+--R 3 3 3 2 4 2 5 2 6 3 n log(x) 2
+--R (2a b d - 6a b c d + 6a b c d - 2b c )n (%e )
+--R +
+--R 4 2 3 3 3 2 2 4 2 5 3 n log(x)
+--R (4a b d - 12a b c d + 12a b c d - 4a b c )n %e
+--R +
+--R 5 3 4 2 2 3 3 2 2 4 3
+--R (2a b d - 6a b c d + 6a b c d - 2a b c )n
+--R Type: Union(Expression(Integer),...)
+--E 511
+
+--S 512 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 n 2 3 n 2 2 n log(x) 2
+--R (- 2b c d (x ) - 4a b c d x - 2a b c d)(%e )
+--R +
+--R 3 n 2 2 2 n 3 n log(x)
+--R (- 4a b c d (x ) - 8a b c d x - 4a b c d)%e
+--R +
+--R 2 2 n 2 3 n 4
+--R - 2a b c d (x ) - 4a b c d x - 2a c d
+--R *
+--R n log(x)
+--R log(d %e + c)
+--R +
+--R 4 n 2 3 n 2 2 n log(x) 2
+--R (2b c d (x ) + 4a b c d x + 2a b c d)(%e )
+--R +
+--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2
+--R (4a b c d (x ) + 8a b c d x + 4a b c d)%e + 2a b c d (x )
+--R +
+--R 3 n 4
+--R 4a b c d x + 2a c d
+--R *
+--R n log(x)
+--R log(b %e + a)
+--R +
+--R 4 n 2 3 n 2 2 n log(x) 2
+--R (2b c d (x ) + 4a b c d x + 2a b c d)(%e )
+--R +
+--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2
+--R (4a b c d (x ) + 8a b c d x + 4a b c d)%e + 2a b c d (x )
+--R +
+--R 3 n 4
+--R 4a b c d x + 2a c d
+--R *
+--R n
+--R log(d x + c)
+--R +
+--R 4 n 2 3 n 2 2 n log(x) 2
+--R (- 2b c d (x ) - 4a b c d x - 2a b c d)(%e )
+--R +
+--R 3 n 2 2 2 n 3 n log(x)
+--R (- 4a b c d (x ) - 8a b c d x - 4a b c d)%e
+--R +
+--R 2 2 n 2 3 n 4
+--R - 2a b c d (x ) - 4a b c d x - 2a c d
+--R *
+--R n
+--R log(b x + a)
+--R +
+--R 3 4 2 n 3 2 3 2 n log(x) 2
+--R ((2a b c d - 2b c )x + a b d - a b c )(%e )
+--R +
+--R 3 4 2 n 2 4 2 3 n log(x)
+--R ((- 2a b c d + 2b c )(x ) + 2a d - 2a b c d)%e
+--R +
+--R 3 2 3 2 n 2 4 2 3 n
+--R (- a b d + a b c )(x ) + (- 2a d + 2a b c d)x
+--R /
+--R 3 4 3 2 5 2 6 2 7 3 n 2
+--R (2a b d - 6a b c d + 6a b c d - 2b c )n (x )
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 n
+--R (4a b d - 12a b c d + 12a b c d - 4a b c )n x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3
+--R (2a b d - 6a b c d + 6a b c d - 2a b c )n
+--R *
+--R n log(x) 2
+--R (%e )
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 n 2
+--R (4a b d - 12a b c d + 12a b c d - 4a b c )n (x )
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 n
+--R (8a b d - 24a b c d + 24a b c d - 8a b c )n x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3
+--R (4a b d - 12a b c d + 12a b c d - 4a b c )n
+--R *
+--R n log(x)
+--R %e
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 n 2
+--R (2a b d - 6a b c d + 6a b c d - 2a b c )n (x )
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 n
+--R (4a b d - 12a b c d + 12a b c d - 4a b c )n x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (2a d - 6a b c d + 6a b c d - 2a b c )n
+--R Type: Expression(Integer)
+--E 512
+
+--S 513 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 513
+
+)clear all
+
+--S 514 of 716
+t0:=x^(-1+3*n)*(a+b*x^n)^3/(c+d*x^n)
+--R
+--R
+--R 3 n 3 2 n 2 2 n 3 3n - 1
+--R (b (x ) + 3a b (x ) + 3a b x + a )x
+--R (1) --------------------------------------------
+--R n
+--R d x + c
+--R Type: Expression(Integer)
+--E 514
+
+--S 515 of 716
+r0:=c*(b*c-a*d)^3*x^n/(d^5*n)-1/2*(b*c-a*d)^3*x^(2*n)/(d^4*n)+_
+ 1/3*b*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*x^(3*n)/(d^3*n)-_
+ 1/4*b^2*(b*c-3*a*d)*x^(4*n)/(d^2*n)+1/5*b^3*x^(5*n)/(d*n)-_
+ c^2*(b*c-a*d)^3*log(c+d*x^n)/(d^6*n)
+--R
+--R
+--R (2)
+--R 3 2 3 2 3 2 2 4 3 5 n 3 5 5n
+--R (60a c d - 180a b c d + 180a b c d - 60b c )log(d x + c) + 12b d x
+--R +
+--R 2 5 3 4 4n 2 5 2 4 3 2 3 3n
+--R (45a b d - 15b c d )x + (60a b d - 60a b c d + 20b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 2n
+--R (30a d - 90a b c d + 90a b c d - 30b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 n
+--R (- 60a c d + 180a b c d - 180a b c d + 60b c d)x
+--R /
+--R 6
+--R 60d n
+--R Type: Expression(Integer)
+--E 515
+
+--S 516 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 3 2 3 2 2 4 3 5 n log(x)
+--R (60a c d - 180a b c d + 180a b c d - 60b c )log(d %e + c)
+--R +
+--R 3 5 n log(x) 5 2 5 3 4 n log(x) 4
+--R 12b d (%e ) + (45a b d - 15b c d )(%e )
+--R +
+--R 2 5 2 4 3 2 3 n log(x) 3
+--R (60a b d - 60a b c d + 20b c d )(%e )
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 n log(x) 2
+--R (30a d - 90a b c d + 90a b c d - 30b c d )(%e )
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 n log(x)
+--R (- 60a c d + 180a b c d - 180a b c d + 60b c d)%e
+--R /
+--R 6
+--R 60d n
+--R Type: Union(Expression(Integer),...)
+--E 516
+
+--S 517 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 2 3 2 3 2 2 4 3 5 n log(x)
+--R (60a c d - 180a b c d + 180a b c d - 60b c )log(d %e + c)
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 n
+--R (- 60a c d + 180a b c d - 180a b c d + 60b c )log(d x + c)
+--R +
+--R 3 5 n log(x) 5 2 5 3 4 n log(x) 4
+--R 12b d (%e ) + (45a b d - 15b c d )(%e )
+--R +
+--R 2 5 2 4 3 2 3 n log(x) 3
+--R (60a b d - 60a b c d + 20b c d )(%e )
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 n log(x) 2
+--R (30a d - 90a b c d + 90a b c d - 30b c d )(%e )
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 n log(x) 3 5 5n
+--R (- 60a c d + 180a b c d - 180a b c d + 60b c d)%e - 12b d x
+--R +
+--R 2 5 3 4 4n 2 5 2 4 3 2 3 3n
+--R (- 45a b d + 15b c d )x + (- 60a b d + 60a b c d - 20b c d )x
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 2n
+--R (- 30a d + 90a b c d - 90a b c d + 30b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 n
+--R (60a c d - 180a b c d + 180a b c d - 60b c d)x
+--R /
+--R 6
+--R 60d n
+--R Type: Expression(Integer)
+--E 517
+
+--S 518 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 518
+
+)clear all
+
+--S 519 of 716
+t0:=x^(-1+3*n)*(a+b*x^n)^2/(c+d*x^n)
+--R
+--R
+--R 2 n 2 n 2 3n - 1
+--R (b (x ) + 2a b x + a )x
+--R (1) -------------------------------
+--R n
+--R d x + c
+--R Type: Expression(Integer)
+--E 519
+
+--S 520 of 716
+r0:=-c*(b*c-a*d)^2*x^n/(d^4*n)+1/2*(b*c-a*d)^2*x^(2*n)/(d^3*n)-_
+ 1/3*b*(b*c-2*a*d)*x^(3*n)/(d^2*n)+1/4*b^2*x^(4*n)/(d*n)+_
+ c^2*(b*c-a*d)^2*log(c+d*x^n)/(d^5*n)
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 4 n 2 4 4n
+--R (12a c d - 24a b c d + 12b c )log(d x + c) + 3b d x
+--R +
+--R 4 2 3 3n 2 4 3 2 2 2 2n
+--R (8a b d - 4b c d )x + (6a d - 12a b c d + 6b c d )x
+--R +
+--R 2 3 2 2 2 3 n
+--R (- 12a c d + 24a b c d - 12b c d)x
+--R /
+--R 5
+--R 12d n
+--R Type: Expression(Integer)
+--E 520
+
+--S 521 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 3 2 4 n log(x) 2 4 n log(x) 4
+--R (12a c d - 24a b c d + 12b c )log(d %e + c) + 3b d (%e )
+--R +
+--R 4 2 3 n log(x) 3
+--R (8a b d - 4b c d )(%e )
+--R +
+--R 2 4 3 2 2 2 n log(x) 2
+--R (6a d - 12a b c d + 6b c d )(%e )
+--R +
+--R 2 3 2 2 2 3 n log(x)
+--R (- 12a c d + 24a b c d - 12b c d)%e
+--R /
+--R 5
+--R 12d n
+--R Type: Union(Expression(Integer),...)
+--E 521
+
+--S 522 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 3 2 4 n log(x)
+--R (12a c d - 24a b c d + 12b c )log(d %e + c)
+--R +
+--R 2 2 2 3 2 4 n 2 4 n log(x) 4
+--R (- 12a c d + 24a b c d - 12b c )log(d x + c) + 3b d (%e )
+--R +
+--R 4 2 3 n log(x) 3
+--R (8a b d - 4b c d )(%e )
+--R +
+--R 2 4 3 2 2 2 n log(x) 2
+--R (6a d - 12a b c d + 6b c d )(%e )
+--R +
+--R 2 3 2 2 2 3 n log(x) 2 4 4n
+--R (- 12a c d + 24a b c d - 12b c d)%e - 3b d x
+--R +
+--R 4 2 3 3n 2 4 3 2 2 2 2n
+--R (- 8a b d + 4b c d )x + (- 6a d + 12a b c d - 6b c d )x
+--R +
+--R 2 3 2 2 2 3 n
+--R (12a c d - 24a b c d + 12b c d)x
+--R /
+--R 5
+--R 12d n
+--R Type: Expression(Integer)
+--E 522
+
+--S 523 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 523
+
+)clear all
+
+--S 524 of 716
+t0:=x^(-1+3*n)*(a+b*x^n)/(c+d*x^n)
+--R
+--R
+--R n 3n - 1
+--R (b x + a)x
+--R (1) -----------------
+--R n
+--R d x + c
+--R Type: Expression(Integer)
+--E 524
+
+--S 525 of 716
+r0:=c*(b*c-a*d)*x^n/(d^3*n)-1/2*(b*c-a*d)*x^(2*n)/(d^2*n)+_
+ 1/3*b*x^(3*n)/(d*n)-c^2*(b*c-a*d)*log(c+d*x^n)/(d^4*n)
+--R
+--R
+--R (2)
+--R 2 3 n 3 3n 3 2 2n
+--R (6a c d - 6b c )log(d x + c) + 2b d x + (3a d - 3b c d )x
+--R +
+--R 2 2 n
+--R (- 6a c d + 6b c d)x
+--R /
+--R 4
+--R 6d n
+--R Type: Expression(Integer)
+--E 525
+
+--S 526 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 n log(x) 3 n log(x) 3
+--R (6a c d - 6b c )log(d %e + c) + 2b d (%e )
+--R +
+--R 3 2 n log(x) 2 2 2 n log(x)
+--R (3a d - 3b c d )(%e ) + (- 6a c d + 6b c d)%e
+--R /
+--R 4
+--R 6d n
+--R Type: Union(Expression(Integer),...)
+--E 526
+
+--S 527 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 n log(x) 2 3 n
+--R (6a c d - 6b c )log(d %e + c) + (- 6a c d + 6b c )log(d x + c)
+--R +
+--R 3 n log(x) 3 3 2 n log(x) 2
+--R 2b d (%e ) + (3a d - 3b c d )(%e )
+--R +
+--R 2 2 n log(x) 3 3n 3 2 2n
+--R (- 6a c d + 6b c d)%e - 2b d x + (- 3a d + 3b c d )x
+--R +
+--R 2 2 n
+--R (6a c d - 6b c d)x
+--R /
+--R 4
+--R 6d n
+--R Type: Expression(Integer)
+--E 527
+
+--S 528 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 528
+
+)clear all
+
+--S 529 of 716
+t0:=x^(-1+3*n)/((a+b*x^n)*(c+d*x^n))
+--R
+--R
+--R 3n - 1
+--R x
+--R (1) -------------------------------
+--R n 2 n
+--R b d (x ) + (a d + b c)x + a c
+--R Type: Expression(Integer)
+--E 529
+
+--S 530 of 716
+r0:=x^n/(b*d*n)+a^2*log(a+b*x^n)/(b^2*(b*c-a*d)*n)-_
+ c^2*log(c+d*x^n)/(d^2*(b*c-a*d)*n)
+--R
+--R
+--R 2 2 n 2 2 n 2 2 n
+--R b c log(d x + c) - a d log(b x + a) + (a b d - b c d)x
+--R (2) ----------------------------------------------------------
+--R 2 3 3 2
+--R (a b d - b c d )n
+--R Type: Expression(Integer)
+--E 530
+
+--S 531 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 n log(x) 2 2 n log(x)
+--R b c log(d %e + c) - a d log(b %e + a)
+--R +
+--R 2 2 n log(x)
+--R (a b d - b c d)%e
+--R /
+--R 2 3 3 2
+--R (a b d - b c d )n
+--R Type: Union(Expression(Integer),...)
+--E 531
+
+--S 532 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 n log(x) 2 2 n log(x) 2 2 n
+--R b c log(d %e + c) - a d log(b %e + a) - b c log(d x + c)
+--R +
+--R 2 2 n 2 2 n log(x) 2 2 n
+--R a d log(b x + a) + (a b d - b c d)%e + (- a b d + b c d)x
+--R /
+--R 2 3 3 2
+--R (a b d - b c d )n
+--R Type: Expression(Integer)
+--E 532
+
+--S 533 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 533
+
+)clear all
+
+--S 534 of 716
+t0:=x^(-1+3*n)/((a+b*x^n)^2*(c+d*x^n))
+--R
+--R
+--R 3n - 1
+--R x
+--R (1) --------------------------------------------------------
+--R 2 n 3 2 n 2 2 n 2
+--R b d (x ) + (2a b d + b c)(x ) + (a d + 2a b c)x + a c
+--R Type: Expression(Integer)
+--E 534
+
+--S 535 of 716
+r0:=-a^2/(b^2*(b*c-a*d)*n*(a+b*x^n))-a*(2*b*c-a*d)*_
+ log(a+b*x^n)/(b^2*(b*c-a*d)^2*n)+c^2*log(c+d*x^n)/(d*(b*c-a*d)^2*n)
+--R
+--R
+--R (2)
+--R 3 2 n 2 2 n
+--R (b c x + a b c )log(d x + c)
+--R +
+--R 2 2 2 n 3 2 2 n 3 2 2
+--R ((a b d - 2a b c d)x + a d - 2a b c d)log(b x + a) + a d - a b c d
+--R /
+--R 2 3 3 4 2 5 2 n 3 2 3 2 3 2 4 2
+--R (a b d - 2a b c d + b c d)n x + (a b d - 2a b c d + a b c d)n
+--R Type: Expression(Integer)
+--E 535
+
+--S 536 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 n log(x) 2 2 n log(x)
+--R (b c %e + a b c )log(d %e + c)
+--R +
+--R 2 2 2 n log(x) 3 2 2 n log(x)
+--R ((a b d - 2a b c d)%e + a d - 2a b c d)log(b %e + a)
+--R +
+--R 3 2 2
+--R a d - a b c d
+--R /
+--R 2 3 3 4 2 5 2 n log(x) 3 2 3 2 3 2 4 2
+--R (a b d - 2a b c d + b c d)n %e + (a b d - 2a b c d + a b c d)n
+--R Type: Union(Expression(Integer),...)
+--E 536
+
+--S 537 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 2 n 3 2 n log(x) 3 2 n 2 2 2 n log(x)
+--R ((b c x + a b c )%e + a b c x + a b c )log(d %e + c)
+--R +
+--R 2 2 2 3 n 3 2 2 2 n log(x)
+--R ((a b d - 2a b c d)x + a b d - 2a b c d)%e
+--R +
+--R 3 2 2 2 n 4 2 3
+--R (a b d - 2a b c d)x + a d - 2a b c d
+--R *
+--R n log(x)
+--R log(b %e + a)
+--R +
+--R 4 2 n 3 2 n log(x) 3 2 n 2 2 2 n
+--R ((- b c x - a b c )%e - a b c x - a b c )log(d x + c)
+--R +
+--R 2 2 2 3 n 3 2 2 2 n log(x)
+--R ((- a b d + 2a b c d)x - a b d + 2a b c d)%e
+--R +
+--R 3 2 2 2 n 4 2 3
+--R (- a b d + 2a b c d)x - a d + 2a b c d
+--R *
+--R n
+--R log(b x + a)
+--R +
+--R 3 2 2 2 n log(x) 3 2 2 2 n
+--R (- a b d + a b c d)%e + (a b d - a b c d)x
+--R /
+--R 2 4 3 5 2 6 2 n 3 3 3 2 4 2 5 2
+--R ((a b d - 2a b c d + b c d)n x + (a b d - 2a b c d + a b c d)n)
+--R *
+--R n log(x)
+--R %e
+--R +
+--R 3 3 3 2 4 2 5 2 n 4 2 3 3 3 2 2 4 2
+--R (a b d - 2a b c d + a b c d)n x + (a b d - 2a b c d + a b c d)n
+--R Type: Expression(Integer)
+--E 537
+
+--S 538 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 538
+
+)clear all
+
+--S 539 of 716
+t0:=x^(-1+3*n)/((a+b*x^n)^3*(c+d*x^n))
+--R
+--R
+--R (1)
+--R 3n - 1
+--R x
+--R /
+--R 3 n 4 2 3 n 3 2 2 n 2
+--R b d (x ) + (3a b d + b c)(x ) + (3a b d + 3a b c)(x )
+--R +
+--R 3 2 n 3
+--R (a d + 3a b c)x + a c
+--R Type: Expression(Integer)
+--E 539
+
+--S 540 of 716
+r0:=-1/2*a^2/(b^2*(b*c-a*d)*n*(a+b*x^n)^2)+a*(2*b*c-a*d)/(b^2*(b*c-a*d)^2*_
+ n*(a+b*x^n))+c^2*log(a+b*x^n)/((b*c-a*d)^3*n)-_
+ c^2*log(c+d*x^n)/((b*c-a*d)^3*n)
+--R
+--R
+--R (2)
+--R 4 2 n 2 3 2 n 2 2 2 n
+--R (2b c (x ) + 4a b c x + 2a b c )log(d x + c)
+--R +
+--R 4 2 n 2 3 2 n 2 2 2 n
+--R (- 2b c (x ) - 4a b c x - 2a b c )log(b x + a)
+--R +
+--R 3 2 2 2 3 2 n 4 2 3 2 2 2
+--R (- 2a b d + 6a b c d - 4a b c )x - a d + 4a b c d - 3a b c
+--R /
+--R 3 4 3 2 5 2 6 2 7 3 n 2
+--R (2a b d - 6a b c d + 6a b c d - 2b c )n (x )
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 n
+--R (4a b d - 12a b c d + 12a b c d - 4a b c )n x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3
+--R (2a b d - 6a b c d + 6a b c d - 2a b c )n
+--R Type: Expression(Integer)
+--E 540
+
+--S 541 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 n log(x) 2 3 2 n log(x) 2 2 2 n log(x)
+--R (2b c (%e ) + 4a b c %e + 2a b c )log(d %e + c)
+--R +
+--R 4 2 n log(x) 2 3 2 n log(x) 2 2 2 n log(x)
+--R (- 2b c (%e ) - 4a b c %e - 2a b c )log(b %e + a)
+--R +
+--R 3 2 2 2 3 2 n log(x) 4 2 3 2 2 2
+--R (- 2a b d + 6a b c d - 4a b c )%e - a d + 4a b c d - 3a b c
+--R /
+--R 3 4 3 2 5 2 6 2 7 3 n log(x) 2
+--R (2a b d - 6a b c d + 6a b c d - 2b c )n (%e )
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 n log(x)
+--R (4a b d - 12a b c d + 12a b c d - 4a b c )n %e
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3
+--R (2a b d - 6a b c d + 6a b c d - 2a b c )n
+--R Type: Union(Expression(Integer),...)
+--E 541
+
+--S 542 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 2 n 2 3 2 n 2 2 2 n log(x) 2
+--R (2b c (x ) + 4a b c x + 2a b c )(%e )
+--R +
+--R 3 2 n 2 2 2 2 n 3 2 n log(x) 2 2 2 n 2
+--R (4a b c (x ) + 8a b c x + 4a b c )%e + 2a b c (x )
+--R +
+--R 3 2 n 4 2
+--R 4a b c x + 2a c
+--R *
+--R n log(x)
+--R log(d %e + c)
+--R +
+--R 4 2 n 2 3 2 n 2 2 2 n log(x) 2
+--R (- 2b c (x ) - 4a b c x - 2a b c )(%e )
+--R +
+--R 3 2 n 2 2 2 2 n 3 2 n log(x) 2 2 2 n 2
+--R (- 4a b c (x ) - 8a b c x - 4a b c )%e - 2a b c (x )
+--R +
+--R 3 2 n 4 2
+--R - 4a b c x - 2a c
+--R *
+--R n log(x)
+--R log(b %e + a)
+--R +
+--R 4 2 n 2 3 2 n 2 2 2 n log(x) 2
+--R (- 2b c (x ) - 4a b c x - 2a b c )(%e )
+--R +
+--R 3 2 n 2 2 2 2 n 3 2 n log(x) 2 2 2 n 2
+--R (- 4a b c (x ) - 8a b c x - 4a b c )%e - 2a b c (x )
+--R +
+--R 3 2 n 4 2
+--R - 4a b c x - 2a c
+--R *
+--R n
+--R log(d x + c)
+--R +
+--R 4 2 n 2 3 2 n 2 2 2 n log(x) 2
+--R (2b c (x ) + 4a b c x + 2a b c )(%e )
+--R +
+--R 3 2 n 2 2 2 2 n 3 2 n log(x) 2 2 2 n 2
+--R (4a b c (x ) + 8a b c x + 4a b c )%e + 2a b c (x )
+--R +
+--R 3 2 n 4 2
+--R 4a b c x + 2a c
+--R *
+--R n
+--R log(b x + a)
+--R +
+--R 3 2 2 2 3 2 n 4 2 3 2 2 2
+--R ((2a b d - 6a b c d + 4a b c )x + a d - 4a b c d + 3a b c )
+--R *
+--R n log(x) 2
+--R (%e )
+--R +
+--R 3 2 2 2 3 2 n 2 4 3 2 n log(x)
+--R ((- 2a b d + 6a b c d - 4a b c )(x ) - 2a c d + 2a b c )%e
+--R +
+--R 4 2 3 2 2 2 n 2 4 3 2 n
+--R (- a d + 4a b c d - 3a b c )(x ) + (2a c d - 2a b c )x
+--R /
+--R 3 4 3 2 5 2 6 2 7 3 n 2
+--R (2a b d - 6a b c d + 6a b c d - 2b c )n (x )
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 n
+--R (4a b d - 12a b c d + 12a b c d - 4a b c )n x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3
+--R (2a b d - 6a b c d + 6a b c d - 2a b c )n
+--R *
+--R n log(x) 2
+--R (%e )
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 n 2
+--R (4a b d - 12a b c d + 12a b c d - 4a b c )n (x )
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 n
+--R (8a b d - 24a b c d + 24a b c d - 8a b c )n x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3
+--R (4a b d - 12a b c d + 12a b c d - 4a b c )n
+--R *
+--R n log(x)
+--R %e
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 n 2
+--R (2a b d - 6a b c d + 6a b c d - 2a b c )n (x )
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 n
+--R (4a b d - 12a b c d + 12a b c d - 4a b c )n x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (2a d - 6a b c d + 6a b c d - 2a b c )n
+--R Type: Expression(Integer)
+--E 542
+
+--S 543 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 543
+
+)clear all
+
+--S 544 of 716
+t0:=x^13*(b+c*x)^13*(b+2*c*x)
+--R
+--R
+--R (1)
+--R 14 27 13 26 2 12 25 3 11 24 4 10 23
+--R 2c x + 27b c x + 169b c x + 650b c x + 1716b c x
+--R +
+--R 5 9 22 6 8 21 7 7 20 8 6 19 9 5 18
+--R 3289b c x + 4719b c x + 5148b c x + 4290b c x + 2717b c x
+--R +
+--R 10 4 17 11 3 16 12 2 15 13 14 14 13
+--R 1287b c x + 442b c x + 104b c x + 15b c x + b x
+--R Type: Polynomial(Integer)
+--E 544
+
+--S 545 of 716
+r0:=1/14*x^14*(b+c*x)^14
+--R
+--R
+--R (2)
+--R 1 14 28 13 27 13 2 12 26 3 11 25 143 4 10 24 5 9 23
+--R -- c x + b c x + -- b c x + 26b c x + --- b c x + 143b c x
+--R 14 2 2
+--R +
+--R 429 6 8 22 1716 7 7 21 429 8 6 20 9 5 19 143 10 4 18
+--R --- b c x + ---- b c x + --- b c x + 143b c x + --- b c x
+--R 2 7 2 2
+--R +
+--R 11 3 17 13 12 2 16 13 15 1 14 14
+--R 26b c x + -- b c x + b c x + -- b x
+--R 2 14
+--R Type: Polynomial(Fraction(Integer))
+--E 545
+
+--S 546 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 14 28 13 27 13 2 12 26 3 11 25 143 4 10 24 5 9 23
+--R -- c x + b c x + -- b c x + 26b c x + --- b c x + 143b c x
+--R 14 2 2
+--R +
+--R 429 6 8 22 1716 7 7 21 429 8 6 20 9 5 19 143 10 4 18
+--R --- b c x + ---- b c x + --- b c x + 143b c x + --- b c x
+--R 2 7 2 2
+--R +
+--R 11 3 17 13 12 2 16 13 15 1 14 14
+--R 26b c x + -- b c x + b c x + -- b x
+--R 2 14
+--R Type: Polynomial(Fraction(Integer))
+--E 546
+
+--S 547 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 547
+
+--S 548 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 548
+
+)clear all
+
+--S 549 of 716
+t0:=x^27*(b+c*x^2)^13*(b+2*c*x^2)
+--R
+--R
+--R (1)
+--R 14 55 13 53 2 12 51 3 11 49 4 10 47
+--R 2c x + 27b c x + 169b c x + 650b c x + 1716b c x
+--R +
+--R 5 9 45 6 8 43 7 7 41 8 6 39 9 5 37
+--R 3289b c x + 4719b c x + 5148b c x + 4290b c x + 2717b c x
+--R +
+--R 10 4 35 11 3 33 12 2 31 13 29 14 27
+--R 1287b c x + 442b c x + 104b c x + 15b c x + b x
+--R Type: Polynomial(Integer)
+--E 549
+
+--S 550 of 716
+r0:=1/28*x^28*(b+c*x^2)^14
+--R
+--R
+--R (2)
+--R 1 14 56 1 13 54 13 2 12 52 3 11 50 143 4 10 48
+--R -- c x + - b c x + -- b c x + 13b c x + --- b c x
+--R 28 2 4 4
+--R +
+--R 143 5 9 46 429 6 8 44 858 7 7 42 429 8 6 40 143 9 5 38
+--R --- b c x + --- b c x + --- b c x + --- b c x + --- b c x
+--R 2 4 7 4 2
+--R +
+--R 143 10 4 36 11 3 34 13 12 2 32 1 13 30 1 14 28
+--R --- b c x + 13b c x + -- b c x + - b c x + -- b x
+--R 4 4 2 28
+--R Type: Polynomial(Fraction(Integer))
+--E 550
+
+--S 551 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 14 56 1 13 54 13 2 12 52 3 11 50 143 4 10 48
+--R -- c x + - b c x + -- b c x + 13b c x + --- b c x
+--R 28 2 4 4
+--R +
+--R 143 5 9 46 429 6 8 44 858 7 7 42 429 8 6 40 143 9 5 38
+--R --- b c x + --- b c x + --- b c x + --- b c x + --- b c x
+--R 2 4 7 4 2
+--R +
+--R 143 10 4 36 11 3 34 13 12 2 32 1 13 30 1 14 28
+--R --- b c x + 13b c x + -- b c x + - b c x + -- b x
+--R 4 4 2 28
+--R Type: Polynomial(Fraction(Integer))
+--E 551
+
+--S 552 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 552
+
+--S 553 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 553
+
+)clear all
+
+--S 554 of 716
+t0:=x^41*(b+c*x^3)^13*(b+2*c*x^3)
+--R
+--R
+--R (1)
+--R 14 83 13 80 2 12 77 3 11 74 4 10 71
+--R 2c x + 27b c x + 169b c x + 650b c x + 1716b c x
+--R +
+--R 5 9 68 6 8 65 7 7 62 8 6 59 9 5 56
+--R 3289b c x + 4719b c x + 5148b c x + 4290b c x + 2717b c x
+--R +
+--R 10 4 53 11 3 50 12 2 47 13 44 14 41
+--R 1287b c x + 442b c x + 104b c x + 15b c x + b x
+--R Type: Polynomial(Integer)
+--E 554
+
+--S 555 of 716
+r0:=1/42*x^42*(b+c*x^3)^14
+--R
+--R
+--R (2)
+--R 1 14 84 1 13 81 13 2 12 78 26 3 11 75 143 4 10 72
+--R -- c x + - b c x + -- b c x + -- b c x + --- b c x
+--R 42 3 6 3 6
+--R +
+--R 143 5 9 69 143 6 8 66 572 7 7 63 143 8 6 60 143 9 5 57
+--R --- b c x + --- b c x + --- b c x + --- b c x + --- b c x
+--R 3 2 7 2 3
+--R +
+--R 143 10 4 54 26 11 3 51 13 12 2 48 1 13 45 1 14 42
+--R --- b c x + -- b c x + -- b c x + - b c x + -- b x
+--R 6 3 6 3 42
+--R Type: Polynomial(Fraction(Integer))
+--E 555
+
+--S 556 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 14 84 1 13 81 13 2 12 78 26 3 11 75 143 4 10 72
+--R -- c x + - b c x + -- b c x + -- b c x + --- b c x
+--R 42 3 6 3 6
+--R +
+--R 143 5 9 69 143 6 8 66 572 7 7 63 143 8 6 60 143 9 5 57
+--R --- b c x + --- b c x + --- b c x + --- b c x + --- b c x
+--R 3 2 7 2 3
+--R +
+--R 143 10 4 54 26 11 3 51 13 12 2 48 1 13 45 1 14 42
+--R --- b c x + -- b c x + -- b c x + - b c x + -- b x
+--R 6 3 6 3 42
+--R Type: Polynomial(Fraction(Integer))
+--E 556
+
+--S 557 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 557
+
+--S 558 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 558
+
+)clear all
+
+--S 559 of 716
+t0:=x^(-1+14*n)*(b+c*x^n)^13*(b+2*c*x^n)
+--R
+--R
+--R (1)
+--R 14 n 14 13 n 13 2 12 n 12 3 11 n 11
+--R 2c (x ) + 27b c (x ) + 169b c (x ) + 650b c (x )
+--R +
+--R 4 10 n 10 5 9 n 9 6 8 n 8 7 7 n 7
+--R 1716b c (x ) + 3289b c (x ) + 4719b c (x ) + 5148b c (x )
+--R +
+--R 8 6 n 6 9 5 n 5 10 4 n 4 11 3 n 3
+--R 4290b c (x ) + 2717b c (x ) + 1287b c (x ) + 442b c (x )
+--R +
+--R 12 2 n 2 13 n 14
+--R 104b c (x ) + 15b c x + b
+--R *
+--R 14n - 1
+--R x
+--R Type: Expression(Integer)
+--E 559
+
+--S 560 of 716
+r0:=1/14*x^(14*n)*(b+c*x^n)^14/n
+--R
+--R
+--R (2)
+--R 14 n 14 13 n 13 2 12 n 12 3 11 n 11
+--R c (x ) + 14b c (x ) + 91b c (x ) + 364b c (x )
+--R +
+--R 4 10 n 10 5 9 n 9 6 8 n 8 7 7 n 7
+--R 1001b c (x ) + 2002b c (x ) + 3003b c (x ) + 3432b c (x )
+--R +
+--R 8 6 n 6 9 5 n 5 10 4 n 4 11 3 n 3
+--R 3003b c (x ) + 2002b c (x ) + 1001b c (x ) + 364b c (x )
+--R +
+--R 12 2 n 2 13 n 14
+--R 91b c (x ) + 14b c x + b
+--R *
+--R 14n
+--R x
+--R /
+--R 14n
+--R Type: Expression(Integer)
+--E 560
+
+--S 561 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 14 n log(x) 28 13 n log(x) 27 2 12 n log(x) 26
+--R c (%e ) + 14b c (%e ) + 91b c (%e )
+--R +
+--R 3 11 n log(x) 25 4 10 n log(x) 24 5 9 n log(x) 23
+--R 364b c (%e ) + 1001b c (%e ) + 2002b c (%e )
+--R +
+--R 6 8 n log(x) 22 7 7 n log(x) 21 8 6 n log(x) 20
+--R 3003b c (%e ) + 3432b c (%e ) + 3003b c (%e )
+--R +
+--R 9 5 n log(x) 19 10 4 n log(x) 18 11 3 n log(x) 17
+--R 2002b c (%e ) + 1001b c (%e ) + 364b c (%e )
+--R +
+--R 12 2 n log(x) 16 13 n log(x) 15 14 n log(x) 14
+--R 91b c (%e ) + 14b c (%e ) + b (%e )
+--R /
+--R 14n
+--R Type: Union(Expression(Integer),...)
+--E 561
+
+--S 562 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 14 n log(x) 28 13 n log(x) 27 2 12 n log(x) 26
+--R c (%e ) + 14b c (%e ) + 91b c (%e )
+--R +
+--R 3 11 n log(x) 25 4 10 n log(x) 24 5 9 n log(x) 23
+--R 364b c (%e ) + 1001b c (%e ) + 2002b c (%e )
+--R +
+--R 6 8 n log(x) 22 7 7 n log(x) 21 8 6 n log(x) 20
+--R 3003b c (%e ) + 3432b c (%e ) + 3003b c (%e )
+--R +
+--R 9 5 n log(x) 19 10 4 n log(x) 18 11 3 n log(x) 17
+--R 2002b c (%e ) + 1001b c (%e ) + 364b c (%e )
+--R +
+--R 12 2 n log(x) 16 13 n log(x) 15 14 n log(x) 14
+--R 91b c (%e ) + 14b c (%e ) + b (%e )
+--R +
+--R 14 n 14 13 n 13 2 12 n 12 3 11 n 11
+--R - c (x ) - 14b c (x ) - 91b c (x ) - 364b c (x )
+--R +
+--R 4 10 n 10 5 9 n 9 6 8 n 8 7 7 n 7
+--R - 1001b c (x ) - 2002b c (x ) - 3003b c (x ) - 3432b c (x )
+--R +
+--R 8 6 n 6 9 5 n 5 10 4 n 4 11 3 n 3
+--R - 3003b c (x ) - 2002b c (x ) - 1001b c (x ) - 364b c (x )
+--R +
+--R 12 2 n 2 13 n 14
+--R - 91b c (x ) - 14b c x - b
+--R *
+--R 14n
+--R x
+--R /
+--R 14n
+--R Type: Expression(Integer)
+--E 562
+
+--S 563 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 563
+
+)clear all
+
+--S 564 of 716
+t0:=x^(-1+m)*(a+b*x^n)^(-1+p)*(a*m+b*(m+n*p)*x^n)
+--R
+--R
+--R m - 1 n m - 1 n p - 1
+--R (1) ((b n p + b m)x x + a m x )(b x + a)
+--R Type: Expression(Integer)
+--E 564
+
+--S 565 of 716
+r0:=x^m*(a+b*x^n)^p
+--R
+--R
+--R m n p
+--R (2) x (b x + a)
+--R Type: Expression(Integer)
+--E 565
+
+--S 566 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R (m - 1)log(x) n log(x) (m - 1)log(x)
+--R (b x %e %e + a x %e )
+--R *
+--R n log(x)
+--R (p - 1)log(b %e + a)
+--R %e
+--R Type: Union(Expression(Integer),...)
+--E 566
+
+--S 567 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R (m - 1)log(x) n log(x) (m - 1)log(x)
+--R (b x %e %e + a x %e )
+--R *
+--R n log(x)
+--R (p - 1)log(b %e + a)
+--R %e
+--R +
+--R m n p
+--R - x (b x + a)
+--R Type: Expression(Integer)
+--E 567
+
+--S 568 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 568
+
+)clear all
+
+--S 569 of 716
+t0:=(b+2*c*x)/(x*(b+c*x))
+--R
+--R
+--R 2c x + b
+--R (1) ----------
+--R 2
+--R c x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 569
+
+--S 570 of 716
+r0a:=log(x*(b+c*x))
+--R
+--R
+--R 2
+--R (2) log(c x + b x)
+--R Type: Expression(Integer)
+--E 570
+
+--S 571 of 716
+r0b:=log(x)+log(b+c*x)
+--R
+--R
+--R (3) log(c x + b) + log(x)
+--R Type: Expression(Integer)
+--E 571
+
+--S 572 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (4) log(c x + b x)
+--R Type: Union(Expression(Integer),...)
+--E 572
+
+--S 573 of 716
+m0a:=a0-r0a
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 573
+
+--S 574 of 716
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 574
+
+--S 575 of 716
+m0b:=a0-r0b
+--R
+--R
+--R 2
+--R (7) log(c x + b x) - log(c x + b) - log(x)
+--R Type: Expression(Integer)
+--E 575
+
+--S 576 of 716
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 576
+
+)clear all
+
+--S 577 of 716
+t0:=(b+2*c*x^2)/(x*(b+c*x^2))
+--R
+--R
+--R 2
+--R 2c x + b
+--R (1) ----------
+--R 3
+--R c x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 577
+
+--S 578 of 716
+r0:=log(x)+1/2*log(b+c*x^2)
+--R
+--R
+--R 2
+--R log(c x + b) + 2log(x)
+--R (2) -----------------------
+--R 2
+--R Type: Expression(Integer)
+--E 578
+
+--S 579 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R log(c x + b) + 2log(x)
+--R (3) -----------------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 579
+
+--S 580 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 580
+
+--S 581 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 581
+
+)clear all
+
+--S 582 of 716
+t0:=(b+2*c*x^3)/(x*(b+c*x^3))
+--R
+--R
+--R 3
+--R 2c x + b
+--R (1) ----------
+--R 4
+--R c x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 582
+
+--S 583 of 716
+r0:=log(x)+1/3*log(b+c*x^3)
+--R
+--R
+--R 3
+--R log(c x + b) + 3log(x)
+--R (2) -----------------------
+--R 3
+--R Type: Expression(Integer)
+--E 583
+
+--S 584 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R log(c x + b) + 3log(x)
+--R (3) -----------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 584
+
+--S 585 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 585
+
+--S 586 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 586
+
+)clear all
+
+--S 587 of 716
+t0:=(b+2*c*x^n)/(x*(b+c*x^n))
+--R
+--R
+--R n
+--R 2c x + b
+--R (1) ------------
+--R n
+--R c x x + b x
+--R Type: Expression(Integer)
+--E 587
+
+--S 588 of 716
+r0:=log(x)+log(b+c*x^n)/n
+--R
+--R
+--R n
+--R log(c x + b) + n log(x)
+--R (2) ------------------------
+--R n
+--R Type: Expression(Integer)
+--E 588
+
+--S 589 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R n log(x)
+--R log(c %e + b) + n log(x)
+--R (3) --------------------------------
+--R n
+--R Type: Union(Expression(Integer),...)
+--E 589
+
+--S 590 of 716
+m0:=a0-r0
+--R
+--R
+--R n log(x) n
+--R log(c %e + b) - log(c x + b)
+--R (4) -------------------------------------
+--R n
+--R Type: Expression(Integer)
+--E 590
+
+--S 591 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 591
+
+)clear all
+
+--S 592 of 716
+t0:=(b+2*c*x)/(x^8*(b+c*x)^8)
+--R
+--R
+--R (1)
+--R 2c x + b
+--R /
+--R 8 16 7 15 2 6 14 3 5 13 4 4 12 5 3 11
+--R c x + 8b c x + 28b c x + 56b c x + 70b c x + 56b c x
+--R +
+--R 6 2 10 7 9 8 8
+--R 28b c x + 8b c x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 592
+
+--S 593 of 716
+r0:=(-1/7)/(x^7*(b+c*x)^7)
+--R
+--R
+--R (2)
+--R -
+--R 1
+--R -
+--R 7
+--R /
+--R 7 14 6 13 2 5 12 3 4 11 4 3 10 5 2 9
+--R c x + 7b c x + 21b c x + 35b c x + 35b c x + 21b c x
+--R +
+--R 6 8 7 7
+--R 7b c x + b x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 593
+
+--S 594 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 1
+--R /
+--R 7 14 6 13 2 5 12 3 4 11 4 3 10 5 2 9
+--R 7c x + 49b c x + 147b c x + 245b c x + 245b c x + 147b c x
+--R +
+--R 6 8 7 7
+--R 49b c x + 7b x
+--R Type: Union(Expression(Integer),...)
+--E 594
+
+--S 595 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 595
+
+--S 596 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 596
+
+)clear all
+
+--S 597 of 716
+t0:=(b+2*c*x^2)/(x^15*(b+c*x^2)^8)
+--R
+--R
+--R (1)
+--R 2
+--R 2c x + b
+--R /
+--R 8 31 7 29 2 6 27 3 5 25 4 4 23 5 3 21
+--R c x + 8b c x + 28b c x + 56b c x + 70b c x + 56b c x
+--R +
+--R 6 2 19 7 17 8 15
+--R 28b c x + 8b c x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 597
+
+--S 598 of 716
+r0:=(-1/14)/(x^14*(b+c*x^2)^7)
+--R
+--R
+--R (2)
+--R -
+--R 1
+--R --
+--R 14
+--R /
+--R 7 28 6 26 2 5 24 3 4 22 4 3 20 5 2 18
+--R c x + 7b c x + 21b c x + 35b c x + 35b c x + 21b c x
+--R +
+--R 6 16 7 14
+--R 7b c x + b x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 598
+
+--S 599 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 1
+--R /
+--R 7 28 6 26 2 5 24 3 4 22 4 3 20
+--R 14c x + 98b c x + 294b c x + 490b c x + 490b c x
+--R +
+--R 5 2 18 6 16 7 14
+--R 294b c x + 98b c x + 14b x
+--R Type: Union(Expression(Integer),...)
+--E 599
+
+--S 600 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 600
+
+--S 601 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 601
+
+)clear all
+
+--S 602 of 716
+t0:=(b+2*c*x^3)/(x^22*(b+c*x^3)^8)
+--R
+--R
+--R (1)
+--R 3
+--R 2c x + b
+--R /
+--R 8 46 7 43 2 6 40 3 5 37 4 4 34 5 3 31
+--R c x + 8b c x + 28b c x + 56b c x + 70b c x + 56b c x
+--R +
+--R 6 2 28 7 25 8 22
+--R 28b c x + 8b c x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 602
+
+--S 603 of 716
+r0:=(-1/21)/(x^21*(b+c*x^3)^7)
+--R
+--R
+--R (2)
+--R -
+--R 1
+--R --
+--R 21
+--R /
+--R 7 42 6 39 2 5 36 3 4 33 4 3 30 5 2 27
+--R c x + 7b c x + 21b c x + 35b c x + 35b c x + 21b c x
+--R +
+--R 6 24 7 21
+--R 7b c x + b x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 603
+
+--S 604 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 1
+--R /
+--R 7 42 6 39 2 5 36 3 4 33 4 3 30
+--R 21c x + 147b c x + 441b c x + 735b c x + 735b c x
+--R +
+--R 5 2 27 6 24 7 21
+--R 441b c x + 147b c x + 21b x
+--R Type: Union(Expression(Integer),...)
+--E 604
+
+--S 605 of 716
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 605
+
+--S 606 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 606
+
+)clear all
+
+--S 607 of 716
+t0:=x^(-1-7*n)*(b+2*c*x^n)/(b+c*x^n)^8
+--R
+--R
+--R (1)
+--R - 7n - 1 n - 7n - 1
+--R 2c x x + b x
+--R /
+--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4
+--R c (x ) + 8b c (x ) + 28b c (x ) + 56b c (x ) + 70b c (x )
+--R +
+--R 5 3 n 3 6 2 n 2 7 n 8
+--R 56b c (x ) + 28b c (x ) + 8b c x + b
+--R Type: Expression(Integer)
+--E 607
+
+--S 608 of 716
+r0:=(-1/7)/(n*x^(7*n)*(b+c*x^n)^7)
+--R
+--R
+--R (2)
+--R -
+--R 1
+--R /
+--R 7 n 7 6 n 6 2 5 n 5 3 4 n 4
+--R 7c n (x ) + 49b c n (x ) + 147b c n (x ) + 245b c n (x )
+--R +
+--R 4 3 n 3 5 2 n 2 6 n 7
+--R 245b c n (x ) + 147b c n (x ) + 49b c n x + 7b n
+--R *
+--R 7n
+--R x
+--R Type: Expression(Integer)
+--E 608
+
+--S 609 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 1
+--R /
+--R 7 n log(x) 14 6 n log(x) 13 2 5 n log(x) 12
+--R 7c n (%e ) + 49b c n (%e ) + 147b c n (%e )
+--R +
+--R 3 4 n log(x) 11 4 3 n log(x) 10
+--R 245b c n (%e ) + 245b c n (%e )
+--R +
+--R 5 2 n log(x) 9 6 n log(x) 8 7 n log(x) 7
+--R 147b c n (%e ) + 49b c n (%e ) + 7b n (%e )
+--R Type: Union(Expression(Integer),...)
+--E 609
+
+--S 610 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 7 n log(x) 14 6 n log(x) 13 2 5 n log(x) 12
+--R c (%e ) + 7b c (%e ) + 21b c (%e )
+--R +
+--R 3 4 n log(x) 11 4 3 n log(x) 10 5 2 n log(x) 9
+--R 35b c (%e ) + 35b c (%e ) + 21b c (%e )
+--R +
+--R 6 n log(x) 8 7 n log(x) 7
+--R 7b c (%e ) + b (%e )
+--R +
+--R 7 n 7 6 n 6 2 5 n 5 3 4 n 4 4 3 n 3
+--R - c (x ) - 7b c (x ) - 21b c (x ) - 35b c (x ) - 35b c (x )
+--R +
+--R 5 2 n 2 6 n 7
+--R - 21b c (x ) - 7b c x - b
+--R *
+--R 7n
+--R x
+--R /
+--R 14 n 7 13 n 6 2 12 n 5 3 11 n 4
+--R 7c n (x ) + 49b c n (x ) + 147b c n (x ) + 245b c n (x )
+--R +
+--R 4 10 n 3 5 9 n 2 6 8 n 7 7
+--R 245b c n (x ) + 147b c n (x ) + 49b c n x + 7b c n
+--R *
+--R 7n n log(x) 14
+--R x (%e )
+--R +
+--R 13 n 7 2 12 n 6 3 11 n 5
+--R 49b c n (x ) + 343b c n (x ) + 1029b c n (x )
+--R +
+--R 4 10 n 4 5 9 n 3 6 8 n 2 7 7 n
+--R 1715b c n (x ) + 1715b c n (x ) + 1029b c n (x ) + 343b c n x
+--R +
+--R 8 6
+--R 49b c n
+--R *
+--R 7n n log(x) 13
+--R x (%e )
+--R +
+--R 2 12 n 7 3 11 n 6 4 10 n 5
+--R 147b c n (x ) + 1029b c n (x ) + 3087b c n (x )
+--R +
+--R 5 9 n 4 6 8 n 3 7 7 n 2 8 6 n
+--R 5145b c n (x ) + 5145b c n (x ) + 3087b c n (x ) + 1029b c n x
+--R +
+--R 9 5
+--R 147b c n
+--R *
+--R 7n n log(x) 12
+--R x (%e )
+--R +
+--R 3 11 n 7 4 10 n 6 5 9 n 5
+--R 245b c n (x ) + 1715b c n (x ) + 5145b c n (x )
+--R +
+--R 6 8 n 4 7 7 n 3 8 6 n 2 9 5 n
+--R 8575b c n (x ) + 8575b c n (x ) + 5145b c n (x ) + 1715b c n x
+--R +
+--R 10 4
+--R 245b c n
+--R *
+--R 7n n log(x) 11
+--R x (%e )
+--R +
+--R 4 10 n 7 5 9 n 6 6 8 n 5 7 7 n 4
+--R 245b c n (x ) + 1715b c n (x ) + 5145b c n (x ) + 8575b c n (x )
+--R +
+--R 8 6 n 3 9 5 n 2 10 4 n 11 3
+--R 8575b c n (x ) + 5145b c n (x ) + 1715b c n x + 245b c n
+--R *
+--R 7n n log(x) 10
+--R x (%e )
+--R +
+--R 5 9 n 7 6 8 n 6 7 7 n 5 8 6 n 4
+--R 147b c n (x ) + 1029b c n (x ) + 3087b c n (x ) + 5145b c n (x )
+--R +
+--R 9 5 n 3 10 4 n 2 11 3 n 12 2
+--R 5145b c n (x ) + 3087b c n (x ) + 1029b c n x + 147b c n
+--R *
+--R 7n n log(x) 9
+--R x (%e )
+--R +
+--R 6 8 n 7 7 7 n 6 8 6 n 5 9 5 n 4
+--R 49b c n (x ) + 343b c n (x ) + 1029b c n (x ) + 1715b c n (x )
+--R +
+--R 10 4 n 3 11 3 n 2 12 2 n 13
+--R 1715b c n (x ) + 1029b c n (x ) + 343b c n x + 49b c n
+--R *
+--R 7n n log(x) 8
+--R x (%e )
+--R +
+--R 7 7 n 7 8 6 n 6 9 5 n 5 10 4 n 4
+--R 7b c n (x ) + 49b c n (x ) + 147b c n (x ) + 245b c n (x )
+--R +
+--R 11 3 n 3 12 2 n 2 13 n 14
+--R 245b c n (x ) + 147b c n (x ) + 49b c n x + 7b n
+--R *
+--R 7n n log(x) 7
+--R x (%e )
+--R Type: Expression(Integer)
+--E 610
+
+--S 611 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 611
+
+)clear all
+
+--S 612 of 716
+t0:=(1+x^6)/(x*(1-x^6))
+--R
+--R
+--R 6
+--R - x - 1
+--R (1) --------
+--R 7
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 612
+
+--S 613 of 716
+r0:=log(x)-1/3*log(1-x^6)
+--R
+--R
+--R 6
+--R 3log(x) - log(- x + 1)
+--R (2) -----------------------
+--R 3
+--R Type: Expression(Integer)
+--E 613
+
+--S 614 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 6
+--R - log(x - 1) + 3log(x)
+--R (3) -----------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 614
+
+--S 615 of 716
+m0:=a0-r0
+--R
+--R
+--R 6 6
+--R - log(x - 1) + log(- x + 1)
+--R (4) -----------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 615
+
+--S 616 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 616
+
+)clear all
+
+--S 617 of 716
+t0:=x^31*sqrt(1+x^16)/(1-x^16)
+--R
+--R
+--R +-------+
+--R 31 | 16
+--R x \|x + 1
+--R (1) - -------------
+--R 16
+--R x - 1
+--R Type: Expression(Integer)
+--E 617
+
+--S 618 of 716
+r0:=-1/24*(1+x^16)^(3/2)+1/4*atanh(sqrt(1+x^16)/sqrt(2))/sqrt(2)-_
+ 1/8*sqrt(1+x^16)
+--R
+--R
+--R +-------+
+--R | 16 +-------+
+--R \|x + 1 16 +-+ | 16
+--R 6atanh(----------) + (- x - 4)\|2 \|x + 1
+--R +-+
+--R \|2
+--R (2) ----------------------------------------------
+--R +-+
+--R 24\|2
+--R Type: Expression(Integer)
+--E 618
+
+--S 619 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R | 16 16 +-+ +-------+
+--R 4\|x + 1 + (x + 3)\|2 16 +-+ | 16
+--R 3log(---------------------------) + (- x - 4)\|2 \|x + 1
+--R 16
+--R x - 1
+--R (3) -------------------------------------------------------------
+--R +-+
+--R 24\|2
+--R Type: Union(Expression(Integer),...)
+--E 619
+
+--S 620 of 716
+m0:=a0-r0
+--R
+--R
+--R +-------+ +-------+
+--R | 16 16 +-+ | 16
+--R 4\|x + 1 + (x + 3)\|2 \|x + 1
+--R log(---------------------------) - 2atanh(----------)
+--R 16 +-+
+--R x - 1 \|2
+--R (4) -----------------------------------------------------
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 620
+
+--S 621 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 621
+
+)clear all
+
+--S 622 of 716
+t0:=sqrt(c+d/x)/(x*sqrt(a+b/x))
+--R
+--R
+--R +-------+
+--R |c x + d
+--R |-------
+--R \| x
+--R (1) -----------
+--R +-------+
+--R |a x + b
+--R x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 622
+
+--S 623 of 716
+r0:=2*atanh(sqrt(c)*sqrt(a+b/x)/(sqrt(a)*sqrt(c+d/x)))*sqrt(c)/sqrt(a)-_
+ 2*atanh(sqrt(d)*sqrt(a+b/x)/(sqrt(b)*sqrt(c+d/x)))*sqrt(d)/sqrt(b)
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +-+ |a x + b +-+
+--R |------- \|d |------- \|c
+--R +-+ +-+ \| x +-+ +-+ \| x
+--R - 2\|a \|d atanh(--------------) + 2\|b \|c atanh(--------------)
+--R +-------+ +-------+
+--R +-+ |c x + d +-+ |c x + d
+--R \|b |------- \|a |-------
+--R \| x \| x
+--R (2) -----------------------------------------------------------------
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 623
+
+--S 624 of 716
+--a0:=integrate(t0,x)
+--E 624
+
+--S 625 of 716
+--m0:=a0-r0
+--E 625
+
+--S 626 of 716
+--d0:=D(m0,x)
+--E 626
+
+)clear all
+
+--S 627 of 716
+t0:=x^(-1+2*n)*(a+b*x^n)^(5/2)/sqrt(c+d*x^n)
+--R
+--R
+--R +--------+
+--R 2 n 2 n 2 2n - 1 | n
+--R (b (x ) + 2a b x + a )x \|b x + a
+--R (1) ------------------------------------------
+--R +--------+
+--R | n
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 627
+
+--S 628 of 716
+r0:=5/64*(b*c-a*d)^3*(7*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*_
+ sqrt(c+d*x^n)))/(b^(3/2)*d^(9/2)*n)+5/96*(b*c-a*d)*(7*b*c+a*d)*_
+ (a+b*x^n)^(3/2)*sqrt(c+d*x^n)/(b*d^3*n)-1/24*(7*b*c+a*d)*_
+ (a+b*x^n)^(5/2)*sqrt(c+d*x^n)/(b*d^2*n)+1/4*(a+b*x^n)^(7/2)*_
+ sqrt(c+d*x^n)/(b*d*n)-5/64*(b*c-a*d)^2*(7*b*c+a*d)*_
+ sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b*d^4*n)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 15a d - 60a b c d + 270a b c d - 300a b c d + 105b c )
+--R *
+--R +--------+
+--R +-+ | n
+--R \|d \|b x + a
+--R atanh(---------------)
+--R +--------+
+--R +-+ | n
+--R \|b \|d x + c
+--R +
+--R 3 3 n 3 2 3 3 2 n 2
+--R 48b d (x ) + (136a b d - 56b c d )(x )
+--R +
+--R 2 3 2 2 3 2 n 3 3 2 2
+--R (118a b d - 172a b c d + 70b c d)x + 15a d - 191a b c d
+--R +
+--R 2 2 3 3
+--R 265a b c d - 105b c
+--R *
+--R +--------+ +--------+
+--R +-+ +-+ | n | n
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 4 +-+ +-+
+--R 192b d n\|b \|d
+--R Type: Expression(Integer)
+--E 628
+
+--S 629 of 716
+--a0:=integrate(t0,x)
+--E 629
+
+--S 630 of 716
+--m0:=a0-r0
+--E 630
+
+--S 631 of 716
+--d0:=D(m0,x)
+--E 631
+
+)clear all
+
+--S 632 of 716
+t0:=x^(-1+2*n)*(a+b*x^n)^(3/2)/sqrt(c+d*x^n)
+--R
+--R
+--R +--------+
+--R n 2n - 1 | n
+--R (b x + a)x \|b x + a
+--R (1) ----------------------------
+--R +--------+
+--R | n
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 632
+
+--S 633 of 716
+r0:=-1/8*(b*c-a*d)^2*(5*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x^n)/_
+ (sqrt(b)*sqrt(c+d*x^n)))/(b^(3/2)*d^(7/2)*n)-_
+ 1/12*(5*b*c+a*d)*(a+b*x^n)^(3/2)*sqrt(c+d*x^n)/(b*d^2*n)+_
+ 1/3*(a+b*x^n)^(5/2)*sqrt(c+d*x^n)/(b*d*n)+1/8*(b*c-a*d)*_
+ (5*b*c+a*d)*sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b*d^3*n)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | n
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (- 3a d - 9a b c d + 27a b c d - 15b c )atanh(---------------)
+--R +--------+
+--R +-+ | n
+--R \|b \|d x + c
+--R +
+--R 2 2 n 2 2 2 n 2 2 2 2 +-+
+--R (8b d (x ) + (14a b d - 10b c d)x + 3a d - 22a b c d + 15b c )\|b
+--R *
+--R +--------+ +--------+
+--R +-+ | n | n
+--R \|d \|b x + a \|d x + c
+--R /
+--R 3 +-+ +-+
+--R 24b d n\|b \|d
+--R Type: Expression(Integer)
+--E 633
+
+--S 634 of 716
+--a0:=integrate(t0,x)
+--E 634
+
+--S 635 of 716
+--m0:=a0-r0
+--E 635
+
+--S 636 of 716
+--d0:=D(m0,x)
+--E 636
+
+)clear all
+
+--S 637 of 716
+t0:=x^(-1+2*n)*sqrt(a+b*x^n)/sqrt(c+d*x^n)
+--R
+--R
+--R +--------+
+--R 2n - 1 | n
+--R x \|b x + a
+--R (1) ------------------
+--R +--------+
+--R | n
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 637
+
+--S 638 of 716
+r0:=1/4*(b*c-a*d)*(3*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x^n)/_
+ (sqrt(b)*sqrt(c+d*x^n)))/(b^(3/2)*d^(5/2)*n)+_
+ 1/2*(a+b*x^n)^(3/2)*sqrt(c+d*x^n)/(b*d*n)-_
+ 1/4*(3*b*c+a*d)*sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b*d^2*n)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | n
+--R 2 2 2 2 \|d \|b x + a
+--R (- a d - 2a b c d + 3b c )atanh(---------------)
+--R +--------+
+--R +-+ | n
+--R \|b \|d x + c
+--R +
+--R +--------+ +--------+
+--R n +-+ +-+ | n | n
+--R (2b d x + a d - 3b c)\|b \|d \|b x + a \|d x + c
+--R /
+--R 2 +-+ +-+
+--R 4b d n\|b \|d
+--R Type: Expression(Integer)
+--E 638
+
+--S 639 of 716
+--a0:=integrate(t0,x)
+--E 639
+
+--S 640 of 716
+--m0:=a0-r0
+--E 640
+
+--S 641 of 716
+--d0:=D(m0,x)
+--E 641
+
+)clear all
+
+--S 642 of 716
+t0:=x^(-1+2*n)/(sqrt(a+b*x^n)*sqrt(c+d*x^n))
+--R
+--R
+--R 2n - 1
+--R x
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | n | n
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 642
+
+--S 643 of 716
+r0:=-(b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/_
+ (b^(3/2)*d^(3/2)*n)+sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b*d*n)
+--R
+--R
+--R +--------+
+--R +-+ | n +--------+ +--------+
+--R \|d \|b x + a +-+ +-+ | n | n
+--R (- a d - b c)atanh(---------------) + \|b \|d \|b x + a \|d x + c
+--R +--------+
+--R +-+ | n
+--R \|b \|d x + c
+--R (2) --------------------------------------------------------------------
+--R +-+ +-+
+--R b d n\|b \|d
+--R Type: Expression(Integer)
+--E 643
+
+--S 644 of 716
+--a0:=integrate(t0,x)
+--E 644
+
+--S 645 of 716
+--m0:=a0-r0
+--E 645
+
+--S 646 of 716
+--d0:=D(m0,x)
+--E 646
+
+)clear all
+
+--S 647 of 716
+t0:=x^(-1+2*n)/((a+b*x^n)^(3/2)*sqrt(c+d*x^n))
+--R
+--R
+--R 2n - 1
+--R x
+--R (1) --------------------------------
+--R +--------+ +--------+
+--R n | n | n
+--R (b x + a)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 647
+
+--S 648 of 716
+r0:=2*atanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/_
+ (b^(3/2)*n*sqrt(d))+2*a*sqrt(c+d*x^n)/(b*(b*c-a*d)*n*sqrt(a+b*x^n))
+--R
+--R
+--R +--------+
+--R +--------+ +-+ | n +--------+
+--R | n \|d \|b x + a +-+ +-+ | n
+--R (2a d - 2b c)\|b x + a atanh(---------------) - 2a\|b \|d \|d x + c
+--R +--------+
+--R +-+ | n
+--R \|b \|d x + c
+--R (2) ----------------------------------------------------------------------
+--R +--------+
+--R 2 +-+ +-+ | n
+--R (a b d - b c)n\|b \|d \|b x + a
+--R Type: Expression(Integer)
+--E 648
+
+--S 649 of 716
+--a0:=integrate(t0,x)
+--E 649
+
+--S 650 of 716
+--m0:=a0-r0
+--E 650
+
+--S 651 of 716
+--d0:=D(m0,x)
+--E 651
+
+)clear all
+
+--S 652 of 716
+t0:=x^(-1+2*n)/((a+b*x^n)^(5/2)*sqrt(c+d*x^n))
+--R
+--R
+--R 2n - 1
+--R x
+--R (1) ----------------------------------------------
+--R +--------+ +--------+
+--R 2 n 2 n 2 | n | n
+--R (b (x ) + 2a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 652
+
+--S 653 of 716
+r0:=2/3*a*sqrt(c+d*x^n)/(b*(b*c-a*d)*n*(a+b*x^n)^(3/2))-_
+ 2/3*(3*b*c-a*d)*sqrt(c+d*x^n)/(b*(b*c-a*d)^2*n*sqrt(a+b*x^n))
+--R
+--R
+--R (2)
+--R +--------+
+--R n | n
+--R ((2a d - 6b c)x - 4a c)\|d x + c
+--R -----------------------------------------------------------------------------
+--R +--------+
+--R 2 2 2 3 2 n 3 2 2 2 2 | n
+--R ((3a b d - 6a b c d + 3b c )n x + (3a d - 6a b c d + 3a b c )n)\|b x + a
+--R Type: Expression(Integer)
+--E 653
+
+--S 654 of 716 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------------+
+--R 2 n log(x) 2 | n log(x)
+--R ((10a d - 30a b c)%e - 20a c)\|b %e + a
+--R *
+--R +----------------+
+--R | n log(x)
+--R \|d %e + c
+--R +
+--R 2 2 2 n log(x) 2 2 2 n log(x)
+--R (- 2b c - 50a b c)(%e ) + (- 4a b c - 100a b c)%e
+--R +
+--R 2 2 3
+--R - 2a c - 50a c
+--R /
+--R 3 2 2 2 3 4 2 n log(x) 2
+--R (15a b d - 30a b c d + 15a b c )n (%e )
+--R +
+--R 4 2 3 2 2 3 2 n log(x)
+--R (30a b d - 60a b c d + 30a b c )n %e
+--R +
+--R 5 2 4 3 2 2
+--R (15a d - 30a b c d + 15a b c )n
+--R Type: Union(Expression(Integer),...)
+--E 654
+
+--S 655 of 716 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 n 3 2 n log(x) 2 n
+--R ((10a b d - 30a b c)x + 10a d - 30a b c)%e - 20a b c x
+--R +
+--R 3
+--R - 20a c
+--R *
+--R +--------+ +----------------+ +----------------+
+--R | n | n log(x) | n log(x)
+--R \|b x + a \|b %e + a \|d %e + c
+--R +
+--R 2 2 3 n 2 2 n log(x) 2
+--R ((- 10a b d + 30a b c)x + 20a b c)(%e )
+--R +
+--R 3 2 2 n 3 n log(x) 4 3 n
+--R ((- 20a b d + 60a b c)x + 40a b c)%e + (- 10a d + 30a b c)x
+--R +
+--R 4
+--R 20a c
+--R *
+--R +--------+
+--R | n
+--R \|d x + c
+--R +
+--R 3 2 3 n 2 2 2 2 n log(x) 2
+--R ((- 2b c - 50a b c)x - 2a b c - 50a b c)(%e )
+--R +
+--R 2 2 2 2 n 2 2 3 n log(x)
+--R ((- 4a b c - 100a b c)x - 4a b c - 100a b c)%e
+--R +
+--R 2 2 3 n 3 2 4
+--R (- 2a b c - 50a b c)x - 2a c - 50a c
+--R *
+--R +--------+
+--R | n
+--R \|b x + a
+--R /
+--R 3 3 2 2 4 5 2 n
+--R (15a b d - 30a b c d + 15a b c )n x
+--R +
+--R 4 2 2 3 3 2 4 2
+--R (15a b d - 30a b c d + 15a b c )n
+--R *
+--R n log(x) 2
+--R (%e )
+--R +
+--R 4 2 2 3 3 2 4 2 n
+--R (30a b d - 60a b c d + 30a b c )n x
+--R +
+--R 5 2 4 2 3 3 2
+--R (30a b d - 60a b c d + 30a b c )n
+--R *
+--R n log(x)
+--R %e
+--R +
+--R 5 2 4 2 3 3 2 n 6 2 5 4 2 2
+--R (15a b d - 30a b c d + 15a b c )n x + (15a d - 30a b c d + 15a b c )n
+--R *
+--R +--------+
+--R | n
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 655
+
+--S 656 of 716
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 656
+
+)clear all
+
+--S 657 of 716
+t0:=x^(-1+3*n)*(a+b*x^n)^(5/2)/sqrt(c+d*x^n)
+--R
+--R
+--R +--------+
+--R 2 n 2 n 2 3n - 1 | n
+--R (b (x ) + 2a b x + a )x \|b x + a
+--R (1) ------------------------------------------
+--R +--------+
+--R | n
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 657
+
+--S 658 of 716
+r0:=-1/128*(b*c-a*d)^3*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(5/2)*d^(11/2)*n)-_
+ 1/192*(b*c-a*d)*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*(a+b*x^n)^(3/2)*_
+ sqrt(c+d*x^n)/(b^2*d^4*n)+1/240*(63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*_
+ (a+b*x^n)^(5/2)*sqrt(c+d*x^n)/(b^2*d^3*n)-3/40*(3*b*c+a*d)*_
+ (a+b*x^n)^(7/2)*sqrt(c+d*x^n)/(b^2*d^2*n)+1/5*x^n*_
+ (a+b*x^n)^(7/2)*sqrt(c+d*x^n)/(b*d*n)+1/128*(b*c-a*d)^2*_
+ (63*b^2*c^2+14*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b^2*d^5*n)
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R 45a d + 75a b c d + 450a b c d - 2250a b c d + 2625a b c d
+--R +
+--R 5 5
+--R - 945b c
+--R *
+--R +--------+
+--R +-+ | n
+--R \|d \|b x + a
+--R atanh(---------------)
+--R +--------+
+--R +-+ | n
+--R \|b \|d x + c
+--R +
+--R 4 4 n 4 3 4 4 3 n 3
+--R 384b d (x ) + (1008a b d - 432b c d )(x )
+--R +
+--R 2 2 4 3 3 4 2 2 n 2
+--R (744a b d - 1184a b c d + 504b c d )(x )
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 n 4 4
+--R (30a b d - 962a b c d + 1498a b c d - 630b c d)x - 45a d
+--R +
+--R 3 3 2 2 2 2 3 3 4 4
+--R - 90a b c d + 1564a b c d - 2310a b c d + 945b c
+--R *
+--R +--------+ +--------+
+--R +-+ +-+ | n | n
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 5 +-+ +-+
+--R 1920b d n\|b \|d
+--R Type: Expression(Integer)
+--E 658
+
+--S 659 of 716
+--a0:=integrate(t0,x)
+--E 659
+
+--S 660 of 716
+--m0:=a0-r0
+--E 660
+
+--S 661 of 716
+--d0:=D(m0,x)
+--E 661
+
+)clear all
+
+--S 662 of 716
+t0:=x^(-1+3*n)*(a+b*x^n)^(3/2)/sqrt(c+d*x^n)
+--R
+--R
+--R +--------+
+--R n 3n - 1 | n
+--R (b x + a)x \|b x + a
+--R (1) ----------------------------
+--R +--------+
+--R | n
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 662
+
+--S 663 of 716
+r0:=1/64*(b*c-a*d)^2*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(5/2)*d^(9/2)*n)+_
+ 1/96*(35*b^2*c^2+10*a*b*c*d+3*a^2*d^2)*(a+b*x^n)^(3/2)*_
+ sqrt(c+d*x^n)/(b^2*d^3*n)-1/24*(7*b*c+3*a*d)*(a+b*x^n)^(5/2)*_
+ sqrt(c+d*x^n)/(b^2*d^2*n)+1/4*x^n*(a+b*x^n)^(5/2)*_
+ sqrt(c+d*x^n)/(b*d*n)-1/64*(b*c-a*d)*(35*b^2*c^2+10*a*b*c*d+_
+ 3*a^2*d^2)*sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b^2*d^4*n)
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (9a d + 12a b c d + 54a b c d - 180a b c d + 105b c )
+--R *
+--R +--------+
+--R +-+ | n
+--R \|d \|b x + a
+--R atanh(---------------)
+--R +--------+
+--R +-+ | n
+--R \|b \|d x + c
+--R +
+--R 3 3 n 3 2 3 3 2 n 2
+--R 48b d (x ) + (72a b d - 56b c d )(x )
+--R +
+--R 2 3 2 2 3 2 n 3 3 2 2 2 2
+--R (6a b d - 92a b c d + 70b c d)x - 9a d - 15a b c d + 145a b c d
+--R +
+--R 3 3
+--R - 105b c
+--R *
+--R +--------+ +--------+
+--R +-+ +-+ | n | n
+--R \|b \|d \|b x + a \|d x + c
+--R /
+--R 2 4 +-+ +-+
+--R 192b d n\|b \|d
+--R Type: Expression(Integer)
+--E 663
+
+--S 664 of 716
+--a0:=integrate(t0,x)
+--E 664
+
+--S 665 of 716
+--m0:=a0-r0
+--E 665
+
+--S 666 of 716
+--d0:=D(m0,x)
+--E 666
+
+)clear all
+
+--S 667 of 716
+t0:=x^(-1+3*n)*sqrt(a+b*x^n)/sqrt(c+d*x^n)
+--R
+--R
+--R +--------+
+--R 3n - 1 | n
+--R x \|b x + a
+--R (1) ------------------
+--R +--------+
+--R | n
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 667
+
+--S 668 of 716
+r0:=-1/8*(b*c-a*d)*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*atanh(sqrt(d)*_
+ sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(5/2)*d^(7/2)*n)-_
+ 1/12*(5*b*c+3*a*d)*(a+b*x^n)^(3/2)*sqrt(c+d*x^n)/(b^2*d^2*n)+_
+ 1/3*x^n*(a+b*x^n)^(3/2)*sqrt(c+d*x^n)/(b*d*n)+_
+ 1/8*(5*b^2*c^2+2*a*b*c*d+a^2*d^2)*sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b^2*d^3*n)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | n
+--R 3 3 2 2 2 2 3 3 \|d \|b x + a
+--R (3a d + 3a b c d + 9a b c d - 15b c )atanh(---------------)
+--R +--------+
+--R +-+ | n
+--R \|b \|d x + c
+--R +
+--R 2 2 n 2 2 2 n 2 2 2 2 +-+
+--R (8b d (x ) + (2a b d - 10b c d)x - 3a d - 4a b c d + 15b c )\|b
+--R *
+--R +--------+ +--------+
+--R +-+ | n | n
+--R \|d \|b x + a \|d x + c
+--R /
+--R 2 3 +-+ +-+
+--R 24b d n\|b \|d
+--R Type: Expression(Integer)
+--E 668
+
+--S 669 of 716
+--a0:=integrate(t0,x)
+--E 669
+
+--S 670 of 716
+--m0:=a0-r0
+--E 670
+
+--S 671 of 716
+--d0:=D(m0,x)
+--E 671
+
+)clear all
+
+--S 672 of 716
+t0:=x^(-1+3*n)/(sqrt(a+b*x^n)*sqrt(c+d*x^n))
+--R
+--R
+--R 3n - 1
+--R x
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | n | n
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 672
+
+--S 673 of 716
+r0:=-1/4*(4*a*b*c*d-3*(b*c+a*d)^2)*atanh(sqrt(d)*sqrt(a+b*x^n)/_
+ (sqrt(b)*sqrt(c+d*x^n)))/(b^(5/2)*d^(5/2)*n)-3/4*(b*c+a*d)*_
+ sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b^2*d^2*n)+1/2*x^n*sqrt(a+b*x^n)*_
+ sqrt(c+d*x^n)/(b*d*n)
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | n
+--R 2 2 2 2 \|d \|b x + a
+--R (3a d + 2a b c d + 3b c )atanh(---------------)
+--R +--------+
+--R +-+ | n
+--R \|b \|d x + c
+--R +
+--R +--------+ +--------+
+--R n +-+ +-+ | n | n
+--R (2b d x - 3a d - 3b c)\|b \|d \|b x + a \|d x + c
+--R /
+--R 2 2 +-+ +-+
+--R 4b d n\|b \|d
+--R Type: Expression(Integer)
+--E 673
+
+--S 674 of 716
+--a0:=integrate(t0,x)
+--E 674
+
+--S 675 of 716
+--m0:=a0-r0
+--E 675
+
+--S 676 of 716
+--d0:=D(m0,x)
+--E 676
+
+)clear all
+
+--S 677 of 716
+t0:=x^(-1+3*n)/((a+b*x^n)^(3/2)*sqrt(c+d*x^n))
+--R
+--R
+--R 3n - 1
+--R x
+--R (1) --------------------------------
+--R +--------+ +--------+
+--R n | n | n
+--R (b x + a)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 677
+
+--S 678 of 716
+r0:=-(b*c+3*a*d)*atanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/_
+ (b^(5/2)*d^(3/2)*n)-2*a^2*sqrt(c+d*x^n)/(b^2*(b*c-a*d)*n*_
+ sqrt(a+b*x^n))+sqrt(a+b*x^n)*sqrt(c+d*x^n)/(b^2*d*n)
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ +-+ | n
+--R 2 2 2 2 | n \|d \|b x + a
+--R (- 3a d + 2a b c d + b c )\|b x + a atanh(---------------)
+--R +--------+
+--R +-+ | n
+--R \|b \|d x + c
+--R +
+--R +--------+
+--R 2 n 2 +-+ +-+ | n
+--R ((a b d - b c)x + 3a d - a b c)\|b \|d \|d x + c
+--R /
+--R +--------+
+--R 2 2 3 +-+ +-+ | n
+--R (a b d - b c d)n\|b \|d \|b x + a
+--R Type: Expression(Integer)
+--E 678
+
+--S 679 of 716
+--a0:=integrate(t0,x)
+--E 679
+
+--S 680 of 716
+--m0:=a0-r0
+--E 680
+
+--S 681 of 716
+--d0:=D(m0,x)
+--E 681
+
+)clear all
+
+--S 682 of 716
+t0:=x^(-1+3*n)/((a+b*x^n)^(5/2)*sqrt(c+d*x^n))
+--R
+--R
+--R 3n - 1
+--R x
+--R (1) ----------------------------------------------
+--R +--------+ +--------+
+--R 2 n 2 n 2 | n | n
+--R (b (x ) + 2a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 682
+
+--S 683 of 716
+r0:=2*atanh(sqrt(d)*sqrt(a+b*x^n)/(sqrt(b)*sqrt(c+d*x^n)))/(b^(5/2)*n*_
+ sqrt(d))-2/3*a^2*sqrt(c+d*x^n)/(b^2*(b*c-a*d)*n*(a+b*x^n)^(3/2))+_
+ 4/3*a*(3*b*c-2*a*d)*sqrt(c+d*x^n)/(b^2*(b*c-a*d)^2*n*sqrt(a+b*x^n))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 n 3 2 2 2 2
+--R ((6a b d - 12a b c d + 6b c )x + 6a d - 12a b c d + 6a b c )
+--R *
+--R +--------+
+--R +--------+ +-+ | n
+--R | n \|d \|b x + a
+--R \|b x + a atanh(---------------)
+--R +--------+
+--R +-+ | n
+--R \|b \|d x + c
+--R +
+--R +--------+
+--R 2 2 n 3 2 +-+ +-+ | n
+--R ((- 8a b d + 12a b c)x - 6a d + 10a b c)\|b \|d \|d x + c
+--R /
+--R 2 3 2 4 5 2 n 3 2 2 2 3 4 2 +-+
+--R ((3a b d - 6a b c d + 3b c )n x + (3a b d - 6a b c d + 3a b c )n)\|b
+--R *
+--R +--------+
+--R +-+ | n
+--R \|d \|b x + a
+--R Type: Expression(Integer)
+--E 683
+
+--S 684 of 716
+--a0:=integrate(t0,x)
+--E 684
+
+--S 685 of 716
+--m0:=a0-r0
+--E 685
+
+--S 686 of 716
+--d0:=D(m0,x)
+--E 686
+
+)clear all
+
+--S 687 of 716
+t0:=x^p*(b+c*x)^p*(b+2*c*x)
+--R
+--R
+--R p p
+--R (1) (2c x + b)x (c x + b)
+--R Type: Expression(Integer)
+--E 687
+
+--S 688 of 716
+r0:=x^(1+p)*(b+c*x)^(1+p)/(1+p)
+--R
+--R
+--R p + 1 p + 1
+--R x (c x + b)
+--R (2) --------------------
+--R p + 1
+--R Type: Expression(Integer)
+--E 688
+
+--S 689 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 p log(x) p log(c x + b)
+--R (c x + b x)%e %e
+--R (3) --------------------------------------
+--R p + 1
+--R Type: Union(Expression(Integer),...)
+--E 689
+
+--S 690 of 716
+m0:=a0-r0
+--R
+--R
+--R 2 p log(x) p log(c x + b) p + 1 p + 1
+--R (c x + b x)%e %e - x (c x + b)
+--R (4) -------------------------------------------------------------
+--R p + 1
+--R Type: Expression(Integer)
+--E 690
+
+--S 691 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 691
+
+)clear all
+
+--S 692 of 716
+t0:=x^(-1+2*(1+p))*(b+c*x^2)^p*(b+2*c*x^2)
+--R
+--R
+--R 2 2p + 1 2 p
+--R (1) (2c x + b)x (c x + b)
+--R Type: Expression(Integer)
+--E 692
+
+--S 693 of 716
+r0:=1/2*x^(2*(1+p))*(b+c*x^2)^(1+p)/(1+p)
+--R
+--R
+--R 2p + 2 2 p + 1
+--R x (c x + b)
+--R (2) ----------------------
+--R 2p + 2
+--R Type: Expression(Integer)
+--E 693
+
+--S 694 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 3 (2p + 1)log(x) p log(c x + b)
+--R (c x + b x)%e %e
+--R (3) ---------------------------------------------
+--R 2p + 2
+--R Type: Union(Expression(Integer),...)
+--E 694
+
+--S 695 of 716
+m0:=a0-r0
+--R
+--R
+--R 2
+--R 3 (2p + 1)log(x) p log(c x + b) 2p + 2 2 p + 1
+--R (c x + b x)%e %e - x (c x + b)
+--R (4) ----------------------------------------------------------------------
+--R 2p + 2
+--R Type: Expression(Integer)
+--E 695
+
+--S 696 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 696
+
+)clear all
+
+--S 697 of 716
+t0:=x^(-1+3*(1+p))*(b+c*x^3)^p*(b+2*c*x^3)
+--R
+--R
+--R 3 3p + 2 3 p
+--R (1) (2c x + b)x (c x + b)
+--R Type: Expression(Integer)
+--E 697
+
+--S 698 of 716
+r0:=1/3*x^(3*(1+p))*(b+c*x^3)^(1+p)/(1+p)
+--R
+--R
+--R 3p + 3 3 p + 1
+--R x (c x + b)
+--R (2) ----------------------
+--R 3p + 3
+--R Type: Expression(Integer)
+--E 698
+
+--S 699 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R 4 (3p + 2)log(x) p log(c x + b)
+--R (c x + b x)%e %e
+--R (3) ---------------------------------------------
+--R 3p + 3
+--R Type: Union(Expression(Integer),...)
+--E 699
+
+--S 700 of 716
+m0:=a0-r0
+--R
+--R
+--R 3
+--R 4 (3p + 2)log(x) p log(c x + b) 3p + 3 3 p + 1
+--R (c x + b x)%e %e - x (c x + b)
+--R (4) ----------------------------------------------------------------------
+--R 3p + 3
+--R Type: Expression(Integer)
+--E 700
+
+--S 701 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 701
+
+)clear all
+
+--S 702 of 716
+t0:=x^(-1+n*(1+p))*(b+c*x^n)^p*(b+2*c*x^n)
+--R
+--R
+--R n n p + n - 1 n p
+--R (1) (2c x + b)x (c x + b)
+--R Type: Expression(Integer)
+--E 702
+
+--S 703 of 716
+r0:=x^(n*(1+p))*(b+c*x^n)^(1+p)/(n*(1+p))
+--R
+--R
+--R n p + n n p + 1
+--R x (c x + b)
+--R (2) -----------------------
+--R n p + n
+--R Type: Expression(Integer)
+--E 703
+
+--S 704 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R n log(x)
+--R n log(x) (n p + n - 1)log(x) p log(c %e + b)
+--R (c x %e + b x)%e %e
+--R (3) --------------------------------------------------------------------
+--R n p + n
+--R Type: Union(Expression(Integer),...)
+--E 704
+
+--S 705 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R n log(x)
+--R n log(x) (n p + n - 1)log(x) p log(c %e + b)
+--R (c x %e + b x)%e %e
+--R +
+--R n p + n n p + 1
+--R - x (c x + b)
+--R /
+--R n p + n
+--R Type: Expression(Integer)
+--E 705
+
+--S 706 of 716
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 706
+
+)clear all
+
+--S 707 of 716
+t0:=(A+B*x^2)*(c+d*x^2)*sqrt(a+b*x^2)/x
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B d x + (A d + B c)x + A c)\|b x + a
+--R (1) -----------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 707
+
+--S 708 of 716
+r0:=1/15*(2*b*B*c+5*A*b*d-2*a*B*d)*(a+b*x^2)^(3/2)/b^2+_
+ 1/5*B*(a+b*x^2)^(3/2)*(c+d*x^2)/b-_
+ A*c*atanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+A*c*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 +-+ \|b x + a
+--R - 15A b c\|a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 4 2 2 2 2
+--R 3B b d x + ((5A b + B a b)d + 5B b c)x + (5A a b - 2B a )d
+--R +
+--R 2
+--R (15A b + 5B a b)c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2
+--R 15b
+--R Type: Expression(Integer)
+--E 708
+
+--S 709 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 3 | 2
+--R (15A a b c x + 180A a b c x + 240A a c)\|b x + a
+--R +
+--R 2 4 2 2 3 +-+
+--R (- 75A a b c x - 300A a b c x - 240A a c)\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 2 8 2 2 2 6
+--R - 15B a b d x + ((- 25A a b - 65B a b)d - 25B a b c)x
+--R +
+--R 2 3 2 2 4
+--R ((- 120A a b - 60B a )d + (- 60A a b - 120B a b)c)x
+--R +
+--R 3 2 3 2
+--R (- 120A a d + (- 120A a b - 120B a )c)x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 10 3 2 3 8
+--R 3B b d x + ((5A b + 40B a b )d + 5B b c)x
+--R +
+--R 2 2 3 2 6
+--R ((70A a b + 95B a b)d + (15A b + 70B a b )c)x
+--R +
+--R 2 3 2 2 4
+--R ((180A a b + 60B a )d + (120A a b + 180B a b)c)x
+--R +
+--R 3 2 3 2
+--R (120A a d + (120A a b + 120B a )c)x
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a
+--R Type: Union(Expression(Integer),...)
+--E 709
+
+--S 710 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 4 4 2 3 2 3 2 | 2
+--R (15A a b c x + 180A a b c x + 240A a b c)\|b x + a
+--R +
+--R 4 4 2 3 2 3 2 +-+
+--R (- 75A a b c x - 300A a b c x - 240A a b c)\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 4 2 3 2 3 2 | 2
+--R (15A a b c x + 180A a b c x + 240A a b c)\|b x + a
+--R +
+--R 4 4 2 3 2 3 2 +-+
+--R (- 75A a b c x - 300A a b c x - 240A a b c)\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 3 3 2 4 2 3 4
+--R ((5A a b - 2B a b )d + (15A a b + 5B a b )c)x
+--R +
+--R 3 2 4 2 3 3 2 2
+--R ((60A a b - 24B a b)d + (180A a b + 60B a b )c)x
+--R +
+--R 4 5 3 2 4
+--R (80A a b - 32B a )d + (240A a b + 80B a b)c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 3 3 2 4 2 3 4
+--R ((- 25A a b + 10B a b )d + (- 75A a b - 25B a b )c)x
+--R +
+--R 3 2 4 2 3 3 2 2
+--R ((- 100A a b + 40B a b)d + (- 300A a b - 100B a b )c)x
+--R +
+--R 4 5 3 2 4
+--R (- 80A a b + 32B a )d + (- 240A a b - 80B a b)c
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +-+ | 2 4 4 2 3 2
+--R (15b x + 180a b x + 240a b )\|a \|b x + a - 75a b x - 300a b x
+--R +
+--R 3 2
+--R - 240a b
+--R Type: Expression(Integer)
+--E 710
+
+--S 711 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 711
+
+)clear all
+
+--S 712 of 716
+t0:=(a+b*x^2)*(A+B*x^2)*sqrt(c+d*x^2)/x
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (B b x + (A b + B a)x + A a)\|d x + c
+--R (1) -----------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 712
+
+--S 713 of 716
+r0:=-1/15*(2*b*B*c-2*A*b*d-5*a*B*d)*(c+d*x^2)^(3/2)/d^2+_
+ 1/5*b*(A+B*x^2)*(c+d*x^2)^(3/2)/d-a*A*atanh(sqrt(c+d*x^2)/_
+ sqrt(c))*sqrt(c)+a*A*sqrt(c+d*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 +-+ \|d x + c
+--R - 15A a d \|c atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 2 4 2 2 2
+--R 3B b d x + ((5A b + 5B a)d + B b c d)x + 15A a d
+--R +
+--R 2
+--R (5A b + 5B a)c d - 2B b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R /
+--R 2
+--R 15d
+--R Type: Expression(Integer)
+--E 713
+
+--S 714 of 716
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 3 | 2
+--R (15A a c d x + 180A a c d x + 240A a c )\|d x + c
+--R +
+--R 2 4 2 2 3 +-+
+--R (- 75A a c d x - 300A a c d x - 240A a c )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R 2 8 2 2 6
+--R - 15B b c d x + ((- 25A b - 25B a)c d - 65B b c d)x
+--R +
+--R 2 2 3 4
+--R (- 60A a c d + (- 120A b - 120B a)c d - 60B b c )x
+--R +
+--R 2 3 2
+--R (- 120A a c d + (- 120A b - 120B a)c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 3 10 3 2 8
+--R 3B b d x + ((5A b + 5B a)d + 40B b c d )x
+--R +
+--R 3 2 2 6
+--R (15A a d + (70A b + 70B a)c d + 95B b c d)x
+--R +
+--R 2 2 3 4
+--R (120A a c d + (180A b + 180B a)c d + 60B b c )x
+--R +
+--R 2 3 2
+--R (120A a c d + (120A b + 120B a)c )x
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (15d x + 180c d x + 240c )\|c \|d x + c - 75c d x - 300c d x - 240c
+--R Type: Union(Expression(Integer),...)
+--E 714
+
+--S 715 of 716
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 4 4 2 3 2 3 2 | 2
+--R (15A a c d x + 180A a c d x + 240A a c d )\|d x + c
+--R +
+--R 4 4 2 3 2 3 2 +-+
+--R (- 75A a c d x - 300A a c d x - 240A a c d )\|c
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|d x + c - \|c
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 4 2 3 2 3 2 | 2
+--R (15A a c d x + 180A a c d x + 240A a c d )\|d x + c
+--R +
+--R 4 4 2 3 2 3 2 +-+
+--R (- 75A a c d x - 300A a c d x - 240A a c d )\|c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R atanh(-----------)
+--R +-+
+--R \|c
+--R +
+--R 4 2 3 3 2 4
+--R (15A a c d + (5A b + 5B a)c d - 2B b c d )x
+--R +
+--R 2 3 3 2 4 2 3 2
+--R (180A a c d + (60A b + 60B a)c d - 24B b c d)x + 240A a c d
+--R +
+--R 4 5
+--R (80A b + 80B a)c d - 32B b c
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 4 2 3 3 2 4
+--R (- 75A a c d + (- 25A b - 25B a)c d + 10B b c d )x
+--R +
+--R 2 3 3 2 4 2 3 2
+--R (- 300A a c d + (- 100A b - 100B a)c d + 40B b c d)x - 240A a c d
+--R +
+--R 4 5
+--R (- 80A b - 80B a)c d + 32B b c
+--R *
+--R +-+
+--R \|c
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +-+ | 2 4 4 2 3 2
+--R (15d x + 180c d x + 240c d )\|c \|d x + c - 75c d x - 300c d x
+--R +
+--R 3 2
+--R - 240c d
+--R Type: Expression(Integer)
+--E 715
+
+--S 716 of 716
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 716
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich6e.input.pdf b/src/axiom-website/CATS/rich6e.input.pdf
new file mode 100644
index 0000000..5113a6c
Binary files /dev/null and b/src/axiom-website/CATS/rich6e.input.pdf differ
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index e912f51..789ea1d 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -4254,6 +4254,8 @@ src/axiom-website/CATS/rich3b
src/axiom-website/CATS/rich3c
20130804.01.tpd.patch
src/axiom-website/CATS/rich4*, src/input/rich4*
+20130811.01.tpd.patch
+src/axiom-website/CATS/rich5,6*, src/input/rich5,6*