diff --git a/changelog b/changelog index 30d4e06..13bb346 100644 --- a/changelog +++ b/changelog @@ -1,4 +1,10 @@ -20130718 tpd src/axiom-website/patches.html 20130718.01.tpd.patch +20130719 tpd src/axiom-website/patches.html 20130719.01.tpd.patch +20130719 tpd src/axiom-website/CATS/index.html +20130719 tpd src/axiom-website/CATS/rich1a.input +20130719 tpd src/axiom-website/CATS/rich1a.input.pdf +20130719 tpd src/axiom-website/CATS/rich1b.input +20130719 tpd src/axiom-website/CATS/rich1b.input.pdf +20130718 tpd 20130718 tpd src/axiom-website/patches.html 20130718.01.tpd.patch 20130718 tpd src/input/rich1b.input 20130718 tpd src/input/rich1a.input 20130718 tpd src/input/Makefile diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html index f5a42a0..c11116e 100644 --- a/src/axiom-website/CATS/index.html +++ b/src/axiom-website/CATS/index.html @@ -287,6 +287,18 @@ This is the Charlwood test suite

This portion of the CATS suite involves Albert Rich's Integration Suite. They have been rewritten using Axiom syntax.

+ (a+b x)^m (c+d x)^n (part 1) + source + pdf
+ (a+b x)^m (c+d x)^n (part 2) + source + pdf
+ +

+

Rich



+This portion of the CATS suite involves Albert Rich's Integration Suite. +They have been rewritten using Axiom syntax. +

algebraic000-099 source pdf
diff --git a/src/axiom-website/CATS/rich1a.input.pamphlet b/src/axiom-website/CATS/rich1a.input.pamphlet new file mode 100644 index 0000000..4ae6691 --- /dev/null +++ b/src/axiom-website/CATS/rich1a.input.pamphlet @@ -0,0 +1,41096 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich1a.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{License} +\begin{chunk}{license} +--Copyright The Numerical Algorithms Group Limited 1991. +\end{chunk} +\section{Integrands of the form $x^m (a+b x)^n$} +\subsection{Integrands of the form $x^m$} +\subsubsection{Integrands of the form $a$} + +\begin{chunk}{*} +)set break resume +)sys rm -f rich1a.output +)spool rich1a.output +)set message test on +)set message auto off +)clear all + +--S 1 of 3330 +t0000:=0 +--R +--R +--R (1) 0 +--R Type: NonNegativeInteger +--E 1 + +--S 2 of 3330 +r0000:=0 +--R +--R +--R (2) 0 +--R Type: NonNegativeInteger +--E 2 + +--S 3 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 3 + +--S 4 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 4 + +--S 5 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 5 + +)clear all + +--S 6 of 3330 +t0000:=1 +--R +--R +--R (1) 1 +--R Type: PositiveInteger +--E 6 + +--S 7 of 3330 +r0000:=x +--R +--R +--R (2) x +--R Type: Variable(x) +--E 7 + +--S 8 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) x +--R Type: Polynomial(Fraction(Integer)) +--E 8 + +--S 9 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 9 + +--S 10 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 10 + +)clear all + +--S 11 of 3330 +t0000:=5 +--R +--R +--R (1) 5 +--R Type: PositiveInteger +--E 11 + +--S 12 of 3330 +r0000:=5*x +--R +--R +--R (2) 5x +--R Type: Polynomial(Integer) +--E 12 + +--S 13 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) 5x +--R Type: Polynomial(Fraction(Integer)) +--E 13 + +--S 14 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 14 + +--S 15 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 15 + +)clear all + +--S 16 of 3330 +t0000:=-2 +--R +--R +--R (1) - 2 +--R Type: Integer +--E 16 + +--S 17 of 3330 +r0000:=-2*x +--R +--R +--R (2) - 2x +--R Type: Polynomial(Integer) +--E 17 + +--S 18 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) - 2x +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 19 + +--S 20 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +)clear all + +--S 21 of 3330 +t0000:=-3/2 +--R +--R +--R 3 +--R (1) - - +--R 2 +--R Type: Fraction(Integer) +--E 21 + +--S 22 of 3330 +r0000:=-3/2*x +--R +--R +--R 3 +--R (2) - - x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3x +--R (3) - -- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 3330 +t0000:=%pi +--R +--R +--R (1) %pi +--R Type: Pi +--E 26 + +--S 27 of 3330 +r0000:=%pi*x +--R +--R +--R (2) %pi x +--R Type: Expression(Integer) +--E 27 + +--S 28 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) %pi x +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 3330 +t0000:=a +--R +--R +--R (1) a +--R Type: Variable(a) +--E 31 + +--S 32 of 3330 +r0000:=a*x +--R +--R +--R (2) a x +--R Type: Polynomial(Integer) +--E 32 + +--S 33 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) a x +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 34 + +--S 35 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +)clear all + +--S 36 of 3330 +t0000:=3*a +--R +--R +--R (1) 3a +--R Type: Polynomial(Integer) +--E 36 + +--S 37 of 3330 +r0000:=3*a*x +--R +--R +--R (2) 3a x +--R Type: Polynomial(Integer) +--E 37 + +--S 38 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) 3a x +--R Type: Polynomial(Fraction(Integer)) +--E 38 + +--S 39 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 39 + +--S 40 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 40 + +)clear all + +--S 41 of 3330 +t0000:=%pi/sqrt(16-%e^2) +--R +--R +--R %pi +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|- %e + 16 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 3330 +r0000:=%pi*x/sqrt(16-%e^2) +--R +--R +--R %pi x +--R (2) ------------- +--R +----------+ +--R | 2 +--R \|- %e + 16 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R %pi x +--R (3) ------------- +--R +----------+ +--R | 2 +--R \|- %e + 16 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 3330 +t0000:=x^m +--R +--R +--R m +--R (1) x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 3330 +r0000:=x^(1+m)/(1+m) +--R +--R +--R m + 1 +--R x +--R (2) ------ +--R m + 1 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R m log(x) +--R x %e +--R (3) ------------ +--R m + 1 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R m log(x) m + 1 +--R x %e - x +--R (4) --------------------- +--R m + 1 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 3330 +d0000:=normalize m0000 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 3330 +t0000:=x^100 +--R +--R +--R 100 +--R (1) x +--R Type: Polynomial(Integer) +--E 51 + +--S 52 of 3330 +r0000:=1/101*x^101 +--R +--R +--R 1 101 +--R (2) --- x +--R 101 +--R Type: Polynomial(Fraction(Integer)) +--E 52 + +--S 53 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 101 +--R (3) --- x +--R 101 +--R Type: Polynomial(Fraction(Integer)) +--E 53 + +--S 54 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 54 + +--S 55 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 55 + +)clear all + +--S 56 of 3330 +t0000:=x^3 +--R +--R +--R 3 +--R (1) x +--R Type: Polynomial(Integer) +--E 56 + +--S 57 of 3330 +r0000:=1/4*x^4 +--R +--R +--R 1 4 +--R (2) - x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 57 + +--S 58 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 4 +--R (3) - x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 58 + +--S 59 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 59 + +--S 60 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 60 + +)clear all + +--S 61 of 3330 +t0000:=x^2 +--R +--R +--R 2 +--R (1) x +--R Type: Polynomial(Integer) +--E 61 + +--S 62 of 3330 +r0000:=1/3*x^3 +--R +--R +--R 1 3 +--R (2) - x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 62 + +--S 63 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 +--R (3) - x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 63 + +--S 64 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 64 + +--S 65 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 65 + +)clear all + +--S 66 of 3330 +t0000:=x +--R +--R +--R (1) x +--R Type: Variable(x) +--E 66 + +--S 67 of 3330 +r0000:=1/2*x^2 +--R +--R +--R 1 2 +--R (2) - x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 67 + +--S 68 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 +--R (3) - x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 68 + +--S 69 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 69 + +--S 70 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 70 + +)clear all + +--S 71 of 3330 +t0000:=1 +--R +--R +--R (1) 1 +--R Type: PositiveInteger +--E 71 + +--S 72 of 3330 +r0000:=x +--R +--R +--R (2) x +--R Type: Variable(x) +--E 72 + +--S 73 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) x +--R Type: Polynomial(Fraction(Integer)) +--E 73 + +--S 74 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 74 + +--S 75 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 75 + +)clear all + +--S 76 of 3330 +t0000:=1/x +--R +--R +--R 1 +--R (1) - +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 3330 +r0000:=log(x) +--R +--R +--R (2) log(x) +--R Type: Expression(Integer) +--E 77 + +--S 78 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) log(x) +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 3330 +t0000:=1/x^2 +--R +--R +--R 1 +--R (1) -- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 3330 +r0000:=(-1)/x +--R +--R +--R 1 +--R (2) - - +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 82 + +--S 83 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - - +--R x +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 3330 +t0000:=1/x^3 +--R +--R +--R 1 +--R (1) -- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 86 + +--S 87 of 3330 +r0000:=(-1/2)/x^2 +--R +--R +--R 1 +--R - +--R 2 +--R (2) - --- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 87 + +--S 88 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - --- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 3330 +t0000:=1/x^4 +--R +--R +--R 1 +--R (1) -- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 3330 +r0000:=(-1/3)/x^3 +--R +--R +--R 1 +--R - +--R 3 +--R (2) - --- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +--S 93 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - --- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 3330 +t0000:=1/x^100 +--R +--R +--R 1 +--R (1) ---- +--R 100 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 96 + +--S 97 of 3330 +r0000:=(-1/99)/x^99 +--R +--R +--R 1 +--R -- +--R 99 +--R (2) - ---- +--R 99 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 97 + +--S 98 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - ----- +--R 99 +--R 99x +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 3330 +t0000:=1/(a*x^n+b*x^n) +--R +--R +--R 1 +--R (1) --------- +--R n +--R (b + a)x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 3330 +r0000:=x^(1-n)/((a+b)*(1-n)) +--R +--R +--R - n + 1 +--R x +--R (2) - ---------------- +--R (b + a)n - b - a +--R Type: Expression(Integer) +--E 102 + +--S 103 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R (3) - ---------------------------- +--R n log(x) +--R ((b + a)n - b - a)%e +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R - n + 1 n log(x) +--R x %e - x +--R (4) ---------------------------- +--R n log(x) +--R ((b + a)n - b - a)%e +--R Type: Expression(Integer) +--E 104 + +--S 105 of 3330 +d0000:=D(m0000,x) +--R +--R +--R - n n log(x) +--R - x %e + 1 +--R (5) -------------------- +--R n log(x) +--R (b + a)%e +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 3330 +t0000:=x^(5/2) +--R +--R +--R 2 +-+ +--R (1) x \|x +--R Type: Expression(Integer) +--E 106 + +--S 107 of 3330 +r0000:=2/7*x^(7/2) +--R +--R +--R 3 +-+ +--R 2x \|x +--R (2) ------- +--R 7 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 +-+ +--R 2x \|x +--R (3) ------- +--R 7 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 3330 +t0000:=x^(3/2) +--R +--R +--R +-+ +--R (1) x\|x +--R Type: Expression(Integer) +--E 111 + +--S 112 of 3330 +r0000:=2/5*x^(5/2) +--R +--R +--R 2 +-+ +--R 2x \|x +--R (2) ------- +--R 5 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +-+ +--R 2x \|x +--R (3) ------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 3330 +t0000:=x^(1/2) +--R +--R +--R +-+ +--R (1) \|x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 3330 +r0000:=2/3*x^(3/2) +--R +--R +--R +-+ +--R 2x\|x +--R (2) ------ +--R 3 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +--R 2x\|x +--R (3) ------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 3330 +t0000:=1/x^(1/2) +--R +--R +--R 1 +--R (1) ---- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 121 + +--S 122 of 3330 +r0000:=2*sqrt(x) +--R +--R +--R +-+ +--R (2) 2\|x +--R Type: Expression(Integer) +--E 122 + +--S 123 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +--R (3) 2\|x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 3330 +t0000:=1/x^(3/2) +--R +--R +--R 1 +--R (1) ----- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 3330 +r0000:=(-2)/sqrt(x) +--R +--R +--R 2 +--R (2) - ---- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 127 + +--S 128 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) - ---- +--R +-+ +--R \|x +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 3330 +t0000:=1/x^(5/2) +--R +--R +--R 1 +--R (1) ------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 131 + +--S 132 of 3330 +r0000:=(-2/3)/x^(3/2) +--R +--R +--R 2 +--R (2) - ------ +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 132 + +--S 133 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) - ------ +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 3330 +t0000:=x^(5/3) +--R +--R +--R 3+-+2 +--R (1) x \|x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 3330 +r0000:=3/8*x^(8/3) +--R +--R +--R 2 3+-+2 +--R 3x \|x +--R (2) -------- +--R 8 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3+-+2 +--R 3x \|x +--R (3) -------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 3330 +t0000:=x^(4/3) +--R +--R +--R 3+-+ +--R (1) x\|x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 3330 +r0000:=3/7*x^(7/3) +--R +--R +--R 2 3+-+ +--R 3x \|x +--R (2) ------- +--R 7 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3+-+ +--R 3x \|x +--R (3) ------- +--R 7 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 3330 +t0000:=x^(2/3) +--R +--R +--R 3+-+2 +--R (1) \|x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 3330 +r0000:=3/5*x^(5/3) +--R +--R +--R 3+-+2 +--R 3x \|x +--R (2) -------- +--R 5 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-+2 +--R 3x \|x +--R (3) -------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 3330 +t0000:=x^(1/3) +--R +--R +--R 3+-+ +--R (1) \|x +--R Type: Expression(Integer) +--E 151 + +--S 152 of 3330 +r0000:=3/4*x^(4/3) +--R +--R +--R 3+-+ +--R 3x\|x +--R (2) ------ +--R 4 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-+ +--R 3x\|x +--R (3) ------ +--R 4 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 3330 +t0000:=1/x^(1/3) +--R +--R +--R 1 +--R (1) ---- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 156 + +--S 157 of 3330 +r0000:=3/2*x^(2/3) +--R +--R +--R 3+-+2 +--R 3\|x +--R (2) ------ +--R 2 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-+2 +--R 3\|x +--R (3) ------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 3330 +t0000:=1/x^(2/3) +--R +--R +--R 1 +--R (1) ----- +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 161 + +--S 162 of 3330 +r0000:=3*x^(1/3) +--R +--R +--R 3+-+ +--R (2) 3\|x +--R Type: Expression(Integer) +--E 162 + +--S 163 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-+ +--R (3) 3\|x +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 3330 +t0000:=1/x^(4/3) +--R +--R +--R 1 +--R (1) ----- +--R 3+-+ +--R x\|x +--R Type: Expression(Integer) +--E 166 + +--S 167 of 3330 +r0000:=(-3)/x^(1/3) +--R +--R +--R 3 +--R (2) - ---- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 +--R (3) - ---- +--R 3+-+ +--R \|x +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 3330 +t0000:=1/x^(5/3) +--R +--R +--R 1 +--R (1) ------- +--R 3+-+2 +--R x \|x +--R Type: Expression(Integer) +--E 171 + +--S 172 of 3330 +r0000:=(-3/2)/x^(2/3) +--R +--R +--R 3 +--R (2) - ------ +--R 3+-+2 +--R 2\|x +--R Type: Expression(Integer) +--E 172 + +--S 173 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 +--R (3) - ------ +--R 3+-+2 +--R 2\|x +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 3330 +t0000:=x^m*(a+b*x) +--R +--R +--R m +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 3330 +r0000:=a*x^(1+m)/(1+m)+b*x^(2+m)/(2+m) +--R +--R +--R m + 2 m + 1 +--R (b m + b)x + (a m + 2a)x +--R (2) ---------------------------------- +--R 2 +--R m + 3m + 2 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 m log(x) +--R ((b m + b)x + (a m + 2a)x)%e +--R (3) ------------------------------------- +--R 2 +--R m + 3m + 2 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 m log(x) m + 2 +--R ((b m + b)x + (a m + 2a)x)%e + (- b m - b)x +--R + +--R m + 1 +--R (- a m - 2a)x +--R / +--R 2 +--R m + 3m + 2 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 3330 +d0000:=normalize m0000 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 3330 +t0000:=x^3*(a+b*x) +--R +--R +--R 4 3 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 181 + +--S 182 of 3330 +r0000:=1/4*a*x^4+1/5*b*x^5 +--R +--R +--R 1 5 1 4 +--R (2) - b x + - a x +--R 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 182 + +--S 183 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 5 1 4 +--R (3) - b x + - a x +--R 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 183 + +--S 184 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 184 + +--S 185 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 185 + +)clear all + +--S 186 of 3330 +t0000:=x^2*(a+b*x) +--R +--R +--R 3 2 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 186 + +--S 187 of 3330 +r0000:=1/3*a*x^3+1/4*b*x^4 +--R +--R +--R 1 4 1 3 +--R (2) - b x + - a x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 187 + +--S 188 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 4 1 3 +--R (3) - b x + - a x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 188 + +--S 189 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 189 + +--S 190 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 190 + +)clear all + +--S 191 of 3330 +t0000:=x*(a+b*x) +--R +--R +--R 2 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 191 + +--S 192 of 3330 +r0000:=1/2*a*x^2+1/3*b*x^3 +--R +--R +--R 1 3 1 2 +--R (2) - b x + - a x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 192 + +--S 193 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 1 2 +--R (3) - b x + - a x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 193 + +--S 194 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 194 + +--S 195 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 195 + +)clear all + +--S 196 of 3330 +t0000:=a+b*x +--R +--R +--R (1) b x + a +--R Type: Polynomial(Integer) +--E 196 + +--S 197 of 3330 +r0000:=a*x+1/2*b*x^2 +--R +--R +--R 1 2 +--R (2) - b x + a x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 197 + +--S 198 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 +--R (3) - b x + a x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 198 + +--S 199 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 199 + +--S 200 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 200 + +)clear all + +--S 201 of 3330 +t0000:=(a+b*x)/x +--R +--R +--R b x + a +--R (1) ------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 3330 +r0000:=b*x+a*log(x) +--R +--R +--R (2) a log(x) + b x +--R Type: Expression(Integer) +--E 202 + +--S 203 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) a log(x) + b x +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 3330 +t0000:=(a+b*x)/x^2 +--R +--R +--R b x + a +--R (1) ------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 3330 +r0000:=-a/x+b*log(x) +--R +--R +--R b x log(x) - a +--R (2) -------------- +--R x +--R Type: Expression(Integer) +--E 207 + +--S 208 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R b x log(x) - a +--R (3) -------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 3330 +t0000:=(a+b*x)/x^3 +--R +--R +--R b x + a +--R (1) ------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 3330 +r0000:=-1/2*a/x^2-b/x +--R +--R +--R 1 +--R - b x - - a +--R 2 +--R (2) ----------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 212 + +--S 213 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 2b x - a +--R (3) ---------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 3330 +t0000:=(a+b*x)/x^4 +--R +--R +--R b x + a +--R (1) ------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 3330 +r0000:=-1/3*a/x^3-1/2*b/x^2 +--R +--R +--R 1 1 +--R - - b x - - a +--R 2 3 +--R (2) ------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 217 + +--S 218 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 3b x - 2a +--R (3) ----------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 3330 +t0000:=(a+b*x)/x^5 +--R +--R +--R b x + a +--R (1) ------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 3330 +r0000:=-1/4*a/x^4-1/3*b/x^3 +--R +--R +--R 1 1 +--R - - b x - - a +--R 3 4 +--R (2) ------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 222 + +--S 223 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 4b x - 3a +--R (3) ----------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 3330 +t0000:=x^m*(a+b*x)^2 +--R +--R +--R 2 2 2 m +--R (1) (b x + 2a b x + a )x +--R Type: Expression(Integer) +--E 226 + +--S 227 of 3330 +r0000:=a^2*x^(1+m)/(1+m)+2*a*b*x^(2+m)/(2+m)+b^2*x^(3+m)/(3+m) +--R +--R +--R (2) +--R 2 2 2 2 m + 3 2 m + 2 +--R (b m + 3b m + 2b )x + (2a b m + 8a b m + 6a b)x +--R + +--R 2 2 2 2 m + 1 +--R (a m + 5a m + 6a )x +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 3 2 2 +--R (b m + 3b m + 2b )x + (2a b m + 8a b m + 6a b)x +--R + +--R 2 2 2 2 +--R (a m + 5a m + 6a )x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 2 2 2 3 2 2 +--R (b m + 3b m + 2b )x + (2a b m + 8a b m + 6a b)x +--R + +--R 2 2 2 2 +--R (a m + 5a m + 6a )x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 2 2 m + 3 2 m + 2 +--R (- b m - 3b m - 2b )x + (- 2a b m - 8a b m - 6a b)x +--R + +--R 2 2 2 2 m + 1 +--R (- a m - 5a m - 6a )x +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 3330 +d0000:=normalize m0000 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 3330 +t0000:=x^3*(a+b*x)^2 +--R +--R +--R 2 5 4 2 3 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 231 + +--S 232 of 3330 +r0000:=1/4*a^2*x^4+2/5*a*b*x^5+1/6*b^2*x^6 +--R +--R +--R 1 2 6 2 5 1 2 4 +--R (2) - b x + - a b x + - a x +--R 6 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 232 + +--S 233 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 6 2 5 1 2 4 +--R (3) - b x + - a b x + - a x +--R 6 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 233 + +--S 234 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 234 + +--S 235 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 235 + +)clear all + +--S 236 of 3330 +t0000:=x^2*(a+b*x)^2 +--R +--R +--R 2 4 3 2 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 236 + +--S 237 of 3330 +r0000:=1/3*a^2*x^3+1/2*a*b*x^4+1/5*b^2*x^5 +--R +--R +--R 1 2 5 1 4 1 2 3 +--R (2) - b x + - a b x + - a x +--R 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 237 + +--S 238 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 5 1 4 1 2 3 +--R (3) - b x + - a b x + - a x +--R 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 238 + +--S 239 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 239 + +--S 240 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 240 + +)clear all + +--S 241 of 3330 +t0000:=x*(a+b*x)^2 +--R +--R +--R 2 3 2 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 241 + +--S 242 of 3330 +r0000:=1/2*a^2*x^2+2/3*a*b*x^3+1/4*b^2*x^4 +--R +--R +--R 1 2 4 2 3 1 2 2 +--R (2) - b x + - a b x + - a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 242 + +--S 243 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 4 2 3 1 2 2 +--R (3) - b x + - a b x + - a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 243 + +--S 244 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 244 + +--S 245 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 245 + +)clear all + +--S 246 of 3330 +t0000:=(a+b*x)^2 +--R +--R +--R 2 2 2 +--R (1) b x + 2a b x + a +--R Type: Polynomial(Integer) +--E 246 + +--S 247 of 3330 +r0000:=1/3*(a+b*x)^3/b +--R +--R +--R 1 3 3 2 2 2 1 3 +--R - b x + a b x + a b x + - a +--R 3 3 +--R (2) ------------------------------ +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 247 + +--S 248 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 3 2 2 +--R (3) - b x + a b x + a x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 248 + +--S 249 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 3 +--R - a +--R 3 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 249 + +--S 250 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 250 + +)clear all + +--S 251 of 3330 +t0000:=(a+b*x)^2/x +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 3330 +r0000:=2*a*b*x+1/2*b^2*x^2+a^2*log(x) +--R +--R +--R 2 2 2 +--R 2a log(x) + b x + 4a b x +--R (2) ------------------------- +--R 2 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 2a log(x) + b x + 4a b x +--R (3) ------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 3330 +t0000:=(a+b*x)^2/x^2 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 3330 +r0000:=-a^2/x+b^2*x+2*a*b*log(x) +--R +--R +--R 2 2 2 +--R 2a b x log(x) + b x - a +--R (2) ------------------------- +--R x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 2a b x log(x) + b x - a +--R (3) ------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 3330 +t0000:=(a+b*x)^2/x^3 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 3330 +r0000:=-1/2*a^2/x^2-2*a*b/x+b^2*log(x) +--R +--R +--R 2 2 2 +--R 2b x log(x) - 4a b x - a +--R (2) ------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 2b x log(x) - 4a b x - a +--R (3) ------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 3330 +t0000:=(a+b*x)^2/x^4 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 3330 +r0000:=-1/3*(a+b*x)^3/(a*x^3) +--R +--R +--R 1 3 3 2 2 2 1 3 +--R - - b x - a b x - a b x - - a +--R 3 3 +--R (2) -------------------------------- +--R 3 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 267 + +--S 268 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 3b x - 3a b x - a +--R (3) --------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 3 +--R b +--R (4) -- +--R 3a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 3330 +t0000:=(a+b*x)^2/x^5 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 3330 +r0000:=-1/4*a^2/x^4-2/3*a*b/x^3-1/2*b^2/x^2 +--R +--R +--R 1 2 2 2 1 2 +--R - - b x - - a b x - - a +--R 2 3 4 +--R (2) ------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 272 + +--S 273 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 6b x - 8a b x - 3a +--R (3) ---------------------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 3330 +t0000:=(a+b*x)^2/x^6 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 3330 +r0000:=-1/5*a^2/x^5-1/2*a*b/x^4-1/3*b^2/x^3 +--R +--R +--R 1 2 2 1 1 2 +--R - - b x - - a b x - - a +--R 3 2 5 +--R (2) ------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 277 + +--S 278 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 10b x - 15a b x - 6a +--R (3) ------------------------ +--R 5 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 3330 +t0000:=(a+b*x)^2/x^7 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 3330 +r0000:=-1/6*a^2/x^6-2/5*a*b/x^5-1/4*b^2/x^4 +--R +--R +--R 1 2 2 2 1 2 +--R - - b x - - a b x - - a +--R 4 5 6 +--R (2) ------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 282 + +--S 283 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 15b x - 24a b x - 10a +--R (3) ------------------------- +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 3330 +t0000:=(a+b*x)^2/x^8 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 3330 +r0000:=-1/7*a^2/x^7-1/3*a*b/x^6-1/5*b^2/x^5 +--R +--R +--R 1 2 2 1 1 2 +--R - - b x - - a b x - - a +--R 5 3 7 +--R (2) ------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 287 + +--S 288 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 21b x - 35a b x - 15a +--R (3) ------------------------- +--R 7 +--R 105x +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 3330 +t0000:=x^m*(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 m +--R (1) (b x + 3a b x + 3a b x + a )x +--R Type: Expression(Integer) +--E 291 + +--S 292 of 3330 +r0000:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(2+m)/(2+m)+3*a*b^2*x^(3+m)/_ + (3+m)+b^3*x^(4+m)/(4+m) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 4 +--R (b m + 6b m + 11b m + 6b )x +--R + +--R 2 3 2 2 2 2 m + 3 +--R (3a b m + 21a b m + 42a b m + 24a b )x +--R + +--R 2 3 2 2 2 2 m + 2 +--R (3a b m + 24a b m + 57a b m + 36a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (a m + 9a m + 26a m + 24a )x +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 4 +--R (b m + 6b m + 11b m + 6b )x +--R + +--R 2 3 2 2 2 2 3 +--R (3a b m + 21a b m + 42a b m + 24a b )x +--R + +--R 2 3 2 2 2 2 2 3 3 3 2 3 3 +--R (3a b m + 24a b m + 57a b m + 36a b)x + (a m + 9a m + 26a m + 24a )x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 3 3 2 3 3 4 +--R (b m + 6b m + 11b m + 6b )x +--R + +--R 2 3 2 2 2 2 3 +--R (3a b m + 21a b m + 42a b m + 24a b )x +--R + +--R 2 3 2 2 2 2 2 +--R (3a b m + 24a b m + 57a b m + 36a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 9a m + 26a m + 24a )x +--R * +--R m log(x) +--R %e +--R + +--R 3 3 3 2 3 3 m + 4 +--R (- b m - 6b m - 11b m - 6b )x +--R + +--R 2 3 2 2 2 2 m + 3 +--R (- 3a b m - 21a b m - 42a b m - 24a b )x +--R + +--R 2 3 2 2 2 2 m + 2 +--R (- 3a b m - 24a b m - 57a b m - 36a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- a m - 9a m - 26a m - 24a )x +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 3330 +d0000:=normalize m0000 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 3330 +t0000:=x^3*(a+b*x)^3 +--R +--R +--R 3 6 2 5 2 4 3 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 296 + +--S 297 of 3330 +r0000:=1/4*a^3*x^4+3/5*a^2*b*x^5+1/2*a*b^2*x^6+1/7*b^3*x^7 +--R +--R +--R 1 3 7 1 2 6 3 2 5 1 3 4 +--R (2) - b x + - a b x + - a b x + - a x +--R 7 2 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 297 + +--S 298 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 7 1 2 6 3 2 5 1 3 4 +--R (3) - b x + - a b x + - a b x + - a x +--R 7 2 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 298 + +--S 299 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 299 + +--S 300 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 300 + +)clear all + +--S 301 of 3330 +t0000:=x^2*(a+b*x)^3 +--R +--R +--R 3 5 2 4 2 3 3 2 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 301 + +--S 302 of 3330 +r0000:=1/3*a^3*x^3+3/4*a^2*b*x^4+3/5*a*b^2*x^5+1/6*b^3*x^6 +--R +--R +--R 1 3 6 3 2 5 3 2 4 1 3 3 +--R (2) - b x + - a b x + - a b x + - a x +--R 6 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 302 + +--S 303 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 6 3 2 5 3 2 4 1 3 3 +--R (3) - b x + - a b x + - a b x + - a x +--R 6 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 303 + +--S 304 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 304 + +--S 305 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 305 + +)clear all + +--S 306 of 3330 +t0000:=x*(a+b*x)^3 +--R +--R +--R 3 4 2 3 2 2 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 306 + +--S 307 of 3330 +r0000:=-1/4*a*(a+b*x)^4/b^2+1/5*(a+b*x)^5/b^2 +--R +--R +--R 1 5 5 3 4 4 2 3 3 1 3 2 2 1 5 +--R - b x + - a b x + a b x + - a b x - -- a +--R 5 4 2 20 +--R (2) --------------------------------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 307 + +--S 308 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 5 3 2 4 2 3 1 3 2 +--R (3) - b x + - a b x + a b x + - a x +--R 5 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 308 + +--S 309 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 5 +--R -- a +--R 20 +--R (4) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 309 + +--S 310 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 310 + +)clear all + +--S 311 of 3330 +t0000:=(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R (1) b x + 3a b x + 3a b x + a +--R Type: Polynomial(Integer) +--E 311 + +--S 312 of 3330 +r0000:=1/4*(a+b*x)^4/b +--R +--R +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - b x + a b x + - a b x + a b x + - a +--R 4 2 4 +--R (2) ----------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 312 + +--S 313 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 4 2 3 3 2 2 3 +--R (3) - b x + a b x + - a b x + a x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 313 + +--S 314 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 4 +--R - a +--R 4 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 314 + +--S 315 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 315 + +)clear all + +--S 316 of 3330 +t0000:=(a+b*x)^3/x +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 3330 +r0000:=3*a^2*b*x+3/2*a*b^2*x^2+1/3*b^3*x^3+a^3*log(x) +--R +--R +--R 3 3 3 2 2 2 +--R 6a log(x) + 2b x + 9a b x + 18a b x +--R (2) ------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 3 2 2 2 +--R 6a log(x) + 2b x + 9a b x + 18a b x +--R (3) ------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 3330 +t0000:=(a+b*x)^3/x^2 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 3330 +r0000:=-a^3/x+3*a*b^2*x+1/2*b^3*x^2+3*a^2*b*log(x) +--R +--R +--R 2 3 3 2 2 3 +--R 6a b x log(x) + b x + 6a b x - 2a +--R (2) ------------------------------------ +--R 2x +--R Type: Expression(Integer) +--E 322 + +--S 323 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 3 2 2 3 +--R 6a b x log(x) + b x + 6a b x - 2a +--R (3) ------------------------------------ +--R 2x +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 3330 +t0000:=(a+b*x)^3/x^3 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 3330 +r0000:=-1/2*a^3/x^2-3*a^2*b/x+b^3*x+3*a*b^2*log(x) +--R +--R +--R 2 2 3 3 2 3 +--R 6a b x log(x) + 2b x - 6a b x - a +--R (2) ----------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 327 + +--S 328 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 3 3 2 3 +--R 6a b x log(x) + 2b x - 6a b x - a +--R (3) ----------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 3330 +t0000:=(a+b*x)^3/x^4 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 3330 +r0000:=-1/3*a^3/x^3-3/2*a^2*b/x^2-3*a*b^2/x+b^3*log(x) +--R +--R +--R 3 3 2 2 2 3 +--R 6b x log(x) - 18a b x - 9a b x - 2a +--R (2) ------------------------------------- +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 332 + +--S 333 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 6b x log(x) - 18a b x - 9a b x - 2a +--R (3) ------------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 3330 +t0000:=(a+b*x)^3/x^5 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 3330 +r0000:=-1/4*(a+b*x)^4/(a*x^4) +--R +--R +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - - b x - a b x - - a b x - a b x - - a +--R 4 2 4 +--R (2) ------------------------------------------- +--R 4 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 337 + +--S 338 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 4b x - 6a b x - 4a b x - a +--R (3) ------------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 4 +--R b +--R (4) -- +--R 4a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 3330 +t0000:=(a+b*x)^3/x^6 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 3330 +r0000:=-1/5*a^3/x^5-3/4*a^2*b/x^4-a*b^2/x^3-1/2*b^3/x^2 +--R +--R +--R 1 3 3 2 2 3 2 1 3 +--R - - b x - a b x - - a b x - - a +--R 2 4 5 +--R (2) ---------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 342 + +--S 343 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 10b x - 20a b x - 15a b x - 4a +--R (3) ----------------------------------- +--R 5 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 3330 +t0000:=(a+b*x)^3/x^7 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 3330 +r0000:=-1/6*a^3/x^6-3/5*a^2*b/x^5-3/4*a*b^2/x^4-1/3*b^3/x^3 +--R +--R +--R 1 3 3 3 2 2 3 2 1 3 +--R - - b x - - a b x - - a b x - - a +--R 3 4 5 6 +--R (2) ------------------------------------ +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 347 + +--S 348 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 20b x - 45a b x - 36a b x - 10a +--R (3) ------------------------------------ +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 3330 +t0000:=(a+b*x)^3/x^8 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 3330 +r0000:=-1/7*a^3/x^7-1/2*a^2*b/x^6-3/5*a*b^2/x^5-1/4*b^3/x^4 +--R +--R +--R 1 3 3 3 2 2 1 2 1 3 +--R - - b x - - a b x - - a b x - - a +--R 4 5 2 7 +--R (2) ------------------------------------ +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 352 + +--S 353 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 35b x - 84a b x - 70a b x - 20a +--R (3) ------------------------------------ +--R 7 +--R 140x +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 3330 +t0000:=x^m*(a+b*x)^7 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 m +--R (b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a )x +--R Type: Expression(Integer) +--E 356 + +--S 357 of 3330 +r0000:=a^7*x^(1+m)/(1+m)+7*a^6*b*x^(2+m)/(2+m)+_ + 21*a^5*b^2*x^(3+m)/(3+m)+35*a^4*b^3*x^(4+m)/(4+m)+_ + 35*a^3*b^4*x^(5+m)/(5+m)+21*a^2*b^5*x^(6+m)/(6+m)+_ + 7*a*b^6*x^(7+m)/(7+m)+b^7*x^(8+m)/(8+m) +--R +--R +--R (2) +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R b m + 28b m + 322b m + 1960b m + 6769b m + 13132b m + 13068b m +--R + +--R 7 +--R 5040b +--R * +--R m + 8 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R 7a b m + 203a b m + 2401a b m + 14945a b m + 52528a b m +--R + +--R 6 2 6 6 +--R 103292a b m + 103824a b m + 40320a b +--R * +--R m + 7 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R 21a b m + 630a b m + 7686a b m + 49140a b m + 176589a b m +--R + +--R 2 5 2 2 5 2 5 +--R 353430a b m + 360024a b m + 141120a b +--R * +--R m + 6 +--R x +--R + +--R 3 4 7 3 4 6 3 4 5 3 4 4 3 4 3 +--R 35a b m + 1085a b m + 13685a b m + 90335a b m + 334040a b m +--R + +--R 3 4 2 3 4 3 4 +--R 684740a b m + 710640a b m + 282240a b +--R * +--R m + 5 +--R x +--R + +--R 4 3 7 4 3 6 4 3 5 4 3 4 4 3 3 +--R 35a b m + 1120a b m + 14630a b m + 100240a b m + 384755a b m +--R + +--R 4 3 2 4 3 4 3 +--R 815920a b m + 870660a b m + 352800a b +--R * +--R m + 4 +--R x +--R + +--R 5 2 7 5 2 6 5 2 5 5 2 4 5 2 3 +--R 21a b m + 693a b m + 9387a b m + 67095a b m + 270144a b m +--R + +--R 5 2 2 5 2 5 2 +--R 602532a b m + 673008a b m + 282240a b +--R * +--R m + 3 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R 7a b m + 238a b m + 3346a b m + 25060a b m + 107023a b m +--R + +--R 6 2 6 6 +--R 256942a b m + 312984a b m + 141120a b +--R * +--R m + 2 +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R a m + 35a m + 511a m + 4025a m + 18424a m + 48860a m + 69264a m +--R + +--R 7 +--R 40320a +--R * +--R m + 1 +--R x +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R b m + 28b m + 322b m + 1960b m + 6769b m + 13132b m +--R + +--R 7 7 +--R 13068b m + 5040b +--R * +--R 8 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R 7a b m + 203a b m + 2401a b m + 14945a b m + 52528a b m +--R + +--R 6 2 6 6 +--R 103292a b m + 103824a b m + 40320a b +--R * +--R 7 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R 21a b m + 630a b m + 7686a b m + 49140a b m + 176589a b m +--R + +--R 2 5 2 2 5 2 5 +--R 353430a b m + 360024a b m + 141120a b +--R * +--R 6 +--R x +--R + +--R 3 4 7 3 4 6 3 4 5 3 4 4 3 4 3 +--R 35a b m + 1085a b m + 13685a b m + 90335a b m + 334040a b m +--R + +--R 3 4 2 3 4 3 4 +--R 684740a b m + 710640a b m + 282240a b +--R * +--R 5 +--R x +--R + +--R 4 3 7 4 3 6 4 3 5 4 3 4 4 3 3 +--R 35a b m + 1120a b m + 14630a b m + 100240a b m + 384755a b m +--R + +--R 4 3 2 4 3 4 3 +--R 815920a b m + 870660a b m + 352800a b +--R * +--R 4 +--R x +--R + +--R 5 2 7 5 2 6 5 2 5 5 2 4 5 2 3 +--R 21a b m + 693a b m + 9387a b m + 67095a b m + 270144a b m +--R + +--R 5 2 2 5 2 5 2 +--R 602532a b m + 673008a b m + 282240a b +--R * +--R 3 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R 7a b m + 238a b m + 3346a b m + 25060a b m + 107023a b m +--R + +--R 6 2 6 6 +--R 256942a b m + 312984a b m + 141120a b +--R * +--R 2 +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R a m + 35a m + 511a m + 4025a m + 18424a m + 48860a m +--R + +--R 7 7 +--R 69264a m + 40320a +--R * +--R x +--R * +--R m log(x) +--R %e +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R b m + 28b m + 322b m + 1960b m + 6769b m + 13132b m +--R + +--R 7 7 +--R 13068b m + 5040b +--R * +--R 8 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R 7a b m + 203a b m + 2401a b m + 14945a b m + 52528a b m +--R + +--R 6 2 6 6 +--R 103292a b m + 103824a b m + 40320a b +--R * +--R 7 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R 21a b m + 630a b m + 7686a b m + 49140a b m + 176589a b m +--R + +--R 2 5 2 2 5 2 5 +--R 353430a b m + 360024a b m + 141120a b +--R * +--R 6 +--R x +--R + +--R 3 4 7 3 4 6 3 4 5 3 4 4 3 4 3 +--R 35a b m + 1085a b m + 13685a b m + 90335a b m + 334040a b m +--R + +--R 3 4 2 3 4 3 4 +--R 684740a b m + 710640a b m + 282240a b +--R * +--R 5 +--R x +--R + +--R 4 3 7 4 3 6 4 3 5 4 3 4 4 3 3 +--R 35a b m + 1120a b m + 14630a b m + 100240a b m + 384755a b m +--R + +--R 4 3 2 4 3 4 3 +--R 815920a b m + 870660a b m + 352800a b +--R * +--R 4 +--R x +--R + +--R 5 2 7 5 2 6 5 2 5 5 2 4 5 2 3 +--R 21a b m + 693a b m + 9387a b m + 67095a b m + 270144a b m +--R + +--R 5 2 2 5 2 5 2 +--R 602532a b m + 673008a b m + 282240a b +--R * +--R 3 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R 7a b m + 238a b m + 3346a b m + 25060a b m + 107023a b m +--R + +--R 6 2 6 6 +--R 256942a b m + 312984a b m + 141120a b +--R * +--R 2 +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R a m + 35a m + 511a m + 4025a m + 18424a m + 48860a m +--R + +--R 7 7 +--R 69264a m + 40320a +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R - b m - 28b m - 322b m - 1960b m - 6769b m - 13132b m +--R + +--R 7 7 +--R - 13068b m - 5040b +--R * +--R m + 8 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R - 7a b m - 203a b m - 2401a b m - 14945a b m - 52528a b m +--R + +--R 6 2 6 6 +--R - 103292a b m - 103824a b m - 40320a b +--R * +--R m + 7 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R - 21a b m - 630a b m - 7686a b m - 49140a b m - 176589a b m +--R + +--R 2 5 2 2 5 2 5 +--R - 353430a b m - 360024a b m - 141120a b +--R * +--R m + 6 +--R x +--R + +--R 3 4 7 3 4 6 3 4 5 3 4 4 3 4 3 +--R - 35a b m - 1085a b m - 13685a b m - 90335a b m - 334040a b m +--R + +--R 3 4 2 3 4 3 4 +--R - 684740a b m - 710640a b m - 282240a b +--R * +--R m + 5 +--R x +--R + +--R 4 3 7 4 3 6 4 3 5 4 3 4 4 3 3 +--R - 35a b m - 1120a b m - 14630a b m - 100240a b m - 384755a b m +--R + +--R 4 3 2 4 3 4 3 +--R - 815920a b m - 870660a b m - 352800a b +--R * +--R m + 4 +--R x +--R + +--R 5 2 7 5 2 6 5 2 5 5 2 4 5 2 3 +--R - 21a b m - 693a b m - 9387a b m - 67095a b m - 270144a b m +--R + +--R 5 2 2 5 2 5 2 +--R - 602532a b m - 673008a b m - 282240a b +--R * +--R m + 3 +--R x +--R + +--R 6 7 6 6 6 5 6 4 6 3 +--R - 7a b m - 238a b m - 3346a b m - 25060a b m - 107023a b m +--R + +--R 6 2 6 6 +--R - 256942a b m - 312984a b m - 141120a b +--R * +--R m + 2 +--R x +--R + +--R 7 7 7 6 7 5 7 4 7 3 7 2 +--R - a m - 35a m - 511a m - 4025a m - 18424a m - 48860a m +--R + +--R 7 7 +--R - 69264a m - 40320a +--R * +--R m + 1 +--R x +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 3330 +d0000:=normalize m0000 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 3330 +t0000:=x^7*(a+b*x)^7 +--R +--R +--R (1) +--R 7 14 6 13 2 5 12 3 4 11 4 3 10 5 2 9 6 8 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x +--R + +--R 7 7 +--R a x +--R Type: Polynomial(Integer) +--E 361 + +--S 362 of 3330 +r0000:=1/8*a^7*x^8+7/9*a^6*b*x^9+21/10*a^5*b^2*x^10+35/11*a^4*b^3*x^11+_ + 35/12*a^3*b^4*x^12+21/13*a^2*b^5*x^13+1/2*a*b^6*x^14+1/15*b^7*x^15 +--R +--R +--R (2) +--R 1 7 15 1 6 14 21 2 5 13 35 3 4 12 35 4 3 11 21 5 2 10 +--R -- b x + - a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 15 2 13 12 11 10 +--R + +--R 7 6 9 1 7 8 +--R - a b x + - a x +--R 9 8 +--R Type: Polynomial(Fraction(Integer)) +--E 362 + +--S 363 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 15 1 6 14 21 2 5 13 35 3 4 12 35 4 3 11 21 5 2 10 +--R -- b x + - a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 15 2 13 12 11 10 +--R + +--R 7 6 9 1 7 8 +--R - a b x + - a x +--R 9 8 +--R Type: Polynomial(Fraction(Integer)) +--E 363 + +--S 364 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 364 + +--S 365 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 365 + +)clear all + +--S 366 of 3330 +t0000:=x^6*(a+b*x)^7 +--R +--R +--R (1) +--R 7 13 6 12 2 5 11 3 4 10 4 3 9 5 2 8 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x +--R + +--R 7 6 +--R a x +--R Type: Polynomial(Integer) +--E 366 + +--S 367 of 3330 +r0000:=1/7*a^7*x^7+7/8*a^6*b*x^8+7/3*a^5*b^2*x^9+7/2*a^4*b^3*x^10+_ + 35/11*a^3*b^4*x^11+7/4*a^2*b^5*x^12+7/13*a*b^6*x^13+1/14*b^7*x^14 +--R +--R +--R (2) +--R 1 7 14 7 6 13 7 2 5 12 35 3 4 11 7 4 3 10 7 5 2 9 +--R -- b x + -- a b x + - a b x + -- a b x + - a b x + - a b x +--R 14 13 4 11 2 3 +--R + +--R 7 6 8 1 7 7 +--R - a b x + - a x +--R 8 7 +--R Type: Polynomial(Fraction(Integer)) +--E 367 + +--S 368 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 14 7 6 13 7 2 5 12 35 3 4 11 7 4 3 10 7 5 2 9 +--R -- b x + -- a b x + - a b x + -- a b x + - a b x + - a b x +--R 14 13 4 11 2 3 +--R + +--R 7 6 8 1 7 7 +--R - a b x + - a x +--R 8 7 +--R Type: Polynomial(Fraction(Integer)) +--E 368 + +--S 369 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 369 + +--S 370 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 370 + +)clear all + +--S 371 of 3330 +t0000:=x^5*(a+b*x)^7 +--R +--R +--R (1) +--R 7 12 6 11 2 5 10 3 4 9 4 3 8 5 2 7 6 6 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x +--R + +--R 7 5 +--R a x +--R Type: Polynomial(Integer) +--E 371 + +--S 372 of 3330 +r0000:=1/6*a^7*x^6+a^6*b*x^7+21/8*a^5*b^2*x^8+35/9*a^4*b^3*x^9+_ + 7/2*a^3*b^4*x^10+21/11*a^2*b^5*x^11+7/12*a*b^6*x^12+1/13*b^7*x^13 +--R +--R +--R (2) +--R 1 7 13 7 6 12 21 2 5 11 7 3 4 10 35 4 3 9 21 5 2 8 +--R -- b x + -- a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 13 12 11 2 9 8 +--R + +--R 6 7 1 7 6 +--R a b x + - a x +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 372 + +--S 373 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 13 7 6 12 21 2 5 11 7 3 4 10 35 4 3 9 21 5 2 8 +--R -- b x + -- a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 13 12 11 2 9 8 +--R + +--R 6 7 1 7 6 +--R a b x + - a x +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 373 + +--S 374 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 374 + +--S 375 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 375 + +)clear all + +--S 376 of 3330 +t0000:=x^4*(a+b*x)^7 +--R +--R +--R (1) +--R 7 11 6 10 2 5 9 3 4 8 4 3 7 5 2 6 6 5 7 4 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial(Integer) +--E 376 + +--S 377 of 3330 +r0000:=1/8*a^4*(a+b*x)^8/b^5-4/9*a^3*(a+b*x)^9/b^5+_ + 3/5*a^2*(a+b*x)^10/b^5-4/11*a*(a+b*x)^11/b^5+1/12*(a+b*x)^12/b^5 +--R +--R +--R (2) +--R 1 12 12 7 11 11 21 2 10 10 35 3 9 9 35 4 8 8 5 7 7 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 3a b x +--R 12 11 10 9 8 +--R + +--R 7 6 6 6 1 7 5 5 1 12 +--R - a b x + - a b x + ---- a +--R 6 5 3960 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 377 + +--S 378 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 12 7 6 11 21 2 5 10 35 3 4 9 35 4 3 8 5 2 7 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 3a b x +--R 12 11 10 9 8 +--R + +--R 7 6 6 1 7 5 +--R - a b x + - a x +--R 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 378 + +--S 379 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 12 +--R ---- a +--R 3960 +--R (4) - -------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 379 + +--S 380 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 380 + +)clear all + +--S 381 of 3330 +t0000:=x^3*(a+b*x)^7 +--R +--R +--R (1) +--R 7 10 6 9 2 5 8 3 4 7 4 3 6 5 2 5 6 4 7 3 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial(Integer) +--E 381 + +--S 382 of 3330 +r0000:=-1/8*a^3*(a+b*x)^8/b^4+1/3*a^2*(a+b*x)^9/b^4-_ + 3/10*a*(a+b*x)^10/b^4+1/11*(a+b*x)^11/b^4 +--R +--R +--R (2) +--R 1 11 11 7 10 10 7 2 9 9 35 3 8 8 4 7 7 7 5 6 6 +--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + - a b x +--R 11 10 3 8 2 +--R + +--R 7 6 5 5 1 7 4 4 1 11 +--R - a b x + - a b x - ---- a +--R 5 4 1320 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 382 + +--S 383 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 11 7 6 10 7 2 5 9 35 3 4 8 4 3 7 7 5 2 6 +--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + - a b x +--R 11 10 3 8 2 +--R + +--R 7 6 5 1 7 4 +--R - a b x + - a x +--R 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 383 + +--S 384 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 11 +--R ---- a +--R 1320 +--R (4) -------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 384 + +--S 385 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 385 + +)clear all + +--S 386 of 3330 +t0000:=x^2*(a+b*x)^7 +--R +--R +--R (1) +--R 7 9 6 8 2 5 7 3 4 6 4 3 5 5 2 4 6 3 7 2 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial(Integer) +--E 386 + +--S 387 of 3330 +r0000:=1/8*a^2*(a+b*x)^8/b^3-2/9*a*(a+b*x)^9/b^3+1/10*(a+b*x)^10/b^3 +--R +--R +--R (2) +--R 1 10 10 7 9 9 21 2 8 8 3 7 7 35 4 6 6 21 5 5 5 +--R -- b x + - a b x + -- a b x + 5a b x + -- a b x + -- a b x +--R 10 9 8 6 5 +--R + +--R 7 6 4 4 1 7 3 3 1 10 +--R - a b x + - a b x + --- a +--R 4 3 360 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 387 + +--S 388 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 10 7 6 9 21 2 5 8 3 4 7 35 4 3 6 21 5 2 5 +--R -- b x + - a b x + -- a b x + 5a b x + -- a b x + -- a b x +--R 10 9 8 6 5 +--R + +--R 7 6 4 1 7 3 +--R - a b x + - a x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 388 + +--S 389 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 10 +--R --- a +--R 360 +--R (4) - ------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 389 + +--S 390 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 390 + +)clear all + +--S 391 of 3330 +t0000:=x*(a+b*x)^7 +--R +--R +--R (1) +--R 7 8 6 7 2 5 6 3 4 5 4 3 4 5 2 3 6 2 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial(Integer) +--E 391 + +--S 392 of 3330 +r0000:=-1/8*a*(a+b*x)^8/b^2+1/9*(a+b*x)^9/b^2 +--R +--R +--R (2) +--R 1 9 9 7 8 8 2 7 7 35 3 6 6 4 5 5 21 5 4 4 7 6 3 3 +--R - b x + - a b x + 3a b x + -- a b x + 7a b x + -- a b x + - a b x +--R 9 8 6 4 3 +--R + +--R 1 7 2 2 1 9 +--R - a b x - -- a +--R 2 72 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 392 + +--S 393 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 9 7 6 8 2 5 7 35 3 4 6 4 3 5 21 5 2 4 7 6 3 +--R - b x + - a b x + 3a b x + -- a b x + 7a b x + -- a b x + - a b x +--R 9 8 6 4 3 +--R + +--R 1 7 2 +--R - a x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 393 + +--S 394 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 9 +--R -- a +--R 72 +--R (4) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 394 + +--S 395 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 395 + +)clear all + +--S 396 of 3330 +t0000:=(a+b*x)^7 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Polynomial(Integer) +--E 396 + +--S 397 of 3330 +r0000:=1/8*(a+b*x)^8/b +--R +--R +--R (2) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - b x + a b x + - a b x + 7a b x + -- a b x + 7a b x + - a b x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R a b x + - a +--R 8 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 397 + +--S 398 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 8 6 7 7 2 5 6 3 4 5 35 4 3 4 5 2 3 7 6 2 7 +--R - b x + a b x + - a b x + 7a b x + -- a b x + 7a b x + - a b x + a x +--R 8 2 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 398 + +--S 399 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 8 +--R - a +--R 8 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 399 + +--S 400 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 400 + +)clear all + +--S 401 of 3330 +t0000:=(a+b*x)^7/x +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 3330 +r0000:=7*a^6*b*x+21/2*a^5*b^2*x^2+35/3*a^4*b^3*x^3+35/4*a^3*b^4*x^4+_ + 21/5*a^2*b^5*x^5+7/6*a*b^6*x^6+1/7*b^7*x^7+a^7*log(x) +--R +--R +--R (2) +--R 7 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420a log(x) + 60b x + 490a b x + 1764a b x + 3675a b x + 4900a b x +--R + +--R 5 2 2 6 +--R 4410a b x + 2940a b x +--R / +--R 420 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420a log(x) + 60b x + 490a b x + 1764a b x + 3675a b x + 4900a b x +--R + +--R 5 2 2 6 +--R 4410a b x + 2940a b x +--R / +--R 420 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 3330 +t0000:=(a+b*x)^7/x^2 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 3330 +r0000:=-a^7/x+21*a^5*b^2*x+35/2*a^4*b^3*x^2+35/3*a^3*b^4*x^3+_ + 21/4*a^2*b^5*x^4+7/5*a*b^6*x^5+1/6*b^7*x^6+7*a^6*b*log(x) +--R +--R +--R (2) +--R 6 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420a b x log(x) + 10b x + 84a b x + 315a b x + 700a b x + 1050a b x +--R + +--R 5 2 2 7 +--R 1260a b x - 60a +--R / +--R 60x +--R Type: Expression(Integer) +--E 407 + +--S 408 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420a b x log(x) + 10b x + 84a b x + 315a b x + 700a b x + 1050a b x +--R + +--R 5 2 2 7 +--R 1260a b x - 60a +--R / +--R 60x +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 3330 +t0000:=(a+b*x)^7/x^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 3330 +r0000:=-1/2*a^7/x^2-7*a^6*b/x+35*a^4*b^3*x+35/2*a^3*b^4*x^2+7*a^2*b^5*x^3+_ + 7/4*a*b^6*x^4+1/5*b^7*x^5+21*a^5*b^2*log(x) +--R +--R +--R (2) +--R 5 2 2 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420a b x log(x) + 4b x + 35a b x + 140a b x + 350a b x + 700a b x +--R + +--R 6 7 +--R - 140a b x - 10a +--R / +--R 2 +--R 20x +--R Type: Expression(Integer) +--E 412 + +--S 413 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 2 2 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420a b x log(x) + 4b x + 35a b x + 140a b x + 350a b x + 700a b x +--R + +--R 6 7 +--R - 140a b x - 10a +--R / +--R 2 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 3330 +t0000:=(a+b*x)^7/x^4 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 3330 +r0000:=-1/3*a^7/x^3-7/2*a^6*b/x^2-21*a^5*b^2/x+35*a^3*b^4*x+21/2*a^2*b^5*x^2+_ + 7/3*a*b^6*x^3+1/4*b^7*x^4+35*a^4*b^3*log(x) +--R +--R +--R (2) +--R 4 3 3 7 7 6 6 2 5 5 3 4 4 5 2 2 +--R 420a b x log(x) + 3b x + 28a b x + 126a b x + 420a b x - 252a b x +--R + +--R 6 7 +--R - 42a b x - 4a +--R / +--R 3 +--R 12x +--R Type: Expression(Integer) +--E 417 + +--S 418 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 3 7 7 6 6 2 5 5 3 4 4 5 2 2 +--R 420a b x log(x) + 3b x + 28a b x + 126a b x + 420a b x - 252a b x +--R + +--R 6 7 +--R - 42a b x - 4a +--R / +--R 3 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 3330 +t0000:=(a+b*x)^7/x^5 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 3330 +r0000:=-1/4*a^7/x^4-7/3*a^6*b/x^3-21/2*a^5*b^2/x^2-35*a^4*b^3/x+_ + 21*a^2*b^5*x+7/2*a*b^6*x^2+1/3*b^7*x^3+35*a^3*b^4*log(x) +--R +--R +--R (2) +--R 3 4 4 7 7 6 6 2 5 5 4 3 3 5 2 2 +--R 420a b x log(x) + 4b x + 42a b x + 252a b x - 420a b x - 126a b x +--R + +--R 6 7 +--R - 28a b x - 3a +--R / +--R 4 +--R 12x +--R Type: Expression(Integer) +--E 422 + +--S 423 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 4 4 7 7 6 6 2 5 5 4 3 3 5 2 2 +--R 420a b x log(x) + 4b x + 42a b x + 252a b x - 420a b x - 126a b x +--R + +--R 6 7 +--R - 28a b x - 3a +--R / +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 3330 +t0000:=(a+b*x)^7/x^6 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 3330 +r0000:=-1/5*a^7/x^5-7/4*a^6*b/x^4-7*a^5*b^2/x^3-35/2*a^4*b^3/x^2-_ + 35*a^3*b^4/x+7*a*b^6*x+1/2*b^7*x^2+21*a^2*b^5*log(x) +--R +--R +--R (2) +--R 2 5 5 7 7 6 6 3 4 4 4 3 3 5 2 2 +--R 420a b x log(x) + 10b x + 140a b x - 700a b x - 350a b x - 140a b x +--R + +--R 6 7 +--R - 35a b x - 4a +--R / +--R 5 +--R 20x +--R Type: Expression(Integer) +--E 427 + +--S 428 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 5 5 7 7 6 6 3 4 4 4 3 3 5 2 2 +--R 420a b x log(x) + 10b x + 140a b x - 700a b x - 350a b x - 140a b x +--R + +--R 6 7 +--R - 35a b x - 4a +--R / +--R 5 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 3330 +t0000:=(a+b*x)^7/x^7 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 431 + +--S 432 of 3330 +r0000:=-1/6*a^7/x^6-7/5*a^6*b/x^5-21/4*a^5*b^2/x^4-35/3*a^4*b^3/x^3-_ + 35/2*a^3*b^4/x^2-21*a^2*b^5/x+b^7*x+7*a*b^6*log(x) +--R +--R +--R (2) +--R 6 6 7 7 2 5 5 3 4 4 4 3 3 +--R 420a b x log(x) + 60b x - 1260a b x - 1050a b x - 700a b x +--R + +--R 5 2 2 6 7 +--R - 315a b x - 84a b x - 10a +--R / +--R 6 +--R 60x +--R Type: Expression(Integer) +--E 432 + +--S 433 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 7 7 2 5 5 3 4 4 4 3 3 +--R 420a b x log(x) + 60b x - 1260a b x - 1050a b x - 700a b x +--R + +--R 5 2 2 6 7 +--R - 315a b x - 84a b x - 10a +--R / +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 3330 +t0000:=(a+b*x)^7/x^8 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 3330 +r0000:=-1/7*a^7/x^7-7/6*a^6*b/x^6-21/5*a^5*b^2/x^5-35/4*a^4*b^3/x^4-_ + 35/3*a^3*b^4/x^3-21/2*a^2*b^5/x^2-7*a*b^6/x+b^7*log(x) +--R +--R +--R (2) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420b x log(x) - 2940a b x - 4410a b x - 4900a b x - 3675a b x +--R + +--R 5 2 2 6 7 +--R - 1764a b x - 490a b x - 60a +--R / +--R 7 +--R 420x +--R Type: Expression(Integer) +--E 437 + +--S 438 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420b x log(x) - 2940a b x - 4410a b x - 4900a b x - 3675a b x +--R + +--R 5 2 2 6 7 +--R - 1764a b x - 490a b x - 60a +--R / +--R 7 +--R 420x +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 3330 +t0000:=(a+b*x)^7/x^9 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 3330 +r0000:=-1/8*(a+b*x)^8/(a*x^8) +--R +--R +--R (2) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - - b x - a b x - - a b x - 7a b x - -- a b x - 7a b x - - a b x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R - a b x - - a +--R 8 +--R / +--R 8 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 442 + +--S 443 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - 8b x - 28a b x - 56a b x - 70a b x - 56a b x - 28a b x - 8a b x - a +--R ---------------------------------------------------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 8 +--R b +--R (4) -- +--R 8a +--R Type: Expression(Integer) +--E 444 + +--S 445 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 3330 +t0000:=(a+b*x)^7/x^10 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 3330 +r0000:=-1/9*(a+b*x)^8/(a*x^9)+1/72*b*(a+b*x)^8/(a^2*x^8) +--R +--R +--R (2) +--R 1 9 9 1 2 7 7 7 3 6 6 21 4 5 5 5 4 4 35 6 3 3 7 2 2 +--R -- b x - - a b x - - a b x - -- a b x - 7a b x - -- a b x - 3a b x +--R 72 2 3 4 6 +--R + +--R 7 8 1 9 +--R - - a b x - - a +--R 8 9 +--R / +--R 2 9 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 447 + +--S 448 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 36b x - 168a b x - 378a b x - 504a b x - 420a b x - 216a b x +--R + +--R 6 7 +--R - 63a b x - 8a +--R / +--R 9 +--R 72x +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 9 +--R b +--R (4) - ---- +--R 2 +--R 72a +--R Type: Expression(Integer) +--E 449 + +--S 450 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 3330 +t0000:=(a+b*x)^7/x^11 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 3330 +r0000:=-1/10*(a+b*x)^8/(a*x^10)+1/45*b*(a+b*x)^8/(a^2*x^9)-_ + 1/360*b^2*(a+b*x)^8/(a^3*x^8) +--R +--R +--R (2) +--R 1 10 10 1 3 7 7 7 4 6 6 21 5 5 5 35 6 4 4 7 3 3 +--R - --- b x - - a b x - - a b x - -- a b x - -- a b x - 5a b x +--R 360 3 4 5 6 +--R + +--R 21 8 2 2 7 9 1 10 +--R - -- a b x - - a b x - -- a +--R 8 9 10 +--R / +--R 3 10 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 452 + +--S 453 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 120b x - 630a b x - 1512a b x - 2100a b x - 1800a b x - 945a b x +--R + +--R 6 7 +--R - 280a b x - 36a +--R / +--R 10 +--R 360x +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 10 +--R b +--R (4) ----- +--R 3 +--R 360a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 3330 +t0000:=(a+b*x)^7/x^12 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 3330 +r0000:=-1/11*(a+b*x)^8/(a*x^11)+3/110*b*(a+b*x)^8/(a^2*x^10)-_ + 1/165*b^2*(a+b*x)^8/(a^3*x^9)+1/1320*b^3*(a+b*x)^8/(a^4*x^8) +--R +--R +--R (2) +--R 1 11 11 1 4 7 7 7 5 6 6 7 6 5 5 7 4 4 35 8 3 3 +--R ---- b x - - a b x - - a b x - - a b x - 5a b x - -- a b x +--R 1320 4 5 2 8 +--R + +--R 7 9 2 2 7 10 1 11 +--R - - a b x - -- a b x - -- a +--R 3 10 11 +--R / +--R 4 11 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 457 + +--S 458 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 330b x - 1848a b x - 4620a b x - 6600a b x - 5775a b x +--R + +--R 5 2 2 6 7 +--R - 3080a b x - 924a b x - 120a +--R / +--R 11 +--R 1320x +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 11 +--R b +--R (4) - ------ +--R 4 +--R 1320a +--R Type: Expression(Integer) +--E 459 + +--S 460 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 3330 +t0000:=(a+b*x)^7/x^13 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 3330 +r0000:=-1/12*a^7/x^12-7/11*a^6*b/x^11-21/10*a^5*b^2/x^10-35/9*a^4*b^3/x^9-_ + 35/8*a^3*b^4/x^8-3*a^2*b^5/x^7-7/6*a*b^6/x^6-1/5*b^7/x^5 +--R +--R +--R (2) +--R 1 7 7 7 6 6 2 5 5 35 3 4 4 35 4 3 3 21 5 2 2 +--R - - b x - - a b x - 3a b x - -- a b x - -- a b x - -- a b x +--R 5 6 8 9 10 +--R + +--R 7 6 1 7 +--R - -- a b x - -- a +--R 11 12 +--R / +--R 12 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 462 + +--S 463 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 792b x - 4620a b x - 11880a b x - 17325a b x - 15400a b x +--R + +--R 5 2 2 6 7 +--R - 8316a b x - 2520a b x - 330a +--R / +--R 12 +--R 3960x +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 3330 +t0000:=(a+b*x)^7/x^14 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 14 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 3330 +r0000:=-1/13*a^7/x^13-7/12*a^6*b/x^12-21/11*a^5*b^2/x^11-7/2*a^4*b^3/x^10-_ + 35/9*a^3*b^4/x^9-21/8*a^2*b^5/x^8-a*b^6/x^7-1/6*b^7/x^6 +--R +--R +--R (2) +--R 1 7 7 6 6 21 2 5 5 35 3 4 4 7 4 3 3 21 5 2 2 +--R - - b x - a b x - -- a b x - -- a b x - - a b x - -- a b x +--R 6 8 9 2 11 +--R + +--R 7 6 1 7 +--R - -- a b x - -- a +--R 12 13 +--R / +--R 13 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 467 + +--S 468 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 1716b x - 10296a b x - 27027a b x - 40040a b x - 36036a b x +--R + +--R 5 2 2 6 7 +--R - 19656a b x - 6006a b x - 792a +--R / +--R 13 +--R 10296x +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 3330 +t0000:=(a+b*x)^7/x^15 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 15 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 3330 +r0000:=-1/14*a^7/x^14-7/13*a^6*b/x^13-7/4*a^5*b^2/x^12-35/11*a^4*b^3/x^11-_ + 7/2*a^3*b^4/x^10-7/3*a^2*b^5/x^9-7/8*a*b^6/x^8-1/7*b^7/x^7 +--R +--R +--R (2) +--R 1 7 7 7 6 6 7 2 5 5 7 3 4 4 35 4 3 3 7 5 2 2 +--R - - b x - - a b x - - a b x - - a b x - -- a b x - - a b x +--R 7 8 3 2 11 4 +--R + +--R 7 6 1 7 +--R - -- a b x - -- a +--R 13 14 +--R / +--R 14 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 472 + +--S 473 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 3432b x - 21021a b x - 56056a b x - 84084a b x - 76440a b x +--R + +--R 5 2 2 6 7 +--R - 42042a b x - 12936a b x - 1716a +--R / +--R 14 +--R 24024x +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 3330 +t0000:=(a+b*x)^7/x^16 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 3330 +r0000:=-1/15*a^7/x^15-1/2*a^6*b/x^14-21/13*a^5*b^2/x^13-35/12*a^4*b^3/x^12-_ + 35/11*a^3*b^4/x^11-21/10*a^2*b^5/x^10-7/9*a*b^6/x^9-1/8*b^7/x^8 +--R +--R +--R (2) +--R 1 7 7 7 6 6 21 2 5 5 35 3 4 4 35 4 3 3 21 5 2 2 +--R - - b x - - a b x - -- a b x - -- a b x - -- a b x - -- a b x +--R 8 9 10 11 12 13 +--R + +--R 1 6 1 7 +--R - - a b x - -- a +--R 2 15 +--R / +--R 15 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 477 + +--S 478 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 6435b x - 40040a b x - 108108a b x - 163800a b x - 150150a b x +--R + +--R 5 2 2 6 7 +--R - 83160a b x - 25740a b x - 3432a +--R / +--R 15 +--R 51480x +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 3330 +t0000:=x^m*(a+b*x)^10 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 481 + +--S 482 of 3330 +r0000:=a^10*x^(1+m)/(1+m)+10*a^9*b*x^(2+m)/(2+m)+45*a^8*b^2*x^(3+m)/(3+m)+_ + 120*a^7*b^3*x^(4+m)/(4+m)+210*a^6*b^4*x^(5+m)/(5+m)+_ + 252*a^5*b^5*x^(6+m)/(6+m)+210*a^4*b^6*x^(7+m)/(7+m)+_ + 120*a^3*b^7*x^(8+m)/(8+m)+45*a^2*b^8*x^(9+m)/(9+m)+_ + 10*a*b^9*x^(10+m)/(10+m)+b^10*x^(11+m)/(11+m) +--R +--R +--R (2) +--R 10 10 10 9 10 8 10 7 10 6 10 5 +--R b m + 55b m + 1320b m + 18150b m + 157773b m + 902055b m +--R + +--R 10 4 10 3 10 2 10 10 +--R 3416930b m + 8409500b m + 12753576b m + 10628640b m + 3628800b +--R * +--R m + 11 +--R x +--R + +--R 9 10 9 9 9 8 9 7 9 6 +--R 10a b m + 560a b m + 13650a b m + 190200a b m + 1672230a b m +--R + +--R 9 5 9 4 9 3 9 2 +--R 9653280a b m + 36862550a b m + 91331800a b m + 139262760a b m +--R + +--R 9 9 +--R 116552160a b m + 39916800a b +--R * +--R m + 10 +--R x +--R + +--R 2 8 10 2 8 9 2 8 8 2 8 7 2 8 6 +--R 45a b m + 2565a b m + 63540a b m + 898290a b m + 7999425a b m +--R + +--R 2 8 5 2 8 4 2 8 3 2 8 2 +--R 46695285a b m + 180021510a b m + 449614260a 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2637558m + 13339535m +--R + +--R 4 3 2 +--R 45995730m + 105258076m + 150917976m + 120543840m + 39916800 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 10 10 10 9 10 8 10 7 10 6 +--R b m + 55b m + 1320b m + 18150b m + 157773b m +--R + +--R 10 5 10 4 10 3 10 2 +--R 902055b m + 3416930b m + 8409500b m + 12753576b m +--R + +--R 10 10 +--R 10628640b m + 3628800b +--R * +--R 11 +--R x +--R + +--R 9 10 9 9 9 8 9 7 +--R 10a b m + 560a b m + 13650a b m + 190200a b m +--R + +--R 9 6 9 5 9 4 9 3 +--R 1672230a b m + 9653280a b m + 36862550a b m + 91331800a b m +--R + +--R 9 2 9 9 +--R 139262760a b m + 116552160a b m + 39916800a b +--R * +--R 10 +--R x +--R + +--R 2 8 10 2 8 9 2 8 8 2 8 7 +--R 45a b m + 2565a b m + 63540a b m + 898290a b m +--R + +--R 2 8 6 2 8 5 2 8 4 +--R 7999425a b m + 46695285a b m + 180021510a b m +--R + +--R 2 8 3 2 8 2 2 8 2 8 +--R 449614260a b m + 690085080a b m + 580543200a b m + 199584000a b +--R * +--R 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9 6 9 5 9 4 9 3 +--R 2992710a b m + 20390160a b m + 92615030a b m + 274727240a b m +--R + +--R 9 2 9 9 +--R 503126280a b m + 502927200a b m + 199584000a b +--R * +--R 2 +--R x +--R + +--R 10 10 10 9 10 8 10 7 10 6 +--R a m + 65a m + 1860a m + 30810a m + 326613a m +--R + +--R 10 5 10 4 10 3 10 2 +--R 2310945a m + 11028590a m + 34967140a m + 70290936a m +--R + +--R 10 10 +--R 80627040a m + 39916800a +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 10 10 10 9 10 8 10 7 10 6 +--R - b m - 55b m - 1320b m - 18150b m - 157773b m +--R + +--R 10 5 10 4 10 3 10 2 +--R - 902055b m - 3416930b m - 8409500b m - 12753576b m +--R + +--R 10 10 +--R - 10628640b m - 3628800b +--R * +--R m + 11 +--R x +--R + +--R 9 10 9 9 9 8 9 7 9 6 +--R - 10a b m - 560a b m - 13650a b m - 190200a b m - 1672230a b m +--R + +--R 9 5 9 4 9 3 9 2 +--R - 9653280a b m - 36862550a b m - 91331800a b m - 139262760a b m +--R + +--R 9 9 +--R - 116552160a b m - 39916800a b +--R * +--R m + 10 +--R x +--R + +--R 2 8 10 2 8 9 2 8 8 2 8 7 2 8 6 +--R - 45a b m - 2565a b m - 63540a b m - 898290a b m - 7999425a b m +--R + +--R 2 8 5 2 8 4 2 8 3 +--R - 46695285a b m - 180021510a b m - 449614260a b m +--R + +--R 2 8 2 2 8 2 8 +--R - 690085080a b m - 580543200a b m - 199584000a b +--R * +--R m + 9 +--R x +--R + +--R 3 7 10 3 7 9 3 7 8 3 7 7 +--R - 120a b m - 6960a b m - 175320a b m - 2517840a b m +--R + +--R 3 7 6 3 7 5 3 7 4 +--R - 22748040a b m - 134522640a b m - 524563080a b m +--R + +--R 3 7 3 3 7 2 3 7 3 7 +--R - 1322982960a b m - 2047105440a b m - 1733313600a b m - 598752000a b +--R * +--R m + 8 +--R x +--R + +--R 4 6 10 4 6 9 4 6 8 4 6 7 +--R - 210a b m - 12390a b m - 317520a b m - 4638060a b m +--R + +--R 4 6 6 4 6 5 4 6 4 +--R - 42592410a b m - 255740310a b m - 1011120180a b m +--R + +--R 4 6 3 4 6 2 4 6 +--R - 2581262040a b m - 4035361680a b m - 3445243200a b m +--R + +--R 4 6 +--R - 1197504000a b +--R * +--R m + 7 +--R x +--R + +--R 5 5 10 5 5 9 5 5 8 5 5 7 +--R - 252a b m - 15120a b m - 394380a b m - 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+--R + +--R 8 2 6 8 2 5 8 2 4 +--R - 12376665a b m - 81560115a b m - 355598730a b m +--R + +--R 8 2 3 8 2 2 8 2 8 2 +--R - 1003011660a b m - 1727578440a b m - 1608573600a b m - 598752000a b +--R * +--R m + 3 +--R x +--R + +--R 9 10 9 9 9 8 9 7 9 6 +--R - 10a b m - 640a b m - 17970a b m - 290760a b m - 2992710a b m +--R + +--R 9 5 9 4 9 3 9 2 +--R - 20390160a b m - 92615030a b m - 274727240a b m - 503126280a b m +--R + +--R 9 9 +--R - 502927200a b m - 199584000a b +--R * +--R m + 2 +--R x +--R + +--R 10 10 10 9 10 8 10 7 10 6 +--R - a m - 65a m - 1860a m - 30810a m - 326613a m +--R + +--R 10 5 10 4 10 3 10 2 +--R - 2310945a m - 11028590a m - 34967140a m - 70290936a m +--R + +--R 10 10 +--R - 80627040a m - 39916800a +--R * +--R m + 1 +--R x +--R / +--R 11 10 9 8 7 6 5 +--R m + 66m + 1925m + 32670m + 357423m + 2637558m + 13339535m +--R + +--R 4 3 2 +--R 45995730m + 105258076m + 150917976m + 120543840m + 39916800 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 3330 +d0000:=normalize m0000 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 3330 +t0000:=x^9*(a+b*x)^10 +--R +--R +--R (1) +--R 10 19 9 18 2 8 17 3 7 16 4 6 15 5 5 14 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 13 7 3 12 8 2 11 9 10 10 9 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 486 + +--S 487 of 3330 +r0000:=1/10*a^10*x^10+10/11*a^9*b*x^11+15/4*a^8*b^2*x^12+_ + 120/13*a^7*b^3*x^13+15*a^6*b^4*x^14+84/5*a^5*b^5*x^15+_ + 105/8*a^4*b^6*x^16+120/17*a^3*b^7*x^17+5/2*a^2*b^8*x^18+_ + 10/19*a*b^9*x^19+1/20*b^10*x^20 +--R +--R +--R (2) +--R 1 10 20 10 9 19 5 2 8 18 120 3 7 17 105 4 6 16 84 5 5 15 +--R -- b x + -- a b x + - a b x + --- a b x + --- a b x + -- a b x +--R 20 19 2 17 8 5 +--R + +--R 6 4 14 120 7 3 13 15 8 2 12 10 9 11 1 10 10 +--R 15a b x + --- a b x + -- a b x + -- a b x + -- a x +--R 13 4 11 10 +--R Type: Polynomial(Fraction(Integer)) +--E 487 + +--S 488 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 20 10 9 19 5 2 8 18 120 3 7 17 105 4 6 16 84 5 5 15 +--R -- b x + -- a b x + - a b x + --- a b x + --- a b x + -- a b x +--R 20 19 2 17 8 5 +--R + +--R 6 4 14 120 7 3 13 15 8 2 12 10 9 11 1 10 10 +--R 15a b x + --- a b x + -- a b x + -- a b x + -- a x +--R 13 4 11 10 +--R Type: Polynomial(Fraction(Integer)) +--E 488 + +--S 489 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 489 + +--S 490 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 490 + +)clear all + +--S 491 of 3330 +t0000:=x^8*(a+b*x)^10 +--R +--R +--R (1) +--R 10 18 9 17 2 8 16 3 7 15 4 6 14 5 5 13 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 12 7 3 11 8 2 10 9 9 10 8 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 491 + +--S 492 of 3330 +r0000:=1/9*a^10*x^9+a^9*b*x^10+45/11*a^8*b^2*x^11+10*a^7*b^3*x^12+_ + 210/13*a^6*b^4*x^13+18*a^5*b^5*x^14+14*a^4*b^6*x^15+_ + 15/2*a^3*b^7*x^16+45/17*a^2*b^8*x^17+5/9*a*b^9*x^18+1/19*b^10*x^19 +--R +--R +--R (2) +--R 1 10 19 5 9 18 45 2 8 17 15 3 7 16 4 6 15 5 5 14 +--R -- b x + - a b x + -- a b x + -- a b x + 14a b x + 18a b x +--R 19 9 17 2 +--R + +--R 210 6 4 13 7 3 12 45 8 2 11 9 10 1 10 9 +--R --- a b x + 10a b x + -- a b x + a b x + - a x +--R 13 11 9 +--R Type: Polynomial(Fraction(Integer)) +--E 492 + +--S 493 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 19 5 9 18 45 2 8 17 15 3 7 16 4 6 15 5 5 14 +--R -- b x + - a b x + -- a b x + -- a b x + 14a b x + 18a b x +--R 19 9 17 2 +--R + +--R 210 6 4 13 7 3 12 45 8 2 11 9 10 1 10 9 +--R --- a b x + 10a b x + -- a b x + a b x + - a x +--R 13 11 9 +--R Type: Polynomial(Fraction(Integer)) +--E 493 + +--S 494 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 494 + +--S 495 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 495 + +)clear all + +--S 496 of 3330 +t0000:=x^7*(a+b*x)^10 +--R +--R +--R (1) +--R 10 17 9 16 2 8 15 3 7 14 4 6 13 5 5 12 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 11 7 3 10 8 2 9 9 8 10 7 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 496 + +--S 497 of 3330 +r0000:=1/8*a^10*x^8+10/9*a^9*b*x^9+9/2*a^8*b^2*x^10+120/11*a^7*b^3*x^11+_ + 35/2*a^6*b^4*x^12+252/13*a^5*b^5*x^13+15*a^4*b^6*x^14+_ + 8*a^3*b^7*x^15+45/16*a^2*b^8*x^16+10/17*a*b^9*x^17+1/18*b^10*x^18 +--R +--R +--R (2) +--R 1 10 18 10 9 17 45 2 8 16 3 7 15 4 6 14 252 5 5 13 +--R -- b x + -- a b x + -- a b x + 8a b x + 15a b x + --- a b x +--R 18 17 16 13 +--R + +--R 35 6 4 12 120 7 3 11 9 8 2 10 10 9 9 1 10 8 +--R -- a b x + --- a b x + - a b x + -- a b x + - a x +--R 2 11 2 9 8 +--R Type: Polynomial(Fraction(Integer)) +--E 497 + +--S 498 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 18 10 9 17 45 2 8 16 3 7 15 4 6 14 252 5 5 13 +--R -- b x + -- a b x + -- a b x + 8a b x + 15a b x + --- a b x +--R 18 17 16 13 +--R + +--R 35 6 4 12 120 7 3 11 9 8 2 10 10 9 9 1 10 8 +--R -- a b x + --- a b x + - a b x + -- a b x + - a x +--R 2 11 2 9 8 +--R Type: Polynomial(Fraction(Integer)) +--E 498 + +--S 499 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 499 + +--S 500 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 500 + +)clear all + +--S 501 of 3330 +t0000:=x^6*(a+b*x)^10 +--R +--R +--R (1) +--R 10 16 9 15 2 8 14 3 7 13 4 6 12 5 5 11 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 10 7 3 9 8 2 8 9 7 10 6 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 501 + +--S 502 of 3330 +r0000:=1/11*a^6*(a+b*x)^11/b^7-1/2*a^5*(a+b*x)^12/b^7+_ + 15/13*a^4*(a+b*x)^13/b^7-10/7*a^3*(a+b*x)^14/b^7+a^2*(a+b*x)^15/b^7-_ + 3/8*a*(a+b*x)^16/b^7+1/17*(a+b*x)^17/b^7 +--R +--R +--R (2) +--R 1 17 17 5 16 16 2 15 15 60 3 14 14 210 4 13 13 +--R -- b x + - a b x + 3a b x + -- a b x + --- a b x +--R 17 8 7 13 +--R + +--R 5 12 12 210 6 11 11 7 10 10 8 9 9 5 9 8 8 1 10 7 7 +--R 21a b x + --- a b x + 12a b x + 5a b x + - a b x + - a b x +--R 11 4 7 +--R + +--R 1 17 +--R ------ a +--R 136136 +--R / +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 502 + +--S 503 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 17 5 9 16 2 8 15 60 3 7 14 210 4 6 13 5 5 12 +--R -- b x + - a b x + 3a b x + -- a b x + --- a b x + 21a b x +--R 17 8 7 13 +--R + +--R 210 6 4 11 7 3 10 8 2 9 5 9 8 1 10 7 +--R --- a b x + 12a b x + 5a b x + - a b x + - a x +--R 11 4 7 +--R Type: Polynomial(Fraction(Integer)) +--E 503 + +--S 504 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 17 +--R ------ a +--R 136136 +--R (4) - ---------- +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 504 + +--S 505 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 505 + +)clear all + +--S 506 of 3330 +t0000:=x^5*(a+b*x)^10 +--R +--R +--R (1) +--R 10 15 9 14 2 8 13 3 7 12 4 6 11 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 9 7 3 8 8 2 7 9 6 10 5 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 506 + +--S 507 of 3330 +r0000:=-1/11*a^5*(a+b*x)^11/b^6+5/12*a^4*(a+b*x)^12/b^6-_ + 10/13*a^3*(a+b*x)^13/b^6+5/7*a^2*(a+b*x)^14/b^6-1/3*a*(a+b*x)^15/b^6+_ + 1/16*(a+b*x)^16/b^6 +--R +--R +--R (2) +--R 1 16 16 2 15 15 45 2 14 14 120 3 13 13 35 4 12 12 +--R -- b x + - a b x + -- a b x + --- a b x + -- a b x +--R 16 3 14 13 2 +--R + +--R 252 5 11 11 6 10 10 40 7 9 9 45 8 8 8 10 9 7 7 1 10 6 6 +--R --- a b x + 21a b x + -- a b x + -- a b x + -- a b x + - a b x +--R 11 3 8 7 6 +--R + +--R 1 16 +--R - ----- a +--R 48048 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 507 + +--S 508 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 16 2 9 15 45 2 8 14 120 3 7 13 35 4 6 12 252 5 5 11 +--R -- b x + - a b x + -- a b x + --- a b x + -- a b x + --- a b x +--R 16 3 14 13 2 11 +--R + +--R 6 4 10 40 7 3 9 45 8 2 8 10 9 7 1 10 6 +--R 21a b x + -- a b x + -- a b x + -- a b x + - a x +--R 3 8 7 6 +--R Type: Polynomial(Fraction(Integer)) +--E 508 + +--S 509 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 16 +--R ----- a +--R 48048 +--R (4) --------- +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 509 + +--S 510 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 510 + +)clear all + +--S 511 of 3330 +t0000:=x^4*(a+b*x)^10 +--R +--R +--R (1) +--R 10 14 9 13 2 8 12 3 7 11 4 6 10 5 5 9 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 7 8 2 6 9 5 10 4 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 511 + +--S 512 of 3330 +r0000:=1/11*a^4*(a+b*x)^11/b^5-1/3*a^3*(a+b*x)^12/b^5+_ + 6/13*a^2*(a+b*x)^13/b^5-2/7*a*(a+b*x)^14/b^5+1/15*(a+b*x)^15/b^5 +--R +--R +--R (2) +--R 1 15 15 5 14 14 45 2 13 13 3 12 12 210 4 11 11 +--R -- b x + - a b x + -- a b x + 10a b x + --- a b x +--R 15 7 13 11 +--R + +--R 126 5 10 10 70 6 9 9 7 8 8 45 8 7 7 5 9 6 6 1 10 5 5 +--R --- a b x + -- a b x + 15a b x + -- a b x + - a b x + - a b x +--R 5 3 7 3 5 +--R + +--R 1 15 +--R ----- a +--R 15015 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 512 + +--S 513 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 15 5 9 14 45 2 8 13 3 7 12 210 4 6 11 126 5 5 10 +--R -- b x + - a b x + -- a b x + 10a b x + --- a b x + --- a b x +--R 15 7 13 11 5 +--R + +--R 70 6 4 9 7 3 8 45 8 2 7 5 9 6 1 10 5 +--R -- a b x + 15a b x + -- a b x + - a b x + - a x +--R 3 7 3 5 +--R Type: Polynomial(Fraction(Integer)) +--E 513 + +--S 514 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 15 +--R ----- a +--R 15015 +--R (4) - --------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 514 + +--S 515 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 515 + +)clear all + +--S 516 of 3330 +t0000:=x^3*(a+b*x)^10 +--R +--R +--R (1) +--R 10 13 9 12 2 8 11 3 7 10 4 6 9 5 5 8 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 7 7 3 6 8 2 5 9 4 10 3 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 516 + +--S 517 of 3330 +r0000:=-1/11*a^3*(a+b*x)^11/b^4+1/4*a^2*(a+b*x)^12/b^4-_ + 3/13*a*(a+b*x)^13/b^4+1/14*(a+b*x)^14/b^4 +--R +--R +--R (2) +--R 1 14 14 10 13 13 15 2 12 12 120 3 11 11 4 10 10 +--R -- b x + -- a b x + -- a b x + --- a b x + 21a b x +--R 14 13 4 11 +--R + +--R 5 9 9 105 6 8 8 120 7 7 7 15 8 6 6 9 5 5 1 10 4 4 +--R 28a b x + --- a b x + --- a b x + -- a b x + 2a b x + - a b x +--R 4 7 2 4 +--R + +--R 1 14 +--R - ---- a +--R 4004 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 517 + +--S 518 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 14 10 9 13 15 2 8 12 120 3 7 11 4 6 10 5 5 9 +--R -- b x + -- a b x + -- a b x + --- a b x + 21a b x + 28a b x +--R 14 13 4 11 +--R + +--R 105 6 4 8 120 7 3 7 15 8 2 6 9 5 1 10 4 +--R --- a b x + --- a b x + -- a b x + 2a b x + - a x +--R 4 7 2 4 +--R Type: Polynomial(Fraction(Integer)) +--E 518 + +--S 519 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 14 +--R ---- a +--R 4004 +--R (4) -------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 519 + +--S 520 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 520 + +)clear all + +--S 521 of 3330 +t0000:=x^2*(a+b*x)^10 +--R +--R +--R (1) +--R 10 12 9 11 2 8 10 3 7 9 4 6 8 5 5 7 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 6 7 3 5 8 2 4 9 3 10 2 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 521 + +--S 522 of 3330 +r0000:=1/11*a^2*(a+b*x)^11/b^3-1/6*a*(a+b*x)^12/b^3+1/13*(a+b*x)^13/b^3 +--R +--R +--R (2) +--R 1 13 13 5 12 12 45 2 11 11 3 10 10 70 4 9 9 63 5 8 8 +--R -- b x + - a b x + -- a b x + 12a b x + -- a b x + -- a b x +--R 13 6 11 3 2 +--R + +--R 6 7 7 7 6 6 8 5 5 5 9 4 4 1 10 3 3 1 13 +--R 30a b x + 20a b x + 9a b x + - a b x + - a b x + --- a +--R 2 3 858 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 522 + +--S 523 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 13 5 9 12 45 2 8 11 3 7 10 70 4 6 9 63 5 5 8 +--R -- b x + - a b x + -- a b x + 12a b x + -- a b x + -- a b x +--R 13 6 11 3 2 +--R + +--R 6 4 7 7 3 6 8 2 5 5 9 4 1 10 3 +--R 30a b x + 20a b x + 9a b x + - a b x + - a x +--R 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 523 + +--S 524 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 13 +--R --- a +--R 858 +--R (4) - ------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 524 + +--S 525 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 525 + +)clear all + +--S 526 of 3330 +t0000:=x*(a+b*x)^10 +--R +--R +--R (1) +--R 10 11 9 10 2 8 9 3 7 8 4 6 7 5 5 6 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 5 7 3 4 8 2 3 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Polynomial(Integer) +--E 526 + +--S 527 of 3330 +r0000:=-1/11*a*(a+b*x)^11/b^2+1/12*(a+b*x)^12/b^2 +--R +--R +--R (2) +--R 1 12 12 10 11 11 9 2 10 10 40 3 9 9 105 4 8 8 5 7 7 +--R -- b x + -- a b x + - a b x + -- a b x + --- a b x + 36a b x +--R 12 11 2 3 4 +--R + +--R 6 6 6 7 5 5 45 8 4 4 10 9 3 3 1 10 2 2 1 12 +--R 35a b x + 24a b x + -- a b x + -- a b x + - a b x - --- a +--R 4 3 2 132 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 527 + +--S 528 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 12 10 9 11 9 2 8 10 40 3 7 9 105 4 6 8 5 5 7 +--R -- b x + -- a b x + - a b x + -- a b x + --- a b x + 36a b x +--R 12 11 2 3 4 +--R + +--R 6 4 6 7 3 5 45 8 2 4 10 9 3 1 10 2 +--R 35a b x + 24a b x + -- a b x + -- a b x + - a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 528 + +--S 529 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 12 +--R --- a +--R 132 +--R (4) ------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 529 + +--S 530 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 530 + +)clear all + +--S 531 of 3330 +t0000:=(a+b*x)^10 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Polynomial(Integer) +--E 531 + +--S 532 of 3330 +r0000:=1/11*(a+b*x)^11/b +--R +--R +--R (2) +--R 1 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R -- b x + a b x + 5a b x + 15a b x + 30a b x + 42a b x +--R 11 +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 1 11 +--R 42a b x + 30a b x + 15a b x + 5a b x + a b x + -- a +--R 11 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 532 + +--S 533 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 11 9 10 2 8 9 3 7 8 4 6 7 5 5 6 6 4 5 +--R -- b x + a b x + 5a b x + 15a b x + 30a b x + 42a b x + 42a b x +--R 11 +--R + +--R 7 3 4 8 2 3 9 2 10 +--R 30a b x + 15a b x + 5a b x + a x +--R Type: Polynomial(Fraction(Integer)) +--E 533 + +--S 534 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 11 +--R -- a +--R 11 +--R (4) - ------ +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 534 + +--S 535 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 535 + +)clear all + +--S 536 of 3330 +t0000:=(a+b*x)^10/x +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 536 + +--S 537 of 3330 +r0000:=10*a^9*b*x+45/2*a^8*b^2*x^2+40*a^7*b^3*x^3+105/2*a^6*b^4*x^4+_ + 252/5*a^5*b^5*x^5+35*a^4*b^6*x^6+120/7*a^3*b^7*x^7+_ + 45/8*a^2*b^8*x^8+10/9*a*b^9*x^9+1/10*b^10*x^10+a^10*log(x) +--R +--R +--R (2) +--R 10 10 10 9 9 2 8 8 3 7 7 +--R 2520a log(x) + 252b x + 2800a b x + 14175a b x + 43200a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R 88200a b x + 127008a b x + 132300a b x + 100800a b x + 56700a b x +--R + +--R 9 +--R 25200a b x +--R / +--R 2520 +--R Type: Expression(Integer) +--E 537 + +--S 538 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 9 2 8 8 3 7 7 +--R 2520a log(x) + 252b x + 2800a b x + 14175a b x + 43200a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R 88200a b x + 127008a b x + 132300a b x + 100800a b x + 56700a b x +--R + +--R 9 +--R 25200a b x +--R / +--R 2520 +--R Type: Union(Expression(Integer),...) +--E 538 + +--S 539 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 539 + +--S 540 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 3330 +t0000:=(a+b*x)^10/x^2 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 541 + +--S 542 of 3330 +r0000:=-a^10/x+45*a^8*b^2*x+60*a^7*b^3*x^2+70*a^6*b^4*x^3+63*a^5*b^5*x^4+_ + 42*a^4*b^6*x^5+20*a^3*b^7*x^6+45/7*a^2*b^8*x^7+5/4*a*b^9*x^8+_ + 1/9*b^10*x^9+10*a^9*b*log(x) +--R +--R +--R (2) +--R 9 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 28b x + 315a b x + 1620a b x + 5040a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R 10584a b x + 15876a b x + 17640a b x + 15120a b x + 11340a b x +--R + +--R 10 +--R - 252a +--R / +--R 252x +--R Type: Expression(Integer) +--E 542 + +--S 543 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 28b x + 315a b x + 1620a b x + 5040a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R 10584a b x + 15876a b x + 17640a b x + 15120a b x + 11340a b x +--R + +--R 10 +--R - 252a +--R / +--R 252x +--R Type: Union(Expression(Integer),...) +--E 543 + +--S 544 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 544 + +--S 545 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 545 + +)clear all + +--S 546 of 3330 +t0000:=(a+b*x)^10/x^3 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 546 + +--S 547 of 3330 +r0000:=-1/2*a^10/x^2-10*a^9*b/x+120*a^7*b^3*x+105*a^6*b^4*x^2+_ + 84*a^5*b^5*x^3+105/2*a^4*b^6*x^4+24*a^3*b^7*x^5+15/2*a^2*b^8*x^6+_ + 10/7*a*b^9*x^7+1/8*b^10*x^8+45*a^8*b^2*log(x) +--R +--R +--R (2) +--R 8 2 2 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 7b x + 80a b x + 420a b x + 1344a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 9 10 +--R 2940a b x + 4704a b x + 5880a b x + 6720a b x - 560a b x - 28a +--R / +--R 2 +--R 56x +--R Type: Expression(Integer) +--E 547 + +--S 548 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 2 2 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 7b x + 80a b x + 420a b x + 1344a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 9 10 +--R 2940a b x + 4704a b x + 5880a b x + 6720a b x - 560a b x - 28a +--R / +--R 2 +--R 56x +--R Type: Union(Expression(Integer),...) +--E 548 + +--S 549 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 550 + +)clear all + +--S 551 of 3330 +t0000:=(a+b*x)^10/x^4 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 551 + +--S 552 of 3330 +r0000:=-1/3*a^10/x^3-5*a^9*b/x^2-45*a^8*b^2/x+210*a^6*b^4*x+_ + 126*a^5*b^5*x^2+70*a^4*b^6*x^3+30*a^3*b^7*x^4+9*a^2*b^8*x^5+_ + 5/3*a*b^9*x^6+1/7*b^10*x^7+120*a^7*b^3*log(x) +--R +--R +--R (2) +--R 7 3 3 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 3b x + 35a b x + 189a b x + 630a b x +--R + +--R 4 6 6 5 5 5 6 4 4 8 2 2 9 10 +--R 1470a b x + 2646a b x + 4410a b x - 945a b x - 105a b x - 7a +--R / +--R 3 +--R 21x +--R Type: Expression(Integer) +--E 552 + +--S 553 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 3 3 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 3b x + 35a b x + 189a b x + 630a b x +--R + +--R 4 6 6 5 5 5 6 4 4 8 2 2 9 10 +--R 1470a b x + 2646a b x + 4410a b x - 945a b x - 105a b x - 7a +--R / +--R 3 +--R 21x +--R Type: Union(Expression(Integer),...) +--E 553 + +--S 554 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 3330 +t0000:=(a+b*x)^10/x^5 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 of 3330 +r0000:=-1/4*a^10/x^4-10/3*a^9*b/x^3-45/2*a^8*b^2/x^2-120*a^7*b^3/x+_ + 252*a^5*b^5*x+105*a^4*b^6*x^2+40*a^3*b^7*x^3+45/4*a^2*b^8*x^4+_ + 2*a*b^9*x^5+1/6*b^10*x^6+210*a^6*b^4*log(x) +--R +--R +--R (2) +--R 6 4 4 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 2b x + 24a b x + 135a b x + 480a b x +--R + +--R 4 6 6 5 5 5 7 3 3 8 2 2 9 10 +--R 1260a b x + 3024a b x - 1440a b x - 270a b x - 40a b x - 3a +--R / +--R 4 +--R 12x +--R Type: Expression(Integer) +--E 557 + +--S 558 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 4 4 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 2b x + 24a b x + 135a b x + 480a b x +--R + +--R 4 6 6 5 5 5 7 3 3 8 2 2 9 10 +--R 1260a b x + 3024a b x - 1440a b x - 270a b x - 40a b x - 3a +--R / +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 558 + +--S 559 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 3330 +t0000:=(a+b*x)^10/x^6 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 561 + +--S 562 of 3330 +r0000:=-1/5*a^10/x^5-5/2*a^9*b/x^4-15*a^8*b^2/x^3-60*a^7*b^3/x^2-_ + 210*a^6*b^4/x+210*a^4*b^6*x+60*a^3*b^7*x^2+15*a^2*b^8*x^3+_ + 5/2*a*b^9*x^4+1/5*b^10*x^5+252*a^5*b^5*log(x) +--R +--R +--R (2) +--R 5 5 5 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 2b x + 25a b x + 150a b x + 600a b x +--R + +--R 4 6 6 6 4 4 7 3 3 8 2 2 9 10 +--R 2100a b x - 2100a b x - 600a b x - 150a b x - 25a b x - 2a +--R / +--R 5 +--R 10x +--R Type: Expression(Integer) +--E 562 + +--S 563 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 5 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 2b x + 25a b x + 150a b x + 600a b x +--R + +--R 4 6 6 6 4 4 7 3 3 8 2 2 9 10 +--R 2100a b x - 2100a b x - 600a b x - 150a b x - 25a b x - 2a +--R / +--R 5 +--R 10x +--R Type: Union(Expression(Integer),...) +--E 563 + +--S 564 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 564 + +--S 565 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 565 + +)clear all + +--S 566 of 3330 +t0000:=(a+b*x)^10/x^7 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 566 + +--S 567 of 3330 +r0000:=-1/6*a^10/x^6-2*a^9*b/x^5-45/4*a^8*b^2/x^4-40*a^7*b^3/x^3-_ + 105*a^6*b^4/x^2-252*a^5*b^5/x+120*a^3*b^7*x+45/2*a^2*b^8*x^2+_ + 10/3*a*b^9*x^3+1/4*b^10*x^4+210*a^4*b^6*log(x) +--R +--R +--R (2) +--R 4 6 6 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 3b x + 40a b x + 270a b x + 1440a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 3024a b x - 1260a b x - 480a b x - 135a b x - 24a b x - 2a +--R / +--R 6 +--R 12x +--R Type: Expression(Integer) +--E 567 + +--S 568 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 6 6 10 10 9 9 2 8 8 3 7 7 +--R 2520a b x log(x) + 3b x + 40a b x + 270a b x + 1440a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 3024a b x - 1260a b x - 480a b x - 135a b x - 24a b x - 2a +--R / +--R 6 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 568 + +--S 569 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 3330 +t0000:=(a+b*x)^10/x^8 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 571 + +--S 572 of 3330 +r0000:=-1/7*a^10/x^7-5/3*a^9*b/x^6-9*a^8*b^2/x^5-30*a^7*b^3/x^4-_ + 70*a^6*b^4/x^3-126*a^5*b^5/x^2-210*a^4*b^6/x+45*a^2*b^8*x+_ + 5*a*b^9*x^2+1/3*b^10*x^3+120*a^3*b^7*log(x) +--R +--R +--R (2) +--R 3 7 7 10 10 9 9 2 8 8 4 6 6 +--R 2520a b x log(x) + 7b x + 105a b x + 945a b x - 4410a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 2646a b x - 1470a b x - 630a b x - 189a b x - 35a b x - 3a +--R / +--R 7 +--R 21x +--R Type: Expression(Integer) +--E 572 + +--S 573 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 7 7 10 10 9 9 2 8 8 4 6 6 +--R 2520a b x log(x) + 7b x + 105a b x + 945a b x - 4410a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 2646a b x - 1470a b x - 630a b x - 189a b x - 35a b x - 3a +--R / +--R 7 +--R 21x +--R Type: Union(Expression(Integer),...) +--E 573 + +--S 574 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 575 + +)clear all + +--S 576 of 3330 +t0000:=(a+b*x)^10/x^9 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 576 + +--S 577 of 3330 +r0000:=-1/8*a^10/x^8-10/7*a^9*b/x^7-15/2*a^8*b^2/x^6-24*a^7*b^3/x^5-_ + 105/2*a^6*b^4/x^4-84*a^5*b^5/x^3-105*a^4*b^6/x^2-120*a^3*b^7/x+_ + 10*a*b^9*x+1/2*b^10*x^2+45*a^2*b^8*log(x) +--R +--R +--R (2) +--R 2 8 8 10 10 9 9 3 7 7 4 6 6 +--R 2520a b x log(x) + 28b x + 560a b x - 6720a b x - 5880a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 4704a b x - 2940a b x - 1344a b x - 420a b x - 80a b x - 7a +--R / +--R 8 +--R 56x +--R Type: Expression(Integer) +--E 577 + +--S 578 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 8 8 10 10 9 9 3 7 7 4 6 6 +--R 2520a b x log(x) + 28b x + 560a b x - 6720a b x - 5880a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 4704a b x - 2940a b x - 1344a b x - 420a b x - 80a b x - 7a +--R / +--R 8 +--R 56x +--R Type: Union(Expression(Integer),...) +--E 578 + +--S 579 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 580 + +)clear all + +--S 581 of 3330 +t0000:=(a+b*x)^10/x^10 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 581 + +--S 582 of 3330 +r0000:=-1/9*a^10/x^9-5/4*a^9*b/x^8-45/7*a^8*b^2/x^7-20*a^7*b^3/x^6-_ + 42*a^6*b^4/x^5-63*a^5*b^5/x^4-70*a^4*b^6/x^3-60*a^3*b^7/x^2-_ + 45*a^2*b^8/x+b^10*x+10*a*b^9*log(x) +--R +--R +--R (2) +--R 9 9 10 10 2 8 8 3 7 7 4 6 6 +--R 2520a b x log(x) + 252b x - 11340a b x - 15120a b x - 17640a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 15876a b x - 10584a b x - 5040a b x - 1620a b x - 315a b x - 28a +--R / +--R 9 +--R 252x +--R Type: Expression(Integer) +--E 582 + +--S 583 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 10 10 2 8 8 3 7 7 4 6 6 +--R 2520a b x log(x) + 252b x - 11340a b x - 15120a b x - 17640a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 15876a b x - 10584a b x - 5040a b x - 1620a b x - 315a b x - 28a +--R / +--R 9 +--R 252x +--R Type: Union(Expression(Integer),...) +--E 583 + +--S 584 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 3330 +t0000:=(a+b*x)^10/x^11 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 586 + +--S 587 of 3330 +r0000:=-1/10*a^10/x^10-10/9*a^9*b/x^9-45/8*a^8*b^2/x^8-120/7*a^7*b^3/x^7-_ + 35*a^6*b^4/x^6-252/5*a^5*b^5/x^5-105/2*a^4*b^6/x^4-40*a^3*b^7/x^3-_ + 45/2*a^2*b^8/x^2-10*a*b^9/x+b^10*log(x) +--R +--R +--R (2) +--R 10 10 9 9 2 8 8 3 7 7 +--R 2520b x log(x) - 25200a b x - 56700a b x - 100800a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R - 132300a b x - 127008a b x - 88200a b x - 43200a b x - 14175a b x +--R + +--R 9 10 +--R - 2800a b x - 252a +--R / +--R 10 +--R 2520x +--R Type: Expression(Integer) +--E 587 + +--S 588 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 +--R 2520b x log(x) - 25200a b x - 56700a b x - 100800a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R - 132300a b x - 127008a b x - 88200a b x - 43200a b x - 14175a b x +--R + +--R 9 10 +--R - 2800a b x - 252a +--R / +--R 10 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 3330 +t0000:=(a+b*x)^10/x^12 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 591 + +--S 592 of 3330 +r0000:=-1/11*(a+b*x)^11/(a*x^11) +--R +--R +--R (2) +--R 1 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R - -- b x - a b x - 5a b x - 15a b x - 30a b x - 42a b x +--R 11 +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 1 11 +--R - 42a b x - 30a b x - 15a b x - 5a b x - a b x - -- a +--R 11 +--R / +--R 11 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 592 + +--S 593 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R - 11b x - 55a b x - 165a b x - 330a b x - 462a b x - 462a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R - 330a b x - 165a b x - 55a b x - 11a b x - a +--R / +--R 11 +--R 11x +--R Type: Union(Expression(Integer),...) +--E 593 + +--S 594 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 11 +--R b +--R (4) --- +--R 11a +--R Type: Expression(Integer) +--E 594 + +--S 595 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 595 + +)clear all + +--S 596 of 3330 +t0000:=(a+b*x)^10/x^13 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 596 + +--S 597 of 3330 +r0000:=-1/12*(a+b*x)^11/(a*x^12)+1/132*b*(a+b*x)^11/(a^2*x^11) +--R +--R +--R (2) +--R 1 12 12 1 2 10 10 10 3 9 9 45 4 8 8 5 7 7 6 6 6 +--R --- b x - - a b x - -- a b x - -- a b x - 24a b x - 35a b x +--R 132 2 3 4 +--R + +--R 7 5 5 105 8 4 4 40 9 3 3 9 10 2 2 10 11 1 12 +--R - 36a b x - --- a b x - -- a b x - - a b x - -- a b x - -- a +--R 4 3 2 11 12 +--R / +--R 2 12 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 597 + +--S 598 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R - 66b x - 440a b x - 1485a b x - 3168a b x - 4620a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 4752a b x - 3465a b x - 1760a b x - 594a b x - 120a b x - 11a +--R / +--R 12 +--R 132x +--R Type: Union(Expression(Integer),...) +--E 598 + +--S 599 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 12 +--R b +--R (4) - ----- +--R 2 +--R 132a +--R Type: Expression(Integer) +--E 599 + +--S 600 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 3330 +t0000:=(a+b*x)^10/x^14 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 14 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 601 + +--S 602 of 3330 +r0000:=-1/13*(a+b*x)^11/(a*x^13)+1/78*b*(a+b*x)^11/(a^2*x^12)-_ + 1/858*b^2*(a+b*x)^11/(a^3*x^11) +--R +--R +--R (2) +--R 1 13 13 1 3 10 10 5 4 9 9 5 8 8 6 7 7 7 6 6 +--R - --- b x - - a b x - - a b x - 9a b x - 20a b x - 30a b x +--R 858 3 2 +--R + +--R 63 8 5 5 70 9 4 4 10 3 3 45 11 2 2 5 12 1 13 +--R - -- a b x - -- a b x - 12a b x - -- a b x - - a b x - -- a +--R 2 3 11 6 13 +--R / +--R 3 13 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 602 + +--S 603 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R - 286b x - 2145a b x - 7722a b x - 17160a b x - 25740a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 27027a b x - 20020a b x - 10296a b x - 3510a b x - 715a b x - 66a +--R / +--R 13 +--R 858x +--R Type: Union(Expression(Integer),...) +--E 603 + +--S 604 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 13 +--R b +--R (4) ----- +--R 3 +--R 858a +--R Type: Expression(Integer) +--E 604 + +--S 605 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 605 + +)clear all + +--S 606 of 3330 +t0000:=(a+b*x)^10/x^15 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 15 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 606 + +--S 607 of 3330 +r0000:=-1/14*(a+b*x)^11/(a*x^14)+3/182*b*(a+b*x)^11/(a^2*x^13)-_ + 1/364*b^2*(a+b*x)^11/(a^3*x^12)+1/4004*b^3*(a+b*x)^11/(a^4*x^11) +--R +--R +--R (2) +--R 1 14 14 1 4 10 10 5 9 9 15 6 8 8 120 7 7 7 105 8 6 6 +--R ---- b x - - a b x - 2a b x - -- a b x - --- a b x - --- a b x +--R 4004 4 2 7 4 +--R + +--R 9 5 5 10 4 4 120 11 3 3 15 12 2 2 10 13 1 14 +--R - 28a b x - 21a b x - --- a b x - -- a b x - -- a b x - -- a +--R 11 4 13 14 +--R / +--R 4 14 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 607 + +--S 608 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R - 1001b x - 8008a b x - 30030a b x - 68640a b x - 105105a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R - 112112a b x - 84084a b x - 43680a b x - 15015a b x - 3080a b x +--R + +--R 10 +--R - 286a +--R / +--R 14 +--R 4004x +--R Type: Union(Expression(Integer),...) +--E 608 + +--S 609 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 14 +--R b +--R (4) - ------ +--R 4 +--R 4004a +--R Type: Expression(Integer) +--E 609 + +--S 610 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 610 + +)clear all + +--S 611 of 3330 +t0000:=(a+b*x)^10/x^16 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 611 + +--S 612 of 3330 +r0000:=-1/15*(a+b*x)^11/(a*x^15)+2/105*b*(a+b*x)^11/(a^2*x^14)-_ + 2/455*b^2*(a+b*x)^11/(a^3*x^13)+1/1365*b^3*(a+b*x)^11/(a^4*x^12)-_ + 1/15015*b^4*(a+b*x)^11/(a^5*x^11) +--R +--R +--R (2) +--R 1 15 15 1 5 10 10 5 6 9 9 45 7 8 8 8 7 7 70 9 6 6 +--R - ----- b x - - a b x - - a b x - -- a b x - 15a b x - -- a b x +--R 15015 5 3 7 3 +--R + +--R 126 10 5 5 210 11 4 4 12 3 3 45 13 2 2 5 14 1 15 +--R - --- a b x - --- a b x - 10a b x - -- a b x - - a b x - -- a +--R 5 11 13 7 15 +--R / +--R 5 15 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 612 + +--S 613 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R - 3003b x - 25025a b x - 96525a b x - 225225a b x - 350350a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R - 378378a b x - 286650a b x - 150150a b x - 51975a b x - 10725a b x +--R + +--R 10 +--R - 1001a +--R / +--R 15 +--R 15015x +--R Type: Union(Expression(Integer),...) +--E 613 + +--S 614 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 15 +--R b +--R (4) ------- +--R 5 +--R 15015a +--R Type: Expression(Integer) +--E 614 + +--S 615 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 3330 +t0000:=(a+b*x)^10/x^17 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 17 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 616 + +--S 617 of 3330 +r0000:=-1/16*(a+b*x)^11/(a*x^16)+1/48*b*(a+b*x)^11/(a^2*x^15)-_ + 1/168*b^2*(a+b*x)^11/(a^3*x^14)+1/728*b^3*(a+b*x)^11/(a^4*x^13)-_ + 1/4368*b^4*(a+b*x)^11/(a^5*x^12)+1/48048*b^5*(a+b*x)^11/(a^6*x^11) +--R +--R +--R (2) +--R 1 16 16 1 6 10 10 10 7 9 9 45 8 8 8 40 9 7 7 10 6 6 +--R ----- b x - - a b x - -- a b x - -- a b x - -- a b x - 21a b x +--R 48048 6 7 8 3 +--R + +--R 252 11 5 5 35 12 4 4 120 13 3 3 45 14 2 2 2 15 1 16 +--R - --- a b x - -- a b x - --- a b x - -- a b x - - a b x - -- a +--R 11 2 13 14 3 16 +--R / +--R 6 16 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 617 + +--S 618 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R - 8008b x - 68640a b x - 270270a b x - 640640a b x - 1009008a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R - 1100736a b x - 840840a b x - 443520a b x - 154440a b x - 32032a b x +--R + +--R 10 +--R - 3003a +--R / +--R 16 +--R 48048x +--R Type: Union(Expression(Integer),...) +--E 618 + +--S 619 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 16 +--R b +--R (4) - ------- +--R 6 +--R 48048a +--R Type: Expression(Integer) +--E 619 + +--S 620 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 620 + +)clear all + +--S 621 of 3330 +t0000:=(a+b*x)^10/x^18 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 18 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 621 + +--S 622 of 3330 +r0000:=-1/17*a^10/x^17-5/8*a^9*b/x^16-3*a^8*b^2/x^15-60/7*a^7*b^3/x^14-_ + 210/13*a^6*b^4/x^13-21*a^5*b^5/x^12-210/11*a^4*b^6/x^11-_ + 12*a^3*b^7/x^10-5*a^2*b^8/x^9-5/4*a*b^9/x^8-1/7*b^10/x^7 +--R +--R +--R (2) +--R 1 10 10 5 9 9 2 8 8 3 7 7 210 4 6 6 5 5 5 +--R - - b x - - a b x - 5a b x - 12a b x - --- a b x - 21a b x +--R 7 4 11 +--R + +--R 210 6 4 4 60 7 3 3 8 2 2 5 9 1 10 +--R - --- a b x - -- a b x - 3a b x - - a b x - -- a +--R 13 7 8 17 +--R / +--R 17 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 622 + +--S 623 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 +--R - 19448b x - 170170a b x - 680680a b x - 1633632a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 +--R - 2598960a b x - 2858856a b x - 2199120a b x - 1166880a b x +--R + +--R 8 2 2 9 10 +--R - 408408a b x - 85085a b x - 8008a +--R / +--R 17 +--R 136136x +--R Type: Union(Expression(Integer),...) +--E 623 + +--S 624 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 624 + +--S 625 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 625 + +)clear all + +--S 626 of 3330 +t0000:=(a+b*x)^10/x^19 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 626 + +--S 627 of 3330 +r0000:=-1/18*a^10/x^18-10/17*a^9*b/x^17-45/16*a^8*b^2/x^16-8*a^7*b^3/x^15-_ + 15*a^6*b^4/x^14-252/13*a^5*b^5/x^13-35/2*a^4*b^6/x^12-_ + 120/11*a^3*b^7/x^11-9/2*a^2*b^8/x^10-10/9*a*b^9/x^9-1/8*b^10/x^8 +--R +--R +--R (2) +--R 1 10 10 10 9 9 9 2 8 8 120 3 7 7 35 4 6 6 252 5 5 5 +--R - - b x - -- a b x - - a b x - --- a b x - -- a b x - --- a b x +--R 8 9 2 11 2 13 +--R + +--R 6 4 4 7 3 3 45 8 2 2 10 9 1 10 +--R - 15a b x - 8a b x - -- a b x - -- a b x - -- a +--R 16 17 18 +--R / +--R 18 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 627 + +--S 628 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 +--R - 43758b x - 388960a b x - 1575288a b x - 3818880a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 +--R - 6126120a b x - 6785856a b x - 5250960a b x - 2800512a b x +--R + +--R 8 2 2 9 10 +--R - 984555a b x - 205920a b x - 19448a +--R / +--R 18 +--R 350064x +--R Type: Union(Expression(Integer),...) +--E 628 + +--S 629 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 629 + +--S 630 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 of 3330 +t0000:=(a+b*x)^10/x^20 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 20 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 631 + +--S 632 of 3330 +r0000:=-1/19*a^10/x^19-5/9*a^9*b/x^18-45/17*a^8*b^2/x^17-15/2*a^7*b^3/x^16-_ + 14*a^6*b^4/x^15-18*a^5*b^5/x^14-210/13*a^4*b^6/x^13-_ + 10*a^3*b^7/x^12-45/11*a^2*b^8/x^11-a*b^9/x^10-1/9*b^10/x^9 +--R +--R +--R (2) +--R 1 10 10 9 9 45 2 8 8 3 7 7 210 4 6 6 5 5 5 +--R - - b x - a b x - -- a b x - 10a b x - --- a b x - 18a b x +--R 9 11 13 +--R + +--R 6 4 4 15 7 3 3 45 8 2 2 5 9 1 10 +--R - 14a b x - -- a b x - -- a b x - - a b x - -- a +--R 2 17 9 19 +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 632 + +--S 633 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 +--R - 92378b x - 831402a b x - 3401190a b x - 8314020a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 +--R - 13430340a b x - 14965236a b x - 11639628a b x - 6235515a b x +--R + +--R 8 2 2 9 10 +--R - 2200770a b x - 461890a b x - 43758a +--R / +--R 19 +--R 831402x +--R Type: Union(Expression(Integer),...) +--E 633 + +--S 634 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 634 + +--S 635 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 635 + +)clear all + +--S 636 of 3330 +t0000:=c*(a+b*x) +--R +--R +--R (1) b c x + a c +--R Type: Polynomial(Integer) +--E 636 + +--S 637 of 3330 +r0000:=1/2*c*(a+b*x)^2/b +--R +--R +--R 1 2 2 1 2 +--R - b c x + a b c x + - a c +--R 2 2 +--R (2) -------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 637 + +--S 638 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 +--R (3) - b c x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 638 + +--S 639 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 2 +--R - a c +--R 2 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 639 + +--S 640 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 640 + +)clear all + +--S 641 of 3330 +t0000:=(c+d)*(a+b*x)/e +--R +--R +--R (b d + b c)x + a d + a c +--R (1) ------------------------ +--R e +--R Type: Fraction(Polynomial(Integer)) +--E 641 + +--S 642 of 3330 +r0000:=1/2*(c+d)*(a+b*x)^2/(b*e) +--R +--R +--R 1 2 1 2 2 1 2 1 2 +--R (- b d + - b c)x + (a b d + a b c)x + - a d + - a c +--R 2 2 2 2 +--R (2) ---------------------------------------------------- +--R b e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 642 + +--S 643 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (b d + b c)x + (2a d + 2a c)x +--R (3) ------------------------------ +--R 2e +--R Type: Union(Expression(Integer),...) +--E 643 + +--S 644 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R - a d - a c +--R (4) ----------- +--R 2b e +--R Type: Expression(Integer) +--E 644 + +--S 645 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 3330 +t0000:=x^m/(a+b*x) +--R +--R +--R m +--R x +--R (1) ------- +--R b x + a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 3330 +--r0000:=x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a*(1+m)) +--E 647 + +--S 648 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | -------- d%N +--R ++ %N b + a +--R Type: Union(Expression(Integer),...) +--E 648 + +--S 649 of 3330 +--m0000:=a0000 - r0000 +--E 649 + +--S 650 of 3330 +--d0000:=D(m0000,x) +--E 650 + +)clear all + +--S 651 of 3330 +t0000:=x^5/(a+b*x) +--R +--R +--R 5 +--R x +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 651 + +--S 652 of 3330 +r0000:=a^4*x/b^5-1/2*a^3*x^2/b^4+1/3*a^2*x^3/b^3-1/4*a*x^4/b^2+1/5*x^5/b-_ + a^5*log(a+b*x)/b^6 +--R +--R +--R 5 5 5 4 4 2 3 3 3 2 2 4 +--R - 60a log(b x + a) + 12b x - 15a b x + 20a b x - 30a b x + 60a b x +--R (2) ---------------------------------------------------------------------- +--R 6 +--R 60b +--R Type: Expression(Integer) +--E 652 + +--S 653 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 5 5 5 4 4 2 3 3 3 2 2 4 +--R - 60a log(b x + a) + 12b x - 15a b x + 20a b x - 30a b x + 60a b x +--R (3) ---------------------------------------------------------------------- +--R 6 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 653 + +--S 654 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 654 + +--S 655 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 655 + +)clear all + +--S 656 of 3330 +t0000:=x^4/(a+b*x) +--R +--R +--R 4 +--R x +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 656 + +--S 657 of 3330 +r0000:=-a^3*x/b^4+1/2*a^2*x^2/b^3-1/3*a*x^3/b^2+1/4*x^4/b+a^4*log(a+b*x)/b^5 +--R +--R +--R 4 4 4 3 3 2 2 2 3 +--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x +--R (2) ------------------------------------------------------ +--R 5 +--R 12b +--R Type: Expression(Integer) +--E 657 + +--S 658 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 4 3 3 2 2 2 3 +--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x +--R (3) ------------------------------------------------------ +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 658 + +--S 659 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 659 + +--S 660 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 of 3330 +t0000:=x^3/(a+b*x) +--R +--R +--R 3 +--R x +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 661 + +--S 662 of 3330 +r0000:=a^2*x/b^3-1/2*a*x^2/b^2+1/3*x^3/b-a^3*log(a+b*x)/b^4 +--R +--R +--R 3 3 3 2 2 2 +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (2) -------------------------------------------- +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 662 + +--S 663 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 3 2 2 2 +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (3) -------------------------------------------- +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 663 + +--S 664 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 664 + +--S 665 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 665 + +)clear all + +--S 666 of 3330 +t0000:=x^2/(a+b*x) +--R +--R +--R 2 +--R x +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 666 + +--S 667 of 3330 +r0000:=-a*x/b^2+1/2*x^2/b+a^2*log(a+b*x)/b^3 +--R +--R +--R 2 2 2 +--R 2a log(b x + a) + b x - 2a b x +--R (2) ------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 667 + +--S 668 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 2a log(b x + a) + b x - 2a b x +--R (3) ------------------------------- +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 668 + +--S 669 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 669 + +--S 670 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 670 + +)clear all + +--S 671 of 3330 +t0000:=x/(a+b*x) +--R +--R +--R x +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 671 + +--S 672 of 3330 +r0000:=x/b-a*log(a+b*x)/b^2 +--R +--R +--R - a log(b x + a) + b x +--R (2) ---------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 672 + +--S 673 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - a log(b x + a) + b x +--R (3) ---------------------- +--R 2 +--R b +--R Type: Union(Expression(Integer),...) +--E 673 + +--S 674 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 674 + +--S 675 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 of 3330 +t0000:=1/(a+b*x) +--R +--R +--R 1 +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 676 + +--S 677 of 3330 +r0000:=log(a+b*x)/b +--R +--R +--R log(b x + a) +--R (2) ------------ +--R b +--R Type: Expression(Integer) +--E 677 + +--S 678 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R log(b x + a) +--R (3) ------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 678 + +--S 679 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 679 + +--S 680 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 680 + +)clear all + +--S 681 of 3330 +t0000:=1/(x*(a+b*x)) +--R +--R +--R 1 +--R (1) ---------- +--R 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 681 + +--S 682 of 3330 +r0000:=log(x)/a-log(a+b*x)/a +--R +--R +--R - log(b x + a) + log(x) +--R (2) ----------------------- +--R a +--R Type: Expression(Integer) +--E 682 + +--S 683 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - log(b x + a) + log(x) +--R (3) ----------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 683 + +--S 684 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 684 + +--S 685 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 685 + +)clear all + +--S 686 of 3330 +t0000:=1/(x^2*(a+b*x)) +--R +--R +--R 1 +--R (1) ----------- +--R 3 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 686 + +--S 687 of 3330 +r0000:=(-1)/(a*x)-b*log(x)/a^2+b*log(a+b*x)/a^2 +--R +--R +--R b x log(b x + a) - b x log(x) - a +--R (2) --------------------------------- +--R 2 +--R a x +--R Type: Expression(Integer) +--E 687 + +--S 688 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R b x log(b x + a) - b x log(x) - a +--R (3) --------------------------------- +--R 2 +--R a x +--R Type: Union(Expression(Integer),...) +--E 688 + +--S 689 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 689 + +--S 690 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 3330 +t0000:=1/(x^3*(a+b*x)) +--R +--R +--R 1 +--R (1) ----------- +--R 4 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 691 + +--S 692 of 3330 +r0000:=(-1/2)/(a*x^2)+b/(a^2*x)+b^2*log(x)/a^3-b^2*log(a+b*x)/a^3 +--R +--R +--R 2 2 2 2 2 +--R - 2b x log(b x + a) + 2b x log(x) + 2a b x - a +--R (2) ----------------------------------------------- +--R 3 2 +--R 2a x +--R Type: Expression(Integer) +--E 692 + +--S 693 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 2 +--R - 2b x log(b x + a) + 2b x log(x) + 2a b x - a +--R (3) ----------------------------------------------- +--R 3 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 693 + +--S 694 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 694 + +--S 695 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 695 + +)clear all + +--S 696 of 3330 +t0000:=1/(x^4*(a+b*x)) +--R +--R +--R 1 +--R (1) ----------- +--R 5 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 696 + +--S 697 of 3330 +r0000:=(-1/3)/(a*x^3)+1/2*b/(a^2*x^2)-b^2/(a^3*x)-_ + b^3*log(x)/a^4+b^3*log(a+b*x)/a^4 +--R +--R +--R 3 3 3 3 2 2 2 3 +--R 6b x log(b x + a) - 6b x log(x) - 6a b x + 3a b x - 2a +--R (2) -------------------------------------------------------- +--R 4 3 +--R 6a x +--R Type: Expression(Integer) +--E 697 + +--S 698 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 3 3 2 2 2 3 +--R 6b x log(b x + a) - 6b x log(x) - 6a b x + 3a b x - 2a +--R (3) -------------------------------------------------------- +--R 4 3 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 698 + +--S 699 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 699 + +--S 700 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 700 + +)clear all + +--S 701 of 3330 +t0000:=1/(x^5*(a+b*x)) +--R +--R +--R 1 +--R (1) ----------- +--R 6 5 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 701 + +--S 702 of 3330 +r0000:=(-1/4)/(a*x^4)+1/3*b/(a^2*x^3)-1/2*b^2/(a^3*x^2)+b^3/(a^4*x)+_ + b^4*log(x)/a^5-b^4*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 4 4 4 4 3 3 2 2 2 3 4 +--R - 12b x log(b x + a) + 12b x log(x) + 12a b x - 6a b x + 4a b x - 3a +--R ----------------------------------------------------------------------- +--R 5 4 +--R 12a x +--R Type: Expression(Integer) +--E 702 + +--S 703 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 4 4 3 3 2 2 2 3 4 +--R - 12b x log(b x + a) + 12b x log(x) + 12a b x - 6a b x + 4a b x - 3a +--R ----------------------------------------------------------------------- +--R 5 4 +--R 12a x +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 3330 +t0000:=x^m/(a+b*x)^2 +--R +--R +--R m +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 3330 +--r0000:=x^(1+m)/(a*(a+b*x))-m*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-b*x/a)/(a^2*(1+m)) +--E 707 + +--S 708 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | -------------------- d%N +--R ++ 2 2 2 +--R %N b + 2%N a b + a +--R Type: Union(Expression(Integer),...) +--E 708 + +--S 709 of 3330 +--m0000:=a0000 - r0000 +--E 709 + +--S 710 of 3330 +--d0000:=D(m0000,x) +--E 710 + +)clear all + +--S 711 of 3330 +t0000:=x^6/(a+b*x)^2 +--R +--R +--R 6 +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 711 + +--S 712 of 3330 +r0000:=5*a^4*x/b^6-2*a^3*x^2/b^5+a^2*x^3/b^4-1/2*a*x^4/b^3+1/5*x^5/b^2-_ + a^6/(b^7*(a+b*x))-6*a^5*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 5 6 6 6 5 5 2 4 4 3 3 3 +--R (- 60a b x - 60a )log(b x + a) + 2b x - 3a b x + 5a b x - 10a b x +--R + +--R 4 2 2 5 6 +--R 30a b x + 50a b x - 10a +--R / +--R 8 7 +--R 10b x + 10a b +--R Type: Expression(Integer) +--E 712 + +--S 713 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 6 6 6 5 5 2 4 4 3 3 3 +--R (- 60a b x - 60a )log(b x + a) + 2b x - 3a b x + 5a b x - 10a b x +--R + +--R 4 2 2 5 6 +--R 30a b x + 50a b x - 10a +--R / +--R 8 7 +--R 10b x + 10a b +--R Type: Union(Expression(Integer),...) +--E 713 + +--S 714 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 714 + +--S 715 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 715 + +)clear all + +--S 716 of 3330 +t0000:=x^5/(a+b*x)^2 +--R +--R +--R 5 +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 716 + +--S 717 of 3330 +r0000:=-4*a^3*x/b^5+3/2*a^2*x^2/b^4-2/3*a*x^3/b^3+1/4*x^4/b^2+_ + a^5/(b^6*(a+b*x))+5*a^4*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 4 5 5 5 4 4 2 3 3 3 2 2 +--R (60a b x + 60a )log(b x + a) + 3b x - 5a b x + 10a b x - 30a b x +--R + +--R 4 5 +--R - 48a b x + 12a +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Expression(Integer) +--E 717 + +--S 718 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 5 5 5 4 4 2 3 3 3 2 2 +--R (60a b x + 60a )log(b x + a) + 3b x - 5a b x + 10a b x - 30a b x +--R + +--R 4 5 +--R - 48a b x + 12a +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 718 + +--S 719 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 719 + +--S 720 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 of 3330 +t0000:=x^4/(a+b*x)^2 +--R +--R +--R 4 +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 721 + +--S 722 of 3330 +r0000:=3*a^2*x/b^4-a*x^2/b^3+1/3*x^3/b^2-a^4/(b^5*(a+b*x))-4*a^3*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 3 4 4 4 3 3 2 2 2 3 4 +--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x - 3a +--R ------------------------------------------------------------------------ +--R 6 5 +--R 3b x + 3a b +--R Type: Expression(Integer) +--E 722 + +--S 723 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 4 4 4 3 3 2 2 2 3 4 +--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x - 3a +--R ------------------------------------------------------------------------ +--R 6 5 +--R 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 723 + +--S 724 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 724 + +--S 725 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 725 + +)clear all + +--S 726 of 3330 +t0000:=x^3/(a+b*x)^2 +--R +--R +--R 3 +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 726 + +--S 727 of 3330 +r0000:=-2*a*x/b^3+1/2*x^2/b^2+a^3/(b^4*(a+b*x))+3*a^2*log(a+b*x)/b^4 +--R +--R +--R 2 3 3 3 2 2 2 3 +--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a +--R (2) ---------------------------------------------------------- +--R 5 4 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 727 + +--S 728 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 3 3 2 2 2 3 +--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a +--R (3) ---------------------------------------------------------- +--R 5 4 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 728 + +--S 729 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 729 + +--S 730 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 730 + +)clear all + +--S 731 of 3330 +t0000:=x^2/(a+b*x)^2 +--R +--R +--R 2 +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 731 + +--S 732 of 3330 +r0000:=x/b^2-a^2/(b^3*(a+b*x))-2*a*log(a+b*x)/b^3 +--R +--R +--R 2 2 2 2 +--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a +--R (2) ------------------------------------------------ +--R 4 3 +--R b x + a b +--R Type: Expression(Integer) +--E 732 + +--S 733 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 +--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a +--R (3) ------------------------------------------------ +--R 4 3 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 733 + +--S 734 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 734 + +--S 735 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 735 + +)clear all + +--S 736 of 3330 +t0000:=x/(a+b*x)^2 +--R +--R +--R x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 736 + +--S 737 of 3330 +r0000:=a/(b^2*(a+b*x))+log(a+b*x)/b^2 +--R +--R +--R (b x + a)log(b x + a) + a +--R (2) ------------------------- +--R 3 2 +--R b x + a b +--R Type: Expression(Integer) +--E 737 + +--S 738 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (b x + a)log(b x + a) + a +--R (3) ------------------------- +--R 3 2 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 738 + +--S 739 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 739 + +--S 740 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 740 + +)clear all + +--S 741 of 3330 +t0000:=1/(a+b*x)^2 +--R +--R +--R 1 +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 741 + +--S 742 of 3330 +r0000:=(-1)/(b*(a+b*x)) +--R +--R +--R 1 +--R (2) - --------- +--R 2 +--R b x + a b +--R Type: Fraction(Polynomial(Integer)) +--E 742 + +--S 743 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - --------- +--R 2 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 743 + +--S 744 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 744 + +--S 745 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 745 + +)clear all + +--S 746 of 3330 +t0000:=1/(x*(a+b*x)^2) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 3 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 746 + +--S 747 of 3330 +r0000:=1/(a*(a+b*x))+log(x)/a^2-log(a+b*x)/a^2 +--R +--R +--R (- b x - a)log(b x + a) + (b x + a)log(x) + a +--R (2) --------------------------------------------- +--R 2 3 +--R a b x + a +--R Type: Expression(Integer) +--E 747 + +--S 748 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (- b x - a)log(b x + a) + (b x + a)log(x) + a +--R (3) --------------------------------------------- +--R 2 3 +--R a b x + a +--R Type: Union(Expression(Integer),...) +--E 748 + +--S 749 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 749 + +--S 750 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 3330 +t0000:=1/(x^2*(a+b*x)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 4 3 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 751 + +--S 752 of 3330 +r0000:=(-1)/(a^2*x)-b/(a^2*(a+b*x))-2*b*log(x)/a^3+2*b*log(a+b*x)/a^3 +--R +--R +--R 2 2 2 2 2 +--R (2b x + 2a b x)log(b x + a) + (- 2b x - 2a b x)log(x) - 2a b x - a +--R (2) --------------------------------------------------------------------- +--R 3 2 4 +--R a b x + a x +--R Type: Expression(Integer) +--E 752 + +--S 753 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 2 +--R (2b x + 2a b x)log(b x + a) + (- 2b x - 2a b x)log(x) - 2a b x - a +--R (3) --------------------------------------------------------------------- +--R 3 2 4 +--R a b x + a x +--R Type: Union(Expression(Integer),...) +--E 753 + +--S 754 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 754 + +--S 755 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 755 + +)clear all + +--S 756 of 3330 +t0000:=1/(x^3*(a+b*x)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 5 4 2 3 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 756 + +--S 757 of 3330 +r0000:=(-1/2)/(a^2*x^2)+2*b/(a^3*x)+b^2/(a^3*(a+b*x))+_ + 3*b^2*log(x)/a^4-3*b^2*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 3 3 2 2 3 3 2 2 2 2 +--R (- 6b x - 6a b x )log(b x + a) + (6b x + 6a b x )log(x) + 6a b x +--R + +--R 2 3 +--R 3a b x - a +--R / +--R 4 3 5 2 +--R 2a b x + 2a x +--R Type: Expression(Integer) +--E 757 + +--S 758 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 3 3 2 2 2 2 +--R (- 6b x - 6a b x )log(b x + a) + (6b x + 6a b x )log(x) + 6a b x +--R + +--R 2 3 +--R 3a b x - a +--R / +--R 4 3 5 2 +--R 2a b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 758 + +--S 759 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 759 + +--S 760 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 760 + +)clear all + +--S 761 of 3330 +t0000:=1/(x^4*(a+b*x)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 6 5 2 4 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 761 + +--S 762 of 3330 +r0000:=(-1/3)/(a^2*x^3)+b/(a^3*x^2)-3*b^2/(a^4*x)-b^3/(a^4*(a+b*x))-_ + 4*b^3*log(x)/a^5+4*b^3*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 4 4 3 3 4 4 3 3 3 3 +--R (12b x + 12a b x )log(b x + a) + (- 12b x - 12a b x )log(x) - 12a b x +--R + +--R 2 2 2 3 4 +--R - 6a b x + 2a b x - a +--R / +--R 5 4 6 3 +--R 3a b x + 3a x +--R Type: Expression(Integer) +--E 762 + +--S 763 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 3 3 4 4 3 3 3 3 +--R (12b x + 12a b x )log(b x + a) + (- 12b x - 12a b x )log(x) - 12a b x +--R + +--R 2 2 2 3 4 +--R - 6a b x + 2a b x - a +--R / +--R 5 4 6 3 +--R 3a b x + 3a x +--R Type: Union(Expression(Integer),...) +--E 763 + +--S 764 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 764 + +--S 765 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 765 + +)clear all + +--S 766 of 3330 +t0000:=1/(x^5*(a+b*x)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 7 6 2 5 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 766 + +--S 767 of 3330 +r0000:=(-1/4)/(a^2*x^4)+2/3*b/(a^3*x^3)-3/2*b^2/(a^4*x^2)+4*b^3/(a^5*x)+_ + b^4/(a^5*(a+b*x))+5*b^4*log(x)/a^6-5*b^4*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 5 5 4 4 5 5 4 4 4 4 +--R (- 60b x - 60a b x )log(b x + a) + (60b x + 60a b x )log(x) + 60a b x +--R + +--R 2 3 3 3 2 2 4 5 +--R 30a b x - 10a b x + 5a b x - 3a +--R / +--R 6 5 7 4 +--R 12a b x + 12a x +--R Type: Expression(Integer) +--E 767 + +--S 768 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 4 4 5 5 4 4 4 4 +--R (- 60b x - 60a b x )log(b x + a) + (60b x + 60a b x )log(x) + 60a b x +--R + +--R 2 3 3 3 2 2 4 5 +--R 30a b x - 10a b x + 5a b x - 3a +--R / +--R 6 5 7 4 +--R 12a b x + 12a x +--R Type: Union(Expression(Integer),...) +--E 768 + +--S 769 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 770 + +)clear all + +--S 771 of 3330 +t0000:=x^m/(a+b*x)^3 +--R +--R +--R m +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 771 + +--S 772 of 3330 +--r0000:=1/2*x^(1+m)/(a*(a+b*x)^2)+1/2*(1-m)*x^(1+m)/(a^2*(a+b*x))-_ +-- 1/2*(1-m)*m*x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a^3*(1+m)) +--E 772 + +--S 773 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | ------------------------------- d%N +--R ++ 3 3 2 2 2 3 +--R %N b + 3%N a b + 3%N a b + a +--R Type: Union(Expression(Integer),...) +--E 773 + +--S 774 of 3330 +--m0000:=a0000 - r0000 +--E 774 + +--S 775 of 3330 +--d0000:=D(m0000,x) +--E 775 + +)clear all + +--S 776 of 3330 +t0000:=x^7/(a+b*x)^3 +--R +--R +--R 7 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 776 + +--S 777 of 3330 +r0000:=15*a^4*x/b^7-5*a^3*x^2/b^6+2*a^2*x^3/b^5-3/4*a*x^4/b^4+1/5*x^5/b^3+_ + 1/2*a^7/(b^8*(a+b*x)^2)-7*a^6/(b^8*(a+b*x))-21*a^5*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 5 2 2 6 7 7 7 6 6 2 5 5 +--R (- 420a b x - 840a b x - 420a )log(b x + a) + 4b x - 7a b x + 14a b x +--R + +--R 3 4 4 4 3 3 5 2 2 6 7 +--R - 35a b x + 140a b x + 500a b x + 160a b x - 130a +--R / +--R 10 2 9 2 8 +--R 20b x + 40a b x + 20a b +--R Type: Expression(Integer) +--E 777 + +--S 778 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 2 2 6 7 7 7 6 6 2 5 5 +--R (- 420a b x - 840a b x - 420a )log(b x + a) + 4b x - 7a b x + 14a b x +--R + +--R 3 4 4 4 3 3 5 2 2 6 7 +--R - 35a b x + 140a b x + 500a b x + 160a b x - 130a +--R / +--R 10 2 9 2 8 +--R 20b x + 40a b x + 20a b +--R Type: Union(Expression(Integer),...) +--E 778 + +--S 779 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 779 + +--S 780 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 780 + +)clear all + +--S 781 of 3330 +t0000:=x^6/(a+b*x)^3 +--R +--R +--R 6 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 781 + +--S 782 of 3330 +r0000:=-10*a^3*x/b^6+3*a^2*x^2/b^5-a*x^3/b^4+1/4*x^4/b^3-_ + 1/2*a^6/(b^7*(a+b*x)^2)+6*a^5/(b^7*(a+b*x))+15*a^4*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 4 2 2 5 6 6 6 5 5 2 4 4 +--R (60a b x + 120a b x + 60a )log(b x + a) + b x - 2a b x + 5a b x +--R + +--R 3 3 3 4 2 2 5 6 +--R - 20a b x - 68a b x - 16a b x + 22a +--R / +--R 9 2 8 2 7 +--R 4b x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 782 + +--S 783 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 2 2 5 6 6 6 5 5 2 4 4 +--R (60a b x + 120a b x + 60a )log(b x + a) + b x - 2a b x + 5a b x +--R + +--R 3 3 3 4 2 2 5 6 +--R - 20a b x - 68a b x - 16a b x + 22a +--R / +--R 9 2 8 2 7 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 783 + +--S 784 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 784 + +--S 785 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 785 + +)clear all + +--S 786 of 3330 +t0000:=x^5/(a+b*x)^3 +--R +--R +--R 5 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 786 + +--S 787 of 3330 +r0000:=6*a^2*x/b^5-3/2*a*x^2/b^4+1/3*x^3/b^3+1/2*a^5/(b^6*(a+b*x)^2)-_ + 5*a^4/(b^6*(a+b*x))-10*a^3*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 3 2 2 4 5 5 5 4 4 2 3 3 +--R (- 60a b x - 120a b x - 60a )log(b x + a) + 2b x - 5a b x + 20a b x +--R + +--R 3 2 2 4 5 +--R 63a b x + 6a b x - 27a +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Expression(Integer) +--E 787 + +--S 788 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 4 5 5 5 4 4 2 3 3 +--R (- 60a b x - 120a b x - 60a )log(b x + a) + 2b x - 5a b x + 20a b x +--R + +--R 3 2 2 4 5 +--R 63a b x + 6a b x - 27a +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 788 + +--S 789 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 789 + +--S 790 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 790 + +)clear all + +--S 791 of 3330 +t0000:=x^4/(a+b*x)^3 +--R +--R +--R 4 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 791 + +--S 792 of 3330 +r0000:=-3*a*x/b^4+1/2*x^2/b^3-1/2*a^4/(b^5*(a+b*x)^2)+4*a^3/(b^5*(a+b*x))+_ + 6*a^2*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 2 2 2 3 4 4 4 3 3 2 2 2 +--R (12a b x + 24a b x + 12a )log(b x + a) + b x - 4a b x - 11a b x +--R + +--R 3 4 +--R 2a b x + 7a +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 792 + +--S 793 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 3 4 4 4 3 3 2 2 2 +--R (12a b x + 24a b x + 12a )log(b x + a) + b x - 4a b x - 11a b x +--R + +--R 3 4 +--R 2a b x + 7a +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 793 + +--S 794 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 794 + +--S 795 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 795 + +)clear all + +--S 796 of 3330 +t0000:=x^3/(a+b*x)^3 +--R +--R +--R 3 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 796 + +--S 797 of 3330 +r0000:=x/b^3+1/2*a^3/(b^4*(a+b*x)^2)-3*a^2/(b^4*(a+b*x))-3*a*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 3 3 2 2 2 3 +--R (- 6a b x - 12a b x - 6a )log(b x + a) + 2b x + 4a b x - 4a b x - 5a +--R ------------------------------------------------------------------------ +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 797 + +--S 798 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 3 3 3 2 2 2 3 +--R (- 6a b x - 12a b x - 6a )log(b x + a) + 2b x + 4a b x - 4a b x - 5a +--R ------------------------------------------------------------------------ +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 798 + +--S 799 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 799 + +--S 800 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 800 + +)clear all + +--S 801 of 3330 +t0000:=x^2/(a+b*x)^3 +--R +--R +--R 2 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 801 + +--S 802 of 3330 +r0000:=-1/2*a^2/(b^3*(a+b*x)^2)+2*a/(b^3*(a+b*x))+log(a+b*x)/b^3 +--R +--R +--R 2 2 2 2 +--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (2) ------------------------------------------------- +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 802 + +--S 803 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 +--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (3) ------------------------------------------------- +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 803 + +--S 804 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 804 + +--S 805 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 805 + +)clear all + +--S 806 of 3330 +t0000:=x/(a+b*x)^3 +--R +--R +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 806 + +--S 807 of 3330 +r0000:=1/2*x^2/(a*(a+b*x)^2) +--R +--R +--R 1 2 +--R - x +--R 2 +--R (2) -------------------- +--R 2 2 2 3 +--R a b x + 2a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 807 + +--S 808 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 2b x - a +--R (3) ---------------------- +--R 4 2 3 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 808 + +--S 809 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ----- +--R 2 +--R 2a b +--R Type: Expression(Integer) +--E 809 + +--S 810 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 810 + +)clear all + +--S 811 of 3330 +t0000:=1/(a+b*x)^3 +--R +--R +--R 1 +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 811 + +--S 812 of 3330 +r0000:=(-1/2)/(b*(a+b*x)^2) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - ------------------- +--R 3 2 2 2 +--R b x + 2a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 812 + +--S 813 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - --------------------- +--R 3 2 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 813 + +--S 814 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 814 + +--S 815 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 815 + +)clear all + +--S 816 of 3330 +t0000:=1/(x*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 4 2 3 2 2 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 816 + +--S 817 of 3330 +r0000:=1/2/(a*(a+b*x)^2)+1/(a^2*(a+b*x))+log(x)/a^3-log(a+b*x)/a^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (- 2b x - 4a b x - 2a )log(b x + a) + (2b x + 4a b x + 2a )log(x) +--R + +--R 2 +--R 2a b x + 3a +--R / +--R 3 2 2 4 5 +--R 2a b x + 4a b x + 2a +--R Type: Expression(Integer) +--E 817 + +--S 818 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R (- 2b x - 4a b x - 2a )log(b x + a) + (2b x + 4a b x + 2a )log(x) +--R + +--R 2 +--R 2a b x + 3a +--R / +--R 3 2 2 4 5 +--R 2a b x + 4a b x + 2a +--R Type: Union(Expression(Integer),...) +--E 818 + +--S 819 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 819 + +--S 820 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 820 + +)clear all + +--S 821 of 3330 +t0000:=1/(x^2*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 5 2 4 2 3 3 2 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 821 + +--S 822 of 3330 +r0000:=(-1)/(a^3*x)-1/2*b/(a^2*(a+b*x)^2)-2*b/(a^3*(a+b*x))-_ + 3*b*log(x)/a^4+3*b*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 3 3 2 2 2 +--R (6b x + 12a b x + 6a b x)log(b x + a) +--R + +--R 3 3 2 2 2 2 2 2 3 +--R (- 6b x - 12a b x - 6a b x)log(x) - 6a b x - 9a b x - 2a +--R / +--R 4 2 3 5 2 6 +--R 2a b x + 4a b x + 2a x +--R Type: Expression(Integer) +--E 822 + +--S 823 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 +--R (6b x + 12a b x + 6a b x)log(b x + a) +--R + +--R 3 3 2 2 2 2 2 2 3 +--R (- 6b x - 12a b x - 6a b x)log(x) - 6a b x - 9a b x - 2a +--R / +--R 4 2 3 5 2 6 +--R 2a b x + 4a b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 823 + +--S 824 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 824 + +--S 825 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +)clear all + +--S 826 of 3330 +t0000:=1/(x^3*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 826 + +--S 827 of 3330 +r0000:=(-1/2)/(a^3*x^2)+3*b/(a^4*x)+1/2*b^2/(a^3*(a+b*x)^2)+_ + 3*b^2/(a^4*(a+b*x))+6*b^2*log(x)/a^5-6*b^2*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 +--R (- 12b x - 24a b x - 12a b x )log(b x + a) +--R + +--R 4 4 3 3 2 2 2 3 3 2 2 2 3 4 +--R (12b x + 24a b x + 12a b x )log(x) + 12a b x + 18a b x + 4a b x - a +--R / +--R 5 2 4 6 3 7 2 +--R 2a b x + 4a b x + 2a x +--R Type: Expression(Integer) +--E 827 + +--S 828 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 +--R (- 12b x - 24a b x - 12a b x )log(b x + a) +--R + +--R 4 4 3 3 2 2 2 3 3 2 2 2 3 4 +--R (12b x + 24a b x + 12a b x )log(x) + 12a b x + 18a b x + 4a b x - a +--R / +--R 5 2 4 6 3 7 2 +--R 2a b x + 4a b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 828 + +--S 829 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 829 + +--S 830 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 830 + +)clear all + +--S 831 of 3330 +t0000:=1/(x^4*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 7 2 6 2 5 3 4 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 831 + +--S 832 of 3330 +r0000:=(-1/3)/(a^3*x^3)+3/2*b/(a^4*x^2)-6*b^2/(a^5*x)-1/2*b^3/(a^4*(a+b*x)^2)-_ + 4*b^3/(a^5*(a+b*x))-10*b^3*log(x)/a^6+10*b^3*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 5 5 4 4 2 3 3 +--R (60b x + 120a b x + 60a b x )log(b x + a) +--R + +--R 5 5 4 4 2 3 3 4 4 2 3 3 3 2 2 +--R (- 60b x - 120a b x - 60a b x )log(x) - 60a b x - 90a b x - 20a b x +--R + +--R 4 5 +--R 5a b x - 2a +--R / +--R 6 2 5 7 4 8 3 +--R 6a b x + 12a b x + 6a x +--R Type: Expression(Integer) +--E 832 + +--S 833 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 +--R (60b x + 120a b x + 60a b x )log(b x + a) +--R + +--R 5 5 4 4 2 3 3 4 4 2 3 3 3 2 2 +--R (- 60b x - 120a b x - 60a b x )log(x) - 60a b x - 90a b x - 20a b x +--R + +--R 4 5 +--R 5a b x - 2a +--R / +--R 6 2 5 7 4 8 3 +--R 6a b x + 12a b x + 6a x +--R Type: Union(Expression(Integer),...) +--E 833 + +--S 834 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 834 + +--S 835 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 835 + +)clear all + +--S 836 of 3330 +t0000:=1/(x^5*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 8 2 7 2 6 3 5 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 836 + +--S 837 of 3330 +r0000:=(-1/4)/(a^3*x^4)+b/(a^4*x^3)-3*b^2/(a^5*x^2)+10*b^3/(a^6*x)+_ + 1/2*b^4/(a^5*(a+b*x)^2)+5*b^4/(a^6*(a+b*x))+_ + 15*b^4*log(x)/a^7-15*b^4*log(a+b*x)/a^7 +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 +--R (- 60b x - 120a b x - 60a b x )log(b x + a) +--R + +--R 6 6 5 5 2 4 4 5 5 2 4 4 3 3 3 +--R (60b x + 120a b x + 60a b x )log(x) + 60a b x + 90a b x + 20a b x +--R + +--R 4 2 2 5 6 +--R - 5a b x + 2a b x - a +--R / +--R 7 2 6 8 5 9 4 +--R 4a b x + 8a b x + 4a x +--R Type: Expression(Integer) +--E 837 + +--S 838 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 +--R (- 60b x - 120a b x - 60a b x )log(b x + a) +--R + +--R 6 6 5 5 2 4 4 5 5 2 4 4 3 3 3 +--R (60b x + 120a b x + 60a b x )log(x) + 60a b x + 90a b x + 20a b x +--R + +--R 4 2 2 5 6 +--R - 5a b x + 2a b x - a +--R / +--R 7 2 6 8 5 9 4 +--R 4a b x + 8a b x + 4a x +--R Type: Union(Expression(Integer),...) +--E 838 + +--S 839 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 839 + +--S 840 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 840 + +)clear all + +--S 841 of 3330 +t0000:=x^8/(a+b*x)^4 +--R +--R +--R 8 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 841 + +--S 842 of 3330 +r0000:=35*a^4*x/b^8-10*a^3*x^2/b^7+10/3*a^2*x^3/b^6-a*x^4/b^5+_ + 1/5*x^5/b^4-1/3*a^8/(b^9*(a+b*x)^3)+4*a^7/(b^9*(a+b*x)^2)-_ + 28*a^6/(b^9*(a+b*x))-56*a^5*log(a+b*x)/b^9 +--R +--R +--R (2) +--R 5 3 3 6 2 2 7 8 8 8 +--R (- 840a b x - 2520a b x - 2520a b x - 840a )log(b x + a) + 3b x +--R + +--R 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R - 6a b x + 14a b x - 42a b x + 210a b x + 1175a b x + 1005a b x +--R + +--R 7 8 +--R - 255a b x - 365a +--R / +--R 12 3 11 2 2 10 3 9 +--R 15b x + 45a b x + 45a b x + 15a b +--R Type: Expression(Integer) +--E 842 + +--S 843 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 3 3 6 2 2 7 8 8 8 +--R (- 840a b x - 2520a b x - 2520a b x - 840a )log(b x + a) + 3b x +--R + +--R 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R - 6a b x + 14a b x - 42a b x + 210a b x + 1175a b x + 1005a b x +--R + +--R 7 8 +--R - 255a b x - 365a +--R / +--R 12 3 11 2 2 10 3 9 +--R 15b x + 45a b x + 45a b x + 15a b +--R Type: Union(Expression(Integer),...) +--E 843 + +--S 844 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 844 + +--S 845 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 845 + +)clear all + +--S 846 of 3330 +t0000:=x^7/(a+b*x)^4 +--R +--R +--R 7 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 846 + +--S 847 of 3330 +r0000:=-20*a^3*x/b^7+5*a^2*x^2/b^6-4/3*a*x^3/b^5+1/4*x^4/b^4+_ + 1/3*a^7/(b^8*(a+b*x)^3)-7/2*a^6/(b^8*(a+b*x)^2)+_ + 21*a^5/(b^8*(a+b*x))+35*a^4*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 4 3 3 5 2 2 6 7 7 7 +--R (420a b x + 1260a b x + 1260a b x + 420a )log(b x + a) + 3b x +--R + +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - 7a b x + 21a b x - 105a b x - 556a b x - 408a b x + 222a b x + 214a +--R / +--R 11 3 10 2 2 9 3 8 +--R 12b x + 36a b x + 36a b x + 12a b +--R Type: Expression(Integer) +--E 847 + +--S 848 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 3 5 2 2 6 7 7 7 +--R (420a b x + 1260a b x + 1260a b x + 420a )log(b x + a) + 3b x +--R + +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - 7a b x + 21a b x - 105a b x - 556a b x - 408a b x + 222a b x + 214a +--R / +--R 11 3 10 2 2 9 3 8 +--R 12b x + 36a b x + 36a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 848 + +--S 849 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 849 + +--S 850 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 850 + +)clear all + +--S 851 of 3330 +t0000:=x^6/(a+b*x)^4 +--R +--R +--R 6 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 851 + +--S 852 of 3330 +r0000:=10*a^2*x/b^6-2*a*x^2/b^5+1/3*x^3/b^4-1/3*a^6/(b^7*(a+b*x)^3)+_ + 3*a^5/(b^7*(a+b*x)^2)-15*a^4/(b^7*(a+b*x))-20*a^3*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 3 3 3 4 2 2 5 6 6 6 5 5 +--R (- 60a b x - 180a b x - 180a b x - 60a )log(b x + a) + b x - 3a b x +--R + +--R 2 4 4 3 3 3 4 2 2 5 6 +--R 15a b x + 73a b x + 39a b x - 51a b x - 37a +--R / +--R 10 3 9 2 2 8 3 7 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Expression(Integer) +--E 852 + +--S 853 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 4 2 2 5 6 6 6 5 5 +--R (- 60a b x - 180a b x - 180a b x - 60a )log(b x + a) + b x - 3a b x +--R + +--R 2 4 4 3 3 3 4 2 2 5 6 +--R 15a b x + 73a b x + 39a b x - 51a b x - 37a +--R / +--R 10 3 9 2 2 8 3 7 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 853 + +--S 854 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 854 + +--S 855 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 855 + +)clear all + +--S 856 of 3330 +t0000:=x^5/(a+b*x)^4 +--R +--R +--R 5 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 856 + +--S 857 of 3330 +r0000:=-4*a*x/b^5+1/2*x^2/b^4+1/3*a^5/(b^6*(a+b*x)^3)-_ + 5/2*a^4/(b^6*(a+b*x)^2)+10*a^3/(b^6*(a+b*x))+10*a^2*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 2 3 3 3 2 2 4 5 5 5 4 4 +--R (60a b x + 180a b x + 180a b x + 60a )log(b x + a) + 3b x - 15a b x +--R + +--R 2 3 3 3 2 2 4 5 +--R - 63a b x - 9a b x + 81a b x + 47a +--R / +--R 9 3 8 2 2 7 3 6 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Expression(Integer) +--E 857 + +--S 858 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 3 3 3 2 2 4 5 5 5 4 4 +--R (60a b x + 180a b x + 180a b x + 60a )log(b x + a) + 3b x - 15a b x +--R + +--R 2 3 3 3 2 2 4 5 +--R - 63a b x - 9a b x + 81a b x + 47a +--R / +--R 9 3 8 2 2 7 3 6 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 858 + +--S 859 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 859 + +--S 860 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 860 + +)clear all + +--S 861 of 3330 +t0000:=x^4/(a+b*x)^4 +--R +--R +--R 4 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 861 + +--S 862 of 3330 +r0000:=x/b^4-1/3*a^4/(b^5*(a+b*x)^3)+2*a^3/(b^5*(a+b*x)^2)-_ + 6*a^2/(b^5*(a+b*x))-4*a*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 3 3 2 2 2 3 4 4 4 3 3 +--R (- 12a b x - 36a b x - 36a b x - 12a )log(b x + a) + 3b x + 9a b x +--R + +--R 2 2 2 3 4 +--R - 9a b x - 27a b x - 13a +--R / +--R 8 3 7 2 2 6 3 5 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Expression(Integer) +--E 862 + +--S 863 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 4 4 4 3 3 +--R (- 12a b x - 36a b x - 36a b x - 12a )log(b x + a) + 3b x + 9a b x +--R + +--R 2 2 2 3 4 +--R - 9a b x - 27a b x - 13a +--R / +--R 8 3 7 2 2 6 3 5 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 863 + +--S 864 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 864 + +--S 865 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 865 + +)clear all + +--S 866 of 3330 +t0000:=x^3/(a+b*x)^4 +--R +--R +--R 3 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 866 + +--S 867 of 3330 +r0000:=1/3*a^3/(b^4*(a+b*x)^3)-3/2*a^2/(b^4*(a+b*x)^2)+_ + 3*a/(b^4*(a+b*x))+log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 2 2 3 +--R (6b x + 18a b x + 18a b x + 6a )log(b x + a) + 18a b x + 27a b x + 11a +--R -------------------------------------------------------------------------- +--R 7 3 6 2 2 5 3 4 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Expression(Integer) +--E 867 + +--S 868 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 2 2 2 3 +--R (6b x + 18a b x + 18a b x + 6a )log(b x + a) + 18a b x + 27a b x + 11a +--R -------------------------------------------------------------------------- +--R 7 3 6 2 2 5 3 4 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 868 + +--S 869 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 869 + +--S 870 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 870 + +)clear all + +--S 871 of 3330 +t0000:=x^2/(a+b*x)^4 +--R +--R +--R 2 +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 871 + +--S 872 of 3330 +r0000:=1/3*x^3/(a*(a+b*x)^3) +--R +--R +--R 1 3 +--R - x +--R 3 +--R (2) ------------------------------ +--R 3 3 2 2 2 3 4 +--R a b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 872 + +--S 873 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 3b x - 3a b x - a +--R (3) -------------------------------- +--R 6 3 5 2 2 4 3 3 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 873 + +--S 874 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ----- +--R 3 +--R 3a b +--R Type: Expression(Integer) +--E 874 + +--S 875 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 875 + +)clear all + +--S 876 of 3330 +t0000:=x/(a+b*x)^4 +--R +--R +--R x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 876 + +--S 877 of 3330 +r0000:=1/3*a/(b^2*(a+b*x)^3)+(-1/2)/(b^2*(a+b*x)^2) +--R +--R +--R 1 1 +--R - - b x - - a +--R 2 6 +--R (2) ------------------------------ +--R 5 3 4 2 2 3 3 2 +--R b x + 3a b x + 3a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 877 + +--S 878 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 3b x - a +--R (3) ---------------------------------- +--R 5 3 4 2 2 3 3 2 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 878 + +--S 879 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 879 + +--S 880 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 880 + +)clear all + +--S 881 of 3330 +t0000:=1/(a+b*x)^4 +--R +--R +--R 1 +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 881 + +--S 882 of 3330 +r0000:=(-1/3)/(b*(a+b*x)^3) +--R +--R +--R 1 +--R - +--R 3 +--R (2) - ----------------------------- +--R 4 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 882 + +--S 883 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - ------------------------------- +--R 4 3 3 2 2 2 3 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 883 + +--S 884 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 884 + +--S 885 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 885 + +)clear all + +--S 886 of 3330 +t0000:=1/(x*(a+b*x)^4) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 4 5 3 4 2 2 3 3 2 4 +--R b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 886 + +--S 887 of 3330 +r0000:=1/3/(a*(a+b*x)^3)+1/2/(a^2*(a+b*x)^2)+1/(a^3*(a+b*x))+log(x)/a^4-_ + log(a+b*x)/a^4 +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (- 6b x - 18a b x - 18a b x - 6a )log(b x + a) +--R + +--R 3 3 2 2 2 3 2 2 2 3 +--R (6b x + 18a b x + 18a b x + 6a )log(x) + 6a b x + 15a b x + 11a +--R / +--R 4 3 3 5 2 2 6 7 +--R 6a b x + 18a b x + 18a b x + 6a +--R Type: Expression(Integer) +--E 887 + +--S 888 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (- 6b x - 18a b x - 18a b x - 6a )log(b x + a) +--R + +--R 3 3 2 2 2 3 2 2 2 3 +--R (6b x + 18a b x + 18a b x + 6a )log(x) + 6a b x + 15a b x + 11a +--R / +--R 4 3 3 5 2 2 6 7 +--R 6a b x + 18a b x + 18a b x + 6a +--R Type: Union(Expression(Integer),...) +--E 888 + +--S 889 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 889 + +--S 890 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 890 + +)clear all + +--S 891 of 3330 +t0000:=1/(x^2*(a+b*x)^4) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 4 6 3 5 2 2 4 3 3 4 2 +--R b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 891 + +--S 892 of 3330 +r0000:=(-1)/(a^4*x)-1/3*b/(a^2*(a+b*x)^3)-b/(a^3*(a+b*x)^2)-_ + 3*b/(a^4*(a+b*x))-4*b*log(x)/a^5+4*b*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 3 +--R (12b x + 36a b x + 36a b x + 12a b x)log(b x + a) +--R + +--R 4 4 3 3 2 2 2 3 3 3 2 2 2 +--R (- 12b x - 36a b x - 36a b x - 12a b x)log(x) - 12a b x - 30a b x +--R + +--R 3 4 +--R - 22a b x - 3a +--R / +--R 5 3 4 6 2 3 7 2 8 +--R 3a b x + 9a b x + 9a b x + 3a x +--R Type: Expression(Integer) +--E 892 + +--S 893 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 3 +--R (12b x + 36a b x + 36a b x + 12a b x)log(b x + a) +--R + +--R 4 4 3 3 2 2 2 3 3 3 2 2 2 +--R (- 12b x - 36a b x - 36a b x - 12a b x)log(x) - 12a b x - 30a b x +--R + +--R 3 4 +--R - 22a b x - 3a +--R / +--R 5 3 4 6 2 3 7 2 8 +--R 3a b x + 9a b x + 9a b x + 3a x +--R Type: Union(Expression(Integer),...) +--E 893 + +--S 894 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 894 + +--S 895 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 895 + +)clear all + +--S 896 of 3330 +t0000:=1/(x^3*(a+b*x)^4) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 4 7 3 6 2 2 5 3 4 4 3 +--R b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 896 + +--S 897 of 3330 +r0000:=(-1/2)/(a^4*x^2)+4*b/(a^5*x)+1/3*b^2/(a^3*(a+b*x)^3)+_ + 3/2*b^2/(a^4*(a+b*x)^2)+6*b^2/(a^5*(a+b*x))+_ + 10*b^2*log(x)/a^6-10*b^2*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 5 5 4 4 2 3 3 3 2 2 +--R (- 60b x - 180a b x - 180a b x - 60a b x )log(b x + a) +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 4 2 3 3 +--R (60b x + 180a b x + 180a b x + 60a b x )log(x) + 60a b x + 150a b x +--R + +--R 3 2 2 4 5 +--R 110a b x + 15a b x - 3a +--R / +--R 6 3 5 7 2 4 8 3 9 2 +--R 6a b x + 18a b x + 18a b x + 6a x +--R Type: Expression(Integer) +--E 897 + +--S 898 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 +--R (- 60b x - 180a b x - 180a b x - 60a b x )log(b x + a) +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 4 2 3 3 +--R (60b x + 180a b x + 180a b x + 60a b x )log(x) + 60a b x + 150a b x +--R + +--R 3 2 2 4 5 +--R 110a b x + 15a b x - 3a +--R / +--R 6 3 5 7 2 4 8 3 9 2 +--R 6a b x + 18a b x + 18a b x + 6a x +--R Type: Union(Expression(Integer),...) +--E 898 + +--S 899 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 899 + +--S 900 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 900 + +)clear all + +--S 901 of 3330 +t0000:=1/(x^4*(a+b*x)^4) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 4 8 3 7 2 2 6 3 5 4 4 +--R b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 901 + +--S 902 of 3330 +r0000:=(-1/3)/(a^4*x^3)+2*b/(a^5*x^2)-10*b^2/(a^6*x)-_ + 1/3*b^3/(a^4*(a+b*x)^3)-2*b^3/(a^5*(a+b*x)^2)-_ + 10*b^3/(a^6*(a+b*x))-20*b^3*log(x)/a^7+20*b^3*log(a+b*x)/a^7 +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 +--R (60b x + 180a b x + 180a b x + 60a b x )log(b x + a) +--R + +--R 6 6 5 5 2 4 4 3 3 3 5 5 +--R (- 60b x - 180a b x - 180a b x - 60a b x )log(x) - 60a b x +--R + +--R 2 4 4 3 3 3 4 2 2 5 6 +--R - 150a b x - 110a b x - 15a b x + 3a b x - a +--R / +--R 7 3 6 8 2 5 9 4 10 3 +--R 3a b x + 9a b x + 9a b x + 3a x +--R Type: Expression(Integer) +--E 902 + +--S 903 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 +--R (60b x + 180a b x + 180a b x + 60a b x )log(b x + a) +--R + +--R 6 6 5 5 2 4 4 3 3 3 5 5 +--R (- 60b x - 180a b x - 180a b x - 60a b x )log(x) - 60a b x +--R + +--R 2 4 4 3 3 3 4 2 2 5 6 +--R - 150a b x - 110a b x - 15a b x + 3a b x - a +--R / +--R 7 3 6 8 2 5 9 4 10 3 +--R 3a b x + 9a b x + 9a b x + 3a x +--R Type: Union(Expression(Integer),...) +--E 903 + +--S 904 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 904 + +--S 905 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 905 + +)clear all + +--S 906 of 3330 +t0000:=1/(x^5*(a+b*x)^4) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 4 9 3 8 2 2 7 3 6 4 5 +--R b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 906 + +--S 907 of 3330 +r0000:=(-1/4)/(a^4*x^4)+4/3*b/(a^5*x^3)-5*b^2/(a^6*x^2)+20*b^3/(a^7*x)+_ + 1/3*b^4/(a^5*(a+b*x)^3)+5/2*b^4/(a^6*(a+b*x)^2)+15*b^4/(a^7*(a+b*x))+_ + 35*b^4*log(x)/a^8-35*b^4*log(a+b*x)/a^8 +--R +--R +--R (2) +--R 7 7 6 6 2 5 5 3 4 4 +--R (- 420b x - 1260a b x - 1260a b x - 420a b x )log(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 6 6 +--R (420b x + 1260a b x + 1260a b x + 420a b x )log(x) + 420a b x +--R + +--R 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R 1050a b x + 770a b x + 105a b x - 21a b x + 7a b x - 3a +--R / +--R 8 3 7 9 2 6 10 5 11 4 +--R 12a b x + 36a b x + 36a b x + 12a x +--R Type: Expression(Integer) +--E 907 + +--S 908 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 +--R (- 420b x - 1260a b x - 1260a b x - 420a b x )log(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 6 6 +--R (420b x + 1260a b x + 1260a b x + 420a b x )log(x) + 420a b x +--R + +--R 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R 1050a b x + 770a b x + 105a b x - 21a b x + 7a b x - 3a +--R / +--R 8 3 7 9 2 6 10 5 11 4 +--R 12a b x + 36a b x + 36a b x + 12a x +--R Type: Union(Expression(Integer),...) +--E 908 + +--S 909 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 909 + +--S 910 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 910 + +)clear all + +--S 911 of 3330 +t0000:=x^10/(a+b*x)^7 +--R +--R +--R (1) +--R 10 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 911 + +--S 912 of 3330 +r0000:=-84*a^3*x/b^10+14*a^2*x^2/b^9-7/3*a*x^3/b^8+1/4*x^4/b^7-_ + 1/6*a^10/(b^11*(a+b*x)^6)+2*a^9/(b^11*(a+b*x)^5)-_ + 45/4*a^8/(b^11*(a+b*x)^4)+40*a^7/(b^11*(a+b*x)^3)-_ + 105*a^6/(b^11*(a+b*x)^2)+252*a^5/(b^11*(a+b*x))+210*a^4*log(a+b*x)/b^11 +--R +--R +--R (2) +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R 2520a b x + 15120a b x + 37800a b x + 50400a b x + 37800a b x +--R + +--R 9 10 +--R 15120a b x + 2520a +--R * +--R log(b x + a) +--R + +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R 3b x - 10a b x + 45a b x - 360a b x - 4043a b x - 9138a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R - 3945a b x + 11540a b x + 18105a b x + 10266a b x + 2131a +--R / +--R 17 6 16 5 2 15 4 3 14 3 4 13 2 5 12 +--R 12b x + 72a b x + 180a b x + 240a b x + 180a b x + 72a b x +--R + +--R 6 11 +--R 12a b +--R Type: Expression(Integer) +--E 912 + +--S 913 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 6 6 5 5 5 6 4 4 7 3 3 8 2 2 +--R 2520a b x + 15120a b x + 37800a b x + 50400a b x + 37800a b x +--R + +--R 9 10 +--R 15120a b x + 2520a +--R * +--R log(b x + a) +--R + +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R 3b x - 10a b x + 45a b x - 360a b x - 4043a b x - 9138a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R - 3945a b x + 11540a b x + 18105a b x + 10266a b x + 2131a +--R / +--R 17 6 16 5 2 15 4 3 14 3 4 13 2 5 12 +--R 12b x + 72a b x + 180a b x + 240a b x + 180a b x + 72a b x +--R + +--R 6 11 +--R 12a b +--R Type: Union(Expression(Integer),...) +--E 913 + +--S 914 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 914 + +--S 915 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 915 + +)clear all + +--S 916 of 3330 +t0000:=x^9/(a+b*x)^7 +--R +--R +--R (1) +--R 9 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 916 + +--S 917 of 3330 +r0000:=28*a^2*x/b^9-7/2*a*x^2/b^8+1/3*x^3/b^7+1/6*a^9/(b^10*(a+b*x)^6)-_ + 9/5*a^8/(b^10*(a+b*x)^5)+9*a^7/(b^10*(a+b*x)^4)-_ + 28*a^6/(b^10*(a+b*x)^3)+63*a^5/(b^10*(a+b*x)^2)-_ + 126*a^4/(b^10*(a+b*x))-84*a^3*log(a+b*x)/b^10 +--R +--R +--R (2) +--R 3 6 6 4 5 5 5 4 4 6 3 3 7 2 2 +--R - 2520a b x - 15120a b x - 37800a b x - 50400a b x - 37800a b x +--R + +--R 8 9 +--R - 15120a b x - 2520a +--R * +--R log(b x + a) +--R + +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R 10b x - 45a b x + 360a b x + 3665a b x + 6870a b x - 1725a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R - 19100a b x - 23775a b x - 12534a b x - 2509a +--R / +--R 16 6 15 5 2 14 4 3 13 3 4 12 2 5 11 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x +--R + +--R 6 10 +--R 30a b +--R Type: Expression(Integer) +--E 917 + +--S 918 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 6 6 4 5 5 5 4 4 6 3 3 7 2 2 +--R - 2520a b x - 15120a b x - 37800a b x - 50400a b x - 37800a b x +--R + +--R 8 9 +--R - 15120a b x - 2520a +--R * +--R log(b x + a) +--R + +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R 10b x - 45a b x + 360a b x + 3665a b x + 6870a b x - 1725a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R - 19100a b x - 23775a b x - 12534a b x - 2509a +--R / +--R 16 6 15 5 2 14 4 3 13 3 4 12 2 5 11 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x +--R + +--R 6 10 +--R 30a b +--R Type: Union(Expression(Integer),...) +--E 918 + +--S 919 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 919 + +--S 920 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 920 + +)clear all + +--S 921 of 3330 +t0000:=x^8/(a+b*x)^7 +--R +--R +--R (1) +--R 8 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 921 + +--S 922 of 3330 +r0000:=-7*a*x/b^8+1/2*x^2/b^7-1/6*a^8/(b^9*(a+b*x)^6)+_ + 8/5*a^7/(b^9*(a+b*x)^5)-7*a^6/(b^9*(a+b*x)^4)+_ + 56/3*a^5/(b^9*(a+b*x)^3)-35*a^4/(b^9*(a+b*x)^2)+_ + 56*a^3/(b^9*(a+b*x))+28*a^2*log(a+b*x)/b^9 +--R +--R +--R (2) +--R 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R 840a b x + 5040a b x + 12600a b x + 16800a b x + 12600a b x +--R + +--R 7 8 +--R 5040a b x + 840a +--R * +--R log(b x + a) +--R + +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R 15b x - 120a b x - 1035a b x - 1170a b x + 3375a b x + 10100a b x +--R + +--R 6 2 2 7 8 +--R 10725a b x + 5298a b x + 1023a +--R / +--R 15 6 14 5 2 13 4 3 12 3 4 11 2 5 10 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x +--R + +--R 6 9 +--R 30a b +--R Type: Expression(Integer) +--E 922 + +--S 923 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R 840a b x + 5040a b x + 12600a b x + 16800a b x + 12600a b x +--R + +--R 7 8 +--R 5040a b x + 840a +--R * +--R log(b x + a) +--R + +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R 15b x - 120a b x - 1035a b x - 1170a b x + 3375a b x + 10100a b x +--R + +--R 6 2 2 7 8 +--R 10725a b x + 5298a b x + 1023a +--R / +--R 15 6 14 5 2 13 4 3 12 3 4 11 2 5 10 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x +--R + +--R 6 9 +--R 30a b +--R Type: Union(Expression(Integer),...) +--E 923 + +--S 924 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 924 + +--S 925 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 925 + +)clear all + +--S 926 of 3330 +t0000:=x^7/(a+b*x)^7 +--R +--R +--R (1) +--R 7 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 926 + +--S 927 of 3330 +r0000:=x/b^7+1/6*a^7/(b^8*(a+b*x)^6)-7/5*a^6/(b^8*(a+b*x)^5)+_ + 21/4*a^5/(b^8*(a+b*x)^4)-35/3*a^4/(b^8*(a+b*x)^3)+_ + 35/2*a^3/(b^8*(a+b*x)^2)-21*a^2/(b^8*(a+b*x))-7*a*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 420a b x - 2520a b x - 6300a b x - 8400a b x - 6300a b x +--R + +--R 6 7 +--R - 2520a b x - 420a +--R * +--R log(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R 60b x + 360a b x - 360a b x - 4050a b x - 8200a b x - 7725a b x +--R + +--R 6 7 +--R - 3594a b x - 669a +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 8 +--R 60a b +--R Type: Expression(Integer) +--E 927 + +--S 928 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 420a b x - 2520a b x - 6300a b x - 8400a b x - 6300a b x +--R + +--R 6 7 +--R - 2520a b x - 420a +--R * +--R log(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R 60b x + 360a b x - 360a b x - 4050a b x - 8200a b x - 7725a b x +--R + +--R 6 7 +--R - 3594a b x - 669a +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 8 +--R 60a b +--R Type: Union(Expression(Integer),...) +--E 928 + +--S 929 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 929 + +--S 930 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 930 + +)clear all + +--S 931 of 3330 +t0000:=x^6/(a+b*x)^7 +--R +--R +--R (1) +--R 6 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 931 + +--S 932 of 3330 +r0000:=-1/6*a^6/(b^7*(a+b*x)^6)+6/5*a^5/(b^7*(a+b*x)^5)-_ + 15/4*a^4/(b^7*(a+b*x)^4)+20/3*a^3/(b^7*(a+b*x)^3)-_ + 15/2*a^2/(b^7*(a+b*x)^2)+6*a/(b^7*(a+b*x))+log(a+b*x)/b^7 +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 +--R 60a +--R * +--R log(b x + a) +--R + +--R 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R 360a b x + 1350a b x + 2200a b x + 1875a b x + 822a b x + 147a +--R / +--R 13 6 12 5 2 11 4 3 10 3 4 9 2 5 8 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 7 +--R 60a b +--R Type: Expression(Integer) +--E 932 + +--S 933 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 +--R 60a +--R * +--R log(b x + a) +--R + +--R 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R 360a b x + 1350a b x + 2200a b x + 1875a b x + 822a b x + 147a +--R / +--R 13 6 12 5 2 11 4 3 10 3 4 9 2 5 8 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 7 +--R 60a b +--R Type: Union(Expression(Integer),...) +--E 933 + +--S 934 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 934 + +--S 935 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 935 + +)clear all + +--S 936 of 3330 +t0000:=x^5/(a+b*x)^7 +--R +--R +--R (1) +--R 5 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 936 + +--S 937 of 3330 +r0000:=1/6*x^6/(a*(a+b*x)^6) +--R +--R +--R 1 6 +--R - x +--R 6 +--R (2) --------------------------------------------------------------- +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R a b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 937 + +--S 938 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R - 6b x - 15a b x - 20a b x - 15a b x - 6a b x - a +--R ----------------------------------------------------------------------- +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 6 6 +--R 6b x + 36a b x + 90a b x + 120a b x + 90a b x + 36a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 938 + +--S 939 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ----- +--R 6 +--R 6a b +--R Type: Expression(Integer) +--E 939 + +--S 940 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 940 + +)clear all + +--S 941 of 3330 +t0000:=x^4/(a+b*x)^7 +--R +--R +--R (1) +--R 4 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 941 + +--S 942 of 3330 +r0000:=1/6*x^5/(a*(a+b*x)^6)+1/30*x^5/(a^2*(a+b*x)^5) +--R +--R +--R 1 6 1 5 +--R -- b x + - a x +--R 30 5 +--R (2) --------------------------------------------------------------- +--R 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 7 8 +--R a b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 942 + +--S 943 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 3 4 +--R - 15b x - 20a b x - 15a b x - 6a b x - a +--R ---------------------------------------------------------------------------- +--R 11 6 10 5 2 9 4 3 8 3 4 7 2 5 6 6 5 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x + 30a b +--R Type: Union(Expression(Integer),...) +--E 943 + +--S 944 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ------ +--R 2 5 +--R 30a b +--R Type: Expression(Integer) +--E 944 + +--S 945 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 945 + +)clear all + +--S 946 of 3330 +t0000:=x^3/(a+b*x)^7 +--R +--R +--R (1) +--R 3 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 946 + +--S 947 of 3330 +r0000:=1/6*x^4/(a*(a+b*x)^6)+1/15*x^4/(a^2*(a+b*x)^5)+_ + 1/60*x^4/(a^3*(a+b*x)^4),1/6*a^3/(b^4*(a+b*x)^6)-_ + 3/5*a^2/(b^4*(a+b*x)^5)+3/4*a/(b^4*(a+b*x)^4)+(-1/3)/(b^4*(a+b*x)^3) +--R +--R +--R (2) +--R 1 2 6 1 5 1 2 4 +--R -- b x + -- a b x + - a x +--R 60 10 4 +--R [---------------------------------------------------------------, +--R 3 6 6 4 5 5 5 4 4 6 3 3 7 2 2 8 9 +--R a b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R 1 3 3 1 2 2 1 2 1 3 +--R - - b x - - a b x - -- a b x - -- a +--R 3 4 10 60 +--R ----------------------------------------------------------------] +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a b +--R Type: Tuple(Fraction(Polynomial(Fraction(Integer)))) +--E 947 + +--S 948 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R - 20b x - 15a b x - 6a b x - a +--R ---------------------------------------------------------------------------- +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x + 60a b +--R Type: Union(Expression(Integer),...) +--E 948 + +--S 949 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ------ +--R 3 4 +--R 60a b +--R Type: Expression(Integer) +--E 949 + +--S 950 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 950 + +)clear all + +--S 951 of 3330 +t0000:=x^2/(a+b*x)^7 +--R +--R +--R (1) +--R 2 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 951 + +--S 952 of 3330 +r0000:=-1/6*a^2/(b^3*(a+b*x)^6)+2/5*a/(b^3*(a+b*x)^5)+(-1/4)/(b^3*(a+b*x)^4) +--R +--R +--R 1 2 2 1 1 2 +--R - - b x - -- a b x - -- a +--R 4 10 60 +--R (2) --------------------------------------------------------------- +--R 9 6 8 5 2 7 4 3 6 3 4 5 2 5 4 6 3 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 952 + +--S 953 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 +--R - 15b x - 6a b x - a +--R --------------------------------------------------------------------------- +--R 9 6 8 5 2 7 4 3 6 3 4 5 2 5 4 6 3 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x + 60a b +--R Type: Union(Expression(Integer),...) +--E 953 + +--S 954 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 954 + +--S 955 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 955 + +)clear all + +--S 956 of 3330 +t0000:=x/(a+b*x)^7 +--R +--R +--R (1) +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 956 + +--S 957 of 3330 +r0000:=1/6*a/(b^2*(a+b*x)^6)+(-1/5)/(b^2*(a+b*x)^5) +--R +--R +--R 1 1 +--R - - b x - -- a +--R 5 30 +--R (2) --------------------------------------------------------------- +--R 8 6 7 5 2 6 4 3 5 3 4 4 2 5 3 6 2 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 957 + +--S 958 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R - 6b x - a +--R -------------------------------------------------------------------------- +--R 8 6 7 5 2 6 4 3 5 3 4 4 2 5 3 6 2 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x + 30a b +--R Type: Union(Expression(Integer),...) +--E 958 + +--S 959 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 959 + +--S 960 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 3330 +t0000:=1/(a+b*x)^7 +--R +--R +--R (1) +--R 1 +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 961 + +--S 962 of 3330 +r0000:=(-1/6)/(b*(a+b*x)^6) +--R +--R +--R 1 +--R - +--R 6 +--R (2) - -------------------------------------------------------------- +--R 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 962 + +--S 963 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - ------------------------------------------------------------------- +--R 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 6 +--R 6b x + 36a b x + 90a b x + 120a b x + 90a b x + 36a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 963 + +--S 964 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 964 + +--S 965 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +)clear all + +--S 966 of 3330 +t0000:=1/(x*(a+b*x)^7) +--R +--R +--R (1) +--R 1 +--R -------------------------------------------------------------------------- +--R 7 8 6 7 2 5 6 3 4 5 4 3 4 5 2 3 6 2 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 966 + +--S 967 of 3330 +r0000:=1/6/(a*(a+b*x)^6)+1/5/(a^2*(a+b*x)^5)+1/4/(a^3*(a+b*x)^4)+_ + 1/3/(a^4*(a+b*x)^3)+1/2/(a^5*(a+b*x)^2)+1/(a^6*(a+b*x))+_ + log(x)/a^7-log(a+b*x)/a^7 +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R - 60b x - 360a b x - 900a b x - 1200a b x - 900a b x - 360a b x +--R + +--R 6 +--R - 60a +--R * +--R log(b x + a) +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 +--R 60a +--R * +--R log(x) +--R + +--R 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R 60a b x + 330a b x + 740a b x + 855a b x + 522a b x + 147a +--R / +--R 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 12 +--R 60a b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 13 +--R 60a +--R Type: Expression(Integer) +--E 967 + +--S 968 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R - 60b x - 360a b x - 900a b x - 1200a b x - 900a b x - 360a b x +--R + +--R 6 +--R - 60a +--R * +--R log(b x + a) +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 +--R 60a +--R * +--R log(x) +--R + +--R 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R 60a b x + 330a b x + 740a b x + 855a b x + 522a b x + 147a +--R / +--R 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 12 +--R 60a b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 13 +--R 60a +--R Type: Union(Expression(Integer),...) +--E 968 + +--S 969 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 969 + +--S 970 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 970 + +)clear all + +--S 971 of 3330 +t0000:=1/(x^2*(a+b*x)^7) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R 7 9 6 8 2 5 7 3 4 6 4 3 5 5 2 4 6 3 7 2 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 971 + +--S 972 of 3330 +r0000:=(-1)/(a^7*x)-1/6*b/(a^2*(a+b*x)^6)-2/5*b/(a^3*(a+b*x)^5)-_ + 3/4*b/(a^4*(a+b*x)^4)-4/3*b/(a^5*(a+b*x)^3)-5/2*b/(a^6*(a+b*x)^2)-_ + 6*b/(a^7*(a+b*x))-7*b*log(x)/a^8+7*b*log(a+b*x)/a^8 +--R +--R +--R (2) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420b x + 2520a b x + 6300a b x + 8400a b x + 6300a b x +--R + +--R 5 2 2 6 +--R 2520a b x + 420a b x +--R * +--R log(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 420b x - 2520a b x - 6300a b x - 8400a b x - 6300a b x +--R + +--R 5 2 2 6 +--R - 2520a b x - 420a b x +--R * +--R log(x) +--R + +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 420a b x - 2310a b x - 5180a b x - 5985a b x - 3654a b x +--R + +--R 6 7 +--R - 1029a b x - 60a +--R / +--R 8 6 7 9 5 6 10 4 5 11 3 4 12 2 3 13 2 +--R 60a b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 14 +--R 60a x +--R Type: Expression(Integer) +--E 972 + +--S 973 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 420b x + 2520a b x + 6300a b x + 8400a b x + 6300a b x +--R + +--R 5 2 2 6 +--R 2520a b x + 420a b x +--R * +--R log(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 420b x - 2520a b x - 6300a b x - 8400a b x - 6300a b x +--R + +--R 5 2 2 6 +--R - 2520a b x - 420a b x +--R * +--R log(x) +--R + +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 420a b x - 2310a b x - 5180a b x - 5985a b x - 3654a b x +--R + +--R 6 7 +--R - 1029a b x - 60a +--R / +--R 8 6 7 9 5 6 10 4 5 11 3 4 12 2 3 13 2 +--R 60a b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 14 +--R 60a x +--R Type: Union(Expression(Integer),...) +--E 973 + +--S 974 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 974 + +--S 975 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 3330 +t0000:=1/(x^3*(a+b*x)^7) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 7 10 6 9 2 5 8 3 4 7 4 3 6 5 2 5 6 4 7 3 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 976 + +--S 977 of 3330 +r0000:=(-1/2)/(a^7*x^2)+7*b/(a^8*x)+1/6*b^2/(a^3*(a+b*x)^6)+_ + 3/5*b^2/(a^4*(a+b*x)^5)+3/2*b^2/(a^5*(a+b*x)^4)+_ + 10/3*b^2/(a^6*(a+b*x)^3)+15/2*b^2/(a^7*(a+b*x)^2)+_ + 21*b^2/(a^8*(a+b*x))+28*b^2*log(x)/a^9-28*b^2*log(a+b*x)/a^9 +--R +--R +--R (2) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 +--R - 840b x - 5040a b x - 12600a b x - 16800a b x - 12600a b x +--R + +--R 5 3 3 6 2 2 +--R - 5040a b x - 840a b x +--R * +--R log(b x + a) +--R + +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 +--R 840b x + 5040a b x + 12600a b x + 16800a b x + 12600a b x +--R + +--R 5 3 3 6 2 2 +--R 5040a b x + 840a b x +--R * +--R log(x) +--R + +--R 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R 840a b x + 4620a b x + 10360a b x + 11970a b x + 7308a b x +--R + +--R 6 2 2 7 8 +--R 2058a b x + 120a b x - 15a +--R / +--R 9 6 8 10 5 7 11 4 6 12 3 5 13 2 4 14 3 +--R 30a b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x +--R + +--R 15 2 +--R 30a x +--R Type: Expression(Integer) +--E 977 + +--S 978 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 +--R - 840b x - 5040a b x - 12600a b x - 16800a b x - 12600a b x +--R + +--R 5 3 3 6 2 2 +--R - 5040a b x - 840a b x +--R * +--R log(b x + a) +--R + +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 +--R 840b x + 5040a b x + 12600a b x + 16800a b x + 12600a b x +--R + +--R 5 3 3 6 2 2 +--R 5040a b x + 840a b x +--R * +--R log(x) +--R + +--R 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R 840a b x + 4620a b x + 10360a b x + 11970a b x + 7308a b x +--R + +--R 6 2 2 7 8 +--R 2058a b x + 120a b x - 15a +--R / +--R 9 6 8 10 5 7 11 4 6 12 3 5 13 2 4 14 3 +--R 30a b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x +--R + +--R 15 2 +--R 30a x +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 979 + +--S 980 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 980 + +)clear all + +--S 981 of 3330 +t0000:=1/(x^4*(a+b*x)^7) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------------- +--R 7 11 6 10 2 5 9 3 4 8 4 3 7 5 2 6 6 5 7 4 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 981 + +--S 982 of 3330 +r0000:=(-1/3)/(a^7*x^3)+7/2*b/(a^8*x^2)-28*b^2/(a^9*x)-_ + 1/6*b^3/(a^4*(a+b*x)^6)-4/5*b^3/(a^5*(a+b*x)^5)-_ + 5/2*b^3/(a^6*(a+b*x)^4)-20/3*b^3/(a^7*(a+b*x)^3)-_ + 35/2*b^3/(a^8*(a+b*x)^2)-56*b^3/(a^9*(a+b*x))-_ + 84*b^3*log(x)/a^10+84*b^3*log(a+b*x)/a^10 +--R +--R +--R (2) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x + 15120a b x + 37800a b x + 50400a b x + 37800a b x +--R + +--R 5 4 4 6 3 3 +--R 15120a b x + 2520a b x +--R * +--R log(b x + a) +--R + +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R - 2520b x - 15120a b x - 37800a b x - 50400a b x - 37800a b x +--R + +--R 5 4 4 6 3 3 +--R - 15120a b x - 2520a b x +--R * +--R log(x) +--R + +--R 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R - 2520a b x - 13860a b x - 31080a b x - 35910a b x - 21924a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R - 6174a b x - 360a b x + 45a b x - 10a +--R / +--R 10 6 9 11 5 8 12 4 7 13 3 6 14 2 5 +--R 30a b x + 180a b x + 450a b x + 600a b x + 450a b x +--R + +--R 15 4 16 3 +--R 180a b x + 30a x +--R Type: Expression(Integer) +--E 982 + +--S 983 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x + 15120a b x + 37800a b x + 50400a b x + 37800a b x +--R + +--R 5 4 4 6 3 3 +--R 15120a b x + 2520a b x +--R * +--R log(b x + a) +--R + +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R - 2520b x - 15120a b x - 37800a b x - 50400a b x - 37800a b x +--R + +--R 5 4 4 6 3 3 +--R - 15120a b x - 2520a b x +--R * +--R log(x) +--R + +--R 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R - 2520a b x - 13860a b x - 31080a b x - 35910a b x - 21924a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R - 6174a b x - 360a b x + 45a b x - 10a +--R / +--R 10 6 9 11 5 8 12 4 7 13 3 6 14 2 5 +--R 30a b x + 180a b x + 450a b x + 600a b x + 450a b x +--R + +--R 15 4 16 3 +--R 180a b x + 30a x +--R Type: Union(Expression(Integer),...) +--E 983 + +--S 984 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 984 + +--S 985 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 985 + +)clear all + +--S 986 of 3330 +t0000:=x^12/(a+b*x)^10 +--R +--R +--R (1) +--R 12 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 986 + +--S 987 of 3330 +r0000:=55*a^2*x/b^12-5*a*x^2/b^11+1/3*x^3/b^10-1/9*a^12/(b^13*(a+b*x)^9)+_ + 3/2*a^11/(b^13*(a+b*x)^8)-66/7*a^10/(b^13*(a+b*x)^7)+_ + 110/3*a^9/(b^13*(a+b*x)^6)-99*a^8/(b^13*(a+b*x)^5)+_ + 198*a^7/(b^13*(a+b*x)^4)-308*a^6/(b^13*(a+b*x)^3)+_ + 396*a^5/(b^13*(a+b*x)^2)-495*a^4/(b^13*(a+b*x))-220*a^3*log(a+b*x)/b^13 +--R +--R +--R (2) +--R 3 9 9 4 8 8 5 7 7 6 6 6 +--R - 27720a b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 7 5 5 8 4 4 9 3 3 10 2 2 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 11 12 +--R - 249480a b x - 27720a +--R * +--R log(b x + a) +--R + +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 +--R 42b x - 252a b x + 2772a b x + 43218a b x + 139482a b x +--R + +--R 5 7 7 6 6 6 7 5 5 8 4 4 +--R 58968a b x - 638568a b x - 1831032a b x - 2529576a b x +--R + +--R 9 3 3 10 2 2 11 12 +--R - 2074464a b x - 1031616a b x - 289089a b x - 35201a +--R / +--R 22 9 21 8 2 20 7 3 19 6 4 18 5 +--R 126b x + 1134a b x + 4536a b x + 10584a b x + 15876a b x +--R + +--R 5 17 4 6 16 3 7 15 2 8 14 9 13 +--R 15876a b x + 10584a b x + 4536a b x + 1134a b x + 126a b +--R Type: Expression(Integer) +--E 987 + +--S 988 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 9 9 4 8 8 5 7 7 6 6 6 +--R - 27720a b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 7 5 5 8 4 4 9 3 3 10 2 2 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 11 12 +--R - 249480a b x - 27720a +--R * +--R log(b x + a) +--R + +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 +--R 42b x - 252a b x + 2772a b x + 43218a b x + 139482a b x +--R + +--R 5 7 7 6 6 6 7 5 5 8 4 4 +--R 58968a b x - 638568a b x - 1831032a b x - 2529576a b x +--R + +--R 9 3 3 10 2 2 11 12 +--R - 2074464a b x - 1031616a b x - 289089a b x - 35201a +--R / +--R 22 9 21 8 2 20 7 3 19 6 4 18 5 +--R 126b x + 1134a b x + 4536a b x + 10584a b x + 15876a b x +--R + +--R 5 17 4 6 16 3 7 15 2 8 14 9 13 +--R 15876a b x + 10584a b x + 4536a b x + 1134a b x + 126a b +--R Type: Union(Expression(Integer),...) +--E 988 + +--S 989 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 989 + +--S 990 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 990 + +)clear all + +--S 991 of 3330 +t0000:=x^11/(a+b*x)^10 +--R +--R +--R (1) +--R 11 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 991 + +--S 992 of 3330 +r0000:=-10*a*x/b^11+1/2*x^2/b^10+1/9*a^11/(b^12*(a+b*x)^9)-_ + 11/8*a^10/(b^12*(a+b*x)^8)+55/7*a^9/(b^12*(a+b*x)^7)-_ + 55/2*a^8/(b^12*(a+b*x)^6)+66*a^7/(b^12*(a+b*x)^5)-_ + 231/2*a^6/(b^12*(a+b*x)^4)+154*a^5/(b^12*(a+b*x)^3)-_ + 165*a^4/(b^12*(a+b*x)^2)+165*a^3/(b^12*(a+b*x))+55*a^2*log(a+b*x)/b^12 +--R +--R +--R (2) +--R 2 9 9 3 8 8 4 7 7 5 6 6 +--R 27720a b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 10 11 +--R 249480a b x + 27720a +--R * +--R log(b x + a) +--R + +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 +--R 252b x - 2772a b x - 36288a b x - 77112a b x + 190512a b x +--R + +--R 5 6 6 6 5 5 7 4 4 8 3 3 +--R 1220688a b x + 2704212a b x + 3402756a b x + 2656584a b x +--R + +--R 9 2 2 10 11 +--R 1281096a b x + 351459a b x + 42131a +--R / +--R 21 9 20 8 2 19 7 3 18 6 4 17 5 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 16 4 6 15 3 7 14 2 8 13 9 12 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Expression(Integer) +--E 992 + +--S 993 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 9 9 3 8 8 4 7 7 5 6 6 +--R 27720a b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 10 11 +--R 249480a b x + 27720a +--R * +--R log(b x + a) +--R + +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 +--R 252b x - 2772a b x - 36288a b x - 77112a b x + 190512a b x +--R + +--R 5 6 6 6 5 5 7 4 4 8 3 3 +--R 1220688a b x + 2704212a b x + 3402756a b x + 2656584a b x +--R + +--R 9 2 2 10 11 +--R 1281096a b x + 351459a b x + 42131a +--R / +--R 21 9 20 8 2 19 7 3 18 6 4 17 5 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 16 4 6 15 3 7 14 2 8 13 9 12 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Union(Expression(Integer),...) +--E 993 + +--S 994 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 994 + +--S 995 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 995 + +)clear all + +--S 996 of 3330 +t0000:=x^10/(a+b*x)^10 +--R +--R +--R (1) +--R 10 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 996 + +--S 997 of 3330 +r0000:=x/b^10-1/9*a^10/(b^11*(a+b*x)^9)+5/4*a^9/(b^11*(a+b*x)^8)-_ + 45/7*a^8/(b^11*(a+b*x)^7)+20*a^7/(b^11*(a+b*x)^6)-_ + 42*a^6/(b^11*(a+b*x)^5)+63*a^5/(b^11*(a+b*x)^4)-_ + 70*a^4/(b^11*(a+b*x)^3)+60*a^3/(b^11*(a+b*x)^2)-_ + 45*a^2/(b^11*(a+b*x))-10*a*log(a+b*x)/b^11 +--R +--R +--R (2) +--R 9 9 2 8 8 3 7 7 4 6 6 +--R - 2520a b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 9 10 +--R - 22680a b x - 2520a +--R * +--R log(b x + a) +--R + +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R 252b x + 2268a b x - 2268a b x - 54432a b x - 197568a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R - 375732a b x - 439236a b x - 328104a b x - 153576a b x - 41229a b x +--R + +--R 10 +--R - 4861a +--R / +--R 20 9 19 8 2 18 7 3 17 6 4 16 5 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 15 4 6 14 3 7 13 2 8 12 9 11 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Expression(Integer) +--E 997 + +--S 998 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 2 8 8 3 7 7 4 6 6 +--R - 2520a b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 9 10 +--R - 22680a b x - 2520a +--R * +--R log(b x + a) +--R + +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R 252b x + 2268a b x - 2268a b x - 54432a b x - 197568a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R - 375732a b x - 439236a b x - 328104a b x - 153576a b x - 41229a b x +--R + +--R 10 +--R - 4861a +--R / +--R 20 9 19 8 2 18 7 3 17 6 4 16 5 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 15 4 6 14 3 7 13 2 8 12 9 11 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Union(Expression(Integer),...) +--E 998 + +--S 999 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1000 + +)clear all + +--S 1001 of 3330 +t0000:=x^9/(a+b*x)^10 +--R +--R +--R (1) +--R 9 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1001 + +--S 1002 of 3330 +r0000:=1/9*a^9/(b^10*(a+b*x)^9)-9/8*a^8/(b^10*(a+b*x)^8)+_ + 36/7*a^7/(b^10*(a+b*x)^7)-14*a^6/(b^10*(a+b*x)^6)+_ + 126/5*a^5/(b^10*(a+b*x)^5)-63/2*a^4/(b^10*(a+b*x)^4)+_ + 28*a^3/(b^10*(a+b*x)^3)-18*a^2/(b^10*(a+b*x)^2)+_ + 9*a/(b^10*(a+b*x))+log(a+b*x)/b^10 +--R +--R +--R (2) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a +--R * +--R log(b x + a) +--R + +--R 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R 22680a b x + 136080a b x + 388080a b x + 661500a b x + 725004a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R 518616a b x + 235224a b x + 61641a b x + 7129a +--R / +--R 19 9 18 8 2 17 7 3 16 6 4 15 5 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 14 4 6 13 3 7 12 2 8 11 9 10 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a b +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a +--R * +--R log(b x + a) +--R + +--R 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R 22680a b x + 136080a b x + 388080a b x + 661500a b x + 725004a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R 518616a b x + 235224a b x + 61641a b x + 7129a +--R / +--R 19 9 18 8 2 17 7 3 16 6 4 15 5 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 14 4 6 13 3 7 12 2 8 11 9 10 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a b +--R Type: Union(Expression(Integer),...) +--E 1003 + +--S 1004 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1005 + +)clear all + +--S 1006 of 3330 +t0000:=x^8/(a+b*x)^10 +--R +--R +--R (1) +--R 8 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1006 + +--S 1007 of 3330 +r0000:=1/9*x^9/(a*(a+b*x)^9) +--R +--R +--R (2) +--R 1 9 +--R - x +--R 9 +--R / +--R 9 9 2 8 8 3 7 7 4 6 6 5 5 5 6 4 4 7 3 3 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 8 2 2 9 10 +--R 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1007 + +--S 1008 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x +--R + +--R 6 2 2 7 8 +--R - 36a b x - 9a b x - a +--R / +--R 18 9 17 8 2 16 7 3 15 6 4 14 5 5 13 4 +--R 9b x + 81a b x + 324a b x + 756a b x + 1134a b x + 1134a b x +--R + +--R 6 12 3 7 11 2 8 10 9 9 +--R 756a b x + 324a b x + 81a b x + 9a b +--R Type: Union(Expression(Integer),...) +--E 1008 + +--S 1009 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ----- +--R 9 +--R 9a b +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1010 + +)clear all + +--S 1011 of 3330 +t0000:=x^7/(a+b*x)^10 +--R +--R +--R (1) +--R 7 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1011 + +--S 1012 of 3330 +r0000:=1/9*x^8/(a*(a+b*x)^9)+1/72*x^8/(a^2*(a+b*x)^8) +--R +--R +--R (2) +--R 1 9 1 8 +--R -- b x + - a x +--R 72 8 +--R / +--R 2 9 9 3 8 8 4 7 7 5 6 6 6 5 5 7 4 4 8 3 3 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 9 2 2 10 11 +--R 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1012 + +--S 1013 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 36b x - 84a b x - 126a b x - 126a b x - 84a b x - 36a b x +--R + +--R 6 7 +--R - 9a b x - a +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 +--R 72b x + 648a b x + 2592a b x + 6048a b x + 9072a b x +--R + +--R 5 12 4 6 11 3 7 10 2 8 9 9 8 +--R 9072a b x + 6048a b x + 2592a b x + 648a b x + 72a b +--R Type: Union(Expression(Integer),...) +--E 1013 + +--S 1014 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ------ +--R 2 8 +--R 72a b +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1015 + +)clear all + +--S 1016 of 3330 +t0000:=x^6/(a+b*x)^10 +--R +--R +--R (1) +--R 6 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1016 + +--S 1017 of 3330 +r0000:=1/9*x^7/(a*(a+b*x)^9)+1/36*x^7/(a^2*(a+b*x)^8)+1/252*x^7/(a^3*(a+b*x)^7) +--R +--R +--R (2) +--R 1 2 9 1 8 1 2 7 +--R --- b x + -- a b x + - a x +--R 252 28 7 +--R / +--R 3 9 9 4 8 8 5 7 7 6 6 6 7 5 5 8 4 4 9 3 3 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 10 2 2 11 12 +--R 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1017 + +--S 1018 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R - 84b x - 126a b x - 126a b x - 84a b x - 36a b x - 9a b x - a +--R / +--R 16 9 15 8 2 14 7 3 13 6 4 12 5 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 11 4 6 10 3 7 9 2 8 8 9 7 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Union(Expression(Integer),...) +--E 1018 + +--S 1019 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ------- +--R 3 7 +--R 252a b +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1020 + +)clear all + +--S 1021 of 3330 +t0000:=x^5/(a+b*x)^10 +--R +--R +--R (1) +--R 5 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1021 + +--S 1022 of 3330 +r0000:=1/9*x^6/(a*(a+b*x)^9)+1/24*x^6/(a^2*(a+b*x)^8)+_ + 1/84*x^6/(a^3*(a+b*x)^7)+1/504*x^6/(a^4*(a+b*x)^6) +--R +--R +--R (2) +--R 1 3 9 1 2 8 1 2 7 1 3 6 +--R --- b x + -- a b x + -- a b x + - a x +--R 504 56 14 6 +--R / +--R 4 9 9 5 8 8 6 7 7 7 6 6 8 5 5 9 4 4 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 10 3 3 11 2 2 12 13 +--R 84a b x + 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1022 + +--S 1023 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R - 126b x - 126a b x - 84a b x - 36a b x - 9a b x - a +--R / +--R 15 9 14 8 2 13 7 3 12 6 4 11 5 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 10 4 6 9 3 7 8 2 8 7 9 6 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Union(Expression(Integer),...) +--E 1023 + +--S 1024 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - ------- +--R 4 6 +--R 504a b +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1025 + +)clear all + +--S 1026 of 3330 +t0000:=x^4/(a+b*x)^10 +--R +--R +--R (1) +--R 4 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1026 + +--S 1027 of 3330 +r0000:=-1/9*a^4/(b^5*(a+b*x)^9)+1/2*a^3/(b^5*(a+b*x)^8)-_ + 6/7*a^2/(b^5*(a+b*x)^7)+2/3*a/(b^5*(a+b*x)^6)+(-1/5)/(b^5*(a+b*x)^5) +--R +--R +--R (2) +--R 1 4 4 2 3 3 2 2 2 2 1 3 1 4 +--R - - b x - -- a b x - -- a b x - -- a b x - --- a +--R 5 15 35 70 630 +--R / +--R 14 9 13 8 2 12 7 3 11 6 4 10 5 5 9 4 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 8 3 7 7 2 8 6 9 5 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1027 + +--S 1028 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 3 4 +--R - 126b x - 84a b x - 36a b x - 9a b x - a +--R / +--R 14 9 13 8 2 12 7 3 11 6 4 10 5 +--R 630b x + 5670a b x + 22680a b x + 52920a b x + 79380a b x +--R + +--R 5 9 4 6 8 3 7 7 2 8 6 9 5 +--R 79380a b x + 52920a b x + 22680a b x + 5670a b x + 630a b +--R Type: Union(Expression(Integer),...) +--E 1028 + +--S 1029 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1030 + +)clear all + +--S 1031 of 3330 +t0000:=x^3/(a+b*x)^10 +--R +--R +--R (1) +--R 3 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1031 + +--S 1032 of 3330 +r0000:=1/9*a^3/(b^4*(a+b*x)^9)-3/8*a^2/(b^4*(a+b*x)^8)+_ + 3/7*a/(b^4*(a+b*x)^7)+(-1/6)/(b^4*(a+b*x)^6) +--R +--R +--R (2) +--R 1 3 3 1 2 2 1 2 1 3 +--R - - b x - -- a b x - -- a b x - --- a +--R 6 14 56 504 +--R / +--R 13 9 12 8 2 11 7 3 10 6 4 9 5 5 8 4 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 7 3 7 6 2 8 5 9 4 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1032 + +--S 1033 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R - 84b x - 36a b x - 9a b x - a +--R / +--R 13 9 12 8 2 11 7 3 10 6 4 9 5 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 8 4 6 7 3 7 6 2 8 5 9 4 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Union(Expression(Integer),...) +--E 1033 + +--S 1034 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1035 + +)clear all + +--S 1036 of 3330 +t0000:=x^2/(a+b*x)^10 +--R +--R +--R (1) +--R 2 +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1036 + +--S 1037 of 3330 +r0000:=-1/9*a^2/(b^3*(a+b*x)^9)+1/4*a/(b^3*(a+b*x)^8)+(-1/7)/(b^3*(a+b*x)^7) +--R +--R +--R (2) +--R 1 2 2 1 1 2 +--R - - b x - -- a b x - --- a +--R 7 28 252 +--R / +--R 12 9 11 8 2 10 7 3 9 6 4 8 5 5 7 4 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 6 3 7 5 2 8 4 9 3 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1037 + +--S 1038 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 +--R - 36b x - 9a b x - a +--R / +--R 12 9 11 8 2 10 7 3 9 6 4 8 5 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 7 4 6 6 3 7 5 2 8 4 9 3 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Union(Expression(Integer),...) +--E 1038 + +--S 1039 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1040 + +)clear all + +--S 1041 of 3330 +t0000:=x/(a+b*x)^10 +--R +--R +--R (1) +--R x +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1041 + +--S 1042 of 3330 +r0000:=1/9*a/(b^2*(a+b*x)^9)+(-1/8)/(b^2*(a+b*x)^8) +--R +--R +--R (2) +--R 1 1 +--R - - b x - -- a +--R 8 72 +--R / +--R 11 9 10 8 2 9 7 3 8 6 4 7 5 5 6 4 6 5 3 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 7 4 2 8 3 9 2 +--R 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1042 + +--S 1043 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R - 9b x - a +--R / +--R 11 9 10 8 2 9 7 3 8 6 4 7 5 5 6 4 +--R 72b x + 648a b x + 2592a b x + 6048a b x + 9072a b x + 9072a b x +--R + +--R 6 5 3 7 4 2 8 3 9 2 +--R 6048a b x + 2592a b x + 648a b x + 72a b +--R Type: Union(Expression(Integer),...) +--E 1043 + +--S 1044 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1045 + +)clear all + +--S 1046 of 3330 +t0000:=1/(a+b*x)^10 +--R +--R +--R (1) +--R 1 +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1046 + +--S 1047 of 3330 +r0000:=(-1/9)/(b*(a+b*x)^9) +--R +--R +--R (2) +--R - +--R 1 +--R - +--R 9 +--R / +--R 10 9 9 8 2 8 7 3 7 6 4 6 5 5 5 4 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 4 3 7 3 2 8 2 9 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1047 + +--S 1048 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R - +--R 1 +--R / +--R 10 9 9 8 2 8 7 3 7 6 4 6 5 5 5 4 +--R 9b x + 81a b x + 324a b x + 756a b x + 1134a b x + 1134a b x +--R + +--R 6 4 3 7 3 2 8 2 9 +--R 756a b x + 324a b x + 81a b x + 9a b +--R Type: Union(Expression(Integer),...) +--E 1048 + +--S 1049 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1050 + +)clear all + +--S 1051 of 3330 +t0000:=1/(x*(a+b*x)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 11 9 10 2 8 9 3 7 8 4 6 7 5 5 6 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 5 7 3 4 8 2 3 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1051 + +--S 1052 of 3330 +r0000:=1/9/(a*(a+b*x)^9)+1/8/(a^2*(a+b*x)^8)+1/7/(a^3*(a+b*x)^7)+_ + 1/6/(a^4*(a+b*x)^6)+1/5/(a^5*(a+b*x)^5)+1/4/(a^6*(a+b*x)^4)+_ + 1/3/(a^7*(a+b*x)^3)+1/2/(a^8*(a+b*x)^2)+1/(a^9*(a+b*x))+_ + log(x)/a^10-log(a+b*x)/a^10 +--R +--R +--R (2) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R - 2520b x - 22680a b x - 90720a b x - 211680a b x - 317520a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R - 317520a b x - 211680a b x - 90720a b x - 22680a b x - 2520a +--R * +--R log(b x + a) +--R + +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a +--R * +--R log(x) +--R + +--R 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R 2520a b x + 21420a b x + 80220a b x + 173250a b x + 236754a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R 210756a b x + 120564a b x + 41481a b x + 7129a +--R / +--R 10 9 9 11 8 8 12 7 7 13 6 6 14 5 5 +--R 2520a b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 15 4 4 16 3 3 17 2 2 18 19 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R - 2520b x - 22680a b x - 90720a b x - 211680a b x - 317520a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R - 317520a b x - 211680a b x - 90720a b x - 22680a b x - 2520a +--R * +--R log(b x + a) +--R + +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a +--R * +--R log(x) +--R + +--R 8 8 2 7 7 3 6 6 4 5 5 5 4 4 +--R 2520a b x + 21420a b x + 80220a b x + 173250a b x + 236754a b x +--R + +--R 6 3 3 7 2 2 8 9 +--R 210756a b x + 120564a b x + 41481a b x + 7129a +--R / +--R 10 9 9 11 8 8 12 7 7 13 6 6 14 5 5 +--R 2520a b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 15 4 4 16 3 3 17 2 2 18 19 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a +--R Type: Union(Expression(Integer),...) +--E 1053 + +--S 1054 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1055 + +)clear all + +--S 1056 of 3330 +t0000:=1/(x^2*(a+b*x)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 12 9 11 2 8 10 3 7 9 4 6 8 5 5 7 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 6 7 3 5 8 2 4 9 3 10 2 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1056 + +--S 1057 of 3330 +r0000:=(-1)/(a^10*x)-1/9*b/(a^2*(a+b*x)^9)-1/4*b/(a^3*(a+b*x)^8)-_ + 3/7*b/(a^4*(a+b*x)^7)-2/3*b/(a^5*(a+b*x)^6)-b/(a^6*(a+b*x)^5)-_ + 3/2*b/(a^7*(a+b*x)^4)-7/3*b/(a^8*(a+b*x)^3)-4*b/(a^9*(a+b*x)^2)-_ + 9*b/(a^10*(a+b*x))-10*b*log(x)/a^11+10*b*log(a+b*x)/a^11 +--R +--R +--R (2) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a b x +--R * +--R log(b x + a) +--R + +--R 10 10 9 9 2 8 8 3 7 7 +--R - 2520b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 8 2 2 9 +--R - 22680a b x - 2520a b x +--R * +--R log(x) +--R + +--R 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R - 2520a b x - 21420a b x - 80220a b x - 173250a b x - 236754a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R - 210756a b x - 120564a b x - 41481a b x - 7129a b x - 252a +--R / +--R 11 9 10 12 8 9 13 7 8 14 6 7 15 5 6 +--R 252a b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 16 4 5 17 3 4 18 2 3 19 2 20 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a x +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x + 317520a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 +--R 317520a b x + 211680a b x + 90720a b x + 22680a b x + 2520a b x +--R * +--R log(b x + a) +--R + +--R 10 10 9 9 2 8 8 3 7 7 +--R - 2520b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 4 6 6 5 5 5 6 4 4 7 3 3 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 8 2 2 9 +--R - 22680a b x - 2520a b x +--R * +--R log(x) +--R + +--R 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R - 2520a b x - 21420a b x - 80220a b x - 173250a b x - 236754a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R - 210756a b x - 120564a b x - 41481a b x - 7129a b x - 252a +--R / +--R 11 9 10 12 8 9 13 7 8 14 6 7 15 5 6 +--R 252a b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 16 4 5 17 3 4 18 2 3 19 2 20 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a x +--R Type: Union(Expression(Integer),...) +--E 1058 + +--S 1059 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1060 + +)clear all + +--S 1061 of 3330 +t0000:=1/(x^3*(a+b*x)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 13 9 12 2 8 11 3 7 10 4 6 9 5 5 8 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 7 7 3 6 8 2 5 9 4 10 3 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1061 + +--S 1062 of 3330 +r0000:=(-1/2)/(a^10*x^2)+10*b/(a^11*x)+1/9*b^2/(a^3*(a+b*x)^9)+_ + 3/8*b^2/(a^4*(a+b*x)^8)+6/7*b^2/(a^5*(a+b*x)^7)+_ + 5/3*b^2/(a^6*(a+b*x)^6)+3*b^2/(a^7*(a+b*x)^5)+_ + 21/4*b^2/(a^8*(a+b*x)^4)+28/3*b^2/(a^9*(a+b*x)^3)+_ + 18*b^2/(a^10*(a+b*x)^2)+45*b^2/(a^11*(a+b*x))+_ + 55*b^2*log(x)/a^12-55*b^2*log(a+b*x)/a^12 +--R +--R +--R (2) +--R 11 11 10 10 2 9 9 3 8 8 +--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 4 7 7 5 6 6 6 5 5 7 4 4 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 8 3 3 9 2 2 +--R - 249480a b x - 27720a b x +--R * +--R log(b x + a) +--R + +--R 11 11 10 10 2 9 9 3 8 8 +--R 27720b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 4 7 7 5 6 6 6 5 5 7 4 4 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 8 3 3 9 2 2 +--R 249480a b x + 27720a b x +--R * +--R log(x) +--R + +--R 10 10 2 9 9 3 8 8 4 7 7 +--R 27720a b x + 235620a b x + 882420a b x + 1905750a b x +--R + +--R 5 6 6 6 5 5 7 4 4 8 3 3 +--R 2604294a b x + 2318316a b x + 1326204a b x + 456291a b x +--R + +--R 9 2 2 10 11 +--R 78419a b x + 2772a b x - 252a +--R / +--R 12 9 11 13 8 10 14 7 9 15 6 8 16 5 7 +--R 504a b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 17 4 6 18 3 5 19 2 4 20 3 21 2 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a x +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 11 11 10 10 2 9 9 3 8 8 +--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 4 7 7 5 6 6 6 5 5 7 4 4 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 8 3 3 9 2 2 +--R - 249480a b x - 27720a b x +--R * +--R log(b x + a) +--R + +--R 11 11 10 10 2 9 9 3 8 8 +--R 27720b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 4 7 7 5 6 6 6 5 5 7 4 4 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 8 3 3 9 2 2 +--R 249480a b x + 27720a b x +--R * +--R log(x) +--R + +--R 10 10 2 9 9 3 8 8 4 7 7 +--R 27720a b x + 235620a b x + 882420a b x + 1905750a b x +--R + +--R 5 6 6 6 5 5 7 4 4 8 3 3 +--R 2604294a b x + 2318316a b x + 1326204a b x + 456291a b x +--R + +--R 9 2 2 10 11 +--R 78419a b x + 2772a b x - 252a +--R / +--R 12 9 11 13 8 10 14 7 9 15 6 8 16 5 7 +--R 504a b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 17 4 6 18 3 5 19 2 4 20 3 21 2 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a x +--R Type: Union(Expression(Integer),...) +--E 1063 + +--S 1064 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1065 + +)clear all + +--S 1066 of 3330 +t0000:=1/(x^4*(a+b*x)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 14 9 13 2 8 12 3 7 11 4 6 10 5 5 9 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 7 8 2 6 9 5 10 4 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1066 + +--S 1067 of 3330 +r0000:=(-1/3)/(a^10*x^3)+5*b/(a^11*x^2)-55*b^2/(a^12*x)-_ + 1/9*b^3/(a^4*(a+b*x)^9)-1/2*b^3/(a^5*(a+b*x)^8)-_ + 10/7*b^3/(a^6*(a+b*x)^7)-10/3*b^3/(a^7*(a+b*x)^6)-_ + 7*b^3/(a^8*(a+b*x)^5)-14*b^3/(a^9*(a+b*x)^4)-_ + 28*b^3/(a^10*(a+b*x)^3)-60*b^3/(a^11*(a+b*x)^2)-_ + 165*b^3/(a^12*(a+b*x))-220*b^3*log(x)/a^13+220*b^3*log(a+b*x)/a^13 +--R +--R +--R (2) +--R 12 12 11 11 2 10 10 3 9 9 +--R 27720b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 4 8 8 5 7 7 6 6 6 7 5 5 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 8 4 4 9 3 3 +--R 249480a b x + 27720a b x +--R * +--R log(b x + a) +--R + +--R 12 12 11 11 2 10 10 3 9 9 +--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 4 8 8 5 7 7 6 6 6 7 5 5 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 8 4 4 9 3 3 +--R - 249480a b x - 27720a b x +--R * +--R log(x) +--R + +--R 11 11 2 10 10 3 9 9 4 8 8 +--R - 27720a b x - 235620a b x - 882420a b x - 1905750a b x +--R + +--R 5 7 7 6 6 6 7 5 5 8 4 4 +--R - 2604294a b x - 2318316a b x - 1326204a b x - 456291a b x +--R + +--R 9 3 3 10 2 2 11 12 +--R - 78419a b x - 2772a b x + 252a b x - 42a +--R / +--R 13 9 12 14 8 11 15 7 10 16 6 9 17 5 8 +--R 126a b x + 1134a b x + 4536a b x + 10584a b x + 15876a b x +--R + +--R 18 4 7 19 3 6 20 2 5 21 4 22 3 +--R 15876a b x + 10584a b x + 4536a b x + 1134a b x + 126a x +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 12 12 11 11 2 10 10 3 9 9 +--R 27720b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 4 8 8 5 7 7 6 6 6 7 5 5 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 8 4 4 9 3 3 +--R 249480a b x + 27720a b x +--R * +--R log(b x + a) +--R + +--R 12 12 11 11 2 10 10 3 9 9 +--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 4 8 8 5 7 7 6 6 6 7 5 5 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 8 4 4 9 3 3 +--R - 249480a b x - 27720a b x +--R * +--R log(x) +--R + +--R 11 11 2 10 10 3 9 9 4 8 8 +--R - 27720a b x - 235620a b x - 882420a b x - 1905750a b x +--R + +--R 5 7 7 6 6 6 7 5 5 8 4 4 +--R - 2604294a b x - 2318316a b x - 1326204a b x - 456291a b x +--R + +--R 9 3 3 10 2 2 11 12 +--R - 78419a b x - 2772a b x + 252a b x - 42a +--R / +--R 13 9 12 14 8 11 15 7 10 16 6 9 17 5 8 +--R 126a b x + 1134a b x + 4536a b x + 10584a b x + 15876a b x +--R + +--R 18 4 7 19 3 6 20 2 5 21 4 22 3 +--R 15876a b x + 10584a b x + 4536a b x + 1134a b x + 126a x +--R Type: Union(Expression(Integer),...) +--E 1068 + +--S 1069 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1070 + +)clear all + +--S 1071 of 3330 +t0000:=(a+b*x)^12/x^10 +--R +--R +--R (1) +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R b x + 12a b x + 66a b x + 220a b x + 495a b x + 792a b x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924a b x + 792a b x + 495a b x + 220a b x + 66a b x + 12a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1071 + +--S 1072 of 3330 +r0000:=-1/9*a^12/x^9-3/2*a^11*b/x^8-66/7*a^10*b^2/x^7-_ + 110/3*a^9*b^3/x^6-99*a^8*b^4/x^5-198*a^7*b^5/x^4-_ + 308*a^6*b^6/x^3-396*a^5*b^7/x^2-495*a^4*b^8/x+66*a^2*b^10*x+_ + 6*a*b^11*x^2+1/3*b^12*x^3+220*a^3*b^9*log(x) +--R +--R +--R (2) +--R 3 9 9 12 12 11 11 2 10 10 4 8 8 +--R 27720a b x log(x) + 42b x + 756a b x + 8316a b x - 62370a b x +--R + +--R 5 7 7 6 6 6 7 5 5 8 4 4 9 3 3 +--R - 49896a b x - 38808a b x - 24948a b x - 12474a b x - 4620a b x +--R + +--R 10 2 2 11 12 +--R - 1188a b x - 189a b x - 14a +--R / +--R 9 +--R 126x +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 9 9 12 12 11 11 2 10 10 4 8 8 +--R 27720a b x log(x) + 42b x + 756a b x + 8316a b x - 62370a b x +--R + +--R 5 7 7 6 6 6 7 5 5 8 4 4 9 3 3 +--R - 49896a b x - 38808a b x - 24948a b x - 12474a b x - 4620a b x +--R + +--R 10 2 2 11 12 +--R - 1188a b x - 189a b x - 14a +--R / +--R 9 +--R 126x +--R Type: Union(Expression(Integer),...) +--E 1073 + +--S 1074 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1075 + +)clear all + +--S 1076 of 3330 +t0000:=(a+b*x)^11/x^10 +--R +--R +--R (1) +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R b x + 11a b x + 55a b x + 165a b x + 330a b x + 462a b x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462a b x + 330a b x + 165a b x + 55a b x + 11a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1076 + +--S 1077 of 3330 +r0000:=-1/9*a^11/x^9-11/8*a^10*b/x^8-55/7*a^9*b^2/x^7-55/2*a^8*b^3/x^6-_ + 66*a^7*b^4/x^5-231/2*a^6*b^5/x^4-154*a^5*b^6/x^3-165*a^4*b^7/x^2-_ + 165*a^3*b^8/x+11*a*b^10*x+1/2*b^11*x^2+55*a^2*b^9*log(x) +--R +--R +--R (2) +--R 2 9 9 11 11 10 10 3 8 8 4 7 7 +--R 27720a b x log(x) + 252b x + 5544a b x - 83160a b x - 83160a b x +--R + +--R 5 6 6 6 5 5 7 4 4 8 3 3 9 2 2 +--R - 77616a b x - 58212a b x - 33264a b x - 13860a b x - 3960a b x +--R + +--R 10 11 +--R - 693a b x - 56a +--R / +--R 9 +--R 504x +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 9 9 11 11 10 10 3 8 8 4 7 7 +--R 27720a b x log(x) + 252b x + 5544a b x - 83160a b x - 83160a b x +--R + +--R 5 6 6 6 5 5 7 4 4 8 3 3 9 2 2 +--R - 77616a b x - 58212a b x - 33264a b x - 13860a b x - 3960a b x +--R + +--R 10 11 +--R - 693a b x - 56a +--R / +--R 9 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 1078 + +--S 1079 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1080 + +)clear all + +--S 1081 of 3330 +t0000:=(a+b*x)^10/x^10 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1081 + +--S 1082 of 3330 +r0000:=-1/9*a^10/x^9-5/4*a^9*b/x^8-45/7*a^8*b^2/x^7-20*a^7*b^3/x^6-_ + 42*a^6*b^4/x^5-63*a^5*b^5/x^4-70*a^4*b^6/x^3-60*a^3*b^7/x^2-_ + 45*a^2*b^8/x+b^10*x+10*a*b^9*log(x) +--R +--R +--R (2) +--R 9 9 10 10 2 8 8 3 7 7 4 6 6 +--R 2520a b x log(x) + 252b x - 11340a b x - 15120a b x - 17640a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 15876a b x - 10584a b x - 5040a b x - 1620a b x - 315a b x - 28a +--R / +--R 9 +--R 252x +--R Type: Expression(Integer) +--E 1082 + +--S 1083 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 10 10 2 8 8 3 7 7 4 6 6 +--R 2520a b x log(x) + 252b x - 11340a b x - 15120a b x - 17640a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R - 15876a b x - 10584a b x - 5040a b x - 1620a b x - 315a b x - 28a +--R / +--R 9 +--R 252x +--R Type: Union(Expression(Integer),...) +--E 1083 + +--S 1084 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1085 + +)clear all + +--S 1086 of 3330 +t0000:=(a+b*x)^9/x^10 +--R +--R +--R (1) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 7 2 2 8 9 +--R 36a b x + 9a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1086 + +--S 1087 of 3330 +r0000:=-1/9*a^9/x^9-9/8*a^8*b/x^8-36/7*a^7*b^2/x^7-14*a^6*b^3/x^6-_ + 126/5*a^5*b^4/x^5-63/2*a^4*b^5/x^4-28*a^3*b^6/x^3-_ + 18*a^2*b^7/x^2-9*a*b^8/x+b^9*log(x) +--R +--R +--R (2) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x log(x) - 22680a b x - 45360a b x - 70560a b x - 79380a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R - 63504a b x - 35280a b x - 12960a b x - 2835a b x - 280a +--R / +--R 9 +--R 2520x +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 2520b x log(x) - 22680a b x - 45360a b x - 70560a b x - 79380a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R - 63504a b x - 35280a b x - 12960a b x - 2835a b x - 280a +--R / +--R 9 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 1088 + +--S 1089 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1090 + +)clear all + +--S 1091 of 3330 +t0000:=(a+b*x)^8/x^10 +--R +--R +--R (1) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 8 +--R 8a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1091 + +--S 1092 of 3330 +r0000:=-1/9*(a+b*x)^9/(a*x^9) +--R +--R +--R (2) +--R 1 9 9 8 8 2 7 7 28 3 6 6 4 5 5 5 4 4 28 6 3 3 +--R - - b x - a b x - 4a b x - -- a b x - 14a b x - 14a b x - -- a b x +--R 9 3 3 +--R + +--R 7 2 2 8 1 9 +--R - 4a b x - a b x - - a +--R 9 +--R / +--R 9 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1092 + +--S 1093 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x +--R + +--R 6 2 2 7 8 +--R - 36a b x - 9a b x - a +--R / +--R 9 +--R 9x +--R Type: Union(Expression(Integer),...) +--E 1093 + +--S 1094 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 9 +--R b +--R (4) -- +--R 9a +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1095 + +)clear all + +--S 1096 of 3330 +t0000:=(a+b*x)^7/x^10 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1096 + +--S 1097 of 3330 +r0000:=-1/9*(a+b*x)^8/(a*x^9)+1/72*b*(a+b*x)^8/(a^2*x^8) +--R +--R +--R (2) +--R 1 9 9 1 2 7 7 7 3 6 6 21 4 5 5 5 4 4 35 6 3 3 7 2 2 +--R -- b x - - a b x - - a b x - -- a b x - 7a b x - -- a b x - 3a b x +--R 72 2 3 4 6 +--R + +--R 7 8 1 9 +--R - - a b x - - a +--R 8 9 +--R / +--R 2 9 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1097 + +--S 1098 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 36b x - 168a b x - 378a b x - 504a b x - 420a b x - 216a b x +--R + +--R 6 7 +--R - 63a b x - 8a +--R / +--R 9 +--R 72x +--R Type: Union(Expression(Integer),...) +--E 1098 + +--S 1099 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 9 +--R b +--R (4) - ---- +--R 2 +--R 72a +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1100 + +)clear all + +--S 1101 of 3330 +t0000:=(a+b*x)^6/x^10 +--R +--R +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R (1) ------------------------------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1101 + +--S 1102 of 3330 +r0000:=-1/9*(a+b*x)^7/(a*x^9)+1/36*b*(a+b*x)^7/(a^2*x^8)-_ + 1/252*b^2*(a+b*x)^7/(a^3*x^7) +--R +--R +--R (2) +--R 1 9 9 1 3 6 6 3 4 5 5 5 4 4 10 6 3 3 15 7 2 2 +--R - --- b x - - a b x - - a b x - 3a b x - -- a b x - -- a b x +--R 252 3 2 3 7 +--R + +--R 3 8 1 9 +--R - - a b x - - a +--R 4 9 +--R / +--R 3 9 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1102 + +--S 1103 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R - 84b x - 378a b x - 756a b x - 840a b x - 540a b x - 189a b x - 28a +--R -------------------------------------------------------------------------- +--R 9 +--R 252x +--R Type: Union(Expression(Integer),...) +--E 1103 + +--S 1104 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 9 +--R b +--R (4) ----- +--R 3 +--R 252a +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1105 + +)clear all + +--S 1106 of 3330 +t0000:=(a+b*x)^5/x^10 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1106 + +--S 1107 of 3330 +r0000:=-1/9*a^5/x^9-5/8*a^4*b/x^8-10/7*a^3*b^2/x^7-5/3*a^2*b^3/x^6-_ + a*b^4/x^5-1/4*b^5/x^4 +--R +--R +--R 1 5 5 4 4 5 2 3 3 10 3 2 2 5 4 1 5 +--R - - b x - a b x - - a b x - -- a b x - - a b x - - a +--R 4 3 7 8 9 +--R (2) --------------------------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1107 + +--S 1108 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R - 126b x - 504a b x - 840a b x - 720a b x - 315a b x - 56a +--R (3) --------------------------------------------------------------- +--R 9 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 1108 + +--S 1109 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1110 + +)clear all + +--S 1111 of 3330 +t0000:=(a+b*x)^4/x^10 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (1) -------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1111 + +--S 1112 of 3330 +r0000:=-1/9*a^4/x^9-1/2*a^3*b/x^8-6/7*a^2*b^2/x^7-2/3*a*b^3/x^6-1/5*b^4/x^5 +--R +--R +--R 1 4 4 2 3 3 6 2 2 2 1 3 1 4 +--R - - b x - - a b x - - a b x - - a b x - - a +--R 5 3 7 2 9 +--R (2) ----------------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1112 + +--S 1113 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R - 126b x - 420a b x - 540a b x - 315a b x - 70a +--R (3) --------------------------------------------------- +--R 9 +--R 630x +--R Type: Union(Expression(Integer),...) +--E 1113 + +--S 1114 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1115 + +)clear all + +--S 1116 of 3330 +t0000:=(a+b*x)^3/x^10 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1116 + +--S 1117 of 3330 +r0000:=-1/9*a^3/x^9-3/8*a^2*b/x^8-3/7*a*b^2/x^7-1/6*b^3/x^6 +--R +--R +--R 1 3 3 3 2 2 3 2 1 3 +--R - - b x - - a b x - - a b x - - a +--R 6 7 8 9 +--R (2) ------------------------------------ +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1117 + +--S 1118 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 84b x - 216a b x - 189a b x - 56a +--R (3) -------------------------------------- +--R 9 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 1118 + +--S 1119 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1119 + +--S 1120 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1120 + +)clear all + +--S 1121 of 3330 +t0000:=(a+b*x)^2/x^10 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1121 + +--S 1122 of 3330 +r0000:=-1/9*a^2/x^9-1/4*a*b/x^8-1/7*b^2/x^7 +--R +--R +--R 1 2 2 1 1 2 +--R - - b x - - a b x - - a +--R 7 4 9 +--R (2) ------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1122 + +--S 1123 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R - 36b x - 63a b x - 28a +--R (3) ------------------------- +--R 9 +--R 252x +--R Type: Union(Expression(Integer),...) +--E 1123 + +--S 1124 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1125 + +)clear all + +--S 1126 of 3330 +t0000:=(a+b*x)/x^10 +--R +--R +--R b x + a +--R (1) ------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1126 + +--S 1127 of 3330 +r0000:=-1/9*a/x^9-1/8*b/x^8 +--R +--R +--R 1 1 +--R - - b x - - a +--R 8 9 +--R (2) ------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1127 + +--S 1128 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 9b x - 8a +--R (3) ----------- +--R 9 +--R 72x +--R Type: Union(Expression(Integer),...) +--E 1128 + +--S 1129 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1130 + +)clear all + +--S 1131 of 3330 +t0000:=1/x^10 +--R +--R +--R 1 +--R (1) --- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1131 + +--S 1132 of 3330 +r0000:=(-1/9)/x^9 +--R +--R +--R 1 +--R - +--R 9 +--R (2) - --- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1132 + +--S 1133 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - --- +--R 9 +--R 9x +--R Type: Union(Expression(Integer),...) +--E 1133 + +--S 1134 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1135 + +)clear all + +--S 1136 of 3330 +t0000:=1/(x^10*(a+b*x)) +--R +--R +--R 1 +--R (1) ------------- +--R 11 10 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1136 + +--S 1137 of 3330 +r0000:=(-1/9)/(a*x^9)+1/8*b/(a^2*x^8)-1/7*b^2/(a^3*x^7)+1/6*b^3/(a^4*x^6)-_ + 1/5*b^4/(a^5*x^5)+1/4*b^5/(a^6*x^4)-1/3*b^6/(a^7*x^3)+_ + 1/2*b^7/(a^8*x^2)-b^8/(a^9*x)-b^9*log(x)/a^10+b^9*log(a+b*x)/a^10 +--R +--R +--R (2) +--R 9 9 9 9 8 8 2 7 7 +--R 2520b x log(b x + a) - 2520b x log(x) - 2520a b x + 1260a b x +--R + +--R 3 6 6 4 5 5 5 4 4 6 3 3 7 2 2 8 +--R - 840a b x + 630a b x - 504a b x + 420a b x - 360a b x + 315a b x +--R + +--R 9 +--R - 280a +--R / +--R 10 9 +--R 2520a x +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 9 9 8 8 2 7 7 +--R 2520b x log(b x + a) - 2520b x log(x) - 2520a b x + 1260a b x +--R + +--R 3 6 6 4 5 5 5 4 4 6 3 3 7 2 2 8 +--R - 840a b x + 630a b x - 504a b x + 420a b x - 360a b x + 315a b x +--R + +--R 9 +--R - 280a +--R / +--R 10 9 +--R 2520a x +--R Type: Union(Expression(Integer),...) +--E 1138 + +--S 1139 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1140 + +)clear all + +--S 1141 of 3330 +t0000:=1/(x^10*(a+b*x)^2) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 12 11 2 10 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1141 + +--S 1142 of 3330 +r0000:=(-1/9)/(a^2*x^9)+1/4*b/(a^3*x^8)-3/7*b^2/(a^4*x^7)+_ + 2/3*b^3/(a^5*x^6)-b^4/(a^6*x^5)+3/2*b^5/(a^7*x^4)-_ + 7/3*b^6/(a^8*x^3)+4*b^7/(a^9*x^2)-9*b^8/(a^10*x)-_ + b^9/(a^10*(a+b*x))-10*b^9*log(x)/a^11+10*b^9*log(a+b*x)/a^11 +--R +--R +--R (2) +--R 10 10 9 9 10 10 9 9 +--R (2520b x + 2520a b x )log(b x + a) + (- 2520b x - 2520a b x )log(x) +--R + +--R 9 9 2 8 8 3 7 7 4 6 6 5 5 5 6 4 4 +--R - 2520a b x - 1260a b x + 420a b x - 210a b x + 126a b x - 84a b x +--R + +--R 7 3 3 8 2 2 9 10 +--R 60a b x - 45a b x + 35a b x - 28a +--R / +--R 11 10 12 9 +--R 252a b x + 252a x +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 10 10 9 9 +--R (2520b x + 2520a b x )log(b x + a) + (- 2520b x - 2520a b x )log(x) +--R + +--R 9 9 2 8 8 3 7 7 4 6 6 5 5 5 6 4 4 +--R - 2520a b x - 1260a b x + 420a b x - 210a b x + 126a b x - 84a b x +--R + +--R 7 3 3 8 2 2 9 10 +--R 60a b x - 45a b x + 35a b x - 28a +--R / +--R 11 10 12 9 +--R 252a b x + 252a x +--R Type: Union(Expression(Integer),...) +--E 1143 + +--S 1144 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1145 + +)clear all + +--S 1146 of 3330 +t0000:=1/(x^10*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 3 13 2 12 2 11 3 10 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1146 + +--S 1147 of 3330 +r0000:=(-1/9)/(a^3*x^9)+3/8*b/(a^4*x^8)-6/7*b^2/(a^5*x^7)+_ + 5/3*b^3/(a^6*x^6)-3*b^4/(a^7*x^5)+21/4*b^5/(a^8*x^4)-_ + 28/3*b^6/(a^9*x^3)+18*b^7/(a^10*x^2)-45*b^8/(a^11*x)-_ + 1/2*b^9/(a^10*(a+b*x)^2)-10*b^9/(a^11*(a+b*x))-_ + 55*b^9*log(x)/a^12+55*b^9*log(a+b*x)/a^12 +--R +--R +--R (2) +--R 11 11 10 10 2 9 9 +--R (27720b x + 55440a b x + 27720a b x )log(b x + a) +--R + +--R 11 11 10 10 2 9 9 10 10 +--R (- 27720b x - 55440a b x - 27720a b x )log(x) - 27720a b x +--R + +--R 2 9 9 3 8 8 4 7 7 5 6 6 6 5 5 +--R - 41580a b x - 9240a b x + 2310a b x - 924a b x + 462a b x +--R + +--R 7 4 4 8 3 3 9 2 2 10 11 +--R - 264a b x + 165a b x - 110a b x + 77a b x - 56a +--R / +--R 12 2 11 13 10 14 9 +--R 504a b x + 1008a b x + 504a x +--R Type: Expression(Integer) +--E 1147 + +--S 1148 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 11 11 10 10 2 9 9 +--R (27720b x + 55440a b x + 27720a b x )log(b x + a) +--R + +--R 11 11 10 10 2 9 9 10 10 +--R (- 27720b x - 55440a b x - 27720a b x )log(x) - 27720a b x +--R + +--R 2 9 9 3 8 8 4 7 7 5 6 6 6 5 5 +--R - 41580a b x - 9240a b x + 2310a b x - 924a b x + 462a b x +--R + +--R 7 4 4 8 3 3 9 2 2 10 11 +--R - 264a b x + 165a b x - 110a b x + 77a b x - 56a +--R / +--R 12 2 11 13 10 14 9 +--R 504a b x + 1008a b x + 504a x +--R Type: Union(Expression(Integer),...) +--E 1148 + +--S 1149 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1150 + +)clear all + +--S 1151 of 3330 +t0000:=1/(x*(2+3*x)) +--R +--R +--R 1 +--R (1) -------- +--R 2 +--R 3x + 2x +--R Type: Fraction(Polynomial(Integer)) +--E 1151 + +--S 1152 of 3330 +r0000:=1/2*log(x)-1/2*log(2+3*x) +--R +--R +--R - log(3x + 2) + log(x) +--R (2) ---------------------- +--R 2 +--R Type: Expression(Integer) +--E 1152 + +--S 1153 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - log(3x + 2) + log(x) +--R (3) ---------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1153 + +--S 1154 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1155 + +)clear all + +--S 1156 of 3330 +t0000:=1/(x*(4+6*x)) +--R +--R +--R 1 +--R (1) -------- +--R 2 +--R 6x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1156 + +--S 1157 of 3330 +r0000:=1/4*log(x)-1/4*log(2+3*x) +--R +--R +--R - log(3x + 2) + log(x) +--R (2) ---------------------- +--R 4 +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - log(3x + 2) + log(x) +--R (3) ---------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 1158 + +--S 1159 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1160 + +)clear all + +--S 1161 of 3330 +t0000:=1/(x^2*(4+6*x)) +--R +--R +--R 1 +--R (1) --------- +--R 3 2 +--R 6x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1161 + +--S 1162 of 3330 +r0000:=(-1/4)/x-3/8*log(x)+3/8*log(2+3*x) +--R +--R +--R 3x log(3x + 2) - 3x log(x) - 2 +--R (2) ------------------------------ +--R 8x +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3x log(3x + 2) - 3x log(x) - 2 +--R (3) ------------------------------ +--R 8x +--R Type: Union(Expression(Integer),...) +--E 1163 + +--S 1164 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1165 + +)clear all + +--S 1166 of 3330 +t0000:=1/(x^3*(4+6*x)) +--R +--R +--R 1 +--R (1) --------- +--R 4 3 +--R 6x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1166 + +--S 1167 of 3330 +r0000:=(-1/8)/x^2+3/8/x+9/16*log(x)-9/16*log(2+3*x) +--R +--R +--R 2 2 +--R - 9x log(3x + 2) + 9x log(x) + 6x - 2 +--R (2) ------------------------------------- +--R 2 +--R 16x +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 +--R - 9x log(3x + 2) + 9x log(x) + 6x - 2 +--R (3) ------------------------------------- +--R 2 +--R 16x +--R Type: Union(Expression(Integer),...) +--E 1168 + +--S 1169 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1170 + +)clear all + +--S 1171 of 3330 +t0000:=1/(x^4*(4+6*x)) +--R +--R +--R 1 +--R (1) --------- +--R 5 4 +--R 6x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1171 + +--S 1172 of 3330 +r0000:=(-1/12)/x^3+3/16/x^2+(-9/16)/x-27/32*log(x)+27/32*log(2+3*x) +--R +--R +--R 3 3 2 +--R 81x log(3x + 2) - 81x log(x) - 54x + 18x - 8 +--R (2) --------------------------------------------- +--R 3 +--R 96x +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 +--R 81x log(3x + 2) - 81x log(x) - 54x + 18x - 8 +--R (3) --------------------------------------------- +--R 3 +--R 96x +--R Type: Union(Expression(Integer),...) +--E 1173 + +--S 1174 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1174 + +--S 1175 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1175 + +)clear all + +--S 1176 of 3330 +t0000:=1/(x^5*(4+6*x)) +--R +--R +--R 1 +--R (1) --------- +--R 6 5 +--R 6x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1176 + +--S 1177 of 3330 +r0000:=(-1/16)/x^4+1/8/x^3+(-9/32)/x^2+27/32/x+81/64*log(x)-81/64*log(2+3*x) +--R +--R +--R 4 4 3 2 +--R - 81x log(3x + 2) + 81x log(x) + 54x - 18x + 8x - 4 +--R (2) ----------------------------------------------------- +--R 4 +--R 64x +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 2 +--R - 81x log(3x + 2) + 81x log(x) + 54x - 18x + 8x - 4 +--R (3) ----------------------------------------------------- +--R 4 +--R 64x +--R Type: Union(Expression(Integer),...) +--E 1178 + +--S 1179 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1179 + +--S 1180 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1180 + +)clear all + +--S 1181 of 3330 +t0000:=1/(x*(4+6*x)^2) +--R +--R +--R 1 +--R (1) ----------------- +--R 3 2 +--R 36x + 48x + 16x +--R Type: Fraction(Polynomial(Integer)) +--E 1181 + +--S 1182 of 3330 +r0000:=1/8/(2+3*x)+1/16*log(x)-1/16*log(2+3*x) +--R +--R +--R (- 3x - 2)log(3x + 2) + (3x + 2)log(x) + 2 +--R (2) ------------------------------------------ +--R 48x + 32 +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (- 3x - 2)log(3x + 2) + (3x + 2)log(x) + 2 +--R (3) ------------------------------------------ +--R 48x + 32 +--R Type: Union(Expression(Integer),...) +--E 1183 + +--S 1184 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1185 + +)clear all + +--S 1186 of 3330 +t0000:=1/(x^2*(4+6*x)^2) +--R +--R +--R 1 +--R (1) ------------------ +--R 4 3 2 +--R 36x + 48x + 16x +--R Type: Fraction(Polynomial(Integer)) +--E 1186 + +--S 1187 of 3330 +r0000:=(-1/16)/x+(-3/16)/(2+3*x)-3/16*log(x)+3/16*log(2+3*x) +--R +--R +--R 2 2 +--R (9x + 6x)log(3x + 2) + (- 9x - 6x)log(x) - 6x - 2 +--R (2) --------------------------------------------------- +--R 2 +--R 48x + 32x +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 +--R (9x + 6x)log(3x + 2) + (- 9x - 6x)log(x) - 6x - 2 +--R (3) --------------------------------------------------- +--R 2 +--R 48x + 32x +--R Type: Union(Expression(Integer),...) +--E 1188 + +--S 1189 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1190 + +)clear all + +--S 1191 of 3330 +t0000:=1/(x^3*(4+6*x)^2) +--R +--R +--R 1 +--R (1) ------------------ +--R 5 4 3 +--R 36x + 48x + 16x +--R Type: Fraction(Polynomial(Integer)) +--E 1191 + +--S 1192 of 3330 +r0000:=(-1/32)/x^2+3/16/x+9/32/(2+3*x)+27/64*log(x)-27/64*log(2+3*x) +--R +--R +--R 3 2 3 2 2 +--R (- 81x - 54x )log(3x + 2) + (81x + 54x )log(x) + 54x + 18x - 4 +--R (2) ----------------------------------------------------------------- +--R 3 2 +--R 192x + 128x +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 2 3 2 2 +--R (- 81x - 54x )log(3x + 2) + (81x + 54x )log(x) + 54x + 18x - 4 +--R (3) ----------------------------------------------------------------- +--R 3 2 +--R 192x + 128x +--R Type: Union(Expression(Integer),...) +--E 1193 + +--S 1194 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 3330 +t0000:=1/(x^4*(4+6*x)^2) +--R +--R +--R 1 +--R (1) ------------------ +--R 6 5 4 +--R 36x + 48x + 16x +--R Type: Fraction(Polynomial(Integer)) +--E 1196 + +--S 1197 of 3330 +r0000:=(-1/48)/x^3+3/32/x^2+(-27/64)/x+(-27/64)/(2+3*x)-_ + 27/32*log(x)+27/32*log(2+3*x) +--R +--R +--R (2) +--R 4 3 4 3 3 2 +--R (243x + 162x )log(3x + 2) + (- 243x - 162x )log(x) - 162x - 54x + 12x - 4 +--R ----------------------------------------------------------------------------- +--R 4 3 +--R 288x + 192x +--R Type: Expression(Integer) +--E 1197 + +--S 1198 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 4 3 3 2 +--R (243x + 162x )log(3x + 2) + (- 243x - 162x )log(x) - 162x - 54x + 12x - 4 +--R ----------------------------------------------------------------------------- +--R 4 3 +--R 288x + 192x +--R Type: Union(Expression(Integer),...) +--E 1198 + +--S 1199 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1200 + +)clear all + +--S 1201 of 3330 +t0000:=1/(x^5*(4+6*x)^2) +--R +--R +--R 1 +--R (1) ------------------ +--R 7 6 5 +--R 36x + 48x + 16x +--R Type: Fraction(Polynomial(Integer)) +--E 1201 + +--S 1202 of 3330 +r0000:=(-1/64)/x^4+1/16/x^3+(-27/128)/x^2+27/32/x+_ + 81/128/(2+3*x)+405/256*log(x)-405/256*log(2+3*x) +--R +--R +--R (2) +--R 5 4 5 4 4 3 +--R (- 1215x - 810x )log(3x + 2) + (1215x + 810x )log(x) + 810x + 270x +--R + +--R 2 +--R - 60x + 20x - 8 +--R / +--R 5 4 +--R 768x + 512x +--R Type: Expression(Integer) +--E 1202 + +--S 1203 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 5 4 4 3 +--R (- 1215x - 810x )log(3x + 2) + (1215x + 810x )log(x) + 810x + 270x +--R + +--R 2 +--R - 60x + 20x - 8 +--R / +--R 5 4 +--R 768x + 512x +--R Type: Union(Expression(Integer),...) +--E 1203 + +--S 1204 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1205 + +)clear all + +--S 1206 of 3330 +t0000:=1/(x*(4+6*x)^3) +--R +--R +--R 1 +--R (1) --------------------------- +--R 4 3 2 +--R 216x + 432x + 288x + 64x +--R Type: Fraction(Polynomial(Integer)) +--E 1206 + +--S 1207 of 3330 +r0000:=1/32/(2+3*x)^2+1/32/(2+3*x)+1/64*log(x)-1/64*log(2+3*x) +--R +--R +--R 2 2 +--R (- 9x - 12x - 4)log(3x + 2) + (9x + 12x + 4)log(x) + 6x + 6 +--R (2) ------------------------------------------------------------- +--R 2 +--R 576x + 768x + 256 +--R Type: Expression(Integer) +--E 1207 + +--S 1208 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 +--R (- 9x - 12x - 4)log(3x + 2) + (9x + 12x + 4)log(x) + 6x + 6 +--R (3) ------------------------------------------------------------- +--R 2 +--R 576x + 768x + 256 +--R Type: Union(Expression(Integer),...) +--E 1208 + +--S 1209 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1210 + +)clear all + +--S 1211 of 3330 +t0000:=1/(x^2*(4+6*x)^3) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 5 4 3 2 +--R 216x + 432x + 288x + 64x +--R Type: Fraction(Polynomial(Integer)) +--E 1211 + +--S 1212 of 3330 +r0000:=(-1/64)/x+(-3/64)/(2+3*x)^2+(-3/32)/(2+3*x)-_ + 9/128*log(x)+9/128*log(2+3*x) +--R +--R +--R (2) +--R 3 2 3 2 2 +--R (81x + 108x + 36x)log(3x + 2) + (- 81x - 108x - 36x)log(x) - 54x +--R + +--R - 54x - 8 +--R / +--R 3 2 +--R 1152x + 1536x + 512x +--R Type: Expression(Integer) +--E 1212 + +--S 1213 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 3 2 2 +--R (81x + 108x + 36x)log(3x + 2) + (- 81x - 108x - 36x)log(x) - 54x +--R + +--R - 54x - 8 +--R / +--R 3 2 +--R 1152x + 1536x + 512x +--R Type: Union(Expression(Integer),...) +--E 1213 + +--S 1214 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1215 + +)clear all + +--S 1216 of 3330 +t0000:=1/(x^3*(4+6*x)^3) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 6 5 4 3 +--R 216x + 432x + 288x + 64x +--R Type: Fraction(Polynomial(Integer)) +--E 1216 + +--S 1217 of 3330 +r0000:=(-1/128)/x^2+9/128/x+9/128/(2+3*x)^2+27/128/(2+3*x)+_ + 27/128*log(x)-27/128*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 4 3 2 +--R (- 243x - 324x - 108x )log(3x + 2) + (243x + 324x + 108x )log(x) +--R + +--R 3 2 +--R 162x + 162x + 24x - 4 +--R / +--R 4 3 2 +--R 1152x + 1536x + 512x +--R Type: Expression(Integer) +--E 1217 + +--S 1218 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 2 4 3 2 +--R (- 243x - 324x - 108x )log(3x + 2) + (243x + 324x + 108x )log(x) +--R + +--R 3 2 +--R 162x + 162x + 24x - 4 +--R / +--R 4 3 2 +--R 1152x + 1536x + 512x +--R Type: Union(Expression(Integer),...) +--E 1218 + +--S 1219 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1220 + +)clear all + +--S 1221 of 3330 +t0000:=1/(x^4*(4+6*x)^3) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 7 6 5 4 +--R 216x + 432x + 288x + 64x +--R Type: Fraction(Polynomial(Integer)) +--E 1221 + +--S 1222 of 3330 +r0000:=(-1/192)/x^3+9/256/x^2+(-27/128)/x+(-27/256)/(2+3*x)^2+_ + (-27/64)/(2+3*x)-135/256*log(x)+135/256*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 +--R (3645x + 4860x + 1620x )log(3x + 2) +--R + +--R 5 4 3 4 3 2 +--R (- 3645x - 4860x - 1620x )log(x) - 2430x - 2430x - 360x + 60x - 16 +--R / +--R 5 4 3 +--R 6912x + 9216x + 3072x +--R Type: Expression(Integer) +--E 1222 + +--S 1223 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 3 +--R (3645x + 4860x + 1620x )log(3x + 2) +--R + +--R 5 4 3 4 3 2 +--R (- 3645x - 4860x - 1620x )log(x) - 2430x - 2430x - 360x + 60x - 16 +--R / +--R 5 4 3 +--R 6912x + 9216x + 3072x +--R Type: Union(Expression(Integer),...) +--E 1223 + +--S 1224 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1225 + +)clear all + +--S 1226 of 3330 +t0000:=1/(x^5*(4+6*x)^3) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 8 7 6 5 +--R 216x + 432x + 288x + 64x +--R Type: Fraction(Polynomial(Integer)) +--E 1226 + +--S 1227 of 3330 +r0000:=(-1/256)/x^4+3/128/x^3+(-27/256)/x^2+135/256/x+81/512/(2+3*x)^2+_ + 405/512/(2+3*x)+1215/1024*log(x)-1215/1024*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 +--R (- 10935x - 14580x - 4860x )log(3x + 2) +--R + +--R 6 5 4 5 4 3 2 +--R (10935x + 14580x + 4860x )log(x) + 7290x + 7290x + 1080x - 180x +--R + +--R 48x - 16 +--R / +--R 6 5 4 +--R 9216x + 12288x + 4096x +--R Type: Expression(Integer) +--E 1227 + +--S 1228 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 5 4 +--R (- 10935x - 14580x - 4860x )log(3x + 2) +--R + +--R 6 5 4 5 4 3 2 +--R (10935x + 14580x + 4860x )log(x) + 7290x + 7290x + 1080x - 180x +--R + +--R 48x - 16 +--R / +--R 6 5 4 +--R 9216x + 12288x + 4096x +--R Type: Union(Expression(Integer),...) +--E 1228 + +--S 1229 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1230 + +--R +--R +)clear all + +--S 1231 of 3330 +t0000:=1/(2+2*x) +--R +--R +--R 1 +--R (1) ------ +--R 2x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1231 + +--S 1232 of 3330 +r0000:=1/2*log(1+x) +--R +--R +--R log(x + 1) +--R (2) ---------- +--R 2 +--R Type: Expression(Integer) +--E 1232 + +--S 1233 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R log(x + 1) +--R (3) ---------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1233 + +--S 1234 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1235 + +)clear all + +--S 1236 of 3330 +t0000:=1/(4-6*x) +--R +--R +--R 1 +--R (1) - ------ +--R 6x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 1236 + +--S 1237 of 3330 +r0000:=-1/6*log(2-3*x) +--R +--R +--R log(- 3x + 2) +--R (2) - ------------- +--R 6 +--R Type: Expression(Integer) +--E 1237 + +--S 1238 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R log(3x - 2) +--R (3) - ----------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1238 + +--S 1239 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R - log(3x - 2) + log(- 3x + 2) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1240 + +)clear all + +--S 1241 of 3330 +t0000:=1/(a+x*sqrt(a)) +--R +--R +--R 1 +--R (1) --------- +--R +-+ +--R x\|a + a +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 3330 +r0000:=log(x+sqrt(a))/sqrt(a) +--R +--R +--R +-+ +--R log(\|a + x) +--R (2) ------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1242 + +--S 1243 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +--R log(x\|a + a) +--R (3) -------------- +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 1243 + +--S 1244 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R +-+ +-+ +--R log(x\|a + a) - log(\|a + x) +--R (4) ------------------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1244 + +--S 1245 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1245 + +)clear all + +--S 1246 of 3330 +t0000:=1/(a+x*sqrt(-a)) +--R +--R +--R 1 +--R (1) ----------- +--R +---+ +--R x\|- a + a +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 3330 +r0000:=log(-x+sqrt(-a))/sqrt(-a) +--R +--R +--R +---+ +--R log(\|- a - x) +--R (2) --------------- +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1247 + +--S 1248 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +---+ +--R log(x\|- a + a) +--R (3) ---------------- +--R +---+ +--R \|- a +--R Type: Union(Expression(Integer),...) +--E 1248 + +--S 1249 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R +---+ +---+ +--R log(x\|- a + a) - log(\|- a - x) +--R (4) ---------------------------------- +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1250 + +)clear all + +--S 1251 of 3330 +t0000:=1/(a^2+x*sqrt(-a)) +--R +--R +--R 1 +--R (1) ------------ +--R +---+ 2 +--R x\|- a + a +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 3330 +r0000:=log((-a)^(3/2)+x)/sqrt(-a) +--R +--R +--R +---+ +--R log(- a\|- a + x) +--R (2) ------------------ +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1252 + +--S 1253 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +---+ 2 +--R log(x\|- a + a ) +--R (3) ----------------- +--R +---+ +--R \|- a +--R Type: Union(Expression(Integer),...) +--E 1253 + +--S 1254 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R +---+ 2 +---+ +--R log(x\|- a + a ) - log(- a\|- a + x) +--R (4) -------------------------------------- +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1254 + +--S 1255 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1255 + +)clear all + +--S 1256 of 3330 +t0000:=1/(a^3+x*sqrt(-a)) +--R +--R +--R 1 +--R (1) ------------ +--R +---+ 3 +--R x\|- a + a +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 3330 +r0000:=log((-a)^(5/2)-x)/sqrt(-a) +--R +--R +--R 2 +---+ +--R log(a \|- a - x) +--R (2) ----------------- +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1257 + +--S 1258 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +---+ 3 +--R log(x\|- a + a ) +--R (3) ----------------- +--R +---+ +--R \|- a +--R Type: Union(Expression(Integer),...) +--E 1258 + +--S 1259 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R +---+ 3 2 +---+ +--R log(x\|- a + a ) - log(a \|- a - x) +--R (4) ------------------------------------- +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1259 + +--S 1260 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1260 + +)clear all + +--S 1261 of 3330 +t0000:=1/(1/a+x*sqrt(-a)) +--R +--R +--R a +--R (1) ------------- +--R +---+ +--R a x\|- a + 1 +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 3330 +r0000:=log(1-(-a)^(3/2)*x)/sqrt(-a) +--R +--R +--R +---+ +--R log(a x\|- a + 1) +--R (2) ------------------ +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1262 + +--S 1263 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +---+ +--R log(a x\|- a + 1) +--R (3) ------------------ +--R +---+ +--R \|- a +--R Type: Union(Expression(Integer),...) +--E 1263 + +--S 1264 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1264 + +--S 1265 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1265 + +)clear all + +--S 1266 of 3330 +t0000:=1/(1/a^2+x*sqrt(-a)) +--R +--R +--R 2 +--R a +--R (1) ------------- +--R 2 +---+ +--R a x\|- a + 1 +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 3330 +r0000:=log(1+(-a)^(5/2)*x)/sqrt(-a) +--R +--R +--R 2 +---+ +--R log(a x\|- a + 1) +--R (2) ------------------ +--R +---+ +--R \|- a +--R Type: Expression(Integer) +--E 1267 + +--S 1268 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +---+ +--R log(a x\|- a + 1) +--R (3) ------------------ +--R +---+ +--R \|- a +--R Type: Union(Expression(Integer),...) +--E 1268 + +--S 1269 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1270 + +)clear all + +--S 1271 of 3330 +t0000:=1/(x*(1+b*x)) +--R +--R +--R 1 +--R (1) -------- +--R 2 +--R b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1271 + +--S 1272 of 3330 +r0000:=log(x)-log(1+b*x) +--R +--R +--R (2) - log(b x + 1) + log(x) +--R Type: Expression(Integer) +--E 1272 + +--S 1273 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) - log(b x + 1) + log(x) +--R Type: Union(Expression(Integer),...) +--E 1273 + +--S 1274 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1275 + +)clear all + +--S 1276 of 3330 +t0000:=1/(x*(-1+b*x)) +--R +--R +--R 1 +--R (1) -------- +--R 2 +--R b x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1276 + +--S 1277 of 3330 +r0000:=-log(x)+log(1-b*x) +--R +--R +--R (2) - log(x) + log(- b x + 1) +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) log(b x - 1) - log(x) +--R Type: Union(Expression(Integer),...) +--E 1278 + +--S 1279 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) log(b x - 1) - log(- b x + 1) +--R Type: Expression(Integer) +--E 1279 + +--S 1280 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1280 + +)clear all + +--S 1281 of 3330 +t0000:=1/(x^2*(1+b*x)) +--R +--R +--R 1 +--R (1) --------- +--R 3 2 +--R b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1281 + +--S 1282 of 3330 +r0000:=(-1)/x-b*log(x)+b*log(1+b*x) +--R +--R +--R b x log(b x + 1) - b x log(x) - 1 +--R (2) --------------------------------- +--R x +--R Type: Expression(Integer) +--E 1282 + +--S 1283 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R b x log(b x + 1) - b x log(x) - 1 +--R (3) --------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 1283 + +--S 1284 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1285 + +)clear all + +--S 1286 of 3330 +t0000:=1/(x^2*(-1+b*x)) +--R +--R +--R 1 +--R (1) --------- +--R 3 2 +--R b x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1286 + +--S 1287 of 3330 +r0000:=1/x-b*log(x)+b*log(1-b*x) +--R +--R +--R - b x log(x) + b x log(- b x + 1) + 1 +--R (2) ------------------------------------- +--R x +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R b x log(b x - 1) - b x log(x) + 1 +--R (3) --------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 1288 + +--S 1289 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) b log(b x - 1) - b log(- b x + 1) +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1290 + +)clear all + +--S 1291 of 3330 +t0000:=b/x+1/(x^2*(1+b*x)) +--R +--R +--R 2 2 +--R b x + b x + 1 +--R (1) -------------- +--R 3 2 +--R b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1291 + +--S 1292 of 3330 +r0000:=(-1)/x+b*log(1+b*x) +--R +--R +--R b x log(b x + 1) - 1 +--R (2) -------------------- +--R x +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R b x log(b x + 1) - 1 +--R (3) -------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 1293 + +--S 1294 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1294 + +--S 1295 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1295 + +)clear all + +--S 1296 of 3330 +t0000:=x^m*sqrt(a+b*x) +--R +--R +--R m +-------+ +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 3330 +--r0000:=2*x^(1+m)*sqrt(a+b*x)/(3+2*m)+2*a*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (b*(3+2*m)*(-b*x/a)^m) +--E 1297 + +--S 1298 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R ++ m +--------+ +--R (2) | %N \|%N b + a d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 1298 + +--S 1299 of 3330 +--m0000:=a0000 - r0000 +--E 1299 + +--S 1300 of 3330 +--d0000:=D(m0000,x) +--E 1300 + +)clear all + +--S 1301 of 3330 +t0000:=x^3*sqrt(a+b*x) +--R +--R +--R 3 +-------+ +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 3330 +r0000:=-2/3*a^3*(a+b*x)^(3/2)/b^4+6/5*a^2*(a+b*x)^(5/2)/b^4-_ + 6/7*a*(a+b*x)^(7/2)/b^4+2/9*(a+b*x)^(9/2)/b^4 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 10a b x - 12a b x + 16a b x - 32a )\|b x + a +--R (2) --------------------------------------------------------- +--R 4 +--R 315b +--R Type: Expression(Integer) +--E 1302 + +--S 1303 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 10a b x - 12a b x + 16a b x - 32a )\|b x + a +--R (3) --------------------------------------------------------- +--R 4 +--R 315b +--R Type: Union(Expression(Integer),...) +--E 1303 + +--S 1304 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1305 + +)clear all + +--S 1306 of 3330 +t0000:=x^2*sqrt(a+b*x) +--R +--R +--R 2 +-------+ +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 3330 +r0000:=2/3*a^2*(a+b*x)^(3/2)/b^3-4/5*a*(a+b*x)^(5/2)/b^3+2/7*(a+b*x)^(7/2)/b^3 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (30b x + 6a b x - 8a b x + 16a )\|b x + a +--R (2) -------------------------------------------- +--R 3 +--R 105b +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (30b x + 6a b x - 8a b x + 16a )\|b x + a +--R (3) -------------------------------------------- +--R 3 +--R 105b +--R Type: Union(Expression(Integer),...) +--E 1308 + +--S 1309 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1309 + +--S 1310 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1310 + +)clear all + +--S 1311 of 3330 +t0000:=x*sqrt(a+b*x) +--R +--R +--R +-------+ +--R (1) x\|b x + a +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 3330 +r0000:=-2/3*a*(a+b*x)^(3/2)/b^2+2/5*(a+b*x)^(5/2)/b^2 +--R +--R +--R 2 2 2 +-------+ +--R (6b x + 2a b x - 4a )\|b x + a +--R (2) -------------------------------- +--R 2 +--R 15b +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +-------+ +--R (6b x + 2a b x - 4a )\|b x + a +--R (3) -------------------------------- +--R 2 +--R 15b +--R Type: Union(Expression(Integer),...) +--E 1313 + +--S 1314 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1315 + +)clear all + +--S 1316 of 3330 +t0000:=sqrt(a+b*x) +--R +--R +--R +-------+ +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 3330 +r0000:=2/3*(a+b*x)^(3/2)/b +--R +--R +--R +-------+ +--R (2b x + 2a)\|b x + a +--R (2) --------------------- +--R 3b +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +--R (2b x + 2a)\|b x + a +--R (3) --------------------- +--R 3b +--R Type: Union(Expression(Integer),...) +--E 1318 + +--S 1319 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1319 + +--S 1320 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1320 + +)clear all + +--S 1321 of 3330 +t0000:=sqrt(a+b*x)/x +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 3330 +r0000:=-2*atanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+2*sqrt(a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x + a +-------+ +--R (2) - 2\|a atanh(----------) + 2\|b x + a +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-------+ +--R [\|a log(----------------------------) + 2\|b x + a , +--R x +--R +-------+ +--R +---+ \|b x + a +-------+ +--R - 2\|- a atan(----------) + 2\|b x + a ] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1323 + +--S 1324 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a +--R (4) \|a log(----------------------------) + 2\|a atanh(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1324 + +--S 1325 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1325 + +--S 1326 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R +-+ \|b x + a +---+ \|b x + a +--R (6) 2\|a atanh(----------) - 2\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1327 + +)clear all + +--S 1328 of 3330 +t0000:=sqrt(a+b*x)/x^2 +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 3330 +r0000:=-b*atanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)-sqrt(a+b*x)/x +--R +--R +--R +-------+ +--R \|b x + a +-+ +-------+ +--R - b x atanh(----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R +-+ +--R x\|a +--R Type: Expression(Integer) +--E 1329 + +--S 1330 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R - 2a\|b x + a + (b x + 2a)\|a +-+ +-------+ +--R b x log(-------------------------------) - 2\|a \|b x + a +--R x +--R [----------------------------------------------------------, +--R +-+ +--R 2x\|a +--R +---+ +-------+ +--R \|- a \|b x + a +---+ +-------+ +--R - b x atan(----------------) - \|- a \|b x + a +--R a +--R -----------------------------------------------] +--R +---+ +--R x\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1330 + +--S 1331 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R b log(-------------------------------) + 2b atanh(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R b\|- a atanh(----------) - b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1334 + +)clear all + +--S 1335 of 3330 +t0000:=sqrt(a+b*x)/x^3 +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 3330 +r0000:=1/4*b^2*atanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-_ + 1/2*sqrt(a+b*x)/x^2-1/4*b*sqrt(a+b*x)/(a*x) +--R +--R +--R +-------+ +--R 2 2 \|b x + a +-+ +-------+ +--R b x atanh(----------) + (- b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) -------------------------------------------------- +--R 2 +-+ +--R 4a x \|a +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R 2 2 2a\|b x + a + (b x + 2a)\|a +-+ +-------+ +--R b x log(-----------------------------) + (- 2b x - 4a)\|a \|b x + a +--R x +--R [--------------------------------------------------------------------, +--R 2 +-+ +--R 8a x \|a +--R +---+ +-------+ +--R 2 2 \|- a \|b x + a +---+ +-------+ +--R b x atan(----------------) + (- b x - 2a)\|- a \|b x + a +--R a +--R ---------------------------------------------------------] +--R 2 +---+ +--R 4a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1337 + +--S 1338 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R b log(-----------------------------) - 2b atanh(----------) +--R x +-+ +--R \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1339 + +--S 1340 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R - b \|- a atanh(----------) + b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 4a\|- a \|a +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1341 + +)clear all + +--S 1342 of 3330 +t0000:=sqrt(a+b*x)/x^4 +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1342 + +--S 1343 of 3330 +r0000:=-1/8*b^3*atanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)-1/3*sqrt(a+b*x)/x^3-_ + 1/12*b*sqrt(a+b*x)/(a*x^2)+1/8*b^2*sqrt(a+b*x)/(a^2*x) +--R +--R +--R +-------+ +--R 3 3 \|b x + a 2 2 2 +-+ +-------+ +--R - 3b x atanh(----------) + (3b x - 2a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------- +--R 2 3 +-+ +--R 24a x \|a +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 3 3 - 2a\|b x + a + (b x + 2a)\|a +--R 3b x log(-------------------------------) +--R x +--R + +--R 2 2 2 +-+ +-------+ +--R (6b x - 4a b x - 16a )\|a \|b x + a +--R / +--R 2 3 +-+ +--R 48a x \|a +--R , +--R +---+ +-------+ +--R 3 3 \|- a \|b x + a 2 2 2 +---+ +-------+ +--R - 3b x atan(----------------) + (3b x - 2a b x - 8a )\|- a \|b x + a +--R a +--R ----------------------------------------------------------------------] +--R 2 3 +---+ +--R 24a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1344 + +--S 1345 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 3 - 2a\|b x + a + (b x + 2a)\|a 3 \|b x + a +--R b log(-------------------------------) + 2b atanh(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 2 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 3 +---+ \|b x + a 3 +-+ \|- a \|b x + a +--R b \|- a atanh(----------) - b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R 2 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1348 + +)clear all + +--S 1349 of 3330 +t0000:=x^m*(a+b*x)^(3/2) +--R +--R +--R m +-------+ +--R (1) (b x + a)x \|b x + a +--R Type: Expression(Integer) +--E 1349 + +--S 1350 of 3330 +--r0000:=2*x^(1+m)*(a+b*x)^(3/2)/(5+2*m)+_ +-- 6*a*x^(1+m)*sqrt(a+b*x)/(15+16*m+4*m^2)+_ +-- 6*a^2*x^m*hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (b*(15+16*m+4*m^2)*(-b*x/a)^m) +--E 1350 + +--S 1351 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R ++ m +--------+ +--R (2) | (%N b + a)%N \|%N b + a d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 1351 + +--S 1352 of 3330 +--m0000:=a0000 - r0000 +--E 1352 + +--S 1353 of 3330 +--d0000:=D(m0000,x) +--E 1353 + +)clear all + +--S 1354 of 3330 +t0000:=x^3*(a+b*x)^(3/2) +--R +--R +--R 4 3 +-------+ +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1354 + +--S 1355 of 3330 +r0000:=-2/5*a^3*(a+b*x)^(5/2)/b^4+6/7*a^2*(a+b*x)^(7/2)/b^4-_ + 2/3*a*(a+b*x)^(9/2)/b^4+2/11*(a+b*x)^(11/2)/b^4 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (210b x + 280a b x + 10a b x - 12a b x + 16a b x - 32a )\|b x + a +--R (2) ---------------------------------------------------------------------- +--R 4 +--R 1155b +--R Type: Expression(Integer) +--E 1355 + +--S 1356 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (210b x + 280a b x + 10a b x - 12a b x + 16a b x - 32a )\|b x + a +--R (3) ---------------------------------------------------------------------- +--R 4 +--R 1155b +--R Type: Union(Expression(Integer),...) +--E 1356 + +--S 1357 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1357 + +--S 1358 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1358 + +)clear all + +--S 1359 of 3330 +t0000:=x^2*(a+b*x)^(3/2) +--R +--R +--R 3 2 +-------+ +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1359 + +--S 1360 of 3330 +r0000:=2/5*a^2*(a+b*x)^(5/2)/b^3-4/7*a*(a+b*x)^(7/2)/b^3+2/9*(a+b*x)^(9/2)/b^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 100a b x + 6a b x - 8a b x + 16a )\|b x + a +--R (2) -------------------------------------------------------- +--R 3 +--R 315b +--R Type: Expression(Integer) +--E 1360 + +--S 1361 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 100a b x + 6a b x - 8a b x + 16a )\|b x + a +--R (3) -------------------------------------------------------- +--R 3 +--R 315b +--R Type: Union(Expression(Integer),...) +--E 1361 + +--S 1362 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1362 + +--S 1363 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1363 + +)clear all + +--S 1364 of 3330 +t0000:=x*(a+b*x)^(3/2) +--R +--R +--R 2 +-------+ +--R (1) (b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1364 + +--S 1365 of 3330 +r0000:=-2/5*a*(a+b*x)^(5/2)/b^2+2/7*(a+b*x)^(7/2)/b^2 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (10b x + 16a b x + 2a b x - 4a )\|b x + a +--R (2) -------------------------------------------- +--R 2 +--R 35b +--R Type: Expression(Integer) +--E 1365 + +--S 1366 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (10b x + 16a b x + 2a b x - 4a )\|b x + a +--R (3) -------------------------------------------- +--R 2 +--R 35b +--R Type: Union(Expression(Integer),...) +--E 1366 + +--S 1367 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1367 + +--S 1368 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1368 + +)clear all + +--S 1369 of 3330 +t0000:=(a+b*x)^(3/2) +--R +--R +--R +-------+ +--R (1) (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1369 + +--S 1370 of 3330 +r0000:=2/5*(a+b*x)^(5/2)/b +--R +--R +--R 2 2 2 +-------+ +--R (2b x + 4a b x + 2a )\|b x + a +--R (2) -------------------------------- +--R 5b +--R Type: Expression(Integer) +--E 1370 + +--S 1371 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +-------+ +--R (2b x + 4a b x + 2a )\|b x + a +--R (3) -------------------------------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 1371 + +--S 1372 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1372 + +--S 1373 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1373 + +)clear all + +--S 1374 of 3330 +t0000:=(a+b*x)^(3/2)/x +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R x +--R Type: Expression(Integer) +--E 1374 + +--S 1375 of 3330 +r0000:=2/3*(a+b*x)^(3/2)-2*a^(3/2)*atanh(sqrt(a+b*x)/sqrt(a))+2*a*sqrt(a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x + a +-------+ +--R - 6a\|a atanh(----------) + (2b x + 8a)\|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1375 + +--S 1376 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-------+ +--R 3a\|a log(----------------------------) + (2b x + 8a)\|b x + a +--R x +--R [---------------------------------------------------------------, +--R 3 +--R +-------+ +--R +---+ \|b x + a +-------+ +--R - 6a\|- a atan(----------) + (2b x + 8a)\|b x + a +--R +---+ +--R \|- a +--R --------------------------------------------------] +--R 3 +--R Type: Union(List(Expression(Integer)),...) +--E 1376 + +--S 1377 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a +--R (4) a\|a log(----------------------------) + 2a\|a atanh(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1377 + +--S 1378 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1378 + +--S 1379 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R +-+ \|b x + a +---+ \|b x + a +--R (6) 2a\|a atanh(----------) - 2a\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1379 + +--S 1380 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1380 + +)clear all + +--S 1381 of 3330 +t0000:=(a+b*x)^(3/2)/x^2 +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1381 + +--S 1382 of 3330 +r0000:=-(a+b*x)^(3/2)/x-3*b*atanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+3*b*sqrt(a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x + a +-------+ +--R - 3b x\|a atanh(----------) + (2b x - a)\|b x + a +--R +-+ +--R \|a +--R (2) -------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 1382 + +--S 1383 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-------+ +--R 3b x\|a log(----------------------------) + (4b x - 2a)\|b x + a +--R x +--R [-----------------------------------------------------------------, +--R 2x +--R +-------+ +--R +---+ \|b x + a +-------+ +--R - 3b x\|- a atan(----------) + (2b x - a)\|b x + a +--R +---+ +--R \|- a +--R ---------------------------------------------------] +--R x +--R Type: Union(List(Expression(Integer)),...) +--E 1383 + +--S 1384 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a +--R 3b\|a log(----------------------------) + 6b\|a atanh(----------) +--R x +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1384 + +--S 1385 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1385 + +--S 1386 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R +-+ \|b x + a +---+ \|b x + a +--R (6) 3b\|a atanh(----------) - 3b\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1386 + +--S 1387 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1387 + +)clear all + +--S 1388 of 3330 +t0000:=(a+b*x)^(3/2)/x^3 +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1388 + +--S 1389 of 3330 +r0000:=-1/2*(a+b*x)^(3/2)/x^2-3/4*b^2*atanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)-_ + 3/4*b*sqrt(a+b*x)/x +--R +--R +--R +-------+ +--R 2 2 \|b x + a +-+ +-------+ +--R - 3b x atanh(----------) + (- 5b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 2 +-+ +--R 4x \|a +--R Type: Expression(Integer) +--E 1389 + +--S 1390 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R 2 2 - 2a\|b x + a + (b x + 2a)\|a +-+ +-------+ +--R 3b x log(-------------------------------) + (- 10b x - 4a)\|a \|b x + a +--R x +--R [------------------------------------------------------------------------, +--R 2 +-+ +--R 8x \|a +--R +---+ +-------+ +--R 2 2 \|- a \|b x + a +---+ +-------+ +--R - 3b x atan(----------------) + (- 5b x - 2a)\|- a \|b x + a +--R a +--R -------------------------------------------------------------] +--R 2 +---+ +--R 4x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1390 + +--S 1391 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2 - 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R 3b log(-------------------------------) + 6b atanh(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 8\|a +--R Type: Expression(Integer) +--E 1391 + +--S 1392 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1392 + +--S 1393 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R 3b \|- a atanh(----------) - 3b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 4\|- a \|a +--R Type: Expression(Integer) +--E 1393 + +--S 1394 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1394 + +)clear all + +--S 1395 of 3330 +t0000:=(a+b*x)^(3/2)/x^4 +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1395 + +--S 1396 of 3330 +r0000:=-1/3*(a+b*x)^(3/2)/x^3+1/8*b^3*atanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-_ + 1/4*b*sqrt(a+b*x)/x^2-1/8*b^2*sqrt(a+b*x)/(a*x) +--R +--R +--R +-------+ +--R 3 3 \|b x + a 2 2 2 +-+ +-------+ +--R 3b x atanh(----------) + (- 3b x - 14a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------------- +--R 3 +-+ +--R 24a x \|a +--R Type: Expression(Integer) +--E 1396 + +--S 1397 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 3 3 2a\|b x + a + (b x + 2a)\|a +--R 3b x log(-----------------------------) +--R x +--R + +--R 2 2 2 +-+ +-------+ +--R (- 6b x - 28a b x - 16a )\|a \|b x + a +--R / +--R 3 +-+ +--R 48a x \|a +--R , +--R +---+ +-------+ +--R 3 3 \|- a \|b x + a 2 2 2 +---+ +-------+ +--R 3b x atan(----------------) + (- 3b x - 14a b x - 8a )\|- a \|b x + a +--R a +--R -----------------------------------------------------------------------] +--R 3 +---+ +--R 24a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1397 + +--S 1398 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 3 2a\|b x + a + (b x + 2a)\|a 3 \|b x + a +--R b log(-----------------------------) - 2b atanh(----------) +--R x +-+ +--R \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 16a\|a +--R Type: Expression(Integer) +--E 1398 + +--S 1399 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1399 + +--S 1400 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 3 +---+ \|b x + a 3 +-+ \|- a \|b x + a +--R - b \|- a atanh(----------) + b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 8a\|- a \|a +--R Type: Expression(Integer) +--E 1400 + +--S 1401 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1401 + +)clear all + +--S 1402 of 3330 +t0000:=x^m*(a+b*x)^(5/2) +--R +--R +--R 2 2 2 m +-------+ +--R (1) (b x + 2a b x + a )x \|b x + a +--R Type: Expression(Integer) +--E 1402 + +--S 1403 of 3330 +--r0000:=10*a*x^(1+m)*(a+b*x)^(3/2)/(35+24*m+4*m^2)+_ +-- 2*x^(1+m)*(a+b*x)^(5/2)/(7+2*m)+_ +-- 30*a^2*x^(1+m)*sqrt(a+b*x)/((7+2*m)*(15+16*m+4*m^2))+_ +-- 30*a^3*x^m*hypergeometric(1/2,-m,3/2,(a+b*x)/a)*_ +-- sqrt(a+b*x)/(b*(7+2*m)*(15+16*m+4*m^2)*(-b*x/a)^m) +--E 1403 + +--S 1404 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R ++ 2 2 2 m +--------+ +--R (2) | (%N b + 2%N a b + a )%N \|%N b + a d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 1404 + +--S 1405 of 3330 +--m0000:=a0000 - r0000 +--E 1405 + +--S 1406 of 3330 +--d0000:=D(m0000,x) +--E 1406 + +)clear all + +--S 1407 of 3330 +t0000:=x^3*(a+b*x)^(5/2) +--R +--R +--R 2 5 4 2 3 +-------+ +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1407 + +--S 1408 of 3330 +r0000:=-2/7*a^3*(a+b*x)^(7/2)/b^4+2/3*a^2*(a+b*x)^(9/2)/b^4-_ + 6/11*a*(a+b*x)^(11/2)/b^4+2/13*(a+b*x)^(13/2)/b^4 +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (462b x + 1134a b x + 742a b x + 10a b x - 12a b x + 16a b x - 32a ) +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 +--R 3003b +--R Type: Expression(Integer) +--E 1408 + +--S 1409 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (462b x + 1134a b x + 742a b x + 10a b x - 12a b x + 16a b x - 32a ) +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 +--R 3003b +--R Type: Union(Expression(Integer),...) +--E 1409 + +--S 1410 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1410 + +--S 1411 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1411 + +)clear all + +--S 1412 of 3330 +t0000:=x^2*(a+b*x)^(5/2) +--R +--R +--R 2 4 3 2 2 +-------+ +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1412 + +--S 1413 of 3330 +r0000:=2/7*a^2*(a+b*x)^(7/2)/b^3-4/9*a*(a+b*x)^(9/2)/b^3+_ + 2/11*(a+b*x)^(11/2)/b^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (126b x + 322a b x + 226a b x + 6a b x - 8a b x + 16a )\|b x + a +--R (2) --------------------------------------------------------------------- +--R 3 +--R 693b +--R Type: Expression(Integer) +--E 1413 + +--S 1414 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (126b x + 322a b x + 226a b x + 6a b x - 8a b x + 16a )\|b x + a +--R (3) --------------------------------------------------------------------- +--R 3 +--R 693b +--R Type: Union(Expression(Integer),...) +--E 1414 + +--S 1415 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1415 + +--S 1416 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1416 + +)clear all + +--S 1417 of 3330 +t0000:=x*(a+b*x)^(5/2) +--R +--R +--R 2 3 2 2 +-------+ +--R (1) (b x + 2a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1417 + +--S 1418 of 3330 +r0000:=-2/7*a*(a+b*x)^(7/2)/b^2+2/9*(a+b*x)^(9/2)/b^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (14b x + 38a b x + 30a b x + 2a b x - 4a )\|b x + a +--R (2) ------------------------------------------------------- +--R 2 +--R 63b +--R Type: Expression(Integer) +--E 1418 + +--S 1419 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (14b x + 38a b x + 30a b x + 2a b x - 4a )\|b x + a +--R (3) ------------------------------------------------------- +--R 2 +--R 63b +--R Type: Union(Expression(Integer),...) +--E 1419 + +--S 1420 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1420 + +--S 1421 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1421 + +)clear all + +--S 1422 of 3330 +t0000:=(a+b*x)^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (1) (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1422 + +--S 1423 of 3330 +r0000:=2/7*(a+b*x)^(7/2)/b +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R (2) ------------------------------------------ +--R 7b +--R Type: Expression(Integer) +--E 1423 + +--S 1424 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R (3) ------------------------------------------ +--R 7b +--R Type: Union(Expression(Integer),...) +--E 1424 + +--S 1425 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1425 + +--S 1426 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1426 + +)clear all + +--S 1427 of 3330 +t0000:=(a+b*x)^(5/2)/x +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R x +--R Type: Expression(Integer) +--E 1427 + +--S 1428 of 3330 +r0000:=2/3*a*(a+b*x)^(3/2)+2/5*(a+b*x)^(5/2)-_ + 2*a^(5/2)*atanh(sqrt(a+b*x)/sqrt(a))+2*a^2*sqrt(a+b*x) +--R +--R +--R +-------+ +--R 2 +-+ \|b x + a 2 2 2 +-------+ +--R - 30a \|a atanh(----------) + (6b x + 22a b x + 46a )\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 1428 + +--S 1429 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 2 +-+ - 2\|a \|b x + a + b x + 2a +--R 15a \|a log(----------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (6b x + 22a b x + 46a )\|b x + a +--R / +--R 15 +--R , +--R +-------+ +--R 2 +---+ \|b x + a 2 2 2 +-------+ +--R - 30a \|- a atan(----------) + (6b x + 22a b x + 46a )\|b x + a +--R +---+ +--R \|- a +--R -----------------------------------------------------------------] +--R 15 +--R Type: Union(List(Expression(Integer)),...) +--E 1429 + +--S 1430 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 +-+ - 2\|a \|b x + a + b x + 2a 2 +-+ \|b x + a +--R (4) a \|a log(----------------------------) + 2a \|a atanh(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1430 + +--S 1431 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1431 + +--S 1432 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 2 +-+ \|b x + a 2 +---+ \|b x + a +--R (6) 2a \|a atanh(----------) - 2a \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1432 + +--S 1433 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1433 + +)clear all + +--S 1434 of 3330 +t0000:=(a+b*x)^(5/2)/x^2 +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 1434 + +--S 1435 of 3330 +r0000:=5/3*b*(a+b*x)^(3/2)-(a+b*x)^(5/2)/x-_ + 5*a^(3/2)*b*atanh(sqrt(a+b*x)/sqrt(a))+5*a*b*sqrt(a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x + a 2 2 2 +-------+ +--R - 15a b x\|a atanh(----------) + (2b x + 14a b x - 3a )\|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------ +--R 3x +--R Type: Expression(Integer) +--E 1435 + +--S 1436 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +--R 15a b x\|a log(----------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (4b x + 28a b x - 6a )\|b x + a +--R / +--R 6x +--R , +--R +-------+ +--R +---+ \|b x + a 2 2 2 +-------+ +--R - 15a b x\|- a atan(----------) + (2b x + 14a b x - 3a )\|b x + a +--R +---+ +--R \|- a +--R -------------------------------------------------------------------] +--R 3x +--R Type: Union(List(Expression(Integer)),...) +--E 1436 + +--S 1437 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a +--R 5a b\|a log(----------------------------) + 10a b\|a atanh(----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1437 + +--S 1438 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1438 + +--S 1439 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R +-+ \|b x + a +---+ \|b x + a +--R (6) 5a b\|a atanh(----------) - 5a b\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1439 + +--S 1440 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1440 + +)clear all + +--S 1441 of 3330 +t0000:=(a+b*x)^(5/2)/x^3 +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 1441 + +--S 1442 of 3330 +r0000:=-5/4*b*(a+b*x)^(3/2)/x-1/2*(a+b*x)^(5/2)/x^2-_ + 15/4*b^2*atanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+15/4*b^2*sqrt(a+b*x) +--R +--R +--R +-------+ +--R 2 2 +-+ \|b x + a 2 2 2 +-------+ +--R - 15b x \|a atanh(----------) + (8b x - 9a b x - 2a )\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 1442 + +--S 1443 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 2 2 +-+ - 2\|a \|b x + a + b x + 2a +--R 15b x \|a log(----------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (16b x - 18a b x - 4a )\|b x + a +--R / +--R 2 +--R 8x +--R , +--R +-------+ +--R 2 2 +---+ \|b x + a 2 2 2 +-------+ +--R - 15b x \|- a atan(----------) + (8b x - 9a b x - 2a )\|b x + a +--R +---+ +--R \|- a +--R -----------------------------------------------------------------] +--R 2 +--R 4x +--R Type: Union(List(Expression(Integer)),...) +--E 1443 + +--S 1444 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 +-+ - 2\|a \|b x + a + b x + 2a 2 +-+ \|b x + a +--R 15b \|a log(----------------------------) + 30b \|a atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 1444 + +--S 1445 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1445 + +--S 1446 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 2 +-+ \|b x + a 2 +---+ \|b x + a +--R 15b \|a atanh(----------) - 15b \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) ------------------------------------------------------ +--R 4 +--R Type: Expression(Integer) +--E 1446 + +--S 1447 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1447 + +)clear all + +--S 1448 of 3330 +t0000:=(a+b*x)^(5/2)/x^4 +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 1448 + +--S 1449 of 3330 +r0000:=-5/12*b*(a+b*x)^(3/2)/x^2-1/3*(a+b*x)^(5/2)/x^3-_ + 5/8*b^3*atanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)-5/8*b^2*sqrt(a+b*x)/x +--R +--R +--R +-------+ +--R 3 3 \|b x + a 2 2 2 +-+ +-------+ +--R - 15b x atanh(----------) + (- 33b x - 26a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------------- +--R 3 +-+ +--R 24x \|a +--R Type: Expression(Integer) +--E 1449 + +--S 1450 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 3 3 - 2a\|b x + a + (b x + 2a)\|a +--R 15b x log(-------------------------------) +--R x +--R + +--R 2 2 2 +-+ +-------+ +--R (- 66b x - 52a b x - 16a )\|a \|b x + a +--R / +--R 3 +-+ +--R 48x \|a +--R , +--R +---+ +-------+ +--R 3 3 \|- a \|b x + a 2 2 2 +---+ +-------+ +--R - 15b x atan(----------------) + (- 33b x - 26a b x - 8a )\|- a \|b x + a +--R a +--R ---------------------------------------------------------------------------] +--R 3 +---+ +--R 24x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1450 + +--S 1451 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 3 - 2a\|b x + a + (b x + 2a)\|a 3 \|b x + a +--R 5b log(-------------------------------) + 10b atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R +-+ +--R 16\|a +--R Type: Expression(Integer) +--E 1451 + +--S 1452 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1452 + +--S 1453 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 3 +---+ \|b x + a 3 +-+ \|- a \|b x + a +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 8\|- a \|a +--R Type: Expression(Integer) +--E 1453 + +--S 1454 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1454 + +)clear all + +--S 1455 of 3330 +t0000:=(a+b*x)^(5/2)/x^5 +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R 5 +--R x +--R Type: Expression(Integer) +--E 1455 + +--S 1456 of 3330 +r0000:=-5/24*b*(a+b*x)^(3/2)/x^3-1/4*(a+b*x)^(5/2)/x^4+_ + 5/64*b^4*atanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-5/32*b^2*sqrt(a+b*x)/x^2-_ + 5/64*b^3*sqrt(a+b*x)/(a*x) +--R +--R +--R (2) +--R +-------+ +--R 4 4 \|b x + a +--R 15b x atanh(----------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +-------+ +--R (- 15b x - 118a b x - 136a b x - 48a )\|a \|b x + a +--R / +--R 4 +-+ +--R 192a x \|a +--R Type: Expression(Integer) +--E 1456 + +--S 1457 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 4 4 2a\|b x + a + (b x + 2a)\|a +--R 15b x log(-----------------------------) +--R x +--R + +--R 3 3 2 2 2 3 +-+ +-------+ +--R (- 30b x - 236a b x - 272a b x - 96a )\|a \|b x + a +--R / +--R 4 +-+ +--R 384a x \|a +--R , +--R +--R +---+ +-------+ +--R 4 4 \|- a \|b x + a +--R 15b x atan(----------------) +--R a +--R + +--R 3 3 2 2 2 3 +---+ +-------+ +--R (- 15b x - 118a b x - 136a b x - 48a )\|- a \|b x + a +--R / +--R 4 +---+ +--R 192a x \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1457 + +--S 1458 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 4 2a\|b x + a + (b x + 2a)\|a 4 \|b x + a +--R 5b log(-----------------------------) - 10b atanh(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R +-+ +--R 128a\|a +--R Type: Expression(Integer) +--E 1458 + +--S 1459 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1459 + +--S 1460 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 4 +---+ \|b x + a 4 +-+ \|- a \|b x + a +--R - 5b \|- a atanh(----------) + 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 64a\|- a \|a +--R Type: Expression(Integer) +--E 1460 + +--S 1461 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1461 + +)clear all + +--S 1462 of 3330 +t0000:=x^7*(a+b*x)^(9/2) +--R +--R +--R 4 11 3 10 2 2 9 3 8 4 7 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1462 + +--S 1463 of 3330 +r0000:=-2/11*a^7*(a+b*x)^(11/2)/b^8+14/13*a^6*(a+b*x)^(13/2)/b^8-_ + 14/5*a^5*(a+b*x)^(15/2)/b^8+70/17*a^4*(a+b*x)^(17/2)/b^8-_ + 70/19*a^3*(a+b*x)^(19/2)/b^8+2*a^2*(a+b*x)^(21/2)/b^8-_ + 14/23*a*(a+b*x)^(23/2)/b^8+2/25*(a+b*x)^(25/2)/b^8 +--R +--R +--R (2) +--R 12 12 11 11 2 10 10 3 9 9 +--R 2124694b x + 9330178a b x + 15519504a b x + 11620180a b x +--R + +--R 4 8 8 5 7 7 6 6 6 7 5 5 8 4 4 +--R 3319030a b x + 858a b x - 924a b x + 1008a b x - 1120a b x +--R + +--R 9 3 3 10 2 2 11 12 +--R 1280a b x - 1536a b x + 2048a b x - 4096a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 8 +--R 26558675b +--R Type: Expression(Integer) +--E 1463 + +--S 1464 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 12 12 11 11 2 10 10 3 9 9 +--R 2124694b x + 9330178a b x + 15519504a b x + 11620180a b x +--R + +--R 4 8 8 5 7 7 6 6 6 7 5 5 8 4 4 +--R 3319030a b x + 858a b x - 924a b x + 1008a b x - 1120a b x +--R + +--R 9 3 3 10 2 2 11 12 +--R 1280a b x - 1536a b x + 2048a b x - 4096a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 8 +--R 26558675b +--R Type: Union(Expression(Integer),...) +--E 1464 + +--S 1465 of 3330 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+--S 1469 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 11 11 10 10 2 9 9 3 8 8 +--R 646646b x + 2863718a b x + 4813380a b x + 3652220a b x +--R + +--R 4 7 7 5 6 6 6 5 5 7 4 4 8 3 3 +--R 1061918a b x + 462a b x - 504a b x + 560a b x - 640a b x +--R + +--R 9 2 2 10 11 +--R 768a b x - 1024a b x + 2048a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 7 +--R 7436429b +--R Type: Union(Expression(Integer),...) +--E 1469 + +--S 1470 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1470 + +--S 1471 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1471 + +)clear all + +--S 1472 of 3330 +t0000:=x^5*(a+b*x)^(9/2) +--R +--R +--R 4 9 3 8 2 2 7 3 6 4 5 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1472 + +--S 1473 of 3330 +r0000:=-2/11*a^5*(a+b*x)^(11/2)/b^6+10/13*a^4*(a+b*x)^(13/2)/b^6-_ + 4/3*a^3*(a+b*x)^(15/2)/b^6+20/17*a^2*(a+b*x)^(17/2)/b^6-_ + 10/19*a*(a+b*x)^(19/2)/b^6+2/21*(a+b*x)^(21/2)/b^6 +--R +--R +--R (2) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R 92378b x + 413270a b x + 703560a b x + 542828a b x + 161546a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R 126a b x - 140a b x + 160a b x - 192a b x + 256a b x - 512a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 6 +--R 969969b +--R Type: Expression(Integer) +--E 1473 + +--S 1474 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 +--R 92378b x + 413270a b x + 703560a b x + 542828a b x + 161546a b x +--R + +--R 5 5 5 6 4 4 7 3 3 8 2 2 9 10 +--R 126a b x - 140a b x + 160a b x - 192a b x + 256a b x - 512a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 6 +--R 969969b +--R Type: Union(Expression(Integer),...) +--E 1474 + +--S 1475 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1475 + +--S 1476 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1476 + +)clear all + +--S 1477 of 3330 +t0000:=x^4*(a+b*x)^(9/2) +--R +--R +--R 4 8 3 7 2 2 6 3 5 4 4 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1477 + +--S 1478 of 3330 +r0000:=2/11*a^4*(a+b*x)^(11/2)/b^5-8/13*a^3*(a+b*x)^(13/2)/b^5+_ + 4/5*a^2*(a+b*x)^(15/2)/b^5-8/17*a*(a+b*x)^(17/2)/b^5+_ + 2/19*(a+b*x)^(19/2)/b^5 +--R +--R +--R (2) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 24310b x + 110110a b x + 190476a b x + 150172a b x + 46126a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R 70a b x - 80a b x + 96a b x - 128a b x + 256a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 5 +--R 230945b +--R Type: Expression(Integer) +--E 1478 + +--S 1479 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 +--R 24310b x + 110110a b x + 190476a b x + 150172a b x + 46126a b x +--R + +--R 5 4 4 6 3 3 7 2 2 8 9 +--R 70a b x - 80a b x + 96a b x - 128a b x + 256a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 5 +--R 230945b +--R Type: Union(Expression(Integer),...) +--E 1479 + +--S 1480 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1480 + +--S 1481 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1481 + +)clear all + +--S 1482 of 3330 +t0000:=x^3*(a+b*x)^(9/2) +--R +--R +--R 4 7 3 6 2 2 5 3 4 4 3 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1482 + +--S 1483 of 3330 +r0000:=-2/11*a^3*(a+b*x)^(11/2)/b^4+6/13*a^2*(a+b*x)^(13/2)/b^4-_ + 2/5*a*(a+b*x)^(15/2)/b^4+2/17*(a+b*x)^(17/2)/b^4 +--R +--R +--R (2) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 +--R 1430b x + 6578a b x + 11616a b x + 9428a b x + 3030a b x +--R + +--R 5 3 3 6 2 2 7 8 +--R 10a b x - 12a b x + 16a b x - 32a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 +--R 12155b +--R Type: Expression(Integer) +--E 1483 + +--S 1484 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 +--R 1430b x + 6578a b x + 11616a b x + 9428a b x + 3030a b x +--R + +--R 5 3 3 6 2 2 7 8 +--R 10a b x - 12a b x + 16a b x - 32a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 +--R 12155b +--R Type: Union(Expression(Integer),...) +--E 1484 + +--S 1485 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1485 + +--S 1486 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1486 + +)clear all + +--S 1487 of 3330 +t0000:=x^2*(a+b*x)^(9/2) +--R +--R +--R 4 6 3 5 2 2 4 3 3 4 2 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1487 + +--S 1488 of 3330 +r0000:=2/11*a^2*(a+b*x)^(11/2)/b^3-4/13*a*(a+b*x)^(13/2)/b^3+_ + 2/15*(a+b*x)^(15/2)/b^3 +--R +--R +--R (2) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R 286b x + 1342a b x + 2436a b x + 2060a b x + 710a b x + 6a b x +--R + +--R 6 7 +--R - 8a b x + 16a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 3 +--R 2145b +--R Type: Expression(Integer) +--E 1488 + +--S 1489 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R 286b x + 1342a b x + 2436a b x + 2060a b x + 710a b x + 6a b x +--R + +--R 6 7 +--R - 8a b x + 16a +--R * +--R +-------+ +--R \|b x + a +--R / +--R 3 +--R 2145b +--R Type: Union(Expression(Integer),...) +--E 1489 + +--S 1490 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1490 + +--S 1491 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1491 + +)clear all + +--S 1492 of 3330 +t0000:=x*(a+b*x)^(9/2) +--R +--R +--R 4 5 3 4 2 2 3 3 2 4 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1492 + +--S 1493 of 3330 +r0000:=-2/11*a*(a+b*x)^(11/2)/b^2+2/13*(a+b*x)^(13/2)/b^2 +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (22b x + 106a b x + 200a b x + 180a b x + 70a b x + 2a b x - 4a ) +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 +--R 143b +--R Type: Expression(Integer) +--E 1493 + +--S 1494 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (22b x + 106a b x + 200a b x + 180a b x + 70a b x + 2a b x - 4a ) +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 +--R 143b +--R Type: Union(Expression(Integer),...) +--E 1494 + +--S 1495 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1495 + +--S 1496 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1496 + +)clear all + +--S 1497 of 3330 +t0000:=(a+b*x)^(9/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1497 + +--S 1498 of 3330 +r0000:=2/11*(a+b*x)^(11/2)/b +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (2b x + 10a b x + 20a b x + 20a b x + 10a b x + 2a )\|b x + a +--R (2) ------------------------------------------------------------------ +--R 11b +--R Type: Expression(Integer) +--E 1498 + +--S 1499 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (2b x + 10a b x + 20a b x + 20a b x + 10a b x + 2a )\|b x + a +--R (3) ------------------------------------------------------------------ +--R 11b +--R Type: Union(Expression(Integer),...) +--E 1499 + +--S 1500 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1500 + +--S 1501 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1501 + +)clear all + +--S 1502 of 3330 +t0000:=(a+b*x)^(9/2)/x +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 1502 + +--S 1503 of 3330 +r0000:=2/3*a^3*(a+b*x)^(3/2)+2/5*a^2*(a+b*x)^(5/2)+2/7*a*(a+b*x)^(7/2)+_ + 2/9*(a+b*x)^(9/2)-2*a^(9/2)*atanh(sqrt(a+b*x)/sqrt(a))+2*a^4*sqrt(a+b*x) +--R +--R +--R (2) +--R +-------+ +--R 4 +-+ \|b x + a +--R - 630a \|a atanh(----------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 370a b x + 816a b x + 1012a b x + 1126a )\|b x + a +--R / +--R 315 +--R Type: Expression(Integer) +--E 1503 + +--S 1504 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 4 +-+ - 2\|a \|b x + a + b x + 2a +--R 315a \|a log(----------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 370a b x + 816a b x + 1012a b x + 1126a )\|b x + a +--R / +--R 315 +--R , +--R +--R +-------+ +--R 4 +---+ \|b x + a +--R - 630a \|- a atan(----------) +--R +---+ +--R \|- a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x + 370a b x + 816a b x + 1012a b x + 1126a )\|b x + a +--R / +--R 315 +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1504 + +--S 1505 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 4 +-+ - 2\|a \|b x + a + b x + 2a 4 +-+ \|b x + a +--R (4) a \|a log(----------------------------) + 2a \|a atanh(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1505 + +--S 1506 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1506 + +--S 1507 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 4 +-+ \|b x + a 4 +---+ \|b x + a +--R (6) 2a \|a atanh(----------) - 2a \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1507 + +--S 1508 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1508 + +)clear all + +--S 1509 of 3330 +t0000:=(a+b*x)^(9/2)/x^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1509 + +--S 1510 of 3330 +r0000:=3*a^2*b*(a+b*x)^(3/2)+9/5*a*b*(a+b*x)^(5/2)+9/7*b*(a+b*x)^(7/2)-_ + (a+b*x)^(9/2)/x-9*a^(7/2)*b*atanh(sqrt(a+b*x)/sqrt(a))+_ + 9*a^3*b*sqrt(a+b*x) +--R +--R +--R (2) +--R +-------+ +--R 3 +-+ \|b x + a +--R - 315a b x\|a atanh(----------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (10b x + 58a b x + 156a b x + 388a b x - 35a )\|b x + a +--R / +--R 35x +--R Type: Expression(Integer) +--E 1510 + +--S 1511 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 3 +-+ - 2\|a \|b x + a + b x + 2a +--R 315a b x\|a log(----------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (20b x + 116a b x + 312a b x + 776a b x - 70a )\|b x + a +--R / +--R 70x +--R , +--R +--R +-------+ +--R 3 +---+ \|b x + a +--R - 315a b x\|- a atan(----------) +--R +---+ +--R \|- a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (10b x + 58a b x + 156a b x + 388a b x - 35a )\|b x + a +--R / +--R 35x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1511 + +--S 1512 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 3 +-+ - 2\|a \|b x + a + b x + 2a 3 +-+ \|b x + a +--R 9a b\|a log(----------------------------) + 18a b\|a atanh(----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1512 + +--S 1513 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1513 + +--S 1514 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 3 +-+ \|b x + a 3 +---+ \|b x + a +--R (6) 9a b\|a atanh(----------) - 9a b\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1514 + +--S 1515 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1515 + +)clear all + +--S 1516 of 3330 +t0000:=(a+b*x)^(9/2)/x^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1516 + +--S 1517 of 3330 +r0000:=21/4*a*b^2*(a+b*x)^(3/2)+63/20*b^2*(a+b*x)^(5/2)-_ + 9/4*b*(a+b*x)^(7/2)/x-1/2*(a+b*x)^(9/2)/x^2-_ + 63/4*a^(5/2)*b^2*atanh(sqrt(a+b*x)/sqrt(a))+63/4*a^2*b^2*sqrt(a+b*x) +--R +--R +--R (2) +--R +-------+ +--R 2 2 2 +-+ \|b x + a +--R - 315a b x \|a atanh(----------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (8b x + 56a b x + 288a b x - 85a b x - 10a )\|b x + a +--R / +--R 2 +--R 20x +--R Type: Expression(Integer) +--E 1517 + +--S 1518 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 2 2 2 +-+ - 2\|a \|b x + a + b x + 2a +--R 315a b x \|a log(----------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (16b x + 112a b x + 576a b x - 170a b x - 20a )\|b x + a +--R / +--R 2 +--R 40x +--R , +--R +--R +-------+ +--R 2 2 2 +---+ \|b x + a +--R - 315a b x \|- a atan(----------) +--R +---+ +--R \|- a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (8b x + 56a b x + 288a b x - 85a b x - 10a )\|b x + a +--R / +--R 2 +--R 20x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1518 + +--S 1519 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-+ +-------+ +-------+ +--R 2 2 +-+ - 2\|a \|b x + a + b x + 2a 2 2 +-+ \|b x + a +--R 63a b \|a log(----------------------------) + 126a b \|a atanh(----------) +--R x +-+ +--R \|a +--R -------------------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 1519 + +--S 1520 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1520 + +--S 1521 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 2 2 +-+ \|b x + a 2 2 +---+ \|b x + a +--R 63a b \|a atanh(----------) - 63a b \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) ---------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 1521 + +--S 1522 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1522 + +)clear all + +--S 1523 of 3330 +t0000:=(a+b*x)^(9/2)/x^4 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1523 + +--S 1524 of 3330 +r0000:=35/8*b^3*(a+b*x)^(3/2)-21/8*b^2*(a+b*x)^(5/2)/x-_ + 3/4*b*(a+b*x)^(7/2)/x^2-1/3*(a+b*x)^(9/2)/x^3-_ + 105/8*a^(3/2)*b^3*atanh(sqrt(a+b*x)/sqrt(a))+105/8*a*b^3*sqrt(a+b*x) +--R +--R +--R (2) +--R +-------+ +--R 3 3 +-+ \|b x + a +--R - 315a b x \|a atanh(----------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (16b x + 208a b x - 165a b x - 50a b x - 8a )\|b x + a +--R / +--R 3 +--R 24x +--R Type: Expression(Integer) +--E 1524 + +--S 1525 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 3 3 +-+ - 2\|a \|b x + a + b x + 2a +--R 315a b x \|a log(----------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (32b x + 416a b x - 330a b x - 100a b x - 16a )\|b x + a +--R / +--R 3 +--R 48x +--R , +--R +--R +-------+ +--R 3 3 +---+ \|b x + a +--R - 315a b x \|- a atan(----------) +--R +---+ +--R \|- a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (16b x + 208a b x - 165a b x - 50a b x - 8a )\|b x + a +--R / +--R 3 +--R 24x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1525 + +--S 1526 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-+ +-------+ +-------+ +--R 3 +-+ - 2\|a \|b x + a + b x + 2a 3 +-+ \|b x + a +--R 105a b \|a log(----------------------------) + 210a b \|a atanh(----------) +--R x +-+ +--R \|a +--R --------------------------------------------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1526 + +--S 1527 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1527 + +--S 1528 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 3 +-+ \|b x + a 3 +---+ \|b x + a +--R 105a b \|a atanh(----------) - 105a b \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) ------------------------------------------------------------ +--R 8 +--R Type: Expression(Integer) +--E 1528 + +--S 1529 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1529 + +)clear all + +--S 1530 of 3330 +t0000:=(a+b*x)^(9/2)/x^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 1530 + +--S 1531 of 3330 +r0000:=-105/64*b^3*(a+b*x)^(3/2)/x-21/32*b^2*(a+b*x)^(5/2)/x^2-_ + 3/8*b*(a+b*x)^(7/2)/x^3-1/4*(a+b*x)^(9/2)/x^4-_ + 315/64*b^4*atanh(sqrt(a+b*x)/sqrt(a))*sqrt(a)+315/64*b^4*sqrt(a+b*x) +--R +--R +--R (2) +--R +-------+ +--R 4 4 +-+ \|b x + a +--R - 315b x \|a atanh(----------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (128b x - 325a b x - 210a b x - 88a b x - 16a )\|b x + a +--R / +--R 4 +--R 64x +--R Type: Expression(Integer) +--E 1531 + +--S 1532 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 4 4 +-+ - 2\|a \|b x + a + b x + 2a +--R 315b x \|a log(----------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (256b x - 650a b x - 420a b x - 176a b x - 32a )\|b x + a +--R / +--R 4 +--R 128x +--R , +--R +--R +-------+ +--R 4 4 +---+ \|b x + a +--R - 315b x \|- a atan(----------) +--R +---+ +--R \|- a +--R + +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (128b x - 325a b x - 210a b x - 88a b x - 16a )\|b x + a +--R / +--R 4 +--R 64x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1532 + +--S 1533 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-+ +-------+ +-------+ +--R 4 +-+ - 2\|a \|b x + a + b x + 2a 4 +-+ \|b x + a +--R 315b \|a log(----------------------------) + 630b \|a atanh(----------) +--R x +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 1533 + +--S 1534 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1534 + +--S 1535 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +-------+ +--R 4 +-+ \|b x + a 4 +---+ \|b x + a +--R 315b \|a atanh(----------) - 315b \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) -------------------------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 1535 + +--S 1536 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1536 + +)clear all + +--S 1537 of 3330 +t0000:=(a+b*x)^(9/2)/x^6 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 1537 + +--S 1538 of 3330 +r0000:=-21/64*b^3*(a+b*x)^(3/2)/x^2-21/80*b^2*(a+b*x)^(5/2)/x^3-_ + 9/40*b*(a+b*x)^(7/2)/x^4-1/5*(a+b*x)^(9/2)/x^5-_ + 63/128*b^5*atanh(sqrt(a+b*x)/sqrt(a))/sqrt(a)-63/128*b^4*sqrt(a+b*x)/x +--R +--R +--R (2) +--R +-------+ +--R 5 5 \|b x + a +--R - 315b x atanh(----------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +-------+ +--R (- 965b x - 1490a b x - 1368a b x - 656a b x - 128a )\|a \|b x + a +--R / +--R 5 +-+ +--R 640x \|a +--R Type: Expression(Integer) +--E 1538 + +--S 1539 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 5 5 - 2a\|b x + a + (b x + 2a)\|a +--R 315b x log(-------------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +-------+ +--R (- 1930b x - 2980a b x - 2736a b x - 1312a b x - 256a )\|a \|b x + a +--R / +--R 5 +-+ +--R 1280x \|a +--R , +--R +--R +---+ +-------+ +--R 5 5 \|- a \|b x + a +--R - 315b x atan(----------------) +--R a +--R + +--R 4 4 3 3 2 2 2 3 4 +---+ +-------+ +--R (- 965b x - 1490a b x - 1368a b x - 656a b x - 128a )\|- a \|b x + a +--R / +--R 5 +---+ +--R 640x \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1539 + +--S 1540 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 5 - 2a\|b x + a + (b x + 2a)\|a 5 \|b x + a +--R 63b log(-------------------------------) + 126b atanh(----------) +--R x +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R +-+ +--R 256\|a +--R Type: Expression(Integer) +--E 1540 + +--S 1541 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1541 + +--S 1542 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 5 +---+ \|b x + a 5 +-+ \|- a \|b x + a +--R 63b \|- a atanh(----------) - 63b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 128\|- a \|a +--R Type: Expression(Integer) +--E 1542 + +--S 1543 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1543 + +)clear all + +--S 1544 of 3330 +t0000:=(a+b*x)^(9/2)/x^7 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 1544 + +--S 1545 of 3330 +r0000:=-7/64*b^3*(a+b*x)^(3/2)/x^3-21/160*b^2*(a+b*x)^(5/2)/x^4-_ + 3/20*b*(a+b*x)^(7/2)/x^5-1/6*(a+b*x)^(9/2)/x^6+_ + 21/512*b^6*atanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-_ + 21/256*b^4*sqrt(a+b*x)/x^2-21/512*b^5*sqrt(a+b*x)/(a*x) +--R +--R +--R (2) +--R +-------+ +--R 6 6 \|b x + a +--R 315b x atanh(----------) +--R +-+ +--R \|a +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 +--R - 315b x - 4910a b x - 11432a b x - 12144a b x - 6272a b x +--R + +--R 5 +--R - 1280a +--R * +--R +-+ +-------+ +--R \|a \|b x + a +--R / +--R 6 +-+ +--R 7680a x \|a +--R Type: Expression(Integer) +--E 1545 + +--S 1546 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 6 6 2a\|b x + a + (b x + 2a)\|a +--R 315b x log(-----------------------------) +--R x +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 +--R - 630b x - 9820a b x - 22864a b x - 24288a b x - 12544a b x +--R + +--R 5 +--R - 2560a +--R * +--R +-+ +-------+ +--R \|a \|b x + a +--R / +--R 6 +-+ +--R 15360a x \|a +--R , +--R +--R +---+ +-------+ +--R 6 6 \|- a \|b x + a +--R 315b x atan(----------------) +--R a +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 +--R - 315b x - 4910a b x - 11432a b x - 12144a b x - 6272a b x +--R + +--R 5 +--R - 1280a +--R * +--R +---+ +-------+ +--R \|- a \|b x + a +--R / +--R 6 +---+ +--R 7680a x \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1546 + +--S 1547 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 6 2a\|b x + a + (b x + 2a)\|a 6 \|b x + a +--R 21b log(-----------------------------) - 42b atanh(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 1024a\|a +--R Type: Expression(Integer) +--E 1547 + +--S 1548 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1548 + +--S 1549 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 6 +---+ \|b x + a 6 +-+ \|- a \|b x + a +--R - 21b \|- a atanh(----------) + 21b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R +---+ +-+ +--R 512a\|- a \|a +--R Type: Expression(Integer) +--E 1549 + +--S 1550 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1550 + +)clear all + +--S 1551 of 3330 +t0000:=(a+b*x)^(9/2)/x^8 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 1551 + +--S 1552 of 3330 +r0000:=-3/64*b^3*(a+b*x)^(3/2)/x^4-3/40*b^2*(a+b*x)^(5/2)/x^5-_ + 3/28*b*(a+b*x)^(7/2)/x^6-1/7*(a+b*x)^(9/2)/x^7-_ + 9/1024*b^7*atanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)-_ + 3/128*b^4*sqrt(a+b*x)/x^3-3/512*b^5*sqrt(a+b*x)/(a*x^2)+_ + 9/1024*b^6*sqrt(a+b*x)/(a^2*x) +--R +--R +--R (2) +--R +-------+ +--R 7 7 \|b x + a +--R - 315b x atanh(----------) +--R +-+ +--R \|a +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R 315b x - 210a b x - 14168a b x - 39056a b x - 44928a b x +--R + +--R 5 6 +--R - 24320a b x - 5120a +--R * +--R +-+ +-------+ +--R \|a \|b x + a +--R / +--R 2 7 +-+ +--R 35840a x \|a +--R Type: Expression(Integer) +--E 1552 + +--S 1553 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 7 7 - 2a\|b x + a + (b x + 2a)\|a +--R 315b x log(-------------------------------) +--R x +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R 630b x - 420a b x - 28336a b x - 78112a b x - 89856a b x +--R + +--R 5 6 +--R - 48640a b x - 10240a +--R * +--R +-+ +-------+ +--R \|a \|b x + a +--R / +--R 2 7 +-+ +--R 71680a x \|a +--R , +--R +--R +---+ +-------+ +--R 7 7 \|- a \|b x + a +--R - 315b x atan(----------------) +--R a +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R 315b x - 210a b x - 14168a b x - 39056a b x - 44928a b x +--R + +--R 5 6 +--R - 24320a b x - 5120a +--R * +--R +---+ +-------+ +--R \|- a \|b x + a +--R / +--R 2 7 +---+ +--R 35840a x \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1553 + +--S 1554 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 7 - 2a\|b x + a + (b x + 2a)\|a 7 \|b x + a +--R 9b log(-------------------------------) + 18b atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R 2 +-+ +--R 2048a \|a +--R Type: Expression(Integer) +--E 1554 + +--S 1555 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1555 + +--S 1556 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 7 +---+ \|b x + a 7 +-+ \|- a \|b x + a +--R 9b \|- a atanh(----------) - 9b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 2 +---+ +-+ +--R 1024a \|- a \|a +--R Type: Expression(Integer) +--E 1556 + +--S 1557 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1557 + +)clear all + +--S 1558 of 3330 +t0000:=sqrt(-a+b*x)/x +--R +--R +--R +-------+ +--R \|b x - a +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 1558 + +--S 1559 of 3330 +r0000:=-2*atan(sqrt(-a+b*x)/sqrt(a))*sqrt(a)+2*sqrt(-a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x - a +-------+ +--R (2) - 2\|a atan(----------) + 2\|b x - a +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1559 + +--S 1560 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +-------+ +--R +---+ - 2\|- a \|b x - a + b x - 2a +-------+ +--R [\|- a log(------------------------------) + 2\|b x - a , +--R x +--R +-------+ +--R +-+ \|b x - a +-------+ +--R - 2\|a atan(----------) + 2\|b x - a ] +--R +-+ +--R \|a +--R Type: Union(List(Expression(Integer)),...) +--E 1560 + +--S 1561 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +-------+ +-------+ +--R +---+ - 2\|- a \|b x - a + b x - 2a +-+ \|b x - a +--R (4) \|- a log(------------------------------) + 2\|a atan(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1561 + +--S 1562 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1562 + +--S 1563 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1563 + +--S 1564 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1564 + +)clear all + +--S 1565 of 3330 +t0000:=sqrt(-a+b*x)/x^2 +--R +--R +--R +-------+ +--R \|b x - a +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1565 + +--S 1566 of 3330 +r0000:=b*atan(sqrt(-a+b*x)/sqrt(a))/sqrt(a)-sqrt(-a+b*x)/x +--R +--R +--R +-------+ +--R \|b x - a +-+ +-------+ +--R b x atan(----------) - \|a \|b x - a +--R +-+ +--R \|a +--R (2) ------------------------------------- +--R +-+ +--R x\|a +--R Type: Expression(Integer) +--E 1566 + +--S 1567 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R 2a\|b x - a + (b x - 2a)\|- a +---+ +-------+ +--R b x log(-------------------------------) - 2\|- a \|b x - a +--R x +--R [------------------------------------------------------------, +--R +---+ +--R 2x\|- a +--R +-+ +-------+ +--R \|a \|b x - a +-+ +-------+ +--R b x atan(--------------) - \|a \|b x - a +--R a +--R -----------------------------------------] +--R +-+ +--R x\|a +--R Type: Union(List(Expression(Integer)),...) +--E 1567 + +--S 1568 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +-+ 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R b\|a log(-------------------------------) - 2b\|- a atan(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R +---+ +-+ +--R 2\|- a \|a +--R Type: Expression(Integer) +--E 1568 + +--S 1569 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1569 + +--S 1570 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R b atan(--------------) - b atan(----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1570 + +--S 1571 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1571 + +)clear all + +--S 1572 of 3330 +t0000:=sqrt(-a+b*x)/x^3 +--R +--R +--R +-------+ +--R \|b x - a +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1572 + +--S 1573 of 3330 +r0000:=1/4*b^2*atan(sqrt(-a+b*x)/sqrt(a))/a^(3/2)-_ + 1/2*sqrt(-a+b*x)/x^2+1/4*b*sqrt(-a+b*x)/(a*x) +--R +--R +--R +-------+ +--R 2 2 \|b x - a +-+ +-------+ +--R b x atan(----------) + (b x - 2a)\|a \|b x - a +--R +-+ +--R \|a +--R (2) ----------------------------------------------- +--R 2 +-+ +--R 4a x \|a +--R Type: Expression(Integer) +--E 1573 + +--S 1574 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R 2 2 2a\|b x - a + (b x - 2a)\|- a +---+ +-------+ +--R b x log(-------------------------------) + (2b x - 4a)\|- a \|b x - a +--R x +--R [----------------------------------------------------------------------, +--R 2 +---+ +--R 8a x \|- a +--R +-+ +-------+ +--R 2 2 \|a \|b x - a +-+ +-------+ +--R b x atan(--------------) + (b x - 2a)\|a \|b x - a +--R a +--R ---------------------------------------------------] +--R 2 +-+ +--R 4a x \|a +--R Type: Union(List(Expression(Integer)),...) +--E 1574 + +--S 1575 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 2 +-+ 2a\|b x - a + (b x - 2a)\|- a 2 +---+ \|b x - a +--R b \|a log(-------------------------------) - 2b \|- a atan(----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------------------------- +--R +---+ +-+ +--R 8a\|- a \|a +--R Type: Expression(Integer) +--E 1575 + +--S 1576 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1576 + +--S 1577 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 \|a \|b x - a 2 \|b x - a +--R b atan(--------------) - b atan(----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 1577 + +--S 1578 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1578 + +)clear all + +--S 1579 of 3330 +t0000:=(-a+b*x)^(3/2)/x +--R +--R +--R +-------+ +--R (b x - a)\|b x - a +--R (1) ------------------- +--R x +--R Type: Expression(Integer) +--E 1579 + +--S 1580 of 3330 +r0000:=2/3*(-a+b*x)^(3/2)+2*a^(3/2)*atan(sqrt(-a+b*x)/sqrt(a))-2*a*sqrt(-a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x - a +-------+ +--R 6a\|a atan(----------) + (2b x - 8a)\|b x - a +--R +-+ +--R \|a +--R (2) ---------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1580 + +--S 1581 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +-------+ +--R +---+ 2\|- a \|b x - a + b x - 2a +-------+ +--R 3a\|- a log(----------------------------) + (2b x - 8a)\|b x - a +--R x +--R [-----------------------------------------------------------------, +--R 3 +--R +-------+ +--R +-+ \|b x - a +-------+ +--R 6a\|a atan(----------) + (2b x - 8a)\|b x - a +--R +-+ +--R \|a +--R ----------------------------------------------] +--R 3 +--R Type: Union(List(Expression(Integer)),...) +--E 1581 + +--S 1582 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +-------+ +-------+ +--R +---+ 2\|- a \|b x - a + b x - 2a +-+ \|b x - a +--R (4) a\|- a log(----------------------------) - 2a\|a atan(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1582 + +--S 1583 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1583 + +--S 1584 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1584 + +--S 1585 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1585 + +)clear all + +--S 1586 of 3330 +t0000:=(-a+b*x)^(3/2)/x^2 +--R +--R +--R +-------+ +--R (b x - a)\|b x - a +--R (1) ------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1586 + +--S 1587 of 3330 +r0000:=-(-a+b*x)^(3/2)/x-3*b*atan(sqrt(-a+b*x)/sqrt(a))*sqrt(a)+_ + 3*b*sqrt(-a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x - a +-------+ +--R - 3b x\|a atan(----------) + (2b x + a)\|b x - a +--R +-+ +--R \|a +--R (2) ------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 1587 + +--S 1588 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +-------+ +--R +---+ - 2\|- a \|b x - a + b x - 2a +-------+ +--R 3b x\|- a log(------------------------------) + (4b x + 2a)\|b x - a +--R x +--R [---------------------------------------------------------------------, +--R 2x +--R +-------+ +--R +-+ \|b x - a +-------+ +--R - 3b x\|a atan(----------) + (2b x + a)\|b x - a +--R +-+ +--R \|a +--R -------------------------------------------------] +--R x +--R Type: Union(List(Expression(Integer)),...) +--E 1588 + +--S 1589 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +-------+ +-------+ +--R +---+ - 2\|- a \|b x - a + b x - 2a +-+ \|b x - a +--R 3b\|- a log(------------------------------) + 6b\|a atan(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1589 + +--S 1590 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1590 + +--S 1591 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1591 + +--S 1592 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1592 + +)clear all + +--S 1593 of 3330 +t0000:=(-a+b*x)^(3/2)/x^3 +--R +--R +--R +-------+ +--R (b x - a)\|b x - a +--R (1) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1593 + +--S 1594 of 3330 +r0000:=-1/2*(-a+b*x)^(3/2)/x^2+3/4*b^2*atan(sqrt(-a+b*x)/sqrt(a))/sqrt(a)-_ + 3/4*b*sqrt(-a+b*x)/x +--R +--R +--R +-------+ +--R 2 2 \|b x - a +-+ +-------+ +--R 3b x atan(----------) + (- 5b x + 2a)\|a \|b x - a +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 2 +-+ +--R 4x \|a +--R Type: Expression(Integer) +--E 1594 + +--S 1595 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R 2 2 2a\|b x - a + (b x - 2a)\|- a +---+ +-------+ +--R 3b x log(-------------------------------) + (- 10b x + 4a)\|- a \|b x - a +--R x +--R [--------------------------------------------------------------------------, +--R 2 +---+ +--R 8x \|- a +--R +-+ +-------+ +--R 2 2 \|a \|b x - a +-+ +-------+ +--R 3b x atan(--------------) + (- 5b x + 2a)\|a \|b x - a +--R a +--R -------------------------------------------------------] +--R 2 +-+ +--R 4x \|a +--R Type: Union(List(Expression(Integer)),...) +--E 1595 + +--S 1596 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-------+ +---+ +-------+ +--R 2 +-+ 2a\|b x - a + (b x - 2a)\|- a 2 +---+ \|b x - a +--R 3b \|a log(-------------------------------) - 6b \|- a atan(----------) +--R x +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R +---+ +-+ +--R 8\|- a \|a +--R Type: Expression(Integer) +--E 1596 + +--S 1597 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1597 + +--S 1598 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 \|a \|b x - a 2 \|b x - a +--R 3b atan(--------------) - 3b atan(----------) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R +-+ +--R 4\|a +--R Type: Expression(Integer) +--E 1598 + +--S 1599 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1599 + +)clear all + +--S 1600 of 3330 +t0000:=(-a+b*x)^(5/2)/x +--R +--R +--R 2 2 2 +-------+ +--R (b x - 2a b x + a )\|b x - a +--R (1) ------------------------------ +--R x +--R Type: Expression(Integer) +--E 1600 + +--S 1601 of 3330 +r0000:=-2/3*a*(-a+b*x)^(3/2)+2/5*(-a+b*x)^(5/2)-_ + 2*a^(5/2)*atan(sqrt(-a+b*x)/sqrt(a))+2*a^2*sqrt(-a+b*x) +--R +--R +--R +-------+ +--R 2 +-+ \|b x - a 2 2 2 +-------+ +--R - 30a \|a atan(----------) + (6b x - 22a b x + 46a )\|b x - a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 1601 + +--S 1602 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +-------+ +--R 2 +---+ - 2\|- a \|b x - a + b x - 2a +--R 15a \|- a log(------------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (6b x - 22a b x + 46a )\|b x - a +--R / +--R 15 +--R , +--R +-------+ +--R 2 +-+ \|b x - a 2 2 2 +-------+ +--R - 30a \|a atan(----------) + (6b x - 22a b x + 46a )\|b x - a +--R +-+ +--R \|a +--R ---------------------------------------------------------------] +--R 15 +--R Type: Union(List(Expression(Integer)),...) +--E 1602 + +--S 1603 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +-------+ +-------+ +--R 2 +---+ - 2\|- a \|b x - a + b x - 2a 2 +-+ \|b x - a +--R (4) a \|- a log(------------------------------) + 2a \|a atan(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 1603 + +--S 1604 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1604 + +--S 1605 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1605 + +--S 1606 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1606 + +)clear all + +--S 1607 of 3330 +t0000:=(-a+b*x)^(5/2)/x^2 +--R +--R +--R 2 2 2 +-------+ +--R (b x - 2a b x + a )\|b x - a +--R (1) ------------------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 1607 + +--S 1608 of 3330 +r0000:=5/3*b*(-a+b*x)^(3/2)-(-a+b*x)^(5/2)/x+_ + 5*a^(3/2)*b*atan(sqrt(-a+b*x)/sqrt(a))-5*a*b*sqrt(-a+b*x) +--R +--R +--R +-------+ +--R +-+ \|b x - a 2 2 2 +-------+ +--R 15a b x\|a atan(----------) + (2b x - 14a b x - 3a )\|b x - a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------- +--R 3x +--R Type: Expression(Integer) +--E 1608 + +--S 1609 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +-------+ +--R +---+ 2\|- a \|b x - a + b x - 2a +--R 15a b x\|- a log(----------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (4b x - 28a b x - 6a )\|b x - a +--R / +--R 6x +--R , +--R +-------+ +--R +-+ \|b x - a 2 2 2 +-------+ +--R 15a b x\|a atan(----------) + (2b x - 14a b x - 3a )\|b x - a +--R +-+ +--R \|a +--R ---------------------------------------------------------------] +--R 3x +--R Type: Union(List(Expression(Integer)),...) +--E 1609 + +--S 1610 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +---+ +-------+ +-------+ +--R +---+ 2\|- a \|b x - a + b x - 2a +-+ \|b x - a +--R 5a b\|- a log(----------------------------) - 10a b\|a atan(----------) +--R x +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1610 + +--S 1611 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1611 + +--S 1612 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1612 + +--S 1613 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1613 + +)clear all + +--S 1614 of 3330 +t0000:=(-a+b*x)^(5/2)/x^3 +--R +--R +--R 2 2 2 +-------+ +--R (b x - 2a b x + a )\|b x - a +--R (1) ------------------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 1614 + +--S 1615 of 3330 +r0000:=-5/4*b*(-a+b*x)^(3/2)/x-1/2*(-a+b*x)^(5/2)/x^2-_ + 15/4*b^2*atan(sqrt(-a+b*x)/sqrt(a))*sqrt(a)+15/4*b^2*sqrt(-a+b*x) +--R +--R +--R +-------+ +--R 2 2 +-+ \|b x - a 2 2 2 +-------+ +--R - 15b x \|a atan(----------) + (8b x + 9a b x - 2a )\|b x - a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 1615 + +--S 1616 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +-------+ +--R 2 2 +---+ - 2\|- a \|b x - a + b x - 2a +--R 15b x \|- a log(------------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (16b x + 18a b x - 4a )\|b x - a +--R / +--R 2 +--R 8x +--R , +--R +-------+ +--R 2 2 +-+ \|b x - a 2 2 2 +-------+ +--R - 15b x \|a atan(----------) + (8b x + 9a b x - 2a )\|b x - a +--R +-+ +--R \|a +--R ---------------------------------------------------------------] +--R 2 +--R 4x +--R Type: Union(List(Expression(Integer)),...) +--E 1616 + +--S 1617 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +---+ +-------+ +-------+ +--R 2 +---+ - 2\|- a \|b x - a + b x - 2a 2 +-+ \|b x - a +--R 15b \|- a log(------------------------------) + 30b \|a atan(----------) +--R x +-+ +--R \|a +--R ------------------------------------------------------------------------ +--R 8 +--R Type: Expression(Integer) +--E 1617 + +--S 1618 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1618 + +--S 1619 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1619 + +--S 1620 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1620 + +)clear all + +--S 1621 of 3330 +t0000:=x^m/sqrt(a+b*x) +--R +--R +--R m +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1621 + +--S 1622 of 3330 +--r0000:=2*x^m*hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/(b*(-b*x/a)^m) +--E 1622 + +--S 1623 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1623 + +--S 1624 of 3330 +--m0000:=a0000 - r0000 +--E 1624 + +--S 1625 of 3330 +--d0000:=D(m0000,x) +--E 1625 + +)clear all + +--S 1626 of 3330 +t0000:=x^4/sqrt(a+b*x) +--R +--R +--R 4 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1626 + +--S 1627 of 3330 +r0000:=-8/3*a^3*(a+b*x)^(3/2)/b^5+12/5*a^2*(a+b*x)^(5/2)/b^5-_ + 8/7*a*(a+b*x)^(7/2)/b^5+2/9*(a+b*x)^(9/2)/b^5+2*a^4*sqrt(a+b*x)/b^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x - 80a b x + 96a b x - 128a b x + 256a )\|b x + a +--R (2) ----------------------------------------------------------- +--R 5 +--R 315b +--R Type: Expression(Integer) +--E 1627 + +--S 1628 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (70b x - 80a b x + 96a b x - 128a b x + 256a )\|b x + a +--R (3) ----------------------------------------------------------- +--R 5 +--R 315b +--R Type: Union(Expression(Integer),...) +--E 1628 + +--S 1629 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1629 + +--S 1630 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1630 + +)clear all + +--S 1631 of 3330 +t0000:=x^3/sqrt(a+b*x) +--R +--R +--R 3 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1631 + +--S 1632 of 3330 +r0000:=2*a^2*(a+b*x)^(3/2)/b^4-6/5*a*(a+b*x)^(5/2)/b^4+_ + 2/7*(a+b*x)^(7/2)/b^4-2*a^3*sqrt(a+b*x)/b^4 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (10b x - 12a b x + 16a b x - 32a )\|b x + a +--R (2) ---------------------------------------------- +--R 4 +--R 35b +--R Type: Expression(Integer) +--E 1632 + +--S 1633 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (10b x - 12a b x + 16a b x - 32a )\|b x + a +--R (3) ---------------------------------------------- +--R 4 +--R 35b +--R Type: Union(Expression(Integer),...) +--E 1633 + +--S 1634 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1634 + +--S 1635 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1635 + +)clear all + +--S 1636 of 3330 +t0000:=x^2/sqrt(a+b*x) +--R +--R +--R 2 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1636 + +--S 1637 of 3330 +r0000:=-4/3*a*(a+b*x)^(3/2)/b^3+2/5*(a+b*x)^(5/2)/b^3+2*a^2*sqrt(a+b*x)/b^3 +--R +--R +--R 2 2 2 +-------+ +--R (6b x - 8a b x + 16a )\|b x + a +--R (2) --------------------------------- +--R 3 +--R 15b +--R Type: Expression(Integer) +--E 1637 + +--S 1638 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +-------+ +--R (6b x - 8a b x + 16a )\|b x + a +--R (3) --------------------------------- +--R 3 +--R 15b +--R Type: Union(Expression(Integer),...) +--E 1638 + +--S 1639 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1639 + +--S 1640 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1640 + +)clear all + +--S 1641 of 3330 +t0000:=x/sqrt(a+b*x) +--R +--R +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1641 + +--S 1642 of 3330 +r0000:=2/3*(a+b*x)^(3/2)/b^2-2*a*sqrt(a+b*x)/b^2 +--R +--R +--R +-------+ +--R (2b x - 4a)\|b x + a +--R (2) --------------------- +--R 2 +--R 3b +--R Type: Expression(Integer) +--E 1642 + +--S 1643 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +--R (2b x - 4a)\|b x + a +--R (3) --------------------- +--R 2 +--R 3b +--R Type: Union(Expression(Integer),...) +--E 1643 + +--S 1644 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1644 + +--S 1645 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1645 + +)clear all + +--S 1646 of 3330 +t0000:=1/sqrt(a+b*x) +--R +--R +--R 1 +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1646 + +--S 1647 of 3330 +r0000:=2*sqrt(a+b*x)/b +--R +--R +--R +-------+ +--R 2\|b x + a +--R (2) ----------- +--R b +--R Type: Expression(Integer) +--E 1647 + +--S 1648 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +--R 2\|b x + a +--R (3) ----------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1648 + +--S 1649 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1649 + +--S 1650 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1650 + +)clear all + +--S 1651 of 3330 +t0000:=1/(x*sqrt(a+b*x)) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R x\|b x + a +--R Type: Expression(Integer) +--E 1651 + +--S 1652 of 3330 +r0000:=-2*atanh(sqrt(a+b*x)/sqrt(a))/sqrt(a) +--R +--R +--R +-------+ +--R \|b x + a +--R 2atanh(----------) +--R +-+ +--R \|a +--R (2) - ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1652 + +--S 1653 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-+ +---+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|- a \|b x + a +--R log(-------------------------------) 2atan(----------------) +--R x a +--R (3) [------------------------------------,- -----------------------] +--R +-+ +---+ +--R \|a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1653 + +--S 1654 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R log(-------------------------------) + 2atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1654 + +--S 1655 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1655 + +--S 1656 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R 2\|- a atanh(----------) - 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1656 + +--S 1657 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1657 + +)clear all + +--S 1658 of 3330 +t0000:=1/(x^2*sqrt(a+b*x)) +--R +--R +--R 1 +--R (1) ------------ +--R 2 +-------+ +--R x \|b x + a +--R Type: Expression(Integer) +--E 1658 + +--S 1659 of 3330 +r0000:=b*atanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)-sqrt(a+b*x)/(a*x) +--R +--R +--R +-------+ +--R \|b x + a +-+ +-------+ +--R b x atanh(----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R +-+ +--R a x\|a +--R Type: Expression(Integer) +--E 1659 + +--S 1660 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R 2a\|b x + a + (b x + 2a)\|a +-+ +-------+ +--R b x log(-----------------------------) - 2\|a \|b x + a +--R x +--R [--------------------------------------------------------, +--R +-+ +--R 2a x\|a +--R +---+ +-------+ +--R \|- a \|b x + a +---+ +-------+ +--R b x atan(----------------) - \|- a \|b x + a +--R a +--R ---------------------------------------------] +--R +---+ +--R a x\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1660 + +--S 1661 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R b log(-----------------------------) - 2b atanh(----------) +--R x +-+ +--R \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 1661 + +--S 1662 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1662 + +--S 1663 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R - b\|- a atanh(----------) + b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R a\|- a \|a +--R Type: Expression(Integer) +--E 1663 + +--S 1664 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1664 + +)clear all + +--S 1665 of 3330 +t0000:=1/(x^3*sqrt(a+b*x)) +--R +--R +--R 1 +--R (1) ------------ +--R 3 +-------+ +--R x \|b x + a +--R Type: Expression(Integer) +--E 1665 + +--S 1666 of 3330 +r0000:=-3/4*b^2*atanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)-_ + 1/2*sqrt(a+b*x)/(a*x^2)+3/4*b*sqrt(a+b*x)/(a^2*x) +--R +--R +--R +-------+ +--R 2 2 \|b x + a +-+ +-------+ +--R - 3b x atanh(----------) + (3b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------- +--R 2 2 +-+ +--R 4a x \|a +--R Type: Expression(Integer) +--E 1666 + +--S 1667 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R 2 2 - 2a\|b x + a + (b x + 2a)\|a +-+ +-------+ +--R 3b x log(-------------------------------) + (6b x - 4a)\|a \|b x + a +--R x +--R [---------------------------------------------------------------------, +--R 2 2 +-+ +--R 8a x \|a +--R +---+ +-------+ +--R 2 2 \|- a \|b x + a +---+ +-------+ +--R - 3b x atan(----------------) + (3b x - 2a)\|- a \|b x + a +--R a +--R -----------------------------------------------------------] +--R 2 2 +---+ +--R 4a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1667 + +--S 1668 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2 - 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R 3b log(-------------------------------) + 6b atanh(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1668 + +--S 1669 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1669 + +--S 1670 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R 3b \|- a atanh(----------) - 3b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 2 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 1670 + +--S 1671 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1671 + +)clear all + +--S 1672 of 3330 +t0000:=1/(x^4*sqrt(a+b*x)) +--R +--R +--R 1 +--R (1) ------------ +--R 4 +-------+ +--R x \|b x + a +--R Type: Expression(Integer) +--E 1672 + +--S 1673 of 3330 +r0000:=5/8*b^3*atanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)-_ + 1/3*sqrt(a+b*x)/(a*x^3)+5/12*b*sqrt(a+b*x)/(a^2*x^2)-_ + 5/8*b^2*sqrt(a+b*x)/(a^3*x) +--R +--R +--R +-------+ +--R 3 3 \|b x + a 2 2 2 +-+ +-------+ +--R 15b x atanh(----------) + (- 15b x + 10a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------ +--R 3 3 +-+ +--R 24a x \|a +--R Type: Expression(Integer) +--E 1673 + +--S 1674 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 3 3 2a\|b x + a + (b x + 2a)\|a +--R 15b x log(-----------------------------) +--R x +--R + +--R 2 2 2 +-+ +-------+ +--R (- 30b x + 20a b x - 16a )\|a \|b x + a +--R / +--R 3 3 +-+ +--R 48a x \|a +--R , +--R +---+ +-------+ +--R 3 3 \|- a \|b x + a 2 2 2 +---+ +-------+ +--R 15b x atan(----------------) + (- 15b x + 10a b x - 8a )\|- a \|b x + a +--R a +--R -------------------------------------------------------------------------] +--R 3 3 +---+ +--R 24a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1674 + +--S 1675 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 3 2a\|b x + a + (b x + 2a)\|a 3 \|b x + a +--R 5b log(-----------------------------) - 10b atanh(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1675 + +--S 1676 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1676 + +--S 1677 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 3 +---+ \|b x + a 3 +-+ \|- a \|b x + a +--R - 5b \|- a atanh(----------) + 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 3 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1677 + +--S 1678 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1678 + +)clear all + +--S 1679 of 3330 +t0000:=x^m/(a+b*x)^(3/2) +--R +--R +--R m +--R x +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1679 + +--S 1680 of 3330 +--r0000:=2*x^(1+m)/(a*sqrt(a+b*x))-2*(1+2*m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/(a*b*(-b*x/a)^m) +--E 1680 + +--S 1681 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | --------------------- d%N +--R ++ +--------+ +--R (%N b + a)\|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1681 + +--S 1682 of 3330 +--m0000:=a0000 - r0000 +--E 1682 + +--S 1683 of 3330 +--d0000:=D(m0000,x) +--E 1683 + +)clear all + +--S 1684 of 3330 +t0000:=x^4/(a+b*x)^(3/2) +--R +--R +--R 4 +--R x +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1684 + +--S 1685 of 3330 +r0000:=4*a^2*(a+b*x)^(3/2)/b^5-8/5*a*(a+b*x)^(5/2)/b^5+_ + 2/7*(a+b*x)^(7/2)/b^5-2*a^4/(b^5*sqrt(a+b*x))-8*a^3*sqrt(a+b*x)/b^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R 10b x - 16a b x + 32a b x - 128a b x - 256a +--R (2) ----------------------------------------------- +--R 5 +-------+ +--R 35b \|b x + a +--R Type: Expression(Integer) +--E 1685 + +--S 1686 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R 10b x - 16a b x + 32a b x - 128a b x - 256a +--R (3) ----------------------------------------------- +--R 5 +-------+ +--R 35b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 1686 + +--S 1687 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1687 + +--S 1688 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1688 + +)clear all + +--S 1689 of 3330 +t0000:=x^3/(a+b*x)^(3/2) +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1689 + +--S 1690 of 3330 +r0000:=-2*a*(a+b*x)^(3/2)/b^4+2/5*(a+b*x)^(5/2)/b^4+_ + 2*a^3/(b^4*sqrt(a+b*x))+6*a^2*sqrt(a+b*x)/b^4 +--R +--R +--R 3 3 2 2 2 3 +--R 2b x - 4a b x + 16a b x + 32a +--R (2) -------------------------------- +--R 4 +-------+ +--R 5b \|b x + a +--R Type: Expression(Integer) +--E 1690 + +--S 1691 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x - 4a b x + 16a b x + 32a +--R (3) -------------------------------- +--R 4 +-------+ +--R 5b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 1691 + +--S 1692 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1692 + +--S 1693 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1693 + +)clear all + +--S 1694 of 3330 +t0000:=x^2/(a+b*x)^(3/2) +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1694 + +--S 1695 of 3330 +r0000:=2/3*(a+b*x)^(3/2)/b^3-2*a^2/(b^3*sqrt(a+b*x))-4*a*sqrt(a+b*x)/b^3 +--R +--R +--R 2 2 2 +--R 2b x - 8a b x - 16a +--R (2) --------------------- +--R 3 +-------+ +--R 3b \|b x + a +--R Type: Expression(Integer) +--E 1695 + +--S 1696 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 2b x - 8a b x - 16a +--R (3) --------------------- +--R 3 +-------+ +--R 3b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 1696 + +--S 1697 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1697 + +--S 1698 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1698 + +)clear all + +--S 1699 of 3330 +t0000:=x/(a+b*x)^(3/2) +--R +--R +--R x +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1699 + +--S 1700 of 3330 +r0000:=2*a/(b^2*sqrt(a+b*x))+2*sqrt(a+b*x)/b^2 +--R +--R +--R 2b x + 4a +--R (2) ------------ +--R 2 +-------+ +--R b \|b x + a +--R Type: Expression(Integer) +--E 1700 + +--S 1701 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2b x + 4a +--R (3) ------------ +--R 2 +-------+ +--R b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 1701 + +--S 1702 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1702 + +--S 1703 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1703 + +)clear all + +--S 1704 of 3330 +t0000:=1/(a+b*x)^(3/2) +--R +--R +--R 1 +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1704 + +--S 1705 of 3330 +r0000:=(-2)/(b*sqrt(a+b*x)) +--R +--R +--R 2 +--R (2) - ----------- +--R +-------+ +--R b\|b x + a +--R Type: Expression(Integer) +--E 1705 + +--S 1706 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) - ----------- +--R +-------+ +--R b\|b x + a +--R Type: Union(Expression(Integer),...) +--E 1706 + +--S 1707 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1707 + +--S 1708 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1708 + +)clear all + +--S 1709 of 3330 +t0000:=1/(x*(a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 +-------+ +--R (b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1709 + +--S 1710 of 3330 +r0000:=-2*atanh(sqrt(a+b*x)/sqrt(a))/a^(3/2)+2/(a*sqrt(a+b*x)) +--R +--R +--R +-------+ +--R +-------+ \|b x + a +-+ +--R - 2\|b x + a atanh(----------) + 2\|a +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R +-+ +-------+ +--R a\|a \|b x + a +--R Type: Expression(Integer) +--E 1710 + +--S 1711 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R +-------+ - 2a\|b x + a + (b x + 2a)\|a +-+ +--R \|b x + a log(-------------------------------) + 2\|a +--R x +--R [------------------------------------------------------, +--R +-+ +-------+ +--R a\|a \|b x + a +--R +---+ +-------+ +--R +-------+ \|- a \|b x + a +---+ +--R - 2\|b x + a atan(----------------) + 2\|- a +--R a +--R ---------------------------------------------] +--R +---+ +-------+ +--R a\|- a \|b x + a +--R Type: Union(List(Expression(Integer)),...) +--E 1711 + +--S 1712 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R log(-------------------------------) + 2atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1712 + +--S 1713 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1713 + +--S 1714 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R 2\|- a atanh(----------) - 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R a\|- a \|a +--R Type: Expression(Integer) +--E 1714 + +--S 1715 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1715 + +)clear all + +--S 1716 of 3330 +t0000:=1/(x^2*(a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 3 2 +-------+ +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1716 + +--S 1717 of 3330 +r0000:=3*b*atanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)+2/(a*x*sqrt(a+b*x))-_ + 3*sqrt(a+b*x)/(a^2*x) +--R +--R +--R +-------+ +--R +-------+ \|b x + a +-+ +--R 3b x\|b x + a atanh(----------) + (- 3b x - a)\|a +--R +-+ +--R \|a +--R (2) -------------------------------------------------- +--R 2 +-+ +-------+ +--R a x\|a \|b x + a +--R Type: Expression(Integer) +--E 1717 + +--S 1718 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R +-------+ 2a\|b x + a + (b x + 2a)\|a +-+ +--R 3b x\|b x + a log(-----------------------------) + (- 6b x - 2a)\|a +--R x +--R [--------------------------------------------------------------------, +--R 2 +-+ +-------+ +--R 2a x\|a \|b x + a +--R +---+ +-------+ +--R +-------+ \|- a \|b x + a +---+ +--R 3b x\|b x + a atan(----------------) + (- 3b x - a)\|- a +--R a +--R ---------------------------------------------------------] +--R 2 +---+ +-------+ +--R a x\|- a \|b x + a +--R Type: Union(List(Expression(Integer)),...) +--E 1718 + +--S 1719 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R 3b log(-----------------------------) - 6b atanh(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------ +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1719 + +--S 1720 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1720 + +--S 1721 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R - 3b\|- a atanh(----------) + 3b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 2 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1721 + +--S 1722 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1722 + +)clear all + +--S 1723 of 3330 +t0000:=1/(x^3*(a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4 3 +-------+ +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1723 + +--S 1724 of 3330 +r0000:=-15/4*b^2*atanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)+2/(a*x^2*sqrt(a+b*x))-_ + 5/2*sqrt(a+b*x)/(a^2*x^2)+15/4*b*sqrt(a+b*x)/(a^3*x) +--R +--R +--R +-------+ +--R 2 2 +-------+ \|b x + a 2 2 2 +-+ +--R - 15b x \|b x + a atanh(----------) + (15b x + 5a b x - 2a )\|a +--R +-+ +--R \|a +--R (2) ----------------------------------------------------------------- +--R 3 2 +-+ +-------+ +--R 4a x \|a \|b x + a +--R Type: Expression(Integer) +--E 1724 + +--S 1725 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 2 2 +-------+ - 2a\|b x + a + (b x + 2a)\|a +--R 15b x \|b x + a log(-------------------------------) +--R x +--R + +--R 2 2 2 +-+ +--R (30b x + 10a b x - 4a )\|a +--R / +--R 3 2 +-+ +-------+ +--R 8a x \|a \|b x + a +--R , +--R +---+ +-------+ +--R 2 2 +-------+ \|- a \|b x + a 2 2 2 +---+ +--R - 15b x \|b x + a atan(----------------) + (15b x + 5a b x - 2a )\|- a +--R a +--R ------------------------------------------------------------------------] +--R 3 2 +---+ +-------+ +--R 4a x \|- a \|b x + a +--R Type: Union(List(Expression(Integer)),...) +--E 1725 + +--S 1726 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2 - 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R 15b log(-------------------------------) + 30b atanh(----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1726 + +--S 1727 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1727 + +--S 1728 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R 15b \|- a atanh(----------) - 15b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 3 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 1728 + +--S 1729 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1729 + +)clear all + +--S 1730 of 3330 +t0000:=x^m/(a+b*x)^(5/2) +--R +--R +--R m +--R x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1730 + +--S 1731 of 3330 +--r0000:=2/3*x^(1+m)/(a*(a+b*x)^(3/2))+2/3*(1-2*m)*x^(1+m)/(a^2*sqrt(a+b*x))-_ +-- 2/3*(1-2*m)*(1+2*m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/(a^2*b*(-b*x/a)^m) +--E 1731 + +--S 1732 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | --------------------------------- d%N +--R ++ 2 2 2 +--------+ +--R (%N b + 2%N a b + a )\|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1732 + +--S 1733 of 3330 +--m0000:=a0000 - r0000 +--E 1733 + +--S 1734 of 3330 +--d0000:=D(m0000,x) +--E 1734 + +)clear all + +--S 1735 of 3330 +--t0000:=x^4/(a+b*x)^(5/2) +--E 1735 + +--S 1736 of 3330 +r0000:=-2/3*a^4/(b^5*(a+b*x)^(3/2))-8/3*a*(a+b*x)^(3/2)/b^5+_ + 2/5*(a+b*x)^(5/2)/b^5+8*a^3/(b^5*sqrt(a+b*x))+12*a^2*sqrt(a+b*x)/b^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R 6b x - 16a b x + 96a b x + 384a b x + 256a +--R (1) ---------------------------------------------- +--R 6 5 +-------+ +--R (15b x + 15a b )\|b x + a +--R Type: Expression(Integer) +--E 1736 + +--S 1737 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (2) t0000 x +--R Type: Polynomial(Fraction(Integer)) +--E 1737 + +--S 1738 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (3) +--R 6 2 5 +-------+ 4 4 3 3 2 2 2 +--R (15b t0000 x + 15a b t0000 x)\|b x + a - 6b x + 16a b x - 96a b x +--R + +--R 3 4 +--R - 384a b x - 256a +--R / +--R 6 5 +-------+ +--R (15b x + 15a b )\|b x + a +--R Type: Expression(Integer) +--E 1738 + +--S 1739 of 3330 +d0000:=D(m0000,x) +--R +--R +--R 2 2 2 +-------+ 4 +--R (b t0000 x + 2a b t0000 x + a t0000)\|b x + a - x +--R (4) ---------------------------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1739 + +)clear all + +--S 1740 of 3330 +t0000:=x^3/(a+b*x)^(5/2) +--R +--R +--R 3 +--R x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1740 + +--S 1741 of 3330 +r0000:=2/3*a^3/(b^4*(a+b*x)^(3/2))+2/3*(a+b*x)^(3/2)/b^4-_ + 6*a^2/(b^4*sqrt(a+b*x))-6*a*sqrt(a+b*x)/b^4 +--R +--R +--R 3 3 2 2 2 3 +--R 2b x - 12a b x - 48a b x - 32a +--R (2) --------------------------------- +--R 5 4 +-------+ +--R (3b x + 3a b )\|b x + a +--R Type: Expression(Integer) +--E 1741 + +--S 1742 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x - 12a b x - 48a b x - 32a +--R (3) --------------------------------- +--R 5 4 +-------+ +--R (3b x + 3a b )\|b x + a +--R Type: Union(Expression(Integer),...) +--E 1742 + +--S 1743 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1743 + +--S 1744 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1744 + +)clear all + +--S 1745 of 3330 +t0000:=x^2/(a+b*x)^(5/2) +--R +--R +--R 2 +--R x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1745 + +--S 1746 of 3330 +r0000:=-2/3*a^2/(b^3*(a+b*x)^(3/2))+4*a/(b^3*sqrt(a+b*x))+2*sqrt(a+b*x)/b^3 +--R +--R +--R 2 2 2 +--R 6b x + 24a b x + 16a +--R (2) ------------------------ +--R 4 3 +-------+ +--R (3b x + 3a b )\|b x + a +--R Type: Expression(Integer) +--E 1746 + +--S 1747 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 6b x + 24a b x + 16a +--R (3) ------------------------ +--R 4 3 +-------+ +--R (3b x + 3a b )\|b x + a +--R Type: Union(Expression(Integer),...) +--E 1747 + +--S 1748 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1748 + +--S 1749 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1749 + +)clear all + +--S 1750 of 3330 +t0000:=x/(a+b*x)^(5/2) +--R +--R +--R x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1750 + +--S 1751 of 3330 +r0000:=2/3*a/(b^2*(a+b*x)^(3/2))+(-2)/(b^2*sqrt(a+b*x)) +--R +--R +--R - 6b x - 4a +--R (2) ------------------------ +--R 3 2 +-------+ +--R (3b x + 3a b )\|b x + a +--R Type: Expression(Integer) +--E 1751 + +--S 1752 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 6b x - 4a +--R (3) ------------------------ +--R 3 2 +-------+ +--R (3b x + 3a b )\|b x + a +--R Type: Union(Expression(Integer),...) +--E 1752 + +--S 1753 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1753 + +--S 1754 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1754 + +)clear all + +--S 1755 of 3330 +t0000:=1/(a+b*x)^(5/2) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1755 + +--S 1756 of 3330 +r0000:=(-2/3)/(b*(a+b*x)^(3/2)) +--R +--R +--R 2 +--R (2) - ----------------------- +--R 2 +-------+ +--R (3b x + 3a b)\|b x + a +--R Type: Expression(Integer) +--E 1756 + +--S 1757 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) - ----------------------- +--R 2 +-------+ +--R (3b x + 3a b)\|b x + a +--R Type: Union(Expression(Integer),...) +--E 1757 + +--S 1758 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1758 + +--S 1759 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1759 + +)clear all + +--S 1760 of 3330 +t0000:=1/(x*(a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 2 3 2 2 +-------+ +--R (b x + 2a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1760 + +--S 1761 of 3330 +r0000:=2/3/(a*(a+b*x)^(3/2))-2*atanh(sqrt(a+b*x)/sqrt(a))/a^(5/2)+_ + 2/(a^2*sqrt(a+b*x)) +--R +--R +--R +-------+ +--R +-------+ \|b x + a +-+ +--R (- 6b x - 6a)\|b x + a atanh(----------) + (6b x + 8a)\|a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------- +--R 2 3 +-+ +-------+ +--R (3a b x + 3a )\|a \|b x + a +--R Type: Expression(Integer) +--E 1761 + +--S 1762 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +-+ +--R +-------+ - 2a\|b x + a + (b x + 2a)\|a +-+ +--R (3b x + 3a)\|b x + a log(-------------------------------) + (6b x + 8a)\|a +--R x +--R [---------------------------------------------------------------------------, +--R 2 3 +-+ +-------+ +--R (3a b x + 3a )\|a \|b x + a +--R +---+ +-------+ +--R +-------+ \|- a \|b x + a +---+ +--R (- 6b x - 6a)\|b x + a atan(----------------) + (6b x + 8a)\|- a +--R a +--R -----------------------------------------------------------------] +--R 2 3 +---+ +-------+ +--R (3a b x + 3a )\|- a \|b x + a +--R Type: Union(List(Expression(Integer)),...) +--E 1762 + +--S 1763 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R log(-------------------------------) + 2atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1763 + +--S 1764 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1764 + +--S 1765 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R 2\|- a atanh(----------) - 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R 2 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1765 + +--S 1766 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1766 + +)clear all + +--S 1767 of 3330 +t0000:=1/(x^2*(a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 4 3 2 2 +-------+ +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1767 + +--S 1768 of 3330 +r0000:=2/3/(a*x*(a+b*x)^(3/2))+5*b*atanh(sqrt(a+b*x)/sqrt(a))/a^(7/2)+_ + 10/3/(a^2*x*sqrt(a+b*x))-5*sqrt(a+b*x)/(a^3*x) +--R +--R +--R (2) +--R +-------+ +--R 2 2 +-------+ \|b x + a +--R (15b x + 15a b x)\|b x + a atanh(----------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R (- 15b x - 20a b x - 3a )\|a +--R / +--R 3 2 4 +-+ +-------+ +--R (3a b x + 3a x)\|a \|b x + a +--R Type: Expression(Integer) +--E 1768 + +--S 1769 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 2 2 +-------+ 2a\|b x + a + (b x + 2a)\|a +--R (15b x + 15a b x)\|b x + a log(-----------------------------) +--R x +--R + +--R 2 2 2 +-+ +--R (- 30b x - 40a b x - 6a )\|a +--R / +--R 3 2 4 +-+ +-------+ +--R (6a b x + 6a x)\|a \|b x + a +--R , +--R +--R +---+ +-------+ +--R 2 2 +-------+ \|- a \|b x + a +--R (15b x + 15a b x)\|b x + a atan(----------------) +--R a +--R + +--R 2 2 2 +---+ +--R (- 15b x - 20a b x - 3a )\|- a +--R / +--R 3 2 4 +---+ +-------+ +--R (3a b x + 3a x)\|- a \|b x + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1769 + +--S 1770 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R 5b log(-----------------------------) - 10b atanh(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1770 + +--S 1771 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1771 + +--S 1772 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R - 5b\|- a atanh(----------) + 5b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 3 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1772 + +--S 1773 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1773 + +)clear all + +--S 1774 of 3330 +t0000:=1/(x^3*(a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 5 4 2 3 +-------+ +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1774 + +--S 1775 of 3330 +r0000:=2/3/(a*x^2*(a+b*x)^(3/2))-_ + 35/4*b^2*atanh(sqrt(a+b*x)/sqrt(a))/a^(9/2)+_ + 14/3/(a^2*x^2*sqrt(a+b*x))-35/6*sqrt(a+b*x)/(a^3*x^2)+_ + 35/4*b*sqrt(a+b*x)/(a^4*x) +--R +--R +--R (2) +--R +-------+ +--R 3 3 2 2 +-------+ \|b x + a +--R (- 105b x - 105a b x )\|b x + a atanh(----------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (105b x + 140a b x + 21a b x - 6a )\|a +--R / +--R 4 3 5 2 +-+ +-------+ +--R (12a b x + 12a x )\|a \|b x + a +--R Type: Expression(Integer) +--E 1775 + +--S 1776 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 3 3 2 2 +-------+ - 2a\|b x + a + (b x + 2a)\|a +--R (105b x + 105a b x )\|b x + a log(-------------------------------) +--R x +--R + +--R 3 3 2 2 2 3 +-+ +--R (210b x + 280a b x + 42a b x - 12a )\|a +--R / +--R 4 3 5 2 +-+ +-------+ +--R (24a b x + 24a x )\|a \|b x + a +--R , +--R +--R +---+ +-------+ +--R 3 3 2 2 +-------+ \|- a \|b x + a +--R (- 105b x - 105a b x )\|b x + a atan(----------------) +--R a +--R + +--R 3 3 2 2 2 3 +---+ +--R (105b x + 140a b x + 21a b x - 6a )\|- a +--R / +--R 4 3 5 2 +---+ +-------+ +--R (12a b x + 12a x )\|- a \|b x + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1776 + +--S 1777 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R 2 - 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R 35b log(-------------------------------) + 70b atanh(----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1777 + +--S 1778 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1778 + +--S 1779 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R 35b \|- a atanh(----------) - 35b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 4 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 1779 + +--S 1780 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1780 + +)clear all + +--S 1781 of 3330 +t0000:=1/(x*sqrt(-a+b*x)) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R x\|b x - a +--R Type: Expression(Integer) +--E 1781 + +--S 1782 of 3330 +r0000:=2*atan(sqrt(-a+b*x)/sqrt(a))/sqrt(a) +--R +--R +--R +-------+ +--R \|b x - a +--R 2atan(----------) +--R +-+ +--R \|a +--R (2) ----------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1782 + +--S 1783 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +---+ +-+ +-------+ +--R 2a\|b x - a + (b x - 2a)\|- a \|a \|b x - a +--R log(-------------------------------) 2atan(--------------) +--R x a +--R (3) [------------------------------------,---------------------] +--R +---+ +-+ +--R \|- a \|a +--R Type: Union(List(Expression(Integer)),...) +--E 1783 + +--S 1784 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +-+ 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R \|a log(-------------------------------) - 2\|- a atan(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------------ +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1784 + +--S 1785 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1785 + +--S 1786 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R 2atan(--------------) - 2atan(----------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1786 + +--S 1787 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1787 + +)clear all + +--S 1788 of 3330 +t0000:=1/(x^2*sqrt(-a+b*x)) +--R +--R +--R 1 +--R (1) ------------ +--R 2 +-------+ +--R x \|b x - a +--R Type: Expression(Integer) +--E 1788 + +--S 1789 of 3330 +r0000:=b*atan(sqrt(-a+b*x)/sqrt(a))/a^(3/2)+sqrt(-a+b*x)/(a*x) +--R +--R +--R +-------+ +--R \|b x - a +-+ +-------+ +--R b x atan(----------) + \|a \|b x - a +--R +-+ +--R \|a +--R (2) ------------------------------------- +--R +-+ +--R a x\|a +--R Type: Expression(Integer) +--E 1789 + +--S 1790 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R 2a\|b x - a + (b x - 2a)\|- a +---+ +-------+ +--R b x log(-------------------------------) + 2\|- a \|b x - a +--R x +--R [------------------------------------------------------------, +--R +---+ +--R 2a x\|- a +--R +-+ +-------+ +--R \|a \|b x - a +-+ +-------+ +--R b x atan(--------------) + \|a \|b x - a +--R a +--R -----------------------------------------] +--R +-+ +--R a x\|a +--R Type: Union(List(Expression(Integer)),...) +--E 1790 + +--S 1791 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +-+ 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R b\|a log(-------------------------------) - 2b\|- a atan(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R +---+ +-+ +--R 2a\|- a \|a +--R Type: Expression(Integer) +--E 1791 + +--S 1792 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1792 + +--S 1793 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R b atan(--------------) - b atan(----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1793 + +--S 1794 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1794 + +)clear all + +--S 1795 of 3330 +t0000:=1/(x^3*sqrt(-a+b*x)) +--R +--R +--R 1 +--R (1) ------------ +--R 3 +-------+ +--R x \|b x - a +--R Type: Expression(Integer) +--E 1795 + +--S 1796 of 3330 +r0000:=3/4*b^2*atan(sqrt(-a+b*x)/sqrt(a))/a^(5/2)+_ + 1/2*sqrt(-a+b*x)/(a*x^2)+3/4*b*sqrt(-a+b*x)/(a^2*x) +--R +--R +--R +-------+ +--R 2 2 \|b x - a +-+ +-------+ +--R 3b x atan(----------) + (3b x + 2a)\|a \|b x - a +--R +-+ +--R \|a +--R (2) ------------------------------------------------- +--R 2 2 +-+ +--R 4a x \|a +--R Type: Expression(Integer) +--E 1796 + +--S 1797 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R 2 2 2a\|b x - a + (b x - 2a)\|- a +---+ +-------+ +--R 3b x log(-------------------------------) + (6b x + 4a)\|- a \|b x - a +--R x +--R [-----------------------------------------------------------------------, +--R 2 2 +---+ +--R 8a x \|- a +--R +-+ +-------+ +--R 2 2 \|a \|b x - a +-+ +-------+ +--R 3b x atan(--------------) + (3b x + 2a)\|a \|b x - a +--R a +--R -----------------------------------------------------] +--R 2 2 +-+ +--R 4a x \|a +--R Type: Union(List(Expression(Integer)),...) +--E 1797 + +--S 1798 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-------+ +---+ +-------+ +--R 2 +-+ 2a\|b x - a + (b x - 2a)\|- a 2 +---+ \|b x - a +--R 3b \|a log(-------------------------------) - 6b \|- a atan(----------) +--R x +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1798 + +--S 1799 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1799 + +--S 1800 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 \|a \|b x - a 2 \|b x - a +--R 3b atan(--------------) - 3b atan(----------) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1800 + +--S 1801 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1801 + +)clear all + +--S 1802 of 3330 +t0000:=1/(x*(-a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 +-------+ +--R (b x - a x)\|b x - a +--R Type: Expression(Integer) +--E 1802 + +--S 1803 of 3330 +r0000:=-2*atan(sqrt(-a+b*x)/sqrt(a))/a^(3/2)+(-2)/(a*sqrt(-a+b*x)) +--R +--R +--R +-------+ +--R +-------+ \|b x - a +-+ +--R - 2\|b x - a atan(----------) - 2\|a +--R +-+ +--R \|a +--R (2) ------------------------------------- +--R +-+ +-------+ +--R a\|a \|b x - a +--R Type: Expression(Integer) +--E 1803 + +--S 1804 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R +-------+ - 2a\|b x - a + (b x - 2a)\|- a +---+ +--R \|b x - a log(---------------------------------) - 2\|- a +--R x +--R [----------------------------------------------------------, +--R +---+ +-------+ +--R a\|- a \|b x - a +--R +-+ +-------+ +--R +-------+ \|a \|b x - a +-+ +--R - 2\|b x - a atan(--------------) - 2\|a +--R a +--R -----------------------------------------] +--R +-+ +-------+ +--R a\|a \|b x - a +--R Type: Union(List(Expression(Integer)),...) +--E 1804 + +--S 1805 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +-+ - 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R \|a log(---------------------------------) + 2\|- a atan(----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R +---+ +-+ +--R a\|- a \|a +--R Type: Expression(Integer) +--E 1805 + +--S 1806 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1806 + +--S 1807 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R - 2atan(--------------) + 2atan(----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1807 + +--S 1808 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1808 + +)clear all + +--S 1809 of 3330 +t0000:=1/(x^2*(-a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 3 2 +-------+ +--R (b x - a x )\|b x - a +--R Type: Expression(Integer) +--E 1809 + +--S 1810 of 3330 +r0000:=-3*b*atan(sqrt(-a+b*x)/sqrt(a))/a^(5/2)+(-2)/(a*x*sqrt(-a+b*x))-_ + 3*sqrt(-a+b*x)/(a^2*x) +--R +--R +--R +-------+ +--R +-------+ \|b x - a +-+ +--R - 3b x\|b x - a atan(----------) + (- 3b x + a)\|a +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 2 +-+ +-------+ +--R a x\|a \|b x - a +--R Type: Expression(Integer) +--E 1810 + +--S 1811 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------+ +---+ +--R +-------+ - 2a\|b x - a + (b x - 2a)\|- a +---+ +--R 3b x\|b x - a log(---------------------------------) + (- 6b x + 2a)\|- a +--R x +--R [--------------------------------------------------------------------------, +--R 2 +---+ +-------+ +--R 2a x\|- a \|b x - a +--R +-+ +-------+ +--R +-------+ \|a \|b x - a +-+ +--R - 3b x\|b x - a atan(--------------) + (- 3b x + a)\|a +--R a +--R -------------------------------------------------------] +--R 2 +-+ +-------+ +--R a x\|a \|b x - a +--R Type: Union(List(Expression(Integer)),...) +--E 1811 + +--S 1812 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-------+ +---+ +-------+ +--R +-+ - 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R 3b\|a log(---------------------------------) + 6b\|- a atan(----------) +--R x +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 2a \|- a \|a +--R Type: Expression(Integer) +--E 1812 + +--S 1813 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1813 + +--S 1814 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R - 3b atan(--------------) + 3b atan(----------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1814 + +--S 1815 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1815 + +)clear all + +--S 1816 of 3330 +t0000:=1/(x^3*(-a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4 3 +-------+ +--R (b x - a x )\|b x - a +--R Type: Expression(Integer) +--E 1816 + +--S 1817 of 3330 +r0000:=-15/4*b^2*atan(sqrt(-a+b*x)/sqrt(a))/a^(7/2)+_ + (-2)/(a*x^2*sqrt(-a+b*x))-5/2*sqrt(-a+b*x)/(a^2*x^2)-_ + 15/4*b*sqrt(-a+b*x)/(a^3*x) +--R +--R +--R +-------+ +--R 2 2 +-------+ \|b x - a 2 2 2 +-+ +--R - 15b x \|b x - a atan(----------) + (- 15b x + 5a b x + 2a )\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------ +--R 3 2 +-+ +-------+ +--R 4a x \|a \|b x - a +--R Type: Expression(Integer) +--E 1817 + +--S 1818 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +---+ +--R 2 2 +-------+ - 2a\|b x - a + (b x - 2a)\|- a +--R 15b x \|b x - a log(---------------------------------) +--R x +--R + +--R 2 2 2 +---+ +--R (- 30b x + 10a b x + 4a )\|- a +--R / +--R 3 2 +---+ +-------+ +--R 8a x \|- a \|b x - a +--R , +--R +-+ +-------+ +--R 2 2 +-------+ \|a \|b x - a 2 2 2 +-+ +--R - 15b x \|b x - a atan(--------------) + (- 15b x + 5a b x + 2a )\|a +--R a +--R ----------------------------------------------------------------------] +--R 3 2 +-+ +-------+ +--R 4a x \|a \|b x - a +--R Type: Union(List(Expression(Integer)),...) +--E 1818 + +--S 1819 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-------+ +---+ +-------+ +--R 2 +-+ - 2a\|b x - a + (b x - 2a)\|- a 2 +---+ \|b x - a +--R 15b \|a log(---------------------------------) + 30b \|- a atan(----------) +--R x +-+ +--R \|a +--R --------------------------------------------------------------------------- +--R 3 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1819 + +--S 1820 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1820 + +--S 1821 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 \|a \|b x - a 2 \|b x - a +--R - 15b atan(--------------) + 15b atan(----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1821 + +--S 1822 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1822 + +)clear all + +--S 1823 of 3330 +t0000:=1/(x*(-a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 2 3 2 2 +-------+ +--R (b x - 2a b x + a x)\|b x - a +--R Type: Expression(Integer) +--E 1823 + +--S 1824 of 3330 +r0000:=(-2/3)/(a*(-a+b*x)^(3/2))+2*atan(sqrt(-a+b*x)/sqrt(a))/a^(5/2)+_ + 2/(a^2*sqrt(-a+b*x)) +--R +--R +--R +-------+ +--R +-------+ \|b x - a +-+ +--R (6b x - 6a)\|b x - a atan(----------) + (6b x - 8a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------- +--R 2 3 +-+ +-------+ +--R (3a b x - 3a )\|a \|b x - a +--R Type: Expression(Integer) +--E 1824 + +--S 1825 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +---+ +--R +-------+ 2a\|b x - a + (b x - 2a)\|- a +--R (3b x - 3a)\|b x - a log(-------------------------------) +--R x +--R + +--R +---+ +--R (6b x - 8a)\|- a +--R / +--R 2 3 +---+ +-------+ +--R (3a b x - 3a )\|- a \|b x - a +--R , +--R +-+ +-------+ +--R +-------+ \|a \|b x - a +-+ +--R (6b x - 6a)\|b x - a atan(--------------) + (6b x - 8a)\|a +--R a +--R -----------------------------------------------------------] +--R 2 3 +-+ +-------+ +--R (3a b x - 3a )\|a \|b x - a +--R Type: Union(List(Expression(Integer)),...) +--E 1825 + +--S 1826 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +-+ 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R \|a log(-------------------------------) - 2\|- a atan(----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------------------ +--R 2 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1826 + +--S 1827 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1827 + +--S 1828 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R 2atan(--------------) - 2atan(----------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1828 + +--S 1829 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1829 + +)clear all + +--S 1830 of 3330 +t0000:=1/(x^2*(-a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 4 3 2 2 +-------+ +--R (b x - 2a b x + a x )\|b x - a +--R Type: Expression(Integer) +--E 1830 + +--S 1831 of 3330 +r0000:=(-2/3)/(a*x*(-a+b*x)^(3/2))+5*b*atan(sqrt(-a+b*x)/sqrt(a))/a^(7/2)+_ + 10/3/(a^2*x*sqrt(-a+b*x))+5*sqrt(-a+b*x)/(a^3*x) +--R +--R +--R (2) +--R +-------+ +--R 2 2 +-------+ \|b x - a 2 2 2 +-+ +--R (15b x - 15a b x)\|b x - a atan(----------) + (15b x - 20a b x + 3a )\|a +--R +-+ +--R \|a +--R --------------------------------------------------------------------------- +--R 3 2 4 +-+ +-------+ +--R (3a b x - 3a x)\|a \|b x - a +--R Type: Expression(Integer) +--E 1831 + +--S 1832 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +---+ +--R 2 2 +-------+ 2a\|b x - a + (b x - 2a)\|- a +--R (15b x - 15a b x)\|b x - a log(-------------------------------) +--R x +--R + +--R 2 2 2 +---+ +--R (30b x - 40a b x + 6a )\|- a +--R / +--R 3 2 4 +---+ +-------+ +--R (6a b x - 6a x)\|- a \|b x - a +--R , +--R +--R +-+ +-------+ +--R 2 2 +-------+ \|a \|b x - a +--R (15b x - 15a b x)\|b x - a atan(--------------) +--R a +--R + +--R 2 2 2 +-+ +--R (15b x - 20a b x + 3a )\|a +--R / +--R 3 2 4 +-+ +-------+ +--R (3a b x - 3a x)\|a \|b x - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1832 + +--S 1833 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +-+ 2a\|b x - a + (b x - 2a)\|- a +---+ \|b x - a +--R 5b\|a log(-------------------------------) - 10b\|- a atan(----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------------------------- +--R 3 +---+ +-+ +--R 2a \|- a \|a +--R Type: Expression(Integer) +--E 1833 + +--S 1834 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1834 + +--S 1835 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R \|a \|b x - a \|b x - a +--R 5b atan(--------------) - 5b atan(----------) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1835 + +--S 1836 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1836 + +)clear all + +--S 1837 of 3330 +t0000:=1/(x^3*(-a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 5 4 2 3 +-------+ +--R (b x - 2a b x + a x )\|b x - a +--R Type: Expression(Integer) +--E 1837 + +--S 1838 of 3330 +r0000:=(-2/3)/(a*x^2*(-a+b*x)^(3/2))+_ + 35/4*b^2*atan(sqrt(-a+b*x)/sqrt(a))/a^(9/2)+_ + 14/3/(a^2*x^2*sqrt(-a+b*x))+35/6*sqrt(-a+b*x)/(a^3*x^2)+_ + 35/4*b*sqrt(-a+b*x)/(a^4*x) +--R +--R +--R (2) +--R +-------+ +--R 3 3 2 2 +-------+ \|b x - a +--R (105b x - 105a b x )\|b x - a atan(----------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (105b x - 140a b x + 21a b x + 6a )\|a +--R / +--R 4 3 5 2 +-+ +-------+ +--R (12a b x - 12a x )\|a \|b x - a +--R Type: Expression(Integer) +--E 1838 + +--S 1839 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-------+ +---+ +--R 3 3 2 2 +-------+ 2a\|b x - a + (b x - 2a)\|- a +--R (105b x - 105a b x )\|b x - a log(-------------------------------) +--R x +--R + +--R 3 3 2 2 2 3 +---+ +--R (210b x - 280a b x + 42a b x + 12a )\|- a +--R / +--R 4 3 5 2 +---+ +-------+ +--R (24a b x - 24a x )\|- a \|b x - a +--R , +--R +--R +-+ +-------+ +--R 3 3 2 2 +-------+ \|a \|b x - a +--R (105b x - 105a b x )\|b x - a atan(--------------) +--R a +--R + +--R 3 3 2 2 2 3 +-+ +--R (105b x - 140a b x + 21a b x + 6a )\|a +--R / +--R 4 3 5 2 +-+ +-------+ +--R (12a b x - 12a x )\|a \|b x - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1839 + +--S 1840 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-------+ +---+ +-------+ +--R 2 +-+ 2a\|b x - a + (b x - 2a)\|- a 2 +---+ \|b x - a +--R 35b \|a log(-------------------------------) - 70b \|- a atan(----------) +--R x +-+ +--R \|a +--R ------------------------------------------------------------------------- +--R 4 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1840 + +--S 1841 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1841 + +--S 1842 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-------+ +-------+ +--R 2 \|a \|b x - a 2 \|b x - a +--R 35b atan(--------------) - 35b atan(----------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1842 + +--S 1843 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1843 + +)clear all + +--S 1844 of 3330 +t0000:=x^(3+m)/sqrt(a+b*x) +--R +--R +--R m + 3 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1844 + +--S 1845 of 3330 +--r0000:=8*a^2*(2+m)*(3+m)*x^(1+m)*sqrt(a+b*x)/(b^3*(3+2*m)*(5+2*m)*(7+2*m))-_ +-- 4*a*(3+m)*x^(2+m)*sqrt(a+b*x)/(b^2*(5+2*m)*(7+2*m))+_ +-- 2*x^(3+m)*sqrt(a+b*x)/(b*(7+2*m))-16*a^3*(1+m)*(2+m)*(3+m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (b^4*(3+2*m)*(5+2*m)*(7+2*m)*(-b*x/a)^m) +--E 1845 + +--S 1846 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m + 3 +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1846 + +--S 1847 of 3330 +--m0000:=a0000 - r0000 +--E 1847 + +--S 1848 of 3330 +--d0000:=D(m0000,x) +--E 1848 + +)clear all + +--S 1849 of 3330 +t0000:=x^(2+m)/sqrt(a+b*x) +--R +--R +--R m + 2 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1849 + +--S 1850 of 3330 +--r0000:=-4*a*(2+m)*x^(1+m)*sqrt(a+b*x)/(b^2*(3+2*m)*(5+2*m))+_ +-- 2*x^(2+m)*sqrt(a+b*x)/(b*(5+2*m))+8*a^2*(1+m)*(2+m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (b^3*(3+2*m)*(5+2*m)*(-b*x/a)^m) +--E 1850 + +--S 1851 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m + 2 +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1851 + +--S 1852 of 3330 +--m0000:=a0000 - r0000 +--E 1852 + +--S 1853 of 3330 +--d0000:=D(m0000,x) +--E 1853 + +)clear all + +--S 1854 of 3330 +t0000:=x^(1+m)/sqrt(a+b*x) +--R +--R +--R m + 1 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1854 + +--S 1855 of 3330 +--r0000:=2*x^(1+m)*sqrt(a+b*x)/(b*(3+2*m))-4*a*(1+m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (b^2*(3+2*m)*(-b*x/a)^m) +--E 1855 + +--S 1856 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m + 1 +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1856 + +--S 1857 of 3330 +--m0000:=a0000 - r0000 +--E 1857 + +--S 1858 of 3330 +--d0000:=D(m0000,x) +--E 1858 + +)clear all + +--S 1859 of 3330 +t0000:=x^m/sqrt(a+b*x) +--R +--R +--R m +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1859 + +--S 1860 of 3330 +--r0000:=2*x^m*hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/(b*(-b*x/a)^m) +--E 1860 + +--S 1861 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1861 + +--S 1862 of 3330 +--m0000:=a0000 - r0000 +--E 1862 + +--S 1863 of 3330 +--d0000:=D(m0000,x) +--E 1863 + +)clear all + +--S 1864 of 3330 +t0000:=x^(-1+m)/sqrt(a+b*x) +--R +--R +--R m - 1 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1864 + +--S 1865 of 3330 +--r0000:=x^m*sqrt(a+b*x)/(a*m)-(1+2*m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/(a*m*(-b*x/a)^m) +--E 1865 + +--S 1866 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m - 1 +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1866 + +--S 1867 of 3330 +--m0000:=a0000 - r0000 +--E 1867 + +--S 1868 of 3330 +--d0000:=D(m0000,x) +--E 1868 + +)clear all + +--S 1869 of 3330 +t0000:=x^(-2+m)/sqrt(a+b*x) +--R +--R +--R m - 2 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1869 + +--S 1870 of 3330 +--r0000:=-x^(-1+m)*sqrt(a+b*x)/(a*(1-m))-1/2*b*(1-2*m)*x^m*_ +-- sqrt(a+b*x)/(a^2*(1-m)*m)+1/2*b*(1-2*m)*(1+2*m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (a^2*(1-m)*m*(-b*x/a)^m) +--E 1870 + +--S 1871 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m - 2 +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1871 + +--S 1872 of 3330 +--m0000:=a0000 - r0000 +--E 1872 + +--S 1873 of 3330 +--d0000:=D(m0000,x) +--E 1873 + +)clear all + +--S 1874 of 3330 +t0000:=x^(-3+m)/sqrt(a+b*x) +--R +--R +--R m - 3 +--R x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1874 + +--S 1875 of 3330 +--r0000:=-x^(-2+m)*sqrt(a+b*x)/(a*(2-m))+1/2*b*(3-2*m)*x^(-1+m)*_ +-- sqrt(a+b*x)/(a^2*(1-m)*(2-m))+1/4*b^2*(1-2*m)*(3-2*m)*x^m*_ +-- sqrt(a+b*x)/(a^3*(1-m)*(2-m)*m)-1/4*b^2*(1-2*m)*(3-2*m)*(1+2*m)*x^m*_ +-- hypergeometric(1/2,-m,3/2,(a+b*x)/a)*sqrt(a+b*x)/_ +-- (a^3*(1-m)*(2-m)*m*(-b*x/a)^m) +--E 1875 + +--S 1876 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R x m - 3 +--R ++ %N +--R (2) | ----------- d%N +--R ++ +--------+ +--R \|%N b + a +--R Type: Union(Expression(Integer),...) +--E 1876 + +--S 1877 of 3330 +--m0000:=a0000 - r0000 +--E 1877 + +--S 1878 of 3330 +--d0000:=D(m0000,x) +--E 1878 + +)clear all + +--S 1879 of 3330 +t0000:=1/2*x^(-1+m)*(2*a*m+b*(-1+2*m)*x)/(a+b*x)^(3/2) +--R +--R +--R m - 1 +--R ((2b m - b)x + 2a m)x +--R (1) -------------------------- +--R +-------+ +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1879 + +--S 1880 of 3330 +r0000:=x^m/sqrt(a+b*x) +--R +--R +--R m +--R x +--R (2) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1880 + +--S 1881 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (m - 1)log(x) +--R x %e +--R (3) ----------------- +--R +-------+ +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 1881 + +--S 1882 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (m - 1)log(x) m +--R x %e - x +--R (4) ---------------------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1882 + +--S 1883 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (m - 1)log(x) m m - 1 +--R ((2b m - b)x + 2a m)%e + b x + (- 2b m x - 2a m)x +--R (5) -------------------------------------------------------------------- +--R +-------+ +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1883 + +)clear all + +--S 1884 of 3330 +t0000:=-1/2*b*x^m/(a+b*x)^(3/2)+m*x^(-1+m)/sqrt(a+b*x) +--R +--R +--R m m - 1 +--R - b x + (2b m x + 2a m)x +--R (1) ------------------------------ +--R +-------+ +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1884 + +--S 1885 of 3330 +r0000:=x^m/sqrt(a+b*x),-b*x^(1+m)/(a*sqrt(a+b*x))+x^m*sqrt(a+b*x)/a +--R +--R +--R m m + 1 m +--R x - b x + (b x + a)x +--R (2) [----------,------------------------] +--R +-------+ +-------+ +--R \|b x + a a\|b x + a +--R Type: Tuple(Expression(Integer)) +--E 1885 + +--S 1886 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (m - 1)log(x) +--R x %e +--R (3) ----------------- +--R +-------+ +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 1886 + +--S 1887 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (m - 1)log(x) m +--R x %e - x +--R (4) ---------------------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1887 + +--S 1888 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (m - 1)log(x) m m - 1 +--R ((2b m - b)x + 2a m)%e + b x + (- 2b m x - 2a m)x +--R (5) -------------------------------------------------------------------- +--R +-------+ +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1888 + +)clear all + +--S 1889 of 3330 +t0000:=x^(1/2*(1-n)+1/2*(-3+n))/sqrt(a+b*x) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R x\|b x + a +--R Type: Expression(Integer) +--E 1889 + +--S 1890 of 3330 +r0000:=-2*atanh(sqrt(a+b*x)/sqrt(a))/sqrt(a) +--R +--R +--R +-------+ +--R \|b x + a +--R 2atanh(----------) +--R +-+ +--R \|a +--R (2) - ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1890 + +--S 1891 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-+ +---+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|- a \|b x + a +--R log(-------------------------------) 2atan(----------------) +--R x a +--R (3) [------------------------------------,- -----------------------] +--R +-+ +---+ +--R \|a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1891 + +--S 1892 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-------+ +-+ +-------+ +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R log(-------------------------------) + 2atanh(----------) +--R x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1892 + +--S 1893 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1893 + +--S 1894 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-------+ +---+ +-------+ +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R 2\|- a atanh(----------) - 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1894 + +--S 1895 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1895 + +)clear all + +--S 1896 of 3330 +t0000:=x^3*(a+b*x)^(1/3) +--R +--R +--R 3 3+-------+ +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1896 + +--S 1897 of 3330 +r0000:=-3/4*a^3*(a+b*x)^(4/3)/b^4+9/7*a^2*(a+b*x)^(7/3)/b^4-_ + 9/10*a*(a+b*x)^(10/3)/b^4+3/13*(a+b*x)^(13/3)/b^4 +--R +--R +--R 4 4 3 3 2 2 2 3 4 3+-------+ +--R (420b x + 42a b x - 54a b x + 81a b x - 243a )\|b x + a +--R (2) ----------------------------------------------------------- +--R 4 +--R 1820b +--R Type: Expression(Integer) +--E 1897 + +--S 1898 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 3+-------+ +--R (420b x + 42a b x - 54a b x + 81a b x - 243a )\|b x + a +--R (3) ----------------------------------------------------------- +--R 4 +--R 1820b +--R Type: Union(Expression(Integer),...) +--E 1898 + +--S 1899 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1899 + +--S 1900 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1900 + +)clear all + +--S 1901 of 3330 +t0000:=x^2*(a+b*x)^(1/3) +--R +--R +--R 2 3+-------+ +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1901 + +--S 1902 of 3330 +r0000:=3/4*a^2*(a+b*x)^(4/3)/b^3-6/7*a*(a+b*x)^(7/3)/b^3+_ + 3/10*(a+b*x)^(10/3)/b^3 +--R +--R +--R 3 3 2 2 2 3 3+-------+ +--R (42b x + 6a b x - 9a b x + 27a )\|b x + a +--R (2) -------------------------------------------- +--R 3 +--R 140b +--R Type: Expression(Integer) +--E 1902 + +--S 1903 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-------+ +--R (42b x + 6a b x - 9a b x + 27a )\|b x + a +--R (3) -------------------------------------------- +--R 3 +--R 140b +--R Type: Union(Expression(Integer),...) +--E 1903 + +--S 1904 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1904 + +--S 1905 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1905 + +)clear all + +--S 1906 of 3330 +t0000:=x*(a+b*x)^(1/3) +--R +--R +--R 3+-------+ +--R (1) x\|b x + a +--R Type: Expression(Integer) +--E 1906 + +--S 1907 of 3330 +r0000:=-3/4*a*(a+b*x)^(4/3)/b^2+3/7*(a+b*x)^(7/3)/b^2 +--R +--R +--R 2 2 2 3+-------+ +--R (12b x + 3a b x - 9a )\|b x + a +--R (2) --------------------------------- +--R 2 +--R 28b +--R Type: Expression(Integer) +--E 1907 + +--S 1908 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-------+ +--R (12b x + 3a b x - 9a )\|b x + a +--R (3) --------------------------------- +--R 2 +--R 28b +--R Type: Union(Expression(Integer),...) +--E 1908 + +--S 1909 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1909 + +--S 1910 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1910 + +)clear all + +--S 1911 of 3330 +t0000:=(a+b*x)^(1/3) +--R +--R +--R 3+-------+ +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 1911 + +--S 1912 of 3330 +r0000:=3/4*(a+b*x)^(4/3)/b +--R +--R +--R 3+-------+ +--R (3b x + 3a)\|b x + a +--R (2) --------------------- +--R 4b +--R Type: Expression(Integer) +--E 1912 + +--S 1913 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+ +--R (3b x + 3a)\|b x + a +--R (3) --------------------- +--R 4b +--R Type: Union(Expression(Integer),...) +--E 1913 + +--S 1914 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1914 + +--S 1915 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1915 + +)clear all + +--S 1916 of 3330 +t0000:=(a+b*x)^(1/3)/x +--R +--R +--R 3+-------+ +--R \|b x + a +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 1916 + +--S 1917 of 3330 +r0000:=3*(a+b*x)^(1/3)+a^(1/3)*log(a^(1/3)-(a+b*x)^(1/3))-_ + 1/2*a^(1/3)*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))-_ + a^(1/3)*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3) +--R +--R +--R (2) +--R 3+-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 3+-+ 3+-------+ 3+-+ +-+3+-+ 2\|b x + a + \|a +--R 2\|a log(- \|b x + a + \|a ) - 2\|3 \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3+-------+ +--R 6\|b x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 1917 + +--S 1918 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3+-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 3+-+ 3+-------+ 3+-+ +-+3+-+ 2\|b x + a + \|a +--R 2\|a log(\|b x + a - \|a ) - 2\|3 \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3+-------+ +--R 6\|b x + a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1918 + +--S 1919 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 3+-+ 3+-------+ 3+-+ 3+-+ 3+-------+ 3+-+ +--R (4) \|a log(\|b x + a - \|a ) - \|a log(- \|b x + a + \|a ) +--R Type: Expression(Integer) +--E 1919 + +--S 1920 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1920 + +)clear all + +--S 1921 of 3330 +t0000:=(a+b*x)^(1/3)/x^2 +--R +--R +--R 3+-------+ +--R \|b x + a +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1921 + +--S 1922 of 3330 +r0000:=-(a+b*x)^(1/3)/x+1/3*b*log(a^(1/3)-(a+b*x)^(1/3))/a^(2/3)-_ + 1/6*b*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(2/3)-_ + b*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b x\|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 3+-------+ 3+-+ 2\|b x + a + \|a +--R 2b x\|3 log(- \|b x + a + \|a ) - 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-------+ +--R - 6\|3 \|a \|b x + a +--R / +--R +-+3+-+2 +--R 6x\|3 \|a +--R Type: Expression(Integer) +--E 1922 + +--S 1923 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +--+2 +--+ +--R +-+ 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b x\|3 log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R +-+ 3| 2 3+-------+ +--R 2b x\|3 log(\|a \|b x + a - a) +--R + +--R +--+ +--R +-+3| 2 3+-------+ +-+ +--+ +--R 2\|3 \|a \|b x + a + a\|3 +-+3| 2 3+-------+ +--R - 6b x atan(----------------------------) - 6\|3 \|a \|b x + a +--R 3a +--R / +--R +--+ +--R +-+3| 2 +--R 6x\|3 \|a +--R Type: Union(Expression(Integer),...) +--E 1923 + +--S 1924 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +--+2 +--+ +--R +-+3+-+2 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b\|3 \|a log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R +-+3| 2 3+-------+2 3+-+3+-------+ 3+-+2 +--R b\|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--+ +--R +-+3+-+2 3| 2 3+-------+ +-+3| 2 3+-------+ 3+-+ +--R 2b\|3 \|a log(\|a \|b x + a - a) - 2b\|3 \|a log(- \|b x + a + \|a ) +--R + +--R +--+ +--R +-+3| 2 3+-------+ +-+ +--R 3+-+2 2\|3 \|a \|b x + a + a\|3 +--R - 6b \|a atan(----------------------------) +--R 3a +--R + +--R +--+ 3+-------+ 3+-+ +--R 3| 2 2\|b x + a + \|a +--R 6b\|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +--+ +--R +-+3+-+2 3| 2 +--R 6\|3 \|a \|a +--R Type: Expression(Integer) +--E 1924 + +--S 1925 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1925 + +)clear all + +--S 1926 of 3330 +t0000:=(a+b*x)^(1/3)/x^3 +--R +--R +--R 3+-------+ +--R \|b x + a +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1926 + +--S 1927 of 3330 +r0000:=-1/2*(a+b*x)^(1/3)/x^2-1/6*b*(a+b*x)^(1/3)/(a*x)-_ + 1/9*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(5/3)+_ + 1/18*b^2*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+_ + (a+b*x)^(2/3))/a^(5/3)+1/3*b^2*_ + atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 +-+ 3+-------+ 3+-+ 2 2 2\|b x + a + \|a +--R - 2b x \|3 log(- \|b x + a + \|a ) + 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-------+ +--R (- 3b x - 9a)\|3 \|a \|b x + a +--R / +--R 2 +-+3+-+2 +--R 18a x \|3 \|a +--R Type: Expression(Integer) +--E 1927 + +--S 1928 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +----+2 +----+ +--R 2 2 +-+ 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b x \|3 log(\|- a \|b x + a - a\|- a \|b x + a + a ) +--R + +--R +----+ +--R 2 2 +-+ 3| 2 3+-------+ +--R 2b x \|3 log(\|- a \|b x + a + a) +--R + +--R +----+ +--R +-+3| 2 3+-------+ +-+ +--R 2 2 2\|3 \|- a \|b x + a - a\|3 +--R 6b x atan(------------------------------) +--R 3a +--R + +--R +----+ +--R +-+3| 2 3+-------+ +--R (- 3b x - 9a)\|3 \|- a \|b x + a +--R / +--R +----+ +--R 2 +-+3| 2 +--R 18a x \|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 1928 + +--S 1929 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +----+2 +----+ +--R 2 +-+3+-+2 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b \|3 \|a log(\|- a \|b x + a - a\|- a \|b x + a + a ) +--R + +--R +----+ +--R 2 +-+3| 2 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b \|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +----+ +--R 2 +-+3+-+2 3| 2 3+-------+ +--R 2b \|3 \|a log(\|- a \|b x + a + a) +--R + +--R +----+ +--R 2 +-+3| 2 3+-------+ 3+-+ +--R 2b \|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +----+ +--R +-+3| 2 3+-------+ +-+ +--R 2 3+-+2 2\|3 \|- a \|b x + a - a\|3 +--R 6b \|a atan(------------------------------) +--R 3a +--R + +--R +----+ 3+-------+ 3+-+ +--R 2 3| 2 2\|b x + a + \|a +--R - 6b \|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +----+ +--R +-+3| 2 3+-+2 +--R 18a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 1929 + +--S 1930 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1930 + +)clear all + +--S 1931 of 3330 +t0000:=x^3*(a+b*x)^(2/3) +--R +--R +--R 3 3+-------+2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1931 + +--S 1932 of 3330 +r0000:=-3/5*a^3*(a+b*x)^(5/3)/b^4+9/8*a^2*(a+b*x)^(8/3)/b^4-_ + 9/11*a*(a+b*x)^(11/3)/b^4+3/14*(a+b*x)^(14/3)/b^4 +--R +--R +--R 4 4 3 3 2 2 2 3 4 3+-------+2 +--R (660b x + 120a b x - 135a b x + 162a b x - 243a )\|b x + a +--R (2) --------------------------------------------------------------- +--R 4 +--R 3080b +--R Type: Expression(Integer) +--E 1932 + +--S 1933 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 3+-------+2 +--R (660b x + 120a b x - 135a b x + 162a b x - 243a )\|b x + a +--R (3) --------------------------------------------------------------- +--R 4 +--R 3080b +--R Type: Union(Expression(Integer),...) +--E 1933 + +--S 1934 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1934 + +--S 1935 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1935 + +)clear all + +--S 1936 of 3330 +t0000:=x^2*(a+b*x)^(2/3) +--R +--R +--R 2 3+-------+2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1936 + +--S 1937 of 3330 +r0000:=3/5*a^2*(a+b*x)^(5/3)/b^3-3/4*a*(a+b*x)^(8/3)/b^3+_ + 3/11*(a+b*x)^(11/3)/b^3 +--R +--R +--R 3 3 2 2 2 3 3+-------+2 +--R (60b x + 15a b x - 18a b x + 27a )\|b x + a +--R (2) ----------------------------------------------- +--R 3 +--R 220b +--R Type: Expression(Integer) +--E 1937 + +--S 1938 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-------+2 +--R (60b x + 15a b x - 18a b x + 27a )\|b x + a +--R (3) ----------------------------------------------- +--R 3 +--R 220b +--R Type: Union(Expression(Integer),...) +--E 1938 + +--S 1939 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1939 + +--S 1940 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1940 + +)clear all + +--S 1941 of 3330 +t0000:=x*(a+b*x)^(2/3) +--R +--R +--R 3+-------+2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 1941 + +--S 1942 of 3330 +r0000:=-3/5*a*(a+b*x)^(5/3)/b^2+3/8*(a+b*x)^(8/3)/b^2 +--R +--R +--R 2 2 2 3+-------+2 +--R (15b x + 6a b x - 9a )\|b x + a +--R (2) ---------------------------------- +--R 2 +--R 40b +--R Type: Expression(Integer) +--E 1942 + +--S 1943 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-------+2 +--R (15b x + 6a b x - 9a )\|b x + a +--R (3) ---------------------------------- +--R 2 +--R 40b +--R Type: Union(Expression(Integer),...) +--E 1943 + +--S 1944 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1944 + +--S 1945 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1945 + +)clear all + +--S 1946 of 3330 +t0000:=(a+b*x)^(2/3) +--R +--R +--R 3+-------+2 +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 1946 + +--S 1947 of 3330 +r0000:=3/5*(a+b*x)^(5/3)/b +--R +--R +--R 3+-------+2 +--R (3b x + 3a)\|b x + a +--R (2) ---------------------- +--R 5b +--R Type: Expression(Integer) +--E 1947 + +--S 1948 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+2 +--R (3b x + 3a)\|b x + a +--R (3) ---------------------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 1948 + +--S 1949 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1949 + +--S 1950 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1950 + +)clear all + +--S 1951 of 3330 +t0000:=(a+b*x)^(2/3)/x +--R +--R +--R 3+-------+2 +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 1951 + +--S 1952 of 3330 +r0000:=3/2*(a+b*x)^(2/3)+a^(2/3)*log(a^(1/3)-(a+b*x)^(1/3))-_ + 1/2*a^(2/3)*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))+_ + a^(2/3)*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3) +--R +--R +--R (2) +--R 3+-+2 3+-------+2 3+-+3+-------+ 3+-+2 +--R - \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 3+-+2 3+-------+ 3+-+ +-+3+-+2 2\|b x + a + \|a +--R 2\|a log(- \|b x + a + \|a ) + 2\|3 \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3+-------+2 +--R 3\|b x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 1952 + +--S 1953 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +--+ +--+2 +--+ +--R 3| 2 3+-------+2 3| 2 3+-------+ 3| 2 +--R - \|a log(a \|b x + a + \|a \|b x + a + a\|a ) +--R + +--R +--+2 +--R +--+ +--+2 +--+ 3+-------+ 3| 2 +--R 3| 2 3+-------+ 3| 2 +-+3| 2 2a\|b x + a + \|a +--R 2\|a log(a\|b x + a - \|a ) + 2\|3 \|a atan(---------------------) +--R +--+2 +--R +-+3| 2 +--R \|3 \|a +--R + +--R 3+-------+2 +--R 3\|b x + a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1953 + +--S 1954 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +--+ +--+2 +--+ +--R 3| 2 3+-------+2 3| 2 3+-------+ 3| 2 +--R - \|a log(a \|b x + a + \|a \|b x + a + a\|a ) +--R + +--R 3+-+2 3+-------+2 3+-+3+-------+ 3+-+2 +--R \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--+2 +--R 3| 2 3+-------+ 3| 2 3+-+2 3+-------+ 3+-+ +--R 2\|a log(a\|b x + a - \|a ) - 2\|a log(- \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+3+-+2 2\|b x + a + \|a +--R - 2\|3 \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--+2 +--R +--+ 3+-------+ 3| 2 +--R +-+3| 2 2a\|b x + a + \|a +--R 2\|3 \|a atan(---------------------) +--R +--+2 +--R +-+3| 2 +--R \|3 \|a +--R / +--R 2 +--R Type: Expression(Integer) +--E 1954 + +--S 1955 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1955 + +)clear all + +--S 1956 of 3330 +t0000:=(a+b*x)^(2/3)/x^2 +--R +--R +--R 3+-------+2 +--R \|b x + a +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1956 + +--S 1957 of 3330 +r0000:=-(a+b*x)^(2/3)/x+2/3*b*log(a^(1/3)-(a+b*x)^(1/3))/a^(1/3)-_ + 1/3*b*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(1/3)+_ + 2*b*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b x\|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 3+-------+ 3+-+ 2\|b x + a + \|a +--R 2b x\|3 log(- \|b x + a + \|a ) + 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-------+2 +--R - 3\|3 \|a \|b x + a +--R / +--R +-+3+-+ +--R 3x\|3 \|a +--R Type: Expression(Integer) +--E 1957 + +--S 1958 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - b x\|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R +-+ 3+-+2 3+-------+ +--R 2b x\|3 log(\|a \|b x + a - a) +--R + +--R +-+3+-+2 3+-------+ +-+ +--R 2\|3 \|a \|b x + a + a\|3 +-+3+-+3+-------+2 +--R 6b x atan(----------------------------) - 3\|3 \|a \|b x + a +--R 3a +--R / +--R +-+3+-+ +--R 3x\|3 \|a +--R Type: Union(Expression(Integer),...) +--E 1958 + +--S 1959 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - b\|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b\|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +-+ 3+-+2 3+-------+ +-+ 3+-------+ 3+-+ +--R 2b\|3 log(\|a \|b x + a - a) - 2b\|3 log(- \|b x + a + \|a ) +--R + +--R +-+3+-+2 3+-------+ +-+ 3+-------+ 3+-+ +--R 2\|3 \|a \|b x + a + a\|3 2\|b x + a + \|a +--R 6b atan(----------------------------) - 6b atan(------------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 3\|3 \|a +--R Type: Expression(Integer) +--E 1959 + +--S 1960 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1960 + +)clear all + +--S 1961 of 3330 +t0000:=(a+b*x)^(2/3)/x^3 +--R +--R +--R 3+-------+2 +--R \|b x + a +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1961 + +--S 1962 of 3330 +r0000:=-1/2*(a+b*x)^(2/3)/x^2-1/3*b*(a+b*x)^(2/3)/(a*x)-_ + 1/9*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(4/3)+1/18*b^2*log(a^(2/3)+_ + a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(4/3)-_ + 1/3*b^2*atan((a^(1/3)+2*(a+b*x)^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 +-+ 3+-------+ 3+-+ 2 2 2\|b x + a + \|a +--R - 2b x \|3 log(- \|b x + a + \|a ) - 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-------+2 +--R (- 6b x - 9a)\|3 \|a \|b x + a +--R / +--R 2 +-+3+-+ +--R 18a x \|3 \|a +--R Type: Expression(Integer) +--E 1962 + +--S 1963 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b x \|3 log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R 2 2 +-+ 3+---+2 3+-------+ +--R 2b x \|3 log(\|- a \|b x + a - a) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 2 2 2\|3 \|- a \|b x + a + a\|3 +--R 6b x atan(------------------------------) +--R 3a +--R + +--R +-+3+---+3+-------+2 +--R (- 6b x - 9a)\|3 \|- a \|b x + a +--R / +--R 2 +-+3+---+ +--R 18a x \|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 1963 + +--S 1964 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 +-+3+-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b \|3 \|a log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R 2 +-+3+---+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b \|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 2 +-+3+-+ 3+---+2 3+-------+ +--R 2b \|3 \|a log(\|- a \|b x + a - a) +--R + +--R 2 +-+3+---+ 3+-------+ 3+-+ +--R 2b \|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 2 3+-+ 2\|3 \|- a \|b x + a + a\|3 +--R 6b \|a atan(------------------------------) +--R 3a +--R + +--R 3+-------+ 3+-+ +--R 2 3+---+ 2\|b x + a + \|a +--R 6b \|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+---+3+-+ +--R 18a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 1964 + +--S 1965 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1965 + +)clear all + +--S 1966 of 3330 +t0000:=x^3*(a+b*x)^(4/3) +--R +--R +--R 4 3 3+-------+ +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1966 + +--S 1967 of 3330 +r0000:=-3/7*a^3*(a+b*x)^(7/3)/b^4+9/10*a^2*(a+b*x)^(10/3)/b^4-_ + 9/13*a*(a+b*x)^(13/3)/b^4+3/16*(a+b*x)^(16/3)/b^4 +--R +--R +--R (2) +--R 5 5 4 4 2 3 3 3 2 2 4 5 3+-------+ +--R (1365b x + 1785a b x + 42a b x - 54a b x + 81a b x - 243a )\|b x + a +--R ------------------------------------------------------------------------- +--R 4 +--R 7280b +--R Type: Expression(Integer) +--E 1967 + +--S 1968 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 4 5 3+-------+ +--R (1365b x + 1785a b x + 42a b x - 54a b x + 81a b x - 243a )\|b x + a +--R ------------------------------------------------------------------------- +--R 4 +--R 7280b +--R Type: Union(Expression(Integer),...) +--E 1968 + +--S 1969 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1969 + +--S 1970 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1970 + +)clear all + +--S 1971 of 3330 +t0000:=x^2*(a+b*x)^(4/3) +--R +--R +--R 3 2 3+-------+ +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1971 + +--S 1972 of 3330 +r0000:=3/7*a^2*(a+b*x)^(7/3)/b^3-3/5*a*(a+b*x)^(10/3)/b^3+_ + 3/13*(a+b*x)^(13/3)/b^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 3+-------+ +--R (105b x + 147a b x + 6a b x - 9a b x + 27a )\|b x + a +--R (2) --------------------------------------------------------- +--R 3 +--R 455b +--R Type: Expression(Integer) +--E 1972 + +--S 1973 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 3+-------+ +--R (105b x + 147a b x + 6a b x - 9a b x + 27a )\|b x + a +--R (3) --------------------------------------------------------- +--R 3 +--R 455b +--R Type: Union(Expression(Integer),...) +--E 1973 + +--S 1974 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1974 + +--S 1975 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1975 + +)clear all + +--S 1976 of 3330 +t0000:=x*(a+b*x)^(4/3) +--R +--R +--R 2 3+-------+ +--R (1) (b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1976 + +--S 1977 of 3330 +r0000:=-3/7*a*(a+b*x)^(7/3)/b^2+3/10*(a+b*x)^(10/3)/b^2 +--R +--R +--R 3 3 2 2 2 3 3+-------+ +--R (21b x + 33a b x + 3a b x - 9a )\|b x + a +--R (2) -------------------------------------------- +--R 2 +--R 70b +--R Type: Expression(Integer) +--E 1977 + +--S 1978 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-------+ +--R (21b x + 33a b x + 3a b x - 9a )\|b x + a +--R (3) -------------------------------------------- +--R 2 +--R 70b +--R Type: Union(Expression(Integer),...) +--E 1978 + +--S 1979 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1979 + +--S 1980 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1980 + +)clear all + +--S 1981 of 3330 +t0000:=(a+b*x)^(4/3) +--R +--R +--R 3+-------+ +--R (1) (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1981 + +--S 1982 of 3330 +r0000:=3/7*(a+b*x)^(7/3)/b +--R +--R +--R 2 2 2 3+-------+ +--R (3b x + 6a b x + 3a )\|b x + a +--R (2) -------------------------------- +--R 7b +--R Type: Expression(Integer) +--E 1982 + +--S 1983 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-------+ +--R (3b x + 6a b x + 3a )\|b x + a +--R (3) -------------------------------- +--R 7b +--R Type: Union(Expression(Integer),...) +--E 1983 + +--S 1984 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1984 + +--S 1985 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1985 + +)clear all + +--S 1986 of 3330 +t0000:=(a+b*x)^(4/3)/x +--R +--R +--R 3+-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R x +--R Type: Expression(Integer) +--E 1986 + +--S 1987 of 3330 +r0000:=3*a*(a+b*x)^(1/3)+3/4*(a+b*x)^(4/3)+a^(4/3)*log(a^(1/3)-_ + (a+b*x)^(1/3))-1/2*a^(4/3)*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+_ + (a+b*x)^(2/3))-a^(4/3)*atan((a^(1/3)+_ + 2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3) +--R +--R +--R (2) +--R 3+-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2a\|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 3+-+ 3+-------+ 3+-+ +-+3+-+ 2\|b x + a + \|a +--R 4a\|a log(- \|b x + a + \|a ) - 4a\|3 \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3+-------+ +--R (3b x + 15a)\|b x + a +--R / +--R 4 +--R Type: Expression(Integer) +--E 1987 + +--S 1988 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3+-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2a\|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 3+-+ 3+-------+ 3+-+ +-+3+-+ 2\|b x + a + \|a +--R 4a\|a log(\|b x + a - \|a ) - 4a\|3 \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3+-------+ +--R (3b x + 15a)\|b x + a +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 1988 + +--S 1989 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R 3+-+ 3+-------+ 3+-+ 3+-+ 3+-------+ 3+-+ +--R (4) a\|a log(\|b x + a - \|a ) - a\|a log(- \|b x + a + \|a ) +--R Type: Expression(Integer) +--E 1989 + +--S 1990 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1990 + +)clear all + +--S 1991 of 3330 +t0000:=(a+b*x)^(4/3)/x^2 +--R +--R +--R 3+-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1991 + +--S 1992 of 3330 +r0000:=4*b*(a+b*x)^(1/3)-(a+b*x)^(4/3)/x+4/3*a^(1/3)*b*log(a^(1/3)-_ + (a+b*x)^(1/3))-2/3*a^(1/3)*b*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+_ + (a+b*x)^(2/3))-4*a^(1/3)*b*atan((a^(1/3)+_ + 2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/sqrt(3) +--R +--R +--R (2) +--R +-+3+-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2b x\|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+3+-+ 3+-------+ 3+-+ 3+-+ 2\|b x + a + \|a +--R 4b x\|3 \|a log(- \|b x + a + \|a ) - 12b x\|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-------+ +--R (9b x - 3a)\|3 \|b x + a +--R / +--R +-+ +--R 3x\|3 +--R Type: Expression(Integer) +--E 1992 + +--S 1993 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+3+-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2b x\|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +-+3+-+ 3+-------+ 3+-+ +--R 4b x\|3 \|a log(\|b x + a - \|a ) +--R + +--R +-+3+-------+ +-+3+-+ +--R 3+-+ 2\|3 \|b x + a + \|3 \|a +-+3+-------+ +--R - 12b x\|a atan(--------------------------) + (9b x - 3a)\|3 \|b x + a +--R 3+-+ +--R 3\|a +--R / +--R +-+ +--R 3x\|3 +--R Type: Union(Expression(Integer),...) +--E 1993 + +--S 1994 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+ 3+-------+ 3+-+ +-+3+-+ 3+-------+ 3+-+ +--R 4b\|3 \|a log(\|b x + a - \|a ) - 4b\|3 \|a log(- \|b x + a + \|a ) +--R + +--R +-+3+-------+ +-+3+-+ 3+-------+ 3+-+ +--R 3+-+ 2\|3 \|b x + a + \|3 \|a 3+-+ 2\|b x + a + \|a +--R - 12b\|a atan(--------------------------) + 12b\|a atan(------------------) +--R 3+-+ +-+3+-+ +--R 3\|a \|3 \|a +--R / +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 1994 + +--S 1995 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1995 + +)clear all + +--S 1996 of 3330 +t0000:=(a+b*x)^(4/3)/x^3 +--R +--R +--R 3+-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1996 + +--S 1997 of 3330 +r0000:=-2/3*b*(a+b*x)^(1/3)/x-1/2*(a+b*x)^(4/3)/x^2+2/9*b^2*log(a^(1/3)-_ + (a+b*x)^(1/3))/a^(2/3)-1/9*b^2*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+_ + (a+b*x)^(2/3))/a^(2/3)-2/3*b^2*atan((a^(1/3)+_ + 2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 +-+ 3+-------+ 3+-+ 2 2 2\|b x + a + \|a +--R 4b x \|3 log(- \|b x + a + \|a ) - 12b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-------+ +--R (- 21b x - 9a)\|3 \|a \|b x + a +--R / +--R 2 +-+3+-+2 +--R 18x \|3 \|a +--R Type: Expression(Integer) +--E 1997 + +--S 1998 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +--+2 +--+ +--R 2 2 +-+ 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - 2b x \|3 log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R 2 2 +-+ 3| 2 3+-------+ +--R 4b x \|3 log(\|a \|b x + a - a) +--R + +--R +--+ +--R +-+3| 2 3+-------+ +-+ +--R 2 2 2\|3 \|a \|b x + a + a\|3 +--R - 12b x atan(----------------------------) +--R 3a +--R + +--R +--+ +--R +-+3| 2 3+-------+ +--R (- 21b x - 9a)\|3 \|a \|b x + a +--R / +--R +--+ +--R 2 +-+3| 2 +--R 18x \|3 \|a +--R Type: Union(Expression(Integer),...) +--E 1998 + +--S 1999 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +--+2 +--+ +--R 2 +-+3+-+2 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b \|3 \|a log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R 2 +-+3| 2 3+-------+2 3+-+3+-------+ 3+-+2 +--R b \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--R 2 +-+3+-+2 3| 2 3+-------+ +--R 2b \|3 \|a log(\|a \|b x + a - a) +--R + +--R +--+ +--R 2 +-+3| 2 3+-------+ 3+-+ +--R - 2b \|3 \|a log(- \|b x + a + \|a ) +--R + +--R +--+ +--R +-+3| 2 3+-------+ +-+ +--R 2 3+-+2 2\|3 \|a \|b x + a + a\|3 +--R - 6b \|a atan(----------------------------) +--R 3a +--R + +--R +--+ 3+-------+ 3+-+ +--R 2 3| 2 2\|b x + a + \|a +--R 6b \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +--+ +--R +-+3+-+2 3| 2 +--R 9\|3 \|a \|a +--R Type: Expression(Integer) +--E 1999 + +--S 2000 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2000 + +)clear all + +--S 2001 of 3330 +t0000:=x^3/(a+b*x)^(1/3) +--R +--R +--R 3 +--R x +--R (1) ---------- +--R 3+-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 2001 + +--S 2002 of 3330 +r0000:=-3/2*a^3*(a+b*x)^(2/3)/b^4+9/5*a^2*(a+b*x)^(5/3)/b^4-_ + 9/8*a*(a+b*x)^(8/3)/b^4+3/11*(a+b*x)^(11/3)/b^4 +--R +--R +--R 3 3 2 2 2 3 3+-------+2 +--R (120b x - 135a b x + 162a b x - 243a )\|b x + a +--R (2) --------------------------------------------------- +--R 4 +--R 440b +--R Type: Expression(Integer) +--E 2002 + +--S 2003 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-------+2 +--R (120b x - 135a b x + 162a b x - 243a )\|b x + a +--R (3) --------------------------------------------------- +--R 4 +--R 440b +--R Type: Union(Expression(Integer),...) +--E 2003 + +--S 2004 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2004 + +--S 2005 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2005 + +)clear all + +--S 2006 of 3330 +t0000:=x^2/(a+b*x)^(1/3) +--R +--R +--R 2 +--R x +--R (1) ---------- +--R 3+-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 2006 + +--S 2007 of 3330 +r0000:=3/2*a^2*(a+b*x)^(2/3)/b^3-6/5*a*(a+b*x)^(5/3)/b^3+3/8*(a+b*x)^(8/3)/b^3 +--R +--R +--R 2 2 2 3+-------+2 +--R (15b x - 18a b x + 27a )\|b x + a +--R (2) ------------------------------------ +--R 3 +--R 40b +--R Type: Expression(Integer) +--E 2007 + +--S 2008 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-------+2 +--R (15b x - 18a b x + 27a )\|b x + a +--R (3) ------------------------------------ +--R 3 +--R 40b +--R Type: Union(Expression(Integer),...) +--E 2008 + +--S 2009 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2009 + +--S 2010 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2010 + +)clear all + +--S 2011 of 3330 +t0000:=x/(a+b*x)^(1/3) +--R +--R +--R x +--R (1) ---------- +--R 3+-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 2011 + +--S 2012 of 3330 +r0000:=-3/2*a*(a+b*x)^(2/3)/b^2+3/5*(a+b*x)^(5/3)/b^2 +--R +--R +--R 3+-------+2 +--R (6b x - 9a)\|b x + a +--R (2) ---------------------- +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 2012 + +--S 2013 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+2 +--R (6b x - 9a)\|b x + a +--R (3) ---------------------- +--R 2 +--R 10b +--R Type: Union(Expression(Integer),...) +--E 2013 + +--S 2014 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2014 + +--S 2015 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2015 + +)clear all + +--S 2016 of 3330 +t0000:=1/(a+b*x)^(1/3) +--R +--R +--R 1 +--R (1) ---------- +--R 3+-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 2016 + +--S 2017 of 3330 +r0000:=3/2*(a+b*x)^(2/3)/b +--R +--R +--R 3+-------+2 +--R 3\|b x + a +--R (2) ------------ +--R 2b +--R Type: Expression(Integer) +--E 2017 + +--S 2018 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+2 +--R 3\|b x + a +--R (3) ------------ +--R 2b +--R Type: Union(Expression(Integer),...) +--E 2018 + +--S 2019 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2019 + +--S 2020 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2020 + +)clear all + +--S 2021 of 3330 +t0000:=1/(x*(a+b*x)^(1/3)) +--R +--R +--R 1 +--R (1) ----------- +--R 3+-------+ +--R x\|b x + a +--R Type: Expression(Integer) +--E 2021 + +--S 2022 of 3330 +r0000:=log(a^(1/3)-(a+b*x)^(1/3))/a^(1/3)-1/2*log(a^(2/3)+_ + a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(1/3)+_ + atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(1/3) +--R +--R +--R (2) +--R 3+-------+2 3+-+3+-------+ 3+-+2 3+-------+ 3+-+ +--R - log(\|b x + a + \|a \|b x + a + \|a ) + 2log(- \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 2\|b x + a + \|a +--R 2\|3 atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+ +--R 2\|a +--R Type: Expression(Integer) +--E 2022 + +--S 2023 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3+-+3+-------+2 3+-+2 3+-------+ 3+-+2 3+-------+ +--R - log(\|a \|b x + a + \|a \|b x + a + a) + 2log(\|a \|b x + a - a) +--R + +--R 3+-+2 3+-------+ +--R +-+ 2\|a \|b x + a + a +--R 2\|3 atan(--------------------) +--R +-+ +--R a\|3 +--R / +--R 3+-+ +--R 2\|a +--R Type: Union(Expression(Integer),...) +--E 2023 + +--S 2024 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3+-+3+-------+2 3+-+2 3+-------+ +--R - log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 3+-------+2 3+-+3+-------+ 3+-+2 3+-+2 3+-------+ +--R log(\|b x + a + \|a \|b x + a + \|a ) + 2log(\|a \|b x + a - a) +--R + +--R 3+-+2 3+-------+ +--R 3+-------+ 3+-+ +-+ 2\|a \|b x + a + a +--R - 2log(- \|b x + a + \|a ) + 2\|3 atan(--------------------) +--R +-+ +--R a\|3 +--R + +--R 3+-------+ 3+-+ +--R +-+ 2\|b x + a + \|a +--R - 2\|3 atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+ +--R 2\|a +--R Type: Expression(Integer) +--E 2024 + +--S 2025 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2025 + +)clear all + +--S 2026 of 3330 +t0000:=1/(x^2*(a+b*x)^(1/3)) +--R +--R +--R 1 +--R (1) ------------ +--R 2 3+-------+ +--R x \|b x + a +--R Type: Expression(Integer) +--E 2026 + +--S 2027 of 3330 +r0000:=-(a+b*x)^(2/3)/(a*x)-1/3*b*log(a^(1/3)-(a+b*x)^(1/3))/a^(4/3)+_ + 1/6*b*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(4/3)-_ + b*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b x\|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 3+-------+ 3+-+ 2\|b x + a + \|a +--R - 2b x\|3 log(- \|b x + a + \|a ) - 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-------+2 +--R - 6\|3 \|a \|b x + a +--R / +--R +-+3+-+ +--R 6a x\|3 \|a +--R Type: Expression(Integer) +--E 2027 + +--S 2028 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b x\|3 log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R +-+ 3+---+2 3+-------+ +--R 2b x\|3 log(\|- a \|b x + a - a) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 2\|3 \|- a \|b x + a + a\|3 +-+3+---+3+-------+2 +--R 6b x atan(------------------------------) - 6\|3 \|- a \|b x + a +--R 3a +--R / +--R +-+3+---+ +--R 6a x\|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 2028 + +--S 2029 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b\|3 \|a log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R +-+3+---+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b\|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +-+3+-+ 3+---+2 3+-------+ +--R 2b\|3 \|a log(\|- a \|b x + a - a) +--R + +--R +-+3+---+ 3+-------+ 3+-+ +--R 2b\|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 3+-+ 2\|3 \|- a \|b x + a + a\|3 +--R 6b\|a atan(------------------------------) +--R 3a +--R + +--R 3+-------+ 3+-+ +--R 3+---+ 2\|b x + a + \|a +--R 6b\|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+---+3+-+ +--R 6a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 2029 + +--S 2030 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2030 + +)clear all + +--S 2031 of 3330 +t0000:=1/(x^3*(a+b*x)^(1/3)) +--R +--R +--R 1 +--R (1) ------------ +--R 3 3+-------+ +--R x \|b x + a +--R Type: Expression(Integer) +--E 2031 + +--S 2032 of 3330 +r0000:=-1/2*(a+b*x)^(2/3)/(a*x^2)+2/3*b*(a+b*x)^(2/3)/(a^2*x)+_ + 2/9*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(7/3)-1/9*b^2*log(a^(2/3)+_ + a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(7/3)+_ + 2/3*b^2*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/_ + (a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 +-+ 3+-------+ 3+-+ 2 2 2\|b x + a + \|a +--R 4b x \|3 log(- \|b x + a + \|a ) + 12b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-------+2 +--R (12b x - 9a)\|3 \|a \|b x + a +--R / +--R 2 2 +-+3+-+ +--R 18a x \|3 \|a +--R Type: Expression(Integer) +--E 2032 + +--S 2033 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +-+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - 2b x \|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 2 2 +-+ 3+-+2 3+-------+ +--R 4b x \|3 log(\|a \|b x + a - a) +--R + +--R +-+3+-+2 3+-------+ +-+ +--R 2 2 2\|3 \|a \|b x + a + a\|3 +-+3+-+3+-------+2 +--R 12b x atan(----------------------------) + (12b x - 9a)\|3 \|a \|b x + a +--R 3a +--R / +--R 2 2 +-+3+-+ +--R 18a x \|3 \|a +--R Type: Union(Expression(Integer),...) +--E 2033 + +--S 2034 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 +-+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - b \|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 2 +-+ 3+-+2 3+-------+ 2 +-+ 3+-------+ 3+-+ +--R 2b \|3 log(\|a \|b x + a - a) - 2b \|3 log(- \|b x + a + \|a ) +--R + +--R +-+3+-+2 3+-------+ +-+ 3+-------+ 3+-+ +--R 2 2\|3 \|a \|b x + a + a\|3 2 2\|b x + a + \|a +--R 6b atan(----------------------------) - 6b atan(------------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+-+ +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 2034 + +--S 2035 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2035 + +)clear all + +--S 2036 of 3330 +t0000:=x^3/(-a+b*x)^(1/3) +--R +--R +--R 3 +--R x +--R (1) ---------- +--R 3+-------+ +--R \|b x - a +--R Type: Expression(Integer) +--E 2036 + +--S 2037 of 3330 +r0000:=3/2*a^3*(-a+b*x)^(2/3)/b^4+9/5*a^2*(-a+b*x)^(5/3)/b^4+_ + 9/8*a*(-a+b*x)^(8/3)/b^4+3/11*(-a+b*x)^(11/3)/b^4 +--R +--R +--R 3 3 2 2 2 3 3+-------+2 +--R (120b x + 135a b x + 162a b x + 243a )\|b x - a +--R (2) --------------------------------------------------- +--R 4 +--R 440b +--R Type: Expression(Integer) +--E 2037 + +--S 2038 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-------+2 +--R (120b x + 135a b x + 162a b x + 243a )\|b x - a +--R (3) --------------------------------------------------- +--R 4 +--R 440b +--R Type: Union(Expression(Integer),...) +--E 2038 + +--S 2039 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2039 + +--S 2040 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2040 + +)clear all + +--S 2041 of 3330 +t0000:=x^2/(-a+b*x)^(1/3) +--R +--R +--R 2 +--R x +--R (1) ---------- +--R 3+-------+ +--R \|b x - a +--R Type: Expression(Integer) +--E 2041 + +--S 2042 of 3330 +r0000:=3/2*a^2*(-a+b*x)^(2/3)/b^3+6/5*a*(-a+b*x)^(5/3)/b^3+_ + 3/8*(-a+b*x)^(8/3)/b^3 +--R +--R +--R 2 2 2 3+-------+2 +--R (15b x + 18a b x + 27a )\|b x - a +--R (2) ------------------------------------ +--R 3 +--R 40b +--R Type: Expression(Integer) +--E 2042 + +--S 2043 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-------+2 +--R (15b x + 18a b x + 27a )\|b x - a +--R (3) ------------------------------------ +--R 3 +--R 40b +--R Type: Union(Expression(Integer),...) +--E 2043 + +--S 2044 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2044 + +--S 2045 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2045 + +)clear all + +--S 2046 of 3330 +t0000:=x/(-a+b*x)^(1/3) +--R +--R +--R x +--R (1) ---------- +--R 3+-------+ +--R \|b x - a +--R Type: Expression(Integer) +--E 2046 + +--S 2047 of 3330 +r0000:=3/2*a*(-a+b*x)^(2/3)/b^2+3/5*(-a+b*x)^(5/3)/b^2 +--R +--R +--R 3+-------+2 +--R (6b x + 9a)\|b x - a +--R (2) ---------------------- +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 2047 + +--S 2048 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+2 +--R (6b x + 9a)\|b x - a +--R (3) ---------------------- +--R 2 +--R 10b +--R Type: Union(Expression(Integer),...) +--E 2048 + +--S 2049 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2049 + +--S 2050 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2050 + +)clear all + +--S 2051 of 3330 +t0000:=1/(-a+b*x)^(1/3) +--R +--R +--R 1 +--R (1) ---------- +--R 3+-------+ +--R \|b x - a +--R Type: Expression(Integer) +--E 2051 + +--S 2052 of 3330 +r0000:=3/2*(-a+b*x)^(2/3)/b +--R +--R +--R 3+-------+2 +--R 3\|b x - a +--R (2) ------------ +--R 2b +--R Type: Expression(Integer) +--E 2052 + +--S 2053 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+2 +--R 3\|b x - a +--R (3) ------------ +--R 2b +--R Type: Union(Expression(Integer),...) +--E 2053 + +--S 2054 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2054 + +--S 2055 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2055 + +)clear all + +--S 2056 of 3330 +t0000:=1/(x*(-a+b*x)^(1/3)) +--R +--R +--R 1 +--R (1) ----------- +--R 3+-------+ +--R x\|b x - a +--R Type: Expression(Integer) +--E 2056 + +--S 2057 of 3330 +r0000:=-log(a^(1/3)+(-a+b*x)^(1/3))/a^(1/3)+1/2*log(a^(2/3)-_ + a^(1/3)*(-a+b*x)^(1/3)+(-a+b*x)^(2/3))/a^(1/3)-_ + atan((a^(1/3)-2*(-a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(1/3) +--R +--R +--R (2) +--R 3+-------+2 3+-+3+-------+ 3+-+2 3+-------+ 3+-+ +--R log(\|b x - a - \|a \|b x - a + \|a ) - 2log(\|b x - a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 2\|b x - a - \|a +--R 2\|3 atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+ +--R 2\|a +--R Type: Expression(Integer) +--E 2057 + +--S 2058 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3+---+3+-------+2 3+---+2 3+-------+ +--R - log(\|- a \|b x - a + \|- a \|b x - a - a) +--R + +--R 3+---+2 3+-------+ +--R 3+---+2 3+-------+ +-+ 2\|- a \|b x - a - a +--R 2log(\|- a \|b x - a + a) - 2\|3 atan(----------------------) +--R +-+ +--R a\|3 +--R / +--R 3+---+ +--R 2\|- a +--R Type: Union(Expression(Integer),...) +--E 2058 + +--S 2059 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3+-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - \|a log(\|- a \|b x - a + \|- a \|b x - a - a) +--R + +--R 3+---+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - \|- a log(\|b x - a - \|a \|b x - a + \|a ) +--R + +--R 3+-+ 3+---+2 3+-------+ 3+---+ 3+-------+ 3+-+ +--R 2\|a log(\|- a \|b x - a + a) + 2\|- a log(\|b x - a + \|a ) +--R + +--R 3+---+2 3+-------+ +--R +-+3+-+ 2\|- a \|b x - a - a +--R - 2\|3 \|a atan(----------------------) +--R +-+ +--R a\|3 +--R + +--R 3+-------+ 3+-+ +--R +-+3+---+ 2\|b x - a - \|a +--R - 2\|3 \|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+---+3+-+ +--R 2\|- a \|a +--R Type: Expression(Integer) +--E 2059 + +--S 2060 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2060 + +)clear all + +--S 2061 of 3330 +t0000:=1/(x^2*(-a+b*x)^(1/3)) +--R +--R +--R 1 +--R (1) ------------ +--R 2 3+-------+ +--R x \|b x - a +--R Type: Expression(Integer) +--E 2061 + +--S 2062 of 3330 +r0000:=(-a+b*x)^(2/3)/(a*x)-1/3*b*log(a^(1/3)+(-a+b*x)^(1/3))/a^(4/3)+_ + 1/6*b*log(a^(2/3)-a^(1/3)*(-a+b*x)^(1/3)+(-a+b*x)^(2/3))/a^(4/3)-_ + b*atan((a^(1/3)-2*(-a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b x\|3 log(\|b x - a - \|a \|b x - a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 3+-------+ 3+-+ 2\|b x - a - \|a +--R - 2b x\|3 log(\|b x - a + \|a ) + 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-------+2 +--R 6\|3 \|a \|b x - a +--R / +--R +-+3+-+ +--R 6a x\|3 \|a +--R Type: Expression(Integer) +--E 2062 + +--S 2063 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b x\|3 log(\|- a \|b x - a + \|- a \|b x - a - a) +--R + +--R +-+ 3+---+2 3+-------+ +--R 2b x\|3 log(\|- a \|b x - a + a) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 2\|3 \|- a \|b x - a - a\|3 +-+3+---+3+-------+2 +--R - 6b x atan(------------------------------) + 6\|3 \|- a \|b x - a +--R 3a +--R / +--R +-+3+---+ +--R 6a x\|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 2063 + +--S 2064 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b\|3 \|a log(\|- a \|b x - a + \|- a \|b x - a - a) +--R + +--R +-+3+---+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b\|3 \|- a log(\|b x - a - \|a \|b x - a + \|a ) +--R + +--R +-+3+-+ 3+---+2 3+-------+ +-+3+---+ 3+-------+ 3+-+ +--R 2b\|3 \|a log(\|- a \|b x - a + a) + 2b\|3 \|- a log(\|b x - a + \|a ) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 3+-+ 2\|3 \|- a \|b x - a - a\|3 +--R - 6b\|a atan(------------------------------) +--R 3a +--R + +--R 3+-------+ 3+-+ +--R 3+---+ 2\|b x - a - \|a +--R - 6b\|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+---+3+-+ +--R 6a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 2064 + +--S 2065 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2065 + +)clear all + +--S 2066 of 3330 +t0000:=1/(x^3*(-a+b*x)^(1/3)) +--R +--R +--R 1 +--R (1) ------------ +--R 3 3+-------+ +--R x \|b x - a +--R Type: Expression(Integer) +--E 2066 + +--S 2067 of 3330 +r0000:=1/2*(-a+b*x)^(2/3)/(a*x^2)+2/3*b*(-a+b*x)^(2/3)/(a^2*x)-_ + 2/9*b^2*log(a^(1/3)+(-a+b*x)^(1/3))/a^(7/3)+1/9*b^2*log(a^(2/3)-_ + a^(1/3)*(-a+b*x)^(1/3)+(-a+b*x)^(2/3))/a^(7/3)-_ + 2/3*b^2*atan((a^(1/3)-2*(-a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/_ + (a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R 2b x \|3 log(\|b x - a - \|a \|b x - a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 +-+ 3+-------+ 3+-+ 2 2 2\|b x - a - \|a +--R - 4b x \|3 log(\|b x - a + \|a ) + 12b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-------+2 +--R (12b x + 9a)\|3 \|a \|b x - a +--R / +--R 2 2 +-+3+-+ +--R 18a x \|3 \|a +--R Type: Expression(Integer) +--E 2067 + +--S 2068 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - 2b x \|3 log(\|- a \|b x - a + \|- a \|b x - a - a) +--R + +--R 2 2 +-+ 3+---+2 3+-------+ +--R 4b x \|3 log(\|- a \|b x - a + a) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 2 2 2\|3 \|- a \|b x - a - a\|3 +--R - 12b x atan(------------------------------) +--R 3a +--R + +--R +-+3+---+3+-------+2 +--R (12b x + 9a)\|3 \|- a \|b x - a +--R / +--R 2 2 +-+3+---+ +--R 18a x \|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 2068 + +--S 2069 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 +-+3+-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - b \|3 \|a log(\|- a \|b x - a + \|- a \|b x - a - a) +--R + +--R 2 +-+3+---+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b \|3 \|- a log(\|b x - a - \|a \|b x - a + \|a ) +--R + +--R 2 +-+3+-+ 3+---+2 3+-------+ +--R 2b \|3 \|a log(\|- a \|b x - a + a) +--R + +--R 2 +-+3+---+ 3+-------+ 3+-+ +--R 2b \|3 \|- a log(\|b x - a + \|a ) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 2 3+-+ 2\|3 \|- a \|b x - a - a\|3 +--R - 6b \|a atan(------------------------------) +--R 3a +--R + +--R 3+-------+ 3+-+ +--R 2 3+---+ 2\|b x - a - \|a +--R - 6b \|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+---+3+-+ +--R 9a \|3 \|- a \|a +--R Type: Expression(Integer) +--E 2069 + +--S 2070 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2070 + +)clear all + +--S 2071 of 3330 +t0000:=x^3/(a+b*x)^(2/3) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R 3+-------+2 +--R \|b x + a +--R Type: Expression(Integer) +--E 2071 + +--S 2072 of 3330 +r0000:=-3*a^3*(a+b*x)^(1/3)/b^4+9/4*a^2*(a+b*x)^(4/3)/b^4-_ + 9/7*a*(a+b*x)^(7/3)/b^4+3/10*(a+b*x)^(10/3)/b^4 +--R +--R +--R 3 3 2 2 2 3 3+-------+ +--R (42b x - 54a b x + 81a b x - 243a )\|b x + a +--R (2) ----------------------------------------------- +--R 4 +--R 140b +--R Type: Expression(Integer) +--E 2072 + +--S 2073 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-------+ +--R (42b x - 54a b x + 81a b x - 243a )\|b x + a +--R (3) ----------------------------------------------- +--R 4 +--R 140b +--R Type: Union(Expression(Integer),...) +--E 2073 + +--S 2074 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2074 + +--S 2075 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2075 + +)clear all + +--S 2076 of 3330 +t0000:=x^2/(a+b*x)^(2/3) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R 3+-------+2 +--R \|b x + a +--R Type: Expression(Integer) +--E 2076 + +--S 2077 of 3330 +r0000:=3*a^2*(a+b*x)^(1/3)/b^3-3/2*a*(a+b*x)^(4/3)/b^3+3/7*(a+b*x)^(7/3)/b^3 +--R +--R +--R 2 2 2 3+-------+ +--R (6b x - 9a b x + 27a )\|b x + a +--R (2) --------------------------------- +--R 3 +--R 14b +--R Type: Expression(Integer) +--E 2077 + +--S 2078 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-------+ +--R (6b x - 9a b x + 27a )\|b x + a +--R (3) --------------------------------- +--R 3 +--R 14b +--R Type: Union(Expression(Integer),...) +--E 2078 + +--S 2079 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2079 + +--S 2080 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2080 + +)clear all + +--S 2081 of 3330 +t0000:=x/(a+b*x)^(2/3) +--R +--R +--R x +--R (1) ----------- +--R 3+-------+2 +--R \|b x + a +--R Type: Expression(Integer) +--E 2081 + +--S 2082 of 3330 +r0000:=-3*a*(a+b*x)^(1/3)/b^2+3/4*(a+b*x)^(4/3)/b^2 +--R +--R +--R 3+-------+ +--R (3b x - 9a)\|b x + a +--R (2) --------------------- +--R 2 +--R 4b +--R Type: Expression(Integer) +--E 2082 + +--S 2083 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+ +--R (3b x - 9a)\|b x + a +--R (3) --------------------- +--R 2 +--R 4b +--R Type: Union(Expression(Integer),...) +--E 2083 + +--S 2084 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2084 + +--S 2085 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2085 + +)clear all + +--S 2086 of 3330 +t0000:=1/(a+b*x)^(2/3) +--R +--R +--R 1 +--R (1) ----------- +--R 3+-------+2 +--R \|b x + a +--R Type: Expression(Integer) +--E 2086 + +--S 2087 of 3330 +r0000:=3*(a+b*x)^(1/3)/b +--R +--R +--R 3+-------+ +--R 3\|b x + a +--R (2) ----------- +--R b +--R Type: Expression(Integer) +--E 2087 + +--S 2088 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-------+ +--R 3\|b x + a +--R (3) ----------- +--R b +--R Type: Union(Expression(Integer),...) +--E 2088 + +--S 2089 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2089 + +--S 2090 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2090 + +)clear all + +--S 2091 of 3330 +t0000:=1/(x*(a+b*x)^(2/3)) +--R +--R +--R 1 +--R (1) ------------- +--R 3+-------+2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 2091 + +--S 2092 of 3330 +r0000:=log(a^(1/3)-(a+b*x)^(1/3))/a^(2/3)-1/2*log(a^(2/3)+_ + a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(2/3)-_ + atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(2/3) +--R +--R +--R (2) +--R 3+-------+2 3+-+3+-------+ 3+-+2 3+-------+ 3+-+ +--R - log(\|b x + a + \|a \|b x + a + \|a ) + 2log(- \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 2\|b x + a + \|a +--R - 2\|3 atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+2 +--R 2\|a +--R Type: Expression(Integer) +--E 2092 + +--S 2093 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +--+2 +--+ +--R 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R +--+ 3| 2 3+-------+ +--R 3| 2 3+-------+ +-+ 2\|a \|b x + a + a +--R 2log(\|a \|b x + a - a) - 2\|3 atan(--------------------) +--R +-+ +--R a\|3 +--R / +--R +--+ +--R 3| 2 +--R 2\|a +--R Type: Union(Expression(Integer),...) +--E 2093 + +--S 2094 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +--+2 +--+ +--R 3+-+2 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - \|a log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R 3| 2 3+-------+2 3+-+3+-------+ 3+-+2 +--R \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--+ +--R 3+-+2 3| 2 3+-------+ 3| 2 3+-------+ 3+-+ +--R 2\|a log(\|a \|b x + a - a) - 2\|a log(- \|b x + a + \|a ) +--R + +--R +--+ +--R 3| 2 3+-------+ +--+ 3+-------+ 3+-+ +--R +-+3+-+2 2\|a \|b x + a + a +-+3| 2 2\|b x + a + \|a +--R - 2\|3 \|a atan(--------------------) + 2\|3 \|a atan(------------------) +--R +-+ +-+3+-+ +--R a\|3 \|3 \|a +--R / +--R +--+ +--R 3+-+2 3| 2 +--R 2\|a \|a +--R Type: Expression(Integer) +--E 2094 + +--S 2095 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2095 + +)clear all + +--S 2096 of 3330 +t0000:=1/(x^2*(a+b*x)^(2/3)) +--R +--R +--R 1 +--R (1) ------------- +--R 2 3+-------+2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 2096 + +--S 2097 of 3330 +r0000:=-(a+b*x)^(1/3)/(a*x)-2/3*b*log(a^(1/3)-(a+b*x)^(1/3))/a^(5/3)+_ + 1/3*b*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(5/3)+_ + 2*b*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R b x\|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+ 3+-------+ 3+-+ 2\|b x + a + \|a +--R - 2b x\|3 log(- \|b x + a + \|a ) + 6b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-------+ +--R - 3\|3 \|a \|b x + a +--R / +--R +-+3+-+2 +--R 3a x\|3 \|a +--R Type: Expression(Integer) +--E 2097 + +--S 2098 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +----+2 +----+ +--R +-+ 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b x\|3 log(\|- a \|b x + a - a\|- a \|b x + a + a ) +--R + +--R +----+ +--R +-+ 3| 2 3+-------+ +--R 2b x\|3 log(\|- a \|b x + a + a) +--R + +--R +----+ +--R +-+3| 2 3+-------+ +-+ +----+ +--R 2\|3 \|- a \|b x + a - a\|3 +-+3| 2 3+-------+ +--R 6b x atan(------------------------------) - 3\|3 \|- a \|b x + a +--R 3a +--R / +--R +----+ +--R +-+3| 2 +--R 3a x\|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 2098 + +--S 2099 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +----+2 +----+ +--R +-+3+-+2 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - b\|3 \|a log(\|- a \|b x + a - a\|- a \|b x + a + a ) +--R + +--R +----+ +--R +-+3| 2 3+-------+2 3+-+3+-------+ 3+-+2 +--R - b\|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +----+ +--R +-+3+-+2 3| 2 3+-------+ +--R 2b\|3 \|a log(\|- a \|b x + a + a) +--R + +--R +----+ +--R +-+3| 2 3+-------+ 3+-+ +--R 2b\|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +----+ +--R +-+3| 2 3+-------+ +-+ +--R 3+-+2 2\|3 \|- a \|b x + a - a\|3 +--R 6b \|a atan(------------------------------) +--R 3a +--R + +--R +----+ 3+-------+ 3+-+ +--R 3| 2 2\|b x + a + \|a +--R - 6b\|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +----+ +--R +-+3| 2 3+-+2 +--R 3a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 2099 + +--S 2100 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2100 + +)clear all + +--S 2101 of 3330 +t0000:=1/(x^3*(a+b*x)^(2/3)) +--R +--R +--R 1 +--R (1) ------------- +--R 3 3+-------+2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 2101 + +--S 2102 of 3330 +r0000:=-1/2*(a+b*x)^(1/3)/(a*x^2)+5/6*b*(a+b*x)^(1/3)/(a^2*x)+_ + 5/9*b^2*log(a^(1/3)-(a+b*x)^(1/3))/a^(8/3)-_ + 5/18*b^2*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(8/3)-_ + 5/3*b^2*atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/_ + (a^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 5b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 +-+ 3+-------+ 3+-+ 2 2 2\|b x + a + \|a +--R 10b x \|3 log(- \|b x + a + \|a ) - 30b x atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-------+ +--R (15b x - 9a)\|3 \|a \|b x + a +--R / +--R 2 2 +-+3+-+2 +--R 18a x \|3 \|a +--R Type: Expression(Integer) +--E 2102 + +--S 2103 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +--+2 +--+ +--R 2 2 +-+ 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - 5b x \|3 log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R 2 2 +-+ 3| 2 3+-------+ +--R 10b x \|3 log(\|a \|b x + a - a) +--R + +--R +--+ +--R +-+3| 2 3+-------+ +-+ +--R 2 2 2\|3 \|a \|b x + a + a\|3 +--R - 30b x atan(----------------------------) +--R 3a +--R + +--R +--+ +--R +-+3| 2 3+-------+ +--R (15b x - 9a)\|3 \|a \|b x + a +--R / +--R +--+ +--R 2 2 +-+3| 2 +--R 18a x \|3 \|a +--R Type: Union(Expression(Integer),...) +--E 2103 + +--S 2104 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +--+2 +--+ +--R 2 +-+3+-+2 3| 2 3+-------+2 3| 2 3+-------+ 2 +--R - 5b \|3 \|a log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--R 2 +-+3| 2 3+-------+2 3+-+3+-------+ 3+-+2 +--R 5b \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--R 2 +-+3+-+2 3| 2 3+-------+ +--R 10b \|3 \|a log(\|a \|b x + a - a) +--R + +--R +--+ +--R 2 +-+3| 2 3+-------+ 3+-+ +--R - 10b \|3 \|a log(- \|b x + a + \|a ) +--R + +--R +--+ +--R +-+3| 2 3+-------+ +-+ +--R 2 3+-+2 2\|3 \|a \|b x + a + a\|3 +--R - 30b \|a atan(----------------------------) +--R 3a +--R + +--R +--+ 3+-------+ 3+-+ +--R 2 3| 2 2\|b x + a + \|a +--R 30b \|a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +--+ +--R 2 +-+3+-+2 3| 2 +--R 18a \|3 \|a \|a +--R Type: Expression(Integer) +--E 2104 + +--S 2105 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2105 + +)clear all + +--S 2106 of 3330 +t0000:=x^3/(a+b*x)^(4/3) +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 3+-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 2106 + +--S 2107 of 3330 +r0000:=3*a^3/(b^4*(a+b*x)^(1/3))+9/2*a^2*(a+b*x)^(2/3)/b^4-_ + 9/5*a*(a+b*x)^(5/3)/b^4+3/8*(a+b*x)^(8/3)/b^4 +--R +--R +--R 3 3 2 2 2 3 +--R 15b x - 27a b x + 81a b x + 243a +--R (2) ----------------------------------- +--R 4 3+-------+ +--R 40b \|b x + a +--R Type: Expression(Integer) +--E 2107 + +--S 2108 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 15b x - 27a b x + 81a b x + 243a +--R (3) ----------------------------------- +--R 4 3+-------+ +--R 40b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 2108 + +--S 2109 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2109 + +--S 2110 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2110 + +)clear all + +--S 2111 of 3330 +t0000:=x^2/(a+b*x)^(4/3) +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 3+-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 2111 + +--S 2112 of 3330 +r0000:=-3*a^2/(b^3*(a+b*x)^(1/3))-3*a*(a+b*x)^(2/3)/b^3+3/5*(a+b*x)^(5/3)/b^3 +--R +--R +--R 2 2 2 +--R 3b x - 9a b x - 27a +--R (2) --------------------- +--R 3 3+-------+ +--R 5b \|b x + a +--R Type: Expression(Integer) +--E 2112 + +--S 2113 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 3b x - 9a b x - 27a +--R (3) --------------------- +--R 3 3+-------+ +--R 5b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 2113 + +--S 2114 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2114 + +--S 2115 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2115 + +)clear all + +--S 2116 of 3330 +t0000:=x/(a+b*x)^(4/3) +--R +--R +--R x +--R (1) ------------------- +--R 3+-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 2116 + +--S 2117 of 3330 +r0000:=3*a/(b^2*(a+b*x)^(1/3))+3/2*(a+b*x)^(2/3)/b^2 +--R +--R +--R 3b x + 9a +--R (2) ------------- +--R 2 3+-------+ +--R 2b \|b x + a +--R Type: Expression(Integer) +--E 2117 + +--S 2118 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3b x + 9a +--R (3) ------------- +--R 2 3+-------+ +--R 2b \|b x + a +--R Type: Union(Expression(Integer),...) +--E 2118 + +--S 2119 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2119 + +--S 2120 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2120 + +)clear all + +--S 2121 of 3330 +t0000:=1/(a+b*x)^(4/3) +--R +--R +--R 1 +--R (1) ------------------- +--R 3+-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 2121 + +--S 2122 of 3330 +r0000:=(-3)/(b*(a+b*x)^(1/3)) +--R +--R +--R 3 +--R (2) - ----------- +--R 3+-------+ +--R b\|b x + a +--R Type: Expression(Integer) +--E 2122 + +--S 2123 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 +--R (3) - ----------- +--R 3+-------+ +--R b\|b x + a +--R Type: Union(Expression(Integer),...) +--E 2123 + +--S 2124 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2124 + +--S 2125 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2125 + +)clear all + +--S 2126 of 3330 +t0000:=1/(x*(a+b*x)^(4/3)) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 3+-------+ +--R (b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 2126 + +--S 2127 of 3330 +r0000:=3/(a*(a+b*x)^(1/3))+log(a^(1/3)-(a+b*x)^(1/3))/a^(4/3)-_ + 1/2*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+(a+b*x)^(2/3))/a^(4/3)+_ + atan((a^(1/3)+2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(4/3) +--R +--R +--R (2) +--R 3+-------+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - \|b x + a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-------+ 3+-+ +--R 2\|b x + a log(- \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R +-+3+-------+ 2\|b x + a + \|a 3+-+ +--R 2\|3 \|b x + a atan(------------------) + 6\|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+3+-------+ +--R 2a\|a \|b x + a +--R Type: Expression(Integer) +--E 2127 + +--S 2128 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3+-------+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - \|b x + a log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 3+-------+ 3+-+2 3+-------+ +--R 2\|b x + a log(\|a \|b x + a - a) +--R + +--R 3+-+2 3+-------+ +--R +-+3+-------+ 2\|a \|b x + a + a 3+-+ +--R 2\|3 \|b x + a atan(--------------------) + 6\|a +--R +-+ +--R a\|3 +--R / +--R 3+-+3+-------+ +--R 2a\|a \|b x + a +--R Type: Union(Expression(Integer),...) +--E 2128 + +--S 2129 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3+-+3+-------+2 3+-+2 3+-------+ +--R - log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 3+-------+2 3+-+3+-------+ 3+-+2 3+-+2 3+-------+ +--R log(\|b x + a + \|a \|b x + a + \|a ) + 2log(\|a \|b x + a - a) +--R + +--R 3+-+2 3+-------+ +--R 3+-------+ 3+-+ +-+ 2\|a \|b x + a + a +--R - 2log(- \|b x + a + \|a ) + 2\|3 atan(--------------------) +--R +-+ +--R a\|3 +--R + +--R 3+-------+ 3+-+ +--R +-+ 2\|b x + a + \|a +--R - 2\|3 atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 2129 + +--S 2130 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2130 + +)clear all + +--S 2131 of 3330 +t0000:=1/(x^2*(a+b*x)^(4/3)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 3 2 3+-------+ +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 2131 + +--S 2132 of 3330 +r0000:=3/(a*x*(a+b*x)^(1/3))-4*(a+b*x)^(2/3)/(a^2*x)-4/3*b*log(a^(1/3)-_ + (a+b*x)^(1/3))/a^(7/3)+2/3*b*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+_ + (a+b*x)^(2/3))/a^(7/3)-4*b*atan((a^(1/3)+2*(a+b*x)^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-------+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R 2b x\|3 \|b x + a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +-+3+-------+ 3+-------+ 3+-+ +--R - 4b x\|3 \|b x + a log(- \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 3+-------+ 2\|b x + a + \|a +-+3+-+ +--R - 12b x\|b x + a atan(------------------) + (- 12b x - 3a)\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+-+3+-------+ +--R 3a x\|3 \|a \|b x + a +--R Type: Expression(Integer) +--E 2132 + +--S 2133 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+3+-------+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - 2b x\|3 \|b x + a log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R +-+3+-------+ 3+---+2 3+-------+ +--R 4b x\|3 \|b x + a log(\|- a \|b x + a - a) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 3+-------+ 2\|3 \|- a \|b x + a + a\|3 +--R 12b x\|b x + a atan(------------------------------) +--R 3a +--R + +--R +-+3+---+ +--R (- 12b x - 3a)\|3 \|- a +--R / +--R 2 +-+3+---+3+-------+ +--R 3a x\|3 \|- a \|b x + a +--R Type: Union(Expression(Integer),...) +--E 2133 + +--S 2134 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+ 3+---+3+-------+2 3+---+2 3+-------+ +--R - 2b\|3 \|a log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R +-+3+---+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 2b\|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +-+3+-+ 3+---+2 3+-------+ +--R 4b\|3 \|a log(\|- a \|b x + a - a) +--R + +--R +-+3+---+ 3+-------+ 3+-+ +--R 4b\|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +-+3+---+2 3+-------+ +-+ +--R 3+-+ 2\|3 \|- a \|b x + a + a\|3 +--R 12b\|a atan(------------------------------) +--R 3a +--R + +--R 3+-------+ 3+-+ +--R 3+---+ 2\|b x + a + \|a +--R 12b\|- a atan(------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+---+3+-+ +--R 3a \|3 \|- a \|a +--R Type: Expression(Integer) +--E 2134 + +--S 2135 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2135 + +)clear all + +--S 2136 of 3330 +t0000:=1/(x^3*(a+b*x)^(4/3)) +--R +--R +--R 1 +--R (1) ----------------------- +--R 4 3 3+-------+ +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 2136 + +--S 2137 of 3330 +r0000:=3/(a*x^2*(a+b*x)^(1/3))-7/2*(a+b*x)^(2/3)/(a^2*x^2)+_ + 14/3*b*(a+b*x)^(2/3)/(a^3*x)+14/9*b^2*log(a^(1/3)-_ + (a+b*x)^(1/3))/a^(10/3)-7/9*b^2*log(a^(2/3)+a^(1/3)*(a+b*x)^(1/3)+_ + (a+b*x)^(2/3))/a^(10/3)+14/3*b^2*atan((a^(1/3)+_ + 2*(a+b*x)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(10/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 +-+3+-------+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - 14b x \|3 \|b x + a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 2 2 +-+3+-------+ 3+-------+ 3+-+ +--R 28b x \|3 \|b x + a log(- \|b x + a + \|a ) +--R + +--R 3+-------+ 3+-+ +--R 2 2 3+-------+ 2\|b x + a + \|a 2 2 2 +-+3+-+ +--R 84b x \|b x + a atan(------------------ + (84b x + 21a b x - 9a )\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 2 +-+3+-+3+-------+ +--R 18a x \|3 \|a \|b x + a +--R Type: Expression(Integer) +--E 2137 + +--S 2138 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +-+3+-------+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - 14b x \|3 \|b x + a log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 2 2 +-+3+-------+ 3+-+2 3+-------+ +--R 28b x \|3 \|b x + a log(\|a \|b x + a - a) +--R + +--R +-+3+-+2 3+-------+ +-+ +--R 2 2 3+-------+ 2\|3 \|a \|b x + a + a\|3 +--R 84b x \|b x + a atan(----------------------------) +--R 3a +--R + +--R 2 2 2 +-+3+-+ +--R (84b x + 21a b x - 9a )\|3 \|a +--R / +--R 3 2 +-+3+-+3+-------+ +--R 18a x \|3 \|a \|b x + a +--R Type: Union(Expression(Integer),...) +--E 2138 + +--S 2139 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 +-+ 3+-+3+-------+2 3+-+2 3+-------+ +--R - 7b \|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R 2 +-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R 7b \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R 2 +-+ 3+-+2 3+-------+ 2 +-+ 3+-------+ 3+-+ +--R 14b \|3 log(\|a \|b x + a - a) - 14b \|3 log(- \|b x + a + \|a ) +--R + +--R +-+3+-+2 3+-------+ +-+ 3+-------+ 3+-+ +--R 2 2\|3 \|a \|b x + a + a\|3 2 2\|b x + a + \|a +--R 42b atan(----------------------------) - 42b atan(------------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R 3 +-+3+-+ +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 2139 + +--S 2140 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2140 + +)clear all + +--S 2141 of 3330 +t0000:=x^m*(a+b*x) +--R +--R +--R m +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 2141 + +--S 2142 of 3330 +r0000:=a*x^(1+m)/(1+m)+b*x^(2+m)/(2+m) +--R +--R +--R m + 2 m + 1 +--R (b m + b)x + (a m + 2a)x +--R (2) ---------------------------------- +--R 2 +--R m + 3m + 2 +--R Type: Expression(Integer) +--E 2142 + +--S 2143 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 m log(x) +--R ((b m + b)x + (a m + 2a)x)%e +--R (3) ------------------------------------- +--R 2 +--R m + 3m + 2 +--R Type: Union(Expression(Integer),...) +--E 2143 + +--S 2144 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 m log(x) m + 2 +--R ((b m + b)x + (a m + 2a)x)%e + (- b m - b)x +--R + +--R m + 1 +--R (- a m - 2a)x +--R / +--R 2 +--R m + 3m + 2 +--R Type: Expression(Integer) +--E 2144 + +--S 2145 of 3330 +d0000:=D(m0000,x) +--R +--R +--R m log(x) m + 1 m +--R (5) (b x + a)%e - b x - a x +--R Type: Expression(Integer) +--E 2145 + +)clear all + +--S 2146 of 3330 +t0000:=x^(5/2)*(a+b*x) +--R +--R +--R 3 2 +-+ +--R (1) (b x + a x )\|x +--R Type: Expression(Integer) +--E 2146 + +--S 2147 of 3330 +r0000:=2/7*a*x^(7/2)+2/9*b*x^(9/2) +--R +--R +--R 4 3 +-+ +--R (14b x + 18a x )\|x +--R (2) --------------------- +--R 63 +--R Type: Expression(Integer) +--E 2147 + +--S 2148 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 4 3 +-+ +--R (14b x + 18a x )\|x +--R (3) --------------------- +--R 63 +--R Type: Union(Expression(Integer),...) +--E 2148 + +--S 2149 of 3330 +m0000:=a0000.1 - r0000 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2149 + +--S 2150 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (4) 0 +--R Type: Polynomial(Integer) +--E 2150 + +--S 2151 of 3330 +m0000:=a0000.2 - r0000 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2151 + +--S 2152 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Integer) +--E 2152 + +)clear all + +--S 2153 of 3330 +t0000:=x^(3/2)*(a+b*x) +--R +--R +--R 2 +-+ +--R (1) (b x + a x)\|x +--R Type: Expression(Integer) +--E 2153 + +--S 2154 of 3330 +r0000:=2/5*a*x^(5/2)+2/7*b*x^(7/2) +--R +--R +--R 3 2 +-+ +--R (10b x + 14a x )\|x +--R (2) --------------------- +--R 35 +--R Type: Expression(Integer) +--E 2154 + +--S 2155 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 2 +-+ +--R (10b x + 14a x )\|x +--R (3) --------------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 2155 + +--S 2156 of 3330 +m0000:=a0000.1 - r0000 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2156 + +--S 2157 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (4) 0 +--R Type: Polynomial(Integer) +--E 2157 + +--S 2158 of 3330 +m0000:=a0000.2 - r0000 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2158 + +--S 2159 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Integer) +--E 2159 + +)clear all + +--S 2160 of 3330 +t0000:=(a+b*x)*sqrt(x) +--R +--R +--R +-+ +--R (1) (b x + a)\|x +--R Type: Expression(Integer) +--E 2160 + +--S 2161 of 3330 +r0000:=2/3*a*x^(3/2)+2/5*b*x^(5/2) +--R +--R +--R 2 +-+ +--R (6b x + 10a x)\|x +--R (2) ------------------- +--R 15 +--R Type: Expression(Integer) +--E 2161 + +--S 2162 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +-+ +--R (6b x + 10a x)\|x +--R (3) ------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 2162 + +--S 2163 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2163 + +--S 2164 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2164 + +)clear all + +--S 2165 of 3330 +t0000:=(a+b*x)/sqrt(x) +--R +--R +--R b x + a +--R (1) ------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2165 + +--S 2166 of 3330 +r0000:=2/3*b*x^(3/2)+2*a*sqrt(x) +--R +--R +--R +-+ +--R (2b x + 6a)\|x +--R (2) --------------- +--R 3 +--R Type: Expression(Integer) +--E 2166 + +--S 2167 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +--R (2b x + 6a)\|x +--R (3) --------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 2167 + +--S 2168 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2168 + +--S 2169 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2169 + +)clear all + +--S 2170 of 3330 +t0000:=(a+b*x)/x^(3/2) +--R +--R +--R b x + a +--R (1) ------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2170 + +--S 2171 of 3330 +r0000:=-2*a/sqrt(x)+2*b*sqrt(x) +--R +--R +--R 2b x - 2a +--R (2) --------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2171 + +--S 2172 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2b x - 2a +--R (3) --------- +--R +-+ +--R \|x +--R Type: Union(Expression(Integer),...) +--E 2172 + +--S 2173 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2173 + +--S 2174 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2174 + +)clear all + +--S 2175 of 3330 +t0000:=(a+b*x)/x^(5/2) +--R +--R +--R b x + a +--R (1) ------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2175 + +--S 2176 of 3330 +r0000:=-2/3*a/x^(3/2)-2*b/sqrt(x) +--R +--R +--R - 6b x - 2a +--R (2) ----------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2176 + +--S 2177 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R - 6b x - 2a +--R (3) ----------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 2177 + +--S 2178 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2178 + +--S 2179 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2179 + +)clear all + +--S 2180 of 3330 +t0000:=x^m*(a+b*x)^2 +--R +--R +--R 2 2 2 m +--R (1) (b x + 2a b x + a )x +--R Type: Expression(Integer) +--E 2180 + +--S 2181 of 3330 +r0000:=a^2*x^(1+m)/(1+m)+2*a*b*x^(2+m)/(2+m)+b^2*x^(3+m)/(3+m) +--R +--R +--R (2) +--R 2 2 2 2 m + 3 2 m + 2 +--R (b m + 3b m + 2b )x + (2a b m + 8a b m + 6a b)x +--R + +--R 2 2 2 2 m + 1 +--R (a m + 5a m + 6a )x +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Expression(Integer) +--E 2181 + +--S 2182 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 3 2 2 +--R (b m + 3b m + 2b )x + (2a b m + 8a b m + 6a b)x +--R + +--R 2 2 2 2 +--R (a m + 5a m + 6a )x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Union(Expression(Integer),...) +--E 2182 + +--S 2183 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 2 2 2 3 2 2 +--R (b m + 3b m + 2b )x + (2a b m + 8a b m + 6a b)x +--R + +--R 2 2 2 2 +--R (a m + 5a m + 6a )x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 2 2 m + 3 2 m + 2 +--R (- b m - 3b m - 2b )x + (- 2a b m - 8a b m - 6a b)x +--R + +--R 2 2 2 2 m + 1 +--R (- a m - 5a m - 6a )x +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Expression(Integer) +--E 2183 + +--S 2184 of 3330 +d0000:=D(m0000,x) +--R +--R +--R 2 2 2 m log(x) 2 m + 2 m + 1 2 m +--R (5) (b x + 2a b x + a )%e - b x - 2a b x - a x +--R Type: Expression(Integer) +--E 2184 + +)clear all + +--S 2185 of 3330 +t0000:=x^(5/2)*(a+b*x)^2 +--R +--R +--R 2 4 3 2 2 +-+ +--R (1) (b x + 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 2185 + +--S 2186 of 3330 +r0000:=2/7*a^2*x^(7/2)+4/9*a*b*x^(9/2)+2/11*b^2*x^(11/2) +--R +--R +--R 2 5 4 2 3 +-+ +--R (126b x + 308a b x + 198a x )\|x +--R (2) ----------------------------------- +--R 693 +--R Type: Expression(Integer) +--E 2186 + +--S 2187 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 5 4 2 3 +-+ +--R (126b x + 308a b x + 198a x )\|x +--R (3) ----------------------------------- +--R 693 +--R Type: Union(Expression(Integer),...) +--E 2187 + +--S 2188 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2188 + +--S 2189 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2189 + +)clear all + +--S 2190 of 3330 +t0000:=x^(3/2)*(a+b*x)^2 +--R +--R +--R 2 3 2 2 +-+ +--R (1) (b x + 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 2190 + +--S 2191 of 3330 +r0000:=2/5*a^2*x^(5/2)+4/7*a*b*x^(7/2)+2/9*b^2*x^(9/2) +--R +--R +--R 2 4 3 2 2 +-+ +--R (70b x + 180a b x + 126a x )\|x +--R (2) ---------------------------------- +--R 315 +--R Type: Expression(Integer) +--E 2191 + +--S 2192 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 4 3 2 2 +-+ +--R (70b x + 180a b x + 126a x )\|x +--R (3) ---------------------------------- +--R 315 +--R Type: Union(Expression(Integer),...) +--E 2192 + +--S 2193 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2193 + +--S 2194 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2194 + +)clear all + +--S 2195 of 3330 +t0000:=(a+b*x)^2*sqrt(x) +--R +--R +--R 2 2 2 +-+ +--R (1) (b x + 2a b x + a )\|x +--R Type: Expression(Integer) +--E 2195 + +--S 2196 of 3330 +r0000:=2/3*a^2*x^(3/2)+4/5*a*b*x^(5/2)+2/7*b^2*x^(7/2) +--R +--R +--R 2 3 2 2 +-+ +--R (30b x + 84a b x + 70a x)\|x +--R (2) ------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 2196 + +--S 2197 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 2 2 +-+ +--R (30b x + 84a b x + 70a x)\|x +--R (3) ------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 2197 + +--S 2198 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2198 + +--S 2199 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2199 + +)clear all + +--S 2200 of 3330 +t0000:=(a+b*x)^2/sqrt(x) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2200 + +--S 2201 of 3330 +r0000:=4/3*a*b*x^(3/2)+2/5*b^2*x^(5/2)+2*a^2*sqrt(x) +--R +--R +--R 2 2 2 +-+ +--R (6b x + 20a b x + 30a )\|x +--R (2) ---------------------------- +--R 15 +--R Type: Expression(Integer) +--E 2201 + +--S 2202 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +-+ +--R (6b x + 20a b x + 30a )\|x +--R (3) ---------------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 2202 + +--S 2203 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2203 + +--S 2204 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2204 + +)clear all + +--S 2205 of 3330 +t0000:=(a+b*x)^2/x^(3/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2205 + +--S 2206 of 3330 +r0000:=2/3*b^2*x^(3/2)-2*a^2/sqrt(x)+4*a*b*sqrt(x) +--R +--R +--R 2 2 2 +--R 2b x + 12a b x - 6a +--R (2) --------------------- +--R +-+ +--R 3\|x +--R Type: Expression(Integer) +--E 2206 + +--S 2207 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 2b x + 12a b x - 6a +--R (3) --------------------- +--R +-+ +--R 3\|x +--R Type: Union(Expression(Integer),...) +--E 2207 + +--S 2208 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2208 + +--S 2209 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2209 + +)clear all + +--S 2210 of 3330 +t0000:=(a+b*x)^2/x^(5/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2210 + +--S 2211 of 3330 +r0000:=-2/3*a^2/x^(3/2)-4*a*b/sqrt(x)+2*b^2*sqrt(x) +--R +--R +--R 2 2 2 +--R 6b x - 12a b x - 2a +--R (2) --------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2211 + +--S 2212 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 6b x - 12a b x - 2a +--R (3) --------------------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 2212 + +--S 2213 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2213 + +--S 2214 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2214 + +)clear all + +--S 2215 of 3330 +t0000:=x^m*(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 m +--R (1) (b x + 3a b x + 3a b x + a )x +--R Type: Expression(Integer) +--E 2215 + +--S 2216 of 3330 +r0000:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(2+m)/(2+m)+3*a*b^2*x^(3+m)/(3+m)+_ + b^3*x^(4+m)/(4+m) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 4 +--R (b m + 6b m + 11b m + 6b )x +--R + +--R 2 3 2 2 2 2 m + 3 +--R (3a b m + 21a b m + 42a b m + 24a b )x +--R + +--R 2 3 2 2 2 2 m + 2 +--R (3a b m + 24a b m + 57a b m + 36a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (a m + 9a m + 26a m + 24a )x +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Expression(Integer) +--E 2216 + +--S 2217 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 4 +--R (b m + 6b m + 11b m + 6b )x +--R + +--R 2 3 2 2 2 2 3 +--R (3a b m + 21a b m + 42a b m + 24a b )x +--R + +--R 2 3 2 2 2 2 2 3 3 3 2 3 3 +--R (3a b m + 24a b m + 57a b m + 36a b)x + (a m + 9a m + 26a m + 24a )x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Union(Expression(Integer),...) +--E 2217 + +--S 2218 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 3 3 2 3 3 4 +--R (b m + 6b m + 11b m + 6b )x +--R + +--R 2 3 2 2 2 2 3 +--R (3a b m + 21a b m + 42a b m + 24a b )x +--R + +--R 2 3 2 2 2 2 2 +--R (3a b m + 24a b m + 57a b m + 36a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 9a m + 26a m + 24a )x +--R * +--R m log(x) +--R %e +--R + +--R 3 3 3 2 3 3 m + 4 +--R (- b m - 6b m - 11b m - 6b )x +--R + +--R 2 3 2 2 2 2 m + 3 +--R (- 3a b m - 21a b m - 42a b m - 24a b )x +--R + +--R 2 3 2 2 2 2 m + 2 +--R (- 3a b m - 24a b m - 57a b m - 36a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- a m - 9a m - 26a m - 24a )x +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Expression(Integer) +--E 2218 + +--S 2219 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 3 3 2 2 2 3 m log(x) 3 m + 3 2 m + 2 +--R (b x + 3a b x + 3a b x + a )%e - b x - 3a b x +--R + +--R 2 m + 1 3 m +--R - 3a b x - a x +--R Type: Expression(Integer) +--E 2219 + +)clear all + +--S 2220 of 3330 +t0000:=x^(5/2)*(a+b*x)^3 +--R +--R +--R 3 5 2 4 2 3 3 2 +-+ +--R (1) (b x + 3a b x + 3a b x + a x )\|x +--R Type: Expression(Integer) +--E 2220 + +--S 2221 of 3330 +r0000:=2/7*a^3*x^(7/2)+2/3*a^2*b*x^(9/2)+6/11*a*b^2*x^(11/2)+2/13*b^3*x^(13/2) +--R +--R +--R 3 6 2 5 2 4 3 3 +-+ +--R (462b x + 1638a b x + 2002a b x + 858a x )\|x +--R (2) ------------------------------------------------- +--R 3003 +--R Type: Expression(Integer) +--E 2221 + +--S 2222 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 6 2 5 2 4 3 3 +-+ +--R (462b x + 1638a b x + 2002a b x + 858a x )\|x +--R (3) ------------------------------------------------- +--R 3003 +--R Type: Union(Expression(Integer),...) +--E 2222 + +--S 2223 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2223 + +--S 2224 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2224 + +)clear all + +--S 2225 of 3330 +t0000:=x^(3/2)*(a+b*x)^3 +--R +--R +--R 3 4 2 3 2 2 3 +-+ +--R (1) (b x + 3a b x + 3a b x + a x)\|x +--R Type: Expression(Integer) +--E 2225 + +--S 2226 of 3330 +r0000:=2/5*a^3*x^(5/2)+6/7*a^2*b*x^(7/2)+2/3*a*b^2*x^(9/2)+2/11*b^3*x^(11/2) +--R +--R +--R 3 5 2 4 2 3 3 2 +-+ +--R (210b x + 770a b x + 990a b x + 462a x )\|x +--R (2) ----------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 2226 + +--S 2227 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 5 2 4 2 3 3 2 +-+ +--R (210b x + 770a b x + 990a b x + 462a x )\|x +--R (3) ----------------------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 2227 + +--S 2228 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2228 + +--S 2229 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2229 + +)clear all + +--S 2230 of 3330 +t0000:=(a+b*x)^3*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (1) (b x + 3a b x + 3a b x + a )\|x +--R Type: Expression(Integer) +--E 2230 + +--S 2231 of 3330 +r0000:=2/3*a^3*x^(3/2)+6/5*a^2*b*x^(5/2)+6/7*a*b^2*x^(7/2)+2/9*b^3*x^(9/2) +--R +--R +--R 3 4 2 3 2 2 3 +-+ +--R (70b x + 270a b x + 378a b x + 210a x)\|x +--R (2) --------------------------------------------- +--R 315 +--R Type: Expression(Integer) +--E 2231 + +--S 2232 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 4 2 3 2 2 3 +-+ +--R (70b x + 270a b x + 378a b x + 210a x)\|x +--R (3) --------------------------------------------- +--R 315 +--R Type: Union(Expression(Integer),...) +--E 2232 + +--S 2233 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2233 + +--S 2234 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2234 + +)clear all + +--S 2235 of 3330 +t0000:=(a+b*x)^3/sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2235 + +--S 2236 of 3330 +r0000:=2*a^2*b*x^(3/2)+6/5*a*b^2*x^(5/2)+2/7*b^3*x^(7/2)+2*a^3*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (10b x + 42a b x + 70a b x + 70a )\|x +--R (2) ---------------------------------------- +--R 35 +--R Type: Expression(Integer) +--E 2236 + +--S 2237 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (10b x + 42a b x + 70a b x + 70a )\|x +--R (3) ---------------------------------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 2237 + +--S 2238 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2238 + +--S 2239 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2239 + +)clear all + +--S 2240 of 3330 +t0000:=(a+b*x)^3/x^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2240 + +--S 2241 of 3330 +r0000:=2*a*b^2*x^(3/2)+2/5*b^3*x^(5/2)-2*a^3/sqrt(x)+6*a^2*b*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x + 10a b x + 30a b x - 10a +--R (2) --------------------------------- +--R +-+ +--R 5\|x +--R Type: Expression(Integer) +--E 2241 + +--S 2242 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x + 10a b x + 30a b x - 10a +--R (3) --------------------------------- +--R +-+ +--R 5\|x +--R Type: Union(Expression(Integer),...) +--E 2242 + +--S 2243 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2243 + +--S 2244 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2244 + +)clear all + +--S 2245 of 3330 +t0000:=(a+b*x)^3/x^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2245 + +--S 2246 of 3330 +r0000:=-2/3*a^3/x^(3/2)+2/3*b^3*x^(3/2)-6*a^2*b/sqrt(x)+6*a*b^2*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x + 18a b x - 18a b x - 2a +--R (2) -------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2246 + +--S 2247 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x + 18a b x - 18a b x - 2a +--R (3) -------------------------------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 2247 + +--S 2248 of 3330 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2248 + +--S 2249 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2249 + +)clear all + +--S 2250 of 3330 +t0000:=x^(5/2)/(a+b*x) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------- +--R b x + a +--R Type: Expression(Integer) +--E 2250 + +--S 2251 of 3330 +r0000:=-2/3*a*x^(3/2)/b^2+2/5*x^(5/2)/b-_ + 2*a^(5/2)*atan(sqrt(b)*sqrt(x)/sqrt(a))/b^(7/2)+2*a^2*sqrt(x)/b^3 +--R +--R +--R +-+ +-+ +--R 2 +-+ \|b \|x 2 2 2 +-+ +-+ +--R - 30a \|a atan(--------) + (6b x - 10a b x + 30a )\|b \|x +--R +-+ +--R \|a +--R (2) ----------------------------------------------------------- +--R 3 +-+ +--R 15b \|b +--R Type: Expression(Integer) +--E 2251 + +--S 2252 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + b x - a +--R 2 | a \| b 2 2 2 +-+ +--R 15a |- - log(------------------------) + (6b x - 10a b x + 30a )\|x +--R \| b b x + a +--R [----------------------------------------------------------------------, +--R 3 +--R 15b +--R +-+ +-+ +--R 2 |a \|x 2 2 2 +-+ +--R - 30a |- atan(----) + (6b x - 10a b x + 30a )\|x +--R \|b +-+ +--R |a +--R |- +--R \|b +--R ---------------------------------------------------] +--R 3 +--R 15b +--R Type: Union(List(Expression(Integer)),...) +--E 2252 + +--S 2253 of 3330 +m0000:=a0000 - r0000 +--R +--R There are 12 exposed and 3 unexposed library operations named - +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op - +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named - +--R with argument type(s) +--R List(Expression(Integer)) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2253 + +--S 2254 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (4) 0 +--R Type: Polynomial(Integer) +--E 2254 + +)clear all + +--S 2255 of 3330 +t0000:=x^(3/2)/(a+b*x) +--R +--R +--R +-+ +--R x\|x +--R (1) ------- +--R b x + a +--R Type: Expression(Integer) +--E 2255 + +--S 2256 of 3330 +r0000:=2/3*x^(3/2)/b+2*a^(3/2)*atan(sqrt(b)*sqrt(x)/sqrt(a))/b^(5/2)-_ + 2*a*sqrt(x)/b^2 +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R 6a\|a atan(--------) + (2b x - 6a)\|b \|x +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R 2 +-+ +--R 3b \|b +--R Type: Expression(Integer) +--E 2256 + +--S 2257 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + b x - a +--R | a \| b +-+ +--R 3a |- - log(----------------------) + (2b x - 6a)\|x +--R \| b b x + a +--R [-----------------------------------------------------, +--R 2 +--R 3b +--R +-+ +-+ +--R |a \|x +-+ +--R 6a |- atan(----) + (2b x - 6a)\|x +--R \|b +-+ +--R |a +--R |- +--R \|b +--R ----------------------------------] +--R 2 +--R 3b +--R Type: Union(List(Expression(Integer)),...) +--E 2257 + +--S 2258 of 3330 +m0000:=a0000 - r0000 +--R +--R There are 12 exposed and 3 unexposed library operations named - +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op - +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named - +--R with argument type(s) +--R List(Expression(Integer)) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2258 + +--S 2259 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (4) 0 +--R Type: Polynomial(Integer) +--E 2259 + +)clear all + +--S 2260 of 3330 +t0000:=sqrt(x)/(a+b*x) +--R +--R +--R +-+ +--R \|x +--R (1) ------- +--R b x + a +--R Type: Expression(Integer) +--E 2260 + +--S 2261 of 3330 +r0000:=-2*atan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(3/2)+2*sqrt(x)/b +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R - 2\|a atan(--------) + 2\|b \|x +--R +-+ +--R \|a +--R (2) --------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 2261 + +--S 2262 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-+ +--R +---+ |a \|x +-+ +--R | a +-+ - 2 |- atan(---- + 2\|x +--R +---+ - 2b |- - \|x + b x - a \|b +-+ +--R | a \| b +-+ |a +--R |- - log(------------------------) + 2\|x |- +--R \| b b x + a \|b +--R [-------------------------------------------,-------------------------] +--R b b +--R Type: Union(List(Expression(Integer)),...) +--E 2262 + +--S 2263 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + b x - a +-+ +-+ +--R | a +-+ \| b +-+ \|b \|x +--R |- - \|b log(------------------------) + 2\|a atan(--------) +--R \| b b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 2263 + +--S 2264 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2264 + +--S 2265 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x |a +-+ \|x +--R 2\|a atan(--------) - 2 |- \|b atan(----) +--R +-+ \|b +-+ +--R \|a |a +--R |- +--R \|b +--R (6) ----------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 2265 + +--S 2266 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2266 + +)clear all + +--S 2267 of 3330 +t0000:=1/((a+b*x)*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------- +--R +-+ +--R (b x + a)\|x +--R Type: Expression(Integer) +--E 2267 + +--S 2268 of 3330 +r0000:=2*atan(sqrt(b)*sqrt(x)/sqrt(a))/(sqrt(a)*sqrt(b)) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2atan(--------) +--R +-+ +--R \|a +--R (2) --------------- +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 2268 + +--S 2269 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-----+ +---+ +-+ +--R 2a b\|x + (b x - a)\|- a b \|a b \|x +--R log(----------------------------) 2atan(----------) +--R b x + a a +--R (3) [---------------------------------,-----------------] +--R +-----+ +---+ +--R \|- a b \|a b +--R Type: Union(List(Expression(Integer)),...) +--E 2269 + +--S 2270 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x - a)\|- a b +-----+ \|b \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 2270 + +--S 2271 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2271 + +--S 2272 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|b \|x +--R 2\|a \|b atan(----------) - 2\|a b atan(--------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------------- +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 2272 + +--S 2273 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2273 + +)clear all + +--S 2274 of 3330 +t0000:=1/(x^(3/2)*(a+b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R 2 +-+ +--R (b x + a x)\|x +--R Type: Expression(Integer) +--E 2274 + +--S 2275 of 3330 +r0000:=-2*atan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(3/2)+(-2)/(a*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R - 2\|b \|x atan(--------) - 2\|a +--R +-+ +--R \|a +--R (2) --------------------------------- +--R +-+ +-+ +--R a\|a \|x +--R Type: Expression(Integer) +--E 2275 + +--S 2276 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-+ +--R +---+ |b +-+ b\|x +--R | b +-+ - 2 |- \|x atan(----- - 2 +--R +---+ - 2a |- - \|x + b x - a \|a +-+ +--R | b +-+ \| a |b +--R |- - \|x log(------------------------) - 2 a |- +--R \| a b x + a \|a +--R [-------------------------------------------,--------------------------] +--R +-+ +-+ +--R a\|x a\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2276 + +--S 2277 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +-+ +-+ +--R | b +-+ \| a +-+ \|b \|x +--R |- - \|a log(------------------------) + 2\|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 2277 + +--S 2278 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2278 + +--S 2279 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x +-+ |b b\|x +--R 2\|b atan(--------) - 2\|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) ------------------------------------------ +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 2279 + +--S 2280 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2280 + +)clear all + +--S 2281 of 3330 +t0000:=1/(x^(5/2)*(a+b*x)) +--R +--R +--R 1 +--R (1) ----------------- +--R 3 2 +-+ +--R (b x + a x )\|x +--R Type: Expression(Integer) +--E 2281 + +--S 2282 of 3330 +r0000:=(-2/3)/(a*x^(3/2))+2*b^(3/2)*atan(sqrt(b)*sqrt(x)/sqrt(a))/a^(5/2)+_ + 2*b/(a^2*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R 6b x\|b \|x atan(--------) + (6b x - 2a)\|a +--R +-+ +--R \|a +--R (2) -------------------------------------------- +--R 2 +-+ +-+ +--R 3a x\|a \|x +--R Type: Expression(Integer) +--E 2282 + +--S 2283 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + b x - a +--R | b +-+ \| a +--R 3b x |- - \|x log(----------------------) + 6b x - 2a +--R \| a b x + a +--R [-----------------------------------------------------, +--R 2 +-+ +--R 3a x\|x +--R +-+ +-+ +--R |b +-+ b\|x +--R 6b x |- \|x atan(-----) + 6b x - 2a +--R \|a +-+ +--R |b +--R a |- +--R \|a +--R -----------------------------------] +--R 2 +-+ +--R 3a x\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2283 + +--S 2284 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + b x - a +-+ +-+ +--R | b +-+ \| a +-+ \|b \|x +--R b |- - \|a log(----------------------) - 2b\|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2284 + +--S 2285 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2285 + +--S 2286 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x +-+ |b b\|x +--R - 2b\|b atan(--------) + 2b\|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) ---------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2286 + +--S 2287 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2287 + +)clear all + +--S 2288 of 3330 +t0000:=1/(x^(7/2)*(a+b*x)) +--R +--R +--R 1 +--R (1) ----------------- +--R 4 3 +-+ +--R (b x + a x )\|x +--R Type: Expression(Integer) +--E 2288 + +--S 2289 of 3330 +r0000:=(-2/5)/(a*x^(5/2))+2/3*b/(a^2*x^(3/2))-_ + 2*b^(5/2)*atan(sqrt(b)*sqrt(x)/sqrt(a))/a^(7/2)-2*b^2/(a^3*sqrt(x)) +--R +--R +--R +-+ +-+ +--R 2 2 +-+ +-+ \|b \|x 2 2 2 +-+ +--R - 30b x \|b \|x atan(--------) + (- 30b x + 10a b x - 6a )\|a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------- +--R 3 2 +-+ +-+ +--R 15a x \|a \|x +--R Type: Expression(Integer) +--E 2289 + +--S 2290 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +--R 2 2 | b +-+ \| a 2 2 2 +--R 15b x |- - \|x log(------------------------) - 30b x + 10a b x - 6a +--R \| a b x + a +--R [----------------------------------------------------------------------, +--R 3 2 +-+ +--R 15a x \|x +--R +-+ +-+ +--R 2 2 |b +-+ b\|x 2 2 2 +--R - 30b x |- \|x atan(-----) - 30b x + 10a b x - 6a +--R \|a +-+ +--R |b +--R a |- +--R \|a +--R ----------------------------------------------------] +--R 3 2 +-+ +--R 15a x \|x +--R Type: Union(List(Expression(Integer)),...) +--E 2290 + +--S 2291 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +-+ +-+ +--R 2 | b +-+ \| a 2 +-+ \|b \|x +--R b |- - \|a log(------------------------) + 2b \|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2291 + +--S 2292 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2292 + +--S 2293 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 +-+ \|b \|x 2 +-+ |b b\|x +--R 2b \|b atan(--------) - 2b \|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) ---------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2293 + +--S 2294 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2294 + +)clear all + +--S 2295 of 3330 +t0000:=x^(5/2)/(a+b*x)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 2295 + +--S 2296 of 3330 +r0000:=5/3*x^(3/2)/b^2-x^(5/2)/(b*(a+b*x))+_ + 5*a^(3/2)*atan(sqrt(b)*sqrt(x)/sqrt(a))/b^(7/2)-5*a*sqrt(x)/b^3 +--R +--R +--R +-+ +-+ +--R 2 +-+ \|b \|x 2 2 2 +-+ +-+ +--R (15a b x + 15a )\|a atan(--------) + (2b x - 10a b x - 15a )\|b \|x +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------------- +--R 4 3 +-+ +--R (3b x + 3a b )\|b +--R Type: Expression(Integer) +--E 2296 + +--S 2297 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + b x - a +--R 2 | a \| b +--R (15a b x + 15a ) |- - log(----------------------) +--R \| b b x + a +--R + +--R 2 2 2 +-+ +--R (4b x - 20a b x - 30a )\|x +--R / +--R 4 3 +--R 6b x + 6a b +--R , +--R +-+ +-+ +--R 2 |a \|x 2 2 2 +-+ +--R (15a b x + 15a ) |- atan(----) + (2b x - 10a b x - 15a )\|x +--R \|b +-+ +--R |a +--R |- +--R \|b +--R -------------------------------------------------------------] +--R 4 3 +--R 3b x + 3a b +--R Type: Union(List(Expression(Integer)),...) +--E 2297 + +--S 2298 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + b x - a +-+ +-+ +--R | a +-+ \| b +-+ \|b \|x +--R 5a |- - \|b log(----------------------) - 10a\|a atan(--------) +--R \| b b x + a +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 2298 + +--S 2299 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2299 + +--S 2300 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x |a +-+ \|x +--R - 5a\|a atan(--------) + 5a |- \|b atan(----) +--R +-+ \|b +-+ +--R \|a |a +--R |- +--R \|b +--R (6) --------------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2300 + +--S 2301 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2301 + +)clear all + +--S 2302 of 3330 +t0000:=x^(3/2)/(a+b*x)^2 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 2302 + +--S 2303 of 3330 +r0000:=-x^(3/2)/(b*(a+b*x))-3*atan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(5/2)+_ + 3*sqrt(x)/b^2 +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R (- 3b x - 3a)\|a atan(--------) + (2b x + 3a)\|b \|x +--R +-+ +--R \|a +--R (2) ----------------------------------------------------- +--R 3 2 +-+ +--R (b x + a b )\|b +--R Type: Expression(Integer) +--E 2303 + +--S 2304 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + b x - a +--R | a \| b +-+ +--R (3b x + 3a) |- - log(------------------------) + (4b x + 6a)\|x +--R \| b b x + a +--R [----------------------------------------------------------------, +--R 3 2 +--R 2b x + 2a b +--R +-+ +-+ +--R |a \|x +-+ +--R (- 3b x - 3a) |- atan(----) + (2b x + 3a)\|x +--R \|b +-+ +--R |a +--R |- +--R \|b +--R ---------------------------------------------] +--R 3 2 +--R b x + a b +--R Type: Union(List(Expression(Integer)),...) +--E 2304 + +--S 2305 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + b x - a +-+ +-+ +--R | a +-+ \| b +-+ \|b \|x +--R 3 |- - \|b log(------------------------ + 6\|a atan(--------) +--R \| b b x + a +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 2305 + +--S 2306 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2306 + +--S 2307 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x |a +-+ \|x +--R 3\|a atan(--------) - 3 |- \|b atan(----) +--R +-+ \|b +-+ +--R \|a |a +--R |- +--R \|b +--R (6) ----------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2307 + +--S 2308 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2308 + +)clear all + +--S 2309 of 3330 +t0000:=sqrt(x)/(a+b*x)^2 +--R +--R +--R +-+ +--R \|x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 2309 + +--S 2310 of 3330 +r0000:=atan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(3/2)*sqrt(a))-sqrt(x)/(b*(a+b*x)) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-+ +--R (b x + a)atan(--------) - \|a \|b \|x +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R 2 +-+ +-+ +--R (b x + a b)\|a \|b +--R Type: Expression(Integer) +--E 2310 + +--S 2311 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-----+ +--R 2a b\|x + (b x - a)\|- a b +-----+ +-+ +--R (b x + a)log(----------------------------) - 2\|- a b \|x +--R b x + a +--R [----------------------------------------------------------, +--R 2 +-----+ +--R (2b x + 2a b)\|- a b +--R +---+ +-+ +--R \|a b \|x +---+ +-+ +--R (b x + a)atan(----------) - \|a b \|x +--R a +--R --------------------------------------] +--R 2 +---+ +--R (b x + a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 2311 + +--S 2312 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x - a)\|- a b +-----+ \|b \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 2312 + +--S 2313 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2313 + +--S 2314 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|b \|x +--R \|a \|b atan(----------) - \|a b atan(--------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R +-+ +-+ +---+ +--R b\|a \|b \|a b +--R Type: Expression(Integer) +--E 2314 + +--S 2315 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2315 + +)clear all + +--S 2316 of 3330 +t0000:=1/((a+b*x)^2*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 2 2 +-+ +--R (b x + 2a b x + a )\|x +--R Type: Expression(Integer) +--E 2316 + +--S 2317 of 3330 +r0000:=atan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*sqrt(b))+sqrt(x)/(a*(a+b*x)) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-+ +--R (b x + a)atan(--------) + \|a \|b \|x +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R 2 +-+ +-+ +--R (a b x + a )\|a \|b +--R Type: Expression(Integer) +--E 2317 + +--S 2318 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-----+ +--R 2a b\|x + (b x - a)\|- a b +-----+ +-+ +--R (b x + a)log(----------------------------) + 2\|- a b \|x +--R b x + a +--R [----------------------------------------------------------, +--R 2 +-----+ +--R (2a b x + 2a )\|- a b +--R +---+ +-+ +--R \|a b \|x +---+ +-+ +--R (b x + a)atan(----------) + \|a b \|x +--R a +--R --------------------------------------] +--R 2 +---+ +--R (a b x + a )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 2318 + +--S 2319 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x - a)\|- a b +-----+ \|b \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 2319 + +--S 2320 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2320 + +--S 2321 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|b \|x +--R \|a \|b atan(----------) - \|a b atan(--------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R +-+ +-+ +---+ +--R a\|a \|b \|a b +--R Type: Expression(Integer) +--E 2321 + +--S 2322 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2322 + +)clear all + +--S 2323 of 3330 +t0000:=1/(x^(3/2)*(a+b*x)^2) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 3 2 2 +-+ +--R (b x + 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 2323 + +--S 2324 of 3330 +r0000:=-3*atan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(5/2)+_ + (-3)/(a^2*sqrt(x))+1/(a*(a+b*x)*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R (- 3b x - 3a)\|b \|x atan(--------) + (- 3b x - 2a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------- +--R 2 3 +-+ +-+ +--R (a b x + a )\|a \|x +--R Type: Expression(Integer) +--E 2324 + +--S 2325 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +--R | b +-+ \| a +--R (3b x + 3a) |- - \|x log(------------------------) - 6b x - 4a +--R \| a b x + a +--R [--------------------------------------------------------------, +--R 2 3 +-+ +--R (2a b x + 2a )\|x +--R +-+ +-+ +--R |b +-+ b\|x +--R (- 3b x - 3a) |- \|x atan(-----) - 3b x - 2a +--R \|a +-+ +--R |b +--R a |- +--R \|a +--R --------------------------------------------] +--R 2 3 +-+ +--R (a b x + a )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2325 + +--S 2326 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +-+ +-+ +--R | b +-+ \| a +-+ \|b \|x +--R 3 |- - \|a log(------------------------ + 6\|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 2326 + +--S 2327 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2327 + +--S 2328 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x +-+ |b b\|x +--R 3\|b atan(--------) - 3\|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) ------------------------------------------ +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2328 + +--S 2329 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2329 + +)clear all + +--S 2330 of 3330 +t0000:=1/(x^(5/2)*(a+b*x)^2) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 4 3 2 2 +-+ +--R (b x + 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 2330 + +--S 2331 of 3330 +r0000:=(-5/3)/(a^2*x^(3/2))+1/(a*x^(3/2)*(a+b*x))+_ + 5*b^(3/2)*atan(sqrt(b)*sqrt(x)/sqrt(a))/a^(7/2)+5*b/(a^3*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 +-+ +-+ \|b \|x 2 2 2 +-+ +--R (15b x + 15a b x)\|b \|x atan(--------) + (15b x + 10a b x - 2a )\|a +--R +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R 3 2 4 +-+ +-+ +--R (3a b x + 3a x)\|a \|x +--R Type: Expression(Integer) +--E 2331 + +--S 2332 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + b x - a +--R 2 2 | b +-+ \| a 2 2 +--R (15b x + 15a b x) |- - \|x log(----------------------) + 30b x +--R \| a b x + a +--R + +--R 2 +--R 20a b x - 4a +--R / +--R 3 2 4 +-+ +--R (6a b x + 6a x)\|x +--R , +--R +-+ +-+ +--R 2 2 |b +-+ b\|x 2 2 2 +--R (15b x + 15a b x) |- \|x atan(-----) + 15b x + 10a b x - 2a +--R \|a +-+ +--R |b +--R a |- +--R \|a +--R --------------------------------------------------------------] +--R 3 2 4 +-+ +--R (3a b x + 3a x)\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2332 + +--S 2333 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + b x - a +-+ +-+ +--R | b +-+ \| a +-+ \|b \|x +--R 5b |- - \|a log(----------------------) - 10b\|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 2333 + +--S 2334 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2334 + +--S 2335 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x +-+ |b b\|x +--R - 5b\|b atan(--------) + 5b\|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) ---------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2335 + +--S 2336 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2336 + +)clear all + +--S 2337 of 3330 +t0000:=x^(7/2)/(a+b*x)^3 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 2337 + +--S 2338 of 3330 +r0000:=35/12*x^(3/2)/b^3-1/2*x^(7/2)/(b*(a+b*x)^2)-_ + 7/4*x^(5/2)/(b^2*(a+b*x))+35/4*a^(3/2)*_ + atan(sqrt(b)*sqrt(x)/sqrt(a))/b^(9/2)-35/4*a*sqrt(x)/b^4 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 3 +-+ \|b \|x +--R (105a b x + 210a b x + 105a )\|a atan(--------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +-+ +--R (8b x - 56a b x - 175a b x - 105a )\|b \|x +--R / +--R 6 2 5 2 4 +-+ +--R (12b x + 24a b x + 12a b )\|b +--R Type: Expression(Integer) +--E 2338 + +--S 2339 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + b x - a +--R 2 2 2 3 | a \| b +--R (105a b x + 210a b x + 105a ) |- - log(----------------------) +--R \| b b x + a +--R + +--R 3 3 2 2 2 3 +-+ +--R (16b x - 112a b x - 350a b x - 210a )\|x +--R / +--R 6 2 5 2 4 +--R 24b x + 48a b x + 24a b +--R , +--R +--R +-+ +-+ +--R 2 2 2 3 |a \|x +--R (105a b x + 210a b x + 105a ) |- atan(----) +--R \|b +-+ +--R |a +--R |- +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (8b x - 56a b x - 175a b x - 105a )\|x +--R / +--R 6 2 5 2 4 +--R 12b x + 24a b x + 12a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 2339 + +--S 2340 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + b x - a +-+ +-+ +--R | a +-+ \| b +-+ \|b \|x +--R 35a |- - \|b log(----------------------) - 70a\|a atan(--------) +--R \| b b x + a +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 2340 + +--S 2341 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2341 + +--S 2342 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x |a +-+ \|x +--R - 35a\|a atan(--------) + 35a |- \|b atan(----) +--R +-+ \|b +-+ +--R \|a |a +--R |- +--R \|b +--R (6) ----------------------------------------------- +--R 4 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 2342 + +--S 2343 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2343 + +)clear all + +--S 2344 of 3330 +t0000:=x^(5/2)/(a+b*x)^3 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 2344 + +--S 2345 of 3330 +r0000:=-1/2*x^(5/2)/(b*(a+b*x)^2)-5/4*x^(3/2)/(b^2*(a+b*x))-_ + 15/4*atan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(7/2)+15/4*sqrt(x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 +-+ \|b \|x +--R (- 15b x - 30a b x - 15a )\|a atan(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +-+ +--R (8b x + 25a b x + 15a )\|b \|x +--R / +--R 5 2 4 2 3 +-+ +--R (4b x + 8a b x + 4a b )\|b +--R Type: Expression(Integer) +--E 2345 + +--S 2346 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + b x - a +--R 2 2 2 | a \| b +--R (15b x + 30a b x + 15a ) |- - log(------------------------) +--R \| b b x + a +--R + +--R 2 2 2 +-+ +--R (16b x + 50a b x + 30a )\|x +--R / +--R 5 2 4 2 3 +--R 8b x + 16a b x + 8a b +--R , +--R +-+ +-+ +--R 2 2 2 |a \|x 2 2 2 +-+ +--R (- 15b x - 30a b x - 15a ) |- atan(----) + (8b x + 25a b x + 15a )\|x +--R \|b +-+ +--R |a +--R |- +--R \|b +--R ------------------------------------------------------------------------] +--R 5 2 4 2 3 +--R 4b x + 8a b x + 4a b +--R Type: Union(List(Expression(Integer)),...) +--E 2346 + +--S 2347 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + b x - a +-+ +-+ +--R | a +-+ \| b +-+ \|b \|x +--R 15 |- - \|b log(------------------------ + 30\|a atan(--------) +--R \| b b x + a +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 2347 + +--S 2348 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2348 + +--S 2349 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x |a +-+ \|x +--R 15\|a atan(--------) - 15 |- \|b atan(----) +--R +-+ \|b +-+ +--R \|a |a +--R |- +--R \|b +--R (6) ------------------------------------------- +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 2349 + +--S 2350 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2350 + +)clear all + +--S 2351 of 3330 +t0000:=x^(3/2)/(a+b*x)^3 +--R +--R +--R +-+ +--R x\|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 2351 + +--S 2352 of 3330 +r0000:=-1/2*x^(3/2)/(b*(a+b*x)^2)+_ + 3/4*atan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(5/2)*sqrt(a))-_ + 3/4*sqrt(x)/(b^2*(a+b*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (3b x + 6a b x + 3a )atan(--------) + (- 5b x - 3a)\|a \|b \|x +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------------- +--R 4 2 3 2 2 +-+ +-+ +--R (4b x + 8a b x + 4a b )\|a \|b +--R Type: Expression(Integer) +--E 2352 + +--S 2353 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-----+ +--R 2 2 2 2a b\|x + (b x - a)\|- a b +--R (3b x + 6a b x + 3a )log(----------------------------) +--R b x + a +--R + +--R +-----+ +-+ +--R (- 10b x - 6a)\|- a b \|x +--R / +--R 4 2 3 2 2 +-----+ +--R (8b x + 16a b x + 8a b )\|- a b +--R , +--R +---+ +-+ +--R 2 2 2 \|a b \|x +---+ +-+ +--R (3b x + 6a b x + 3a )atan(----------) + (- 5b x - 3a)\|a b \|x +--R a +--R ----------------------------------------------------------------] +--R 4 2 3 2 2 +---+ +--R (4b x + 8a b x + 4a b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 2353 + +--S 2354 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x - a)\|- a b +-----+ \|b \|x +--R 3\|a \|b log(----------------------------) - 6\|- a b atan(--------) +--R b x + a +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 8b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 2354 + +--S 2355 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2355 + +--S 2356 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|b \|x +--R 3\|a \|b atan(----------) - 3\|a b atan(--------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 4b \|a \|b \|a b +--R Type: Expression(Integer) +--E 2356 + +--S 2357 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2357 + +)clear all + +--S 2358 of 3330 +t0000:=sqrt(x)/(a+b*x)^3 +--R +--R +--R +-+ +--R \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 2358 + +--S 2359 of 3330 +r0000:=1/4*atan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*b^(3/2))-_ + 1/2*sqrt(x)/(b*(a+b*x)^2)+1/4*sqrt(x)/(a*b*(a+b*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (b x + 2a b x + a )atan(--------) + (b x - a)\|a \|b \|x +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------- +--R 3 2 2 2 3 +-+ +-+ +--R (4a b x + 8a b x + 4a b)\|a \|b +--R Type: Expression(Integer) +--E 2359 + +--S 2360 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-----+ +--R 2 2 2 2a b\|x + (b x - a)\|- a b +--R (b x + 2a b x + a )log(----------------------------) +--R b x + a +--R + +--R +-----+ +-+ +--R (2b x - 2a)\|- a b \|x +--R / +--R 3 2 2 2 3 +-----+ +--R (8a b x + 16a b x + 8a b)\|- a b +--R , +--R +---+ +-+ +--R 2 2 2 \|a b \|x +---+ +-+ +--R (b x + 2a b x + a )atan(----------) + (b x - a)\|a b \|x +--R a +--R ----------------------------------------------------------] +--R 3 2 2 2 3 +---+ +--R (4a b x + 8a b x + 4a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 2360 + +--S 2361 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x - a)\|- a b +-----+ \|b \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R b x + a +-+ +--R \|a +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 8a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 2361 + +--S 2362 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2362 + +--S 2363 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|b \|x +--R \|a \|b atan(----------) - \|a b atan(--------) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R +-+ +-+ +---+ +--R 4a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 2363 + +--S 2364 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2364 + +)clear all + +--S 2365 of 3330 +t0000:=1/((a+b*x)^3*sqrt(x)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 3 3 2 2 2 3 +-+ +--R (b x + 3a b x + 3a b x + a )\|x +--R Type: Expression(Integer) +--E 2365 + +--S 2366 of 3330 +r0000:=3/4*atan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(5/2)*sqrt(b))+_ + 1/2*sqrt(x)/(a*(a+b*x)^2)+3/4*sqrt(x)/(a^2*(a+b*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (3b x + 6a b x + 3a )atan(--------) + (3b x + 5a)\|a \|b \|x +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------- +--R 2 2 2 3 4 +-+ +-+ +--R (4a b x + 8a b x + 4a )\|a \|b +--R Type: Expression(Integer) +--E 2366 + +--S 2367 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +-----+ +--R 2 2 2 2a b\|x + (b x - a)\|- a b +--R (3b x + 6a b x + 3a )log(----------------------------) +--R b x + a +--R + +--R +-----+ +-+ +--R (6b x + 10a)\|- a b \|x +--R / +--R 2 2 2 3 4 +-----+ +--R (8a b x + 16a b x + 8a )\|- a b +--R , +--R +---+ +-+ +--R 2 2 2 \|a b \|x +---+ +-+ +--R (3b x + 6a b x + 3a )atan(----------) + (3b x + 5a)\|a b \|x +--R a +--R --------------------------------------------------------------] +--R 2 2 2 3 4 +---+ +--R (4a b x + 8a b x + 4a )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 2367 + +--S 2368 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x - a)\|- a b +-----+ \|b \|x +--R 3\|a \|b log(----------------------------) - 6\|- a b atan(--------) +--R b x + a +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 8a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 2368 + +--S 2369 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2369 + +--S 2370 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|b \|x +--R 3\|a \|b atan(----------) - 3\|a b atan(--------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 4a \|a \|b \|a b +--R Type: Expression(Integer) +--E 2370 + +--S 2371 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2371 + +)clear all + +--S 2372 of 3330 +t0000:=1/(x^(3/2)*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 4 2 3 2 2 3 +-+ +--R (b x + 3a b x + 3a b x + a x)\|x +--R Type: Expression(Integer) +--E 2372 + +--S 2373 of 3330 +r0000:=-15/4*atan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(7/2)+_ + (-15/4)/(a^3*sqrt(x))+1/2/(a*(a+b*x)^2*sqrt(x))+_ + 5/4/(a^2*(a+b*x)*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 +-+ +-+ \|b \|x +--R (- 15b x - 30a b x - 15a )\|b \|x atan(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R (- 15b x - 25a b x - 8a )\|a +--R / +--R 3 2 2 4 5 +-+ +-+ +--R (4a b x + 8a b x + 4a )\|a \|x +--R Type: Expression(Integer) +--E 2373 + +--S 2374 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +--R 2 2 2 | b +-+ \| a +--R (15b x + 30a b x + 15a ) |- - \|x log(------------------------) +--R \| a b x + a +--R + +--R 2 2 2 +--R - 30b x - 50a b x - 16a +--R / +--R 3 2 2 4 5 +-+ +--R (8a b x + 16a b x + 8a )\|x +--R , +--R +-+ +-+ +--R 2 2 2 |b +-+ b\|x 2 2 2 +--R (- 15b x - 30a b x - 15a ) |- \|x atan(-----) - 15b x - 25a b x - 8a +--R \|a +-+ +--R |b +--R a |- +--R \|a +--R -----------------------------------------------------------------------] +--R 3 2 2 4 5 +-+ +--R (4a b x + 8a b x + 4a )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2374 + +--S 2375 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + b x - a +-+ +-+ +--R | b +-+ \| a +-+ \|b \|x +--R 15 |- - \|a log(------------------------ + 30\|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 2375 + +--S 2376 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2376 + +--S 2377 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x +-+ |b b\|x +--R 15\|b atan(--------) - 15\|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) -------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 2377 + +--S 2378 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2378 + +)clear all + +--S 2379 of 3330 +t0000:=1/(x^(5/2)*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 5 2 4 2 3 3 2 +-+ +--R (b x + 3a b x + 3a b x + a x )\|x +--R Type: Expression(Integer) +--E 2379 + +--S 2380 of 3330 +r0000:=(-35/12)/(a^3*x^(3/2))+1/2/(a*x^(3/2)*(a+b*x)^2)+_ + 7/4/(a^2*x^(3/2)*(a+b*x))+35/4*b^(3/2)*_ + atan(sqrt(b)*sqrt(x)/sqrt(a))/a^(9/2)+35/4*b/(a^4*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 3 3 2 2 2 +-+ +-+ \|b \|x +--R (105b x + 210a b x + 105a b x)\|b \|x atan(--------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (105b x + 175a b x + 56a b x - 8a )\|a +--R / +--R 4 2 3 5 2 6 +-+ +-+ +--R (12a b x + 24a b x + 12a x)\|a \|x +--R Type: Expression(Integer) +--E 2380 + +--S 2381 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + b x - a +--R 3 3 2 2 2 | b +-+ \| a +--R (105b x + 210a b x + 105a b x) |- - \|x log(----------------------) +--R \| a b x + a +--R + +--R 3 3 2 2 2 3 +--R 210b x + 350a b x + 112a b x - 16a +--R / +--R 4 2 3 5 2 6 +-+ +--R (24a b x + 48a b x + 24a x)\|x +--R , +--R +--R +-+ +-+ +--R 3 3 2 2 2 |b +-+ b\|x 3 3 +--R (105b x + 210a b x + 105a b x) |- \|x atan(-----) + 105b x +--R \|a +-+ +--R |b +--R a |- +--R \|a +--R + +--R 2 2 2 3 +--R 175a b x + 56a b x - 8a +--R / +--R 4 2 3 5 2 6 +-+ +--R (12a b x + 24a b x + 12a x)\|x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 2381 + +--S 2382 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + b x - a +-+ +-+ +--R | b +-+ \| a +-+ \|b \|x +--R 35b |- - \|a log(----------------------) - 70b\|b atan(--------) +--R \| a b x + a +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 2382 + +--S 2383 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2383 + +--S 2384 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ \|b \|x +-+ |b b\|x +--R - 35b\|b atan(--------) + 35b\|a |- atan(-----) +--R +-+ \|a +-+ +--R \|a |b +--R a |- +--R \|a +--R (6) ------------------------------------------------ +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 2384 + +--S 2385 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2385 + +)clear all + +--S 2386 of 3330 +t0000:=x^(5/2)/(-a+b*x) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------- +--R b x - a +--R Type: Expression(Integer) +--E 2386 + +--S 2387 of 3330 +r0000:=2/3*a*x^(3/2)/b^2+2/5*x^(5/2)/b-_ + 2*a^(5/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/b^(7/2)+2*a^2*sqrt(x)/b^3 +--R +--R +--R +-+ +-+ +--R 2 +-+ \|b \|x 2 2 2 +-+ +-+ +--R - 30a \|a atanh(--------) + (6b x + 10a b x + 30a )\|b \|x +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------ +--R 3 +-+ +--R 15b \|b +--R Type: Expression(Integer) +--E 2387 + +--S 2388 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 |a \|b 2 2 2 +-+ +--R 15a |- log(----------------------) + (6b x + 10a b x + 30a )\|x +--R \|b b x - a +--R [------------------------------------------------------------------, +--R 3 +--R 15b +--R +---+ +-+ +--R 2 | a \|x 2 2 2 +-+ +--R - 30a |- - atan(------) + (6b x + 10a b x + 30a )\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R -------------------------------------------------------] +--R 3 +--R 15b +--R Type: Union(List(Expression(Integer)),...) +--E 2388 + +--S 2389 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R 2 |a +-+ \|b 2 +-+ \|b \|x +--R a |- \|b log(----------------------) + 2a \|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2389 + +--S 2390 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2390 + +--S 2391 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R 2 +-+ \|b \|x 2 | a +-+ \|x +--R 2a \|a atanh(--------) - 2a |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) -------------------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2391 + +--S 2392 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2392 + +)clear all + +--S 2393 of 3330 +t0000:=x^(3/2)/(-a+b*x) +--R +--R +--R +-+ +--R x\|x +--R (1) ------- +--R b x - a +--R Type: Expression(Integer) +--E 2393 + +--S 2394 of 3330 +r0000:=2/3*x^(3/2)/b-2*a^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/b^(5/2)+_ + 2*a*sqrt(x)/b^2 +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R - 6a\|a atanh(--------) + (2b x + 6a)\|b \|x +--R +-+ +--R \|a +--R (2) --------------------------------------------- +--R 2 +-+ +--R 3b \|b +--R Type: Expression(Integer) +--E 2394 + +--S 2395 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R |a \|b +-+ +--R 3a |- log(----------------------) + (2b x + 6a)\|x +--R \|b b x - a +--R [---------------------------------------------------, +--R 2 +--R 3b +--R +---+ +-+ +--R | a \|x +-+ +--R - 6a |- - atan(------) + (2b x + 6a)\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R ----------------------------------------] +--R 2 +--R 3b +--R Type: Union(List(Expression(Integer)),...) +--E 2395 + +--S 2396 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R a |- \|b log(----------------------) + 2a\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------ +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2396 + +--S 2397 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2397 + +--S 2398 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 2a\|a atanh(--------) - 2a |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) ------------------------------------------------ +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2398 + +--S 2399 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2399 + +)clear all + +--S 2400 of 3330 +t0000:=sqrt(x)/(-a+b*x) +--R +--R +--R +-+ +--R \|x +--R (1) ------- +--R b x - a +--R Type: Expression(Integer) +--E 2400 + +--S 2401 of 3330 +r0000:=-2*atanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(3/2)+2*sqrt(x)/b +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R - 2\|a atanh(--------) + 2\|b \|x +--R +-+ +--R \|a +--R (2) ---------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 2401 + +--S 2402 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +-+ +--R +-+ | a \|x +-+ +--R |a +-+ - 2 |- - atan(------ + 2\|x +--R +-+ - 2b |- \|x + b x + a \| b +---+ +--R |a \|b +-+ | a +--R |- log(----------------------) + 2\|x |- - +--R \|b b x - a \| b +--R [---------------------------------------,-----------------------------] +--R b b +--R Type: Union(List(Expression(Integer)),...) +--E 2402 + +--S 2403 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R |- \|b log(----------------------) + 2\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) ---------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 2403 + +--S 2404 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2404 + +--S 2405 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 2\|a atanh(--------) - 2 |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) ---------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 2405 + +--S 2406 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2406 + +)clear all + +--S 2407 of 3330 +t0000:=1/((-a+b*x)*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------- +--R +-+ +--R (b x - a)\|x +--R Type: Expression(Integer) +--E 2407 + +--S 2408 of 3330 +r0000:=-2*atanh(sqrt(b)*sqrt(x)/sqrt(a))/(sqrt(a)*sqrt(b)) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2atanh(--------) +--R +-+ +--R \|a +--R (2) - ---------------- +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 2408 + +--S 2409 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +---+ +-----+ +-+ +--R - 2a b\|x + (b x + a)\|a b \|- a b \|x +--R log(----------------------------) 2atan(------------) +--R b x - a a +--R (3) [---------------------------------,- -------------------] +--R +---+ +-----+ +--R \|a b \|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 2409 + +--S 2410 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(----------------------------) + 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------------ +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 2410 + +--S 2411 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2411 + +--S 2412 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R 2\|- a b atanh(--------) - 2\|a \|b atan(------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 2412 + +--S 2413 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2413 + +)clear all + +--S 2414 of 3330 +t0000:=1/(x^(3/2)*(-a+b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R 2 +-+ +--R (b x - a x)\|x +--R Type: Expression(Integer) +--E 2414 + +--S 2415 of 3330 +r0000:=-2*atanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(3/2)+2/(a*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R - 2\|b \|x atanh(--------) + 2\|a +--R +-+ +--R \|a +--R (2) ---------------------------------- +--R +-+ +-+ +--R a\|a \|x +--R Type: Expression(Integer) +--E 2415 + +--S 2416 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +-+ +--R +-+ | b +-+ b\|x +--R |b +-+ - 2 |- - \|x atan(------- + 2 +--R +-+ - 2a |- \|x + b x + a \| a +---+ +--R |b +-+ \|a | b +--R |- \|x log(----------------------) + 2 a |- - +--R \|a b x - a \| a +--R [---------------------------------------,------------------------------] +--R +-+ +-+ +--R a\|x a\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2416 + +--S 2417 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R \|a |- log(----------------------) + 2\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) ---------------------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 2417 + +--S 2418 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2418 + +--S 2419 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 2\|b atanh(--------) - 2 |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) ----------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 2419 + +--S 2420 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2420 + +)clear all + +--S 2421 of 3330 +t0000:=1/(x^(5/2)*(-a+b*x)) +--R +--R +--R 1 +--R (1) ----------------- +--R 3 2 +-+ +--R (b x - a x )\|x +--R Type: Expression(Integer) +--E 2421 + +--S 2422 of 3330 +r0000:=2/3/(a*x^(3/2))-2*b^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/a^(5/2)+_ + 2*b/(a^2*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R - 6b x\|b \|x atanh(--------) + (6b x + 2a)\|a +--R +-+ +--R \|a +--R (2) ----------------------------------------------- +--R 2 +-+ +-+ +--R 3a x\|a \|x +--R Type: Expression(Integer) +--E 2422 + +--S 2423 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R |b +-+ \|a +--R 3b x |- \|x log(----------------------) + 6b x + 2a +--R \|a b x - a +--R [---------------------------------------------------, +--R 2 +-+ +--R 3a x\|x +--R +---+ +-+ +--R | b +-+ b\|x +--R - 6b x |- - \|x atan(-------) + 6b x + 2a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R -----------------------------------------] +--R 2 +-+ +--R 3a x\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2423 + +--S 2424 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R b\|a |- log(----------------------) + 2b\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------ +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2424 + +--S 2425 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2425 + +--S 2426 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 2b\|b atanh(--------) - 2b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) ------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2426 + +--S 2427 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2427 + +)clear all + +--S 2428 of 3330 +t0000:=1/(x^(7/2)*(-a+b*x)) +--R +--R +--R 1 +--R (1) ----------------- +--R 4 3 +-+ +--R (b x - a x )\|x +--R Type: Expression(Integer) +--E 2428 + +--S 2429 of 3330 +r0000:=2/5/(a*x^(5/2))+2/3*b/(a^2*x^(3/2))-_ + 2*b^(5/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/a^(7/2)+2*b^2/(a^3*sqrt(x)) +--R +--R +--R +-+ +-+ +--R 2 2 +-+ +-+ \|b \|x 2 2 2 +-+ +--R - 30b x \|b \|x atanh(--------) + (30b x + 10a b x + 6a )\|a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------- +--R 3 2 +-+ +-+ +--R 15a x \|a \|x +--R Type: Expression(Integer) +--E 2429 + +--S 2430 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R 2 2 |b +-+ \|a 2 2 2 +--R 15b x |- \|x log(----------------------) + 30b x + 10a b x + 6a +--R \|a b x - a +--R [------------------------------------------------------------------, +--R 3 2 +-+ +--R 15a x \|x +--R +---+ +-+ +--R 2 2 | b +-+ b\|x 2 2 2 +--R - 30b x |- - \|x atan(-------) + 30b x + 10a b x + 6a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R --------------------------------------------------------] +--R 3 2 +-+ +--R 15a x \|x +--R Type: Union(List(Expression(Integer)),...) +--E 2430 + +--S 2431 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R 2 +-+ |b \|a 2 +-+ \|b \|x +--R b \|a |- log(----------------------) + 2b \|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2431 + +--S 2432 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2432 + +--S 2433 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R 2 +-+ \|b \|x 2 | b +-+ b\|x +--R 2b \|b atanh(--------) - 2b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) --------------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2433 + +--S 2434 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2434 + +)clear all + +--S 2435 of 3330 +t0000:=x^(5/2)/(-a+b*x)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression(Integer) +--E 2435 + +--S 2436 of 3330 +r0000:=5/3*x^(3/2)/b^2+x^(5/2)/(b*(a-b*x))-_ + 5*a^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/b^(7/2)+5*a*sqrt(x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 +-+ \|b \|x 2 2 2 +-+ +-+ +--R (- 15a b x + 15a )\|a atanh(--------) + (2b x + 10a b x - 15a )\|b \|x +--R +-+ +--R \|a +--R ------------------------------------------------------------------------ +--R 4 3 +-+ +--R (3b x - 3a b )\|b +--R Type: Expression(Integer) +--E 2436 + +--S 2437 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 |a \|b +--R (15a b x - 15a ) |- log(----------------------) +--R \|b b x - a +--R + +--R 2 2 2 +-+ +--R (4b x + 20a b x - 30a )\|x +--R / +--R 4 3 +--R 6b x - 6a b +--R , +--R +---+ +-+ +--R 2 | a \|x 2 2 2 +-+ +--R (- 15a b x + 15a ) |- - atan(------) + (2b x + 10a b x - 15a )\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R -------------------------------------------------------------------] +--R 4 3 +--R 3b x - 3a b +--R Type: Union(List(Expression(Integer)),...) +--E 2437 + +--S 2438 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 5a |- \|b log(----------------------) + 10a\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 2438 + +--S 2439 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2439 + +--S 2440 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 5a\|a atanh(--------) - 5a |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) ------------------------------------------------ +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2440 + +--S 2441 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2441 + +)clear all + +--S 2442 of 3330 +t0000:=x^(3/2)/(-a+b*x)^2 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression(Integer) +--E 2442 + +--S 2443 of 3330 +r0000:=x^(3/2)/(b*(a-b*x))-3*atanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(5/2)+_ + 3*sqrt(x)/b^2 +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R (- 3b x + 3a)\|a atanh(--------) + (2b x - 3a)\|b \|x +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 3 2 +-+ +--R (b x - a b )\|b +--R Type: Expression(Integer) +--E 2443 + +--S 2444 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R |a \|b +-+ +--R (3b x - 3a) |- log(----------------------) + (4b x - 6a)\|x +--R \|b b x - a +--R [------------------------------------------------------------, +--R 3 2 +--R 2b x - 2a b +--R +---+ +-+ +--R | a \|x +-+ +--R (- 3b x + 3a) |- - atan(------) + (2b x - 3a)\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R -------------------------------------------------] +--R 3 2 +--R b x - a b +--R Type: Union(List(Expression(Integer)),...) +--E 2444 + +--S 2445 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 3 |- \|b log(---------------------- + 6\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) ----------------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 2445 + +--S 2446 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2446 + +--S 2447 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 3\|a atanh(--------) - 3 |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) ---------------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 2447 + +--S 2448 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2448 + +)clear all + +--S 2449 of 3330 +t0000:=sqrt(x)/(-a+b*x)^2 +--R +--R +--R +-+ +--R \|x +--R (1) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression(Integer) +--E 2449 + +--S 2450 of 3330 +r0000:=-atanh(sqrt(b)*sqrt(x)/sqrt(a))/(b^(3/2)*sqrt(a))+sqrt(x)/(b*(a-b*x)) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-+ +--R (- b x + a)atanh(--------) - \|a \|b \|x +--R +-+ +--R \|a +--R (2) ----------------------------------------- +--R 2 +-+ +-+ +--R (b x - a b)\|a \|b +--R Type: Expression(Integer) +--E 2450 + +--S 2451 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +---+ +--R - 2a b\|x + (b x + a)\|a b +---+ +-+ +--R (b x - a)log(----------------------------) - 2\|a b \|x +--R b x - a +--R [--------------------------------------------------------, +--R 2 +---+ +--R (2b x - 2a b)\|a b +--R +-----+ +-+ +--R \|- a b \|x +-----+ +-+ +--R (- b x + a)atan(------------) - \|- a b \|x +--R a +--R --------------------------------------------] +--R 2 +-----+ +--R (b x - a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 2451 + +--S 2452 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(----------------------------) + 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 2b\|a \|b \|a b +--R Type: Expression(Integer) +--E 2452 + +--S 2453 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2453 + +--S 2454 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R \|- a b atanh(--------) - \|a \|b atan(------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------- +--R +-----+ +-+ +-+ +--R b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 2454 + +--S 2455 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2455 + +)clear all + +--S 2456 of 3330 +t0000:=1/((-a+b*x)^2*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 2 2 +-+ +--R (b x - 2a b x + a )\|x +--R Type: Expression(Integer) +--E 2456 + +--S 2457 of 3330 +r0000:=atanh(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*sqrt(b))+sqrt(x)/(a*(a-b*x)) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-+ +--R (b x - a)atanh(--------) - \|a \|b \|x +--R +-+ +--R \|a +--R (2) --------------------------------------- +--R 2 +-+ +-+ +--R (a b x - a )\|a \|b +--R Type: Expression(Integer) +--E 2457 + +--S 2458 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +---+ +--R 2a b\|x + (b x + a)\|a b +---+ +-+ +--R (b x - a)log(--------------------------) - 2\|a b \|x +--R b x - a +--R [------------------------------------------------------, +--R 2 +---+ +--R (2a b x - 2a )\|a b +--R +-----+ +-+ +--R \|- a b \|x +-----+ +-+ +--R (b x - a)atan(------------) - \|- a b \|x +--R a +--R ------------------------------------------] +--R 2 +-----+ +--R (a b x - a )\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 2458 + +--S 2459 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(--------------------------) - 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R +-+ +-+ +---+ +--R 2a\|a \|b \|a b +--R Type: Expression(Integer) +--E 2459 + +--S 2460 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2460 + +--S 2461 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R - \|- a b atanh(--------) + \|a \|b atan(------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +-----+ +-+ +-+ +--R a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 2461 + +--S 2462 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2462 + +)clear all + +--S 2463 of 3330 +t0000:=1/(x^(3/2)*(-a+b*x)^2) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 3 2 2 +-+ +--R (b x - 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 2463 + +--S 2464 of 3330 +r0000:=3*atanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(5/2)+_ + (-3)/(a^2*sqrt(x))+1/(a*(a-b*x)*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R (3b x - 3a)\|b \|x atanh(--------) + (- 3b x + 2a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 2 3 +-+ +-+ +--R (a b x - a )\|a \|x +--R Type: Expression(Integer) +--E 2464 + +--S 2465 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +--R |b +-+ \|a +--R (3b x - 3a) |- \|x log(--------------------) - 6b x + 4a +--R \|a b x - a +--R [--------------------------------------------------------, +--R 2 3 +-+ +--R (2a b x - 2a )\|x +--R +---+ +-+ +--R | b +-+ b\|x +--R (3b x - 3a) |- - \|x atan(-------) - 3b x + 2a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ----------------------------------------------] +--R 2 3 +-+ +--R (a b x - a )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2465 + +--S 2466 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 3\|a |- log(--------------------) - 6\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 2466 + +--S 2467 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2467 + +--S 2468 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R - 3\|b atanh(--------) + 3 |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) ------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2468 + +--S 2469 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2469 + +)clear all + +--S 2470 of 3330 +t0000:=1/(x^(5/2)*(-a+b*x)^2) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 4 3 2 2 +-+ +--R (b x - 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 2470 + +--S 2471 of 3330 +r0000:=(-5/3)/(a^2*x^(3/2))+1/(a*x^(3/2)*(a-b*x))+_ + 5*b^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/a^(7/2)-5*b/(a^3*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 +-+ +-+ \|b \|x 2 2 2 +-+ +--R (15b x - 15a b x)\|b \|x atanh(--------) + (- 15b x + 10a b x + 2a )\|a +--R +-+ +--R \|a +--R -------------------------------------------------------------------------- +--R 3 2 4 +-+ +-+ +--R (3a b x - 3a x)\|a \|x +--R Type: Expression(Integer) +--E 2471 + +--S 2472 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +--R 2 2 |b +-+ \|a 2 2 2 +--R (15b x - 15a b x) |- \|x log(--------------------) - 30b x + 20a b x + 4a +--R \|a b x - a +--R [---------------------------------------------------------------------------- +--R 3 2 4 +-+ +--R (6a b x - 6a x)\|x +--R , +--R +---+ +-+ +--R 2 2 | b +-+ b\|x 2 2 2 +--R (15b x - 15a b x) |- - \|x atan(-------) - 15b x + 10a b x + 2a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ------------------------------------------------------------------] +--R 3 2 4 +-+ +--R (3a b x - 3a x)\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2472 + +--S 2473 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 5b\|a |- log(--------------------) - 10b\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------ +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 2473 + +--S 2474 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2474 + +--S 2475 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R - 5b\|b atanh(--------) + 5b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) --------------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 2475 + +--S 2476 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2476 + +)clear all + +--S 2477 of 3330 +t0000:=x^(7/2)/(-a+b*x)^3 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 2477 + +--S 2478 of 3330 +r0000:=35/12*x^(3/2)/b^3-1/2*x^(7/2)/(b*(a-b*x)^2)+_ + 7/4*x^(5/2)/(b^2*(a-b*x))-_ + 35/4*a^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/b^(9/2)+35/4*a*sqrt(x)/b^4 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 3 +-+ \|b \|x +--R (- 105a b x + 210a b x - 105a )\|a atanh(--------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +-+ +--R (8b x + 56a b x - 175a b x + 105a )\|b \|x +--R / +--R 6 2 5 2 4 +-+ +--R (12b x - 24a b x + 12a b )\|b +--R Type: Expression(Integer) +--E 2478 + +--S 2479 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 2 2 3 |a \|b +--R (105a b x - 210a b x + 105a ) |- log(----------------------) +--R \|b b x - a +--R + +--R 3 3 2 2 2 3 +-+ +--R (16b x + 112a b x - 350a b x + 210a )\|x +--R / +--R 6 2 5 2 4 +--R 24b x - 48a b x + 24a b +--R , +--R +--R +---+ +-+ +--R 2 2 2 3 | a \|x +--R (- 105a b x + 210a b x - 105a ) |- - atan(------) +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R + +--R 3 3 2 2 2 3 +-+ +--R (8b x + 56a b x - 175a b x + 105a )\|x +--R / +--R 6 2 5 2 4 +--R 12b x - 24a b x + 12a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 2479 + +--S 2480 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 35a |- \|b log(----------------------) + 70a\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 2480 + +--S 2481 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2481 + +--S 2482 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 35a\|a atanh(--------) - 35a |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) -------------------------------------------------- +--R 4 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 2482 + +--S 2483 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2483 + +)clear all + +--S 2484 of 3330 +t0000:=x^(5/2)/(-a+b*x)^3 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 2484 + +--S 2485 of 3330 +r0000:=-1/2*x^(5/2)/(b*(a-b*x)^2)+5/4*x^(3/2)/(b^2*(a-b*x))-_ + 15/4*atanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(7/2)+15/4*sqrt(x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 +-+ \|b \|x +--R (- 15b x + 30a b x - 15a )\|a atanh(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +-+ +--R (8b x - 25a b x + 15a )\|b \|x +--R / +--R 5 2 4 2 3 +-+ +--R (4b x - 8a b x + 4a b )\|b +--R Type: Expression(Integer) +--E 2485 + +--S 2486 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 2 2 |a \|b +--R (15b x - 30a b x + 15a ) |- log(----------------------) +--R \|b b x - a +--R + +--R 2 2 2 +-+ +--R (16b x - 50a b x + 30a )\|x +--R / +--R 5 2 4 2 3 +--R 8b x - 16a b x + 8a b +--R , +--R +---+ +-+ +--R 2 2 2 | a \|x 2 2 2 +-+ +--R (- 15b x + 30a b x - 15a ) |- - atan(------) + (8b x - 25a b x + 15a )\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R ---------------------------------------------------------------------------- +--R 5 2 4 2 3 +--R 4b x - 8a b x + 4a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 2486 + +--S 2487 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 15 |- \|b log(---------------------- + 30\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 2487 + +--S 2488 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2488 + +--S 2489 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 15\|a atanh(--------) - 15 |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (6) ------------------------------------------------ +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 2489 + +--S 2490 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2490 + +)clear all + +--S 2491 of 3330 +t0000:=x^(3/2)/(-a+b*x)^3 +--R +--R +--R +-+ +--R x\|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 2491 + +--S 2492 of 3330 +r0000:=-1/2*x^(3/2)/(b*(a-b*x)^2)-_ + 3/4*atanh(sqrt(b)*sqrt(x)/sqrt(a))/(b^(5/2)*sqrt(a))+_ + 3/4*sqrt(x)/(b^2*(a-b*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (- 3b x + 6a b x - 3a )atanh(--------) + (- 5b x + 3a)\|a \|b \|x +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------- +--R 4 2 3 2 2 +-+ +-+ +--R (4b x - 8a b x + 4a b )\|a \|b +--R Type: Expression(Integer) +--E 2492 + +--S 2493 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +---+ +--R 2 2 2 - 2a b\|x + (b x + a)\|a b +--R (3b x - 6a b x + 3a )log(----------------------------) +--R b x - a +--R + +--R +---+ +-+ +--R (- 10b x + 6a)\|a b \|x +--R / +--R 4 2 3 2 2 +---+ +--R (8b x - 16a b x + 8a b )\|a b +--R , +--R +-----+ +-+ +--R 2 2 2 \|- a b \|x +-----+ +-+ +--R (- 3b x + 6a b x - 3a )atan(------------) + (- 5b x + 3a)\|- a b \|x +--R a +--R ----------------------------------------------------------------------] +--R 4 2 3 2 2 +-----+ +--R (4b x - 8a b x + 4a b )\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 2493 + +--S 2494 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R 3\|a \|b log(----------------------------) + 6\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8b \|a \|b \|a b +--R Type: Expression(Integer) +--E 2494 + +--S 2495 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2495 + +--S 2496 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R 3\|- a b atanh(--------) - 3\|a \|b atan(------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R 2 +-----+ +-+ +-+ +--R 4b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 2496 + +--S 2497 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2497 + +)clear all + +--S 2498 of 3330 +t0000:=sqrt(x)/(-a+b*x)^3 +--R +--R +--R +-+ +--R \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 2498 + +--S 2499 of 3330 +r0000:=1/4*atanh(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*b^(3/2))-_ + 1/2*sqrt(x)/(b*(a-b*x)^2)+1/4*sqrt(x)/(a*b*(a-b*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (b x - 2a b x + a )atanh(--------) + (- b x - a)\|a \|b \|x +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------- +--R 3 2 2 2 3 +-+ +-+ +--R (4a b x - 8a b x + 4a b)\|a \|b +--R Type: Expression(Integer) +--E 2499 + +--S 2500 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +---+ +--R 2 2 2 2a b\|x + (b x + a)\|a b +--R (b x - 2a b x + a )log(--------------------------) +--R b x - a +--R + +--R +---+ +-+ +--R (- 2b x - 2a)\|a b \|x +--R / +--R 3 2 2 2 3 +---+ +--R (8a b x - 16a b x + 8a b)\|a b +--R , +--R +-----+ +-+ +--R 2 2 2 \|- a b \|x +-----+ +-+ +--R (b x - 2a b x + a )atan(------------) + (- b x - a)\|- a b \|x +--R a +--R ----------------------------------------------------------------] +--R 3 2 2 2 3 +-----+ +--R (4a b x - 8a b x + 4a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 2500 + +--S 2501 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(--------------------------) - 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R +-+ +-+ +---+ +--R 8a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 2501 + +--S 2502 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2502 + +--S 2503 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R - \|- a b atanh(--------) + \|a \|b atan(------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +-----+ +-+ +-+ +--R 4a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 2503 + +--S 2504 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2504 + +)clear all + +--S 2505 of 3330 +t0000:=1/((-a+b*x)^3*sqrt(x)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 3 3 2 2 2 3 +-+ +--R (b x - 3a b x + 3a b x - a )\|x +--R Type: Expression(Integer) +--E 2505 + +--S 2506 of 3330 +r0000:=-3/4*atanh(sqrt(b)*sqrt(x)/sqrt(a))/(a^(5/2)*sqrt(b))-_ + 1/2*sqrt(x)/(a*(a-b*x)^2)-3/4*sqrt(x)/(a^2*(a-b*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (- 3b x + 6a b x - 3a )atanh(--------) + (3b x - 5a)\|a \|b \|x +--R +-+ +--R \|a +--R (2) ----------------------------------------------------------------- +--R 2 2 2 3 4 +-+ +-+ +--R (4a b x - 8a b x + 4a )\|a \|b +--R Type: Expression(Integer) +--E 2506 + +--S 2507 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +---+ +--R 2 2 2 - 2a b\|x + (b x + a)\|a b +--R (3b x - 6a b x + 3a )log(----------------------------) +--R b x - a +--R + +--R +---+ +-+ +--R (6b x - 10a)\|a b \|x +--R / +--R 2 2 2 3 4 +---+ +--R (8a b x - 16a b x + 8a )\|a b +--R , +--R +-----+ +-+ +--R 2 2 2 \|- a b \|x +-----+ +-+ +--R (- 3b x + 6a b x - 3a )atan(------------) + (3b x - 5a)\|- a b \|x +--R a +--R --------------------------------------------------------------------] +--R 2 2 2 3 4 +-----+ +--R (4a b x - 8a b x + 4a )\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 2507 + +--S 2508 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R 3\|a \|b log(----------------------------) + 6\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8a \|a \|b \|a b +--R Type: Expression(Integer) +--E 2508 + +--S 2509 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2509 + +--S 2510 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R 3\|- a b atanh(--------) - 3\|a \|b atan(------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R 2 +-----+ +-+ +-+ +--R 4a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 2510 + +--S 2511 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2511 + +)clear all + +--S 2512 of 3330 +t0000:=1/(x^(3/2)*(-a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 4 2 3 2 2 3 +-+ +--R (b x - 3a b x + 3a b x - a x)\|x +--R Type: Expression(Integer) +--E 2512 + +--S 2513 of 3330 +r0000:=-15/4*atanh(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(7/2)+_ + 15/4/(a^3*sqrt(x))+(-1/2)/(a*(a-b*x)^2*sqrt(x))+_ + (-5/4)/(a^2*(a-b*x)*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 +-+ +-+ \|b \|x +--R (- 15b x + 30a b x - 15a )\|b \|x atanh(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R (15b x - 25a b x + 8a )\|a +--R / +--R 3 2 2 4 5 +-+ +-+ +--R (4a b x - 8a b x + 4a )\|a \|x +--R Type: Expression(Integer) +--E 2513 + +--S 2514 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R 2 2 2 |b +-+ \|a 2 2 +--R (15b x - 30a b x + 15a ) |- \|x log(----------------------) + 30b x +--R \|a b x - a +--R + +--R 2 +--R - 50a b x + 16a +--R / +--R 3 2 2 4 5 +-+ +--R (8a b x - 16a b x + 8a )\|x +--R , +--R +---+ +-+ +--R 2 2 2 | b +-+ b\|x 2 2 2 +--R (- 15b x + 30a b x - 15a ) |- - \|x atan(-------) + 15b x - 25a b x + 8a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ---------------------------------------------------------------------------] +--R 3 2 2 4 5 +-+ +--R (4a b x - 8a b x + 4a )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 2514 + +--S 2515 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 15\|a |- log(----------------------) + 30\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 2515 + +--S 2516 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2516 + +--S 2517 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 15\|b atanh(--------) - 15 |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) ------------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 2517 + +--S 2518 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2518 + +)clear all + +--S 2519 of 3330 +t0000:=1/(x^(5/2)*(-a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 5 2 4 2 3 3 2 +-+ +--R (b x - 3a b x + 3a b x - a x )\|x +--R Type: Expression(Integer) +--E 2519 + +--S 2520 of 3330 +r0000:=35/12/(a^3*x^(3/2))+(-1/2)/(a*x^(3/2)*(a-b*x)^2)+_ + (-7/4)/(a^2*x^(3/2)*(a-b*x))-_ + 35/4*b^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a))/a^(9/2)+35/4*b/(a^4*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 3 3 2 2 2 +-+ +-+ \|b \|x +--R (- 105b x + 210a b x - 105a b x)\|b \|x atanh(--------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (105b x - 175a b x + 56a b x + 8a )\|a +--R / +--R 4 2 3 5 2 6 +-+ +-+ +--R (12a b x - 24a b x + 12a x)\|a \|x +--R Type: Expression(Integer) +--E 2520 + +--S 2521 of 3330 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R 3 3 2 2 2 |b +-+ \|a +--R (105b x - 210a b x + 105a b x) |- \|x log(----------------------) +--R \|a b x - a +--R + +--R 3 3 2 2 2 3 +--R 210b x - 350a b x + 112a b x + 16a +--R / +--R 4 2 3 5 2 6 +-+ +--R (24a b x - 48a b x + 24a x)\|x +--R , +--R +--R +---+ +-+ +--R 3 3 2 2 2 | b +-+ b\|x 3 3 +--R (- 105b x + 210a b x - 105a b x) |- - \|x atan(-------) + 105b x +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R + +--R 2 2 2 3 +--R - 175a b x + 56a b x + 8a +--R / +--R 4 2 3 5 2 6 +-+ +--R (12a b x - 24a b x + 12a x)\|x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 2521 + +--S 2522 of 3330 +m0000:=a0000.1 - r0000 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 35b\|a |- log(----------------------) + 70b\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 2522 + +--S 2523 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2523 + +--S 2524 of 3330 +m0000:=a0000.2 - r0000 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 35b\|b atanh(--------) - 35b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (6) --------------------------------------------------- +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 2524 + +--S 2525 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 2525 + +)clear all + +--S 2526 of 3330 +t0000:=x^(5/2)*sqrt(a+b*x) +--R +--R +--R 2 +-+ +-------+ +--R (1) x \|x \|b x + a +--R Type: Expression(Integer) +--E 2526 + +--S 2527 of 3330 +r0000:=-5/64*a^4*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-_ + 5/96*a^2*x^(3/2)*sqrt(a+b*x)/b^2+_ + 1/24*a*x^(5/2)*sqrt(a+b*x)/b+1/4*x^(7/2)*sqrt(a+b*x)+_ + 5/64*a^3*sqrt(x)*sqrt(a+b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 4 \|b \|x +--R - 15a atanh(----------) +--R +-------+ +--R \|b x + a +--R + +--R 3 3 2 2 2 3 +-+ +-+ +-------+ +--R (48b x + 8a b x - 10a b x + 15a )\|b \|x \|b x + a +--R / +--R 3 +-+ +--R 192b \|b +--R Type: Expression(Integer) +--E 2527 + +--S 2528 of 3330 +--a0000:=integrate(t0000,x) +--E 2528 + +--S 2529 of 3330 +--m0000:=a0000 - r0000 +--E 2529 + +--S 2530 of 3330 +--d0000:=D(m0000,x) +--E 2530 + +)clear all + +--S 2531 of 3330 +t0000:=x^(3/2)*sqrt(a+b*x) +--R +--R +--R +-+ +-------+ +--R (1) x\|x \|b x + a +--R Type: Expression(Integer) +--E 2531 + +--S 2532 of 3330 +r0000:=1/8*a^3*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+_ + 1/12*a*x^(3/2)*sqrt(a+b*x)/b+1/3*x^(5/2)*sqrt(a+b*x)-_ + 1/8*a^2*sqrt(x)*sqrt(a+b*x)/b^2 +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R 3a atanh(----------) + (8b x + 2a b x - 3a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) --------------------------------------------------------------- +--R 2 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 2532 + +--S 2533 of 3330 +--a0000:=integrate(t0000,x) +--E 2533 + +--S 2534 of 3330 +--m0000:=a0000 - r0000 +--E 2534 + +--S 2535 of 3330 +--d0000:=D(m0000,x) +--E 2535 + +)clear all + +--S 2536 of 3330 +t0000:=sqrt(x)*sqrt(a+b*x) +--R +--R +--R +-+ +-------+ +--R (1) \|x \|b x + a +--R Type: Expression(Integer) +--E 2536 + +--S 2537 of 3330 +r0000:=-1/4*a^2*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+_ + 1/2*x^(3/2)*sqrt(a+b*x)+1/4*a*sqrt(x)*sqrt(a+b*x)/b +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R - a atanh(----------) + (2b x + a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) ---------------------------------------------------- +--R +-+ +--R 4b\|b +--R Type: Expression(Integer) +--E 2537 + +--S 2538 of 3330 +--a0000:=integrate(t0000,x) +--E 2538 + +--S 2539 of 3330 +--m0000:=a0000 - r0000 +--E 2539 + +--S 2540 of 3330 +--d0000:=D(m0000,x) +--E 2540 + +)clear all + +--S 2541 of 3330 +t0000:=sqrt(a+b*x)/sqrt(x) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2541 + +--S 2542 of 3330 +r0000:=a*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b)+sqrt(x)*sqrt(a+b*x) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R a atanh(----------) + \|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) ---------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 2542 + +--S 2543 of 3330 +--a0000:=integrate(t0000,x) +--E 2543 + +--S 2544 of 3330 +--m0000:=a0000 - r0000 +--E 2544 + +--S 2545 of 3330 +--d0000:=D(m0000,x) +--E 2545 + +)clear all + +--S 2546 of 3330 +t0000:=sqrt(a+b*x)/x^(3/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2546 + +--S 2547 of 3330 +r0000:=2*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))*sqrt(b)-2*sqrt(a+b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 2\|b \|x atanh(----------) - 2\|b x + a +--R +-------+ +--R \|b x + a +--R (2) ---------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2547 + +--S 2548 of 3330 +--a0000:=integrate(t0000,x) +--E 2548 + +--S 2549 of 3330 +--m0000:=a0000 - r0000 +--E 2549 + +--S 2550 of 3330 +--d0000:=D(m0000,x) +--E 2550 + +)clear all + +--S 2551 of 3330 +t0000:=sqrt(a+b*x)/x^(5/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2551 + +--S 2552 of 3330 +r0000:=-2/3*(a+b*x)^(3/2)/(a*x^(3/2)) +--R +--R +--R +-------+ +--R (- 2b x - 2a)\|b x + a +--R (2) ----------------------- +--R +-+ +--R 3a x\|x +--R Type: Expression(Integer) +--E 2552 + +--S 2553 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-------+ 2 2 2 +--R (- 4b x - 4a)\|x \|b x + a + (- b + (- 2a - 4)b - a - 4a)x +--R (3) -------------------------------------------------------------- +--R 2 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 2553 + +--S 2554 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R - b + (- 2a - 4)b - a - 4a +--R (4) ---------------------------- +--R 6a +--R Type: Expression(Integer) +--E 2554 + +--S 2555 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2555 + +)clear all + +--S 2556 of 3330 +t0000:=sqrt(a+b*x)/x^(7/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2556 + +--S 2557 of 3330 +r0000:=-2/5*(a+b*x)^(3/2)/(a*x^(5/2))+4/15*b*(a+b*x)^(3/2)/(a^2*x^(3/2)) +--R +--R +--R 2 2 2 +-------+ +--R (4b x - 2a b x - 6a )\|b x + a +--R (2) -------------------------------- +--R 2 2 +-+ +--R 15a x \|x +--R Type: Expression(Integer) +--E 2557 + +--S 2558 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 +-+ +-------+ +--R (4b x - 2a b x - 6a )\|x \|b x + a +--R + +--R 3 2 2 3 2 3 +--R (2b + (a + 2)b + (- 4a - a)b - 3a - 3a )x +--R / +--R 2 3 +--R 15a x +--R Type: Union(Expression(Integer),...) +--E 2558 + +--S 2559 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 2 3 2 +--R 2b + (a + 2)b + (- 4a - a)b - 3a - 3a +--R (4) ------------------------------------------ +--R 2 +--R 15a +--R Type: Expression(Integer) +--E 2559 + +--S 2560 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2560 + +)clear all + +--S 2561 of 3330 +t0000:=sqrt(a+b*x)/x^(9/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2561 + +--S 2562 of 3330 +r0000:=-2/7*(a+b*x)^(3/2)/(a*x^(7/2))+8/35*b*(a+b*x)^(3/2)/(a^2*x^(5/2))-_ + 16/105*b^2*(a+b*x)^(3/2)/(a^3*x^(3/2)) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (- 16b x + 8a b x - 6a b x - 30a )\|b x + a +--R (2) ---------------------------------------------- +--R 3 3 +-+ +--R 105a x \|x +--R Type: Expression(Integer) +--E 2562 + +--S 2563 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +-------+ +--R (- 80b x + 40a b x - 30a b x - 150a )\|x \|b x + a +--R + +--R 4 3 2 2 3 2 4 +--R - 8b + (- 4a - 200)b + (a + 100a)b + (- 18a - 75a )b - 15a +--R + +--R 3 +--R - 375a +--R * +--R 4 +--R x +--R / +--R 3 4 +--R 525a x +--R Type: Union(Expression(Integer),...) +--E 2563 + +--S 2564 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 4 3 2 2 3 2 4 3 +--R - 8b + (- 4a - 200)b + (a + 100a)b + (- 18a - 75a )b - 15a - 375a +--R ------------------------------------------------------------------------ +--R 3 +--R 525a +--R Type: Expression(Integer) +--E 2564 + +--S 2565 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2565 + +)clear all + +--S 2566 of 3330 +t0000:=x^(5/2)*sqrt(a-b*x) +--R +--R +--R 2 +---------+ +-+ +--R (1) x \|- b x + a \|x +--R Type: Expression(Integer) +--E 2566 + +--S 2567 of 3330 +r0000:=5/64*a^4*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)-_ + 5/96*a^2*x^(3/2)*sqrt(a-b*x)/b^2-1/24*a*x^(5/2)*sqrt(a-b*x)/b+_ + 1/4*x^(7/2)*sqrt(a-b*x)-5/64*a^3*sqrt(x)*sqrt(a-b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 4 \|b \|x +--R 15a atan(------------) +--R +---------+ +--R \|- b x + a +--R + +--R 3 3 2 2 2 3 +---------+ +-+ +-+ +--R (48b x - 8a b x - 10a b x - 15a )\|- b x + a \|b \|x +--R / +--R 3 +-+ +--R 192b \|b +--R Type: Expression(Integer) +--E 2567 + +--S 2568 of 3330 +--a0000:=integrate(t0000,x) +--E 2568 + +--S 2569 of 3330 +--m0000:=a0000 - r0000 +--E 2569 + +--S 2570 of 3330 +--d0000:=D(m0000,x) +--E 2570 + +)clear all + +--S 2571 of 3330 +t0000:=x^(3/2)*sqrt(a-b*x) +--R +--R +--R +---------+ +-+ +--R (1) x\|- b x + a \|x +--R Type: Expression(Integer) +--E 2571 + +--S 2572 of 3330 +r0000:=1/8*a^3*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)-_ + 1/12*a*x^(3/2)*sqrt(a-b*x)/b+1/3*x^(5/2)*sqrt(a-b*x)-_ + 1/8*a^2*sqrt(x)*sqrt(a-b*x)/b^2 +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +---------+ +-+ +-+ +--R 3a atan(------------) + (8b x - 2a b x - 3a )\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (2) ------------------------------------------------------------------ +--R 2 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 2572 + +--S 2573 of 3330 +--a0000:=integrate(t0000,x) +--E 2573 + +--S 2574 of 3330 +--m0000:=a0000 - r0000 +--E 2574 + +--S 2575 of 3330 +--d0000:=D(m0000,x) +--E 2575 + +)clear all + +--S 2576 of 3330 +t0000:=sqrt(x)*sqrt(a-b*x) +--R +--R +--R +---------+ +-+ +--R (1) \|- b x + a \|x +--R Type: Expression(Integer) +--E 2576 + +--S 2577 of 3330 +r0000:=1/4*a^2*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(3/2)+_ + 1/2*x^(3/2)*sqrt(a-b*x)-1/4*a*sqrt(x)*sqrt(a-b*x)/b +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +---------+ +-+ +-+ +--R a atan(------------) + (2b x - a)\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (2) ----------------------------------------------------- +--R +-+ +--R 4b\|b +--R Type: Expression(Integer) +--E 2577 + +--S 2578 of 3330 +--a0000:=integrate(t0000,x) +--E 2578 + +--S 2579 of 3330 +--m0000:=a0000 - r0000 +--E 2579 + +--S 2580 of 3330 +--d0000:=D(m0000,x) +--E 2580 + +)clear all + +--S 2581 of 3330 +t0000:=sqrt(a-b*x)/sqrt(x) +--R +--R +--R +---------+ +--R \|- b x + a +--R (1) ------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2581 + +--S 2582 of 3330 +r0000:=a*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/sqrt(b)+sqrt(x)*sqrt(a-b*x) +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R a atan(------------) + \|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (2) ------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 2582 + +--S 2583 of 3330 +--a0000:=integrate(t0000,x) +--E 2583 + +--S 2584 of 3330 +--m0000:=a0000 - r0000 +--E 2584 + +--S 2585 of 3330 +--d0000:=D(m0000,x) +--E 2585 + +)clear all + +--S 2586 of 3330 +t0000:=sqrt(a-b*x)/x^(3/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (1) ------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2586 + +--S 2587 of 3330 +r0000:=-2*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))*sqrt(b)-2*sqrt(a-b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R - 2\|b \|x atan(------------) - 2\|- b x + a +--R +---------+ +--R \|- b x + a +--R (2) --------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2587 + +--S 2588 of 3330 +--a0000:=integrate(t0000,x) +--E 2588 + +--S 2589 of 3330 +--m0000:=a0000 - r0000 +--E 2589 + +--S 2590 of 3330 +--d0000:=D(m0000,x) +--E 2590 + +)clear all + +--S 2591 of 3330 +t0000:=sqrt(a-b*x)/x^(5/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (1) ------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2591 + +--S 2592 of 3330 +r0000:=-2/3*(a-b*x)^(3/2)/(a*x^(3/2)) +--R +--R +--R +---------+ +--R (2b x - 2a)\|- b x + a +--R (2) ----------------------- +--R +-+ +--R 3a x\|x +--R Type: Expression(Integer) +--E 2592 + +--S 2593 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +---------+ +-+ 2 2 2 +--R (10b x - 10a)\|- b x + a \|x + (25b + (- 50a - 1)b + 25a + a)x +--R (3) ------------------------------------------------------------------ +--R 2 +--R 15a x +--R Type: Union(Expression(Integer),...) +--E 2593 + +--S 2594 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R 25b + (- 50a - 1)b + 25a + a +--R (4) ------------------------------ +--R 15a +--R Type: Expression(Integer) +--E 2594 + +--S 2595 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2595 + +)clear all + +--S 2596 of 3330 +t0000:=sqrt(a-b*x)/x^(7/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (1) ------------ +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2596 + +--S 2597 of 3330 +r0000:=-2/5*(a-b*x)^(3/2)/(a*x^(5/2))-4/15*b*(a-b*x)^(3/2)/(a^2*x^(3/2)) +--R +--R +--R 2 2 2 +---------+ +--R (4b x + 2a b x - 6a )\|- b x + a +--R (2) ---------------------------------- +--R 2 2 +-+ +--R 15a x \|x +--R Type: Expression(Integer) +--E 2597 + +--S 2598 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 +---------+ +-+ +--R (8b x + 4a b x - 12a )\|- b x + a \|x +--R + +--R 3 2 2 3 2 3 +--R (8b + (- 4a - 2)b + (- 16a - a)b + 12a + 3a )x +--R / +--R 2 3 +--R 30a x +--R Type: Union(Expression(Integer),...) +--E 2598 + +--S 2599 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 2 3 2 +--R 8b + (- 4a - 2)b + (- 16a - a)b + 12a + 3a +--R (4) ----------------------------------------------- +--R 2 +--R 30a +--R Type: Expression(Integer) +--E 2599 + +--S 2600 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2600 + +)clear all + +--S 2601 of 3330 +t0000:=sqrt(a-b*x)/x^(9/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (1) ------------ +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2601 + +--S 2602 of 3330 +r0000:=-2/7*(a-b*x)^(3/2)/(a*x^(7/2))-8/35*b*(a-b*x)^(3/2)/(a^2*x^(5/2))-_ + 16/105*b^2*(a-b*x)^(3/2)/(a^3*x^(3/2)) +--R +--R +--R 3 3 2 2 2 3 +---------+ +--R (16b x + 8a b x + 6a b x - 30a )\|- b x + a +--R (2) ---------------------------------------------- +--R 3 3 +-+ +--R 105a x \|x +--R Type: Expression(Integer) +--E 2602 + +--S 2603 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +---------+ +-+ +--R (48b x + 24a b x + 18a b x - 90a )\|- b x + a \|x +--R + +--R 4 3 2 2 3 2 4 3 4 +--R (72b + (- 36a - 8)b + (- 9a - 4a)b + (- 162a - 3a )b + 135a + 15a )x +--R / +--R 3 4 +--R 315a x +--R Type: Union(Expression(Integer),...) +--E 2603 + +--S 2604 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 4 3 2 2 3 2 4 3 +--R 72b + (- 36a - 8)b + (- 9a - 4a)b + (- 162a - 3a )b + 135a + 15a +--R ----------------------------------------------------------------------- +--R 3 +--R 315a +--R Type: Expression(Integer) +--E 2604 + +--S 2605 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2605 + +)clear all + +--S 2606 of 3330 +t0000:=x^(5/2)*sqrt(2+b*x) +--R +--R +--R 2 +-+ +-------+ +--R (1) x \|x \|b x + 2 +--R Type: Expression(Integer) +--E 2606 + +--S 2607 of 3330 +r0000:=-5/4*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 5/24*x^(3/2)*sqrt(2+b*x)/b^2+1/12*x^(5/2)*sqrt(2+b*x)/b+_ + 1/4*x^(7/2)*sqrt(2+b*x)+5/8*sqrt(x)*sqrt(2+b*x)/b^3 +--R +--R +--R +-+ +-+ +--R \|b \|x 3 3 2 2 +-+ +-+ +-------+ +--R - 30asinh(--------) + (6b x + 2b x - 5b x + 15)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------------- +--R 3 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 2607 + +--S 2608 of 3330 +--a0000:=integrate(t0000,x) +--E 2608 + +--S 2609 of 3330 +--m0000:=a0000 - r0000 +--E 2609 + +--S 2610 of 3330 +--d0000:=D(m0000,x) +--E 2610 + +)clear all + +--S 2611 of 3330 +t0000:=x^(3/2)*sqrt(2+b*x) +--R +--R +--R +-+ +-------+ +--R (1) x\|x \|b x + 2 +--R Type: Expression(Integer) +--E 2611 + +--S 2612 of 3330 +r0000:=asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)+1/6*x^(3/2)*sqrt(2+b*x)/b+_ + 1/3*x^(5/2)*sqrt(2+b*x)-1/2*sqrt(x)*sqrt(2+b*x)/b^2 +--R +--R +--R +-+ +-+ +--R \|b \|x 2 2 +-+ +-+ +-------+ +--R 6asinh(--------) + (2b x + b x - 3)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------ +--R 2 +-+ +--R 6b \|b +--R Type: Expression(Integer) +--E 2612 + +--S 2613 of 3330 +--a0000:=integrate(t0000,x) +--E 2613 + +--S 2614 of 3330 +--m0000:=a0000 - r0000 +--E 2614 + +--S 2615 of 3330 +--d0000:=D(m0000,x) +--E 2615 + +)clear all + +--S 2616 of 3330 +t0000:=sqrt(x)*sqrt(2+b*x) +--R +--R +--R +-+ +-------+ +--R (1) \|x \|b x + 2 +--R Type: Expression(Integer) +--E 2616 + +--S 2617 of 3330 +r0000:=-asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+1/2*x^(3/2)*sqrt(2+b*x)+_ + 1/2*sqrt(x)*sqrt(2+b*x)/b +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R - 2asinh(--------) + (b x + 1)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) ------------------------------------------------ +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 2617 + +--S 2618 of 3330 +--a0000:=integrate(t0000,x) +--E 2618 + +--S 2619 of 3330 +--m0000:=a0000 - r0000 +--E 2619 + +--S 2620 of 3330 +--d0000:=D(m0000,x) +--E 2620 + +)clear all + +--S 2621 of 3330 +t0000:=sqrt(2+b*x)/sqrt(x) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (1) ---------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2621 + +--S 2622 of 3330 +r0000:=2*asinh(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+sqrt(x)*sqrt(2+b*x) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R 2asinh(--------) + \|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) ------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 2622 + +--S 2623 of 3330 +--a0000:=integrate(t0000,x) +--E 2623 + +--S 2624 of 3330 +--m0000:=a0000 - r0000 +--E 2624 + +--S 2625 of 3330 +--d0000:=D(m0000,x) +--E 2625 + +)clear all + +--S 2626 of 3330 +t0000:=sqrt(2+b*x)/x^(3/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (1) ---------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2626 + +--S 2627 of 3330 +r0000:=2*asinh(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-2*sqrt(2+b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 2\|b \|x asinh(--------) - 2\|b x + 2 +--R +-+ +--R \|2 +--R (2) -------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2627 + +--S 2628 of 3330 +--a0000:=integrate(t0000,x) +--E 2628 + +--S 2629 of 3330 +--m0000:=a0000 - r0000 +--E 2629 + +--S 2630 of 3330 +--d0000:=D(m0000,x) +--E 2630 + +)clear all + +--S 2631 of 3330 +t0000:=sqrt(2+b*x)/x^(5/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (1) ---------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2631 + +--S 2632 of 3330 +r0000:=-1/3*(2+b*x)^(3/2)/x^(3/2) +--R +--R +--R +-------+ +--R (- b x - 2)\|b x + 2 +--R (2) --------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2632 + +--S 2633 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-------+ 2 2 +--R (- 8b x - 16)\|x \|b x + 2 + (- b - 20b - 36)x +--R (3) ------------------------------------------------- +--R 2 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 2633 + +--S 2634 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R - b - 20b - 36 +--R (4) --------------- +--R 24 +--R Type: Expression(Integer) +--E 2634 + +--S 2635 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2635 + +)clear all + +--S 2636 of 3330 +t0000:=sqrt(2+b*x)/x^(7/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (1) ---------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2636 + +--S 2637 of 3330 +r0000:=-1/5*(2+b*x)^(3/2)/x^(5/2)+1/15*b*(2+b*x)^(3/2)/x^(3/2) +--R +--R +--R 2 2 +-------+ +--R (b x - b x - 6)\|b x + 2 +--R (2) -------------------------- +--R 2 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 2637 + +--S 2638 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 +-+ +-------+ 3 2 3 +--R (2b x - 2b x - 12)\|x \|b x + 2 + (b + 2b - 9b - 18)x +--R (3) ---------------------------------------------------------- +--R 3 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 2638 + +--S 2639 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 +--R b + 2b - 9b - 18 +--R (4) ------------------ +--R 30 +--R Type: Expression(Integer) +--E 2639 + +--S 2640 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2640 + +)clear all + +--S 2641 of 3330 +t0000:=sqrt(2+b*x)/x^(9/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (1) ---------- +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2641 + +--S 2642 of 3330 +r0000:=-1/7*(2+b*x)^(3/2)/x^(7/2)+2/35*b*(2+b*x)^(3/2)/x^(5/2)-_ + 2/105*b^2*(2+b*x)^(3/2)/x^(3/2) +--R +--R +--R 3 3 2 2 +-------+ +--R (- 2b x + 2b x - 3b x - 30)\|b x + 2 +--R (2) --------------------------------------- +--R 3 +-+ +--R 105x \|x +--R Type: Expression(Integer) +--E 2642 + +--S 2643 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 +-+ +-------+ +--R (- 12b x + 12b x - 18b x - 180)\|x \|b x + 2 +--R + +--R 4 3 2 4 +--R (- 2b - 20b + 19b - 63b - 330)x +--R / +--R 4 +--R 630x +--R Type: Union(Expression(Integer),...) +--E 2643 + +--S 2644 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 4 3 2 +--R - 2b - 20b + 19b - 63b - 330 +--R (4) ------------------------------- +--R 630 +--R Type: Expression(Integer) +--E 2644 + +--S 2645 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2645 + +)clear all + +--S 2646 of 3330 +t0000:=x^(5/2)*sqrt(2-b*x) +--R +--R +--R 2 +---------+ +-+ +--R (1) x \|- b x + 2 \|x +--R Type: Expression(Integer) +--E 2646 + +--S 2647 of 3330 +r0000:=5/4*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 5/24*x^(3/2)*sqrt(2-b*x)/b^2-1/12*x^(5/2)*sqrt(2-b*x)/b+_ + 1/4*x^(7/2)*sqrt(2-b*x)-5/8*sqrt(x)*sqrt(2-b*x)/b^3 +--R +--R +--R +-+ +-+ +--R \|b \|x 3 3 2 2 +---------+ +-+ +-+ +--R 30asin(--------) + (6b x - 2b x - 5b x - 15)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------------ +--R 3 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 2647 + +--S 2648 of 3330 +--a0000:=integrate(t0000,x) +--E 2648 + +--S 2649 of 3330 +--m0000:=a0000 - r0000 +--E 2649 + +--S 2650 of 3330 +--d0000:=D(m0000,x) +--E 2650 + +)clear all + +--S 2651 of 3330 +t0000:=x^(3/2)*sqrt(2-b*x) +--R +--R +--R +---------+ +-+ +--R (1) x\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 2651 + +--S 2652 of 3330 +r0000:=asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-_ + 1/6*x^(3/2)*sqrt(2-b*x)/b+1/3*x^(5/2)*sqrt(2-b*x)-_ + 1/2*sqrt(x)*sqrt(2-b*x)/b^2 +--R +--R +--R +-+ +-+ +--R \|b \|x 2 2 +---------+ +-+ +-+ +--R 6asin(--------) + (2b x - b x - 3)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------- +--R 2 +-+ +--R 6b \|b +--R Type: Expression(Integer) +--E 2652 + +--S 2653 of 3330 +--a0000:=integrate(t0000,x) +--E 2653 + +--S 2654 of 3330 +--m0000:=a0000 - r0000 +--E 2654 + +--S 2655 of 3330 +--d0000:=D(m0000,x) +--E 2655 + +)clear all + +--S 2656 of 3330 +t0000:=sqrt(x)*sqrt(2-b*x) +--R +--R +--R +---------+ +-+ +--R (1) \|- b x + 2 \|x +--R Type: Expression(Integer) +--E 2656 + +--S 2657 of 3330 +r0000:=asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+1/2*x^(3/2)*sqrt(2-b*x)-_ + 1/2*sqrt(x)*sqrt(2-b*x)/b +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R 2asin(--------) + (b x - 1)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) ----------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 2657 + +--S 2658 of 3330 +--a0000:=integrate(t0000,x) +--E 2658 + +--S 2659 of 3330 +--m0000:=a0000 - r0000 +--E 2659 + +--S 2660 of 3330 +--d0000:=D(m0000,x) +--E 2660 + +)clear all + +--S 2661 of 3330 +t0000:=sqrt(2-b*x)/sqrt(x) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (1) ------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2661 + +--S 2662 of 3330 +r0000:=2*asin(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+sqrt(x)*sqrt(2-b*x) +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R 2asin(--------) + \|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) -------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 2662 + +--S 2663 of 3330 +--a0000:=integrate(t0000,x) +--E 2663 + +--S 2664 of 3330 +--m0000:=a0000 - r0000 +--E 2664 + +--S 2665 of 3330 +--d0000:=D(m0000,x) +--E 2665 + +)clear all + +--S 2666 of 3330 +t0000:=sqrt(2-b*x)/x^(3/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (1) ------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2666 + +--S 2667 of 3330 +r0000:=-2*asin(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-2*sqrt(2-b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R - 2\|b \|x asin(--------) - 2\|- b x + 2 +--R +-+ +--R \|2 +--R (2) ----------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2667 + +--S 2668 of 3330 +--a0000:=integrate(t0000,x) +--E 2668 + +--S 2669 of 3330 +--m0000:=a0000 - r0000 +--E 2669 + +--S 2670 of 3330 +--d0000:=D(m0000,x) +--E 2670 + +)clear all + +--S 2671 of 3330 +t0000:=sqrt(2-b*x)/x^(5/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (1) ------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2671 + +--S 2672 of 3330 +r0000:=-1/3*(2-b*x)^(3/2)/x^(3/2) +--R +--R +--R +---------+ +--R (b x - 2)\|- b x + 2 +--R (2) --------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2672 + +--S 2673 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +---------+ +-+ 2 2 +--R (8b x - 16)\|- b x + 2 \|x + (- 16b + 65b - 66)x +--R (3) --------------------------------------------------- +--R 2 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 2673 + +--S 2674 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R - 16b + 65b - 66 +--R (4) ----------------- +--R 24 +--R Type: Expression(Integer) +--E 2674 + +--S 2675 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2675 + +)clear all + +--S 2676 of 3330 +t0000:=sqrt(2-b*x)/x^(7/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (1) ------------ +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2676 + +--S 2677 of 3330 +r0000:=-1/5*(2-b*x)^(3/2)/x^(5/2)-1/15*b*(2-b*x)^(3/2)/x^(3/2) +--R +--R +--R 2 2 +---------+ +--R (b x + b x - 6)\|- b x + 2 +--R (2) ---------------------------- +--R 2 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 2677 + +--S 2678 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 +---------+ +-+ 3 2 3 +--R (2b x + 2b x - 12)\|- b x + 2 \|x + (- b + 2b + 9b - 18)x +--R (3) -------------------------------------------------------------- +--R 3 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 2678 + +--S 2679 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 +--R - b + 2b + 9b - 18 +--R (4) -------------------- +--R 30 +--R Type: Expression(Integer) +--E 2679 + +--S 2680 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2680 + +)clear all + +--S 2681 of 3330 +t0000:=sqrt(2-b*x)/x^(9/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (1) ------------ +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2681 + +--S 2682 of 3330 +r0000:=-1/7*(2-b*x)^(3/2)/x^(7/2)-2/35*b*(2-b*x)^(3/2)/x^(5/2)-_ + 2/105*b^2*(2-b*x)^(3/2)/x^(3/2) +--R +--R +--R 3 3 2 2 +---------+ +--R (2b x + 2b x + 3b x - 30)\|- b x + 2 +--R (2) --------------------------------------- +--R 3 +-+ +--R 105x \|x +--R Type: Expression(Integer) +--E 2682 + +--S 2683 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 +---------+ +-+ 4 3 2 4 +--R (4b x + 4b x + 6b x - 60)\|- b x + 2 \|x + (2b - 4b - 3b - 39b + 90)x +--R ---------------------------------------------------------------------------- +--R 4 +--R 210x +--R Type: Union(Expression(Integer),...) +--E 2683 + +--S 2684 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 4 3 2 +--R 2b - 4b - 3b - 39b + 90 +--R (4) -------------------------- +--R 210 +--R Type: Expression(Integer) +--E 2684 + +--S 2685 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2685 + +)clear all + +--S 2686 of 3330 +t0000:=x^(5/2)*(a+b*x)^(3/2) +--R +--R +--R 3 2 +-+ +-------+ +--R (1) (b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 2686 + +--S 2687 of 3330 +r0000:=1/5*x^(7/2)*(a+b*x)^(3/2)-_ + 3/128*a^5*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-_ + 1/64*a^3*x^(3/2)*sqrt(a+b*x)/b^2+1/80*a^2*x^(5/2)*sqrt(a+b*x)/b+_ + 3/40*a*x^(7/2)*sqrt(a+b*x)+3/128*a^4*sqrt(x)*sqrt(a+b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 5 \|b \|x +--R - 15a atanh(----------) +--R +-------+ +--R \|b x + a +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +-+ +-------+ +--R (128b x + 176a b x + 8a b x - 10a b x + 15a )\|b \|x \|b x + a +--R / +--R 3 +-+ +--R 640b \|b +--R Type: Expression(Integer) +--E 2687 + +--S 2688 of 3330 +--a0000:=integrate(t0000,x) +--E 2688 + +--S 2689 of 3330 +--m0000:=a0000 - r0000 +--E 2689 + +--S 2690 of 3330 +--d0000:=D(m0000,x) +--E 2690 + +)clear all + +--S 2691 of 3330 +t0000:=x^(3/2)*(a+b*x)^(3/2) +--R +--R +--R 2 +-+ +-------+ +--R (1) (b x + a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 2691 + +--S 2692 of 3330 +r0000:=1/4*x^(5/2)*(a+b*x)^(3/2)+_ + 3/64*a^4*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+_ + 1/32*a^2*x^(3/2)*sqrt(a+b*x)/b+1/8*a*x^(5/2)*sqrt(a+b*x)-_ + 3/64*a^3*sqrt(x)*sqrt(a+b*x)/b^2 +--R +--R +--R (2) +--R +-+ +-+ +--R 4 \|b \|x 3 3 2 2 2 3 +-+ +-+ +-------+ +--R 3a atanh(----------) + (16b x + 24a b x + 2a b x - 3a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R --------------------------------------------------------------------------- +--R 2 +-+ +--R 64b \|b +--R Type: Expression(Integer) +--E 2692 + +--S 2693 of 3330 +--a0000:=integrate(t0000,x) +--E 2693 + +--S 2694 of 3330 +--m0000:=a0000 - r0000 +--E 2694 + +--S 2695 of 3330 +--d0000:=D(m0000,x) +--E 2695 + +)clear all + +--S 2696 of 3330 +t0000:=(a+b*x)^(3/2)*sqrt(x) +--R +--R +--R +-+ +-------+ +--R (1) (b x + a)\|x \|b x + a +--R Type: Expression(Integer) +--E 2696 + +--S 2697 of 3330 +r0000:=1/3*x^(3/2)*(a+b*x)^(3/2)-_ + 1/8*a^3*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+_ + 1/4*a*x^(3/2)*sqrt(a+b*x)+1/8*a^2*sqrt(x)*sqrt(a+b*x)/b +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R - 3a atanh(----------) + (8b x + 14a b x + 3a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) ------------------------------------------------------------------ +--R +-+ +--R 24b\|b +--R Type: Expression(Integer) +--E 2697 + +--S 2698 of 3330 +--a0000:=integrate(t0000,x) +--E 2698 + +--S 2699 of 3330 +--m0000:=a0000 - r0000 +--E 2699 + +--S 2700 of 3330 +--d0000:=D(m0000,x) +--E 2700 + +)clear all + +--S 2701 of 3330 +t0000:=(a+b*x)^(3/2)/sqrt(x) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2701 + +--S 2702 of 3330 +r0000:=3/4*a^2*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b)+_ + 1/2*(a+b*x)^(3/2)*sqrt(x)+3/4*a*sqrt(x)*sqrt(a+b*x) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R 3a atanh(----------) + (2b x + 5a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) ---------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression(Integer) +--E 2702 + +--S 2703 of 3330 +--a0000:=integrate(t0000,x) +--E 2703 + +--S 2704 of 3330 +--m0000:=a0000 - r0000 +--E 2704 + +--S 2705 of 3330 +--d0000:=D(m0000,x) +--E 2705 + +)clear all + +--S 2706 of 3330 +t0000:=(a+b*x)^(3/2)/x^(3/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2706 + +--S 2707 of 3330 +r0000:=3*a*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))*sqrt(b)-_ + 2*(a+b*x)^(3/2)/sqrt(x)+3*b*sqrt(x)*sqrt(a+b*x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 3a\|b \|x atanh(----------) + (b x - 2a)\|b x + a +--R +-------+ +--R \|b x + a +--R (2) -------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2707 + +--S 2708 of 3330 +--a0000:=integrate(t0000,x) +--E 2708 + +--S 2709 of 3330 +--m0000:=a0000 - r0000 +--E 2709 + +--S 2710 of 3330 +--d0000:=D(m0000,x) +--E 2710 + +)clear all + +--S 2711 of 3330 +t0000:=(a+b*x)^(3/2)/x^(5/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2711 + +--S 2712 of 3330 +r0000:=-2/3*(a+b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))-2*b*sqrt(a+b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 6b x\|b \|x atanh(----------) + (- 8b x - 2a)\|b x + a +--R +-------+ +--R \|b x + a +--R (2) ------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2712 + +--S 2713 of 3330 +--a0000:=integrate(t0000,x) +--E 2713 + +--S 2714 of 3330 +--m0000:=a0000 - r0000 +--E 2714 + +--S 2715 of 3330 +--d0000:=D(m0000,x) +--E 2715 + +)clear all + +--S 2716 of 3330 +t0000:=x^(5/2)*(a-b*x)^(3/2) +--R +--R +--R 3 2 +---------+ +-+ +--R (1) (- b x + a x )\|- b x + a \|x +--R Type: Expression(Integer) +--E 2716 + +--S 2717 of 3330 +r0000:=1/5*x^(7/2)*(a-b*x)^(3/2)+_ + 3/128*a^5*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)-_ + 1/64*a^3*x^(3/2)*sqrt(a-b*x)/b^2-1/80*a^2*x^(5/2)*sqrt(a-b*x)/b+_ + 3/40*a*x^(7/2)*sqrt(a-b*x)-3/128*a^4*sqrt(x)*sqrt(a-b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 5 \|b \|x +--R 15a atan(------------) +--R +---------+ +--R \|- b x + a +--R + +--R 4 4 3 3 2 2 2 3 4 +---------+ +-+ +-+ +--R (- 128b x + 176a b x - 8a b x - 10a b x - 15a )\|- b x + a \|b \|x +--R / +--R 3 +-+ +--R 640b \|b +--R Type: Expression(Integer) +--E 2717 + +--S 2718 of 3330 +--a0000:=integrate(t0000,x) +--E 2718 + +--S 2719 of 3330 +--m0000:=a0000 - r0000 +--E 2719 + +--S 2720 of 3330 +--d0000:=D(m0000,x) +--E 2720 + +)clear all + +--S 2721 of 3330 +t0000:=x^(3/2)*(a-b*x)^(3/2) +--R +--R +--R 2 +---------+ +-+ +--R (1) (- b x + a x)\|- b x + a \|x +--R Type: Expression(Integer) +--E 2721 + +--S 2722 of 3330 +r0000:=1/4*x^(5/2)*(a-b*x)^(3/2)+_ + 3/64*a^4*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)-_ + 1/32*a^2*x^(3/2)*sqrt(a-b*x)/b+1/8*a*x^(5/2)*sqrt(a-b*x)-_ + 3/64*a^3*sqrt(x)*sqrt(a-b*x)/b^2 +--R +--R +--R (2) +--R +-+ +-+ +--R 4 \|b \|x +--R 3a atan(------------) +--R +---------+ +--R \|- b x + a +--R + +--R 3 3 2 2 2 3 +---------+ +-+ +-+ +--R (- 16b x + 24a b x - 2a b x - 3a )\|- b x + a \|b \|x +--R / +--R 2 +-+ +--R 64b \|b +--R Type: Expression(Integer) +--E 2722 + +--S 2723 of 3330 +--a0000:=integrate(t0000,x) +--E 2723 + +--S 2724 of 3330 +--m0000:=a0000 - r0000 +--E 2724 + +--S 2725 of 3330 +--d0000:=D(m0000,x) +--E 2725 + +)clear all + +--S 2726 of 3330 +t0000:=(a-b*x)^(3/2)*sqrt(x) +--R +--R +--R +---------+ +-+ +--R (1) (- b x + a)\|- b x + a \|x +--R Type: Expression(Integer) +--E 2726 + +--S 2727 of 3330 +r0000:=1/3*x^(3/2)*(a-b*x)^(3/2)+_ + 1/8*a^3*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(3/2)+_ + 1/4*a*x^(3/2)*sqrt(a-b*x)-1/8*a^2*sqrt(x)*sqrt(a-b*x)/b +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +---------+ +-+ +-+ +--R 3a atan(------------) + (- 8b x + 14a b x - 3a )\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (2) --------------------------------------------------------------------- +--R +-+ +--R 24b\|b +--R Type: Expression(Integer) +--E 2727 + +--S 2728 of 3330 +--a0000:=integrate(t0000,x) +--E 2728 + +--S 2729 of 3330 +--m0000:=a0000 - r0000 +--E 2729 + +--S 2730 of 3330 +--d0000:=D(m0000,x) +--E 2730 + +)clear all + +--S 2731 of 3330 +t0000:=(a-b*x)^(3/2)/sqrt(x) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (1) ----------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2731 + +--S 2732 of 3330 +r0000:=3/4*a^2*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/sqrt(b)+_ + 1/2*(a-b*x)^(3/2)*sqrt(x)+3/4*a*sqrt(x)*sqrt(a-b*x) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +---------+ +-+ +-+ +--R 3a atan(------------) + (- 2b x + 5a)\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (2) --------------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression(Integer) +--E 2732 + +--S 2733 of 3330 +--a0000:=integrate(t0000,x) +--E 2733 + +--S 2734 of 3330 +--m0000:=a0000 - r0000 +--E 2734 + +--S 2735 of 3330 +--d0000:=D(m0000,x) +--E 2735 + +)clear all + +--S 2736 of 3330 +t0000:=(a-b*x)^(3/2)/x^(3/2) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (1) ----------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2736 + +--S 2737 of 3330 +r0000:=-3*a*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))*sqrt(b)-2*(a-b*x)^(3/2)/sqrt(x)-_ + 3*b*sqrt(x)*sqrt(a-b*x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R - 3a\|b \|x atan(------------) + (- b x - 2a)\|- b x + a +--R +---------+ +--R \|- b x + a +--R (2) --------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2737 + +--S 2738 of 3330 +--a0000:=integrate(t0000,x) +--E 2738 + +--S 2739 of 3330 +--m0000:=a0000 - r0000 +--E 2739 + +--S 2740 of 3330 +--d0000:=D(m0000,x) +--E 2740 + +)clear all + +--S 2741 of 3330 +t0000:=(a-b*x)^(3/2)/x^(5/2) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (1) ----------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2741 + +--S 2742 of 3330 +r0000:=-2/3*(a-b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))+2*b*sqrt(a-b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R 6b x\|b \|x atan(------------) + (8b x - 2a)\|- b x + a +--R +---------+ +--R \|- b x + a +--R (2) -------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2742 + +--S 2743 of 3330 +--a0000:=integrate(t0000,x) +--E 2743 + +--S 2744 of 3330 +--m0000:=a0000 - r0000 +--E 2744 + +--S 2745 of 3330 +--d0000:=D(m0000,x) +--E 2745 + +)clear all + +--S 2746 of 3330 +t0000:=x^(5/2)*(2+b*x)^(3/2) +--R +--R +--R 3 2 +-+ +-------+ +--R (1) (b x + 2x )\|x \|b x + 2 +--R Type: Expression(Integer) +--E 2746 + +--S 2747 of 3330 +r0000:=1/5*x^(7/2)*(2+b*x)^(3/2)-_ + 3/4*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 1/8*x^(3/2)*sqrt(2+b*x)/b^2+1/20*x^(5/2)*sqrt(2+b*x)/b+_ + 3/20*x^(7/2)*sqrt(2+b*x)+3/8*sqrt(x)*sqrt(2+b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R \|b \|x 4 4 3 3 2 2 +-+ +-+ +-------+ +--R - 30asinh(--------) + (8b x + 22b x + 2b x - 5b x + 15)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R ---------------------------------------------------------------------------- +--R 3 +-+ +--R 40b \|b +--R Type: Expression(Integer) +--E 2747 + +--S 2748 of 3330 +--a0000:=integrate(t0000,x) +--E 2748 + +--S 2749 of 3330 +--m0000:=a0000 - r0000 +--E 2749 + +--S 2750 of 3330 +--d0000:=D(m0000,x) +--E 2750 + +)clear all + +--S 2751 of 3330 +t0000:=x^(3/2)*(2+b*x)^(3/2) +--R +--R +--R 2 +-+ +-------+ +--R (1) (b x + 2x)\|x \|b x + 2 +--R Type: Expression(Integer) +--E 2751 + +--S 2752 of 3330 +r0000:=1/4*x^(5/2)*(2+b*x)^(3/2)+_ + 3/4*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)+_ + 1/8*x^(3/2)*sqrt(2+b*x)/b+1/4*x^(5/2)*sqrt(2+b*x)-_ + 3/8*sqrt(x)*sqrt(2+b*x)/b^2 +--R +--R +--R +-+ +-+ +--R \|b \|x 3 3 2 2 +-+ +-+ +-------+ +--R 6asinh(--------) + (2b x + 6b x + b x - 3)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) -------------------------------------------------------------- +--R 2 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 2752 + +--S 2753 of 3330 +--a0000:=integrate(t0000,x) +--E 2753 + +--S 2754 of 3330 +--m0000:=a0000 - r0000 +--E 2754 + +--S 2755 of 3330 +--d0000:=D(m0000,x) +--E 2755 + +)clear all + +--S 2756 of 3330 +t0000:=(2+b*x)^(3/2)*sqrt(x) +--R +--R +--R +-+ +-------+ +--R (1) (b x + 2)\|x \|b x + 2 +--R Type: Expression(Integer) +--E 2756 + +--S 2757 of 3330 +r0000:=1/3*x^(3/2)*(2+b*x)^(3/2)-asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+_ + 1/2*x^(3/2)*sqrt(2+b*x)+1/2*sqrt(x)*sqrt(2+b*x)/b +--R +--R +--R +-+ +-+ +--R \|b \|x 2 2 +-+ +-+ +-------+ +--R - 6asinh(--------) + (2b x + 7b x + 3)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) --------------------------------------------------------- +--R +-+ +--R 6b\|b +--R Type: Expression(Integer) +--E 2757 + +--S 2758 of 3330 +--a0000:=integrate(t0000,x) +--E 2758 + +--S 2759 of 3330 +--m0000:=a0000 - r0000 +--E 2759 + +--S 2760 of 3330 +--d0000:=D(m0000,x) +--E 2760 + +)clear all + +--S 2761 of 3330 +t0000:=(2+b*x)^(3/2)/sqrt(x) +--R +--R +--R +-------+ +--R (b x + 2)\|b x + 2 +--R (1) ------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2761 + +--S 2762 of 3330 +r0000:=3*asinh(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+_ + 1/2*(2+b*x)^(3/2)*sqrt(x)+3/2*sqrt(x)*sqrt(2+b*x) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R 6asinh(--------) + (b x + 5)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) ---------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 2762 + +--S 2763 of 3330 +--a0000:=integrate(t0000,x) +--E 2763 + +--S 2764 of 3330 +--m0000:=a0000 - r0000 +--E 2764 + +--S 2765 of 3330 +--d0000:=D(m0000,x) +--E 2765 + +)clear all + +--S 2766 of 3330 +t0000:=(2+b*x)^(3/2)/x^(3/2) +--R +--R +--R +-------+ +--R (b x + 2)\|b x + 2 +--R (1) ------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2766 + +--S 2767 of 3330 +r0000:=6*asinh(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-_ + 2*(2+b*x)^(3/2)/sqrt(x)+3*b*sqrt(x)*sqrt(2+b*x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 6\|b \|x asinh(--------) + (b x - 4)\|b x + 2 +--R +-+ +--R \|2 +--R (2) ---------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2767 + +--S 2768 of 3330 +--a0000:=integrate(t0000,x) +--E 2768 + +--S 2769 of 3330 +--m0000:=a0000 - r0000 +--E 2769 + +--S 2770 of 3330 +--d0000:=D(m0000,x) +--E 2770 + +)clear all + +--S 2771 of 3330 +t0000:=(2+b*x)^(3/2)/x^(5/2) +--R +--R +--R +-------+ +--R (b x + 2)\|b x + 2 +--R (1) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2771 + +--S 2772 of 3330 +r0000:=-2/3*(2+b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*asinh(sqrt(b)*sqrt(x)/sqrt(2))-2*b*sqrt(2+b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 6b x\|b \|x asinh(--------) + (- 8b x - 4)\|b x + 2 +--R +-+ +--R \|2 +--R (2) ---------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2772 + +--S 2773 of 3330 +--a0000:=integrate(t0000,x) +--E 2773 + +--S 2774 of 3330 +--m0000:=a0000 - r0000 +--E 2774 + +--S 2775 of 3330 +--d0000:=D(m0000,x) +--E 2775 + +)clear all + +--S 2776 of 3330 +t0000:=x^(5/2)*(2-b*x)^(3/2) +--R +--R +--R 3 2 +---------+ +-+ +--R (1) (- b x + 2x )\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 2776 + +--S 2777 of 3330 +r0000:=1/5*x^(7/2)*(2-b*x)^(3/2)+_ + 3/4*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 1/8*x^(3/2)*sqrt(2-b*x)/b^2-1/20*x^(5/2)*sqrt(2-b*x)/b+_ + 3/20*x^(7/2)*sqrt(2-b*x)-3/8*sqrt(x)*sqrt(2-b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R \|b \|x 4 4 3 3 2 2 +---------+ +-+ +-+ +--R 30asin(--------) + (- 8b x + 22b x - 2b x - 5b x - 15)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R ----------------------------------------------------------------------------- +--R 3 +-+ +--R 40b \|b +--R Type: Expression(Integer) +--E 2777 + +--S 2778 of 3330 +--a0000:=integrate(t0000,x) +--E 2778 + +--S 2779 of 3330 +--m0000:=a0000 - r0000 +--E 2779 + +--S 2780 of 3330 +--d0000:=D(m0000,x) +--E 2780 + +)clear all + +--S 2781 of 3330 +t0000:=x^(3/2)*(2-b*x)^(3/2) +--R +--R +--R 2 +---------+ +-+ +--R (1) (- b x + 2x)\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 2781 + +--S 2782 of 3330 +r0000:=1/4*x^(5/2)*(2-b*x)^(3/2)+3/4*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-_ + 1/8*x^(3/2)*sqrt(2-b*x)/b+1/4*x^(5/2)*sqrt(2-b*x)-_ + 3/8*sqrt(x)*sqrt(2-b*x)/b^2 +--R +--R +--R +-+ +-+ +--R \|b \|x 3 3 2 2 +---------+ +-+ +-+ +--R 6asin(--------) + (- 2b x + 6b x - b x - 3)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) ----------------------------------------------------------------- +--R 2 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 2782 + +--S 2783 of 3330 +--a0000:=integrate(t0000,x) +--E 2783 + +--S 2784 of 3330 +--m0000:=a0000 - r0000 +--E 2784 + +--S 2785 of 3330 +--d0000:=D(m0000,x) +--E 2785 + +)clear all + +--S 2786 of 3330 +t0000:=(2-b*x)^(3/2)*sqrt(x) +--R +--R +--R +---------+ +-+ +--R (1) (- b x + 2)\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 2786 + +--S 2787 of 3330 +r0000:=1/3*x^(3/2)*(2-b*x)^(3/2)+asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+_ + 1/2*x^(3/2)*sqrt(2-b*x)-1/2*sqrt(x)*sqrt(2-b*x)/b +--R +--R +--R +-+ +-+ +--R \|b \|x 2 2 +---------+ +-+ +-+ +--R 6asin(--------) + (- 2b x + 7b x - 3)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) ---------------------------------------------------------- +--R +-+ +--R 6b\|b +--R Type: Expression(Integer) +--E 2787 + +--S 2788 of 3330 +--a0000:=integrate(t0000,x) +--E 2788 + +--S 2789 of 3330 +--m0000:=a0000 - r0000 +--E 2789 + +--S 2790 of 3330 +--d0000:=D(m0000,x) +--E 2790 + +)clear all + +--S 2791 of 3330 +t0000:=(2-b*x)^(3/2)/sqrt(x) +--R +--R +--R +---------+ +--R (- b x + 2)\|- b x + 2 +--R (1) ----------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2791 + +--S 2792 of 3330 +r0000:=3*asin(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+1/2*(2-b*x)^(3/2)*sqrt(x)+_ + 3/2*sqrt(x)*sqrt(2-b*x) +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R 6asin(--------) + (- b x + 5)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) ------------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 2792 + +--S 2793 of 3330 +--a0000:=integrate(t0000,x) +--E 2793 + +--S 2794 of 3330 +--m0000:=a0000 - r0000 +--E 2794 + +--S 2795 of 3330 +--d0000:=D(m0000,x) +--E 2795 + +)clear all + +--S 2796 of 3330 +t0000:=(2-b*x)^(3/2)/x^(3/2) +--R +--R +--R +---------+ +--R (- b x + 2)\|- b x + 2 +--R (1) ----------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2796 + +--S 2797 of 3330 +r0000:=-6*asin(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-2*(2-b*x)^(3/2)/sqrt(x)-_ + 3*b*sqrt(x)*sqrt(2-b*x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R - 6\|b \|x asin(--------) + (- b x - 4)\|- b x + 2 +--R +-+ +--R \|2 +--R (2) --------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2797 + +--S 2798 of 3330 +--a0000:=integrate(t0000,x) +--E 2798 + +--S 2799 of 3330 +--m0000:=a0000 - r0000 +--E 2799 + +--S 2800 of 3330 +--d0000:=D(m0000,x) +--E 2800 + +)clear all + +--S 2801 of 3330 +t0000:=(2-b*x)^(3/2)/x^(5/2) +--R +--R +--R +---------+ +--R (- b x + 2)\|- b x + 2 +--R (1) ----------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2801 + +--S 2802 of 3330 +r0000:=-2/3*(2-b*x)^(3/2)/x^(3/2)+2*b^(3/2)*asin(sqrt(b)*sqrt(x)/sqrt(2))+_ + 2*b*sqrt(2-b*x)/sqrt(x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R 6b x\|b \|x asin(--------) + (8b x - 4)\|- b x + 2 +--R +-+ +--R \|2 +--R (2) --------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2802 + +--S 2803 of 3330 +--a0000:=integrate(t0000,x) +--E 2803 + +--S 2804 of 3330 +--m0000:=a0000 - r0000 +--E 2804 + +--S 2805 of 3330 +--d0000:=D(m0000,x) +--E 2805 + +)clear all + +--S 2806 of 3330 +t0000:=x^(5/2)*(a+b*x)^(5/2) +--R +--R +--R 2 4 3 2 2 +-+ +-------+ +--R (1) (b x + 2a b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 2806 + +--S 2807 of 3330 +r0000:=1/12*a*x^(7/2)*(a+b*x)^(3/2)+1/6*x^(7/2)*(a+b*x)^(5/2)-_ + 5/512*a^6*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-_ + 5/768*a^4*x^(3/2)*sqrt(a+b*x)/b^2+1/192*a^3*x^(5/2)*sqrt(a+b*x)/b+_ + 1/32*a^2*x^(7/2)*sqrt(a+b*x)+5/512*a^5*sqrt(x)*sqrt(a+b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 6 \|b \|x +--R - 15a atanh(----------) +--R +-------+ +--R \|b x + a +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-+ +-+ +--R (256b x + 640a b x + 432a b x + 8a b x - 10a b x + 15a )\|b \|x +--R * +--R +-------+ +--R \|b x + a +--R / +--R 3 +-+ +--R 1536b \|b +--R Type: Expression(Integer) +--E 2807 + +--S 2808 of 3330 +--a0000:=integrate(t0000,x) +--E 2808 + +--S 2809 of 3330 +--m0000:=a0000 - r0000 +--E 2809 + +--S 2810 of 3330 +--d0000:=D(m0000,x) +--E 2810 + +)clear all + +--S 2811 of 3330 +t0000:=x^(3/2)*(a+b*x)^(5/2) +--R +--R +--R 2 3 2 2 +-+ +-------+ +--R (1) (b x + 2a b x + a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 2811 + +--S 2812 of 3330 +r0000:=1/8*a*x^(5/2)*(a+b*x)^(3/2)+1/5*x^(5/2)*(a+b*x)^(5/2)+_ + 3/128*a^5*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+_ + 1/64*a^3*x^(3/2)*sqrt(a+b*x)/b+1/16*a^2*x^(5/2)*sqrt(a+b*x)-_ + 3/128*a^4*sqrt(x)*sqrt(a+b*x)/b^2 +--R +--R +--R (2) +--R +-+ +-+ +--R 5 \|b \|x +--R 15a atanh(----------) +--R +-------+ +--R \|b x + a +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +-+ +-------+ +--R (128b x + 336a b x + 248a b x + 10a b x - 15a )\|b \|x \|b x + a +--R / +--R 2 +-+ +--R 640b \|b +--R Type: Expression(Integer) +--E 2812 + +--S 2813 of 3330 +--a0000:=integrate(t0000,x) +--E 2813 + +--S 2814 of 3330 +--m0000:=a0000 - r0000 +--E 2814 + +--S 2815 of 3330 +--d0000:=D(m0000,x) +--E 2815 + +)clear all + +--S 2816 of 3330 +t0000:=(a+b*x)^(5/2)*sqrt(x) +--R +--R +--R 2 2 2 +-+ +-------+ +--R (1) (b x + 2a b x + a )\|x \|b x + a +--R Type: Expression(Integer) +--E 2816 + +--S 2817 of 3330 +r0000:=5/24*a*x^(3/2)*(a+b*x)^(3/2)+1/4*x^(3/2)*(a+b*x)^(5/2)-_ + 5/64*a^4*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+_ + 5/32*a^2*x^(3/2)*sqrt(a+b*x)+5/64*a^3*sqrt(x)*sqrt(a+b*x)/b +--R +--R +--R (2) +--R +-+ +-+ +--R 4 \|b \|x +--R - 15a atanh(----------) +--R +-------+ +--R \|b x + a +--R + +--R 3 3 2 2 2 3 +-+ +-+ +-------+ +--R (48b x + 136a b x + 118a b x + 15a )\|b \|x \|b x + a +--R / +--R +-+ +--R 192b\|b +--R Type: Expression(Integer) +--E 2817 + +--S 2818 of 3330 +--a0000:=integrate(t0000,x) +--E 2818 + +--S 2819 of 3330 +--m0000:=a0000 - r0000 +--E 2819 + +--S 2820 of 3330 +--d0000:=D(m0000,x) +--E 2820 + +)clear all + +--S 2821 of 3330 +t0000:=(a+b*x)^(5/2)/sqrt(x) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2821 + +--S 2822 of 3330 +r0000:=5/8*a^3*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b)+_ + 5/12*a*(a+b*x)^(3/2)*sqrt(x)+1/3*(a+b*x)^(5/2)*sqrt(x)+_ + 5/8*a^2*sqrt(x)*sqrt(a+b*x) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R 15a atanh(----------) + (8b x + 26a b x + 33a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) ------------------------------------------------------------------ +--R +-+ +--R 24\|b +--R Type: Expression(Integer) +--E 2822 + +--S 2823 of 3330 +--a0000:=integrate(t0000,x) +--E 2823 + +--S 2824 of 3330 +--m0000:=a0000 - r0000 +--E 2824 + +--S 2825 of 3330 +--d0000:=D(m0000,x) +--E 2825 + +)clear all + +--S 2826 of 3330 +t0000:=(a+b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2826 + +--S 2827 of 3330 +r0000:=15/4*a^2*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))*sqrt(b)-_ + 2*(a+b*x)^(5/2)/sqrt(x)+5/2*b*(a+b*x)^(3/2)*sqrt(x)+_ + 15/4*a*b*sqrt(x)*sqrt(a+b*x) +--R +--R +--R +-+ +-+ +--R 2 +-+ +-+ \|b \|x 2 2 2 +-------+ +--R 15a \|b \|x atanh(----------) + (2b x + 9a b x - 8a )\|b x + a +--R +-------+ +--R \|b x + a +--R (2) ---------------------------------------------------------------- +--R +-+ +--R 4\|x +--R Type: Expression(Integer) +--E 2827 + +--S 2828 of 3330 +--a0000:=integrate(t0000,x) +--E 2828 + +--S 2829 of 3330 +--m0000:=a0000 - r0000 +--E 2829 + +--S 2830 of 3330 +--d0000:=D(m0000,x) +--E 2830 + +)clear all + +--S 2831 of 3330 +t0000:=(a+b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2831 + +--S 2832 of 3330 +r0000:=-2/3*(a+b*x)^(5/2)/x^(3/2)+_ + 5*a*b^(3/2)*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))-_ + 10/3*b*(a+b*x)^(3/2)/sqrt(x)+5*b^2*sqrt(x)*sqrt(a+b*x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x 2 2 2 +-------+ +--R 15a b x\|b \|x atanh(----------) + (3b x - 14a b x - 2a )\|b x + a +--R +-------+ +--R \|b x + a +--R (2) -------------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2832 + +--S 2833 of 3330 +--a0000:=integrate(t0000,x) +--E 2833 + +--S 2834 of 3330 +--m0000:=a0000 - r0000 +--E 2834 + +--S 2835 of 3330 +--d0000:=D(m0000,x) +--E 2835 + +)clear all + +--S 2836 of 3330 +t0000:=x^(5/2)*(a-b*x)^(5/2) +--R +--R +--R 2 4 3 2 2 +---------+ +-+ +--R (1) (b x - 2a b x + a x )\|- b x + a \|x +--R Type: Expression(Integer) +--E 2836 + +--S 2837 of 3330 +r0000:=1/12*a*x^(7/2)*(a-b*x)^(3/2)+1/6*x^(7/2)*(a-b*x)^(5/2)+_ + 5/512*a^6*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)-_ + 5/768*a^4*x^(3/2)*sqrt(a-b*x)/b^2-1/192*a^3*x^(5/2)*sqrt(a-b*x)/b+_ + 1/32*a^2*x^(7/2)*sqrt(a-b*x)-5/512*a^5*sqrt(x)*sqrt(a-b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 6 \|b \|x +--R 15a atan(------------) +--R +---------+ +--R \|- b x + a +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (256b x - 640a b x + 432a b x - 8a b x - 10a b x - 15a ) +--R * +--R +---------+ +-+ +-+ +--R \|- b x + a \|b \|x +--R / +--R 3 +-+ +--R 1536b \|b +--R Type: Expression(Integer) +--E 2837 + +--S 2838 of 3330 +--a0000:=integrate(t0000,x) +--E 2838 + +--S 2839 of 3330 +--m0000:=a0000 - r0000 +--E 2839 + +--S 2840 of 3330 +--d0000:=D(m0000,x) +--E 2840 + +)clear all + +--S 2841 of 3330 +t0000:=x^(3/2)*(a-b*x)^(5/2) +--R +--R +--R 2 3 2 2 +---------+ +-+ +--R (1) (b x - 2a b x + a x)\|- b x + a \|x +--R Type: Expression(Integer) +--E 2841 + +--S 2842 of 3330 +r0000:=1/8*a*x^(5/2)*(a-b*x)^(3/2)+1/5*x^(5/2)*(a-b*x)^(5/2)+_ + 3/128*a^5*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)-_ + 1/64*a^3*x^(3/2)*sqrt(a-b*x)/b+1/16*a^2*x^(5/2)*sqrt(a-b*x)-_ + 3/128*a^4*sqrt(x)*sqrt(a-b*x)/b^2 +--R +--R +--R (2) +--R +-+ +-+ +--R 5 \|b \|x +--R 15a atan(------------) +--R +---------+ +--R \|- b x + a +--R + +--R 4 4 3 3 2 2 2 3 4 +---------+ +-+ +-+ +--R (128b x - 336a b x + 248a b x - 10a b x - 15a )\|- b x + a \|b \|x +--R / +--R 2 +-+ +--R 640b \|b +--R Type: Expression(Integer) +--E 2842 + +--S 2843 of 3330 +--a0000:=integrate(t0000,x) +--E 2843 + +--S 2844 of 3330 +--m0000:=a0000 - r0000 +--E 2844 + +--S 2845 of 3330 +--d0000:=D(m0000,x) +--E 2845 + +)clear all + +--S 2846 of 3330 +t0000:=(a-b*x)^(5/2)*sqrt(x) +--R +--R +--R 2 2 2 +---------+ +-+ +--R (1) (b x - 2a b x + a )\|- b x + a \|x +--R Type: Expression(Integer) +--E 2846 + +--S 2847 of 3330 +r0000:=5/24*a*x^(3/2)*(a-b*x)^(3/2)+1/4*x^(3/2)*(a-b*x)^(5/2)+_ + 5/64*a^4*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(3/2)+_ + 5/32*a^2*x^(3/2)*sqrt(a-b*x)-5/64*a^3*sqrt(x)*sqrt(a-b*x)/b +--R +--R +--R (2) +--R +-+ +-+ +--R 4 \|b \|x +--R 15a atan(------------) +--R +---------+ +--R \|- b x + a +--R + +--R 3 3 2 2 2 3 +---------+ +-+ +-+ +--R (48b x - 136a b x + 118a b x - 15a )\|- b x + a \|b \|x +--R / +--R +-+ +--R 192b\|b +--R Type: Expression(Integer) +--E 2847 + +--S 2848 of 3330 +--a0000:=integrate(t0000,x) +--E 2848 + +--S 2849 of 3330 +--m0000:=a0000 - r0000 +--E 2849 + +--S 2850 of 3330 +--d0000:=D(m0000,x) +--E 2850 + +)clear all + +--S 2851 of 3330 +t0000:=(a-b*x)^(5/2)/sqrt(x) +--R +--R +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R (1) -------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2851 + +--S 2852 of 3330 +r0000:=5/8*a^3*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/sqrt(b)+_ + 5/12*a*(a-b*x)^(3/2)*sqrt(x)+1/3*(a-b*x)^(5/2)*sqrt(x)+_ + 5/8*a^2*sqrt(x)*sqrt(a-b*x) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +---------+ +-+ +-+ +--R 15a atan(------------) + (8b x - 26a b x + 33a )\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (2) --------------------------------------------------------------------- +--R +-+ +--R 24\|b +--R Type: Expression(Integer) +--E 2852 + +--S 2853 of 3330 +--a0000:=integrate(t0000,x) +--E 2853 + +--S 2854 of 3330 +--m0000:=a0000 - r0000 +--E 2854 + +--S 2855 of 3330 +--d0000:=D(m0000,x) +--E 2855 + +)clear all + +--S 2856 of 3330 +t0000:=(a-b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R (1) -------------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2856 + +--S 2857 of 3330 +r0000:=-15/4*a^2*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))*sqrt(b)-_ + 2*(a-b*x)^(5/2)/sqrt(x)-5/2*b*(a-b*x)^(3/2)*sqrt(x)-_ + 15/4*a*b*sqrt(x)*sqrt(a-b*x) +--R +--R +--R +-+ +-+ +--R 2 +-+ +-+ \|b \|x 2 2 2 +---------+ +--R - 15a \|b \|x atan(------------) + (2b x - 9a b x - 8a )\|- b x + a +--R +---------+ +--R \|- b x + a +--R (2) --------------------------------------------------------------------- +--R +-+ +--R 4\|x +--R Type: Expression(Integer) +--E 2857 + +--S 2858 of 3330 +--a0000:=integrate(t0000,x) +--E 2858 + +--S 2859 of 3330 +--m0000:=a0000 - r0000 +--E 2859 + +--S 2860 of 3330 +--d0000:=D(m0000,x) +--E 2860 + +)clear all + +--S 2861 of 3330 +t0000:=(a-b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R (1) -------------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2861 + +--S 2862 of 3330 +r0000:=-2/3*(a-b*x)^(5/2)/x^(3/2)+_ + 5*a*b^(3/2)*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))+_ + 10/3*b*(a-b*x)^(3/2)/sqrt(x)+5*b^2*sqrt(x)*sqrt(a-b*x) +--R +--R +--R (2) +--R +-+ +-+ +--R +-+ +-+ \|b \|x 2 2 2 +---------+ +--R 15a b x\|b \|x atan(------------) + (3b x + 14a b x - 2a )\|- b x + a +--R +---------+ +--R \|- b x + a +--R ----------------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2862 + +--S 2863 of 3330 +--a0000:=integrate(t0000,x) +--E 2863 + +--S 2864 of 3330 +--m0000:=a0000 - r0000 +--E 2864 + +--S 2865 of 3330 +--d0000:=D(m0000,x) +--E 2865 + +)clear all + +--S 2866 of 3330 +t0000:=x^(5/2)*(2+b*x)^(5/2) +--R +--R +--R 2 4 3 2 +-+ +-------+ +--R (1) (b x + 4b x + 4x )\|x \|b x + 2 +--R Type: Expression(Integer) +--E 2866 + +--S 2867 of 3330 +r0000:=1/6*x^(7/2)*(2+b*x)^(3/2)+1/6*x^(7/2)*(2+b*x)^(5/2)-_ + 5/8*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 5/48*x^(3/2)*sqrt(2+b*x)/b^2+1/24*x^(5/2)*sqrt(2+b*x)/b+_ + 1/8*x^(7/2)*sqrt(2+b*x)+5/16*sqrt(x)*sqrt(2+b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R \|b \|x +--R - 30asinh(--------) +--R +-+ +--R \|2 +--R + +--R 5 5 4 4 3 3 2 2 +-+ +-+ +-------+ +--R (8b x + 40b x + 54b x + 2b x - 5b x + 15)\|b \|x \|b x + 2 +--R / +--R 3 +-+ +--R 48b \|b +--R Type: Expression(Integer) +--E 2867 + +--S 2868 of 3330 +--a0000:=integrate(t0000,x) +--E 2868 + +--S 2869 of 3330 +--m0000:=a0000 - r0000 +--E 2869 + +--S 2870 of 3330 +--d0000:=D(m0000,x) +--E 2870 + +)clear all + +--S 2871 of 3330 +t0000:=x^(3/2)*(2+b*x)^(5/2) +--R +--R +--R 2 3 2 +-+ +-------+ +--R (1) (b x + 4b x + 4x)\|x \|b x + 2 +--R Type: Expression(Integer) +--E 2871 + +--S 2872 of 3330 +r0000:=1/4*x^(5/2)*(2+b*x)^(3/2)+1/5*x^(5/2)*(2+b*x)^(5/2)+_ + 3/4*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)+1/8*x^(3/2)*sqrt(2+b*x)/b+_ + 1/4*x^(5/2)*sqrt(2+b*x)-3/8*sqrt(x)*sqrt(2+b*x)/b^2 +--R +--R +--R (2) +--R +-+ +-+ +--R \|b \|x 4 4 3 3 2 2 +-+ +-+ +-------+ +--R 30asinh(--------) + (8b x + 42b x + 62b x + 5b x - 15)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R --------------------------------------------------------------------------- +--R 2 +-+ +--R 40b \|b +--R Type: Expression(Integer) +--E 2872 + +--S 2873 of 3330 +--a0000:=integrate(t0000,x) +--E 2873 + +--S 2874 of 3330 +--m0000:=a0000 - r0000 +--E 2874 + +--S 2875 of 3330 +--d0000:=D(m0000,x) +--E 2875 + +)clear all + +--S 2876 of 3330 +t0000:=(2+b*x)^(5/2)*sqrt(x) +--R +--R +--R 2 2 +-+ +-------+ +--R (1) (b x + 4b x + 4)\|x \|b x + 2 +--R Type: Expression(Integer) +--E 2876 + +--S 2877 of 3330 +r0000:=5/12*x^(3/2)*(2+b*x)^(3/2)+1/4*x^(3/2)*(2+b*x)^(5/2)-_ + 5/4*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+5/8*x^(3/2)*sqrt(2+b*x)+_ + 5/8*sqrt(x)*sqrt(2+b*x)/b +--R +--R +--R +-+ +-+ +--R \|b \|x 3 3 2 2 +-+ +-+ +-------+ +--R - 30asinh(--------) + (6b x + 34b x + 59b x + 15)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) --------------------------------------------------------------------- +--R +-+ +--R 24b\|b +--R Type: Expression(Integer) +--E 2877 + +--S 2878 of 3330 +--a0000:=integrate(t0000,x) +--E 2878 + +--S 2879 of 3330 +--m0000:=a0000 - r0000 +--E 2879 + +--S 2880 of 3330 +--d0000:=D(m0000,x) +--E 2880 + +)clear all + +--S 2881 of 3330 +t0000:=(2+b*x)^(5/2)/sqrt(x) +--R +--R +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R (1) --------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2881 + +--S 2882 of 3330 +r0000:=5*asinh(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+_ + 5/6*(2+b*x)^(3/2)*sqrt(x)+1/3*(2+b*x)^(5/2)*sqrt(x)+_ + 5/2*sqrt(x)*sqrt(2+b*x) +--R +--R +--R +-+ +-+ +--R \|b \|x 2 2 +-+ +-+ +-------+ +--R 30asinh(--------) + (2b x + 13b x + 33)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) ---------------------------------------------------------- +--R +-+ +--R 6\|b +--R Type: Expression(Integer) +--E 2882 + +--S 2883 of 3330 +--a0000:=integrate(t0000,x) +--E 2883 + +--S 2884 of 3330 +--m0000:=a0000 - r0000 +--E 2884 + +--S 2885 of 3330 +--d0000:=D(m0000,x) +--E 2885 + +)clear all + +--S 2886 of 3330 +t0000:=(2+b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R (1) --------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2886 + +--S 2887 of 3330 +r0000:=15*asinh(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-_ + 2*(2+b*x)^(5/2)/sqrt(x)+5/2*b*(2+b*x)^(3/2)*sqrt(x)+_ + 15/2*b*sqrt(x)*sqrt(2+b*x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x 2 2 +-------+ +--R 30\|b \|x asinh(--------) + (b x + 9b x - 16)\|b x + 2 +--R +-+ +--R \|2 +--R (2) -------------------------------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression(Integer) +--E 2887 + +--S 2888 of 3330 +--a0000:=integrate(t0000,x) +--E 2888 + +--S 2889 of 3330 +--m0000:=a0000 - r0000 +--E 2889 + +--S 2890 of 3330 +--d0000:=D(m0000,x) +--E 2890 + +)clear all + +--S 2891 of 3330 +t0000:=(2+b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R (1) --------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2891 + +--S 2892 of 3330 +r0000:=-2/3*(2+b*x)^(5/2)/x^(3/2)+10*b^(3/2)*asinh(sqrt(b)*sqrt(x)/sqrt(2))-_ + 10/3*b*(2+b*x)^(3/2)/sqrt(x)+5*b^2*sqrt(x)*sqrt(2+b*x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x 2 2 +-------+ +--R 30b x\|b \|x asinh(--------) + (3b x - 28b x - 8)\|b x + 2 +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------ +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2892 + +--S 2893 of 3330 +--a0000:=integrate(t0000,x) +--E 2893 + +--S 2894 of 3330 +--m0000:=a0000 - r0000 +--E 2894 + +--S 2895 of 3330 +--d0000:=D(m0000,x) +--E 2895 + +)clear all + +--S 2896 of 3330 +t0000:=x^(5/2)*(2-b*x)^(5/2) +--R +--R +--R 2 4 3 2 +---------+ +-+ +--R (1) (b x - 4b x + 4x )\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 2896 + +--S 2897 of 3330 +r0000:=1/6*x^(7/2)*(2-b*x)^(3/2)+1/6*x^(7/2)*(2-b*x)^(5/2)+_ + 5/8*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 5/48*x^(3/2)*sqrt(2-b*x)/b^2-1/24*x^(5/2)*sqrt(2-b*x)/b+_ + 1/8*x^(7/2)*sqrt(2-b*x)-5/16*sqrt(x)*sqrt(2-b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R \|b \|x +--R 30asin(--------) +--R +-+ +--R \|2 +--R + +--R 5 5 4 4 3 3 2 2 +---------+ +-+ +-+ +--R (8b x - 40b x + 54b x - 2b x - 5b x - 15)\|- b x + 2 \|b \|x +--R / +--R 3 +-+ +--R 48b \|b +--R Type: Expression(Integer) +--E 2897 + +--S 2898 of 3330 +--a0000:=integrate(t0000,x) +--E 2898 + +--S 2899 of 3330 +--m0000:=a0000 - r0000 +--E 2899 + +--S 2900 of 3330 +--d0000:=D(m0000,x) +--E 2900 + +)clear all + +--S 2901 of 3330 +t0000:=x^(3/2)*(2-b*x)^(5/2) +--R +--R +--R 2 3 2 +---------+ +-+ +--R (1) (b x - 4b x + 4x)\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 2901 + +--S 2902 of 3330 +r0000:=1/4*x^(5/2)*(2-b*x)^(3/2)+1/5*x^(5/2)*(2-b*x)^(5/2)+_ + 3/4*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-_ + 1/8*x^(3/2)*sqrt(2-b*x)/b+1/4*x^(5/2)*sqrt(2-b*x)-_ + 3/8*sqrt(x)*sqrt(2-b*x)/b^2 +--R +--R +--R (2) +--R +-+ +-+ +--R \|b \|x 4 4 3 3 2 2 +---------+ +-+ +-+ +--R 30asin(--------) + (8b x - 42b x + 62b x - 5b x - 15)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R ---------------------------------------------------------------------------- +--R 2 +-+ +--R 40b \|b +--R Type: Expression(Integer) +--E 2902 + +--S 2903 of 3330 +--a0000:=integrate(t0000,x) +--E 2903 + +--S 2904 of 3330 +--m0000:=a0000 - r0000 +--E 2904 + +--S 2905 of 3330 +--d0000:=D(m0000,x) +--E 2905 + +)clear all + +--S 2906 of 3330 +t0000:=(2-b*x)^(5/2)*sqrt(x) +--R +--R +--R 2 2 +---------+ +-+ +--R (1) (b x - 4b x + 4)\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 2906 + +--S 2907 of 3330 +r0000:=5/12*x^(3/2)*(2-b*x)^(3/2)+1/4*x^(3/2)*(2-b*x)^(5/2)+_ + 5/4*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+_ + 5/8*x^(3/2)*sqrt(2-b*x)-5/8*sqrt(x)*sqrt(2-b*x)/b +--R +--R +--R +-+ +-+ +--R \|b \|x 3 3 2 2 +---------+ +-+ +-+ +--R 30asin(--------) + (6b x - 34b x + 59b x - 15)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) -------------------------------------------------------------------- +--R +-+ +--R 24b\|b +--R Type: Expression(Integer) +--E 2907 + +--S 2908 of 3330 +--a0000:=integrate(t0000,x) +--E 2908 + +--S 2909 of 3330 +--m0000:=a0000 - r0000 +--E 2909 + +--S 2910 of 3330 +--d0000:=D(m0000,x) +--E 2910 + +)clear all + +--S 2911 of 3330 +t0000:=(2-b*x)^(5/2)/sqrt(x) +--R +--R +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R (1) ----------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 2911 + +--S 2912 of 3330 +r0000:=5*asin(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b)+_ + 5/6*(2-b*x)^(3/2)*sqrt(x)+1/3*(2-b*x)^(5/2)*sqrt(x)+_ + 5/2*sqrt(x)*sqrt(2-b*x) +--R +--R +--R +-+ +-+ +--R \|b \|x 2 2 +---------+ +-+ +-+ +--R 30asin(--------) + (2b x - 13b x + 33)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) ----------------------------------------------------------- +--R +-+ +--R 6\|b +--R Type: Expression(Integer) +--E 2912 + +--S 2913 of 3330 +--a0000:=integrate(t0000,x) +--E 2913 + +--S 2914 of 3330 +--m0000:=a0000 - r0000 +--E 2914 + +--S 2915 of 3330 +--d0000:=D(m0000,x) +--E 2915 + +)clear all + +--S 2916 of 3330 +t0000:=(2-b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R (1) ----------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2916 + +--S 2917 of 3330 +r0000:=-15*asin(sqrt(b)*sqrt(x)/sqrt(2))*sqrt(b)-_ + 2*(2-b*x)^(5/2)/sqrt(x)-5/2*b*(2-b*x)^(3/2)*sqrt(x)-_ + 15/2*b*sqrt(x)*sqrt(2-b*x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x 2 2 +---------+ +--R - 30\|b \|x asin(--------) + (b x - 9b x - 16)\|- b x + 2 +--R +-+ +--R \|2 +--R (2) ----------------------------------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression(Integer) +--E 2917 + +--S 2918 of 3330 +--a0000:=integrate(t0000,x) +--E 2918 + +--S 2919 of 3330 +--m0000:=a0000 - r0000 +--E 2919 + +--S 2920 of 3330 +--d0000:=D(m0000,x) +--E 2920 + +)clear all + +--S 2921 of 3330 +t0000:=(2-b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R (1) ----------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 2921 + +--S 2922 of 3330 +r0000:=-2/3*(2-b*x)^(5/2)/x^(3/2)+10*b^(3/2)*asin(sqrt(b)*sqrt(x)/sqrt(2))+_ + 10/3*b*(2-b*x)^(3/2)/sqrt(x)+5*b^2*sqrt(x)*sqrt(2-b*x) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x 2 2 +---------+ +--R 30b x\|b \|x asin(--------) + (3b x + 28b x - 8)\|- b x + 2 +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 2922 + +--S 2923 of 3330 +--a0000:=integrate(t0000,x) +--E 2923 + +--S 2924 of 3330 +--m0000:=a0000 - r0000 +--E 2924 + +--S 2925 of 3330 +--d0000:=D(m0000,x) +--E 2925 + +)clear all + +--S 2926 of 3330 +t0000:=x^(5/2)/sqrt(a+b*x) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 2926 + +--S 2927 of 3330 +r0000:=-5/8*a^3*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-_ + 5/12*a*x^(3/2)*sqrt(a+b*x)/b^2+1/3*x^(5/2)*sqrt(a+b*x)/b+_ + 5/8*a^2*sqrt(x)*sqrt(a+b*x)/b^3 +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R - 15a atanh(----------) + (8b x - 10a b x + 15a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) -------------------------------------------------------------------- +--R 3 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 2927 + +--S 2928 of 3330 +--a0000:=integrate(t0000,x) +--E 2928 + +--S 2929 of 3330 +--m0000:=a0000 - r0000 +--E 2929 + +--S 2930 of 3330 +--d0000:=D(m0000,x) +--E 2930 + +)clear all + +--S 2931 of 3330 +t0000:=x^(3/2)/sqrt(a+b*x) +--R +--R +--R +-+ +--R x\|x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 2931 + +--S 2932 of 3330 +r0000:=3/4*a^2*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)+_ + 1/2*x^(3/2)*sqrt(a+b*x)/b-3/4*a*sqrt(x)*sqrt(a+b*x)/b^2 +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R 3a atanh(----------) + (2b x - 3a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) ---------------------------------------------------- +--R 2 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 2932 + +--S 2933 of 3330 +--a0000:=integrate(t0000,x) +--E 2933 + +--S 2934 of 3330 +--m0000:=a0000 - r0000 +--E 2934 + +--S 2935 of 3330 +--d0000:=D(m0000,x) +--E 2935 + +)clear all + +--S 2936 of 3330 +t0000:=sqrt(x)/sqrt(a+b*x) +--R +--R +--R +-+ +--R \|x +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 2936 + +--S 2937 of 3330 +r0000:=-a*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)+_ + sqrt(x)*sqrt(a+b*x)/b +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R - a atanh(----------) + \|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (2) ------------------------------------------ +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 2937 + +--S 2938 of 3330 +--a0000:=integrate(t0000,x) +--E 2938 + +--S 2939 of 3330 +--m0000:=a0000 - r0000 +--E 2939 + +--S 2940 of 3330 +--d0000:=D(m0000,x) +--E 2940 + +)clear all + +--S 2941 of 3330 +t0000:=1/(sqrt(x)*sqrt(a+b*x)) +--R +--R +--R 1 +--R (1) -------------- +--R +-+ +-------+ +--R \|x \|b x + a +--R Type: Expression(Integer) +--E 2941 + +--S 2942 of 3330 +r0000:=2*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/sqrt(b) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2atanh(----------) +--R +-------+ +--R \|b x + a +--R (2) ------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 2942 + +--S 2943 of 3330 +--a0000:=integrate(t0000,x) +--E 2943 + +--S 2944 of 3330 +--m0000:=a0000 - r0000 +--E 2944 + +--S 2945 of 3330 +--d0000:=D(m0000,x) +--E 2945 + +)clear all + +--S 2946 of 3330 +t0000:=1/(x^(3/2)*sqrt(a+b*x)) +--R +--R +--R 1 +--R (1) --------------- +--R +-+ +-------+ +--R x\|x \|b x + a +--R Type: Expression(Integer) +--E 2946 + +--S 2947 of 3330 +r0000:=-2*sqrt(a+b*x)/(a*sqrt(x)) +--R +--R +--R +-------+ +--R 2\|b x + a +--R (2) - ----------- +--R +-+ +--R a\|x +--R Type: Expression(Integer) +--E 2947 + +--S 2948 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-------+ +--R - 2\|x \|b x + a + (- b - a - 1)x +--R (3) ---------------------------------- +--R a x +--R Type: Union(Expression(Integer),...) +--E 2948 + +--S 2949 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R - b - a - 1 +--R (4) ----------- +--R a +--R Type: Expression(Integer) +--E 2949 + +--S 2950 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2950 + +)clear all + +--S 2951 of 3330 +t0000:=1/(x^(5/2)*sqrt(a+b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R 2 +-+ +-------+ +--R x \|x \|b x + a +--R Type: Expression(Integer) +--E 2951 + +--S 2952 of 3330 +r0000:=-2/3*sqrt(a+b*x)/(a*x^(3/2))+4/3*b*sqrt(a+b*x)/(a^2*sqrt(x)) +--R +--R +--R +-------+ +--R (4b x - 2a)\|b x + a +--R (2) --------------------- +--R 2 +-+ +--R 3a x\|x +--R Type: Expression(Integer) +--E 2952 + +--S 2953 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-------+ 2 2 2 +--R (4b x - 2a)\|x \|b x + a + (- 2b + (- a - 2)b + a + a)x +--R (3) ----------------------------------------------------------- +--R 2 2 +--R 3a x +--R Type: Union(Expression(Integer),...) +--E 2953 + +--S 2954 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R - 2b + (- a - 2)b + a + a +--R (4) --------------------------- +--R 2 +--R 3a +--R Type: Expression(Integer) +--E 2954 + +--S 2955 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2955 + +)clear all + +--S 2956 of 3330 +t0000:=1/(x^(7/2)*sqrt(a+b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R 3 +-+ +-------+ +--R x \|x \|b x + a +--R Type: Expression(Integer) +--E 2956 + +--S 2957 of 3330 +r0000:=-2/5*sqrt(a+b*x)/(a*x^(5/2))+8/15*b*sqrt(a+b*x)/(a^2*x^(3/2))-_ + 16/15*b^2*sqrt(a+b*x)/(a^3*sqrt(x)) +--R +--R +--R 2 2 2 +-------+ +--R (- 16b x + 8a b x - 6a )\|b x + a +--R (2) ----------------------------------- +--R 3 2 +-+ +--R 15a x \|x +--R Type: Expression(Integer) +--E 2957 + +--S 2958 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 +-+ +-------+ +--R (- 32b x + 16a b x - 12a )\|x \|b x + a +--R + +--R 3 2 2 3 2 3 +--R (- 8b + (- 4a - 32)b + (a + 16a)b - 3a - 12a )x +--R / +--R 3 3 +--R 30a x +--R Type: Union(Expression(Integer),...) +--E 2958 + +--S 2959 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 2 3 2 +--R - 8b + (- 4a - 32)b + (a + 16a)b - 3a - 12a +--R (4) ------------------------------------------------ +--R 3 +--R 30a +--R Type: Expression(Integer) +--E 2959 + +--S 2960 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2960 + +)clear all + +--S 2961 of 3330 +t0000:=1/(x^(9/2)*sqrt(a+b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R 4 +-+ +-------+ +--R x \|x \|b x + a +--R Type: Expression(Integer) +--E 2961 + +--S 2962 of 3330 +r0000:=-2/7*sqrt(a+b*x)/(a*x^(7/2))+12/35*b*sqrt(a+b*x)/(a^2*x^(5/2))-_ + 16/35*b^2*sqrt(a+b*x)/(a^3*x^(3/2))+32/35*b^3*sqrt(a+b*x)/(a^4*sqrt(x)) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (32b x - 16a b x + 12a b x - 10a )\|b x + a +--R (2) ---------------------------------------------- +--R 4 3 +-+ +--R 35a x \|x +--R Type: Expression(Integer) +--E 2962 + +--S 2963 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +-------+ +--R (128b x - 64a b x + 48a b x - 40a )\|x \|b x + a +--R + +--R 4 3 2 2 3 2 4 3 4 +--R (16b + (8a + 256)b + (- 2a - 128a)b + (a + 96a )b - 5a - 80a )x +--R / +--R 4 4 +--R 140a x +--R Type: Union(Expression(Integer),...) +--E 2963 + +--S 2964 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 4 3 2 2 3 2 4 3 +--R 16b + (8a + 256)b + (- 2a - 128a)b + (a + 96a )b - 5a - 80a +--R (4) ------------------------------------------------------------------ +--R 4 +--R 140a +--R Type: Expression(Integer) +--E 2964 + +--S 2965 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2965 + +)clear all + +--S 2966 of 3330 +t0000:=x^(5/2)/(a+b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 2966 + +--S 2967 of 3330 +r0000:=15/4*a^2*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-_ + 2*x^(5/2)/(b*sqrt(a+b*x))+5/2*x^(3/2)*sqrt(a+b*x)/b^2-_ + 15/4*a*sqrt(x)*sqrt(a+b*x)/b^3 +--R +--R +--R +-+ +-+ +--R 2 +-------+ \|b \|x 2 2 2 +-+ +-+ +--R 15a \|b x + a atanh(----------) + (2b x - 5a b x - 15a )\|b \|x +--R +-------+ +--R \|b x + a +--R (2) ----------------------------------------------------------------- +--R 3 +-+ +-------+ +--R 4b \|b \|b x + a +--R Type: Expression(Integer) +--E 2967 + +--S 2968 of 3330 +--a0000:=integrate(t0000,x) +--E 2968 + +--S 2969 of 3330 +--m0000:=a0000 - r0000 +--E 2969 + +--S 2970 of 3330 +--d0000:=D(m0000,x) +--E 2970 + +)clear all + +--S 2971 of 3330 +t0000:=x^(3/2)/(a+b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 2971 + +--S 2972 of 3330 +r0000:=-3*a*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)-_ + 2*x^(3/2)/(b*sqrt(a+b*x))+3*sqrt(x)*sqrt(a+b*x)/b^2 +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R - 3a\|b x + a atanh(----------) + (b x + 3a)\|b \|x +--R +-------+ +--R \|b x + a +--R (2) ---------------------------------------------------- +--R 2 +-+ +-------+ +--R b \|b \|b x + a +--R Type: Expression(Integer) +--E 2972 + +--S 2973 of 3330 +--a0000:=integrate(t0000,x) +--E 2973 + +--S 2974 of 3330 +--m0000:=a0000 - r0000 +--E 2974 + +--S 2975 of 3330 +--d0000:=D(m0000,x) +--E 2975 + +)clear all + +--S 2976 of 3330 +t0000:=sqrt(x)/(a+b*x)^(3/2) +--R +--R +--R +-+ +--R \|x +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 2976 + +--S 2977 of 3330 +r0000:=2*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(3/2)-2*sqrt(x)/(b*sqrt(a+b*x)) +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R 2\|b x + a atanh(----------) - 2\|b \|x +--R +-------+ +--R \|b x + a +--R (2) ---------------------------------------- +--R +-+ +-------+ +--R b\|b \|b x + a +--R Type: Expression(Integer) +--E 2977 + +--S 2978 of 3330 +--a0000:=integrate(t0000,x) +--E 2978 + +--S 2979 of 3330 +--m0000:=a0000 - r0000 +--E 2979 + +--S 2980 of 3330 +--d0000:=D(m0000,x) +--E 2980 + +)clear all + +--S 2981 of 3330 +t0000:=1/((a+b*x)^(3/2)*sqrt(x)) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-+ +-------+ +--R (b x + a)\|x \|b x + a +--R Type: Expression(Integer) +--E 2981 + +--S 2982 of 3330 +r0000:=2*sqrt(x)/(a*sqrt(a+b*x)) +--R +--R +--R +-+ +--R 2\|x +--R (2) ----------- +--R +-------+ +--R a\|b x + a +--R Type: Expression(Integer) +--E 2982 + +--S 2983 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-------+ 2 2 +--R (8b + 8a)\|x \|b x + a + (- b + (- a - 16)b)x - a b - a - 16a +--R (3) ---------------------------------------------------------------- +--R 2 2 2 3 +--R (4a b + 4a b)x + 4a b + 4a +--R Type: Union(Expression(Integer),...) +--E 2983 + +--S 2984 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R - b - a - 16 +--R (4) ------------ +--R 2 +--R 4a b + 4a +--R Type: Expression(Integer) +--E 2984 + +--S 2985 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2985 + +)clear all + +--S 2986 of 3330 +t0000:=1/(x^(3/2)*(a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 +-+ +-------+ +--R (b x + a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 2986 + +--S 2987 of 3330 +r0000:=2/(a*sqrt(x)*sqrt(a+b*x))-4*sqrt(a+b*x)/(a^2*sqrt(x)) +--R +--R +--R - 4b x - 2a +--R (2) ---------------- +--R 2 +-+ +-------+ +--R a \|x \|b x + a +--R Type: Expression(Integer) +--E 2987 + +--S 2988 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +-+ +-------+ +--R ((- 12b - 12a b)x - 6a b - 6a )\|x \|b x + a +--R + +--R 3 2 2 2 +--R (- 2b + (- 3a - 18)b + (- a - 9a)b)x +--R + +--R 2 2 3 2 +--R (- 2a b + (- 3a - 18a)b - a - 9a )x +--R / +--R 2 2 3 2 3 4 +--R (3a b + 3a b)x + (3a b + 3a )x +--R Type: Union(Expression(Integer),...) +--E 2988 + +--S 2989 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R - 2b + (- 3a - 18)b - a - 9a +--R (4) ------------------------------ +--R 2 3 +--R 3a b + 3a +--R Type: Expression(Integer) +--E 2989 + +--S 2990 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2990 + +)clear all + +--S 2991 of 3330 +t0000:=1/(x^(5/2)*(a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 3 2 +-+ +-------+ +--R (b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 2991 + +--S 2992 of 3330 +r0000:=2/(a*x^(3/2)*sqrt(a+b*x))-8/3*sqrt(a+b*x)/(a^2*x^(3/2))+_ + 16/3*b*sqrt(a+b*x)/(a^3*sqrt(x)) +--R +--R +--R 2 2 2 +--R 16b x + 8a b x - 2a +--R (2) --------------------- +--R 3 +-+ +-------+ +--R 3a x\|x \|b x + a +--R Type: Expression(Integer) +--E 2992 + +--S 2993 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 2 2 2 3 +-+ +-------+ +--R ((48b + 48a b )x + (24a b + 24a b)x - 6a b - 6a )\|x \|b x + a +--R + +--R 4 3 2 2 3 2 3 +--R (8b + (12a + 72)b + (3a + 36a)b + (- a - 9a )b)x +--R + +--R 3 2 2 3 2 4 3 2 +--R (8a b + (12a + 72a)b + (3a + 36a )b - a - 9a )x +--R / +--R 3 2 4 3 4 5 2 +--R (9a b + 9a b)x + (9a b + 9a )x +--R Type: Union(Expression(Integer),...) +--E 2993 + +--S 2994 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 2 3 2 +--R 8b + (12a + 72)b + (3a + 36a)b - a - 9a +--R (4) -------------------------------------------- +--R 3 4 +--R 9a b + 9a +--R Type: Expression(Integer) +--E 2994 + +--S 2995 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2995 + +)clear all + +--S 2996 of 3330 +t0000:=1/(x^(7/2)*(a+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 4 3 +-+ +-------+ +--R (b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 2996 + +--S 2997 of 3330 +r0000:=2/(a*x^(5/2)*sqrt(a+b*x))-12/5*sqrt(a+b*x)/(a^2*x^(5/2))+_ + 16/5*b*sqrt(a+b*x)/(a^3*x^(3/2))-32/5*b^2*sqrt(a+b*x)/(a^4*sqrt(x)) +--R +--R +--R 3 3 2 2 2 3 +--R - 32b x - 16a b x + 4a b x - 2a +--R (2) ---------------------------------- +--R 4 2 +-+ +-------+ +--R 5a x \|x \|b x + a +--R Type: Expression(Integer) +--E 2997 + +--S 2998 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 3 3 2 2 2 2 2 3 3 +--R (- 64b - 64a b )x + (- 32a b - 32a b )x + (8a b + 8a b)x - 4a b +--R + +--R 4 +--R - 4a +--R * +--R +-+ +-------+ +--R \|x \|b x + a +--R + +--R 5 4 2 3 3 2 2 4 3 4 +--R (16b + (24a + 64)b + (6a + 32a)b + (- a - 8a )b + (a + 4a )b)x +--R + +--R 4 2 3 3 2 2 4 3 5 4 3 +--R (16a b + (24a + 64a)b + (6a + 32a )b + (- a - 8a )b + a + 4a )x +--R / +--R 4 2 5 4 5 6 3 +--R (10a b + 10a b)x + (10a b + 10a )x +--R Type: Union(Expression(Integer),...) +--E 2998 + +--S 2999 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 4 3 2 2 3 2 4 3 +--R 16b + (24a + 64)b + (6a + 32a)b + (- a - 8a )b + a + 4a +--R (4) -------------------------------------------------------------- +--R 4 5 +--R 10a b + 10a +--R Type: Expression(Integer) +--E 2999 + +--S 3000 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3000 + +)clear all + +--S 3001 of 3330 +t0000:=x^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 3001 + +--S 3002 of 3330 +r0000:=-2/3*x^(5/2)/(b*(a+b*x)^(3/2))-_ + 5*a*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(7/2)-_ + 10/3*x^(3/2)/(b^2*sqrt(a+b*x))+5*sqrt(x)*sqrt(a+b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 +-------+ \|b \|x +--R (- 15a b x - 15a )\|b x + a atanh(----------) +--R +-------+ +--R \|b x + a +--R + +--R 2 2 2 +-+ +-+ +--R (3b x + 20a b x + 15a )\|b \|x +--R / +--R 4 3 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 3002 + +--S 3003 of 3330 +--a0000:=integrate(t0000,x) +--E 3003 + +--S 3004 of 3330 +--m0000:=a0000 - r0000 +--E 3004 + +--S 3005 of 3330 +--d0000:=D(m0000,x) +--E 3005 + +)clear all + +--S 3006 of 3330 +t0000:=x^(3/2)/(a+b*x)^(5/2) +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 3006 + +--S 3007 of 3330 +r0000:=-2/3*x^(3/2)/(b*(a+b*x)^(3/2))+_ + 2*atanh(sqrt(b)*sqrt(x)/sqrt(a+b*x))/b^(5/2)-_ + 2*sqrt(x)/(b^2*sqrt(a+b*x)) +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R (6b x + 6a)\|b x + a atanh(----------) + (- 8b x - 6a)\|b \|x +--R +-------+ +--R \|b x + a +--R (2) -------------------------------------------------------------- +--R 3 2 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 3007 + +--S 3008 of 3330 +--a0000:=integrate(t0000,x) +--E 3008 + +--S 3009 of 3330 +--m0000:=a0000 - r0000 +--E 3009 + +--S 3010 of 3330 +--d0000:=D(m0000,x) +--E 3010 + +)clear all + +--S 3011 of 3330 +t0000:=sqrt(x)/(a+b*x)^(5/2) +--R +--R +--R +-+ +--R \|x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 3011 + +--S 3012 of 3330 +r0000:=2/3*x^(3/2)/(a*(a+b*x)^(3/2)) +--R +--R +--R +-+ +--R 2x\|x +--R (2) ------------------------ +--R 2 +-------+ +--R (3a b x + 3a )\|b x + a +--R Type: Expression(Integer) +--E 3012 + +--S 3013 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +-+ +-------+ 3 2 2 +--R (4b + 8a b + 4a )x\|x \|b x + a + (b + (a + 4)b )x +--R + +--R 2 2 2 3 2 +--R (2a b + (2a + 8a)b)x + a b + a + 4a +--R / +--R 4 2 3 3 2 2 2 3 3 2 4 3 2 4 +--R (6a b + 12a b + 6a b )x + (12a b + 24a b + 12a b)x + 6a b + 12a b +--R + +--R 5 +--R 6a +--R Type: Union(Expression(Integer),...) +--E 3013 + +--S 3014 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R b + a + 4 +--R (4) ------------------- +--R 2 2 3 +--R 6a b + 12a b + 6a +--R Type: Expression(Integer) +--E 3014 + +--S 3015 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3015 + +)clear all + +--S 3016 of 3330 +t0000:=1/((a+b*x)^(5/2)*sqrt(x)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 2 2 2 +-+ +-------+ +--R (b x + 2a b x + a )\|x \|b x + a +--R Type: Expression(Integer) +--E 3016 + +--S 3017 of 3330 +r0000:=2/3*sqrt(x)/(a*(a+b*x)^(3/2))+4/3*sqrt(x)/(a^2*sqrt(a+b*x)) +--R +--R +--R +-+ +--R (4b x + 6a)\|x +--R (2) ------------------------ +--R 2 3 +-------+ +--R (3a b x + 3a )\|b x + a +--R Type: Expression(Integer) +--E 3017 + +--S 3018 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 2 2 3 +-+ +-------+ +--R ((4b + 8a b + 4a b)x + 6a b + 12a b + 6a )\|x \|b x + a +--R + +--R 4 3 2 2 2 +--R (2b + (5a + 2)b + (3a + 3a)b )x +--R + +--R 3 2 2 3 2 2 2 3 2 4 3 +--R (4a b + (10a + 4a)b + (6a + 6a )b)x + 2a b + (5a + 2a )b + 3a + 3a +--R / +--R 2 4 3 3 4 2 2 3 3 4 2 5 4 2 5 6 +--R (3a b + 6a b + 3a b )x + (6a b + 12a b + 6a b)x + 3a b + 6a b + 3a +--R Type: Union(Expression(Integer),...) +--E 3018 + +--S 3019 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R 2b + (5a + 2)b + 3a + 3a +--R (4) -------------------------- +--R 2 2 3 4 +--R 3a b + 6a b + 3a +--R Type: Expression(Integer) +--E 3019 + +--S 3020 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3020 + +)clear all + +--S 3021 of 3330 +t0000:=1/(x^(3/2)*(a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 2 3 2 2 +-+ +-------+ +--R (b x + 2a b x + a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 3021 + +--S 3022 of 3330 +r0000:=2/3/(a*(a+b*x)^(3/2)*sqrt(x))+8/3/(a^2*sqrt(x)*sqrt(a+b*x))-_ + 16/3*sqrt(a+b*x)/(a^3*sqrt(x)) +--R +--R +--R 2 2 2 +--R - 16b x - 24a b x - 6a +--R (2) ---------------------------- +--R 3 4 +-+ +-------+ +--R (3a b x + 3a )\|x \|b x + a +--R Type: Expression(Integer) +--E 3022 + +--S 3023 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 2 2 2 3 2 2 3 2 2 +--R (- 48b - 96a b - 48a b )x + (- 72a b - 144a b - 72a b)x - 18a b +--R + +--R 3 4 +--R - 36a b - 18a +--R * +--R +-+ +-------+ +--R \|x \|b x + a +--R + +--R 5 4 2 3 3 2 2 3 +--R (- 8b + (- 20a - 72)b + (- 15a - 108a)b + (- 3a - 27a )b )x +--R + +--R 4 2 3 3 2 2 4 3 2 +--R (- 16a b + (- 40a - 144a)b + (- 30a - 216a )b + (- 6a - 54a )b)x +--R + +--R 2 3 3 2 2 4 3 5 4 +--R (- 8a b + (- 20a - 72a )b + (- 15a - 108a )b - 3a - 27a )x +--R / +--R 3 4 4 3 5 2 3 4 3 5 2 6 2 +--R (9a b + 18a b + 9a b )x + (18a b + 36a b + 18a b)x +--R + +--R 5 2 6 7 +--R (9a b + 18a b + 9a )x +--R Type: Union(Expression(Integer),...) +--E 3023 + +--S 3024 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 2 3 2 +--R - 8b + (- 20a - 72)b + (- 15a - 108a)b - 3a - 27a +--R (4) ------------------------------------------------------ +--R 3 2 4 5 +--R 9a b + 18a b + 9a +--R Type: Expression(Integer) +--E 3024 + +--S 3025 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3025 + +)clear all + +--S 3026 of 3330 +t0000:=1/(x^(5/2)*(a+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 2 4 3 2 2 +-+ +-------+ +--R (b x + 2a b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 3026 + +--S 3027 of 3330 +r0000:=2/3/(a*x^(3/2)*(a+b*x)^(3/2))+4/(a^2*x^(3/2)*sqrt(a+b*x))-_ + 16/3*sqrt(a+b*x)/(a^3*x^(3/2))+32/3*b*sqrt(a+b*x)/(a^4*sqrt(x)) +--R +--R +--R 3 3 2 2 2 3 +--R 32b x + 48a b x + 12a b x - 2a +--R (2) --------------------------------- +--R 4 2 5 +-+ +-------+ +--R (3a b x + 3a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 3027 + +--random failure... +-->> Error detected within library code: +--(1 . failed) cannot be coerced to mode (SparseUnivariatePolynomial (Integer)) +--R +--S 3028 of 3330 +--a0000:=integrate(t0000,x) +--E 3028 + +--S 3029 of 3330 +--m0000:=a0000 - r0000 +--E 3029 + +--S 3030 of 3330 +--d0000:=D(m0000,x) +--E 3030 + +)clear all + +--S 3031 of 3330 +t0000:=x^(5/2)/sqrt(a-b*x) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------ +--R +---------+ +--R \|- b x + a +--R Type: Expression(Integer) +--E 3031 + +--S 3032 of 3330 +r0000:=5/8*a^3*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)-_ + 5/12*a*x^(3/2)*sqrt(a-b*x)/b^2-1/3*x^(5/2)*sqrt(a-b*x)/b-_ + 5/8*a^2*sqrt(x)*sqrt(a-b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +---------+ +-+ +-+ +--R 15a atan(------------) + (- 8b x - 10a b x - 15a )\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R ----------------------------------------------------------------------- +--R 3 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 3032 + +--S 3033 of 3330 +--a0000:=integrate(t0000,x) +--E 3033 + +--S 3034 of 3330 +--m0000:=a0000 - r0000 +--E 3034 + +--S 3035 of 3330 +--d0000:=D(m0000,x) +--E 3035 + +)clear all + +--S 3036 of 3330 +t0000:=x^(3/2)/sqrt(a-b*x) +--R +--R +--R +-+ +--R x\|x +--R (1) ------------ +--R +---------+ +--R \|- b x + a +--R Type: Expression(Integer) +--E 3036 + +--S 3037 of 3330 +r0000:=3/4*a^2*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)-_ + 1/2*x^(3/2)*sqrt(a-b*x)/b-3/4*a*sqrt(x)*sqrt(a-b*x)/b^2 +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +---------+ +-+ +-+ +--R 3a atan(------------) + (- 2b x - 3a)\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (2) --------------------------------------------------------- +--R 2 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 3037 + +--S 3038 of 3330 +--a0000:=integrate(t0000,x) +--E 3038 + +--S 3039 of 3330 +--m0000:=a0000 - r0000 +--E 3039 + +--S 3040 of 3330 +--d0000:=D(m0000,x) +--E 3040 + +)clear all + +--S 3041 of 3330 +t0000:=sqrt(x)/sqrt(a-b*x) +--R +--R +--R +-+ +--R \|x +--R (1) ------------ +--R +---------+ +--R \|- b x + a +--R Type: Expression(Integer) +--E 3041 + +--S 3042 of 3330 +r0000:=a*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(3/2)-sqrt(x)*sqrt(a-b*x)/b +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R a atan(------------) - \|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (2) ------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 3042 + +--S 3043 of 3330 +--a0000:=integrate(t0000,x) +--E 3043 + +--S 3044 of 3330 +--m0000:=a0000 - r0000 +--E 3044 + +--S 3045 of 3330 +--d0000:=D(m0000,x) +--E 3045 + +)clear all + +--S 3046 of 3330 +t0000:=1/(sqrt(x)*sqrt(a-b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R +---------+ +-+ +--R \|- b x + a \|x +--R Type: Expression(Integer) +--E 3046 + +--S 3047 of 3330 +r0000:=2*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/sqrt(b) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2atan(------------) +--R +---------+ +--R \|- b x + a +--R (2) ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 3047 + +--S 3048 of 3330 +--a0000:=integrate(t0000,x) +--E 3048 + +--S 3049 of 3330 +--m0000:=a0000 - r0000 +--E 3049 + +--S 3050 of 3330 +--d0000:=D(m0000,x) +--E 3050 + +)clear all + +--S 3051 of 3330 +t0000:=1/(x^(3/2)*sqrt(a-b*x)) +--R +--R +--R 1 +--R (1) ----------------- +--R +---------+ +-+ +--R x\|- b x + a \|x +--R Type: Expression(Integer) +--E 3051 + +--S 3052 of 3330 +r0000:=-2*sqrt(a-b*x)/(a*sqrt(x)) +--R +--R +--R +---------+ +--R 2\|- b x + a +--R (2) - ------------- +--R +-+ +--R a\|x +--R Type: Expression(Integer) +--E 3052 + +--S 3053 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +---------+ +-+ +--R - 2\|- b x + a \|x + (- b + a + 1)x +--R (3) ------------------------------------ +--R a x +--R Type: Union(Expression(Integer),...) +--E 3053 + +--S 3054 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R - b + a + 1 +--R (4) ----------- +--R a +--R Type: Expression(Integer) +--E 3054 + +--S 3055 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3055 + +)clear all + +--S 3056 of 3330 +t0000:=1/(x^(5/2)*sqrt(a-b*x)) +--R +--R +--R 1 +--R (1) ------------------ +--R 2 +---------+ +-+ +--R x \|- b x + a \|x +--R Type: Expression(Integer) +--E 3056 + +--S 3057 of 3330 +r0000:=-2/3*sqrt(a-b*x)/(a*x^(3/2))-4/3*b*sqrt(a-b*x)/(a^2*sqrt(x)) +--R +--R +--R +---------+ +--R (- 4b x - 2a)\|- b x + a +--R (2) ------------------------- +--R 2 +-+ +--R 3a x\|x +--R Type: Expression(Integer) +--E 3057 + +--S 3058 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +---------+ +-+ 2 2 2 +--R (- 16b x - 8a)\|- b x + a \|x + (32b + (- 16a - 2)b - 16a - a)x +--R (3) ------------------------------------------------------------------- +--R 2 2 +--R 12a x +--R Type: Union(Expression(Integer),...) +--E 3058 + +--S 3059 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R 32b + (- 16a - 2)b - 16a - a +--R (4) ------------------------------ +--R 2 +--R 12a +--R Type: Expression(Integer) +--E 3059 + +--S 3060 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3060 + +)clear all + +--S 3061 of 3330 +t0000:=x^(5/2)/(a-b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) - --------------------- +--R +---------+ +--R (b x - a)\|- b x + a +--R Type: Expression(Integer) +--E 3061 + +--S 3062 of 3330 +r0000:=-15/4*a^2*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)+_ + 2*x^(5/2)/(b*sqrt(a-b*x))+5/2*x^(3/2)*sqrt(a-b*x)/b^2+_ + 15/4*a*sqrt(x)*sqrt(a-b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 +---------+ \|b \|x 2 2 2 +-+ +-+ +--R - 15a \|- b x + a atan(------------) + (- 2b x - 5a b x + 15a )\|b \|x +--R +---------+ +--R \|- b x + a +--R ------------------------------------------------------------------------ +--R 3 +---------+ +-+ +--R 4b \|- b x + a \|b +--R Type: Expression(Integer) +--E 3062 + +--S 3063 of 3330 +--a0000:=integrate(t0000,x) +--E 3063 + +--S 3064 of 3330 +--m0000:=a0000 - r0000 +--E 3064 + +--S 3065 of 3330 +--d0000:=D(m0000,x) +--E 3065 + +)clear all + +--S 3066 of 3330 +t0000:=x^(3/2)/(a-b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (1) - --------------------- +--R +---------+ +--R (b x - a)\|- b x + a +--R Type: Expression(Integer) +--E 3066 + +--S 3067 of 3330 +r0000:=-3*a*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)+_ + 2*x^(3/2)/(b*sqrt(a-b*x))+3*sqrt(x)*sqrt(a-b*x)/b^2 +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R - 3a\|- b x + a atan(------------) + (- b x + 3a)\|b \|x +--R +---------+ +--R \|- b x + a +--R (2) --------------------------------------------------------- +--R 2 +---------+ +-+ +--R b \|- b x + a \|b +--R Type: Expression(Integer) +--E 3067 + +--S 3068 of 3330 +--a0000:=integrate(t0000,x) +--E 3068 + +--S 3069 of 3330 +--m0000:=a0000 - r0000 +--E 3069 + +--S 3070 of 3330 +--d0000:=D(m0000,x) +--E 3070 + +)clear all + +--S 3071 of 3330 +t0000:=sqrt(x)/(a-b*x)^(3/2) +--R +--R +--R +-+ +--R \|x +--R (1) - --------------------- +--R +---------+ +--R (b x - a)\|- b x + a +--R Type: Expression(Integer) +--E 3071 + +--S 3072 of 3330 +r0000:=-2*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(3/2)+2*sqrt(x)/(b*sqrt(a-b*x)) +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R - 2\|- b x + a atan(------------) + 2\|b \|x +--R +---------+ +--R \|- b x + a +--R (2) --------------------------------------------- +--R +---------+ +-+ +--R b\|- b x + a \|b +--R Type: Expression(Integer) +--E 3072 + +--S 3073 of 3330 +--a0000:=integrate(t0000,x) +--E 3073 + +--S 3074 of 3330 +--m0000:=a0000 - r0000 +--E 3074 + +--S 3075 of 3330 +--d0000:=D(m0000,x) +--E 3075 + +)clear all + +--S 3076 of 3330 +t0000:=1/((a-b*x)^(3/2)*sqrt(x)) +--R +--R +--R 1 +--R (1) - ------------------------- +--R +---------+ +-+ +--R (b x - a)\|- b x + a \|x +--R Type: Expression(Integer) +--E 3076 + +--S 3077 of 3330 +r0000:=2*sqrt(x)/(a*sqrt(a-b*x)) +--R +--R +--R +-+ +--R 2\|x +--R (2) ------------- +--R +---------+ +--R a\|- b x + a +--R Type: Expression(Integer) +--E 3077 + +--S 3078 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +---------+ +-+ 2 2 +--R (- 6b + 6a)\|- b x + a \|x + (9b + (- 9a - 1)b)x - 9a b + 9a + a +--R (3) ------------------------------------------------------------------- +--R 2 2 2 3 +--R (3a b - 3a b)x - 3a b + 3a +--R Type: Union(Expression(Integer),...) +--E 3078 + +--S 3079 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 9b - 9a - 1 +--R (4) ----------- +--R 2 +--R 3a b - 3a +--R Type: Expression(Integer) +--E 3079 + +--S 3080 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3080 + +)clear all + +--S 3081 of 3330 +t0000:=1/(x^(3/2)*(a-b*x)^(3/2)) +--R +--R +--R 1 +--R (1) - ---------------------------- +--R 2 +---------+ +-+ +--R (b x - a x)\|- b x + a \|x +--R Type: Expression(Integer) +--E 3081 + +--S 3082 of 3330 +r0000:=2/(a*sqrt(x)*sqrt(a-b*x))-4*sqrt(a-b*x)/(a^2*sqrt(x)) +--R +--R +--R 4b x - 2a +--R (2) ------------------ +--R 2 +---------+ +-+ +--R a \|- b x + a \|x +--R Type: Expression(Integer) +--E 3082 + +--S 3083 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +---------+ +-+ +--R ((- 4b + 4a b)x + 2a b - 2a )\|- b x + a \|x +--R + +--R 3 2 2 2 2 2 3 2 +--R (- 2b + (3a + 2)b + (- a - a)b)x + (2a b + (- 3a - 2a)b + a + a )x +--R / +--R 2 2 3 2 3 4 +--R (a b - a b)x + (- a b + a )x +--R Type: Union(Expression(Integer),...) +--E 3083 + +--S 3084 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R - 2b + (3a + 2)b - a - a +--R (4) -------------------------- +--R 2 3 +--R a b - a +--R Type: Expression(Integer) +--E 3084 + +--S 3085 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3085 + +)clear all + +--S 3086 of 3330 +t0000:=1/(x^(5/2)*(a-b*x)^(3/2)) +--R +--R +--R 1 +--R (1) - ----------------------------- +--R 3 2 +---------+ +-+ +--R (b x - a x )\|- b x + a \|x +--R Type: Expression(Integer) +--E 3086 + +--S 3087 of 3330 +r0000:=2/(a*x^(3/2)*sqrt(a-b*x))-8/3*sqrt(a-b*x)/(a^2*x^(3/2))-_ + 16/3*b*sqrt(a-b*x)/(a^3*sqrt(x)) +--R +--R +--R 2 2 2 +--R 16b x - 8a b x - 2a +--R (2) --------------------- +--R 3 +---------+ +-+ +--R 3a x\|- b x + a \|x +--R Type: Expression(Integer) +--E 3087 + +--S 3088 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 2 2 2 3 +---------+ +-+ +--R ((- 64b + 64a b )x + (32a b - 32a b)x + 8a b - 8a )\|- b x + a \|x +--R + +--R 4 3 2 2 3 2 3 +--R (- 128b + (192a + 8)b + (- 48a - 4a)b + (- 16a - a )b)x +--R + +--R 3 2 2 3 2 4 3 2 +--R (128a b + (- 192a - 8a)b + (48a + 4a )b + 16a + a )x +--R / +--R 3 2 4 3 4 5 2 +--R (12a b - 12a b)x + (- 12a b + 12a )x +--R Type: Union(Expression(Integer),...) +--E 3088 + +--S 3089 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 2 3 2 +--R - 128b + (192a + 8)b + (- 48a - 4a)b - 16a - a +--R (4) --------------------------------------------------- +--R 3 4 +--R 12a b - 12a +--R Type: Expression(Integer) +--E 3089 + +--S 3090 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3090 + +)clear all + +--S 3091 of 3330 +t0000:=x^(5/2)/(a-b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) -------------------------------- +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R Type: Expression(Integer) +--E 3091 + +--S 3092 of 3330 +r0000:=2/3*x^(5/2)/(b*(a-b*x)^(3/2))+_ + 5*a*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(7/2)-_ + 10/3*x^(3/2)/(b^2*sqrt(a-b*x))-5*sqrt(x)*sqrt(a-b*x)/b^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 +---------+ \|b \|x +--R (15a b x - 15a )\|- b x + a atan(------------) +--R +---------+ +--R \|- b x + a +--R + +--R 2 2 2 +-+ +-+ +--R (3b x - 20a b x + 15a )\|b \|x +--R / +--R 4 3 +---------+ +-+ +--R (3b x - 3a b )\|- b x + a \|b +--R Type: Expression(Integer) +--E 3092 + +--S 3093 of 3330 +--a0000:=integrate(t0000,x) +--E 3093 + +--S 3094 of 3330 +--m0000:=a0000 - r0000 +--E 3094 + +--S 3095 of 3330 +--d0000:=D(m0000,x) +--E 3095 + +)clear all + +--S 3096 of 3330 +t0000:=x^(3/2)/(a-b*x)^(5/2) +--R +--R +--R +-+ +--R x\|x +--R (1) -------------------------------- +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R Type: Expression(Integer) +--E 3096 + +--S 3097 of 3330 +r0000:=2/3*x^(3/2)/(b*(a-b*x)^(3/2))+_ + 2*atan(sqrt(b)*sqrt(x)/sqrt(a-b*x))/b^(5/2)-2*sqrt(x)/(b^2*sqrt(a-b*x)) +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R (6b x - 6a)\|- b x + a atan(------------) + (- 8b x + 6a)\|b \|x +--R +---------+ +--R \|- b x + a +--R (2) ----------------------------------------------------------------- +--R 3 2 +---------+ +-+ +--R (3b x - 3a b )\|- b x + a \|b +--R Type: Expression(Integer) +--E 3097 + +--S 3098 of 3330 +--a0000:=integrate(t0000,x) +--E 3098 + +--S 3099 of 3330 +--m0000:=a0000 - r0000 +--E 3099 + +--S 3100 of 3330 +--d0000:=D(m0000,x) +--E 3100 + +)clear all + +--S 3101 of 3330 +t0000:=sqrt(x)/(a-b*x)^(5/2) +--R +--R +--R +-+ +--R \|x +--R (1) -------------------------------- +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R Type: Expression(Integer) +--E 3101 + +--S 3102 of 3330 +r0000:=2/3*x^(3/2)/(a*(a-b*x)^(3/2)) +--R +--R +--R +-+ +--R 2x\|x +--R (2) - -------------------------- +--R 2 +---------+ +--R (3a b x - 3a )\|- b x + a +--R Type: Expression(Integer) +--E 3102 + +--S 3103 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +---------+ +-+ 3 2 2 +--R (6b - 12a b + 6a )x\|- b x + a \|x + (- 9b + (9a + 1)b )x +--R + +--R 2 2 2 3 2 +--R (18a b + (- 18a - 2a)b)x - 9a b + 9a + a +--R / +--R 4 2 3 3 2 2 2 3 3 2 4 3 2 4 +--R (9a b - 18a b + 9a b )x + (- 18a b + 36a b - 18a b)x + 9a b - 18a b +--R + +--R 5 +--R 9a +--R Type: Union(Expression(Integer),...) +--E 3103 + +--S 3104 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R - 9b + 9a + 1 +--R (4) ------------------- +--R 2 2 3 +--R 9a b - 18a b + 9a +--R Type: Expression(Integer) +--E 3104 + +--S 3105 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3105 + +)clear all + +--S 3106 of 3330 +t0000:=1/((a-b*x)^(5/2)*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 2 2 2 +---------+ +-+ +--R (b x - 2a b x + a )\|- b x + a \|x +--R Type: Expression(Integer) +--E 3106 + +--S 3107 of 3330 +r0000:=2/3*sqrt(x)/(a*(a-b*x)^(3/2))+4/3*sqrt(x)/(a^2*sqrt(a-b*x)) +--R +--R +--R +-+ +--R (4b x - 6a)\|x +--R (2) -------------------------- +--R 2 3 +---------+ +--R (3a b x - 3a )\|- b x + a +--R Type: Expression(Integer) +--E 3107 + +--S 3108 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 2 2 3 +---------+ +-+ +--R ((- 12b + 24a b - 12a b)x + 18a b - 36a b + 18a )\|- b x + a \|x +--R + +--R 4 3 2 2 2 +--R (18b + (- 45a - 2)b + (27a + 3a)b )x +--R + +--R 3 2 2 3 2 2 2 3 2 +--R (- 36a b + (90a + 4a)b + (- 54a - 6a )b)x + 18a b + (- 45a - 2a )b +--R + +--R 4 3 +--R 27a + 3a +--R / +--R 2 4 3 3 4 2 2 3 3 4 2 5 4 2 5 +--R (9a b - 18a b + 9a b )x + (- 18a b + 36a b - 18a b)x + 9a b - 18a b +--R + +--R 6 +--R 9a +--R Type: Union(Expression(Integer),...) +--E 3108 + +--S 3109 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R 18b + (- 45a - 2)b + 27a + 3a +--R (4) ------------------------------- +--R 2 2 3 4 +--R 9a b - 18a b + 9a +--R Type: Expression(Integer) +--E 3109 + +--S 3110 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3110 + +)clear all + +--S 3111 of 3330 +t0000:=1/(x^(3/2)*(a-b*x)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------------- +--R 2 3 2 2 +---------+ +-+ +--R (b x - 2a b x + a x)\|- b x + a \|x +--R Type: Expression(Integer) +--E 3111 + +--S 3112 of 3330 +r0000:=2/3/(a*(a-b*x)^(3/2)*sqrt(x))+_ + 8/3/(a^2*sqrt(x)*sqrt(a-b*x))-16/3*sqrt(a-b*x)/(a^3*sqrt(x)) +--R +--R +--R 2 2 2 +--R 16b x - 24a b x + 6a +--R (2) ------------------------------ +--R 3 4 +---------+ +-+ +--R (3a b x - 3a )\|- b x + a \|x +--R Type: Expression(Integer) +--E 3112 + +--S 3113 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 2 2 2 3 2 2 3 +--R (- 80b + 160a b - 80a b )x + (120a b - 240a b + 120a b)x +--R + +--R 2 2 3 4 +--R - 30a b + 60a b - 30a +--R * +--R +---------+ +-+ +--R \|- b x + a \|x +--R + +--R 5 4 2 3 3 2 2 3 +--R (200b + (- 500a - 8)b + (375a + 12a)b + (- 75a - 3a )b )x +--R + +--R 4 2 3 3 2 2 4 3 2 +--R (- 400a b + (1000a + 16a)b + (- 750a - 24a )b + (150a + 6a )b)x +--R + +--R 2 3 3 2 2 4 3 5 4 +--R (200a b + (- 500a - 8a )b + (375a + 12a )b - 75a - 3a )x +--R / +--R 3 4 4 3 5 2 3 4 3 5 2 6 2 +--R (15a b - 30a b + 15a b )x + (- 30a b + 60a b - 30a b)x +--R + +--R 5 2 6 7 +--R (15a b - 30a b + 15a )x +--R Type: Union(Expression(Integer),...) +--E 3113 + +--S 3114 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 2 3 2 +--R 200b + (- 500a - 8)b + (375a + 12a)b - 75a - 3a +--R (4) ---------------------------------------------------- +--R 3 2 4 5 +--R 15a b - 30a b + 15a +--R Type: Expression(Integer) +--E 3114 + +--S 3115 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3115 + +)clear all + +--S 3116 of 3330 +t0000:=1/(x^(5/2)*(a-b*x)^(5/2)) +--R +--R +--R 1 +--R (1) --------------------------------------- +--R 2 4 3 2 2 +---------+ +-+ +--R (b x - 2a b x + a x )\|- b x + a \|x +--R Type: Expression(Integer) +--E 3116 + +--S 3117 of 3330 +r0000:=2/3/(a*x^(3/2)*(a-b*x)^(3/2))+4/(a^2*x^(3/2)*sqrt(a-b*x))-_ + 16/3*sqrt(a-b*x)/(a^3*x^(3/2))-32/3*b*sqrt(a-b*x)/(a^4*sqrt(x)) +--R +--R +--R 3 3 2 2 2 3 +--R 32b x - 48a b x + 12a b x + 2a +--R (2) --------------------------------- +--R 4 2 5 +---------+ +-+ +--R (3a b x - 3a x)\|- b x + a \|x +--R Type: Expression(Integer) +--E 3117 + +--S 3118 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 2 3 3 4 2 3 3 2 2 +--R (- 32b + 64a b - 32a b )x + (48a b - 96a b + 48a b )x +--R + +--R 2 3 3 2 4 3 2 4 5 +--R (- 12a b + 24a b - 12a b)x - 2a b + 4a b - 2a +--R * +--R +---------+ +-+ +--R \|- b x + a \|x +--R + +--R 6 5 2 4 3 2 3 +--R 16b + (- 40a - 16)b + (30a + 24a)b + (- 5a - 6a )b +--R + +--R 4 3 2 +--R (- a - a )b +--R * +--R 4 +--R x +--R + +--R 5 2 4 3 2 3 4 3 2 +--R - 32a b + (80a + 32a)b + (- 60a - 48a )b + (10a + 12a )b +--R + +--R 5 4 +--R (2a + 2a )b +--R * +--R 3 +--R x +--R + +--R 2 4 3 2 3 4 3 2 5 4 6 5 2 +--R (16a b + (- 40a - 16a )b + (30a + 24a )b + (- 5a - 6a )b - a - a )x +--R / +--R 4 4 5 3 6 2 4 5 3 6 2 7 3 +--R (3a b - 6a b + 3a b )x + (- 6a b + 12a b - 6a b)x +--R + +--R 6 2 7 8 2 +--R (3a b - 6a b + 3a )x +--R Type: Union(Expression(Integer),...) +--E 3118 + +--S 3119 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 4 3 2 2 3 2 4 3 +--R 16b + (- 40a - 16)b + (30a + 24a)b + (- 5a - 6a )b - a - a +--R (4) ----------------------------------------------------------------- +--R 4 2 5 6 +--R 3a b - 6a b + 3a +--R Type: Expression(Integer) +--E 3119 + +--S 3120 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3120 + +)clear all + +--S 3121 of 3330 +t0000:=x^(5/2)/sqrt(2+b*x) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ---------- +--R +-------+ +--R \|b x + 2 +--R Type: Expression(Integer) +--E 3121 + +--S 3122 of 3330 +r0000:=-5*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 5/6*x^(3/2)*sqrt(2+b*x)/b^2+1/3*x^(5/2)*sqrt(2+b*x)/b+_ + 5/2*sqrt(x)*sqrt(2+b*x)/b^3 +--R +--R +--R +-+ +-+ +--R \|b \|x 2 2 +-+ +-+ +-------+ +--R - 30asinh(--------) + (2b x - 5b x + 15)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) ----------------------------------------------------------- +--R 3 +-+ +--R 6b \|b +--R Type: Expression(Integer) +--E 3122 + +--S 3123 of 3330 +--a0000:=integrate(t0000,x) +--E 3123 + +--S 3124 of 3330 +--m0000:=a0000 - r0000 +--E 3124 + +--S 3125 of 3330 +--d0000:=D(m0000,x) +--E 3125 + +)clear all + +--S 3126 of 3330 +t0000:=x^(3/2)/sqrt(2+b*x) +--R +--R +--R +-+ +--R x\|x +--R (1) ---------- +--R +-------+ +--R \|b x + 2 +--R Type: Expression(Integer) +--E 3126 + +--S 3127 of 3330 +r0000:=3*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)+_ + 1/2*x^(3/2)*sqrt(2+b*x)/b-3/2*sqrt(x)*sqrt(2+b*x)/b^2 +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R 6asinh(--------) + (b x - 3)\|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) ---------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 3127 + +--S 3128 of 3330 +--a0000:=integrate(t0000,x) +--E 3128 + +--S 3129 of 3330 +--m0000:=a0000 - r0000 +--E 3129 + +--S 3130 of 3330 +--d0000:=D(m0000,x) +--E 3130 + +)clear all + +--S 3131 of 3330 +t0000:=sqrt(x)/sqrt(2+b*x) +--R +--R +--R +-+ +--R \|x +--R (1) ---------- +--R +-------+ +--R \|b x + 2 +--R Type: Expression(Integer) +--E 3131 + +--S 3132 of 3330 +r0000:=-2*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+sqrt(x)*sqrt(2+b*x)/b +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R - 2asinh(--------) + \|b \|x \|b x + 2 +--R +-+ +--R \|2 +--R (2) --------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 3132 + +--S 3133 of 3330 +--a0000:=integrate(t0000,x) +--E 3133 + +--S 3134 of 3330 +--m0000:=a0000 - r0000 +--E 3134 + +--S 3135 of 3330 +--d0000:=D(m0000,x) +--E 3135 + +)clear all + +--S 3136 of 3330 +t0000:=1/(sqrt(x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) -------------- +--R +-+ +-------+ +--R \|x \|b x + 2 +--R Type: Expression(Integer) +--E 3136 + +--S 3137 of 3330 +r0000:=2*asinh(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2asinh(--------) +--R +-+ +--R \|2 +--R (2) ---------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 3137 + +--S 3138 of 3330 +--a0000:=integrate(t0000,x) +--E 3138 + +--S 3139 of 3330 +--m0000:=a0000 - r0000 +--E 3139 + +--S 3140 of 3330 +--d0000:=D(m0000,x) +--E 3140 + +)clear all + +--S 3141 of 3330 +t0000:=1/(x^(3/2)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) --------------- +--R +-+ +-------+ +--R x\|x \|b x + 2 +--R Type: Expression(Integer) +--E 3141 + +--S 3142 of 3330 +r0000:=-sqrt(2+b*x)/sqrt(x) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (2) - ---------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 3142 + +--S 3143 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-------+ +--R - 4\|x \|b x + 2 + (b + 6)x +--R (3) ---------------------------- +--R 4x +--R Type: Union(Expression(Integer),...) +--E 3143 + +--S 3144 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R b + 6 +--R (4) ----- +--R 4 +--R Type: Expression(Integer) +--E 3144 + +--S 3145 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3145 + +)clear all + +--S 3146 of 3330 +t0000:=1/(x^(5/2)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R 2 +-+ +-------+ +--R x \|x \|b x + 2 +--R Type: Expression(Integer) +--E 3146 + +--S 3147 of 3330 +r0000:=-1/3*sqrt(2+b*x)/x^(3/2)+1/3*b*sqrt(2+b*x)/sqrt(x) +--R +--R +--R +-------+ +--R (b x - 1)\|b x + 2 +--R (2) ------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 3147 + +--S 3148 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-------+ 2 2 +--R (4b x - 4)\|x \|b x + 2 + (- b - 5b + 6)x +--R (3) -------------------------------------------- +--R 2 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 3148 + +--S 3149 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R - b - 5b + 6 +--R (4) ------------- +--R 12 +--R Type: Expression(Integer) +--E 3149 + +--S 3150 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3150 + +)clear all + +--S 3151 of 3330 +t0000:=1/(x^(7/2)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R 3 +-+ +-------+ +--R x \|x \|b x + 2 +--R Type: Expression(Integer) +--E 3151 + +--S 3152 of 3330 +r0000:=-1/5*sqrt(2+b*x)/x^(5/2)+2/15*b*sqrt(2+b*x)/x^(3/2)-_ + 2/15*b^2*sqrt(2+b*x)/sqrt(x) +--R +--R +--R 2 2 +-------+ +--R (- 2b x + 2b x - 3)\|b x + 2 +--R (2) ------------------------------ +--R 2 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 3152 + +--S 3153 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 +-+ +-------+ 3 2 3 +--R (- 4b x + 4b x - 6)\|x \|b x + 2 + (- 2b - 4b + 3b - 9)x +--R (3) ------------------------------------------------------------- +--R 3 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 3153 + +--S 3154 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 +--R - 2b - 4b + 3b - 9 +--R (4) -------------------- +--R 30 +--R Type: Expression(Integer) +--E 3154 + +--S 3155 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3155 + +)clear all + +--S 3156 of 3330 +t0000:=1/(x^(9/2)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R 4 +-+ +-------+ +--R x \|x \|b x + 2 +--R Type: Expression(Integer) +--E 3156 + +--S 3157 of 3330 +r0000:=-1/7*sqrt(2+b*x)/x^(7/2)+3/35*b*sqrt(2+b*x)/x^(5/2)-_ + 2/35*b^2*sqrt(2+b*x)/x^(3/2)+2/35*b^3*sqrt(2+b*x)/sqrt(x) +--R +--R +--R 3 3 2 2 +-------+ +--R (2b x - 2b x + 3b x - 5)\|b x + 2 +--R (2) ------------------------------------ +--R 3 +-+ +--R 35x \|x +--R Type: Expression(Integer) +--E 3157 + +--S 3158 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 +-+ +-------+ 4 3 2 4 +--R (4b x - 4b x + 6b x - 10)\|x \|b x + 2 + (2b + 4b - 3b + 4b - 15)x +--R ------------------------------------------------------------------------- +--R 4 +--R 70x +--R Type: Union(Expression(Integer),...) +--E 3158 + +--S 3159 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 4 3 2 +--R 2b + 4b - 3b + 4b - 15 +--R (4) ------------------------- +--R 70 +--R Type: Expression(Integer) +--E 3159 + +--S 3160 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3160 + +)clear all + +--S 3161 of 3330 +t0000:=x^(5/2)/(2+b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------- +--R +-------+ +--R (b x + 2)\|b x + 2 +--R Type: Expression(Integer) +--E 3161 + +--S 3162 of 3330 +r0000:=15*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 2*x^(5/2)/(b*sqrt(2+b*x))+5/2*x^(3/2)*sqrt(2+b*x)/b^2-_ + 15/2*sqrt(x)*sqrt(2+b*x)/b^3 +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x 2 2 +-+ +-+ +--R 30\|b x + 2 asinh(--------) + (b x - 5b x - 30)\|b \|x +--R +-+ +--R \|2 +--R (2) -------------------------------------------------------- +--R 3 +-+ +-------+ +--R 2b \|b \|b x + 2 +--R Type: Expression(Integer) +--E 3162 + +--S 3163 of 3330 +--a0000:=integrate(t0000,x) +--E 3163 + +--S 3164 of 3330 +--m0000:=a0000 - r0000 +--E 3164 + +--S 3165 of 3330 +--d0000:=D(m0000,x) +--E 3165 + +)clear all + +--S 3166 of 3330 +t0000:=x^(3/2)/(2+b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------- +--R +-------+ +--R (b x + 2)\|b x + 2 +--R Type: Expression(Integer) +--E 3166 + +--S 3167 of 3330 +r0000:=-6*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-_ + 2*x^(3/2)/(b*sqrt(2+b*x))+3*sqrt(x)*sqrt(2+b*x)/b^2 +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R - 6\|b x + 2 asinh(--------) + (b x + 6)\|b \|x +--R +-+ +--R \|2 +--R (2) ------------------------------------------------ +--R 2 +-+ +-------+ +--R b \|b \|b x + 2 +--R Type: Expression(Integer) +--E 3167 + +--S 3168 of 3330 +--a0000:=integrate(t0000,x) +--E 3168 + +--S 3169 of 3330 +--m0000:=a0000 - r0000 +--E 3169 + +--S 3170 of 3330 +--d0000:=D(m0000,x) +--E 3170 + +)clear all + +--S 3171 of 3330 +t0000:=sqrt(x)/(2+b*x)^(3/2) +--R +--R +--R +-+ +--R \|x +--R (1) ------------------- +--R +-------+ +--R (b x + 2)\|b x + 2 +--R Type: Expression(Integer) +--E 3171 + +--S 3172 of 3330 +r0000:=2*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)-2*sqrt(x)/(b*sqrt(2+b*x)) +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R 2\|b x + 2 asinh(--------) - 2\|b \|x +--R +-+ +--R \|2 +--R (2) -------------------------------------- +--R +-+ +-------+ +--R b\|b \|b x + 2 +--R Type: Expression(Integer) +--E 3172 + +--S 3173 of 3330 +--a0000:=integrate(t0000,x) +--E 3173 + +--S 3174 of 3330 +--m0000:=a0000 - r0000 +--E 3174 + +--S 3175 of 3330 +--d0000:=D(m0000,x) +--E 3175 + +)clear all + +--S 3176 of 3330 +t0000:=1/((2+b*x)^(3/2)*sqrt(x)) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-+ +-------+ +--R (b x + 2)\|x \|b x + 2 +--R Type: Expression(Integer) +--E 3176 + +--S 3177 of 3330 +r0000:=sqrt(x)/sqrt(2+b*x) +--R +--R +--R +-+ +--R \|x +--R (2) ---------- +--R +-------+ +--R \|b x + 2 +--R Type: Expression(Integer) +--E 3177 + +--S 3178 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-------+ 2 +--R (10b + 20)\|x \|b x + 2 + (b + 27b)x + 2b + 54 +--R (3) ------------------------------------------------ +--R 2 +--R (10b + 20b)x + 20b + 40 +--R Type: Union(Expression(Integer),...) +--E 3178 + +--S 3179 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R b + 27 +--R (4) -------- +--R 10b + 20 +--R Type: Expression(Integer) +--E 3179 + +--S 3180 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3180 + +)clear all + +--S 3181 of 3330 +t0000:=1/(x^(3/2)*(2+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------- +--R 2 +-+ +-------+ +--R (b x + 2x)\|x \|b x + 2 +--R Type: Expression(Integer) +--E 3181 + +--S 3182 of 3330 +r0000:=1/(sqrt(x)*sqrt(2+b*x))-sqrt(2+b*x)/sqrt(x) +--R +--R +--R - b x - 1 +--R (2) -------------- +--R +-+ +-------+ +--R \|x \|b x + 2 +--R Type: Expression(Integer) +--E 3182 + +--S 3183 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 +-+ +-------+ 3 2 2 +--R ((- 8b - 16b)x - 8b - 16)\|x \|b x + 2 + (- b - 19b - 18b)x +--R + +--R 2 +--R (- 2b - 38b - 36)x +--R / +--R 2 2 +--R (8b + 16b)x + (16b + 32)x +--R Type: Union(Expression(Integer),...) +--E 3183 + +--S 3184 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R - b - 19b - 18 +--R (4) --------------- +--R 8b + 16 +--R Type: Expression(Integer) +--E 3184 + +--S 3185 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3185 + +)clear all + +--S 3186 of 3330 +t0000:=1/(x^(5/2)*(2+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) -------------------------- +--R 3 2 +-+ +-------+ +--R (b x + 2x )\|x \|b x + 2 +--R Type: Expression(Integer) +--E 3186 + +--S 3187 of 3330 +r0000:=1/(x^(3/2)*sqrt(2+b*x))-2/3*sqrt(2+b*x)/x^(3/2)+_ + 2/3*b*sqrt(2+b*x)/sqrt(x) +--R +--R +--R 2 2 +--R 2b x + 2b x - 1 +--R (2) ---------------- +--R +-+ +-------+ +--R 3x\|x \|b x + 2 +--R Type: Expression(Integer) +--E 3187 + +--S 3188 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 2 +-+ +-------+ +--R ((16b + 32b )x + (16b + 32b)x - 8b - 16)\|x \|b x + 2 +--R + +--R 4 3 2 3 3 2 2 +--R (2b + 38b + 35b - 18b)x + (4b + 76b + 70b - 36)x +--R / +--R 2 3 2 +--R (24b + 48b)x + (48b + 96)x +--R Type: Union(Expression(Integer),...) +--E 3188 + +--S 3189 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 +--R 2b + 38b + 35b - 18 +--R (4) --------------------- +--R 24b + 48 +--R Type: Expression(Integer) +--E 3189 + +--S 3190 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3190 + +)clear all + +--S 3191 of 3330 +t0000:=1/(x^(7/2)*(2+b*x)^(3/2)) +--R +--R +--R 1 +--R (1) -------------------------- +--R 4 3 +-+ +-------+ +--R (b x + 2x )\|x \|b x + 2 +--R Type: Expression(Integer) +--E 3191 + +--S 3192 of 3330 +r0000:=1/(x^(5/2)*sqrt(2+b*x))-3/5*sqrt(2+b*x)/x^(5/2)+_ + 2/5*b*sqrt(2+b*x)/x^(3/2)-2/5*b^2*sqrt(2+b*x)/sqrt(x) +--R +--R +--R 3 3 2 2 +--R - 2b x - 2b x + b x - 1 +--R (2) ------------------------- +--R 2 +-+ +-------+ +--R 5x \|x \|b x + 2 +--R Type: Expression(Integer) +--E 3192 + +--S 3193 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 3 3 2 2 2 +-+ +--R ((- 8b - 16b )x + (- 8b - 16b )x + (4b + 8b)x - 4b - 8)\|x +--R * +--R +-------+ +--R \|b x + 2 +--R + +--R 5 4 3 2 4 4 3 2 3 +--R (2b + 14b + 11b - 5b + 6b)x + (4b + 28b + 22b - 10b + 12)x +--R / +--R 2 4 3 +--R (20b + 40b)x + (40b + 80)x +--R Type: Union(Expression(Integer),...) +--E 3193 + +--S 3194 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 4 3 2 +--R 2b + 14b + 11b - 5b + 6 +--R (4) -------------------------- +--R 20b + 40 +--R Type: Expression(Integer) +--E 3194 + +--S 3195 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3195 + +)clear all + +--S 3196 of 3330 +t0000:=x^(5/2)/(2+b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) --------------------------- +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R Type: Expression(Integer) +--E 3196 + +--S 3197 of 3330 +r0000:=-2/3*x^(5/2)/(b*(2+b*x)^(3/2))-_ + 10*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 10/3*x^(3/2)/(b^2*sqrt(2+b*x))+5*sqrt(x)*sqrt(2+b*x)/b^3 +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x 2 2 +-+ +-+ +--R (- 30b x - 60)\|b x + 2 asinh(--------) + (3b x + 40b x + 60)\|b \|x +--R +-+ +--R \|2 +--R (2) ---------------------------------------------------------------------- +--R 4 3 +-+ +-------+ +--R (3b x + 6b )\|b \|b x + 2 +--R Type: Expression(Integer) +--E 3197 + +--S 3198 of 3330 +--a0000:=integrate(t0000,x) +--E 3198 + +--S 3199 of 3330 +--m0000:=a0000 - r0000 +--E 3199 + +--S 3200 of 3330 +--d0000:=D(m0000,x) +--E 3200 + +)clear all + +--S 3201 of 3330 +t0000:=x^(3/2)/(2+b*x)^(5/2) +--R +--R +--R +-+ +--R x\|x +--R (1) --------------------------- +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R Type: Expression(Integer) +--E 3201 + +--S 3202 of 3330 +r0000:=-2/3*x^(3/2)/(b*(2+b*x)^(3/2))+_ + 2*asinh(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-2*sqrt(x)/(b^2*sqrt(2+b*x)) +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R (6b x + 12)\|b x + 2 asinh(--------) + (- 8b x - 12)\|b \|x +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------ +--R 3 2 +-+ +-------+ +--R (3b x + 6b )\|b \|b x + 2 +--R Type: Expression(Integer) +--E 3202 + +--S 3203 of 3330 +--a0000:=integrate(t0000,x) +--E 3203 + +--S 3204 of 3330 +--m0000:=a0000 - r0000 +--E 3204 + +--S 3205 of 3330 +--d0000:=D(m0000,x) +--E 3205 + +)clear all + +--S 3206 of 3330 +t0000:=sqrt(x)/(2+b*x)^(5/2) +--R +--R +--R +-+ +--R \|x +--R (1) --------------------------- +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R Type: Expression(Integer) +--E 3206 + +--S 3207 of 3330 +r0000:=1/3*x^(3/2)/(2+b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (2) -------------------- +--R +-------+ +--R (3b x + 6)\|b x + 2 +--R Type: Expression(Integer) +--E 3207 + +--S 3208 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 +-+ +-------+ 3 2 2 2 +--R (8b + 32b + 32)x\|x \|b x + 2 + (b + 18b )x + (4b + 72b)x + 4b + 72 +--R ------------------------------------------------------------------------ +--R 4 3 2 2 3 2 2 +--R (24b + 96b + 96b )x + (96b + 384b + 384b)x + 96b + 384b + 384 +--R Type: Union(Expression(Integer),...) +--E 3208 + +--S 3209 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R b + 18 +--R (4) --------------- +--R 2 +--R 24b + 96b + 96 +--R Type: Expression(Integer) +--E 3209 + +--S 3210 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3210 + +)clear all + +--S 3211 of 3330 +t0000:=1/((2+b*x)^(5/2)*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 2 2 +-+ +-------+ +--R (b x + 4b x + 4)\|x \|b x + 2 +--R Type: Expression(Integer) +--E 3211 + +--S 3212 of 3330 +r0000:=1/3*sqrt(x)/(2+b*x)^(3/2)+1/3*sqrt(x)/sqrt(2+b*x) +--R +--R +--R +-+ +--R (b x + 3)\|x +--R (2) -------------------- +--R +-------+ +--R (3b x + 6)\|b x + 2 +--R Type: Expression(Integer) +--E 3212 + +--S 3213 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 +-+ +-------+ +--R ((6b + 24b + 24b)x + 18b + 72b + 72)\|x \|b x + 2 +--R + +--R 4 3 2 2 3 2 2 +--R (b + 14b + 33b )x + (4b + 56b + 132b)x + 4b + 56b + 132 +--R / +--R 4 3 2 2 3 2 2 +--R (18b + 72b + 72b )x + (72b + 288b + 288b)x + 72b + 288b + 288 +--R Type: Union(Expression(Integer),...) +--E 3213 + +--S 3214 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R b + 14b + 33 +--R (4) --------------- +--R 2 +--R 18b + 72b + 72 +--R Type: Expression(Integer) +--E 3214 + +--S 3215 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3215 + +)clear all + +--S 3216 of 3330 +t0000:=1/(x^(3/2)*(2+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 3 2 +-+ +-------+ +--R (b x + 4b x + 4x)\|x \|b x + 2 +--R Type: Expression(Integer) +--E 3216 + +--S 3217 of 3330 +r0000:=1/3/((2+b*x)^(3/2)*sqrt(x))+2/3/(sqrt(x)*sqrt(2+b*x))-_ + 2/3*sqrt(2+b*x)/sqrt(x) +--R +--R +--R 2 2 +--R - 2b x - 6b x - 3 +--R (2) ------------------------ +--R +-+ +-------+ +--R (3b x + 6)\|x \|b x + 2 +--R Type: Expression(Integer) +--E 3217 + +--S 3218 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 2 2 3 2 2 +--R (- 20b - 80b - 80b )x + (- 60b - 240b - 240b)x - 30b - 120b +--R + +--R - 120 +--R * +--R +-+ +-------+ +--R \|x \|b x + 2 +--R + +--R 5 4 3 2 3 4 3 2 2 +--R (- 2b - 60b - 165b - 81b )x + (- 8b - 240b - 660b - 324b)x +--R + +--R 3 2 +--R (- 8b - 240b - 660b - 324)x +--R / +--R 4 3 2 3 3 2 2 2 +--R (30b + 120b + 120b )x + (120b + 480b + 480b)x + (120b + 480b + 480)x +--R Type: Union(Expression(Integer),...) +--E 3218 + +--S 3219 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 +--R - 2b - 60b - 165b - 81 +--R (4) ------------------------ +--R 2 +--R 30b + 120b + 120 +--R Type: Expression(Integer) +--E 3219 + +--S 3220 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3220 + +)clear all + +--S 3221 of 3330 +t0000:=1/(x^(5/2)*(2+b*x)^(5/2)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 2 4 3 2 +-+ +-------+ +--R (b x + 4b x + 4x )\|x \|b x + 2 +--R Type: Expression(Integer) +--E 3221 + +--S 3222 of 3330 +r0000:=1/3/(x^(3/2)*(2+b*x)^(3/2))+1/(x^(3/2)*sqrt(2+b*x))-_ + 2/3*sqrt(2+b*x)/x^(3/2)+2/3*b*sqrt(2+b*x)/sqrt(x) +--R +--R +--R 3 3 2 2 +--R 2b x + 6b x + 3b x - 1 +--R (2) -------------------------- +--R 2 +-+ +-------+ +--R (3b x + 6x)\|x \|b x + 2 +--R Type: Expression(Integer) +--E 3222 + +--S 3223 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 3 3 4 3 2 2 3 2 +--R (4b + 16b + 16b )x + (12b + 48b + 48b )x + (6b + 24b + 24b)x +--R + +--R 2 +--R - 2b - 8b - 8 +--R * +--R +-+ +-------+ +--R \|x \|b x + 2 +--R + +--R 6 5 4 3 2 4 5 4 3 2 3 +--R (2b + 12b + 21b + 8b - 3b )x + (8b + 48b + 84b + 32b - 12b)x +--R + +--R 4 3 2 2 +--R (8b + 48b + 84b + 32b - 12)x +--R / +--R 4 3 2 4 3 2 3 2 2 +--R (6b + 24b + 24b )x + (24b + 96b + 96b)x + (24b + 96b + 96)x +--R Type: Union(Expression(Integer),...) +--E 3223 + +--S 3224 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 4 3 2 +--R 2b + 12b + 21b + 8b - 3 +--R (4) -------------------------- +--R 2 +--R 6b + 24b + 24 +--R Type: Expression(Integer) +--E 3224 + +--S 3225 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3225 + +)clear all + +--S 3226 of 3330 +t0000:=x^(5/2)/sqrt(2-b*x) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------ +--R +---------+ +--R \|- b x + 2 +--R Type: Expression(Integer) +--E 3226 + +--S 3227 of 3330 +r0000:=5*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 5/6*x^(3/2)*sqrt(2-b*x)/b^2-1/3*x^(5/2)*sqrt(2-b*x)/b-_ + 5/2*sqrt(x)*sqrt(2-b*x)/b^3 +--R +--R +--R +-+ +-+ +--R \|b \|x 2 2 +---------+ +-+ +-+ +--R 30asin(--------) + (- 2b x - 5b x - 15)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------ +--R 3 +-+ +--R 6b \|b +--R Type: Expression(Integer) +--E 3227 + +--S 3228 of 3330 +--a0000:=integrate(t0000,x) +--E 3228 + +--S 3229 of 3330 +--m0000:=a0000 - r0000 +--E 3229 + +--S 3230 of 3330 +--d0000:=D(m0000,x) +--E 3230 + +)clear all + +--S 3231 of 3330 +t0000:=x^(3/2)/sqrt(2-b*x) +--R +--R +--R +-+ +--R x\|x +--R (1) ------------ +--R +---------+ +--R \|- b x + 2 +--R Type: Expression(Integer) +--E 3231 + +--S 3232 of 3330 +r0000:=3*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-_ + 1/2*x^(3/2)*sqrt(2-b*x)/b-3/2*sqrt(x)*sqrt(2-b*x)/b^2 +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R 6asin(--------) + (- b x - 3)\|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) ------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 3232 + +--S 3233 of 3330 +--a0000:=integrate(t0000,x) +--E 3233 + +--S 3234 of 3330 +--m0000:=a0000 - r0000 +--E 3234 + +--S 3235 of 3330 +--d0000:=D(m0000,x) +--E 3235 + +)clear all + +--S 3236 of 3330 +t0000:=sqrt(x)/sqrt(2-b*x) +--R +--R +--R +-+ +--R \|x +--R (1) ------------ +--R +---------+ +--R \|- b x + 2 +--R Type: Expression(Integer) +--E 3236 + +--S 3237 of 3330 +r0000:=2*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)-sqrt(x)*sqrt(2-b*x)/b +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R 2asin(--------) - \|- b x + 2 \|b \|x +--R +-+ +--R \|2 +--R (2) -------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 3237 + +--S 3238 of 3330 +--a0000:=integrate(t0000,x) +--E 3238 + +--S 3239 of 3330 +--m0000:=a0000 - r0000 +--E 3239 + +--S 3240 of 3330 +--d0000:=D(m0000,x) +--E 3240 + +)clear all + +--S 3241 of 3330 +t0000:=1/(sqrt(x)*sqrt(2-b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R +---------+ +-+ +--R \|- b x + 2 \|x +--R Type: Expression(Integer) +--E 3241 + +--S 3242 of 3330 +r0000:=2*asin(sqrt(b)*sqrt(x)/sqrt(2))/sqrt(b) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2asin(--------) +--R +-+ +--R \|2 +--R (2) --------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 3242 + +--S 3243 of 3330 +--a0000:=integrate(t0000,x) +--E 3243 + +--S 3244 of 3330 +--m0000:=a0000 - r0000 +--E 3244 + +--S 3245 of 3330 +--d0000:=D(m0000,x) +--E 3245 + +)clear all + +--S 3246 of 3330 +t0000:=1/(x^(3/2)*sqrt(2-b*x)) +--R +--R +--R 1 +--R (1) ----------------- +--R +---------+ +-+ +--R x\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 3246 + +--S 3247 of 3330 +r0000:=-sqrt(2-b*x)/sqrt(x) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (2) - ------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 3247 + +--S 3248 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +---------+ +-+ +--R - 4\|- b x + 2 \|x + (- 4b + 9)x +--R (3) --------------------------------- +--R 4x +--R Type: Union(Expression(Integer),...) +--E 3248 + +--S 3249 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R - 4b + 9 +--R (4) -------- +--R 4 +--R Type: Expression(Integer) +--E 3249 + +--S 3250 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3250 + +)clear all + +--S 3251 of 3330 +t0000:=1/(x^(5/2)*sqrt(2-b*x)) +--R +--R +--R 1 +--R (1) ------------------ +--R 2 +---------+ +-+ +--R x \|- b x + 2 \|x +--R Type: Expression(Integer) +--E 3251 + +--S 3252 of 3330 +r0000:=-1/3*sqrt(2-b*x)/x^(3/2)-1/3*b*sqrt(2-b*x)/sqrt(x) +--R +--R +--R +---------+ +--R (- b x - 1)\|- b x + 2 +--R (2) ----------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 3252 + +--S 3253 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +---------+ +-+ 2 2 +--R (- 8b x - 8)\|- b x + 2 \|x + (- 16b + 17b + 33)x +--R (3) ---------------------------------------------------- +--R 2 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 3253 + +--S 3254 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R - 16b + 17b + 33 +--R (4) ----------------- +--R 24 +--R Type: Expression(Integer) +--E 3254 + +--S 3255 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3255 + +)clear all + +--S 3256 of 3330 +t0000:=x^(5/2)/(2-b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) - --------------------- +--R +---------+ +--R (b x - 2)\|- b x + 2 +--R Type: Expression(Integer) +--E 3256 + +--S 3257 of 3330 +r0000:=-15*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)+_ + 2*x^(5/2)/(b*sqrt(2-b*x))+5/2*x^(3/2)*sqrt(2-b*x)/b^2+_ + 15/2*sqrt(x)*sqrt(2-b*x)/b^3 +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x 2 2 +-+ +-+ +--R - 30\|- b x + 2 asin(--------) + (- b x - 5b x + 30)\|b \|x +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------- +--R 3 +---------+ +-+ +--R 2b \|- b x + 2 \|b +--R Type: Expression(Integer) +--E 3257 + +--S 3258 of 3330 +--a0000:=integrate(t0000,x) +--E 3258 + +--S 3259 of 3330 +--m0000:=a0000 - r0000 +--E 3259 + +--S 3260 of 3330 +--d0000:=D(m0000,x) +--E 3260 + +)clear all + +--S 3261 of 3330 +t0000:=x^(3/2)/(2-b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (1) - --------------------- +--R +---------+ +--R (b x - 2)\|- b x + 2 +--R Type: Expression(Integer) +--E 3261 + +--S 3262 of 3330 +r0000:=-6*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)+_ + 2*x^(3/2)/(b*sqrt(2-b*x))+3*sqrt(x)*sqrt(2-b*x)/b^2 +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R - 6\|- b x + 2 asin(--------) + (- b x + 6)\|b \|x +--R +-+ +--R \|2 +--R (2) --------------------------------------------------- +--R 2 +---------+ +-+ +--R b \|- b x + 2 \|b +--R Type: Expression(Integer) +--E 3262 + +--S 3263 of 3330 +--a0000:=integrate(t0000,x) +--E 3263 + +--S 3264 of 3330 +--m0000:=a0000 - r0000 +--E 3264 + +--S 3265 of 3330 +--d0000:=D(m0000,x) +--E 3265 + +)clear all + +--S 3266 of 3330 +t0000:=sqrt(x)/(2-b*x)^(3/2) +--R +--R +--R +-+ +--R \|x +--R (1) - --------------------- +--R +---------+ +--R (b x - 2)\|- b x + 2 +--R Type: Expression(Integer) +--E 3266 + +--S 3267 of 3330 +r0000:=-2*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(3/2)+2*sqrt(x)/(b*sqrt(2-b*x)) +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R - 2\|- b x + 2 asin(--------) + 2\|b \|x +--R +-+ +--R \|2 +--R (2) ----------------------------------------- +--R +---------+ +-+ +--R b\|- b x + 2 \|b +--R Type: Expression(Integer) +--E 3267 + +--S 3268 of 3330 +--a0000:=integrate(t0000,x) +--E 3268 + +--S 3269 of 3330 +--m0000:=a0000 - r0000 +--E 3269 + +--S 3270 of 3330 +--d0000:=D(m0000,x) +--E 3270 + +)clear all + +--S 3271 of 3330 +t0000:=1/((2-b*x)^(3/2)*sqrt(x)) +--R +--R +--R 1 +--R (1) - ------------------------- +--R +---------+ +-+ +--R (b x - 2)\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 3271 + +--S 3272 of 3330 +r0000:=sqrt(x)/sqrt(2-b*x) +--R +--R +--R +-+ +--R \|x +--R (2) ------------ +--R +---------+ +--R \|- b x + 2 +--R Type: Expression(Integer) +--E 3272 + +--S 3273 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +---------+ +-+ 2 +--R (- 10b + 20)\|- b x + 2 \|x + (25b - 51b)x - 50b + 102 +--R (3) -------------------------------------------------------- +--R 2 +--R (10b - 20b)x - 20b + 40 +--R Type: Union(Expression(Integer),...) +--E 3273 + +--S 3274 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 25b - 51 +--R (4) -------- +--R 10b - 20 +--R Type: Expression(Integer) +--E 3274 + +--S 3275 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3275 + +)clear all + +--S 3276 of 3330 +t0000:=1/(x^(3/2)*(2-b*x)^(3/2)) +--R +--R +--R 1 +--R (1) - --------------------------- +--R 2 +---------+ +-+ +--R (b x - 2x)\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 3276 + +--S 3277 of 3330 +r0000:=1/(sqrt(x)*sqrt(2-b*x))-sqrt(2-b*x)/sqrt(x) +--R +--R +--R b x - 1 +--R (2) ---------------- +--R +---------+ +-+ +--R \|- b x + 2 \|x +--R Type: Expression(Integer) +--E 3277 + +--S 3278 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 +---------+ +-+ 3 2 2 +--R ((- 4b + 8b)x + 4b - 8)\|- b x + 2 \|x + (- 4b + 13b - 9b)x +--R + +--R 2 +--R (8b - 26b + 18)x +--R / +--R 2 2 +--R (4b - 8b)x + (- 8b + 16)x +--R Type: Union(Expression(Integer),...) +--E 3278 + +--S 3279 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R - 4b + 13b - 9 +--R (4) --------------- +--R 4b - 8 +--R Type: Expression(Integer) +--E 3279 + +--S 3280 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3280 + +)clear all + +--S 3281 of 3330 +t0000:=1/(x^(5/2)*(2-b*x)^(3/2)) +--R +--R +--R 1 +--R (1) - ---------------------------- +--R 3 2 +---------+ +-+ +--R (b x - 2x )\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 3281 + +--S 3282 of 3330 +r0000:=1/(x^(3/2)*sqrt(2-b*x))-2/3*sqrt(2-b*x)/x^(3/2)-_ + 2/3*b*sqrt(2-b*x)/sqrt(x) +--R +--R +--R 2 2 +--R 2b x - 2b x - 1 +--R (2) ------------------ +--R +---------+ +-+ +--R 3x\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 3282 + +--S 3283 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 2 +---------+ +-+ +--R ((- 4b + 8b )x + (4b - 8b)x + 2b - 4)\|- b x + 2 \|x +--R + +--R 4 3 2 3 3 2 2 +--R (- 2b + 8b - 5b - 3b)x + (4b - 16b + 10b + 6)x +--R / +--R 2 3 2 +--R (6b - 12b)x + (- 12b + 24)x +--R Type: Union(Expression(Integer),...) +--E 3283 + +--S 3284 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 +--R - 2b + 8b - 5b - 3 +--R (4) -------------------- +--R 6b - 12 +--R Type: Expression(Integer) +--E 3284 + +--S 3285 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3285 + +)clear all + +--S 3286 of 3330 +t0000:=x^(5/2)/(2-b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ----------------------------- +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R Type: Expression(Integer) +--E 3286 + +--S 3287 of 3330 +r0000:=2/3*x^(5/2)/(b*(2-b*x)^(3/2))+_ + 10*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(7/2)-_ + 10/3*x^(3/2)/(b^2*sqrt(2-b*x))-5*sqrt(x)*sqrt(2-b*x)/b^3 +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x 2 2 +-+ +-+ +--R (30b x - 60)\|- b x + 2 asin(--------) + (3b x - 40b x + 60)\|b \|x +--R +-+ +--R \|2 +--R (2) --------------------------------------------------------------------- +--R 4 3 +---------+ +-+ +--R (3b x - 6b )\|- b x + 2 \|b +--R Type: Expression(Integer) +--E 3287 + +--S 3288 of 3330 +--a0000:=integrate(t0000,x) +--E 3288 + +--S 3289 of 3330 +--m0000:=a0000 - r0000 +--E 3289 + +--S 3290 of 3330 +--d0000:=D(m0000,x) +--E 3290 + +)clear all + +--S 3291 of 3330 +t0000:=x^(3/2)/(2-b*x)^(5/2) +--R +--R +--R +-+ +--R x\|x +--R (1) ----------------------------- +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R Type: Expression(Integer) +--E 3291 + +--S 3292 of 3330 +r0000:=2/3*x^(3/2)/(b*(2-b*x)^(3/2))+_ + 2*asin(sqrt(b)*sqrt(x)/sqrt(2))/b^(5/2)-2*sqrt(x)/(b^2*sqrt(2-b*x)) +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R (6b x - 12)\|- b x + 2 asin(--------) + (- 8b x + 12)\|b \|x +--R +-+ +--R \|2 +--R (2) ------------------------------------------------------------- +--R 3 2 +---------+ +-+ +--R (3b x - 6b )\|- b x + 2 \|b +--R Type: Expression(Integer) +--E 3292 + +--S 3293 of 3330 +--a0000:=integrate(t0000,x) +--E 3293 + +--S 3294 of 3330 +--m0000:=a0000 - r0000 +--E 3294 + +--S 3295 of 3330 +--d0000:=D(m0000,x) +--E 3295 + +)clear all + +--S 3296 of 3330 +t0000:=sqrt(x)/(2-b*x)^(5/2) +--R +--R +--R +-+ +--R \|x +--R (1) ----------------------------- +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R Type: Expression(Integer) +--E 3296 + +--S 3297 of 3330 +r0000:=1/3*x^(3/2)/(2-b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (2) - ---------------------- +--R +---------+ +--R (3b x - 6)\|- b x + 2 +--R Type: Expression(Integer) +--E 3297 + +--S 3298 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 +---------+ +-+ 3 2 2 2 +--R (2b - 8b + 8)x\|- b x + 2 \|x + (- b + 3b )x + (4b - 12b)x - 4b + 12 +--R ------------------------------------------------------------------------- +--R 4 3 2 2 3 2 2 +--R (6b - 24b + 24b )x + (- 24b + 96b - 96b)x + 24b - 96b + 96 +--R Type: Union(Expression(Integer),...) +--E 3298 + +--S 3299 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R - b + 3 +--R (4) -------------- +--R 2 +--R 6b - 24b + 24 +--R Type: Expression(Integer) +--E 3299 + +--S 3300 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3300 + +)clear all + +--S 3301 of 3330 +t0000:=1/((2-b*x)^(5/2)*sqrt(x)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 2 +---------+ +-+ +--R (b x - 4b x + 4)\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 3301 + +--S 3302 of 3330 +r0000:=1/3*sqrt(x)/(2-b*x)^(3/2)+1/3*sqrt(x)/sqrt(2-b*x) +--R +--R +--R +-+ +--R (b x - 3)\|x +--R (2) ---------------------- +--R +---------+ +--R (3b x - 6)\|- b x + 2 +--R Type: Expression(Integer) +--E 3302 + +--S 3303 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 +---------+ +-+ +--R ((- 6b + 24b - 24b)x + 18b - 72b + 72)\|- b x + 2 \|x +--R + +--R 4 3 2 2 3 2 2 +--R (9b - 46b + 57b )x + (- 36b + 184b - 228b)x + 36b - 184b + 228 +--R / +--R 4 3 2 2 3 2 2 +--R (18b - 72b + 72b )x + (- 72b + 288b - 288b)x + 72b - 288b + 288 +--R Type: Union(Expression(Integer),...) +--E 3303 + +--S 3304 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R 9b - 46b + 57 +--R (4) --------------- +--R 2 +--R 18b - 72b + 72 +--R Type: Expression(Integer) +--E 3304 + +--S 3305 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3305 + +)clear all + +--S 3306 of 3330 +t0000:=1/(x^(3/2)*(2-b*x)^(5/2)) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 2 3 2 +---------+ +-+ +--R (b x - 4b x + 4x)\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 3306 + +--S 3307 of 3330 +r0000:=1/3/((2-b*x)^(3/2)*sqrt(x))+2/3/(sqrt(x)*sqrt(2-b*x))-_ + 2/3*sqrt(2-b*x)/sqrt(x) +--R +--R +--R 2 2 +--R 2b x - 6b x + 3 +--R (2) -------------------------- +--R +---------+ +-+ +--R (3b x - 6)\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 3307 + +--S 3308 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 2 2 3 2 2 +--R ((- 8b + 32b - 32b )x + (24b - 96b + 96b)x - 12b + 48b - 48) +--R * +--R +---------+ +-+ +--R \|- b x + 2 \|x +--R + +--R 5 4 3 2 3 4 3 2 2 +--R (- 8b + 42b - 66b + 27b )x + (32b - 168b + 264b - 108b)x +--R + +--R 3 2 +--R (- 32b + 168b - 264b + 108)x +--R / +--R 4 3 2 3 3 2 2 2 +--R (12b - 48b + 48b )x + (- 48b + 192b - 192b)x + (48b - 192b + 192)x +--R Type: Union(Expression(Integer),...) +--E 3308 + +--S 3309 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 +--R - 8b + 42b - 66b + 27 +--R (4) ----------------------- +--R 2 +--R 12b - 48b + 48 +--R Type: Expression(Integer) +--E 3309 + +--S 3310 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3310 + +)clear all + +--S 3311 of 3330 +t0000:=1/(x^(5/2)*(2-b*x)^(5/2)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 2 4 3 2 +---------+ +-+ +--R (b x - 4b x + 4x )\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 3311 + +--S 3312 of 3330 +r0000:=1/3/(x^(3/2)*(2-b*x)^(3/2))+1/(x^(3/2)*sqrt(2-b*x))-_ + 2/3*sqrt(2-b*x)/x^(3/2)-2/3*b*sqrt(2-b*x)/sqrt(x) +--R +--R +--R 3 3 2 2 +--R 2b x - 6b x + 3b x + 1 +--R (2) ---------------------------- +--R 2 +---------+ +-+ +--R (3b x - 6x)\|- b x + 2 \|x +--R Type: Expression(Integer) +--E 3312 + +--S 3313 of 3330 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 3 3 4 3 2 2 +--R (- 12b + 48b - 48b )x + (36b - 144b + 144b )x +--R + +--R 3 2 2 +--R (- 18b + 72b - 72b)x - 6b + 24b - 24 +--R * +--R +---------+ +-+ +--R \|- b x + 2 \|x +--R + +--R 6 5 4 3 2 4 +--R (- 18b + 92b - 141b + 48b + 19b )x +--R + +--R 5 4 3 2 3 +--R (72b - 368b + 564b - 192b - 76b)x +--R + +--R 4 3 2 2 +--R (- 72b + 368b - 564b + 192b + 76)x +--R / +--R 4 3 2 4 3 2 3 2 2 +--R (18b - 72b + 72b )x + (- 72b + 288b - 288b)x + (72b - 288b + 288)x +--R Type: Union(Expression(Integer),...) +--E 3313 + +--S 3314 of 3330 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 4 3 2 +--R - 18b + 92b - 141b + 48b + 19 +--R (4) -------------------------------- +--R 2 +--R 18b - 72b + 72 +--R Type: Expression(Integer) +--E 3314 + +--S 3315 of 3330 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 3315 + +)clear all + +--S 3316 of 3330 +t0000:=sqrt(x)/sqrt(1-x) +--R +--R +--R +-+ +--R \|x +--R (1) ---------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 3316 + +--S 3317 of 3330 +r0000:=-1/2*asin(1-2*x)-sqrt(1-x)*sqrt(x) +--R +--R +--R +-------+ +-+ +--R - 2\|- x + 1 \|x + asin(2x - 1) +--R (2) -------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 3317 + +--S 3318 of 3330 +--a0000:=integrate(t0000,x) +--E 3318 + +--S 3319 of 3330 +--m0000:=a0000 - r0000 +--E 3319 + +--S 3320 of 3330 +--d0000:=D(m0000,x) +--E 3320 + +)clear all + +--S 3321 of 3330 +t0000:=1/(sqrt(1-x)*sqrt(x)) +--R +--R +--R 1 +--R (1) -------------- +--R +-------+ +-+ +--R \|- x + 1 \|x +--R Type: Expression(Integer) +--E 3321 + +--S 3322 of 3330 +r0000:=-asin(1-2*x) +--R +--R +--R (2) asin(2x - 1) +--R Type: Expression(Integer) +--E 3322 + +--S 3323 of 3330 +--a0000:=integrate(t0000,x) +--E 3323 + +--S 3324 of 3330 +--m0000:=a0000 - r0000 +--E 3324 + +--S 3325 of 3330 +--d0000:=D(m0000,x) +--E 3325 + +)clear all + +--S 3326 of 3330 +t0000:=1/(sqrt(x)*sqrt(1-b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R +---------+ +-+ +--R \|- b x + 1 \|x +--R Type: Expression(Integer) +--E 3326 + +--S 3327 of 3330 +r0000:=2*asin(sqrt(b)*sqrt(x))/sqrt(b) +--R +--R +--R +-+ +-+ +--R 2asin(\|b \|x ) +--R (2) --------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 3327 + +--S 3328 of 3330 +--a0000:=integrate(t0000,x) +--E 3328 + +--S 3329 of 3330 +--m0000:=a0000 - r0000 +--E 3329 + +--S 3330 of 3330 +--d0000:=D(m0000,x) +--E 3330 + +)spool + +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich1a.input.pdf b/src/axiom-website/CATS/rich1a.input.pdf new file mode 100644 index 0000000..166743b Binary files /dev/null and b/src/axiom-website/CATS/rich1a.input.pdf differ diff --git a/src/axiom-website/CATS/rich1b.input.pamphlet b/src/axiom-website/CATS/rich1b.input.pamphlet new file mode 100644 index 0000000..40252a5 --- /dev/null +++ b/src/axiom-website/CATS/rich1b.input.pamphlet @@ -0,0 +1,61612 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich1b.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{Integrands of the form $x^m (a+b x)^n$} +\subsection{Integrands of the form $x^m$} +\subsubsection{Integrands of the form $a$} + +\begin{chunk}{*} +)set break resume +)sys rm -f rich1b.output +)spool rich1b.output +)set message test on +)set message auto off +)clear all + + +--S 1 of 2952 +t0000:=x^(5/3)*(a+b*x) +--R +--R +--R 2 3+-+2 +--R (1) (b x + a x)\|x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 2952 +r0000:=3/8*a*x^(8/3)+3/11*b*x^(11/3) +--R +--R +--R 3 2 3+-+2 +--R (24b x + 33a x )\|x +--R (2) ---------------------- +--R 88 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 2 3+-+2 +--R (24b x + 33a x )\|x +--R (3) ---------------------- +--R 88 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 2952 +t0000:=x^(4/3)*(a+b*x) +--R +--R +--R 2 3+-+ +--R (1) (b x + a x)\|x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 2952 +r0000:=3/7*a*x^(7/3)+3/10*b*x^(10/3) +--R +--R +--R 3 2 3+-+ +--R (21b x + 30a x )\|x +--R (2) --------------------- +--R 70 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 2 3+-+ +--R (21b x + 30a x )\|x +--R (3) --------------------- +--R 70 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 2952 +t0000:=x^(2/3)*(a+b*x) +--R +--R +--R 3+-+2 +--R (1) (b x + a)\|x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 2952 +r0000:=3/5*a*x^(5/3)+3/8*b*x^(8/3) +--R +--R +--R 2 3+-+2 +--R (15b x + 24a x)\|x +--R (2) --------------------- +--R 40 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3+-+2 +--R (15b x + 24a x)\|x +--R (3) --------------------- +--R 40 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 2952 +t0000:=x^(1/3)*(a+b*x) +--R +--R +--R 3+-+ +--R (1) (b x + a)\|x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 2952 +r0000:=3/4*a*x^(4/3)+3/7*b*x^(7/3) +--R +--R +--R 2 3+-+ +--R (12b x + 21a x)\|x +--R (2) -------------------- +--R 28 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3+-+ +--R (12b x + 21a x)\|x +--R (3) -------------------- +--R 28 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 2952 +t0000:=(a+b*x)/x^(1/3) +--R +--R +--R b x + a +--R (1) ------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 2952 +r0000:=3/2*a*x^(2/3)+3/5*b*x^(5/3) +--R +--R +--R 3+-+2 +--R (6b x + 15a)\|x +--R (2) ----------------- +--R 10 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-+2 +--R (6b x + 15a)\|x +--R (3) ----------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 2952 +t0000:=(a+b*x)/x^(2/3) +--R +--R +--R b x + a +--R (1) ------- +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 26 + +--S 27 of 2952 +r0000:=3*a*x^(1/3)+3/4*b*x^(4/3) +--R +--R +--R 3+-+ +--R (3b x + 12a)\|x +--R (2) ---------------- +--R 4 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3+-+ +--R (3b x + 12a)\|x +--R (3) ---------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 2952 +t0000:=(a+b*x)/x^(4/3) +--R +--R +--R b x + a +--R (1) ------- +--R 3+-+ +--R x\|x +--R Type: Expression(Integer) +--E 31 + +--S 32 of 2952 +r0000:=-3*a/x^(1/3)+3/2*b*x^(2/3) +--R +--R +--R 3b x - 6a +--R (2) --------- +--R 3+-+ +--R 2\|x +--R Type: Expression(Integer) +--E 32 + +--S 33 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3b x - 6a +--R (3) --------- +--R 3+-+ +--R 2\|x +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 2952 +t0000:=(a+b*x)/x^(5/3) +--R +--R +--R b x + a +--R (1) ------- +--R 3+-+2 +--R x \|x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 2952 +r0000:=-3/2*a/x^(2/3)+3*b*x^(1/3) +--R +--R +--R 6b x - 3a +--R (2) --------- +--R 3+-+2 +--R 2\|x +--R Type: Expression(Integer) +--E 37 + +--S 38 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 6b x - 3a +--R (3) --------- +--R 3+-+2 +--R 2\|x +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 2952 +t0000:=x^(5/3)*(a+b*x)^2 +--R +--R +--R 2 3 2 2 3+-+2 +--R (1) (b x + 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 2952 +r0000:=3/8*a^2*x^(8/3)+6/11*a*b*x^(11/3)+3/14*b^2*x^(14/3) +--R +--R +--R 2 4 3 2 2 3+-+2 +--R (132b x + 336a b x + 231a x )\|x +--R (2) ------------------------------------ +--R 616 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 4 3 2 2 3+-+2 +--R (132b x + 336a b x + 231a x )\|x +--R (3) ------------------------------------ +--R 616 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 2952 +t0000:=x^(4/3)*(a+b*x)^2 +--R +--R +--R 2 3 2 2 3+-+ +--R (1) (b x + 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 2952 +r0000:=3/7*a^2*x^(7/3)+3/5*a*b*x^(10/3)+3/13*b^2*x^(13/3) +--R +--R +--R 2 4 3 2 2 3+-+ +--R (105b x + 273a b x + 195a x )\|x +--R (2) ----------------------------------- +--R 455 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 4 3 2 2 3+-+ +--R (105b x + 273a b x + 195a x )\|x +--R (3) ----------------------------------- +--R 455 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 2952 +t0000:=x^(2/3)*(a+b*x)^2 +--R +--R +--R 2 2 2 3+-+2 +--R (1) (b x + 2a b x + a )\|x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 2952 +r0000:=3/5*a^2*x^(5/3)+3/4*a*b*x^(8/3)+3/11*b^2*x^(11/3) +--R +--R +--R 2 3 2 2 3+-+2 +--R (60b x + 165a b x + 132a x)\|x +--R (2) ---------------------------------- +--R 220 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 2 2 3+-+2 +--R (60b x + 165a b x + 132a x)\|x +--R (3) ---------------------------------- +--R 220 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 2952 +t0000:=x^(1/3)*(a+b*x)^2 +--R +--R +--R 2 2 2 3+-+ +--R (1) (b x + 2a b x + a )\|x +--R Type: Expression(Integer) +--E 56 + +--S 57 of 2952 +r0000:=3/4*a^2*x^(4/3)+6/7*a*b*x^(7/3)+3/10*b^2*x^(10/3) +--R +--R +--R 2 3 2 2 3+-+ +--R (42b x + 120a b x + 105a x)\|x +--R (2) --------------------------------- +--R 140 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 2 2 3+-+ +--R (42b x + 120a b x + 105a x)\|x +--R (3) --------------------------------- +--R 140 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 2952 +t0000:=(a+b*x)^2/x^(1/3) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 61 + +--S 62 of 2952 +r0000:=3/2*a^2*x^(2/3)+6/5*a*b*x^(5/3)+3/8*b^2*x^(8/3) +--R +--R +--R 2 2 2 3+-+2 +--R (15b x + 48a b x + 60a )\|x +--R (2) ------------------------------ +--R 40 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-+2 +--R (15b x + 48a b x + 60a )\|x +--R (3) ------------------------------ +--R 40 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 2952 +t0000:=(a+b*x)^2/x^(2/3) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 2952 +r0000:=3*a^2*x^(1/3)+3/2*a*b*x^(4/3)+3/7*b^2*x^(7/3) +--R +--R +--R 2 2 2 3+-+ +--R (6b x + 21a b x + 42a )\|x +--R (2) ---------------------------- +--R 14 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 3+-+ +--R (6b x + 21a b x + 42a )\|x +--R (3) ---------------------------- +--R 14 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 2952 +t0000:=(a+b*x)^2/x^(4/3) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 3+-+ +--R x\|x +--R Type: Expression(Integer) +--E 71 + +--S 72 of 2952 +r0000:=-3*a^2/x^(1/3)+3*a*b*x^(2/3)+3/5*b^2*x^(5/3) +--R +--R +--R 2 2 2 +--R 3b x + 15a b x - 15a +--R (2) ---------------------- +--R 3+-+ +--R 5\|x +--R Type: Expression(Integer) +--E 72 + +--S 73 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 3b x + 15a b x - 15a +--R (3) ---------------------- +--R 3+-+ +--R 5\|x +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 2952 +t0000:=(a+b*x)^2/x^(5/3) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 3+-+2 +--R x \|x +--R Type: Expression(Integer) +--E 76 + +--S 77 of 2952 +r0000:=-3/2*a^2/x^(2/3)+6*a*b*x^(1/3)+3/4*b^2*x^(4/3) +--R +--R +--R 2 2 2 +--R 3b x + 24a b x - 6a +--R (2) --------------------- +--R 3+-+2 +--R 4\|x +--R Type: Expression(Integer) +--E 77 + +--S 78 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +--R 3b x + 24a b x - 6a +--R (3) --------------------- +--R 3+-+2 +--R 4\|x +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 2952 +t0000:=x^(5/3)*(a+b*x)^3 +--R +--R +--R 3 4 2 3 2 2 3 3+-+2 +--R (1) (b x + 3a b x + 3a b x + a x)\|x +--R Type: Expression(Integer) +--E 81 + +--S 82 of 2952 +r0000:=3/8*a^3*x^(8/3)+9/11*a^2*b*x^(11/3)+_ + 9/14*a*b^2*x^(14/3)+3/17*b^3*x^(17/3) +--R +--R +--R 3 5 2 4 2 3 3 2 3+-+2 +--R (1848b x + 6732a b x + 8568a b x + 3927a x )\|x +--R (2) ---------------------------------------------------- +--R 10472 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 5 2 4 2 3 3 2 3+-+2 +--R (1848b x + 6732a b x + 8568a b x + 3927a x )\|x +--R (3) ---------------------------------------------------- +--R 10472 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 2952 +t0000:=x^(4/3)*(a+b*x)^3 +--R +--R +--R 3 4 2 3 2 2 3 3+-+ +--R (1) (b x + 3a b x + 3a b x + a x)\|x +--R Type: Expression(Integer) +--E 86 + +--S 87 of 2952 +r0000:=3/7*a^3*x^(7/3)+9/10*a^2*b*x^(10/3)+9/13*a*b^2*x^(13/3)+_ + 3/16*b^3*x^(16/3) +--R +--R +--R 3 5 2 4 2 3 3 2 3+-+ +--R (1365b x + 5040a b x + 6552a b x + 3120a x )\|x +--R (2) --------------------------------------------------- +--R 7280 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 5 2 4 2 3 3 2 3+-+ +--R (1365b x + 5040a b x + 6552a b x + 3120a x )\|x +--R (3) --------------------------------------------------- +--R 7280 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 2952 +t0000:=x^(2/3)*(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 3+-+2 +--R (1) (b x + 3a b x + 3a b x + a )\|x +--R Type: Expression(Integer) +--E 91 + +--S 92 of 2952 +r0000:=3/5*a^3*x^(5/3)+9/8*a^2*b*x^(8/3)+9/11*a*b^2*x^(11/3)+_ + 3/14*b^3*x^(14/3) +--R +--R +--R 3 4 2 3 2 2 3 3+-+2 +--R (660b x + 2520a b x + 3465a b x + 1848a x)\|x +--R (2) -------------------------------------------------- +--R 3080 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 4 2 3 2 2 3 3+-+2 +--R (660b x + 2520a b x + 3465a b x + 1848a x)\|x +--R (3) -------------------------------------------------- +--R 3080 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 2952 +t0000:=x^(1/3)*(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 3+-+ +--R (1) (b x + 3a b x + 3a b x + a )\|x +--R Type: Expression(Integer) +--E 96 + +--S 97 of 2952 +r0000:=3/4*a^3*x^(4/3)+9/7*a^2*b*x^(7/3)+9/10*a*b^2*x^(10/3)+_ + 3/13*b^3*x^(13/3) +--R +--R +--R 3 4 2 3 2 2 3 3+-+ +--R (420b x + 1638a b x + 2340a b x + 1365a x)\|x +--R (2) ------------------------------------------------- +--R 1820 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 4 2 3 2 2 3 3+-+ +--R (420b x + 1638a b x + 2340a b x + 1365a x)\|x +--R (3) ------------------------------------------------- +--R 1820 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 2952 +t0000:=(a+b*x)^3/x^(1/3) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 2952 +r0000:=3/2*a^3*x^(2/3)+9/5*a^2*b*x^(5/3)+9/8*a*b^2*x^(8/3)+3/11*b^3*x^(11/3) +--R +--R +--R 3 3 2 2 2 3 3+-+2 +--R (120b x + 495a b x + 792a b x + 660a )\|x +--R (2) --------------------------------------------- +--R 440 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-+2 +--R (120b x + 495a b x + 792a b x + 660a )\|x +--R (3) --------------------------------------------- +--R 440 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 2952 +t0000:=(a+b*x)^3/x^(2/3) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 106 + +--S 107 of 2952 +r0000:=3*a^3*x^(1/3)+9/4*a^2*b*x^(4/3)+9/7*a*b^2*x^(7/3)+3/10*b^3*x^(10/3) +--R +--R +--R 3 3 2 2 2 3 3+-+ +--R (42b x + 180a b x + 315a b x + 420a )\|x +--R (2) ------------------------------------------- +--R 140 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 3+-+ +--R (42b x + 180a b x + 315a b x + 420a )\|x +--R (3) ------------------------------------------- +--R 140 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 2952 +t0000:=(a+b*x)^3/x^(4/3) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 3+-+ +--R x\|x +--R Type: Expression(Integer) +--E 111 + +--S 112 of 2952 +r0000:=-3*a^3/x^(1/3)+9/2*a^2*b*x^(2/3)+9/5*a*b^2*x^(5/3)+3/8*b^3*x^(8/3) +--R +--R +--R 3 3 2 2 2 3 +--R 15b x + 72a b x + 180a b x - 120a +--R (2) ------------------------------------ +--R 3+-+ +--R 40\|x +--R Type: Expression(Integer) +--E 112 + +--S 113 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 15b x + 72a b x + 180a b x - 120a +--R (3) ------------------------------------ +--R 3+-+ +--R 40\|x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 2952 +t0000:=(a+b*x)^3/x^(5/3) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 3+-+2 +--R x \|x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 2952 +r0000:=-3/2*a^3/x^(2/3)+9*a^2*b*x^(1/3)+9/4*a*b^2*x^(4/3)+3/7*b^3*x^(7/3) +--R +--R +--R 3 3 2 2 2 3 +--R 12b x + 63a b x + 252a b x - 42a +--R (2) ----------------------------------- +--R 3+-+2 +--R 28\|x +--R Type: Expression(Integer) +--E 117 + +--S 118 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +--R 12b x + 63a b x + 252a b x - 42a +--R (3) ----------------------------------- +--R 3+-+2 +--R 28\|x +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 2952 +t0000:=x^(5/3)/(a+b*x) +--R +--R +--R 3+-+2 +--R x \|x +--R (1) ------- +--R b x + a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 2952 +r0000:=-3/2*a*x^(2/3)/b^2+3/5*x^(5/3)/b-a^(5/3)*log(a^(1/3)+_ + b^(1/3)*x^(1/3))/b^(8/3)+1/2*a^(5/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/b^(8/3)-_ + a^(5/3)*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/_ + (a^(1/3)*sqrt(3)))*sqrt(3)/b^(8/3) +--R +--R +--R (2) +--R 3+-+2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R 5a \|a log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 3+-+2 3+-+3+-+ 3+-+ +-+3+-+2 2\|b \|x - \|a +--R - 10a \|a log(\|b \|x + \|a ) + 10a\|3 \|a atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3+-+2 3+-+2 +--R (6b x - 15a)\|b \|x +--R / +--R 2 3+-+2 +--R 10b \|b +--R Type: Expression(Integer) +--E 122 + +--S 123 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R | a 3+-+2 | a 3+-+ | a +--R - 5a |- -- log(a \|x - b |- -- \|x - a |- --) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +----+ +----+2 +--R | 2 | 2 +--R | a 3+-+ | a +--R 10a |- -- log(a\|x + b |- -- ) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R +----+2 +--R | 2 +--R 3+-+ | a +--R +----+ 2a\|x - b |- -- +--R | 2 3| 2 +--R +-+ | a \| b 3+-+2 +--R - 10a\|3 |- -- atan(------------------- + (6b x - 15a)\|x +--R 3| 2 +----+2 +--R \| b | 2 +--R +-+ | a +--R b\|3 |- -- +--R 3| 2 +--R \| b +--R / +--R 2 +--R 10b +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3+-+2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - a \|a log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R | a 3+-+2 3+-+2 | a 3+-+ | a +--R - a |- -- \|b log(a \|x - b |- -- \|x - a |- --) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +----+ +----+2 +--R | 2 | 2 +--R 3+-+2 3+-+3+-+ 3+-+ | a 3+-+2 3+-+ | a +--R 2a \|a log(\|b \|x + \|a ) + 2a |- -- \|b log(a\|x + b |- -- ) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R 3+-+3+-+ 3+-+ +--R +-+3+-+2 2\|b \|x - \|a +--R - 2a\|3 \|a atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+2 +--R | 2 +--R 3+-+ | a +--R +----+ 2a\|x - b |- -- +--R | 2 3| 2 +--R +-+ | a 3+-+2 \| b +--R - 2a\|3 |- -- \|b atan(-------------------) +--R 3| 2 +----+2 +--R \| b | 2 +--R +-+ | a +--R b\|3 |- -- +--R 3| 2 +--R \| b +--R / +--R 2 3+-+2 +--R 2b \|b +--R Type: Expression(Integer) +--E 124 + +--S 125 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 2952 +t0000:=x^(4/3)/(a+b*x) +--R +--R +--R 3+-+ +--R x\|x +--R (1) ------- +--R b x + a +--R Type: Expression(Integer) +--E 126 + +--S 127 of 2952 +r0000:=-3*a*x^(1/3)/b^2+3/4*x^(4/3)/b+a^(4/3)*log(a^(1/3)+_ + b^(1/3)*x^(1/3))/b^(7/3)-1/2*a^(4/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/b^(7/3)-_ + a^(4/3)*atan((a^(1/3)-_ + 2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(7/3) +--R +--R +--R (2) +--R 3+-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - 2a\|a log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 3+-+ 3+-+3+-+ 3+-+ +-+3+-+ 2\|b \|x - \|a +--R 4a\|a log(\|b \|x + \|a ) + 4a\|3 \|a atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3+-+3+-+ +--R (3b x - 12a)\|b \|x +--R / +--R 2 3+-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 127 + +--S 128 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-+ +-+2 +-+ +-+ +--R |a 3+-+2 |a 3+-+ |a |a 3+-+ |a +--R - 2a 3|- log(\|x - 3|- \|x + 3|- + 4a 3|- log(\|x + 3|- ) +--R \|b \|b \|b \|b \|b +--R + +--R +-+ +--R 3+-+ |a +--R +-+ 2\|x - 3|- +--R +-+ |a \|b 3+-+ +--R 4a\|3 3|- atan(------------ + (3b x - 12a)\|x +--R \|b +-+ +--R +-+ |a +--R \|3 3|- +--R \|b +--R / +--R 2 +--R 4b +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3+-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R a\|a log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +-+ +-+ +-+2 +--R |a 3+-+ 3+-+2 |a 3+-+ |a 3+-+ 3+-+3+-+ 3+-+ +--R - a 3|- \|b log(\|x - 3|- \|x + 3|- - 2a\|a log(\|b \|x + \|a ) +--R \|b \|b \|b +--R + +--R +-+ +-+ 3+-+3+-+ 3+-+ +--R |a 3+-+ 3+-+ |a +-+3+-+ 2\|b \|x - \|a +--R 2a 3|- \|b log(\|x + 3|- - 2a\|3 \|a atan(----------------) +--R \|b \|b +-+3+-+ +--R \|3 \|a +--R + +--R +-+ +--R 3+-+ |a +--R +-+ 2\|x - 3|- +--R +-+ |a 3+-+ \|b +--R 2a\|3 3|- \|b atan(------------) +--R \|b +-+ +--R +-+ |a +--R \|3 3|- +--R \|b +--R / +--R 2 3+-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 129 + +--S 130 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 2952 +t0000:=x^(2/3)/(a+b*x) +--R +--R +--R 3+-+2 +--R \|x +--R (1) ------- +--R b x + a +--R Type: Expression(Integer) +--E 131 + +--S 132 of 2952 +r0000:=3/2*x^(2/3)/b+a^(2/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/b^(5/3)-_ + 1/2*a^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3)+_ + b^(2/3)*x^(2/3))/b^(5/3)+a^(2/3)*atan((a^(1/3)-_ + 2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(5/3) +--R +--R +--R (2) +--R 3+-+2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - \|a log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 3+-+2 3+-+3+-+ 3+-+ +-+3+-+2 2\|b \|x - \|a 3+-+2 3+-+2 +--R 2\|a log(\|b \|x + \|a ) - 2\|3 \|a atan(----------------) + 3\|b \|x +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+2 +--R 2b \|b +--R Type: Expression(Integer) +--E 132 + +--S 133 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +--+ +--+2 +--+ +--+ +--+2 +--R | 2 | 2 | 2 | 2 | 2 +--R |a 3+-+2 |a 3+-+ |a |a 3+-+ |a +--R - |-- log(a \|x - b |-- \|x + a |--) + 2 |-- log(a\|x + b |-- ) +--R 3| 2 3| 2 3| 2 3| 2 3| 2 +--R \|b \|b \|b \|b \|b +--R + +--R +--+2 +--R | 2 +--R 3+-+ |a +--R +--+ 2a\|x - b |-- +--R | 2 3| 2 +--R +-+ |a \|b 3+-+2 +--R - 2\|3 |-- atan(----------------- + 3\|x +--R 3| 2 +--+2 +--R \|b | 2 +--R +-+ |a +--R b\|3 |-- +--R 3| 2 +--R \|b +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3+-+2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R \|a log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R |a 3+-+2 3+-+2 |a 3+-+ |a +--R - |-- \|b log(a \|x - b |-- \|x + a |--) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +--+ +--+2 +--R | 2 | 2 +--R 3+-+2 3+-+3+-+ 3+-+ |a 3+-+2 3+-+ |a +--R - 2\|a log(\|b \|x + \|a ) + 2 |-- \|b log(a\|x + b |-- ) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+2 +--R | 2 +--R 3+-+ |a +--R +--+ 2a\|x - b |-- +--R 3+-+3+-+ 3+-+ | 2 3| 2 +--R +-+3+-+2 2\|b \|x - \|a +-+ |a 3+-+2 \|b +--R 2\|3 \|a atan(----------------) - 2\|3 |-- \|b atan(-----------------) +--R +-+3+-+ 3| 2 +--+2 +--R \|3 \|a \|b | 2 +--R +-+ |a +--R b\|3 |-- +--R 3| 2 +--R \|b +--R / +--R 3+-+2 +--R 2b \|b +--R Type: Expression(Integer) +--E 134 + +--S 135 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 2952 +t0000:=x^(1/3)/(a+b*x) +--R +--R +--R 3+-+ +--R \|x +--R (1) ------- +--R b x + a +--R Type: Expression(Integer) +--E 136 + +--S 137 of 2952 +r0000:=3*x^(1/3)/b-a^(1/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/b^(4/3)+_ + 1/2*a^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3)+_ + b^(2/3)*x^(2/3))/b^(4/3)+a^(1/3)*atan((a^(1/3)-_ + 2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(4/3) +--R +--R +--R (2) +--R 3+-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 3+-+ 3+-+3+-+ 3+-+ +--R \|a log(\|b \|x - \|a \|b \|x + \|a ) - 2\|a log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R +-+3+-+ 2\|b \|x - \|a 3+-+3+-+ +--R - 2\|3 \|a atan(----------------) + 6\|b \|x +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 137 + +--S 138 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +---+ +---+2 +---+ +---+ +--R | a 3+-+2 | a 3+-+ | a | a 3+-+ | a +--R - 3|- - log(\|x + 3|- - \|x + 3|- - ) + 2 3|- - log(\|x - 3|- - ) +--R \| b \| b \| b \| b \| b +--R + +--R +---+ +--R 3+-+ | a +--R +---+ 2\|x + 3|- - +--R +-+ | a \| b 3+-+ +--R - 2\|3 3|- - atan(-------------- + 6\|x +--R \| b +---+ +--R +-+ | a +--R \|3 3|- - +--R \| b +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3+-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - \|a log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +---+ +---+ +---+2 +--R | a 3+-+ 3+-+2 | a 3+-+ | a 3+-+ 3+-+3+-+ 3+-+ +--R - 3|- - \|b log(\|x + 3|- - \|x + 3|- - ) + 2\|a log(\|b \|x + \|a ) +--R \| b \| b \| b +--R + +--R +---+ +---+ 3+-+3+-+ 3+-+ +--R | a 3+-+ 3+-+ | a +-+3+-+ 2\|b \|x - \|a +--R 2 3|- - \|b log(\|x - 3|- - + 2\|3 \|a atan(----------------) +--R \| b \| b +-+3+-+ +--R \|3 \|a +--R + +--R +---+ +--R 3+-+ | a +--R +---+ 2\|x + 3|- - +--R +-+ | a 3+-+ \| b +--R - 2\|3 3|- - \|b atan(--------------) +--R \| b +---+ +--R +-+ | a +--R \|3 3|- - +--R \| b +--R / +--R 3+-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 139 + +--S 140 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 2952 +t0000:=1/(x^(1/3)*(a+b*x)) +--R +--R +--R 1 +--R (1) ------------- +--R 3+-+ +--R (b x + a)\|x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 2952 +r0000:=-log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(1/3)*b^(2/3))+_ + 1/2*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/_ + (a^(1/3)*b^(2/3))-atan((a^(1/3)-2*b^(1/3)*x^(1/3))/_ + (a^(1/3)*sqrt(3)))*sqrt(3)/(a^(1/3)*b^(2/3)) +--R +--R +--R (2) +--R 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 3+-+3+-+ 3+-+ +--R log(\|b \|x - \|a \|b \|x + \|a ) - 2log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R +-+ 2\|b \|x - \|a +--R 2\|3 atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+3+-+2 +--R 2\|a \|b +--R Type: Expression(Integer) +--E 142 + +--S 143 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +------+ +------+2 +--R 3| 2 3+-+2 3| 2 3+-+ +--R - log(b\|- a b \|x + \|- a b \|x - a b) +--R + +--R +------+2 +--R +------+2 3| 2 3+-+ +--R 3| 2 3+-+ +-+ 2\|- a b \|x - a b +--R 2log(\|- a b \|x + a b) - 2\|3 atan(---------------------) +--R +-+ +--R a b\|3 +--R / +--R +------+ +--R 3| 2 +--R 2\|- a b +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +------+ +--R 3| 2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - \|- a b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +------+ +------+2 +--R 3+-+3+-+2 3| 2 3+-+2 3| 2 3+-+ +--R - \|a \|b log(b\|- a b \|x + \|- a b \|x - a b) +--R + +--R +------+ +------+2 +--R 3| 2 3+-+3+-+ 3+-+ 3+-+3+-+2 3| 2 3+-+ +--R 2\|- a b log(\|b \|x + \|a ) + 2\|a \|b log(\|- a b \|x + a b) +--R + +--R +------+ 3+-+3+-+ 3+-+ +--R +-+3| 2 2\|b \|x - \|a +--R - 2\|3 \|- a b atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R 3| 2 3+-+ +--R +-+3+-+3+-+2 2\|- a b \|x - a b +--R - 2\|3 \|a \|b atan(---------------------) +--R +-+ +--R a b\|3 +--R / +--R +------+ +--R 3| 2 3+-+3+-+2 +--R 2\|- a b \|a \|b +--R Type: Expression(Integer) +--E 144 + +--S 145 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 2952 +t0000:=1/(x^(2/3)*(a+b*x)) +--R +--R +--R 1 +--R (1) -------------- +--R 3+-+2 +--R (b x + a)\|x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 2952 +r0000:=log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(2/3)*b^(1/3))-_ + 1/2*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/_ + (a^(2/3)*b^(1/3))-atan((a^(1/3)-2*b^(1/3)*x^(1/3))/_ + (a^(1/3)*sqrt(3)))*sqrt(3)/(a^(2/3)*b^(1/3)) +--R +--R +--R (2) +--R 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 3+-+3+-+ 3+-+ +--R - log(\|b \|x - \|a \|b \|x + \|a ) + 2log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R +-+ 2\|b \|x - \|a +--R 2\|3 atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+2 3+-+ +--R 2\|a \|b +--R Type: Expression(Integer) +--E 147 + +--S 148 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+2 +---+ +---+ +--R 3| 2 3+-+2 3| 2 3+-+ 2 3| 2 3+-+ +--R - log(\|a b \|x - a\|a b \|x + a ) + 2log(\|a b \|x + a) +--R + +--R +---+ +--R 3| 2 3+-+ +--R +-+ 2\|a b \|x - a +--R 2\|3 atan(---------------) +--R +-+ +--R a\|3 +--R / +--R +---+ +--R 3| 2 +--R 2\|a b +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +---+2 +---+ +--R 3+-+2 3+-+ 3| 2 3+-+2 3| 2 3+-+ 2 +--R - \|a \|b log(\|a b \|x - a\|a b \|x + a ) +--R + +--R +---+ +--R 3| 2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R \|a b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +---+ +---+ +--R 3+-+2 3+-+ 3| 2 3+-+ 3| 2 3+-+3+-+ 3+-+ +--R 2\|a \|b log(\|a b \|x + a - 2\|a b log(\|b \|x + \|a ) +--R + +--R +---+ +--R 3| 2 3+-+ +---+ 3+-+3+-+ 3+-+ +--R +-+3+-+2 3+-+ 2\|a b \|x - a +-+3| 2 2\|b \|x - \|a +--R 2\|3 \|a \|b atan(--------------- - 2\|3 \|a b atan(----------------) +--R +-+ +-+3+-+ +--R a\|3 \|3 \|a +--R / +--R +---+ +--R 3+-+2 3+-+3| 2 +--R 2\|a \|b \|a b +--R Type: Expression(Integer) +--E 149 + +--S 150 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 2952 +t0000:=1/(x^(4/3)*(a+b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R 2 3+-+ +--R (b x + a x)\|x +--R Type: Expression(Integer) +--E 151 + +--S 152 of 2952 +r0000:=(-3)/(a*x^(1/3))+b^(1/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/a^(4/3)-_ + 1/2*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3)+_ + b^(2/3)*x^(2/3))/a^(4/3)+b^(1/3)*atan((a^(1/3)-_ + 2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(4/3) +--R +--R +--R (2) +--R 3+-+3+-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - \|b \|x log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 3+-+3+-+ 3+-+3+-+ 3+-+ +-+3+-+3+-+ 2\|b \|x - \|a 3+-+ +--R 2\|b \|x log(\|b \|x + \|a ) - 2\|3 \|b \|x atan(----------------) - 6\|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+3+-+ +--R 2a\|a \|x +--R Type: Expression(Integer) +--E 152 + +--S 153 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-+2 +-+ +--R |b 3+-+ 3+-+2 |b 3+-+ |b +--R - 3|- \|x log(b \|x - a 3|- \|x + a 3|-) +--R \|a \|a \|a +--R + +--R +-+2 +--R 3+-+ |b +--R +-+ +-+2 +-+ 2b\|x - a 3|- +--R |b 3+-+ 3+-+ |b +-+ |b 3+-+ \|a +--R 2 3|- \|x log(b\|x + a 3|- - 2\|3 3|- \|x atan(---------------- - 6 +--R \|a \|a \|a +-+2 +--R +-+ |b +--R a\|3 3|- +--R \|a +--R / +--R 3+-+ +--R 2a\|x +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3+-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R \|b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +-+ +-+2 +-+ +--R 3+-+ |b 3+-+2 |b 3+-+ |b 3+-+ 3+-+3+-+ 3+-+ +--R - \|a 3|- log(b \|x - a 3|- \|x + a 3|- - 2\|b log(\|b \|x + \|a ) +--R \|a \|a \|a +--R + +--R +-+ +-+2 3+-+3+-+ 3+-+ +--R 3+-+ |b 3+-+ |b +-+3+-+ 2\|b \|x - \|a +--R 2\|a 3|- log(b\|x + a 3|- + 2\|3 \|b atan(----------------) +--R \|a \|a +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R 3+-+ |b +--R +-+ 2b\|x - a 3|- +--R +-+3+-+ |b \|a +--R - 2\|3 \|a 3|- atan(----------------) +--R \|a +-+2 +--R +-+ |b +--R a\|3 3|- +--R \|a +--R / +--R 3+-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 154 + +--S 155 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 2952 +t0000:=1/(x^(5/3)*(a+b*x)) +--R +--R +--R 1 +--R (1) ----------------- +--R 2 3+-+2 +--R (b x + a x)\|x +--R Type: Expression(Integer) +--E 156 + +--S 157 of 2952 +r0000:=(-3/2)/(a*x^(2/3))-b^(2/3)*log(a^(1/3)+_ + b^(1/3)*x^(1/3))/a^(5/3)+1/2*b^(2/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/a^(5/3)+_ + b^(2/3)*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))*_ + sqrt(3)/a^(5/3) +--R +--R +--R (2) +--R 3+-+2 3+-+2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R \|b \|x log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 3+-+2 3+-+2 3+-+3+-+ 3+-+ +-+3+-+2 3+-+2 2\|b \|x - \|a +--R - 2\|b \|x log(\|b \|x + \|a - 2\|3 \|b \|x atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3+-+2 +--R - 3\|a +--R / +--R 3+-+2 3+-+2 +--R 2a \|a \|x +--R Type: Expression(Integer) +--E 157 + +--S 158 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +----+ +----+ +----+2 +--R | 2 | 2 | 2 +--R | b 3+-+2 2 3+-+2 | b 3+-+ 2 | b +--R - |- -- \|x log(b \|x + a b |- -- \|x + a |- -- ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R | b 3+-+2 3+-+ | b +--R 2 |- -- \|x log(b\|x - a |- --) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R 3+-+ | b +--R +----+ 2b\|x + a |- -- +--R | 2 3| 2 +--R +-+ | b 3+-+2 \| a +--R - 2\|3 |- -- \|x atan(----------------- - 3 +--R 3| 2 +----+ +--R \| a | 2 +--R +-+ | b +--R a\|3 |- -- +--R 3| 2 +--R \| a +--R / +--R 3+-+2 +--R 2a \|x +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3+-+2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - \|b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +----+ +----+ +----+2 +--R | 2 | 2 | 2 +--R | b 3+-+2 2 3+-+2 | b 3+-+ 2 | b +--R - |- -- \|a log(b \|x + a b |- -- \|x + a |- -- ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 3+-+2 3+-+3+-+ 3+-+ | b 3+-+2 3+-+ | b +--R 2\|b log(\|b \|x + \|a ) + 2 |- -- \|a log(b\|x - a |- --) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R 3+-+ | b +--R +----+ 2b\|x + a |- -- +--R 3+-+3+-+ 3+-+ | 2 3| 2 +--R +-+3+-+2 2\|b \|x - \|a +-+ | b 3+-+2 \| a +--R 2\|3 \|b atan(----------------) - 2\|3 |- -- \|a atan(-----------------) +--R +-+3+-+ 3| 2 +----+ +--R \|3 \|a \| a | 2 +--R +-+ | b +--R a\|3 |- -- +--R 3| 2 +--R \| a +--R / +--R 3+-+2 +--R 2a \|a +--R Type: Expression(Integer) +--E 159 + +--S 160 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 2952 +t0000:=x^(5/3)/(a+b*x)^2 +--R +--R +--R 3+-+2 +--R x \|x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 161 + +--S 162 of 2952 +r0000:=5/2*x^(2/3)/b^2-x^(5/3)/(b*(a+b*x))+5/3*a^(2/3)*log(a^(1/3)+_ + b^(1/3)*x^(1/3))/b^(8/3)-5/6*a^(2/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/b^(8/3)+_ + 5*a^(2/3)*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*_ + sqrt(3)))/(b^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (- 5b x - 5a)\|3 \|a log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +-+3+-+2 3+-+3+-+ 3+-+ +--R (10b x + 10a)\|3 \|a log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 3+-+2 2\|b \|x - \|a +-+3+-+2 3+-+2 +--R (- 30b x - 30a)\|a atan(----------------) + (9b x + 15a)\|3 \|b \|x +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 2 +-+3+-+2 +--R (6b x + 6a b )\|3 \|b +--R Type: Expression(Integer) +--E 162 + +--S 163 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+ |a 3+-+2 |a 3+-+ |a +--R (- 5b x - 5a)\|3 |-- log(a \|x - b |-- \|x + a |--) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |a 3+-+ |a +--R (10b x + 10a)\|3 |-- log(a\|x + b |-- ) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+3+-+ +-+ |a +--R +--+ 2a\|3 \|x - b\|3 |-- +--R | 2 3| 2 +--R |a \|b +-+3+-+2 +--R (- 30b x - 30a) |-- atan(------------------------ + (9b x + 15a)\|3 \|x +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R 3 2 +-+ +--R (6b x + 6a b )\|3 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R 5\|3 \|a log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+ |a 3+-+2 3+-+2 |a 3+-+ |a +--R - 5\|3 |-- \|b log(a \|x - b |-- \|x + a |--) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +--+ +--+2 +--R | 2 | 2 +--R +-+3+-+2 3+-+3+-+ 3+-+ +-+ |a 3+-+2 3+-+ |a +--R - 10\|3 \|a log(\|b \|x + \|a ) + 10\|3 |-- \|b log(a\|x + b |-- ) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+3+-+ +-+ |a +--R +--+ 2a\|3 \|x - b\|3 |-- +--R 3+-+3+-+ 3+-+ | 2 3| 2 +--R 3+-+2 2\|b \|x - \|a |a 3+-+2 \|b +--R 30\|a atan(----------------) - 30 |-- \|b atan(------------------------) +--R +-+3+-+ 3| 2 +--+2 +--R \|3 \|a \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R 2 +-+3+-+2 +--R 6b \|3 \|b +--R Type: Expression(Integer) +--E 164 + +--S 165 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 2952 +t0000:=x^(4/3)/(a+b*x)^2 +--R +--R +--R 3+-+ +--R x\|x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 166 + +--S 167 of 2952 +r0000:=4*x^(1/3)/b^2-x^(4/3)/(b*(a+b*x))-4/3*a^(1/3)*log(a^(1/3)+_ + b^(1/3)*x^(1/3))/b^(7/3)+2/3*a^(1/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/b^(7/3)+_ + 4*a^(1/3)*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/_ + (b^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (2b x + 2a)\|3 \|a log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +-+3+-+ 3+-+3+-+ 3+-+ +--R (- 4b x - 4a)\|3 \|a log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 3+-+ 2\|b \|x - \|a +-+3+-+3+-+ +--R (- 12b x - 12a)\|a atan(----------------) + (9b x + 12a)\|3 \|b \|x +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 2 +-+3+-+ +--R (3b x + 3a b )\|3 \|b +--R Type: Expression(Integer) +--E 167 + +--S 168 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+ +---+ +---+2 +--R +-+ | a 3+-+2 | a 3+-+ | a +--R (- 2b x - 2a)\|3 3|- - log(\|x + 3|- - \|x + 3|- - ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R +-+ | a 3+-+ | a +--R (4b x + 4a)\|3 3|- - log(\|x - 3|- - ) +--R \| b \| b +--R + +--R +---+ +--R +-+3+-+ +-+ | a +--R +---+ 2\|3 \|x + \|3 3|- - +--R | a \| b +-+3+-+ +--R (- 12b x - 12a) 3|- - atan(---------------------- + (9b x + 12a)\|3 \|x +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R 3 2 +-+ +--R (3b x + 3a b )\|3 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - 2\|3 \|a log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +---+ +---+ +---+2 +--R +-+ | a 3+-+ 3+-+2 | a 3+-+ | a +--R - 2\|3 3|- - \|b log(\|x + 3|- - \|x + 3|- - ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R +-+3+-+ 3+-+3+-+ 3+-+ +-+ | a 3+-+ 3+-+ | a +--R 4\|3 \|a log(\|b \|x + \|a ) + 4\|3 3|- - \|b log(\|x - 3|- - ) +--R \| b \| b +--R + +--R +---+ +--R +-+3+-+ +-+ | a +--R 3+-+3+-+ 3+-+ +---+ 2\|3 \|x + \|3 3|- - +--R 3+-+ 2\|b \|x - \|a | a 3+-+ \| b +--R 12\|a atan(----------------) - 12 3|- - \|b atan(----------------------) +--R +-+3+-+ \| b +---+ +--R \|3 \|a | a +--R 3 3|- - +--R \| b +--R / +--R 2 +-+3+-+ +--R 3b \|3 \|b +--R Type: Expression(Integer) +--E 169 + +--S 170 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 2952 +t0000:=x^(2/3)/(a+b*x)^2 +--R +--R +--R 3+-+2 +--R \|x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 171 + +--S 172 of 2952 +r0000:=-x^(2/3)/(b*(a+b*x))-2/3*log(a^(1/3)+_ + b^(1/3)*x^(1/3))/(a^(1/3)*b^(5/3))+1/3*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/(a^(1/3)*b^(5/3))-_ + 2*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/_ + (a^(1/3)*b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (b x + a)\|3 log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R +-+ 3+-+3+-+ 3+-+ 2\|b \|x - \|a +--R (- 2b x - 2a)\|3 log(\|b \|x + \|a ) + (6b x + 6a)atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-+2 3+-+2 +--R - 3\|3 \|a \|b \|x +--R / +--R 2 +-+3+-+3+-+2 +--R (3b x + 3a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 172 + +--S 173 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +------+ +------+2 +--R +-+ 3| 2 3+-+2 3| 2 3+-+ +--R (- b x - a)\|3 log(b\|- a b \|x + \|- a b \|x - a b) +--R + +--R +------+2 +--R +-+ 3| 2 3+-+ +--R (2b x + 2a)\|3 log(\|- a b \|x + a b) +--R + +--R +------+2 +--R +-+3| 2 3+-+ +-+ +------+ +--R 2\|3 \|- a b \|x - a b\|3 +-+3| 2 3+-+2 +--R (- 6b x - 6a)atan(-----------------------------) - 3\|3 \|- a b \|x +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 +--R (3b x + 3a b)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +------+ +------+2 +--R +-+3+-+3+-+2 3| 2 3+-+2 3| 2 3+-+ +--R - \|3 \|a \|b log(b\|- a b \|x + \|- a b \|x - a b) +--R + +--R +------+ +--R +-+3| 2 3+-+3+-+ 3+-+ +--R 2\|3 \|- a b log(\|b \|x + \|a ) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 3+-+ +--R 2\|3 \|a \|b log(\|- a b \|x + a b) +--R + +--R +------+ 3+-+3+-+ 3+-+ +--R 3| 2 2\|b \|x - \|a +--R - 6\|- a b atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 3+-+ +-+ +--R 3+-+3+-+2 2\|3 \|- a b \|x - a b\|3 +--R - 6\|a \|b atan(-----------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 3b\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 174 + +--S 175 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 2952 +t0000:=x^(1/3)/(a+b*x)^2 +--R +--R +--R 3+-+ +--R \|x +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 176 + +--S 177 of 2952 +r0000:=-x^(1/3)/(b*(a+b*x))+1/3*log(a^(1/3)+_ + b^(1/3)*x^(1/3))/(a^(2/3)*b^(4/3))-1/6*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/(a^(2/3)*b^(4/3))-_ + atan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/_ + (a^(2/3)*b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (- b x - a)\|3 log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R +-+ 3+-+3+-+ 3+-+ 2\|b \|x - \|a +--R (2b x + 2a)\|3 log(\|b \|x + \|a ) + (6b x + 6a)atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+3+-+ +--R - 6\|3 \|a \|b \|x +--R / +--R 2 +-+3+-+2 3+-+ +--R (6b x + 6a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 177 + +--S 178 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R +-+ 3| 2 3+-+2 3| 2 3+-+ 2 +--R (- b x - a)\|3 log(\|a b \|x - a\|a b \|x + a ) +--R + +--R +---+ +--R +-+ 3| 2 3+-+ +--R (2b x + 2a)\|3 log(\|a b \|x + a) +--R + +--R +---+ +--R +-+3| 2 3+-+ +-+ +---+ +--R 2\|3 \|a b \|x - a\|3 +-+3| 2 3+-+ +--R (6b x + 6a)atan(-----------------------) - 6\|3 \|a b \|x +--R 3a +--R / +--R +---+ +--R 2 +-+3| 2 +--R (6b x + 6a b)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 3| 2 3+-+2 3| 2 3+-+ 2 +--R - \|3 \|a \|b log(\|a b \|x - a\|a b \|x + a ) +--R + +--R +---+ +--R +-+3| 2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R \|3 \|a b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +---+ +---+ +--R +-+3+-+2 3+-+ 3| 2 3+-+ +-+3| 2 3+-+3+-+ 3+-+ +--R 2\|3 \|a \|b log(\|a b \|x + a - 2\|3 \|a b log(\|b \|x + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ +-+ +---+ 3+-+3+-+ 3+-+ +--R 3+-+2 3+-+ 2\|3 \|a b \|x - a\|3 3| 2 2\|b \|x - \|a +--R 6\|a \|b atan(----------------------- - 6\|a b atan(----------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 6b\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 179 + +--S 180 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 2952 +t0000:=1/(x^(1/3)*(a+b*x)^2) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 2 2 3+-+ +--R (b x + 2a b x + a )\|x +--R Type: Expression(Integer) +--E 181 + +--S 182 of 2952 +r0000:=x^(2/3)/(a*(a+b*x))-1/3*log(a^(1/3)+_ + b^(1/3)*x^(1/3))/(a^(4/3)*b^(2/3))+1/6*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/(a^(4/3)*b^(2/3))-_ + atan((a^(1/3)-2*b^(1/3)*x^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(4/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (b x + a)\|3 log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R +-+ 3+-+3+-+ 3+-+ 2\|b \|x - \|a +--R (- 2b x - 2a)\|3 log(\|b \|x + \|a ) + (6b x + 6a)atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-+2 3+-+2 +--R 6\|3 \|a \|b \|x +--R / +--R 2 +-+3+-+3+-+2 +--R (6a b x + 6a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 182 + +--S 183 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +------+ +------+2 +--R +-+ 3| 2 3+-+2 3| 2 3+-+ +--R (- b x - a)\|3 log(b\|- a b \|x + \|- a b \|x - a b) +--R + +--R +------+2 +--R +-+ 3| 2 3+-+ +--R (2b x + 2a)\|3 log(\|- a b \|x + a b) +--R + +--R +------+2 +--R +-+3| 2 3+-+ +-+ +------+ +--R 2\|3 \|- a b \|x - a b\|3 +-+3| 2 3+-+2 +--R (- 6b x - 6a)atan(-----------------------------) + 6\|3 \|- a b \|x +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 +--R (6a b x + 6a )\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +------+ +------+2 +--R +-+3+-+3+-+2 3| 2 3+-+2 3| 2 3+-+ +--R - \|3 \|a \|b log(b\|- a b \|x + \|- a b \|x - a b) +--R + +--R +------+ +--R +-+3| 2 3+-+3+-+ 3+-+ +--R 2\|3 \|- a b log(\|b \|x + \|a ) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 3+-+ +--R 2\|3 \|a \|b log(\|- a b \|x + a b) +--R + +--R +------+ 3+-+3+-+ 3+-+ +--R 3| 2 2\|b \|x - \|a +--R - 6\|- a b atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 3+-+ +-+ +--R 3+-+3+-+2 2\|3 \|- a b \|x - a b\|3 +--R - 6\|a \|b atan(-----------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 6a\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 184 + +--S 185 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 2952 +t0000:=1/(x^(2/3)*(a+b*x)^2) +--R +--R +--R 1 +--R (1) ------------------------- +--R 2 2 2 3+-+2 +--R (b x + 2a b x + a )\|x +--R Type: Expression(Integer) +--E 186 + +--S 187 of 2952 +r0000:=x^(1/3)/(a*(a+b*x))+2/3*log(a^(1/3)+b^(1/3)*x^(1/3))/_ + (a^(5/3)*b^(1/3))-1/3*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + x^(1/3)+b^(2/3)*x^(2/3))/(a^(5/3)*b^(1/3))-2*atan((a^(1/3)-_ + 2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (- b x - a)\|3 log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R +-+ 3+-+3+-+ 3+-+ 2\|b \|x - \|a +--R (2b x + 2a)\|3 log(\|b \|x + \|a ) + (6b x + 6a)atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+3+-+ +--R 3\|3 \|a \|b \|x +--R / +--R 2 +-+3+-+2 3+-+ +--R (3a b x + 3a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 187 + +--S 188 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R +-+ 3| 2 3+-+2 3| 2 3+-+ 2 +--R (- b x - a)\|3 log(\|a b \|x - a\|a b \|x + a ) +--R + +--R +---+ +--R +-+ 3| 2 3+-+ +--R (2b x + 2a)\|3 log(\|a b \|x + a) +--R + +--R +---+ +--R +-+3| 2 3+-+ +-+ +---+ +--R 2\|3 \|a b \|x - a\|3 +-+3| 2 3+-+ +--R (6b x + 6a)atan(-----------------------) + 3\|3 \|a b \|x +--R 3a +--R / +--R +---+ +--R 2 +-+3| 2 +--R (3a b x + 3a )\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 3| 2 3+-+2 3| 2 3+-+ 2 +--R - \|3 \|a \|b log(\|a b \|x - a\|a b \|x + a ) +--R + +--R +---+ +--R +-+3| 2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R \|3 \|a b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +---+ +---+ +--R +-+3+-+2 3+-+ 3| 2 3+-+ +-+3| 2 3+-+3+-+ 3+-+ +--R 2\|3 \|a \|b log(\|a b \|x + a - 2\|3 \|a b log(\|b \|x + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ +-+ +---+ 3+-+3+-+ 3+-+ +--R 3+-+2 3+-+ 2\|3 \|a b \|x - a\|3 3| 2 2\|b \|x - \|a +--R 6\|a \|b atan(----------------------- - 6\|a b atan(----------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 3a\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 189 + +--S 190 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 2952 +t0000:=1/(x^(4/3)*(a+b*x)^2) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 3 2 2 3+-+ +--R (b x + 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 191 + +--S 192 of 2952 +r0000:=(-4)/(a^2*x^(1/3))+1/(a*x^(1/3)*(a+b*x))+_ + 4/3*b^(1/3)*log(a^(1/3)+b^(1/3)*x^(1/3))/a^(7/3)-_ + 2/3*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3)+_ + b^(2/3)*x^(2/3))/a^(7/3)+4*b^(1/3)*atan((a^(1/3)-_ + 2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+3+-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (- 2b x - 2a)\|3 \|b \|x log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +-+3+-+3+-+ 3+-+3+-+ 3+-+ +--R (4b x + 4a)\|3 \|b \|x log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 3+-+3+-+ 2\|b \|x - \|a +-+3+-+ +--R (- 12b x - 12a)\|b \|x atan(----------------) + (- 12b x - 9a)\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 3 +-+3+-+3+-+ +--R (3a b x + 3a )\|3 \|a \|x +--R Type: Expression(Integer) +--E 192 + +--S 193 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-+2 +-+ +--R +-+ |b 3+-+ 3+-+2 |b 3+-+ |b +--R (- 2b x - 2a)\|3 3|- \|x log(b \|x - a 3|- \|x + a 3|-) +--R \|a \|a \|a +--R + +--R +-+ +-+2 +--R +-+ |b 3+-+ 3+-+ |b +--R (4b x + 4a)\|3 3|- \|x log(b\|x + a 3|- ) +--R \|a \|a +--R + +--R +-+2 +--R +-+3+-+ +-+ |b +--R +-+ 2b\|3 \|x - a\|3 3|- +--R |b 3+-+ \|a +-+ +--R (- 12b x - 12a) 3|- \|x atan(----------------------- + (- 12b x - 9a)\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 3 +-+3+-+ +--R (3a b x + 3a )\|3 \|x +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R 2\|3 \|b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +-+ +-+2 +-+ +--R +-+3+-+ |b 3+-+2 |b 3+-+ |b +--R - 2\|3 \|a 3|- log(b \|x - a 3|- \|x + a 3|-) +--R \|a \|a \|a +--R + +--R +-+ +-+2 +--R +-+3+-+ 3+-+3+-+ 3+-+ +-+3+-+ |b 3+-+ |b +--R - 4\|3 \|b log(\|b \|x + \|a ) + 4\|3 \|a 3|- log(b\|x + a 3|- ) +--R \|a \|a +--R + +--R +-+2 +--R +-+3+-+ +-+ |b +--R 3+-+3+-+ 3+-+ +-+ 2b\|3 \|x - a\|3 3|- +--R 3+-+ 2\|b \|x - \|a 3+-+ |b \|a +--R 12\|b atan(----------------) - 12\|a 3|- atan(-----------------------) +--R +-+3+-+ \|a +-+2 +--R \|3 \|a |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+3+-+ +--R 3a \|3 \|a +--R Type: Expression(Integer) +--E 194 + +--S 195 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 2952 +t0000:=1/(x^(5/3)*(a+b*x)^2) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 3 2 2 3+-+2 +--R (b x + 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 196 + +--S 197 of 2952 +r0000:=(-5/2)/(a^2*x^(2/3))+1/(a*x^(2/3)*(a+b*x))-5/3*b^(2/3)*log(a^(1/3)+_ + b^(1/3)*x^(1/3))/a^(8/3)+5/6*b^(2/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/a^(8/3)+_ + 5*b^(2/3)*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/(a^(1/3)*sqrt(3)))/_ + (a^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+2 3+-+2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (5b x + 5a)\|3 \|b \|x log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +-+3+-+2 3+-+2 3+-+3+-+ 3+-+ +--R (- 10b x - 10a)\|3 \|b \|x log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 3+-+2 3+-+2 2\|b \|x - \|a +-+3+-+2 +--R (- 30b x - 30a)\|b \|x atan(---------------- + (- 15b x - 9a)\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 3 +-+3+-+2 3+-+2 +--R (6a b x + 6a )\|3 \|a \|x +--R Type: Expression(Integer) +--E 197 + +--S 198 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +----+ +----+ +----+2 +--R | 2 | 2 | 2 +--R +-+ | b 3+-+2 2 3+-+2 | b 3+-+ 2 | b +--R (- 5b x - 5a)\|3 |- -- \|x log(b \|x + a b |- -- \|x + a |- -- ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 3+-+ | b +--R (10b x + 10a)\|3 |- -- \|x log(b\|x - a |- --) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+3+-+ +-+ | b +--R +----+ 2b\|3 \|x + a\|3 |- -- +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R (- 30b x - 30a) |- -- \|x atan(-------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R +-+ +--R (- 15b x - 9a)\|3 +--R / +--R 2 3 +-+3+-+2 +--R (6a b x + 6a )\|3 \|x +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - 5\|3 \|b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +----+ +----+ +----+2 +--R | 2 | 2 | 2 +--R +-+ | b 3+-+2 2 3+-+2 | b 3+-+ 2 | b +--R - 5\|3 |- -- \|a log(b \|x + a b |- -- \|x + a |- -- ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+3+-+2 3+-+3+-+ 3+-+ +-+ | b 3+-+2 3+-+ | b +--R 10\|3 \|b log(\|b \|x + \|a ) + 10\|3 |- -- \|a log(b\|x - a |- --) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+3+-+ 3+-+ +--R 3+-+2 2\|b \|x - \|a +--R 30\|b atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+3+-+ +-+ | b +--R +----+ 2b\|3 \|x + a\|3 |- -- +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 30 |- -- \|a atan(-------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+3+-+2 +--R 6a \|3 \|a +--R Type: Expression(Integer) +--E 199 + +--S 200 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 2952 +t0000:=x^(5/3)/(a+b*x)^3 +--R +--R +--R 3+-+2 +--R x \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 201 + +--S 202 of 2952 +r0000:=-1/2*x^(5/3)/(b*(a+b*x)^2)-5/6*x^(2/3)/(b^2*(a+b*x))-_ + 5/9*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(1/3)*b^(8/3))+_ + 5/18*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/_ + (a^(1/3)*b^(8/3))-5/3*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(1/3)*b^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 2 +-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (5b x + 10a b x + 5a )\|3 log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 2 2 2 +-+ 3+-+3+-+ 3+-+ +--R (- 10b x - 20a b x - 10a )\|3 log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 2 2 2 2\|b \|x - \|a +--R (30b x + 60a b x + 30a )atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-+2 3+-+2 +--R (- 24b x - 15a)\|3 \|a \|b \|x +--R / +--R 4 2 3 2 2 +-+3+-+3+-+2 +--R (18b x + 36a b x + 18a b )\|3 \|a \|b +--R Type: Expression(Integer) +--E 202 + +--S 203 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +------+ +------+2 +--R 2 2 2 +-+ 3| 2 3+-+2 3| 2 3+-+ +--R (- 5b x - 10a b x - 5a )\|3 log(b\|- a b \|x + \|- a b \|x - a b) +--R + +--R +------+2 +--R 2 2 2 +-+ 3| 2 3+-+ +--R (10b x + 20a b x + 10a )\|3 log(\|- a b \|x + a b) +--R + +--R +------+2 +--R +-+3| 2 3+-+ +-+ +--R 2 2 2 2\|3 \|- a b \|x - a b\|3 +--R (- 30b x - 60a b x - 30a )atan(-----------------------------) +--R 3a b +--R + +--R +------+ +--R +-+3| 2 3+-+2 +--R (- 24b x - 15a)\|3 \|- a b \|x +--R / +--R +------+ +--R 4 2 3 2 2 +-+3| 2 +--R (18b x + 36a b x + 18a b )\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - 5\|3 \|- a b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +------+ +------+2 +--R +-+3+-+3+-+2 3| 2 3+-+2 3| 2 3+-+ +--R - 5\|3 \|a \|b log(b\|- a b \|x + \|- a b \|x - a b) +--R + +--R +------+ +--R +-+3| 2 3+-+3+-+ 3+-+ +--R 10\|3 \|- a b log(\|b \|x + \|a ) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 3+-+ +--R 10\|3 \|a \|b log(\|- a b \|x + a b) +--R + +--R +------+ 3+-+3+-+ 3+-+ +--R 3| 2 2\|b \|x - \|a +--R - 30\|- a b atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 3+-+ +-+ +--R 3+-+3+-+2 2\|3 \|- a b \|x - a b\|3 +--R - 30\|a \|b atan(-----------------------------) +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 3+-+3+-+2 +--R 18b \|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 204 + +--S 205 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 2952 +t0000:=x^(4/3)/(a+b*x)^3 +--R +--R +--R 3+-+ +--R x\|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 206 + +--S 207 of 2952 +r0000:=-1/2*x^(4/3)/(b*(a+b*x)^2)-2/3*x^(1/3)/(b^2*(a+b*x))+_ + 2/9*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(2/3)*b^(7/3))-_ + 1/9*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/_ + (a^(2/3)*b^(7/3))-2/3*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(2/3)*b^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 2 +-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (- 2b x - 4a b x - 2a )\|3 log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 2 2 2 +-+ 3+-+3+-+ 3+-+ +--R (4b x + 8a b x + 4a )\|3 log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 2 2 2 2\|b \|x - \|a +--R (12b x + 24a b x + 12a )atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+3+-+ +--R (- 21b x - 12a)\|3 \|a \|b \|x +--R / +--R 4 2 3 2 2 +-+3+-+2 3+-+ +--R (18b x + 36a b x + 18a b )\|3 \|a \|b +--R Type: Expression(Integer) +--E 207 + +--S 208 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 2 2 2 +-+ 3| 2 3+-+2 3| 2 3+-+ 2 +--R (- 2b x - 4a b x - 2a )\|3 log(\|a b \|x - a\|a b \|x + a ) +--R + +--R +---+ +--R 2 2 2 +-+ 3| 2 3+-+ +--R (4b x + 8a b x + 4a )\|3 log(\|a b \|x + a) +--R + +--R +---+ +--R +-+3| 2 3+-+ +-+ +--R 2 2 2 2\|3 \|a b \|x - a\|3 +--R (12b x + 24a b x + 12a )atan(-----------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 3+-+ +--R (- 21b x - 12a)\|3 \|a b \|x +--R / +--R +---+ +--R 4 2 3 2 2 +-+3| 2 +--R (18b x + 36a b x + 18a b )\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 3| 2 3+-+2 3| 2 3+-+ 2 +--R - \|3 \|a \|b log(\|a b \|x - a\|a b \|x + a ) +--R + +--R +---+ +--R +-+3| 2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R \|3 \|a b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +---+ +---+ +--R +-+3+-+2 3+-+ 3| 2 3+-+ +-+3| 2 3+-+3+-+ 3+-+ +--R 2\|3 \|a \|b log(\|a b \|x + a - 2\|3 \|a b log(\|b \|x + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ +-+ +---+ 3+-+3+-+ 3+-+ +--R 3+-+2 3+-+ 2\|3 \|a b \|x - a\|3 3| 2 2\|b \|x - \|a +--R 6\|a \|b atan(----------------------- - 6\|a b atan(----------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R 2 +-+3+-+2 3+-+3| 2 +--R 9b \|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 209 + +--S 210 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 2952 +t0000:=x^(2/3)/(a+b*x)^3 +--R +--R +--R 3+-+2 +--R \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 211 + +--S 212 of 2952 +r0000:=-1/2*x^(2/3)/(b*(a+b*x)^2)+1/3*x^(2/3)/(a*b*(a+b*x))-_ + 1/9*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(4/3)*b^(5/3))+_ + 1/18*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/_ + (a^(4/3)*b^(5/3))-1/3*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(4/3)*b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 2 +-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (b x + 2a b x + a )\|3 log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 2 2 2 +-+ 3+-+3+-+ 3+-+ +--R (- 2b x - 4a b x - 2a )\|3 log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 2 2 2 2\|b \|x - \|a +--R (6b x + 12a b x + 6a )atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-+2 3+-+2 +--R (6b x - 3a)\|3 \|a \|b \|x +--R / +--R 3 2 2 2 3 +-+3+-+3+-+2 +--R (18a b x + 36a b x + 18a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 212 + +--S 213 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +------+ +------+2 +--R 2 2 2 +-+ 3| 2 3+-+2 3| 2 3+-+ +--R (- b x - 2a b x - a )\|3 log(b\|- a b \|x + \|- a b \|x - a b) +--R + +--R +------+2 +--R 2 2 2 +-+ 3| 2 3+-+ +--R (2b x + 4a b x + 2a )\|3 log(\|- a b \|x + a b) +--R + +--R +------+2 +--R +-+3| 2 3+-+ +-+ +--R 2 2 2 2\|3 \|- a b \|x - a b\|3 +--R (- 6b x - 12a b x - 6a )atan(-----------------------------) +--R 3a b +--R + +--R +------+ +--R +-+3| 2 3+-+2 +--R (6b x - 3a)\|3 \|- a b \|x +--R / +--R +------+ +--R 3 2 2 2 3 +-+3| 2 +--R (18a b x + 36a b x + 18a b)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +------+ +------+2 +--R +-+3+-+3+-+2 3| 2 3+-+2 3| 2 3+-+ +--R - \|3 \|a \|b log(b\|- a b \|x + \|- a b \|x - a b) +--R + +--R +------+ +--R +-+3| 2 3+-+3+-+ 3+-+ +--R 2\|3 \|- a b log(\|b \|x + \|a ) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 3+-+ +--R 2\|3 \|a \|b log(\|- a b \|x + a b) +--R + +--R +------+ 3+-+3+-+ 3+-+ +--R 3| 2 2\|b \|x - \|a +--R - 6\|- a b atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 3+-+ +-+ +--R 3+-+3+-+2 2\|3 \|- a b \|x - a b\|3 +--R - 6\|a \|b atan(-----------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 18a b\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 214 + +--S 215 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 2952 +t0000:=x^(1/3)/(a+b*x)^3 +--R +--R +--R 3+-+ +--R \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 216 + +--S 217 of 2952 +r0000:=-1/2*x^(1/3)/(b*(a+b*x)^2)+1/6*x^(1/3)/(a*b*(a+b*x))+_ + 1/9*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(5/3)*b^(4/3))-_ + 1/18*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/_ + (a^(5/3)*b^(4/3))-1/3*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(5/3)*b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 2 +-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (- b x - 2a b x - a )\|3 log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 2 2 2 +-+ 3+-+3+-+ 3+-+ +--R (2b x + 4a b x + 2a )\|3 log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 2 2 2 2\|b \|x - \|a +--R (6b x + 12a b x + 6a )atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+3+-+ +--R (3b x - 6a)\|3 \|a \|b \|x +--R / +--R 3 2 2 2 3 +-+3+-+2 3+-+ +--R (18a b x + 36a b x + 18a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 217 + +--S 218 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 2 2 2 +-+ 3| 2 3+-+2 3| 2 3+-+ 2 +--R (- b x - 2a b x - a )\|3 log(\|a b \|x - a\|a b \|x + a ) +--R + +--R +---+ +--R 2 2 2 +-+ 3| 2 3+-+ +--R (2b x + 4a b x + 2a )\|3 log(\|a b \|x + a) +--R + +--R +---+ +--R +-+3| 2 3+-+ +-+ +--R 2 2 2 2\|3 \|a b \|x - a\|3 +--R (6b x + 12a b x + 6a )atan(-----------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 3+-+ +--R (3b x - 6a)\|3 \|a b \|x +--R / +--R +---+ +--R 3 2 2 2 3 +-+3| 2 +--R (18a b x + 36a b x + 18a b)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 3| 2 3+-+2 3| 2 3+-+ 2 +--R - \|3 \|a \|b log(\|a b \|x - a\|a b \|x + a ) +--R + +--R +---+ +--R +-+3| 2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R \|3 \|a b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +---+ +---+ +--R +-+3+-+2 3+-+ 3| 2 3+-+ +-+3| 2 3+-+3+-+ 3+-+ +--R 2\|3 \|a \|b log(\|a b \|x + a - 2\|3 \|a b log(\|b \|x + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ +-+ +---+ 3+-+3+-+ 3+-+ +--R 3+-+2 3+-+ 2\|3 \|a b \|x - a\|3 3| 2 2\|b \|x - \|a +--R 6\|a \|b atan(----------------------- - 6\|a b atan(----------------) +--R 3a +-+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 219 + +--S 220 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 2952 +t0000:=1/(x^(1/3)*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 3 3 2 2 2 3 3+-+ +--R (b x + 3a b x + 3a b x + a )\|x +--R Type: Expression(Integer) +--E 221 + +--S 222 of 2952 +r0000:=1/2*x^(2/3)/(a*(a+b*x)^2)+2/3*x^(2/3)/(a^2*(a+b*x))-_ + 2/9*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(7/3)*b^(2/3))+_ + 1/9*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/_ + (a^(7/3)*b^(2/3))-2/3*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(7/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 2 +-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (2b x + 4a b x + 2a )\|3 log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 2 2 2 +-+ 3+-+3+-+ 3+-+ +--R (- 4b x - 8a b x - 4a )\|3 log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 2 2 2 2\|b \|x - \|a +--R (12b x + 24a b x + 12a )atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+3+-+2 3+-+2 +--R (12b x + 21a)\|3 \|a \|b \|x +--R / +--R 2 2 2 3 4 +-+3+-+3+-+2 +--R (18a b x + 36a b x + 18a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 222 + +--S 223 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +------+ +------+2 +--R 2 2 2 +-+ 3| 2 3+-+2 3| 2 3+-+ +--R (- 2b x - 4a b x - 2a )\|3 log(b\|- a b \|x + \|- a b \|x - a b) +--R + +--R +------+2 +--R 2 2 2 +-+ 3| 2 3+-+ +--R (4b x + 8a b x + 4a )\|3 log(\|- a b \|x + a b) +--R + +--R +------+2 +--R +-+3| 2 3+-+ +-+ +--R 2 2 2 2\|3 \|- a b \|x - a b\|3 +--R (- 12b x - 24a b x - 12a )atan(-----------------------------) +--R 3a b +--R + +--R +------+ +--R +-+3| 2 3+-+2 +--R (12b x + 21a)\|3 \|- a b \|x +--R / +--R +------+ +--R 2 2 2 3 4 +-+3| 2 +--R (18a b x + 36a b x + 18a )\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +------+ +------+2 +--R +-+3+-+3+-+2 3| 2 3+-+2 3| 2 3+-+ +--R - \|3 \|a \|b log(b\|- a b \|x + \|- a b \|x - a b) +--R + +--R +------+ +--R +-+3| 2 3+-+3+-+ 3+-+ +--R 2\|3 \|- a b log(\|b \|x + \|a ) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 3+-+ +--R 2\|3 \|a \|b log(\|- a b \|x + a b) +--R + +--R +------+ 3+-+3+-+ 3+-+ +--R 3| 2 2\|b \|x - \|a +--R - 6\|- a b atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 3+-+ +-+ +--R 3+-+3+-+2 2\|3 \|- a b \|x - a b\|3 +--R - 6\|a \|b atan(-----------------------------) +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 3+-+3+-+2 +--R 9a \|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 224 + +--S 225 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 2952 +t0000:=1/(x^(2/3)*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 3 3 2 2 2 3 3+-+2 +--R (b x + 3a b x + 3a b x + a )\|x +--R Type: Expression(Integer) +--E 226 + +--S 227 of 2952 +r0000:=1/2*x^(1/3)/(a*(a+b*x)^2)+5/6*x^(1/3)/(a^2*(a+b*x))+_ + 5/9*log(a^(1/3)+b^(1/3)*x^(1/3))/(a^(8/3)*b^(1/3))-_ + 5/18*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/_ + (a^(8/3)*b^(1/3))-5/3*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(8/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 2 +-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R (- 5b x - 10a b x - 5a )\|3 log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 2 2 2 +-+ 3+-+3+-+ 3+-+ +--R (10b x + 20a b x + 10a )\|3 log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 2 2 2 2\|b \|x - \|a +--R (30b x + 60a b x + 30a )atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+3+-+ +--R (15b x + 24a)\|3 \|a \|b \|x +--R / +--R 2 2 2 3 4 +-+3+-+2 3+-+ +--R (18a b x + 36a b x + 18a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 227 + +--S 228 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 2 2 2 +-+ 3| 2 3+-+2 3| 2 3+-+ 2 +--R (- 5b x - 10a b x - 5a )\|3 log(\|a b \|x - a\|a b \|x + a ) +--R + +--R +---+ +--R 2 2 2 +-+ 3| 2 3+-+ +--R (10b x + 20a b x + 10a )\|3 log(\|a b \|x + a) +--R + +--R +---+ +--R +-+3| 2 3+-+ +-+ +--R 2 2 2 2\|3 \|a b \|x - a\|3 +--R (30b x + 60a b x + 30a )atan(-----------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 3+-+ +--R (15b x + 24a)\|3 \|a b \|x +--R / +--R +---+ +--R 2 2 2 3 4 +-+3| 2 +--R (18a b x + 36a b x + 18a )\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 3| 2 3+-+2 3| 2 3+-+ 2 +--R - 5\|3 \|a \|b log(\|a b \|x - a\|a b \|x + a ) +--R + +--R +---+ +--R +-+3| 2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R 5\|3 \|a b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +---+ +---+ +--R +-+3+-+2 3+-+ 3| 2 3+-+ +-+3| 2 3+-+3+-+ 3+-+ +--R 10\|3 \|a \|b log(\|a b \|x + a - 10\|3 \|a b log(\|b \|x + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ +-+ +---+ 3+-+3+-+ 3+-+ +--R 3+-+2 3+-+ 2\|3 \|a b \|x - a\|3 3| 2 2\|b \|x - \|a +--R 30\|a \|b atan(----------------------- - 30\|a b atan(----------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R 2 +-+3+-+2 3+-+3| 2 +--R 18a \|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 229 + +--S 230 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 2952 +t0000:=1/(x^(4/3)*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 4 2 3 2 2 3 3+-+ +--R (b x + 3a b x + 3a b x + a x)\|x +--R Type: Expression(Integer) +--E 231 + +--S 232 of 2952 +r0000:=(-14/3)/(a^3*x^(1/3))+1/2/(a*x^(1/3)*(a+b*x)^2)+_ + 7/6/(a^2*x^(1/3)*(a+b*x))+14/9*b^(1/3)*log(a^(1/3)+_ + b^(1/3)*x^(1/3))/a^(10/3)-7/9*b^(1/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/a^(10/3)+_ + 14/3*b^(1/3)*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(10/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 2 +-+3+-+3+-+ +--R (- 14b x - 28a b x - 14a )\|3 \|b \|x +--R * +--R 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 2 2 2 +-+3+-+3+-+ 3+-+3+-+ 3+-+ +--R (28b x + 56a b x + 28a )\|3 \|b \|x log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 2 2 2 3+-+3+-+ 2\|b \|x - \|a +--R (- 84b x - 168a b x - 84a )\|b \|x atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 2 2 +-+3+-+ +--R (- 84b x - 147a b x - 54a )\|3 \|a +--R / +--R 3 2 2 4 5 +-+3+-+3+-+ +--R (18a b x + 36a b x + 18a )\|3 \|a \|x +--R Type: Expression(Integer) +--E 232 + +--S 233 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-+ +-+2 +-+ +--R 2 2 2 +-+ |b 3+-+ 3+-+2 |b 3+-+ |b +--R (- 14b x - 28a b x - 14a )\|3 3|- \|x log(b \|x - a 3|- \|x + a 3|-) +--R \|a \|a \|a +--R + +--R +-+ +-+2 +--R 2 2 2 +-+ |b 3+-+ 3+-+ |b +--R (28b x + 56a b x + 28a )\|3 3|- \|x log(b\|x + a 3|- ) +--R \|a \|a +--R + +--R +-+2 +--R +-+3+-+ +-+ |b +--R +-+ 2b\|3 \|x - a\|3 3|- +--R 2 2 2 |b 3+-+ \|a +--R (- 84b x - 168a b x - 84a ) 3|- \|x atan(-----------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R + +--R 2 2 2 +-+ +--R (- 84b x - 147a b x - 54a )\|3 +--R / +--R 3 2 2 4 5 +-+3+-+ +--R (18a b x + 36a b x + 18a )\|3 \|x +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+ 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R 7\|3 \|b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +-+ +-+2 +-+ +--R +-+3+-+ |b 3+-+2 |b 3+-+ |b +--R - 7\|3 \|a 3|- log(b \|x - a 3|- \|x + a 3|-) +--R \|a \|a \|a +--R + +--R +-+ +-+2 +--R +-+3+-+ 3+-+3+-+ 3+-+ +-+3+-+ |b 3+-+ |b +--R - 14\|3 \|b log(\|b \|x + \|a ) + 14\|3 \|a 3|- log(b\|x + a 3|- ) +--R \|a \|a +--R + +--R +-+2 +--R +-+3+-+ +-+ |b +--R 3+-+3+-+ 3+-+ +-+ 2b\|3 \|x - a\|3 3|- +--R 3+-+ 2\|b \|x - \|a 3+-+ |b \|a +--R 42\|b atan(----------------) - 42\|a 3|- atan(-----------------------) +--R +-+3+-+ \|a +-+2 +--R \|3 \|a |b +--R 3a 3|- +--R \|a +--R / +--R 3 +-+3+-+ +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 234 + +--S 235 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 2952 +t0000:=1/(x^(5/3)*(a+b*x)^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 4 2 3 2 2 3 3+-+2 +--R (b x + 3a b x + 3a b x + a x)\|x +--R Type: Expression(Integer) +--E 236 + +--S 237 of 2952 +r0000:=(-10/3)/(a^3*x^(2/3))+1/2/(a*x^(2/3)*(a+b*x)^2)+_ + 4/3/(a^2*x^(2/3)*(a+b*x))-20/9*b^(2/3)*log(a^(1/3)+_ + b^(1/3)*x^(1/3))/a^(11/3)+10/9*b^(2/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^(1/3)+b^(2/3)*x^(2/3))/a^(11/3)+_ + 20/3*b^(2/3)*atan((a^(1/3)-2*b^(1/3)*x^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(11/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 2 2 +-+3+-+2 3+-+2 +--R (20b x + 40a b x + 20a )\|3 \|b \|x +--R * +--R 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R 2 2 2 +-+3+-+2 3+-+2 3+-+3+-+ 3+-+ +--R (- 40b x - 80a b x - 40a )\|3 \|b \|x log(\|b \|x + \|a ) +--R + +--R 3+-+3+-+ 3+-+ +--R 2 2 2 3+-+2 3+-+2 2\|b \|x - \|a +--R (- 120b x - 240a b x - 120a )\|b \|x atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 2 2 +-+3+-+2 +--R (- 60b x - 96a b x - 27a )\|3 \|a +--R / +--R 3 2 2 4 5 +-+3+-+2 3+-+2 +--R (18a b x + 36a b x + 18a )\|3 \|a \|x +--R Type: Expression(Integer) +--E 237 + +--S 238 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +----+ +--R | 2 +--R 2 2 2 +-+ | b 3+-+2 +--R (- 20b x - 40a b x - 20a )\|3 |- -- \|x +--R 3| 2 +--R \| a +--R * +--R +----+ +----+2 +--R | 2 | 2 +--R 2 3+-+2 | b 3+-+ 2 | b +--R log(b \|x + a b |- -- \|x + a |- -- ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 2 2 2 +-+ | b 3+-+2 3+-+ | b +--R (40b x + 80a b x + 40a )\|3 |- -- \|x log(b\|x - a |- --) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+3+-+ +-+ | b +--R +----+ 2b\|3 \|x + a\|3 |- -- +--R | 2 3| 2 +--R 2 2 2 | b 3+-+2 \| a +--R (- 120b x - 240a b x - 120a ) |- -- \|x atan(-------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 2 2 2 +-+ +--R (- 60b x - 96a b x - 27a )\|3 +--R / +--R 3 2 2 4 5 +-+3+-+2 +--R (18a b x + 36a b x + 18a )\|3 \|x +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-+3+-+2 3+-+2 3+-+2 3+-+3+-+3+-+ 3+-+2 +--R - 10\|3 \|b log(\|b \|x - \|a \|b \|x + \|a ) +--R + +--R +----+ +----+ +----+2 +--R | 2 | 2 | 2 +--R +-+ | b 3+-+2 2 3+-+2 | b 3+-+ 2 | b +--R - 10\|3 |- -- \|a log(b \|x + a b |- -- \|x + a |- -- ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+3+-+2 3+-+3+-+ 3+-+ +-+ | b 3+-+2 3+-+ | b +--R 20\|3 \|b log(\|b \|x + \|a ) + 20\|3 |- -- \|a log(b\|x - a |- --) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+3+-+ 3+-+ +--R 3+-+2 2\|b \|x - \|a +--R 60\|b atan(----------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+3+-+ +-+ | b +--R +----+ 2b\|3 \|x + a\|3 |- -- +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 60 |- -- \|a atan(-------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 3 +-+3+-+2 +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 239 + +--S 240 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 2952 +t0000:=(1-x)^(1/4)/(1+x) +--R +--R +--R 4+-------+ +--R \|- x + 1 +--R (1) ---------- +--R x + 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 2952 +r0000:=4*(1-x)^(1/4)-2*2^(1/4)*atan((1-x)^(1/4)/2^(1/4))-_ + 2*2^(1/4)*atanh((1-x)^(1/4)/2^(1/4)) +--R +--R +--R 4+-------+ 4+-------+ +--R 4+-+ \|- x + 1 4+-+ \|- x + 1 4+-------+ +--R (2) - 2\|2 atanh(----------) - 2\|2 atan(----------) + 4\|- x + 1 +--R 4+-+ 4+-+ +--R \|2 \|2 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4+-+ 4+-------+ 4+-+ 4+-+ 4+-------+ 4+-+ +--R - \|2 log(\|- x + 1 + \|2 ) + \|2 log(\|- x + 1 - \|2 ) +--R + +--R 4+-+ +--R 4+-+ \|2 4+-------+ +--R 2\|2 atan(----------) + 4\|- x + 1 +--R 4+-------+ +--R \|- x + 1 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 4+-+ 4+-------+ 4+-+ 4+-+ 4+-------+ 4+-+ +--R - \|2 log(\|- x + 1 + \|2 ) + \|2 log(\|- x + 1 - \|2 ) +--R + +--R 4+-------+ 4+-------+ 4+-+ +--R 4+-+ \|- x + 1 4+-+ \|- x + 1 4+-+ \|2 +--R 2\|2 atanh(----------) + 2\|2 atan(----------) + 2\|2 atan(----------) +--R 4+-+ 4+-+ 4+-------+ +--R \|2 \|2 \|- x + 1 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 2952 +t0000:=x^3*(a+b*x)^n +--R +--R +--R 3 n +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 246 + +--S 247 of 2952 +r0000:=-a^3*(a+b*x)^(1+n)/(b^4*(1+n))+3*a^2*(a+b*x)^(2+n)/(b^4*(2+n))-_ + 3*a*(a+b*x)^(3+n)/(b^4*(3+n))+(a+b*x)^(4+n)/(b^4*(4+n)) +--R +--R +--R (2) +--R 3 2 n + 4 +--R (n + 6n + 11n + 6)(b x + a) +--R + +--R 3 2 n + 3 +--R (- 3a n - 21a n - 42a n - 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 n + 2 +--R (3a n + 24a n + 57a n + 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 n + 1 +--R (- a n - 9a n - 26a n - 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 247 + +--S 248 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 4 3 3 3 2 3 3 +--R (b n + 6b n + 11b n + 6b )x + (a b n + 3a b n + 2a b n)x +--R + +--R 2 2 2 2 2 2 3 4 +--R (- 3a b n - 3a b n)x + 6a b n x - 6a +--R * +--R n log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 3 3 3 2 3 3 +--R (b n + 6b n + 11b n + 6b )x + (a b n + 3a b n + 2a b n)x +--R + +--R 2 2 2 2 2 2 3 4 +--R (- 3a b n - 3a b n)x + 6a b n x - 6a +--R * +--R n log(b x + a) +--R %e +--R + +--R 3 2 n + 4 +--R (- n - 6n - 11n - 6)(b x + a) +--R + +--R 3 2 n + 3 +--R (3a n + 21a n + 42a n + 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 n + 2 +--R (- 3a n - 24a n - 57a n - 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 n + 1 +--R (a n + 9a n + 26a n + 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 249 + +--S 250 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 3 3 n log(b x + a) n + 3 n + 2 +--R b x %e - (b x + a) + 3a (b x + a) +--R + +--R 2 n + 1 3 n +--R - 3a (b x + a) + a (b x + a) +--R / +--R 3 +--R b +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 2952 +t0000:=x^2*(a+b*x)^n +--R +--R +--R 2 n +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 251 + +--S 252 of 2952 +r0000:=a^2*(a+b*x)^(1+n)/(b^3*(1+n))-2*a*(a+b*x)^(2+n)/(b^3*(2+n))+_ + (a+b*x)^(3+n)/(b^3*(3+n)) +--R +--R +--R (2) +--R 2 n + 3 2 n + 2 +--R (n + 3n + 2)(b x + a) + (- 2a n - 8a n - 6a)(b x + a) +--R + +--R 2 2 2 2 n + 1 +--R (a n + 5a n + 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 252 + +--S 253 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 3 3 3 2 2 2 2 2 3 n log(b x + a) +--R ((b n + 3b n + 2b )x + (a b n + a b n)x - 2a b n x + 2a )%e +--R ----------------------------------------------------------------------------- +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 2 3 3 3 2 2 2 2 2 3 +--R ((b n + 3b n + 2b )x + (a b n + a b n)x - 2a b n x + 2a ) +--R * +--R n log(b x + a) +--R %e +--R + +--R 2 n + 3 2 n + 2 +--R (- n - 3n - 2)(b x + a) + (2a n + 8a n + 6a)(b x + a) +--R + +--R 2 2 2 2 n + 1 +--R (- a n - 5a n - 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 254 + +--S 255 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 2 2 n log(b x + a) n + 2 n + 1 2 n +--R b x %e - (b x + a) + 2a (b x + a) - a (b x + a) +--R ------------------------------------------------------------------------ +--R 2 +--R b +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 2952 +t0000:=x*(a+b*x)^n +--R +--R +--R n +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 256 + +--S 257 of 2952 +r0000:=-a*(a+b*x)^(1+n)/(b^2*(1+n))+(a+b*x)^(2+n)/(b^2*(2+n)) +--R +--R +--R n + 2 n + 1 +--R (n + 1)(b x + a) + (- a n - 2a)(b x + a) +--R (2) -------------------------------------------------- +--R 2 2 2 2 +--R b n + 3b n + 2b +--R Type: Expression(Integer) +--E 257 + +--S 258 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 n log(b x + a) +--R ((b n + b )x + a b n x - a )%e +--R (3) --------------------------------------------- +--R 2 2 2 2 +--R b n + 3b n + 2b +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 2 2 2 n log(b x + a) n + 2 +--R ((b n + b )x + a b n x - a )%e + (- n - 1)(b x + a) +--R + +--R n + 1 +--R (a n + 2a)(b x + a) +--R / +--R 2 2 2 2 +--R b n + 3b n + 2b +--R Type: Expression(Integer) +--E 259 + +--S 260 of 2952 +d0000:=D(m0000,x) +--R +--R +--R n log(b x + a) n + 1 n +--R b x %e - (b x + a) + a (b x + a) +--R (5) ---------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 2952 +t0000:=(a+b*x)^n +--R +--R +--R n +--R (1) (b x + a) +--R Type: Expression(Integer) +--E 261 + +--S 262 of 2952 +r0000:=(a+b*x)^(1+n)/(b*(1+n)) +--R +--R +--R n + 1 +--R (b x + a) +--R (2) -------------- +--R b n + b +--R Type: Expression(Integer) +--E 262 + +--S 263 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R n log(b x + a) +--R (b x + a)%e +--R (3) ------------------------- +--R b n + b +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R n log(b x + a) n + 1 +--R (b x + a)%e - (b x + a) +--R (4) ------------------------------------------ +--R b n + b +--R Type: Expression(Integer) +--E 264 + +--S 265 of 2952 +d0000:=D(m0000,x) +--R +--R +--R n log(b x + a) n +--R (5) %e - (b x + a) +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 2952 +t0000:=(a+b*x)^n/x +--R +--R +--R n +--R (b x + a) +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 266 + +--S 267 of 2952 +--r0000:=-(a+b*x)^(1+n)*hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n)) +--E 267 + +--S 268 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n +--R ++ (%BJ b + a) +--R (2) | ------------ d%BJ +--R ++ %BJ +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 2952 +--m0000:=a0000 - r0000 +--E 269 + +--S 270 of 2952 +--d0000:=D(m0000,x) +--E 270 + +)clear all + +--S 271 of 2952 +t0000:=(a+b*x)^n/x^2 +--R +--R +--R n +--R (b x + a) +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 271 + +--S 272 of 2952 +--r0000:=-(a+b*x)^(1+n)/(a*x)-b*n*(a+b*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a^2*(1+n)) +--E 272 + +--S 273 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n +--R ++ (%BJ b + a) +--R (2) | ------------ d%BJ +--R ++ 2 +--R %BJ +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 2952 +--m0000:=a0000 - r0000 +--E 274 + +--S 275 of 2952 +--d0000:=D(m0000,x) +--E 275 + +)clear all + +--S 276 of 2952 +t0000:=(a+b*x)^n/x^3 +--R +--R +--R n +--R (b x + a) +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 276 + +--S 277 of 2952 +--r0000:=-1/2*(a+b*x)^(1+n)/(a*x^2)+1/2*b*(1-n)*(a+b*x)^(1+n)/(a^2*x)+_ +-- 1/2*b^2*(1-n)*n*(a+b*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a^3*(1+n)) +--E 277 + +--S 278 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n +--R ++ (%BJ b + a) +--R (2) | ------------ d%BJ +--R ++ 3 +--R %BJ +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 2952 +--m0000:=a0000 - r0000 +--E 279 + +--S 280 of 2952 +--d0000:=D(m0000,x) +--E 280 + +)clear all + +--S 281 of 2952 +t0000:=x^(-4+n)/(a+b*x)^n +--R +--R +--R n - 4 +--R x +--R (1) ---------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 281 + +--S 282 of 2952 +r0000:=-x^(-3+n)*(a+b*x)^(1-n)/(a*(3-n))+_ + 2*b*x^(-2+n)*(a+b*x)^(1-n)/(a^2*(2-n)*(3-n))-_ + 2*b^2*x^(-1+n)*(a+b*x)^(1-n)/(a^3*(1-n)*(2-n)*(3-n)) +--R +--R +--R (2) +--R 2 n - 1 n - 2 2 2 2 2 n - 3 +--R (2b x + (2a b n - 2a b)x + (a n - 3a n + 2a )x ) +--R * +--R - n + 1 +--R (b x + a) +--R / +--R 3 3 3 2 3 3 +--R a n - 6a n + 11a n - 6a +--R Type: Expression(Integer) +--E 282 + +--S 283 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 4 2 3 2 2 2 2 3 2 3 3 +--R (2b x + 2a b n x + (a b n - a b n)x + (a n - 3a n + 2a )x) +--R * +--R (n - 4)log(x) +--R %e +--R / +--R 3 3 3 2 3 3 n log(b x + a) +--R (a n - 6a n + 11a n - 6a )%e +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 n - 1 n - 2 2 2 2 2 n - 3 +--R (- 2b x + (- 2a b n + 2a b)x + (- a n + 3a n - 2a )x ) +--R * +--R - n + 1 n log(b x + a) +--R (b x + a) %e +--R + +--R 3 4 2 3 2 2 2 2 3 2 3 3 +--R (2b x + 2a b n x + (a b n - a b n)x + (a n - 3a n + 2a )x) +--R * +--R (n - 4)log(x) +--R %e +--R / +--R 3 3 3 2 3 3 n log(b x + a) +--R (a n - 6a n + 11a n - 6a )%e +--R Type: Expression(Integer) +--E 284 + +--S 285 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 2 n - 2 n - 3 +--R - 2b x + (- 2a b n + 4a b)x +--R + +--R 2 2 2 2 n - 4 +--R (- a n + 5a n - 6a )x +--R * +--R - n + 1 +--R (b x + a) +--R + +--R 3 n - 1 2 2 n - 2 +--R 2b x + (2a b n - 2a b )x +--R + +--R 2 2 2 2 n - 3 +--R (a b n - 3a b n + 2a b)x +--R * +--R - n +--R (b x + a) +--R * +--R n log(b x + a) +--R %e +--R + +--R 3 2 3 3 (n - 4)log(x) +--R (a n - 5a n + 6a )%e +--R / +--R 3 2 3 3 n log(b x + a) +--R (a n - 5a n + 6a )%e +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 2952 +t0000:=x^(-3+n)/(a+b*x)^n +--R +--R +--R n - 3 +--R x +--R (1) ---------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 286 + +--S 287 of 2952 +r0000:=-x^(-2+n)*(a+b*x)^(1-n)/(a*(2-n))+_ + b*x^(-1+n)*(a+b*x)^(1-n)/(a^2*(1-n)*(2-n)) +--R +--R +--R n - 1 n - 2 - n + 1 +--R (b x + (a n - a)x )(b x + a) +--R (2) -------------------------------------------- +--R 2 2 2 2 +--R a n - 3a n + 2a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 2 2 2 (n - 3)log(x) +--R (b x + a b n x + (a n - a )x)%e +--R (3) ---------------------------------------------- +--R 2 2 2 2 n log(b x + a) +--R (a n - 3a n + 2a )%e +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R n - 1 n - 2 - n + 1 n log(b x + a) +--R (- b x + (- a n + a)x )(b x + a) %e +--R + +--R 2 3 2 2 2 (n - 3)log(x) +--R (b x + a b n x + (a n - a )x)%e +--R / +--R 2 2 2 2 n log(b x + a) +--R (a n - 3a n + 2a )%e +--R Type: Expression(Integer) +--E 289 + +--S 290 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R n - 2 n - 3 - n + 1 +--R (- b x + (- a n + 2a)x )(b x + a) +--R + +--R 2 n - 1 n - 2 - n +--R (b x + (a b n - a b)x )(b x + a) +--R * +--R n log(b x + a) +--R %e +--R + +--R 2 2 (n - 3)log(x) +--R (a n - 2a )%e +--R / +--R 2 2 n log(b x + a) +--R (a n - 2a )%e +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 2952 +t0000:=x^(-2+n)/(a+b*x)^n +--R +--R +--R n - 2 +--R x +--R (1) ---------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 291 + +--S 292 of 2952 +r0000:=-x^(-1+n)*(a+b*x)^(1-n)/(a*(1-n)) +--R +--R +--R n - 1 - n + 1 +--R x (b x + a) +--R (2) ---------------------- +--R a n - a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 (n - 2)log(x) +--R (b x + a x)%e +--R (3) --------------------------- +--R n log(b x + a) +--R (a n - a)%e +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R n - 1 - n + 1 n log(b x + a) 2 (n - 2)log(x) +--R - x (b x + a) %e + (b x + a x)%e +--R (4) ---------------------------------------------------------------------- +--R n log(b x + a) +--R (a n - a)%e +--R Type: Expression(Integer) +--E 294 + +--S 295 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R n - 2 - n + 1 n - 1 - n n log(b x + a) +--R (- x (b x + a) + b x (b x + a) )%e +--R + +--R (n - 2)log(x) +--R a %e +--R / +--R n log(b x + a) +--R a %e +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 2952 +t0000:=x^(-1+n)/(a+b*x)^n +--R +--R +--R n - 1 +--R x +--R (1) ---------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 296 + +--S 297 of 2952 +--r0000:=x^n*(a+b*x)^(1-n)/(a*n)-x^n*(a+b*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,(a+b*x)/a)/(a*(1-n)*n*(-b*x/a)^n) +--E 297 + +--S 298 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n - 1 +--R ++ %BJ +--R (2) | ------------ d%BJ +--R ++ n +--R (%BJ b + a) +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 2952 +--m0000:=a0000 - r0000 +--E 299 + +--S 300 of 2952 +--d0000:=D(m0000,x) +--E 300 + +)clear all + +--S 301 of 2952 +t0000:=x^n/(a+b*x)^n +--R +--R +--R n +--R x +--R (1) ---------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 301 + +--S 302 of 2952 +--r0000:=x^n*(a+b*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,(a+b*x)/a)/(b*(1-n)*(-b*x/a)^n) +--E 302 + +--S 303 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n +--R ++ %BJ +--R (2) | ------------ d%BJ +--R ++ n +--R (%BJ b + a) +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 2952 +--m0000:=a0000 - r0000 +--E 304 + +--S 305 of 2952 +--d0000:=D(m0000,x) +--E 305 + +)clear all + +--S 306 of 2952 +t0000:=x^(1+n)/(a+b*x)^n +--R +--R +--R n + 1 +--R x +--R (1) ---------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 306 + +--S 307 of 2952 +--r0000:=1/2*x^(1+n)*(a+b*x)^(1-n)/b-1/2*a*(1+n)*x^n*(a+b*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,(a+b*x)/a)/(b^2*(1-n)*(-b*x/a)^n) +--E 307 + +--S 308 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n + 1 +--R ++ %BJ +--R (2) | ------------ d%BJ +--R ++ n +--R (%BJ b + a) +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 2952 +--m0000:=a0000 - r0000 +--E 309 + +--S 310 of 2952 +--d0000:=D(m0000,x) +--E 310 + +)clear all + +--S 311 of 2952 +t0000:=x^(2+n)/(a+b*x)^n +--R +--R +--R n + 2 +--R x +--R (1) ---------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 311 + +--S 312 of 2952 +--r0000:=-1/6*a*(2+n)*x^(1+n)*(a+b*x)^(1-n)/b^2+_ +-- 1/3*x^(2+n)*(a+b*x)^(1-n)/b+1/6*a^2*(1+n)*(2+n)*x^n*(a+b*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,(a+b*x)/a)/(b^3*(1-n)*(-b*x/a)^n) +--E 312 + +--S 313 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n + 2 +--R ++ %BJ +--R (2) | ------------ d%BJ +--R ++ n +--R (%BJ b + a) +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 2952 +--m0000:=a0000 - r0000 +--E 314 + +--S 315 of 2952 +--d0000:=D(m0000,x) +--E 315 + +)clear all + +--S 316 of 2952 +t0000:=x^(3/2)*(a+b*x)^n +--R +--R +--R n +-+ +--R (1) x (b x + a) \|x +--R Type: Expression(Integer) +--E 316 + +--S 317 of 2952 +--r0000:=2*x^(3/2)*(a+b*x)^(1+n)/(b*(5+2*n))-_ +-- 6*a*(a+b*x)^(1+n)*sqrt(x)/(b^2*(3+2*n)*(5+2*n))+_ +-- 3*a^2*(a+b*x)^(1+n)*_ +-- hypergeometric(1/2,1+n,2+n,(a+b*x)/a)*sqrt(-b*x/a)/_ +-- (b^3*(1+n)*(3+2*n)*(5+2*n)*sqrt(x)) +--E 317 + +--S 318 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R ++ n +---+ +--R (2) | %BJ (%BJ b + a) \|%BJ d%BJ +--R ++ +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 2952 +--m0000:=a0000 - r0000 +--E 319 + +--S 320 of 2952 +--d0000:=D(m0000,x) +--E 320 + +)clear all + +--S 321 of 2952 +t0000:=x^(1/2)*(a+b*x)^n +--R +--R +--R n +-+ +--R (1) (b x + a) \|x +--R Type: Expression(Integer) +--E 321 + +--S 322 of 2952 +--r0000:=2*(a+b*x)^(1+n)*sqrt(x)/(b*(3+2*n))-_ +-- a*(a+b*x)^(1+n)*hypergeometric(1/2,1+n,2+n,(a+b*x)/a)*_ +-- sqrt(-b*x/a)/(b^2*(1+n)*(3+2*n)*sqrt(x)) +--E 322 + +--S 323 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R ++ n +---+ +--R (2) | (%BJ b + a) \|%BJ d%BJ +--R ++ +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 2952 +--m0000:=a0000 - r0000 +--E 324 + +--S 325 of 2952 +--d0000:=D(m0000,x) +--E 325 + +)clear all + +--S 326 of 2952 +t0000:=(a+b*x)^n/x^(1/2) +--R +--R +--R n +--R (b x + a) +--R (1) ---------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 326 + +--S 327 of 2952 +--r0000:=(a+b*x)^(1+n)*_ +-- hypergeometric(1/2,1+n,2+n,(a+b*x)/a)*sqrt(-b*x/a)/(b*(1+n)*sqrt(x)) +--E 327 + +--S 328 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n +--R ++ (%BJ b + a) +--R (2) | ------------ d%BJ +--R ++ +---+ +--R \|%BJ +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 2952 +--m0000:=a0000 - r0000 +--E 329 + +--S 330 of 2952 +--d0000:=D(m0000,x) +--E 330 + +)clear all + +--S 331 of 2952 +t0000:=(a+b*x)^n/x^(3/2) +--R +--R +--R n +--R (b x + a) +--R (1) ---------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 331 + +--S 332 of 2952 +--r0000:=-2*(a+b*x)^(1+n)/(a*sqrt(x))+(1+2*n)*(a+b*x)^(1+n)*_ +-- hypergeometric(1/2,1+n,2+n,(a+b*x)/a)*sqrt(-b*x/a)/(a*(1+n)*sqrt(x)) +--E 332 + +--S 333 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n +--R ++ (%BJ b + a) +--R (2) | ------------ d%BJ +--R ++ +---+ +--R %BJ\|%BJ +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 2952 +--m0000:=a0000 - r0000 +--E 334 + +--S 335 of 2952 +--d0000:=D(m0000,x) +--E 335 + +)clear all + +--S 336 of 2952 +t0000:=(a+b*x)^n/x^(5/2) +--R +--R +--R n +--R (b x + a) +--R (1) ---------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 336 + +--S 337 of 2952 +--r0000:=-2/3*(a+b*x)^(1+n)/(a*x^(3/2))+_ +-- 2/3*b*(1-2*n)*(a+b*x)^(1+n)/(a^2*sqrt(x))-_ +-- 1/3*b*(1-2*n)*(1+2*n)*(a+b*x)^(1+n)*_ +-- hypergeometric(1/2,1+n,2+n,(a+b*x)/a)*sqrt(-b*x/a)/(a^2*(1+n)*sqrt(x)) +--E 337 + +--S 338 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n +--R ++ (%BJ b + a) +--R (2) | ------------ d%BJ +--R ++ 2 +---+ +--R %BJ \|%BJ +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 2952 +--m0000:=a0000 - r0000 +--E 339 + +--S 340 of 2952 +--d0000:=D(m0000,x) +--E 340 + +)clear all + +--S 341 of 2952 +t0000:=x^(-1+n)*(a+b*x)^(-1-n) +--R +--R +--R n - 1 - n - 1 +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 341 + +--S 342 of 2952 +r0000:=x^n/(a*n*(a+b*x)^n) +--R +--R +--R n +--R x +--R (2) -------------- +--R n +--R a n (b x + a) +--R Type: Expression(Integer) +--E 342 + +--S 343 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 (- n - 1)log(b x + a) (n - 1)log(x) +--R (b x + a x)%e %e +--R (3) -------------------------------------------------- +--R a n +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 2 n (- n - 1)log(b x + a) (n - 1)log(x) n +--R (b x + a x)(b x + a) %e %e - x +--R (4) ----------------------------------------------------------------- +--R n +--R a n (b x + a) +--R Type: Expression(Integer) +--E 344 + +--S 345 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R n 2 (- n - 1)log(b x + a) (n - 1)log(x) n - 1 n +--R a ((b x + a) ) %e %e - x (b x + a) +--R + +--R n n - 1 +--R b x (b x + a) +--R / +--R n 2 +--R a ((b x + a) ) +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 2952 +t0000:=x^(-3-n)*(a+b*x)^n +--R +--R +--R - n - 3 n +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 346 + +--S 347 of 2952 +r0000:=-x^(-2-n)*(a+b*x)^(1+n)/(a*(2+n))+_ + b*x^(-1-n)*(a+b*x)^(1+n)/(a^2*(1+n)*(2+n)) +--R +--R +--R - n - 1 - n - 2 n + 1 +--R (b x + (- a n - a)x )(b x + a) +--R (2) ------------------------------------------------ +--R 2 2 2 2 +--R a n + 3a n + 2a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 2 2 2 (- n - 3)log(x) n log(b x + a) +--R (b x - a b n x + (- a n - a )x)%e %e +--R (3) ------------------------------------------------------------------ +--R 2 2 2 2 +--R a n + 3a n + 2a +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 3 2 2 2 (- n - 3)log(x) n log(b x + a) +--R (b x - a b n x + (- a n - a )x)%e %e +--R + +--R - n - 1 - n - 2 n + 1 +--R (- b x + (a n + a)x )(b x + a) +--R / +--R 2 2 2 2 +--R a n + 3a n + 2a +--R Type: Expression(Integer) +--E 349 + +--S 350 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 2 2 (- n - 3)log(x) n log(b x + a) +--R (a n + 2a )%e %e +--R + +--R - n - 2 - n - 3 n + 1 +--R (b x + (- a n - 2a)x )(b x + a) +--R + +--R 2 - n - 1 - n - 2 n +--R (- b x + (a b n + a b)x )(b x + a) +--R / +--R 2 2 +--R a n + 2a +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 2952 +t0000:=x^(2*n-3*(1+n))*(a+b*x)^n +--R +--R +--R - n - 3 n +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 351 + +--S 352 of 2952 +r0000:=-x^(-2-n)*(a+b*x)^(1+n)/(a*(2+n))+_ + b*x^(-1-n)*(a+b*x)^(1+n)/(a^2*(1+n)*(2+n)) +--R +--R +--R - n - 1 - n - 2 n + 1 +--R (b x + (- a n - a)x )(b x + a) +--R (2) ------------------------------------------------ +--R 2 2 2 2 +--R a n + 3a n + 2a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 2 2 2 (- n - 3)log(x) n log(b x + a) +--R (b x - a b n x + (- a n - a )x)%e %e +--R (3) ------------------------------------------------------------------ +--R 2 2 2 2 +--R a n + 3a n + 2a +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 3 2 2 2 (- n - 3)log(x) n log(b x + a) +--R (b x - a b n x + (- a n - a )x)%e %e +--R + +--R - n - 1 - n - 2 n + 1 +--R (- b x + (a n + a)x )(b x + a) +--R / +--R 2 2 2 2 +--R a n + 3a n + 2a +--R Type: Expression(Integer) +--E 354 + +--S 355 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 2 2 (- n - 3)log(x) n log(b x + a) +--R (a n + 2a )%e %e +--R + +--R - n - 2 - n - 3 n + 1 +--R (b x + (- a n - 2a)x )(b x + a) +--R + +--R 2 - n - 1 - n - 2 n +--R (- b x + (a b n + a b)x )(b x + a) +--R / +--R 2 2 +--R a n + 2a +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 2952 +t0000:=1/(e*(c+d*x)+sqrt(-a)) +--R +--R +--R 1 +--R (1) -------------------- +--R +---+ +--R \|- a + d e x + c e +--R Type: Expression(Integer) +--E 356 + +--S 357 of 2952 +r0000:=log(e*(c+d*x)+sqrt(-a))/(d*e) +--R +--R +--R +---+ +--R log(\|- a + d e x + c e) +--R (2) ------------------------- +--R d e +--R Type: Expression(Integer) +--E 357 + +--S 358 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +---+ +--R log(\|- a + d e x + c e) +--R (3) ------------------------- +--R d e +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 2952 +t0000:=(c+d*(a+b*x))^(5/2) +--R +--R +--R 2 2 2 2 2 2 2 +---------------+ +--R (1) (b d x + (2a b d + 2b c d)x + a d + 2a c d + c )\|b d x + a d + c +--R Type: Expression(Integer) +--E 361 + +--S 362 of 2952 +r0000:=2/7*(c+d*(a+b*x))^(7/2)/(b*d) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 2 2 3 2 2 +--R 2b d x + (6a b d + 6b c d )x + (6a b d + 12a b c d + 6b c d)x +--R + +--R 3 3 2 2 2 3 +--R 2a d + 6a c d + 6a c d + 2c +--R * +--R +---------------+ +--R \|b d x + a d + c +--R / +--R 7b d +--R Type: Expression(Integer) +--E 362 + +--S 363 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 2 2 2 2 3 2 2 +--R 2b d x + (6a b d + 6b c d )x + (6a b d + 12a b c d + 6b c d)x +--R + +--R 3 3 2 2 2 3 +--R 2a d + 6a c d + 6a c d + 2c +--R * +--R +---------------+ +--R \|b d x + a d + c +--R / +--R 7b d +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 2952 +t0000:=(c+d*(a+b*x))^(3/2) +--R +--R +--R +---------------+ +--R (1) (b d x + a d + c)\|b d x + a d + c +--R Type: Expression(Integer) +--E 366 + +--S 367 of 2952 +r0000:=2/5*(c+d*(a+b*x))^(5/2)/(b*d) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +---------------+ +--R (2b d x + (4a b d + 4b c d)x + 2a d + 4a c d + 2c )\|b d x + a d + c +--R ------------------------------------------------------------------------ +--R 5b d +--R Type: Expression(Integer) +--E 367 + +--S 368 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 +---------------+ +--R (2b d x + (4a b d + 4b c d)x + 2a d + 4a c d + 2c )\|b d x + a d + c +--R ------------------------------------------------------------------------ +--R 5b d +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 2952 +t0000:=(c+d*(a+b*x))^(1/2) +--R +--R +--R +---------------+ +--R (1) \|b d x + a d + c +--R Type: Expression(Integer) +--E 371 + +--S 372 of 2952 +r0000:=2/3*(c+d*(a+b*x))^(3/2)/(b*d) +--R +--R +--R +---------------+ +--R (2b d x + 2a d + 2c)\|b d x + a d + c +--R (2) -------------------------------------- +--R 3b d +--R Type: Expression(Integer) +--E 372 + +--S 373 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +---------------+ +--R (2b d x + 2a d + 2c)\|b d x + a d + c +--R (3) -------------------------------------- +--R 3b d +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 2952 +t0000:=1/(c+d*(a+b*x))^(1/2) +--R +--R +--R 1 +--R (1) ------------------ +--R +---------------+ +--R \|b d x + a d + c +--R Type: Expression(Integer) +--E 376 + +--S 377 of 2952 +r0000:=2*sqrt(c+d*(a+b*x))/(b*d) +--R +--R +--R +---------------+ +--R 2\|b d x + a d + c +--R (2) ------------------- +--R b d +--R Type: Expression(Integer) +--E 377 + +--S 378 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +---------------+ +--R 2\|b d x + a d + c +--R (3) ------------------- +--R b d +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 2952 +t0000:=1/(c+d*(a+b*x))^(3/2) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R +---------------+ +--R (b d x + a d + c)\|b d x + a d + c +--R Type: Expression(Integer) +--E 381 + +--S 382 of 2952 +r0000:=(-2)/(b*d*sqrt(c+d*(a+b*x))) +--R +--R +--R 2 +--R (2) - --------------------- +--R +---------------+ +--R b d\|b d x + a d + c +--R Type: Expression(Integer) +--E 382 + +--S 383 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) - --------------------- +--R +---------------+ +--R b d\|b d x + a d + c +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 2952 +t0000:=1/(c+d*(a+b*x))^(5/2) +--R +--R +--R 1 +--R (1) --------------------------------------------------------------------- +--R 2 2 2 2 2 2 2 +---------------+ +--R (b d x + (2a b d + 2b c d)x + a d + 2a c d + c )\|b d x + a d + c +--R Type: Expression(Integer) +--E 386 + +--S 387 of 2952 +r0000:=(-2/3)/(b*d*(c+d*(a+b*x))^(3/2)) +--R +--R +--R 2 +--R (2) - --------------------------------------------- +--R 2 2 2 +---------------+ +--R (3b d x + 3a b d + 3b c d)\|b d x + a d + c +--R Type: Expression(Integer) +--E 387 + +--S 388 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) - --------------------------------------------- +--R 2 2 2 +---------------+ +--R (3b d x + 3a b d + 3b c d)\|b d x + a d + c +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 2952 +t0000:=(a+b*x)^m*(c+d*x) +--R +--R +--R m +--R (1) (d x + c)(b x + a) +--R Type: Expression(Integer) +--E 391 + +--S 392 of 2952 +r0000:=(b*c-a*d)*(a+b*x)^(1+m)/(b^2*(1+m))+d*(a+b*x)^(2+m)/(b^2*(2+m)) +--R +--R +--R m + 2 m + 1 +--R (d m + d)(b x + a) + ((- a d + b c)m - 2a d + 2b c)(b x + a) +--R (2) ---------------------------------------------------------------------- +--R 2 2 2 2 +--R b m + 3b m + 2b +--R Type: Expression(Integer) +--E 392 + +--S 393 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R ((b d m + b d)x + ((a b d + b c)m + 2b c)x + a b c m - a d + 2a b c) +--R * +--R m log(b x + a) +--R %e +--R / +--R 2 2 2 2 +--R b m + 3b m + 2b +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 2 2 2 2 2 +--R ((b d m + b d)x + ((a b d + b c)m + 2b c)x + a b c m - a d + 2a b c) +--R * +--R m log(b x + a) +--R %e +--R + +--R m + 2 m + 1 +--R (- d m - d)(b x + a) + ((a d - b c)m + 2a d - 2b c)(b x + a) +--R / +--R 2 2 2 2 +--R b m + 3b m + 2b +--R Type: Expression(Integer) +--E 394 + +--S 395 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R m log(b x + a) m + 1 m +--R (b d x + b c)%e - d (b x + a) + (a d - b c)(b x + a) +--R ------------------------------------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 2952 +t0000:=(a+b*x)^4*(c+d*x) +--R +--R +--R (1) +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b d x + (4a b d + b c)x + (6a b d + 4a b c)x + (4a b d + 6a b c)x +--R + +--R 4 3 4 +--R (a d + 4a b c)x + a c +--R Type: Polynomial(Integer) +--E 396 + +--S 397 of 2952 +r0000:=1/5*(b*c-a*d)*(a+b*x)^5/b^2+1/6*d*(a+b*x)^6/b^2 +--R +--R +--R (2) +--R 1 6 6 4 5 1 6 5 3 2 4 5 4 +--R - b d x + (- a b d + - b c)x + (- a b d + a b c)x +--R 6 5 5 2 +--R + +--R 4 3 3 2 4 3 1 4 2 3 3 2 4 2 1 6 1 5 +--R (- a b d + 2a b c)x + (- a b d + 2a b c)x + a b c x - -- a d + - a b c +--R 3 2 30 5 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 397 + +--S 398 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 4 6 4 3 1 4 5 3 2 2 3 4 4 3 2 2 3 +--R - b d x + (- a b d + - b c)x + (- a b d + a b c)x + (- a b d + 2a b c)x +--R 6 5 5 2 3 +--R + +--R 1 4 3 2 4 +--R (- a d + 2a b c)x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 398 + +--S 399 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 6 1 5 +--R -- a d - - a b c +--R 30 5 +--R (4) ---------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 399 + +--S 400 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 400 + +)clear all + +--S 401 of 2952 +t0000:=(a+b*x)^3*(c+d*x) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 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 401 + +--S 402 of 2952 +r0000:=1/4*(b*c-a*d)*(a+b*x)^4/b^2+1/5*d*(a+b*x)^5/b^2 +--R +--R +--R (2) +--R 1 5 5 3 4 1 5 4 2 3 4 3 +--R - b d x + (- a b d + - b c)x + (a b d + a b c)x +--R 5 4 4 +--R + +--R 1 3 2 3 2 3 2 3 2 1 5 1 4 +--R (- a b d + - a b c)x + a b c x - -- a d + - a b c +--R 2 2 20 4 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 402 + +--S 403 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 3 5 3 2 1 3 4 2 2 3 1 3 3 2 2 +--R - b d x + (- a b d + - b c)x + (a b d + a b c)x + (- a d + - a b c)x +--R 5 4 4 2 2 +--R + +--R 3 +--R a c x +--R Type: Polynomial(Fraction(Integer)) +--E 403 + +--S 404 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 5 1 4 +--R -- a d - - a b c +--R 20 4 +--R (4) ---------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 404 + +--S 405 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 405 + +)clear all + +--S 406 of 2952 +t0000:=(a+b*x)^2*(c+d*x) +--R +--R +--R 2 3 2 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 406 + +--S 407 of 2952 +r0000:=1/3*(b*c-a*d)*(a+b*x)^3/b^2+1/4*d*(a+b*x)^4/b^2 +--R +--R +--R (2) +--R 1 4 4 2 3 1 4 3 1 2 2 3 2 2 2 1 4 +--R - b d x + (- a b d + - b c)x + (- a b d + a b c)x + a b c x - -- a d +--R 4 3 3 2 12 +--R + +--R 1 3 +--R - a b c +--R 3 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 407 + +--S 408 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 4 2 1 2 3 1 2 2 2 +--R (3) - b d x + (- a b d + - b c)x + (- a d + a b c)x + a c x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 408 + +--S 409 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 4 1 3 +--R -- a d - - a b c +--R 12 3 +--R (4) ---------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 409 + +--S 410 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 410 + +)clear all + +--S 411 of 2952 +t0000:=(a+b*x)*(c+d*x) +--R +--R +--R 2 +--R (1) b d x + (a d + b c)x + a c +--R Type: Polynomial(Integer) +--E 411 + +--S 412 of 2952 +r0000:=a*c*x+1/2*(b*c+a*d)*x^2+1/3*b*d*x^3 +--R +--R +--R 1 3 1 1 2 +--R (2) - b d x + (- a d + - b c)x + a c x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 412 + +--S 413 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 1 1 2 +--R (3) - b d x + (- a d + - b c)x + a c x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 413 + +--S 414 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 414 + +--S 415 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 415 + +)clear all + +--S 416 of 2952 +t0000:=c+d*x +--R +--R +--R (1) d x + c +--R Type: Polynomial(Integer) +--E 416 + +--S 417 of 2952 +r0000:=c*x+1/2*d*x^2 +--R +--R +--R 1 2 +--R (2) - d x + c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 417 + +--S 418 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 +--R (3) - d x + c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 418 + +--S 419 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 419 + +--S 420 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 420 + +)clear all + +--S 421 of 2952 +t0000:=(c+d*x)/(a+b*x) +--R +--R +--R d x + c +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 2952 +r0000:=d*x/b+(b*c-a*d)*log(a+b*x)/b^2 +--R +--R +--R (- a d + b c)log(b x + a) + b d x +--R (2) --------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 422 + +--S 423 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (- a d + b c)log(b x + a) + b d x +--R (3) --------------------------------- +--R 2 +--R b +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 2952 +t0000:=(c+d*x)/(a+b*x)^2 +--R +--R +--R d x + c +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 2952 +r0000:=(-b*c+a*d)/(b^2*(a+b*x))+d*log(a+b*x)/b^2 +--R +--R +--R (b d x + a d)log(b x + a) + a d - b c +--R (2) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Expression(Integer) +--E 427 + +--S 428 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (b d x + a d)log(b x + a) + a d - b c +--R (3) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 2952 +t0000:=(c+d*x)/(a+b*x)^3 +--R +--R +--R d x + c +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 431 + +--S 432 of 2952 +r0000:=-1/2*(c+d*x)^2/((b*c-a*d)*(a+b*x)^2) +--R +--R +--R 1 2 2 1 2 +--R - d x + c d x + - c +--R 2 2 +--R (2) -------------------------------------------------- +--R 2 3 2 2 2 3 2 +--R (a b d - b c)x + (2a b d - 2a b c)x + a d - a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 432 + +--S 433 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R - 2b d x - a d - b c +--R (3) ---------------------- +--R 4 2 3 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R d +--R (4) - ------------- +--R 2 3 +--R 2a b d - 2b c +--R Type: Expression(Integer) +--E 434 + +--S 435 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 2952 +t0000:=(c+d*x)/(a+b*x)^4 +--R +--R +--R d x + c +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 2952 +r0000:=1/3*(-b*c+a*d)/(b^2*(a+b*x)^3)-1/2*d/(b^2*(a+b*x)^2) +--R +--R +--R 1 1 1 +--R - - b d x - - a d - - b c +--R 2 6 3 +--R (2) ------------------------------ +--R 5 3 4 2 2 3 3 2 +--R b x + 3a b x + 3a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 437 + +--S 438 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R - 3b d x - a d - 2b c +--R (3) ---------------------------------- +--R 5 3 4 2 2 3 3 2 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 2952 +t0000:=(c+d*x)/(a+b*x)^5 +--R +--R +--R d x + c +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 2952 +r0000:=1/4*(-b*c+a*d)/(b^2*(a+b*x)^4)-1/3*d/(b^2*(a+b*x)^3) +--R +--R +--R 1 1 1 +--R - - b d x - -- a d - - b c +--R 3 12 4 +--R (2) ---------------------------------------- +--R 6 4 5 3 2 4 2 3 3 4 2 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 442 + +--S 443 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R - 4b d x - a d - 3b c +--R (3) ----------------------------------------------- +--R 6 4 5 3 2 4 2 3 3 4 2 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 2952 +t0000:=(a+b*x)^m*(c+d*x)^2 +--R +--R +--R 2 2 2 m +--R (1) (d x + 2c d x + c )(b x + a) +--R Type: Expression(Integer) +--E 446 + +--S 447 of 2952 +r0000:=(b*c-a*d)^2*(a+b*x)^(1+m)/(b^3*(1+m))+_ + 2*d*(b*c-a*d)*(a+b*x)^(2+m)/(b^3*(2+m))+d^2*(a+b*x)^(3+m)/(b^3*(3+m)) +--R +--R +--R (2) +--R 2 2 2 2 m + 3 +--R (d m + 3d m + 2d )(b x + a) +--R + +--R 2 2 2 2 +--R ((- 2a d + 2b c d)m + (- 8a d + 8b c d)m - 6a d + 6b c d) +--R * +--R m + 2 +--R (b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )m + (5a d - 10a b c d + 5b c )m + 6a d +--R + +--R 2 2 +--R - 12a b c d + 6b c +--R * +--R m + 1 +--R (b x + a) +--R / +--R 3 3 3 2 3 3 +--R b m + 6b m + 11b m + 6b +--R Type: Expression(Integer) +--E 447 + +--S 448 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 3 2 3 2 3 +--R (b d m + 3b d m + 2b d )x +--R + +--R 2 2 3 2 2 2 3 3 2 +--R ((a b d + 2b c d)m + (a b d + 8b c d)m + 6b c d)x +--R + +--R 2 3 2 2 2 2 2 3 2 3 2 +--R ((2a b c d + b c )m + (- 2a b d + 6a b c d + 5b c )m + 6b c )x +--R + +--R 2 2 2 2 2 2 3 2 2 2 2 +--R a b c m + (- 2a b c d + 5a b c )m + 2a d - 6a b c d + 6a b c +--R * +--R m log(b x + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R b m + 6b m + 11b m + 6b +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 2 2 3 2 3 2 3 +--R (b d m + 3b d m + 2b d )x +--R + +--R 2 2 3 2 2 2 3 3 2 +--R ((a b d + 2b c d)m + (a b d + 8b c d)m + 6b c d)x +--R + +--R 2 3 2 2 2 2 2 3 2 3 2 +--R ((2a b c d + b c )m + (- 2a b d + 6a b c d + 5b c )m + 6b c )x +--R + +--R 2 2 2 2 2 2 3 2 2 2 2 +--R a b c m + (- 2a b c d + 5a b c )m + 2a d - 6a b c d + 6a b c +--R * +--R m log(b x + a) +--R %e +--R + +--R 2 2 2 2 m + 3 +--R (- d m - 3d m - 2d )(b x + a) +--R + +--R 2 2 2 2 m + 2 +--R ((2a d - 2b c d)m + (8a d - 8b c d)m + 6a d - 6b c d)(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (- a d + 2a b c d - b c )m + (- 5a d + 10a b c d - 5b c )m - 6a d +--R + +--R 2 2 +--R 12a b c d - 6b c +--R * +--R m + 1 +--R (b x + a) +--R / +--R 3 3 3 2 3 3 +--R b m + 6b m + 11b m + 6b +--R Type: Expression(Integer) +--E 449 + +--S 450 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 2 2 2 2 2 2 m log(b x + a) 2 m + 2 +--R (b d x + 2b c d x + b c )%e - d (b x + a) +--R + +--R 2 m + 1 2 2 2 2 m +--R (2a d - 2b c d)(b x + a) + (- a d + 2a b c d - b c )(b x + a) +--R / +--R 2 +--R b +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 2952 +t0000:=(a+b*x)^4*(c+d*x)^2 +--R +--R +--R (1) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b d x + (4a b d + 2b c d)x + (6a b d + 8a b c d + b c )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b d + 12a b c d + 4a b c )x + (a d + 8a b c d + 6a b c )x +--R + +--R 4 3 2 4 2 +--R (2a c d + 4a b c )x + a c +--R Type: Polynomial(Integer) +--E 451 + +--S 452 of 2952 +r0000:=1/5*(b*c-a*d)^2*(a+b*x)^5/b^3+_ + 1/3*d*(b*c-a*d)*(a+b*x)^6/b^3+1/7*d^2*(a+b*x)^7/b^3 +--R +--R +--R (2) +--R 1 7 2 7 2 6 2 1 7 6 6 2 5 2 8 6 1 7 2 5 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 7 3 3 5 5 5 +--R + +--R 3 4 2 2 5 6 2 4 1 4 3 2 8 3 4 2 5 2 3 +--R (a b d + 3a b c d + a b c )x + (- a b d + - a b c d + 2a b c )x +--R 3 3 +--R + +--R 4 3 3 4 2 2 4 3 2 1 7 2 1 6 1 5 2 2 +--R (a b c d + 2a b c )x + a b c x + --- a d - -- a b c d + - a b c +--R 105 15 5 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 452 + +--S 453 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 4 2 7 2 3 2 1 4 6 6 2 2 2 8 3 1 4 2 5 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 7 3 3 5 5 5 +--R + +--R 3 2 2 2 3 2 4 1 4 2 8 3 2 2 2 3 +--R (a b d + 3a b c d + a b c )x + (- a d + - a b c d + 2a b c )x +--R 3 3 +--R + +--R 4 3 2 2 4 2 +--R (a c d + 2a b c )x + a c x +--R Type: Polynomial(Fraction(Integer)) +--E 453 + +--S 454 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 7 2 1 6 1 5 2 2 +--R - --- a d + -- a b c d - - a b c +--R 105 15 5 +--R (4) ---------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 454 + +--S 455 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 455 + +)clear all + +--S 456 of 2952 +t0000:=(a+b*x)^3*(c+d*x)^2 +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--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 2 3 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 456 + +--S 457 of 2952 +r0000:=1/4*(b*c-a*d)^2*(a+b*x)^4/b^3+2/5*d*(b*c-a*d)*(a+b*x)^5/b^3+_ + 1/6*d^2*(a+b*x)^6/b^3 +--R +--R +--R (2) +--R 1 6 2 6 3 5 2 2 6 5 3 2 4 2 3 5 1 6 2 4 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 6 5 5 4 2 4 +--R + +--R 1 3 3 2 2 4 5 2 3 3 3 3 2 4 2 2 3 3 2 +--R (- a b d + 2a b c d + a b c )x + (a b c d + - a b c )x + a b c x +--R 3 2 +--R + +--R 1 6 2 1 5 1 4 2 2 +--R -- a d - -- a b c d + - a b c +--R 60 10 4 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 457 + +--S 458 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 3 2 6 3 2 2 2 3 5 3 2 2 3 2 1 3 2 4 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 6 5 5 4 2 4 +--R + +--R 1 3 2 2 2 2 3 3 3 2 2 2 3 2 +--R (- a d + 2a b c d + a b c )x + (a c d + - a b c )x + a c x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 458 + +--S 459 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 6 2 1 5 1 4 2 2 +--R - -- a d + -- a b c d - - a b c +--R 60 10 4 +--R (4) --------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 459 + +--S 460 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 460 + +)clear all + +--S 461 of 2952 +t0000:=(a+b*x)^2*(c+d*x)^2 +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--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 +--R (2a c d + 2a b c )x + a c +--R Type: Polynomial(Integer) +--E 461 + +--S 462 of 2952 +r0000:=1/3*(b*c-a*d)^2*(a+b*x)^3/b^3+1/2*d*(b*c-a*d)*(a+b*x)^4/b^3+_ + 1/5*d^2*(a+b*x)^5/b^3 +--R +--R +--R (2) +--R 1 5 2 5 1 4 2 1 5 4 1 2 3 2 4 4 1 5 2 3 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 5 2 2 3 3 3 +--R + +--R 2 3 4 2 2 2 3 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 30 6 3 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 462 + +--S 463 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 2 2 5 1 2 1 2 4 1 2 2 4 1 2 2 3 +--R - b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x +--R 5 2 2 3 3 3 +--R + +--R 2 2 2 2 2 +--R (a c d + a b c )x + a c x +--R Type: Polynomial(Fraction(Integer)) +--E 463 + +--S 464 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 5 2 1 4 1 3 2 2 +--R - -- a d + - a b c d - - a b c +--R 30 6 3 +--R (4) -------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 464 + +--S 465 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 465 + +)clear all + +--S 466 of 2952 +t0000:=(a+b*x)*(c+d*x)^2 +--R +--R +--R 2 3 2 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 466 + +--S 467 of 2952 +r0000:=-1/3*(b*c-a*d)*(c+d*x)^3/d^2+1/4*b*(c+d*x)^4/d^2 +--R +--R +--R (2) +--R 1 4 4 1 4 2 3 3 3 1 2 2 2 2 2 +--R - b d x + (- a d + - b c d )x + (a c d + - b c d )x + a c d x +--R 4 3 3 2 +--R + +--R 1 3 1 4 +--R - a c d - -- b c +--R 3 12 +--R / +--R 2 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 467 + +--S 468 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 4 1 2 2 3 1 2 2 2 +--R (3) - b d x + (- a d + - b c d)x + (a c d + - b c )x + a c x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 468 + +--S 469 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 3 1 4 +--R - - a c d + -- b c +--R 3 12 +--R (4) ------------------- +--R 2 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 469 + +--S 470 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 470 + +)clear all + +--S 471 of 2952 +t0000:=(c+d*x)^2 +--R +--R +--R 2 2 2 +--R (1) d x + 2c d x + c +--R Type: Polynomial(Integer) +--E 471 + +--S 472 of 2952 +r0000:=1/3*(c+d*x)^3/d +--R +--R +--R 1 3 3 2 2 2 1 3 +--R - d x + c d x + c d x + - c +--R 3 3 +--R (2) ------------------------------ +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 472 + +--S 473 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 2 3 2 2 +--R (3) - d x + c d x + c x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 473 + +--S 474 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 3 +--R - c +--R 3 +--R (4) - ---- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 474 + +--S 475 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 475 + +)clear all + +--S 476 of 2952 +t0000:=(c+d*x)^2/(a+b*x) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 2952 +r0000:=d*(b*c-a*d)*x/b^2+1/2*(c+d*x)^2/b+(b*c-a*d)^2*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 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 2b +--R Type: Expression(Integer) +--E 477 + +--S 478 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 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 2b +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R c +--R (4) - -- +--R 2b +--R Type: Expression(Integer) +--E 479 + +--S 480 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 2952 +t0000:=(c+d*x)^2/(a+b*x)^2 +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 2952 +r0000:=d^2*x/b^2-(b*c-a*d)^2/(b^3*(a+b*x))+2*d*(b*c-a*d)*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R ((- 2a b d + 2b c d)x - 2a d + 2a b c d)log(b x + a) + b d x + a b d x +--R + +--R 2 2 2 2 +--R - a d + 2a b c d - b c +--R / +--R 4 3 +--R b x + a b +--R Type: Expression(Integer) +--E 482 + +--S 483 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 +--R ((- 2a b d + 2b c d)x - 2a d + 2a b c d)log(b x + a) + b d x + a b d x +--R + +--R 2 2 2 2 +--R - a d + 2a b c d - b c +--R / +--R 4 3 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 2952 +t0000:=(c+d*x)^2/(a+b*x)^3 +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 2952 +r0000:=-1/2*(b*c-a*d)^2/(b^3*(a+b*x)^2)-2*d*(b*c-a*d)/(b^3*(a+b*x))+_ + d^2*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 2 +--R (2b d x + 4a b d x + 2a d )log(b x + a) + (4a b d - 4b c d)x + 3a d +--R + +--R 2 2 +--R - 2a b c d - b c +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 487 + +--S 488 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 2 +--R (2b d x + 4a b d x + 2a d )log(b x + a) + (4a b d - 4b c d)x + 3a d +--R + +--R 2 2 +--R - 2a b c d - b c +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 2952 +t0000:=(c+d*x)^2/(a+b*x)^4 +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 2952 +r0000:=-1/3*(c+d*x)^3/((b*c-a*d)*(a+b*x)^3) +--R +--R +--R (2) +--R 1 3 3 2 2 2 1 3 +--R - d x + c d x + c d x + - c +--R 3 3 +--R ------------------------------------------------------------------------ +--R 3 4 3 2 2 3 2 3 2 2 4 3 +--R (a b d - b c)x + (3a b d - 3a b c)x + (3a b d - 3a b c)x + a d - a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 492 + +--S 493 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 3b d x + (- 3a b d - 3b c d)x - a d - a b c d - b c +--R (3) --------------------------------------------------------- +--R 6 3 5 2 2 4 3 3 +--R 3b x + 9a b x + 9a b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 3 +--R d +--R (4) - ------------- +--R 3 4 +--R 3a b d - 3b c +--R Type: Expression(Integer) +--E 494 + +--S 495 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 2952 +t0000:=(c+d*x)^2/(a+b*x)^5 +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 2952 +r0000:=-1/4*(b*c-a*d)^2/(b^3*(a+b*x)^4)-2/3*d*(b*c-a*d)/(b^3*(a+b*x)^3)-_ + 1/2*d^2/(b^3*(a+b*x)^2) +--R +--R +--R 1 2 2 2 1 2 2 2 1 2 2 1 1 2 2 +--R - - b d x + (- - a b d - - b c d)x - -- a d - - a b c d - - b c +--R 2 3 3 12 6 4 +--R (2) ------------------------------------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R b x + 4a b x + 6a b x + 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 497 + +--S 498 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 6b d x + (- 4a b d - 8b c d)x - a d - 2a b c d - 3b c +--R (3) ----------------------------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)clear all + +--S 501 of 2952 +t0000:=(c+d*x)^2/(a+b*x)^6 +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 501 + +--S 502 of 2952 +r0000:=-1/5*(b*c-a*d)^2/(b^3*(a+b*x)^5)-1/2*d*(b*c-a*d)/(b^3*(a+b*x)^4)-_ + 1/3*d^2/(b^3*(a+b*x)^3) +--R +--R +--R 1 2 2 2 1 2 1 2 1 2 2 1 1 2 2 +--R - - b d x + (- - a b d - - b c d)x - -- a d - -- a b c d - - b c +--R 3 6 2 30 10 5 +--R (2) -------------------------------------------------------------------- +--R 8 5 7 4 2 6 3 3 5 2 4 4 5 3 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 502 + +--S 503 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R - 10b d x + (- 5a b d - 15b c d)x - a d - 3a b c d - 6b c +--R (3) -------------------------------------------------------------- +--R 8 5 7 4 2 6 3 3 5 2 4 4 5 3 +--R 30b x + 150a b x + 300a b x + 300a b x + 150a b x + 30a b +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 505 + +)clear all + +--S 506 of 2952 +t0000:=(c+d*x)^2/(a+b*x)^7 +--R +--R +--R (1) +--R 2 2 2 +--R d x + 2c d x + c +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 506 + +--S 507 of 2952 +r0000:=-1/6*(b*c-a*d)^2/(b^3*(a+b*x)^6)-2/5*d*(b*c-a*d)/(b^3*(a+b*x)^5)-_ + 1/4*d^2/(b^3*(a+b*x)^4) +--R +--R +--R 1 2 2 2 1 2 2 2 1 2 2 1 1 2 2 +--R - - b d x + (- -- a b d - - b c d)x - -- a d - -- a b c d - - b c +--R 4 10 5 60 15 6 +--R (2) --------------------------------------------------------------------- +--R 9 6 8 5 2 7 4 3 6 3 4 5 2 5 4 6 3 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 507 + +--S 508 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R - 15b d x + (- 6a b d - 24b c d)x - a d - 4a b c d - 10b c +--R --------------------------------------------------------------------------- +--R 9 6 8 5 2 7 4 3 6 3 4 5 2 5 4 6 3 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x + 60a b +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 2952 +t0000:=(a+b*x)^m*(c+d*x)^3 +--R +--R +--R 3 3 2 2 2 3 m +--R (1) (d x + 3c d x + 3c d x + c )(b x + a) +--R Type: Expression(Integer) +--E 511 + +--S 512 of 2952 +r0000:=(b*c-a*d)^3*(a+b*x)^(1+m)/(b^4*(1+m))+_ + 3*d*(b*c-a*d)^2*(a+b*x)^(2+m)/(b^4*(2+m))+_ + 3*d^2*(b*c-a*d)*(a+b*x)^(3+m)/(b^4*(3+m))+_ + d^3*(a+b*x)^(4+m)/(b^4*(4+m)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 4 +--R (d m + 6d m + 11d m + 6d )(b x + a) +--R + +--R 3 2 3 3 2 2 +--R (- 3a d + 3b c d )m + (- 21a d + 21b c d )m +--R + +--R 3 2 3 2 +--R (- 42a d + 42b c d )m - 24a d + 24b c d +--R * +--R m + 3 +--R (b x + a) +--R + +--R 2 3 2 2 2 3 2 3 2 2 2 2 +--R (3a d - 6a b c d + 3b c d)m + (24a d - 48a b c d + 24b c d)m +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R (57a d - 114a b c d + 57b c d)m + 36a d - 72a b c d + 36b c d +--R * +--R m + 2 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a d + 3a b c d - 3a b c d + b c )m +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 9a d + 27a b c d - 27a b c d + 9b c )m +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (- 26a d + 78a b c d - 78a b c d + 26b c )m - 24a d + 72a b c d +--R + +--R 2 2 3 3 +--R - 72a b c d + 24b c +--R * +--R m + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b m + 10b m + 35b m + 50b m + 24b +--R Type: Expression(Integer) +--E 512 + +--S 513 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 3 4 3 2 4 3 4 3 4 +--R (b d m + 6b d m + 11b d m + 6b d )x +--R + +--R 3 3 4 2 3 3 3 4 2 2 +--R (a b d + 3b c d )m + (3a b d + 21b c d )m +--R + +--R 3 3 4 2 4 2 +--R (2a b d + 42b c d )m + 24b c d +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 3 2 2 3 3 2 4 2 2 +--R (3a b c d + 3b c d)m + (- 3a b d + 15a b c d + 24b c d)m +--R + +--R 2 2 3 3 2 4 2 4 2 +--R (- 3a b d + 12a b c d + 57b c d)m + 36b c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 3 2 2 2 3 2 4 3 2 +--R (3a b c d + b c )m + (- 6a b c d + 21a b c d + 9b c )m +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (6a b d - 24a b c d + 36a b c d + 26b c )m + 24b c +--R * +--R x +--R + +--R 3 3 3 2 2 2 3 3 2 +--R a b c m + (- 3a b c d + 9a b c )m +--R + +--R 3 2 2 2 2 3 3 4 3 3 2 2 2 2 +--R (6a b c d - 21a b c d + 26a b c )m - 6a d + 24a b c d - 36a b c d +--R + +--R 3 3 +--R 24a b c +--R * +--R m log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R b m + 10b m + 35b m + 50b m + 24b +--R Type: Union(Expression(Integer),...) +--E 513 + +--S 514 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 4 3 3 4 3 2 4 3 4 3 4 +--R (b d m + 6b d m + 11b d m + 6b d )x +--R + +--R 3 3 4 2 3 3 3 4 2 2 +--R (a b d + 3b c d )m + (3a b d + 21b c d )m +--R + +--R 3 3 4 2 4 2 +--R (2a b d + 42b c d )m + 24b c d +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 3 2 2 3 3 2 4 2 2 +--R (3a b c d + 3b c d)m + (- 3a b d + 15a b c d + 24b c d)m +--R + +--R 2 2 3 3 2 4 2 4 2 +--R (- 3a b d + 12a b c d + 57b c d)m + 36b c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 3 2 2 2 3 2 4 3 2 +--R (3a b c d + b c )m + (- 6a b c d + 21a b c d + 9b c )m +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (6a b d - 24a b c d + 36a b c d + 26b c )m + 24b c +--R * +--R x +--R + +--R 3 3 3 2 2 2 3 3 2 +--R a b c m + (- 3a b c d + 9a b c )m +--R + +--R 3 2 2 2 2 3 3 4 3 3 2 2 2 2 +--R (6a b c d - 21a b c d + 26a b c )m - 6a d + 24a b c d - 36a b c d +--R + +--R 3 3 +--R 24a b c +--R * +--R m log(b x + a) +--R %e +--R + +--R 3 3 3 2 3 3 m + 4 +--R (- d m - 6d m - 11d m - 6d )(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a d - 3b c d )m + (21a d - 21b c d )m + (42a d - 42b c d )m +--R + +--R 3 2 +--R 24a d - 24b c d +--R * +--R m + 3 +--R (b x + a) +--R + +--R 2 3 2 2 2 3 +--R (- 3a d + 6a b c d - 3b c d)m +--R + +--R 2 3 2 2 2 2 +--R (- 24a d + 48a b c d - 24b c d)m +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R (- 57a d + 114a b c d - 57b c d)m - 36a d + 72a b c d - 36b c d +--R * +--R m + 2 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )m +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (9a d - 27a b c d + 27a b c d - 9b c )m +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (26a d - 78a b c d + 78a b c d - 26b c )m + 24a d - 72a b c d +--R + +--R 2 2 3 3 +--R 72a b c d - 24b c +--R * +--R m + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b m + 10b m + 35b m + 50b m + 24b +--R Type: Expression(Integer) +--E 514 + +--S 515 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 3 3 3 3 2 2 3 2 3 3 m log(b x + a) 3 m + 3 +--R (b d x + 3b c d x + 3b c d x + b c )%e - d (b x + a) +--R + +--R 3 2 m + 2 +--R (3a d - 3b c d )(b x + a) +--R + +--R 2 3 2 2 2 m + 1 +--R (- 3a d + 6a b c d - 3b c d)(b x + a) +--R + +--R 3 3 2 2 2 2 3 3 m +--R (a d - 3a b c d + 3a b c d - b c )(b x + a) +--R / +--R 3 +--R b +--R Type: Expression(Integer) +--E 515 + +)clear all + +--S 516 of 2952 +t0000:=(a+b*x)^5*(c+d*x)^3 +--R +--R +--R (1) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b d x + (5a b d + 3b c d )x + (10a b d + 15a b c d + 3b c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b d + 30a b c d + 15a b c d + b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b d + 30a b c d + 30a b c d + 5a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a d + 15a b c d + 30a b c d + 10a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a c d + 15a b c d + 10a b c )x + (3a c d + 5a b c )x + a c +--R Type: Polynomial(Integer) +--E 516 + +--S 517 of 2952 +r0000:=1/6*(b*c-a*d)^3*(a+b*x)^6/b^4+3/7*d*(b*c-a*d)^2*(a+b*x)^7/b^4+_ + 3/8*d^2*(b*c-a*d)*(a+b*x)^8/b^4+1/9*d^3*(a+b*x)^9/b^4 +--R +--R +--R (2) +--R 1 9 3 9 5 8 3 3 9 2 8 +--R - b d x + (- a b d + - b c d )x +--R 9 8 8 +--R + +--R 10 2 7 3 15 8 2 3 9 2 7 +--R (-- a b d + -- a b c d + - b c d)x +--R 7 7 7 +--R + +--R 5 3 6 3 2 7 2 5 8 2 1 9 3 6 +--R (- a b d + 5a b c d + - a b c d + - b c )x +--R 3 2 6 +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (a b d + 6a b c d + 6a b c d + a b c )x +--R + +--R 1 5 4 3 15 4 5 2 15 3 6 2 5 2 7 3 4 +--R (- a b d + -- a b c d + -- a b c d + - a b c )x +--R 4 4 2 2 +--R + +--R 5 4 2 4 5 2 10 3 6 3 3 3 5 4 2 5 4 5 3 2 5 4 3 +--R (a b c d + 5a b c d + -- a b c )x + (- a b c d + - a b c )x + a b c x +--R 3 2 2 +--R + +--R 1 9 3 1 8 2 1 7 2 2 1 6 3 3 +--R - --- a d + -- a b c d - -- a b c d + - a b c +--R 504 56 14 6 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 517 + +--S 518 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 5 3 9 5 4 3 3 5 2 8 10 2 3 3 15 4 2 3 5 2 7 +--R - b d x + (- a b d + - b c d )x + (-- a b d + -- a b c d + - b c d)x +--R 9 8 8 7 7 7 +--R + +--R 5 3 2 3 2 3 2 5 4 2 1 5 3 6 +--R (- a b d + 5a b c d + - a b c d + - b c )x +--R 3 2 6 +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 +--R (a b d + 6a b c d + 6a b c d + a b c )x +--R + +--R 1 5 3 15 4 2 15 3 2 2 5 2 3 3 4 +--R (- a d + -- a b c d + -- a b c d + - a b c )x +--R 4 4 2 2 +--R + +--R 5 2 4 2 10 3 2 3 3 3 5 2 5 4 3 2 5 3 +--R (a c d + 5a b c d + -- a b c )x + (- a c d + - a b c )x + a c x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 518 + +--S 519 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 9 3 1 8 2 1 7 2 2 1 6 3 3 +--R --- a d - -- a b c d + -- a b c d - - a b c +--R 504 56 14 6 +--R (4) ---------------------------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 519 + +--S 520 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 520 + +)clear all + +--S 521 of 2952 +t0000:=(a+b*x)^4*(c+d*x)^3 +--R +--R +--R (1) +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b d x + (4a b d + 3b c d )x + (6a b d + 12a b c d + 3b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b d + 18a b c d + 12a b c d + b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a d + 12a b c d + 18a b c d + 4a b c )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a c d + 12a b c d + 6a b c )x + (3a c d + 4a b c )x + a c +--R Type: Polynomial(Integer) +--E 521 + +--S 522 of 2952 +r0000:=1/5*(b*c-a*d)^3*(a+b*x)^5/b^4+1/2*d*(b*c-a*d)^2*(a+b*x)^6/b^4+_ + 3/7*d^2*(b*c-a*d)*(a+b*x)^7/b^4+1/8*d^3*(a+b*x)^8/b^4 +--R +--R +--R (2) +--R 1 8 3 8 4 7 3 3 8 2 7 2 6 3 7 2 1 8 2 6 +--R - b d x + (- a b d + - b c d )x + (a b d + 2a b c d + - b c d)x +--R 8 7 7 2 +--R + +--R 4 3 5 3 18 2 6 2 12 7 2 1 8 3 5 +--R (- a b d + -- a b c d + -- a b c d + - b c )x +--R 5 5 5 5 +--R + +--R 1 4 4 3 3 5 2 9 2 6 2 7 3 4 +--R (- a b d + 3a b c d + - a b c d + a b c )x +--R 4 2 +--R + +--R 4 4 2 3 5 2 2 6 3 3 3 4 4 2 3 5 3 2 4 4 3 +--R (a b c d + 4a b c d + 2a b c )x + (- a b c d + 2a b c )x + a b c x +--R 2 +--R + +--R 1 8 3 1 7 2 1 6 2 2 1 5 3 3 +--R - --- a d + -- a b c d - -- a b c d + - a b c +--R 280 35 10 5 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 522 + +--S 523 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 4 3 8 4 3 3 3 4 2 7 2 2 3 3 2 1 4 2 6 +--R - b d x + (- a b d + - b c d )x + (a b d + 2a b c d + - b c d)x +--R 8 7 7 2 +--R + +--R 4 3 3 18 2 2 2 12 3 2 1 4 3 5 +--R (- a b d + -- a b c d + -- a b c d + - b c )x +--R 5 5 5 5 +--R + +--R 1 4 3 3 2 9 2 2 2 3 3 4 +--R (- a d + 3a b c d + - a b c d + a b c )x +--R 4 2 +--R + +--R 4 2 3 2 2 2 3 3 3 4 2 3 3 2 4 3 +--R (a c d + 4a b c d + 2a b c )x + (- a c d + 2a b c )x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 523 + +--S 524 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 8 3 1 7 2 1 6 2 2 1 5 3 3 +--R --- a d - -- a b c d + -- a b c d - - a b c +--R 280 35 10 5 +--R (4) ---------------------------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 524 + +--S 525 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 525 + +)clear all + +--S 526 of 2952 +t0000:=(a+b*x)^3*(c+d*x)^3 +--R +--R +--R (1) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--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 3 3 2 2 2 2 3 2 +--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 3 3 +--R (3a c d + 3a b c )x + a c +--R Type: Polynomial(Integer) +--E 526 + +--S 527 of 2952 +r0000:=1/4*(b*c-a*d)^3*(a+b*x)^4/b^4+3/5*d*(b*c-a*d)^2*(a+b*x)^5/b^4+_ + 1/2*d^2*(b*c-a*d)*(a+b*x)^6/b^4+1/7*d^3*(a+b*x)^7/b^4 +--R +--R +--R (2) +--R 1 7 3 7 1 6 3 1 7 2 6 3 2 5 3 9 6 2 3 7 2 5 +--R - b d x + (- a b d + - b c d )x + (- a b d + - a b c d + - b c d)x +--R 7 2 2 5 5 5 +--R + +--R 1 3 4 3 9 2 5 2 9 6 2 1 7 3 4 +--R (- a b d + - a b c d + - a b c d + - b c )x +--R 4 4 4 4 +--R + +--R 3 4 2 2 5 2 6 3 3 3 3 4 2 3 2 5 3 2 3 4 3 +--R (a b c d + 3a b c d + a b c )x + (- a b c d + - a b c )x + a b c x +--R 2 2 +--R + +--R 1 7 3 1 6 2 3 5 2 2 1 4 3 3 +--R - --- a d + -- a b c d - -- a b c d + - a b c +--R 140 20 20 4 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 527 + +--S 528 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 3 3 7 1 2 3 1 3 2 6 3 2 3 9 2 2 3 3 2 5 +--R - b d x + (- a b d + - b c d )x + (- a b d + - a b c d + - b c d)x +--R 7 2 2 5 5 5 +--R + +--R 1 3 3 9 2 2 9 2 2 1 3 3 4 +--R (- a d + - a b c d + - a b c d + - b c )x +--R 4 4 4 4 +--R + +--R 3 2 2 2 2 3 3 3 3 2 3 2 3 2 3 3 +--R (a c d + 3a b c d + a b c )x + (- a c d + - a b c )x + a c x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 528 + +--S 529 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 7 3 1 6 2 3 5 2 2 1 4 3 3 +--R --- a d - -- a b c d + -- a b c d - - a b c +--R 140 20 20 4 +--R (4) ---------------------------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 529 + +--S 530 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 530 + +)clear all + +--S 531 of 2952 +t0000:=(a+b*x)^2*(c+d*x)^3 +--R +--R +--R (1) +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--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 2 2 2 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 531 + +--S 532 of 2952 +r0000:=1/4*(b*c-a*d)^2*(c+d*x)^4/d^3-2/5*b*(b*c-a*d)*(c+d*x)^5/d^3+_ + 1/6*b^2*(c+d*x)^6/d^3 +--R +--R +--R (2) +--R 1 2 6 6 2 6 3 2 5 5 1 2 6 3 5 3 2 2 4 4 +--R - b d x + (- a b d + - b c d )x + (- a d + - a b c d + - b c d )x +--R 6 5 5 4 2 4 +--R + +--R 2 5 2 4 1 2 3 3 3 3 2 2 4 3 3 2 2 3 3 +--R (a c d + 2a b c d + - b c d )x + (- a c d + a b c d )x + a c d x +--R 3 2 +--R + +--R 1 2 4 2 1 5 1 2 6 +--R - a c d - -- a b c d + -- b c +--R 4 10 60 +--R / +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 532 + +--S 533 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 2 3 6 2 3 3 2 2 5 1 2 3 3 2 3 2 2 4 +--R - b d x + (- a b d + - b c d )x + (- a d + - a b c d + - b c d)x +--R 6 5 5 4 2 4 +--R + +--R 2 2 2 1 2 3 3 3 2 2 3 2 2 3 +--R (a c d + 2a b c d + - b c )x + (- a c d + a b c )x + a c x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 533 + +--S 534 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 2 4 2 1 5 1 2 6 +--R - - a c d + -- a b c d - -- b c +--R 4 10 60 +--R (4) --------------------------------- +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 534 + +--S 535 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 535 + +)clear all + +--S 536 of 2952 +t0000:=(a+b*x)*(c+d*x)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 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 + a c +--R Type: Polynomial(Integer) +--E 536 + +--S 537 of 2952 +r0000:=-1/4*(b*c-a*d)*(c+d*x)^4/d^2+1/5*b*(c+d*x)^5/d^2 +--R +--R +--R (2) +--R 1 5 5 1 5 3 4 4 4 2 3 3 +--R - b d x + (- a d + - b c d )x + (a c d + b c d )x +--R 5 4 4 +--R + +--R 3 2 3 1 3 2 2 3 2 1 4 1 5 +--R (- a c d + - b c d )x + a c d x + - a c d - -- b c +--R 2 2 4 20 +--R / +--R 2 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 537 + +--S 538 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 3 5 1 3 3 2 4 2 2 3 +--R - b d x + (- a d + - b c d )x + (a c d + b c d)x +--R 5 4 4 +--R + +--R 3 2 1 3 2 3 +--R (- a c d + - b c )x + a c x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 538 + +--S 539 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 4 1 5 +--R - - a c d + -- b c +--R 4 20 +--R (4) ------------------- +--R 2 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 539 + +--S 540 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 540 + +)clear all + +--S 541 of 2952 +t0000:=(c+d*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R (1) d x + 3c d x + 3c d x + c +--R Type: Polynomial(Integer) +--E 541 + +--S 542 of 2952 +r0000:=1/4*(c+d*x)^4/d +--R +--R +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - d x + c d x + - c d x + c d x + - c +--R 4 2 4 +--R (2) ----------------------------------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 542 + +--S 543 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 3 4 2 3 3 2 2 3 +--R (3) - d x + c d x + - c d x + c x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 543 + +--S 544 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 4 +--R - c +--R 4 +--R (4) - ---- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 544 + +--S 545 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 545 + +)clear all + +--S 546 of 2952 +t0000:=(c+d*x)^3/(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 546 + +--S 547 of 2952 +r0000:=d*(b*c-a*d)^2*x/b^3+1/2*(b*c-a*d)*(c+d*x)^2/b^2+1/3*(c+d*x)^3/b+_ + (b*c-a*d)^3*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 3 +--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 2 2 3 2 2 3 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 6b +--R Type: Expression(Integer) +--E 547 + +--S 548 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 3 3 +--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 2 2 3 2 2 3 2 +--R (- 3a b d + 9b c d )x + (6a b d - 18a b c d + 18b c d)x +--R / +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 548 + +--S 549 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 2 3 +--R 3a c d - 5b c +--R (4) -------------- +--R 2 +--R 6b +--R Type: Expression(Integer) +--E 549 + +--S 550 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 550 + +)clear all + +--S 551 of 2952 +t0000:=(c+d*x)^3/(a+b*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 551 + +--S 552 of 2952 +r0000:=d^2*(3*b*c-2*a*d)*x/b^3+1/2*d^3*x^2/b^2-(b*c-a*d)^3/(b^4*(a+b*x))+_ + 3*d*(b*c-a*d)^2*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 3 2 2 3 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 log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 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 4 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 552 + +--S 553 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 3 2 2 3 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 log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 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 4 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 553 + +--S 554 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 2952 +t0000:=(c+d*x)^3/(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 of 2952 +r0000:=d^3*x/b^3-1/2*(b*c-a*d)^3/(b^4*(a+b*x)^2)-_ + 3*d*(b*c-a*d)^2/(b^4*(a+b*x))+3*d^2*(b*c-a*d)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (- 6a b d + 6b c d )x + (- 12a b d + 12a b c d )x - 6a d +--R + +--R 2 2 +--R 6a b c d +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 2 2 3 2 2 3 2 3 3 +--R 2b d x + 4a b d x + (- 4a b d + 12a b c d - 6b c d)x - 5a d +--R + +--R 2 2 2 2 3 3 +--R 9a b c d - 3a b c d - b c +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 557 + +--S 558 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (- 6a b d + 6b c d )x + (- 12a b d + 12a b c d )x - 6a d +--R + +--R 2 2 +--R 6a b c d +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 2 2 3 2 2 3 2 3 3 +--R 2b d x + 4a b d x + (- 4a b d + 12a b c d - 6b c d)x - 5a d +--R + +--R 2 2 2 2 3 3 +--R 9a b c d - 3a b c d - b c +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 558 + +--S 559 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 2952 +t0000:=(c+d*x)^3/(a+b*x)^4 +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 561 + +--S 562 of 2952 +r0000:=-1/3*(b*c-a*d)^3/(b^4*(a+b*x)^3)-3/2*d*(b*c-a*d)^2/(b^4*(a+b*x)^2)-_ + 3*d^2*(b*c-a*d)/(b^4*(a+b*x))+d^3*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b d x + 18a b d x + 18a b d x + 6a d )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (18a b d - 18b c d )x + (27a b d - 18a b c d - 9b c d)x + 11a d +--R + +--R 2 2 2 2 3 3 +--R - 6a b c d - 3a b c d - 2b c +--R / +--R 7 3 6 2 2 5 3 4 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Expression(Integer) +--E 562 + +--S 563 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b d x + 18a b d x + 18a b d x + 6a d )log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (18a b d - 18b c d )x + (27a b d - 18a b c d - 9b c d)x + 11a d +--R + +--R 2 2 2 2 3 3 +--R - 6a b c d - 3a b c d - 2b c +--R / +--R 7 3 6 2 2 5 3 4 +--R 6b x + 18a b x + 18a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 563 + +--S 564 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 564 + +--S 565 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 565 + +)clear all + +--S 566 of 2952 +t0000:=(c+d*x)^3/(a+b*x)^5 +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 566 + +--S 567 of 2952 +r0000:=-1/4*(c+d*x)^4/((b*c-a*d)*(a+b*x)^4) +--R +--R +--R (2) +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - d x + c d x + - c d x + c d x + - c +--R 4 2 4 +--R / +--R 4 5 4 2 3 4 3 3 2 2 3 2 +--R (a b d - b c)x + (4a b d - 4a b c)x + (6a b d - 6a b c)x +--R + +--R 4 3 2 5 4 +--R (4a b d - 4a b c)x + a d - a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 567 + +--S 568 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R - 4b d x + (- 6a b d - 6b c d )x + (- 4a b d - 4a b c d - 4b c d)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - a d - a b c d - a b c d - b c +--R / +--R 8 4 7 3 2 6 2 3 5 4 4 +--R 4b x + 16a b x + 24a b x + 16a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 568 + +--S 569 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 4 +--R d +--R (4) - ------------- +--R 4 5 +--R 4a b d - 4b c +--R Type: Expression(Integer) +--E 569 + +--S 570 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 2952 +t0000:=(c+d*x)^3/(a+b*x)^6 +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 571 + +--S 572 of 2952 +r0000:=-1/5*(c+d*x)^4/((b*c-a*d)*(a+b*x)^5)+_ + 1/20*d*(c+d*x)^4/((b*c-a*d)^2*(a+b*x)^4) +--R +--R +--R (2) +--R 1 5 5 1 5 4 4 1 2 3 3 3 2 3 3 2 2 +--R -- b d x + - a d x + (a c d - - b c d )x + (- a c d - b c d )x +--R 20 4 2 2 +--R + +--R 3 2 3 4 1 4 1 5 +--R (a c d - - b c d)x + - a c d - - b c +--R 4 4 5 +--R / +--R 2 5 2 6 7 2 5 3 4 2 2 5 6 2 4 +--R (a b d - 2a b c d + b c )x + (5a b d - 10a b c d + 5a b c )x +--R + +--R 4 3 2 3 4 2 5 2 3 5 2 2 4 3 3 4 2 2 +--R (10a b d - 20a b c d + 10a b c )x + (10a b d - 20a b c d + 10a b c )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 5 2 2 +--R (5a b d - 10a b c d + 5a b c )x + a d - 2a b c d + a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 572 + +--S 573 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 +--R - 10b d x + (- 10a b d - 20b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 3 3 +--R (- 5a b d - 10a b c d - 15b c d)x - a d - 2a b c d - 3a b c d - 4b c +--R / +--R 9 5 8 4 2 7 3 3 6 2 4 5 5 4 +--R 20b x + 100a b x + 200a b x + 200a b x + 100a b x + 20a b +--R Type: Union(Expression(Integer),...) +--E 573 + +--S 574 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 5 +--R d +--R (4) - ----------------------------- +--R 2 4 2 5 6 2 +--R 20a b d - 40a b c d + 20b c +--R Type: Expression(Integer) +--E 574 + +--S 575 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 575 + +)clear all + +--S 576 of 2952 +t0000:=(c+d*x)^3/(a+b*x)^7 +--R +--R +--R (1) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 576 + +--S 577 of 2952 +r0000:=-1/6*(b*c-a*d)^3/(b^4*(a+b*x)^6)-3/5*d*(b*c-a*d)^2/(b^4*(a+b*x)^5)-_ + 3/4*d^2*(b*c-a*d)/(b^4*(a+b*x)^4)-1/3*d^3/(b^4*(a+b*x)^3) +--R +--R +--R (2) +--R 1 3 3 3 1 2 3 3 3 2 2 +--R - - b d x + (- - a b d - - b c d )x +--R 3 4 4 +--R + +--R 1 2 3 3 2 2 3 3 2 1 3 3 1 2 2 +--R (- -- a b d - -- a b c d - - b c d)x - -- a d - -- a b c d +--R 10 10 5 60 20 +--R + +--R 1 2 2 1 3 3 +--R - -- a b c d - - b c +--R 10 6 +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 6 4 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 577 + +--S 578 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 +--R - 20b d x + (- 15a b d - 45b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 3 3 +--R (- 6a b d - 18a b c d - 36b c d)x - a d - 3a b c d - 6a b c d - 10b c +--R / +--R 10 6 9 5 2 8 4 3 7 3 4 6 2 5 5 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 4 +--R 60a b +--R Type: Union(Expression(Integer),...) +--E 578 + +--S 579 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 580 + +)clear all + +--S 581 of 2952 +t0000:=(c+d*x)^3/(a+b*x)^8 +--R +--R +--R (1) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 8 +--R 8a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 581 + +--S 582 of 2952 +r0000:=-1/7*(b*c-a*d)^3/(b^4*(a+b*x)^7)-1/2*d*(b*c-a*d)^2/(b^4*(a+b*x)^6)-_ + 3/5*d^2*(b*c-a*d)/(b^4*(a+b*x)^5)-1/4*d^3/(b^4*(a+b*x)^4) +--R +--R +--R (2) +--R 1 3 3 3 3 2 3 3 3 2 2 +--R - - b d x + (- -- a b d - - b c d )x +--R 4 20 5 +--R + +--R 1 2 3 1 2 2 1 3 2 1 3 3 1 2 2 +--R (- -- a b d - - a b c d - - b c d)x - --- a d - -- a b c d +--R 20 5 2 140 35 +--R + +--R 1 2 2 1 3 3 +--R - -- a b c d - - b c +--R 14 7 +--R / +--R 11 7 10 6 2 9 5 3 8 4 4 7 3 5 6 2 6 5 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x +--R + +--R 7 4 +--R a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 582 + +--S 583 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 +--R - 35b d x + (- 21a b d - 84b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 3 3 +--R (- 7a b d - 28a b c d - 70b c d)x - a d - 4a b c d - 10a b c d - 20b c +--R / +--R 11 7 10 6 2 9 5 3 8 4 4 7 3 5 6 2 +--R 140b x + 980a b x + 2940a b x + 4900a b x + 4900a b x + 2940a b x +--R + +--R 6 5 7 4 +--R 980a b x + 140a b +--R Type: Union(Expression(Integer),...) +--E 583 + +--S 584 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 2952 +t0000:=(c+d*x)^3/(a+b*x)^9 +--R +--R +--R (1) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 7 2 2 8 9 +--R 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 586 + +--S 587 of 2952 +r0000:=-1/8*(b*c-a*d)^3/(b^4*(a+b*x)^8)-3/7*d*(b*c-a*d)^2/(b^4*(a+b*x)^7)-_ + 1/2*d^2*(b*c-a*d)/(b^4*(a+b*x)^6)-1/5*d^3/(b^4*(a+b*x)^5) +--R +--R +--R (2) +--R 1 3 3 3 1 2 3 1 3 2 2 +--R - - b d x + (- -- a b d - - b c d )x +--R 5 10 2 +--R + +--R 1 2 3 1 2 2 3 3 2 1 3 3 1 2 2 +--R (- -- a b d - - a b c d - - b c d)x - --- a d - -- a b c d +--R 35 7 7 280 56 +--R + +--R 3 2 2 1 3 3 +--R - -- a b c d - - b c +--R 56 8 +--R / +--R 12 8 11 7 2 10 6 3 9 5 4 8 4 5 7 3 6 6 2 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 5 8 4 +--R 8a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 587 + +--S 588 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 +--R - 56b d x + (- 28a b d - 140b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 8a b d - 40a b c d - 120b c d)x - a d - 5a b c d - 15a b c d +--R + +--R 3 3 +--R - 35b c +--R / +--R 12 8 11 7 2 10 6 3 9 5 4 8 4 +--R 280b x + 2240a b x + 7840a b x + 15680a b x + 19600a b x +--R + +--R 5 7 3 6 6 2 7 5 8 4 +--R 15680a b x + 7840a b x + 2240a b x + 280a b +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 2952 +t0000:=(a+b*x)^m*(c+d*x)^7 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R (d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c ) +--R * +--R m +--R (b x + a) +--R Type: Expression(Integer) +--E 591 + +--S 592 of 2952 +r0000:=(b*c-a*d)^7*(a+b*x)^(1+m)/(b^8*(1+m))+_ + 7*d*(b*c-a*d)^6*(a+b*x)^(2+m)/(b^8*(2+m))+_ + 21*d^2*(b*c-a*d)^5*(a+b*x)^(3+m)/(b^8*(3+m))+_ + 35*d^3*(b*c-a*d)^4*(a+b*x)^(4+m)/(b^8*(4+m))+_ + 35*d^4*(b*c-a*d)^3*(a+b*x)^(5+m)/(b^8*(5+m))+_ + 21*d^5*(b*c-a*d)^2*(a+b*x)^(6+m)/(b^8*(6+m))+_ + 7*d^6*(b*c-a*d)*(a+b*x)^(7+m)/(b^8*(7+m))+_ + d^7*(a+b*x)^(8+m)/(b^8*(8+m)) +--R +--R +--R (2) +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R d m + 28d m + 322d m + 1960d m + 6769d m + 13132d m + 13068d m +--R + +--R 7 +--R 5040d +--R * +--R m + 8 +--R (b x + a) +--R + +--R 7 6 7 7 6 6 +--R (- 7a d + 7b c d )m + (- 203a d + 203b c d )m +--R + +--R 7 6 5 7 6 4 +--R (- 2401a d + 2401b c d )m + (- 14945a d + 14945b c d )m +--R + +--R 7 6 3 7 6 2 +--R (- 52528a d + 52528b c d )m + (- 103292a d + 103292b c d )m +--R + +--R 7 6 7 6 +--R (- 103824a d + 103824b c d )m - 40320a d + 40320b c d +--R * +--R m + 7 +--R (b x + a) +--R + +--R 2 7 6 2 2 5 7 +--R (21a d - 42a b c d + 21b c d )m +--R + +--R 2 7 6 2 2 5 6 +--R (630a d - 1260a b c d + 630b c d )m +--R + +--R 2 7 6 2 2 5 5 +--R (7686a d - 15372a b c d + 7686b c d )m +--R + +--R 2 7 6 2 2 5 4 +--R (49140a d - 98280a b c d + 49140b c d )m +--R + +--R 2 7 6 2 2 5 3 +--R (176589a d - 353178a b c d + 176589b c d )m +--R + +--R 2 7 6 2 2 5 2 +--R (353430a d - 706860a b c d + 353430b c d )m +--R + +--R 2 7 6 2 2 5 2 7 +--R (360024a d - 720048a b c d + 360024b c d )m + 141120a d +--R + +--R 6 2 2 5 +--R - 282240a b c d + 141120b c d +--R * +--R m + 6 +--R (b x + a) +--R + +--R 3 7 2 6 2 2 5 3 3 4 7 +--R (- 35a d + 105a b c d - 105a b c d + 35b c d )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 6 +--R (- 1085a d + 3255a b c d - 3255a b c d + 1085b c d )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 5 +--R (- 13685a d + 41055a b c d - 41055a b c d + 13685b c d )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 4 +--R (- 90335a d + 271005a b c d - 271005a b c d + 90335b c d )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 3 +--R (- 334040a d + 1002120a b c d - 1002120a b c d + 334040b c d )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 2 +--R (- 684740a d + 2054220a b c d - 2054220a b c d + 684740b c d )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 +--R (- 710640a d + 2131920a b c d - 2131920a b c d + 710640b c d )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 +--R - 282240a d + 846720a b c d - 846720a b c d + 282240b c d +--R * +--R m + 5 +--R (b x + a) +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 7 +--R (35a d - 140a b c d + 210a b c d - 140a b c d + 35b c d )m +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 1120a d - 4480a b c d + 6720a b c d - 4480a b c d +--R + +--R 4 4 3 +--R 1120b c d +--R * +--R 6 +--R m +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 14630a d - 58520a b c d + 87780a b c d - 58520a b c d +--R + +--R 4 4 3 +--R 14630b c d +--R * +--R 5 +--R m +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 100240a d - 400960a b c d + 601440a b c d - 400960a b c d +--R + +--R 4 4 3 +--R 100240b c d +--R * +--R 4 +--R m +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 384755a d - 1539020a b c d + 2308530a b c d - 1539020a b c d +--R + +--R 4 4 3 +--R 384755b c d +--R * +--R 3 +--R m +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 815920a d - 3263680a b c d + 4895520a b c d - 3263680a b c d +--R + +--R 4 4 3 +--R 815920b c d +--R * +--R 2 +--R m +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 870660a d - 3482640a b c d + 5223960a b c d - 3482640a b c d +--R + +--R 4 4 3 +--R 870660b c d +--R * +--R m +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R 352800a d - 1411200a b c d + 2116800a b c d - 1411200a b c d +--R + +--R 4 4 3 +--R 352800b c d +--R * +--R m + 4 +--R (b x + a) +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 +--R - 21a d + 105a b c d - 210a b c d + 210a b c d - 105a b c d +--R + +--R 5 5 2 +--R 21b c d +--R * +--R 7 +--R m +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R - 693a d + 3465a b c d - 6930a b c d + 6930a b c d +--R + +--R 4 4 3 5 5 2 +--R - 3465a b c d + 693b c d +--R * +--R 6 +--R m +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R - 9387a d + 46935a b c d - 93870a b c d + 93870a b c d +--R + +--R 4 4 3 5 5 2 +--R - 46935a b c d + 9387b c d +--R * +--R 5 +--R m +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R - 67095a d + 335475a b c d - 670950a b c d + 670950a b c d +--R + +--R 4 4 3 5 5 2 +--R - 335475a b c d + 67095b c d +--R * +--R 4 +--R m +--R + +--R 5 7 4 6 3 2 2 5 +--R - 270144a d + 1350720a b c d - 2701440a b c d +--R + +--R 2 3 3 4 4 4 3 5 5 2 +--R 2701440a b c d - 1350720a b c d + 270144b c d +--R * +--R 3 +--R m +--R + +--R 5 7 4 6 3 2 2 5 +--R - 602532a d + 3012660a b c d - 6025320a b c d +--R + +--R 2 3 3 4 4 4 3 5 5 2 +--R 6025320a b c d - 3012660a b c d + 602532b c d +--R * +--R 2 +--R m +--R + +--R 5 7 4 6 3 2 2 5 +--R - 673008a d + 3365040a b c d - 6730080a b c d +--R + +--R 2 3 3 4 4 4 3 5 5 2 +--R 6730080a b c d - 3365040a b c d + 673008b c d +--R * +--R m +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R - 282240a d + 1411200a b c d - 2822400a b c d + 2822400a b c d +--R + +--R 4 4 3 5 5 2 +--R - 1411200a b c d + 282240b c d +--R * +--R m + 3 +--R (b x + a) +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R 7a d - 42a b c d + 105a b c d - 140a b c d + 105a b c d +--R + +--R 5 5 2 6 6 +--R - 42a b c d + 7b c d +--R * +--R 7 +--R m +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 238a d - 1428a b c d + 3570a b c d - 4760a b c d +--R + +--R 2 4 4 3 5 5 2 6 6 +--R 3570a b c d - 1428a b c d + 238b c d +--R * +--R 6 +--R m +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 3346a d - 20076a b c d + 50190a b c d - 66920a b c d +--R + +--R 2 4 4 3 5 5 2 6 6 +--R 50190a b c d - 20076a b c d + 3346b c d +--R * +--R 5 +--R m +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 25060a d - 150360a b c d + 375900a b c d - 501200a b c d +--R + +--R 2 4 4 3 5 5 2 6 6 +--R 375900a b c d - 150360a b c d + 25060b c d +--R * +--R 4 +--R m +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 107023a d - 642138a b c d + 1605345a b c d - 2140460a b c d +--R + +--R 2 4 4 3 5 5 2 6 6 +--R 1605345a b c d - 642138a b c d + 107023b c d +--R * +--R 3 +--R m +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 256942a d - 1541652a b c d + 3854130a b c d - 5138840a b c d +--R + +--R 2 4 4 3 5 5 2 6 6 +--R 3854130a b c d - 1541652a b c d + 256942b c d +--R * +--R 2 +--R m +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 312984a d - 1877904a b c d + 4694760a b c d - 6259680a b c d +--R + +--R 2 4 4 3 5 5 2 6 6 +--R 4694760a b c d - 1877904a b c d + 312984b c d +--R * +--R m +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 141120a d - 846720a b c d + 2116800a b c d - 2822400a b c d +--R + +--R 2 4 4 3 5 5 2 6 6 +--R 2116800a b c d - 846720a b c d + 141120b c d +--R * +--R m + 2 +--R (b x + a) +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - a d + 7a b c d - 21a b c d + 35a b c d - 35a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 21a b c d - 7a b c d + b c +--R * +--R 7 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 35a d + 245a b c d - 735a b c d + 1225a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 1225a b c d + 735a b c d - 245a b c d + 35b c +--R * +--R 6 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 511a d + 3577a b c d - 10731a b c d + 17885a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 17885a b c d + 10731a b c d - 3577a b c d + 511b c +--R * +--R 5 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 4025a d + 28175a b c d - 84525a b c d + 140875a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 140875a b c d + 84525a b c d - 28175a b c d + 4025b c +--R * +--R 4 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 18424a d + 128968a b c d - 386904a b c d + 644840a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 644840a b c d + 386904a b c d - 128968a b c d + 18424b c +--R * +--R 3 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 48860a d + 342020a b c d - 1026060a b c d + 1710100a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 1710100a b c d + 1026060a b c d - 342020a b c d + 48860b c +--R * +--R 2 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 69264a d + 484848a b c d - 1454544a b c d + 2424240a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 2424240a b c d + 1454544a b c d - 484848a b c d + 69264b c +--R * +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 40320a d + 282240a b c d - 846720a b c d + 1411200a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 1411200a b c d + 846720a b c d - 282240a b c d + 40320b c +--R * +--R m + 1 +--R (b x + a) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R b m + 36b m + 546b m + 4536b m + 22449b m + 67284b m + 118124b m +--R + +--R 8 8 +--R 109584b m + 40320b +--R Type: Expression(Integer) +--E 592 + +--S 593 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 7 7 8 7 6 8 7 5 8 7 4 8 7 3 +--R b d m + 28b d m + 322b d m + 1960b d m + 6769b d m +--R + +--R 8 7 2 8 7 8 7 +--R 13132b d m + 13068b d m + 5040b d +--R * +--R 8 +--R x +--R + +--R 7 7 8 6 7 7 7 8 6 6 +--R (a b d + 7b c d )m + (21a b d + 203b c d )m +--R + +--R 7 7 8 6 5 7 7 8 6 4 +--R (175a b d + 2401b c d )m + (735a b d + 14945b c d )m +--R + +--R 7 7 8 6 3 7 7 8 6 2 +--R (1624a b d + 52528b c d )m + (1764a b d + 103292b c d )m +--R + +--R 7 7 8 6 8 6 +--R (720a b d + 103824b c d )m + 40320b c d +--R * +--R 7 +--R x +--R + +--R 7 6 8 2 5 7 2 6 7 7 6 8 2 5 6 +--R (7a b c d + 21b c d )m + (- 7a b d + 161a b c d + 630b c d )m +--R + +--R 2 6 7 7 6 8 2 5 5 +--R (- 105a b d + 1435a b c d + 7686b c d )m +--R + +--R 2 6 7 7 6 8 2 5 4 +--R (- 595a b d + 6335a b c d + 49140b c d )m +--R + +--R 2 6 7 7 6 8 2 5 3 +--R (- 1575a b d + 14518a b c d + 176589b c d )m +--R + +--R 2 6 7 7 6 8 2 5 2 +--R (- 1918a b d + 16184a b c d + 353430b c d )m +--R + +--R 2 6 7 7 6 8 2 5 8 2 5 +--R (- 840a b d + 6720a b c d + 360024b c d )m + 141120b c d +--R * +--R 6 +--R x +--R + +--R 7 2 5 8 3 4 7 +--R (21a b c d + 35b c d )m +--R + +--R 2 6 6 7 2 5 8 3 4 6 +--R (- 42a b c d + 525a b c d + 1085b c d )m +--R + +--R 3 5 7 2 6 6 7 2 5 8 3 4 5 +--R (42a b d - 756a b c d + 5061a b c d + 13685b c d )m +--R + +--R 3 5 7 2 6 6 7 2 5 8 3 4 4 +--R (420a b d - 4830a b c d + 23835a b c d + 90335b c d )m +--R + +--R 3 5 7 2 6 6 7 2 5 8 3 4 3 +--R (1470a b d - 13860a b c d + 57414a b c d + 334040b c d )m +--R + +--R 3 5 7 2 6 6 7 2 5 8 3 4 2 +--R (2100a b d - 17808a b c d + 66360a b c d + 684740b c d )m +--R + +--R 3 5 7 2 6 6 7 2 5 8 3 4 +--R (1008a b d - 8064a b c d + 28224a b c d + 710640b c d )m +--R + +--R 8 3 4 +--R 282240b c d +--R * +--R 5 +--R x +--R + +--R 7 3 4 8 4 3 7 +--R (35a b c d + 35b c d )m +--R + +--R 2 6 2 5 7 3 4 8 4 3 6 +--R (- 105a b c d + 945a b c d + 1120b c d )m +--R + +--R 3 5 6 2 6 2 5 7 3 4 8 4 3 5 +--R (210a b c d - 2205a b c d + 9905a b c d + 14630b c d )m +--R + +--R 4 4 7 3 5 6 2 6 2 5 7 3 4 +--R - 210a b d + 2940a b c d - 16485a b c d + 50715a b c d +--R + +--R 8 4 3 +--R 100240b c d +--R * +--R 4 +--R m +--R + +--R 4 4 7 3 5 6 2 6 2 5 7 3 4 +--R - 1260a b d + 12390a b c d - 53235a b c d + 131180a b c d +--R + +--R 8 4 3 +--R 384755b c d +--R * +--R 3 +--R m +--R + +--R 4 4 7 3 5 6 2 6 2 5 7 3 4 +--R - 2310a b d + 19740a b c d - 74130a b c d + 160020a b c d +--R + +--R 8 4 3 +--R 815920b c d +--R * +--R 2 +--R m +--R + +--R 4 4 7 3 5 6 2 6 2 5 7 3 4 +--R - 1260a b d + 10080a b c d - 35280a b c d + 70560a b c d +--R + +--R 8 4 3 +--R 870660b c d +--R * +--R m +--R + 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b c d + 140a b c d - 35b c d )m +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 1120a d + 4480a b c d - 6720a b c d + 4480a b c d +--R + +--R 4 4 3 +--R - 1120b c d +--R * +--R 6 +--R m +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 14630a d + 58520a b c d - 87780a b c d + 58520a b c d +--R + +--R 4 4 3 +--R - 14630b c d +--R * +--R 5 +--R m +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 100240a d + 400960a b c d - 601440a b c d + 400960a b c d +--R + +--R 4 4 3 +--R - 100240b c d +--R * +--R 4 +--R m +--R + +--R 4 7 3 6 2 2 2 5 +--R - 384755a d + 1539020a b c d - 2308530a b c d +--R + +--R 3 3 4 4 4 3 +--R 1539020a b c d - 384755b c d +--R * +--R 3 +--R m +--R + +--R 4 7 3 6 2 2 2 5 +--R - 815920a d + 3263680a b c d - 4895520a b c d +--R + +--R 3 3 4 4 4 3 +--R 3263680a b c d - 815920b c d +--R * +--R 2 +--R m +--R + +--R 4 7 3 6 2 2 2 5 +--R - 870660a d + 3482640a b c d - 5223960a b c d +--R + +--R 3 3 4 4 4 3 +--R 3482640a b c d - 870660b c d +--R * +--R m +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 +--R - 352800a d + 1411200a b c d - 2116800a b c d + 1411200a b c d +--R + +--R 4 4 3 +--R - 352800b c d +--R * +--R m + 4 +--R (b x + a) +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 +--R 21a d - 105a b c d + 210a b c d - 210a b c d + 105a b c d +--R + +--R 5 5 2 +--R - 21b c d +--R * +--R 7 +--R m +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 693a d - 3465a b c d + 6930a b c d - 6930a b c d +--R + +--R 4 4 3 5 5 2 +--R 3465a b c d - 693b c d +--R * +--R 6 +--R m +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 9387a d - 46935a b c d + 93870a b c d - 93870a b c d +--R + +--R 4 4 3 5 5 2 +--R 46935a b c d - 9387b c d +--R * +--R 5 +--R m +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 67095a d - 335475a b c d + 670950a b c d - 670950a b c d +--R + +--R 4 4 3 5 5 2 +--R 335475a b c d - 67095b c d +--R * +--R 4 +--R m +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 270144a d - 1350720a b c d + 2701440a b c d - 2701440a b c d +--R + +--R 4 4 3 5 5 2 +--R 1350720a b c d - 270144b c d +--R * +--R 3 +--R m +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 602532a d - 3012660a b c d + 6025320a b c d - 6025320a b c d +--R + +--R 4 4 3 5 5 2 +--R 3012660a b c d - 602532b c d +--R * +--R 2 +--R m +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 673008a d - 3365040a b c d + 6730080a b c d - 6730080a b c d +--R + +--R 4 4 3 5 5 2 +--R 3365040a b c d - 673008b c d +--R * +--R m +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 282240a d - 1411200a b c d + 2822400a b c d - 2822400a b c d +--R + +--R 4 4 3 5 5 2 +--R 1411200a b c d - 282240b c d +--R * +--R m + 3 +--R (b x + a) +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R - 7a d + 42a b c d - 105a b c d + 140a b c d - 105a b c d +--R + +--R 5 5 2 6 6 +--R 42a b c d - 7b c d +--R * +--R 7 +--R m +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R - 238a d + 1428a b c d - 3570a b c d + 4760a b c d +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 3570a b c d + 1428a b c d - 238b c d +--R * +--R 6 +--R m +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R - 3346a d + 20076a b c d - 50190a b c d + 66920a b c d +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 50190a b c d + 20076a b c d - 3346b c d +--R * +--R 5 +--R m +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R - 25060a d + 150360a b c d - 375900a b c d + 501200a b c d +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 375900a b c d + 150360a b c d - 25060b c d +--R * +--R 4 +--R m +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R - 107023a d + 642138a b c d - 1605345a b c d + 2140460a b c d +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 1605345a b c d + 642138a b c d - 107023b c d +--R * +--R 3 +--R m +--R + +--R 6 7 5 6 4 2 2 5 +--R - 256942a d + 1541652a b c d - 3854130a b c d +--R + +--R 3 3 3 4 2 4 4 3 5 5 2 6 6 +--R 5138840a b c d - 3854130a b c d + 1541652a b c d - 256942b c d +--R * +--R 2 +--R m +--R + +--R 6 7 5 6 4 2 2 5 +--R - 312984a d + 1877904a b c d - 4694760a b c d +--R + +--R 3 3 3 4 2 4 4 3 5 5 2 6 6 +--R 6259680a b c d - 4694760a b c d + 1877904a b c d - 312984b c d +--R * +--R m +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R - 141120a d + 846720a b c d - 2116800a b c d + 2822400a b c d +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 2116800a b c d + 846720a b c d - 141120b c d +--R * +--R m + 2 +--R (b x + a) +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R a d - 7a b c d + 21a b c d - 35a b c d + 35a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 21a b c d + 7a b c d - b c +--R * +--R 7 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 35a d - 245a b c d + 735a b c d - 1225a b c d + 1225a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 735a b c d + 245a b c d - 35b c +--R * +--R 6 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 511a d - 3577a b c d + 10731a b c d - 17885a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 17885a b c d - 10731a b c d + 3577a b c d - 511b c +--R * +--R 5 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 4025a d - 28175a b c d + 84525a b c d - 140875a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 140875a b c d - 84525a b c d + 28175a b c d - 4025b c +--R * +--R 4 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 18424a d - 128968a b c d + 386904a b c d - 644840a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 644840a b c d - 386904a b c d + 128968a b c d - 18424b c +--R * +--R 3 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 48860a d - 342020a b c d + 1026060a b c d - 1710100a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 1710100a b c d - 1026060a b c d + 342020a b c d - 48860b c +--R * +--R 2 +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 69264a d - 484848a b c d + 1454544a b c d - 2424240a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 2424240a b c d - 1454544a b c d + 484848a b c d - 69264b c +--R * +--R m +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 40320a d - 282240a b c d + 846720a b c d - 1411200a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 1411200a b c d - 846720a b c d + 282240a b c d - 40320b c +--R * +--R m + 1 +--R (b x + a) +--R / +--R 8 8 8 7 8 6 8 5 8 4 8 3 8 2 +--R b m + 36b m + 546b m + 4536b m + 22449b m + 67284b m + 118124b m +--R + +--R 8 8 +--R 109584b m + 40320b +--R Type: Expression(Integer) +--E 594 + +--S 595 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 7 4 3 3 +--R b d x + 7b c d x + 21b c d x + 35b c d x + 35b c d x +--R + +--R 7 5 2 2 7 6 7 7 +--R 21b c d x + 7b c d x + b c +--R * +--R m log(b x + a) +--R %e +--R + +--R 7 m + 7 7 6 m + 6 +--R - d (b x + a) + (7a d - 7b c d )(b x + a) +--R + +--R 2 7 6 2 2 5 m + 5 +--R (- 21a d + 42a b c d - 21b c d )(b x + a) +--R + +--R 3 7 2 6 2 2 5 3 3 4 m + 4 +--R (35a d - 105a b c d + 105a b c d - 35b c d )(b x + a) +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 +--R (- 35a d + 140a b c d - 210a b c d + 140a b c d - 35b c d ) +--R * +--R m + 3 +--R (b x + a) +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 +--R 21a d - 105a b c d + 210a b c d - 210a b c d + 105a b c d +--R + +--R 5 5 2 +--R - 21b c d +--R * +--R m + 2 +--R (b x + a) +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R - 7a d + 42a b c d - 105a b c d + 140a b c d - 105a b c d +--R + +--R 5 5 2 6 6 +--R 42a b c d - 7b c d +--R * +--R m + 1 +--R (b x + a) +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R a d - 7a b c d + 21a b c d - 35a b c d + 35a b c d - 21a b c d +--R + +--R 6 6 7 7 +--R 7a b c d - b c +--R * +--R m +--R (b x + a) +--R / +--R 7 +--R b +--R Type: Expression(Integer) +--E 595 + +)clear all + +--S 596 of 2952 +t0000:=(a+b*x)^9*(c+d*x)^7 +--R +--R +--R (1) +--R 9 7 16 8 7 9 6 15 2 7 7 8 6 9 2 5 14 +--R b d x + (9a b d + 7b c d )x + (36a b d + 63a b c d + 21b c d )x +--R + +--R 3 6 7 2 7 6 8 2 5 9 3 4 13 +--R (84a b d + 252a b c d + 189a b c d + 35b c d )x +--R + +--R 4 5 7 3 6 6 2 7 2 5 8 3 4 9 4 3 12 +--R (126a b d + 588a b c d + 756a b c d + 315a b c d + 35b c d )x +--R + +--R 5 4 7 4 5 6 3 6 2 5 2 7 3 4 8 4 3 +--R 126a b d + 882a b c d + 1764a b c d + 1260a b c d + 315a b c d +--R + +--R 9 5 2 +--R 21b c d +--R * +--R 11 +--R x +--R + +--R 6 3 7 5 4 6 4 5 2 5 3 6 3 4 2 7 4 3 +--R 84a b d + 882a b c d + 2646a b c d + 2940a b c d + 1260a b c d +--R + +--R 8 5 2 9 6 +--R 189a b c d + 7b c d +--R * +--R 10 +--R x +--R + +--R 7 2 7 6 3 6 5 4 2 5 4 5 3 4 3 6 4 3 +--R 36a b d + 588a b c d + 2646a b c d + 4410a b c d + 2940a b c d +--R + +--R 2 7 5 2 8 6 9 7 +--R 756a b c d + 63a b c d + b c +--R * +--R 9 +--R x +--R + +--R 8 7 7 2 6 6 3 2 5 5 4 3 4 4 5 4 3 +--R 9a b d + 252a b c d + 1764a b c d + 4410a b c d + 4410a b c d +--R + +--R 3 6 5 2 2 7 6 8 7 +--R 1764a b c d + 252a b c d + 9a b c +--R * +--R 8 +--R x +--R + +--R 9 7 8 6 7 2 2 5 6 3 3 4 5 4 4 3 +--R a d + 63a b c d + 756a b c d + 2940a b c d + 4410a b c d +--R + +--R 4 5 5 2 3 6 6 2 7 7 +--R 2646a b c d + 588a b c d + 36a b c +--R * +--R 7 +--R x +--R + +--R 9 6 8 2 5 7 2 3 4 6 3 4 3 5 4 5 2 +--R 7a c d + 189a b c d + 1260a b c d + 2940a b c d + 2646a b c d +--R + +--R 4 5 6 3 6 7 +--R 882a b c d + 84a b c +--R * +--R 6 +--R x +--R + +--R 9 2 5 8 3 4 7 2 4 3 6 3 5 2 5 4 6 +--R 21a c d + 315a b c d + 1260a b c d + 1764a b c d + 882a b c d +--R + +--R 4 5 7 +--R 126a b c +--R * +--R 5 +--R x +--R + +--R 9 3 4 8 4 3 7 2 5 2 6 3 6 5 4 7 4 +--R (35a c d + 315a b c d + 756a b c d + 588a b c d + 126a b c )x +--R + +--R 9 4 3 8 5 2 7 2 6 6 3 7 3 +--R (35a c d + 189a b c d + 252a b c d + 84a b c )x +--R + +--R 9 5 2 8 6 7 2 7 2 9 6 8 7 9 7 +--R (21a c d + 63a b c d + 36a b c )x + (7a c d + 9a b c )x + a c +--R Type: Polynomial(Integer) +--E 596 + +--S 597 of 2952 +r0000:=1/10*(b*c-a*d)^7*(a+b*x)^10/b^8+7/11*d*(b*c-a*d)^6*(a+b*x)^11/b^8+_ + 7/4*d^2*(b*c-a*d)^5*(a+b*x)^12/b^8+_ + 35/13*d^3*(b*c-a*d)^4*(a+b*x)^13/b^8+_ + 5/2*d^4*(b*c-a*d)^3*(a+b*x)^14/b^8+_ + 7/5*d^5*(b*c-a*d)^2*(a+b*x)^15/b^8+_ + 7/16*d^6*(b*c-a*d)*(a+b*x)^16/b^8+1/17*d^7*(a+b*x)^17/b^8 +--R +--R +--R (2) +--R 1 17 7 17 9 16 7 7 17 6 16 +--R -- b d x + (-- a b d + -- b c d )x +--R 17 16 16 +--R + +--R 12 2 15 7 21 16 6 7 17 2 5 15 +--R (-- a b d + -- a b c d + - b c d )x +--R 5 5 5 +--R + +--R 3 14 7 2 15 6 27 16 2 5 5 17 3 4 14 +--R (6a b d + 18a b c d + -- a b c d + - b c d )x +--R 2 2 +--R + +--R 126 4 13 7 588 3 14 6 756 2 15 2 5 315 16 3 4 +--R --- a b d + --- a b c d + --- a b c d + --- a b c d +--R 13 13 13 13 +--R + +--R 35 17 4 3 +--R -- b c d +--R 13 +--R * +--R 13 +--R x +--R + +--R 21 5 12 7 147 4 13 6 3 14 2 5 2 15 3 4 +--R -- a b d + --- a b c d + 147a b c d + 105a b c d +--R 2 2 +--R + +--R 105 16 4 3 7 17 5 2 +--R --- a b c d + - b c d +--R 4 4 +--R * +--R 12 +--R x +--R + +--R 84 6 11 7 882 5 12 6 2646 4 13 2 5 2940 3 14 3 4 +--R -- a b d + --- a b c d + ---- a b c d + ---- a b c d +--R 11 11 11 11 +--R + +--R 1260 2 15 4 3 189 16 5 2 7 17 6 +--R ---- a b c d + --- a b c d + -- b c d +--R 11 11 11 +--R * +--R 11 +--R x +--R + +--R 18 7 10 7 294 6 11 6 1323 5 12 2 5 4 13 3 4 +--R -- a b d + --- a b c d + ---- a b c d + 441a b c d +--R 5 5 5 +--R + +--R 3 14 4 3 378 2 15 5 2 63 16 6 1 17 7 +--R 294a b c d + --- a b c d + -- a b c d + -- b c +--R 5 10 10 +--R * +--R 10 +--R x +--R + +--R 8 9 7 7 10 6 6 11 2 5 5 12 3 4 4 13 4 3 +--R a b d + 28a b c d + 196a b c d + 490a b c d + 490a b c d +--R + +--R 3 14 5 2 2 15 6 16 7 +--R 196a b c d + 28a b c d + a b c +--R * +--R 9 +--R x +--R + +--R 1 9 8 7 63 8 9 6 189 7 10 2 5 735 6 11 3 4 +--R - a b d + -- a b c d + --- a b c d + --- a b c d +--R 8 8 2 2 +--R + +--R 2205 5 12 4 3 1323 4 13 5 2 147 3 14 6 9 2 15 7 +--R ---- a b c d + ---- a b c d + --- a b c d + - a b c +--R 4 4 2 2 +--R * +--R 8 +--R x +--R + +--R 9 8 6 8 9 2 5 7 10 3 4 6 11 4 3 5 12 5 2 +--R a b c d + 27a b c d + 180a b c d + 420a b c d + 378a b c d +--R + +--R 4 13 6 3 14 7 +--R 126a b c d + 12a b c +--R * +--R 7 +--R x +--R + +--R 7 9 8 2 5 105 8 9 3 4 7 10 4 3 6 11 5 2 5 12 6 +--R - a b c d + --- a b c d + 210a b c d + 294a b c d + 147a b c d +--R 2 2 +--R + +--R 4 13 7 +--R 21a b c +--R * +--R 6 +--R x +--R + +--R 9 8 3 4 8 9 4 3 756 7 10 5 2 588 6 11 6 126 5 12 7 5 +--R (7a b c d + 63a b c d + --- a b c d + --- a b c d + --- a b c )x +--R 5 5 5 +--R + +--R 35 9 8 4 3 189 8 9 5 2 7 10 6 6 11 7 4 +--R (-- a b c d + --- a b c d + 63a b c d + 21a b c )x +--R 4 4 +--R + +--R 9 8 5 2 8 9 6 7 10 7 3 7 9 8 6 9 8 9 7 2 +--R (7a b c d + 21a b c d + 12a b c )x + (- a b c d + - a b c )x +--R 2 2 +--R + +--R 9 8 7 1 17 7 1 16 6 1 15 2 2 5 1 14 3 3 4 +--R a b c x - ------ a d + ----- a b c d - ---- a b c d + --- a b c d +--R 194480 11440 1430 286 +--R + +--R 7 13 4 4 3 7 12 5 5 2 7 11 6 6 1 10 7 7 +--R - --- a b c d + --- a b c d - --- a b c d + -- a b c +--R 572 220 110 10 +--R / +--R 8 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 597 + +--S 598 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 9 7 17 9 8 7 7 9 6 16 +--R -- b d x + (-- a b d + -- b c d )x +--R 17 16 16 +--R + +--R 12 2 7 7 21 8 6 7 9 2 5 15 +--R (-- a b d + -- a b c d + - b c d )x +--R 5 5 5 +--R + +--R 3 6 7 2 7 6 27 8 2 5 5 9 3 4 14 +--R (6a b d + 18a b c d + -- a b c d + - b c d )x +--R 2 2 +--R + +--R 126 4 5 7 588 3 6 6 756 2 7 2 5 315 8 3 4 35 9 4 3 13 +--R (--- a b d + --- a b c d + --- a b c d + --- a b c d + -- b c d )x +--R 13 13 13 13 13 +--R + +--R 21 5 4 7 147 4 5 6 3 6 2 5 2 7 3 4 105 8 4 3 +--R -- a b d + --- a b c d + 147a b c d + 105a b c d + --- a b c d +--R 2 2 4 +--R + +--R 7 9 5 2 +--R - b c d +--R 4 +--R * +--R 12 +--R x +--R + +--R 84 6 3 7 882 5 4 6 2646 4 5 2 5 2940 3 6 3 4 +--R -- a b d + --- a b c d + ---- a b c d + ---- a b c d +--R 11 11 11 11 +--R + +--R 1260 2 7 4 3 189 8 5 2 7 9 6 +--R ---- a b c d + --- a b c d + -- b c d +--R 11 11 11 +--R * +--R 11 +--R x +--R + +--R 18 7 2 7 294 6 3 6 1323 5 4 2 5 4 5 3 4 3 6 4 3 +--R -- a b d + --- a b c d + ---- a b c d + 441a b c d + 294a b c d +--R 5 5 5 +--R + +--R 378 2 7 5 2 63 8 6 1 9 7 +--R --- a b c d + -- a b c d + -- b c +--R 5 10 10 +--R * +--R 10 +--R x +--R + +--R 8 7 7 2 6 6 3 2 5 5 4 3 4 4 5 4 3 +--R a b d + 28a b c d + 196a b c d + 490a b c d + 490a b c d +--R + +--R 3 6 5 2 2 7 6 8 7 +--R 196a b c d + 28a b c d + a b c +--R * +--R 9 +--R x +--R + +--R 1 9 7 63 8 6 189 7 2 2 5 735 6 3 3 4 2205 5 4 4 3 +--R - a d + -- a b c d + --- a b c d + --- a b c d + ---- a b c d +--R 8 8 2 2 4 +--R + +--R 1323 4 5 5 2 147 3 6 6 9 2 7 7 +--R ---- a b c d + --- a b c d + - a b c +--R 4 2 2 +--R * +--R 8 +--R x +--R + +--R 9 6 8 2 5 7 2 3 4 6 3 4 3 5 4 5 2 +--R a c d + 27a b c d + 180a b c d + 420a b c d + 378a b c d +--R + +--R 4 5 6 3 6 7 +--R 126a b c d + 12a b c +--R * +--R 7 +--R x +--R + +--R 7 9 2 5 105 8 3 4 7 2 4 3 6 3 5 2 5 4 6 +--R - a c d + --- a b c d + 210a b c d + 294a b c d + 147a b c d +--R 2 2 +--R + +--R 4 5 7 +--R 21a b c +--R * +--R 6 +--R x +--R + +--R 9 3 4 8 4 3 756 7 2 5 2 588 6 3 6 126 5 4 7 5 +--R (7a c d + 63a b c d + --- a b c d + --- a b c d + --- a b c )x +--R 5 5 5 +--R + +--R 35 9 4 3 189 8 5 2 7 2 6 6 3 7 4 +--R (-- a c d + --- a b c d + 63a b c d + 21a b c )x +--R 4 4 +--R + +--R 9 5 2 8 6 7 2 7 3 7 9 6 9 8 7 2 9 7 +--R (7a c d + 21a b c d + 12a b c )x + (- a c d + - a b c )x + a c x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 598 + +--S 599 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 17 7 1 16 6 1 15 2 2 5 1 14 3 3 4 +--R ------ a d - ----- a b c d + ---- a b c d - --- a b c d +--R 194480 11440 1430 286 +--R + +--R 7 13 4 4 3 7 12 5 5 2 7 11 6 6 1 10 7 7 +--R --- a b c d - --- a b c d + --- a b c d - -- a b c +--R 572 220 110 10 +--R / +--R 8 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 599 + +--S 600 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 600 + +)clear all + +--S 601 of 2952 +t0000:=(a+b*x)^8*(c+d*x)^7 +--R +--R +--R (1) +--R 8 7 15 7 7 8 6 14 2 6 7 7 6 8 2 5 13 +--R b d x + (8a b d + 7b c d )x + (28a b d + 56a b c d + 21b c d )x +--R + +--R 3 5 7 2 6 6 7 2 5 8 3 4 12 +--R (56a b d + 196a b c d + 168a b c d + 35b c d )x +--R + +--R 4 4 7 3 5 6 2 6 2 5 7 3 4 8 4 3 11 +--R (70a b d + 392a b c d + 588a b c d + 280a b c d + 35b c d )x +--R + +--R 5 3 7 4 4 6 3 5 2 5 2 6 3 4 7 4 3 +--R 56a b d + 490a b c d + 1176a b c d + 980a b c d + 280a b c d +--R + +--R 8 5 2 +--R 21b c d +--R * +--R 10 +--R x +--R + +--R 6 2 7 5 3 6 4 4 2 5 3 5 3 4 2 6 4 3 +--R 28a b d + 392a b c d + 1470a b c d + 1960a b c d + 980a b c d +--R + +--R 7 5 2 8 6 +--R 168a b c d + 7b c d +--R * +--R 9 +--R x +--R + +--R 7 7 6 2 6 5 3 2 5 4 4 3 4 3 5 4 3 +--R 8a b d + 196a b c d + 1176a b c d + 2450a b c d + 1960a b c d +--R + +--R 2 6 5 2 7 6 8 7 +--R 588a b c d + 56a b c d + b c +--R * +--R 8 +--R x +--R + +--R 8 7 7 6 6 2 2 5 5 3 3 4 4 4 4 3 +--R a d + 56a b c d + 588a b c d + 1960a b c d + 2450a b c d +--R + +--R 3 5 5 2 2 6 6 7 7 +--R 1176a b c d + 196a b c d + 8a b c +--R * +--R 7 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 4 4 5 2 +--R 7a c d + 168a b c d + 980a b c d + 1960a b c d + 1470a b c d +--R + +--R 3 5 6 2 6 7 +--R 392a b c d + 28a b c +--R * +--R 6 +--R x +--R + +--R 8 2 5 7 3 4 6 2 4 3 5 3 5 2 4 4 6 +--R 21a c d + 280a b c d + 980a b c d + 1176a b c d + 490a b c d +--R + +--R 3 5 7 +--R 56a b c +--R * +--R 5 +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 4 +--R (35a c d + 280a b c d + 588a b c d + 392a b c d + 70a b c )x +--R + +--R 8 4 3 7 5 2 6 2 6 5 3 7 3 +--R (35a c d + 168a b c d + 196a b c d + 56a b c )x +--R + +--R 8 5 2 7 6 6 2 7 2 8 6 7 7 8 7 +--R (21a c d + 56a b c d + 28a b c )x + (7a c d + 8a b c )x + a c +--R Type: Polynomial(Integer) +--E 601 + +--S 602 of 2952 +r0000:=1/9*(b*c-a*d)^7*(a+b*x)^9/b^8+7/10*d*(b*c-a*d)^6*(a+b*x)^10/b^8+_ + 21/11*d^2*(b*c-a*d)^5*(a+b*x)^11/b^8+_ + 35/12*d^3*(b*c-a*d)^4*(a+b*x)^12/b^8+_ + 35/13*d^4*(b*c-a*d)^3*(a+b*x)^13/b^8+_ + 3/2*d^5*(b*c-a*d)^2*(a+b*x)^14/b^8+_ + 7/15*d^6*(b*c-a*d)*(a+b*x)^15/b^8+1/16*d^7*(a+b*x)^16/b^8 +--R +--R +--R (2) +--R 1 16 7 16 8 15 7 7 16 6 15 +--R -- b d x + (-- a b d + -- b c d )x +--R 16 15 15 +--R + +--R 2 14 7 15 6 3 16 2 5 14 +--R (2a b d + 4a b c d + - b c d )x +--R 2 +--R + +--R 56 3 13 7 196 2 14 6 168 15 2 5 35 16 3 4 13 +--R (-- a b d + --- a b c d + --- a b c d + -- b c d )x +--R 13 13 13 13 +--R + +--R 35 4 12 7 98 3 13 6 2 14 2 5 70 15 3 4 35 16 4 3 12 +--R (-- a b d + -- a b c d + 49a b c d + -- a b c d + -- b c d )x +--R 6 3 3 12 +--R + +--R 56 5 11 7 490 4 12 6 1176 3 13 2 5 980 2 14 3 4 +--R -- a b d + --- a b c d + ---- a b c d + --- a b c d +--R 11 11 11 11 +--R + +--R 280 15 4 3 21 16 5 2 +--R --- a b c d + -- b c d +--R 11 11 +--R * +--R 11 +--R x +--R + +--R 14 6 10 7 196 5 11 6 4 12 2 5 3 13 3 4 +--R -- a b d + --- a b c d + 147a b c d + 196a b c d +--R 5 5 +--R + +--R 2 14 4 3 84 15 5 2 7 16 6 +--R 98a b c d + -- a b c d + -- b c d +--R 5 10 +--R * +--R 10 +--R x +--R + +--R 8 7 9 7 196 6 10 6 392 5 11 2 5 2450 4 12 3 4 +--R - a b d + --- a b c d + --- a b c d + ---- a b c d +--R 9 9 3 9 +--R + +--R 1960 3 13 4 3 196 2 14 5 2 56 15 6 1 16 7 +--R ---- a b c d + --- a b c d + -- a b c d + - b c +--R 9 3 9 9 +--R * +--R 9 +--R x +--R + +--R 1 8 8 7 7 9 6 147 6 10 2 5 5 11 3 4 1225 4 12 4 3 +--R - a b d + 7a b c d + --- a b c d + 245a b c d + ---- a b c d +--R 8 2 4 +--R + +--R 3 13 5 2 49 2 14 6 15 7 +--R 147a b c d + -- a b c d + a b c +--R 2 +--R * +--R 8 +--R x +--R + +--R 8 8 6 7 9 2 5 6 10 3 4 5 11 4 3 4 12 5 2 +--R a b c d + 24a b c d + 140a b c d + 280a b c d + 210a b c d +--R + +--R 3 13 6 2 14 7 +--R 56a b c d + 4a b c +--R * +--R 7 +--R x +--R + +--R 7 8 8 2 5 140 7 9 3 4 490 6 10 4 3 5 11 5 2 +--R - a b c d + --- a b c d + --- a b c d + 196a b c d +--R 2 3 3 +--R + +--R 245 4 12 6 28 3 13 7 +--R --- a b c d + -- a b c +--R 3 3 +--R * +--R 6 +--R x +--R + +--R 8 8 3 4 7 9 4 3 588 6 10 5 2 392 5 11 6 4 12 7 5 +--R (7a b c d + 56a b c d + --- a b c d + --- a b c d + 14a b c )x +--R 5 5 +--R + +--R 35 8 8 4 3 7 9 5 2 6 10 6 5 11 7 4 +--R (-- a b c d + 42a b c d + 49a b c d + 14a b c )x +--R 4 +--R + +--R 8 8 5 2 56 7 9 6 28 6 10 7 3 7 8 8 6 7 9 7 2 +--R (7a b c d + -- a b c d + -- a b c )x + (- a b c d + 4a b c )x +--R 3 3 2 +--R + +--R 8 8 7 1 16 7 1 15 6 1 14 2 2 5 7 13 3 3 4 +--R a b c x - ------ a d + ---- a b c d - --- a b c d + ---- a b c d +--R 102960 6435 858 1287 +--R + +--R 7 12 4 4 3 7 11 5 5 2 7 10 6 6 1 9 7 7 +--R - --- a b c d + --- a b c d - -- a b c d + - a b c +--R 396 165 90 9 +--R / +--R 8 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 602 + +--S 603 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 8 7 16 8 7 7 7 8 6 15 +--R -- b d x + (-- a b d + -- b c d )x +--R 16 15 15 +--R + +--R 2 6 7 7 6 3 8 2 5 14 +--R (2a b d + 4a b c d + - b c d )x +--R 2 +--R + +--R 56 3 5 7 196 2 6 6 168 7 2 5 35 8 3 4 13 +--R (-- a b d + --- a b c d + --- a b c d + -- b c d )x +--R 13 13 13 13 +--R + +--R 35 4 4 7 98 3 5 6 2 6 2 5 70 7 3 4 35 8 4 3 12 +--R (-- a b d + -- a b c d + 49a b c d + -- a b c d + -- b c d )x +--R 6 3 3 12 +--R + +--R 56 5 3 7 490 4 4 6 1176 3 5 2 5 980 2 6 3 4 280 7 4 3 +--R -- a b d + --- a b c d + ---- a b c d + --- a b c d + --- a b c d +--R 11 11 11 11 11 +--R + +--R 21 8 5 2 +--R -- b c d +--R 11 +--R * +--R 11 +--R x +--R + +--R 14 6 2 7 196 5 3 6 4 4 2 5 3 5 3 4 2 6 4 3 +--R -- a b d + --- a b c d + 147a b c d + 196a b c d + 98a b c d +--R 5 5 +--R + +--R 84 7 5 2 7 8 6 +--R -- a b c d + -- b c d +--R 5 10 +--R * +--R 10 +--R x +--R + +--R 8 7 7 196 6 2 6 392 5 3 2 5 2450 4 4 3 4 1960 3 5 4 3 +--R - a b d + --- a b c d + --- a b c d + ---- a b c d + ---- a b c d +--R 9 9 3 9 9 +--R + +--R 196 2 6 5 2 56 7 6 1 8 7 +--R --- a b c d + -- a b c d + - b c +--R 3 9 9 +--R * +--R 9 +--R x +--R + +--R 1 8 7 7 6 147 6 2 2 5 5 3 3 4 1225 4 4 4 3 +--R - a d + 7a b c d + --- a b c d + 245a b c d + ---- a b c d +--R 8 2 4 +--R + +--R 3 5 5 2 49 2 6 6 7 7 +--R 147a b c d + -- a b c d + a b c +--R 2 +--R * +--R 8 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 4 4 5 2 +--R a c d + 24a b c d + 140a b c d + 280a b c d + 210a b c d +--R + +--R 3 5 6 2 6 7 +--R 56a b c d + 4a b c +--R * +--R 7 +--R x +--R + +--R 7 8 2 5 140 7 3 4 490 6 2 4 3 5 3 5 2 245 4 4 6 +--R - a c d + --- a b c d + --- a b c d + 196a b c d + --- a b c d +--R 2 3 3 3 +--R + +--R 28 3 5 7 +--R -- a b c +--R 3 +--R * +--R 6 +--R x +--R + +--R 8 3 4 7 4 3 588 6 2 5 2 392 5 3 6 4 4 7 5 +--R (7a c d + 56a b c d + --- a b c d + --- a b c d + 14a b c )x +--R 5 5 +--R + +--R 35 8 4 3 7 5 2 6 2 6 5 3 7 4 +--R (-- a c d + 42a b c d + 49a b c d + 14a b c )x +--R 4 +--R + +--R 8 5 2 56 7 6 28 6 2 7 3 7 8 6 7 7 2 8 7 +--R (7a c d + -- a b c d + -- a b c )x + (- a c d + 4a b c )x + a c x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 603 + +--S 604 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 16 7 1 15 6 1 14 2 2 5 7 13 3 3 4 +--R ------ a d - ---- a b c d + --- a b c d - ---- a b c d +--R 102960 6435 858 1287 +--R + +--R 7 12 4 4 3 7 11 5 5 2 7 10 6 6 1 9 7 7 +--R --- a b c d - --- a b c d + -- a b c d - - a b c +--R 396 165 90 9 +--R / +--R 8 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 604 + +--S 605 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 605 + +)clear all + +--S 606 of 2952 +t0000:=(a+b*x)^7*(c+d*x)^7 +--R +--R +--R (1) +--R 7 7 14 6 7 7 6 13 2 5 7 6 6 7 2 5 12 +--R b d x + (7a b d + 7b c d )x + (21a b d + 49a b c d + 21b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 11 +--R (35a b d + 147a b c d + 147a b c d + 35b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 10 +--R (35a b d + 245a b c d + 441a b c d + 245a b c d + 35b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 21a b d + 245a b c d + 735a b c d + 735a b c d + 245a b c d +--R + +--R 7 5 2 +--R 21b c d +--R * +--R 9 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 7a b d + 147a b c d + 735a b c d + 1225a b c d + 735a b c d +--R + +--R 6 5 2 7 6 +--R 147a b c d + 7b c d +--R * +--R 8 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R a d + 49a b c d + 441a b c d + 1225a b c d + 1225a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 441a b c d + 49a b c d + b c +--R * +--R 7 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 +--R 7a c d + 147a b c d + 735a b c d + 1225a b c d + 735a b c d +--R + +--R 2 5 6 6 7 +--R 147a b c d + 7a b c +--R * +--R 6 +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 21a c d + 245a b c d + 735a b c d + 735a b c d + 245a b c d +--R + +--R 2 5 7 +--R 21a b c +--R * +--R 5 +--R x +--R + +--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 4 +--R (35a c d + 245a b c d + 441a b c d + 245a b c d + 35a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 3 +--R (35a c d + 147a b c d + 147a b c d + 35a b c )x +--R + +--R 7 5 2 6 6 5 2 7 2 7 6 6 7 7 7 +--R (21a c d + 49a b c d + 21a b c )x + (7a c d + 7a b c )x + a c +--R Type: Polynomial(Integer) +--E 606 + +--S 607 of 2952 +r0000:=1/8*(b*c-a*d)^7*(a+b*x)^8/b^8+7/9*d*(b*c-a*d)^6*(a+b*x)^9/b^8+_ + 21/10*d^2*(b*c-a*d)^5*(a+b*x)^10/b^8+_ + 35/11*d^3*(b*c-a*d)^4*(a+b*x)^11/b^8+_ + 35/12*d^4*(b*c-a*d)^3*(a+b*x)^12/b^8+_ + 21/13*d^5*(b*c-a*d)^2*(a+b*x)^13/b^8+_ + 1/2*d^6*(b*c-a*d)*(a+b*x)^14/b^8+1/15*d^7*(a+b*x)^15/b^8 +--R +--R +--R (2) +--R 1 15 7 15 1 14 7 1 15 6 14 +--R -- b d x + (- a b d + - b c d )x +--R 15 2 2 +--R + +--R 21 2 13 7 49 14 6 21 15 2 5 13 +--R (-- a b d + -- a b c d + -- b c d )x +--R 13 13 13 +--R + +--R 35 3 12 7 49 2 13 6 49 14 2 5 35 15 3 4 12 +--R (-- a b d + -- a b c d + -- a b c d + -- b c d )x +--R 12 4 4 12 +--R + +--R 35 4 11 7 245 3 12 6 441 2 13 2 5 245 14 3 4 +--R -- a b d + --- a b c d + --- a b c d + --- a b c d +--R 11 11 11 11 +--R + +--R 35 15 4 3 +--R -- b c d +--R 11 +--R * +--R 11 +--R x +--R + +--R 21 5 10 7 49 4 11 6 147 3 12 2 5 147 2 13 3 4 +--R -- a b d + -- a b c d + --- a b c d + --- a b c d +--R 10 2 2 2 +--R + +--R 49 14 4 3 21 15 5 2 +--R -- a b c d + -- b c d +--R 2 10 +--R * +--R 10 +--R x +--R + +--R 7 6 9 7 49 5 10 6 245 4 11 2 5 1225 3 12 3 4 +--R - a b d + -- a b c d + --- a b c d + ---- a b c d +--R 9 3 3 9 +--R + +--R 245 2 13 4 3 49 14 5 2 7 15 6 +--R --- a b c d + -- a b c d + - b c d +--R 3 3 9 +--R * +--R 9 +--R x +--R + +--R 1 7 8 7 49 6 9 6 441 5 10 2 5 1225 4 11 3 4 +--R - a b d + -- a b c d + --- a b c d + ---- a b c d +--R 8 8 8 8 +--R + +--R 1225 3 12 4 3 441 2 13 5 2 49 14 6 1 15 7 +--R ---- a b c d + --- a b c d + -- a b c d + - b c +--R 8 8 8 8 +--R * +--R 8 +--R x +--R + +--R 7 8 6 6 9 2 5 5 10 3 4 4 11 4 3 3 12 5 2 +--R a b c d + 21a b c d + 105a b c d + 175a b c d + 105a b c d +--R + +--R 2 13 6 14 7 +--R 21a b c d + a b c +--R * +--R 7 +--R x +--R + +--R 7 7 8 2 5 245 6 9 3 4 245 5 10 4 3 245 4 11 5 2 +--R - a b c d + --- a b c d + --- a b c d + --- a b c d +--R 2 6 2 2 +--R + +--R 245 3 12 6 7 2 13 7 +--R --- a b c d + - a b c +--R 6 2 +--R * +--R 6 +--R x +--R + +--R 7 8 3 4 6 9 4 3 441 5 10 5 2 4 11 6 3 12 7 5 +--R (7a b c d + 49a b c d + --- a b c d + 49a b c d + 7a b c )x +--R 5 +--R + +--R 35 7 8 4 3 147 6 9 5 2 147 5 10 6 35 4 11 7 4 +--R (-- a b c d + --- a b c d + --- a b c d + -- a b c )x +--R 4 4 4 4 +--R + +--R 7 8 5 2 49 6 9 6 5 10 7 3 7 7 8 6 7 6 9 7 2 +--R (7a b c d + -- a b c d + 7a b c )x + (- a b c d + - a b c )x +--R 3 2 2 +--R + +--R 7 8 7 1 15 7 1 14 6 7 13 2 2 5 7 12 3 3 4 +--R a b c x - ----- a d + ---- a b c d - ---- a b c d + --- a b c d +--R 51480 3432 3432 792 +--R + +--R 7 11 4 4 3 7 10 5 5 2 7 9 6 6 1 8 7 7 +--R - --- a b c d + --- a b c d - -- a b c d + - a b c +--R 264 120 72 8 +--R / +--R 8 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 607 + +--S 608 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 7 15 1 6 7 1 7 6 14 +--R -- b d x + (- a b d + - b c d )x +--R 15 2 2 +--R + +--R 21 2 5 7 49 6 6 21 7 2 5 13 +--R (-- a b d + -- a b c d + -- b c d )x +--R 13 13 13 +--R + +--R 35 3 4 7 49 2 5 6 49 6 2 5 35 7 3 4 12 +--R (-- a b d + -- a b c d + -- a b c d + -- b c d )x +--R 12 4 4 12 +--R + +--R 35 4 3 7 245 3 4 6 441 2 5 2 5 245 6 3 4 35 7 4 3 11 +--R (-- a b d + --- a b c d + --- a b c d + --- a b c d + -- b c d )x +--R 11 11 11 11 11 +--R + +--R 21 5 2 7 49 4 3 6 147 3 4 2 5 147 2 5 3 4 49 6 4 3 +--R -- a b d + -- a b c d + --- a b c d + --- a b c d + -- a b c d +--R 10 2 2 2 2 +--R + +--R 21 7 5 2 +--R -- b c d +--R 10 +--R * +--R 10 +--R x +--R + +--R 7 6 7 49 5 2 6 245 4 3 2 5 1225 3 4 3 4 245 2 5 4 3 +--R - a b d + -- a b c d + --- a b c d + ---- a b c d + --- a b c d +--R 9 3 3 9 3 +--R + +--R 49 6 5 2 7 7 6 +--R -- a b c d + - b c d +--R 3 9 +--R * +--R 9 +--R x +--R + +--R 1 7 7 49 6 6 441 5 2 2 5 1225 4 3 3 4 1225 3 4 4 3 +--R - a d + -- a b c d + --- a b c d + ---- a b c d + ---- a b c d +--R 8 8 8 8 8 +--R + +--R 441 2 5 5 2 49 6 6 1 7 7 +--R --- a b c d + -- a b c d + - b c +--R 8 8 8 +--R * +--R 8 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 +--R a c d + 21a b c d + 105a b c d + 175a b c d + 105a b c d +--R + +--R 2 5 6 6 7 +--R 21a b c d + a b c +--R * +--R 7 +--R x +--R + +--R 7 7 2 5 245 6 3 4 245 5 2 4 3 245 4 3 5 2 245 3 4 6 +--R - a c d + --- a b c d + --- a b c d + --- a b c d + --- a b c d +--R 2 6 2 2 6 +--R + +--R 7 2 5 7 +--R - a b c +--R 2 +--R * +--R 6 +--R x +--R + +--R 7 3 4 6 4 3 441 5 2 5 2 4 3 6 3 4 7 5 +--R (7a c d + 49a b c d + --- a b c d + 49a b c d + 7a b c )x +--R 5 +--R + +--R 35 7 4 3 147 6 5 2 147 5 2 6 35 4 3 7 4 +--R (-- a c d + --- a b c d + --- a b c d + -- a b c )x +--R 4 4 4 4 +--R + +--R 7 5 2 49 6 6 5 2 7 3 7 7 6 7 6 7 2 7 7 +--R (7a c d + -- a b c d + 7a b c )x + (- a c d + - a b c )x + a c x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 608 + +--S 609 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 15 7 1 14 6 7 13 2 2 5 7 12 3 3 4 +--R ----- a d - ---- a b c d + ---- a b c d - --- a b c d +--R 51480 3432 3432 792 +--R + +--R 7 11 4 4 3 7 10 5 5 2 7 9 6 6 1 8 7 7 +--R --- a b c d - --- a b c d + -- a b c d - - a b c +--R 264 120 72 8 +--R / +--R 8 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 609 + +--S 610 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 610 + +)clear all + +--S 611 of 2952 +t0000:=(a+b*x)^6*(c+d*x)^7 +--R +--R +--R (1) +--R 6 7 13 5 7 6 6 12 2 4 7 5 6 6 2 5 11 +--R b d x + (6a b d + 7b c d )x + (15a b d + 42a b c d + 21b c d )x +--R + +--R 3 3 7 2 4 6 5 2 5 6 3 4 10 +--R (20a b d + 105a b c d + 126a b c d + 35b c d )x +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 6 4 3 9 +--R (15a b d + 140a b c d + 315a b c d + 210a b c d + 35b c d )x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 6a b d + 105a b c d + 420a b c d + 525a b c d + 210a b c d +--R + +--R 6 5 2 +--R 21b c d +--R * +--R 8 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R a d + 42a b c d + 315a b c d + 700a b c d + 525a b c d +--R + +--R 5 5 2 6 6 +--R 126a b c d + 7b c d +--R * +--R 7 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 +--R 7a c d + 126a b c d + 525a b c d + 700a b c d + 315a b c d +--R + +--R 5 6 6 7 +--R 42a b c d + b c +--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 21a c d + 210a b c d + 525a b c d + 420a b c d + 105a b c d +--R + +--R 5 7 +--R 6a b c +--R * +--R 5 +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 4 +--R (35a c d + 210a b c d + 315a b c d + 140a b c d + 15a b c )x +--R + +--R 6 4 3 5 5 2 4 2 6 3 3 7 3 +--R (35a c d + 126a b c d + 105a b c d + 20a b c )x +--R + +--R 6 5 2 5 6 4 2 7 2 6 6 5 7 6 7 +--R (21a c d + 42a b c d + 15a b c )x + (7a c d + 6a b c )x + a c +--R Type: Polynomial(Integer) +--E 611 + +--S 612 of 2952 +r0000:=1/8*(b*c-a*d)^6*(c+d*x)^8/d^7-2/3*b*(b*c-a*d)^5*(c+d*x)^9/d^7+_ + 3/2*b^2*(b*c-a*d)^4*(c+d*x)^10/d^7-_ + 20/11*b^3*(b*c-a*d)^3*(c+d*x)^11/d^7+_ + 5/4*b^4*(b*c-a*d)^2*(c+d*x)^12/d^7-_ + 6/13*b^5*(b*c-a*d)*(c+d*x)^13/d^7+1/14*b^6*(c+d*x)^14/d^7 +--R +--R +--R (2) +--R 1 6 14 14 6 5 14 7 6 13 13 +--R -- b d x + (-- a b d + -- b c d )x +--R 14 13 13 +--R + +--R 5 2 4 14 7 5 13 7 6 2 12 12 +--R (- a b d + - a b c d + - b c d )x +--R 4 2 4 +--R + +--R 20 3 3 14 105 2 4 13 126 5 2 12 35 6 3 11 11 +--R (-- a b d + --- a b c d + --- a b c d + -- b c d )x +--R 11 11 11 11 +--R + +--R 3 4 2 14 3 3 13 63 2 4 2 12 5 3 11 7 6 4 10 10 +--R (- a b d + 14a b c d + -- a b c d + 21a b c d + - b c d )x +--R 2 2 2 +--R + +--R 2 5 14 35 4 2 13 140 3 3 2 12 175 2 4 3 11 +--R - a b d + -- a b c d + --- a b c d + --- a b c d +--R 3 3 3 3 +--R + +--R 70 5 4 10 7 6 5 9 +--R -- a b c d + - b c d +--R 3 3 +--R * +--R 9 +--R x +--R + +--R 1 6 14 21 5 13 315 4 2 2 12 175 3 3 3 11 +--R - a d + -- a b c d + --- a b c d + --- a b c d +--R 8 4 8 2 +--R + +--R 525 2 4 4 10 63 5 5 9 7 6 6 8 +--R --- a b c d + -- a b c d + - b c d +--R 8 4 8 +--R * +--R 8 +--R x +--R + +--R 6 13 5 2 12 4 2 3 11 3 3 4 10 2 4 5 9 +--R a c d + 18a b c d + 75a b c d + 100a b c d + 45a b c d +--R + +--R 5 6 8 1 6 7 7 +--R 6a b c d + - b c d +--R 7 +--R * +--R 7 +--R x +--R + +--R 7 6 2 12 5 3 11 175 4 2 4 10 3 3 5 9 35 2 4 6 8 +--R - a c d + 35a b c d + --- a b c d + 70a b c d + -- a b c d +--R 2 2 2 +--R + +--R 5 7 7 +--R a b c d +--R * +--R 6 +--R x +--R + +--R 6 3 11 5 4 10 4 2 5 9 3 3 6 8 2 4 7 7 5 +--R (7a c d + 42a b c d + 63a b c d + 28a b c d + 3a b c d )x +--R + +--R 35 6 4 10 63 5 5 9 105 4 2 6 8 3 3 7 7 4 +--R (-- a c d + -- a b c d + --- a b c d + 5a b c d )x +--R 4 2 4 +--R + +--R 6 5 9 5 6 8 4 2 7 7 3 7 6 6 8 5 7 7 2 6 7 7 +--R (7a c d + 14a b c d + 5a b c d )x + (- a c d + 3a b c d )x + a c d x +--R 2 +--R + +--R 1 6 8 6 1 5 9 5 1 4 2 10 4 1 3 3 11 3 1 2 4 12 2 +--R - a c d - -- a b c d + -- a b c d - -- a b c d + --- a b c d +--R 8 12 24 66 264 +--R + +--R 1 5 13 1 6 14 +--R - ---- a b c d + ----- b c +--R 1716 24024 +--R / +--R 7 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 612 + +--S 613 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 6 7 14 6 5 7 7 6 6 13 +--R -- b d x + (-- a b d + -- b c d )x +--R 14 13 13 +--R + +--R 5 2 4 7 7 5 6 7 6 2 5 12 +--R (- a b d + - a b c d + - b c d )x +--R 4 2 4 +--R + +--R 20 3 3 7 105 2 4 6 126 5 2 5 35 6 3 4 11 +--R (-- a b d + --- a b c d + --- a b c d + -- b c d )x +--R 11 11 11 11 +--R + +--R 3 4 2 7 3 3 6 63 2 4 2 5 5 3 4 7 6 4 3 10 +--R (- a b d + 14a b c d + -- a b c d + 21a b c d + - b c d )x +--R 2 2 2 +--R + +--R 2 5 7 35 4 2 6 140 3 3 2 5 175 2 4 3 4 70 5 4 3 +--R - a b d + -- a b c d + --- a b c d + --- a b c d + -- a b c d +--R 3 3 3 3 3 +--R + +--R 7 6 5 2 +--R - b c d +--R 3 +--R * +--R 9 +--R x +--R + +--R 1 6 7 21 5 6 315 4 2 2 5 175 3 3 3 4 525 2 4 4 3 +--R - a d + -- a b c d + --- a b c d + --- a b c d + --- a b c d +--R 8 4 8 2 8 +--R + +--R 63 5 5 2 7 6 6 +--R -- a b c d + - b c d +--R 4 8 +--R * +--R 8 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 5 6 +--R a c d + 18a b c d + 75a b c d + 100a b c d + 45a b c d + 6a b c d +--R + +--R 1 6 7 +--R - b c +--R 7 +--R * +--R 7 +--R x +--R + +--R 7 6 2 5 5 3 4 175 4 2 4 3 3 3 5 2 35 2 4 6 5 7 6 +--R (- a c d + 35a b c d + --- a b c d + 70a b c d + -- a b c d + a b c )x +--R 2 2 2 +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 5 +--R (7a c d + 42a b c d + 63a b c d + 28a b c d + 3a b c )x +--R + +--R 35 6 4 3 63 5 5 2 105 4 2 6 3 3 7 4 +--R (-- a c d + -- a b c d + --- a b c d + 5a b c )x +--R 4 2 4 +--R + +--R 6 5 2 5 6 4 2 7 3 7 6 6 5 7 2 6 7 +--R (7a c d + 14a b c d + 5a b c )x + (- a c d + 3a b c )x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 613 + +--S 614 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 6 8 6 1 5 9 5 1 4 2 10 4 1 3 3 11 3 1 2 4 12 2 +--R - - a c d + -- a b c d - -- a b c d + -- a b c d - --- a b c d +--R 8 12 24 66 264 +--R + +--R 1 5 13 1 6 14 +--R ---- a b c d - ----- b c +--R 1716 24024 +--R / +--R 7 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 614 + +--S 615 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 615 + +)clear all + +--S 616 of 2952 +t0000:=(a+b*x)^5*(c+d*x)^7 +--R +--R +--R (1) +--R 5 7 12 4 7 5 6 11 2 3 7 4 6 5 2 5 10 +--R b d x + (5a b d + 7b c d )x + (10a b d + 35a b c d + 21b c d )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 9 +--R (10a b d + 70a b c d + 105a b c d + 35b c d )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 8 +--R (5a b d + 70a b c d + 210a b c d + 175a b c d + 35b c d )x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 7 +--R (a d + 35a b c d + 210a b c d + 350a b c d + 175a b c d + 21b c d )x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2 +--R 7a c d + 105a b c d + 350a b c d + 350a b c d + 105a b c d +--R + +--R 5 6 +--R 7b c d +--R * +--R 6 +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 5 7 5 +--R (21a c d + 175a b c d + 350a b c d + 210a b c d + 35a b c d + b c )x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 4 +--R (35a c d + 175a b c d + 210a b c d + 70a b c d + 5a b c )x +--R + +--R 5 4 3 4 5 2 3 2 6 2 3 7 3 +--R (35a c d + 105a b c d + 70a b c d + 10a b c )x +--R + +--R 5 5 2 4 6 3 2 7 2 5 6 4 7 5 7 +--R (21a c d + 35a b c d + 10a b c )x + (7a c d + 5a b c )x + a c +--R Type: Polynomial(Integer) +--E 616 + +--S 617 of 2952 +r0000:=-1/8*(b*c-a*d)^5*(c+d*x)^8/d^6+5/9*b*(b*c-a*d)^4*(c+d*x)^9/d^6-_ + b^2*(b*c-a*d)^3*(c+d*x)^10/d^6+10/11*b^3*(b*c-a*d)^2*(c+d*x)^11/d^6-_ + 5/12*b^4*(b*c-a*d)*(c+d*x)^12/d^6+1/13*b^5*(c+d*x)^13/d^6 +--R +--R +--R (2) +--R 1 5 13 13 5 4 13 7 5 12 12 +--R -- b d x + (-- a b d + -- b c d )x +--R 13 12 12 +--R + +--R 10 2 3 13 35 4 12 21 5 2 11 11 +--R (-- a b d + -- a b c d + -- b c d )x +--R 11 11 11 +--R + +--R 3 2 13 2 3 12 21 4 2 11 7 5 3 10 10 +--R (a b d + 7a b c d + -- a b c d + - b c d )x +--R 2 2 +--R + +--R 5 4 13 70 3 2 12 70 2 3 2 11 175 4 3 10 35 5 4 9 9 +--R (- a b d + -- a b c d + -- a b c d + --- a b c d + -- b c d )x +--R 9 9 3 9 9 +--R + +--R 1 5 13 35 4 12 105 3 2 2 11 175 2 3 3 10 175 4 4 9 +--R - a d + -- a b c d + --- a b c d + --- a b c d + --- a b c d +--R 8 8 4 4 8 +--R + +--R 21 5 5 8 +--R -- b c d +--R 8 +--R * +--R 8 +--R x +--R + +--R 5 12 4 2 11 3 2 3 10 2 3 4 9 4 5 8 +--R a c d + 15a b c d + 50a b c d + 50a b c d + 15a b c d +--R + +--R 5 6 7 +--R b c d +--R * +--R 7 +--R x +--R + +--R 7 5 2 11 175 4 3 10 175 3 2 4 9 2 3 5 8 35 4 6 7 +--R - a c d + --- a b c d + --- a b c d + 35a b c d + -- a b c d +--R 2 6 3 6 +--R + +--R 1 5 7 6 +--R - b c d +--R 6 +--R * +--R 6 +--R x +--R + +--R 5 3 10 4 4 9 3 2 5 8 2 3 6 7 4 7 6 5 +--R (7a c d + 35a b c d + 42a b c d + 14a b c d + a b c d )x +--R + +--R 35 5 4 9 105 4 5 8 35 3 2 6 7 5 2 3 7 6 4 +--R (-- a c d + --- a b c d + -- a b c d + - a b c d )x +--R 4 4 2 2 +--R + +--R 5 5 8 35 4 6 7 10 3 2 7 6 3 7 5 6 7 5 4 7 6 2 +--R (7a c d + -- a b c d + -- a b c d )x + (- a c d + - a b c d )x +--R 3 3 2 2 +--R + +--R 5 7 6 1 5 8 5 5 4 9 4 1 3 2 10 3 1 2 3 11 2 +--R a c d x + - a c d - -- a b c d + -- a b c d - --- a b c d +--R 8 72 36 132 +--R + +--R 1 4 12 1 5 13 +--R --- a b c d - ----- b c +--R 792 10296 +--R / +--R 6 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 617 + +--S 618 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 5 7 13 5 4 7 7 5 6 12 +--R -- b d x + (-- a b d + -- b c d )x +--R 13 12 12 +--R + +--R 10 2 3 7 35 4 6 21 5 2 5 11 +--R (-- a b d + -- a b c d + -- b c d )x +--R 11 11 11 +--R + +--R 3 2 7 2 3 6 21 4 2 5 7 5 3 4 10 +--R (a b d + 7a b c d + -- a b c d + - b c d )x +--R 2 2 +--R + +--R 5 4 7 70 3 2 6 70 2 3 2 5 175 4 3 4 35 5 4 3 9 +--R (- a b d + -- a b c d + -- a b c d + --- a b c d + -- b c d )x +--R 9 9 3 9 9 +--R + +--R 1 5 7 35 4 6 105 3 2 2 5 175 2 3 3 4 175 4 4 3 +--R - a d + -- a b c d + --- a b c d + --- a b c d + --- a b c d +--R 8 8 4 4 8 +--R + +--R 21 5 5 2 +--R -- b c d +--R 8 +--R * +--R 8 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2 5 6 7 +--R (a c d + 15a b c d + 50a b c d + 50a b c d + 15a b c d + b c d)x +--R + +--R 7 5 2 5 175 4 3 4 175 3 2 4 3 2 3 5 2 35 4 6 +--R - a c d + --- a b c d + --- a b c d + 35a b c d + -- a b c d +--R 2 6 3 6 +--R + +--R 1 5 7 +--R - b c +--R 6 +--R * +--R 6 +--R x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 5 +--R (7a c d + 35a b c d + 42a b c d + 14a b c d + a b c )x +--R + +--R 35 5 4 3 105 4 5 2 35 3 2 6 5 2 3 7 4 +--R (-- a c d + --- a b c d + -- a b c d + - a b c )x +--R 4 4 2 2 +--R + +--R 5 5 2 35 4 6 10 3 2 7 3 7 5 6 5 4 7 2 5 7 +--R (7a c d + -- a b c d + -- a b c )x + (- a c d + - a b c )x + a c x +--R 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 618 + +--S 619 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 5 8 5 5 4 9 4 1 3 2 10 3 1 2 3 11 2 1 4 12 +--R - - a c d + -- a b c d - -- a b c d + --- a b c d - --- a b c d +--R 8 72 36 132 792 +--R + +--R 1 5 13 +--R ----- b c +--R 10296 +--R / +--R 6 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 619 + +--S 620 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 620 + +)clear all + +--S 621 of 2952 +t0000:=(a+b*x)^4*(c+d*x)^7 +--R +--R +--R (1) +--R 4 7 11 3 7 4 6 10 2 2 7 3 6 4 2 5 9 +--R b d x + (4a b d + 7b c d )x + (6a b d + 28a b c d + 21b c d )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 8 +--R (4a b d + 42a b c d + 84a b c d + 35b c d )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 7 +--R (a d + 28a b c d + 126a b c d + 140a b c d + 35b c d )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 6 +--R (7a c d + 84a b c d + 210a b c d + 140a b c d + 21b c d )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 5 +--R (21a c d + 140a b c d + 210a b c d + 84a b c d + 7b c d)x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 4 +--R (35a c d + 140a b c d + 126a b c d + 28a b c d + b c )x +--R + +--R 4 4 3 3 5 2 2 2 6 3 7 3 +--R (35a c d + 84a b c d + 42a b c d + 4a b c )x +--R + +--R 4 5 2 3 6 2 2 7 2 4 6 3 7 4 7 +--R (21a c d + 28a b c d + 6a b c )x + (7a c d + 4a b c )x + a c +--R Type: Polynomial(Integer) +--E 621 + +--S 622 of 2952 +r0000:=1/8*(b*c-a*d)^4*(c+d*x)^8/d^5-4/9*b*(b*c-a*d)^3*(c+d*x)^9/d^5+_ + 3/5*b^2*(b*c-a*d)^2*(c+d*x)^10/d^5-4/11*b^3*(b*c-a*d)*(c+d*x)^11/d^5+_ + 1/12*b^4*(c+d*x)^12/d^5 +--R +--R +--R (2) +--R 1 4 12 12 4 3 12 7 4 11 11 +--R -- b d x + (-- a b d + -- b c d )x +--R 12 11 11 +--R + +--R 3 2 2 12 14 3 11 21 4 2 10 10 +--R (- a b d + -- a b c d + -- b c d )x +--R 5 5 10 +--R + +--R 4 3 12 14 2 2 11 28 3 2 10 35 4 3 9 9 +--R (- a b d + -- a b c d + -- a b c d + -- b c d )x +--R 9 3 3 9 +--R + +--R 1 4 12 7 3 11 63 2 2 2 10 35 3 3 9 35 4 4 8 8 +--R (- a d + - a b c d + -- a b c d + -- a b c d + -- b c d )x +--R 8 2 4 2 8 +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 4 5 7 7 +--R (a c d + 12a b c d + 30a b c d + 20a b c d + 3b c d )x +--R + +--R 7 4 2 10 70 3 3 9 2 2 4 8 3 5 7 7 4 6 6 6 +--R (- a c d + -- a b c d + 35a b c d + 14a b c d + - b c d )x +--R 2 3 6 +--R + +--R 4 3 9 3 4 8 126 2 2 5 7 28 3 6 6 1 4 7 5 5 +--R (7a c d + 28a b c d + --- a b c d + -- a b c d + - b c d )x +--R 5 5 5 +--R + +--R 35 4 4 8 3 5 7 21 2 2 6 6 3 7 5 4 +--R (-- a c d + 21a b c d + -- a b c d + a b c d )x +--R 4 2 +--R + +--R 4 5 7 28 3 6 6 2 2 7 5 3 7 4 6 6 3 7 5 2 +--R (7a c d + -- a b c d + 2a b c d )x + (- a c d + 2a b c d )x +--R 3 2 +--R + +--R 4 7 5 1 4 8 4 1 3 9 3 1 2 2 10 2 1 3 11 1 4 12 +--R a c d x + - a c d - -- a b c d + -- a b c d - --- a b c d + ---- b c +--R 8 18 60 330 3960 +--R / +--R 5 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 622 + +--S 623 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 4 7 12 4 3 7 7 4 6 11 +--R -- b d x + (-- a b d + -- b c d )x +--R 12 11 11 +--R + +--R 3 2 2 7 14 3 6 21 4 2 5 10 +--R (- a b d + -- a b c d + -- b c d )x +--R 5 5 10 +--R + +--R 4 3 7 14 2 2 6 28 3 2 5 35 4 3 4 9 +--R (- a b d + -- a b c d + -- a b c d + -- b c d )x +--R 9 3 3 9 +--R + +--R 1 4 7 7 3 6 63 2 2 2 5 35 3 3 4 35 4 4 3 8 +--R (- a d + - a b c d + -- a b c d + -- a b c d + -- b c d )x +--R 8 2 4 2 8 +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 7 +--R (a c d + 12a b c d + 30a b c d + 20a b c d + 3b c d )x +--R + +--R 7 4 2 5 70 3 3 4 2 2 4 3 3 5 2 7 4 6 6 +--R (- a c d + -- a b c d + 35a b c d + 14a b c d + - b c d)x +--R 2 3 6 +--R + +--R 4 3 4 3 4 3 126 2 2 5 2 28 3 6 1 4 7 5 +--R (7a c d + 28a b c d + --- a b c d + -- a b c d + - b c )x +--R 5 5 5 +--R + +--R 35 4 4 3 3 5 2 21 2 2 6 3 7 4 +--R (-- a c d + 21a b c d + -- a b c d + a b c )x +--R 4 2 +--R + +--R 4 5 2 28 3 6 2 2 7 3 7 4 6 3 7 2 4 7 +--R (7a c d + -- a b c d + 2a b c )x + (- a c d + 2a b c )x + a c x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 623 + +--S 624 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 4 8 4 1 3 9 3 1 2 2 10 2 1 3 11 1 4 12 +--R - - a c d + -- a b c d - -- a b c d + --- a b c d - ---- b c +--R 8 18 60 330 3960 +--R (4) ------------------------------------------------------------------- +--R 5 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 624 + +--S 625 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 625 + +)clear all + +--S 626 of 2952 +t0000:=(a+b*x)^3*(c+d*x)^7 +--R +--R +--R (1) +--R 3 7 10 2 7 3 6 9 2 7 2 6 3 2 5 8 +--R b d x + (3a b d + 7b c d )x + (3a b d + 21a b c d + 21b c d )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 7 +--R (a d + 21a b c d + 63a b c d + 35b c d )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 6 +--R (7a c d + 63a b c d + 105a b c d + 35b c d )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 5 +--R (21a c d + 105a b c d + 105a b c d + 21b c d )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 4 +--R (35a c d + 105a b c d + 63a b c d + 7b c d)x +--R + +--R 3 4 3 2 5 2 2 6 3 7 3 +--R (35a c d + 63a b c d + 21a b c d + b c )x +--R + +--R 3 5 2 2 6 2 7 2 3 6 2 7 3 7 +--R (21a c d + 21a b c d + 3a b c )x + (7a c d + 3a b c )x + a c +--R Type: Polynomial(Integer) +--E 626 + +--S 627 of 2952 +r0000:=-1/8*(b*c-a*d)^3*(c+d*x)^8/d^4+1/3*b*(b*c-a*d)^2*(c+d*x)^9/d^4-_ + 3/10*b^2*(b*c-a*d)*(c+d*x)^10/d^4+1/11*b^3*(c+d*x)^11/d^4 +--R +--R +--R (2) +--R 1 3 11 11 3 2 11 7 3 10 10 +--R -- b d x + (-- a b d + -- b c d )x +--R 11 10 10 +--R + +--R 1 2 11 7 2 10 7 3 2 9 9 +--R (- a b d + - a b c d + - b c d )x +--R 3 3 3 +--R + +--R 1 3 11 21 2 10 63 2 2 9 35 3 3 8 8 +--R (- a d + -- a b c d + -- a b c d + -- b c d )x +--R 8 8 8 8 +--R + +--R 3 10 2 2 9 2 3 8 3 4 7 7 +--R (a c d + 9a b c d + 15a b c d + 5b c d )x +--R + +--R 7 3 2 9 35 2 3 8 35 2 4 7 7 3 5 6 6 +--R (- a c d + -- a b c d + -- a b c d + - b c d )x +--R 2 2 2 2 +--R + +--R 3 3 8 2 4 7 63 2 5 6 7 3 6 5 5 +--R (7a c d + 21a b c d + -- a b c d + - b c d )x +--R 5 5 +--R + +--R 35 3 4 7 63 2 5 6 21 2 6 5 1 3 7 4 4 +--R (-- a c d + -- a b c d + -- a b c d + - b c d )x +--R 4 4 4 4 +--R + +--R 3 5 6 2 6 5 2 7 4 3 7 3 6 5 3 2 7 4 2 3 7 4 +--R (7a c d + 7a b c d + a b c d )x + (- a c d + - a b c d )x + a c d x +--R 2 2 +--R + +--R 1 3 8 3 1 2 9 2 1 2 10 1 3 11 +--R - a c d - -- a b c d + --- a b c d - ---- b c +--R 8 24 120 1320 +--R / +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 627 + +--S 628 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 3 7 11 3 2 7 7 3 6 10 +--R -- b d x + (-- a b d + -- b c d )x +--R 11 10 10 +--R + +--R 1 2 7 7 2 6 7 3 2 5 9 +--R (- a b d + - a b c d + - b c d )x +--R 3 3 3 +--R + +--R 1 3 7 21 2 6 63 2 2 5 35 3 3 4 8 +--R (- a d + -- a b c d + -- a b c d + -- b c d )x +--R 8 8 8 8 +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 7 +--R (a c d + 9a b c d + 15a b c d + 5b c d )x +--R + +--R 7 3 2 5 35 2 3 4 35 2 4 3 7 3 5 2 6 +--R (- a c d + -- a b c d + -- a b c d + - b c d )x +--R 2 2 2 2 +--R + +--R 3 3 4 2 4 3 63 2 5 2 7 3 6 5 +--R (7a c d + 21a b c d + -- a b c d + - b c d)x +--R 5 5 +--R + +--R 35 3 4 3 63 2 5 2 21 2 6 1 3 7 4 +--R (-- a c d + -- a b c d + -- a b c d + - b c )x +--R 4 4 4 4 +--R + +--R 3 5 2 2 6 2 7 3 7 3 6 3 2 7 2 3 7 +--R (7a c d + 7a b c d + a b c )x + (- a c d + - a b c )x + a c x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 628 + +--S 629 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 3 8 3 1 2 9 2 1 2 10 1 3 11 +--R - - a c d + -- a b c d - --- a b c d + ---- b c +--R 8 24 120 1320 +--R (4) ---------------------------------------------------- +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 629 + +--S 630 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 630 + +)clear all + +--S 631 of 2952 +t0000:=(a+b*x)^2*(c+d*x)^7 +--R +--R +--R (1) +--R 2 7 9 7 2 6 8 2 7 6 2 2 5 7 +--R b d x + (2a b d + 7b c d )x + (a d + 14a b c d + 21b c d )x +--R + +--R 2 6 2 5 2 3 4 6 2 2 5 3 4 2 4 3 5 +--R (7a c d + 42a b c d + 35b c d )x + (21a c d + 70a b c d + 35b c d )x +--R + +--R 2 3 4 4 3 2 5 2 4 2 4 3 5 2 2 6 3 +--R (35a c d + 70a b c d + 21b c d )x + (35a c d + 42a b c d + 7b c d)x +--R + +--R 2 5 2 6 2 7 2 2 6 7 2 7 +--R (21a c d + 14a b c d + b c )x + (7a c d + 2a b c )x + a c +--R Type: Polynomial(Integer) +--E 631 + +--S 632 of 2952 +r0000:=1/8*(b*c-a*d)^2*(c+d*x)^8/d^3-2/9*b*(b*c-a*d)*(c+d*x)^9/d^3+_ + 1/10*b^2*(c+d*x)^10/d^3 +--R +--R +--R (2) +--R 1 2 10 10 2 10 7 2 9 9 +--R -- b d x + (- a b d + - b c d )x +--R 10 9 9 +--R + +--R 1 2 10 7 9 21 2 2 8 8 2 9 2 8 2 3 7 7 +--R (- a d + - a b c d + -- b c d )x + (a c d + 6a b c d + 5b c d )x +--R 8 4 8 +--R + +--R 7 2 2 8 35 3 7 35 2 4 6 6 +--R (- a c d + -- a b c d + -- b c d )x +--R 2 3 6 +--R + +--R 2 3 7 4 6 21 2 5 5 5 +--R (7a c d + 14a b c d + -- b c d )x +--R 5 +--R + +--R 35 2 4 6 21 5 5 7 2 6 4 4 +--R (-- a c d + -- a b c d + - b c d )x +--R 4 2 4 +--R + +--R 2 5 5 14 6 4 1 2 7 3 3 7 2 6 4 7 3 2 2 7 3 +--R (7a c d + -- a b c d + - b c d )x + (- a c d + a b c d )x + a c d x +--R 3 3 2 +--R + +--R 1 2 8 2 1 9 1 2 10 +--R - a c d - -- a b c d + --- b c +--R 8 36 360 +--R / +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 632 + +--S 633 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 2 7 10 2 7 7 2 6 9 1 2 7 7 6 21 2 2 5 8 +--R -- b d x + (- a b d + - b c d )x + (- a d + - a b c d + -- b c d )x +--R 10 9 9 8 4 8 +--R + +--R 2 6 2 5 2 3 4 7 7 2 2 5 35 3 4 35 2 4 3 6 +--R (a c d + 6a b c d + 5b c d )x + (- a c d + -- a b c d + -- b c d )x +--R 2 3 6 +--R + +--R 2 3 4 4 3 21 2 5 2 5 +--R (7a c d + 14a b c d + -- b c d )x +--R 5 +--R + +--R 35 2 4 3 21 5 2 7 2 6 4 2 5 2 14 6 1 2 7 3 +--R (-- a c d + -- a b c d + - b c d)x + (7a c d + -- a b c d + - b c )x +--R 4 2 4 3 3 +--R + +--R 7 2 6 7 2 2 7 +--R (- a c d + a b c )x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 633 + +--S 634 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 2 8 2 1 9 1 2 10 +--R - - a c d + -- a b c d - --- b c +--R 8 36 360 +--R (4) ----------------------------------- +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 634 + +--S 635 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 635 + +)clear all + +--S 636 of 2952 +t0000:=(a+b*x)*(c+d*x)^7 +--R +--R +--R (1) +--R 7 8 7 6 7 6 2 5 6 +--R b d x + (a d + 7b c d )x + (7a c d + 21b c d )x +--R + +--R 2 5 3 4 5 3 4 4 3 4 4 3 5 2 3 +--R (21a c d + 35b c d )x + (35a c d + 35b c d )x + (35a c d + 21b c d )x +--R + +--R 5 2 6 2 6 7 7 +--R (21a c d + 7b c d)x + (7a c d + b c )x + a c +--R Type: Polynomial(Integer) +--E 636 + +--S 637 of 2952 +r0000:=-1/8*(b*c-a*d)*(c+d*x)^8/d^2+1/9*b*(c+d*x)^9/d^2 +--R +--R +--R (2) +--R 1 9 9 1 9 7 8 8 8 2 7 7 +--R - b d x + (- a d + - b c d )x + (a c d + 3b c d )x +--R 9 8 8 +--R + +--R 7 2 7 35 3 6 6 3 6 4 5 5 +--R (- a c d + -- b c d )x + (7a c d + 7b c d )x +--R 2 6 +--R + +--R 35 4 5 21 5 4 4 5 4 7 6 3 3 +--R (-- a c d + -- b c d )x + (7a c d + - b c d )x +--R 4 4 3 +--R + +--R 7 6 3 1 7 2 2 7 2 1 8 1 9 +--R (- a c d + - b c d )x + a c d x + - a c d - -- b c +--R 2 2 8 72 +--R / +--R 2 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 637 + +--S 638 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 9 1 7 7 6 8 6 2 5 7 +--R - b d x + (- a d + - b c d )x + (a c d + 3b c d )x +--R 9 8 8 +--R + +--R 7 2 5 35 3 4 6 3 4 4 3 5 +--R (- a c d + -- b c d )x + (7a c d + 7b c d )x +--R 2 6 +--R + +--R 35 4 3 21 5 2 4 5 2 7 6 3 7 6 1 7 2 +--R (-- a c d + -- b c d )x + (7a c d + - b c d)x + (- a c d + - b c )x +--R 4 4 3 2 2 +--R + +--R 7 +--R a c x +--R Type: Polynomial(Fraction(Integer)) +--E 638 + +--S 639 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 8 1 9 +--R - - a c d + -- b c +--R 8 72 +--R (4) ------------------- +--R 2 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 639 + +--S 640 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 640 + +)clear all + +--S 641 of 2952 +t0000:=(c+d*x)^7 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R Type: Polynomial(Integer) +--E 641 + +--S 642 of 2952 +r0000:=1/8*(c+d*x)^8/d +--R +--R +--R (2) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - d x + c d x + - c d x + 7c d x + -- c d x + 7c d x + - c d x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R c d x + - c +--R 8 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 642 + +--S 643 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 8 6 7 7 2 5 6 3 4 5 35 4 3 4 5 2 3 7 6 2 7 +--R - d x + c d x + - c d x + 7c d x + -- c d x + 7c d x + - c d x + c x +--R 8 2 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 643 + +--S 644 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 8 +--R - c +--R 8 +--R (4) - ---- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 644 + +--S 645 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 645 + +)clear all + +--S 646 of 2952 +t0000:=(c+d*x)^7/(a+b*x) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R ------------------------------------------------------------------------ +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 646 + +--S 647 of 2952 +r0000:=d*(b*c-a*d)^6*x/b^7+1/2*(b*c-a*d)^5*(c+d*x)^2/b^6+_ + 1/3*(b*c-a*d)^4*(c+d*x)^3/b^5+1/4*(b*c-a*d)^3*(c+d*x)^4/b^4+_ + 1/5*(b*c-a*d)^2*(c+d*x)^5/b^3+1/6*(b*c-a*d)*(c+d*x)^6/b^2+_ + 1/7*(c+d*x)^7/b+(b*c-a*d)^7*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 420a d + 2940a b c d - 8820a b c d + 14700a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 14700a b c d + 8820a b c d - 2940a b c d + 420b c +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 7 6 6 +--R 60b d x + (- 70a b d + 490b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (84a b d - 588a b c d + 1764b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 105a b d + 735a b c d - 2205a b c d + 3675b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (140a b d - 980a b c d + 2940a b c d - 4900a b c d + 4900b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 210a b d + 1470a b c d - 4410a b c d + 7350a b c d +--R + +--R 6 4 3 7 5 2 +--R - 7350a b c d + 4410b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b d - 2940a b c d + 8820a b c d - 14700a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 14700a b c d - 8820a b c d + 2940b c d +--R * +--R x +--R + +--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 6 6 +--R - 210a b c d + 1190a b c d - 2765a b c d + 3339a b c d - 2163a b c d +--R + +--R 7 7 +--R 669b c +--R / +--R 8 +--R 420b +--R Type: Expression(Integer) +--E 647 + +--S 648 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 420a d + 2940a b c d - 8820a b c d + 14700a b c d +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 14700a b c d + 8820a b c d - 2940a b c d + 420b c +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 7 6 6 +--R 60b d x + (- 70a b d + 490b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (84a b d - 588a b c d + 1764b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 105a b d + 735a b c d - 2205a b c d + 3675b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (140a b d - 980a b c d + 2940a b c d - 4900a b c d + 4900b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 210a b d + 1470a b c d - 4410a b c d + 7350a b c d +--R + +--R 6 4 3 7 5 2 +--R - 7350a b c d + 4410b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b d - 2940a b c d + 8820a b c d - 14700a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 14700a b c d - 8820a b c d + 2940b c d +--R * +--R x +--R / +--R 8 +--R 420b +--R Type: Union(Expression(Integer),...) +--E 648 + +--S 649 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 +--R 210a c d - 1190a b c d + 2765a b c d - 3339a b c d + 2163a b c d +--R + +--R 5 7 +--R - 669b c +--R / +--R 6 +--R 420b +--R Type: Expression(Integer) +--E 649 + +--S 650 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 650 + +)clear all + +--S 651 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^2 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R ------------------------------------------------------------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 651 + +--S 652 of 2952 +r0000:=21*d^2*(b*c-a*d)^5*x/b^7-(b*c-a*d)^7/(b^8*(a+b*x))+_ + 35/2*d^3*(b*c-a*d)^4*(a+b*x)^2/b^8+35/3*d^4*(b*c-a*d)^3*(a+b*x)^3/b^8+_ + 21/4*d^5*(b*c-a*d)^2*(a+b*x)^4/b^8+7/5*d^6*(b*c-a*d)*(a+b*x)^5/b^8+_ + 1/6*d^7*(a+b*x)^6/b^8+7*d*(b*c-a*d)^6*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b d - 2520a b c d + 6300a b c d - 8400a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 6300a b c d - 2520a b c d + 420b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a d - 2520a b c d + 6300a b c d - 8400a b c d + 6300a b c d +--R + +--R 2 5 5 2 6 6 +--R - 2520a b c d + 420a b c d +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b d x + (- 14a b d + 84b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (21a b d - 126a b c d + 315b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 35a b d + 210a b c d - 525a b c d + 700b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (70a b d - 420a b c d + 1050a b c d - 1400a b c d + 1050b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 210a b d + 1260a b c d - 3150a b c d + 4200a b c d +--R + +--R 6 4 3 7 5 2 +--R - 3150a b c d + 1260b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 231a b d - 546a b c d - 525a b c d + 2800a b c d - 3150a b c d +--R + +--R 6 5 2 +--R 1260a b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 651a d - 3066a b c d + 5775a b c d - 5600a b c d + 3150a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 1260a b c d + 420a b c d - 60b c +--R / +--R 9 8 +--R 60b x + 60a b +--R Type: Expression(Integer) +--E 652 + +--S 653 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b d - 2520a b c d + 6300a b c d - 8400a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 6300a b c d - 2520a b c d + 420b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a d - 2520a b c d + 6300a b c d - 8400a b c d + 6300a b c d +--R + +--R 2 5 5 2 6 6 +--R - 2520a b c d + 420a b c d +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b d x + (- 14a b d + 84b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (21a b d - 126a b c d + 315b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 35a b d + 210a b c d - 525a b c d + 700b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (70a b d - 420a b c d + 1050a b c d - 1400a b c d + 1050b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 210a b d + 1260a b c d - 3150a b c d + 4200a b c d +--R + +--R 6 4 3 7 5 2 +--R - 3150a b c d + 1260b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 360a b d + 2100a b c d - 5040a b c d + 6300a b c d +--R + +--R 2 5 4 3 6 5 2 +--R - 4200a b c d + 1260a b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 60a d - 420a b c d + 1260a b c d - 2100a b c d + 2100a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 1260a b c d + 420a b c d - 60b c +--R / +--R 9 8 +--R 60b x + 60a b +--R Type: Union(Expression(Integer),...) +--E 653 + +--S 654 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R - 591a d + 2646a b c d - 4515a b c d + 3500a b c d - 1050a b c d +--R (4) --------------------------------------------------------------------- +--R 8 +--R 60b +--R Type: Expression(Integer) +--E 654 + +--S 655 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 655 + +)clear all + +--S 656 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^3 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R ------------------------------------------------------------------------ +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 656 + +--S 657 of 2952 +r0000:=35*d^3*(b*c-a*d)^4*x/b^7-1/2*(b*c-a*d)^7/(b^8*(a+b*x)^2)-_ + 7*d*(b*c-a*d)^6/(b^8*(a+b*x))+35/2*d^4*(b*c-a*d)^3*(a+b*x)^2/b^8+_ + 7*d^5*(b*c-a*d)^2*(a+b*x)^3/b^8+7/4*d^6*(b*c-a*d)*(a+b*x)^4/b^8+_ + 1/5*d^7*(a+b*x)^5/b^8+21*d^2*(b*c-a*d)^5*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 420a b d + 2100a b c d - 4200a b c d + 4200a b c d +--R + +--R 6 4 3 7 5 2 +--R - 2100a b c d + 420b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 840a b d + 4200a b c d - 8400a b c d + 8400a b c d +--R + +--R 2 5 4 3 6 5 2 +--R - 4200a b c d + 840a b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 420a d + 2100a b c d - 4200a b c d + 4200a b c d - 2100a b c d +--R + +--R 2 5 5 2 +--R 420a b c d +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 7 6 6 +--R 4b d x + (- 7a b d + 35b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (14a b d - 70a b c d + 140b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 35a b d + 175a b c d - 350a b c d + 350b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (140a b d - 700a b c d + 1400a b c d - 1400a b c d + 700b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 2 +--R (259a b d - 1575a b c d + 3500a b c d - 3500a b c d + 1400a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 322a b d + 1050a b c d - 1400a b c d + 1400a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 1400a b c d + 840a b c d - 140b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 371a d + 1575a b c d - 2800a b c d + 2800a b c d - 1750a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 630a b c d - 70a b c d - 10b c +--R / +--R 10 2 9 2 8 +--R 20b x + 40a b x + 20a b +--R Type: Expression(Integer) +--E 657 + +--S 658 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 420a b d + 2100a b c d - 4200a b c d + 4200a b c d +--R + +--R 6 4 3 7 5 2 +--R - 2100a b c d + 420b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 840a b d + 4200a b c d - 8400a b c d + 8400a b c d +--R + +--R 2 5 4 3 6 5 2 +--R - 4200a b c d + 840a b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 420a d + 2100a b c d - 4200a b c d + 4200a b c d - 2100a b c d +--R + +--R 2 5 5 2 +--R 420a b c d +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 7 6 6 +--R 4b d x + (- 7a b d + 35b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (14a b d - 70a b c d + 140b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 35a b d + 175a b c d - 350a b c d + 350b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (140a b d - 700a b c d + 1400a b c d - 1400a b c d + 700b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 2 +--R (500a b d - 2380a b c d + 4410a b c d - 3850a b c d + 1400a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 160a b d - 560a b c d + 420a b c d + 700a b c d - 1400a b c d +--R + +--R 6 5 2 7 6 +--R 840a b c d - 140b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 130a d + 770a b c d - 1890a b c d + 2450a b c d - 1750a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 630a b c d - 70a b c d - 10b c +--R / +--R 10 2 9 2 8 +--R 20b x + 40a b x + 20a b +--R Type: Union(Expression(Integer),...) +--E 658 + +--S 659 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 241a d - 805a b c d + 910a b c d - 350a b c d +--R (4) ------------------------------------------------- +--R 8 +--R 20b +--R Type: Expression(Integer) +--E 659 + +--S 660 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^4 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R ------------------------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 661 + +--S 662 of 2952 +r0000:=35*d^4*(b*c-a*d)^3*x/b^7-1/3*(b*c-a*d)^7/(b^8*(a+b*x)^3)-_ + 7/2*d*(b*c-a*d)^6/(b^8*(a+b*x)^2)-21*d^2*(b*c-a*d)^5/(b^8*(a+b*x))+_ + 21/2*d^5*(b*c-a*d)^2*(a+b*x)^2/b^8+7/3*d^6*(b*c-a*d)*(a+b*x)^3/b^8+_ + 1/4*d^7*(a+b*x)^4/b^8+35*d^3*(b*c-a*d)^4*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 420a b d - 1680a b c d + 2520a b c d - 1680a b c d +--R + +--R 7 4 3 +--R 420b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 1260a b d - 5040a b c d + 7560a b c d - 5040a b c d +--R + +--R 6 4 3 +--R 1260a b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 1260a b d - 5040a b c d + 7560a b c d - 5040a b c d +--R + +--R 2 5 4 3 +--R 1260a b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a d - 1680a b c d + 2520a b c d - 1680a b c d + 420a b c d +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 7 6 6 +--R 3b d x + (- 7a b d + 28b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (21a b d - 84a b c d + 126b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 105a b d + 420a b c d - 630a b c d + 420b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (- 455a b d + 1820a b c d - 2520a b c d + 1260a b c d )x +--R + +--R 5 2 7 4 3 6 2 5 3 4 6 4 3 7 5 2 2 +--R (- 105a b d + 420a b c d - 1260a b c d + 1260a b c d - 252b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 525a b d - 2100a b c d + 3780a b c d - 3780a b c d + 1890a b c d +--R + +--R 6 5 2 7 6 +--R - 252a b c d - 42b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 315a d - 1260a b c d + 2100a b c d - 1820a b c d + 770a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 84a b c d - 14a b c d - 4b c +--R / +--R 11 3 10 2 2 9 3 8 +--R 12b x + 36a b x + 36a b x + 12a b +--R Type: Expression(Integer) +--E 662 + +--S 663 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 420a b d - 1680a b c d + 2520a b c d - 1680a b c d +--R + +--R 7 4 3 +--R 420b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 1260a b d - 5040a b c d + 7560a b c d - 5040a b c d +--R + +--R 6 4 3 +--R 1260a b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 1260a b d - 5040a b c d + 7560a b c d - 5040a b c d +--R + +--R 2 5 4 3 +--R 1260a b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a d - 1680a b c d + 2520a b c d - 1680a b c d + 420a b c d +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 7 6 6 +--R 3b d x + (- 7a b d + 28b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (21a b d - 84a b c d + 126b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 105a b d + 420a b c d - 630a b c d + 420b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (- 556a b d + 2044a b c d - 2646a b c d + 1260a b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 408a b d + 1092a b c d - 378a b c d - 1260a b c d +--R + +--R 6 4 3 7 5 2 +--R 1260a b c d - 252b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 222a b d - 1428a b c d + 3402a b c d - 3780a b c d + 1890a b c d +--R + +--R 6 5 2 7 6 +--R - 252a b c d - 42b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 214a d - 1036a b c d + 1974a b c d - 1820a b c d + 770a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 84a b c d - 14a b c d - 4b c +--R / +--R 11 3 10 2 2 9 3 8 +--R 12b x + 36a b x + 36a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 663 + +--S 664 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 4 7 3 6 2 2 2 5 +--R - 101a d + 224a b c d - 126a b c d +--R (4) ------------------------------------- +--R 8 +--R 12b +--R Type: Expression(Integer) +--E 664 + +--S 665 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 665 + +)clear all + +--S 666 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^5 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R ------------------------------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 666 + +--S 667 of 2952 +r0000:=21*d^5*(b*c-a*d)^2*x/b^7-1/4*(b*c-a*d)^7/(b^8*(a+b*x)^4)-_ + 7/3*d*(b*c-a*d)^6/(b^8*(a+b*x)^3)-21/2*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^2)-_ + 35*d^3*(b*c-a*d)^4/(b^8*(a+b*x))+7/2*d^6*(b*c-a*d)*(a+b*x)^2/b^8+_ + 1/3*d^7*(a+b*x)^3/b^8+35*d^4*(b*c-a*d)^3*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 420a b d + 1260a b c d - 1260a b c d + 420b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (- 1680a b d + 5040a b c d - 5040a b c d + 1680a b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 2 +--R (- 2520a b d + 7560a b c d - 7560a b c d + 2520a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R (- 1680a b d + 5040a b c d - 5040a b c d + 1680a b c d )x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 420a d + 1260a b c d - 1260a b c d + 420a b c d +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 7 6 6 +--R 4b d x + (- 14a b d + 42b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (84a b d - 252a b c d + 252b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 4 +--R (518a b d - 1386a b c d + 1008a b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (392a b d - 504a b c d - 1008a b c d + 1680a b c d - 420b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 672a b d + 3024a b c d - 5292a b c d + 3780a b c d +--R + +--R 6 4 3 7 5 2 +--R - 630a b c d - 126b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 1008a b d + 3696a b c d - 5208a b c d + 3080a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 420a b c d - 84a b c d - 28b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 357a d + 1239a b c d - 1617a b c d + 875a b c d - 105a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 21a b c d - 7a b c d - 3b c +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Expression(Integer) +--E 667 + +--S 668 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 420a b d + 1260a b c d - 1260a b c d + 420b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 3 +--R (- 1680a b d + 5040a b c d - 5040a b c d + 1680a b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 2 +--R (- 2520a b d + 7560a b c d - 7560a b c d + 2520a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R (- 1680a b d + 5040a b c d - 5040a b c d + 1680a b c d )x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R - 420a d + 1260a b c d - 1260a b c d + 420a b c d +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 7 6 6 +--R 4b d x + (- 14a b d + 42b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (84a b d - 252a b c d + 252b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 4 +--R (556a b d - 1428a b c d + 1008a b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (544a b d - 672a b c d - 1008a b c d + 1680a b c d - 420b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 444a b d + 2772a b c d - 5292a b c d + 3780a b c d +--R + +--R 6 4 3 7 5 2 +--R - 630a b c d - 126b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 856a b d + 3528a b c d - 5208a b c d + 3080a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 420a b c d - 84a b c d - 28b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 319a d + 1197a b c d - 1617a b c d + 875a b c d - 105a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 21a b c d - 7a b c d - 3b c +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 668 + +--S 669 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 3 7 2 6 +--R 19a d - 21a b c d +--R (4) ------------------- +--R 8 +--R 6b +--R Type: Expression(Integer) +--E 669 + +--S 670 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 670 + +)clear all + +--S 671 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^6 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R ------------------------------------------------------------------------ +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 671 + +--S 672 of 2952 +r0000:=d^6*(7*b*c-6*a*d)*x/b^7+1/2*d^7*x^2/b^6-_ + 1/5*(b*c-a*d)^7/(b^8*(a+b*x)^5)-7/4*d*(b*c-a*d)^6/(b^8*(a+b*x)^4)-_ + 7*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^3)-_ + 35/2*d^3*(b*c-a*d)^4/(b^8*(a+b*x)^2)-_ + 35*d^4*(b*c-a*d)^3/(b^8*(a+b*x))+21*d^5*(b*c-a*d)^2*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 2 5 7 6 6 7 2 5 5 +--R (420a b d - 840a b c d + 420b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 4 +--R (2100a b d - 4200a b c d + 2100a b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 3 +--R (4200a b d - 8400a b c d + 4200a b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 +--R (4200a b d - 8400a b c d + 4200a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 7 7 6 6 +--R (2100a b d - 4200a b c d + 2100a b c d )x + 420a d - 840a b c d +--R + +--R 5 2 2 5 +--R 420a b c d +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 5 +--R 10b d x + (- 70a b d + 140b c d )x + (- 500a b d + 700a b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 400a b d - 700a b c d + 2100a b c d - 700b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1300a b d - 5600a b c d + 6300a b c d - 1400a b c d - 350b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 2700a b d - 8400a b c d + 7700a b c d - 1400a b c d - 350a b c d +--R + +--R 7 5 2 +--R - 140b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 1875a b d - 5250a b c d + 4375a b c d - 700a b c d - 175a b c d +--R + +--R 6 5 2 7 6 +--R - 70a b c d - 35b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 459a d - 1218a b c d + 959a b c d - 140a b c d - 35a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 14a b c d - 7a b c d - 4b c +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20b x + 100a b x + 200a b x + 200a b x + 100a b x + 20a b +--R Type: Expression(Integer) +--E 672 + +--S 673 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 5 7 6 6 7 2 5 5 +--R (420a b d - 840a b c d + 420b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 4 +--R (2100a b d - 4200a b c d + 2100a b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 3 +--R (4200a b d - 8400a b c d + 4200a b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 +--R (4200a b d - 8400a b c d + 4200a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 7 7 6 6 +--R (2100a b d - 4200a b c d + 2100a b c d )x + 420a d - 840a b c d +--R + +--R 5 2 2 5 +--R 420a b c d +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 5 +--R 10b d x + (- 70a b d + 140b c d )x + (- 500a b d + 700a b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 400a b d - 700a b c d + 2100a b c d - 700b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1300a b d - 5600a b c d + 6300a b c d - 1400a b c d - 350b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 2700a b d - 8400a b c d + 7700a b c d - 1400a b c d - 350a b c d +--R + +--R 7 5 2 +--R - 140b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 1875a b d - 5250a b c d + 4375a b c d - 700a b c d - 175a b c d +--R + +--R 6 5 2 7 6 +--R - 70a b c d - 35b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 459a d - 1218a b c d + 959a b c d - 140a b c d - 35a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 14a b c d - 7a b c d - 4b c +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20b x + 100a b x + 200a b x + 200a b x + 100a b x + 20a b +--R Type: Union(Expression(Integer),...) +--E 673 + +--S 674 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 674 + +--S 675 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^7 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 676 + +--S 677 of 2952 +r0000:=d^7*x/b^7-1/6*(b*c-a*d)^7/(b^8*(a+b*x)^6)-_ + 7/5*d*(b*c-a*d)^6/(b^8*(a+b*x)^5)-_ + 21/4*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^4)-_ + 35/3*d^3*(b*c-a*d)^4/(b^8*(a+b*x)^3)-_ + 35/2*d^4*(b*c-a*d)^3/(b^8*(a+b*x)^2)-_ + 21*d^5*(b*c-a*d)^2/(b^8*(a+b*x))+7*d^6*(b*c-a*d)*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 6 7 7 6 6 2 5 7 6 6 5 +--R (- 420a b d + 420b c d )x + (- 2520a b d + 2520a b c d )x +--R + +--R 3 4 7 2 5 6 4 4 3 7 3 4 6 3 +--R (- 6300a b d + 6300a b c d )x + (- 8400a b d + 8400a b c d )x +--R + +--R 5 2 7 4 3 6 2 6 7 5 2 6 +--R (- 6300a b d + 6300a b c d )x + (- 2520a b d + 2520a b c d )x +--R + +--R 7 7 6 6 +--R - 420a d + 420a b c d +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 6 2 5 7 6 6 7 2 5 5 +--R 60b d x + 360a b d x + (- 360a b d + 2520a b c d - 1260b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 4050a b d + 9450a b c d - 3150a b c d - 1050b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 8200a b d + 15400a b c d - 4200a b c d - 1400a b c d +--R + +--R 7 4 3 +--R - 700b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 7725a b d + 13125a b c d - 3150a b c d - 1050a b c d +--R + +--R 6 4 3 7 5 2 +--R - 525a b c d - 315b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 3594a b d + 5754a b c d - 1260a b c d - 420a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 210a b c d - 126a b c d - 84b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 669a d + 1029a b c d - 210a b c d - 70a b c d - 35a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 21a b c d - 14a b c d - 10b c +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 8 +--R 60a b +--R Type: Expression(Integer) +--E 677 + +--S 678 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 7 7 6 6 2 5 7 6 6 5 +--R (- 420a b d + 420b c d )x + (- 2520a b d + 2520a b c d )x +--R + +--R 3 4 7 2 5 6 4 4 3 7 3 4 6 3 +--R (- 6300a b d + 6300a b c d )x + (- 8400a b d + 8400a b c d )x +--R + +--R 5 2 7 4 3 6 2 6 7 5 2 6 +--R (- 6300a b d + 6300a b c d )x + (- 2520a b d + 2520a b c d )x +--R + +--R 7 7 6 6 +--R - 420a d + 420a b c d +--R * +--R log(b x + a) +--R + +--R 7 7 7 6 7 6 2 5 7 6 6 7 2 5 5 +--R 60b d x + 360a b d x + (- 360a b d + 2520a b c d - 1260b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 4050a b d + 9450a b c d - 3150a b c d - 1050b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 8200a b d + 15400a b c d - 4200a b c d - 1400a b c d +--R + +--R 7 4 3 +--R - 700b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 7725a b d + 13125a b c d - 3150a b c d - 1050a b c d +--R + +--R 6 4 3 7 5 2 +--R - 525a b c d - 315b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 3594a b d + 5754a b c d - 1260a b c d - 420a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R - 210a b c d - 126a b c d - 84b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 669a d + 1029a b c d - 210a b c d - 70a b c d - 35a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 21a b c d - 14a b c d - 10b c +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60b x + 360a b x + 900a b x + 1200a b x + 900a b x + 360a b x +--R + +--R 6 8 +--R 60a b +--R Type: Union(Expression(Integer),...) +--E 678 + +--S 679 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 679 + +--S 680 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 680 + +)clear all + +--S 681 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^8 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 8 +--R 8a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 681 + +--S 682 of 2952 +r0000:=-1/7*(b*c-a*d)^7/(b^8*(a+b*x)^7)-7/6*d*(b*c-a*d)^6/(b^8*(a+b*x)^6)-_ + 21/5*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^5)-_ + 35/4*d^3*(b*c-a*d)^4/(b^8*(a+b*x)^4)-_ + 35/3*d^4*(b*c-a*d)^3/(b^8*(a+b*x)^3)-_ + 21/2*d^5*(b*c-a*d)^2/(b^8*(a+b*x)^2)-_ + 7*d^6*(b*c-a*d)/(b^8*(a+b*x))+d^7*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 7 7 7 6 7 6 2 5 7 5 3 4 7 4 +--R 420b d x + 2940a b d x + 8820a b d x + 14700a b d x +--R + +--R 4 3 7 3 5 2 7 2 6 7 7 7 +--R 14700a b d x + 8820a b d x + 2940a b d x + 420a d +--R * +--R log(b x + a) +--R + +--R 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R (2940a b d - 2940b c d )x + (13230a b d - 8820a b c d - 4410b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (26950a b d - 14700a b c d - 7350a b c d - 4900b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 30625a b d - 14700a b c d - 7350a b c d - 4900a b c d +--R + +--R 7 4 3 +--R - 3675b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 20139a b d - 8820a b c d - 4410a b c d - 2940a b c d +--R + +--R 6 4 3 7 5 2 +--R - 2205a b c d - 1764b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 7203a b d - 2940a b c d - 1470a b c d - 980a b c d - 735a b c d +--R + +--R 6 5 2 7 6 +--R - 588a b c d - 490b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 1089a d - 420a b c d - 210a b c d - 140a b c d - 105a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 84a b c d - 70a b c d - 60b c +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420b x + 2940a b x + 8820a b x + 14700a b x + 14700a b x +--R + +--R 5 10 2 6 9 7 8 +--R 8820a b x + 2940a b x + 420a b +--R Type: Expression(Integer) +--E 682 + +--S 683 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 6 7 6 2 5 7 5 3 4 7 4 +--R 420b d x + 2940a b d x + 8820a b d x + 14700a b d x +--R + +--R 4 3 7 3 5 2 7 2 6 7 7 7 +--R 14700a b d x + 8820a b d x + 2940a b d x + 420a d +--R * +--R log(b x + a) +--R + +--R 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R (2940a b d - 2940b c d )x + (13230a b d - 8820a b c d - 4410b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (26950a b d - 14700a b c d - 7350a b c d - 4900b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 30625a b d - 14700a b c d - 7350a b c d - 4900a b c d +--R + +--R 7 4 3 +--R - 3675b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 20139a b d - 8820a b c d - 4410a b c d - 2940a b c d +--R + +--R 6 4 3 7 5 2 +--R - 2205a b c d - 1764b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 7203a b d - 2940a b c d - 1470a b c d - 980a b c d - 735a b c d +--R + +--R 6 5 2 7 6 +--R - 588a b c d - 490b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 1089a d - 420a b c d - 210a b c d - 140a b c d - 105a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 84a b c d - 70a b c d - 60b c +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420b x + 2940a b x + 8820a b x + 14700a b x + 14700a b x +--R + +--R 5 10 2 6 9 7 8 +--R 8820a b x + 2940a b x + 420a b +--R Type: Union(Expression(Integer),...) +--E 683 + +--S 684 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 684 + +--S 685 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 685 + +)clear all + +--S 686 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^9 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 7 2 2 8 9 +--R 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 686 + +--S 687 of 2952 +r0000:=-1/8*(c+d*x)^8/((b*c-a*d)*(a+b*x)^8) +--R +--R +--R (2) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - d x + c d x + - c d x + 7c d x + -- c d x + 7c d x + - c d x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R c d x + - c +--R 8 +--R / +--R 8 9 8 2 7 8 7 3 6 2 7 6 +--R (a b d - b c)x + (8a b d - 8a b c)x + (28a b d - 28a b c)x +--R + +--R 4 5 3 6 5 5 4 4 5 4 6 3 5 4 3 +--R (56a b d - 56a b c)x + (70a b d - 70a b c)x + (56a b d - 56a b c)x +--R + +--R 7 2 6 3 2 8 7 2 9 8 +--R (28a b d - 28a b c)x + (8a b d - 8a b c)x + a d - a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 687 + +--S 688 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R - 8b d x + (- 28a b d - 28b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 56a b d - 56a b c d - 56b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 70a b d - 70a b c d - 70a b c d - 70b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 56a b d - 56a b c d - 56a b c d - 56a b c d - 56b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 28a b d - 28a b c d - 28a b c d - 28a b c d - 28a b c d +--R + +--R 7 5 2 +--R - 28b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R - 8a b d - 8a b c d - 8a b c d - 8a b c d - 8a b c d - 8a b c d +--R + +--R 7 6 +--R - 8b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 6 6 +--R - a d - a b c d - a b c d - a b c d - a b c d - a b c d - a b c d +--R + +--R 7 7 +--R - b c +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 5 11 3 +--R 8b x + 64a b x + 224a b x + 448a b x + 560a b x + 448a b x +--R + +--R 6 10 2 7 9 8 8 +--R 224a b x + 64a b x + 8a b +--R Type: Union(Expression(Integer),...) +--E 688 + +--S 689 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 8 +--R d +--R (4) - ------------- +--R 8 9 +--R 8a b d - 8b c +--R Type: Expression(Integer) +--E 689 + +--S 690 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^10 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 691 + +--S 692 of 2952 +r0000:=-1/9*(c+d*x)^8/((b*c-a*d)*(a+b*x)^9)+_ + 1/72*d*(c+d*x)^8/((b*c-a*d)^2*(a+b*x)^8) +--R +--R +--R (2) +--R 1 9 9 1 9 8 8 1 2 7 7 7 2 7 7 3 6 6 +--R -- b d x + - a d x + (a c d - - b c d )x + (- a c d - - b c d )x +--R 72 8 2 2 3 +--R + +--R 3 6 21 4 5 5 35 4 5 5 4 4 +--R (7a c d - -- b c d )x + (-- a c d - 7b c d )x +--R 4 4 +--R + +--R 5 4 35 6 3 3 7 6 3 7 2 2 7 2 7 8 +--R (7a c d - -- b c d )x + (- a c d - 3b c d )x + (a c d - - b c d)x +--R 6 2 8 +--R + +--R 1 8 1 9 +--R - a c d - - b c +--R 8 9 +--R / +--R 2 9 2 10 11 2 9 3 8 2 2 9 10 2 8 +--R (a b d - 2a b c d + b c )x + (9a b d - 18a b c d + 9a b c )x +--R + +--R 4 7 2 3 8 2 9 2 7 +--R (36a b d - 72a b c d + 36a b c )x +--R + +--R 5 6 2 4 7 3 8 2 6 +--R (84a b d - 168a b c d + 84a b c )x +--R + +--R 6 5 2 5 6 4 7 2 5 +--R (126a b d - 252a b c d + 126a b c )x +--R + +--R 7 4 2 6 5 5 6 2 4 +--R (126a b d - 252a b c d + 126a b c )x +--R + +--R 8 3 2 7 4 6 5 2 3 +--R (84a b d - 168a b c d + 84a b c )x +--R + +--R 9 2 2 8 3 7 4 2 2 10 2 9 2 8 3 2 +--R (36a b d - 72a b c d + 36a b c )x + (9a b d - 18a b c d + 9a b c )x +--R + +--R 11 2 10 9 2 2 +--R a d - 2a b c d + a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 692 + +--S 693 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R - 36b d x + (- 84a b d - 168b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 126a b d - 252a b c d - 378b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 126a b d - 252a b c d - 378a b c d - 504b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 84a b d - 168a b c d - 252a b c d - 336a b c d - 420b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 36a b d - 72a b c d - 108a b c d - 144a b c d - 180a b c d +--R + +--R 7 5 2 +--R - 216b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 9a b d - 18a b c d - 27a b c d - 36a b c d - 45a b c d +--R + +--R 6 5 2 7 6 +--R - 54a b c d - 63b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R - a d - 2a b c d - 3a b c d - 4a b c d - 5a b c d - 6a b c d +--R + +--R 6 6 7 7 +--R - 7a b c d - 8b c +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 +--R 72b x + 648a b x + 2592a b x + 6048a b x + 9072a b x +--R + +--R 5 12 4 6 11 3 7 10 2 8 9 9 8 +--R 9072a b x + 6048a b x + 2592a b x + 648a b x + 72a b +--R Type: Union(Expression(Integer),...) +--E 693 + +--S 694 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 9 +--R d +--R (4) - ------------------------------- +--R 2 8 2 9 10 2 +--R 72a b d - 144a b c d + 72b c +--R Type: Expression(Integer) +--E 694 + +--S 695 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 695 + +)clear all + +--S 696 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^11 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R b x + 11a b x + 55a b x + 165a b x + 330a b x + 462a b x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462a b x + 330a b x + 165a b x + 55a b x + 11a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 696 + +--S 697 of 2952 +r0000:=-1/10*(c+d*x)^8/((b*c-a*d)*(a+b*x)^10)+_ + 1/45*d*(c+d*x)^8/((b*c-a*d)^2*(a+b*x)^9)-_ + 1/360*d^2*(c+d*x)^8/((b*c-a*d)^3*(a+b*x)^8) +--R +--R +--R (2) +--R 1 2 10 10 1 10 9 1 2 10 8 +--R --- b d x + -- a b d x + - a d x +--R 360 36 8 +--R + +--R 2 9 2 8 1 2 3 7 7 7 2 2 8 14 3 7 7 2 4 6 6 +--R (a c d - a b c d + - b c d )x + (- a c d - -- a b c d + - b c d )x +--R 3 2 3 4 +--R + +--R 2 3 7 21 4 6 21 2 5 5 5 +--R (7a c d - -- a b c d + -- b c d )x +--R 2 5 +--R + +--R 35 2 4 6 5 5 35 2 6 4 4 +--R (-- a c d - 14a b c d + -- b c d )x +--R 4 6 +--R + +--R 2 5 5 35 6 4 2 7 3 3 +--R (7a c d - -- a b c d + 5b c d )x +--R 3 +--R + +--R 7 2 6 4 7 3 21 2 8 2 2 2 7 3 7 8 2 7 2 9 +--R (- a c d - 6a b c d + -- b c d )x + (a c d - - a b c d + - b c d)x +--R 2 8 4 9 +--R + +--R 1 2 8 2 2 9 1 2 10 +--R - a c d - - a b c d + -- b c +--R 8 9 10 +--R / +--R 3 10 3 2 11 2 12 2 13 3 10 +--R (a b d - 3a b c d + 3a b c d - b c )x +--R + +--R 4 9 3 3 10 2 2 11 2 12 3 9 +--R (10a b d - 30a b c d + 30a b c d - 10a b c )x +--R + +--R 5 8 3 4 9 2 3 10 2 2 11 3 8 +--R (45a b d - 135a b c d + 135a b c d - 45a b c )x +--R + +--R 6 7 3 5 8 2 4 9 2 3 10 3 7 +--R (120a b d - 360a b c d + 360a b c d - 120a b c )x +--R + +--R 7 6 3 6 7 2 5 8 2 4 9 3 6 +--R (210a b d - 630a b c d + 630a b c d - 210a b c )x +--R + +--R 8 5 3 7 6 2 6 7 2 5 8 3 5 +--R (252a b d - 756a b c d + 756a b c d - 252a b c )x +--R + +--R 9 4 3 8 5 2 7 6 2 6 7 3 4 +--R (210a b d - 630a b c d + 630a b c d - 210a b c )x +--R + +--R 10 3 3 9 4 2 8 5 2 7 6 3 3 +--R (120a b d - 360a b c d + 360a b c d - 120a b c )x +--R + +--R 11 2 3 10 3 2 9 4 2 8 5 3 2 +--R (45a b d - 135a b c d + 135a b c d - 45a b c )x +--R + +--R 12 3 11 2 2 10 3 2 9 4 3 13 3 12 2 +--R (10a b d - 30a b c d + 30a b c d - 10a b c )x + a d - 3a b c d +--R + +--R 11 2 2 10 3 3 +--R 3a b c d - a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 697 + +--S 698 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R - 120b d x + (- 210a b d - 630b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 252a b d - 756a b c d - 1512b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 210a b d - 630a b c d - 1260a b c d - 2100b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 120a b d - 360a b c d - 720a b c d - 1200a b c d - 1800b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 45a b d - 135a b c d - 270a b c d - 450a b c d - 675a b c d +--R + +--R 7 5 2 +--R - 945b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 10a b d - 30a b c d - 60a b c d - 100a b c d - 150a b c d +--R + +--R 6 5 2 7 6 +--R - 210a b c d - 280b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R - a d - 3a b c d - 6a b c d - 10a b c d - 15a b c d - 21a b c d +--R + +--R 6 6 7 7 +--R - 28a b c d - 36b c +--R / +--R 18 10 17 9 2 16 8 3 15 7 4 14 6 +--R 360b x + 3600a b x + 16200a b x + 43200a b x + 75600a b x +--R + +--R 5 13 5 6 12 4 7 11 3 8 10 2 9 9 +--R 90720a b x + 75600a b x + 43200a b x + 16200a b x + 3600a b x +--R + +--R 10 8 +--R 360a b +--R Type: Union(Expression(Integer),...) +--E 698 + +--S 699 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 10 +--R d +--R (4) - -------------------------------------------------- +--R 3 8 3 2 9 2 10 2 11 3 +--R 360a b d - 1080a b c d + 1080a b c d - 360b c +--R Type: Expression(Integer) +--E 699 + +--S 700 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 700 + +)clear all + +--S 701 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^12 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R b x + 12a b x + 66a b x + 220a b x + 495a b x + 792a b x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924a b x + 792a b x + 495a b x + 220a b x + 66a b x + 12a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 701 + +--S 702 of 2952 +r0000:=-1/11*(c+d*x)^8/((b*c-a*d)*(a+b*x)^11)+_ + 3/110*d*(c+d*x)^8/((b*c-a*d)^2*(a+b*x)^10)-_ + 1/165*d^2*(c+d*x)^8/((b*c-a*d)^3*(a+b*x)^9)+_ + 1/1320*d^3*(c+d*x)^8/((b*c-a*d)^4*(a+b*x)^8) +--R +--R +--R (2) +--R 1 3 11 11 1 2 11 10 1 2 11 9 1 3 11 8 +--R ---- b d x + --- a b d x + -- a b d x + - a d x +--R 1320 120 24 8 +--R + +--R 3 10 3 2 2 9 2 3 8 1 3 4 7 7 +--R (a c d - - a b c d + a b c d - - b c d )x +--R 2 4 +--R + +--R 7 3 2 9 2 3 8 21 2 4 7 7 3 5 6 6 +--R (- a c d - 7a b c d + -- a b c d - - b c d )x +--R 2 4 5 +--R + +--R 3 3 8 63 2 4 7 63 2 5 6 7 3 6 5 5 +--R (7a c d - -- a b c d + -- a b c d - - b c d )x +--R 4 5 2 +--R + +--R 35 3 4 7 2 5 6 35 2 6 5 3 7 4 4 +--R (-- a c d - 21a b c d + -- a b c d - 5b c d )x +--R 4 2 +--R + +--R 3 5 6 35 2 6 5 2 7 4 35 3 8 3 3 +--R (7a c d - -- a b c d + 15a b c d - -- b c d )x +--R 2 8 +--R + +--R 7 3 6 5 2 7 4 63 2 8 3 7 3 9 2 2 +--R (- a c d - 9a b c d + -- a b c d - - b c d )x +--R 2 8 3 +--R + +--R 3 7 4 21 2 8 3 7 2 9 2 7 3 10 1 3 8 3 1 2 9 2 +--R (a c d - -- a b c d + - a b c d - -- b c d)x + - a c d - - a b c d +--R 8 3 10 8 3 +--R + +--R 3 2 10 1 3 11 +--R -- a b c d - -- b c +--R 10 11 +--R / +--R 4 11 4 3 12 3 2 13 2 2 14 3 15 4 11 +--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c )x +--R + +--R 5 10 4 4 11 3 3 12 2 2 2 13 3 14 4 10 +--R (11a b d - 44a b c d + 66a b c d - 44a b c d + 11a b c )x +--R + +--R 6 9 4 5 10 3 4 11 2 2 3 12 3 2 13 4 9 +--R (55a b d - 220a b c d + 330a b c d - 220a b c d + 55a b c )x +--R + +--R 7 8 4 6 9 3 5 10 2 2 4 11 3 3 12 4 8 +--R (165a b d - 660a b c d + 990a b c d - 660a b c d + 165a b c )x +--R + +--R 8 7 4 7 8 3 6 9 2 2 5 10 3 4 11 4 7 +--R (330a b d - 1320a b c d + 1980a b c d - 1320a b c d + 330a b c )x +--R + +--R 9 6 4 8 7 3 7 8 2 2 6 9 3 5 10 4 6 +--R (462a b d - 1848a b c d + 2772a b c d - 1848a b c d + 462a b c )x +--R + +--R 10 5 4 9 6 3 8 7 2 2 7 8 3 6 9 4 5 +--R (462a b d - 1848a b c d + 2772a b c d - 1848a b c d + 462a b c )x +--R + +--R 11 4 4 10 5 3 9 6 2 2 8 7 3 7 8 4 4 +--R (330a b d - 1320a b c d + 1980a b c d - 1320a b c d + 330a b c )x +--R + +--R 12 3 4 11 4 3 10 5 2 2 9 6 3 8 7 4 3 +--R (165a b d - 660a b c d + 990a b c d - 660a b c d + 165a b c )x +--R + +--R 13 2 4 12 3 3 11 4 2 2 10 5 3 9 6 4 2 +--R (55a b d - 220a b c d + 330a b c d - 220a b c d + 55a b c )x +--R + +--R 14 4 13 2 3 12 3 2 2 11 4 3 10 5 4 15 4 +--R (11a b d - 44a b c d + 66a b c d - 44a b c d + 11a b c )x + a d +--R + +--R 14 3 13 2 2 2 12 3 3 11 4 4 +--R - 4a b c d + 6a b c d - 4a b c d + a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 702 + +--S 703 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R - 330b d x + (- 462a b d - 1848b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 462a b d - 1848a b c d - 4620b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 330a b d - 1320a b c d - 3300a b c d - 6600b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 165a b d - 660a b c d - 1650a b c d - 3300a b c d - 5775b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 55a b d - 220a b c d - 550a b c d - 1100a b c d - 1925a b c d +--R + +--R 7 5 2 +--R - 3080b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 11a b d - 44a b c d - 110a b c d - 220a b c d - 385a b c d +--R + +--R 6 5 2 7 6 +--R - 616a b c d - 924b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R - a d - 4a b c d - 10a b c d - 20a b c d - 35a b c d - 56a b c d +--R + +--R 6 6 7 7 +--R - 84a b c d - 120b c +--R / +--R 19 11 18 10 2 17 9 3 16 8 4 15 7 +--R 1320b x + 14520a b x + 72600a b x + 217800a b x + 435600a b x +--R + +--R 5 14 6 6 13 5 7 12 4 8 11 3 +--R 609840a b x + 609840a b x + 435600a b x + 217800a b x +--R + +--R 9 10 2 10 9 11 8 +--R 72600a b x + 14520a b x + 1320a b +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 11 +--R d +--R (4) - -------------------------------------------------------------------- +--R 4 8 4 3 9 3 2 10 2 2 11 3 12 4 +--R 1320a b d - 5280a b c d + 7920a b c d - 5280a b c d + 1320b c +--R Type: Expression(Integer) +--E 704 + +--S 705 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^13 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R / +--R 13 13 12 12 2 11 11 3 10 10 4 9 9 5 8 8 +--R b x + 13a b x + 78a b x + 286a b x + 715a b x + 1287a b x +--R + +--R 6 7 7 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 +--R 1716a b x + 1716a b x + 1287a b x + 715a b x + 286a b x + 78a b x +--R + +--R 12 13 +--R 13a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 706 + +--S 707 of 2952 +r0000:=-1/12*(c+d*x)^8/((b*c-a*d)*(a+b*x)^12)+_ + 1/33*d*(c+d*x)^8/((b*c-a*d)^2*(a+b*x)^11)-_ + 1/110*d^2*(c+d*x)^8/((b*c-a*d)^3*(a+b*x)^10)+_ + 1/495*d^3*(c+d*x)^8/((b*c-a*d)^4*(a+b*x)^9)-_ + 1/3960*d^4*(c+d*x)^8/((b*c-a*d)^5*(a+b*x)^8) +--R +--R +--R (2) +--R 1 4 12 12 1 3 12 11 1 2 2 12 10 1 3 12 9 1 4 12 8 +--R ---- b d x + --- a b d x + -- a b d x + -- a b d x + - a d x +--R 3960 330 60 18 8 +--R + +--R 4 11 3 2 10 2 2 3 9 3 4 8 1 4 5 7 7 +--R (a c d - 2a b c d + 2a b c d - a b c d + - b c d )x +--R 5 +--R + +--R 7 4 2 10 28 3 3 9 21 2 2 4 8 28 3 5 7 7 4 6 6 6 +--R (- a c d - -- a b c d + -- a b c d - -- a b c d + - b c d )x +--R 2 3 2 5 6 +--R + +--R 4 3 9 3 4 8 126 2 2 5 7 3 6 6 4 7 5 5 +--R (7a c d - 21a b c d + --- a b c d - 14a b c d + 3b c d )x +--R 5 +--R + +--R 35 4 4 8 3 5 7 2 2 6 6 3 7 5 35 4 8 4 4 +--R (-- a c d - 28a b c d + 35a b c d - 20a b c d + -- b c d )x +--R 4 8 +--R + +--R 4 5 7 70 3 6 6 2 2 7 5 35 3 8 4 35 4 9 3 3 +--R (7a c d - -- a b c d + 30a b c d - -- a b c d + -- b c d )x +--R 3 2 9 +--R + +--R 7 4 6 6 3 7 5 63 2 2 8 4 28 3 9 3 21 4 10 2 2 +--R (- a c d - 12a b c d + -- a b c d - -- a b c d + -- b c d )x +--R 2 4 3 10 +--R + +--R 4 7 5 7 3 8 4 14 2 2 9 3 14 3 10 2 7 4 11 +--R (a c d - - a b c d + -- a b c d - -- a b c d + -- b c d)x +--R 2 3 5 11 +--R + +--R 1 4 8 4 4 3 9 3 3 2 2 10 2 4 3 11 1 4 12 +--R - a c d - - a b c d + - a b c d - -- a b c d + -- b c +--R 8 9 5 11 12 +--R / +--R 5 12 5 4 13 4 3 14 2 3 2 15 3 2 16 4 17 5 12 +--R (a b d - 5a b c d + 10a b c d - 10a b c d + 5a b c d - b c )x +--R + +--R 6 11 5 5 12 4 4 13 2 3 3 14 3 2 2 15 4 +--R 12a b d - 60a b c d + 120a b c d - 120a b c d + 60a b c d +--R + +--R 16 5 +--R - 12a b c +--R * +--R 11 +--R x +--R + +--R 7 10 5 6 11 4 5 12 2 3 4 13 3 2 3 14 4 +--R 66a b d - 330a b c d + 660a b c d - 660a b c d + 330a b c d +--R + +--R 2 15 5 +--R - 66a b c +--R * +--R 10 +--R x +--R + +--R 8 9 5 7 10 4 6 11 2 3 5 12 3 2 +--R 220a b d - 1100a b c d + 2200a b c d - 2200a b c d +--R + +--R 4 13 4 3 14 5 +--R 1100a b c d - 220a b c +--R * +--R 9 +--R x +--R + +--R 9 8 5 8 9 4 7 10 2 3 6 11 3 2 +--R 495a b d - 2475a b c d + 4950a b c d - 4950a b c d +--R + +--R 5 12 4 4 13 5 +--R 2475a b c d - 495a b c +--R * +--R 8 +--R x +--R + +--R 10 7 5 9 8 4 8 9 2 3 7 10 3 2 +--R 792a b d - 3960a b c d + 7920a b c d - 7920a b c d +--R + +--R 6 11 4 5 12 5 +--R 3960a b c d - 792a b c +--R * +--R 7 +--R x +--R + +--R 11 6 5 10 7 4 9 8 2 3 8 9 3 2 +--R 924a b d - 4620a b c d + 9240a b c d - 9240a b c d +--R + +--R 7 10 4 6 11 5 +--R 4620a b c d - 924a b c +--R * +--R 6 +--R x +--R + +--R 12 5 5 11 6 4 10 7 2 3 9 8 3 2 +--R 792a b d - 3960a b c d + 7920a b c d - 7920a b c d +--R + +--R 8 9 4 7 10 5 +--R 3960a b c d - 792a b c +--R * +--R 5 +--R x +--R + +--R 13 4 5 12 5 4 11 6 2 3 10 7 3 2 +--R 495a b d - 2475a b c d + 4950a b c d - 4950a b c d +--R + +--R 9 8 4 8 9 5 +--R 2475a b c d - 495a b c +--R * +--R 4 +--R x +--R + +--R 14 3 5 13 4 4 12 5 2 3 11 6 3 2 +--R 220a b d - 1100a b c d + 2200a b c d - 2200a b c d +--R + +--R 10 7 4 9 8 5 +--R 1100a b c d - 220a b c +--R * +--R 3 +--R x +--R + +--R 15 2 5 14 3 4 13 4 2 3 12 5 3 2 11 6 4 +--R 66a b d - 330a b c d + 660a b c d - 660a b c d + 330a b c d +--R + +--R 10 7 5 +--R - 66a b c +--R * +--R 2 +--R x +--R + +--R 16 5 15 2 4 14 3 2 3 13 4 3 2 12 5 4 +--R 12a b d - 60a b c d + 120a b c d - 120a b c d + 60a b c d +--R + +--R 11 6 5 +--R - 12a b c +--R * +--R x +--R + +--R 17 5 16 4 15 2 2 3 14 3 3 2 13 4 4 12 5 5 +--R a d - 5a b c d + 10a b c d - 10a b c d + 5a b c d - a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 707 + +--S 708 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R - 792b d x + (- 924a b d - 4620b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 792a b d - 3960a b c d - 11880b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 495a b d - 2475a b c d - 7425a b c d - 17325b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 220a b d - 1100a b c d - 3300a b c d - 7700a b c d +--R + +--R 7 4 3 +--R - 15400b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 66a b d - 330a b c d - 990a b c d - 2310a b c d - 4620a b c d +--R + +--R 7 5 2 +--R - 8316b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 12a b d - 60a b c d - 180a b c d - 420a b c d - 840a b c d +--R + +--R 6 5 2 7 6 +--R - 1512a b c d - 2520b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R - a d - 5a b c d - 15a b c d - 35a b c d - 70a b c d - 126a b c d +--R + +--R 6 6 7 7 +--R - 210a b c d - 330b c +--R / +--R 20 12 19 11 2 18 10 3 17 9 +--R 3960b x + 47520a b x + 261360a b x + 871200a b x +--R + +--R 4 16 8 5 15 7 6 14 6 7 13 5 +--R 1960200a b x + 3136320a b x + 3659040a b x + 3136320a b x +--R + +--R 8 12 4 9 11 3 10 10 2 11 9 12 8 +--R 1960200a b x + 871200a b x + 261360a b x + 47520a b x + 3960a b +--R Type: Union(Expression(Integer),...) +--E 708 + +--S 709 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R - +--R 12 +--R d +--R / +--R 5 8 5 4 9 4 3 10 2 3 2 11 3 2 +--R 3960a b d - 19800a b c d + 39600a b c d - 39600a b c d +--R + +--R 12 4 13 5 +--R 19800a b c d - 3960b c +--R Type: Expression(Integer) +--E 709 + +--S 710 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 710 + +)clear all + +--S 711 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^14 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R / +--R 14 14 13 13 2 12 12 3 11 11 4 10 10 +--R b x + 14a b x + 91a b x + 364a b x + 1001a b x +--R + +--R 5 9 9 6 8 8 7 7 7 8 6 6 9 5 5 +--R 2002a b x + 3003a b x + 3432a b x + 3003a b x + 2002a b x +--R + +--R 10 4 4 11 3 3 12 2 2 13 14 +--R 1001a b x + 364a b x + 91a b x + 14a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 711 + +--S 712 of 2952 +r0000:=-1/13*(b*c-a*d)^7/(b^8*(a+b*x)^13)-_ + 7/12*d*(b*c-a*d)^6/(b^8*(a+b*x)^12)-_ + 21/11*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^11)-_ + 7/2*d^3*(b*c-a*d)^4/(b^8*(a+b*x)^10)-_ + 35/9*d^4*(b*c-a*d)^3/(b^8*(a+b*x)^9)-_ + 21/8*d^5*(b*c-a*d)^2/(b^8*(a+b*x)^8)-_ + d^6*(b*c-a*d)/(b^8*(a+b*x)^7)-1/6*d^7/(b^8*(a+b*x)^6) +--R +--R +--R (2) +--R 1 7 7 7 1 6 7 7 6 6 +--R - - b d x + (- - a b d - b c d )x +--R 6 6 +--R + +--R 1 2 5 7 3 6 6 21 7 2 5 5 +--R (- - a b d - - a b c d - -- b c d )x +--R 8 4 8 +--R + +--R 5 3 4 7 5 2 5 6 35 6 2 5 35 7 3 4 4 +--R (- -- a b d - -- a b c d - -- a b c d - -- b c d )x +--R 72 12 24 9 +--R + +--R 1 4 3 7 1 3 4 6 7 2 5 2 5 14 6 3 4 7 7 4 3 3 +--R (- -- a b d - - a b c d - -- a b c d - -- a b c d - - b c d )x +--R 36 6 12 9 2 +--R + +--R 1 5 2 7 1 4 3 6 7 3 4 2 5 14 2 5 3 4 21 6 4 3 +--R - --- a b d - -- a b c d - -- a b c d - -- a b c d - -- a b c d +--R 132 22 44 33 22 +--R + +--R 21 7 5 2 +--R - -- b c d +--R 11 +--R * +--R 2 +--R x +--R + +--R 1 6 7 1 5 2 6 7 4 3 2 5 7 3 4 3 4 +--R - --- a b d - --- a b c d - --- a b c d - -- a b c d +--R 792 132 264 99 +--R + +--R 7 2 5 4 3 7 6 5 2 7 7 6 +--R - -- a b c d - -- a b c d - -- b c d +--R 44 22 12 +--R * +--R x +--R + +--R 1 7 7 1 6 6 7 5 2 2 5 7 4 3 3 4 +--R - ----- a d - ---- a b c d - ---- a b c d - ---- a b c d +--R 10296 1716 3432 1287 +--R + +--R 7 3 4 4 3 7 2 5 5 2 7 6 6 1 7 7 +--R - --- a b c d - --- a b c d - --- a b c d - -- b c +--R 572 286 156 13 +--R / +--R 21 13 20 12 2 19 11 3 18 10 4 17 9 5 16 8 +--R b x + 13a b x + 78a b x + 286a b x + 715a b x + 1287a b x +--R + +--R 6 15 7 7 14 6 8 13 5 9 12 4 10 11 3 +--R 1716a b x + 1716a b x + 1287a b x + 715a b x + 286a b x +--R + +--R 11 10 2 12 9 13 8 +--R 78a b x + 13a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 712 + +--S 713 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R - 1716b d x + (- 1716a b d - 10296b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 1287a b d - 7722a b c d - 27027b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 715a b d - 4290a b c d - 15015a b c d - 40040b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 286a b d - 1716a b c d - 6006a b c d - 16016a b c d +--R + +--R 7 4 3 +--R - 36036b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 78a b d - 468a b c d - 1638a b c d - 4368a b c d - 9828a b c d +--R + +--R 7 5 2 +--R - 19656b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 13a b d - 78a b c d - 273a b c d - 728a b c d - 1638a b c d +--R + +--R 6 5 2 7 6 +--R - 3276a b c d - 6006b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R - a d - 6a b c d - 21a b c d - 56a b c d - 126a b c d - 252a b c d +--R + +--R 6 6 7 7 +--R - 462a b c d - 792b c +--R / +--R 21 13 20 12 2 19 11 3 18 10 +--R 10296b x + 133848a b x + 803088a b x + 2944656a b x +--R + +--R 4 17 9 5 16 8 6 15 7 7 14 6 +--R 7361640a b x + 13250952a b x + 17667936a b x + 17667936a b x +--R + +--R 8 13 5 9 12 4 10 11 3 11 10 2 +--R 13250952a b x + 7361640a b x + 2944656a b x + 803088a b x +--R + +--R 12 9 13 8 +--R 133848a b x + 10296a b +--R Type: Union(Expression(Integer),...) +--E 713 + +--S 714 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 714 + +--S 715 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 715 + +)clear all + +--S 716 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^15 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R / +--R 15 15 14 14 2 13 13 3 12 12 4 11 11 +--R b x + 15a b x + 105a b x + 455a b x + 1365a b x +--R + +--R 5 10 10 6 9 9 7 8 8 8 7 7 9 6 6 +--R 3003a b x + 5005a b x + 6435a b x + 6435a b x + 5005a b x +--R + +--R 10 5 5 11 4 4 12 3 3 13 2 2 14 15 +--R 3003a b x + 1365a b x + 455a b x + 105a b x + 15a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 716 + +--S 717 of 2952 +r0000:=-1/14*(b*c-a*d)^7/(b^8*(a+b*x)^14)-_ + 7/13*d*(b*c-a*d)^6/(b^8*(a+b*x)^13)-_ + 7/4*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^12)-_ + 35/11*d^3*(b*c-a*d)^4/(b^8*(a+b*x)^11)-_ + 7/2*d^4*(b*c-a*d)^3/(b^8*(a+b*x)^10)-_ + 7/3*d^5*(b*c-a*d)^2/(b^8*(a+b*x)^9)-_ + 7/8*d^6*(b*c-a*d)/(b^8*(a+b*x)^8)-1/7*d^7/(b^8*(a+b*x)^7) +--R +--R +--R (2) +--R 1 7 7 7 1 6 7 7 7 6 6 +--R - - b d x + (- - a b d - - b c d )x +--R 7 8 8 +--R + +--R 1 2 5 7 7 6 6 7 7 2 5 5 +--R (- -- a b d - -- a b c d - - b c d )x +--R 12 12 3 +--R + +--R 1 3 4 7 7 2 5 6 7 6 2 5 7 7 3 4 4 +--R (- -- a b d - -- a b c d - - a b c d - - b c d )x +--R 24 24 6 2 +--R + +--R 1 4 3 7 7 3 4 6 14 2 5 2 5 14 6 3 4 35 7 4 3 3 +--R (- -- a b d - -- a b c d - -- a b c d - -- a b c d - -- b c d )x +--R 66 66 33 11 11 +--R + +--R 1 5 2 7 7 4 3 6 7 3 4 2 5 7 2 5 3 4 35 6 4 3 +--R - --- a b d - --- a b c d - -- a b c d - -- a b c d - -- a b c d +--R 264 264 66 22 44 +--R + +--R 7 7 5 2 +--R - - b c d +--R 4 +--R * +--R 2 +--R x +--R + +--R 1 6 7 7 5 2 6 7 4 3 2 5 7 3 4 3 4 +--R - ---- a b d - ---- a b c d - --- a b c d - --- a b c d +--R 1716 1716 429 143 +--R + +--R 35 2 5 4 3 7 6 5 2 7 7 6 +--R - --- a b c d - -- a b c d - -- b c d +--R 286 26 13 +--R * +--R x +--R + +--R 1 7 7 1 6 6 1 5 2 2 5 1 4 3 3 4 5 3 4 4 3 +--R - ----- a d - ---- a b c d - --- a b c d - --- a b c d - --- a b c d +--R 24024 3432 858 286 572 +--R + +--R 1 2 5 5 2 1 6 6 1 7 7 +--R - -- a b c d - -- a b c d - -- b c +--R 52 26 14 +--R / +--R 22 14 21 13 2 20 12 3 19 11 4 18 10 +--R b x + 14a b x + 91a b x + 364a b x + 1001a b x +--R + +--R 5 17 9 6 16 8 7 15 7 8 14 6 9 13 5 +--R 2002a b x + 3003a b x + 3432a b x + 3003a b x + 2002a b x +--R + +--R 10 12 4 11 11 3 12 10 2 13 9 14 8 +--R 1001a b x + 364a b x + 91a b x + 14a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 717 + +--S 718 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R - 3432b d x + (- 3003a b d - 21021b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 2002a b d - 14014a b c d - 56056b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1001a b d - 7007a b c d - 28028a b c d - 84084b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 364a b d - 2548a b c d - 10192a b c d - 30576a b c d +--R + +--R 7 4 3 +--R - 76440b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 91a b d - 637a b c d - 2548a b c d - 7644a b c d +--R + +--R 6 4 3 7 5 2 +--R - 19110a b c d - 42042b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 14a b d - 98a b c d - 392a b c d - 1176a b c d - 2940a b c d +--R + +--R 6 5 2 7 6 +--R - 6468a b c d - 12936b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R - a d - 7a b c d - 28a b c d - 84a b c d - 210a b c d - 462a b c d +--R + +--R 6 6 7 7 +--R - 924a b c d - 1716b c +--R / +--R 22 14 21 13 2 20 12 3 19 11 +--R 24024b x + 336336a b x + 2186184a b x + 8744736a b x +--R + +--R 4 18 10 5 17 9 6 16 8 7 15 7 +--R 24048024a b x + 48096048a b x + 72144072a b x + 82450368a b x +--R + +--R 8 14 6 9 13 5 10 12 4 11 11 3 +--R 72144072a b x + 48096048a b x + 24048024a b x + 8744736a b x +--R + +--R 12 10 2 13 9 14 8 +--R 2186184a b x + 336336a b x + 24024a b +--R Type: Union(Expression(Integer),...) +--E 718 + +--S 719 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 719 + +--S 720 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 of 2952 +t0000:=(c+d*x)^7/(a+b*x)^16 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R / +--R 16 16 15 15 2 14 14 3 13 13 4 12 12 +--R b x + 16a b x + 120a b x + 560a b x + 1820a b x +--R + +--R 5 11 11 6 10 10 7 9 9 8 8 8 9 7 7 +--R 4368a b x + 8008a b x + 11440a b x + 12870a b x + 11440a b x +--R + +--R 10 6 6 11 5 5 12 4 4 13 3 3 14 2 2 +--R 8008a b x + 4368a b x + 1820a b x + 560a b x + 120a b x +--R + +--R 15 16 +--R 16a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 721 + +--S 722 of 2952 +r0000:=-1/15*(b*c-a*d)^7/(b^8*(a+b*x)^15)-_ + 1/2*d*(b*c-a*d)^6/(b^8*(a+b*x)^14)-_ + 21/13*d^2*(b*c-a*d)^5/(b^8*(a+b*x)^13)-_ + 35/12*d^3*(b*c-a*d)^4/(b^8*(a+b*x)^12)-_ + 35/11*d^4*(b*c-a*d)^3/(b^8*(a+b*x)^11)-_ + 21/10*d^5*(b*c-a*d)^2/(b^8*(a+b*x)^10)-_ + 7/9*d^6*(b*c-a*d)/(b^8*(a+b*x)^9)-1/8*d^7/(b^8*(a+b*x)^8) +--R +--R +--R (2) +--R 1 7 7 7 7 6 7 7 7 6 6 +--R - - b d x + (- -- a b d - - b c d )x +--R 8 72 9 +--R + +--R 7 2 5 7 7 6 6 21 7 2 5 5 +--R (- --- a b d - -- a b c d - -- b c d )x +--R 120 15 10 +--R + +--R 7 3 4 7 7 2 5 6 21 6 2 5 35 7 3 4 4 +--R (- --- a b d - -- a b c d - -- a b c d - -- b c d )x +--R 264 33 22 11 +--R + +--R 7 4 3 7 7 3 4 6 7 2 5 2 5 35 6 3 4 35 7 4 3 3 +--R (- --- a b d - -- a b c d - -- a b c d - -- a b c d - -- b c d )x +--R 792 99 22 33 12 +--R + +--R 7 5 2 7 7 4 3 6 21 3 4 2 5 35 2 5 3 4 +--R - ---- a b d - --- a b c d - --- a b c d - --- a b c d +--R 3432 429 286 143 +--R + +--R 35 6 4 3 21 7 5 2 +--R - -- a b c d - -- b c d +--R 52 13 +--R * +--R 2 +--R x +--R + +--R 1 6 7 1 5 2 6 3 4 3 2 5 5 3 4 3 4 +--R - ---- a b d - --- a b c d - --- a b c d - --- a b c d +--R 3432 429 286 143 +--R + +--R 5 2 5 4 3 3 6 5 2 1 7 6 +--R - -- a b c d - -- a b c d - - b c d +--R 52 13 2 +--R * +--R x +--R + +--R 1 7 7 1 6 6 1 5 2 2 5 1 4 3 3 4 +--R - ----- a d - ---- a b c d - ---- a b c d - --- a b c d +--R 51480 6435 1430 429 +--R + +--R 1 3 4 4 3 1 2 5 5 2 1 6 6 1 7 7 +--R - --- a b c d - -- a b c d - -- a b c d - -- b c +--R 156 65 30 15 +--R / +--R 23 15 22 14 2 21 13 3 20 12 4 19 11 +--R b x + 15a b x + 105a b x + 455a b x + 1365a b x +--R + +--R 5 18 10 6 17 9 7 16 8 8 15 7 9 14 6 +--R 3003a b x + 5005a b x + 6435a b x + 6435a b x + 5005a b x +--R + +--R 10 13 5 11 12 4 12 11 3 13 10 2 14 9 15 8 +--R 3003a b x + 1365a b x + 455a b x + 105a b x + 15a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 722 + +--S 723 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 6 7 7 6 6 +--R - 6435b d x + (- 5005a b d - 40040b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 3003a b d - 24024a b c d - 108108b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1365a b d - 10920a b c d - 49140a b c d - 163800b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 455a b d - 3640a b c d - 16380a b c d - 54600a b c d +--R + +--R 7 4 3 +--R - 150150b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 105a b d - 840a b c d - 3780a b c d - 12600a b c d +--R + +--R 6 4 3 7 5 2 +--R - 34650a b c d - 83160b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 15a b d - 120a b c d - 540a b c d - 1800a b c d - 4950a b c d +--R + +--R 6 5 2 7 6 +--R - 11880a b c d - 25740b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R - a d - 8a b c d - 36a b c d - 120a b c d - 330a b c d - 792a b c d +--R + +--R 6 6 7 7 +--R - 1716a b c d - 3432b c +--R / +--R 23 15 22 14 2 21 13 3 20 12 +--R 51480b x + 772200a b x + 5405400a b x + 23423400a b x +--R + +--R 4 19 11 5 18 10 6 17 9 +--R 70270200a b x + 154594440a b x + 257657400a b x +--R + +--R 7 16 8 8 15 7 9 14 6 +--R 331273800a b x + 331273800a b x + 257657400a b x +--R + +--R 10 13 5 11 12 4 12 11 3 13 10 2 +--R 154594440a b x + 70270200a b x + 23423400a b x + 5405400a b x +--R + +--R 14 9 15 8 +--R 772200a b x + 51480a b +--R Type: Union(Expression(Integer),...) +--E 723 + +--S 724 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 724 + +--S 725 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 725 + +)clear all + +--S 726 of 2952 +t0000:=(a+b*x)^m*(c+d*x)^10 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R * +--R m +--R (b x + a) +--R Type: Expression(Integer) +--E 726 + +--S 727 of 2952 +r0000:=(b*c-a*d)^10*(a+b*x)^(1+m)/(b^11*(1+m))+_ + 10*d*(b*c-a*d)^9*(a+b*x)^(2+m)/(b^11*(2+m))+_ + 45*d^2*(b*c-a*d)^8*(a+b*x)^(3+m)/(b^11*(3+m))+_ + 120*d^3*(b*c-a*d)^7*(a+b*x)^(4+m)/(b^11*(4+m))+_ + 210*d^4*(b*c-a*d)^6*(a+b*x)^(5+m)/(b^11*(5+m))+_ + 252*d^5*(b*c-a*d)^5*(a+b*x)^(6+m)/(b^11*(6+m))+_ + 210*d^6*(b*c-a*d)^4*(a+b*x)^(7+m)/(b^11*(7+m))+_ + 120*d^7*(b*c-a*d)^3*(a+b*x)^(8+m)/(b^11*(8+m))+_ + 45*d^8*(b*c-a*d)^2*(a+b*x)^(9+m)/(b^11*(9+m))+_ + 10*d^9*(b*c-a*d)*(a+b*x)^(10+m)/(b^11*(10+m))+_ + d^10*(a+b*x)^(11+m)/(b^11*(11+m)) +--R +--R +--R (2) +--R 10 10 10 9 10 8 10 7 10 6 10 5 +--R d m + 55d m + 1320d m + 18150d m + 157773d m + 902055d m +--R + +--R 10 4 10 3 10 2 10 10 +--R 3416930d m + 8409500d m + 12753576d m + 10628640d m + 3628800d +--R * +--R m + 11 +--R (b x + a) +--R + +--R 10 9 10 10 9 9 +--R (- 10a d + 10b c d )m + (- 560a d + 560b c d )m +--R + +--R 10 9 8 10 9 7 +--R (- 13650a d + 13650b c d )m + (- 190200a d + 190200b c d )m +--R + +--R 10 9 6 +--R (- 1672230a d + 1672230b c d )m +--R + +--R 10 9 5 +--R (- 9653280a d + 9653280b c d )m +--R + +--R 10 9 4 +--R (- 36862550a d + 36862550b c d )m +--R + +--R 10 9 3 +--R (- 91331800a d + 91331800b c d )m +--R + +--R 10 9 2 +--R (- 139262760a d + 139262760b c d )m +--R + +--R 10 9 10 9 +--R (- 116552160a d + 116552160b c d )m - 39916800a d + 39916800b c d +--R * +--R m + 10 +--R (b x + a) +--R + +--R 2 10 9 2 2 8 10 +--R (45a d - 90a b c d + 45b c d )m +--R + +--R 2 10 9 2 2 8 9 +--R (2565a d - 5130a b c d + 2565b c d )m +--R + +--R 2 10 9 2 2 8 8 +--R (63540a d - 127080a b c d + 63540b c d )m +--R + +--R 2 10 9 2 2 8 7 +--R (898290a d - 1796580a b c d + 898290b c d )m +--R + +--R 2 10 9 2 2 8 6 +--R (7999425a d - 15998850a b c d + 7999425b c d )m +--R + +--R 2 10 9 2 2 8 5 +--R (46695285a d - 93390570a b c d + 46695285b c d )m +--R + +--R 2 10 9 2 2 8 4 +--R (180021510a d - 360043020a b c d + 180021510b c d )m +--R + +--R 2 10 9 2 2 8 3 +--R (449614260a d - 899228520a b c d + 449614260b c d )m +--R + +--R 2 10 9 2 2 8 2 +--R (690085080a d - 1380170160a b c d + 690085080b c d )m +--R + +--R 2 10 9 2 2 8 +--R (580543200a d - 1161086400a b c d + 580543200b c d )m +--R + +--R 2 10 9 2 2 8 +--R 199584000a d - 399168000a b c d + 199584000b c d +--R * +--R m + 9 +--R (b x + a) +--R + +--R 3 10 2 9 2 2 8 3 3 7 10 +--R (- 120a d + 360a b c d - 360a b c d + 120b c d )m +--R + +--R 3 10 2 9 2 2 8 3 3 7 9 +--R (- 6960a d + 20880a b c d - 20880a b c d + 6960b c d )m +--R + +--R 3 10 2 9 2 2 8 3 3 7 8 +--R (- 175320a d + 525960a b c d - 525960a b c d + 175320b c d )m +--R + +--R 3 10 2 9 2 2 8 +--R - 2517840a d + 7553520a b c d - 7553520a b c d +--R + +--R 3 3 7 +--R 2517840b c d +--R * +--R 7 +--R m +--R + +--R 3 10 2 9 2 2 8 +--R - 22748040a d + 68244120a b c d - 68244120a b c d +--R + +--R 3 3 7 +--R 22748040b c d +--R * +--R 6 +--R m +--R + +--R 3 10 2 9 2 2 8 +--R - 134522640a d + 403567920a b c d - 403567920a b c d +--R + +--R 3 3 7 +--R 134522640b c d +--R * +--R 5 +--R m +--R + +--R 3 10 2 9 2 2 8 +--R - 524563080a d + 1573689240a b c d - 1573689240a b c d +--R + +--R 3 3 7 +--R 524563080b c d +--R * +--R 4 +--R m +--R + +--R 3 10 2 9 2 2 8 +--R - 1322982960a d + 3968948880a b c d - 3968948880a b c d +--R + +--R 3 3 7 +--R 1322982960b c d +--R * +--R 3 +--R m +--R + +--R 3 10 2 9 2 2 8 +--R - 2047105440a d + 6141316320a b c d - 6141316320a b c d +--R + +--R 3 3 7 +--R 2047105440b c d +--R * +--R 2 +--R m +--R + +--R 3 10 2 9 2 2 8 +--R - 1733313600a d + 5199940800a b c d - 5199940800a b c d +--R + +--R 3 3 7 +--R 1733313600b c d +--R * +--R m +--R + +--R 3 10 2 9 2 2 8 +--R - 598752000a d + 1796256000a b c d - 1796256000a b c d +--R + +--R 3 3 7 +--R 598752000b c d +--R * +--R m + 8 +--R (b x + a) +--R + +--R 4 10 3 9 2 2 2 8 3 3 7 4 4 6 10 +--R (210a d - 840a b c d + 1260a b c d - 840a b c d + 210b c d )m +--R + +--R 4 10 3 9 2 2 2 8 3 3 7 +--R 12390a d - 49560a b c d + 74340a b c d - 49560a b c d +--R + +--R 4 4 6 +--R 12390b c d +--R * +--R 9 +--R m +--R + +--R 4 10 3 9 2 2 2 8 3 3 7 +--R 317520a d - 1270080a b c d + 1905120a b c d - 1270080a b c d +--R + +--R 4 4 6 +--R 317520b c d +--R * +--R 8 +--R m +--R + +--R 4 10 3 9 2 2 2 8 +--R 4638060a d - 18552240a b c d + 27828360a b c d +--R + +--R 3 3 7 4 4 6 +--R - 18552240a b c d + 4638060b c d +--R * +--R 7 +--R m +--R + +--R 4 10 3 9 2 2 2 8 +--R 42592410a d - 170369640a b c d + 255554460a b c d +--R + +--R 3 3 7 4 4 6 +--R - 170369640a b c d + 42592410b c d +--R * +--R 6 +--R m +--R + +--R 4 10 3 9 2 2 2 8 +--R 255740310a d - 1022961240a b c d + 1534441860a b c d +--R + +--R 3 3 7 4 4 6 +--R - 1022961240a b c d + 255740310b c d +--R * +--R 5 +--R m +--R + +--R 4 10 3 9 2 2 2 8 +--R 1011120180a d - 4044480720a b c d + 6066721080a b c d +--R + +--R 3 3 7 4 4 6 +--R - 4044480720a b c d + 1011120180b c d +--R * +--R 4 +--R m +--R + +--R 4 10 3 9 2 2 2 8 +--R 2581262040a d - 10325048160a b c d + 15487572240a b c d +--R + +--R 3 3 7 4 4 6 +--R - 10325048160a b c d + 2581262040b c d +--R * +--R 3 +--R m +--R + +--R 4 10 3 9 2 2 2 8 +--R 4035361680a d - 16141446720a b c d + 24212170080a b c d +--R + +--R 3 3 7 4 4 6 +--R - 16141446720a b c d + 4035361680b c d +--R * +--R 2 +--R m +--R + +--R 4 10 3 9 2 2 2 8 +--R 3445243200a d - 13780972800a b c d + 20671459200a b c d +--R + +--R 3 3 7 4 4 6 +--R - 13780972800a b c d + 3445243200b c d +--R * +--R m +--R + +--R 4 10 3 9 2 2 2 8 +--R 1197504000a d - 4790016000a b c d + 7185024000a b c d +--R + +--R 3 3 7 4 4 6 +--R - 4790016000a b c d + 1197504000b c d +--R * +--R m + 7 +--R (b x + a) +--R + +--R 5 10 4 9 3 2 2 8 2 3 3 7 +--R - 252a d + 1260a b c d - 2520a b c d + 2520a b c d +--R + +--R 4 4 6 5 5 5 +--R - 1260a b c d + 252b c d +--R * +--R 10 +--R m +--R + +--R 5 10 4 9 3 2 2 8 2 3 3 7 +--R - 15120a d + 75600a b c d - 151200a b c d + 151200a b c d +--R + +--R 4 4 6 5 5 5 +--R - 75600a b c d + 15120b c d +--R * +--R 9 +--R m +--R + +--R 5 10 4 9 3 2 2 8 +--R - 394380a d + 1971900a b c d - 3943800a b c d +--R + +--R 2 3 3 7 4 4 6 5 5 5 +--R 3943800a b c d - 1971900a b c d + 394380b c d +--R * +--R 8 +--R m +--R + +--R 5 10 4 9 3 2 2 8 +--R - 5866560a d + 29332800a b c d - 58665600a b c d +--R + +--R 2 3 3 7 4 4 6 5 5 5 +--R 58665600a b c d - 29332800a b c d + 5866560b c d +--R * +--R 7 +--R m +--R + +--R 5 10 4 9 3 2 2 8 +--R - 54871236a d + 274356180a b c d - 548712360a b c d +--R + +--R 2 3 3 7 4 4 6 5 5 5 +--R 548712360a b c d - 274356180a b c d + 54871236b c d +--R * +--R 6 +--R m +--R + +--R 5 10 4 9 3 2 2 8 +--R - 335437200a d + 1677186000a b c d - 3354372000a b c d +--R + +--R 2 3 3 7 4 4 6 5 5 5 +--R 3354372000a b c d - 1677186000a b c d + 335437200b c d +--R * +--R 5 +--R m +--R + +--R 5 10 4 9 3 2 2 8 +--R - 1348939620a d + 6744698100a b c d - 13489396200a b c d +--R + +--R 2 3 3 7 4 4 6 5 5 5 +--R 13489396200a b c d - 6744698100a b c d + 1348939620b c d +--R * +--R 4 +--R m +--R + +--R 5 10 4 9 3 2 2 8 +--R - 3497286240a d + 17486431200a b c d - 34972862400a b c d +--R + +--R 2 3 3 7 4 4 6 5 5 5 +--R 34972862400a b c d - 17486431200a b c d + 3497286240b c d +--R * +--R 3 +--R m +--R + +--R 5 10 4 9 3 2 2 8 +--R - 5541317712a d + 27706588560a b c d - 55413177120a b c d +--R + +--R 2 3 3 7 4 4 6 5 5 5 +--R 55413177120a b c d - 27706588560a b c d + 5541317712b c d +--R * +--R 2 +--R m +--R + +--R 5 10 4 9 3 2 2 8 +--R - 4783423680a d + 23917118400a b c d - 47834236800a b c d +--R + +--R 2 3 3 7 4 4 6 5 5 5 +--R 47834236800a b c d - 23917118400a b c d + 4783423680b c d +--R * +--R m +--R + +--R 5 10 4 9 3 2 2 8 +--R - 1676505600a d + 8382528000a b c d - 16765056000a b c d +--R + +--R 2 3 3 7 4 4 6 5 5 5 +--R 16765056000a b c d - 8382528000a b c d + 1676505600b c d +--R * +--R m + 6 +--R (b x + a) +--R + +--R 6 10 5 9 4 2 2 8 3 3 3 7 +--R 210a d - 1260a b c d + 3150a b c d - 4200a b c d +--R + +--R 2 4 4 6 5 5 5 6 6 4 +--R 3150a b c d - 1260a b c d + 210b c d +--R * +--R 10 +--R m +--R + 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+--R 6 3 3 7 5 4 4 6 4 5 5 5 +--R - 23077088160a b c d + 34615632240a b c d - 34615632240a b c d +--R + +--R 3 6 6 4 2 7 7 3 8 8 2 +--R 23077088160a b c d - 9890180640a b c d + 2472545160a b c d +--R + +--R 9 9 +--R - 274727240b c d +--R * +--R 3 +--R m +--R + +--R 9 10 8 9 7 2 2 8 +--R 503126280a d - 4528136520a b c d + 18112546080a b c d +--R + +--R 6 3 3 7 5 4 4 6 4 5 5 5 +--R - 42262607520a b c d + 63393911280a b c d - 63393911280a b c d +--R + +--R 3 6 6 4 2 7 7 3 8 8 2 +--R 42262607520a b c d - 18112546080a b c d + 4528136520a b c d +--R + +--R 9 9 +--R - 503126280b c d +--R * +--R 2 +--R m +--R + +--R 9 10 8 9 7 2 2 8 +--R 502927200a d - 4526344800a b c d + 18105379200a b c d +--R + +--R 6 3 3 7 5 4 4 6 4 5 5 5 +--R - 42245884800a b c d + 63368827200a b c d - 63368827200a b c d +--R + +--R 3 6 6 4 2 7 7 3 8 8 2 +--R 42245884800a b c d - 18105379200a b c d + 4526344800a b c d +--R + +--R 9 9 +--R - 502927200b c d +--R * +--R m +--R + +--R 9 10 8 9 7 2 2 8 +--R 199584000a d - 1796256000a b c d + 7185024000a b c d +--R + +--R 6 3 3 7 5 4 4 6 4 5 5 5 +--R - 16765056000a b c d + 25147584000a b c d - 25147584000a b c d +--R + +--R 3 6 6 4 2 7 7 3 8 8 2 +--R 16765056000a b c d - 7185024000a b c d + 1796256000a b c d +--R + +--R 9 9 +--R - 199584000b c d +--R * +--R m + 2 +--R (b x + a) +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R - a d + 10a b c d - 45a b c d + 120a b c d - 210a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 +--R 252a b c d - 210a b c d + 120a b c d - 45a b c d + 10a b c d +--R + +--R 10 10 +--R - b c +--R * +--R 10 +--R m +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 65a d + 650a b c d - 2925a b c d + 7800a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R - 13650a b c d + 16380a b c d - 13650a b c d + 7800a b c d +--R + +--R 2 8 8 2 9 9 10 10 +--R - 2925a b c d + 650a b c d - 65b c +--R * +--R 9 +--R m +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 1860a d + 18600a b c d - 83700a b c d + 223200a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 +--R - 390600a b c d + 468720a b c d - 390600a b c d +--R + +--R 3 7 7 3 2 8 8 2 9 9 10 10 +--R 223200a b c d - 83700a b c d + 18600a b c d - 1860b c +--R * +--R 8 +--R m +--R + +--R 10 10 9 9 8 2 2 8 +--R - 30810a d + 308100a b c d - 1386450a b c d +--R + +--R 7 3 3 7 6 4 4 6 5 5 5 5 +--R 3697200a b c d - 6470100a b c d + 7764120a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 6470100a b c d + 3697200a b c d - 1386450a b c d +--R + +--R 9 9 10 10 +--R 308100a b c d - 30810b c +--R * +--R 7 +--R m +--R + +--R 10 10 9 9 8 2 2 8 +--R - 326613a d + 3266130a b c d - 14697585a b c d +--R + +--R 7 3 3 7 6 4 4 6 5 5 5 5 +--R 39193560a b c d - 68588730a b c d + 82306476a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 68588730a b c d + 39193560a b c d - 14697585a b c d +--R + +--R 9 9 10 10 +--R 3266130a b c d - 326613b c +--R * +--R 6 +--R m +--R + +--R 10 10 9 9 8 2 2 8 +--R - 2310945a d + 23109450a b c d - 103992525a b c d +--R + +--R 7 3 3 7 6 4 4 6 5 5 5 5 +--R 277313400a b c d - 485298450a b c d + 582358140a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 485298450a b c d + 277313400a b c d - 103992525a b c d +--R + +--R 9 9 10 10 +--R 23109450a b c d - 2310945b c +--R * +--R 5 +--R m +--R + +--R 10 10 9 9 8 2 2 8 +--R - 11028590a d + 110285900a b c d - 496286550a b c d +--R + +--R 7 3 3 7 6 4 4 6 5 5 5 5 +--R 1323430800a b c d - 2316003900a b c d + 2779204680a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 2316003900a b c d + 1323430800a b c d - 496286550a b c d +--R + +--R 9 9 10 10 +--R 110285900a b c d - 11028590b c +--R * +--R 4 +--R m +--R + +--R 10 10 9 9 8 2 2 8 +--R - 34967140a d + 349671400a b c d - 1573521300a b c d +--R + +--R 7 3 3 7 6 4 4 6 5 5 5 5 +--R 4196056800a b c d - 7343099400a b c d + 8811719280a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 7343099400a b c d + 4196056800a b c d - 1573521300a b c d +--R + +--R 9 9 10 10 +--R 349671400a b c d - 34967140b c +--R * +--R 3 +--R m +--R + +--R 10 10 9 9 8 2 2 8 +--R - 70290936a d + 702909360a b c d - 3163092120a b c d +--R + +--R 7 3 3 7 6 4 4 6 5 5 5 5 +--R 8434912320a b c d - 14761096560a b c d + 17713315872a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 14761096560a b c d + 8434912320a b c d - 3163092120a b c d +--R + +--R 9 9 10 10 +--R 702909360a b c d - 70290936b c +--R * +--R 2 +--R m +--R + +--R 10 10 9 9 8 2 2 8 +--R - 80627040a d + 806270400a b c d - 3628216800a b c d +--R + +--R 7 3 3 7 6 4 4 6 5 5 5 5 +--R 9675244800a b c d - 16931678400a b c d + 20318014080a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 16931678400a b c d + 9675244800a b c d - 3628216800a b c d +--R + +--R 9 9 10 10 +--R 806270400a b c d - 80627040b c +--R * +--R m +--R + +--R 10 10 9 9 8 2 2 8 +--R - 39916800a d + 399168000a b c d - 1796256000a b c d +--R + +--R 7 3 3 7 6 4 4 6 5 5 5 5 +--R 4790016000a b c d - 8382528000a b c d + 10059033600a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 8382528000a b c d + 4790016000a b c d - 1796256000a b c d +--R + +--R 9 9 10 10 +--R 399168000a b c d - 39916800b c +--R * +--R m + 1 +--R (b x + a) +--R / +--R 11 11 11 10 11 9 11 8 11 7 11 6 +--R b m + 66b m + 1925b m + 32670b m + 357423b m + 2637558b m +--R + +--R 11 5 11 4 11 3 11 2 +--R 13339535b m + 45995730b m + 105258076b m + 150917976b m +--R + +--R 11 11 +--R 120543840b m + 39916800b +--R Type: Expression(Integer) +--E 729 + +--S 730 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 10 10 10 10 9 9 10 2 8 8 10 3 7 7 10 4 6 6 +--R b d x + 10b c d x + 45b c d x + 120b c d x + 210b c d x +--R + +--R 10 5 5 5 10 6 4 4 10 7 3 3 10 8 2 2 10 9 +--R 252b c d x + 210b c d x + 120b c d x + 45b c d x + 10b c d x +--R + +--R 10 10 +--R b c +--R * +--R m log(b x + a) +--R %e +--R + +--R 10 m + 10 10 9 m + 9 +--R - d (b x + a) + (10a d - 10b c d )(b x + a) +--R + +--R 2 10 9 2 2 8 m + 8 +--R (- 45a d + 90a b c d - 45b c d )(b x + a) +--R + +--R 3 10 2 9 2 2 8 3 3 7 m + 7 +--R (120a d - 360a b c d + 360a b c d - 120b c d )(b x + a) +--R + +--R 4 10 3 9 2 2 2 8 3 3 7 4 4 6 +--R (- 210a d + 840a b c d - 1260a b c d + 840a b c d - 210b c d ) +--R * +--R m + 6 +--R (b x + a) +--R + +--R 5 10 4 9 3 2 2 8 2 3 3 7 4 4 6 +--R 252a d - 1260a b c d + 2520a b c d - 2520a b c d + 1260a b c d +--R + +--R 5 5 5 +--R - 252b c d +--R * +--R m + 5 +--R (b x + a) +--R + +--R 6 10 5 9 4 2 2 8 3 3 3 7 +--R - 210a d + 1260a b c d - 3150a b c d + 4200a b c d +--R + +--R 2 4 4 6 5 5 5 6 6 4 +--R - 3150a b c d + 1260a b c d - 210b c d +--R * +--R m + 4 +--R (b x + a) +--R + +--R 7 10 6 9 5 2 2 8 4 3 3 7 3 4 4 6 +--R 120a d - 840a b c d + 2520a b c d - 4200a b c d + 4200a b c d +--R + +--R 2 5 5 5 6 6 4 7 7 3 +--R - 2520a b c d + 840a b c d - 120b c d +--R * +--R m + 3 +--R (b x + a) +--R + +--R 8 10 7 9 6 2 2 8 5 3 3 7 4 4 4 6 +--R - 45a d + 360a b c d - 1260a b c d + 2520a b c d - 3150a b c d +--R + +--R 3 5 5 5 2 6 6 4 7 7 3 8 8 2 +--R 2520a b c d - 1260a b c d + 360a b c d - 45b c d +--R * +--R m + 2 +--R (b x + a) +--R + +--R 9 10 8 9 7 2 2 8 6 3 3 7 5 4 4 6 +--R 10a d - 90a b c d + 360a b c d - 840a b c d + 1260a b c d +--R + +--R 4 5 5 5 3 6 6 4 2 7 7 3 8 8 2 9 9 +--R - 1260a b c d + 840a b c d - 360a b c d + 90a b c d - 10b c d +--R * +--R m + 1 +--R (b x + a) +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R - a d + 10a b c d - 45a b c d + 120a b c d - 210a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 +--R 252a b c d - 210a b c d + 120a b c d - 45a b c d + 10a b c d +--R + +--R 10 10 +--R - b c +--R * +--R m +--R (b x + a) +--R / +--R 10 +--R b +--R Type: Expression(Integer) +--E 730 + +)clear all + +--S 731 of 2952 +t0000:=(a+b*x)^12*(c+d*x)^10 +--R +--R +--R (1) +--R 12 10 22 11 10 12 9 21 +--R b d x + (12a b d + 10b c d )x +--R + +--R 2 10 10 11 9 12 2 8 20 +--R (66a b d + 120a b c d + 45b c d )x +--R + +--R 3 9 10 2 10 9 11 2 8 12 3 7 19 +--R (220a b d + 660a b c d + 540a b c d + 120b c d )x +--R + +--R 4 8 10 3 9 9 2 10 2 8 11 3 7 12 4 6 18 +--R (495a b d + 2200a b c d + 2970a b c d + 1440a b c d + 210b c d )x +--R + +--R 5 7 10 4 8 9 3 9 2 8 2 10 3 7 +--R 792a b d + 4950a b c d + 9900a b c d + 7920a b c d +--R + +--R 11 4 6 12 5 5 +--R 2520a b c d + 252b c d +--R * +--R 17 +--R x +--R + +--R 6 6 10 5 7 9 4 8 2 8 3 9 3 7 +--R 924a b d + 7920a b c d + 22275a b c d + 26400a b c d +--R + +--R 2 10 4 6 11 5 5 12 6 4 +--R 13860a b c d + 3024a b c d + 210b c d +--R * +--R 16 +--R x +--R + +--R 7 5 10 6 6 9 5 7 2 8 4 8 3 7 +--R 792a b d + 9240a b c d + 35640a b c d + 59400a b c d +--R + +--R 3 9 4 6 2 10 5 5 11 6 4 12 7 3 +--R 46200a b c d + 16632a b c d + 2520a b c d + 120b c d +--R * +--R 15 +--R x +--R + +--R 8 4 10 7 5 9 6 6 2 8 5 7 3 7 +--R 495a b d + 7920a b c d + 41580a b c d + 95040a b c d +--R + +--R 4 8 4 6 3 9 5 5 2 10 6 4 11 7 3 +--R 103950a b c d + 55440a b c d + 13860a b c d + 1440a b c d +--R + +--R 12 8 2 +--R 45b c d +--R * +--R 14 +--R x +--R + +--R 9 3 10 8 4 9 7 5 2 8 6 6 3 7 +--R 220a b d + 4950a b c d + 35640a b c d + 110880a b c d +--R + +--R 5 7 4 6 4 8 5 5 3 9 6 4 2 10 7 3 +--R 166320a b c d + 124740a b c d + 46200a b c d + 7920a b c d +--R + +--R 11 8 2 12 9 +--R 540a b c d + 10b c d +--R * +--R 13 +--R x +--R + +--R 10 2 10 9 3 9 8 4 2 8 7 5 3 7 +--R 66a b d + 2200a b c d + 22275a b c d + 95040a b c d +--R + +--R 6 6 4 6 5 7 5 5 4 8 6 4 3 9 7 3 +--R 194040a b c d + 199584a b c d + 103950a b c d + 26400a b c d +--R + +--R 2 10 8 2 11 9 12 10 +--R 2970a b c d + 120a b c d + b c +--R * +--R 12 +--R x +--R + +--R 11 10 10 2 9 9 3 2 8 8 4 3 7 +--R 12a b d + 660a b c d + 9900a b c d + 59400a b c d +--R + +--R 7 5 4 6 6 6 5 5 5 7 6 4 4 8 7 3 +--R 166320a b c d + 232848a b c d + 166320a b c d + 59400a b c d +--R + +--R 3 9 8 2 2 10 9 11 10 +--R 9900a b c d + 660a b c d + 12a b c +--R * +--R 11 +--R x +--R + +--R 12 10 11 9 10 2 2 8 9 3 3 7 8 4 4 6 +--R a d + 120a b c d + 2970a b c d + 26400a b c d + 103950a b c d +--R + +--R 7 5 5 5 6 6 6 4 5 7 7 3 4 8 8 2 +--R 199584a b c d + 194040a b c d + 95040a b c d + 22275a b c d +--R + +--R 3 9 9 2 10 10 +--R 2200a b c d + 66a b c +--R * +--R 10 +--R x +--R + +--R 12 9 11 2 8 10 2 3 7 9 3 4 6 +--R 10a c d + 540a b c d + 7920a b c d + 46200a b c d +--R + +--R 8 4 5 5 7 5 6 4 6 6 7 3 5 7 8 2 +--R 124740a b c d + 166320a b c d + 110880a b c d + 35640a b c d +--R + +--R 4 8 9 3 9 10 +--R 4950a b c d + 220a b c +--R * +--R 9 +--R x +--R + +--R 12 2 8 11 3 7 10 2 4 6 9 3 5 5 +--R 45a c d + 1440a b c d + 13860a b c d + 55440a b c d +--R + +--R 8 4 6 4 7 5 7 3 6 6 8 2 5 7 9 4 8 10 +--R 103950a b c d + 95040a b c d + 41580a b c d + 7920a b c d + 495a b c +--R * +--R 8 +--R x +--R + +--R 12 3 7 11 4 6 10 2 5 5 9 3 6 4 +--R 120a c d + 2520a b c d + 16632a b c d + 46200a b c d +--R + +--R 8 4 7 3 7 5 8 2 6 6 9 5 7 10 +--R 59400a b c d + 35640a b c d + 9240a b c d + 792a b c +--R * +--R 7 +--R x +--R + +--R 12 4 6 11 5 5 10 2 6 4 9 3 7 3 +--R 210a c d + 3024a b c d + 13860a b c d + 26400a b c d +--R + +--R 8 4 8 2 7 5 9 6 6 10 +--R 22275a b c d + 7920a b c d + 924a b c +--R * +--R 6 +--R x +--R + +--R 12 5 5 11 6 4 10 2 7 3 9 3 8 2 8 4 9 +--R 252a c d + 2520a b c d + 7920a b c d + 9900a b c d + 4950a b c d +--R + +--R 7 5 10 +--R 792a b c +--R * +--R 5 +--R x +--R + +--R 12 6 4 11 7 3 10 2 8 2 9 3 9 8 4 10 4 +--R (210a c d + 1440a b c d + 2970a b c d + 2200a b c d + 495a b c )x +--R + +--R 12 7 3 11 8 2 10 2 9 9 3 10 3 +--R (120a c d + 540a b c d + 660a b c d + 220a b c )x +--R + +--R 12 8 2 11 9 10 2 10 2 12 9 11 10 12 10 +--R (45a c d + 120a b c d + 66a b c )x + (10a c d + 12a b c )x + a c +--R Type: Polynomial(Integer) +--E 731 + +--S 732 of 2952 +r0000:=1/13*(b*c-a*d)^10*(a+b*x)^13/b^11+_ + 5/7*d*(b*c-a*d)^9*(a+b*x)^14/b^11+_ + 3*d^2*(b*c-a*d)^8*(a+b*x)^15/b^11+_ + 15/2*d^3*(b*c-a*d)^7*(a+b*x)^16/b^11+_ + 210/17*d^4*(b*c-a*d)^6*(a+b*x)^17/b^11+_ + 14*d^5*(b*c-a*d)^5*(a+b*x)^18/b^11+_ + 210/19*d^6*(b*c-a*d)^4*(a+b*x)^19/b^11+_ + 6*d^7*(b*c-a*d)^3*(a+b*x)^20/b^11+_ + 15/7*d^8*(b*c-a*d)^2*(a+b*x)^21/b^11+_ + 5/11*d^9*(b*c-a*d)*(a+b*x)^22/b^11+1/23*d^10*(a+b*x)^23/b^11 +--R +--R +--R (2) +--R 1 23 10 23 6 22 10 5 23 9 22 +--R -- b d x + (-- a b d + -- b c d )x +--R 23 11 11 +--R + +--R 22 2 21 10 40 22 9 15 23 2 8 21 +--R (-- a b d + -- a b c d + -- b c d )x +--R 7 7 7 +--R + +--R 3 20 10 2 21 9 22 2 8 23 3 7 20 +--R (11a b d + 33a b c d + 27a b c d + 6b c d )x +--R + +--R 495 4 19 10 2200 3 20 9 2970 2 21 2 8 1440 22 3 7 +--R --- a b d + ---- a b c d + ---- a b c d + ---- a b c d +--R 19 19 19 19 +--R + +--R 210 23 4 6 +--R --- b c d +--R 19 +--R * +--R 19 +--R x +--R + +--R 5 18 10 4 19 9 3 20 2 8 2 21 3 7 +--R 44a b d + 275a b c d + 550a b c d + 440a b c d +--R + +--R 22 4 6 23 5 5 +--R 140a b c d + 14b c d +--R * +--R 18 +--R x +--R + +--R 924 6 17 10 7920 5 18 9 22275 4 19 2 8 26400 3 20 3 7 +--R --- a b d + ---- a b c d + ----- a b c d + ----- a b c d +--R 17 17 17 17 +--R + +--R 13860 2 21 4 6 3024 22 5 5 210 23 6 4 +--R ----- a b c d + ---- a b c d + --- b c d +--R 17 17 17 +--R * +--R 17 +--R x +--R + +--R 99 7 16 10 1155 6 17 9 4455 5 18 2 8 7425 4 19 3 7 +--R -- a b d + ---- a b c d + ---- a b c d + ---- a b c d +--R 2 2 2 2 +--R + +--R 5775 3 20 4 6 2079 2 21 5 5 315 22 6 4 15 23 7 3 +--R ---- a b c d + ---- a b c d + --- a b c d + -- b c d +--R 2 2 2 2 +--R * +--R 16 +--R x +--R + +--R 8 15 10 7 16 9 6 17 2 8 5 18 3 7 +--R 33a b d + 528a b c d + 2772a b c d + 6336a b c d +--R + +--R 4 19 4 6 3 20 5 5 2 21 6 4 22 7 3 23 8 2 +--R 6930a b c d + 3696a b c d + 924a b c d + 96a b c d + 3b c d +--R * +--R 15 +--R x +--R + +--R 110 9 14 10 2475 8 15 9 17820 7 16 2 8 6 17 3 7 +--R --- a b d + ---- a b c d + ----- a b c d + 7920a b c d +--R 7 7 7 +--R + +--R 5 18 4 6 4 19 5 5 3 20 6 4 3960 2 21 7 3 +--R 11880a b c d + 8910a b c d + 3300a b c d + ---- a b c d +--R 7 +--R + +--R 270 22 8 2 5 23 9 +--R --- a b c d + - b c d +--R 7 7 +--R * +--R 14 +--R x +--R + +--R 66 10 13 10 2200 9 14 9 22275 8 15 2 8 95040 7 16 3 7 +--R -- a b d + ---- a b c d + ----- a b c d + ----- a b c d +--R 13 13 13 13 +--R + +--R 194040 6 17 4 6 199584 5 18 5 5 103950 4 19 6 4 +--R ------ a b c d + ------ a b c d + ------ a b c d +--R 13 13 13 +--R + +--R 26400 3 20 7 3 2970 2 21 8 2 120 22 9 1 23 10 +--R ----- a b c d + ---- a b c d + --- a b c d + -- b c +--R 13 13 13 13 +--R * +--R 13 +--R x +--R + +--R 11 12 10 10 13 9 9 14 2 8 8 15 3 7 +--R a b d + 55a b c d + 825a b c d + 4950a b c d +--R + +--R 7 16 4 6 6 17 5 5 5 18 6 4 4 19 7 3 +--R 13860a b c d + 19404a b c d + 13860a b c d + 4950a b c d +--R + +--R 3 20 8 2 2 21 9 22 10 +--R 825a b c d + 55a b c d + a b c +--R * +--R 12 +--R x +--R + +--R 1 12 11 10 120 11 12 9 10 13 2 8 9 14 3 7 +--R -- a b d + --- a b c d + 270a b c d + 2400a b c d +--R 11 11 +--R + +--R 8 15 4 6 7 16 5 5 6 17 6 4 5 18 7 3 +--R 9450a b c d + 18144a b c d + 17640a b c d + 8640a b c d +--R + +--R 4 19 8 2 3 20 9 2 21 10 +--R 2025a b c d + 200a b c d + 6a b c +--R * +--R 11 +--R x +--R + +--R 12 11 9 11 12 2 8 10 13 3 7 9 14 4 6 +--R a b c d + 54a b c d + 792a b c d + 4620a b c d +--R + +--R 8 15 5 5 7 16 6 4 6 17 7 3 5 18 8 2 +--R 12474a b c d + 16632a b c d + 11088a b c d + 3564a b c d +--R + +--R 4 19 9 3 20 10 +--R 495a b c d + 22a b c +--R * +--R 10 +--R x +--R + +--R 12 11 2 8 11 12 3 7 10 13 4 6 9 14 5 5 +--R 5a b c d + 160a b c d + 1540a b c d + 6160a b c d +--R + +--R 8 15 6 4 7 16 7 3 6 17 8 2 5 18 9 +--R 11550a b c d + 10560a b c d + 4620a b c d + 880a b c d +--R + +--R 4 19 10 +--R 55a b c +--R * +--R 9 +--R x +--R + +--R 12 11 3 7 11 12 4 6 10 13 5 5 9 14 6 4 +--R 15a b c d + 315a b c d + 2079a b c d + 5775a b c d +--R + +--R 8 15 7 3 7 16 8 2 6 17 9 5 18 10 +--R 7425a b c d + 4455a b c d + 1155a b c d + 99a b c +--R * +--R 8 +--R x +--R + +--R 12 11 4 6 11 12 5 5 10 13 6 4 26400 9 14 7 3 +--R 30a b c d + 432a b c d + 1980a b c d + ----- a b c d +--R 7 +--R + +--R 22275 8 15 8 2 7920 7 16 9 6 17 10 +--R ----- a b c d + ---- a b c d + 132a b c +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 12 11 5 5 11 12 6 4 10 13 7 3 9 14 8 2 +--R 42a b c d + 420a b c d + 1320a b c d + 1650a b c d +--R + +--R 8 15 9 7 16 10 +--R 825a b c d + 132a b c +--R * +--R 6 +--R x +--R + +--R 12 11 6 4 11 12 7 3 10 13 8 2 9 14 9 +--R 42a b c d + 288a b c d + 594a b c d + 440a b c d +--R + +--R 8 15 10 +--R 99a b c +--R * +--R 5 +--R x +--R + +--R 12 11 7 3 11 12 8 2 10 13 9 9 14 10 4 +--R (30a b c d + 135a b c d + 165a b c d + 55a b c )x +--R + +--R 12 11 8 2 11 12 9 10 13 10 3 +--R (15a b c d + 40a b c d + 22a b c )x +--R + +--R 12 11 9 11 12 10 2 12 11 10 1 23 10 +--R (5a b c d + 6a b c )x + a b c x + -------- a d +--R 14872858 +--R + +--R 1 22 9 1 21 2 2 8 1 20 3 3 7 5 19 4 4 6 +--R - ------ a b c d + ----- a b c d - ---- a b c d + ---- a b c d +--R 646646 58786 8398 8398 +--R + +--R 1 18 5 5 5 3 17 6 6 4 3 16 7 7 3 3 15 8 8 2 +--R - --- a b c d + --- a b c d - --- a b c d + -- a b c d +--R 442 442 182 91 +--R + +--R 5 14 9 9 1 13 10 10 +--R - -- a b c d + -- a b c +--R 91 13 +--R / +--R 11 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 732 + +--S 733 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 12 10 23 6 11 10 5 12 9 22 +--R -- b d x + (-- a b d + -- b c d )x +--R 23 11 11 +--R + +--R 22 2 10 10 40 11 9 15 12 2 8 21 +--R (-- a b d + -- a b c d + -- b c d )x +--R 7 7 7 +--R + +--R 3 9 10 2 10 9 11 2 8 12 3 7 20 +--R (11a b d + 33a b c d + 27a b c d + 6b c d )x +--R + +--R 495 4 8 10 2200 3 9 9 2970 2 10 2 8 1440 11 3 7 +--R --- a b d + ---- a b c d + ---- a b c d + ---- a b c d +--R 19 19 19 19 +--R + +--R 210 12 4 6 +--R --- b c d +--R 19 +--R * +--R 19 +--R x +--R + +--R 5 7 10 4 8 9 3 9 2 8 2 10 3 7 11 4 6 +--R 44a b d + 275a b c d + 550a b c d + 440a b c d + 140a b c d +--R + +--R 12 5 5 +--R 14b c d +--R * +--R 18 +--R x +--R + +--R 924 6 6 10 7920 5 7 9 22275 4 8 2 8 26400 3 9 3 7 +--R --- a b d + ---- a b c d + ----- a b c d + ----- a b c d +--R 17 17 17 17 +--R + +--R 13860 2 10 4 6 3024 11 5 5 210 12 6 4 +--R ----- a b c d + ---- a b c d + --- b c d +--R 17 17 17 +--R * +--R 17 +--R x +--R + +--R 99 7 5 10 1155 6 6 9 4455 5 7 2 8 7425 4 8 3 7 +--R -- a b d + ---- a b c d + ---- a b c d + ---- a b c d +--R 2 2 2 2 +--R + +--R 5775 3 9 4 6 2079 2 10 5 5 315 11 6 4 15 12 7 3 +--R ---- a b c d + ---- a b c d + --- a b c d + -- b c d +--R 2 2 2 2 +--R * +--R 16 +--R x +--R + +--R 8 4 10 7 5 9 6 6 2 8 5 7 3 7 4 8 4 6 +--R 33a b d + 528a b c d + 2772a b c d + 6336a b c d + 6930a b c d +--R + +--R 3 9 5 5 2 10 6 4 11 7 3 12 8 2 +--R 3696a b c d + 924a b c d + 96a b c d + 3b c d +--R * +--R 15 +--R x +--R + +--R 110 9 3 10 2475 8 4 9 17820 7 5 2 8 6 6 3 7 +--R --- a b d + ---- a b c d + ----- a b c d + 7920a b c d +--R 7 7 7 +--R + +--R 5 7 4 6 4 8 5 5 3 9 6 4 3960 2 10 7 3 +--R 11880a b c d + 8910a b c d + 3300a b c d + ---- a b c d +--R 7 +--R + +--R 270 11 8 2 5 12 9 +--R --- a b c d + - b c d +--R 7 7 +--R * +--R 14 +--R x +--R + +--R 66 10 2 10 2200 9 3 9 22275 8 4 2 8 95040 7 5 3 7 +--R -- a b d + ---- a b c d + ----- a b c d + ----- a b c d +--R 13 13 13 13 +--R + +--R 194040 6 6 4 6 199584 5 7 5 5 103950 4 8 6 4 26400 3 9 7 3 +--R ------ a b c d + ------ a b c d + ------ a b c d + ----- a b c d +--R 13 13 13 13 +--R + +--R 2970 2 10 8 2 120 11 9 1 12 10 +--R ---- a b c d + --- a b c d + -- b c +--R 13 13 13 +--R * +--R 13 +--R x +--R + +--R 11 10 10 2 9 9 3 2 8 8 4 3 7 7 5 4 6 +--R a b d + 55a b c d + 825a b c d + 4950a b c d + 13860a b c d +--R + +--R 6 6 5 5 5 7 6 4 4 8 7 3 3 9 8 2 2 10 9 +--R 19404a b c d + 13860a b c d + 4950a b c d + 825a b c d + 55a b c d +--R + +--R 11 10 +--R a b c +--R * +--R 12 +--R x +--R + +--R 1 12 10 120 11 9 10 2 2 8 9 3 3 7 8 4 4 6 +--R -- a d + --- a b c d + 270a b c d + 2400a b c d + 9450a b c d +--R 11 11 +--R + +--R 7 5 5 5 6 6 6 4 5 7 7 3 4 8 8 2 +--R 18144a b c d + 17640a b c d + 8640a b c d + 2025a b c d +--R + +--R 3 9 9 2 10 10 +--R 200a b c d + 6a b c +--R * +--R 11 +--R x +--R + +--R 12 9 11 2 8 10 2 3 7 9 3 4 6 8 4 5 5 +--R a c d + 54a b c d + 792a b c d + 4620a b c d + 12474a b c d +--R + +--R 7 5 6 4 6 6 7 3 5 7 8 2 4 8 9 3 9 10 +--R 16632a b c d + 11088a b c d + 3564a b c d + 495a b c d + 22a b c +--R * +--R 10 +--R x +--R + +--R 12 2 8 11 3 7 10 2 4 6 9 3 5 5 8 4 6 4 +--R 5a c d + 160a b c d + 1540a b c d + 6160a b c d + 11550a b c d +--R + +--R 7 5 7 3 6 6 8 2 5 7 9 4 8 10 +--R 10560a b c d + 4620a b c d + 880a b c d + 55a b c +--R * +--R 9 +--R x +--R + +--R 12 3 7 11 4 6 10 2 5 5 9 3 6 4 8 4 7 3 +--R 15a c d + 315a b c d + 2079a b c d + 5775a b c d + 7425a b c d +--R + +--R 7 5 8 2 6 6 9 5 7 10 +--R 4455a b c d + 1155a b c d + 99a b c +--R * +--R 8 +--R x +--R + +--R 12 4 6 11 5 5 10 2 6 4 26400 9 3 7 3 +--R 30a c d + 432a b c d + 1980a b c d + ----- a b c d +--R 7 +--R + +--R 22275 8 4 8 2 7920 7 5 9 6 6 10 +--R ----- a b c d + ---- a b c d + 132a b c +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 12 5 5 11 6 4 10 2 7 3 9 3 8 2 8 4 9 +--R 42a c d + 420a b c d + 1320a b c d + 1650a b c d + 825a b c d +--R + +--R 7 5 10 +--R 132a b c +--R * +--R 6 +--R x +--R + +--R 12 6 4 11 7 3 10 2 8 2 9 3 9 8 4 10 5 +--R (42a c d + 288a b c d + 594a b c d + 440a b c d + 99a b c )x +--R + +--R 12 7 3 11 8 2 10 2 9 9 3 10 4 +--R (30a c d + 135a b c d + 165a b c d + 55a b c )x +--R + +--R 12 8 2 11 9 10 2 10 3 12 9 11 10 2 12 10 +--R (15a c d + 40a b c d + 22a b c )x + (5a c d + 6a b c )x + a c x +--R Type: Polynomial(Fraction(Integer)) +--E 733 + +--S 734 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 23 10 1 22 9 1 21 2 2 8 1 20 3 3 7 +--R - -------- a d + ------ a b c d - ----- a b c d + ---- a b c d +--R 14872858 646646 58786 8398 +--R + +--R 5 19 4 4 6 1 18 5 5 5 3 17 6 6 4 3 16 7 7 3 +--R - ---- a b c d + --- a b c d - --- a b c d + --- a b c d +--R 8398 442 442 182 +--R + +--R 3 15 8 8 2 5 14 9 9 1 13 10 10 +--R - -- a b c d + -- a b c d - -- a b c +--R 91 91 13 +--R / +--R 11 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 734 + +--S 735 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 735 + +)clear all + +--S 736 of 2952 +t0000:=(a+b*x)^11*(c+d*x)^10 +--R +--R +--R (1) +--R 11 10 21 10 10 11 9 20 +--R b d x + (11a b d + 10b c d )x +--R + +--R 2 9 10 10 9 11 2 8 19 +--R (55a b d + 110a b c d + 45b c d )x +--R + +--R 3 8 10 2 9 9 10 2 8 11 3 7 18 +--R (165a b d + 550a b c d + 495a b c d + 120b c d )x +--R + +--R 4 7 10 3 8 9 2 9 2 8 10 3 7 11 4 6 17 +--R (330a b d + 1650a b c d + 2475a b c d + 1320a b c d + 210b c d )x +--R + +--R 5 6 10 4 7 9 3 8 2 8 2 9 3 7 10 4 6 +--R 462a b d + 3300a b c d + 7425a b c d + 6600a b c d + 2310a b c d +--R + +--R 11 5 5 +--R 252b c d +--R * +--R 16 +--R x +--R + +--R 6 5 10 5 6 9 4 7 2 8 3 8 3 7 +--R 462a b d + 4620a b c d + 14850a b c d + 19800a b c d +--R + +--R 2 9 4 6 10 5 5 11 6 4 +--R 11550a b c d + 2772a b c d + 210b c d +--R * +--R 15 +--R x +--R + +--R 7 4 10 6 5 9 5 6 2 8 4 7 3 7 +--R 330a b d + 4620a b c d + 20790a b c d + 39600a b c d +--R + +--R 3 8 4 6 2 9 5 5 10 6 4 11 7 3 +--R 34650a b c d + 13860a b c d + 2310a b c d + 120b c d +--R * +--R 14 +--R x +--R + +--R 8 3 10 7 4 9 6 5 2 8 5 6 3 7 +--R 165a b d + 3300a b c d + 20790a b c d + 55440a b c d +--R + +--R 4 7 4 6 3 8 5 5 2 9 6 4 10 7 3 11 8 2 +--R 69300a b c d + 41580a b c d + 11550a b c d + 1320a b c d + 45b c d +--R * +--R 13 +--R x +--R + +--R 9 2 10 8 3 9 7 4 2 8 6 5 3 7 +--R 55a b d + 1650a b c d + 14850a b c d + 55440a b c d +--R + +--R 5 6 4 6 4 7 5 5 3 8 6 4 2 9 7 3 +--R 97020a b c d + 83160a b c d + 34650a b c d + 6600a b c d +--R + +--R 10 8 2 11 9 +--R 495a b c d + 10b c d +--R * +--R 12 +--R x +--R + +--R 10 10 9 2 9 8 3 2 8 7 4 3 7 6 5 4 6 +--R 11a b d + 550a b c d + 7425a b c d + 39600a b c d + 97020a b c d +--R + +--R 5 6 5 5 4 7 6 4 3 8 7 3 2 9 8 2 +--R 116424a b c d + 69300a b c d + 19800a b c d + 2475a b c d +--R + +--R 10 9 11 10 +--R 110a b c d + b c +--R * +--R 11 +--R x +--R + +--R 11 10 10 9 9 2 2 8 8 3 3 7 7 4 4 6 +--R a d + 110a b c d + 2475a b c d + 19800a b c d + 69300a b c d +--R + +--R 6 5 5 5 5 6 6 4 4 7 7 3 3 8 8 2 +--R 116424a b c d + 97020a b c d + 39600a b c d + 7425a b c d +--R + +--R 2 9 9 10 10 +--R 550a b c d + 11a b c +--R * +--R 10 +--R x +--R + +--R 11 9 10 2 8 9 2 3 7 8 3 4 6 7 4 5 5 +--R 10a c d + 495a b c d + 6600a b c d + 34650a b c d + 83160a b c d +--R + +--R 6 5 6 4 5 6 7 3 4 7 8 2 3 8 9 2 9 10 +--R 97020a b c d + 55440a b c d + 14850a b c d + 1650a b c d + 55a b c +--R * +--R 9 +--R x +--R + +--R 11 2 8 10 3 7 9 2 4 6 8 3 5 5 +--R 45a c d + 1320a b c d + 11550a b c d + 41580a b c d +--R + +--R 7 4 6 4 6 5 7 3 5 6 8 2 4 7 9 3 8 10 +--R 69300a b c d + 55440a b c d + 20790a b c d + 3300a b c d + 165a b c +--R * +--R 8 +--R x +--R + +--R 11 3 7 10 4 6 9 2 5 5 8 3 6 4 +--R 120a c d + 2310a b c d + 13860a b c d + 34650a b c d +--R + +--R 7 4 7 3 6 5 8 2 5 6 9 4 7 10 +--R 39600a b c d + 20790a b c d + 4620a b c d + 330a b c +--R * +--R 7 +--R x +--R + +--R 11 4 6 10 5 5 9 2 6 4 8 3 7 3 +--R 210a c d + 2772a b c d + 11550a b c d + 19800a b c d +--R + +--R 7 4 8 2 6 5 9 5 6 10 +--R 14850a b c d + 4620a b c d + 462a b c +--R * +--R 6 +--R x +--R + +--R 11 5 5 10 6 4 9 2 7 3 8 3 8 2 7 4 9 +--R 252a c d + 2310a b c d + 6600a b c d + 7425a b c d + 3300a b c d +--R + +--R 6 5 10 +--R 462a b c +--R * +--R 5 +--R x +--R + +--R 11 6 4 10 7 3 9 2 8 2 8 3 9 7 4 10 4 +--R (210a c d + 1320a b c d + 2475a b c d + 1650a b c d + 330a b c )x +--R + +--R 11 7 3 10 8 2 9 2 9 8 3 10 3 +--R (120a c d + 495a b c d + 550a b c d + 165a b c )x +--R + +--R 11 8 2 10 9 9 2 10 2 11 9 10 10 11 10 +--R (45a c d + 110a b c d + 55a b c )x + (10a c d + 11a b c )x + a c +--R Type: Polynomial(Integer) +--E 736 + +--S 737 of 2952 +r0000:=1/12*(b*c-a*d)^10*(a+b*x)^12/b^11+_ + 10/13*d*(b*c-a*d)^9*(a+b*x)^13/b^11+_ + 45/14*d^2*(b*c-a*d)^8*(a+b*x)^14/b^11+_ + 8*d^3*(b*c-a*d)^7*(a+b*x)^15/b^11+_ + 105/8*d^4*(b*c-a*d)^6*(a+b*x)^16/b^11+_ + 252/17*d^5*(b*c-a*d)^5*(a+b*x)^17/b^11+_ + 35/3*d^6*(b*c-a*d)^4*(a+b*x)^18/b^11+_ + 120/19*d^7*(b*c-a*d)^3*(a+b*x)^19/b^11+_ + 9/4*d^8*(b*c-a*d)^2*(a+b*x)^20/b^11+_ + 10/21*d^9*(b*c-a*d)*(a+b*x)^21/b^11+1/22*d^10*(a+b*x)^22/b^11 +--R +--R +--R (2) +--R 1 22 10 22 11 21 10 10 22 9 21 +--R -- b d x + (-- a b d + -- b c d )x +--R 22 21 21 +--R + +--R 11 2 20 10 11 21 9 9 22 2 8 20 +--R (-- a b d + -- a b c d + - b c d )x +--R 4 2 4 +--R + +--R 165 3 19 10 550 2 20 9 495 21 2 8 120 22 3 7 19 +--R (--- a b d + --- a b c d + --- a b c d + --- b c d )x +--R 19 19 19 19 +--R + +--R 55 4 18 10 275 3 19 9 275 2 20 2 8 220 21 3 7 +--R -- a b d + --- a b c d + --- a b c d + --- a b c d +--R 3 3 2 3 +--R + +--R 35 22 4 6 +--R -- b c d +--R 3 +--R * +--R 18 +--R x +--R + +--R 462 5 17 10 3300 4 18 9 7425 3 19 2 8 6600 2 20 3 7 +--R --- a b d + ---- a b c d + ---- a b c d + ---- a b c d +--R 17 17 17 17 +--R + +--R 2310 21 4 6 252 22 5 5 +--R ---- a b c d + --- b c d +--R 17 17 +--R * +--R 17 +--R x +--R + +--R 231 6 16 10 1155 5 17 9 7425 4 18 2 8 2475 3 19 3 7 +--R --- a b d + ---- a b c d + ---- a b c d + ---- a b c d +--R 8 4 8 2 +--R + +--R 5775 2 20 4 6 693 21 5 5 105 22 6 4 +--R ---- a b c d + --- a b c d + --- b c d +--R 8 4 8 +--R * +--R 16 +--R x +--R + +--R 7 15 10 6 16 9 5 17 2 8 4 18 3 7 +--R 22a b d + 308a b c d + 1386a b c d + 2640a b c d +--R + +--R 3 19 4 6 2 20 5 5 21 6 4 22 7 3 +--R 2310a b c d + 924a b c d + 154a b c d + 8b c d +--R * +--R 15 +--R x +--R + +--R 165 8 14 10 1650 7 15 9 6 16 2 8 5 17 3 7 +--R --- a b d + ---- a b c d + 1485a b c d + 3960a b c d +--R 14 7 +--R + +--R 4 18 4 6 3 19 5 5 2 20 6 4 660 21 7 3 +--R 4950a b c d + 2970a b c d + 825a b c d + --- a b c d +--R 7 +--R + +--R 45 22 8 2 +--R -- b c d +--R 14 +--R * +--R 14 +--R x +--R + +--R 55 9 13 10 1650 8 14 9 14850 7 15 2 8 55440 6 16 3 7 +--R -- a b d + ---- a b c d + ----- a b c d + ----- a b c d +--R 13 13 13 13 +--R + +--R 97020 5 17 4 6 83160 4 18 5 5 34650 3 19 6 4 6600 2 20 7 3 +--R ----- a b c d + ----- a b c d + ----- a b c d + ---- a b c d +--R 13 13 13 13 +--R + +--R 495 21 8 2 10 22 9 +--R --- a b c d + -- b c d +--R 13 13 +--R * +--R 13 +--R x +--R + +--R 11 10 12 10 275 9 13 9 2475 8 14 2 8 7 15 3 7 +--R -- a b d + --- a b c d + ---- a b c d + 3300a b c d +--R 12 6 4 +--R + +--R 6 16 4 6 5 17 5 5 4 18 6 4 3 19 7 3 +--R 8085a b c d + 9702a b c d + 5775a b c d + 1650a b c d +--R + +--R 825 2 20 8 2 55 21 9 1 22 10 +--R --- a b c d + -- a b c d + -- b c +--R 4 6 12 +--R * +--R 12 +--R x +--R + +--R 1 11 11 10 10 12 9 9 13 2 8 8 14 3 7 +--R -- a b d + 10a b c d + 225a b c d + 1800a b c d +--R 11 +--R + +--R 7 15 4 6 6 16 5 5 5 17 6 4 4 18 7 3 +--R 6300a b c d + 10584a b c d + 8820a b c d + 3600a b c d +--R + +--R 3 19 8 2 2 20 9 21 10 +--R 675a b c d + 50a b c d + a b c +--R * +--R 11 +--R x +--R + +--R 11 11 9 99 10 12 2 8 9 13 3 7 8 14 4 6 +--R a b c d + -- a b c d + 660a b c d + 3465a b c d +--R 2 +--R + +--R 7 15 5 5 6 16 6 4 5 17 7 3 4 18 8 2 +--R 8316a b c d + 9702a b c d + 5544a b c d + 1485a b c d +--R + +--R 3 19 9 11 2 20 10 +--R 165a b c d + -- a b c +--R 2 +--R * +--R 10 +--R x +--R + +--R 11 11 2 8 440 10 12 3 7 3850 9 13 4 6 8 14 5 5 +--R 5a b c d + --- a b c d + ---- a b c d + 4620a b c d +--R 3 3 +--R + +--R 7 15 6 4 6 16 7 3 5 17 8 2 1100 4 18 9 +--R 7700a b c d + 6160a b c d + 2310a b c d + ---- a b c d +--R 3 +--R + +--R 55 3 19 10 +--R -- a b c +--R 3 +--R * +--R 9 +--R x +--R + +--R 11 11 3 7 1155 10 12 4 6 3465 9 13 5 5 17325 8 14 6 4 +--R 15a b c d + ---- a b c d + ---- a b c d + ----- a b c d +--R 4 2 4 +--R + +--R 7 15 7 3 10395 6 16 8 2 1155 5 17 9 165 4 18 10 +--R 4950a b c d + ----- a b c d + ---- a b c d + --- a b c +--R 4 2 4 +--R * +--R 8 +--R x +--R + +--R 11 11 4 6 10 12 5 5 9 13 6 4 19800 8 14 7 3 +--R 30a b c d + 396a b c d + 1650a b c d + ----- a b c d +--R 7 +--R + +--R 14850 7 15 8 2 6 16 9 5 17 10 +--R ----- a b c d + 660a b c d + 66a b c +--R 7 +--R * +--R 7 +--R x +--R + +--R 11 11 5 5 10 12 6 4 9 13 7 3 2475 8 14 8 2 +--R 42a b c d + 385a b c d + 1100a b c d + ---- a b c d +--R 2 +--R + +--R 7 15 9 6 16 10 +--R 550a b c d + 77a b c +--R * +--R 6 +--R x +--R + +--R 11 11 6 4 10 12 7 3 9 13 8 2 8 14 9 +--R 42a b c d + 264a b c d + 495a b c d + 330a b c d +--R + +--R 7 15 10 +--R 66a b c +--R * +--R 5 +--R x +--R + +--R 11 11 7 3 495 10 12 8 2 275 9 13 9 165 8 14 10 4 +--R (30a b c d + --- a b c d + --- a b c d + --- a b c )x +--R 4 2 4 +--R + +--R 11 11 8 2 110 10 12 9 55 9 13 10 3 +--R (15a b c d + --- a b c d + -- a b c )x +--R 3 3 +--R + +--R 11 11 9 11 10 12 10 2 11 11 10 1 22 10 +--R (5a b c d + -- a b c )x + a b c x + ------- a d +--R 2 7759752 +--R + +--R 1 21 9 1 20 2 2 8 5 19 3 3 7 5 18 4 4 6 +--R - ------ a b c d + ----- a b c d - ----- a b c d + ---- a b c d +--R 352716 33592 25194 5304 +--R + +--R 3 17 5 5 5 1 16 6 6 4 2 15 7 7 3 15 14 8 8 2 +--R - --- a b c d + --- a b c d - -- a b c d + --- a b c d +--R 884 104 91 364 +--R + +--R 5 13 9 9 1 12 10 10 +--R - -- a b c d + -- a b c +--R 78 12 +--R / +--R 11 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 737 + +--S 738 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 11 10 22 11 10 10 10 11 9 21 +--R -- b d x + (-- a b d + -- b c d )x +--R 22 21 21 +--R + +--R 11 2 9 10 11 10 9 9 11 2 8 20 +--R (-- a b d + -- a b c d + - b c d )x +--R 4 2 4 +--R + +--R 165 3 8 10 550 2 9 9 495 10 2 8 120 11 3 7 19 +--R (--- a b d + --- a b c d + --- a b c d + --- b c d )x +--R 19 19 19 19 +--R + +--R 55 4 7 10 275 3 8 9 275 2 9 2 8 220 10 3 7 35 11 4 6 18 +--R (-- a b d + --- a b c d + --- a b c d + --- a b c d + -- b c d )x +--R 3 3 2 3 3 +--R + +--R 462 5 6 10 3300 4 7 9 7425 3 8 2 8 6600 2 9 3 7 +--R --- a b d + ---- a b c d + ---- a b c d + ---- a b c d +--R 17 17 17 17 +--R + +--R 2310 10 4 6 252 11 5 5 +--R ---- a b c d + --- b c d +--R 17 17 +--R * +--R 17 +--R x +--R + +--R 231 6 5 10 1155 5 6 9 7425 4 7 2 8 2475 3 8 3 7 +--R --- a b d + ---- a b c d + ---- a b c d + ---- a b c d +--R 8 4 8 2 +--R + +--R 5775 2 9 4 6 693 10 5 5 105 11 6 4 +--R ---- a b c d + --- a b c d + --- b c d +--R 8 4 8 +--R * +--R 16 +--R x +--R + +--R 7 4 10 6 5 9 5 6 2 8 4 7 3 7 3 8 4 6 +--R 22a b d + 308a b c d + 1386a b c d + 2640a b c d + 2310a b c d +--R + +--R 2 9 5 5 10 6 4 11 7 3 +--R 924a b c d + 154a b c d + 8b c d +--R * +--R 15 +--R x +--R + +--R 165 8 3 10 1650 7 4 9 6 5 2 8 5 6 3 7 +--R --- a b d + ---- a b c d + 1485a b c d + 3960a b c d +--R 14 7 +--R + +--R 4 7 4 6 3 8 5 5 2 9 6 4 660 10 7 3 45 11 8 2 +--R 4950a b c d + 2970a b c d + 825a b c d + --- a b c d + -- b c d +--R 7 14 +--R * +--R 14 +--R x +--R + +--R 55 9 2 10 1650 8 3 9 14850 7 4 2 8 55440 6 5 3 7 +--R -- a b d + ---- a b c d + ----- a b c d + ----- a b c d +--R 13 13 13 13 +--R + +--R 97020 5 6 4 6 83160 4 7 5 5 34650 3 8 6 4 6600 2 9 7 3 +--R ----- a b c d + ----- a b c d + ----- a b c d + ---- a b c d +--R 13 13 13 13 +--R + +--R 495 10 8 2 10 11 9 +--R --- a b c d + -- b c d +--R 13 13 +--R * +--R 13 +--R x +--R + +--R 11 10 10 275 9 2 9 2475 8 3 2 8 7 4 3 7 +--R -- a b d + --- a b c d + ---- a b c d + 3300a b c d +--R 12 6 4 +--R + +--R 6 5 4 6 5 6 5 5 4 7 6 4 3 8 7 3 +--R 8085a b c d + 9702a b c d + 5775a b c d + 1650a b c d +--R + +--R 825 2 9 8 2 55 10 9 1 11 10 +--R --- a b c d + -- a b c d + -- b c +--R 4 6 12 +--R * +--R 12 +--R x +--R + +--R 1 11 10 10 9 9 2 2 8 8 3 3 7 7 4 4 6 +--R -- a d + 10a b c d + 225a b c d + 1800a b c d + 6300a b c d +--R 11 +--R + +--R 6 5 5 5 5 6 6 4 4 7 7 3 3 8 8 2 2 9 9 +--R 10584a b c d + 8820a b c d + 3600a b c d + 675a b c d + 50a b c d +--R + +--R 10 10 +--R a b c +--R * +--R 11 +--R x +--R + +--R 11 9 99 10 2 8 9 2 3 7 8 3 4 6 7 4 5 5 +--R a c d + -- a b c d + 660a b c d + 3465a b c d + 8316a b c d +--R 2 +--R + +--R 6 5 6 4 5 6 7 3 4 7 8 2 3 8 9 11 2 9 10 +--R 9702a b c d + 5544a b c d + 1485a b c d + 165a b c d + -- a b c +--R 2 +--R * +--R 10 +--R x +--R + +--R 11 2 8 440 10 3 7 3850 9 2 4 6 8 3 5 5 7 4 6 4 +--R 5a c d + --- a b c d + ---- a b c d + 4620a b c d + 7700a b c d +--R 3 3 +--R + +--R 6 5 7 3 5 6 8 2 1100 4 7 9 55 3 8 10 +--R 6160a b c d + 2310a b c d + ---- a b c d + -- a b c +--R 3 3 +--R * +--R 9 +--R x +--R + +--R 11 3 7 1155 10 4 6 3465 9 2 5 5 17325 8 3 6 4 +--R 15a c d + ---- a b c d + ---- a b c d + ----- a b c d +--R 4 2 4 +--R + +--R 7 4 7 3 10395 6 5 8 2 1155 5 6 9 165 4 7 10 +--R 4950a b c d + ----- a b c d + ---- a b c d + --- a b c +--R 4 2 4 +--R * +--R 8 +--R x +--R + +--R 11 4 6 10 5 5 9 2 6 4 19800 8 3 7 3 +--R 30a c d + 396a b c d + 1650a b c d + ----- a b c d +--R 7 +--R + +--R 14850 7 4 8 2 6 5 9 5 6 10 +--R ----- a b c d + 660a b c d + 66a b c +--R 7 +--R * +--R 7 +--R x +--R + +--R 11 5 5 10 6 4 9 2 7 3 2475 8 3 8 2 7 4 9 +--R 42a c d + 385a b c d + 1100a b c d + ---- a b c d + 550a b c d +--R 2 +--R + +--R 6 5 10 +--R 77a b c +--R * +--R 6 +--R x +--R + +--R 11 6 4 10 7 3 9 2 8 2 8 3 9 7 4 10 5 +--R (42a c d + 264a b c d + 495a b c d + 330a b c d + 66a b c )x +--R + +--R 11 7 3 495 10 8 2 275 9 2 9 165 8 3 10 4 +--R (30a c d + --- a b c d + --- a b c d + --- a b c )x +--R 4 2 4 +--R + +--R 11 8 2 110 10 9 55 9 2 10 3 11 9 11 10 10 2 +--R (15a c d + --- a b c d + -- a b c )x + (5a c d + -- a b c )x +--R 3 3 2 +--R + +--R 11 10 +--R a c x +--R Type: Polynomial(Fraction(Integer)) +--E 738 + +--S 739 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 22 10 1 21 9 1 20 2 2 8 5 19 3 3 7 +--R - ------- a d + ------ a b c d - ----- a b c d + ----- a b c d +--R 7759752 352716 33592 25194 +--R + +--R 5 18 4 4 6 3 17 5 5 5 1 16 6 6 4 2 15 7 7 3 +--R - ---- a b c d + --- a b c d - --- a b c d + -- a b c d +--R 5304 884 104 91 +--R + +--R 15 14 8 8 2 5 13 9 9 1 12 10 10 +--R - --- a b c d + -- a b c d - -- a b c +--R 364 78 12 +--R / +--R 11 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 739 + +--S 740 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 740 + +)clear all + +--S 741 of 2952 +t0000:=(a+b*x)^10*(c+d*x)^10 +--R +--R +--R (1) +--R 10 10 20 9 10 10 9 19 +--R b d x + (10a b d + 10b c d )x +--R + +--R 2 8 10 9 9 10 2 8 18 +--R (45a b d + 100a b c d + 45b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 17 +--R (120a b d + 450a b c d + 450a b c d + 120b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 10 4 6 16 +--R (210a b d + 1200a b c d + 2025a b c d + 1200a b c d + 210b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 9 4 6 +--R 252a b d + 2100a b c d + 5400a b c d + 5400a b c d + 2100a b c d +--R + +--R 10 5 5 +--R 252b c d +--R * +--R 15 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 2 8 4 6 +--R 210a b d + 2520a b c d + 9450a b c d + 14400a b c d + 9450a b c d +--R + +--R 9 5 5 10 6 4 +--R 2520a b c d + 210b c d +--R * +--R 14 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R 120a b d + 2100a b c d + 11340a b c d + 25200a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R 25200a b c d + 11340a b c d + 2100a b c d + 120b c d +--R * +--R 13 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 4 6 4 6 +--R 45a b d + 1200a b c d + 9450a b c d + 30240a b c d + 44100a b c d +--R + +--R 3 7 5 5 2 8 6 4 9 7 3 10 8 2 +--R 30240a b c d + 9450a b c d + 1200a b c d + 45b c d +--R * +--R 12 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 5 5 4 6 +--R 10a b d + 450a b c d + 5400a b c d + 25200a b c d + 52920a b c d +--R + +--R 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 10 9 +--R 52920a b c d + 25200a b c d + 5400a b c d + 450a b c d + 10b c d +--R * +--R 11 +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R a d + 100a b c d + 2025a b c d + 14400a b c d + 44100a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 +--R 63504a b c d + 44100a b c d + 14400a b c d + 2025a b c d +--R + +--R 9 9 10 10 +--R 100a b c d + b c +--R * +--R 10 +--R x +--R + +--R 10 9 9 2 8 8 2 3 7 7 3 4 6 6 4 5 5 +--R 10a c d + 450a b c d + 5400a b c d + 25200a b c d + 52920a b c d +--R + +--R 5 5 6 4 4 6 7 3 3 7 8 2 2 8 9 9 10 +--R 52920a b c d + 25200a b c d + 5400a b c d + 450a b c d + 10a b c +--R * +--R 9 +--R x +--R + +--R 10 2 8 9 3 7 8 2 4 6 7 3 5 5 6 4 6 4 +--R 45a c d + 1200a b c d + 9450a b c d + 30240a b c d + 44100a b c d +--R + +--R 5 5 7 3 4 6 8 2 3 7 9 2 8 10 +--R 30240a b c d + 9450a b c d + 1200a b c d + 45a b c +--R * +--R 8 +--R x +--R + +--R 10 3 7 9 4 6 8 2 5 5 7 3 6 4 +--R 120a c d + 2100a b c d + 11340a b c d + 25200a b c d +--R + +--R 6 4 7 3 5 5 8 2 4 6 9 3 7 10 +--R 25200a b c d + 11340a b c d + 2100a b c d + 120a b c +--R * +--R 7 +--R x +--R + +--R 10 4 6 9 5 5 8 2 6 4 7 3 7 3 6 4 8 2 +--R 210a c d + 2520a b c d + 9450a b c d + 14400a b c d + 9450a b c d +--R + +--R 5 5 9 4 6 10 +--R 2520a b c d + 210a b c +--R * +--R 6 +--R x +--R + +--R 10 5 5 9 6 4 8 2 7 3 7 3 8 2 6 4 9 +--R 252a c d + 2100a b c d + 5400a b c d + 5400a b c d + 2100a b c d +--R + +--R 5 5 10 +--R 252a b c +--R * +--R 5 +--R x +--R + +--R 10 6 4 9 7 3 8 2 8 2 7 3 9 6 4 10 4 +--R (210a c d + 1200a b c d + 2025a b c d + 1200a b c d + 210a b c )x +--R + +--R 10 7 3 9 8 2 8 2 9 7 3 10 3 +--R (120a c d + 450a b c d + 450a b c d + 120a b c )x +--R + +--R 10 8 2 9 9 8 2 10 2 10 9 9 10 10 10 +--R (45a c d + 100a b c d + 45a b c )x + (10a c d + 10a b c )x + a c +--R Type: Polynomial(Integer) +--E 741 + +--S 742 of 2952 +r0000:=1/11*(b*c-a*d)^10*(a+b*x)^11/b^11+5/6*d*(b*c-a*d)^9*(a+b*x)^12/b^11+_ + 45/13*d^2*(b*c-a*d)^8*(a+b*x)^13/b^11+_ + 60/7*d^3*(b*c-a*d)^7*(a+b*x)^14/b^11+_ + 14*d^4*(b*c-a*d)^6*(a+b*x)^15/b^11+_ + 63/4*d^5*(b*c-a*d)^5*(a+b*x)^16/b^11+_ + 210/17*d^6*(b*c-a*d)^4*(a+b*x)^17/b^11+_ + 20/3*d^7*(b*c-a*d)^3*(a+b*x)^18/b^11+_ + 45/19*d^8*(b*c-a*d)^2*(a+b*x)^19/b^11+_ + 1/2*d^9*(b*c-a*d)*(a+b*x)^20/b^11+1/21*d^10*(a+b*x)^21/b^11 +--R +--R +--R (2) +--R 1 21 10 21 1 20 10 1 21 9 20 +--R -- b d x + (- a b d + - b c d )x +--R 21 2 2 +--R + +--R 45 2 19 10 100 20 9 45 21 2 8 19 +--R (-- a b d + --- a b c d + -- b c d )x +--R 19 19 19 +--R + +--R 20 3 18 10 2 19 9 20 2 8 20 21 3 7 18 +--R (-- a b d + 25a b c d + 25a b c d + -- b c d )x +--R 3 3 +--R + +--R 210 4 17 10 1200 3 18 9 2025 2 19 2 8 1200 20 3 7 +--R --- a b d + ---- a b c d + ---- a b c d + ---- a b c d +--R 17 17 17 17 +--R + +--R 210 21 4 6 +--R --- b c d +--R 17 +--R * +--R 17 +--R x +--R + +--R 63 5 16 10 525 4 17 9 675 3 18 2 8 675 2 19 3 7 +--R -- a b d + --- a b c d + --- a b c d + --- a b c d +--R 4 4 2 2 +--R + +--R 525 20 4 6 63 21 5 5 +--R --- a b c d + -- b c d +--R 4 4 +--R * +--R 16 +--R x +--R + +--R 6 15 10 5 16 9 4 17 2 8 3 18 3 7 +--R 14a b d + 168a b c d + 630a b c d + 960a b c d +--R + +--R 2 19 4 6 20 5 5 21 6 4 +--R 630a b c d + 168a b c d + 14b c d +--R * +--R 15 +--R x +--R + +--R 60 7 14 10 6 15 9 5 16 2 8 4 17 3 7 +--R -- a b d + 150a b c d + 810a b c d + 1800a b c d +--R 7 +--R + +--R 3 18 4 6 2 19 5 5 20 6 4 60 21 7 3 +--R 1800a b c d + 810a b c d + 150a b c d + -- b c d +--R 7 +--R * +--R 14 +--R x +--R + +--R 45 8 13 10 1200 7 14 9 9450 6 15 2 8 30240 5 16 3 7 +--R -- a b d + ---- a b c d + ---- a b c d + ----- a b c d +--R 13 13 13 13 +--R + +--R 44100 4 17 4 6 30240 3 18 5 5 9450 2 19 6 4 1200 20 7 3 +--R ----- a b c d + ----- a b c d + ---- a b c d + ---- a b c d +--R 13 13 13 13 +--R + +--R 45 21 8 2 +--R -- b c d +--R 13 +--R * +--R 13 +--R x +--R + +--R 5 9 12 10 75 8 13 9 7 14 2 8 6 15 3 7 +--R - a b d + -- a b c d + 450a b c d + 2100a b c d +--R 6 2 +--R + +--R 5 16 4 6 4 17 5 5 3 18 6 4 2 19 7 3 +--R 4410a b c d + 4410a b c d + 2100a b c d + 450a b c d +--R + +--R 75 20 8 2 5 21 9 +--R -- a b c d + - b c d +--R 2 6 +--R * +--R 12 +--R x +--R + +--R 1 10 11 10 100 9 12 9 2025 8 13 2 8 14400 7 14 3 7 +--R -- a b d + --- a b c d + ---- a b c d + ----- a b c d +--R 11 11 11 11 +--R + +--R 44100 6 15 4 6 63504 5 16 5 5 44100 4 17 6 4 14400 3 18 7 3 +--R ----- a b c d + ----- a b c d + ----- a b c d + ----- a b c d +--R 11 11 11 11 +--R + +--R 2025 2 19 8 2 100 20 9 1 21 10 +--R ---- a b c d + --- a b c d + -- b c +--R 11 11 11 +--R * +--R 11 +--R x +--R + +--R 10 11 9 9 12 2 8 8 13 3 7 7 14 4 6 +--R a b c d + 45a b c d + 540a b c d + 2520a b c d +--R + +--R 6 15 5 5 5 16 6 4 4 17 7 3 3 18 8 2 +--R 5292a b c d + 5292a b c d + 2520a b c d + 540a b c d +--R + +--R 2 19 9 20 10 +--R 45a b c d + a b c +--R * +--R 10 +--R x +--R + +--R 10 11 2 8 400 9 12 3 7 8 13 4 6 7 14 5 5 +--R 5a b c d + --- a b c d + 1050a b c d + 3360a b c d +--R 3 +--R + +--R 6 15 6 4 5 16 7 3 4 17 8 2 400 3 18 9 +--R 4900a b c d + 3360a b c d + 1050a b c d + --- a b c d +--R 3 +--R + +--R 2 19 10 +--R 5a b c +--R * +--R 9 +--R x +--R + +--R 10 11 3 7 525 9 12 4 6 2835 8 13 5 5 7 14 6 4 +--R 15a b c d + --- a b c d + ---- a b c d + 3150a b c d +--R 2 2 +--R + +--R 6 15 7 3 2835 5 16 8 2 525 4 17 9 3 18 10 +--R 3150a b c d + ---- a b c d + --- a b c d + 15a b c +--R 2 2 +--R * +--R 8 +--R x +--R + +--R 10 11 4 6 9 12 5 5 8 13 6 4 14400 7 14 7 3 +--R 30a b c d + 360a b c d + 1350a b c d + ----- a b c d +--R 7 +--R + +--R 6 15 8 2 5 16 9 4 17 10 +--R 1350a b c d + 360a b c d + 30a b c +--R * +--R 7 +--R x +--R + +--R 10 11 5 5 9 12 6 4 8 13 7 3 7 14 8 2 +--R 42a b c d + 350a b c d + 900a b c d + 900a b c d +--R + +--R 6 15 9 5 16 10 +--R 350a b c d + 42a b c +--R * +--R 6 +--R x +--R + +--R 10 11 6 4 9 12 7 3 8 13 8 2 7 14 9 6 15 10 5 +--R (42a b c d + 240a b c d + 405a b c d + 240a b c d + 42a b c )x +--R + +--R 10 11 7 3 225 9 12 8 2 225 8 13 9 7 14 10 4 +--R (30a b c d + --- a b c d + --- a b c d + 30a b c )x +--R 2 2 +--R + +--R 10 11 8 2 100 9 12 9 8 13 10 3 10 11 9 9 12 10 2 +--R (15a b c d + --- a b c d + 15a b c )x + (5a b c d + 5a b c )x +--R 3 +--R + +--R 10 11 10 1 21 10 1 20 9 5 19 2 2 8 +--R a b c x + ------- a d - ------ a b c d + ----- a b c d +--R 3879876 184756 92378 +--R + +--R 5 18 3 3 7 15 17 4 4 6 3 16 5 5 5 2 15 6 6 4 +--R - ----- a b c d + ---- a b c d - --- a b c d + --- a b c d +--R 14586 9724 572 143 +--R + +--R 30 14 7 7 3 15 13 8 8 2 5 12 9 9 1 11 10 10 +--R - ---- a b c d + --- a b c d - -- a b c d + -- a b c +--R 1001 286 66 11 +--R / +--R 11 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 742 + +--S 743 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 10 21 1 9 10 1 10 9 20 +--R -- b d x + (- a b d + - b c d )x +--R 21 2 2 +--R + +--R 45 2 8 10 100 9 9 45 10 2 8 19 +--R (-- a b d + --- a b c d + -- b c d )x +--R 19 19 19 +--R + +--R 20 3 7 10 2 8 9 9 2 8 20 10 3 7 18 +--R (-- a b d + 25a b c d + 25a b c d + -- b c d )x +--R 3 3 +--R + +--R 210 4 6 10 1200 3 7 9 2025 2 8 2 8 1200 9 3 7 +--R --- a b d + ---- a b c d + ---- a b c d + ---- a b c d +--R 17 17 17 17 +--R + +--R 210 10 4 6 +--R --- b c d +--R 17 +--R * +--R 17 +--R x +--R + +--R 63 5 5 10 525 4 6 9 675 3 7 2 8 675 2 8 3 7 525 9 4 6 +--R -- a b d + --- a b c d + --- a b c d + --- a b c d + --- a b c d +--R 4 4 2 2 4 +--R + +--R 63 10 5 5 +--R -- b c d +--R 4 +--R * +--R 16 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 2 8 4 6 +--R 14a b d + 168a b c d + 630a b c d + 960a b c d + 630a b c d +--R + +--R 9 5 5 10 6 4 +--R 168a b c d + 14b c d +--R * +--R 15 +--R x +--R + +--R 60 7 3 10 6 4 9 5 5 2 8 4 6 3 7 3 7 4 6 +--R -- a b d + 150a b c d + 810a b c d + 1800a b c d + 1800a b c d +--R 7 +--R + +--R 2 8 5 5 9 6 4 60 10 7 3 +--R 810a b c d + 150a b c d + -- b c d +--R 7 +--R * +--R 14 +--R x +--R + +--R 45 8 2 10 1200 7 3 9 9450 6 4 2 8 30240 5 5 3 7 +--R -- a b d + ---- a b c d + ---- a b c d + ----- a b c d +--R 13 13 13 13 +--R + +--R 44100 4 6 4 6 30240 3 7 5 5 9450 2 8 6 4 1200 9 7 3 +--R ----- a b c d + ----- a b c d + ---- a b c d + ---- a b c d +--R 13 13 13 13 +--R + +--R 45 10 8 2 +--R -- b c d +--R 13 +--R * +--R 13 +--R x +--R + +--R 5 9 10 75 8 2 9 7 3 2 8 6 4 3 7 5 5 4 6 +--R - a b d + -- a b c d + 450a b c d + 2100a b c d + 4410a b c d +--R 6 2 +--R + +--R 4 6 5 5 3 7 6 4 2 8 7 3 75 9 8 2 5 10 9 +--R 4410a b c d + 2100a b c d + 450a b c d + -- a b c d + - b c d +--R 2 6 +--R * +--R 12 +--R x +--R + +--R 1 10 10 100 9 9 2025 8 2 2 8 14400 7 3 3 7 +--R -- a d + --- a b c d + ---- a b c d + ----- a b c d +--R 11 11 11 11 +--R + +--R 44100 6 4 4 6 63504 5 5 5 5 44100 4 6 6 4 14400 3 7 7 3 +--R ----- a b c d + ----- a b c d + ----- a b c d + ----- a b c d +--R 11 11 11 11 +--R + +--R 2025 2 8 8 2 100 9 9 1 10 10 +--R ---- a b c d + --- a b c d + -- b c +--R 11 11 11 +--R * +--R 11 +--R x +--R + +--R 10 9 9 2 8 8 2 3 7 7 3 4 6 6 4 5 5 +--R a c d + 45a b c d + 540a b c d + 2520a b c d + 5292a b c d +--R + +--R 5 5 6 4 4 6 7 3 3 7 8 2 2 8 9 9 10 +--R 5292a b c d + 2520a b c d + 540a b c d + 45a b c d + a b c +--R * +--R 10 +--R x +--R + +--R 10 2 8 400 9 3 7 8 2 4 6 7 3 5 5 6 4 6 4 +--R 5a c d + --- a b c d + 1050a b c d + 3360a b c d + 4900a b c d +--R 3 +--R + +--R 5 5 7 3 4 6 8 2 400 3 7 9 2 8 10 +--R 3360a b c d + 1050a b c d + --- a b c d + 5a b c +--R 3 +--R * +--R 9 +--R x +--R + +--R 10 3 7 525 9 4 6 2835 8 2 5 5 7 3 6 4 6 4 7 3 +--R 15a c d + --- a b c d + ---- a b c d + 3150a b c d + 3150a b c d +--R 2 2 +--R + +--R 2835 5 5 8 2 525 4 6 9 3 7 10 +--R ---- a b c d + --- a b c d + 15a b c +--R 2 2 +--R * +--R 8 +--R x +--R + +--R 10 4 6 9 5 5 8 2 6 4 14400 7 3 7 3 6 4 8 2 +--R 30a c d + 360a b c d + 1350a b c d + ----- a b c d + 1350a b c d +--R 7 +--R + +--R 5 5 9 4 6 10 +--R 360a b c d + 30a b c +--R * +--R 7 +--R x +--R + +--R 10 5 5 9 6 4 8 2 7 3 7 3 8 2 6 4 9 +--R 42a c d + 350a b c d + 900a b c d + 900a b c d + 350a b c d +--R + +--R 5 5 10 +--R 42a b c +--R * +--R 6 +--R x +--R + +--R 10 6 4 9 7 3 8 2 8 2 7 3 9 6 4 10 5 +--R (42a c d + 240a b c d + 405a b c d + 240a b c d + 42a b c )x +--R + +--R 10 7 3 225 9 8 2 225 8 2 9 7 3 10 4 +--R (30a c d + --- a b c d + --- a b c d + 30a b c )x +--R 2 2 +--R + +--R 10 8 2 100 9 9 8 2 10 3 10 9 9 10 2 10 10 +--R (15a c d + --- a b c d + 15a b c )x + (5a c d + 5a b c )x + a c x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 743 + +--S 744 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 21 10 1 20 9 5 19 2 2 8 5 18 3 3 7 +--R - ------- a d + ------ a b c d - ----- a b c d + ----- a b c d +--R 3879876 184756 92378 14586 +--R + +--R 15 17 4 4 6 3 16 5 5 5 2 15 6 6 4 30 14 7 7 3 +--R - ---- a b c d + --- a b c d - --- a b c d + ---- a b c d +--R 9724 572 143 1001 +--R + +--R 15 13 8 8 2 5 12 9 9 1 11 10 10 +--R - --- a b c d + -- a b c d - -- a b c +--R 286 66 11 +--R / +--R 11 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 744 + +--S 745 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 745 + +)clear all + +--S 746 of 2952 +t0000:=(a+b*x)^9*(c+d*x)^10 +--R +--R +--R (1) +--R 9 10 19 8 10 9 9 18 +--R b d x + (9a b d + 10b c d )x +--R + +--R 2 7 10 8 9 9 2 8 17 +--R (36a b d + 90a b c d + 45b c d )x +--R + +--R 3 6 10 2 7 9 8 2 8 9 3 7 16 +--R (84a b d + 360a b c d + 405a b c d + 120b c d )x +--R + +--R 4 5 10 3 6 9 2 7 2 8 8 3 7 9 4 6 15 +--R (126a b d + 840a b c d + 1620a b c d + 1080a b c d + 210b c d )x +--R + +--R 5 4 10 4 5 9 3 6 2 8 2 7 3 7 8 4 6 +--R 126a b d + 1260a b c d + 3780a b c d + 4320a b c d + 1890a b c d +--R + +--R 9 5 5 +--R 252b c d +--R * +--R 14 +--R x +--R + +--R 6 3 10 5 4 9 4 5 2 8 3 6 3 7 2 7 4 6 +--R 84a b d + 1260a b c d + 5670a b c d + 10080a b c d + 7560a b c d +--R + +--R 8 5 5 9 6 4 +--R 2268a b c d + 210b c d +--R * +--R 13 +--R x +--R + +--R 7 2 10 6 3 9 5 4 2 8 4 5 3 7 3 6 4 6 +--R 36a b d + 840a b c d + 5670a b c d + 15120a b c d + 17640a b c d +--R + +--R 2 7 5 5 8 6 4 9 7 3 +--R 9072a b c d + 1890a b c d + 120b c d +--R * +--R 12 +--R x +--R + +--R 8 10 7 2 9 6 3 2 8 5 4 3 7 4 5 4 6 +--R 9a b d + 360a b c d + 3780a b c d + 15120a b c d + 26460a b c d +--R + +--R 3 6 5 5 2 7 6 4 8 7 3 9 8 2 +--R 21168a b c d + 7560a b c d + 1080a b c d + 45b c d +--R * +--R 11 +--R x +--R + +--R 9 10 8 9 7 2 2 8 6 3 3 7 5 4 4 6 +--R a d + 90a b c d + 1620a b c d + 10080a b c d + 26460a b c d +--R + +--R 4 5 5 5 3 6 6 4 2 7 7 3 8 8 2 9 9 +--R 31752a b c d + 17640a b c d + 4320a b c d + 405a b c d + 10b c d +--R * +--R 10 +--R x +--R + +--R 9 9 8 2 8 7 2 3 7 6 3 4 6 5 4 5 5 +--R 10a c d + 405a b c d + 4320a b c d + 17640a b c d + 31752a b c d +--R + +--R 4 5 6 4 3 6 7 3 2 7 8 2 8 9 9 10 +--R 26460a b c d + 10080a b c d + 1620a b c d + 90a b c d + b c +--R * +--R 9 +--R x +--R + +--R 9 2 8 8 3 7 7 2 4 6 6 3 5 5 5 4 6 4 +--R 45a c d + 1080a b c d + 7560a b c d + 21168a b c d + 26460a b c d +--R + +--R 4 5 7 3 3 6 8 2 2 7 9 8 10 +--R 15120a b c d + 3780a b c d + 360a b c d + 9a b c +--R * +--R 8 +--R x +--R + +--R 9 3 7 8 4 6 7 2 5 5 6 3 6 4 5 4 7 3 +--R 120a c d + 1890a b c d + 9072a b c d + 17640a b c d + 15120a b c d +--R + +--R 4 5 8 2 3 6 9 2 7 10 +--R 5670a b c d + 840a b c d + 36a b c +--R * +--R 7 +--R x +--R + +--R 9 4 6 8 5 5 7 2 6 4 6 3 7 3 5 4 8 2 +--R 210a c d + 2268a b c d + 7560a b c d + 10080a b c d + 5670a b c d +--R + +--R 4 5 9 3 6 10 +--R 1260a b c d + 84a b c +--R * +--R 6 +--R x +--R + +--R 9 5 5 8 6 4 7 2 7 3 6 3 8 2 5 4 9 +--R 252a c d + 1890a b c d + 4320a b c d + 3780a b c d + 1260a b c d +--R + +--R 4 5 10 +--R 126a b c +--R * +--R 5 +--R x +--R + +--R 9 6 4 8 7 3 7 2 8 2 6 3 9 5 4 10 4 +--R (210a c d + 1080a b c d + 1620a b c d + 840a b c d + 126a b c )x +--R + +--R 9 7 3 8 8 2 7 2 9 6 3 10 3 +--R (120a c d + 405a b c d + 360a b c d + 84a b c )x +--R + +--R 9 8 2 8 9 7 2 10 2 9 9 8 10 9 10 +--R (45a c d + 90a b c d + 36a b c )x + (10a c d + 9a b c )x + a c +--R Type: Polynomial(Integer) +--E 746 + +--S 747 of 2952 +r0000:=-1/11*(b*c-a*d)^9*(c+d*x)^11/d^10+3/4*b*(b*c-a*d)^8*(c+d*x)^12/d^10-_ + 36/13*b^2*(b*c-a*d)^7*(c+d*x)^13/d^10+_ + 6*b^3*(b*c-a*d)^6*(c+d*x)^14/d^10-_ + 42/5*b^4*(b*c-a*d)^5*(c+d*x)^15/d^10+_ + 63/8*b^5*(b*c-a*d)^4*(c+d*x)^16/d^10-_ + 84/17*b^6*(b*c-a*d)^3*(c+d*x)^17/d^10+_ + 2*b^7*(b*c-a*d)^2*(c+d*x)^18/d^10-_ + 9/19*b^8*(b*c-a*d)*(c+d*x)^19/d^10+1/20*b^9*(c+d*x)^20/d^10 +--R +--R +--R (2) +--R 1 9 20 20 9 8 20 10 9 19 19 +--R -- b d x + (-- a b d + -- b c d )x +--R 20 19 19 +--R + +--R 2 7 20 8 19 5 9 2 18 18 +--R (2a b d + 5a b c d + - b c d )x +--R 2 +--R + +--R 84 3 6 20 360 2 7 19 405 8 2 18 120 9 3 17 17 +--R (-- a b d + --- a b c d + --- a b c d + --- b c d )x +--R 17 17 17 17 +--R + +--R 63 4 5 20 105 3 6 19 405 2 7 2 18 135 8 3 17 +--R -- a b d + --- a b c d + --- a b c d + --- a b c d +--R 8 2 4 2 +--R + +--R 105 9 4 16 +--R --- b c d +--R 8 +--R * +--R 16 +--R x +--R + +--R 42 5 4 20 4 5 19 3 6 2 18 2 7 3 17 8 4 16 +--R -- a b d + 84a b c d + 252a b c d + 288a b c d + 126a b c d +--R 5 +--R + +--R 84 9 5 15 +--R -- b c d +--R 5 +--R * +--R 15 +--R x +--R + +--R 6 3 20 5 4 19 4 5 2 18 3 6 3 17 2 7 4 16 +--R 6a b d + 90a b c d + 405a b c d + 720a b c d + 540a b c d +--R + +--R 8 5 15 9 6 14 +--R 162a b c d + 15b c d +--R * +--R 14 +--R x +--R + +--R 36 7 2 20 840 6 3 19 5670 5 4 2 18 15120 4 5 3 17 +--R -- a b d + --- a b c d + ---- a b c d + ----- a b c d +--R 13 13 13 13 +--R + +--R 17640 3 6 4 16 9072 2 7 5 15 1890 8 6 14 120 9 7 13 +--R ----- a b c d + ---- a b c d + ---- a b c d + --- b c d +--R 13 13 13 13 +--R * +--R 13 +--R x +--R + +--R 3 8 20 7 2 19 6 3 2 18 5 4 3 17 +--R - a b d + 30a b c d + 315a b c d + 1260a b c d +--R 4 +--R + +--R 4 5 4 16 3 6 5 15 2 7 6 14 8 7 13 15 9 8 12 +--R 2205a b c d + 1764a b c d + 630a b c d + 90a b c d + -- b c d +--R 4 +--R * +--R 12 +--R x +--R + +--R 1 9 20 90 8 19 1620 7 2 2 18 10080 6 3 3 17 +--R -- a d + -- a b c d + ---- a b c d + ----- a b c d +--R 11 11 11 11 +--R + +--R 26460 5 4 4 16 31752 4 5 5 15 17640 3 6 6 14 4320 2 7 7 13 +--R ----- a b c d + ----- a b c d + ----- a b c d + ---- a b c d +--R 11 11 11 11 +--R + +--R 405 8 8 12 10 9 9 11 +--R --- a b c d + -- b c d +--R 11 11 +--R * +--R 11 +--R x +--R + +--R 9 19 81 8 2 18 7 2 3 17 6 3 4 16 +--R a c d + -- a b c d + 432a b c d + 1764a b c d +--R 2 +--R + +--R 15876 5 4 5 15 4 5 6 14 3 6 7 13 2 7 8 12 +--R ----- a b c d + 2646a b c d + 1008a b c d + 162a b c d +--R 5 +--R + +--R 8 9 11 1 9 10 10 +--R 9a b c d + -- b c d +--R 10 +--R * +--R 10 +--R x +--R + +--R 9 2 18 8 3 17 7 2 4 16 6 3 5 15 +--R 5a c d + 120a b c d + 840a b c d + 2352a b c d +--R + +--R 5 4 6 14 4 5 7 13 3 6 8 12 2 7 9 11 8 10 10 +--R 2940a b c d + 1680a b c d + 420a b c d + 40a b c d + a b c d +--R * +--R 9 +--R x +--R + +--R 9 3 17 945 8 4 16 7 2 5 15 6 3 6 14 +--R 15a c d + --- a b c d + 1134a b c d + 2205a b c d +--R 4 +--R + +--R 5 4 7 13 2835 4 5 8 12 3 6 9 11 9 2 7 10 10 +--R 1890a b c d + ---- a b c d + 105a b c d + - a b c d +--R 4 2 +--R * +--R 8 +--R x +--R + +--R 9 4 16 8 5 15 7 2 6 14 6 3 7 13 +--R 30a c d + 324a b c d + 1080a b c d + 1440a b c d +--R + +--R 5 4 8 12 4 5 9 11 3 6 10 10 +--R 810a b c d + 180a b c d + 12a b c d +--R * +--R 7 +--R x +--R + +--R 9 5 15 8 6 14 7 2 7 13 6 3 8 12 5 4 9 11 +--R 42a c d + 315a b c d + 720a b c d + 630a b c d + 210a b c d +--R + +--R 4 5 10 10 +--R 21a b c d +--R * +--R 6 +--R x +--R + +--R 9 6 14 8 7 13 7 2 8 12 6 3 9 11 +--R 42a c d + 216a b c d + 324a b c d + 168a b c d +--R + +--R 126 5 4 10 10 +--R --- a b c d +--R 5 +--R * +--R 5 +--R x +--R + +--R 9 7 13 405 8 8 12 7 2 9 11 6 3 10 10 4 +--R (30a c d + --- a b c d + 90a b c d + 21a b c d )x +--R 4 +--R + +--R 9 8 12 8 9 11 7 2 10 10 3 9 9 11 9 8 10 10 2 +--R (15a c d + 30a b c d + 12a b c d )x + (5a c d + - a b c d )x +--R 2 +--R + +--R 9 10 10 1 9 11 9 3 8 12 8 6 7 2 13 7 3 6 3 14 6 +--R a c d x + -- a c d - -- a b c d + --- a b c d - --- a b c d +--R 11 44 143 143 +--R + +--R 6 5 4 15 5 3 4 5 16 4 3 3 6 17 3 1 2 7 18 2 +--R --- a b c d - ---- a b c d + ---- a b c d - ---- a b c d +--R 715 1144 4862 9724 +--R + +--R 1 8 19 1 9 20 +--R ----- a b c d - ------- b c +--R 92378 1847560 +--R / +--R 10 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 747 + +--S 748 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 9 10 20 9 8 10 10 9 9 19 +--R -- b d x + (-- a b d + -- b c d )x +--R 20 19 19 +--R + +--R 2 7 10 8 9 5 9 2 8 18 +--R (2a b d + 5a b c d + - b c d )x +--R 2 +--R + +--R 84 3 6 10 360 2 7 9 405 8 2 8 120 9 3 7 17 +--R (-- a b d + --- a b c d + --- a b c d + --- b c d )x +--R 17 17 17 17 +--R + +--R 63 4 5 10 105 3 6 9 405 2 7 2 8 135 8 3 7 105 9 4 6 16 +--R (-- a b d + --- a b c d + --- a b c d + --- a b c d + --- b c d )x +--R 8 2 4 2 8 +--R + +--R 42 5 4 10 4 5 9 3 6 2 8 2 7 3 7 8 4 6 +--R -- a b d + 84a b c d + 252a b c d + 288a b c d + 126a b c d +--R 5 +--R + +--R 84 9 5 5 +--R -- b c d +--R 5 +--R * +--R 15 +--R x +--R + +--R 6 3 10 5 4 9 4 5 2 8 3 6 3 7 2 7 4 6 +--R 6a b d + 90a b c d + 405a b c d + 720a b c d + 540a b c d +--R + +--R 8 5 5 9 6 4 +--R 162a b c d + 15b c d +--R * +--R 14 +--R x +--R + +--R 36 7 2 10 840 6 3 9 5670 5 4 2 8 15120 4 5 3 7 +--R -- a b d + --- a b c d + ---- a b c d + ----- a b c d +--R 13 13 13 13 +--R + +--R 17640 3 6 4 6 9072 2 7 5 5 1890 8 6 4 120 9 7 3 +--R ----- a b c d + ---- a b c d + ---- a b c d + --- b c d +--R 13 13 13 13 +--R * +--R 13 +--R x +--R + +--R 3 8 10 7 2 9 6 3 2 8 5 4 3 7 4 5 4 6 +--R - a b d + 30a b c d + 315a b c d + 1260a b c d + 2205a b c d +--R 4 +--R + +--R 3 6 5 5 2 7 6 4 8 7 3 15 9 8 2 +--R 1764a b c d + 630a b c d + 90a b c d + -- b c d +--R 4 +--R * +--R 12 +--R x +--R + +--R 1 9 10 90 8 9 1620 7 2 2 8 10080 6 3 3 7 +--R -- a d + -- a b c d + ---- a b c d + ----- a b c d +--R 11 11 11 11 +--R + +--R 26460 5 4 4 6 31752 4 5 5 5 17640 3 6 6 4 4320 2 7 7 3 +--R ----- a b c d + ----- a b c d + ----- a b c d + ---- a b c d +--R 11 11 11 11 +--R + +--R 405 8 8 2 10 9 9 +--R --- a b c d + -- b c d +--R 11 11 +--R * +--R 11 +--R x +--R + +--R 9 9 81 8 2 8 7 2 3 7 6 3 4 6 15876 5 4 5 5 +--R a c d + -- a b c d + 432a b c d + 1764a b c d + ----- a b c d +--R 2 5 +--R + +--R 4 5 6 4 3 6 7 3 2 7 8 2 8 9 1 9 10 +--R 2646a b c d + 1008a b c d + 162a b c d + 9a b c d + -- b c +--R 10 +--R * +--R 10 +--R x +--R + +--R 9 2 8 8 3 7 7 2 4 6 6 3 5 5 5 4 6 4 +--R 5a c d + 120a b c d + 840a b c d + 2352a b c d + 2940a b c d +--R + +--R 4 5 7 3 3 6 8 2 2 7 9 8 10 +--R 1680a b c d + 420a b c d + 40a b c d + a b c +--R * +--R 9 +--R x +--R + +--R 9 3 7 945 8 4 6 7 2 5 5 6 3 6 4 5 4 7 3 +--R 15a c d + --- a b c d + 1134a b c d + 2205a b c d + 1890a b c d +--R 4 +--R + +--R 2835 4 5 8 2 3 6 9 9 2 7 10 +--R ---- a b c d + 105a b c d + - a b c +--R 4 2 +--R * +--R 8 +--R x +--R + +--R 9 4 6 8 5 5 7 2 6 4 6 3 7 3 5 4 8 2 +--R 30a c d + 324a b c d + 1080a b c d + 1440a b c d + 810a b c d +--R + +--R 4 5 9 3 6 10 +--R 180a b c d + 12a b c +--R * +--R 7 +--R x +--R + +--R 9 5 5 8 6 4 7 2 7 3 6 3 8 2 5 4 9 +--R 42a c d + 315a b c d + 720a b c d + 630a b c d + 210a b c d +--R + +--R 4 5 10 +--R 21a b c +--R * +--R 6 +--R x +--R + +--R 9 6 4 8 7 3 7 2 8 2 6 3 9 126 5 4 10 5 +--R (42a c d + 216a b c d + 324a b c d + 168a b c d + --- a b c )x +--R 5 +--R + +--R 9 7 3 405 8 8 2 7 2 9 6 3 10 4 +--R (30a c d + --- a b c d + 90a b c d + 21a b c )x +--R 4 +--R + +--R 9 8 2 8 9 7 2 10 3 9 9 9 8 10 2 9 10 +--R (15a c d + 30a b c d + 12a b c )x + (5a c d + - a b c )x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 748 + +--S 749 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 9 11 9 3 8 12 8 6 7 2 13 7 3 6 3 14 6 +--R - -- a c d + -- a b c d - --- a b c d + --- a b c d +--R 11 44 143 143 +--R + +--R 6 5 4 15 5 3 4 5 16 4 3 3 6 17 3 1 2 7 18 2 +--R - --- a b c d + ---- a b c d - ---- a b c d + ---- a b c d +--R 715 1144 4862 9724 +--R + +--R 1 8 19 1 9 20 +--R - ----- a b c d + ------- b c +--R 92378 1847560 +--R / +--R 10 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 749 + +--S 750 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 750 + +)clear all + +--S 751 of 2952 +t0000:=(a+b*x)^8*(c+d*x)^10 +--R +--R +--R (1) +--R 8 10 18 7 10 8 9 17 +--R b d x + (8a b d + 10b c d )x +--R + +--R 2 6 10 7 9 8 2 8 16 +--R (28a b d + 80a b c d + 45b c d )x +--R + +--R 3 5 10 2 6 9 7 2 8 8 3 7 15 +--R (56a b d + 280a b c d + 360a b c d + 120b c d )x +--R + +--R 4 4 10 3 5 9 2 6 2 8 7 3 7 8 4 6 14 +--R (70a b d + 560a b c d + 1260a b c d + 960a b c d + 210b c d )x +--R + +--R 5 3 10 4 4 9 3 5 2 8 2 6 3 7 7 4 6 +--R 56a b d + 700a b c d + 2520a b c d + 3360a b c d + 1680a b c d +--R + +--R 8 5 5 +--R 252b c d +--R * +--R 13 +--R x +--R + +--R 6 2 10 5 3 9 4 4 2 8 3 5 3 7 2 6 4 6 +--R 28a b d + 560a b c d + 3150a b c d + 6720a b c d + 5880a b c d +--R + +--R 7 5 5 8 6 4 +--R 2016a b c d + 210b c d +--R * +--R 12 +--R x +--R + +--R 7 10 6 2 9 5 3 2 8 4 4 3 7 3 5 4 6 +--R 8a b d + 280a b c d + 2520a b c d + 8400a b c d + 11760a b c d +--R + +--R 2 6 5 5 7 6 4 8 7 3 +--R 7056a b c d + 1680a b c d + 120b c d +--R * +--R 11 +--R x +--R + +--R 8 10 7 9 6 2 2 8 5 3 3 7 4 4 4 6 +--R a d + 80a b c d + 1260a b c d + 6720a b c d + 14700a b c d +--R + +--R 3 5 5 5 2 6 6 4 7 7 3 8 8 2 +--R 14112a b c d + 5880a b c d + 960a b c d + 45b c d +--R * +--R 10 +--R x +--R + +--R 8 9 7 2 8 6 2 3 7 5 3 4 6 4 4 5 5 +--R 10a c d + 360a b c d + 3360a b c d + 11760a b c d + 17640a b c d +--R + +--R 3 5 6 4 2 6 7 3 7 8 2 8 9 +--R 11760a b c d + 3360a b c d + 360a b c d + 10b c d +--R * +--R 9 +--R x +--R + +--R 8 2 8 7 3 7 6 2 4 6 5 3 5 5 4 4 6 4 +--R 45a c d + 960a b c d + 5880a b c d + 14112a b c d + 14700a b c d +--R + +--R 3 5 7 3 2 6 8 2 7 9 8 10 +--R 6720a b c d + 1260a b c d + 80a b c d + b c +--R * +--R 8 +--R x +--R + +--R 8 3 7 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 +--R 120a c d + 1680a b c d + 7056a b c d + 11760a b c d + 8400a b c d +--R + +--R 3 5 8 2 2 6 9 7 10 +--R 2520a b c d + 280a b c d + 8a b c +--R * +--R 7 +--R x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 210a c d + 2016a b c d + 5880a b c d + 6720a b c d + 3150a b c d +--R + +--R 3 5 9 2 6 10 +--R 560a b c d + 28a b c +--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 252a c d + 1680a b c d + 3360a b c d + 2520a b c d + 700a b c d +--R + +--R 3 5 10 +--R 56a 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 4 +--R (210a c d + 960a b c d + 1260a b c d + 560a b c d + 70a b c )x +--R + +--R 8 7 3 7 8 2 6 2 9 5 3 10 3 +--R (120a c d + 360a b c d + 280a b c d + 56a b c )x +--R + +--R 8 8 2 7 9 6 2 10 2 8 9 7 10 8 10 +--R (45a c d + 80a b c d + 28a b c )x + (10a c d + 8a b c )x + a c +--R Type: Polynomial(Integer) +--E 751 + +--S 752 of 2952 +r0000:=1/11*(b*c-a*d)^8*(c+d*x)^11/d^9-2/3*b*(b*c-a*d)^7*(c+d*x)^12/d^9+_ + 28/13*b^2*(b*c-a*d)^6*(c+d*x)^13/d^9-4*b^3*(b*c-a*d)^5*(c+d*x)^14/d^9+_ + 14/3*b^4*(b*c-a*d)^4*(c+d*x)^15/d^9-7/2*b^5*(b*c-a*d)^3*(c+d*x)^16/d^9+_ + 28/17*b^6*(b*c-a*d)^2*(c+d*x)^17/d^9-4/9*b^7*(b*c-a*d)*(c+d*x)^18/d^9+_ + 1/19*b^8*(c+d*x)^19/d^9 +--R +--R +--R (2) +--R 1 8 19 19 4 7 19 5 8 18 18 +--R -- b d x + (- a b d + - b c d )x +--R 19 9 9 +--R + +--R 28 2 6 19 80 7 18 45 8 2 17 17 +--R (-- a b d + -- a b c d + -- b c d )x +--R 17 17 17 +--R + +--R 7 3 5 19 35 2 6 18 45 7 2 17 15 8 3 16 16 +--R (- a b d + -- a b c d + -- a b c d + -- b c d )x +--R 2 2 2 2 +--R + +--R 14 4 4 19 112 3 5 18 2 6 2 17 7 3 16 8 4 15 15 +--R (-- a b d + --- a b c d + 84a b c d + 64a b c d + 14b c d )x +--R 3 3 +--R + +--R 5 3 19 4 4 18 3 5 2 17 2 6 3 16 7 4 15 +--R 4a b d + 50a b c d + 180a b c d + 240a b c d + 120a b c d +--R + +--R 8 5 14 +--R 18b c d +--R * +--R 14 +--R x +--R + +--R 28 6 2 19 560 5 3 18 3150 4 4 2 17 6720 3 5 3 16 +--R -- a b d + --- a b c d + ---- a b c d + ---- a b c d +--R 13 13 13 13 +--R + +--R 5880 2 6 4 15 2016 7 5 14 210 8 6 13 +--R ---- a b c d + ---- a b c d + --- b c d +--R 13 13 13 +--R * +--R 13 +--R x +--R + +--R 2 7 19 70 6 2 18 5 3 2 17 4 4 3 16 3 5 4 15 +--R - a b d + -- a b c d + 210a b c d + 700a b c d + 980a b c d +--R 3 3 +--R + +--R 2 6 5 14 7 6 13 8 7 12 +--R 588a b c d + 140a b c d + 10b c d +--R * +--R 12 +--R x +--R + +--R 1 8 19 80 7 18 1260 6 2 2 17 6720 5 3 3 16 +--R -- a d + -- a b c d + ---- a b c d + ---- a b c d +--R 11 11 11 11 +--R + +--R 14700 4 4 4 15 14112 3 5 5 14 5880 2 6 6 13 960 7 7 12 +--R ----- a b c d + ----- a b c d + ---- a b c d + --- a b c d +--R 11 11 11 11 +--R + +--R 45 8 8 11 +--R -- b c d +--R 11 +--R * +--R 11 +--R x +--R + +--R 8 18 7 2 17 6 2 3 16 5 3 4 15 4 4 5 14 +--R a c d + 36a b c d + 336a b c d + 1176a b c d + 1764a b c d +--R + +--R 3 5 6 13 2 6 7 12 7 8 11 8 9 10 +--R 1176a b c d + 336a b c d + 36a b c d + b c d +--R * +--R 10 +--R x +--R + +--R 8 2 17 320 7 3 16 1960 6 2 4 15 5 3 5 14 +--R 5a c d + --- a b c d + ---- a b c d + 1568a b c d +--R 3 3 +--R + +--R 4900 4 4 6 13 2240 3 5 7 12 2 6 8 11 80 7 9 10 +--R ---- a b c d + ---- a b c d + 140a b c d + -- a b c d +--R 3 3 9 +--R + +--R 1 8 10 9 +--R - b c d +--R 9 +--R * +--R 9 +--R x +--R + +--R 8 3 16 7 4 15 6 2 5 14 5 3 6 13 +--R 15a c d + 210a b c d + 882a b c d + 1470a b c d +--R + +--R 4 4 7 12 3 5 8 11 2 6 9 10 7 10 9 +--R 1050a b c d + 315a b c d + 35a b c d + a b c d +--R * +--R 8 +--R x +--R + +--R 8 4 15 7 5 14 6 2 6 13 5 3 7 12 4 4 8 11 +--R 30a c d + 288a b c d + 840a b c d + 960a b c d + 450a b c d +--R + +--R 3 5 9 10 2 6 10 9 +--R 80a b c d + 4a b c d +--R * +--R 7 +--R x +--R + +--R 8 5 14 7 6 13 6 2 7 12 5 3 8 11 +--R 42a c d + 280a b c d + 560a b c d + 420a b c d +--R + +--R 350 4 4 9 10 28 3 5 10 9 +--R --- a b c d + -- a b c d +--R 3 3 +--R * +--R 6 +--R x +--R + +--R 8 6 13 7 7 12 6 2 8 11 5 3 9 10 4 4 10 9 5 +--R (42a c d + 192a b c d + 252a b c d + 112a b c d + 14a b c d )x +--R + +--R 8 7 12 7 8 11 6 2 9 10 5 3 10 9 4 +--R (30a c d + 90a b c d + 70a b c d + 14a b c d )x +--R + +--R 8 8 11 80 7 9 10 28 6 2 10 9 3 8 9 10 7 10 9 2 +--R (15a c d + -- a b c d + -- a b c d )x + (5a c d + 4a b c d )x +--R 3 3 +--R + +--R 8 10 9 1 8 11 8 2 7 12 7 14 6 2 13 6 2 5 3 14 5 +--R a c d x + -- a c d - -- a b c d + --- a b c d - --- a b c d +--R 11 33 429 143 +--R + +--R 2 4 4 15 4 1 3 5 16 3 1 2 6 17 2 1 7 18 +--R --- a b c d - --- a b c d + ---- a b c d - ----- a b c d +--R 429 858 4862 43758 +--R + +--R 1 8 19 +--R ------ b c +--R 831402 +--R / +--R 9 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 752 + +--S 753 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 8 10 19 4 7 10 5 8 9 18 +--R -- b d x + (- a b d + - b c d )x +--R 19 9 9 +--R + +--R 28 2 6 10 80 7 9 45 8 2 8 17 +--R (-- a b d + -- a b c d + -- b c d )x +--R 17 17 17 +--R + +--R 7 3 5 10 35 2 6 9 45 7 2 8 15 8 3 7 16 +--R (- a b d + -- a b c d + -- a b c d + -- b c d )x +--R 2 2 2 2 +--R + +--R 14 4 4 10 112 3 5 9 2 6 2 8 7 3 7 8 4 6 15 +--R (-- a b d + --- a b c d + 84a b c d + 64a b c d + 14b c d )x +--R 3 3 +--R + +--R 5 3 10 4 4 9 3 5 2 8 2 6 3 7 7 4 6 +--R 4a b d + 50a b c d + 180a b c d + 240a b c d + 120a b c d +--R + +--R 8 5 5 +--R 18b c d +--R * +--R 14 +--R x +--R + +--R 28 6 2 10 560 5 3 9 3150 4 4 2 8 6720 3 5 3 7 +--R -- a b d + --- a b c d + ---- a b c d + ---- a b c d +--R 13 13 13 13 +--R + +--R 5880 2 6 4 6 2016 7 5 5 210 8 6 4 +--R ---- a b c d + ---- a b c d + --- b c d +--R 13 13 13 +--R * +--R 13 +--R x +--R + +--R 2 7 10 70 6 2 9 5 3 2 8 4 4 3 7 3 5 4 6 +--R - a b d + -- a b c d + 210a b c d + 700a b c d + 980a b c d +--R 3 3 +--R + +--R 2 6 5 5 7 6 4 8 7 3 +--R 588a b c d + 140a b c d + 10b c d +--R * +--R 12 +--R x +--R + +--R 1 8 10 80 7 9 1260 6 2 2 8 6720 5 3 3 7 14700 4 4 4 6 +--R -- a d + -- a b c d + ---- a b c d + ---- a b c d + ----- a b c d +--R 11 11 11 11 11 +--R + +--R 14112 3 5 5 5 5880 2 6 6 4 960 7 7 3 45 8 8 2 +--R ----- a b c d + ---- a b c d + --- a b c d + -- b c d +--R 11 11 11 11 +--R * +--R 11 +--R x +--R + +--R 8 9 7 2 8 6 2 3 7 5 3 4 6 4 4 5 5 +--R a c d + 36a b c d + 336a b c d + 1176a b c d + 1764a b c d +--R + +--R 3 5 6 4 2 6 7 3 7 8 2 8 9 +--R 1176a b c d + 336a b c d + 36a b c d + b c d +--R * +--R 10 +--R x +--R + +--R 8 2 8 320 7 3 7 1960 6 2 4 6 5 3 5 5 4900 4 4 6 4 +--R 5a c d + --- a b c d + ---- a b c d + 1568a b c d + ---- a b c d +--R 3 3 3 +--R + +--R 2240 3 5 7 3 2 6 8 2 80 7 9 1 8 10 +--R ---- a b c d + 140a b c d + -- a b c d + - b c +--R 3 9 9 +--R * +--R 9 +--R x +--R + +--R 8 3 7 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 +--R 15a c d + 210a b c d + 882a b c d + 1470a b c d + 1050a b c d +--R + +--R 3 5 8 2 2 6 9 7 10 +--R 315a b c d + 35a b c d + a b c +--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 30a c d + 288a b c d + 840a b c d + 960a b c d + 450a b c d +--R + +--R 3 5 9 2 6 10 +--R 80a b c d + 4a b c +--R * +--R 7 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 350 4 4 9 +--R 42a c d + 280a b c d + 560a b c d + 420a b c d + --- a b c d +--R 3 +--R + +--R 28 3 5 10 +--R -- a b c +--R 3 +--R * +--R 6 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 5 +--R (42a c d + 192a b c d + 252a b c d + 112a b c d + 14a b c )x +--R + +--R 8 7 3 7 8 2 6 2 9 5 3 10 4 +--R (30a c d + 90a b c d + 70a b c d + 14a b c )x +--R + +--R 8 8 2 80 7 9 28 6 2 10 3 8 9 7 10 2 8 10 +--R (15a c d + -- a b c d + -- a b c )x + (5a c d + 4a b c )x + a c x +--R 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 753 + +--S 754 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 8 11 8 2 7 12 7 14 6 2 13 6 2 5 3 14 5 +--R - -- a c d + -- a b c d - --- a b c d + --- a b c d +--R 11 33 429 143 +--R + +--R 2 4 4 15 4 1 3 5 16 3 1 2 6 17 2 1 7 18 +--R - --- a b c d + --- a b c d - ---- a b c d + ----- a b c d +--R 429 858 4862 43758 +--R + +--R 1 8 19 +--R - ------ b c +--R 831402 +--R / +--R 9 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 754 + +--S 755 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 755 + +)clear all + +--S 756 of 2952 +t0000:=(a+b*x)^7*(c+d*x)^10 +--R +--R +--R (1) +--R 7 10 17 6 10 7 9 16 +--R b d x + (7a b d + 10b c d )x +--R + +--R 2 5 10 6 9 7 2 8 15 +--R (21a b d + 70a b c d + 45b c d )x +--R + +--R 3 4 10 2 5 9 6 2 8 7 3 7 14 +--R (35a b d + 210a b c d + 315a b c d + 120b c d )x +--R + +--R 4 3 10 3 4 9 2 5 2 8 6 3 7 7 4 6 13 +--R (35a b d + 350a b c d + 945a b c d + 840a b c d + 210b c d )x +--R + +--R 5 2 10 4 3 9 3 4 2 8 2 5 3 7 6 4 6 +--R 21a b d + 350a b c d + 1575a b c d + 2520a b c d + 1470a b c d +--R + +--R 7 5 5 +--R 252b c d +--R * +--R 12 +--R x +--R + +--R 6 10 5 2 9 4 3 2 8 3 4 3 7 2 5 4 6 +--R 7a b d + 210a b c d + 1575a b c d + 4200a b c d + 4410a b c d +--R + +--R 6 5 5 7 6 4 +--R 1764a b c d + 210b c d +--R * +--R 11 +--R x +--R + +--R 7 10 6 9 5 2 2 8 4 3 3 7 3 4 4 6 +--R a d + 70a b c d + 945a b c d + 4200a b c d + 7350a b c d +--R + +--R 2 5 5 5 6 6 4 7 7 3 +--R 5292a b c d + 1470a b c d + 120b c d +--R * +--R 10 +--R x +--R + +--R 7 9 6 2 8 5 2 3 7 4 3 4 6 3 4 5 5 +--R 10a c d + 315a b c d + 2520a b c d + 7350a b c d + 8820a b c d +--R + +--R 2 5 6 4 6 7 3 7 8 2 +--R 4410a b c d + 840a b c d + 45b c d +--R * +--R 9 +--R x +--R + +--R 7 2 8 6 3 7 5 2 4 6 4 3 5 5 3 4 6 4 +--R 45a c d + 840a b c d + 4410a b c d + 8820a b c d + 7350a b c d +--R + +--R 2 5 7 3 6 8 2 7 9 +--R 2520a b c d + 315a b c d + 10b c d +--R * +--R 8 +--R x +--R + +--R 7 3 7 6 4 6 5 2 5 5 4 3 6 4 3 4 7 3 +--R 120a c d + 1470a b c d + 5292a b c d + 7350a b c d + 4200a b c d +--R + +--R 2 5 8 2 6 9 7 10 +--R 945a b c d + 70a b c d + b c +--R * +--R 7 +--R x +--R + +--R 7 4 6 6 5 5 5 2 6 4 4 3 7 3 3 4 8 2 +--R 210a c d + 1764a b c d + 4410a b c d + 4200a b c d + 1575a b c d +--R + +--R 2 5 9 6 10 +--R 210a b c d + 7a b c +--R * +--R 6 +--R x +--R + +--R 7 5 5 6 6 4 5 2 7 3 4 3 8 2 3 4 9 +--R 252a c d + 1470a b c d + 2520a b c d + 1575a b c d + 350a b c d +--R + +--R 2 5 10 +--R 21a b c +--R * +--R 5 +--R x +--R + +--R 7 6 4 6 7 3 5 2 8 2 4 3 9 3 4 10 4 +--R (210a c d + 840a b c d + 945a b c d + 350a b c d + 35a b c )x +--R + +--R 7 7 3 6 8 2 5 2 9 4 3 10 3 +--R (120a c d + 315a b c d + 210a b c d + 35a b c )x +--R + +--R 7 8 2 6 9 5 2 10 2 7 9 6 10 7 10 +--R (45a c d + 70a b c d + 21a b c )x + (10a c d + 7a b c )x + a c +--R Type: Polynomial(Integer) +--E 756 + +--S 757 of 2952 +r0000:=-1/11*(b*c-a*d)^7*(c+d*x)^11/d^8+7/12*b*(b*c-a*d)^6*(c+d*x)^12/d^8-_ + 21/13*b^2*(b*c-a*d)^5*(c+d*x)^13/d^8+_ + 5/2*b^3*(b*c-a*d)^4*(c+d*x)^14/d^8-_ + 7/3*b^4*(b*c-a*d)^3*(c+d*x)^15/d^8+_ + 21/16*b^5*(b*c-a*d)^2*(c+d*x)^16/d^8-_ + 7/17*b^6*(b*c-a*d)*(c+d*x)^17/d^8+1/18*b^7*(c+d*x)^18/d^8 +--R +--R +--R (2) +--R 1 7 18 18 7 6 18 10 7 17 17 +--R -- b d x + (-- a b d + -- b c d )x +--R 18 17 17 +--R + +--R 21 2 5 18 35 6 17 45 7 2 16 16 +--R (-- a b d + -- a b c d + -- b c d )x +--R 16 8 16 +--R + +--R 7 3 4 18 2 5 17 6 2 16 7 3 15 15 +--R (- a b d + 14a b c d + 21a b c d + 8b c d )x +--R 3 +--R + +--R 5 4 3 18 3 4 17 135 2 5 2 16 6 3 15 7 4 14 14 +--R (- a b d + 25a b c d + --- a b c d + 60a b c d + 15b c d )x +--R 2 2 +--R + +--R 21 5 2 18 350 4 3 17 1575 3 4 2 16 2520 2 5 3 15 +--R -- a b d + --- a b c d + ---- a b c d + ---- a b c d +--R 13 13 13 13 +--R + +--R 1470 6 4 14 252 7 5 13 +--R ---- a b c d + --- b c d +--R 13 13 +--R * +--R 13 +--R x +--R + +--R 7 6 18 35 5 2 17 525 4 3 2 16 3 4 3 15 +--R -- a b d + -- a b c d + --- a b c d + 350a b c d +--R 12 2 4 +--R + +--R 735 2 5 4 14 6 5 13 35 7 6 12 +--R --- a b c d + 147a b c d + -- b c d +--R 2 2 +--R * +--R 12 +--R x +--R + +--R 1 7 18 70 6 17 945 5 2 2 16 4200 4 3 3 15 +--R -- a d + -- a b c d + --- a b c d + ---- a b c d +--R 11 11 11 11 +--R + +--R 7350 3 4 4 14 5292 2 5 5 13 1470 6 6 12 120 7 7 11 +--R ---- a b c d + ---- a b c d + ---- a b c d + --- b c d +--R 11 11 11 11 +--R * +--R 11 +--R x +--R + +--R 7 17 63 6 2 16 5 2 3 15 4 3 4 14 3 4 5 13 +--R a c d + -- a b c d + 252a b c d + 735a b c d + 882a b c d +--R 2 +--R + +--R 2 5 6 12 6 7 11 9 7 8 10 +--R 441a b c d + 84a b c d + - b c d +--R 2 +--R * +--R 10 +--R x +--R + +--R 7 2 16 280 6 3 15 5 2 4 14 4 3 5 13 +--R 5a c d + --- a b c d + 490a b c d + 980a b c d +--R 3 +--R + +--R 2450 3 4 6 12 2 5 7 11 6 8 10 10 7 9 9 +--R ---- a b c d + 280a b c d + 35a b c d + -- b c d +--R 3 9 +--R * +--R 9 +--R x +--R + +--R 7 3 15 735 6 4 14 1323 5 2 5 13 3675 4 3 6 12 +--R 15a c d + --- a b c d + ---- a b c d + ---- a b c d +--R 4 2 4 +--R + +--R 3 4 7 11 945 2 5 8 10 35 6 9 9 1 7 10 8 +--R 525a b c d + --- a b c d + -- a b c d + - b c d +--R 8 4 8 +--R * +--R 8 +--R x +--R + +--R 7 4 14 6 5 13 5 2 6 12 4 3 7 11 3 4 8 10 +--R 30a c d + 252a b c d + 630a b c d + 600a b c d + 225a b c d +--R + +--R 2 5 9 9 6 10 8 +--R 30a b c d + a b c d +--R * +--R 7 +--R x +--R + +--R 7 5 13 6 6 12 5 2 7 11 525 4 3 8 10 +--R 42a c d + 245a b c d + 420a b c d + --- a b c d +--R 2 +--R + +--R 175 3 4 9 9 7 2 5 10 8 +--R --- a b c d + - a b c d +--R 3 2 +--R * +--R 6 +--R x +--R + +--R 7 6 12 6 7 11 5 2 8 10 4 3 9 9 3 4 10 8 5 +--R (42a c d + 168a b c d + 189a b c d + 70a b c d + 7a b c d )x +--R + +--R 7 7 11 315 6 8 10 105 5 2 9 9 35 4 3 10 8 4 +--R (30a c d + --- a b c d + --- a b c d + -- a b c d )x +--R 4 2 4 +--R + +--R 7 8 10 70 6 9 9 5 2 10 8 3 7 9 9 7 6 10 8 2 +--R (15a c d + -- a b c d + 7a b c d )x + (5a c d + - a b c d )x +--R 3 2 +--R + +--R 7 10 8 1 7 11 7 7 6 12 6 7 5 2 13 5 5 4 3 14 4 +--R a c d x + -- a c d - --- a b c d + --- a b c d - --- a b c d +--R 11 132 286 572 +--R + +--R 1 3 4 15 3 1 2 5 16 2 1 6 17 1 7 18 +--R --- a b c d - ---- a b c d + ----- a b c d - ------ b c +--R 429 2288 19448 350064 +--R / +--R 8 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 757 + +--S 758 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 10 18 7 6 10 10 7 9 17 +--R -- b d x + (-- a b d + -- b c d )x +--R 18 17 17 +--R + +--R 21 2 5 10 35 6 9 45 7 2 8 16 +--R (-- a b d + -- a b c d + -- b c d )x +--R 16 8 16 +--R + +--R 7 3 4 10 2 5 9 6 2 8 7 3 7 15 +--R (- a b d + 14a b c d + 21a b c d + 8b c d )x +--R 3 +--R + +--R 5 4 3 10 3 4 9 135 2 5 2 8 6 3 7 7 4 6 14 +--R (- a b d + 25a b c d + --- a b c d + 60a b c d + 15b c d )x +--R 2 2 +--R + +--R 21 5 2 10 350 4 3 9 1575 3 4 2 8 2520 2 5 3 7 +--R -- a b d + --- a b c d + ---- a b c d + ---- a b c d +--R 13 13 13 13 +--R + +--R 1470 6 4 6 252 7 5 5 +--R ---- a b c d + --- b c d +--R 13 13 +--R * +--R 13 +--R x +--R + +--R 7 6 10 35 5 2 9 525 4 3 2 8 3 4 3 7 735 2 5 4 6 +--R -- a b d + -- a b c d + --- a b c d + 350a b c d + --- a b c d +--R 12 2 4 2 +--R + +--R 6 5 5 35 7 6 4 +--R 147a b c d + -- b c d +--R 2 +--R * +--R 12 +--R x +--R + +--R 1 7 10 70 6 9 945 5 2 2 8 4200 4 3 3 7 7350 3 4 4 6 +--R -- a d + -- a b c d + --- a b c d + ---- a b c d + ---- a b c d +--R 11 11 11 11 11 +--R + +--R 5292 2 5 5 5 1470 6 6 4 120 7 7 3 +--R ---- a b c d + ---- a b c d + --- b c d +--R 11 11 11 +--R * +--R 11 +--R x +--R + +--R 7 9 63 6 2 8 5 2 3 7 4 3 4 6 3 4 5 5 +--R a c d + -- a b c d + 252a b c d + 735a b c d + 882a b c d +--R 2 +--R + +--R 2 5 6 4 6 7 3 9 7 8 2 +--R 441a b c d + 84a b c d + - b c d +--R 2 +--R * +--R 10 +--R x +--R + +--R 7 2 8 280 6 3 7 5 2 4 6 4 3 5 5 2450 3 4 6 4 +--R 5a c d + --- a b c d + 490a b c d + 980a b c d + ---- a b c d +--R 3 3 +--R + +--R 2 5 7 3 6 8 2 10 7 9 +--R 280a b c d + 35a b c d + -- b c d +--R 9 +--R * +--R 9 +--R x +--R + +--R 7 3 7 735 6 4 6 1323 5 2 5 5 3675 4 3 6 4 3 4 7 3 +--R 15a c d + --- a b c d + ---- a b c d + ---- a b c d + 525a b c d +--R 4 2 4 +--R + +--R 945 2 5 8 2 35 6 9 1 7 10 +--R --- a b c d + -- a b c d + - b c +--R 8 4 8 +--R * +--R 8 +--R x +--R + +--R 7 4 6 6 5 5 5 2 6 4 4 3 7 3 3 4 8 2 +--R 30a c d + 252a b c d + 630a b c d + 600a b c d + 225a b c d +--R + +--R 2 5 9 6 10 +--R 30a b c d + a b c +--R * +--R 7 +--R x +--R + +--R 7 5 5 6 6 4 5 2 7 3 525 4 3 8 2 175 3 4 9 +--R 42a c d + 245a b c d + 420a b c d + --- a b c d + --- a b c d +--R 2 3 +--R + +--R 7 2 5 10 +--R - a b c +--R 2 +--R * +--R 6 +--R x +--R + +--R 7 6 4 6 7 3 5 2 8 2 4 3 9 3 4 10 5 +--R (42a c d + 168a b c d + 189a b c d + 70a b c d + 7a b c )x +--R + +--R 7 7 3 315 6 8 2 105 5 2 9 35 4 3 10 4 +--R (30a c d + --- a b c d + --- a b c d + -- a b c )x +--R 4 2 4 +--R + +--R 7 8 2 70 6 9 5 2 10 3 7 9 7 6 10 2 7 10 +--R (15a c d + -- a b c d + 7a b c )x + (5a c d + - a b c )x + a c x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 758 + +--S 759 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 7 11 7 7 6 12 6 7 5 2 13 5 5 4 3 14 4 +--R - -- a c d + --- a b c d - --- a b c d + --- a b c d +--R 11 132 286 572 +--R + +--R 1 3 4 15 3 1 2 5 16 2 1 6 17 1 7 18 +--R - --- a b c d + ---- a b c d - ----- a b c d + ------ b c +--R 429 2288 19448 350064 +--R / +--R 8 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 759 + +--S 760 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 760 + +)clear all + +--S 761 of 2952 +t0000:=(a+b*x)^6*(c+d*x)^10 +--R +--R +--R (1) +--R 6 10 16 5 10 6 9 15 +--R b d x + (6a b d + 10b c d )x +--R + +--R 2 4 10 5 9 6 2 8 14 +--R (15a b d + 60a b c d + 45b c d )x +--R + +--R 3 3 10 2 4 9 5 2 8 6 3 7 13 +--R (20a b d + 150a b c d + 270a b c d + 120b c d )x +--R + +--R 4 2 10 3 3 9 2 4 2 8 5 3 7 6 4 6 12 +--R (15a b d + 200a b c d + 675a b c d + 720a b c d + 210b c d )x +--R + +--R 5 10 4 2 9 3 3 2 8 2 4 3 7 5 4 6 +--R 6a b d + 150a b c d + 900a b c d + 1800a b c d + 1260a b c d +--R + +--R 6 5 5 +--R 252b c d +--R * +--R 11 +--R x +--R + +--R 6 10 5 9 4 2 2 8 3 3 3 7 2 4 4 6 +--R a d + 60a b c d + 675a b c d + 2400a b c d + 3150a b c d +--R + +--R 5 5 5 6 6 4 +--R 1512a b c d + 210b c d +--R * +--R 10 +--R x +--R + +--R 6 9 5 2 8 4 2 3 7 3 3 4 6 2 4 5 5 +--R 10a c d + 270a b c d + 1800a b c d + 4200a b c d + 3780a b c d +--R + +--R 5 6 4 6 7 3 +--R 1260a b c d + 120b c d +--R * +--R 9 +--R x +--R + +--R 6 2 8 5 3 7 4 2 4 6 3 3 5 5 2 4 6 4 +--R 45a c d + 720a b c d + 3150a b c d + 5040a b c d + 3150a b c d +--R + +--R 5 7 3 6 8 2 +--R 720a b c d + 45b c d +--R * +--R 8 +--R x +--R + +--R 6 3 7 5 4 6 4 2 5 5 3 3 6 4 2 4 7 3 +--R 120a c d + 1260a b c d + 3780a b c d + 4200a b c d + 1800a b c d +--R + +--R 5 8 2 6 9 +--R 270a b c d + 10b c d +--R * +--R 7 +--R x +--R + +--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3 2 4 8 2 +--R 210a c d + 1512a b c d + 3150a b c d + 2400a b c d + 675a b c d +--R + +--R 5 9 6 10 +--R 60a b c d + b c +--R * +--R 6 +--R x +--R + +--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2 2 4 9 +--R 252a c d + 1260a b c d + 1800a b c d + 900a b c d + 150a b c d +--R + +--R 5 10 +--R 6a b c +--R * +--R 5 +--R x +--R + +--R 6 6 4 5 7 3 4 2 8 2 3 3 9 2 4 10 4 +--R (210a c d + 720a b c d + 675a b c d + 200a b c d + 15a b c )x +--R + +--R 6 7 3 5 8 2 4 2 9 3 3 10 3 +--R (120a c d + 270a b c d + 150a b c d + 20a b c )x +--R + +--R 6 8 2 5 9 4 2 10 2 6 9 5 10 6 10 +--R (45a c d + 60a b c d + 15a b c )x + (10a c d + 6a b c )x + a c +--R Type: Polynomial(Integer) +--E 761 + +--S 762 of 2952 +r0000:=1/11*(b*c-a*d)^6*(c+d*x)^11/d^7-1/2*b*(b*c-a*d)^5*(c+d*x)^12/d^7+_ + 15/13*b^2*(b*c-a*d)^4*(c+d*x)^13/d^7-_ + 10/7*b^3*(b*c-a*d)^3*(c+d*x)^14/d^7+b^4*(b*c-a*d)^2*(c+d*x)^15/d^7-_ + 3/8*b^5*(b*c-a*d)*(c+d*x)^16/d^7+1/17*b^6*(c+d*x)^17/d^7 +--R +--R +--R (2) +--R 1 6 17 17 3 5 17 5 6 16 16 +--R -- b d x + (- a b d + - b c d )x +--R 17 8 8 +--R + +--R 2 4 17 5 16 6 2 15 15 +--R (a b d + 4a b c d + 3b c d )x +--R + +--R 10 3 3 17 75 2 4 16 135 5 2 15 60 6 3 14 14 +--R (-- a b d + -- a b c d + --- a b c d + -- b c d )x +--R 7 7 7 7 +--R + +--R 15 4 2 17 200 3 3 16 675 2 4 2 15 720 5 3 14 +--R -- a b d + --- a b c d + --- a b c d + --- a b c d +--R 13 13 13 13 +--R + +--R 210 6 4 13 +--R --- b c d +--R 13 +--R * +--R 13 +--R x +--R + +--R 1 5 17 25 4 2 16 3 3 2 15 2 4 3 14 5 4 13 +--R - a b d + -- a b c d + 75a b c d + 150a b c d + 105a b c d +--R 2 2 +--R + +--R 6 5 12 +--R 21b c d +--R * +--R 12 +--R x +--R + +--R 1 6 17 60 5 16 675 4 2 2 15 2400 3 3 3 14 +--R -- a d + -- a b c d + --- a b c d + ---- a b c d +--R 11 11 11 11 +--R + +--R 3150 2 4 4 13 1512 5 5 12 210 6 6 11 +--R ---- a b c d + ---- a b c d + --- b c d +--R 11 11 11 +--R * +--R 11 +--R x +--R + +--R 6 16 5 2 15 4 2 3 14 3 3 4 13 2 4 5 12 +--R a c d + 27a b c d + 180a b c d + 420a b c d + 378a b c d +--R + +--R 5 6 11 6 7 10 +--R 126a b c d + 12b c d +--R * +--R 10 +--R x +--R + +--R 6 2 15 5 3 14 4 2 4 13 3 3 5 12 2 4 6 11 +--R 5a c d + 80a b c d + 350a b c d + 560a b c d + 350a b c d +--R + +--R 5 7 10 6 8 9 +--R 80a b c d + 5b c d +--R * +--R 9 +--R x +--R + +--R 6 3 14 315 5 4 13 945 4 2 5 12 3 3 6 11 +--R 15a c d + --- a b c d + --- a b c d + 525a b c d +--R 2 2 +--R + +--R 2 4 7 10 135 5 8 9 5 6 9 8 +--R 225a b c d + --- a b c d + - b c d +--R 4 4 +--R * +--R 8 +--R x +--R + +--R 6 4 13 5 5 12 4 2 6 11 2400 3 3 7 10 +--R 30a c d + 216a b c d + 450a b c d + ---- a b c d +--R 7 +--R + +--R 675 2 4 8 9 60 5 9 8 1 6 10 7 +--R --- a b c d + -- a b c d + - b c d +--R 7 7 7 +--R * +--R 7 +--R x +--R + +--R 6 5 12 5 6 11 4 2 7 10 3 3 8 9 2 4 9 8 +--R 42a c d + 210a b c d + 300a b c d + 150a b c d + 25a b c d +--R + +--R 5 10 7 +--R a b c d +--R * +--R 6 +--R x +--R + +--R 6 6 11 5 7 10 4 2 8 9 3 3 9 8 2 4 10 7 5 +--R (42a c d + 144a b c d + 135a b c d + 40a b c d + 3a b c d )x +--R + +--R 6 7 10 135 5 8 9 75 4 2 9 8 3 3 10 7 4 +--R (30a c d + --- a b c d + -- a b c d + 5a b c d )x +--R 2 2 +--R + +--R 6 8 9 5 9 8 4 2 10 7 3 6 9 8 5 10 7 2 +--R (15a c d + 20a b c d + 5a b c d )x + (5a c d + 3a b c d )x +--R + +--R 6 10 7 1 6 11 6 1 5 12 5 5 4 2 13 4 5 3 3 14 3 +--R a c d x + -- a c d - -- a b c d + --- a b c d - ---- a b c d +--R 11 22 286 1001 +--R + +--R 1 2 4 15 2 1 5 16 1 6 17 +--R ---- a b c d - ---- a b c d + ------ b c +--R 1001 8008 136136 +--R / +--R 7 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 762 + +--S 763 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 6 10 17 3 5 10 5 6 9 16 +--R -- b d x + (- a b d + - b c d )x +--R 17 8 8 +--R + +--R 2 4 10 5 9 6 2 8 15 +--R (a b d + 4a b c d + 3b c d )x +--R + +--R 10 3 3 10 75 2 4 9 135 5 2 8 60 6 3 7 14 +--R (-- a b d + -- a b c d + --- a b c d + -- b c d )x +--R 7 7 7 7 +--R + +--R 15 4 2 10 200 3 3 9 675 2 4 2 8 720 5 3 7 210 6 4 6 13 +--R (-- a b d + --- a b c d + --- a b c d + --- a b c d + --- b c d )x +--R 13 13 13 13 13 +--R + +--R 1 5 10 25 4 2 9 3 3 2 8 2 4 3 7 5 4 6 +--R - a b d + -- a b c d + 75a b c d + 150a b c d + 105a b c d +--R 2 2 +--R + +--R 6 5 5 +--R 21b c d +--R * +--R 12 +--R x +--R + +--R 1 6 10 60 5 9 675 4 2 2 8 2400 3 3 3 7 3150 2 4 4 6 +--R -- a d + -- a b c d + --- a b c d + ---- a b c d + ---- a b c d +--R 11 11 11 11 11 +--R + +--R 1512 5 5 5 210 6 6 4 +--R ---- a b c d + --- b c d +--R 11 11 +--R * +--R 11 +--R x +--R + +--R 6 9 5 2 8 4 2 3 7 3 3 4 6 2 4 5 5 +--R a c d + 27a b c d + 180a b c d + 420a b c d + 378a b c d +--R + +--R 5 6 4 6 7 3 +--R 126a b c d + 12b c d +--R * +--R 10 +--R x +--R + +--R 6 2 8 5 3 7 4 2 4 6 3 3 5 5 2 4 6 4 +--R 5a c d + 80a b c d + 350a b c d + 560a b c d + 350a b c d +--R + +--R 5 7 3 6 8 2 +--R 80a b c d + 5b c d +--R * +--R 9 +--R x +--R + +--R 6 3 7 315 5 4 6 945 4 2 5 5 3 3 6 4 2 4 7 3 +--R 15a c d + --- a b c d + --- a b c d + 525a b c d + 225a b c d +--R 2 2 +--R + +--R 135 5 8 2 5 6 9 +--R --- a b c d + - b c d +--R 4 4 +--R * +--R 8 +--R x +--R + +--R 6 4 6 5 5 5 4 2 6 4 2400 3 3 7 3 675 2 4 8 2 +--R 30a c d + 216a b c d + 450a b c d + ---- a b c d + --- a b c d +--R 7 7 +--R + +--R 60 5 9 1 6 10 +--R -- a b c d + - b c +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2 2 4 9 +--R 42a c d + 210a b c d + 300a b c d + 150a b c d + 25a b c d +--R + +--R 5 10 +--R a b c +--R * +--R 6 +--R x +--R + +--R 6 6 4 5 7 3 4 2 8 2 3 3 9 2 4 10 5 +--R (42a c d + 144a b c d + 135a b c d + 40a b c d + 3a b c )x +--R + +--R 6 7 3 135 5 8 2 75 4 2 9 3 3 10 4 +--R (30a c d + --- a b c d + -- a b c d + 5a b c )x +--R 2 2 +--R + +--R 6 8 2 5 9 4 2 10 3 6 9 5 10 2 6 10 +--R (15a c d + 20a b c d + 5a b c )x + (5a c d + 3a b c )x + a c x +--R Type: Polynomial(Fraction(Integer)) +--E 763 + +--S 764 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 6 11 6 1 5 12 5 5 4 2 13 4 5 3 3 14 3 +--R - -- a c d + -- a b c d - --- a b c d + ---- a b c d +--R 11 22 286 1001 +--R + +--R 1 2 4 15 2 1 5 16 1 6 17 +--R - ---- a b c d + ---- a b c d - ------ b c +--R 1001 8008 136136 +--R / +--R 7 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 764 + +--S 765 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 765 + +)clear all + +--S 766 of 2952 +t0000:=(a+b*x)^5*(c+d*x)^10 +--R +--R +--R (1) +--R 5 10 15 4 10 5 9 14 +--R b d x + (5a b d + 10b c d )x +--R + +--R 2 3 10 4 9 5 2 8 13 +--R (10a b d + 50a b c d + 45b c d )x +--R + +--R 3 2 10 2 3 9 4 2 8 5 3 7 12 +--R (10a b d + 100a b c d + 225a b c d + 120b c d )x +--R + +--R 4 10 3 2 9 2 3 2 8 4 3 7 5 4 6 11 +--R (5a b d + 100a b c d + 450a b c d + 600a b c d + 210b c d )x +--R + +--R 5 10 4 9 3 2 2 8 2 3 3 7 4 4 6 +--R a d + 50a b c d + 450a b c d + 1200a b c d + 1050a b c d +--R + +--R 5 5 5 +--R 252b c d +--R * +--R 10 +--R x +--R + +--R 5 9 4 2 8 3 2 3 7 2 3 4 6 4 5 5 +--R 10a c d + 225a b c d + 1200a b c d + 2100a b c d + 1260a b c d +--R + +--R 5 6 4 +--R 210b c d +--R * +--R 9 +--R x +--R + +--R 5 2 8 4 3 7 3 2 4 6 2 3 5 5 4 6 4 +--R 45a c d + 600a b c d + 2100a b c d + 2520a b c d + 1050a b c d +--R + +--R 5 7 3 +--R 120b c d +--R * +--R 8 +--R x +--R + +--R 5 3 7 4 4 6 3 2 5 5 2 3 6 4 4 7 3 +--R 120a c d + 1050a b c d + 2520a b c d + 2100a b c d + 600a b c d +--R + +--R 5 8 2 +--R 45b c d +--R * +--R 7 +--R x +--R + +--R 5 4 6 4 5 5 3 2 6 4 2 3 7 3 4 8 2 +--R 210a c d + 1260a b c d + 2100a b c d + 1200a b c d + 225a b c d +--R + +--R 5 9 +--R 10b c d +--R * +--R 6 +--R x +--R + +--R 5 5 5 4 6 4 3 2 7 3 2 3 8 2 4 9 +--R 252a c d + 1050a b c d + 1200a b c d + 450a b c d + 50a b c d +--R + +--R 5 10 +--R b c +--R * +--R 5 +--R x +--R + +--R 5 6 4 4 7 3 3 2 8 2 2 3 9 4 10 4 +--R (210a c d + 600a b c d + 450a b c d + 100a b c d + 5a b c )x +--R + +--R 5 7 3 4 8 2 3 2 9 2 3 10 3 +--R (120a c d + 225a b c d + 100a b c d + 10a b c )x +--R + +--R 5 8 2 4 9 3 2 10 2 5 9 4 10 5 10 +--R (45a c d + 50a b c d + 10a b c )x + (10a c d + 5a b c )x + a c +--R Type: Polynomial(Integer) +--E 766 + +--S 767 of 2952 +r0000:=-1/11*(b*c-a*d)^5*(c+d*x)^11/d^6+5/12*b*(b*c-a*d)^4*(c+d*x)^12/d^6-_ + 10/13*b^2*(b*c-a*d)^3*(c+d*x)^13/d^6+_ + 5/7*b^3*(b*c-a*d)^2*(c+d*x)^14/d^6-_ + 1/3*b^4*(b*c-a*d)*(c+d*x)^15/d^6+1/16*b^5*(c+d*x)^16/d^6 +--R +--R +--R (2) +--R 1 5 16 16 1 4 16 2 5 15 15 +--R -- b d x + (- a b d + - b c d )x +--R 16 3 3 +--R + +--R 5 2 3 16 25 4 15 45 5 2 14 14 +--R (- a b d + -- a b c d + -- b c d )x +--R 7 7 14 +--R + +--R 10 3 2 16 100 2 3 15 225 4 2 14 120 5 3 13 13 +--R (-- a b d + --- a b c d + --- a b c d + --- b c d )x +--R 13 13 13 13 +--R + +--R 5 4 16 25 3 2 15 75 2 3 2 14 4 3 13 35 5 4 12 12 +--R (-- a b d + -- a b c d + -- a b c d + 50a b c d + -- b c d )x +--R 12 3 2 2 +--R + +--R 1 5 16 50 4 15 450 3 2 2 14 1200 2 3 3 13 +--R -- a d + -- a b c d + --- a b c d + ---- a b c d +--R 11 11 11 11 +--R + +--R 1050 4 4 12 252 5 5 11 +--R ---- a b c d + --- b c d +--R 11 11 +--R * +--R 11 +--R x +--R + +--R 5 15 45 4 2 14 3 2 3 13 2 3 4 12 4 5 11 +--R a c d + -- a b c d + 120a b c d + 210a b c d + 126a b c d +--R 2 +--R + +--R 5 6 10 +--R 21b c d +--R * +--R 10 +--R x +--R + +--R 5 2 14 200 4 3 13 700 3 2 4 12 2 3 5 11 +--R 5a c d + --- a b c d + --- a b c d + 280a b c d +--R 3 3 +--R + +--R 350 4 6 10 40 5 7 9 +--R --- a b c d + -- b c d +--R 3 3 +--R * +--R 9 +--R x +--R + +--R 5 3 13 525 4 4 12 3 2 5 11 525 2 3 6 10 4 7 9 +--R 15a c d + --- a b c d + 315a b c d + --- a b c d + 75a b c d +--R 4 2 +--R + +--R 45 5 8 8 +--R -- b c d +--R 8 +--R * +--R 8 +--R x +--R + +--R 5 4 12 4 5 11 3 2 6 10 1200 2 3 7 9 +--R 30a c d + 180a b c d + 300a b c d + ---- a b c d +--R 7 +--R + +--R 225 4 8 8 10 5 9 7 +--R --- a b c d + -- b c d +--R 7 7 +--R * +--R 7 +--R x +--R + +--R 5 5 11 4 6 10 3 2 7 9 2 3 8 8 25 4 9 7 +--R 42a c d + 175a b c d + 200a b c d + 75a b c d + -- a b c d +--R 3 +--R + +--R 1 5 10 6 +--R - b c d +--R 6 +--R * +--R 6 +--R x +--R + +--R 5 6 10 4 7 9 3 2 8 8 2 3 9 7 4 10 6 5 +--R (42a c d + 120a b c d + 90a b c d + 20a b c d + a b c d )x +--R + +--R 5 7 9 225 4 8 8 3 2 9 7 5 2 3 10 6 4 +--R (30a c d + --- a b c d + 25a b c d + - a b c d )x +--R 4 2 +--R + +--R 5 8 8 50 4 9 7 10 3 2 10 6 3 5 9 7 5 4 10 6 2 +--R (15a c d + -- a b c d + -- a b c d )x + (5a c d + - a b c d )x +--R 3 3 2 +--R + +--R 5 10 6 1 5 11 5 5 4 12 4 5 3 2 13 3 5 2 3 14 2 +--R a c d x + -- a c d - --- a b c d + --- a b c d - ---- a b c d +--R 11 132 429 2002 +--R + +--R 1 4 15 1 5 16 +--R ---- a b c d - ----- b c +--R 3003 48048 +--R / +--R 6 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 767 + +--S 768 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 5 10 16 1 4 10 2 5 9 15 +--R -- b d x + (- a b d + - b c d )x +--R 16 3 3 +--R + +--R 5 2 3 10 25 4 9 45 5 2 8 14 +--R (- a b d + -- a b c d + -- b c d )x +--R 7 7 14 +--R + +--R 10 3 2 10 100 2 3 9 225 4 2 8 120 5 3 7 13 +--R (-- a b d + --- a b c d + --- a b c d + --- b c d )x +--R 13 13 13 13 +--R + +--R 5 4 10 25 3 2 9 75 2 3 2 8 4 3 7 35 5 4 6 12 +--R (-- a b d + -- a b c d + -- a b c d + 50a b c d + -- b c d )x +--R 12 3 2 2 +--R + +--R 1 5 10 50 4 9 450 3 2 2 8 1200 2 3 3 7 1050 4 4 6 +--R -- a d + -- a b c d + --- a b c d + ---- a b c d + ---- a b c d +--R 11 11 11 11 11 +--R + +--R 252 5 5 5 +--R --- b c d +--R 11 +--R * +--R 11 +--R x +--R + +--R 5 9 45 4 2 8 3 2 3 7 2 3 4 6 4 5 5 +--R a c d + -- a b c d + 120a b c d + 210a b c d + 126a b c d +--R 2 +--R + +--R 5 6 4 +--R 21b c d +--R * +--R 10 +--R x +--R + +--R 5 2 8 200 4 3 7 700 3 2 4 6 2 3 5 5 350 4 6 4 +--R 5a c d + --- a b c d + --- a b c d + 280a b c d + --- a b c d +--R 3 3 3 +--R + +--R 40 5 7 3 +--R -- b c d +--R 3 +--R * +--R 9 +--R x +--R + +--R 5 3 7 525 4 4 6 3 2 5 5 525 2 3 6 4 4 7 3 +--R 15a c d + --- a b c d + 315a b c d + --- a b c d + 75a b c d +--R 4 2 +--R + +--R 45 5 8 2 +--R -- b c d +--R 8 +--R * +--R 8 +--R x +--R + +--R 5 4 6 4 5 5 3 2 6 4 1200 2 3 7 3 225 4 8 2 +--R 30a c d + 180a b c d + 300a b c d + ---- a b c d + --- a b c d +--R 7 7 +--R + +--R 10 5 9 +--R -- b c d +--R 7 +--R * +--R 7 +--R x +--R + +--R 5 5 5 4 6 4 3 2 7 3 2 3 8 2 25 4 9 +--R 42a c d + 175a b c d + 200a b c d + 75a b c d + -- a b c d +--R 3 +--R + +--R 1 5 10 +--R - b c +--R 6 +--R * +--R 6 +--R x +--R + +--R 5 6 4 4 7 3 3 2 8 2 2 3 9 4 10 5 +--R (42a c d + 120a b c d + 90a b c d + 20a b c d + a b c )x +--R + +--R 5 7 3 225 4 8 2 3 2 9 5 2 3 10 4 +--R (30a c d + --- a b c d + 25a b c d + - a b c )x +--R 4 2 +--R + +--R 5 8 2 50 4 9 10 3 2 10 3 5 9 5 4 10 2 5 10 +--R (15a c d + -- a b c d + -- a b c )x + (5a c d + - a b c )x + a c x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 768 + +--S 769 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 5 11 5 5 4 12 4 5 3 2 13 3 5 2 3 14 2 +--R - -- a c d + --- a b c d - --- a b c d + ---- a b c d +--R 11 132 429 2002 +--R + +--R 1 4 15 1 5 16 +--R - ---- a b c d + ----- b c +--R 3003 48048 +--R / +--R 6 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 769 + +--S 770 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 770 + +)clear all + +--S 771 of 2952 +t0000:=(a+b*x)^4*(c+d*x)^10 +--R +--R +--R (1) +--R 4 10 14 3 10 4 9 13 2 2 10 3 9 4 2 8 12 +--R b d x + (4a b d + 10b c d )x + (6a b d + 40a b c d + 45b c d )x +--R + +--R 3 10 2 2 9 3 2 8 4 3 7 11 +--R (4a b d + 60a b c d + 180a b c d + 120b c d )x +--R + +--R 4 10 3 9 2 2 2 8 3 3 7 4 4 6 10 +--R (a d + 40a b c d + 270a b c d + 480a b c d + 210b c d )x +--R + +--R 4 9 3 2 8 2 2 3 7 3 4 6 4 5 5 9 +--R (10a c d + 180a b c d + 720a b c d + 840a b c d + 252b c d )x +--R + +--R 4 2 8 3 3 7 2 2 4 6 3 5 5 4 6 4 8 +--R (45a c d + 480a b c d + 1260a b c d + 1008a b c d + 210b c d )x +--R + +--R 4 3 7 3 4 6 2 2 5 5 3 6 4 4 7 3 7 +--R (120a c d + 840a b c d + 1512a b c d + 840a b c d + 120b c d )x +--R + +--R 4 4 6 3 5 5 2 2 6 4 3 7 3 4 8 2 6 +--R (210a c d + 1008a b c d + 1260a b c d + 480a b c d + 45b c d )x +--R + +--R 4 5 5 3 6 4 2 2 7 3 3 8 2 4 9 5 +--R (252a c d + 840a b c d + 720a b c d + 180a b c d + 10b c d)x +--R + +--R 4 6 4 3 7 3 2 2 8 2 3 9 4 10 4 +--R (210a c d + 480a b c d + 270a b c d + 40a b c d + b c )x +--R + +--R 4 7 3 3 8 2 2 2 9 3 10 3 +--R (120a c d + 180a b c d + 60a b c d + 4a b c )x +--R + +--R 4 8 2 3 9 2 2 10 2 4 9 3 10 4 10 +--R (45a c d + 40a b c d + 6a b c )x + (10a c d + 4a b c )x + a c +--R Type: Polynomial(Integer) +--E 771 + +--S 772 of 2952 +r0000:=1/11*(b*c-a*d)^4*(c+d*x)^11/d^5-1/3*b*(b*c-a*d)^3*(c+d*x)^12/d^5+_ + 6/13*b^2*(b*c-a*d)^2*(c+d*x)^13/d^5-2/7*b^3*(b*c-a*d)*(c+d*x)^14/d^5+_ + 1/15*b^4*(c+d*x)^15/d^5 +--R +--R +--R (2) +--R 1 4 15 15 2 3 15 5 4 14 14 +--R -- b d x + (- a b d + - b c d )x +--R 15 7 7 +--R + +--R 6 2 2 15 40 3 14 45 4 2 13 13 +--R (-- a b d + -- a b c d + -- b c d )x +--R 13 13 13 +--R + +--R 1 3 15 2 2 14 3 2 13 4 3 12 12 +--R (- a b d + 5a b c d + 15a b c d + 10b c d )x +--R 3 +--R + +--R 1 4 15 40 3 14 270 2 2 2 13 480 3 3 12 210 4 4 11 +--R (-- a d + -- a b c d + --- a b c d + --- a b c d + --- b c d ) +--R 11 11 11 11 11 +--R * +--R 11 +--R x +--R + +--R 4 14 3 2 13 2 2 3 12 3 4 11 126 4 5 10 10 +--R (a c d + 18a b c d + 72a b c d + 84a b c d + --- b c d )x +--R 5 +--R + +--R 4 2 13 160 3 3 12 2 2 4 11 3 5 10 70 4 6 9 9 +--R (5a c d + --- a b c d + 140a b c d + 112a b c d + -- b c d )x +--R 3 3 +--R + +--R 4 3 12 3 4 11 2 2 5 10 3 6 9 4 7 8 8 +--R (15a c d + 105a b c d + 189a b c d + 105a b c d + 15b c d )x +--R + +--R 4 4 11 3 5 10 2 2 6 9 480 3 7 8 45 4 8 7 7 +--R (30a c d + 144a b c d + 180a b c d + --- a b c d + -- b c d )x +--R 7 7 +--R + +--R 4 5 10 3 6 9 2 2 7 8 3 8 7 5 4 9 6 6 +--R (42a c d + 140a b c d + 120a b c d + 30a b c d + - b c d )x +--R 3 +--R + +--R 4 6 9 3 7 8 2 2 8 7 3 9 6 1 4 10 5 5 +--R (42a c d + 96a b c d + 54a b c d + 8a b c d + - b c d )x +--R 5 +--R + +--R 4 7 8 3 8 7 2 2 9 6 3 10 5 4 +--R (30a c d + 45a b c d + 15a b c d + a b c d )x +--R + +--R 4 8 7 40 3 9 6 2 2 10 5 3 4 9 6 3 10 5 2 +--R (15a c d + -- a b c d + 2a b c d )x + (5a c d + 2a b c d )x +--R 3 +--R + +--R 4 10 5 1 4 11 4 1 3 12 3 1 2 2 13 2 1 3 14 +--R a c d x + -- a c d - -- a b c d + --- a b c d - ---- a b c d +--R 11 33 143 1001 +--R + +--R 1 4 15 +--R ----- b c +--R 15015 +--R / +--R 5 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 772 + +--S 773 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 4 10 15 2 3 10 5 4 9 14 +--R -- b d x + (- a b d + - b c d )x +--R 15 7 7 +--R + +--R 6 2 2 10 40 3 9 45 4 2 8 13 +--R (-- a b d + -- a b c d + -- b c d )x +--R 13 13 13 +--R + +--R 1 3 10 2 2 9 3 2 8 4 3 7 12 +--R (- a b d + 5a b c d + 15a b c d + 10b c d )x +--R 3 +--R + +--R 1 4 10 40 3 9 270 2 2 2 8 480 3 3 7 210 4 4 6 11 +--R (-- a d + -- a b c d + --- a b c d + --- a b c d + --- b c d )x +--R 11 11 11 11 11 +--R + +--R 4 9 3 2 8 2 2 3 7 3 4 6 126 4 5 5 10 +--R (a c d + 18a b c d + 72a b c d + 84a b c d + --- b c d )x +--R 5 +--R + +--R 4 2 8 160 3 3 7 2 2 4 6 3 5 5 70 4 6 4 9 +--R (5a c d + --- a b c d + 140a b c d + 112a b c d + -- b c d )x +--R 3 3 +--R + +--R 4 3 7 3 4 6 2 2 5 5 3 6 4 4 7 3 8 +--R (15a c d + 105a b c d + 189a b c d + 105a b c d + 15b c d )x +--R + +--R 4 4 6 3 5 5 2 2 6 4 480 3 7 3 45 4 8 2 7 +--R (30a c d + 144a b c d + 180a b c d + --- a b c d + -- b c d )x +--R 7 7 +--R + +--R 4 5 5 3 6 4 2 2 7 3 3 8 2 5 4 9 6 +--R (42a c d + 140a b c d + 120a b c d + 30a b c d + - b c d)x +--R 3 +--R + +--R 4 6 4 3 7 3 2 2 8 2 3 9 1 4 10 5 +--R (42a c d + 96a b c d + 54a b c d + 8a b c d + - b c )x +--R 5 +--R + +--R 4 7 3 3 8 2 2 2 9 3 10 4 +--R (30a c d + 45a b c d + 15a b c d + a b c )x +--R + +--R 4 8 2 40 3 9 2 2 10 3 4 9 3 10 2 4 10 +--R (15a c d + -- a b c d + 2a b c )x + (5a c d + 2a b c )x + a c x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 773 + +--S 774 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 1 4 11 4 1 3 12 3 1 2 2 13 2 1 3 14 1 4 15 +--R - -- a c d + -- a b c d - --- a b c d + ---- a b c d - ----- b c +--R 11 33 143 1001 15015 +--R ------------------------------------------------------------------------- +--R 5 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 774 + +--S 775 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 775 + +)clear all + +--S 776 of 2952 +t0000:=(a+b*x)^3*(c+d*x)^10 +--R +--R +--R (1) +--R 3 10 13 2 10 3 9 12 2 10 2 9 3 2 8 11 +--R b d x + (3a b d + 10b c d )x + (3a b d + 30a b c d + 45b c d )x +--R + +--R 3 10 2 9 2 2 8 3 3 7 10 +--R (a d + 30a b c d + 135a b c d + 120b c d )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 9 +--R (10a c d + 135a b c d + 360a b c d + 210b c d )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 8 +--R (45a c d + 360a b c d + 630a b c d + 252b c d )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 7 +--R (120a c d + 630a b c d + 756a b c d + 210b c d )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 6 +--R (210a c d + 756a b c d + 630a b c d + 120b c d )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 5 +--R (252a c d + 630a b c d + 360a b c d + 45b c d )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 4 +--R (210a c d + 360a b c d + 135a b c d + 10b c d)x +--R + +--R 3 7 3 2 8 2 2 9 3 10 3 +--R (120a c d + 135a b c d + 30a b c d + b c )x +--R + +--R 3 8 2 2 9 2 10 2 3 9 2 10 3 10 +--R (45a c d + 30a b c d + 3a b c )x + (10a c d + 3a b c )x + a c +--R Type: Polynomial(Integer) +--E 776 + +--S 777 of 2952 +r0000:=-1/11*(b*c-a*d)^3*(c+d*x)^11/d^4+_ + 1/4*b*(b*c-a*d)^2*(c+d*x)^12/d^4-3/13*b^2*(b*c-a*d)*(c+d*x)^13/d^4+_ + 1/14*b^3*(c+d*x)^14/d^4 +--R +--R +--R (2) +--R 1 3 14 14 3 2 14 10 3 13 13 +--R -- b d x + (-- a b d + -- b c d )x +--R 14 13 13 +--R + +--R 1 2 14 5 2 13 15 3 2 12 12 +--R (- a b d + - a b c d + -- b c d )x +--R 4 2 4 +--R + +--R 1 3 14 30 2 13 135 2 2 12 120 3 3 11 11 +--R (-- a d + -- a b c d + --- a b c d + --- b c d )x +--R 11 11 11 11 +--R + +--R 3 13 27 2 2 12 2 3 11 3 4 10 10 +--R (a c d + -- a b c d + 36a b c d + 21b c d )x +--R 2 +--R + +--R 3 2 12 2 3 11 2 4 10 3 5 9 9 +--R (5a c d + 40a b c d + 70a b c d + 28b c d )x +--R + +--R 3 3 11 315 2 4 10 189 2 5 9 105 3 6 8 8 +--R (15a c d + --- a b c d + --- a b c d + --- b c d )x +--R 4 2 4 +--R + +--R 3 4 10 2 5 9 2 6 8 120 3 7 7 7 +--R (30a c d + 108a b c d + 90a b c d + --- b c d )x +--R 7 +--R + +--R 3 5 9 2 6 8 2 7 7 15 3 8 6 6 +--R (42a c d + 105a b c d + 60a b c d + -- b c d )x +--R 2 +--R + +--R 3 6 8 2 7 7 2 8 6 3 9 5 5 +--R (42a c d + 72a b c d + 27a b c d + 2b c d )x +--R + +--R 3 7 7 135 2 8 6 15 2 9 5 1 3 10 4 4 +--R (30a c d + --- a b c d + -- a b c d + - b c d )x +--R 4 2 4 +--R + +--R 3 8 6 2 9 5 2 10 4 3 3 9 5 3 2 10 4 2 +--R (15a c d + 10a b c d + a b c d )x + (5a c d + - a b c d )x +--R 2 +--R + +--R 3 10 4 1 3 11 3 1 2 12 2 1 2 13 1 3 14 +--R a c d x + -- a c d - -- a b c d + --- a b c d - ---- b c +--R 11 44 286 4004 +--R / +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 777 + +--S 778 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 3 10 14 3 2 10 10 3 9 13 +--R -- b d x + (-- a b d + -- b c d )x +--R 14 13 13 +--R + +--R 1 2 10 5 2 9 15 3 2 8 12 +--R (- a b d + - a b c d + -- b c d )x +--R 4 2 4 +--R + +--R 1 3 10 30 2 9 135 2 2 8 120 3 3 7 11 +--R (-- a d + -- a b c d + --- a b c d + --- b c d )x +--R 11 11 11 11 +--R + +--R 3 9 27 2 2 8 2 3 7 3 4 6 10 +--R (a c d + -- a b c d + 36a b c d + 21b c d )x +--R 2 +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 9 +--R (5a c d + 40a b c d + 70a b c d + 28b c d )x +--R + +--R 3 3 7 315 2 4 6 189 2 5 5 105 3 6 4 8 +--R (15a c d + --- a b c d + --- a b c d + --- b c d )x +--R 4 2 4 +--R + +--R 3 4 6 2 5 5 2 6 4 120 3 7 3 7 +--R (30a c d + 108a b c d + 90a b c d + --- b c d )x +--R 7 +--R + +--R 3 5 5 2 6 4 2 7 3 15 3 8 2 6 +--R (42a c d + 105a b c d + 60a b c d + -- b c d )x +--R 2 +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 5 +--R (42a c d + 72a b c d + 27a b c d + 2b c d)x +--R + +--R 3 7 3 135 2 8 2 15 2 9 1 3 10 4 +--R (30a c d + --- a b c d + -- a b c d + - b c )x +--R 4 2 4 +--R + +--R 3 8 2 2 9 2 10 3 3 9 3 2 10 2 3 10 +--R (15a c d + 10a b c d + a b c )x + (5a c d + - a b c )x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 778 + +--S 779 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 3 11 3 1 2 12 2 1 2 13 1 3 14 +--R - -- a c d + -- a b c d - --- a b c d + ---- b c +--R 11 44 286 4004 +--R (4) ------------------------------------------------------- +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 779 + +--S 780 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 780 + +)clear all + +--S 781 of 2952 +t0000:=(a+b*x)^2*(c+d*x)^10 +--R +--R +--R (1) +--R 2 10 12 10 2 9 11 2 10 9 2 2 8 10 +--R b d x + (2a b d + 10b c d )x + (a d + 20a b c d + 45b c d )x +--R + +--R 2 9 2 8 2 3 7 9 +--R (10a c d + 90a b c d + 120b c d )x +--R + +--R 2 2 8 3 7 2 4 6 8 +--R (45a c d + 240a b c d + 210b c d )x +--R + +--R 2 3 7 4 6 2 5 5 7 +--R (120a c d + 420a b c d + 252b c d )x +--R + +--R 2 4 6 5 5 2 6 4 6 +--R (210a c d + 504a b c d + 210b c d )x +--R + +--R 2 5 5 6 4 2 7 3 5 +--R (252a c d + 420a b c d + 120b c d )x +--R + +--R 2 6 4 7 3 2 8 2 4 +--R (210a c d + 240a b c d + 45b c d )x +--R + +--R 2 7 3 8 2 2 9 3 2 8 2 9 2 10 2 +--R (120a c d + 90a b c d + 10b c d)x + (45a c d + 20a b c d + b c )x +--R + +--R 2 9 10 2 10 +--R (10a c d + 2a b c )x + a c +--R Type: Polynomial(Integer) +--E 781 + +--S 782 of 2952 +r0000:=1/11*(b*c-a*d)^2*(c+d*x)^11/d^3-_ + 1/6*b*(b*c-a*d)*(c+d*x)^12/d^3+1/13*b^2*(c+d*x)^13/d^3 +--R +--R +--R (2) +--R 1 2 13 13 1 13 5 2 12 12 +--R -- b d x + (- a b d + - b c d )x +--R 13 6 6 +--R + +--R 1 2 13 20 12 45 2 2 11 11 +--R (-- a d + -- a b c d + -- b c d )x +--R 11 11 11 +--R + +--R 2 12 2 11 2 3 10 10 +--R (a c d + 9a b c d + 12b c d )x +--R + +--R 2 2 11 80 3 10 70 2 4 9 9 +--R (5a c d + -- a b c d + -- b c d )x +--R 3 3 +--R + +--R 2 3 10 105 4 9 63 2 5 8 8 +--R (15a c d + --- a b c d + -- b c d )x +--R 2 2 +--R + +--R 2 4 9 5 8 2 6 7 7 +--R (30a c d + 72a b c d + 30b c d )x +--R + +--R 2 5 8 6 7 2 7 6 6 +--R (42a c d + 70a b c d + 20b c d )x +--R + +--R 2 6 7 7 6 2 8 5 5 +--R (42a c d + 48a b c d + 9b c d )x +--R + +--R 2 7 6 45 8 5 5 2 9 4 4 +--R (30a c d + -- a b c d + - b c d )x +--R 2 2 +--R + +--R 2 8 5 20 9 4 1 2 10 3 3 2 9 4 10 3 2 +--R (15a c d + -- a b c d + - b c d )x + (5a c d + a b c d )x +--R 3 3 +--R + +--R 2 10 3 1 2 11 2 1 12 1 2 13 +--R a c d x + -- a c d - -- a b c d + --- b c +--R 11 66 858 +--R / +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 782 + +--S 783 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 2 10 13 1 10 5 2 9 12 +--R -- b d x + (- a b d + - b c d )x +--R 13 6 6 +--R + +--R 1 2 10 20 9 45 2 2 8 11 +--R (-- a d + -- a b c d + -- b c d )x +--R 11 11 11 +--R + +--R 2 9 2 8 2 3 7 10 2 2 8 80 3 7 70 2 4 6 9 +--R (a c d + 9a b c d + 12b c d )x + (5a c d + -- a b c d + -- b c d )x +--R 3 3 +--R + +--R 2 3 7 105 4 6 63 2 5 5 8 +--R (15a c d + --- a b c d + -- b c d )x +--R 2 2 +--R + +--R 2 4 6 5 5 2 6 4 7 2 5 5 6 4 2 7 3 6 +--R (30a c d + 72a b c d + 30b c d )x + (42a c d + 70a b c d + 20b c d )x +--R + +--R 2 6 4 7 3 2 8 2 5 2 7 3 45 8 2 5 2 9 4 +--R (42a c d + 48a b c d + 9b c d )x + (30a c d + -- a b c d + - b c d)x +--R 2 2 +--R + +--R 2 8 2 20 9 1 2 10 3 2 9 10 2 2 10 +--R (15a c d + -- a b c d + - b c )x + (5a c d + a b c )x + a c x +--R 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 783 + +--S 784 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 2 11 2 1 12 1 2 13 +--R - -- a c d + -- a b c d - --- b c +--R 11 66 858 +--R (4) -------------------------------------- +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 784 + +--S 785 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 785 + +)clear all + +--S 786 of 2952 +t0000:=(a+b*x)*(c+d*x)^10 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R b d x + (a d + 10b c d )x + (10a c d + 45b c d )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45a c d + 120b c d )x + (120a c d + 210b c d )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210a c d + 252b c d )x + (252a c d + 210b c d )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210a c d + 120b c d )x + (120a c d + 45b c d )x +--R + +--R 8 2 9 2 9 10 10 +--R (45a c d + 10b c d)x + (10a c d + b c )x + a c +--R Type: Polynomial(Integer) +--E 786 + +--S 787 of 2952 +r0000:=-1/11*(b*c-a*d)*(c+d*x)^11/d^2+1/12*b*(c+d*x)^12/d^2 +--R +--R +--R (2) +--R 1 12 12 1 12 10 11 11 11 9 2 10 10 +--R -- b d x + (-- a d + -- b c d )x + (a c d + - b c d )x +--R 12 11 11 2 +--R + +--R 2 10 40 3 9 9 3 9 105 4 8 8 +--R (5a c d + -- b c d )x + (15a c d + --- b c d )x +--R 3 4 +--R + +--R 4 8 5 7 7 5 7 6 6 6 +--R (30a c d + 36b c d )x + (42a c d + 35b c d )x +--R + +--R 6 6 7 5 5 7 5 45 8 4 4 +--R (42a c d + 24b c d )x + (30a c d + -- b c d )x +--R 4 +--R + +--R 8 4 10 9 3 3 9 3 1 10 2 2 10 2 1 11 +--R (15a c d + -- b c d )x + (5a c d + - b c d )x + a c d x + -- a c d +--R 3 2 11 +--R + +--R 1 12 +--R - --- b c +--R 132 +--R / +--R 2 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 787 + +--S 788 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 12 1 10 10 9 11 9 9 2 8 10 +--R -- b d x + (-- a d + -- b c d )x + (a c d + - b c d )x +--R 12 11 11 2 +--R + +--R 2 8 40 3 7 9 3 7 105 4 6 8 +--R (5a c d + -- b c d )x + (15a c d + --- b c d )x +--R 3 4 +--R + +--R 4 6 5 5 7 5 5 6 4 6 6 4 7 3 5 +--R (30a c d + 36b c d )x + (42a c d + 35b c d )x + (42a c d + 24b c d )x +--R + +--R 7 3 45 8 2 4 8 2 10 9 3 9 1 10 2 +--R (30a c d + -- b c d )x + (15a c d + -- b c d)x + (5a c d + - b c )x +--R 4 3 2 +--R + +--R 10 +--R a c x +--R Type: Polynomial(Fraction(Integer)) +--E 788 + +--S 789 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 11 1 12 +--R - -- a c d + --- b c +--R 11 132 +--R (4) ----------------------- +--R 2 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 789 + +--S 790 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 790 + +)clear all + +--S 791 of 2952 +t0000:=(c+d*x)^10 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R Type: Polynomial(Integer) +--E 791 + +--S 792 of 2952 +r0000:=1/11*(c+d*x)^11/d +--R +--R +--R (2) +--R 1 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R -- d x + c d x + 5c d x + 15c d x + 30c d x + 42c d x +--R 11 +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 1 11 +--R 42c d x + 30c d x + 15c d x + 5c d x + c d x + -- c +--R 11 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 792 + +--S 793 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 10 11 9 10 2 8 9 3 7 8 4 6 7 5 5 6 6 4 5 +--R -- d x + c d x + 5c d x + 15c d x + 30c d x + 42c d x + 42c d x +--R 11 +--R + +--R 7 3 4 8 2 3 9 2 10 +--R 30c d x + 15c d x + 5c d x + c x +--R Type: Polynomial(Fraction(Integer)) +--E 793 + +--S 794 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 11 +--R -- c +--R 11 +--R (4) - ------ +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 794 + +--S 795 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 795 + +)clear all + +--S 796 of 2952 +t0000:=(c+d*x)^10/(a+b*x) +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 796 + +--S 797 of 2952 +r0000:=d*(b*c-a*d)^9*x/b^10+1/2*(b*c-a*d)^8*(c+d*x)^2/b^9+_ + 1/3*(b*c-a*d)^7*(c+d*x)^3/b^8+1/4*(b*c-a*d)^6*(c+d*x)^4/b^7+_ + 1/5*(b*c-a*d)^5*(c+d*x)^5/b^6+1/6*(b*c-a*d)^4*(c+d*x)^6/b^5+_ + 1/7*(b*c-a*d)^3*(c+d*x)^7/b^4+1/8*(b*c-a*d)^2*(c+d*x)^8/b^3+_ + 1/9*(b*c-a*d)*(c+d*x)^9/b^2+1/10*(c+d*x)^10/b+_ + (b*c-a*d)^10*log(a+b*x)/b^11 +--R +--R +--R (2) +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R 2520a d - 25200a b c d + 113400a b c d - 302400a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R 529200a b c d - 635040a b c d + 529200a b c d - 302400a b c d +--R + +--R 2 8 8 2 9 9 10 10 +--R 113400a b c d - 25200a b c d + 2520b c +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 252b d x + (- 280a b d + 2800b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (315a b d - 3150a b c d + 14175b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 360a b d + 3600a b c d - 16200a b c d + 43200b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R 420a b d - 4200a b c d + 18900a b c d - 50400a b c d +--R + +--R 10 4 6 +--R 88200b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 504a b d + 5040a b c d - 22680a b c d + 60480a b c d +--R + +--R 9 4 6 10 5 5 +--R - 105840a b c d + 127008b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 630a b d - 6300a b c d + 28350a b c d - 75600a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R 132300a b c d - 158760a b c d + 132300b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 840a b d + 8400a b c d - 37800a b c d + 100800a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 176400a b c d + 211680a b c d - 176400a b c d + 100800b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 1260a b d - 12600a b c d + 56700a b c d - 151200a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R 264600a b c d - 317520a b c d + 264600a b c d - 151200a b c d +--R + +--R 10 8 2 +--R 56700b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 2520a b d + 25200a b c d - 113400a b c d + 302400a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 529200a b c d + 635040a b c d - 529200a b c d + 302400a b c d +--R + +--R 9 8 2 10 9 +--R - 113400a b c d + 25200b c d +--R * +--R x +--R + +--R 8 2 2 8 7 3 3 7 6 4 4 6 5 5 5 5 +--R 1260a b c d - 10920a b c d + 41790a b c d - 92484a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R 129990a b c d - 119640a b c d + 71325a b c d - 25930a b c d + 4861b c +--R / +--R 11 +--R 2520b +--R Type: Expression(Integer) +--E 797 + +--S 798 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R 2520a d - 25200a b c d + 113400a b c d - 302400a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R 529200a b c d - 635040a b c d + 529200a b c d - 302400a b c d +--R + +--R 2 8 8 2 9 9 10 10 +--R 113400a b c d - 25200a b c d + 2520b c +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 252b d x + (- 280a b d + 2800b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (315a b d - 3150a b c d + 14175b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 360a b d + 3600a b c d - 16200a b c d + 43200b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R 420a b d - 4200a b c d + 18900a b c d - 50400a b c d +--R + +--R 10 4 6 +--R 88200b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 504a b d + 5040a b c d - 22680a b c d + 60480a b c d +--R + +--R 9 4 6 10 5 5 +--R - 105840a b c d + 127008b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 630a b d - 6300a b c d + 28350a b c d - 75600a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R 132300a b c d - 158760a b c d + 132300b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 840a b d + 8400a b c d - 37800a b c d + 100800a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 176400a b c d + 211680a b c d - 176400a b c d + 100800b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 1260a b d - 12600a b c d + 56700a b c d - 151200a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R 264600a b c d - 317520a b c d + 264600a b c d - 151200a b c d +--R + +--R 10 8 2 +--R 56700b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 2520a b d + 25200a b c d - 113400a b c d + 302400a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 529200a b c d + 635040a b c d - 529200a b c d + 302400a b c d +--R + +--R 9 8 2 10 9 +--R - 113400a b c d + 25200b c d +--R * +--R x +--R / +--R 11 +--R 2520b +--R Type: Union(Expression(Integer),...) +--E 798 + +--S 799 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 8 2 8 7 3 7 6 2 4 6 5 3 5 5 +--R - 1260a c d + 10920a b c d - 41790a b c d + 92484a b c d +--R + +--R 4 4 6 4 3 5 7 3 2 6 8 2 7 9 +--R - 129990a b c d + 119640a b c d - 71325a b c d + 25930a b c d +--R + +--R 8 10 +--R - 4861b c +--R / +--R 9 +--R 2520b +--R Type: Expression(Integer) +--E 799 + +--S 800 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 800 + +)clear all + +--S 801 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^2 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 801 + +--S 802 of 2952 +r0000:=45*d^2*(b*c-a*d)^8*x/b^10-(b*c-a*d)^10/(b^11*(a+b*x))+_ + 60*d^3*(b*c-a*d)^7*(a+b*x)^2/b^11+70*d^4*(b*c-a*d)^6*(a+b*x)^3/b^11+_ + 63*d^5*(b*c-a*d)^5*(a+b*x)^4/b^11+42*d^6*(b*c-a*d)^4*(a+b*x)^5/b^11+_ + 20*d^7*(b*c-a*d)^3*(a+b*x)^6/b^11+45/7*d^8*(b*c-a*d)^2*(a+b*x)^7/b^11+_ + 5/4*d^9*(b*c-a*d)*(a+b*x)^8/b^11+1/9*d^10*(a+b*x)^9/b^11+_ + 10*d*(b*c-a*d)^9*log(a+b*x)/b^11 +--R +--R +--R (2) +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 2520a b d + 22680a b c d - 90720a b c d + 211680a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 +--R - 317520a b c d + 317520a b c d - 211680a b c d +--R + +--R 2 8 7 3 9 8 2 10 9 +--R 90720a b c d - 22680a b c d + 2520b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 2520a d + 22680a b c d - 90720a b c d + 211680a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R - 317520a b c d + 317520a b c d - 211680a b c d + 90720a b c d +--R + +--R 2 8 8 2 9 9 +--R - 22680a b c d + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 28b d x + (- 35a b d + 315b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (45a b d - 405a b c d + 1620b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 60a b d + 540a b c d - 2160a b c d + 5040b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 10 4 6 6 +--R (84a b d - 756a b c d + 3024a b c d - 7056a b c d + 10584b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 126a b d + 1134a b c d - 4536a b c d + 10584a b c d +--R + +--R 9 4 6 10 5 5 +--R - 15876a b c d + 15876b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 210a b d - 1890a b c d + 7560a b c d - 17640a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R 26460a b c d - 26460a b c d + 17640b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 420a b d + 3780a b c d - 15120a b c d + 35280a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 52920a b c d + 52920a b c d - 35280a b c d + 15120b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 1260a b d - 11340a b c d + 45360a b c d - 105840a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R 158760a b c d - 158760a b c d + 105840a b c d - 45360a b c d +--R + +--R 10 8 2 +--R 11340b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 4211a b d + 29079a b c d - 82296a b c d + 116424a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 68796a b c d - 26460a b c d + 70560a b c d - 45360a b c d +--R + +--R 9 8 2 +--R 11340a b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 6731a d + 51759a b c d - 173016a b c d + 328104a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R - 386316a b c d + 291060a b c d - 141120a b c d + 45360a b c d +--R + +--R 2 8 8 2 9 9 10 10 +--R - 11340a b c d + 2520a b c d - 252b c +--R / +--R 12 11 +--R 252b x + 252a b +--R Type: Expression(Integer) +--E 802 + +--S 803 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 2520a b d + 22680a b c d - 90720a b c d + 211680a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 +--R - 317520a b c d + 317520a b c d - 211680a b c d +--R + +--R 2 8 7 3 9 8 2 10 9 +--R 90720a b c d - 22680a b c d + 2520b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 2520a d + 22680a b c d - 90720a b c d + 211680a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R - 317520a b c d + 317520a b c d - 211680a b c d + 90720a b c d +--R + +--R 2 8 8 2 9 9 +--R - 22680a b c d + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 28b d x + (- 35a b d + 315b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (45a b d - 405a b c d + 1620b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 60a b d + 540a b c d - 2160a b c d + 5040b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 10 4 6 6 +--R (84a b d - 756a b c d + 3024a b c d - 7056a b c d + 10584b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 126a b d + 1134a b c d - 4536a b c d + 10584a b c d +--R + +--R 9 4 6 10 5 5 +--R - 15876a b c d + 15876b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 210a b d - 1890a b c d + 7560a b c d - 17640a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R 26460a b c d - 26460a b c d + 17640b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 420a b d + 3780a b c d - 15120a b c d + 35280a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 52920a b c d + 52920a b c d - 35280a b c d + 15120b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 1260a b d - 11340a b c d + 45360a b c d - 105840a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R 158760a b c d - 158760a b c d + 105840a b c d - 45360a b c d +--R + +--R 10 8 2 +--R 11340b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 2268a b d - 20160a b c d + 79380a b c d - 181440a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R 264600a b c d - 254016a b c d + 158760a b c d - 60480a b c d +--R + +--R 9 8 2 +--R 11340a b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 252a d + 2520a b c d - 11340a b c d + 30240a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R - 52920a b c d + 63504a b c d - 52920a b c d + 30240a b c d +--R + +--R 2 8 8 2 9 9 10 10 +--R - 11340a b c d + 2520a b c d - 252b c +--R / +--R 12 11 +--R 252b x + 252a b +--R Type: Union(Expression(Integer),...) +--E 803 + +--S 804 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 9 10 8 9 7 2 2 8 6 3 3 7 +--R 6479a d - 49239a b c d + 161676a b c d - 297864a b c d +--R + +--R 5 4 4 6 4 5 5 5 3 6 6 4 2 7 7 3 +--R 333396a b c d - 227556a b c d + 88200a b c d - 15120a b c d +--R / +--R 11 +--R 252b +--R Type: Expression(Integer) +--E 804 + +--S 805 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 805 + +)clear all + +--S 806 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^3 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 806 + +--S 807 of 2952 +r0000:=120*d^3*(b*c-a*d)^7*x/b^10-1/2*(b*c-a*d)^10/(b^11*(a+b*x)^2)-_ + 10*d*(b*c-a*d)^9/(b^11*(a+b*x))+105*d^4*(b*c-a*d)^6*(a+b*x)^2/b^11+_ + 84*d^5*(b*c-a*d)^5*(a+b*x)^3/b^11+105/2*d^6*(b*c-a*d)^4*(a+b*x)^4/b^11+_ + 24*d^7*(b*c-a*d)^3*(a+b*x)^5/b^11+15/2*d^8*(b*c-a*d)^2*(a+b*x)^6/b^11+_ + 10/7*d^9*(b*c-a*d)*(a+b*x)^7/b^11+1/8*d^10*(a+b*x)^8/b^11+_ + 45*d^2*(b*c-a*d)^8*log(a+b*x)/b^11 +--R +--R +--R (2) +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 2520a b d - 20160a b c d + 70560a b c d - 141120a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R 176400a b c d - 141120a b c d + 70560a b c d - 20160a b c d +--R + +--R 10 8 2 +--R 2520b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 5040a b d - 40320a b c d + 141120a b c d - 282240a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R 352800a b c d - 282240a b c d + 141120a b c d - 40320a b c d +--R + +--R 9 8 2 +--R 5040a b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R 2520a d - 20160a b c d + 70560a b c d - 141120a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R 176400a b c d - 141120a b c d + 70560a b c d - 20160a b c d +--R + +--R 2 8 8 2 +--R 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 7b d x + (- 10a b d + 80b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (15a b d - 120a b c d + 420b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 24a b d + 192a b c d - 672a b c d + 1344b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 10 4 6 6 +--R (42a b d - 336a b c d + 1176a b c d - 2352a b c d + 2940b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 84a b d + 672a b c d - 2352a b c d + 4704a b c d +--R + +--R 9 4 6 10 5 5 +--R - 5880a b c d + 4704b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 210a b d - 1680a b c d + 5880a b c d - 11760a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R 14700a b c d - 11760a b c d + 5880b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 840a b d + 6720a b c d - 23520a b c d + 47040a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 58800a b c d + 47040a b c d - 23520a b c d + 6720b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 129a b d + 5232a b c d - 31752a b c d + 87024a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 132300a b c d + 117600a b c d - 58800a b c d + 13440a b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 4782a b d - 29856a b c d + 77616a b c d - 108192a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R 88200a b c d - 47040a b c d + 23520a b c d - 13440a b c d +--R + +--R 9 8 2 10 9 +--R 5040a b c d - 560b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R 3651a d - 25008a b c d + 74088a b c d - 124656a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R 132300a b c d - 94080a b c d + 47040a b c d - 16800a b c d +--R + +--R 2 8 8 2 9 9 10 10 +--R 3780a b c d - 280a b c d - 28b c +--R / +--R 13 2 12 2 11 +--R 56b x + 112a b x + 56a b +--R Type: Expression(Integer) +--E 807 + +--S 808 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 2520a b d - 20160a b c d + 70560a b c d - 141120a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R 176400a b c d - 141120a b c d + 70560a b c d - 20160a b c d +--R + +--R 10 8 2 +--R 2520b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 5040a b d - 40320a b c d + 141120a b c d - 282240a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R 352800a b c d - 282240a b c d + 141120a b c d - 40320a b c d +--R + +--R 9 8 2 +--R 5040a b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R 2520a d - 20160a b c d + 70560a b c d - 141120a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R 176400a b c d - 141120a b c d + 70560a b c d - 20160a b c d +--R + +--R 2 8 8 2 +--R 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 7b d x + (- 10a b d + 80b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (15a b d - 120a b c d + 420b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 24a b d + 192a b c d - 672a b c d + 1344b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 10 4 6 6 +--R (42a b d - 336a b c d + 1176a b c d - 2352a b c d + 2940b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 84a b d + 672a b c d - 2352a b c d + 4704a b c d +--R + +--R 9 4 6 10 5 5 +--R - 5880a b c d + 4704b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 210a b d - 1680a b c d + 5880a b c d - 11760a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R 14700a b c d - 11760a b c d + 5880b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 840a b d + 6720a b c d - 23520a b c d + 47040a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 58800a b c d + 47040a b c d - 23520a b c d + 6720b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 3248a b d + 25480a b c d - 86940a b c d + 168000a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 199920a b c d + 148176a b c d - 64680a b c d + 13440a b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 1456a b d + 10640a b c d - 32760a b c d + 53760a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 47040a b c d + 14112a b c d + 11760a b c d - 13440a b c d +--R + +--R 9 8 2 10 9 +--R 5040a b c d - 560b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R 532a d - 4760a b c d + 18900a b c d - 43680a b c d + 64680a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 63504a b c d + 41160a b c d - 16800a b c d + 3780a b c d +--R + +--R 9 9 10 10 +--R - 280a b c d - 28b c +--R / +--R 13 2 12 2 11 +--R 56b x + 112a b x + 56a b +--R Type: Union(Expression(Integer),...) +--E 808 + +--S 809 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 8 10 7 9 6 2 2 8 5 3 3 7 +--R - 3119a d + 20248a b c d - 55188a b c d + 80976a b c d +--R + +--R 4 4 4 6 3 5 5 5 2 6 6 4 +--R - 67620a b c d + 30576a b c d - 5880a b c d +--R / +--R 11 +--R 56b +--R Type: Expression(Integer) +--E 809 + +--S 810 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 810 + +)clear all + +--S 811 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^4 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 811 + +--S 812 of 2952 +r0000:=210*d^4*(b*c-a*d)^6*x/b^10-1/3*(b*c-a*d)^10/(b^11*(a+b*x)^3)-_ + 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+--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 2520a d + 17640a b c d - 52920a b c d + 88200a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R - 88200a b c d + 52920a b c d - 17640a b c d + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 3b d x + (- 5a b d + 35b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (9a b d - 63a b c d + 189b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 18a b d + 126a b c d - 378a b c d + 630b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 10 4 6 6 +--R (42a b d - 294a b c d + 882a b c d - 1470a b c d + 1470b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 126a b d + 882a b c d - 2646a b c d + 4410a b c d +--R + +--R 9 4 6 10 5 5 +--R - 4410a b c d + 2646b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 630a b d - 4410a b c d + 13230a b c d - 22050a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R 22050a b c d - 13230a b c d + 4410b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R 2124a b d - 16758a b c d + 54684a b c d - 95550a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 +--R 95550a b c d - 52920a b c d + 13230a b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 1188a b d + 2646a b c d + 5292a b c d - 22050a b c d +--R + +--R 4 6 4 6 2 8 6 4 9 7 3 10 8 2 +--R 22050a b c d - 13230a b c d + 7560a b c d - 945b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 4968a b d + 29106a b c d - 74088a b c d + 110250a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 110250a b c d + 79380a b c d - 39690a b c d + 11340a b c d +--R + +--R 9 8 2 10 9 +--R - 945a b c d - 105b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 2496a d + 15582a b c d - 42336a b c d + 66150a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R - 66150a b c d + 44100a b c d - 19110a b c d + 4620a b c d +--R + +--R 2 8 8 2 9 9 10 10 +--R - 315a b c d - 35a b c d - 7b c +--R / +--R 14 3 13 2 2 12 3 11 +--R 21b x + 63a b x + 63a b x + 21a b +--R Type: Expression(Integer) +--E 812 + +--S 813 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 2520a b d + 17640a b c d - 52920a b c d + 88200a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 88200a b c d + 52920a b c d - 17640a b c d + 2520b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 7560a b d + 52920a b c d - 158760a b c d + 264600a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 264600a b c d + 158760a b c d - 52920a b c d + 7560a b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 7560a b d + 52920a b c d - 158760a b c d + 264600a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 264600a b c d + 158760a b c d - 52920a b c d + 7560a b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 2520a d + 17640a b c d - 52920a b c d + 88200a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R - 88200a b c d + 52920a b c d - 17640a b c d + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 3b d x + (- 5a b d + 35b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (9a b d - 63a b c d + 189b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 18a b d + 126a b c d - 378a b c d + 630b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 10 4 6 6 +--R (42a b d - 294a b c d + 882a b c d - 1470a b c d + 1470b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 126a b d + 882a b c d - 2646a b c d + 4410a b c d +--R + +--R 9 4 6 10 5 5 +--R - 4410a b c d + 2646b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 630a b d - 4410a b c d + 13230a b c d - 22050a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R 22050a b c d - 13230a b c d + 4410b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R 3773a b d - 25655a b c d + 74025a b c d - 116760a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 +--R 107310a b c d - 55566a b c d + 13230a b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 3759a b d - 24045a b c d + 63315a b c d - 85680a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R 57330a b c d - 7938a b c d - 13230a b c d + 7560a b c d +--R + +--R 10 8 2 +--R - 945b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 21a b d + 2415a b c d - 16065a b c d + 46620a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 74970a b c d + 71442a b c d - 39690a b c d + 11340a b c d +--R + +--R 9 8 2 10 9 +--R - 945a b c d - 105b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 847a d + 6685a b c d - 22995a b c d + 44940a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 +--R - 54390a b c d + 41454a b c d - 19110a b c d + 4620a b c d +--R + +--R 2 8 8 2 9 9 10 10 +--R - 315a b c d - 35a b c d - 7b c +--R / +--R 14 3 13 2 2 12 3 11 +--R 21b x + 63a b x + 63a b x + 21a b +--R Type: Union(Expression(Integer),...) +--E 813 + +--S 814 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 7 10 6 9 5 2 2 8 4 3 3 7 3 4 4 6 +--R 1649a d - 8897a b c d + 19341a b c d - 21210a b c d + 11760a b c d +--R + +--R 2 5 5 5 +--R - 2646a b c d +--R / +--R 11 +--R 21b +--R Type: Expression(Integer) +--E 814 + +--S 815 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 815 + +)clear all + +--S 816 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^5 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 816 + +--S 817 of 2952 +r0000:=252*d^5*(b*c-a*d)^5*x/b^10-1/4*(b*c-a*d)^10/(b^11*(a+b*x)^4)-_ + 10/3*d*(b*c-a*d)^9/(b^11*(a+b*x)^3)-_ + 45/2*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^2)-_ + 120*d^3*(b*c-a*d)^7/(b^11*(a+b*x))+_ + 105*d^6*(b*c-a*d)^4*(a+b*x)^2/b^11+_ + 40*d^7*(b*c-a*d)^3*(a+b*x)^3/b^11+_ + 45/4*d^8*(b*c-a*d)^2*(a+b*x)^4/b^11+_ + 2*d^9*(b*c-a*d)*(a+b*x)^5/b^11+_ + 1/6*d^10*(a+b*x)^6/b^11+210*d^4*(b*c-a*d)^6*log(a+b*x)/b^11 +--R +--R +--R (2) +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 2520a b d - 15120a b c d + 37800a b c d - 50400a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R 37800a b c d - 15120a b c d + 2520b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R 10080a b d - 60480a b c d + 151200a b c d - 201600a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 +--R 151200a b c d - 60480a b c d + 10080a b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 15120a b d - 90720a b c d + 226800a b c d - 302400a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 +--R 226800a b c d - 90720a b c d + 15120a b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 10080a b d - 60480a b c d + 151200a b c d - 201600a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 +--R 151200a b c d - 60480a b c d + 10080a b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R 2520a d - 15120a b c d + 37800a b c d - 50400a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 +--R 37800a b c d - 15120a b c d + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 2b d x + (- 4a b d + 24b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (9a b d - 54a b c d + 135b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 24a b d + 144a b c d - 360a b c d + 480b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 10 4 6 6 +--R (84a b d - 504a b c d + 1260a b c d - 1680a b c d + 1260b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 504a b d + 3024a b c d - 7560a b c d + 10080a b c d +--R + +--R 9 4 6 10 5 5 +--R - 7560a b c d + 3024b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 3150a b d + 19404a b c d - 48510a b c d + 62160a b c d +--R + +--R 2 8 4 6 9 5 5 +--R - 41580a b c d + 12096a b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 2520a b d + 17136a b c d - 42840a b c d + 47040a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 15120a b c d - 12096a b c d + 10080a b c d - 1440b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 3780a b d - 19656a b c d + 49140a b c d - 80640a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R 90720a b c d - 63504a b c d + 22680a b c d - 2160a b c d +--R + +--R 10 8 2 +--R - 270b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 5880a b d - 33264a b c d + 83160a b c d - 120960a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R 110880a b c d - 62496a b c d + 18480a b c d - 1440a b c d +--R + +--R 9 8 2 10 9 +--R - 180a b c d - 40b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R 2100a d - 12096a b c d + 30240a b c d - 42840a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 +--R 37170a b c d - 19404a b c d + 5250a b c d - 360a b c d - 45a b c d +--R + +--R 9 9 10 10 +--R - 10a b c d - 3b c +--R / +--R 15 4 14 3 2 13 2 3 12 4 11 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Expression(Integer) 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- 1440b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 1578a b d + 3420a b c d + 11610a b c d - 53280a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R 83160a b c d - 63504a b c d + 22680a b c d - 2160a b c d +--R + +--R 10 8 2 +--R - 270b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 2308a b d - 17880a b c d + 58140a b c d - 102720a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R 105840a b c d - 62496a b c d + 18480a b c d - 1440a b c d +--R + +--R 9 8 2 10 9 +--R - 180a b c d - 40b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R 1207a d - 8250a b c d + 23985a b c d - 38280a b c d + 35910a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 +--R - 19404a b c d + 5250a b c d - 360a b c d - 45a b c d - 10a b c d +--R + +--R 10 10 +--R - 3b c +--R / +--R 15 4 14 3 2 13 2 3 12 4 11 +--R 12b x + 48a b x + 72a b x + 48a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 818 + +--S 819 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 6 10 5 9 4 2 2 8 3 3 3 7 2 4 4 6 +--R - 893a d + 3846a b c d - 6255a b c d + 4560a b c d - 1260a b c d +--R (4) ---------------------------------------------------------------------- +--R 11 +--R 12b +--R Type: Expression(Integer) +--E 819 + +--S 820 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 820 + +)clear all + +--S 821 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^6 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 821 + +--S 822 of 2952 +r0000:=210*d^6*(b*c-a*d)^4*x/b^10-1/5*(b*c-a*d)^10/(b^11*(a+b*x)^5)-_ + 5/2*d*(b*c-a*d)^9/(b^11*(a+b*x)^4)-_ + 15*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^3)-_ + 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* +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 12600a b d + 63000a b c d - 126000a b c d + 126000a b c d +--R + +--R 5 5 4 6 4 6 5 5 +--R - 63000a b c d + 12600a b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 2520a d + 12600a b c d - 25200a b c d + 25200a b c d +--R + +--R 6 4 4 6 5 5 5 5 +--R - 12600a b c d + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 2b d x + (- 5a b d + 25b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (15a b d - 75a b c d + 150b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 60a b d + 300a b c d - 600a b c d + 600b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 10 4 6 6 +--R (420a b d - 2100a b c d + 4200a b c d - 4200a b c d + 2100b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R 3654a b d - 17850a b c d + 33600a b c d - 29400a b c d +--R + +--R 9 4 6 +--R 10500a b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 5670a b d - 26250a b c d + 42000a b c d - 21000a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 10500a b c d + 12600a b c d - 2100b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 1260a b d + 10500a b c d - 42000a b c d + 84000a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 84000a b c d + 37800a b c d - 4200a b c d - 600b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 9660a b d + 52500a b c d - 126000a b c d + 168000a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 126000a b c d + 46200a b c d - 4200a b c d - 600a b c d +--R + +--R 10 8 2 +--R - 150b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 7980a b d + 42000a b c d - 94500a b c d + 115500a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 78750a b c d + 26250a b c d - 2100a b c d - 300a b c d +--R + +--R 9 8 2 10 9 +--R - 75a b c d - 25b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 2100a d + 10920a b c d - 23940a b c d + 28140a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 18270a b c d + 5754a b c d - 420a b c d - 60a b c d - 15a b c d +--R + +--R 9 9 10 10 +--R - 5a b c d - 2b c +--R / +--R 16 5 15 4 2 14 3 3 13 2 4 12 5 11 +--R 10b x + 50a b x + 100a b x + 100a b x + 50a b x + 10a b +--R Type: Expression(Integer) +--E 822 + +--S 823 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 2520a b d + 12600a b c d - 25200a b c d + 25200a b c d +--R + +--R 9 4 6 10 5 5 +--R - 12600a b c d + 2520b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 12600a b d + 63000a b c d - 126000a b c d + 126000a b c d +--R + +--R 2 8 4 6 9 5 5 +--R - 63000a b c d + 12600a b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 25200a b d + 126000a b c d - 252000a b c d + 252000a b c d +--R + +--R 3 7 4 6 2 8 5 5 +--R - 126000a b c d + 25200a b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 25200a b d + 126000a b c d - 252000a b c d + 252000a b c d +--R + +--R 4 6 4 6 3 7 5 5 +--R - 126000a b c d + 25200a b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 12600a b d + 63000a b c d - 126000a b c d + 126000a b c d +--R + +--R 5 5 4 6 4 6 5 5 +--R - 63000a b c d + 12600a b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 2520a d + 12600a b c d - 25200a b c d + 25200a b c d +--R + +--R 6 4 4 6 5 5 5 5 +--R - 12600a b c d + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 2b d x + (- 5a b d + 25b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (15a b d - 75a b c d + 150b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 60a b d + 300a b c d - 600a b c d + 600b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 10 4 6 6 +--R (420a b d - 2100a b c d + 4200a b c d - 4200a b c d + 2100b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R 4127a b d - 19375a b c d + 35250a b c d - 30000a b c d +--R + +--R 9 4 6 +--R 10500a b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 8035a b d - 33875a b c d + 50250a b c d - 24000a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 10500a b c d + 12600a b c d - 2100b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R 3470a b d - 4750a b c d - 25500a b c d + 78000a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 84000a b c d + 37800a b c d - 4200a b c d - 600b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 4930a b d + 37250a b c d - 109500a b c d + 162000a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 126000a b c d + 46200a b c d - 4200a b c d - 600a b c d +--R + +--R 10 8 2 +--R - 150b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 5615a b d + 34375a b c d - 86250a b c d + 112500a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 78750a b c d + 26250a b c d - 2100a b c d - 300a b c d +--R + +--R 9 8 2 10 9 +--R - 75a b c d - 25b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 1627a d + 9395a b c d - 22290a b c d + 27540a b c d +--R + +--R 6 4 4 6 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 18270a b c d + 5754a b c d - 420a b c d - 60a b c d - 15a b c d +--R + +--R 9 9 10 10 +--R - 5a b c d - 2b c +--R / +--R 16 5 15 4 2 14 3 3 13 2 4 12 5 11 +--R 10b x + 50a b x + 100a b x + 100a b x + 50a b x + 10a b +--R Type: Union(Expression(Integer),...) +--E 823 + +--S 824 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 5 10 4 9 3 2 2 8 2 3 3 7 +--R 473a d - 1525a b c d + 1650a b c d - 600a b c d +--R (4) ---------------------------------------------------- +--R 11 +--R 10b +--R Type: Expression(Integer) +--E 824 + +--S 825 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +)clear all + +--S 826 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^7 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 826 + +--S 827 of 2952 +r0000:=120*d^7*(b*c-a*d)^3*x/b^10-1/6*(b*c-a*d)^10/(b^11*(a+b*x)^6)-_ + 2*d*(b*c-a*d)^9/(b^11*(a+b*x)^5)-_ + 45/4*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^4)-_ + 40*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^3)-_ + 105*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^2)-_ + 252*d^5*(b*c-a*d)^5/(b^11*(a+b*x))+_ + 45/2*d^8*(b*c-a*d)^2*(a+b*x)^2/b^11+_ + 10/3*d^9*(b*c-a*d)*(a+b*x)^3/b^11+1/4*d^10*(a+b*x)^4/b^11+_ + 210*d^6*(b*c-a*d)^4*log(a+b*x)/b^11 +--R +--R +--R (2) +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R 2520a b d - 10080a b c d + 15120a b c d - 10080a b c d +--R + +--R 10 4 6 +--R 2520b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R 15120a b d - 60480a b c d + 90720a b c d - 60480a b c d +--R + +--R 9 4 6 +--R 15120a b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 37800a b d - 151200a b c d + 226800a b c d - 151200a b c d +--R + +--R 2 8 4 6 +--R 37800a b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R 50400a b d - 201600a b c d + 302400a b c d - 201600a b c d +--R + +--R 3 7 4 6 +--R 50400a b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 37800a b d - 151200a b c d + 226800a b c d - 151200a b c d +--R + +--R 4 6 4 6 +--R 37800a b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 15120a b d - 60480a b c d + 90720a b c d - 60480a b c d +--R + +--R 5 5 4 6 +--R 15120a b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R 2520a d - 10080a b c d + 15120a b c d - 10080a b c d +--R + +--R 6 4 4 6 +--R 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 3b d x + (- 10a b d + 40b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (45a b d - 180a b c d + 270b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 360a b d + 1440a b c d - 2160a b c d + 1440b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 6 +--R (- 3810a b d + 14160a b c d - 18360a b c d + 8640a b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 7740a b d + 24480a b c d - 19440a b c d - 8640a b c d +--R + +--R 9 4 6 10 5 5 +--R 15120a b c d - 3024b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 450a b d - 14400a b c d + 64800a b c d - 97200a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R 56700a b c d - 7560a b c d - 1260b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R 16200a b d - 86400a b c d + 187200a b c d - 196800a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R 92400a b c d - 10080a b c d - 1680a b c d - 480b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 21600a b d - 102600a b c d + 197100a b c d - 185400a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 10 8 2 +--R 78750a b c d - 7560a b c d - 1260a b c d - 360a b c d - 135b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 11664a b d - 53136a b c d + 96984a b c d - 86256a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 +--R 34524a b c d - 3024a b c d - 504a b c d - 144a b c d - 54a b c d +--R + +--R 10 9 +--R - 24b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R 2364a d - 10536a b c d + 18684a b c d - 16056a b c d + 6174a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R - 504a b c d - 84a b c d - 24a b c d - 9a b c d - 4a b c d - 2b c +--R / +--R 17 6 16 5 2 15 4 3 14 3 4 13 2 5 12 +--R 12b x + 72a b x + 180a b x + 240a b x + 180a b x + 72a b x +--R + +--R 6 11 +--R 12a b +--R Type: Expression(Integer) +--E 827 + +--S 828 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R 2520a b d - 10080a b c d + 15120a b c d - 10080a b c d +--R + +--R 10 4 6 +--R 2520b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R 15120a b d - 60480a b c d + 90720a b c d - 60480a b c d +--R + +--R 9 4 6 +--R 15120a b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 37800a b d - 151200a b c d + 226800a b c d - 151200a b c d +--R + +--R 2 8 4 6 +--R 37800a b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R 50400a b d - 201600a b c d + 302400a b c d - 201600a b c d +--R + +--R 3 7 4 6 +--R 50400a b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 37800a b d - 151200a b c d + 226800a b c d - 151200a b c d +--R + +--R 4 6 4 6 +--R 37800a b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 15120a b d - 60480a b c d + 90720a b c d - 60480a b c d +--R + +--R 5 5 4 6 +--R 15120a b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R 2520a d - 10080a b c d + 15120a b c d - 10080a b c d +--R + +--R 6 4 4 6 +--R 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 3b d x + (- 10a b d + 40b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (45a b d - 180a b c d + 270b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 360a b d + 1440a b c d - 2160a b c d + 1440b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 6 +--R (- 4043a b d + 14660a b c d - 18630a b c d + 8640a b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 9138a b d + 27480a b c d - 21060a b c d - 8640a b c d +--R + +--R 9 4 6 10 5 5 +--R 15120a b c d - 3024b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 3945a b d - 6900a b c d + 60750a b c d - 97200a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R 56700a b c d - 7560a b c d - 1260b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R 11540a b d - 76400a b c d + 181800a b c d - 196800a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R 92400a b c d - 10080a b c d - 1680a b c d - 480b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 18105a b d - 95100a b c d + 193050a b c d - 185400a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 10 8 2 +--R 78750a b c d - 7560a b c d - 1260a b c d - 360a b c d - 135b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 10266a b d - 50136a b c d + 95364a b c d - 86256a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 +--R 34524a b c d - 3024a b c d - 504a b c d - 144a b c d - 54a b c d +--R + +--R 10 9 +--R - 24b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R 2131a d - 10036a b c d + 18414a b c d - 16056a b c d + 6174a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R - 504a b c d - 84a b c d - 24a b c d - 9a b c d - 4a b c d - 2b c +--R / +--R 17 6 16 5 2 15 4 3 14 3 4 13 2 5 12 +--R 12b x + 72a b x + 180a b x + 240a b x + 180a b x + 72a b x +--R + +--R 6 11 +--R 12a b +--R Type: Union(Expression(Integer),...) +--E 828 + +--S 829 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 4 10 3 9 2 2 2 8 +--R - 233a d + 500a b c d - 270a b c d +--R (4) -------------------------------------- +--R 11 +--R 12b +--R Type: Expression(Integer) +--E 829 + +--S 830 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 830 + +)clear all + +--S 831 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^8 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 8 +--R 8a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 831 + +--S 832 of 2952 +r0000:=45*d^8*(b*c-a*d)^2*x/b^10-1/7*(b*c-a*d)^10/(b^11*(a+b*x)^7)-_ + 5/3*d*(b*c-a*d)^9/(b^11*(a+b*x)^6)-9*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^5)-_ + 30*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^4)-_ + 70*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^3)-_ + 126*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^2)-_ + 210*d^6*(b*c-a*d)^4/(b^11*(a+b*x))+_ + 5*d^9*(b*c-a*d)*(a+b*x)^2/b^11+_ + 1/3*d^10*(a+b*x)^3/b^11+120*d^7*(b*c-a*d)^3*log(a+b*x)/b^11 +--R +--R +--R (2) +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 2520a b d + 7560a b c d - 7560a b c d + 2520b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 6 +--R (- 17640a b d + 52920a b c d - 52920a b c d + 17640a b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 5 +--R (- 52920a b d + 158760a b c d - 158760a b c d + 52920a b c d )x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 4 +--R (- 88200a b d + 264600a b c d - 264600a b c d + 88200a b c d )x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 3 +--R (- 88200a b d + 264600a b c d - 264600a b c d + 88200a b c d )x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 2 +--R (- 52920a b d + 158760a b c d - 158760a b c d + 52920a b c d )x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R (- 17640a b d + 52920a b c d - 52920a b c d + 17640a b c d )x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 2520a d + 7560a b c d - 7560a b c d + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 7b d x + (- 35a b d + 105b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (315a b d - 945a b c d + 945b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 7 +--R (3675a b d - 9450a b c d + 6615a b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R 8085a b d - 13230a b c d - 6615a b c d + 17640a b c d +--R + +--R 10 4 6 +--R - 4410b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 2205a b d + 39690a b c d - 99225a b c d + 79380a b c d +--R + +--R 9 4 6 10 5 5 +--R - 13230a b c d - 2646b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 33075a b d + 154350a b c d - 253575a b c d + 161700a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 22050a b c d - 4410a b c d - 1470b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 55125a b d + 220500a b c d - 319725a b c d + 183750a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 22050a b c d - 4410a b c d - 1470a b c d - 630b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 43659a b d + 164052a b c d - 223587a b c d + 120834a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 10 8 2 +--R - 13230a b c d - 2646a b c d - 882a b c d - 378a b c d - 189b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 17493a b d + 63504a b c d - 83349a b c d + 43218a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 +--R - 4410a b c d - 882a b c d - 294a b c d - 126a b c d - 63a b c d +--R + +--R 10 9 +--R - 35b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R - 2859a d + 10152a b c d - 12987a b c d + 6534a b c d - 630a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R - 126a b c d - 42a b c d - 18a b c d - 9a b c d - 5a b c d - 3b c +--R / +--R 18 7 17 6 2 16 5 3 15 4 4 14 3 5 13 2 +--R 21b x + 147a b x + 441a b x + 735a b x + 735a b x + 441a b x +--R + +--R 6 12 7 11 +--R 147a b x + 21a b +--R Type: Expression(Integer) +--E 832 + +--S 833 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 2520a b d + 7560a b c d - 7560a b c d + 2520b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 6 +--R (- 17640a b d + 52920a b c d - 52920a b c d + 17640a b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 5 +--R (- 52920a b d + 158760a b c d - 158760a b c d + 52920a b c d )x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 4 +--R (- 88200a b d + 264600a b c d - 264600a b c d + 88200a b c d )x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 3 +--R (- 88200a b d + 264600a b c d - 264600a b c d + 88200a b c d )x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 2 +--R (- 52920a b d + 158760a b c d - 158760a b c d + 52920a b c d )x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R (- 17640a b d + 52920a b c d - 52920a b c d + 17640a b c d )x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 +--R - 2520a d + 7560a b c d - 7560a b c d + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 7b d x + (- 35a b d + 105b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (315a b d - 945a b c d + 945b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 7 +--R (3773a b d - 9555a b c d + 6615a b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R 8771a b d - 13965a b c d - 6615a b c d + 17640a b c d +--R + +--R 10 4 6 +--R - 4410b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 147a b d + 37485a b c d - 99225a b c d + 79380a b c d +--R + +--R 9 4 6 10 5 5 +--R - 13230a b c d - 2646b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 29645a b d + 150675a b c d - 253575a b c d + 161700a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 22050a b c d - 4410a b c d - 1470b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 51695a b d + 216825a b c d - 319725a b c d + 183750a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 22050a b c d - 4410a b c d - 1470a b c d - 630b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 41601a b d + 161847a b c d - 223587a b c d + 120834a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 10 8 2 +--R - 13230a b c d - 2646a b c d - 882a b c d - 378a b c d - 189b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 16807a b d + 62769a b c d - 83349a b c d + 43218a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 +--R - 4410a b c d - 882a b c d - 294a b c d - 126a b c d - 63a b c d +--R + +--R 10 9 +--R - 35b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R - 2761a d + 10047a b c d - 12987a b c d + 6534a b c d - 630a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R - 126a b c d - 42a b c d - 18a b c d - 9a b c d - 5a b c d - 3b c +--R / +--R 18 7 17 6 2 16 5 3 15 4 4 14 3 5 13 2 +--R 21b x + 147a b x + 441a b x + 735a b x + 735a b x + 441a b x +--R + +--R 6 12 7 11 +--R 147a b x + 21a b +--R Type: Union(Expression(Integer),...) +--E 833 + +--S 834 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 3 10 2 9 +--R 14a d - 15a b c d +--R (4) -------------------- +--R 11 +--R 3b +--R Type: Expression(Integer) +--E 834 + +--S 835 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 835 + +)clear all + +--S 836 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^9 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 7 2 2 8 9 +--R 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 836 + +--S 837 of 2952 +r0000:=d^9*(10*b*c-9*a*d)*x/b^10+1/2*d^10*x^2/b^9-_ + 1/8*(b*c-a*d)^10/(b^11*(a+b*x)^8)-_ + 10/7*d*(b*c-a*d)^9/(b^11*(a+b*x)^7)-_ + 15/2*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^6)-_ + 24*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^5)-_ + 105/2*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^4)-_ + 84*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^3)-_ + 105*d^6*(b*c-a*d)^4/(b^11*(a+b*x)^2)-_ + 120*d^7*(b*c-a*d)^3/(b^11*(a+b*x))+45*d^8*(b*c-a*d)^2*log(a+b*x)/b^11 +--R +--R +--R (2) +--R 2 8 10 9 9 10 2 8 8 +--R (2520a b d - 5040a b c d + 2520b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 7 +--R (20160a b d - 40320a b c d + 20160a b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 6 +--R (70560a b d - 141120a b c d + 70560a b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 5 +--R (141120a b d - 282240a b c d + 141120a b c d )x +--R + +--R 6 4 10 5 5 9 4 6 2 8 4 +--R (176400a b d - 352800a b c d + 176400a b c d )x +--R + +--R 7 3 10 6 4 9 5 5 2 8 3 +--R (141120a b d - 282240a b c d + 141120a b c d )x +--R + +--R 8 2 10 7 3 9 6 4 2 8 2 +--R (70560a b d - 141120a b c d + 70560a b c d )x +--R + +--R 9 10 8 2 9 7 3 2 8 10 10 +--R (20160a b d - 40320a b c d + 20160a b c d )x + 2520a d +--R + +--R 9 9 8 2 2 8 +--R - 5040a b c d + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 28b d x + (- 280a b d + 560b c d )x +--R + +--R 2 8 10 9 9 8 +--R (- 3248a b d + 4480a b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 5824a b d - 4480a b c d + 20160a b c d - 6720b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R 14896a b d - 86240a b c d + 105840a b c d - 23520a b c d +--R + +--R 10 4 6 +--R - 5880b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R 76832a b d - 266560a b c d + 258720a b c d - 47040a b c d +--R + +--R 9 4 6 10 5 5 +--R - 11760a b c d - 4704b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 140140a b d - 421400a b c d + 367500a b c d - 58800a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 14700a b c d - 5880a b c d - 2940b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R 140336a b d - 393568a b c d + 322224a b c d - 47040a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 11760a b c d - 4704a b c d - 2352a b c d - 1344b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 81928a b d - 220304a b c d + 172872a b c d - 23520a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 10 8 2 +--R - 5880a b c d - 2352a b c d - 1176a b c d - 672a b c d - 420b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 26288a b d - 68704a b c d + 52272a b c d - 6720a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 1680a b c d - 672a b c d - 336a b c d - 192a b c d +--R + +--R 9 8 2 10 9 +--R - 120a b c d - 80b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R 3601a d - 9218a b c d + 6849a b c d - 840a b c d - 210a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R - 84a b c d - 42a b c d - 24a b c d - 15a b c d - 10a b c d - 7b c +--R / +--R 19 8 18 7 2 17 6 3 16 5 4 15 4 +--R 56b x + 448a b x + 1568a b x + 3136a b x + 3920a b x +--R + +--R 5 14 3 6 13 2 7 12 8 11 +--R 3136a b x + 1568a b x + 448a b x + 56a b +--R Type: Expression(Integer) +--E 837 + +--S 838 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 8 10 9 9 10 2 8 8 +--R (2520a b d - 5040a b c d + 2520b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 7 +--R (20160a b d - 40320a b c d + 20160a b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 6 +--R (70560a b d - 141120a b c d + 70560a b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 5 +--R (141120a b d - 282240a b c d + 141120a b c d )x +--R + +--R 6 4 10 5 5 9 4 6 2 8 4 +--R (176400a b d - 352800a b c d + 176400a b c d )x +--R + +--R 7 3 10 6 4 9 5 5 2 8 3 +--R (141120a b d - 282240a b c d + 141120a b c d )x +--R + +--R 8 2 10 7 3 9 6 4 2 8 2 +--R (70560a b d - 141120a b c d + 70560a b c d )x +--R + +--R 9 10 8 2 9 7 3 2 8 10 10 +--R (20160a b d - 40320a b c d + 20160a b c d )x + 2520a d +--R + +--R 9 9 8 2 2 8 +--R - 5040a b c d + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 10 9 9 +--R 28b d x + (- 280a b d + 560b c d )x +--R + +--R 2 8 10 9 9 8 +--R (- 3248a b d + 4480a b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 5824a b d - 4480a b c d + 20160a b c d - 6720b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R 14896a b d - 86240a b c d + 105840a b c d - 23520a b c d +--R + +--R 10 4 6 +--R - 5880b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R 76832a b d - 266560a b c d + 258720a b c d - 47040a b c d +--R + +--R 9 4 6 10 5 5 +--R - 11760a b c d - 4704b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 140140a b d - 421400a b c d + 367500a b c d - 58800a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 14700a b c d - 5880a b c d - 2940b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R 140336a b d - 393568a b c d + 322224a b c d - 47040a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 11760a b c d - 4704a b c d - 2352a b c d - 1344b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 81928a b d - 220304a b c d + 172872a b c d - 23520a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 10 8 2 +--R - 5880a b c d - 2352a b c d - 1176a b c d - 672a b c d - 420b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 26288a b d - 68704a b c d + 52272a b c d - 6720a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 1680a b c d - 672a b c d - 336a b c d - 192a b c d +--R + +--R 9 8 2 10 9 +--R - 120a b c d - 80b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R 3601a d - 9218a b c d + 6849a b c d - 840a b c d - 210a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R - 84a b c d - 42a b c d - 24a b c d - 15a b c d - 10a b c d - 7b c +--R / +--R 19 8 18 7 2 17 6 3 16 5 4 15 4 +--R 56b x + 448a b x + 1568a b x + 3136a b x + 3920a b x +--R + +--R 5 14 3 6 13 2 7 12 8 11 +--R 3136a b x + 1568a b x + 448a b x + 56a b +--R Type: Union(Expression(Integer),...) +--E 838 + +--S 839 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 839 + +--S 840 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 840 + +)clear all + +--S 841 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^10 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 841 + +--S 842 of 2952 +r0000:=d^10*x/b^10-1/9*(b*c-a*d)^10/(b^11*(a+b*x)^9)-_ + 5/4*d*(b*c-a*d)^9/(b^11*(a+b*x)^8)-_ + 45/7*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^7)-_ + 20*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^6)-_ + 42*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^5)-_ + 63*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^4)-_ + 70*d^6*(b*c-a*d)^4/(b^11*(a+b*x)^3)-_ + 60*d^7*(b*c-a*d)^3/(b^11*(a+b*x)^2)-_ + 45*d^8*(b*c-a*d)^2/(b^11*(a+b*x))+10*d^9*(b*c-a*d)*log(a+b*x)/b^11 +--R +--R +--R (2) +--R 9 10 10 9 9 2 8 10 9 9 8 +--R (- 2520a b d + 2520b c d )x + (- 22680a b d + 22680a b c d )x +--R + +--R 3 7 10 2 8 9 7 +--R (- 90720a b d + 90720a b c d )x +--R + +--R 4 6 10 3 7 9 6 +--R (- 211680a b d + 211680a b c d )x +--R + +--R 5 5 10 4 6 9 5 +--R (- 317520a b d + 317520a b c d )x +--R + +--R 6 4 10 5 5 9 4 +--R (- 317520a b d + 317520a b c d )x +--R + +--R 7 3 10 6 4 9 3 +--R (- 211680a b d + 211680a b c d )x +--R + +--R 8 2 10 7 3 9 2 +--R (- 90720a b d + 90720a b c d )x +--R + +--R 9 10 8 2 9 10 10 9 9 +--R (- 22680a b d + 22680a b c d )x - 2520a d + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 9 +--R 252b d x + 2268a b d x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (- 2268a b d + 22680a b c d - 11340b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 54432a b d + 136080a b c d - 45360a b c d - 15120b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R - 197568a b d + 388080a b c d - 105840a b c d - 35280a b c d +--R + +--R 10 4 6 +--R - 17640b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 375732a b d + 661500a b c d - 158760a b c d - 52920a b c d +--R + +--R 9 4 6 10 5 5 +--R - 26460a b c d - 15876b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 439236a b d + 725004a b c d - 158760a b c d - 52920a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 26460a b c d - 15876a b c d - 10584b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 328104a b d + 518616a b c d - 105840a b c d - 35280a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 17640a b c d - 10584a b c d - 7056a b c d - 5040b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 153576a b d + 235224a b c d - 45360a b c d - 15120a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 7560a b c d - 4536a b c d - 3024a b c d - 2160a b c d +--R + +--R 10 8 2 +--R - 1620b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 41229a b d + 61641a b c d - 11340a b c d - 3780a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 1890a b c d - 1134a b c d - 756a b c d - 540a b c d +--R + +--R 9 8 2 10 9 +--R - 405a b c d - 315b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R - 4861a d + 7129a b c d - 1260a b c d - 420a b c d - 210a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R - 126a b c d - 84a b c d - 60a b c d - 45a b c d - 35a b c d - 28b c +--R / +--R 20 9 19 8 2 18 7 3 17 6 4 16 5 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 15 4 6 14 3 7 13 2 8 12 9 11 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Expression(Integer) +--E 842 + +--S 843 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 10 10 9 9 2 8 10 9 9 8 +--R (- 2520a b d + 2520b c d )x + (- 22680a b d + 22680a b c d )x +--R + +--R 3 7 10 2 8 9 7 +--R (- 90720a b d + 90720a b c d )x +--R + +--R 4 6 10 3 7 9 6 +--R (- 211680a b d + 211680a b c d )x +--R + +--R 5 5 10 4 6 9 5 +--R (- 317520a b d + 317520a b c d )x +--R + +--R 6 4 10 5 5 9 4 +--R (- 317520a b d + 317520a b c d )x +--R + +--R 7 3 10 6 4 9 3 +--R (- 211680a b d + 211680a b c d )x +--R + +--R 8 2 10 7 3 9 2 +--R (- 90720a b d + 90720a b c d )x +--R + +--R 9 10 8 2 9 10 10 9 9 +--R (- 22680a b d + 22680a b c d )x - 2520a d + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 10 10 10 9 10 9 +--R 252b d x + 2268a b d x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (- 2268a b d + 22680a b c d - 11340b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 54432a b d + 136080a b c d - 45360a b c d - 15120b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R - 197568a b d + 388080a b c d - 105840a b c d - 35280a b c d +--R + +--R 10 4 6 +--R - 17640b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 375732a b d + 661500a b c d - 158760a b c d - 52920a b c d +--R + +--R 9 4 6 10 5 5 +--R - 26460a b c d - 15876b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 439236a b d + 725004a b c d - 158760a b c d - 52920a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 26460a b c d - 15876a b c d - 10584b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 328104a b d + 518616a b c d - 105840a b c d - 35280a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 17640a b c d - 10584a b c d - 7056a b c d - 5040b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 153576a b d + 235224a b c d - 45360a b c d - 15120a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 7560a b c d - 4536a b c d - 3024a b c d - 2160a b c d +--R + +--R 10 8 2 +--R - 1620b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 41229a b d + 61641a b c d - 11340a b c d - 3780a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 1890a b c d - 1134a b c d - 756a b c d - 540a b c d +--R + +--R 9 8 2 10 9 +--R - 405a b c d - 315b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R - 4861a d + 7129a b c d - 1260a b c d - 420a b c d - 210a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R - 126a b c d - 84a b c d - 60a b c d - 45a b c d - 35a b c d - 28b c +--R / +--R 20 9 19 8 2 18 7 3 17 6 4 16 5 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 15 4 6 14 3 7 13 2 8 12 9 11 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Union(Expression(Integer),...) +--E 843 + +--S 844 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 844 + +--S 845 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 845 + +)clear all + +--S 846 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^11 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R b x + 11a b x + 55a b x + 165a b x + 330a b x + 462a b x +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 11 +--R 462a b x + 330a b x + 165a b x + 55a b x + 11a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 846 + +--S 847 of 2952 +r0000:=-1/10*(b*c-a*d)^10/(b^11*(a+b*x)^10)-_ + 10/9*d*(b*c-a*d)^9/(b^11*(a+b*x)^9)-_ + 45/8*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^8)-_ + 120/7*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^7)-_ + 35*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^6)-_ + 252/5*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^5)-_ + 105/2*d^6*(b*c-a*d)^4/(b^11*(a+b*x)^4)-_ + 40*d^7*(b*c-a*d)^3/(b^11*(a+b*x)^3)-_ + 45/2*d^8*(b*c-a*d)^2/(b^11*(a+b*x)^2)-_ + 10*d^9*(b*c-a*d)/(b^11*(a+b*x))+d^10*log(a+b*x)/b^11 +--R +--R +--R (2) +--R 10 10 10 9 10 9 2 8 10 8 3 7 10 7 +--R 2520b d x + 25200a b d x + 113400a b d x + 302400a b d x +--R + +--R 4 6 10 6 5 5 10 5 6 4 10 4 7 3 10 3 +--R 529200a b d x + 635040a b d x + 529200a b d x + 302400a b d x +--R + +--R 8 2 10 2 9 10 10 10 +--R 113400a b d x + 25200a b d x + 2520a d +--R * +--R log(b x + a) +--R + +--R 9 10 10 9 9 +--R (25200a b d - 25200b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (170100a b d - 113400a b c d - 56700b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (554400a b d - 302400a b c d - 151200a b c d - 100800b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R 1102500a b d - 529200a b c d - 264600a b c d - 176400a b c d +--R + +--R 10 4 6 +--R - 132300b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R 1450008a b d - 635040a b c d - 317520a b c d - 211680a b c d +--R + +--R 9 4 6 10 5 5 +--R - 158760a b c d - 127008b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 1296540a b d - 529200a b c d - 264600a b c d - 176400a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 132300a b c d - 105840a b c d - 88200b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R 784080a b d - 302400a b c d - 151200a b c d - 100800a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 75600a b c d - 60480a b c d - 50400a b c d - 43200b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 308205a b d - 113400a b c d - 56700a b c d - 37800a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 28350a b c d - 22680a b c d - 18900a b c d - 16200a b c d +--R + +--R 10 8 2 +--R - 14175b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 71290a b d - 25200a b c d - 12600a b c d - 8400a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 6300a b c d - 5040a b c d - 4200a b c d - 3600a b c d +--R + +--R 9 8 2 10 9 +--R - 3150a b c d - 2800b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R 7381a d - 2520a b c d - 1260a b c d - 840a b c d - 630a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 +--R - 504a b c d - 420a b c d - 360a b c d - 315a b c d - 280a b c d +--R + +--R 10 10 +--R - 252b c +--R / +--R 21 10 20 9 2 19 8 3 18 7 4 17 6 +--R 2520b x + 25200a b x + 113400a b x + 302400a b x + 529200a b x +--R + +--R 5 16 5 6 15 4 7 14 3 8 13 2 +--R 635040a b x + 529200a b x + 302400a b x + 113400a b x +--R + +--R 9 12 10 11 +--R 25200a b x + 2520a b +--R Type: Expression(Integer) +--E 847 + +--S 848 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 10 9 2 8 10 8 3 7 10 7 +--R 2520b d x + 25200a b d x + 113400a b d x + 302400a b d x +--R + +--R 4 6 10 6 5 5 10 5 6 4 10 4 7 3 10 3 +--R 529200a b d x + 635040a b d x + 529200a b d x + 302400a b d x +--R + +--R 8 2 10 2 9 10 10 10 +--R 113400a b d x + 25200a b d x + 2520a d +--R * +--R log(b x + a) +--R + +--R 9 10 10 9 9 +--R (25200a b d - 25200b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (170100a b d - 113400a b c d - 56700b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (554400a b d - 302400a b c d - 151200a b c d - 100800b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R 1102500a b d - 529200a b c d - 264600a b c d - 176400a b c d +--R + +--R 10 4 6 +--R - 132300b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R 1450008a b d - 635040a b c d - 317520a b c d - 211680a b c d +--R + +--R 9 4 6 10 5 5 +--R - 158760a b c d - 127008b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R 1296540a b d - 529200a b c d - 264600a b c d - 176400a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 132300a b c d - 105840a b c d - 88200b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R 784080a b d - 302400a b c d - 151200a b c d - 100800a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 75600a b c d - 60480a b c d - 50400a b c d - 43200b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R 308205a b d - 113400a b c d - 56700a b c d - 37800a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 28350a b c d - 22680a b c d - 18900a b c d - 16200a b c d +--R + +--R 10 8 2 +--R - 14175b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R 71290a b d - 25200a b c d - 12600a b c d - 8400a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 6300a b c d - 5040a b c d - 4200a b c d - 3600a b c d +--R + +--R 9 8 2 10 9 +--R - 3150a b c d - 2800b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R 7381a d - 2520a b c d - 1260a b c d - 840a b c d - 630a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 +--R - 504a b c d - 420a b c d - 360a b c d - 315a b c d - 280a b c d +--R + +--R 10 10 +--R - 252b c +--R / +--R 21 10 20 9 2 19 8 3 18 7 4 17 6 +--R 2520b x + 25200a b x + 113400a b x + 302400a b x + 529200a b x +--R + +--R 5 16 5 6 15 4 7 14 3 8 13 2 +--R 635040a b x + 529200a b x + 302400a b x + 113400a b x +--R + +--R 9 12 10 11 +--R 25200a b x + 2520a b +--R Type: Union(Expression(Integer),...) +--E 848 + +--S 849 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 849 + +--S 850 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 850 + +)clear all + +--S 851 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^12 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 12 12 11 11 2 10 10 3 9 9 4 8 8 5 7 7 +--R b x + 12a b x + 66a b x + 220a b x + 495a b x + 792a b x +--R + +--R 6 6 6 7 5 5 8 4 4 9 3 3 10 2 2 11 12 +--R 924a b x + 792a b x + 495a b x + 220a b x + 66a b x + 12a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 851 + +--S 852 of 2952 +r0000:=-1/11*(c+d*x)^11/((b*c-a*d)*(a+b*x)^11) +--R +--R +--R (2) +--R 1 11 11 10 10 2 9 9 3 8 8 4 7 7 5 6 6 +--R -- d x + c d x + 5c d x + 15c d x + 30c d x + 42c d x +--R 11 +--R + +--R 6 5 5 7 4 4 8 3 3 9 2 2 10 1 11 +--R 42c d x + 30c d x + 15c d x + 5c d x + c d x + -- c +--R 11 +--R / +--R 11 12 11 2 10 11 10 3 9 2 10 9 +--R (a b d - b c)x + (11a b d - 11a b c)x + (55a b d - 55a b c)x +--R + +--R 4 8 3 9 8 5 7 4 8 7 +--R (165a b d - 165a b c)x + (330a b d - 330a b c)x +--R + +--R 6 6 5 7 6 7 5 6 6 5 +--R (462a b d - 462a b c)x + (462a b d - 462a b c)x +--R + +--R 8 4 7 5 4 9 3 8 4 3 +--R (330a b d - 330a b c)x + (165a b d - 165a b c)x +--R + +--R 10 2 9 3 2 11 10 2 12 11 +--R (55a b d - 55a b c)x + (11a b d - 11a b c)x + a d - a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 852 + +--S 853 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 10 10 9 9 +--R - 11b d x + (- 55a b d - 55b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (- 165a b d - 165a b c d - 165b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 330a b d - 330a b c d - 330a b c d - 330b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 10 4 6 6 +--R (- 462a b d - 462a b c d - 462a b c d - 462a b c d - 462b c d )x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 9 4 6 +--R - 462a b d - 462a b c d - 462a b c d - 462a b c d - 462a b c d +--R + +--R 10 5 5 +--R - 462b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 2 8 4 6 +--R - 330a b d - 330a b c d - 330a b c d - 330a b c d - 330a b c d +--R + +--R 9 5 5 10 6 4 +--R - 330a b c d - 330b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 3 7 4 6 +--R - 165a b d - 165a b c d - 165a b c d - 165a b c d - 165a b c d +--R + +--R 2 8 5 5 9 6 4 10 7 3 +--R - 165a b c d - 165a b c d - 165b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 4 6 4 6 +--R - 55a b d - 55a b c d - 55a b c d - 55a b c d - 55a b c d +--R + +--R 3 7 5 5 2 8 6 4 9 7 3 10 8 2 +--R - 55a b c d - 55a b c d - 55a b c d - 55b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 5 5 4 6 +--R - 11a b d - 11a b c d - 11a b c d - 11a b c d - 11a b c d +--R + +--R 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 10 9 +--R - 11a b c d - 11a b c d - 11a b c d - 11a b c d - 11b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 5 5 5 5 +--R - a d - a b c d - a b c d - a b c d - a b c d - a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R - a b c d - a b c d - a b c d - a b c d - b c +--R / +--R 22 11 21 10 2 20 9 3 19 8 4 18 7 +--R 11b x + 121a b x + 605a b x + 1815a b x + 3630a b x +--R + +--R 5 17 6 6 16 5 7 15 4 8 14 3 9 13 2 +--R 5082a b x + 5082a b x + 3630a b x + 1815a b x + 605a b x +--R + +--R 10 12 11 11 +--R 121a b x + 11a b +--R Type: Union(Expression(Integer),...) +--E 853 + +--S 854 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 11 +--R d +--R (4) - ----------------- +--R 11 12 +--R 11a b d - 11b c +--R Type: Expression(Integer) +--E 854 + +--S 855 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 855 + +)clear all + +--S 856 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^13 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 13 13 12 12 2 11 11 3 10 10 4 9 9 5 8 8 +--R b x + 13a b x + 78a b x + 286a b x + 715a b x + 1287a b x +--R + +--R 6 7 7 7 6 6 8 5 5 9 4 4 10 3 3 11 2 2 +--R 1716a b x + 1716a b x + 1287a b x + 715a b x + 286a b x + 78a b x +--R + +--R 12 13 +--R 13a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 856 + +--S 857 of 2952 +r0000:=-1/12*(c+d*x)^11/((b*c-a*d)*(a+b*x)^12)+_ + 1/132*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^11) +--R +--R +--R (2) +--R 1 12 12 1 12 11 11 1 2 10 10 +--R --- b d x + -- a d x + (a c d - - b c d )x +--R 132 11 2 +--R + +--R 2 10 10 3 9 9 3 9 45 4 8 8 +--R (5a c d - -- b c d )x + (15a c d - -- b c d )x +--R 3 4 +--R + +--R 4 8 5 7 7 5 7 6 6 6 +--R (30a c d - 24b c d )x + (42a c d - 35b c d )x +--R + +--R 6 6 7 5 5 7 5 105 8 4 4 +--R (42a c d - 36b c d )x + (30a c d - --- b c d )x +--R 4 +--R + +--R 8 4 40 9 3 3 9 3 9 10 2 2 +--R (15a c d - -- b c d )x + (5a c d - - b c d )x +--R 3 2 +--R + +--R 10 2 10 11 1 11 1 12 +--R (a c d - -- b c d)x + -- a c d - -- b c +--R 11 11 12 +--R / +--R 2 12 2 13 14 2 12 +--R (a b d - 2a b c d + b c )x +--R + +--R 3 11 2 2 12 13 2 11 +--R (12a b d - 24a b c d + 12a b c )x +--R + +--R 4 10 2 3 11 2 12 2 10 +--R (66a b d - 132a b c d + 66a b c )x +--R + +--R 5 9 2 4 10 3 11 2 9 +--R (220a b d - 440a b c d + 220a b c )x +--R + +--R 6 8 2 5 9 4 10 2 8 +--R (495a b d - 990a b c d + 495a b c )x +--R + +--R 7 7 2 6 8 5 9 2 7 +--R (792a b d - 1584a b c d + 792a b c )x +--R + +--R 8 6 2 7 7 6 8 2 6 +--R (924a b d - 1848a b c d + 924a b c )x +--R + +--R 9 5 2 8 6 7 7 2 5 +--R (792a b d - 1584a b c d + 792a b c )x +--R + +--R 10 4 2 9 5 8 6 2 4 +--R (495a b d - 990a b c d + 495a b c )x +--R + +--R 11 3 2 10 4 9 5 2 3 +--R (220a b d - 440a b c d + 220a b c )x +--R + +--R 12 2 2 11 3 10 4 2 2 +--R (66a b d - 132a b c d + 66a b c )x +--R + +--R 13 2 12 2 11 3 2 14 2 13 12 2 2 +--R (12a b d - 24a b c d + 12a b c )x + a d - 2a b c d + a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 857 + +--S 858 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 10 10 9 9 +--R - 66b d x + (- 220a b d - 440b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (- 495a b d - 990a b c d - 1485b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 792a b d - 1584a b c d - 2376a b c d - 3168b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R - 924a b d - 1848a b c d - 2772a b c d - 3696a b c d +--R + +--R 10 4 6 +--R - 4620b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 792a b d - 1584a b c d - 2376a b c d - 3168a b c d +--R + +--R 9 4 6 10 5 5 +--R - 3960a b c d - 4752b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 495a b d - 990a b c d - 1485a b c d - 1980a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 2475a b c d - 2970a b c d - 3465b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 3 7 4 6 +--R - 220a b d - 440a b c d - 660a b c d - 880a b c d - 1100a b c d +--R + +--R 2 8 5 5 9 6 4 10 7 3 +--R - 1320a b c d - 1540a b c d - 1760b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 4 6 4 6 +--R - 66a b d - 132a b c d - 198a b c d - 264a b c d - 330a b c d +--R + +--R 3 7 5 5 2 8 6 4 9 7 3 10 8 2 +--R - 396a b c d - 462a b c d - 528a b c d - 594b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 5 5 4 6 +--R - 12a b d - 24a b c d - 36a b c d - 48a b c d - 60a b c d +--R + +--R 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 10 9 +--R - 72a b c d - 84a b c d - 96a b c d - 108a b c d - 120b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 5 5 5 5 +--R - a d - 2a b c d - 3a b c d - 4a b c d - 5a b c d - 6a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R - 7a b c d - 8a b c d - 9a b c d - 10a b c d - 11b c +--R / +--R 23 12 22 11 2 21 10 3 20 9 4 19 8 +--R 132b x + 1584a b x + 8712a b x + 29040a b x + 65340a b x +--R + +--R 5 18 7 6 17 6 7 16 5 8 15 4 +--R 104544a b x + 121968a b x + 104544a b x + 65340a b x +--R + +--R 9 14 3 10 13 2 11 12 12 11 +--R 29040a b x + 8712a b x + 1584a b x + 132a b +--R Type: Union(Expression(Integer),...) +--E 858 + +--S 859 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 12 +--R d +--R (4) - ----------------------------------- +--R 2 11 2 12 13 2 +--R 132a b d - 264a b c d + 132b c +--R Type: Expression(Integer) +--E 859 + +--S 860 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 860 + +)clear all + +--S 861 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^14 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 14 14 13 13 2 12 12 3 11 11 4 10 10 +--R b x + 14a b x + 91a b x + 364a b x + 1001a b x +--R + +--R 5 9 9 6 8 8 7 7 7 8 6 6 9 5 5 +--R 2002a b x + 3003a b x + 3432a b x + 3003a b x + 2002a b x +--R + +--R 10 4 4 11 3 3 12 2 2 13 14 +--R 1001a b x + 364a b x + 91a b x + 14a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 861 + +--S 862 of 2952 +r0000:=-1/13*(c+d*x)^11/((b*c-a*d)*(a+b*x)^13)+_ + 1/78*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^12)-_ + 1/858*d^2*(c+d*x)^11/((b*c-a*d)^3*(a+b*x)^11) +--R +--R +--R (2) +--R 1 2 13 13 1 13 12 1 2 13 11 +--R --- b d x + -- a b d x + -- a d x +--R 858 66 11 +--R + +--R 2 12 2 11 1 2 3 10 10 +--R (a c d - a b c d + - b c d )x +--R 3 +--R + +--R 2 2 11 20 3 10 5 2 4 9 9 +--R (5a c d - -- a b c d + - b c d )x +--R 3 2 +--R + +--R 2 3 10 45 4 9 2 5 8 8 +--R (15a c d - -- a b c d + 9b c d )x +--R 2 +--R + +--R 2 4 9 5 8 2 6 7 7 +--R (30a c d - 48a b c d + 20b c d )x +--R + +--R 2 5 8 6 7 2 7 6 6 +--R (42a c d - 70a b c d + 30b c d )x +--R + +--R 2 6 7 7 6 63 2 8 5 5 +--R (42a c d - 72a b c d + -- b c d )x +--R 2 +--R + +--R 2 7 6 105 8 5 70 2 9 4 4 +--R (30a c d - --- a b c d + -- b c d )x +--R 2 3 +--R + +--R 2 8 5 80 9 4 2 10 3 3 +--R (15a c d - -- a b c d + 12b c d )x +--R 3 +--R + +--R 2 9 4 10 3 45 2 11 2 2 +--R (5a c d - 9a b c d + -- b c d )x +--R 11 +--R + +--R 2 10 3 20 11 2 5 2 12 1 2 11 2 1 12 1 2 13 +--R (a c d - -- a b c d + - b c d)x + -- a c d - - a b c d + -- b c +--R 11 6 11 6 13 +--R / +--R 3 13 3 2 14 2 15 2 16 3 13 +--R (a b d - 3a b c d + 3a b c d - b c )x +--R + +--R 4 12 3 3 13 2 2 14 2 15 3 12 +--R (13a b d - 39a b c d + 39a b c d - 13a b c )x +--R + +--R 5 11 3 4 12 2 3 13 2 2 14 3 11 +--R (78a b d - 234a b c d + 234a b c d - 78a b c )x +--R + +--R 6 10 3 5 11 2 4 12 2 3 13 3 10 +--R (286a b d - 858a b c d + 858a b c d - 286a b c )x +--R + +--R 7 9 3 6 10 2 5 11 2 4 12 3 9 +--R (715a b d - 2145a b c d + 2145a b c d - 715a b c )x +--R + +--R 8 8 3 7 9 2 6 10 2 5 11 3 8 +--R (1287a b d - 3861a b c d + 3861a b c d - 1287a b c )x +--R + +--R 9 7 3 8 8 2 7 9 2 6 10 3 7 +--R (1716a b d - 5148a b c d + 5148a b c d - 1716a b c )x +--R + +--R 10 6 3 9 7 2 8 8 2 7 9 3 6 +--R (1716a b d - 5148a b c d + 5148a b c d - 1716a b c )x +--R + +--R 11 5 3 10 6 2 9 7 2 8 8 3 5 +--R (1287a b d - 3861a b c d + 3861a b c d - 1287a b c )x +--R + +--R 12 4 3 11 5 2 10 6 2 9 7 3 4 +--R (715a b d - 2145a b c d + 2145a b c d - 715a b c )x +--R + +--R 13 3 3 12 4 2 11 5 2 10 6 3 3 +--R (286a b d - 858a b c d + 858a b c d - 286a b c )x +--R + +--R 14 2 3 13 3 2 12 4 2 11 5 3 2 +--R (78a b d - 234a b c d + 234a b c d - 78a b c )x +--R + +--R 15 3 14 2 2 13 3 2 12 4 3 16 3 15 2 +--R (13a b d - 39a b c d + 39a b c d - 13a b c )x + a d - 3a b c d +--R + +--R 14 2 2 13 3 3 +--R 3a b c d - a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 862 + +--S 863 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 10 10 9 9 +--R - 286b d x + (- 715a b d - 2145b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (- 1287a b d - 3861a b c d - 7722b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 1716a b d - 5148a b c d - 10296a b c d - 17160b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R - 1716a b d - 5148a b c d - 10296a b c d - 17160a b c d +--R + +--R 10 4 6 +--R - 25740b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 1287a b d - 3861a b c d - 7722a b c d - 12870a b c d +--R + +--R 9 4 6 10 5 5 +--R - 19305a b c d - 27027b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 715a b d - 2145a b c d - 4290a b c d - 7150a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 10725a b c d - 15015a b c d - 20020b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 286a b d - 858a b c d - 1716a b c d - 2860a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 4290a b c d - 6006a b c d - 8008a b c d - 10296b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 4 6 4 6 +--R - 78a b d - 234a b c d - 468a b c d - 780a b c d - 1170a b c d +--R + +--R 3 7 5 5 2 8 6 4 9 7 3 10 8 2 +--R - 1638a b c d - 2184a b c d - 2808a b c d - 3510b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 5 5 4 6 +--R - 13a b d - 39a b c d - 78a b c d - 130a b c d - 195a b c d +--R + +--R 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 10 9 +--R - 273a b c d - 364a b c d - 468a b c d - 585a b c d - 715b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 5 5 5 5 +--R - a d - 3a b c d - 6a b c d - 10a b c d - 15a b c d - 21a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R - 28a b c d - 36a b c d - 45a b c d - 55a b c d - 66b c +--R / +--R 24 13 23 12 2 22 11 3 21 10 +--R 858b x + 11154a b x + 66924a b x + 245388a b x +--R + +--R 4 20 9 5 19 8 6 18 7 7 17 6 +--R 613470a b x + 1104246a b x + 1472328a b x + 1472328a b x +--R + +--R 8 16 5 9 15 4 10 14 3 11 13 2 +--R 1104246a b x + 613470a b x + 245388a b x + 66924a b x +--R + +--R 12 12 13 11 +--R 11154a b x + 858a b +--R Type: Union(Expression(Integer),...) +--E 863 + +--S 864 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 13 +--R d +--R (4) - ---------------------------------------------------- +--R 3 11 3 2 12 2 13 2 14 3 +--R 858a b d - 2574a b c d + 2574a b c d - 858b c +--R Type: Expression(Integer) +--E 864 + +--S 865 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 865 + +)clear all + +--S 866 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^15 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 15 15 14 14 2 13 13 3 12 12 4 11 11 +--R b x + 15a b x + 105a b x + 455a b x + 1365a b x +--R + +--R 5 10 10 6 9 9 7 8 8 8 7 7 9 6 6 +--R 3003a b x + 5005a b x + 6435a b x + 6435a b x + 5005a b x +--R + +--R 10 5 5 11 4 4 12 3 3 13 2 2 14 15 +--R 3003a b x + 1365a b x + 455a b x + 105a b x + 15a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 866 + +--S 867 of 2952 +r0000:=-1/14*(c+d*x)^11/((b*c-a*d)*(a+b*x)^14)+_ + 3/182*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^13)-_ + 1/364*d^2*(c+d*x)^11/((b*c-a*d)^3*(a+b*x)^12)+_ + 1/4004*d^3*(c+d*x)^11/((b*c-a*d)^4*(a+b*x)^11) +--R +--R +--R (2) +--R 1 3 14 14 1 2 14 13 1 2 14 12 1 3 14 11 +--R ---- b d x + --- a b d x + -- a b d x + -- a d x +--R 4004 286 44 11 +--R + +--R 3 13 3 2 2 12 2 3 11 1 3 4 10 10 +--R (a c d - - a b c d + a b c d - - b c d )x +--R 2 4 +--R + +--R 3 2 12 2 3 11 15 2 4 10 3 5 9 9 +--R (5a c d - 10a b c d + -- a b c d - 2b c d )x +--R 2 +--R + +--R 3 3 11 135 2 4 10 2 5 9 15 3 6 8 8 +--R (15a c d - --- a b c d + 27a b c d - -- b c d )x +--R 4 2 +--R + +--R 3 4 10 2 5 9 2 6 8 120 3 7 7 7 +--R (30a c d - 72a b c d + 60a b c d - --- b c d )x +--R 7 +--R + +--R 3 5 9 2 6 8 2 7 7 105 3 8 6 6 +--R (42a c d - 105a b c d + 90a b c d - --- b c d )x +--R 4 +--R + +--R 3 6 8 2 7 7 189 2 8 6 3 9 5 5 +--R (42a c d - 108a b c d + --- a b c d - 28b c d )x +--R 2 +--R + +--R 3 7 7 315 2 8 6 2 9 5 3 10 4 4 +--R (30a c d - --- a b c d + 70a b c d - 21b c d )x +--R 4 +--R + +--R 3 8 6 2 9 5 2 10 4 120 3 11 3 3 +--R (15a c d - 40a b c d + 36a b c d - --- b c d )x +--R 11 +--R + +--R 3 9 5 27 2 10 4 135 2 11 3 15 3 12 2 2 +--R (5a c d - -- a b c d + --- a b c d - -- b c d )x +--R 2 11 4 +--R + +--R 3 10 4 30 2 11 3 5 2 12 2 10 3 13 1 3 11 3 +--R (a c d - -- a b c d + - a b c d - -- b c d)x + -- a c d +--R 11 2 13 11 +--R + +--R 1 2 12 2 3 2 13 1 3 14 +--R - - a b c d + -- a b c d - -- b c +--R 4 13 14 +--R / +--R 4 14 4 3 15 3 2 16 2 2 17 3 18 4 14 +--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c )x +--R + +--R 5 13 4 4 14 3 3 15 2 2 2 16 3 17 4 13 +--R (14a b d - 56a b c d + 84a b c d - 56a b c d + 14a b c )x +--R + +--R 6 12 4 5 13 3 4 14 2 2 3 15 3 2 16 4 12 +--R (91a b d - 364a b c d + 546a b c d - 364a b c d + 91a b c )x +--R + +--R 7 11 4 6 12 3 5 13 2 2 4 14 3 +--R 364a b d - 1456a b c d + 2184a b c d - 1456a b c d +--R + +--R 3 15 4 +--R 364a b c +--R * +--R 11 +--R x +--R + +--R 8 10 4 7 11 3 6 12 2 2 5 13 3 +--R 1001a b d - 4004a b c d + 6006a b c d - 4004a b c d +--R + +--R 4 14 4 +--R 1001a b c +--R * +--R 10 +--R x +--R + +--R 9 9 4 8 10 3 7 11 2 2 6 12 3 +--R 2002a b d - 8008a b c d + 12012a b c d - 8008a b c d +--R + +--R 5 13 4 +--R 2002a b c +--R * +--R 9 +--R x +--R + +--R 10 8 4 9 9 3 8 10 2 2 7 11 3 +--R 3003a b d - 12012a b c d + 18018a b c d - 12012a b c d +--R + +--R 6 12 4 +--R 3003a b c +--R * +--R 8 +--R x +--R + +--R 11 7 4 10 8 3 9 9 2 2 8 10 3 +--R 3432a b d - 13728a b c d + 20592a b c d - 13728a b c d +--R + +--R 7 11 4 +--R 3432a b c +--R * +--R 7 +--R x +--R + +--R 12 6 4 11 7 3 10 8 2 2 9 9 3 +--R 3003a b d - 12012a b c d + 18018a b c d - 12012a b c d +--R + +--R 8 10 4 +--R 3003a b c +--R * +--R 6 +--R x +--R + +--R 13 5 4 12 6 3 11 7 2 2 10 8 3 +--R 2002a b d - 8008a b c d + 12012a b c d - 8008a b c d +--R + +--R 9 9 4 +--R 2002a b c +--R * +--R 5 +--R x +--R + +--R 14 4 4 13 5 3 12 6 2 2 11 7 3 +--R 1001a b d - 4004a b c d + 6006a b c d - 4004a b c d +--R + +--R 10 8 4 +--R 1001a b c +--R * +--R 4 +--R x +--R + +--R 15 3 4 14 4 3 13 5 2 2 12 6 3 +--R 364a b d - 1456a b c d + 2184a b c d - 1456a b c d +--R + +--R 11 7 4 +--R 364a b c +--R * +--R 3 +--R x +--R + +--R 16 2 4 15 3 3 14 4 2 2 13 5 3 12 6 4 2 +--R (91a b d - 364a b c d + 546a b c d - 364a b c d + 91a b c )x +--R + +--R 17 4 16 2 3 15 3 2 2 14 4 3 13 5 4 18 4 +--R (14a b d - 56a b c d + 84a b c d - 56a b c d + 14a b c )x + a d +--R + +--R 17 3 16 2 2 2 15 3 3 14 4 4 +--R - 4a b c d + 6a b c d - 4a b c d + a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 867 + +--S 868 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 10 10 9 9 +--R - 1001b d x + (- 2002a b d - 8008b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (- 3003a b d - 12012a b c d - 30030b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 3432a b d - 13728a b c d - 34320a b c d - 68640b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R - 3003a b d - 12012a b c d - 30030a b c d - 60060a b c d +--R + +--R 10 4 6 +--R - 105105b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 2002a b d - 8008a b c d - 20020a b c d - 40040a b c d +--R + +--R 9 4 6 10 5 5 +--R - 70070a b c d - 112112b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 1001a b d - 4004a b c d - 10010a b c d - 20020a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 35035a b c d - 56056a b c d - 84084b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 364a b d - 1456a b c d - 3640a b c d - 7280a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 12740a b c d - 20384a b c d - 30576a b c d - 43680b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 4 6 4 6 +--R - 91a b d - 364a b c d - 910a b c d - 1820a b c d - 3185a b c d +--R + +--R 3 7 5 5 2 8 6 4 9 7 3 10 8 2 +--R - 5096a b c d - 7644a b c d - 10920a b c d - 15015b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 5 5 4 6 +--R - 14a b d - 56a b c d - 140a b c d - 280a b c d - 490a b c d +--R + +--R 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 10 9 +--R - 784a b c d - 1176a b c d - 1680a b c d - 2310a b c d - 3080b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 5 5 5 5 +--R - a d - 4a b c d - 10a b c d - 20a b c d - 35a b c d - 56a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R - 84a b c d - 120a b c d - 165a b c d - 220a b c d - 286b c +--R / +--R 25 14 24 13 2 23 12 3 22 11 +--R 4004b x + 56056a b x + 364364a b x + 1457456a b x +--R + +--R 4 21 10 5 20 9 6 19 8 7 18 7 +--R 4008004a b x + 8016008a b x + 12024012a b x + 13741728a b x +--R + +--R 8 17 6 9 16 5 10 15 4 11 14 3 +--R 12024012a b x + 8016008a b x + 4008004a b x + 1457456a b x +--R + +--R 12 13 2 13 12 14 11 +--R 364364a b x + 56056a b x + 4004a b +--R Type: Union(Expression(Integer),...) +--E 868 + +--S 869 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 14 +--R d +--R - ------------------------------------------------------------------------- +--R 4 11 4 3 12 3 2 13 2 2 14 3 15 4 +--R 4004a b d - 16016a b c d + 24024a b c d - 16016a b c d + 4004b c +--R Type: Expression(Integer) +--E 869 + +--S 870 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 870 + +)clear all + +--S 871 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^16 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 16 16 15 15 2 14 14 3 13 13 4 12 12 +--R b x + 16a b x + 120a b x + 560a b x + 1820a b x +--R + +--R 5 11 11 6 10 10 7 9 9 8 8 8 9 7 7 +--R 4368a b x + 8008a b x + 11440a b x + 12870a b x + 11440a b x +--R + +--R 10 6 6 11 5 5 12 4 4 13 3 3 14 2 2 +--R 8008a b x + 4368a b x + 1820a b x + 560a b x + 120a b x +--R + +--R 15 16 +--R 16a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 871 + +--S 872 of 2952 +r0000:=-1/15*(c+d*x)^11/((b*c-a*d)*(a+b*x)^15)+_ + 2/105*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^14)-_ + 2/455*d^2*(c+d*x)^11/((b*c-a*d)^3*(a+b*x)^13)+_ + 1/1365*d^3*(c+d*x)^11/((b*c-a*d)^4*(a+b*x)^12)-_ + 1/15015*d^4*(c+d*x)^11/((b*c-a*d)^5*(a+b*x)^11) +--R +--R +--R (2) +--R 1 4 15 15 1 3 15 14 1 2 2 15 13 1 3 15 12 +--R ----- b d x + ---- a b d x + --- a b d x + -- a b d x +--R 15015 1001 143 33 +--R + +--R 1 4 15 11 +--R -- a d x +--R 11 +--R + +--R 4 14 3 2 13 2 2 3 12 3 4 11 1 4 5 10 10 +--R (a c d - 2a b c d + 2a b c d - a b c d + - b c d )x +--R 5 +--R + +--R 4 2 13 40 3 3 12 2 2 4 11 3 5 10 5 4 6 9 9 +--R (5a c d - -- a b c d + 15a b c d - 8a b c d + - b c d )x +--R 3 3 +--R + +--R 4 3 12 3 4 11 2 2 5 10 3 6 9 45 4 7 8 8 +--R (15a c d - 45a b c d + 54a b c d - 30a b c d + -- b c d )x +--R 7 +--R + +--R 4 4 11 3 5 10 2 2 6 9 480 3 7 8 4 8 7 7 +--R (30a c d - 96a b c d + 120a b c d - --- a b c d + 15b c d )x +--R 7 +--R + +--R 4 5 10 3 6 9 2 2 7 8 3 8 7 70 4 9 6 6 +--R (42a c d - 140a b c d + 180a b c d - 105a b c d + -- b c d )x +--R 3 +--R + +--R 4 6 9 3 7 8 2 2 8 7 3 9 6 126 4 10 5 5 +--R (42a c d - 144a b c d + 189a b c d - 112a b c d + --- b c d )x +--R 5 +--R + +--R 4 7 8 3 8 7 2 2 9 6 3 10 5 210 4 11 4 4 +--R (30a c d - 105a b c d + 140a b c d - 84a b c d + --- b c d )x +--R 11 +--R + +--R 4 8 7 160 3 9 6 2 2 10 5 480 3 11 4 4 12 3 3 +--R (15a c d - --- a b c d + 72a b c d - --- a b c d + 10b c d )x +--R 3 11 +--R + +--R 4 9 6 3 10 5 270 2 2 11 4 3 12 3 45 4 13 2 2 +--R (5a c d - 18a b c d + --- a b c d - 15a b c d + -- b c d )x +--R 11 13 +--R + +--R 4 10 5 40 3 11 4 2 2 12 3 40 3 13 2 5 4 14 +--R (a c d - -- a b c d + 5a b c d - -- a b c d + - b c d)x +--R 11 13 7 +--R + +--R 1 4 11 4 1 3 12 3 6 2 2 13 2 2 3 14 1 4 15 +--R -- a c d - - a b c d + -- a b c d - - a b c d + -- b c +--R 11 3 13 7 15 +--R / +--R 5 15 5 4 16 4 3 17 2 3 2 18 3 2 19 4 20 5 15 +--R (a b d - 5a b c d + 10a b c d - 10a b c d + 5a b c d - b c )x +--R + +--R 6 14 5 5 15 4 4 16 2 3 3 17 3 2 2 18 4 +--R 15a b d - 75a b c d + 150a b c d - 150a b c d + 75a b c d +--R + +--R 19 5 +--R - 15a b c +--R * +--R 14 +--R x +--R + +--R 7 13 5 6 14 4 5 15 2 3 4 16 3 2 +--R 105a b d - 525a b c d + 1050a b c d - 1050a b c d +--R + +--R 3 17 4 2 18 5 +--R 525a b c d - 105a b c +--R * +--R 13 +--R x +--R + +--R 8 12 5 7 13 4 6 14 2 3 5 15 3 2 +--R 455a b d - 2275a b c d + 4550a b c d - 4550a b c d +--R + +--R 4 16 4 3 17 5 +--R 2275a b c d - 455a b c +--R * +--R 12 +--R x +--R + +--R 9 11 5 8 12 4 7 13 2 3 6 14 3 2 +--R 1365a b d - 6825a b c d + 13650a b c d - 13650a b c d +--R + +--R 5 15 4 4 16 5 +--R 6825a b c d - 1365a b c +--R * +--R 11 +--R x +--R + +--R 10 10 5 9 11 4 8 12 2 3 7 13 3 2 +--R 3003a b d - 15015a b c d + 30030a b c d - 30030a b c d +--R + +--R 6 14 4 5 15 5 +--R 15015a b c d - 3003a b c +--R * +--R 10 +--R x +--R + +--R 11 9 5 10 10 4 9 11 2 3 8 12 3 2 +--R 5005a b d - 25025a b c d + 50050a b c d - 50050a b c d +--R + +--R 7 13 4 6 14 5 +--R 25025a b c d - 5005a b c +--R * +--R 9 +--R x +--R + +--R 12 8 5 11 9 4 10 10 2 3 9 11 3 2 +--R 6435a b d - 32175a b c d + 64350a b c d - 64350a b c d +--R + +--R 8 12 4 7 13 5 +--R 32175a b c d - 6435a b c +--R * +--R 8 +--R x +--R + +--R 13 7 5 12 8 4 11 9 2 3 10 10 3 2 +--R 6435a b d - 32175a b c d + 64350a b c d - 64350a b c d +--R + +--R 9 11 4 8 12 5 +--R 32175a b c d - 6435a b c +--R * +--R 7 +--R x +--R + +--R 14 6 5 13 7 4 12 8 2 3 11 9 3 2 +--R 5005a b d - 25025a b c d + 50050a b c d - 50050a b c d +--R + +--R 10 10 4 9 11 5 +--R 25025a b c d - 5005a b c +--R * +--R 6 +--R x +--R + +--R 15 5 5 14 6 4 13 7 2 3 12 8 3 2 +--R 3003a b d - 15015a b c d + 30030a b c d - 30030a b c d +--R + +--R 11 9 4 10 10 5 +--R 15015a b c d - 3003a b c +--R * +--R 5 +--R x +--R + +--R 16 4 5 15 5 4 14 6 2 3 13 7 3 2 +--R 1365a b d - 6825a b c d + 13650a b c d - 13650a b c d +--R + +--R 12 8 4 11 9 5 +--R 6825a b c d - 1365a b c +--R * +--R 4 +--R x +--R + +--R 17 3 5 16 4 4 15 5 2 3 14 6 3 2 +--R 455a b d - 2275a b c d + 4550a b c d - 4550a b c d +--R + +--R 13 7 4 12 8 5 +--R 2275a b c d - 455a b c +--R * +--R 3 +--R x +--R + +--R 18 2 5 17 3 4 16 4 2 3 15 5 3 2 +--R 105a b d - 525a b c d + 1050a b c d - 1050a b c d +--R + +--R 14 6 4 13 7 5 +--R 525a b c d - 105a b c +--R * +--R 2 +--R x +--R + +--R 19 5 18 2 4 17 3 2 3 16 4 3 2 15 5 4 +--R 15a b d - 75a b c d + 150a b c d - 150a b c d + 75a b c d +--R + +--R 14 6 5 +--R - 15a b c +--R * +--R x +--R + +--R 20 5 19 4 18 2 2 3 17 3 3 2 16 4 4 15 5 5 +--R a d - 5a b c d + 10a b c d - 10a b c d + 5a b c d - a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 872 + +--S 873 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 10 10 9 9 +--R - 3003b d x + (- 5005a b d - 25025b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (- 6435a b d - 32175a b c d - 96525b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 6435a b d - 32175a b c d - 96525a b c d - 225225b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R - 5005a b d - 25025a b c d - 75075a b c d - 175175a b c d +--R + +--R 10 4 6 +--R - 350350b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 3003a b d - 15015a b c d - 45045a b c d - 105105a b c d +--R + +--R 9 4 6 10 5 5 +--R - 210210a b c d - 378378b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 1365a b d - 6825a b c d - 20475a b c d - 47775a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 95550a b c d - 171990a b c d - 286650b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 455a b d - 2275a b c d - 6825a b c d - 15925a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 31850a b c d - 57330a b c d - 95550a b c d - 150150b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 105a b d - 525a b c d - 1575a b c d - 3675a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 7350a b c d - 13230a b c d - 22050a b c d - 34650a b c d +--R + +--R 10 8 2 +--R - 51975b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 5 5 4 6 +--R - 15a b d - 75a b c d - 225a b c d - 525a b c d - 1050a b c d +--R + +--R 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 +--R - 1890a b c d - 3150a b c d - 4950a b c d - 7425a b c d +--R + +--R 10 9 +--R - 10725b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 5 5 5 5 +--R - a d - 5a b c d - 15a b c d - 35a b c d - 70a b c d - 126a b c d +--R + +--R 4 6 6 4 3 7 7 3 2 8 8 2 9 9 10 10 +--R - 210a b c d - 330a b c d - 495a b c d - 715a b c d - 1001b c +--R / +--R 26 15 25 14 2 24 13 3 23 12 +--R 15015b x + 225225a b x + 1576575a b x + 6831825a b x +--R + +--R 4 22 11 5 21 10 6 20 9 7 19 8 +--R 20495475a b x + 45090045a b x + 75150075a b x + 96621525a b x +--R + +--R 8 18 7 9 17 6 10 16 5 11 15 4 +--R 96621525a b x + 75150075a b x + 45090045a b x + 20495475a b x +--R + +--R 12 14 3 13 13 2 14 12 15 11 +--R 6831825a b x + 1576575a b x + 225225a b x + 15015a b +--R Type: Union(Expression(Integer),...) +--E 873 + +--S 874 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R - +--R 15 +--R d +--R / +--R 5 11 5 4 12 4 3 13 2 3 2 14 3 2 +--R 15015a b d - 75075a b c d + 150150a b c d - 150150a b c d +--R + +--R 15 4 16 5 +--R 75075a b c d - 15015b c +--R Type: Expression(Integer) +--E 874 + +--S 875 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 875 + +)clear all + +--S 876 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^17 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 17 17 16 16 2 15 15 3 14 14 4 13 13 +--R b x + 17a b x + 136a b x + 680a b x + 2380a b x +--R + +--R 5 12 12 6 11 11 7 10 10 8 9 9 9 8 8 +--R 6188a b x + 12376a b x + 19448a b x + 24310a b x + 24310a b x +--R + +--R 10 7 7 11 6 6 12 5 5 13 4 4 14 3 3 +--R 19448a b x + 12376a b x + 6188a b x + 2380a b x + 680a b x +--R + +--R 15 2 2 16 17 +--R 136a b x + 17a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 876 + +--S 877 of 2952 +r0000:=-1/16*(c+d*x)^11/((b*c-a*d)*(a+b*x)^16)+_ + 1/48*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^15)-_ + 1/168*d^2*(c+d*x)^11/((b*c-a*d)^3*(a+b*x)^14)+_ + 1/728*d^3*(c+d*x)^11/((b*c-a*d)^4*(a+b*x)^13)-_ + 1/4368*d^4*(c+d*x)^11/((b*c-a*d)^5*(a+b*x)^12)+_ + 1/48048*d^5*(c+d*x)^11/((b*c-a*d)^6*(a+b*x)^11) +--R +--R +--R (2) +--R 1 5 16 16 1 4 16 15 5 2 3 16 14 5 3 2 16 13 +--R ----- b d x + ---- a b d x + ---- a b d x + --- a b d x +--R 48048 3003 2002 429 +--R + +--R 5 4 16 12 1 5 16 11 +--R --- a b d x + -- a d x +--R 132 11 +--R + +--R 5 15 5 4 2 14 10 3 2 3 13 5 2 3 4 12 4 5 11 +--R a c d - - a b c d + -- a b c d - - a b c d + a b c d +--R 2 3 2 +--R + +--R 1 5 6 10 +--R - - b c d +--R 6 +--R * +--R 10 +--R x +--R + +--R 5 2 14 50 4 3 13 3 2 4 12 2 3 5 11 25 4 6 10 +--R 5a c d - -- a b c d + 25a b c d - 20a b c d + -- a b c d +--R 3 3 +--R + +--R 10 5 7 9 +--R - -- b c d +--R 7 +--R * +--R 9 +--R x +--R + +--R 5 3 13 225 4 4 12 3 2 5 11 2 3 6 10 225 4 7 9 +--R 15a c d - --- a b c d + 90a b c d - 75a b c d + --- a b c d +--R 4 7 +--R + +--R 45 5 8 8 +--R - -- b c d +--R 8 +--R * +--R 8 +--R x +--R + +--R 5 4 12 4 5 11 3 2 6 10 1200 2 3 7 9 4 8 8 +--R 30a c d - 120a b c d + 200a b c d - ---- a b c d + 75a b c d +--R 7 +--R + +--R 40 5 9 7 +--R - -- b c d +--R 3 +--R * +--R 7 +--R x +--R + +--R 5 5 11 4 6 10 3 2 7 9 525 2 3 8 8 350 4 9 7 +--R 42a c d - 175a b c d + 300a b c d - --- a b c d + --- a b c d +--R 2 3 +--R + +--R 5 10 6 +--R - 21b c d +--R * +--R 6 +--R x +--R + +--R 5 6 10 4 7 9 3 2 8 8 2 3 9 7 4 10 6 +--R 42a c d - 180a b c d + 315a b c d - 280a b c d + 126a b c d +--R + +--R 252 5 11 5 +--R - --- b c d +--R 11 +--R * +--R 5 +--R x +--R + +--R 5 7 9 525 4 8 8 700 3 2 9 7 2 3 10 6 +--R 30a c d - --- a b c d + --- a b c d - 210a b c d +--R 4 3 +--R + +--R 1050 4 11 5 35 5 12 4 +--R ---- a b c d - -- b c d +--R 11 2 +--R * +--R 4 +--R x +--R + +--R 5 8 8 200 4 9 7 3 2 10 6 1200 2 3 11 5 4 12 4 +--R 15a c d - --- a b c d + 120a b c d - ---- a b c d + 50a b c d +--R 3 11 +--R + +--R 120 5 13 3 +--R - --- b c d +--R 13 +--R * +--R 3 +--R x +--R + +--R 5 9 7 45 4 10 6 450 3 2 11 5 75 2 3 12 4 225 4 13 3 +--R 5a c d - -- a b c d + --- a b c d - -- a b c d + --- a b c d +--R 2 11 2 13 +--R + +--R 45 5 14 2 +--R - -- b c d +--R 14 +--R * +--R 2 +--R x +--R + +--R 5 10 6 50 4 11 5 25 3 2 12 4 100 2 3 13 3 25 4 14 2 +--R a c d - -- a b c d + -- a b c d - --- a b c d + -- a b c d +--R 11 3 13 7 +--R + +--R 2 5 15 +--R - - b c d +--R 3 +--R * +--R x +--R + +--R 1 5 11 5 5 4 12 4 10 3 2 13 3 5 2 3 14 2 1 4 15 +--R -- a c d - -- a b c d + -- a b c d - - a b c d + - a b c d +--R 11 12 13 7 3 +--R + +--R 1 5 16 +--R - -- b c +--R 16 +--R / +--R 6 16 6 5 17 5 4 18 2 4 3 19 3 3 2 20 4 2 +--R a b d - 6a b c d + 15a b c d - 20a b c d + 15a b c d +--R + +--R 21 5 22 6 +--R - 6a b c d + b c +--R * +--R 16 +--R x +--R + +--R 7 15 6 6 16 5 5 17 2 4 4 18 3 3 3 19 4 2 +--R 16a b d - 96a b c d + 240a b c d - 320a b c d + 240a b c d +--R + +--R 2 20 5 21 6 +--R - 96a b c d + 16a b c +--R * +--R 15 +--R x +--R + +--R 8 14 6 7 15 5 6 16 2 4 5 17 3 3 +--R 120a b d - 720a b c d + 1800a b c d - 2400a b c d +--R + +--R 4 18 4 2 3 19 5 2 20 6 +--R 1800a b c d - 720a b c d + 120a b c +--R * +--R 14 +--R x +--R + +--R 9 13 6 8 14 5 7 15 2 4 6 16 3 3 +--R 560a b d - 3360a b c d + 8400a b c d - 11200a b c d +--R + +--R 5 17 4 2 4 18 5 3 19 6 +--R 8400a b c d - 3360a b c d + 560a b c +--R * +--R 13 +--R x +--R + +--R 10 12 6 9 13 5 8 14 2 4 7 15 3 3 +--R 1820a b d - 10920a b c d + 27300a b c d - 36400a b c d +--R + +--R 6 16 4 2 5 17 5 4 18 6 +--R 27300a b c d - 10920a b c d + 1820a b c +--R * +--R 12 +--R x +--R + +--R 11 11 6 10 12 5 9 13 2 4 8 14 3 3 +--R 4368a b d - 26208a b c d + 65520a b c d - 87360a b c d +--R + +--R 7 15 4 2 6 16 5 5 17 6 +--R 65520a b c d - 26208a b c d + 4368a b c +--R * +--R 11 +--R x +--R + +--R 12 10 6 11 11 5 10 12 2 4 9 13 3 3 +--R 8008a b d - 48048a b c d + 120120a b c d - 160160a b c d +--R + +--R 8 14 4 2 7 15 5 6 16 6 +--R 120120a b c d - 48048a b c d + 8008a b c +--R * +--R 10 +--R x +--R + +--R 13 9 6 12 10 5 11 11 2 4 10 12 3 3 +--R 11440a b d - 68640a b c d + 171600a b c d - 228800a b c d +--R + +--R 9 13 4 2 8 14 5 7 15 6 +--R 171600a b c d - 68640a b c d + 11440a b c +--R * +--R 9 +--R x +--R + +--R 14 8 6 13 9 5 12 10 2 4 11 11 3 3 +--R 12870a b d - 77220a b c d + 193050a b c d - 257400a b c d +--R + +--R 10 12 4 2 9 13 5 8 14 6 +--R 193050a b c d - 77220a b c d + 12870a b c +--R * +--R 8 +--R x +--R + +--R 15 7 6 14 8 5 13 9 2 4 12 10 3 3 +--R 11440a b d - 68640a b c d + 171600a b c d - 228800a b c d +--R + +--R 11 11 4 2 10 12 5 9 13 6 +--R 171600a b c d - 68640a b c d + 11440a b c +--R * +--R 7 +--R x +--R + +--R 16 6 6 15 7 5 14 8 2 4 13 9 3 3 +--R 8008a b d - 48048a b c d + 120120a b c d - 160160a b c d +--R + +--R 12 10 4 2 11 11 5 10 12 6 +--R 120120a b c d - 48048a b c d + 8008a b c +--R * +--R 6 +--R x +--R + +--R 17 5 6 16 6 5 15 7 2 4 14 8 3 3 +--R 4368a b d - 26208a b c d + 65520a b c d - 87360a b c d +--R + +--R 13 9 4 2 12 10 5 11 11 6 +--R 65520a b c d - 26208a b c d + 4368a b c +--R * +--R 5 +--R x +--R + +--R 18 4 6 17 5 5 16 6 2 4 15 7 3 3 +--R 1820a b d - 10920a b c d + 27300a b c d - 36400a b c d +--R + +--R 14 8 4 2 13 9 5 12 10 6 +--R 27300a b c d - 10920a b c d + 1820a b c +--R * +--R 4 +--R x +--R + +--R 19 3 6 18 4 5 17 5 2 4 16 6 3 3 +--R 560a b d - 3360a b c d + 8400a b c d - 11200a b c d +--R + +--R 15 7 4 2 14 8 5 13 9 6 +--R 8400a b c d - 3360a b c d + 560a b c +--R * +--R 3 +--R x +--R + +--R 20 2 6 19 3 5 18 4 2 4 17 5 3 3 +--R 120a b d - 720a b c d + 1800a b c d - 2400a b c d +--R + +--R 16 6 4 2 15 7 5 14 8 6 +--R 1800a b c d - 720a b c d + 120a b c +--R * +--R 2 +--R x +--R + +--R 21 6 20 2 5 19 3 2 4 18 4 3 3 17 5 4 2 +--R 16a b d - 96a b c d + 240a b c d - 320a b c d + 240a b c d +--R + +--R 16 6 5 15 7 6 +--R - 96a b c d + 16a b c +--R * +--R x +--R + +--R 22 6 21 5 20 2 2 4 19 3 3 3 18 4 4 2 17 5 5 +--R a d - 6a b c d + 15a b c d - 20a b c d + 15a b c d - 6a b c d +--R + +--R 16 6 6 +--R a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 877 + +--S 878 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 10 10 9 9 +--R - 8008b d x + (- 11440a b d - 68640b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (- 12870a b d - 77220a b c d - 270270b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 11440a b d - 68640a b c d - 240240a b c d - 640640b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R - 8008a b d - 48048a b c d - 168168a b c d - 448448a b c d +--R + +--R 10 4 6 +--R - 1009008b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 4368a b d - 26208a b c d - 91728a b c d - 244608a b c d +--R + +--R 9 4 6 10 5 5 +--R - 550368a b c d - 1100736b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 1820a b d - 10920a b c d - 38220a b c d - 101920a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 229320a b c d - 458640a b c d - 840840b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 560a b d - 3360a b c d - 11760a b c d - 31360a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 70560a b c d - 141120a b c d - 258720a b c d - 443520b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 120a b d - 720a b c d - 2520a b c d - 6720a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 15120a b c d - 30240a b c d - 55440a b c d - 95040a b c d +--R + +--R 10 8 2 +--R - 154440b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 5 5 4 6 +--R - 16a b d - 96a b c d - 336a b c d - 896a b c d - 2016a b c d +--R + +--R 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 +--R - 4032a b c d - 7392a b c d - 12672a b c d - 20592a b c d +--R + +--R 10 9 +--R - 32032b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R - a d - 6a b c d - 21a b c d - 56a b c d - 126a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 +--R - 252a b c d - 462a b c d - 792a b c d - 1287a b c d - 2002a b c d +--R + +--R 10 10 +--R - 3003b c +--R / +--R 27 16 26 15 2 25 14 3 24 13 +--R 48048b x + 768768a b x + 5765760a b x + 26906880a b x +--R + +--R 4 23 12 5 22 11 6 21 10 +--R 87447360a b x + 209873664a b x + 384768384a b x +--R + +--R 7 20 9 8 19 8 9 18 7 +--R 549669120a b x + 618377760a b x + 549669120a b x +--R + +--R 10 17 6 11 16 5 12 15 4 +--R 384768384a b x + 209873664a b x + 87447360a b x +--R + +--R 13 14 3 14 13 2 15 12 16 11 +--R 26906880a b x + 5765760a b x + 768768a b x + 48048a b +--R Type: Union(Expression(Integer),...) +--E 878 + +--S 879 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R - +--R 16 +--R d +--R / +--R 6 11 6 5 12 5 4 13 2 4 3 14 3 3 +--R 48048a b d - 288288a b c d + 720720a b c d - 960960a b c d +--R + +--R 2 15 4 2 16 5 17 6 +--R 720720a b c d - 288288a b c d + 48048b c +--R Type: Expression(Integer) +--E 879 + +--S 880 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 880 + +)clear all + +--S 881 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^18 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 18 18 17 17 2 16 16 3 15 15 4 14 14 +--R b x + 18a b x + 153a b x + 816a b x + 3060a b x +--R + +--R 5 13 13 6 12 12 7 11 11 8 10 10 +--R 8568a b x + 18564a b x + 31824a b x + 43758a b x +--R + +--R 9 9 9 10 8 8 11 7 7 12 6 6 13 5 5 +--R 48620a b x + 43758a b x + 31824a b x + 18564a b x + 8568a b x +--R + +--R 14 4 4 15 3 3 16 2 2 17 18 +--R 3060a b x + 816a b x + 153a b x + 18a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 881 + +--S 882 of 2952 +r0000:=-1/17*(c+d*x)^11/((b*c-a*d)*(a+b*x)^17)+_ + 3/136*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^16)-_ + 1/136*d^2*(c+d*x)^11/((b*c-a*d)^3*(a+b*x)^15)+_ + 1/476*d^3*(c+d*x)^11/((b*c-a*d)^4*(a+b*x)^14)-_ + 3/6188*d^4*(c+d*x)^11/((b*c-a*d)^5*(a+b*x)^13)+_ + 1/12376*d^5*(c+d*x)^11/((b*c-a*d)^6*(a+b*x)^12)-_ + 1/136136*d^6*(c+d*x)^11/((b*c-a*d)^7*(a+b*x)^11) +--R +--R +--R (2) +--R 1 6 17 17 1 5 17 16 1 2 4 17 15 5 3 3 17 14 +--R ------ b d x + ---- a b d x + ---- a b d x + ---- a b d x +--R 136136 8008 1001 1001 +--R + +--R 5 4 2 17 13 1 5 17 12 1 6 17 11 +--R --- a b d x + -- a b d x + -- a d x +--R 286 22 11 +--R + +--R 6 16 5 2 15 4 2 3 14 3 3 4 13 2 4 5 12 +--R a c d - 3a b c d + 5a b c d - 5a b c d + 3a b c d +--R + +--R 5 6 11 1 6 7 10 +--R - a b c d + - b c d +--R 7 +--R * +--R 10 +--R x +--R + +--R 6 2 15 5 3 14 75 4 2 4 13 3 3 5 12 2 4 6 11 +--R 5a c d - 20a b c d + -- a b c d - 40a b c d + 25a b c d +--R 2 +--R + +--R 60 5 7 10 5 6 8 9 +--R - -- a b c d + - b c d +--R 7 4 +--R * +--R 9 +--R x +--R + +--R 6 3 14 135 5 4 13 4 2 5 12 3 3 6 11 +--R 15a c d - --- a b c d + 135a b c d - 150a b c d +--R 2 +--R + +--R 675 2 4 7 10 135 5 8 9 6 9 8 +--R --- a b c d - --- a b c d + 5b c d +--R 7 4 +--R * +--R 8 +--R x +--R + +--R 6 4 13 5 5 12 4 2 6 11 2400 3 3 7 10 +--R 30a c d - 144a b c d + 300a b c d - ---- a b c d +--R 7 +--R + +--R 2 4 8 9 5 9 8 6 10 7 +--R 225a b c d - 80a b c d + 12b c d +--R * +--R 7 +--R x +--R + +--R 6 5 12 5 6 11 4 2 7 10 3 3 8 9 2 4 9 8 +--R 42a c d - 210a b c d + 450a b c d - 525a b c d + 350a b c d +--R + +--R 5 10 7 210 6 11 6 +--R - 126a b c d + --- b c d +--R 11 +--R * +--R 6 +--R x +--R + +--R 6 6 11 5 7 10 945 4 2 8 9 3 3 9 8 2 4 10 7 +--R 42a c d - 216a b c d + --- a b c d - 560a b c d + 378a b c d +--R 2 +--R + +--R 1512 5 11 6 6 12 5 +--R - ---- a b c d + 21b c d +--R 11 +--R * +--R 5 +--R x +--R + +--R 6 7 10 315 5 8 9 4 2 9 8 3 3 10 7 +--R 30a c d - --- a b c d + 350a b c d - 420a b c d +--R 2 +--R + +--R 3150 2 4 11 6 5 12 5 210 6 13 4 +--R ---- a b c d - 105a b c d + --- b c d +--R 11 13 +--R * +--R 4 +--R x +--R + +--R 6 8 9 5 9 8 4 2 10 7 2400 3 3 11 6 2 4 12 5 +--R 15a c d - 80a b c d + 180a b c d - ---- a b c d + 150a b c d +--R 11 +--R + +--R 720 5 13 4 60 6 14 3 +--R - --- a b c d + -- b c d +--R 13 7 +--R * +--R 3 +--R x +--R + +--R 6 9 8 5 10 7 675 4 2 11 6 3 3 12 5 675 2 4 13 4 +--R 5a c d - 27a b c d + --- a b c d - 75a b c d + --- a b c d +--R 11 13 +--R + +--R 135 5 14 3 6 15 2 +--R - --- a b c d + 3b c d +--R 7 +--R * +--R 2 +--R x +--R + +--R 6 10 7 60 5 11 6 25 4 2 12 5 200 3 3 13 4 75 2 4 14 3 +--R a c d - -- a b c d + -- a b c d - --- a b c d + -- a b c d +--R 11 2 13 7 +--R + +--R 5 15 2 5 6 16 +--R - 4a b c d + - b c d +--R 8 +--R * +--R x +--R + +--R 1 6 11 6 1 5 12 5 15 4 2 13 4 10 3 3 14 3 2 4 15 2 +--R -- a c d - - a b c d + -- a b c d - -- a b c d + a b c d +--R 11 2 13 7 +--R + +--R 3 5 16 1 6 17 +--R - - a b c d + -- b c +--R 8 17 +--R / +--R 7 17 7 6 18 6 5 19 2 5 4 20 3 4 3 21 4 3 +--R a b d - 7a b c d + 21a b c d - 35a b c d + 35a b c d +--R + +--R 2 22 5 2 23 6 24 7 +--R - 21a b c d + 7a b c d - b c +--R * +--R 17 +--R x +--R + +--R 8 16 7 7 17 6 6 18 2 5 5 19 3 4 4 20 4 3 +--R 17a b d - 119a b c d + 357a b c d - 595a b c d + 595a b c d +--R + +--R 3 21 5 2 2 22 6 23 7 +--R - 357a b c d + 119a b c d - 17a b c +--R * +--R 16 +--R x +--R + +--R 9 15 7 8 16 6 7 17 2 5 6 18 3 4 +--R 136a b d - 952a b c d + 2856a b c d - 4760a b c d +--R + +--R 5 19 4 3 4 20 5 2 3 21 6 2 22 7 +--R 4760a b c d - 2856a b c d + 952a b c d - 136a b c +--R * +--R 15 +--R x +--R + +--R 10 14 7 9 15 6 8 16 2 5 7 17 3 4 +--R 680a b d - 4760a b c d + 14280a b c d - 23800a b c d +--R + +--R 6 18 4 3 5 19 5 2 4 20 6 3 21 7 +--R 23800a b c d - 14280a b c d + 4760a b c d - 680a b c +--R * +--R 14 +--R x +--R + +--R 11 13 7 10 14 6 9 15 2 5 8 16 3 4 +--R 2380a b d - 16660a b c d + 49980a b c d - 83300a b c d +--R + +--R 7 17 4 3 6 18 5 2 5 19 6 4 20 7 +--R 83300a b c d - 49980a b c d + 16660a b c d - 2380a b c +--R * +--R 13 +--R x +--R + +--R 12 12 7 11 13 6 10 14 2 5 9 15 3 4 +--R 6188a b d - 43316a b c d + 129948a b c d - 216580a b c d +--R + +--R 8 16 4 3 7 17 5 2 6 18 6 5 19 7 +--R 216580a b c d - 129948a b c d + 43316a b c d - 6188a b c +--R * +--R 12 +--R x +--R + +--R 13 11 7 12 12 6 11 13 2 5 10 14 3 4 +--R 12376a b d - 86632a b c d + 259896a b c d - 433160a b c d +--R + +--R 9 15 4 3 8 16 5 2 7 17 6 6 18 7 +--R 433160a b c d - 259896a b c d + 86632a b c d - 12376a b c +--R * +--R 11 +--R x +--R + +--R 14 10 7 13 11 6 12 12 2 5 +--R 19448a b d - 136136a b c d + 408408a b c d +--R + +--R 11 13 3 4 10 14 4 3 9 15 5 2 +--R - 680680a b c d + 680680a b c d - 408408a b c d +--R + +--R 8 16 6 7 17 7 +--R 136136a b c d - 19448a b c +--R * +--R 10 +--R x +--R + +--R 15 9 7 14 10 6 13 11 2 5 12 12 3 4 +--R 24310a b d - 170170a b c d + 510510a b c d - 850850a b c d +--R + +--R 11 13 4 3 10 14 5 2 9 15 6 8 16 7 +--R 850850a b c d - 510510a b c d + 170170a b c d - 24310a b c +--R * +--R 9 +--R x +--R + +--R 16 8 7 15 9 6 14 10 2 5 13 11 3 4 +--R 24310a b d - 170170a b c d + 510510a b c d - 850850a b c d +--R + +--R 12 12 4 3 11 13 5 2 10 14 6 9 15 7 +--R 850850a b c d - 510510a b c d + 170170a b c d - 24310a b c +--R * +--R 8 +--R x +--R + +--R 17 7 7 16 8 6 15 9 2 5 14 10 3 4 +--R 19448a b d - 136136a b c d + 408408a b c d - 680680a b c d +--R + +--R 13 11 4 3 12 12 5 2 11 13 6 10 14 7 +--R 680680a b c d - 408408a b c d + 136136a b c d - 19448a b c +--R * +--R 7 +--R x +--R + +--R 18 6 7 17 7 6 16 8 2 5 15 9 3 4 +--R 12376a b d - 86632a b c d + 259896a b c d - 433160a b c d +--R + +--R 14 10 4 3 13 11 5 2 12 12 6 11 13 7 +--R 433160a b c d - 259896a b c d + 86632a b c d - 12376a b c +--R * +--R 6 +--R x +--R + +--R 19 5 7 18 6 6 17 7 2 5 16 8 3 4 +--R 6188a b d - 43316a b c d + 129948a b c d - 216580a b c d +--R + +--R 15 9 4 3 14 10 5 2 13 11 6 12 12 7 +--R 216580a b c d - 129948a b c d + 43316a b c d - 6188a b c +--R * +--R 5 +--R x +--R + +--R 20 4 7 19 5 6 18 6 2 5 17 7 3 4 +--R 2380a b d - 16660a b c d + 49980a b c d - 83300a b c d +--R + +--R 16 8 4 3 15 9 5 2 14 10 6 13 11 7 +--R 83300a b c d - 49980a b c d + 16660a b c d - 2380a b c +--R * +--R 4 +--R x +--R + +--R 21 3 7 20 4 6 19 5 2 5 18 6 3 4 +--R 680a b d - 4760a b c d + 14280a b c d - 23800a b c d +--R + +--R 17 7 4 3 16 8 5 2 15 9 6 14 10 7 +--R 23800a b c d - 14280a b c d + 4760a b c d - 680a b c +--R * +--R 3 +--R x +--R + +--R 22 2 7 21 3 6 20 4 2 5 19 5 3 4 +--R 136a b d - 952a b c d + 2856a b c d - 4760a b c d +--R + +--R 18 6 4 3 17 7 5 2 16 8 6 15 9 7 +--R 4760a b c d - 2856a b c d + 952a b c d - 136a b c +--R * +--R 2 +--R x +--R + +--R 23 7 22 2 6 21 3 2 5 20 4 3 4 19 5 4 3 +--R 17a b d - 119a b c d + 357a b c d - 595a b c d + 595a b c d +--R + +--R 18 6 5 2 17 7 6 16 8 7 +--R - 357a b c d + 119a b c d - 17a b c +--R * +--R x +--R + +--R 24 7 23 6 22 2 2 5 21 3 3 4 20 4 4 3 +--R a d - 7a b c d + 21a b c d - 35a b c d + 35a b c d +--R + +--R 19 5 5 2 18 6 6 17 7 7 +--R - 21a b c d + 7a b c d - a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 882 + +--S 883 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 10 10 9 9 +--R - 19448b d x + (- 24310a b d - 170170b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (- 24310a b d - 170170a b c d - 680680b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 19448a b d - 136136a b c d - 544544a b c d - 1633632b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R - 12376a b d - 86632a b c d - 346528a b c d - 1039584a b c d +--R + +--R 10 4 6 +--R - 2598960b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 6188a b d - 43316a b c d - 173264a b c d - 519792a b c d +--R + +--R 9 4 6 10 5 5 +--R - 1299480a b c d - 2858856b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 2380a b d - 16660a b c d - 66640a b c d - 199920a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 499800a b c d - 1099560a b c d - 2199120b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 680a b d - 4760a b c d - 19040a b c d - 57120a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 142800a b c d - 314160a b c d - 628320a b c d - 1166880b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 136a b d - 952a b c d - 3808a b c d - 11424a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 28560a b c d - 62832a b c d - 125664a b c d - 233376a b c d +--R + +--R 10 8 2 +--R - 408408b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 5 5 4 6 +--R - 17a b d - 119a b c d - 476a b c d - 1428a b c d - 3570a b c d +--R + +--R 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 +--R - 7854a b c d - 15708a b c d - 29172a b c d - 51051a b c d +--R + +--R 10 9 +--R - 85085b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R - a d - 7a b c d - 28a b c d - 84a b c d - 210a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 +--R - 462a b c d - 924a b c d - 1716a b c d - 3003a b c d - 5005a b c d +--R + +--R 10 10 +--R - 8008b c +--R / +--R 28 17 27 16 2 26 15 3 25 14 +--R 136136b x + 2314312a b x + 18514496a b x + 92572480a b x +--R + +--R 4 24 13 5 23 12 6 22 11 +--R 324003680a b x + 842409568a b x + 1684819136a b x +--R + +--R 7 21 10 8 20 9 9 19 8 +--R 2647572928a b x + 3309466160a b x + 3309466160a b x +--R + +--R 10 18 7 11 17 6 12 16 5 +--R 2647572928a b x + 1684819136a b x + 842409568a b x +--R + +--R 13 15 4 14 14 3 15 13 2 16 12 +--R 324003680a b x + 92572480a b x + 18514496a b x + 2314312a b x +--R + +--R 17 11 +--R 136136a b +--R Type: Union(Expression(Integer),...) +--E 883 + +--S 884 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R - +--R 17 +--R d +--R / +--R 7 11 7 6 12 6 5 13 2 5 4 14 3 4 +--R 136136a b d - 952952a b c d + 2858856a b c d - 4764760a b c d +--R + +--R 3 15 4 3 2 16 5 2 17 6 18 7 +--R 4764760a b c d - 2858856a b c d + 952952a b c d - 136136b c +--R Type: Expression(Integer) +--E 884 + +--S 885 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 885 + +)clear all + +--S 886 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^19 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 19 19 18 18 2 17 17 3 16 16 4 15 15 +--R b x + 19a b x + 171a b x + 969a b x + 3876a b x +--R + +--R 5 14 14 6 13 13 7 12 12 8 11 11 +--R 11628a b x + 27132a b x + 50388a b x + 75582a b x +--R + +--R 9 10 10 10 9 9 11 8 8 12 7 7 13 6 6 +--R 92378a b x + 92378a b x + 75582a b x + 50388a b x + 27132a b x +--R + +--R 14 5 5 15 4 4 16 3 3 17 2 2 18 19 +--R 11628a b x + 3876a b x + 969a b x + 171a b x + 19a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 886 + +--S 887 of 2952 +r0000:=-1/18*(c+d*x)^11/((b*c-a*d)*(a+b*x)^18)+_ + 7/306*d*(c+d*x)^11/((b*c-a*d)^2*(a+b*x)^17)-_ + 7/816*d^2*(c+d*x)^11/((b*c-a*d)^3*(a+b*x)^16)+_ + 7/2448*d^3*(c+d*x)^11/((b*c-a*d)^4*(a+b*x)^15)-_ + 1/1224*d^4*(c+d*x)^11/((b*c-a*d)^5*(a+b*x)^14)+_ + 1/5304*d^5*(c+d*x)^11/((b*c-a*d)^6*(a+b*x)^13)-_ + 1/31824*d^6*(c+d*x)^11/((b*c-a*d)^7*(a+b*x)^12)+_ + 1/350064*d^7*(c+d*x)^11/((b*c-a*d)^8*(a+b*x)^11) +--R +--R +--R (2) +--R 1 7 18 18 1 6 18 17 1 2 5 18 16 1 3 4 18 15 +--R ------ b d x + ----- a b d x + ---- a b d x + --- a b d x +--R 350064 19448 2288 429 +--R + +--R 5 4 3 18 14 7 5 2 18 13 7 6 18 12 1 7 18 11 +--R --- a b d x + --- a b d x + --- a b d x + -- a d x +--R 572 286 132 11 +--R + +--R 7 17 7 6 2 16 5 2 3 15 35 4 3 4 14 3 4 5 13 +--R a c d - - a b c d + 7a b c d - -- a b c d + 7a b c d +--R 2 4 +--R + +--R 7 2 5 6 12 6 7 11 1 7 8 10 +--R - - a b c d + a b c d - - b c d +--R 2 8 +--R * +--R 10 +--R x +--R + +--R 7 2 16 70 6 3 15 105 5 2 4 14 4 3 5 13 175 3 4 6 12 +--R 5a c d - -- a b c d + --- a b c d - 70a b c d + --- a b c d +--R 3 2 3 +--R + +--R 2 5 7 11 35 6 8 10 10 7 9 9 +--R - 30a b c d + -- a b c d - -- b c d +--R 4 9 +--R * +--R 9 +--R x +--R + +--R 7 3 15 315 6 4 14 5 2 5 13 525 4 3 6 12 +--R 15a c d - --- a b c d + 189a b c d - --- a b c d +--R 4 2 +--R + +--R 3 4 7 11 945 2 5 8 10 6 9 9 9 7 10 8 +--R 225a b c d - --- a b c d + 35a b c d - - b c d +--R 8 2 +--R * +--R 8 +--R x +--R + +--R 7 4 14 6 5 13 5 2 6 12 4 3 7 11 3 4 8 10 +--R 30a c d - 168a b c d + 420a b c d - 600a b c d + 525a b c d +--R + +--R 2 5 9 9 6 10 8 120 7 11 7 +--R - 280a b c d + 84a b c d - --- b c d +--R 11 +--R * +--R 7 +--R x +--R + +--R 7 5 13 6 6 12 5 2 7 11 3675 4 3 8 10 +--R 42a c d - 245a b c d + 630a b c d - ---- a b c d +--R 4 +--R + +--R 2450 3 4 9 9 2 5 10 8 1470 6 11 7 35 7 12 6 +--R ---- a b c d - 441a b c d + ---- a b c d - -- b c d +--R 3 11 2 +--R * +--R 6 +--R x +--R + +--R 7 6 12 6 7 11 1323 5 2 8 10 4 3 9 9 +--R 42a c d - 252a b c d + ---- a b c d - 980a b c d +--R 2 +--R + +--R 3 4 10 8 5292 2 5 11 7 6 12 6 252 7 13 5 +--R 882a b c d - ---- a b c d + 147a b c d - --- b c d +--R 11 13 +--R * +--R 5 +--R x +--R + +--R 7 7 11 735 6 8 10 5 2 9 9 4 3 10 8 +--R 30a c d - --- a b c d + 490a b c d - 735a b c d +--R 4 +--R + +--R 7350 3 4 11 7 735 2 5 12 6 1470 6 13 5 7 14 4 +--R ---- a b c d - --- a b c d + ---- a b c d - 15b c d +--R 11 2 13 +--R * +--R 4 +--R x +--R + +--R 7 8 10 280 6 9 9 5 2 10 8 4200 4 3 11 7 +--R 15a c d - --- a b c d + 252a b c d - ---- a b c d +--R 3 11 +--R + +--R 3 4 12 6 2520 2 5 13 5 6 14 4 7 15 3 +--R 350a b c d - ---- a b c d + 60a b c d - 8b c d +--R 13 +--R * +--R 3 +--R x +--R + +--R 7 9 9 63 6 10 8 945 5 2 11 7 525 4 3 12 6 +--R 5a c d - -- a b c d + --- a b c d - --- a b c d +--R 2 11 4 +--R + +--R 1575 3 4 13 5 135 2 5 14 4 6 15 3 45 7 16 2 +--R ---- a b c d - --- a b c d + 21a b c d - -- b c d +--R 13 2 16 +--R * +--R 2 +--R x +--R + +--R 7 10 8 70 6 11 7 35 5 2 12 6 350 4 3 13 5 3 4 14 4 +--R a c d - -- a b c d + -- a b c d - --- a b c d + 25a b c d +--R 11 2 13 +--R + +--R 2 5 15 3 35 6 16 2 10 7 17 +--R - 14a b c d + -- a b c d - -- b c d +--R 8 17 +--R * +--R x +--R + +--R 1 7 11 7 7 6 12 6 21 5 2 13 5 5 4 3 14 4 7 3 4 15 3 +--R -- a c d - -- a b c d + -- a b c d - - a b c d + - a b c d +--R 11 12 13 2 3 +--R + +--R 21 2 5 16 2 7 6 17 1 7 18 +--R - -- a b c d + -- a b c d - -- b c +--R 16 17 18 +--R / +--R 8 18 8 7 19 7 6 20 2 6 5 21 3 5 4 22 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 23 5 3 2 24 6 2 25 7 26 8 +--R - 56a b c d + 28a b c d - 8a b c d + b c +--R * +--R 18 +--R x +--R + +--R 9 17 8 8 18 7 7 19 2 6 6 20 3 5 +--R 18a b d - 144a b c d + 504a b c d - 1008a b c d +--R + +--R 5 21 4 4 4 22 5 3 3 23 6 2 2 24 7 25 8 +--R 1260a b c d - 1008a b c d + 504a b c d - 144a b c d + 18a b c +--R * +--R 17 +--R x +--R + +--R 10 16 8 9 17 7 8 18 2 6 7 19 3 5 +--R 153a b d - 1224a b c d + 4284a b c d - 8568a b c d +--R + +--R 6 20 4 4 5 21 5 3 4 22 6 2 3 23 7 +--R 10710a b c d - 8568a b c d + 4284a b c d - 1224a b c d +--R + +--R 2 24 8 +--R 153a b c +--R * +--R 16 +--R x +--R + +--R 11 15 8 10 16 7 9 17 2 6 8 18 3 5 +--R 816a b d - 6528a b c d + 22848a b c d - 45696a b c d +--R + +--R 7 19 4 4 6 20 5 3 5 21 6 2 4 22 7 +--R 57120a b c d - 45696a b c d + 22848a b c d - 6528a b c d +--R + +--R 3 23 8 +--R 816a b c +--R * +--R 15 +--R x +--R + +--R 12 14 8 11 15 7 10 16 2 6 9 17 3 5 +--R 3060a b d - 24480a b c d + 85680a b c d - 171360a b c d +--R + +--R 8 18 4 4 7 19 5 3 6 20 6 2 5 21 7 +--R 214200a b c d - 171360a b c d + 85680a b c d - 24480a b c d +--R + +--R 4 22 8 +--R 3060a b c +--R * +--R 14 +--R x +--R + +--R 13 13 8 12 14 7 11 15 2 6 10 16 3 5 +--R 8568a b d - 68544a b c d + 239904a b c d - 479808a b c d +--R + +--R 9 17 4 4 8 18 5 3 7 19 6 2 6 20 7 +--R 599760a b c d - 479808a b c d + 239904a b c d - 68544a b c d +--R + +--R 5 21 8 +--R 8568a b c +--R * +--R 13 +--R x +--R + +--R 14 12 8 13 13 7 12 14 2 6 +--R 18564a b d - 148512a b c d + 519792a b c d +--R + +--R 11 15 3 5 10 16 4 4 9 17 5 3 +--R - 1039584a b c d + 1299480a b c d - 1039584a b c d +--R + +--R 8 18 6 2 7 19 7 6 20 8 +--R 519792a b c d - 148512a b c d + 18564a b c +--R * +--R 12 +--R x +--R + +--R 15 11 8 14 12 7 13 13 2 6 +--R 31824a b d - 254592a b c d + 891072a b c d +--R + +--R 12 14 3 5 11 15 4 4 10 16 5 3 +--R - 1782144a b c d + 2227680a b c d - 1782144a b c d +--R + +--R 9 17 6 2 8 18 7 7 19 8 +--R 891072a b c d - 254592a b c d + 31824a b c +--R * +--R 11 +--R x +--R + +--R 16 10 8 15 11 7 14 12 2 6 +--R 43758a b d - 350064a b c d + 1225224a b c d +--R + +--R 13 13 3 5 12 14 4 4 11 15 5 3 +--R - 2450448a b c d + 3063060a b c d - 2450448a b c d +--R + +--R 10 16 6 2 9 17 7 8 18 8 +--R 1225224a b c d - 350064a b c d + 43758a b c +--R * +--R 10 +--R x +--R + +--R 17 9 8 16 10 7 15 11 2 6 +--R 48620a b d - 388960a b c d + 1361360a b c d +--R + +--R 14 12 3 5 13 13 4 4 12 14 5 3 +--R - 2722720a b c d + 3403400a b c d - 2722720a b c d +--R + +--R 11 15 6 2 10 16 7 9 17 8 +--R 1361360a b c d - 388960a b c d + 48620a b c +--R * +--R 9 +--R x +--R + +--R 18 8 8 17 9 7 16 10 2 6 +--R 43758a b d - 350064a b c d + 1225224a b c d +--R + +--R 15 11 3 5 14 12 4 4 13 13 5 3 +--R - 2450448a b c d + 3063060a b c d - 2450448a b c d +--R + +--R 12 14 6 2 11 15 7 10 16 8 +--R 1225224a b c d - 350064a b c d + 43758a b c +--R * +--R 8 +--R x +--R + +--R 19 7 8 18 8 7 17 9 2 6 16 10 3 5 +--R 31824a b d - 254592a b c d + 891072a b c d - 1782144a b c d +--R + +--R 15 11 4 4 14 12 5 3 13 13 6 2 +--R 2227680a b c d - 1782144a b c d + 891072a b c d +--R + +--R 12 14 7 11 15 8 +--R - 254592a b c d + 31824a b c +--R * +--R 7 +--R x +--R + +--R 20 6 8 19 7 7 18 8 2 6 17 9 3 5 +--R 18564a b d - 148512a b c d + 519792a b c d - 1039584a b c d +--R + +--R 16 10 4 4 15 11 5 3 14 12 6 2 +--R 1299480a b c d - 1039584a b c d + 519792a b c d +--R + +--R 13 13 7 12 14 8 +--R - 148512a b c d + 18564a b c +--R * +--R 6 +--R x +--R + +--R 21 5 8 20 6 7 19 7 2 6 18 8 3 5 +--R 8568a b d - 68544a b c d + 239904a b c d - 479808a b c d +--R + +--R 17 9 4 4 16 10 5 3 15 11 6 2 +--R 599760a b c d - 479808a b c d + 239904a b c d +--R + +--R 14 12 7 13 13 8 +--R - 68544a b c d + 8568a b c +--R * +--R 5 +--R x +--R + +--R 22 4 8 21 5 7 20 6 2 6 19 7 3 5 +--R 3060a b d - 24480a b c d + 85680a b c d - 171360a b c d +--R + +--R 18 8 4 4 17 9 5 3 16 10 6 2 15 11 7 +--R 214200a b c d - 171360a b c d + 85680a b c d - 24480a b c d +--R + +--R 14 12 8 +--R 3060a b c +--R * +--R 4 +--R x +--R + +--R 23 3 8 22 4 7 21 5 2 6 20 6 3 5 +--R 816a b d - 6528a b c d + 22848a b c d - 45696a b c d +--R + +--R 19 7 4 4 18 8 5 3 17 9 6 2 16 10 7 +--R 57120a b c d - 45696a b c d + 22848a b c d - 6528a b c d +--R + +--R 15 11 8 +--R 816a b c +--R * +--R 3 +--R x +--R + +--R 24 2 8 23 3 7 22 4 2 6 21 5 3 5 +--R 153a b d - 1224a b c d + 4284a b c d - 8568a b c d +--R + +--R 20 6 4 4 19 7 5 3 18 8 6 2 17 9 7 +--R 10710a b c d - 8568a b c d + 4284a b c d - 1224a b c d +--R + +--R 16 10 8 +--R 153a b c +--R * +--R 2 +--R x +--R + +--R 25 8 24 2 7 23 3 2 6 22 4 3 5 +--R 18a b d - 144a b c d + 504a b c d - 1008a b c d +--R + +--R 21 5 4 4 20 6 5 3 19 7 6 2 18 8 7 17 9 8 +--R 1260a b c d - 1008a b c d + 504a b c d - 144a b c d + 18a b c +--R * +--R x +--R + +--R 26 8 25 7 24 2 2 6 23 3 3 5 22 4 4 4 +--R a d - 8a b c d + 28a b c d - 56a b c d + 70a b c d +--R + +--R 21 5 5 3 20 6 6 2 19 7 7 18 8 8 +--R - 56a b c d + 28a b c d - 8a b c d + a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 887 + +--S 888 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 10 10 9 9 +--R - 43758b d x + (- 48620a b d - 388960b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (- 43758a b d - 350064a b c d - 1575288b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 31824a b d - 254592a b c d - 1145664a b c d - 3818880b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R - 18564a b d - 148512a b c d - 668304a b c d - 2227680a b c d +--R + +--R 10 4 6 +--R - 6126120b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 8568a b d - 68544a b c d - 308448a b c d - 1028160a b c d +--R + +--R 9 4 6 10 5 5 +--R - 2827440a b c d - 6785856b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 3060a b d - 24480a b c d - 110160a b c d - 367200a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 1009800a b c d - 2423520a b c d - 5250960b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 816a b d - 6528a b c d - 29376a b c d - 97920a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 269280a b c d - 646272a b c d - 1400256a b c d - 2800512b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 153a b d - 1224a b c d - 5508a b c d - 18360a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 50490a b c d - 121176a b c d - 262548a b c d - 525096a b c d +--R + +--R 10 8 2 +--R - 984555b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 5 5 4 6 +--R - 18a b d - 144a b c d - 648a b c d - 2160a b c d - 5940a b c d +--R + +--R 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 +--R - 14256a b c d - 30888a b c d - 61776a b c d - 115830a b c d +--R + +--R 10 9 +--R - 205920b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R - a d - 8a b c d - 36a b c d - 120a b c d - 330a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 9 9 +--R - 792a b c d - 1716a b c d - 3432a b c d - 6435a b c d - 11440a b c d +--R + +--R 10 10 +--R - 19448b c +--R / +--R 29 18 28 17 2 27 16 3 26 15 +--R 350064b x + 6301152a b x + 53559792a b x + 285652224a b x +--R + +--R 4 25 14 5 24 13 6 23 12 +--R 1071195840a b x + 2999348352a b x + 6498588096a b x +--R + +--R 7 22 11 8 21 10 9 20 9 +--R 11140436736a b x + 15318100512a b x + 17020111680a b x +--R + +--R 10 19 8 11 18 7 12 17 6 +--R 15318100512a b x + 11140436736a b x + 6498588096a b x +--R + +--R 13 16 5 14 15 4 15 14 3 +--R 2999348352a b x + 1071195840a b x + 285652224a b x +--R + +--R 16 13 2 17 12 18 11 +--R 53559792a b x + 6301152a b x + 350064a b +--R Type: Union(Expression(Integer),...) +--E 888 + +--S 889 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R - +--R 18 +--R d +--R / +--R 8 11 8 7 12 7 6 13 2 6 +--R 350064a b d - 2800512a b c d + 9801792a b c d +--R + +--R 5 14 3 5 4 15 4 4 3 16 5 3 +--R - 19603584a b c d + 24504480a b c d - 19603584a b c d +--R + +--R 2 17 6 2 18 7 19 8 +--R 9801792a b c d - 2800512a b c d + 350064b c +--R Type: Expression(Integer) +--E 889 + +--S 890 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 890 + +)clear all + +--S 891 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^20 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 20 20 19 19 2 18 18 3 17 17 4 16 16 +--R b x + 20a b x + 190a b x + 1140a b x + 4845a b x +--R + +--R 5 15 15 6 14 14 7 13 13 8 12 12 +--R 15504a b x + 38760a b x + 77520a b x + 125970a b x +--R + +--R 9 11 11 10 10 10 11 9 9 12 8 8 +--R 167960a b x + 184756a b x + 167960a b x + 125970a b x +--R + +--R 13 7 7 14 6 6 15 5 5 16 4 4 17 3 3 +--R 77520a b x + 38760a b x + 15504a b x + 4845a b x + 1140a b x +--R + +--R 18 2 2 19 20 +--R 190a b x + 20a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 891 + +--S 892 of 2952 +r0000:=-1/19*(b*c-a*d)^10/(b^11*(a+b*x)^19)-_ + 5/9*d*(b*c-a*d)^9/(b^11*(a+b*x)^18)-_ + 45/17*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^17)-_ + 15/2*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^16)-_ + 14*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^15)-_ + 18*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^14)-_ + 210/13*d^6*(b*c-a*d)^4/(b^11*(a+b*x)^13)-_ + 10*d^7*(b*c-a*d)^3/(b^11*(a+b*x)^12)-_ + 45/11*d^8*(b*c-a*d)^2/(b^11*(a+b*x)^11)-_ + d^9*(b*c-a*d)/(b^11*(a+b*x)^10)-1/9*d^10/(b^11*(a+b*x)^9) +--R +--R +--R (2) +--R 1 10 10 10 1 9 10 10 9 9 +--R - - b d x + (- - a b d - b c d )x +--R 9 9 +--R + +--R 1 2 8 10 9 9 9 45 10 2 8 8 +--R (- -- a b d - -- a b c d - -- b c d )x +--R 11 11 11 +--R + +--R 2 3 7 10 6 2 8 9 30 9 2 8 10 3 7 7 +--R (- -- a b d - -- a b c d - -- a b c d - 10b c d )x +--R 33 11 11 +--R + +--R 14 4 6 10 42 3 7 9 210 2 8 2 8 70 9 3 7 +--R - --- a b d - --- a b c d - --- a b c d - -- a b c d +--R 429 143 143 13 +--R + +--R 210 10 4 6 +--R - --- b c d +--R 13 +--R * +--R 6 +--R x +--R + +--R 2 5 5 10 18 4 6 9 90 3 7 2 8 30 2 8 3 7 +--R - --- a b d - --- a b c d - --- a b c d - -- a b c d +--R 143 143 143 13 +--R + +--R 90 9 4 6 10 5 5 +--R - -- a b c d - 18b c d +--R 13 +--R * +--R 5 +--R x +--R + +--R 2 6 4 10 6 5 5 9 30 4 6 2 8 10 3 7 3 7 +--R - --- a b d - --- a b c d - --- a b c d - -- a b c d +--R 429 143 143 13 +--R + +--R 30 2 8 4 6 9 5 5 10 6 4 +--R - -- a b c d - 6a b c d - 14b c d +--R 13 +--R * +--R 4 +--R x +--R + +--R 1 7 3 10 3 6 4 9 15 5 5 2 8 5 4 6 3 7 +--R - --- a b d - --- a b c d - --- a b c d - -- a b c d +--R 858 286 286 26 +--R + +--R 15 3 7 4 6 3 2 8 5 5 7 9 6 4 15 10 7 3 +--R - -- a b c d - - a b c d - - a b c d - -- b c d +--R 26 2 2 2 +--R * +--R 3 +--R x +--R + +--R 1 8 2 10 9 7 3 9 45 6 4 2 8 15 5 5 3 7 +--R - ---- a b d - ---- a b c d - ---- a b c d - --- a b c d +--R 4862 4862 4862 442 +--R + +--R 45 4 6 4 6 9 3 7 5 5 21 2 8 6 4 45 9 7 3 45 10 8 2 +--R - --- a b c d - -- a b c d - -- a b c d - -- a b c d - -- b c d +--R 442 34 34 34 17 +--R * +--R 2 +--R x +--R + +--R 1 9 10 1 8 2 9 5 7 3 2 8 5 6 4 3 7 +--R - ----- a b d - ---- a b c d - ---- a b c d - ---- a b c d +--R 43758 4862 4862 1326 +--R + +--R 5 5 5 4 6 1 4 6 5 5 7 3 7 6 4 5 2 8 7 3 +--R - --- a b c d - -- a b c d - --- a b c d - -- a b c d +--R 442 34 102 34 +--R + +--R 5 9 8 2 5 10 9 +--R - -- a b c d - - b c d +--R 17 9 +--R * +--R x +--R + +--R 1 10 10 1 9 9 5 8 2 2 8 5 7 3 3 7 +--R - ------ a d - ----- a b c d - ----- a b c d - ----- a b c d +--R 831402 92378 92378 25194 +--R + +--R 5 6 4 4 6 1 5 5 5 5 7 4 6 6 4 5 3 7 7 3 +--R - ---- a b c d - --- a b c d - ---- a b c d - --- a b c d +--R 8398 646 1938 646 +--R + +--R 5 2 8 8 2 5 9 9 1 10 10 +--R - --- a b c d - --- a b c d - -- b c +--R 323 171 19 +--R / +--R 30 19 29 18 2 28 17 3 27 16 4 26 15 +--R b x + 19a b x + 171a b x + 969a b x + 3876a b x +--R + +--R 5 25 14 6 24 13 7 23 12 8 22 11 +--R 11628a b x + 27132a b x + 50388a b x + 75582a b x +--R + +--R 9 21 10 10 20 9 11 19 8 12 18 7 +--R 92378a b x + 92378a b x + 75582a b x + 50388a b x +--R + +--R 13 17 6 14 16 5 15 15 4 16 14 3 17 13 2 +--R 27132a b x + 11628a b x + 3876a b x + 969a b x + 171a b x +--R + +--R 18 12 19 11 +--R 19a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 892 + +--S 893 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 10 10 9 9 +--R - 92378b d x + (- 92378a b d - 831402b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (- 75582a b d - 680238a b c d - 3401190b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 50388a b d - 453492a b c d - 2267460a b c d - 8314020b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R - 27132a b d - 244188a b c d - 1220940a b c d - 4476780a b c d +--R + +--R 10 4 6 +--R - 13430340b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 11628a b d - 104652a b c d - 523260a b c d - 1918620a b c d +--R + +--R 9 4 6 10 5 5 +--R - 5755860a b c d - 14965236b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 3876a b d - 34884a b c d - 174420a b c d - 639540a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 1918620a b c d - 4988412a b c d - 11639628b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 969a b d - 8721a b c d - 43605a b c d - 159885a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 479655a b c d - 1247103a b c d - 2909907a b c d - 6235515b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 171a b d - 1539a b c d - 7695a b c d - 28215a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 84645a b c d - 220077a b c d - 513513a b c d - 1100385a b c d +--R + +--R 10 8 2 +--R - 2200770b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 5 5 4 6 +--R - 19a b d - 171a b c d - 855a b c d - 3135a b c d - 9405a b c d +--R + +--R 4 6 5 5 3 7 6 4 2 8 7 3 9 8 2 +--R - 24453a b c d - 57057a b c d - 122265a b c d - 244530a b c d +--R + +--R 10 9 +--R - 461890b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R - a d - 9a b c d - 45a b c d - 165a b c d - 495a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 1287a b c d - 3003a b c d - 6435a b c d - 12870a b c d +--R + +--R 9 9 10 10 +--R - 24310a b c d - 43758b c +--R / +--R 30 19 29 18 2 28 17 3 27 16 +--R 831402b x + 15796638a b x + 142169742a b x + 805628538a b x +--R + +--R 4 26 15 5 25 14 6 24 13 +--R 3222514152a b x + 9667542456a b x + 22557599064a b x +--R + +--R 7 23 12 8 22 11 9 21 10 +--R 41892683976a b x + 62839025964a b x + 76803253956a b x +--R + +--R 10 20 9 11 19 8 12 18 7 +--R 76803253956a b x + 62839025964a b x + 41892683976a b x +--R + +--R 13 17 6 14 16 5 15 15 4 +--R 22557599064a b x + 9667542456a b x + 3222514152a b x +--R + +--R 16 14 3 17 13 2 18 12 19 11 +--R 805628538a b x + 142169742a b x + 15796638a b x + 831402a b +--R Type: Union(Expression(Integer),...) +--E 893 + +--S 894 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 894 + +--S 895 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 895 + +)clear all + +--S 896 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^21 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 21 21 20 20 2 19 19 3 18 18 4 17 17 +--R b x + 21a b x + 210a b x + 1330a b x + 5985a b x +--R + +--R 5 16 16 6 15 15 7 14 14 8 13 13 +--R 20349a b x + 54264a b x + 116280a b x + 203490a b x +--R + +--R 9 12 12 10 11 11 11 10 10 12 9 9 +--R 293930a b x + 352716a b x + 352716a b x + 293930a b x +--R + +--R 13 8 8 14 7 7 15 6 6 16 5 5 17 4 4 +--R 203490a b x + 116280a b x + 54264a b x + 20349a b x + 5985a b x +--R + +--R 18 3 3 19 2 2 20 21 +--R 1330a b x + 210a b x + 21a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 896 + +--S 897 of 2952 +r0000:=-1/20*(b*c-a*d)^10/(b^11*(a+b*x)^20)-_ + 10/19*d*(b*c-a*d)^9/(b^11*(a+b*x)^19)-_ + 5/2*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^18)-_ + 120/17*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^17)-_ + 105/8*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^16)-_ + 84/5*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^15)-_ + 15*d^6*(b*c-a*d)^4/(b^11*(a+b*x)^14)-_ + 120/13*d^7*(b*c-a*d)^3/(b^11*(a+b*x)^13)-_ + 15/4*d^8*(b*c-a*d)^2/(b^11*(a+b*x)^12)-_ + 10/11*d^9*(b*c-a*d)/(b^11*(a+b*x)^11)-1/10*d^10/(b^11*(a+b*x)^10) +--R +--R +--R (2) +--R 1 10 10 10 1 9 10 10 10 9 9 +--R - -- b d x + (- -- a b d - -- b c d )x +--R 10 11 11 +--R + +--R 3 2 8 10 15 9 9 15 10 2 8 8 +--R (- -- a b d - -- a b c d - -- b c d )x +--R 44 22 4 +--R + +--R 6 3 7 10 60 2 8 9 30 9 2 8 120 10 3 7 7 +--R (- --- a b d - --- a b c d - -- a b c d - --- b c d )x +--R 143 143 13 13 +--R + +--R 3 4 6 10 30 3 7 9 15 2 8 2 8 60 9 3 7 10 4 6 6 +--R (- --- a b d - --- a b c d - -- a b c d - -- a b c d - 15b c d )x +--R 143 143 13 13 +--R + +--R 6 5 5 10 12 4 6 9 6 3 7 2 8 24 2 8 3 7 9 4 6 +--R - --- a b d - --- a b c d - -- a b c d - -- a b c d - 6a b c d +--R 715 143 13 13 +--R + +--R 84 10 5 5 +--R - -- b c d +--R 5 +--R * +--R 5 +--R x +--R + +--R 3 6 4 10 15 5 5 9 15 4 6 2 8 15 3 7 3 7 +--R - ---- a b d - --- a b c d - --- a b c d - -- a b c d +--R 1144 572 104 26 +--R + +--R 15 2 8 4 6 21 9 5 5 105 10 6 4 +--R - -- a b c d - -- a b c d - --- b c d +--R 8 4 8 +--R * +--R 4 +--R x +--R + +--R 3 7 3 10 15 6 4 9 15 5 5 2 8 30 4 6 3 7 +--R - ---- a b d - ---- a b c d - --- a b c d - --- a b c d +--R 4862 2431 442 221 +--R + +--R 15 3 7 4 6 21 2 8 5 5 105 9 6 4 120 10 7 3 +--R - -- a b c d - -- a b c d - --- a b c d - --- b c d +--R 34 17 34 17 +--R * +--R 3 +--R x +--R + +--R 1 8 2 10 5 7 3 9 5 6 4 2 8 5 5 5 3 7 +--R - ---- a b d - ---- a b c d - --- a b c d - --- a b c d +--R 9724 4862 884 221 +--R + +--R 5 4 6 4 6 7 3 7 5 5 35 2 8 6 4 20 9 7 3 5 10 8 2 +--R - -- a b c d - -- a b c d - -- a b c d - -- a b c d - - b c d +--R 68 34 68 17 2 +--R * +--R 2 +--R x +--R + +--R 1 9 10 5 8 2 9 5 7 3 2 8 10 6 4 3 7 +--R - ----- a b d - ----- a b c d - ---- a b c d - ---- a b c d +--R 92378 46189 8398 4199 +--R + +--R 5 5 5 4 6 7 4 6 5 5 35 3 7 6 4 40 2 8 7 3 +--R - --- a b c d - --- a b c d - --- a b c d - --- a b c d +--R 646 323 646 323 +--R + +--R 5 9 8 2 10 10 9 +--R - -- a b c d - -- b c d +--R 19 19 +--R * +--R x +--R + +--R 1 10 10 1 9 9 1 8 2 2 8 1 7 3 3 7 +--R - ------- a d - ------ a b c d - ----- a b c d - ---- a b c d +--R 1847560 184756 33592 8398 +--R + +--R 1 6 4 4 6 7 5 5 5 5 7 4 6 6 4 2 3 7 7 3 +--R - ---- a b c d - ---- a b c d - ---- a b c d - --- a b c d +--R 2584 6460 2584 323 +--R + +--R 1 2 8 8 2 1 9 9 1 10 10 +--R - -- a b c d - -- a b c d - -- b c +--R 76 38 20 +--R / +--R 31 20 30 19 2 29 18 3 28 17 4 27 16 +--R b x + 20a b x + 190a b x + 1140a b x + 4845a b x +--R + +--R 5 26 15 6 25 14 7 24 13 8 23 12 +--R 15504a b x + 38760a b x + 77520a b x + 125970a b x +--R + +--R 9 22 11 10 21 10 11 20 9 12 19 8 +--R 167960a b x + 184756a b x + 167960a b x + 125970a b x +--R + +--R 13 18 7 14 17 6 15 16 5 16 15 4 +--R 77520a b x + 38760a b x + 15504a b x + 4845a b x +--R + +--R 17 14 3 18 13 2 19 12 20 11 +--R 1140a b x + 190a b x + 20a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 897 + +--S 898 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 10 10 9 9 +--R - 184756b d x + (- 167960a b d - 1679600b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (- 125970a b d - 1259700a b c d - 6928350b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 77520a b d - 775200a b c d - 4263600a b c d - 17054400b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R - 38760a b d - 387600a b c d - 2131800a b c d - 8527200a b c d +--R + +--R 10 4 6 +--R - 27713400b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 15504a b d - 155040a b c d - 852720a b c d - 3410880a b c d +--R + +--R 9 4 6 10 5 5 +--R - 11085360a b c d - 31039008b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 4845a b d - 48450a b c d - 266475a b c d - 1065900a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 3464175a b c d - 9699690a b c d - 24249225b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 1140a b d - 11400a b c d - 62700a b c d - 250800a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 10 7 3 +--R - 815100a b c d - 2282280a b c d - 5705700a b c d - 13041600b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 190a b d - 1900a b c d - 10450a b c d - 41800a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 135850a b c d - 380380a b c d - 950950a b c d - 2173600a b c d +--R + +--R 10 8 2 +--R - 4618900b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 20a b d - 200a b c d - 1100a b c d - 4400a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 14300a b c d - 40040a b c d - 100100a b c d - 228800a b c d +--R + +--R 9 8 2 10 9 +--R - 486200a b c d - 972400b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R - a d - 10a b c d - 55a b c d - 220a b c d - 715a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 2002a b c d - 5005a b c d - 11440a b c d - 24310a b c d +--R + +--R 9 9 10 10 +--R - 48620a b c d - 92378b c +--R / +--R 31 20 30 19 2 29 18 3 28 17 +--R 1847560b x + 36951200a b x + 351036400a b x + 2106218400a b x +--R + +--R 4 27 16 5 26 15 6 25 14 +--R 8951428200a b x + 28644570240a b x + 71611425600a b x +--R + +--R 7 24 13 8 23 12 9 22 11 +--R 143222851200a b x + 232737133200a b x + 310316177600a b x +--R + +--R 10 21 10 11 20 9 12 19 8 +--R 341347795360a b x + 310316177600a b x + 232737133200a b x +--R + +--R 13 18 7 14 17 6 15 16 5 +--R 143222851200a b x + 71611425600a b x + 28644570240a b x +--R + +--R 16 15 4 17 14 3 18 13 2 +--R 8951428200a b x + 2106218400a b x + 351036400a b x +--R + +--R 19 12 20 11 +--R 36951200a b x + 1847560a b +--R Type: Union(Expression(Integer),...) +--E 898 + +--S 899 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 899 + +--S 900 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 900 + +)clear all + +--S 901 of 2952 +t0000:=(c+d*x)^10/(a+b*x)^22 +--R +--R +--R (1) +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R / +--R 22 22 21 21 2 20 20 3 19 19 4 18 18 +--R b x + 22a b x + 231a b x + 1540a b x + 7315a b x +--R + +--R 5 17 17 6 16 16 7 15 15 8 14 14 +--R 26334a b x + 74613a b x + 170544a b x + 319770a b x +--R + +--R 9 13 13 10 12 12 11 11 11 12 10 10 +--R 497420a b x + 646646a b x + 705432a b x + 646646a b x +--R + +--R 13 9 9 14 8 8 15 7 7 16 6 6 +--R 497420a b x + 319770a b x + 170544a b x + 74613a b x +--R + +--R 17 5 5 18 4 4 19 3 3 20 2 2 21 22 +--R 26334a b x + 7315a b x + 1540a b x + 231a b x + 22a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 901 + +--S 902 of 2952 +r0000:=-1/21*(b*c-a*d)^10/(b^11*(a+b*x)^21)-_ + 1/2*d*(b*c-a*d)^9/(b^11*(a+b*x)^20)-_ + 45/19*d^2*(b*c-a*d)^8/(b^11*(a+b*x)^19)-_ + 20/3*d^3*(b*c-a*d)^7/(b^11*(a+b*x)^18)-_ + 210/17*d^4*(b*c-a*d)^6/(b^11*(a+b*x)^17)-_ + 63/4*d^5*(b*c-a*d)^5/(b^11*(a+b*x)^16)-_ + 14*d^6*(b*c-a*d)^4/(b^11*(a+b*x)^15)-_ + 60/7*d^7*(b*c-a*d)^3/(b^11*(a+b*x)^14)-_ + 45/13*d^8*(b*c-a*d)^2/(b^11*(a+b*x)^13)-_ + 5/6*d^9*(b*c-a*d)/(b^11*(a+b*x)^12)-1/11*d^10/(b^11*(a+b*x)^11) +--R +--R +--R (2) +--R 1 10 10 10 5 9 10 5 10 9 9 +--R - -- b d x + (- -- a b d - - b c d )x +--R 11 66 6 +--R + +--R 15 2 8 10 15 9 9 45 10 2 8 8 +--R (- --- a b d - -- a b c d - -- b c d )x +--R 286 26 13 +--R + +--R 30 3 7 10 30 2 8 9 180 9 2 8 60 10 3 7 7 +--R (- ---- a b d - -- a b c d - --- a b c d - -- b c d )x +--R 1001 91 91 7 +--R + +--R 2 4 6 10 2 3 7 9 12 2 8 2 8 9 3 7 10 4 6 6 +--R (- --- a b d - -- a b c d - -- a b c d - 4a b c d - 14b c d )x +--R 143 13 13 +--R + +--R 3 5 5 10 3 4 6 9 9 3 7 2 8 3 2 8 3 7 21 9 4 6 +--R - --- a b d - -- a b c d - -- a b c d - - a b c d - -- a b c d +--R 572 52 26 2 4 +--R + +--R 63 10 5 5 +--R - -- b c d +--R 4 +--R * +--R 5 +--R x +--R + +--R 15 6 4 10 15 5 5 9 45 4 6 2 8 15 3 7 3 7 +--R - ---- a b d - --- a b c d - --- a b c d - -- a b c d +--R 9724 884 442 34 +--R + +--R 105 2 8 4 6 315 9 5 5 210 10 6 4 +--R - --- a b c d - --- a b c d - --- b c d +--R 68 68 17 +--R * +--R 4 +--R x +--R + +--R 5 7 3 10 5 6 4 9 5 5 5 2 8 5 4 6 3 7 +--R - ----- a b d - ---- a b c d - --- a b c d - -- a b c d +--R 14586 1326 221 51 +--R + +--R 35 3 7 4 6 35 2 8 5 5 140 9 6 4 20 10 7 3 +--R - --- a b c d - -- a b c d - --- a b c d - -- b c d +--R 102 34 51 3 +--R * +--R 3 +--R x +--R + +--R 5 8 2 10 5 7 3 9 15 6 4 2 8 5 5 5 3 7 +--R - ----- a b d - ---- a b c d - ---- a b c d - --- a b c d +--R 92378 8398 4199 323 +--R + +--R 35 4 6 4 6 105 3 7 5 5 140 2 8 6 4 20 9 7 3 45 10 8 2 +--R - --- a b c d - --- a b c d - --- a b c d - -- a b c d - -- b c d +--R 646 646 323 19 19 +--R * +--R 2 +--R x +--R + +--R 1 9 10 1 8 2 9 3 7 3 2 8 1 6 4 3 7 +--R - ------ a b d - ----- a b c d - ---- a b c d - --- a b c d +--R 184756 16796 8398 646 +--R + +--R 7 5 5 4 6 21 4 6 5 5 14 3 7 6 4 2 2 8 7 3 +--R - ---- a b c d - ---- a b c d - --- a b c d - -- a b c d +--R 1292 1292 323 19 +--R + +--R 9 9 8 2 1 10 9 +--R - -- a b c d - - b c d +--R 38 2 +--R * +--R x +--R + +--R 1 10 10 1 9 9 1 8 2 2 8 1 7 3 3 7 +--R - ------- a d - ------ a b c d - ----- a b c d - ----- a b c d +--R 3879876 352716 58786 13566 +--R + +--R 1 6 4 4 6 1 5 5 5 5 2 4 6 6 4 2 3 7 7 3 +--R - ---- a b c d - ---- a b c d - --- a b c d - --- a b c d +--R 3876 1292 969 399 +--R + +--R 3 2 8 8 2 1 9 9 1 10 10 +--R - --- a b c d - -- a b c d - -- b c +--R 266 42 21 +--R / +--R 32 21 31 20 2 30 19 3 29 18 4 28 17 +--R b x + 21a b x + 210a b x + 1330a b x + 5985a b x +--R + +--R 5 27 16 6 26 15 7 25 14 8 24 13 +--R 20349a b x + 54264a b x + 116280a b x + 203490a b x +--R + +--R 9 23 12 10 22 11 11 21 10 12 20 9 +--R 293930a b x + 352716a b x + 352716a b x + 293930a b x +--R + +--R 13 19 8 14 18 7 15 17 6 16 16 5 +--R 203490a b x + 116280a b x + 54264a b x + 20349a b x +--R + +--R 17 15 4 18 14 3 19 13 2 20 12 21 11 +--R 5985a b x + 1330a b x + 210a b x + 21a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 902 + +--S 903 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 10 10 10 9 10 10 9 9 +--R - 352716b d x + (- 293930a b d - 3233230b c d )x +--R + +--R 2 8 10 9 9 10 2 8 8 +--R (- 203490a b d - 2238390a b c d - 13430340b c d )x +--R + +--R 3 7 10 2 8 9 9 2 8 10 3 7 7 +--R (- 116280a b d - 1279080a b c d - 7674480a b c d - 33256080b c d )x +--R + +--R 4 6 10 3 7 9 2 8 2 8 9 3 7 +--R - 54264a b d - 596904a b c d - 3581424a b c d - 15519504a b c d +--R + +--R 10 4 6 +--R - 54318264b c d +--R * +--R 6 +--R x +--R + +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 +--R - 20349a b d - 223839a b c d - 1343034a b c d - 5819814a b c d +--R + +--R 9 4 6 10 5 5 +--R - 20369349a b c d - 61108047b c d +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 3 7 3 7 +--R - 5985a b d - 65835a b c d - 395010a b c d - 1711710a b c d +--R + +--R 2 8 4 6 9 5 5 10 6 4 +--R - 5990985a b c d - 17972955a b c d - 47927880b c d +--R * +--R 4 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 +--R - 1330a b d - 14630a b c d - 87780a b c d - 380380a b c d +--R + +--R 3 7 4 6 2 8 5 5 9 6 4 +--R - 1331330a b c d - 3993990a b c d - 10650640a b c d +--R + +--R 10 7 3 +--R - 25865840b c d +--R * +--R 3 +--R x +--R + +--R 8 2 10 7 3 9 6 4 2 8 5 5 3 7 +--R - 210a b d - 2310a b c d - 13860a b c d - 60060a b c d +--R + +--R 4 6 4 6 3 7 5 5 2 8 6 4 9 7 3 +--R - 210210a b c d - 630630a b c d - 1681680a b c d - 4084080a b c d +--R + +--R 10 8 2 +--R - 9189180b c d +--R * +--R 2 +--R x +--R + +--R 9 10 8 2 9 7 3 2 8 6 4 3 7 +--R - 21a b d - 231a b c d - 1386a b c d - 6006a b c d +--R + +--R 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R - 21021a b c d - 63063a b c d - 168168a b c d - 408408a b c d +--R + +--R 9 8 2 10 9 +--R - 918918a b c d - 1939938b c d +--R * +--R x +--R + +--R 10 10 9 9 8 2 2 8 7 3 3 7 6 4 4 6 +--R - a d - 11a b c d - 66a b c d - 286a b c d - 1001a b c d +--R + +--R 5 5 5 5 4 6 6 4 3 7 7 3 2 8 8 2 +--R - 3003a b c d - 8008a b c d - 19448a b c d - 43758a b c d +--R + +--R 9 9 10 10 +--R - 92378a b c d - 184756b c +--R / +--R 32 21 31 20 2 30 19 3 29 18 +--R 3879876b x + 81477396a b x + 814773960a b x + 5160235080a b x +--R + +--R 4 28 17 5 27 16 6 26 15 +--R 23221057860a b x + 78951596724a b x + 210537591264a b x +--R + +--R 7 25 14 8 24 13 9 23 12 +--R 451151981280a b x + 789515967240a b x + 1140411952680a b x +--R + +--R 10 22 11 11 21 10 12 20 9 +--R 1368494343216a b x + 1368494343216a b x + 1140411952680a b x +--R + +--R 13 19 8 14 18 7 15 17 6 +--R 789515967240a b x + 451151981280a b x + 210537591264a b x +--R + +--R 16 16 5 17 15 4 18 14 3 +--R 78951596724a b x + 23221057860a b x + 5160235080a b x +--R + +--R 19 13 2 20 12 21 11 +--R 814773960a b x + 81477396a b x + 3879876a b +--R Type: Union(Expression(Integer),...) +--E 903 + +--S 904 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 904 + +--S 905 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 905 + +)clear all + +--S 906 of 2952 +t0000:=(a+b*x)^m/(c+d*x) +--R +--R +--R m +--R (b x + a) +--R (1) ---------- +--R d x + c +--R Type: Expression(Integer) +--E 906 + +--S 907 of 2952 +--r0000:=(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)*(1+m)) +--E 907 + +--S 908 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ (%BJ b + a) +--R (2) | ------------ d%BJ +--R ++ %BJ d + c +--R Type: Union(Expression(Integer),...) +--E 908 + +--S 909 of 2952 +--m0000:=a0000 - r0000 +--E 909 + +--S 910 of 2952 +--d0000:=D(m0000,x) +--E 910 + +)clear all + +--S 911 of 2952 +t0000:=(a+b*x)^5/(c+d*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 911 + +--S 912 of 2952 +r0000:=b*(b*c-a*d)^4*x/d^5-1/2*(b*c-a*d)^3*(a+b*x)^2/d^4+_ + 1/3*(b*c-a*d)^2*(a+b*x)^3/d^3-1/4*(b*c-a*d)*(a+b*x)^4/d^2+_ + 1/5*(a+b*x)^5/d-(b*c-a*d)^5*log(c+d*x)/d^6 +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 60a d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 5 5 +--R - 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 +--R 12b d x + (75a b d - 15b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (200a b d - 100a b c d + 20b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (300a b d - 300a b c d + 150a b c d - 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (300a b d - 600a b c d + 600a b c d - 300a b c d + 60b c d)x + 77a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 +--R - 145a b c d + 110a b c d - 30a b c d +--R / +--R 6 +--R 60d +--R Type: Expression(Integer) +--E 912 + +--S 913 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 60a d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 5 5 +--R - 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 +--R 12b d x + (75a b d - 15b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (200a b d - 100a b c d + 20b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (300a b d - 300a b c d + 150a b c d - 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (300a b d - 600a b c d + 600a b c d - 300a b c d + 60b c d)x +--R / +--R 6 +--R 60d +--R Type: Union(Expression(Integer),...) +--E 913 + +--S 914 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 5 3 4 2 3 2 2 2 3 3 +--R - 77a d + 145a b c d - 110a b c d + 30a b c +--R (4) ---------------------------------------------- +--R 4 +--R 60d +--R Type: Expression(Integer) +--E 914 + +--S 915 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 915 + +)clear all + +--S 916 of 2952 +t0000:=(a+b*x)^4/(c+d*x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (1) -------------------------------------- +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 916 + +--S 917 of 2952 +r0000:=-b*(b*c-a*d)^3*x/d^4+1/2*(b*c-a*d)^2*(a+b*x)^2/d^3-_ + 1/3*(b*c-a*d)*(a+b*x)^3/d^2+1/4*(a+b*x)^4/d+(b*c-a*d)^4*log(c+d*x)/d^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a d - 48a b c d + 72a b c d - 48a b c d + 12b c )log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b d x + (16a b d - 4b c d )x + (36a b d - 24a b c d + 6b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (48a b d - 72a b c d + 48a b c d - 12b c d)x + 13a d - 16a b c d +--R + +--R 2 2 2 2 +--R 6a b c d +--R / +--R 5 +--R 12d +--R Type: Expression(Integer) +--E 917 + +--S 918 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a d - 48a b c d + 72a b c d - 48a b c d + 12b c )log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b d x + (16a b d - 4b c d )x + (36a b d - 24a b c d + 6b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 +--R (48a b d - 72a b c d + 48a b c d - 12b c d)x +--R / +--R 5 +--R 12d +--R Type: Union(Expression(Integer),...) +--E 918 + +--S 919 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 4 2 3 2 2 2 +--R - 13a d + 16a b c d - 6a b c +--R (4) ------------------------------ +--R 3 +--R 12d +--R Type: Expression(Integer) +--E 919 + +--S 920 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 920 + +)clear all + +--S 921 of 2952 +t0000:=(a+b*x)^3/(c+d*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 921 + +--S 922 of 2952 +r0000:=b*(b*c-a*d)^2*x/d^3-1/2*(b*c-a*d)*(a+b*x)^2/d^2+1/3*(a+b*x)^3/d-_ + (b*c-a*d)^3*log(c+d*x)/d^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )log(d x + c) + 2b d x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (9a b d - 3b c d )x + (18a b d - 18a b c d + 6b c d)x + 5a d +--R + +--R 2 2 +--R - 3a b c d +--R / +--R 4 +--R 6d +--R Type: Expression(Integer) +--E 922 + +--S 923 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )log(d x + c) + 2b d x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (9a b d - 3b c d )x + (18a b d - 18a b c d + 6b c d)x +--R / +--R 4 +--R 6d +--R Type: Union(Expression(Integer),...) +--E 923 + +--S 924 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 3 2 +--R - 5a d + 3a b c +--R (4) --------------- +--R 2 +--R 6d +--R Type: Expression(Integer) +--E 924 + +--S 925 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 925 + +)clear all + +--S 926 of 2952 +t0000:=(a+b*x)^2/(c+d*x) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 926 + +--S 927 of 2952 +r0000:=-b*(b*c-a*d)*x/d^2+1/2*(a+b*x)^2/d+(b*c-a*d)^2*log(c+d*x)/d^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 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 + a d +--R ---------------------------------------------------------------------------- +--R 3 +--R 2d +--R Type: Expression(Integer) +--E 927 + +--S 928 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 2 2 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 (3) --------------------------------------------------------------------- +--R 3 +--R 2d +--R Type: Union(Expression(Integer),...) +--E 928 + +--S 929 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R a +--R (4) - -- +--R 2d +--R Type: Expression(Integer) +--E 929 + +--S 930 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 930 + +)clear all + +--S 931 of 2952 +t0000:=(a+b*x)/(c+d*x) +--R +--R +--R b x + a +--R (1) ------- +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 931 + +--S 932 of 2952 +r0000:=b*x/d-(b*c-a*d)*log(c+d*x)/d^2 +--R +--R +--R (a d - b c)log(d x + c) + b d x +--R (2) ------------------------------- +--R 2 +--R d +--R Type: Expression(Integer) +--E 932 + +--S 933 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (a d - b c)log(d x + c) + b d x +--R (3) ------------------------------- +--R 2 +--R d +--R Type: Union(Expression(Integer),...) +--E 933 + +--S 934 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 934 + +--S 935 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 935 + +)clear all + +--S 936 of 2952 +t0000:=1/(c+d*x) +--R +--R +--R 1 +--R (1) ------- +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 936 + +--S 937 of 2952 +r0000:=log(c+d*x)/d +--R +--R +--R log(d x + c) +--R (2) ------------ +--R d +--R Type: Expression(Integer) +--E 937 + +--S 938 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R log(d x + c) +--R (3) ------------ +--R d +--R Type: Union(Expression(Integer),...) +--E 938 + +--S 939 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 939 + +--S 940 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 940 + +)clear all + +--S 941 of 2952 +t0000:=1/((a+b*x)*(c+d*x)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 941 + +--S 942 of 2952 +r0000:=log(a+b*x)/(b*c-a*d)-log(c+d*x)/(b*c-a*d) +--R +--R +--R log(d x + c) - log(b x + a) +--R (2) --------------------------- +--R a d - b c +--R Type: Expression(Integer) +--E 942 + +--S 943 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R log(d x + c) - log(b x + a) +--R (3) --------------------------- +--R a d - b c +--R Type: Union(Expression(Integer),...) +--E 943 + +--S 944 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 944 + +--S 945 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 945 + +)clear all + +--S 946 of 2952 +t0000:=1/((a+b*x)^2*(c+d*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------- +--R 2 3 2 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 946 + +--S 947 of 2952 +r0000:=(-1)/((b*c-a*d)*(a+b*x))-d*log(a+b*x)/(b*c-a*d)^2+_ + d*log(c+d*x)/(b*c-a*d)^2 +--R +--R +--R (b d x + a d)log(d x + c) + (- b d x - a d)log(b x + a) + a d - b c +--R (2) ------------------------------------------------------------------- +--R 2 2 2 3 2 3 2 2 2 2 +--R (a b d - 2a b c d + b c )x + a d - 2a b c d + a b c +--R Type: Expression(Integer) +--E 947 + +--S 948 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (b d x + a d)log(d x + c) + (- b d x - a d)log(b x + a) + a d - b c +--R (3) ------------------------------------------------------------------- +--R 2 2 2 3 2 3 2 2 2 2 +--R (a b d - 2a b c d + b c )x + a d - 2a b c d + a b c +--R Type: Union(Expression(Integer),...) +--E 948 + +--S 949 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 949 + +--S 950 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 950 + +)clear all + +--S 951 of 2952 +t0000:=1/((a+b*x)^3*(c+d*x)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 3 4 2 3 3 2 2 2 3 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 951 + +--S 952 of 2952 +r0000:=(-1/2)/((b*c-a*d)*(a+b*x)^2)+d/((b*c-a*d)^2*(a+b*x))+_ + d^2*log(a+b*x)/(b*c-a*d)^3-d^2*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (2b d x + 4a b d x + 2a d )log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b d x - 4a b d x - 2a d )log(b x + a) + (2a b d - 2b c d)x + 3a d +--R + +--R 2 2 +--R - 4a b c d + b c +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (4a b d - 12a b c d + 12a b c d - 4a b c )x + 2a d - 6a b c d +--R + +--R 3 2 2 2 3 3 +--R 6a b c d - 2a b c +--R Type: Expression(Integer) +--E 952 + +--S 953 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R (2b d x + 4a b d x + 2a d )log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b d x - 4a b d x - 2a d )log(b x + a) + (2a b d - 2b c d)x + 3a d +--R + +--R 2 2 +--R - 4a b c d + b c +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (4a b d - 12a b c d + 12a b c d - 4a b c )x + 2a d - 6a b c d +--R + +--R 3 2 2 2 3 3 +--R 6a b c d - 2a b c +--R Type: Union(Expression(Integer),...) +--E 953 + +--S 954 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 954 + +--S 955 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 955 + +)clear all + +--S 956 of 2952 +t0000:=(a+b*x)^m/(c+d*x)^2 +--R +--R +--R m +--R (b x + a) +--R (1) ------------------ +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Expression(Integer) +--E 956 + +--S 957 of 2952 +--r0000:=(a+b*x)^(1+m)/((b*c-a*d)*(c+d*x))-b*m*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^2*(1+m)) +--E 957 + +--S 958 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ (%BJ b + a) +--R (2) | ---------------------- d%BJ +--R ++ 2 2 2 +--R %BJ d + 2%BJ c d + c +--R Type: Union(Expression(Integer),...) +--E 958 + +--S 959 of 2952 +--m0000:=a0000 - r0000 +--E 959 + +--S 960 of 2952 +--d0000:=D(m0000,x) +--E 960 + +)clear all + +--S 961 of 2952 +t0000:=(a+b*x)^5/(c+d*x)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 961 + +--S 962 of 2952 +r0000:=-10*b^2*(b*c-a*d)^3*x/d^5+(b*c-a*d)^5/(d^6*(c+d*x))+_ + 5*b^3*(b*c-a*d)^2*(c+d*x)^2/d^6-5/3*b^4*(b*c-a*d)*(c+d*x)^3/d^6+_ + 1/4*b^5*(c+d*x)^4/d^6+5*b*(b*c-a*d)^4*log(c+d*x)/d^6 +--R +--R +--R (2) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (60a b d - 240a b c d + 360a b c d - 240a b c d + 60b c d)x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b c d - 240a b c d + 360a b c d - 240a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 3b d x + (20a b d - 5b c d )x + (60a b d - 40a b c d + 10b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (120a b d - 180a b c d + 120a b c d - 30b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 5 5 4 4 +--R (120a b c d - 180a b c d + 80a b c d - 5b c d)x - 12a d + 60a b c d +--R + +--R 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 120a b c d + 180a b c d - 160a b c d + 55b c +--R / +--R 7 6 +--R 12d x + 12c d +--R Type: Expression(Integer) +--E 962 + +--S 963 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (60a b d - 240a b c d + 360a b c d - 240a b c d + 60b c d)x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b c d - 240a b c d + 360a b c d - 240a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 3b d x + (20a b d - 5b c d )x + (60a b d - 40a b c d + 10b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (120a b d - 180a b c d + 120a b c d - 30b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (120a b c d - 240a b c d + 180a b c d - 48b c d)x - 12a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b c d - 120a b c d + 120a b c d - 60a b c d + 12b c +--R / +--R 7 6 +--R 12d x + 12c d +--R Type: Union(Expression(Integer),...) +--E 963 + +--S 964 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 2 3 2 2 4 3 5 4 +--R - 60a b c d + 100a b c d - 43b c +--R (4) ---------------------------------- +--R 6 +--R 12d +--R Type: Expression(Integer) +--E 964 + +--S 965 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +)clear all + +--S 966 of 2952 +t0000:=(a+b*x)^4/(c+d*x)^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (1) -------------------------------------- +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 966 + +--S 967 of 2952 +r0000:=6*b^2*(b*c-a*d)^2*x/d^4-(b*c-a*d)^4/(d^5*(c+d*x))-_ + 2*b^3*(b*c-a*d)*(c+d*x)^2/d^5+1/3*b^4*(c+d*x)^3/d^5-_ + 4*b*(b*c-a*d)^3*log(c+d*x)/d^5 +--R +--R +--R (2) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (12a b d - 36a b c d + 36a b c d - 12b c d)x + 12a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R - 36a b c d + 36a b c d - 12b c +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b d x + (6a b d - 2b c d )x + (18a b d - 18a b c d + 6b c d )x +--R + +--R 2 2 3 3 2 2 4 3 4 4 3 3 2 2 2 2 +--R (18a b c d - 18a b c d + 4b c d)x - 3a d + 12a b c d - 18a b c d +--R + +--R 3 3 4 4 +--R 18a b c d - 8b c +--R / +--R 6 5 +--R 3d x + 3c d +--R Type: Expression(Integer) +--E 967 + +--S 968 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (12a b d - 36a b c d + 36a b c d - 12b c d)x + 12a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R - 36a b c d + 36a b c d - 12b c +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b d x + (6a b d - 2b c d )x + (18a b d - 18a b c d + 6b c d )x +--R + +--R 2 2 3 3 2 2 4 3 4 4 3 3 2 2 2 2 +--R (18a b c d - 24a b c d + 9b c d)x - 3a d + 12a b c d - 18a b c d +--R + +--R 3 3 4 4 +--R 12a b c d - 3b c +--R / +--R 6 5 +--R 3d x + 3c d +--R Type: Union(Expression(Integer),...) +--E 968 + +--S 969 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 3 2 4 3 +--R - 6a b c d + 5b c +--R (4) ------------------ +--R 5 +--R 3d +--R Type: Expression(Integer) +--E 969 + +--S 970 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 970 + +)clear all + +--S 971 of 2952 +t0000:=(a+b*x)^3/(c+d*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 971 + +--S 972 of 2952 +r0000:=-b^2*(2*b*c-3*a*d)*x/d^3+1/2*b^3*x^2/d^2+(b*c-a*d)^3/(d^4*(c+d*x))+_ + 3*b*(b*c-a*d)^2*log(c+d*x)/d^4 +--R +--R +--R (2) +--R 2 3 2 2 3 2 2 2 2 2 3 3 +--R ((6a b d - 12a b c d + 6b c d)x + 6a b c d - 12a b c d + 6b c ) +--R * +--R log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 3 3 +--R b d x + (6a b d - 3b c d )x + (6a b c d - 4b 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 4 +--R 2d x + 2c d +--R Type: Expression(Integer) +--E 972 + +--S 973 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 3 2 2 3 2 2 2 2 2 3 3 +--R ((6a b d - 12a b c d + 6b c d)x + 6a b c d - 12a b c d + 6b c ) +--R * +--R log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 3 3 +--R b d x + (6a b d - 3b c d )x + (6a b c d - 4b 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 4 +--R 2d x + 2c d +--R Type: Union(Expression(Integer),...) +--E 973 + +--S 974 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 974 + +--S 975 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 2952 +t0000:=(a+b*x)^2/(c+d*x)^2 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 976 + +--S 977 of 2952 +r0000:=b^2*x/d^2-(b*c-a*d)^2/(d^3*(c+d*x))-2*b*(b*c-a*d)*log(c+d*x)/d^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R ((2a b d - 2b c d)x + 2a b c d - 2b c )log(d x + c) + b d x + b c d x +--R + +--R 2 2 2 2 +--R - a d + 2a b c d - b c +--R / +--R 4 3 +--R d x + c d +--R Type: Expression(Integer) +--E 977 + +--S 978 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 +--R ((2a b d - 2b c d)x + 2a b c d - 2b c )log(d x + c) + b d x + b c d x +--R + +--R 2 2 2 2 +--R - a d + 2a b c d - b c +--R / +--R 4 3 +--R d x + c d +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 979 + +--S 980 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 980 + +)clear all + +--S 981 of 2952 +t0000:=(a+b*x)/(c+d*x)^2 +--R +--R +--R b x + a +--R (1) ------------------ +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 981 + +--S 982 of 2952 +r0000:=(b*c-a*d)/(d^2*(c+d*x))+b*log(c+d*x)/d^2 +--R +--R +--R (b d x + b c)log(d x + c) - a d + b c +--R (2) ------------------------------------- +--R 3 2 +--R d x + c d +--R Type: Expression(Integer) +--E 982 + +--S 983 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (b d x + b c)log(d x + c) - a d + b c +--R (3) ------------------------------------- +--R 3 2 +--R d x + c d +--R Type: Union(Expression(Integer),...) +--E 983 + +--S 984 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 984 + +--S 985 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 985 + +)clear all + +--S 986 of 2952 +t0000:=1/(c+d*x)^2 +--R +--R +--R 1 +--R (1) ------------------ +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 986 + +--S 987 of 2952 +r0000:=(-1)/(d*(c+d*x)) +--R +--R +--R 1 +--R (2) - --------- +--R 2 +--R d x + c d +--R Type: Fraction(Polynomial(Integer)) +--E 987 + +--S 988 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - --------- +--R 2 +--R d x + c d +--R Type: Union(Expression(Integer),...) +--E 988 + +--S 989 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 989 + +--S 990 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 990 + +)clear all + +--S 991 of 2952 +t0000:=1/((a+b*x)*(c+d*x)^2) +--R +--R +--R 1 +--R (1) ---------------------------------------------------- +--R 2 3 2 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 991 + +--S 992 of 2952 +r0000:=1/((b*c-a*d)*(c+d*x))+b*log(a+b*x)/(b*c-a*d)^2-b*log(c+d*x)/(b*c-a*d)^2 +--R +--R +--R (- b d x - b c)log(d x + c) + (b d x + b c)log(b x + a) - a d + b c +--R (2) ------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +--R (a d - 2a b c d + b c d)x + a c d - 2a b c d + b c +--R Type: Expression(Integer) +--E 992 + +--S 993 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (- b d x - b c)log(d x + c) + (b d x + b c)log(b x + a) - a d + b c +--R (3) ------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +--R (a d - 2a b c d + b c d)x + a c d - 2a b c d + b c +--R Type: Union(Expression(Integer),...) +--E 993 + +--S 994 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 994 + +--S 995 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 995 + +)clear all + +--S 996 of 2952 +t0000:=1/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--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 +--R (2a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 996 + +--S 997 of 2952 +r0000:=-b/((b*c-a*d)^2*(a+b*x))-d/((b*c-a*d)^2*(c+d*x))-_ + 2*b*d*log(a+b*x)/(b*c-a*d)^3+2*b*d*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 2 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 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 +--R (- 2a b d + 2b c d)x - a d + b c +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R Type: Expression(Integer) +--E 997 + +--S 998 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 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 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 +--R (- 2a b d + 2b c d)x - a d + b c +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R Type: Union(Expression(Integer),...) +--E 998 + +--S 999 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1000 + +)clear all + +--S 1001 of 2952 +t0000:=1/((a+b*x)^3*(c+d*x)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--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 2 3 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 1001 + +--S 1002 of 2952 +r0000:=-1/2*b/((b*c-a*d)^2*(a+b*x)^2)+2*b*d/((b*c-a*d)^3*(a+b*x))+_ + d^2/((b*c-a*d)^3*(c+d*x))+3*b*d^2*log(a+b*x)/(b*c-a*d)^4-_ + 3*b*d^2*log(c+d*x)/(b*c-a*d)^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R - 6b d x + (- 12a b d - 6b c d )x + (- 6a b d - 12a b c d )x +--R + +--R 2 2 +--R - 6a b c d +--R * +--R log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 6b d x + (12a b d + 6b c d )x + (6a b d + 12a b c d )x +--R + +--R 2 2 +--R 6a b c d +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b d + 6b c d )x + (- 9a b d + 6a b c d + 3b c d)x - 2a d +--R + +--R 2 2 2 2 3 3 +--R - 3a b c d + 6a b c d - b c +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R - 6b d x + (- 12a b d - 6b c d )x + (- 6a b d - 12a b c d )x +--R + +--R 2 2 +--R - 6a b c d +--R * +--R log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 6b d x + (12a b d + 6b c d )x + (6a b d + 12a b c d )x +--R + +--R 2 2 +--R 6a b c d +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (- 6a b d + 6b c d )x + (- 9a b d + 6a b c d + 3b c d)x - 2a d +--R + +--R 2 2 2 2 3 3 +--R - 3a b c d + 6a b c d - b c +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Union(Expression(Integer),...) +--E 1003 + +--S 1004 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1005 + +)clear all + +--S 1006 of 2952 +t0000:=(a+b*x)^m/(c+d*x)^3 +--R +--R +--R m +--R (b x + a) +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 2952 +--r0000:=1/2*(a+b*x)^(1+m)/((b*c-a*d)*(c+d*x)^2)+_ +-- 1/2*b*(1-m)*(a+b*x)^(1+m)/((b*c-a*d)^2*(c+d*x))-_ +-- 1/2*b^2*(1-m)*m*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)^3*(1+m)) +--E 1007 + +--S 1008 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x m +--R ++ (%BJ b + a) +--R (2) | ---------------------------------- d%BJ +--R ++ 3 3 2 2 2 3 +--R %BJ d + 3%BJ c d + 3%BJ c d + c +--R Type: Union(Expression(Integer),...) +--E 1008 + +--S 1009 of 2952 +--m0000:=a0000 - r0000 +--E 1009 + +--S 1010 of 2952 +--d0000:=D(m0000,x) +--E 1010 + +)clear all + +--S 1011 of 2952 +t0000:=(a+b*x)^6/(c+d*x)^3 +--R +--R +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R (1) ------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1011 + +--S 1012 of 2952 +r0000:=-20*b^3*(b*c-a*d)^3*x/d^6-1/2*(b*c-a*d)^6/(d^7*(c+d*x)^2)+_ + 6*b*(b*c-a*d)^5/(d^7*(c+d*x))+15/2*b^4*(b*c-a*d)^2*(c+d*x)^2/d^7-_ + 2*b^5*(b*c-a*d)*(c+d*x)^3/d^7+1/4*b^6*(c+d*x)^4/d^7+_ + 15*b^2*(b*c-a*d)^4*log(c+d*x)/d^7 +--R +--R +--R (2) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (60a b d - 240a b c d + 360a b c d - 240a b c d + 60b c d )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (120a b c d - 480a b c d + 720a b c d - 480a b c d + 120b c d)x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R 60a b c d - 240a b c d + 360a b c d - 240a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b d x + (8a b d - 2b c d )x + (30a b d - 20a b c d + 5b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b d - 120a b c d + 80a b c d - 20b c d )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (160a b c d - 300a b c d + 200a b c d - 45b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 24a b d + 120a b c d - 160a b c d + 120a b c d - 80a b c d +--R + +--R 6 5 +--R 30b c d +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 2a d - 12a b c d + 90a b c d - 200a b c d + 240a b c d +--R + +--R 5 5 6 6 +--R - 160a b c d + 45b c +--R / +--R 9 2 8 2 7 +--R 4d x + 8c d x + 4c d +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (60a b d - 240a b c d + 360a b c d - 240a b c d + 60b c d )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (120a b c d - 480a b c d + 720a b c d - 480a b c d + 120b c d)x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R 60a b c d - 240a b c d + 360a b c d - 240a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b d x + (8a b d - 2b c d )x + (30a b d - 20a b c d + 5b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b d - 120a b c d + 80a b c d - 20b c d )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (160a b c d - 330a b c d + 252a b c d - 68b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 24a b d + 120a b c d - 160a b c d + 60a b c d + 24a b c d +--R + +--R 6 5 +--R - 16b c d +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 2a d - 12a b c d + 90a b c d - 200a b c d + 210a b c d +--R + +--R 5 5 6 6 +--R - 108a b c d + 22b c +--R / +--R 9 2 8 2 7 +--R 4d x + 8c d x + 4c d +--R Type: Union(Expression(Integer),...) +--E 1013 + +--S 1014 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 2 4 2 2 5 3 6 4 +--R - 30a b c d + 52a b c d - 23b c +--R (4) --------------------------------- +--R 7 +--R 4d +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1015 + +)clear all + +--S 1016 of 2952 +t0000:=(a+b*x)^5/(c+d*x)^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1016 + +--S 1017 of 2952 +r0000:=10*b^3*(b*c-a*d)^2*x/d^5+1/2*(b*c-a*d)^5/(d^6*(c+d*x)^2)-_ + 5*b*(b*c-a*d)^4/(d^6*(c+d*x))-5/2*b^4*(b*c-a*d)*(c+d*x)^2/d^6+_ + 1/3*b^5*(c+d*x)^3/d^6-10*b^2*(b*c-a*d)^3*log(c+d*x)/d^6 +--R +--R +--R (2) +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (60a b d - 180a b c d + 180a b c d - 60b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 3 2 2 3 +--R (120a b c d - 360a b c d + 360a b c d - 120b c d)x + 60a b c d +--R + +--R 2 3 3 2 4 4 5 5 +--R - 180a b c d + 180a b c d - 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 2b d x + (15a b d - 5b c d )x + (60a b d - 60a b c d + 20b c d )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (120a b c d - 150a b c d + 50b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 30a b d + 120a b c d - 120a b c d + 60a b c d - 20b c d)x - 3a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 15a b c d + 90a b c d - 150a b c d + 120a b c d - 40b c +--R / +--R 8 2 7 2 6 +--R 6d x + 12c d x + 6c d +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (60a b d - 180a b c d + 180a b c d - 60b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 3 2 2 3 +--R (120a b c d - 360a b c d + 360a b c d - 120b c d)x + 60a b c d +--R + +--R 2 3 3 2 4 4 5 5 +--R - 180a b c d + 180a b c d - 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 2b d x + (15a b d - 5b c d )x + (60a b d - 60a b c d + 20b c d )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (120a b c d - 165a b c d + 63b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 30a b d + 120a b c d - 120a b c d + 30a b c d + 6b c d)x - 3a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 15a b c d + 90a b c d - 150a b c d + 105a b c d - 27b c +--R / +--R 8 2 7 2 6 +--R 6d x + 12c d x + 6c d +--R Type: Union(Expression(Integer),...) +--E 1018 + +--S 1019 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 4 2 5 3 +--R - 15a b c d + 13b c +--R (4) -------------------- +--R 6 +--R 6d +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1020 + +)clear all + +--S 1021 of 2952 +t0000:=(a+b*x)^4/(c+d*x)^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (1) -------------------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1021 + +--S 1022 of 2952 +r0000:=-b^3*(3*b*c-4*a*d)*x/d^4+1/2*b^4*x^2/d^3-_ + 1/2*(b*c-a*d)^4/(d^5*(c+d*x)^2)+4*b*(b*c-a*d)^3/(d^5*(c+d*x))+_ + 6*b^2*(b*c-a*d)^2*log(c+d*x)/d^5 +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b d - 24a b c d + 12b c d )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 4 4 +--R (24a b c d - 48a b c d + 24b c d)x + 12a b c d - 24a b c d + 12b c +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 3 3 4 2 2 2 +--R b d x + (8a b d - 4b c d )x + (16a b c d - 11b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 8a b d + 24a b c d - 16a b c d + 2b c d)x - a d - 4a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b c d - 20a b c d + 7b c +--R / +--R 7 2 6 2 5 +--R 2d x + 4c d x + 2c d +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b d - 24a b c d + 12b c d )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 4 4 +--R (24a b c d - 48a b c d + 24b c d)x + 12a b c d - 24a b c d + 12b c +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 3 3 4 2 2 2 +--R b d x + (8a b d - 4b c d )x + (16a b c d - 11b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 8a b d + 24a b c d - 16a b c d + 2b c d)x - a d - 4a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b c d - 20a b c d + 7b c +--R / +--R 7 2 6 2 5 +--R 2d x + 4c d x + 2c d +--R Type: Union(Expression(Integer),...) +--E 1023 + +--S 1024 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1025 + +)clear all + +--S 1026 of 2952 +t0000:=(a+b*x)^3/(c+d*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1026 + +--S 1027 of 2952 +r0000:=b^3*x/d^3+1/2*(b*c-a*d)^3/(d^4*(c+d*x)^2)-_ + 3*b*(b*c-a*d)^2/(d^4*(c+d*x))-3*b^2*(b*c-a*d)*log(c+d*x)/d^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 2 3 2 2 2 3 3 +--R ((6a b d - 6b c d )x + (12a b c d - 12b c d)x + 6a b c d - 6b c ) +--R * +--R log(d x + c) +--R + +--R 3 3 3 3 2 2 2 3 2 2 3 2 3 3 +--R 2b d x + 4b c d x + (- 6a b d + 12a b c d - 4b c d)x - a d +--R + +--R 2 2 2 2 3 3 +--R - 3a b c d + 9a b c d - 5b c +--R / +--R 6 2 5 2 4 +--R 2d x + 4c d x + 2c d +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 2 3 2 2 2 3 3 +--R ((6a b d - 6b c d )x + (12a b c d - 12b c d)x + 6a b c d - 6b c ) +--R * +--R log(d x + c) +--R + +--R 3 3 3 3 2 2 2 3 2 2 3 2 3 3 +--R 2b d x + 4b c d x + (- 6a b d + 12a b c d - 4b c d)x - a d +--R + +--R 2 2 2 2 3 3 +--R - 3a b c d + 9a b c d - 5b c +--R / +--R 6 2 5 2 4 +--R 2d x + 4c d x + 2c d +--R Type: Union(Expression(Integer),...) +--E 1028 + +--S 1029 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1030 + +)clear all + +--S 1031 of 2952 +t0000:=(a+b*x)^2/(c+d*x)^3 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1031 + +--S 1032 of 2952 +r0000:=-1/2*(b*c-a*d)^2/(d^3*(c+d*x)^2)+2*b*(b*c-a*d)/(d^3*(c+d*x))+_ + b^2*log(c+d*x)/d^3 +--R +--R +--R (2) +--R 2 2 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 - a d +--R + +--R 2 2 +--R - 2a b c d + 3b c +--R / +--R 5 2 4 2 3 +--R 2d x + 4c d x + 2c d +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 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 - a d +--R + +--R 2 2 +--R - 2a b c d + 3b c +--R / +--R 5 2 4 2 3 +--R 2d x + 4c d x + 2c d +--R Type: Union(Expression(Integer),...) +--E 1033 + +--S 1034 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1035 + +)clear all + +--S 1036 of 2952 +t0000:=(a+b*x)/(c+d*x)^3 +--R +--R +--R b x + a +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1036 + +--S 1037 of 2952 +r0000:=1/2*(a+b*x)^2/((b*c-a*d)*(c+d*x)^2) +--R +--R +--R 1 2 2 1 2 +--R - - b x - a b x - - a +--R 2 2 +--R (2) ------------------------------------------------------ +--R 3 2 2 2 2 2 3 +--R (a d - b c d )x + (2a c d - 2b c d)x + a c d - b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1037 + +--S 1038 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R - 2b d x - a d - b c +--R (3) ---------------------- +--R 4 2 3 2 2 +--R 2d x + 4c d x + 2c d +--R Type: Union(Expression(Integer),...) +--E 1038 + +--S 1039 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R b +--R (4) --------------- +--R 3 2 +--R 2a d - 2b c d +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1040 + +)clear all + +--S 1041 of 2952 +t0000:=1/(c+d*x)^3 +--R +--R +--R 1 +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1041 + +--S 1042 of 2952 +r0000:=(-1/2)/(d*(c+d*x)^2) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - ------------------- +--R 3 2 2 2 +--R d x + 2c d x + c d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1042 + +--S 1043 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - --------------------- +--R 3 2 2 2 +--R 2d x + 4c d x + 2c d +--R Type: Union(Expression(Integer),...) +--E 1043 + +--S 1044 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1045 + +)clear all + +--S 1046 of 2952 +t0000:=1/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 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 + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1046 + +--S 1047 of 2952 +r0000:=1/2/((b*c-a*d)*(c+d*x)^2)+b/((b*c-a*d)^2*(c+d*x))+_ + b^2*log(a+b*x)/(b*c-a*d)^3-b^2*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (2b d x + 4b c d x + 2b c )log(d x + c) +--R + +--R 2 2 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 - a d +--R + +--R 2 2 +--R 4a b c d - 3b c +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a c d - 12a b c d + 12a b c d - 4b c d)x + 2a c d - 6a b c d +--R + +--R 2 4 3 5 +--R 6a b c d - 2b c +--R Type: Expression(Integer) +--E 1047 + +--S 1048 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R (2b d x + 4b c d x + 2b c )log(d x + c) +--R + +--R 2 2 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 - a d +--R + +--R 2 2 +--R 4a b c d - 3b c +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a c d - 12a b c d + 12a b c d - 4b c d)x + 2a c d - 6a b c d +--R + +--R 2 4 3 5 +--R 6a b c d - 2b c +--R Type: Union(Expression(Integer),...) +--E 1048 + +--S 1049 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1050 + +)clear all + +--S 1051 of 2952 +t0000:=1/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--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 2 2 2 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: Fraction(Polynomial(Integer)) +--E 1051 + +--S 1052 of 2952 +r0000:=-b^2/((b*c-a*d)^3*(a+b*x))-1/2*d/((b*c-a*d)^2*(c+d*x)^2)-_ + 2*b*d/((b*c-a*d)^3*(c+d*x))-3*b^2*d*log(a+b*x)/(b*c-a*d)^4+_ + 3*b^2*d*log(c+d*x)/(b*c-a*d)^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 2 3 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 log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 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 log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 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 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 2 3 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 log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 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 log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 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 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Union(Expression(Integer),...) +--E 1053 + +--S 1054 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1055 + +)clear all + +--S 1056 of 2952 +t0000:=1/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--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 3 3 2 2 2 2 3 2 +--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 3 3 +--R (3a c d + 3a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1056 + +--S 1057 of 2952 +r0000:=-1/2*b^2/((b*c-a*d)^3*(a+b*x)^2)+3*b^2*d/((b*c-a*d)^4*(a+b*x))+_ + 1/2*d^2/((b*c-a*d)^3*(c+d*x)^2)+3*b*d^2/((b*c-a*d)^4*(c+d*x))+_ + 6*b^2*d^2*log(a+b*x)/(b*c-a*d)^5-6*b^2*d^2*log(c+d*x)/(b*c-a*d)^5 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 12b d x + (24a b d + 24b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (12a b d + 48a b c d + 12b c d )x + (24a b c d + 24a b c d )x +--R + +--R 2 2 2 2 +--R 12a b c d +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 12b d x + (- 24a b d - 24b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (- 12a b d - 48a b c d - 12b c d )x + (- 24a b c d - 24a b c d )x +--R + +--R 2 2 2 2 +--R - 12a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 4 2 2 2 +--R (12a b d - 12b c d )x + (18a b d - 18b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b d + 24a b c d - 24a b c d - 4b c d)x - a d + 8a b c d +--R + +--R 3 3 4 4 +--R - 8a b c d + b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 12b d x + (24a b d + 24b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (12a b d + 48a b c d + 12b c d )x + (24a b c d + 24a b c d )x +--R + +--R 2 2 2 2 +--R 12a b c d +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 12b d x + (- 24a b d - 24b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (- 12a b d - 48a b c d - 12b c d )x + (- 24a b c d - 24a b c d )x +--R + +--R 2 2 2 2 +--R - 12a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 4 2 2 2 +--R (12a b d - 12b c d )x + (18a b d - 18b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b d + 24a b c d - 24a b c d - 4b c d)x - a d + 8a b c d +--R + +--R 3 3 4 4 +--R - 8a b c d + b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Union(Expression(Integer),...) +--E 1058 + +--S 1059 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1060 + +)clear all + +--S 1061 of 2952 +t0000:=(a+b*x)^9/(c+d*x)^8 +--R +--R +--R (1) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 7 2 2 8 9 +--R 36a b x + 9a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1061 + +--S 1062 of 2952 +r0000:=-b^8*(8*b*c-9*a*d)*x/d^9+1/2*b^9*x^2/d^8+_ + 1/7*(b*c-a*d)^9/(d^10*(c+d*x)^7)-_ + 3/2*b*(b*c-a*d)^8/(d^10*(c+d*x)^6)+_ + 36/5*b^2*(b*c-a*d)^7/(d^10*(c+d*x)^5)-_ + 21*b^3*(b*c-a*d)^6/(d^10*(c+d*x)^4)+_ + 42*b^4*(b*c-a*d)^5/(d^10*(c+d*x)^3)-_ + 63*b^5*(b*c-a*d)^4/(d^10*(c+d*x)^2)+_ + 84*b^6*(b*c-a*d)^3/(d^10*(c+d*x))+36*b^7*(b*c-a*d)^2*log(c+d*x)/d^10 +--R +--R +--R (2) +--R 2 7 9 8 8 9 2 7 7 +--R (2520a b d - 5040a b c d + 2520b c d )x +--R + +--R 2 7 8 8 2 7 9 3 6 6 +--R (17640a b c d - 35280a b c d + 17640b c d )x +--R + +--R 2 7 2 7 8 3 6 9 4 5 5 +--R (52920a b c d - 105840a b c d + 52920b c d )x +--R + +--R 2 7 3 6 8 4 5 9 5 4 4 +--R (88200a b c d - 176400a b c d + 88200b c d )x +--R + +--R 2 7 4 5 8 5 4 9 6 3 3 +--R (88200a b c d - 176400a b c d + 88200b c d )x +--R + +--R 2 7 5 4 8 6 3 9 7 2 2 +--R (52920a b c d - 105840a b c d + 52920b c d )x +--R + +--R 2 7 6 3 8 7 2 9 8 2 7 7 2 +--R (17640a b c d - 35280a b c d + 17640b c d)x + 2520a b c d +--R + +--R 8 8 9 9 +--R - 5040a b c d + 2520b c +--R * +--R log(d x + c) +--R + +--R 9 9 9 8 9 9 8 8 8 8 9 2 7 7 +--R 35b d x + (630a b d - 315b c d )x + (4410a b c d - 3185b c d )x +--R + +--R 3 6 9 2 7 8 8 2 7 9 3 6 6 +--R (- 5880a b d + 17640a b c d - 4410a b c d - 4655b c d )x +--R + +--R 4 5 9 3 6 8 2 7 2 7 8 3 6 +--R - 4410a b d - 17640a b c d + 79380a b c d - 66150a b c d +--R + +--R 9 4 5 +--R 12495b c d +--R * +--R 5 +--R x +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 +--R - 2940a b d - 7350a b c d - 29400a b c d + 161700a b c d +--R + +--R 8 4 5 9 5 4 +--R - 169050a b c d + 50225b c d +--R * +--R 4 +--R x +--R + +--R 6 3 9 5 4 8 4 5 2 7 3 6 3 6 +--R - 1470a b d - 2940a b c d - 7350a b c d - 29400a b c d +--R + +--R 2 7 4 5 8 5 4 9 6 3 +--R 183750a b c d - 213150a b c d + 72275b c d +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 +--R - 504a b d - 882a b c d - 1764a b c d - 4410a b c d +--R + +--R 3 6 4 5 2 7 5 4 8 6 3 9 7 2 +--R - 17640a b c d + 120834a b c d - 149058a b c d + 53949b c d +--R * +--R 2 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 4 5 4 5 +--R - 105a b d - 168a b c d - 294a b c d - 588a b c d - 1470a b c d +--R + +--R 3 6 5 4 2 7 6 3 8 7 2 9 8 +--R - 5880a b c d + 43218a b c d - 55566a b c d + 20923b c d +--R * +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 +--R - 10a d - 15a b c d - 24a b c d - 42a b c d - 84a b c d +--R + +--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9 +--R - 210a b c d - 840a b c d + 6534a b c d - 8658a b c d + 3349b c +--R / +--R 17 7 16 6 2 15 5 3 14 4 4 13 3 +--R 70d x + 490c d x + 1470c d x + 2450c d x + 2450c d x +--R + +--R 5 12 2 6 11 7 10 +--R 1470c d x + 490c d x + 70c d +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 7 9 8 8 9 2 7 7 +--R (2520a b d - 5040a b c d + 2520b c d )x +--R + +--R 2 7 8 8 2 7 9 3 6 6 +--R (17640a b c d - 35280a b c d + 17640b c d )x +--R + +--R 2 7 2 7 8 3 6 9 4 5 5 +--R (52920a b c d - 105840a b c d + 52920b c d )x +--R + +--R 2 7 3 6 8 4 5 9 5 4 4 +--R (88200a b c d - 176400a b c d + 88200b c d )x +--R + +--R 2 7 4 5 8 5 4 9 6 3 3 +--R (88200a b c d - 176400a b c d + 88200b c d )x +--R + +--R 2 7 5 4 8 6 3 9 7 2 2 +--R (52920a b c d - 105840a b c d + 52920b c d )x +--R + +--R 2 7 6 3 8 7 2 9 8 2 7 7 2 +--R (17640a b c d - 35280a b c d + 17640b c d)x + 2520a b c d +--R + +--R 8 8 9 9 +--R - 5040a b c d + 2520b c +--R * +--R log(d x + c) +--R + +--R 9 9 9 8 9 9 8 8 8 8 9 2 7 7 +--R 35b d x + (630a b d - 315b c d )x + (4410a b c d - 3185b c d )x +--R + +--R 3 6 9 2 7 8 8 2 7 9 3 6 6 +--R (- 5880a b d + 17640a b c d - 4410a b c d - 4655b c d )x +--R + +--R 4 5 9 3 6 8 2 7 2 7 8 3 6 +--R - 4410a b d - 17640a b c d + 79380a b c d - 66150a b c d +--R + +--R 9 4 5 +--R 12495b c d +--R * +--R 5 +--R x +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 +--R - 2940a b d - 7350a b c d - 29400a b c d + 161700a b c d +--R + +--R 8 4 5 9 5 4 +--R - 169050a b c d + 50225b c d +--R * +--R 4 +--R x +--R + +--R 6 3 9 5 4 8 4 5 2 7 3 6 3 6 +--R - 1470a b d - 2940a b c d - 7350a b c d - 29400a b c d +--R + +--R 2 7 4 5 8 5 4 9 6 3 +--R 183750a b c d - 213150a b c d + 72275b c d +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 +--R - 504a b d - 882a b c d - 1764a b c d - 4410a b c d +--R + +--R 3 6 4 5 2 7 5 4 8 6 3 9 7 2 +--R - 17640a b c d + 120834a b c d - 149058a b c d + 53949b c d +--R * +--R 2 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 4 5 4 5 +--R - 105a b d - 168a b c d - 294a b c d - 588a b c d - 1470a b c d +--R + +--R 3 6 5 4 2 7 6 3 8 7 2 9 8 +--R - 5880a b c d + 43218a b c d - 55566a b c d + 20923b c d +--R * +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 +--R - 10a d - 15a b c d - 24a b c d - 42a b c d - 84a b c d +--R + +--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9 +--R - 210a b c d - 840a b c d + 6534a b c d - 8658a b c d + 3349b c +--R / +--R 17 7 16 6 2 15 5 3 14 4 4 13 3 +--R 70d x + 490c d x + 1470c d x + 2450c d x + 2450c d x +--R + +--R 5 12 2 6 11 7 10 +--R 1470c d x + 490c d x + 70c d +--R Type: Union(Expression(Integer),...) +--E 1063 + +--S 1064 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1065 + +)clear all + +--S 1066 of 2952 +t0000:=(a+b*x)^8/(c+d*x)^8 +--R +--R +--R (1) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 8 +--R 8a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1066 + +--S 1067 of 2952 +r0000:=b^8*x/d^8-1/7*(b*c-a*d)^8/(d^9*(c+d*x)^7)+_ + 4/3*b*(b*c-a*d)^7/(d^9*(c+d*x)^6)-_ + 28/5*b^2*(b*c-a*d)^6/(d^9*(c+d*x)^5)+_ + 14*b^3*(b*c-a*d)^5/(d^9*(c+d*x)^4)-_ + 70/3*b^4*(b*c-a*d)^4/(d^9*(c+d*x)^3)+_ + 28*b^5*(b*c-a*d)^3/(d^9*(c+d*x)^2)-_ + 28*b^6*(b*c-a*d)^2/(d^9*(c+d*x))-_ + 8*b^7*(b*c-a*d)*log(c+d*x)/d^9 +--R +--R +--R (2) +--R 7 8 8 7 7 7 7 8 2 6 6 +--R (840a b d - 840b c d )x + (5880a b c d - 5880b c d )x +--R + +--R 7 2 6 8 3 5 5 7 3 5 8 4 4 4 +--R (17640a b c d - 17640b c d )x + (29400a b c d - 29400b c d )x +--R + +--R 7 4 4 8 5 3 3 7 5 3 8 6 2 2 +--R (29400a b c d - 29400b c d )x + (17640a b c d - 17640b c d )x +--R + +--R 7 6 2 8 7 7 7 8 8 +--R (5880a b c d - 5880b c d)x + 840a b c d - 840b c +--R * +--R log(d x + c) +--R + +--R 8 8 8 8 7 7 2 6 8 7 7 8 2 6 6 +--R 105b d x + 735b c d x + (- 2940a b d + 5880a b c d - 735b c d )x +--R + +--R 3 5 8 2 6 7 7 2 6 8 3 5 5 +--R (- 2940a b d - 8820a b c d + 26460a b c d - 11025b c d )x +--R + +--R 4 4 8 3 5 7 2 6 2 6 7 3 5 +--R - 2450a b d - 4900a b c d - 14700a b c d + 53900a b c d +--R + +--R 8 4 4 +--R - 28175b c d +--R * +--R 4 +--R x +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 +--R - 1470a b d - 2450a b c d - 4900a b c d - 14700a b c d +--R + +--R 7 4 4 8 5 3 +--R 61250a b c d - 35525b c d +--R * +--R 3 +--R x +--R + +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 +--R - 588a b d - 882a b c d - 1470a b c d - 2940a b c d +--R + +--R 2 6 4 4 7 5 3 8 6 2 +--R - 8820a b c d + 40278a b c d - 24843b c d +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 140a b d - 196a b c d - 294a b c d - 490a b c d - 980a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R - 2940a b c d + 14406a b c d - 9261b c d +--R * +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R - 15a d - 20a b c d - 28a b c d - 42a b c d - 70a b c d +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R - 140a b c d - 420a b c d + 2178a b c d - 1443b c +--R / +--R 16 7 15 6 2 14 5 3 13 4 4 12 3 +--R 105d x + 735c d x + 2205c d x + 3675c d x + 3675c d x +--R + +--R 5 11 2 6 10 7 9 +--R 2205c d x + 735c d x + 105c d +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 8 8 7 7 7 7 8 2 6 6 +--R (840a b d - 840b c d )x + (5880a b c d - 5880b c d )x +--R + +--R 7 2 6 8 3 5 5 7 3 5 8 4 4 4 +--R (17640a b c d - 17640b c d )x + (29400a b c d - 29400b c d )x +--R + +--R 7 4 4 8 5 3 3 7 5 3 8 6 2 2 +--R (29400a b c d - 29400b c d )x + (17640a b c d - 17640b c d )x +--R + +--R 7 6 2 8 7 7 7 8 8 +--R (5880a b c d - 5880b c d)x + 840a b c d - 840b c +--R * +--R log(d x + c) +--R + +--R 8 8 8 8 7 7 2 6 8 7 7 8 2 6 6 +--R 105b d x + 735b c d x + (- 2940a b d + 5880a b c d - 735b c d )x +--R + +--R 3 5 8 2 6 7 7 2 6 8 3 5 5 +--R (- 2940a b d - 8820a b c d + 26460a b c d - 11025b c d )x +--R + +--R 4 4 8 3 5 7 2 6 2 6 7 3 5 +--R - 2450a b d - 4900a b c d - 14700a b c d + 53900a b c d +--R + +--R 8 4 4 +--R - 28175b c d +--R * +--R 4 +--R x +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 +--R - 1470a b d - 2450a b c d - 4900a b c d - 14700a b c d +--R + +--R 7 4 4 8 5 3 +--R 61250a b c d - 35525b c d +--R * +--R 3 +--R x +--R + +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 +--R - 588a b d - 882a b c d - 1470a b c d - 2940a b c d +--R + +--R 2 6 4 4 7 5 3 8 6 2 +--R - 8820a b c d + 40278a b c d - 24843b c d +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 140a b d - 196a b c d - 294a b c d - 490a b c d - 980a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R - 2940a b c d + 14406a b c d - 9261b c d +--R * +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R - 15a d - 20a b c d - 28a b c d - 42a b c d - 70a b c d +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R - 140a b c d - 420a b c d + 2178a b c d - 1443b c +--R / +--R 16 7 15 6 2 14 5 3 13 4 4 12 3 +--R 105d x + 735c d x + 2205c d x + 3675c d x + 3675c d x +--R + +--R 5 11 2 6 10 7 9 +--R 2205c d x + 735c d x + 105c d +--R Type: Union(Expression(Integer),...) +--E 1068 + +--S 1069 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1070 + +)clear all + +--S 1071 of 2952 +t0000:=(a+b*x)^7/(c+d*x)^8 +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1071 + +--S 1072 of 2952 +r0000:=1/7*(b*c-a*d)^7/(d^8*(c+d*x)^7)-7/6*b*(b*c-a*d)^6/(d^8*(c+d*x)^6)+_ + 21/5*b^2*(b*c-a*d)^5/(d^8*(c+d*x)^5)-_ + 35/4*b^3*(b*c-a*d)^4/(d^8*(c+d*x)^4)+_ + 35/3*b^4*(b*c-a*d)^3/(d^8*(c+d*x)^3)-_ + 21/2*b^5*(b*c-a*d)^2/(d^8*(c+d*x)^2)+_ + 7*b^6*(b*c-a*d)/(d^8*(c+d*x))+b^7*log(c+d*x)/d^8 +--R +--R +--R (2) +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R 420b d x + 2940b c d x + 8820b c d x + 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R 14700b c d x + 8820b c d x + 2940b c d x + 420b c +--R * +--R log(d x + c) +--R + +--R 6 7 7 6 6 +--R (- 2940a b d + 2940b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 4410a b d - 8820a b c d + 13230b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 4900a b d - 7350a b c d - 14700a b c d + 26950b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 3675a b d - 4900a b c d - 7350a b c d - 14700a b c d +--R + +--R 7 4 3 +--R 30625b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1764a b d - 2205a b c d - 2940a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8820a b c d + 20139b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 490a b d - 588a b c d - 735a b c d - 980a b c d - 1470a b c d +--R + +--R 6 5 2 7 6 +--R - 2940a b c d + 7203b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d - 70a b c d - 84a b c d - 105a b c d - 140a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d - 420a b c d + 1089b c +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420d x + 2940c d x + 8820c d x + 14700c d x + 14700c d x +--R + +--R 5 10 2 6 9 7 8 +--R 8820c d x + 2940c d x + 420c d +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R 420b d x + 2940b c d x + 8820b c d x + 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R 14700b c d x + 8820b c d x + 2940b c d x + 420b c +--R * +--R log(d x + c) +--R + +--R 6 7 7 6 6 +--R (- 2940a b d + 2940b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 4410a b d - 8820a b c d + 13230b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 4900a b d - 7350a b c d - 14700a b c d + 26950b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 3675a b d - 4900a b c d - 7350a b c d - 14700a b c d +--R + +--R 7 4 3 +--R 30625b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1764a b d - 2205a b c d - 2940a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8820a b c d + 20139b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 490a b d - 588a b c d - 735a b c d - 980a b c d - 1470a b c d +--R + +--R 6 5 2 7 6 +--R - 2940a b c d + 7203b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d - 70a b c d - 84a b c d - 105a b c d - 140a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d - 420a b c d + 1089b c +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420d x + 2940c d x + 8820c d x + 14700c d x + 14700c d x +--R + +--R 5 10 2 6 9 7 8 +--R 8820c d x + 2940c d x + 420c d +--R Type: Union(Expression(Integer),...) +--E 1073 + +--S 1074 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1075 + +)clear all + +--S 1076 of 2952 +t0000:=(a+b*x)^6/(c+d*x)^8 +--R +--R +--R (1) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1076 + +--S 1077 of 2952 +r0000:=1/7*(a+b*x)^7/((b*c-a*d)*(c+d*x)^7) +--R +--R +--R (2) +--R 1 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 1 7 +--R - - b x - a b x - 3a b x - 5a b x - 5a b x - 3a b x - a b x - - a +--R 7 7 +--R / +--R 8 7 7 7 2 6 6 2 6 3 5 5 +--R (a d - b c d )x + (7a c d - 7b c d )x + (21a c d - 21b c d )x +--R + +--R 3 5 4 4 4 4 4 5 3 3 +--R (35a c d - 35b c d )x + (35a c d - 35b c d )x +--R + +--R 5 3 6 2 2 6 2 7 7 8 +--R (21a c d - 21b c d )x + (7a c d - 7b c d)x + a c d - b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1077 + +--S 1078 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 6 5 6 6 5 5 +--R - 7b d x + (- 21a b d - 21b c d )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 35a b d - 35a b c d - 35b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 35a b d - 35a b c d - 35a b c d - 35b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 21a b d - 21a b c d - 21a b c d - 21a b c d - 21b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (- 7a b d - 7a b c d - 7a b c d - 7a b c d - 7a b c d - 7b c d)x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R - a d - a b c d - a b c d - a b c d - a b c d - a b c d - b c +--R / +--R 14 7 13 6 2 12 5 3 11 4 4 10 3 5 9 2 +--R 7d x + 49c d x + 147c d x + 245c d x + 245c d x + 147c d x +--R + +--R 6 8 7 7 +--R 49c d x + 7c d +--R Type: Union(Expression(Integer),...) +--E 1078 + +--S 1079 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 7 +--R b +--R (4) --------------- +--R 8 7 +--R 7a d - 7b c d +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1080 + +)clear all + +--S 1081 of 2952 +t0000:=(a+b*x)^5/(c+d*x)^8 +--R +--R +--R (1) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1081 + +--S 1082 of 2952 +r0000:=1/7*(a+b*x)^6/((b*c-a*d)*(c+d*x)^7)+_ + 1/42*b*(a+b*x)^6/((b*c-a*d)^2*(c+d*x)^6) +--R +--R +--R (2) +--R 1 7 7 1 7 6 1 2 5 6 5 5 3 4 5 2 5 4 +--R -- b d x + - b c x + (- - a b d + a b c)x + (- - a b d + - a b c)x +--R 42 6 2 3 2 +--R + +--R 5 4 3 10 3 4 3 5 2 5 4 3 2 5 6 5 2 +--R (- - a b d + -- a b c)x + (- 2a b d + - a b c)x + (- - a b d + a b c)x +--R 2 3 2 6 +--R + +--R 1 7 1 6 +--R - - a d + - a b c +--R 7 6 +--R / +--R 2 9 8 2 2 7 7 2 8 2 7 2 3 6 6 +--R (a d - 2a b c d + b c d )x + (7a c d - 14a b c d + 7b c d )x +--R + +--R 2 2 7 3 6 2 4 5 5 +--R (21a c d - 42a b c d + 21b c d )x +--R + +--R 2 3 6 4 5 2 5 4 4 +--R (35a c d - 70a b c d + 35b c d )x +--R + +--R 2 4 5 5 4 2 6 3 3 +--R (35a c d - 70a b c d + 35b c d )x +--R + +--R 2 5 4 6 3 2 7 2 2 2 6 3 7 2 2 8 +--R (21a c d - 42a b c d + 21b c d )x + (7a c d - 14a b c d + 7b c d)x +--R + +--R 2 7 2 8 2 9 +--R a c d - 2a b c d + b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1082 + +--S 1083 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R - 21b d x + (- 70a b d - 35b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 105a b d - 70a b c d - 35b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 84a b d - 63a b c d - 42a b c d - 21b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 35a b d - 28a b c d - 21a b c d - 14a b c d - 7b c d)x - 6a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 5a b c d - 4a b c d - 3a b c d - 2a b c d - b c +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 5 8 2 +--R 42d x + 294c d x + 882c d x + 1470c d x + 1470c d x + 882c d x +--R + +--R 6 7 7 6 +--R 294c d x + 42c d +--R Type: Union(Expression(Integer),...) +--E 1083 + +--S 1084 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 7 +--R b +--R (4) - ------------------------------ +--R 2 8 7 2 2 6 +--R 42a d - 84a b c d + 42b c d +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1085 + +)clear all + +--S 1086 of 2952 +t0000:=(a+b*x)^4/(c+d*x)^8 +--R +--R +--R (1) +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1086 + +--S 1087 of 2952 +r0000:=1/7*(a+b*x)^5/((b*c-a*d)*(c+d*x)^7)+_ + 1/21*b*(a+b*x)^5/((b*c-a*d)^2*(c+d*x)^6)+_ + 1/105*b^2*(a+b*x)^5/((b*c-a*d)^3*(c+d*x)^5) +--R +--R +--R (2) +--R 1 7 2 7 1 7 6 1 7 2 5 1 3 4 2 2 5 6 2 4 +--R - --- b d x - -- b c d x - - b c x + (- - a b d + a b c d - a b c )x +--R 105 15 5 3 +--R + +--R 4 3 2 8 3 4 2 5 2 3 6 5 2 2 4 3 3 4 2 2 +--R (- a b d + - a b c d - 2a b c )x + (- - a b d + 3a b c d - 2a b c )x +--R 3 5 +--R + +--R 2 6 2 8 5 2 4 3 2 1 7 2 1 6 1 5 2 2 +--R (- - a b d + - a b c d - a b c )x - - a d + - a b c d - - a b c +--R 3 5 7 3 5 +--R / +--R 3 10 2 9 2 2 8 3 3 7 7 +--R (a d - 3a b c d + 3a b c d - b c d )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 6 +--R (7a c d - 21a b c d + 21a b c d - 7b c d )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 5 +--R (21a c d - 63a b c d + 63a b c d - 21b c d )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (35a c d - 105a b c d + 105a b c d - 35b c d )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (35a c d - 105a b c d + 105a b c d - 35b c d )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (21a c d - 63a b c d + 63a b c d - 21b c d )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 2 8 2 +--R (7a c d - 21a b c d + 21a b c d - 7b c d)x + a c d - 3a b c d +--R + +--R 2 9 3 10 +--R 3a b c d - b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1087 + +--S 1088 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R - 35b d x + (- 105a b d - 35b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 126a b d - 63a b c d - 21b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 70a b d - 42a b c d - 21a b c d - 7b c d)x - 15a d - 10a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b c d - 3a b c d - b c +--R / +--R 12 7 11 6 2 10 5 3 9 4 4 8 3 +--R 105d x + 735c d x + 2205c d x + 3675c d x + 3675c d x +--R + +--R 5 7 2 6 6 7 5 +--R 2205c d x + 735c d x + 105c d +--R Type: Union(Expression(Integer),...) +--E 1088 + +--S 1089 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 7 +--R b +--R (4) ----------------------------------------------- +--R 3 8 2 7 2 2 6 3 3 5 +--R 105a d - 315a b c d + 315a b c d - 105b c d +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1090 + +)clear all + +--S 1091 of 2952 +t0000:=(a+b*x)^3/(c+d*x)^8 +--R +--R +--R (1) +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1091 + +--S 1092 of 2952 +r0000:=1/7*(b*c-a*d)^3/(d^4*(c+d*x)^7)-1/2*b*(b*c-a*d)^2/(d^4*(c+d*x)^6)+_ + 3/5*b^2*(b*c-a*d)/(d^4*(c+d*x)^5)-1/4*b^3/(d^4*(c+d*x)^4) +--R +--R +--R (2) +--R 1 3 3 3 3 2 3 3 3 2 2 +--R - - b d x + (- - a b d - -- b c d )x +--R 4 5 20 +--R + +--R 1 2 3 1 2 2 1 3 2 1 3 3 1 2 2 1 2 2 +--R (- - a b d - - a b c d - -- b c d)x - - a d - -- a b c d - -- a b c d +--R 2 5 20 7 14 35 +--R + +--R 1 3 3 +--R - --- b c +--R 140 +--R / +--R 11 7 10 6 2 9 5 3 8 4 4 7 3 5 6 2 6 5 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x +--R + +--R 7 4 +--R c d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1092 + +--S 1093 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 +--R - 35b d x + (- 84a b d - 21b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 3 3 +--R (- 70a b d - 28a b c d - 7b c d)x - 20a d - 10a b c d - 4a b c d - b c +--R / +--R 11 7 10 6 2 9 5 3 8 4 4 7 3 5 6 2 +--R 140d x + 980c d x + 2940c d x + 4900c d x + 4900c d x + 2940c d x +--R + +--R 6 5 7 4 +--R 980c d x + 140c d +--R Type: Union(Expression(Integer),...) +--E 1093 + +--S 1094 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1095 + +)clear all + +--S 1096 of 2952 +t0000:=(a+b*x)^2/(c+d*x)^8 +--R +--R +--R (1) +--R 2 2 2 +--R b x + 2a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1096 + +--S 1097 of 2952 +r0000:=-1/7*(b*c-a*d)^2/(d^3*(c+d*x)^7)+1/3*b*(b*c-a*d)/(d^3*(c+d*x)^6)-_ + 1/5*b^2/(d^3*(c+d*x)^5) +--R +--R +--R (2) +--R 1 2 2 2 1 2 1 2 1 2 2 1 1 2 2 +--R - - b d x + (- - a b d - -- b c d)x - - a d - -- a b c d - --- b c +--R 5 3 15 7 21 105 +--R --------------------------------------------------------------------------- +--R 10 7 9 6 2 8 5 3 7 4 4 6 3 5 5 2 6 4 7 3 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1097 + +--S 1098 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R - 21b d x + (- 35a b d - 7b c d)x - 15a d - 5a b c d - b c +--R / +--R 10 7 9 6 2 8 5 3 7 4 4 6 3 5 5 2 +--R 105d x + 735c d x + 2205c d x + 3675c d x + 3675c d x + 2205c d x +--R + +--R 6 4 7 3 +--R 735c d x + 105c d +--R Type: Union(Expression(Integer),...) +--E 1098 + +--S 1099 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1100 + +)clear all + +--S 1101 of 2952 +t0000:=(a+b*x)/(c+d*x)^8 +--R +--R +--R (1) +--R b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1101 + +--S 1102 of 2952 +r0000:=1/7*(b*c-a*d)/(d^2*(c+d*x)^7)-1/6*b/(d^2*(c+d*x)^6) +--R +--R +--R (2) +--R 1 1 1 +--R - - b d x - - a d - -- b c +--R 6 7 42 +--R -------------------------------------------------------------------------- +--R 9 7 8 6 2 7 5 3 6 4 4 5 3 5 4 2 6 3 7 2 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1102 + +--S 1103 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R - 7b d x - 6a d - b c +--R / +--R 9 7 8 6 2 7 5 3 6 4 4 5 3 5 4 2 +--R 42d x + 294c d x + 882c d x + 1470c d x + 1470c d x + 882c d x +--R + +--R 6 3 7 2 +--R 294c d x + 42c d +--R Type: Union(Expression(Integer),...) +--E 1103 + +--S 1104 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1105 + +)clear all + +--S 1106 of 2952 +t0000:=1/(c+d*x)^8 +--R +--R +--R (1) +--R 1 +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1106 + +--S 1107 of 2952 +r0000:=(-1/7)/(d*(c+d*x)^7) +--R +--R +--R (2) +--R 1 +--R - +--R 7 +--R - ------------------------------------------------------------------------- +--R 8 7 7 6 2 6 5 3 5 4 4 4 3 5 3 2 6 2 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1107 + +--S 1108 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R - +--R 1 +--R / +--R 8 7 7 6 2 6 5 3 5 4 4 4 3 5 3 2 +--R 7d x + 49c d x + 147c d x + 245c d x + 245c d x + 147c d x +--R + +--R 6 2 7 +--R 49c d x + 7c d +--R Type: Union(Expression(Integer),...) +--E 1108 + +--S 1109 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1110 + +)clear all + +--S 1111 of 2952 +t0000:=1/((a+b*x)*(c+d*x)^8) +--R +--R +--R (1) +--R 1 +--R / +--R 8 9 8 7 8 7 2 6 7 +--R b d x + (a d + 8b c d )x + (8a c d + 28b c d )x +--R + +--R 2 6 3 5 6 3 5 4 4 5 +--R (28a c d + 56b c d )x + (56a c d + 70b c d )x +--R + +--R 4 4 5 3 4 5 3 6 2 3 6 2 7 2 +--R (70a c d + 56b c d )x + (56a c d + 28b c d )x + (28a c d + 8b c d)x +--R + +--R 7 8 8 +--R (8a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1111 + +--S 1112 of 2952 +r0000:=1/7/((b*c-a*d)*(c+d*x)^7)+1/6*b/((b*c-a*d)^2*(c+d*x)^6)+_ + 1/5*b^2/((b*c-a*d)^3*(c+d*x)^5)+1/4*b^3/((b*c-a*d)^4*(c+d*x)^4)+_ + 1/3*b^4/((b*c-a*d)^5*(c+d*x)^3)+1/2*b^5/((b*c-a*d)^6*(c+d*x)^2)+_ + b^6/((b*c-a*d)^7*(c+d*x))+b^7*log(a+b*x)/(b*c-a*d)^8-_ + b^7*log(c+d*x)/(b*c-a*d)^8 +--R +--R +--R (2) +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R - 420b d x - 2940b c d x - 8820b c d x - 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R - 14700b c d x - 8820b c d x - 2940b c d x - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R 420b d x + 2940b c d x + 8820b c d x + 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R 14700b c d x + 8820b c d x + 2940b c d x + 420b c +--R * +--R log(b x + a) +--R + +--R 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R (- 420a b d + 420b c d )x + (210a b d - 2940a b c d + 2730b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 140a b d + 1470a b c d - 8820a b c d + 7490b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (105a b d - 980a b c d + 4410a b c d - 14700a b c d + 11165b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 84a b d + 735a b c d - 2940a b c d + 7350a b c d +--R + +--R 6 4 3 7 5 2 +--R - 14700a b c d + 9639b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 70a b d - 588a b c d + 2205a b c d - 4900a b c d + 7350a b c d +--R + +--R 6 5 2 7 6 +--R - 8820a b c d + 4683b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d + 490a b c d - 1764a b c d + 3675a b c d - 4900a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 4410a b c d - 2940a b c d + 1089b c +--R / +--R 8 15 7 14 6 2 2 13 5 3 3 12 +--R 420a d - 3360a b c d + 11760a b c d - 23520a b c d +--R + +--R 4 4 4 11 3 5 5 10 2 6 6 9 7 7 8 +--R 29400a b c d - 23520a b c d + 11760a b c d - 3360a b c d +--R + +--R 8 8 7 +--R 420b c d +--R * +--R 7 +--R x +--R + +--R 8 14 7 2 13 6 2 3 12 5 3 4 11 +--R 2940a c d - 23520a b c d + 82320a b c d - 164640a b c d +--R + +--R 4 4 5 10 3 5 6 9 2 6 7 8 7 8 7 +--R 205800a b c d - 164640a b c d + 82320a b c d - 23520a b c d +--R + +--R 8 9 6 +--R 2940b c d +--R * +--R 6 +--R x +--R + +--R 8 2 13 7 3 12 6 2 4 11 5 3 5 10 +--R 8820a c d - 70560a b c d + 246960a b c d - 493920a b c d +--R + +--R 4 4 6 9 3 5 7 8 2 6 8 7 7 9 6 +--R 617400a b c d - 493920a b c d + 246960a b c d - 70560a b c d +--R + +--R 8 10 5 +--R 8820b c d +--R * +--R 5 +--R x +--R + +--R 8 3 12 7 4 11 6 2 5 10 5 3 6 9 +--R 14700a c d - 117600a b c d + 411600a b c d - 823200a b c d +--R + +--R 4 4 7 8 3 5 8 7 2 6 9 6 7 10 5 +--R 1029000a b c d - 823200a b c d + 411600a b c d - 117600a b c d +--R + +--R 8 11 4 +--R 14700b c d +--R * +--R 4 +--R x +--R + +--R 8 4 11 7 5 10 6 2 6 9 5 3 7 8 +--R 14700a c d - 117600a b c d + 411600a b c d - 823200a b c d +--R + +--R 4 4 8 7 3 5 9 6 2 6 10 5 7 11 4 +--R 1029000a b c d - 823200a b c d + 411600a b c d - 117600a b c d +--R + +--R 8 12 3 +--R 14700b c d +--R * +--R 3 +--R x +--R + +--R 8 5 10 7 6 9 6 2 7 8 5 3 8 7 +--R 8820a c d - 70560a b c d + 246960a b c d - 493920a b c d +--R + +--R 4 4 9 6 3 5 10 5 2 6 11 4 7 12 3 +--R 617400a b c d - 493920a b c d + 246960a b c d - 70560a b c d +--R + +--R 8 13 2 +--R 8820b c d +--R * +--R 2 +--R x +--R + +--R 8 6 9 7 7 8 6 2 8 7 5 3 9 6 +--R 2940a c d - 23520a b c d + 82320a b c d - 164640a b c d +--R + +--R 4 4 10 5 3 5 11 4 2 6 12 3 7 13 2 +--R 205800a b c d - 164640a b c d + 82320a b c d - 23520a b c d +--R + +--R 8 14 +--R 2940b c d +--R * +--R x +--R + +--R 8 7 8 7 8 7 6 2 9 6 5 3 10 5 +--R 420a c d - 3360a b c d + 11760a b c d - 23520a b c d +--R + +--R 4 4 11 4 3 5 12 3 2 6 13 2 7 14 8 15 +--R 29400a b c d - 23520a b c d + 11760a b c d - 3360a b c d + 420b c +--R Type: Expression(Integer) +--E 1112 + +--S 1113 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R - 420b d x - 2940b c d x - 8820b c d x - 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R - 14700b c d x - 8820b c d x - 2940b c d x - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R 420b d x + 2940b c d x + 8820b c d x + 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R 14700b c d x + 8820b c d x + 2940b c d x + 420b c +--R * +--R log(b x + a) +--R + +--R 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R (- 420a b d + 420b c d )x + (210a b d - 2940a b c d + 2730b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 140a b d + 1470a b c d - 8820a b c d + 7490b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (105a b d - 980a b c d + 4410a b c d - 14700a b c d + 11165b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 84a b d + 735a b c d - 2940a b c d + 7350a b c d +--R + +--R 6 4 3 7 5 2 +--R - 14700a b c d + 9639b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 70a b d - 588a b c d + 2205a b c d - 4900a b c d + 7350a b c d +--R + +--R 6 5 2 7 6 +--R - 8820a b c d + 4683b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d + 490a b c d - 1764a b c d + 3675a b c d - 4900a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 4410a b c d - 2940a b c d + 1089b c +--R / +--R 8 15 7 14 6 2 2 13 5 3 3 12 +--R 420a d - 3360a b c d + 11760a b c d - 23520a b c d +--R + +--R 4 4 4 11 3 5 5 10 2 6 6 9 7 7 8 +--R 29400a b c d - 23520a b c d + 11760a b c d - 3360a b c d +--R + +--R 8 8 7 +--R 420b c d +--R * +--R 7 +--R x +--R + +--R 8 14 7 2 13 6 2 3 12 5 3 4 11 +--R 2940a c d - 23520a b c d + 82320a b c d - 164640a b c d +--R + +--R 4 4 5 10 3 5 6 9 2 6 7 8 7 8 7 +--R 205800a b c d - 164640a b c d + 82320a b c d - 23520a b c d +--R + +--R 8 9 6 +--R 2940b c d +--R * +--R 6 +--R x +--R + +--R 8 2 13 7 3 12 6 2 4 11 5 3 5 10 +--R 8820a c d - 70560a b c d + 246960a b c d - 493920a b c d +--R + +--R 4 4 6 9 3 5 7 8 2 6 8 7 7 9 6 +--R 617400a b c d - 493920a b c d + 246960a b c d - 70560a b c d +--R + +--R 8 10 5 +--R 8820b c d +--R * +--R 5 +--R x +--R + +--R 8 3 12 7 4 11 6 2 5 10 5 3 6 9 +--R 14700a c d - 117600a b c d + 411600a b c d - 823200a b c d +--R + +--R 4 4 7 8 3 5 8 7 2 6 9 6 7 10 5 +--R 1029000a b c d - 823200a b c d + 411600a b c d - 117600a b c d +--R + +--R 8 11 4 +--R 14700b c d +--R * +--R 4 +--R x +--R + +--R 8 4 11 7 5 10 6 2 6 9 5 3 7 8 +--R 14700a c d - 117600a b c d + 411600a b c d - 823200a b c d +--R + +--R 4 4 8 7 3 5 9 6 2 6 10 5 7 11 4 +--R 1029000a b c d - 823200a b c d + 411600a b c d - 117600a b c d +--R + +--R 8 12 3 +--R 14700b c d +--R * +--R 3 +--R x +--R + +--R 8 5 10 7 6 9 6 2 7 8 5 3 8 7 +--R 8820a c d - 70560a b c d + 246960a b c d - 493920a b c d +--R + +--R 4 4 9 6 3 5 10 5 2 6 11 4 7 12 3 +--R 617400a b c d - 493920a b c d + 246960a b c d - 70560a b c d +--R + +--R 8 13 2 +--R 8820b c d +--R * +--R 2 +--R x +--R + +--R 8 6 9 7 7 8 6 2 8 7 5 3 9 6 +--R 2940a c d - 23520a b c d + 82320a b c d - 164640a b c d +--R + +--R 4 4 10 5 3 5 11 4 2 6 12 3 7 13 2 +--R 205800a b c d - 164640a b c d + 82320a b c d - 23520a b c d +--R + +--R 8 14 +--R 2940b c d +--R * +--R x +--R + +--R 8 7 8 7 8 7 6 2 9 6 5 3 10 5 +--R 420a c d - 3360a b c d + 11760a b c d - 23520a b c d +--R + +--R 4 4 11 4 3 5 12 3 2 6 13 2 7 14 8 15 +--R 29400a b c d - 23520a b c d + 11760a b c d - 3360a b c d + 420b c +--R Type: Union(Expression(Integer),...) +--E 1113 + +--S 1114 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1115 + +)clear all + +--S 1116 of 2952 +t0000:=1/((a+b*x)^2*(c+d*x)^8) +--R +--R +--R (1) +--R 1 +--R / +--R 2 8 10 8 2 7 9 2 8 7 2 2 6 8 +--R b d x + (2a b d + 8b c d )x + (a d + 16a b c d + 28b c d )x +--R + +--R 2 7 2 6 2 3 5 7 +--R (8a c d + 56a b c d + 56b c d )x +--R + +--R 2 2 6 3 5 2 4 4 6 +--R (28a c d + 112a b c d + 70b c d )x +--R + +--R 2 3 5 4 4 2 5 3 5 +--R (56a c d + 140a b c d + 56b c d )x +--R + +--R 2 4 4 5 3 2 6 2 4 +--R (70a c d + 112a b c d + 28b c d )x +--R + +--R 2 5 3 6 2 2 7 3 2 6 2 7 2 8 2 +--R (56a c d + 56a b c d + 8b c d)x + (28a c d + 16a b c d + b c )x +--R + +--R 2 7 8 2 8 +--R (8a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1116 + +--S 1117 of 2952 +r0000:=-b^7/((b*c-a*d)^8*(a+b*x))-1/7*d/((b*c-a*d)^2*(c+d*x)^7)-_ + 1/3*b*d/((b*c-a*d)^3*(c+d*x)^6)-3/5*b^2*d/((b*c-a*d)^4*(c+d*x)^5)-_ + b^3*d/((b*c-a*d)^5*(c+d*x)^4)-5/3*b^4*d/((b*c-a*d)^6*(c+d*x)^3)-_ + 3*b^5*d/((b*c-a*d)^7*(c+d*x)^2)-7*b^6*d/((b*c-a*d)^8*(c+d*x))-_ + 8*b^7*d*log(a+b*x)/(b*c-a*d)^9+8*b^7*d*log(c+d*x)/(b*c-a*d)^9 +--R +--R +--R (2) +--R 8 8 8 7 8 8 7 7 +--R - 840b d x + (- 840a b d - 5880b c d )x +--R + +--R 7 7 8 2 6 6 7 2 6 8 3 5 5 +--R (- 5880a b c d - 17640b c d )x + (- 17640a b c d - 29400b c d )x +--R + +--R 7 3 5 8 4 4 4 7 4 4 8 5 3 3 +--R (- 29400a b c d - 29400b c d )x + (- 29400a b c d - 17640b c d )x +--R + +--R 7 5 3 8 6 2 2 7 6 2 8 7 +--R (- 17640a b c d - 5880b c d )x + (- 5880a b c d - 840b c d)x +--R + +--R 7 7 +--R - 840a b c d +--R * +--R log(d x + c) +--R + +--R 8 8 8 7 8 8 7 7 +--R 840b d x + (840a b d + 5880b c d )x +--R + +--R 7 7 8 2 6 6 7 2 6 8 3 5 5 +--R (5880a b c d + 17640b c d )x + (17640a b c d + 29400b c d )x +--R + +--R 7 3 5 8 4 4 4 7 4 4 8 5 3 3 +--R (29400a b c d + 29400b c d )x + (29400a b c d + 17640b c d )x +--R + +--R 7 5 3 8 6 2 2 7 6 2 8 7 +--R (17640a b c d + 5880b c d )x + (5880a b c d + 840b c d)x +--R + +--R 7 7 +--R 840a b c d +--R * +--R log(b x + a) +--R + +--R 7 8 8 7 7 2 6 8 7 7 8 2 6 6 +--R (- 840a b d + 840b c d )x + (- 420a b d - 5040a b c d + 5460b c d )x +--R + +--R 3 5 8 2 6 7 7 2 6 8 3 5 5 +--R (140a b d - 2940a b c d - 12180a b c d + 14980b c d )x +--R + +--R 4 4 8 3 5 7 2 6 2 6 7 3 5 8 4 4 4 +--R (- 70a b d + 980a b c d - 8820a b c d - 14420a b c d + 22330b c d )x +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 7 4 4 +--R 42a b d - 490a b c d + 2940a b c d - 14700a b c d - 7070a b c d +--R + +--R 8 5 3 +--R 19278b c d +--R * +--R 3 +--R x +--R + +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 +--R - 28a b d + 294a b c d - 1470a b c d + 4900a b c d +--R + +--R 2 6 4 4 7 5 3 8 6 2 +--R - 14700a b c d + 1638a b c d + 9366b c d +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R 20a b d - 196a b c d + 882a b c d - 2450a b c d + 4900a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R - 8820a b c d + 3486a b c d + 2178b c d +--R * +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R - 15a d + 140a b c d - 588a b c d + 1470a b c d - 2450a b c d +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R 2940a b c d - 2940a b c d + 1338a b c d + 105b c +--R / +--R 9 16 8 2 15 7 3 2 14 6 4 3 13 +--R 105a b d - 945a b c d + 3780a b c d - 8820a b c d +--R + +--R 5 5 4 12 4 6 5 11 3 7 6 10 2 8 7 9 +--R 13230a b c d - 13230a b c d + 8820a b c d - 3780a b c d +--R + +--R 9 8 8 10 9 7 +--R 945a b c d - 105b c d +--R * +--R 8 +--R x +--R + +--R 10 16 9 15 8 2 2 14 7 3 3 13 +--R 105a d - 210a b c d - 2835a b c d + 17640a b c d +--R + +--R 6 4 4 12 5 5 5 11 4 6 6 10 3 7 7 9 +--R - 48510a b c d + 79380a b c d - 83790a b c d + 57960a b c d +--R + +--R 2 8 8 8 9 9 7 10 10 6 +--R - 25515a b c d + 6510a b c d - 735b c d +--R * +--R 7 +--R x +--R + +--R 10 15 9 2 14 8 2 3 13 7 3 4 12 +--R 735a c d - 4410a b c d + 6615a b c d + 17640a b c d +--R + +--R 6 4 5 11 5 5 6 10 4 6 7 9 3 7 8 8 +--R - 92610a b c d + 185220a b c d - 216090a b c d + 158760a b c d +--R + +--R 2 8 9 7 9 10 6 10 11 5 +--R - 72765a b c d + 19110a b c d - 2205b c d +--R * +--R 6 +--R x +--R + +--R 10 2 14 9 3 13 8 2 4 12 7 3 5 11 +--R 2205a c d - 16170a b c d + 46305a b c d - 52920a b c d +--R + +--R 6 4 6 10 5 5 7 9 4 6 8 8 3 7 9 7 +--R - 30870a b c d + 185220a b c d - 277830a b c d + 229320a b c d +--R + +--R 2 8 10 6 9 11 5 10 12 4 +--R - 112455a b c d + 30870a b c d - 3675b c d +--R * +--R 5 +--R x +--R + +--R 10 3 13 9 4 12 8 2 5 11 7 3 6 10 +--R 3675a c d - 29400a b c d + 99225a b c d - 176400a b c d +--R + +--R 6 4 7 9 4 6 9 7 3 7 10 6 2 8 11 5 +--R 154350a b c d - 154350a b c d + 176400a b c d - 99225a b c d +--R + +--R 9 12 4 10 13 3 +--R 29400a b c d - 3675b c d +--R * +--R 4 +--R x +--R + +--R 10 4 12 9 5 11 8 2 6 10 7 3 7 9 +--R 3675a c d - 30870a b c d + 112455a b c d - 229320a b c d +--R + +--R 6 4 8 8 5 5 9 7 4 6 10 6 3 7 11 5 +--R 277830a b c d - 185220a b c d + 30870a b c d + 52920a b c d +--R + +--R 2 8 12 4 9 13 3 10 14 2 +--R - 46305a b c d + 16170a b c d - 2205b c d +--R * +--R 3 +--R x +--R + +--R 10 5 11 9 6 10 8 2 7 9 7 3 8 8 +--R 2205a c d - 19110a b c d + 72765a b c d - 158760a b c d +--R + +--R 6 4 9 7 5 5 10 6 4 6 11 5 3 7 12 4 +--R 216090a b c d - 185220a b c d + 92610a b c d - 17640a b c d +--R + +--R 2 8 13 3 9 14 2 10 15 +--R - 6615a b c d + 4410a b c d - 735b c d +--R * +--R 2 +--R x +--R + +--R 10 6 10 9 7 9 8 2 8 8 7 3 9 7 +--R 735a c d - 6510a b c d + 25515a b c d - 57960a b c d +--R + +--R 6 4 10 6 5 5 11 5 4 6 12 4 3 7 13 3 +--R 83790a b c d - 79380a b c d + 48510a b c d - 17640a b c d +--R + +--R 2 8 14 2 9 15 10 16 +--R 2835a b c d + 210a b c d - 105b c +--R * +--R x +--R + +--R 10 7 9 9 8 8 8 2 9 7 7 3 10 6 6 4 11 5 +--R 105a c d - 945a b c d + 3780a b c d - 8820a b c d + 13230a b c d +--R + +--R 5 5 12 4 4 6 13 3 3 7 14 2 2 8 15 9 16 +--R - 13230a b c d + 8820a b c d - 3780a b c d + 945a b c d - 105a b c +--R Type: Expression(Integer) +--E 1117 + +--S 1118 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 8 8 7 8 8 7 7 +--R - 840b d x + (- 840a b d - 5880b c d )x +--R + +--R 7 7 8 2 6 6 7 2 6 8 3 5 5 +--R (- 5880a b c d - 17640b c d )x + (- 17640a b c d - 29400b c d )x +--R + +--R 7 3 5 8 4 4 4 7 4 4 8 5 3 3 +--R (- 29400a b c d - 29400b c d )x + (- 29400a b c d - 17640b c d )x +--R + +--R 7 5 3 8 6 2 2 7 6 2 8 7 +--R (- 17640a b c d - 5880b c d )x + (- 5880a b c d - 840b c d)x +--R + +--R 7 7 +--R - 840a b c d +--R * +--R log(d x + c) +--R + +--R 8 8 8 7 8 8 7 7 +--R 840b d x + (840a b d + 5880b c d )x +--R + +--R 7 7 8 2 6 6 7 2 6 8 3 5 5 +--R (5880a b c d + 17640b c d )x + (17640a b c d + 29400b c d )x +--R + +--R 7 3 5 8 4 4 4 7 4 4 8 5 3 3 +--R (29400a b c d + 29400b c d )x + (29400a b c d + 17640b c d )x +--R + +--R 7 5 3 8 6 2 2 7 6 2 8 7 +--R (17640a b c d + 5880b c d )x + (5880a b c d + 840b c d)x +--R + +--R 7 7 +--R 840a b c d +--R * +--R log(b x + a) +--R + +--R 7 8 8 7 7 2 6 8 7 7 8 2 6 6 +--R (- 840a b d + 840b c d )x + (- 420a b d - 5040a b c d + 5460b c d )x +--R + +--R 3 5 8 2 6 7 7 2 6 8 3 5 5 +--R (140a b d - 2940a b c d - 12180a b c d + 14980b c d )x +--R + +--R 4 4 8 3 5 7 2 6 2 6 7 3 5 8 4 4 4 +--R (- 70a b d + 980a b c d - 8820a b c d - 14420a b c d + 22330b c d )x +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 7 4 4 +--R 42a b d - 490a b c d + 2940a b c d - 14700a b c d - 7070a b c d +--R + +--R 8 5 3 +--R 19278b c d +--R * +--R 3 +--R x +--R + +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 +--R - 28a b d + 294a b c d - 1470a b c d + 4900a b c d +--R + +--R 2 6 4 4 7 5 3 8 6 2 +--R - 14700a b c d + 1638a b c d + 9366b c d +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R 20a b d - 196a b c d + 882a b c d - 2450a b c d + 4900a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R - 8820a b c d + 3486a b c d + 2178b c d +--R * +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R - 15a d + 140a b c d - 588a b c d + 1470a b c d - 2450a b c d +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R 2940a b c d - 2940a b c d + 1338a b c d + 105b c +--R / +--R 9 16 8 2 15 7 3 2 14 6 4 3 13 +--R 105a b d - 945a b c d + 3780a b c d - 8820a b c d +--R + +--R 5 5 4 12 4 6 5 11 3 7 6 10 2 8 7 9 +--R 13230a b c d - 13230a b c d + 8820a b c d - 3780a b c d +--R + +--R 9 8 8 10 9 7 +--R 945a b c d - 105b c d +--R * +--R 8 +--R x +--R + +--R 10 16 9 15 8 2 2 14 7 3 3 13 +--R 105a d - 210a b c d - 2835a b c d + 17640a b c d +--R + +--R 6 4 4 12 5 5 5 11 4 6 6 10 3 7 7 9 +--R - 48510a b c d + 79380a b c d - 83790a b c d + 57960a b c d +--R + +--R 2 8 8 8 9 9 7 10 10 6 +--R - 25515a b c d + 6510a b c d - 735b c d +--R * +--R 7 +--R x +--R + +--R 10 15 9 2 14 8 2 3 13 7 3 4 12 +--R 735a c d - 4410a b c d + 6615a b c d + 17640a b c d +--R + +--R 6 4 5 11 5 5 6 10 4 6 7 9 3 7 8 8 +--R - 92610a b c d + 185220a b c d - 216090a b c d + 158760a b c d +--R + +--R 2 8 9 7 9 10 6 10 11 5 +--R - 72765a b c d + 19110a b c d - 2205b c d +--R * +--R 6 +--R x +--R + +--R 10 2 14 9 3 13 8 2 4 12 7 3 5 11 +--R 2205a c d - 16170a b c d + 46305a b c d - 52920a b c d +--R + +--R 6 4 6 10 5 5 7 9 4 6 8 8 3 7 9 7 +--R - 30870a b c d + 185220a b c d - 277830a b c d + 229320a b c d +--R + +--R 2 8 10 6 9 11 5 10 12 4 +--R - 112455a b c d + 30870a b c d - 3675b c d +--R * +--R 5 +--R x +--R + +--R 10 3 13 9 4 12 8 2 5 11 7 3 6 10 +--R 3675a c d - 29400a b c d + 99225a b c d - 176400a b c d +--R + +--R 6 4 7 9 4 6 9 7 3 7 10 6 2 8 11 5 +--R 154350a b c d - 154350a b c d + 176400a b c d - 99225a b c d +--R + +--R 9 12 4 10 13 3 +--R 29400a b c d - 3675b c d +--R * +--R 4 +--R x +--R + +--R 10 4 12 9 5 11 8 2 6 10 7 3 7 9 +--R 3675a c d - 30870a b c d + 112455a b c d - 229320a b c d +--R + +--R 6 4 8 8 5 5 9 7 4 6 10 6 3 7 11 5 +--R 277830a b c d - 185220a b c d + 30870a b c d + 52920a b c d +--R + +--R 2 8 12 4 9 13 3 10 14 2 +--R - 46305a b c d + 16170a b c d - 2205b c d +--R * +--R 3 +--R x +--R + +--R 10 5 11 9 6 10 8 2 7 9 7 3 8 8 +--R 2205a c d - 19110a b c d + 72765a b c d - 158760a b c d +--R + +--R 6 4 9 7 5 5 10 6 4 6 11 5 3 7 12 4 +--R 216090a b c d - 185220a b c d + 92610a b c d - 17640a b c d +--R + +--R 2 8 13 3 9 14 2 10 15 +--R - 6615a b c d + 4410a b c d - 735b c d +--R * +--R 2 +--R x +--R + +--R 10 6 10 9 7 9 8 2 8 8 7 3 9 7 +--R 735a c d - 6510a b c d + 25515a b c d - 57960a b c d +--R + +--R 6 4 10 6 5 5 11 5 4 6 12 4 3 7 13 3 +--R 83790a b c d - 79380a b c d + 48510a b c d - 17640a b c d +--R + +--R 2 8 14 2 9 15 10 16 +--R 2835a b c d + 210a b c d - 105b c +--R * +--R x +--R + +--R 10 7 9 9 8 8 8 2 9 7 7 3 10 6 6 4 11 5 +--R 105a c d - 945a b c d + 3780a b c d - 8820a b c d + 13230a b c d +--R + +--R 5 5 12 4 4 6 13 3 3 7 14 2 2 8 15 9 16 +--R - 13230a b c d + 8820a b c d - 3780a b c d + 945a b c d - 105a b c +--R Type: Union(Expression(Integer),...) +--E 1118 + +--S 1119 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1119 + +--S 1120 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1120 + +)clear all + +--S 1121 of 2952 +t0000:=1/((a+b*x)^3*(c+d*x)^8) +--R +--R +--R (1) +--R 1 +--R / +--R 3 8 11 2 8 3 7 10 2 8 2 7 3 2 6 9 +--R b d x + (3a b d + 8b c d )x + (3a b d + 24a b c d + 28b c d )x +--R + +--R 3 8 2 7 2 2 6 3 3 5 8 +--R (a d + 24a b c d + 84a b c d + 56b c d )x +--R + +--R 3 7 2 2 6 2 3 5 3 4 4 7 +--R (8a c d + 84a b c d + 168a b c d + 70b c d )x +--R + +--R 3 2 6 2 3 5 2 4 4 3 5 3 6 +--R (28a c d + 168a b c d + 210a b c d + 56b c d )x +--R + +--R 3 3 5 2 4 4 2 5 3 3 6 2 5 +--R (56a c d + 210a b c d + 168a b c d + 28b c d )x +--R + +--R 3 4 4 2 5 3 2 6 2 3 7 4 +--R (70a c d + 168a b c d + 84a b c d + 8b c d)x +--R + +--R 3 5 3 2 6 2 2 7 3 8 3 +--R (56a c d + 84a b c d + 24a b c d + b c )x +--R + +--R 3 6 2 2 7 2 8 2 3 7 2 8 3 8 +--R (28a c d + 24a b c d + 3a b c )x + (8a c d + 3a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1121 + +--S 1122 of 2952 +r0000:=-1/2*b^7/((b*c-a*d)^8*(a+b*x)^2)+8*b^7*d/((b*c-a*d)^9*(a+b*x))+_ + 1/7*d^2/((b*c-a*d)^3*(c+d*x)^7)+1/2*b*d^2/((b*c-a*d)^4*(c+d*x)^6)+_ + 6/5*b^2*d^2/((b*c-a*d)^5*(c+d*x)^5)+_ + 5/2*b^3*d^2/((b*c-a*d)^6*(c+d*x)^4)+_ + 5*b^4*d^2/((b*c-a*d)^7*(c+d*x)^3)+_ + 21/2*b^5*d^2/((b*c-a*d)^8*(c+d*x)^2)+_ + 28*b^6*d^2/((b*c-a*d)^9*(c+d*x))+_ + 36*b^7*d^2*log(a+b*x)/(b*c-a*d)^10-_ + 36*b^7*d^2*log(c+d*x)/(b*c-a*d)^10 +--R +--R +--R (2) +--R 9 9 9 8 9 9 8 8 +--R - 2520b d x + (- 5040a b d - 17640b c d )x +--R + +--R 2 7 9 8 8 9 2 7 7 +--R (- 2520a b d - 35280a b c d - 52920b c d )x +--R + +--R 2 7 8 8 2 7 9 3 6 6 +--R (- 17640a b c d - 105840a b c d - 88200b c d )x +--R + +--R 2 7 2 7 8 3 6 9 4 5 5 +--R (- 52920a b c d - 176400a b c d - 88200b c d )x +--R + +--R 2 7 3 6 8 4 5 9 5 4 4 +--R (- 88200a b c d - 176400a b c d - 52920b c d )x +--R + +--R 2 7 4 5 8 5 4 9 6 3 3 +--R (- 88200a b c d - 105840a b c d - 17640b c d )x +--R + +--R 2 7 5 4 8 6 3 9 7 2 2 +--R (- 52920a b c d - 35280a b c d - 2520b c d )x +--R + +--R 2 7 6 3 8 7 2 2 7 7 2 +--R (- 17640a b c d - 5040a b c d )x - 2520a b c d +--R * +--R log(d x + c) +--R + +--R 9 9 9 8 9 9 8 8 +--R 2520b d x + (5040a b d + 17640b c d )x +--R + +--R 2 7 9 8 8 9 2 7 7 +--R (2520a b d + 35280a b c d + 52920b c d )x +--R + +--R 2 7 8 8 2 7 9 3 6 6 +--R (17640a b c d + 105840a b c d + 88200b c d )x +--R + +--R 2 7 2 7 8 3 6 9 4 5 5 +--R (52920a b c d + 176400a b c d + 88200b c d )x +--R + +--R 2 7 3 6 8 4 5 9 5 4 4 +--R (88200a b c d + 176400a b c d + 52920b c d )x +--R + +--R 2 7 4 5 8 5 4 9 6 3 3 +--R (88200a b c d + 105840a b c d + 17640b c d )x +--R + +--R 2 7 5 4 8 6 3 9 7 2 2 +--R (52920a b c d + 35280a b c d + 2520b c d )x +--R + +--R 2 7 6 3 8 7 2 2 7 7 2 +--R (17640a b c d + 5040a b c d )x + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 8 9 9 8 8 +--R (- 2520a b d + 2520b c d )x +--R + +--R 2 7 9 8 8 9 2 7 7 +--R (- 3780a b d - 12600a b c d + 16380b c d )x +--R + +--R 3 6 9 2 7 8 8 2 7 9 3 6 6 +--R (- 840a b d - 23940a b c d - 20160a b c d + 44940b c d )x +--R + +--R 4 5 9 3 6 8 2 7 2 7 8 3 6 9 4 5 5 +--R (210a b d - 5880a b c d - 63000a b c d + 1680a b c d + 66990b c d )x +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 +--R - 84a b d + 1470a b c d - 17640a b c d - 87360a b c d +--R + +--R 8 4 5 9 5 4 +--R 45780a b c d + 57834b c d +--R * +--R 4 +--R x +--R + +--R 6 3 9 5 4 8 4 5 2 7 3 6 3 6 2 7 4 5 +--R 42a b d - 588a b c d + 4410a b c d - 29400a b c d - 65310a b c d +--R + +--R 8 5 4 9 6 3 +--R 62748a b c d + 28098b c d +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 +--R - 24a b d + 294a b c d - 1764a b c d + 7350a b c d +--R + +--R 3 6 4 5 2 7 5 4 8 6 3 9 7 2 +--R - 29400a b c d - 21546a b c d + 38556a b c d + 6534b c d +--R * +--R 2 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 4 5 4 5 +--R 15a b d - 168a b c d + 882a b c d - 2940a b c d + 7350a b c d +--R + +--R 3 6 5 4 2 7 6 3 8 7 2 9 8 +--R - 17640a b c d + 1638a b c d + 10548a b c d + 315b c d +--R * +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 +--R - 10a d + 105a b c d - 504a b c d + 1470a b c d - 2940a b c d +--R + +--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9 +--R 4410a b c d - 5880a b c d + 2754a b c d + 630a b c d - 35b c +--R / +--R 10 2 17 9 3 16 8 4 2 15 7 5 3 14 +--R 70a b d - 700a b c d + 3150a b c d - 8400a b c d +--R + +--R 6 6 4 13 5 7 5 12 4 8 6 11 3 9 7 10 +--R 14700a b c d - 17640a b c d + 14700a b c d - 8400a b c d +--R + +--R 2 10 8 9 11 9 8 12 10 7 +--R 3150a b c d - 700a b c d + 70b c d +--R * +--R 9 +--R x +--R + +--R 11 17 10 2 16 9 3 2 15 8 4 3 14 +--R 140a b d - 910a b c d + 1400a b c d + 5250a b c d +--R + +--R 7 5 4 13 6 6 5 12 5 7 6 11 4 8 7 10 +--R - 29400a b c d + 67620a b c d - 94080a b c d + 86100a b c d +--R + +--R 3 9 8 9 2 10 9 8 11 10 7 12 11 6 +--R - 52500a b c d + 20650a b c d - 4760a b c d + 490b c d +--R * +--R 8 +--R x +--R + +--R 12 17 11 16 10 2 2 15 9 3 3 14 +--R 70a d + 280a b c d - 5180a b c d + 21000a b c d +--R + +--R 8 4 4 13 7 5 5 12 6 6 6 11 5 7 7 10 +--R - 36750a b c d + 11760a b c d + 76440a b c d - 173040a b c d +--R + +--R 4 8 8 9 3 9 9 8 2 10 10 7 11 11 6 +--R 194250a b c d - 133000a b c d + 56420a b c d - 13720a b c d +--R + +--R 12 12 5 +--R 1470b c d +--R * +--R 7 +--R x +--R + +--R 12 16 11 2 15 10 2 3 14 9 3 4 13 +--R 490a c d - 1960a b c d - 4900a b c d + 49000a b c d +--R + +--R 8 4 5 12 7 5 6 11 6 6 7 10 5 7 8 9 +--R - 139650a b c d + 199920a b c d - 123480a b c d - 58800a b c d +--R + +--R 4 8 9 8 3 9 10 7 2 10 11 6 11 12 5 +--R 183750a b c d - 166600a b c d + 81340a b c d - 21560a b c d +--R + +--R 12 13 4 +--R 2450b c d +--R * +--R 6 +--R x +--R + +--R 12 2 15 11 3 14 10 2 4 13 9 3 5 12 +--R 1470a c d - 9800a b c d + 19600a b c d + 19600a b c d +--R + +--R 8 4 6 11 7 5 7 10 6 6 8 9 5 7 9 8 +--R - 169050a b c d + 364560a b c d - 411600a b c d + 235200a b c d +--R + +--R 4 8 10 7 3 9 11 6 2 10 12 5 11 13 4 +--R - 7350a b c d - 88200a b c d + 62720a b c d - 19600a b c d +--R + +--R 12 14 3 +--R 2450b c d +--R * +--R 5 +--R x +--R + +--R 12 3 14 11 4 13 10 2 5 12 9 3 6 11 +--R 2450a c d - 19600a b c d + 62720a b c d - 88200a b c d +--R + +--R 8 4 7 10 7 5 8 9 6 6 9 8 5 7 10 7 +--R - 7350a b c d + 235200a b c d - 411600a b c d + 364560a b c d +--R + +--R 4 8 11 6 3 9 12 5 2 10 13 4 11 14 3 +--R - 169050a b c d + 19600a b c d + 19600a b c d - 9800a b c d +--R + +--R 12 15 2 +--R 1470b c d +--R * +--R 4 +--R x +--R + +--R 12 4 13 11 5 12 10 2 6 11 9 3 7 10 +--R 2450a c d - 21560a b c d + 81340a b c d - 166600a b c d +--R + +--R 8 4 8 9 7 5 9 8 6 6 10 7 5 7 11 6 +--R 183750a b c d - 58800a b c d - 123480a b c d + 199920a b c d +--R + +--R 4 8 12 5 3 9 13 4 2 10 14 3 11 15 2 +--R - 139650a b c d + 49000a b c d - 4900a b c d - 1960a b c d +--R + +--R 12 16 +--R 490b c d +--R * +--R 3 +--R x +--R + +--R 12 5 12 11 6 11 10 2 7 10 9 3 8 9 +--R 1470a c d - 13720a b c d + 56420a b c d - 133000a b c d +--R + +--R 8 4 9 8 7 5 10 7 6 6 11 6 5 7 12 5 +--R 194250a b c d - 173040a b c d + 76440a b c d + 11760a b c d +--R + +--R 4 8 13 4 3 9 14 3 2 10 15 2 11 16 +--R - 36750a b c d + 21000a b c d - 5180a b c d + 280a b c d +--R + +--R 12 17 +--R 70b c +--R * +--R 2 +--R x +--R + +--R 12 6 11 11 7 10 10 2 8 9 9 3 9 8 +--R 490a c d - 4760a b c d + 20650a b c d - 52500a b c d +--R + +--R 8 4 10 7 7 5 11 6 6 6 12 5 5 7 13 4 +--R 86100a b c d - 94080a b c d + 67620a b c d - 29400a b c d +--R + +--R 4 8 14 3 3 9 15 2 2 10 16 11 17 +--R 5250a b c d + 1400a b c d - 910a b c d + 140a b c +--R * +--R x +--R + +--R 12 7 10 11 8 9 10 2 9 8 9 3 10 7 +--R 70a c d - 700a b c d + 3150a b c d - 8400a b c d +--R + +--R 8 4 11 6 7 5 12 5 6 6 13 4 5 7 14 3 +--R 14700a b c d - 17640a b c d + 14700a b c d - 8400a b c d +--R + +--R 4 8 15 2 3 9 16 2 10 17 +--R 3150a b c d - 700a b c d + 70a b c +--R Type: Expression(Integer) +--E 1122 + +--S 1123 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 9 9 9 8 9 9 8 8 +--R - 2520b d x + (- 5040a b d - 17640b c d )x +--R + +--R 2 7 9 8 8 9 2 7 7 +--R (- 2520a b d - 35280a b c d - 52920b c d )x +--R + +--R 2 7 8 8 2 7 9 3 6 6 +--R (- 17640a b c d - 105840a b c d - 88200b c d )x +--R + +--R 2 7 2 7 8 3 6 9 4 5 5 +--R (- 52920a b c d - 176400a b c d - 88200b c d )x +--R + +--R 2 7 3 6 8 4 5 9 5 4 4 +--R (- 88200a b c d - 176400a b c d - 52920b c d )x +--R + +--R 2 7 4 5 8 5 4 9 6 3 3 +--R (- 88200a b c d - 105840a b c d - 17640b c d )x +--R + +--R 2 7 5 4 8 6 3 9 7 2 2 +--R (- 52920a b c d - 35280a b c d - 2520b c d )x +--R + +--R 2 7 6 3 8 7 2 2 7 7 2 +--R (- 17640a b c d - 5040a b c d )x - 2520a b c d +--R * +--R log(d x + c) +--R + +--R 9 9 9 8 9 9 8 8 +--R 2520b d x + (5040a b d + 17640b c d )x +--R + +--R 2 7 9 8 8 9 2 7 7 +--R (2520a b d + 35280a b c d + 52920b c d )x +--R + +--R 2 7 8 8 2 7 9 3 6 6 +--R (17640a b c d + 105840a b c d + 88200b c d )x +--R + +--R 2 7 2 7 8 3 6 9 4 5 5 +--R (52920a b c d + 176400a b c d + 88200b c d )x +--R + +--R 2 7 3 6 8 4 5 9 5 4 4 +--R (88200a b c d + 176400a b c d + 52920b c d )x +--R + +--R 2 7 4 5 8 5 4 9 6 3 3 +--R (88200a b c d + 105840a b c d + 17640b c d )x +--R + +--R 2 7 5 4 8 6 3 9 7 2 2 +--R (52920a b c d + 35280a b c d + 2520b c d )x +--R + +--R 2 7 6 3 8 7 2 2 7 7 2 +--R (17640a b c d + 5040a b c d )x + 2520a b c d +--R * +--R log(b x + a) +--R + +--R 8 9 9 8 8 +--R (- 2520a b d + 2520b c d )x +--R + +--R 2 7 9 8 8 9 2 7 7 +--R (- 3780a b d - 12600a b c d + 16380b c d )x +--R + +--R 3 6 9 2 7 8 8 2 7 9 3 6 6 +--R (- 840a b d - 23940a b c d - 20160a b c d + 44940b c d )x +--R + +--R 4 5 9 3 6 8 2 7 2 7 8 3 6 9 4 5 5 +--R (210a b d - 5880a b c d - 63000a b c d + 1680a b c d + 66990b c d )x +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 +--R - 84a b d + 1470a b c d - 17640a b c d - 87360a b c d +--R + +--R 8 4 5 9 5 4 +--R 45780a b c d + 57834b c d +--R * +--R 4 +--R x +--R + +--R 6 3 9 5 4 8 4 5 2 7 3 6 3 6 2 7 4 5 +--R 42a b d - 588a b c d + 4410a b c d - 29400a b c d - 65310a b c d +--R + +--R 8 5 4 9 6 3 +--R 62748a b c d + 28098b c d +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 +--R - 24a b d + 294a b c d - 1764a b c d + 7350a b c d +--R + +--R 3 6 4 5 2 7 5 4 8 6 3 9 7 2 +--R - 29400a b c d - 21546a b c d + 38556a b c d + 6534b c d +--R * +--R 2 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 4 5 4 5 +--R 15a b d - 168a b c d + 882a b c d - 2940a b c d + 7350a b c d +--R + +--R 3 6 5 4 2 7 6 3 8 7 2 9 8 +--R - 17640a b c d + 1638a b c d + 10548a b c d + 315b c d +--R * +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 +--R - 10a d + 105a b c d - 504a b c d + 1470a b c d - 2940a b c d +--R + +--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9 +--R 4410a b c d - 5880a b c d + 2754a b c d + 630a b c d - 35b c +--R / +--R 10 2 17 9 3 16 8 4 2 15 7 5 3 14 +--R 70a b d - 700a b c d + 3150a b c d - 8400a b c d +--R + +--R 6 6 4 13 5 7 5 12 4 8 6 11 3 9 7 10 +--R 14700a b c d - 17640a b c d + 14700a b c d - 8400a b c d +--R + +--R 2 10 8 9 11 9 8 12 10 7 +--R 3150a b c d - 700a b c d + 70b c d +--R * +--R 9 +--R x +--R + +--R 11 17 10 2 16 9 3 2 15 8 4 3 14 +--R 140a b d - 910a b c d + 1400a b c d + 5250a b c d +--R + +--R 7 5 4 13 6 6 5 12 5 7 6 11 4 8 7 10 +--R - 29400a b c d + 67620a b c d - 94080a b c d + 86100a b c d +--R + +--R 3 9 8 9 2 10 9 8 11 10 7 12 11 6 +--R - 52500a b c d + 20650a b c d - 4760a b c d + 490b c d +--R * +--R 8 +--R x +--R + +--R 12 17 11 16 10 2 2 15 9 3 3 14 +--R 70a d + 280a b c d - 5180a b c d + 21000a b c d +--R + +--R 8 4 4 13 7 5 5 12 6 6 6 11 5 7 7 10 +--R - 36750a b c d + 11760a b c d + 76440a b c d - 173040a b c d +--R + +--R 4 8 8 9 3 9 9 8 2 10 10 7 11 11 6 +--R 194250a b c d - 133000a b c d + 56420a b c d - 13720a b c d +--R + +--R 12 12 5 +--R 1470b c d +--R * +--R 7 +--R x +--R + +--R 12 16 11 2 15 10 2 3 14 9 3 4 13 +--R 490a c d - 1960a b c d - 4900a b c d + 49000a b c d +--R + +--R 8 4 5 12 7 5 6 11 6 6 7 10 5 7 8 9 +--R - 139650a b c d + 199920a b c d - 123480a b c d - 58800a b c d +--R + +--R 4 8 9 8 3 9 10 7 2 10 11 6 11 12 5 +--R 183750a b c d - 166600a b c d + 81340a b c d - 21560a b c d +--R + +--R 12 13 4 +--R 2450b c d +--R * +--R 6 +--R x +--R + +--R 12 2 15 11 3 14 10 2 4 13 9 3 5 12 +--R 1470a c d - 9800a b c d + 19600a b c d + 19600a b c d +--R + +--R 8 4 6 11 7 5 7 10 6 6 8 9 5 7 9 8 +--R - 169050a b c d + 364560a b c d - 411600a b c d + 235200a b c d +--R + +--R 4 8 10 7 3 9 11 6 2 10 12 5 11 13 4 +--R - 7350a b c d - 88200a b c d + 62720a b c d - 19600a b c d +--R + +--R 12 14 3 +--R 2450b c d +--R * +--R 5 +--R x +--R + +--R 12 3 14 11 4 13 10 2 5 12 9 3 6 11 +--R 2450a c d - 19600a b c d + 62720a b c d - 88200a b c d +--R + +--R 8 4 7 10 7 5 8 9 6 6 9 8 5 7 10 7 +--R - 7350a b c d + 235200a b c d - 411600a b c d + 364560a b c d +--R + +--R 4 8 11 6 3 9 12 5 2 10 13 4 11 14 3 +--R - 169050a b c d + 19600a b c d + 19600a b c d - 9800a b c d +--R + +--R 12 15 2 +--R 1470b c d +--R * +--R 4 +--R x +--R + +--R 12 4 13 11 5 12 10 2 6 11 9 3 7 10 +--R 2450a c d - 21560a b c d + 81340a b c d - 166600a b c d +--R + +--R 8 4 8 9 7 5 9 8 6 6 10 7 5 7 11 6 +--R 183750a b c d - 58800a b c d - 123480a b c d + 199920a b c d +--R + +--R 4 8 12 5 3 9 13 4 2 10 14 3 11 15 2 +--R - 139650a b c d + 49000a b c d - 4900a b c d - 1960a b c d +--R + +--R 12 16 +--R 490b c d +--R * +--R 3 +--R x +--R + +--R 12 5 12 11 6 11 10 2 7 10 9 3 8 9 +--R 1470a c d - 13720a b c d + 56420a b c d - 133000a b c d +--R + +--R 8 4 9 8 7 5 10 7 6 6 11 6 5 7 12 5 +--R 194250a b c d - 173040a b c d + 76440a b c d + 11760a b c d +--R + +--R 4 8 13 4 3 9 14 3 2 10 15 2 11 16 +--R - 36750a b c d + 21000a b c d - 5180a b c d + 280a b c d +--R + +--R 12 17 +--R 70b c +--R * +--R 2 +--R x +--R + +--R 12 6 11 11 7 10 10 2 8 9 9 3 9 8 +--R 490a c d - 4760a b c d + 20650a b c d - 52500a b c d +--R + +--R 8 4 10 7 7 5 11 6 6 6 12 5 5 7 13 4 +--R 86100a b c d - 94080a b c d + 67620a b c d - 29400a b c d +--R + +--R 4 8 14 3 3 9 15 2 2 10 16 11 17 +--R 5250a b c d + 1400a b c d - 910a b c d + 140a b c +--R * +--R x +--R + +--R 12 7 10 11 8 9 10 2 9 8 9 3 10 7 +--R 70a c d - 700a b c d + 3150a b c d - 8400a b c d +--R + +--R 8 4 11 6 7 5 12 5 6 6 13 4 5 7 14 3 +--R 14700a b c d - 17640a b c d + 14700a b c d - 8400a b c d +--R + +--R 4 8 15 2 3 9 16 2 10 17 +--R 3150a b c d - 700a b c d + 70a b c +--R Type: Union(Expression(Integer),...) +--E 1123 + +--S 1124 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1125 + +)clear all + +--S 1126 of 2952 +t0000:=(a+b*x)^5*(c+d*x)^(1/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|d x + c +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 2952 +r0000:=-2/3*(b*c-a*d)^5*(c+d*x)^(3/2)/d^6+2*b*(b*c-a*d)^4*(c+d*x)^(5/2)/d^6-_ + 20/7*b^2*(b*c-a*d)^3*(c+d*x)^(7/2)/d^6+_ + 20/9*b^3*(b*c-a*d)^2*(c+d*x)^(9/2)/d^6-_ + 10/11*b^4*(b*c-a*d)*(c+d*x)^(11/2)/d^6+2/13*b^5*(c+d*x)^(13/2)/d^6 +--R +--R +--R (2) +--R 5 6 6 4 6 5 5 5 +--R 1386b d x + (8190a b d + 126b c d )x +--R + +--R 2 3 6 4 5 5 2 4 4 +--R (20020a b d + 910a b c d - 140b c d )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (25740a b d + 2860a b c d - 1040a b c d + 160b c d )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 18018a b d + 5148a b c d - 3432a b c d + 1248a b c d +--R + +--R 5 4 2 +--R - 192b c d +--R * +--R 2 +--R x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 6006a d + 6006a b c d - 6864a b c d + 4576a b c d +--R + +--R 4 4 2 5 5 +--R - 1664a b c d + 256b c d +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 6006a c d - 12012a b c d + 13728a b c d - 9152a b c d + 3328a b c d +--R + +--R 5 6 +--R - 512b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 +--R 9009d +--R Type: Expression(Integer) +--E 1127 + +--S 1128 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 6 6 4 6 5 5 5 +--R 1386b d x + (8190a b d + 126b c d )x +--R + +--R 2 3 6 4 5 5 2 4 4 +--R (20020a b d + 910a b c d - 140b c d )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (25740a b d + 2860a b c d - 1040a b c d + 160b c d )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 +--R 18018a b d + 5148a b c d - 3432a b c d + 1248a b c d +--R + +--R 5 4 2 +--R - 192b c d +--R * +--R 2 +--R x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 +--R 6006a d + 6006a b c d - 6864a b c d + 4576a b c d +--R + +--R 4 4 2 5 5 +--R - 1664a b c d + 256b c d +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 6006a c d - 12012a b c d + 13728a b c d - 9152a b c d + 3328a b c d +--R + +--R 5 6 +--R - 512b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 +--R 9009d +--R Type: Union(Expression(Integer),...) +--E 1128 + +--S 1129 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1130 + +)clear all + +--S 1131 of 2952 +t0000:=(a+b*x)^4*(c+d*x)^(1/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (1) (b x + 4a b x + 6a b x + 4a b x + a )\|d x + c +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 2952 +r0000:=2/3*(b*c-a*d)^4*(c+d*x)^(3/2)/d^5-_ + 8/5*b*(b*c-a*d)^3*(c+d*x)^(5/2)/d^5+_ + 12/7*b^2*(b*c-a*d)^2*(c+d*x)^(7/2)/d^5-_ + 8/9*b^3*(b*c-a*d)*(c+d*x)^(9/2)/d^5+2/11*b^4*(c+d*x)^(11/2)/d^5 +--R +--R +--R (2) +--R 4 5 5 3 5 4 4 4 +--R 630b d x + (3080a b d + 70b c d )x +--R + +--R 2 2 5 3 4 4 2 3 3 +--R (5940a b d + 440a b c d - 80b c d )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (5544a b d + 1188a b c d - 528a b c d + 96b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (2310a d + 1848a b c d - 1584a b c d + 704a b c d - 128b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R 2310a c d - 3696a b c d + 3168a b c d - 1408a b c d + 256b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 +--R 3465d +--R Type: Expression(Integer) +--E 1132 + +--S 1133 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 5 5 3 5 4 4 4 +--R 630b d x + (3080a b d + 70b c d )x +--R + +--R 2 2 5 3 4 4 2 3 3 +--R (5940a b d + 440a b c d - 80b c d )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (5544a b d + 1188a b c d - 528a b c d + 96b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (2310a d + 1848a b c d - 1584a b c d + 704a b c d - 128b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R 2310a c d - 3696a b c d + 3168a b c d - 1408a b c d + 256b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 +--R 3465d +--R Type: Union(Expression(Integer),...) +--E 1133 + +--S 1134 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1135 + +)clear all + +--S 1136 of 2952 +t0000:=(a+b*x)^3*(c+d*x)^(1/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (1) (b x + 3a b x + 3a b x + a )\|d x + c +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 2952 +r0000:=-2/3*(b*c-a*d)^3*(c+d*x)^(3/2)/d^4+_ + 6/5*b*(b*c-a*d)^2*(c+d*x)^(5/2)/d^4-_ + 6/7*b^2*(b*c-a*d)*(c+d*x)^(7/2)/d^4+2/9*b^3*(c+d*x)^(9/2)/d^4 +--R +--R +--R (2) +--R 3 4 4 2 4 3 3 3 +--R 70b d x + (270a b d + 10b c d )x +--R + +--R 2 4 2 3 3 2 2 2 +--R (378a b d + 54a b c d - 12b c d )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 +--R (210a d + 126a b c d - 72a b c d + 16b c d)x + 210a c d +--R + +--R 2 2 2 2 3 3 4 +--R - 252a b c d + 144a b c d - 32b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 +--R 315d +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 4 4 2 4 3 3 3 +--R 70b d x + (270a b d + 10b c d )x +--R + +--R 2 4 2 3 3 2 2 2 +--R (378a b d + 54a b c d - 12b c d )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 +--R (210a d + 126a b c d - 72a b c d + 16b c d)x + 210a c d +--R + +--R 2 2 2 2 3 3 4 +--R - 252a b c d + 144a b c d - 32b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 +--R 315d +--R Type: Union(Expression(Integer),...) +--E 1138 + +--S 1139 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1140 + +)clear all + +--S 1141 of 2952 +t0000:=(a+b*x)^2*(c+d*x)^(1/2) +--R +--R +--R 2 2 2 +-------+ +--R (1) (b x + 2a b x + a )\|d x + c +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 2952 +r0000:=2/3*(b*c-a*d)^2*(c+d*x)^(3/2)/d^3-4/5*b*(b*c-a*d)*(c+d*x)^(5/2)/d^3+_ + 2/7*b^2*(c+d*x)^(7/2)/d^3 +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 30b d x + (84a b d + 6b c d )x + (70a d + 28a b c d - 8b c d)x +--R + +--R 2 2 2 2 3 +--R 70a c d - 56a b c d + 16b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +--R 105d +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 30b d x + (84a b d + 6b c d )x + (70a d + 28a b c d - 8b c d)x +--R + +--R 2 2 2 2 3 +--R 70a c d - 56a b c d + 16b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +--R 105d +--R Type: Union(Expression(Integer),...) +--E 1143 + +--S 1144 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1145 + +)clear all + +--S 1146 of 2952 +t0000:=(a+b*x)*(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R (1) (b x + a)\|d x + c +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 2952 +r0000:=-2/3*(b*c-a*d)*(c+d*x)^(3/2)/d^2+2/5*b*(c+d*x)^(5/2)/d^2 +--R +--R +--R 2 2 2 2 +-------+ +--R (6b d x + (10a d + 2b c d)x + 10a c d - 4b c )\|d x + c +--R (2) ---------------------------------------------------------- +--R 2 +--R 15d +--R Type: Expression(Integer) +--E 1147 + +--S 1148 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 +-------+ +--R (6b d x + (10a d + 2b c d)x + 10a c d - 4b c )\|d x + c +--R (3) ---------------------------------------------------------- +--R 2 +--R 15d +--R Type: Union(Expression(Integer),...) +--E 1148 + +--S 1149 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1150 + +)clear all + +--S 1151 of 2952 +t0000:=(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R (1) \|d x + c +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 2952 +r0000:=2/3*(c+d*x)^(3/2)/d +--R +--R +--R +-------+ +--R (2d x + 2c)\|d x + c +--R (2) --------------------- +--R 3d +--R Type: Expression(Integer) +--E 1152 + +--S 1153 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +--R (2d x + 2c)\|d x + c +--R (3) --------------------- +--R 3d +--R Type: Union(Expression(Integer),...) +--E 1153 + +--S 1154 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1155 + +)clear all + +--S 1156 of 2952 +t0000:=(c+d*x)^(1/2)/(a+b*x) +--R +--R +--R +-------+ +--R \|d x + c +--R (1) ---------- +--R b x + a +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 2952 +r0000:=-2*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b*c-a*d)/_ + b^(3/2)+2*sqrt(c+d*x)/b +--R +--R +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +-+ +-------+ +--R - 2\|- a d + b c atanh(--------------) + 2\|b \|d x + c +--R +-----------+ +--R \|- a d + b c +--R (2) -------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ - 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R +-------+ +--R 2\|d x + c +--R / +--R b +--R , +--R +---------+ +-------+ +--R |a d - b c \|d x + c +-------+ +--R - 2 |--------- atan(------------ + 2\|d x + c +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R -----------------------------------------------] +--R b +--R Type: Union(List(Expression(Integer)),...) +--E 1158 + +--S 1159 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ - 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c +-+ \| b +--R |----------- \|b log(-------------------------------------------------) +--R \| b b x + a +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R 2\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +---------+ +-------+ +--R +-----------+ \|b \|d x + c +-+ |a d - b c \|d x + c +--R 2\|- a d + b c atanh(--------------) - 2\|b |--------- atan(------------) +--R +-----------+ \| b +---------+ +--R \|- a d + b c |a d - b c +--R |--------- +--R \| b +--R -------------------------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1162 + +)clear all + +--S 1163 of 2952 +t0000:=(c+d*x)^(1/2)/(a+b*x)^2 +--R +--R +--R +-------+ +--R \|d x + c +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 2952 +r0000:=-d*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(3/2)*sqrt(b*c-a*d))-_ + sqrt(c+d*x)/(b*(a+b*x)) +--R +--R +--R +-+ +-------+ +--R \|b \|d x + c +-----------+ +-+ +-------+ +--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 +-----------+ +-+ +--R (b x + a b)\|- a d + b c \|b +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R (b d x + a d) +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b d + b c \|d x + c +--R / +--R +-------------+ +--R 2 | 2 +--R (2b x + 2a b)\|- a b d + b c +--R , +--R +-----------+ +--R | 2 +-------+ +-----------+ +--R \|a b d - b c \|d x + c | 2 +-------+ +--R (b d x + a d)atan(------------------------) - \|a b d - b c \|d x + c +--R a d - b c +--R ----------------------------------------------------------------------] +--R +-----------+ +--R 2 | 2 +--R (b x + a b)\|a b d - b c +--R Type: Union(List(Expression(Integer)),...) +--E 1165 + +--S 1166 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +-+ +--R d\|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|d x + c +--R 2d\|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R | 2 +-----------+ +-+ +--R 2b\|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|d x + c +--R d\|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b d - b c \|d x + c +--R d\|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R +-----------+ +--R +-----------+ +-+ | 2 +--R b\|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1168 + +--S 1169 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1169 + +)clear all + +--S 1170 of 2952 +t0000:=(c+d*x)^(1/2)/(a+b*x)^3 +--R +--R +--R +-------+ +--R \|d x + c +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 2952 +r0000:=1/4*d^2*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (b^(3/2)*(b*c-a*d)^(3/2))-1/2*sqrt(c+d*x)/(b*(a+b*x)^2)-_ + 1/4*d*sqrt(c+d*x)/(b*(b*c-a*d)*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|d x + c +--R (- b d x - 2a b d x - a d )atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +-+ +-------+ +--R (b d x - a d + 2b c)\|- a d + b c \|b \|d x + c +--R / +--R 3 4 2 2 2 3 3 2 2 +-----------+ +--R ((4a b d - 4b c)x + (8a b d - 8a b c)x + 4a b d - 4a b c)\|- a d + b c +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 2 2 +--R (b d x + 2a b d x + a d ) +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (2b d x - 2a d + 4b c)\|- a b d + b c \|d x + c +--R / +--R 3 4 2 2 2 3 3 2 2 +--R ((8a b d - 8b c)x + (16a b d - 16a b c)x + 8a b d - 8a b c) +--R * +--R +-------------+ +--R | 2 +--R \|- a b d + b c +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 2 2 2 2 2 2 \|a b d - b c \|d x + c +--R (b d x + 2a b d x + a d )atan(------------------------) +--R a d - b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R (b d x - a d + 2b c)\|a b d - b c \|d x + c +--R / +--R +-----------+ +--R 3 4 2 2 2 3 3 2 2 | 2 +--R ((4a b d - 4b c)x + (8a b d - 8a b c)x + 4a b d - 4a b c)\|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1172 + +--S 1173 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|d x + c +--R 2d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R (8a b d - 8b c)\|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1174 + +--S 1175 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|d x + c +--R d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 2 +-----------+ +-+ \|a b d - b c \|d x + c +--R d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R (4a b d - 4b c)\|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1176 + +)clear all + +--S 1177 of 2952 +t0000:=(c+d*x)^(1/2)/(a+b*x)^4 +--R +--R +--R +-------+ +--R \|d x + c +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 2952 +r0000:=-1/8*d^3*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (b^(3/2)*(b*c-a*d)^(5/2))-1/3*sqrt(c+d*x)/(b*(a+b*x)^3)-_ + 1/12*d*sqrt(c+d*x)/(b*(b*c-a*d)*(a+b*x)^2)+_ + 1/8*d^2*sqrt(c+d*x)/(b*(b*c-a*d)^2*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|d x + c +--R (- 3b d x - 9a b d x - 9a b d x - 3a d )atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b d x + (8a b d - 2b c d)x - 3a d + 14a b c d - 8b c ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|b \|d x + c +--R / +--R 2 4 2 5 6 2 3 +--R (24a b d - 48a b c d + 24b c )x +--R + +--R 3 3 2 2 4 5 2 2 +--R (72a b d - 144a b c d + 72a b c )x +--R + +--R 4 2 2 3 3 2 4 2 5 2 4 2 3 3 2 +--R (72a b d - 144a b c d + 72a b c )x + 24a b d - 48a b c d + 24a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 2 3 3 3 +--R (3b d x + 9a b d x + 9a b d x + 3a d ) +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b d x + (16a b d - 4b c d)x - 6a d + 28a b c d - 16b c ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b d + b c \|d x + c +--R / +--R 2 4 2 5 6 2 3 +--R (48a b d - 96a b c d + 48b c )x +--R + +--R 3 3 2 2 4 5 2 2 +--R (144a b d - 288a b c d + 144a b c )x +--R + +--R 4 2 2 3 3 2 4 2 5 2 4 2 3 3 2 +--R (144a b d - 288a b c d + 144a b c )x + 48a b d - 96a b c d + 48a b c +--R * +--R +-------------+ +--R | 2 +--R \|- a b d + b c +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|a b d - b c \|d x + c +--R (3b d x + 9a b d x + 9a b d x + 3a d )atan(------------------------) +--R a d - b c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b d x + (8a b d - 2b c d)x - 3a d + 14a b c d - 8b c ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R / +--R 2 4 2 5 6 2 3 +--R (24a b d - 48a b c d + 24b c )x +--R + +--R 3 3 2 2 4 5 2 2 +--R (72a b d - 144a b c d + 72a b c )x +--R + +--R 4 2 2 3 3 2 4 2 5 2 4 2 3 3 2 +--R (72a b d - 144a b c d + 72a b c )x + 24a b d - 48a b c d + 24a b c +--R * +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1179 + +--S 1180 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 3 +-----------+ +-+ +--R d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 | 2 \|b \|d x + c +--R 2d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R 2 2 2 3 2 | 2 +-----------+ +-+ +--R (16a b d - 32a b c d + 16b c )\|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 | 2 \|b \|d x + c +--R d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 3 +-----------+ +-+ \|a b d - b c \|d x + c +--R d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R +-----------+ +--R 2 2 2 3 2 +-----------+ +-+ | 2 +--R (8a b d - 16a b c d + 8b c )\|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1183 + +)clear all + +--S 1184 of 2952 +t0000:=(c+d*x)^(1/2)/(a+b*x)^5 +--R +--R +--R +-------+ +--R \|d x + c +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 2952 +r0000:=5/64*d^4*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (b^(3/2)*(b*c-a*d)^(7/2))-1/4*sqrt(c+d*x)/(b*(a+b*x)^4)-_ + 1/24*d*sqrt(c+d*x)/(b*(b*c-a*d)*(a+b*x)^3)+_ + 5/96*d^2*sqrt(c+d*x)/(b*(b*c-a*d)^2*(a+b*x)^2)-_ + 5/64*d^3*sqrt(c+d*x)/(b*(b*c-a*d)^3*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 15b d x - 60a b d x - 90a b d x - 60a b d x - 15a d ) +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b d x + (55a b d - 10b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (73a b d - 36a b c d + 8b c d)x - 15a d + 118a b c d - 136a b c d +--R + +--R 3 3 +--R 48b c +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|b \|d x + c +--R / +--R 3 5 3 2 6 2 7 2 8 3 4 +--R (192a b d - 576a b c d + 576a b c d - 192b c )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 3 +--R (768a b d - 2304a b c d + 2304a b c d - 768a b c )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 2 +--R (1152a b d - 3456a b c d + 3456a b c d - 1152a b c )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 7 3 +--R (768a b d - 2304a b c d + 2304a b c d - 768a b c )x + 192a b d +--R + +--R 6 2 2 5 3 2 4 4 3 +--R - 576a b c d + 576a b c d - 192a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (15b d x + 60a b d x + 90a b d x + 60a b d x + 15a d ) +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b d x + (110a b d - 20b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (146a b d - 72a b c d + 16b c d)x - 30a d + 236a b c d +--R + +--R 2 2 3 3 +--R - 272a b c d + 96b c +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b d + b c \|d x + c +--R / +--R 3 5 3 2 6 2 7 2 8 3 4 +--R (384a b d - 1152a b c d + 1152a b c d - 384b c )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 3 +--R (1536a b d - 4608a b c d + 4608a b c d - 1536a b c )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 2 +--R (2304a b d - 6912a b c d + 6912a b c d - 2304a b c )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 7 3 +--R (1536a b d - 4608a b c d + 4608a b c d - 1536a b c )x + 384a b d +--R + +--R 6 2 2 5 3 2 4 4 3 +--R - 1152a b c d + 1152a b c d - 384a b c +--R * +--R +-------------+ +--R | 2 +--R \|- a b d + b c +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (15b d x + 60a b d x + 90a b d x + 60a b d x + 15a d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R atan(------------------------) +--R a d - b c +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b d x + (55a b d - 10b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (73a b d - 36a b c d + 8b c d)x - 15a d + 118a b c d +--R + +--R 2 2 3 3 +--R - 136a b c d + 48b c +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R / +--R 3 5 3 2 6 2 7 2 8 3 4 +--R (192a b d - 576a b c d + 576a b c d - 192b c )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 3 +--R (768a b d - 2304a b c d + 2304a b c d - 768a b c )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 2 +--R (1152a b d - 3456a b c d + 3456a b c d - 1152a b c )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 7 3 +--R (768a b d - 2304a b c d + 2304a b c d - 768a b c )x + 192a b d +--R + +--R 6 2 2 5 3 2 4 4 3 +--R - 576a b c d + 576a b c d - 192a b c +--R * +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1186 + +--S 1187 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 5d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|d x + c +--R 10d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R 3 3 2 2 2 3 2 4 3 | 2 +--R (128a b d - 384a b c d + 384a b c d - 128b c )\|- a b d + b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|d x + c +--R 5d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b d - b c \|d x + c +--R 5d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R 3 3 2 2 2 3 2 4 3 +-----------+ +-+ +--R (64a b d - 192a b c d + 192a b c d - 64b c )\|- a d + b c \|b +--R * +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1190 + +)clear all + +--S 1191 of 2952 +t0000:=(c+d*x)^(1/2)/(a+b*x)^6 +--R +--R +--R +-------+ +--R \|d x + c +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 2952 +r0000:=-7/128*d^5*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (b^(3/2)*(b*c-a*d)^(9/2))-1/5*sqrt(c+d*x)/(b*(a+b*x)^5)-_ + 1/40*d*sqrt(c+d*x)/(b*(b*c-a*d)*(a+b*x)^4)+_ + 7/240*d^2*sqrt(c+d*x)/(b*(b*c-a*d)^2*(a+b*x)^3)-_ + 7/192*d^3*sqrt(c+d*x)/(b*(b*c-a*d)^3*(a+b*x)^2)+_ + 7/128*d^4*sqrt(c+d*x)/(b*(b*c-a*d)^4*(a+b*x)) +--R +--R +--R (2) +--R 5 5 5 4 5 4 2 3 5 3 3 2 5 2 4 5 +--R - 105b d x - 525a b d x - 1050a b d x - 1050a b d x - 525a b d x +--R + +--R 5 5 +--R - 105a d +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 4 4 3 4 4 3 3 +--R 105b d x + (490a b d - 70b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (896a b d - 322a b c d + 56b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (790a b d - 578a b c d + 256a b c d - 48b c d)x - 105a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 1210a b c d - 2104a b c d + 1488a b c d - 384b c +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|b \|d x + c +--R / +--R 4 6 4 3 7 3 2 8 2 2 9 3 10 4 5 +--R (1920a b d - 7680a b c d + 11520a b c d - 7680a b c d + 1920b c )x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R 9600a b d - 38400a b c d + 57600a b c d - 38400a b c d +--R + +--R 9 4 +--R 9600a b c +--R * +--R 4 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 +--R 19200a b d - 76800a b c d + 115200a b c d - 76800a b c d +--R + +--R 2 8 4 +--R 19200a b c +--R * +--R 3 +--R x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 +--R 19200a b d - 76800a b c d + 115200a b c d - 76800a b c d +--R + +--R 3 7 4 +--R 19200a b c +--R * +--R 2 +--R x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 +--R 9600a b d - 38400a b c d + 57600a b c d - 38400a b c d +--R + +--R 4 6 4 +--R 9600a b c +--R * +--R x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 5 5 4 +--R 1920a b d - 7680a b c d + 11520a b c d - 7680a b c d + 1920a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 5 5 5 4 5 4 2 3 5 3 3 2 5 2 4 5 +--R 105b d x + 525a b d x + 1050a b d x + 1050a b d x + 525a b d x +--R + +--R 5 5 +--R 105a d +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R 210b d x + (980a b d - 140b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1792a b d - 644a b c d + 112b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (1580a b d - 1156a b c d + 512a b c d - 96b c d)x - 210a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 2420a b c d - 4208a b c d + 2976a b c d - 768b c +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b d + b c \|d x + c +--R / +--R 4 6 4 3 7 3 2 8 2 2 9 3 +--R 3840a b d - 15360a b c d + 23040a b c d - 15360a b c d +--R + +--R 10 4 +--R 3840b c +--R * +--R 5 +--R x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R 19200a b d - 76800a b c d + 115200a b c d - 76800a b c d +--R + +--R 9 4 +--R 19200a b c +--R * +--R 4 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 +--R 38400a b d - 153600a b c d + 230400a b c d - 153600a b c d +--R + +--R 2 8 4 +--R 38400a b c +--R * +--R 3 +--R x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 +--R 38400a b d - 153600a b c d + 230400a b c d - 153600a b c d +--R + +--R 3 7 4 +--R 38400a b c +--R * +--R 2 +--R x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 +--R 19200a b d - 76800a b c d + 115200a b c d - 76800a b c d +--R + +--R 4 6 4 +--R 19200a b c +--R * +--R x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 5 5 4 +--R 3840a b d - 15360a b c d + 23040a b c d - 15360a b c d + 3840a b c +--R * +--R +-------------+ +--R | 2 +--R \|- a b d + b c +--R , +--R +--R 5 5 5 4 5 4 2 3 5 3 3 2 5 2 4 5 +--R 105b d x + 525a b d x + 1050a b d x + 1050a b d x + 525a b d x +--R + +--R 5 5 +--R 105a d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R atan(------------------------) +--R a d - b c +--R + +--R 4 4 4 3 4 4 3 3 +--R 105b d x + (490a b d - 70b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (896a b d - 322a b c d + 56b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (790a b d - 578a b c d + 256a b c d - 48b c d)x - 105a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 1210a b c d - 2104a b c d + 1488a b c d - 384b c +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R / +--R 4 6 4 3 7 3 2 8 2 2 9 3 +--R 1920a b d - 7680a b c d + 11520a b c d - 7680a b c d +--R + +--R 10 4 +--R 1920b c +--R * +--R 5 +--R x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R 9600a b d - 38400a b c d + 57600a b c d - 38400a b c d +--R + +--R 9 4 +--R 9600a b c +--R * +--R 4 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 +--R 19200a b d - 76800a b c d + 115200a b c d - 76800a b c d +--R + +--R 2 8 4 +--R 19200a b c +--R * +--R 3 +--R x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 +--R 19200a b d - 76800a b c d + 115200a b c d - 76800a b c d +--R + +--R 3 7 4 +--R 19200a b c +--R * +--R 2 +--R x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 +--R 9600a b d - 38400a b c d + 57600a b c d - 38400a b c d +--R + +--R 4 6 4 +--R 9600a b c +--R * +--R x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 5 5 4 +--R 1920a b d - 7680a b c d + 11520a b c d - 7680a b c d + 1920a b c +--R * +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1193 + +--S 1194 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 5 +-----------+ +-+ +--R 7d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 | 2 \|b \|d x + c +--R 14d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 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 +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 | 2 \|b \|d x + c +--R 7d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 5 +-----------+ +-+ \|a b d - b c \|d x + c +--R 7d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (128a b d - 512a b c d + 768a b c d - 512a b c d + 128b c ) +--R * +--R +-----------+ +--R +-----------+ +-+ | 2 +--R \|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1197 + +)clear all + +--S 1198 of 2952 +t0000:=(a+b*x)^5*(c+d*x)^(3/2) +--R +--R +--R (1) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b d x + (5a b d + b c)x + (10a b d + 5a b c)x + (10a b d + 10a b c)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b d + 10a b c)x + (a d + 5a b c)x + a c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 2952 +r0000:=-2/5*(b*c-a*d)^5*(c+d*x)^(5/2)/d^6+10/7*b*(b*c-a*d)^4*_ + (c+d*x)^(7/2)/d^6-20/9*b^2*(b*c-a*d)^3*(c+d*x)^(9/2)/d^6+_ + 20/11*b^3*(b*c-a*d)^2*(c+d*x)^(11/2)/d^6-_ + 10/13*b^4*(b*c-a*d)*(c+d*x)^(13/2)/d^6+2/15*b^5*(c+d*x)^(15/2)/d^6 +--R +--R +--R (2) +--R 5 7 7 4 7 5 6 6 +--R 6006b d x + (34650a b d + 7392b c d )x +--R + +--R 2 3 7 4 6 5 2 5 5 +--R (81900a b d + 44100a b c d + 126b c d )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 4 +--R (100100a b d + 109200a b c d + 1050a b c d - 140b c d )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 +--R 64350a b d + 143000a b c d + 3900a b c d - 1200a b c d +--R + +--R 5 4 3 +--R 160b c d +--R * +--R 3 +--R x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 18018a d + 102960a b c d + 8580a b c d - 4680a b c d +--R + +--R 4 4 3 5 5 2 +--R 1440a b c d - 192b c d +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 +--R 36036a c d + 12870a b c d - 11440a b c d + 6240a b c d +--R + +--R 4 5 2 5 6 +--R - 1920a b c d + 256b c d +--R * +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 +--R 18018a c d - 25740a b c d + 22880a b c d - 12480a b c d +--R + +--R 4 6 5 7 +--R 3840a b c d - 512b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 +--R 45045d +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 7 7 4 7 5 6 6 +--R 6006b d x + (34650a b d + 7392b c d )x +--R + +--R 2 3 7 4 6 5 2 5 5 +--R (81900a b d + 44100a b c d + 126b c d )x +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 4 +--R (100100a b d + 109200a b c d + 1050a b c d - 140b c d )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 +--R 64350a b d + 143000a b c d + 3900a b c d - 1200a b c d +--R + +--R 5 4 3 +--R 160b c d +--R * +--R 3 +--R x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 +--R 18018a d + 102960a b c d + 8580a b c d - 4680a b c d +--R + +--R 4 4 3 5 5 2 +--R 1440a b c d - 192b c d +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 +--R 36036a c d + 12870a b c d - 11440a b c d + 6240a b c d +--R + +--R 4 5 2 5 6 +--R - 1920a b c d + 256b c d +--R * +--R x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 +--R 18018a c d - 25740a b c d + 22880a b c d - 12480a b c d +--R + +--R 4 6 5 7 +--R 3840a b c d - 512b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 +--R 45045d +--R Type: Union(Expression(Integer),...) +--E 1200 + +--S 1201 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1202 + +)clear all + +--S 1203 of 2952 +t0000:=(a+b*x)^4*(c+d*x)^(3/2) +--R +--R +--R (1) +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b d x + (4a b d + b c)x + (6a b d + 4a b c)x + (4a b d + 6a b c)x +--R + +--R 4 3 4 +--R (a d + 4a b c)x + a c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 2952 +r0000:=2/5*(b*c-a*d)^4*(c+d*x)^(5/2)/d^5-8/7*b*(b*c-a*d)^3*(c+d*x)^(7/2)/d^5+_ + 4/3*b^2*(b*c-a*d)^2*(c+d*x)^(9/2)/d^5-_ + 8/11*b^3*(b*c-a*d)*(c+d*x)^(11/2)/d^5+2/13*b^4*(c+d*x)^(13/2)/d^5 +--R +--R +--R (2) +--R 4 6 6 3 6 4 5 5 +--R 2310b d x + (10920a b d + 2940b c d )x +--R + +--R 2 2 6 3 5 4 2 4 4 +--R (20020a b d + 14560a b c d + 70b c d )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (17160a b d + 28600a b c d + 520a b c d - 80b c d )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (6006a d + 27456a b c d + 1716a b c d - 624a b c d + 96b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (12012a c d + 3432a b c d - 2288a b c d + 832a b c d - 128b c d)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 6006a c d - 6864a b c d + 4576a b c d - 1664a b c d + 256b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 +--R 15015d +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 6 6 3 6 4 5 5 +--R 2310b d x + (10920a b d + 2940b c d )x +--R + +--R 2 2 6 3 5 4 2 4 4 +--R (20020a b d + 14560a b c d + 70b c d )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (17160a b d + 28600a b c d + 520a b c d - 80b c d )x +--R + +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (6006a d + 27456a b c d + 1716a b c d - 624a b c d + 96b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (12012a c d + 3432a b c d - 2288a b c d + 832a b c d - 128b c d)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 6006a c d - 6864a b c d + 4576a b c d - 1664a b c d + 256b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 +--R 15015d +--R Type: Union(Expression(Integer),...) +--E 1205 + +--S 1206 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1207 + +)clear all + +--S 1208 of 2952 +t0000:=(a+b*x)^3*(c+d*x)^(3/2) +--R +--R +--R (1) +--R 3 4 2 3 3 2 2 2 3 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 * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 2952 +r0000:=-2/5*(b*c-a*d)^3*(c+d*x)^(5/2)/d^4+_ + 6/7*b*(b*c-a*d)^2*(c+d*x)^(7/2)/d^4-_ + 2/3*b^2*(b*c-a*d)*(c+d*x)^(9/2)/d^4+2/11*b^3*(c+d*x)^(11/2)/d^4 +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 210b d x + (770a b d + 280b c d )x +--R + +--R 2 5 2 4 3 2 3 3 +--R (990a b d + 1100a b c d + 10b c d )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (462a d + 1584a b c d + 66a b c d - 12b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (924a c d + 198a b c d - 88a b c d + 16b c d)x + 462a c d +--R + +--R 2 3 2 2 4 3 5 +--R - 396a b c d + 176a b c d - 32b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 +--R 1155d +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 5 5 2 5 3 4 4 +--R 210b d x + (770a b d + 280b c d )x +--R + +--R 2 5 2 4 3 2 3 3 +--R (990a b d + 1100a b c d + 10b c d )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (462a d + 1584a b c d + 66a b c d - 12b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (924a c d + 198a b c d - 88a b c d + 16b c d)x + 462a c d +--R + +--R 2 3 2 2 4 3 5 +--R - 396a b c d + 176a b c d - 32b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 +--R 1155d +--R Type: Union(Expression(Integer),...) +--E 1210 + +--S 1211 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1212 + +)clear all + +--S 1213 of 2952 +t0000:=(a+b*x)^2*(c+d*x)^(3/2) +--R +--R +--R 2 3 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 1213 + +--S 1214 of 2952 +r0000:=2/5*(b*c-a*d)^2*(c+d*x)^(5/2)/d^3-4/7*b*(b*c-a*d)*(c+d*x)^(7/2)/d^3+_ + 2/9*b^2*(c+d*x)^(9/2)/d^3 +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 +--R 70b d x + (180a b d + 100b c d )x +--R + +--R 2 4 3 2 2 2 2 +--R (126a d + 288a b c d + 6b c d )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (252a c d + 36a b c d - 8b c d)x + 126a c d - 72a b c d + 16b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +--R 315d +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 4 4 4 2 3 3 +--R 70b d x + (180a b d + 100b c d )x +--R + +--R 2 4 3 2 2 2 2 +--R (126a d + 288a b c d + 6b c d )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (252a c d + 36a b c d - 8b c d)x + 126a c d - 72a b c d + 16b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +--R 315d +--R Type: Union(Expression(Integer),...) +--E 1215 + +--S 1216 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1217 + +)clear all + +--S 1218 of 2952 +t0000:=(a+b*x)*(c+d*x)^(3/2) +--R +--R +--R 2 +-------+ +--R (1) (b d x + (a d + b c)x + a c)\|d x + c +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 2952 +r0000:=-2/5*(b*c-a*d)*(c+d*x)^(5/2)/d^2+2/7*b*(c+d*x)^(7/2)/d^2 +--R +--R +--R (2) +--R 3 3 3 2 2 2 2 2 +--R 10b d x + (14a d + 16b c d )x + (28a c d + 2b c d)x + 14a c d +--R + +--R 3 +--R - 4b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 2 +--R 35d +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 2 2 2 2 +--R 10b d x + (14a d + 16b c d )x + (28a c d + 2b c d)x + 14a c d +--R + +--R 3 +--R - 4b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 2 +--R 35d +--R Type: Union(Expression(Integer),...) +--E 1220 + +--S 1221 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1222 + +)clear all + +--S 1223 of 2952 +t0000:=(c+d*x)^(3/2) +--R +--R +--R +-------+ +--R (1) (d x + c)\|d x + c +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 2952 +r0000:=2/5*(c+d*x)^(5/2)/d +--R +--R +--R 2 2 2 +-------+ +--R (2d x + 4c d x + 2c )\|d x + c +--R (2) -------------------------------- +--R 5d +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +-------+ +--R (2d x + 4c d x + 2c )\|d x + c +--R (3) -------------------------------- +--R 5d +--R Type: Union(Expression(Integer),...) +--E 1225 + +--S 1226 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1227 + +)clear all + +--S 1228 of 2952 +t0000:=(c+d*x)^(3/2)/(a+b*x) +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) ------------------- +--R b x + a +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 2952 +r0000:=2/3*(c+d*x)^(3/2)/b-2*(b*c-a*d)^(3/2)*atanh(sqrt(b)*_ + sqrt(c+d*x)/sqrt(b*c-a*d))/b^(5/2)+2*(b*c-a*d)*sqrt(c+d*x)/b^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R (6a d - 6b c)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-+ +-------+ +--R (2b d x - 6a d + 8b c)\|b \|d x + c +--R / +--R 2 +-+ +--R 3b \|b +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- a d + b c +--R (3a d - 3b c) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R (2b d x - 6a d + 8b c)\|d x + c +--R / +--R 2 +--R 3b +--R , +--R +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R (6a d - 6b c) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R +-------+ +--R (2b d x - 6a d + 8b c)\|d x + c +--R / +--R 2 +--R 3b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1230 + +--S 1231 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R |- a d + b c +-+ +--R (a d - b c) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R (- 2a d + 2b c)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1232 + +--S 1233 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R (- 2a d + 2b c)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R +-+ |a d - b c \|d x + c +--R (2a d - 2b c)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1234 + +)clear all + +--S 1235 of 2952 +t0000:=(c+d*x)^(3/2)/(a+b*x)^2 +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) ------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 2952 +r0000:=-(c+d*x)^(3/2)/(b*(a+b*x))-_ + 3*d*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*_ + sqrt(b*c-a*d)/b^(5/2)+3*d*sqrt(c+d*x)/b^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R (- 3b d x - 3a d)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-+ +-------+ +--R (2b d x + 3a d - b c)\|b \|d x + c +--R / +--R 3 2 +-+ +--R (b x + a b )\|b +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- a d + b c +--R (3b d x + 3a d) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R (4b d x + 6a d - 2b c)\|d x + c +--R / +--R 3 2 +--R 2b x + 2a b +--R , +--R +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R (- 3b d x - 3a d) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R +-------+ +--R (2b d x + 3a d - b c)\|d x + c +--R / +--R 3 2 +--R b x + a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1237 + +--S 1238 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R |- a d + b c +-+ +--R 3d |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R 6d\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +---------+ +-------+ +--R +-----------+ \|b \|d x + c +-+ |a d - b c \|d x + c +--R 3d\|- a d + b c atanh(--------------) - 3d\|b |--------- atan(------------) +--R +-----------+ \| b +---------+ +--R \|- a d + b c |a d - b c +--R |--------- +--R \| b +--R ---------------------------------------------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1240 + +--S 1241 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1241 + +)clear all + +--S 1242 of 2952 +t0000:=(c+d*x)^(3/2)/(a+b*x)^3 +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 1242 + +--S 1243 of 2952 +r0000:=-1/2*(c+d*x)^(3/2)/(b*(a+b*x)^2)-_ + 3/4*d^2*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (b^(5/2)*sqrt(b*c-a*d))-3/4*d*sqrt(c+d*x)/(b^2*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|d x + c +--R (- 3b d x - 6a b d x - 3a d )atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +-+ +-------+ +--R (- 5b d x - 3a d - 2b c)\|- a d + b c \|b \|d x + c +--R / +--R 4 2 3 2 2 +-----------+ +-+ +--R (4b x + 8a b x + 4a b )\|- a d + b c \|b +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 2 2 +--R (3b d x + 6a b d x + 3a d ) +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (- 10b d x - 6a d - 4b c)\|- a b d + b c \|d x + c +--R / +--R +-------------+ +--R 4 2 3 2 2 | 2 +--R (8b x + 16a b x + 8a b )\|- a b d + b c +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 2 2 2 2 2 2 \|a b d - b c \|d x + c +--R (3b d x + 6a b d x + 3a d )atan(------------------------) +--R a d - b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R (- 5b d x - 3a d - 2b c)\|a b d - b c \|d x + c +--R / +--R +-----------+ +--R 4 2 3 2 2 | 2 +--R (4b x + 8a b x + 4a b )\|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1244 + +--S 1245 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R 3d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|d x + c +--R 6d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R 8b \|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1245 + +--S 1246 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|d x + c +--R 3d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 2 +-----------+ +-+ \|a b d - b c \|d x + c +--R 3d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R 4b \|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1247 + +--S 1248 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1248 + +)clear all + +--S 1249 of 2952 +t0000:=(c+d*x)^(3/2)/(a+b*x)^4 +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 2952 +r0000:=-1/3*(c+d*x)^(3/2)/(b*(a+b*x)^3)+_ + 1/8*d^3*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (b^(5/2)*(b*c-a*d)^(3/2))-_ + 1/4*d*sqrt(c+d*x)/(b^2*(a+b*x)^2)-_ + 1/8*d^2*sqrt(c+d*x)/(b^2*(b*c-a*d)*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|d x + c +--R (- 3b d x - 9a b d x - 9a b d x - 3a d )atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b d x + (- 8a b d + 14b c d)x - 3a d - 2a b c d + 8b c ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|b \|d x + c +--R / +--R 5 6 3 2 4 5 2 3 3 2 4 +--R (24a b d - 24b c)x + (72a b d - 72a b c)x + (72a b d - 72a b c)x +--R + +--R 4 2 3 3 +--R 24a b d - 24a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 2 3 3 3 +--R (3b d x + 9a b d x + 9a b d x + 3a d ) +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b d x + (- 16a b d + 28b c d)x - 6a d - 4a b c d + 16b c ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b d + b c \|d x + c +--R / +--R 5 6 3 2 4 5 2 +--R (48a b d - 48b c)x + (144a b d - 144a b c)x +--R + +--R 3 3 2 4 4 2 3 3 +--R (144a b d - 144a b c)x + 48a b d - 48a b c +--R * +--R +-------------+ +--R | 2 +--R \|- a b d + b c +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|a b d - b c \|d x + c +--R (3b d x + 9a b d x + 9a b d x + 3a d )atan(------------------------) +--R a d - b c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (3b d x + (- 8a b d + 14b c d)x - 3a d - 2a b c d + 8b c ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R / +--R 5 6 3 2 4 5 2 3 3 2 4 +--R (24a b d - 24b c)x + (72a b d - 72a b c)x + (72a b d - 72a b c)x +--R + +--R 4 2 3 3 +--R 24a b d - 24a b c +--R * +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1251 + +--S 1252 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 3 +-----------+ +-+ +--R d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 | 2 \|b \|d x + c +--R 2d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R 2 3 | 2 +-----------+ +-+ +--R (16a b d - 16b c)\|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1252 + +--S 1253 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 | 2 \|b \|d x + c +--R d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 3 +-----------+ +-+ \|a b d - b c \|d x + c +--R d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R +-----------+ +--R 2 3 +-----------+ +-+ | 2 +--R (8a b d - 8b c)\|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1254 + +--S 1255 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1255 + +)clear all + +--S 1256 of 2952 +t0000:=(c+d*x)^(3/2)/(a+b*x)^5 +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 2952 +r0000:=-1/4*(c+d*x)^(3/2)/(b*(a+b*x)^4)-_ + 3/64*d^4*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (b^(5/2)*(b*c-a*d)^(5/2))-1/8*d*sqrt(c+d*x)/(b^2*(a+b*x)^3)-_ + 1/32*d^2*sqrt(c+d*x)/(b^2*(b*c-a*d)*(a+b*x)^2)+_ + 3/64*d^3*sqrt(c+d*x)/(b^2*(b*c-a*d)^2*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 3b d x - 12a b d x - 18a b d x - 12a b d x - 3a d ) +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 3 3 2 3 3 2 2 +--R 3b d x + (11a b d - 2b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 11a b d + 44a b c d - 24b c d)x - 3a d - 2a b c d + 24a b c d +--R + +--R 3 3 +--R - 16b c +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|b \|d x + c +--R / +--R 2 6 2 7 8 2 4 +--R (64a b d - 128a b c d + 64b c )x +--R + +--R 3 5 2 2 6 7 2 3 +--R (256a b d - 512a b c d + 256a b c )x +--R + +--R 4 4 2 3 5 2 6 2 2 +--R (384a b d - 768a b c d + 384a b c )x +--R + +--R 5 3 2 4 4 3 5 2 6 2 2 5 3 4 4 2 +--R (256a b d - 512a b c d + 256a b c )x + 64a b d - 128a b c d + 64a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1257 + +--S 1258 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (3b d x + 12a b d x + 18a b d x + 12a b d x + 3a d ) +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 6b d x + (22a b d - 4b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 22a b d + 88a b c d - 48b c d)x - 6a d - 4a b c d +--R + +--R 2 2 3 3 +--R 48a b c d - 32b c +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b d + b c \|d x + c +--R / +--R 2 6 2 7 8 2 4 +--R (128a b d - 256a b c d + 128b c )x +--R + +--R 3 5 2 2 6 7 2 3 +--R (512a b d - 1024a b c d + 512a b c )x +--R + +--R 4 4 2 3 5 2 6 2 2 +--R (768a b d - 1536a b c d + 768a b c )x +--R + +--R 5 3 2 4 4 3 5 2 6 2 2 5 3 +--R (512a b d - 1024a b c d + 512a b c )x + 128a b d - 256a b c d +--R + +--R 4 4 2 +--R 128a b c +--R * +--R +-------------+ +--R | 2 +--R \|- a b d + b c +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (3b d x + 12a b d x + 18a b d x + 12a b d x + 3a d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R atan(------------------------) +--R a d - b c +--R + +--R 3 3 3 2 3 3 2 2 +--R 3b d x + (11a b d - 2b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 11a b d + 44a b c d - 24b c d)x - 3a d - 2a b c d +--R + +--R 2 2 3 3 +--R 24a b c d - 16b c +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R / +--R 2 6 2 7 8 2 4 +--R (64a b d - 128a b c d + 64b c )x +--R + +--R 3 5 2 2 6 7 2 3 +--R (256a b d - 512a b c d + 256a b c )x +--R + +--R 4 4 2 3 5 2 6 2 2 +--R (384a b d - 768a b c d + 384a b c )x +--R + +--R 5 3 2 4 4 3 5 2 6 2 2 5 3 +--R (256a b d - 512a b c d + 256a b c )x + 64a b d - 128a b c d +--R + +--R 4 4 2 +--R 64a b c +--R * +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1258 + +--S 1259 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 3d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|d x + c +--R 6d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R 2 2 2 3 4 2 | 2 +-----------+ +-+ +--R (128a b d - 256a b c d + 128b c )\|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1259 + +--S 1260 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|d x + c +--R 3d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b d - b c \|d x + c +--R 3d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R +-----------+ +--R 2 2 2 3 4 2 +-----------+ +-+ | 2 +--R (64a b d - 128a b c d + 64b c )\|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1262 + +)clear all + +--S 1263 of 2952 +t0000:=(c+d*x)^(3/2)/(a+b*x)^6 +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 2952 +r0000:=-1/5*(c+d*x)^(3/2)/(b*(a+b*x)^5)+_ + 3/128*d^5*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (b^(5/2)*(b*c-a*d)^(7/2))-3/40*d*sqrt(c+d*x)/(b^2*(a+b*x)^4)-_ + 1/80*d^2*sqrt(c+d*x)/(b^2*(b*c-a*d)*(a+b*x)^3)+_ + 1/64*d^3*sqrt(c+d*x)/(b^2*(b*c-a*d)^2*(a+b*x)^2)-_ + 3/128*d^4*sqrt(c+d*x)/(b^2*(b*c-a*d)^3*(a+b*x)) +--R +--R +--R (2) +--R 5 5 5 4 5 4 2 3 5 3 3 2 5 2 4 5 +--R - 15b d x - 75a b d x - 150a b d x - 150a b d x - 75a b d x +--R + +--R 5 5 +--R - 15a d +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 4 4 3 4 4 3 3 +--R 15b d x + (70a b d - 10b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (128a b d - 46a b c d + 8b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 70a b d + 466a b c d - 512a b c d + 176b c d)x - 15a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 10a b c d + 248a b c d - 336a b c d + 128b c +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|b \|d x + c +--R / +--R 3 7 3 2 8 2 9 2 10 3 5 +--R (640a b d - 1920a b c d + 1920a b c d - 640b c )x +--R + +--R 4 6 3 3 7 2 2 8 2 9 3 4 +--R (3200a b d - 9600a b c d + 9600a b c d - 3200a b c )x +--R + +--R 5 5 3 4 6 2 3 7 2 2 8 3 3 +--R (6400a b d - 19200a b c d + 19200a b c d - 6400a b c )x +--R + +--R 6 4 3 5 5 2 4 6 2 3 7 3 2 +--R (6400a b d - 19200a b c d + 19200a b c d - 6400a b c )x +--R + +--R 7 3 3 6 4 2 5 5 2 4 6 3 8 2 3 +--R (3200a b d - 9600a b c d + 9600a b c d - 3200a b c )x + 640a b d +--R + +--R 7 3 2 6 4 2 5 5 3 +--R - 1920a b c d + 1920a b c d - 640a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1264 + +--S 1265 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 5 5 5 4 5 4 2 3 5 3 3 2 5 2 4 5 +--R 15b d x + 75a b d x + 150a b d x + 150a b d x + 75a b d x +--R + +--R 5 5 +--R 15a d +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R 30b d x + (140a b d - 20b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (256a b d - 92a b c d + 16b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 140a b d + 932a b c d - 1024a b c d + 352b c d)x - 30a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 20a b c d + 496a b c d - 672a b c d + 256b c +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b d + b c \|d x + c +--R / +--R 3 7 3 2 8 2 9 2 10 3 5 +--R (1280a b d - 3840a b c d + 3840a b c d - 1280b c )x +--R + +--R 4 6 3 3 7 2 2 8 2 9 3 4 +--R (6400a b d - 19200a b c d + 19200a b c d - 6400a b c )x +--R + +--R 5 5 3 4 6 2 3 7 2 2 8 3 3 +--R (12800a b d - 38400a b c d + 38400a b c d - 12800a b c )x +--R + +--R 6 4 3 5 5 2 4 6 2 3 7 3 2 +--R (12800a b d - 38400a b c d + 38400a b c d - 12800a b c )x +--R + +--R 7 3 3 6 4 2 5 5 2 4 6 3 +--R (6400a b d - 19200a b c d + 19200a b c d - 6400a b c )x +--R + +--R 8 2 3 7 3 2 6 4 2 5 5 3 +--R 1280a b d - 3840a b c d + 3840a b c d - 1280a b c +--R * +--R +-------------+ +--R | 2 +--R \|- a b d + b c +--R , +--R +--R 5 5 5 4 5 4 2 3 5 3 3 2 5 2 4 5 +--R 15b d x + 75a b d x + 150a b d x + 150a b d x + 75a b d x +--R + +--R 5 5 +--R 15a d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R atan(------------------------) +--R a d - b c +--R + +--R 4 4 4 3 4 4 3 3 +--R 15b d x + (70a b d - 10b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (128a b d - 46a b c d + 8b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 70a b d + 466a b c d - 512a b c d + 176b c d)x - 15a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 10a b c d + 248a b c d - 336a b c d + 128b c +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R / +--R 3 7 3 2 8 2 9 2 10 3 5 +--R (640a b d - 1920a b c d + 1920a b c d - 640b c )x +--R + +--R 4 6 3 3 7 2 2 8 2 9 3 4 +--R (3200a b d - 9600a b c d + 9600a b c d - 3200a b c )x +--R + +--R 5 5 3 4 6 2 3 7 2 2 8 3 3 +--R (6400a b d - 19200a b c d + 19200a b c d - 6400a b c )x +--R + +--R 6 4 3 5 5 2 4 6 2 3 7 3 2 +--R (6400a b d - 19200a b c d + 19200a b c d - 6400a b c )x +--R + +--R 7 3 3 6 4 2 5 5 2 4 6 3 8 2 3 +--R (3200a b d - 9600a b c d + 9600a b c d - 3200a b c )x + 640a b d +--R + +--R 7 3 2 6 4 2 5 5 3 +--R - 1920a b c d + 1920a b c d - 640a b c +--R * +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1265 + +--S 1266 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 5 +-----------+ +-+ +--R 3d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 | 2 \|b \|d x + c +--R 6d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R 3 2 3 2 3 2 4 2 5 3 | 2 +--R (256a b d - 768a b c d + 768a b c d - 256b c )\|- a b d + b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1267 + +--S 1268 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 | 2 \|b \|d x + c +--R 3d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 5 +-----------+ +-+ \|a b d - b c \|d x + c +--R 3d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R 3 2 3 2 3 2 4 2 5 3 +-----------+ +-+ +--R (128a b d - 384a b c d + 384a b c d - 128b c )\|- a d + b c \|b +--R * +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1269 + +)clear all + +--S 1270 of 2952 +t0000:=(a+b*x)^5*(c+d*x)^(5/2) +--R +--R +--R (1) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b d x + (5a b d + 2b c d)x + (10a b d + 10a b c d + b c )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b d + 20a b c d + 5a b c )x + (5a b d + 20a b c d + 10a b c )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a d + 10a b c d + 10a b c )x + (2a c d + 5a b c )x + a c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 2952 +r0000:=-2/7*(b*c-a*d)^5*(c+d*x)^(7/2)/d^6+10/9*b*(b*c-a*d)^4*_ + (c+d*x)^(9/2)/d^6-20/11*b^2*(b*c-a*d)^3*(c+d*x)^(11/2)/d^6+_ + 20/13*b^3*(b*c-a*d)^2*(c+d*x)^(13/2)/d^6-_ + 2/3*b^4*(b*c-a*d)*(c+d*x)^(15/2)/d^6+2/17*b^5*(c+d*x)^(17/2)/d^6 +--R +--R +--R (2) +--R 5 8 8 4 8 5 7 7 +--R 18018b d x + (102102a b d + 42042b c d )x +--R + +--R 2 3 8 4 7 5 2 6 6 +--R (235620a b d + 243474a b c d + 25410b c d )x +--R + +--R 3 2 8 2 3 7 4 2 6 5 3 5 5 +--R (278460a b d + 578340a b c d + 152082a b c d + 126b c d )x +--R + +--R 4 8 3 2 7 2 3 2 6 4 3 5 +--R 170170a b d + 711620a b c d + 378420a b c d + 1190a b c d +--R + +--R 5 4 4 +--R - 140b c d +--R * +--R 4 +--R x +--R + +--R 5 8 4 7 3 2 2 6 2 3 3 5 +--R 43758a d + 461890a b c d + 499460a b c d + 5100a b c d +--R + +--R 4 4 4 5 5 3 +--R - 1360a b c d + 160b c d +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 +--R 131274a c d + 364650a b c d + 13260a b c d - 6120a b c d +--R + +--R 4 5 3 5 6 2 +--R 1632a b c d - 192b c d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 +--R 131274a c d + 24310a b c d - 17680a b c d + 8160a b c d +--R + +--R 4 6 2 5 7 +--R - 2176a b c d + 256b c d +--R * +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 +--R 43758a c d - 48620a b c d + 35360a b c d - 16320a b c d +--R + +--R 4 7 5 8 +--R 4352a b c d - 512b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 +--R 153153d +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 8 8 4 8 5 7 7 +--R 18018b d x + (102102a b d + 42042b c d )x +--R + +--R 2 3 8 4 7 5 2 6 6 +--R (235620a b d + 243474a b c d + 25410b c d )x +--R + +--R 3 2 8 2 3 7 4 2 6 5 3 5 5 +--R (278460a b d + 578340a b c d + 152082a b c d + 126b c d )x +--R + +--R 4 8 3 2 7 2 3 2 6 4 3 5 +--R 170170a b d + 711620a b c d + 378420a b c d + 1190a b c d +--R + +--R 5 4 4 +--R - 140b c d +--R * +--R 4 +--R x +--R + +--R 5 8 4 7 3 2 2 6 2 3 3 5 +--R 43758a d + 461890a b c d + 499460a b c d + 5100a b c d +--R + +--R 4 4 4 5 5 3 +--R - 1360a b c d + 160b c d +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 +--R 131274a c d + 364650a b c d + 13260a b c d - 6120a b c d +--R + +--R 4 5 3 5 6 2 +--R 1632a b c d - 192b c d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 +--R 131274a c d + 24310a b c d - 17680a b c d + 8160a b c d +--R + +--R 4 6 2 5 7 +--R - 2176a b c d + 256b c d +--R * +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 +--R 43758a c d - 48620a b c d + 35360a b c d - 16320a b c d +--R + +--R 4 7 5 8 +--R 4352a b c d - 512b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 +--R 153153d +--R Type: Union(Expression(Integer),...) +--E 1272 + +--S 1273 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1274 + +)clear all + +--S 1275 of 2952 +t0000:=(a+b*x)^4*(c+d*x)^(5/2) +--R +--R +--R (1) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b d x + (4a b d + 2b c d)x + (6a b d + 8a b c d + b c )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b d + 12a b c d + 4a b c )x + (a d + 8a b c d + 6a b c )x +--R + +--R 4 3 2 4 2 +--R (2a c d + 4a b c )x + a c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1275 + +--S 1276 of 2952 +r0000:=2/7*(b*c-a*d)^4*(c+d*x)^(7/2)/d^5-_ + 8/9*b*(b*c-a*d)^3*(c+d*x)^(9/2)/d^5+_ + 12/11*b^2*(b*c-a*d)^2*(c+d*x)^(11/2)/d^5-_ + 8/13*b^3*(b*c-a*d)*(c+d*x)^(13/2)/d^5+2/15*b^4*(c+d*x)^(15/2)/d^5 +--R +--R +--R (2) +--R 4 7 7 3 7 4 6 6 +--R 6006b d x + (27720a b d + 14322b c d )x +--R + +--R 2 2 7 3 6 4 2 5 5 +--R (49140a b d + 68040a b c d + 8946b c d )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 4 +--R (40040a b d + 125580a b c d + 44520a b c d + 70b c d )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (12870a d + 108680a b c d + 88140a b c d + 600a b c d - 80b c d )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (38610a c d + 85800a b c d + 2340a b c d - 720a b c d + 96b c d )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 +--R (38610a c d + 5720a b c d - 3120a b c d + 960a b c d - 128b c d)x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 12870a c d - 11440a b c d + 6240a b c d - 1920a b c d + 256b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 +--R 45045d +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 7 7 3 7 4 6 6 +--R 6006b d x + (27720a b d + 14322b c d )x +--R + +--R 2 2 7 3 6 4 2 5 5 +--R (49140a b d + 68040a b c d + 8946b c d )x +--R + +--R 3 7 2 2 6 3 2 5 4 3 4 4 +--R (40040a b d + 125580a b c d + 44520a b c d + 70b c d )x +--R + +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (12870a d + 108680a b c d + 88140a b c d + 600a b c d - 80b c d )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (38610a c d + 85800a b c d + 2340a b c d - 720a b c d + 96b c d )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 +--R (38610a c d + 5720a b c d - 3120a b c d + 960a b c d - 128b c d)x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 12870a c d - 11440a b c d + 6240a b c d - 1920a b c d + 256b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 +--R 45045d +--R Type: Union(Expression(Integer),...) +--E 1277 + +--S 1278 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1279 + +)clear all + +--S 1280 of 2952 +t0000:=(a+b*x)^3*(c+d*x)^(5/2) +--R +--R +--R (1) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--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 2 3 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 * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 2952 +r0000:=-2/7*(b*c-a*d)^3*(c+d*x)^(7/2)/d^4+_ + 2/3*b*(b*c-a*d)^2*(c+d*x)^(9/2)/d^4-_ + 6/11*b^2*(b*c-a*d)*(c+d*x)^(11/2)/d^4+2/13*b^3*(c+d*x)^(13/2)/d^4 +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 462b d x + (1638a b d + 1134b c d )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (2002a b d + 4186a b c d + 742b c d )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (858a d + 5434a b c d + 2938a b c d + 10b c d )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (2574a c d + 4290a b c d + 78a b c d - 12b c d )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (2574a c d + 286a b c d - 104a b c d + 16b c d)x + 858a c d +--R + +--R 2 4 2 2 5 3 6 +--R - 572a b c d + 208a b c d - 32b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 +--R 3003d +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 6 6 2 6 3 5 5 +--R 462b d x + (1638a b d + 1134b c d )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (2002a b d + 4186a b c d + 742b c d )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (858a d + 5434a b c d + 2938a b c d + 10b c d )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (2574a c d + 4290a b c d + 78a b c d - 12b c d )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (2574a c d + 286a b c d - 104a b c d + 16b c d)x + 858a c d +--R + +--R 2 4 2 2 5 3 6 +--R - 572a b c d + 208a b c d - 32b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 +--R 3003d +--R Type: Union(Expression(Integer),...) +--E 1282 + +--S 1283 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1284 + +)clear all + +--S 1285 of 2952 +t0000:=(a+b*x)^2*(c+d*x)^(5/2) +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--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 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 2952 +r0000:=2/7*(b*c-a*d)^2*(c+d*x)^(7/2)/d^3-4/9*b*(b*c-a*d)*(c+d*x)^(9/2)/d^3+_ + 2/11*b^2*(c+d*x)^(11/2)/d^3 +--R +--R +--R (2) +--R 2 5 5 5 2 4 4 +--R 126b d x + (308a b d + 322b c d )x +--R + +--R 2 5 4 2 2 3 3 +--R (198a d + 836a b c d + 226b c d )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (594a c d + 660a b c d + 6b c d )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (594a c d + 44a b c d - 8b c d)x + 198a c d - 88a b c d + 16b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +--R 693d +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 5 5 5 2 4 4 +--R 126b d x + (308a b d + 322b c d )x +--R + +--R 2 5 4 2 2 3 3 +--R (198a d + 836a b c d + 226b c d )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (594a c d + 660a b c d + 6b c d )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (594a c d + 44a b c d - 8b c d)x + 198a c d - 88a b c d + 16b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +--R 693d +--R Type: Union(Expression(Integer),...) +--E 1287 + +--S 1288 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1289 + +)clear all + +--S 1290 of 2952 +t0000:=(a+b*x)*(c+d*x)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (1) (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 1290 + +--S 1291 of 2952 +r0000:=-2/7*(b*c-a*d)*(c+d*x)^(7/2)/d^2+2/9*b*(c+d*x)^(9/2)/d^2 +--R +--R +--R (2) +--R 4 4 4 3 3 3 2 2 2 +--R 14b d x + (18a d + 38b c d )x + (54a c d + 30b c d )x +--R + +--R 2 2 3 3 4 +--R (54a c d + 2b c d)x + 18a c d - 4b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 2 +--R 63d +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 4 3 3 3 2 2 2 +--R 14b d x + (18a d + 38b c d )x + (54a c d + 30b c d )x +--R + +--R 2 2 3 3 4 +--R (54a c d + 2b c d)x + 18a c d - 4b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 2 +--R 63d +--R Type: Union(Expression(Integer),...) +--E 1292 + +--S 1293 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 2952 +t0000:=(c+d*x)^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (1) (d x + 2c d x + c )\|d x + c +--R Type: Expression(Integer) +--E 1295 + +--S 1296 of 2952 +r0000:=2/7*(c+d*x)^(7/2)/d +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (2d x + 6c d x + 6c d x + 2c )\|d x + c +--R (2) ------------------------------------------ +--R 7d +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (2d x + 6c d x + 6c d x + 2c )\|d x + c +--R (3) ------------------------------------------ +--R 7d +--R Type: Union(Expression(Integer),...) +--E 1297 + +--S 1298 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1299 + +)clear all + +--S 1300 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R b x + a +--R Type: Expression(Integer) +--E 1300 + +--S 1301 of 2952 +r0000:=2/3*(b*c-a*d)*(c+d*x)^(3/2)/b^2+2/5*(c+d*x)^(5/2)/b-_ + 2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+_ + 2*(b*c-a*d)^2*sqrt(c+d*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 30a d + 60a b c d - 30b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (6b d x + (- 10a b d + 22b c d)x + 30a d - 70a b c d + 46b c )\|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +-+ +--R 15b \|b +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R (15a d - 30a b c d + 15b c ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b d x + (- 10a b d + 22b c d)x + 30a d - 70a b c d + 46b c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +--R 15b +--R , +--R +--R +---------+ +-------+ +--R 2 2 2 2 |a d - b c \|d x + c +--R (- 30a d + 60a b c d - 30b c ) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b d x + (- 10a b d + 22b c d)x + 30a d - 70a b c d + 46b c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +--R 15b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1302 + +--S 1303 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (a d - 2a b c d + b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (2a d - 4a b c d + 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (2a d - 4a b c d + 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (- 2a d + 4a b c d - 2b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1305 + +--S 1306 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1306 + +)clear all + +--S 1307 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x)^2 +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 2952 +r0000:=5/3*d*(c+d*x)^(3/2)/b^2-(c+d*x)^(5/2)/(b*(a+b*x))-_ + 5*d*(b*c-a*d)^(3/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+_ + 5*d*(b*c-a*d)*sqrt(c+d*x)/b^3 +--R +--R +--R (2) +--R 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 \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 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 \|d x + c +--R / +--R 4 3 +-+ +--R (3b x + 3a b )\|b +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R ((15a b d - 15b c d)x + 15a d - 15a b c d) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (4b d x + (- 20a b d + 28b c d)x - 30a d + 40a b c d - 6b c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 +--R 6b x + 6a b +--R , +--R +--R +---------+ +--R 2 2 2 2 |a d - b c +--R ((15a b d - 15b c d)x + 15a d - 15a b c d) |--------- +--R \| b +--R * +--R +-------+ +--R \|d x + c +--R atan(------------) +--R +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 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 ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 +--R 3b x + 3a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1309 + +--S 1310 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R 2 |- a d + b c +-+ +--R (5a d - 5b c d) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-----------+ \|b \|d x + c +--R (- 10a d + 10b c d)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-----------+ \|b \|d x + c +--R (- 5a d + 5b c d)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 2 +-+ |a d - b c \|d x + c +--R (5a d - 5b c d)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1313 + +)clear all + +--S 1314 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x)^3 +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 2952 +r0000:=-5/4*d*(c+d*x)^(3/2)/(b^2*(a+b*x))-1/2*(c+d*x)^(5/2)/(b*(a+b*x)^2)-_ + 15/4*d^2*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*_ + sqrt(b*c-a*d)/b^(7/2)+15/4*d^2*sqrt(c+d*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 15b d x - 30a b d x - 15a d )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-------+ +--R (8b d x + (25a b d - 9b c d)x + 15a d - 5a b c d - 2b c )\|b \|d x + c +--R / +--R 5 2 4 2 3 +-+ +--R (4b x + 8a b x + 4a b )\|b +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 2 2 |- a d + b c +--R (15b d x + 30a b d x + 15a d ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (16b d x + (50a b d - 18b c d)x + 30a d - 10a b c d - 4b c )\|d x + c +--R / +--R 5 2 4 2 3 +--R 8b x + 16a b x + 8a b +--R , +--R +--R +---------+ +-------+ +--R 2 2 2 2 2 2 |a d - b c \|d x + c +--R (- 15b d x - 30a b d x - 15a d ) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (8b d x + (25a b d - 9b c d)x + 15a d - 5a b c d - 2b c )\|d x + c +--R / +--R 5 2 4 2 3 +--R 4b x + 8a b x + 4a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1316 + +--S 1317 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R 2 |- a d + b c +-+ +--R 15d |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-----------+ \|b \|d x + c +--R 30d \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-----------+ \|b \|d x + c +--R 15d \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 2 +-+ |a d - b c \|d x + c +--R - 15d \|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 1319 + +--S 1320 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1320 + +)clear all + +--S 1321 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x)^4 +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 2952 +r0000:=-5/12*d*(c+d*x)^(3/2)/(b^2*(a+b*x)^2)-1/3*(c+d*x)^(5/2)/(b*(a+b*x)^3)-_ + 5/8*d^3*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(7/2)*_ + sqrt(b*c-a*d))-5/8*d^2*sqrt(c+d*x)/(b^3*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|d x + c +--R (- 15b d x - 45a b d x - 45a b d x - 15a d )atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 33b d x + (- 40a b d - 26b c d)x - 15a d - 10a b c d - 8b c ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|b \|d x + c +--R / +--R 6 3 5 2 2 4 3 3 +-----------+ +-+ +--R (24b x + 72a b x + 72a b x + 24a b )\|- a d + b c \|b +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 2 3 3 3 +--R (15b d x + 45a b d x + 45a b d x + 15a d ) +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 66b d x + (- 80a b d - 52b c d)x - 30a d - 20a b c d - 16b c ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b d + b c \|d x + c +--R / +--R +-------------+ +--R 6 3 5 2 2 4 3 3 | 2 +--R (48b x + 144a b x + 144a b x + 48a b )\|- a b d + b c +--R , +--R +--R 3 3 3 2 3 2 2 3 3 3 +--R (15b d x + 45a b d x + 45a b d x + 15a d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R atan(------------------------) +--R a d - b c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 33b d x + (- 40a b d - 26b c d)x - 15a d - 10a b c d - 8b c ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R / +--R +-----------+ +--R 6 3 5 2 2 4 3 3 | 2 +--R (24b x + 72a b x + 72a b x + 24a b )\|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1323 + +--S 1324 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 3 +-----------+ +-+ +--R 5d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 | 2 \|b \|d x + c +--R 10d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R 3 | 2 +-----------+ +-+ +--R 16b \|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1324 + +--S 1325 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1325 + +--S 1326 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 | 2 \|b \|d x + c +--R 5d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 3 +-----------+ +-+ \|a b d - b c \|d x + c +--R 5d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R +-----------+ +--R 3 +-----------+ +-+ | 2 +--R 8b \|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1327 + +)clear all + +--S 1328 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x)^5 +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 2952 +r0000:=-5/24*d*(c+d*x)^(3/2)/(b^2*(a+b*x)^3)-1/4*(c+d*x)^(5/2)/(b*(a+b*x)^4)+_ + 5/64*d^4*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(b^(7/2)*_ + (b*c-a*d)^(3/2))-5/32*d^2*sqrt(c+d*x)/(b^3*(a+b*x)^2)-_ + 5/64*d^3*sqrt(c+d*x)/(b^3*(b*c-a*d)*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 15b d x - 60a b d x - 90a b d x - 60a b d x - 15a d ) +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b d x + (- 73a b d + 118b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 55a b d - 36a b c d + 136b c d)x - 15a d - 10a b c d +--R + +--R 2 2 3 3 +--R - 8a b c d + 48b c +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|b \|d x + c +--R / +--R 7 8 4 2 6 7 3 +--R (192a b d - 192b c)x + (768a b d - 768a b c)x +--R + +--R 3 5 2 6 2 4 4 3 5 5 3 4 4 +--R (1152a b d - 1152a b c)x + (768a b d - 768a b c)x + 192a b d - 192a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1329 + +--S 1330 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (15b d x + 60a b d x + 90a b d x + 60a b d x + 15a d ) +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b d x + (- 146a b d + 236b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 110a b d - 72a b c d + 272b c d)x - 30a d - 20a b c d +--R + +--R 2 2 3 3 +--R - 16a b c d + 96b c +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b d + b c \|d x + c +--R / +--R 7 8 4 2 6 7 3 +--R (384a b d - 384b c)x + (1536a b d - 1536a b c)x +--R + +--R 3 5 2 6 2 4 4 3 5 5 3 +--R (2304a b d - 2304a b c)x + (1536a b d - 1536a b c)x + 384a b d +--R + +--R 4 4 +--R - 384a b c +--R * +--R +-------------+ +--R | 2 +--R \|- a b d + b c +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (15b d x + 60a b d x + 90a b d x + 60a b d x + 15a d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R atan(------------------------) +--R a d - b c +--R + +--R 3 3 3 2 3 3 2 2 +--R 15b d x + (- 73a b d + 118b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 55a b d - 36a b c d + 136b c d)x - 15a d - 10a b c d +--R + +--R 2 2 3 3 +--R - 8a b c d + 48b c +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R / +--R 7 8 4 2 6 7 3 +--R (192a b d - 192b c)x + (768a b d - 768a b c)x +--R + +--R 3 5 2 6 2 4 4 3 5 5 3 +--R (1152a b d - 1152a b c)x + (768a b d - 768a b c)x + 192a b d +--R + +--R 4 4 +--R - 192a b c +--R * +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1330 + +--S 1331 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 5d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|d x + c +--R 10d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R 3 4 | 2 +-----------+ +-+ +--R (128a b d - 128b c)\|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|d x + c +--R 5d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b d - b c \|d x + c +--R 5d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R +-----------+ +--R 3 4 +-----------+ +-+ | 2 +--R (64a b d - 64b c)\|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1334 + +)clear all + +--S 1335 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x)^6 +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 2952 +r0000:=-1/8*d*(c+d*x)^(3/2)/(b^2*(a+b*x)^4)-1/5*(c+d*x)^(5/2)/_ + (b*(a+b*x)^5)-3/128*d^5*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (b^(7/2)*(b*c-a*d)^(5/2))-1/16*d^2*sqrt(c+d*x)/(b^3*(a+b*x)^3)-_ + 1/64*d^3*sqrt(c+d*x)/(b^3*(b*c-a*d)*(a+b*x)^2)+_ + 3/128*d^4*sqrt(c+d*x)/(b^3*(b*c-a*d)^2*(a+b*x)) +--R +--R +--R (2) +--R 5 5 5 4 5 4 2 3 5 3 3 2 5 2 4 5 +--R - 15b d x - 75a b d x - 150a b d x - 150a b d x - 75a b d x +--R + +--R 5 5 +--R - 15a d +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 4 4 3 4 4 3 3 +--R 15b d x + (70a b d - 10b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 128a b d + 466a b c d - 248b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 70a b d - 46a b c d + 512a b c d - 336b c d)x - 15a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 10a b c d - 8a b c d + 176a b c d - 128b c +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|b \|d x + c +--R / +--R 2 8 2 9 10 2 5 +--R (640a b d - 1280a b c d + 640b c )x +--R + +--R 3 7 2 2 8 9 2 4 +--R (3200a b d - 6400a b c d + 3200a b c )x +--R + +--R 4 6 2 3 7 2 8 2 3 +--R (6400a b d - 12800a b c d + 6400a b c )x +--R + +--R 5 5 2 4 6 3 7 2 2 +--R (6400a b d - 12800a b c d + 6400a b c )x +--R + +--R 6 4 2 5 5 4 6 2 7 3 2 6 4 +--R (3200a b d - 6400a b c d + 3200a b c )x + 640a b d - 1280a b c d +--R + +--R 5 5 2 +--R 640a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 5 5 5 4 5 4 2 3 5 3 3 2 5 2 4 5 +--R 15b d x + 75a b d x + 150a b d x + 150a b d x + 75a b d x +--R + +--R 5 5 +--R 15a d +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R 30b d x + (140a b d - 20b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 256a b d + 932a b c d - 496b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 140a b d - 92a b c d + 1024a b c d - 672b c d)x - 30a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 20a b c d - 16a b c d + 352a b c d - 256b c +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b d + b c \|d x + c +--R / +--R 2 8 2 9 10 2 5 +--R (1280a b d - 2560a b c d + 1280b c )x +--R + +--R 3 7 2 2 8 9 2 4 +--R (6400a b d - 12800a b c d + 6400a b c )x +--R + +--R 4 6 2 3 7 2 8 2 3 +--R (12800a b d - 25600a b c d + 12800a b c )x +--R + +--R 5 5 2 4 6 3 7 2 2 +--R (12800a b d - 25600a b c d + 12800a b c )x +--R + +--R 6 4 2 5 5 4 6 2 7 3 2 6 4 +--R (6400a b d - 12800a b c d + 6400a b c )x + 1280a b d - 2560a b c d +--R + +--R 5 5 2 +--R 1280a b c +--R * +--R +-------------+ +--R | 2 +--R \|- a b d + b c +--R , +--R +--R 5 5 5 4 5 4 2 3 5 3 3 2 5 2 4 5 +--R 15b d x + 75a b d x + 150a b d x + 150a b d x + 75a b d x +--R + +--R 5 5 +--R 15a d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R atan(------------------------) +--R a d - b c +--R + +--R 4 4 4 3 4 4 3 3 +--R 15b d x + (70a b d - 10b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 128a b d + 466a b c d - 248b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 70a b d - 46a b c d + 512a b c d - 336b c d)x - 15a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 10a b c d - 8a b c d + 176a b c d - 128b c +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R / +--R 2 8 2 9 10 2 5 +--R (640a b d - 1280a b c d + 640b c )x +--R + +--R 3 7 2 2 8 9 2 4 +--R (3200a b d - 6400a b c d + 3200a b c )x +--R + +--R 4 6 2 3 7 2 8 2 3 +--R (6400a b d - 12800a b c d + 6400a b c )x +--R + +--R 5 5 2 4 6 3 7 2 2 +--R (6400a b d - 12800a b c d + 6400a b c )x +--R + +--R 6 4 2 5 5 4 6 2 7 3 2 6 4 +--R (3200a b d - 6400a b c d + 3200a b c )x + 640a b d - 1280a b c d +--R + +--R 5 5 2 +--R 640a b c +--R * +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1337 + +--S 1338 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 5 +-----------+ +-+ +--R 3d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 5 | 2 \|b \|d x + c +--R 6d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R 2 3 2 4 5 2 | 2 +-----------+ +-+ +--R (256a b d - 512a b c d + 256b c )\|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1339 + +--S 1340 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 5 | 2 \|b \|d x + c +--R 3d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 5 +-----------+ +-+ \|a b d - b c \|d x + c +--R 3d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R +-----------+ +--R 2 3 2 4 5 2 +-----------+ +-+ | 2 +--R (128a b d - 256a b c d + 128b c )\|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1341 + +)clear all + +--S 1342 of 2952 +t0000:=sqrt(-1+x)/(1+x)^2 +--R +--R +--R +-----+ +--R \|x - 1 +--R (1) ----------- +--R 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 1342 + +--S 1343 of 2952 +r0000:=atan(sqrt(-1+x)/sqrt(2))/sqrt(2)-sqrt(-1+x)/(1+x) +--R +--R +--R +-----+ +--R \|x - 1 +-+ +-----+ +--R (x + 1)atan(--------) - \|2 \|x - 1 +--R +-+ +--R \|2 +--R (2) ------------------------------------ +--R +-+ +--R (x + 1)\|2 +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-----+ +--R \|2 \|x - 1 +-+ +-----+ +--R (x + 1)atan(------------) - \|2 \|x - 1 +--R 2 +--R (3) ---------------------------------------- +--R +-+ +--R (x + 1)\|2 +--R Type: Union(Expression(Integer),...) +--E 1344 + +--S 1345 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +-+ +-----+ +-----+ +--R \|2 \|x - 1 \|x - 1 +--R atan(------------) - atan(--------) +--R 2 +-+ +--R \|2 +--R (4) ----------------------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1346 + +)clear all + +--S 1347 of 2952 +t0000:=sqrt(-1+x)/(1+x)^3 +--R +--R +--R +-----+ +--R \|x - 1 +--R (1) ----------------- +--R 3 2 +--R x + 3x + 3x + 1 +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 2952 +r0000:=1/8*atan(sqrt(-1+x)/sqrt(2))/sqrt(2)-_ + 1/2*sqrt(-1+x)/(1+x)^2+1/8*sqrt(-1+x)/(1+x) +--R +--R +--R +-----+ +--R 2 \|x - 1 +-+ +-----+ +--R (x + 2x + 1)atan(--------) + (x - 3)\|2 \|x - 1 +--R +-+ +--R \|2 +--R (2) ------------------------------------------------- +--R 2 +-+ +--R (8x + 16x + 8)\|2 +--R Type: Expression(Integer) +--E 1348 + +--S 1349 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +-----+ +--R 2 \|2 \|x - 1 +-+ +-----+ +--R (x + 2x + 1)atan(------------) + (x - 3)\|2 \|x - 1 +--R 2 +--R (3) ----------------------------------------------------- +--R 2 +-+ +--R (8x + 16x + 8)\|2 +--R Type: Union(Expression(Integer),...) +--E 1349 + +--S 1350 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +-+ +-----+ +-----+ +--R \|2 \|x - 1 \|x - 1 +--R atan(------------) - atan(--------) +--R 2 +-+ +--R \|2 +--R (4) ----------------------------------- +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1351 + +)clear all + +--S 1352 of 2952 +t0000:=(a+b*x)^5/(c+d*x)^(1/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1352 + +--S 1353 of 2952 +r0000:=10/3*b*(b*c-a*d)^4*(c+d*x)^(3/2)/d^6-_ + 4*b^2*(b*c-a*d)^3*(c+d*x)^(5/2)/d^6+_ + 20/7*b^3*(b*c-a*d)^2*(c+d*x)^(7/2)/d^6-_ + 10/9*b^4*(b*c-a*d)*(c+d*x)^(9/2)/d^6+2/11*b^5*(c+d*x)^(11/2)/d^6-_ + 2*(b*c-a*d)^5*sqrt(c+d*x)/d^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 126b d x + (770a b d - 140b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (1980a b d - 880a b c d + 160b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (2772a b d - 2376a b c d + 1056a b c d - 192b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b d - 3696a b c d + 3168a b c d - 1408a b c d + 256b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 1386a d - 4620a b c d + 7392a b c d - 6336a b c d + 2816a b c d +--R + +--R 5 5 +--R - 512b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 +--R 693d +--R Type: Expression(Integer) +--E 1353 + +--S 1354 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R 126b d x + (770a b d - 140b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (1980a b d - 880a b c d + 160b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (2772a b d - 2376a b c d + 1056a b c d - 192b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b d - 3696a b c d + 3168a b c d - 1408a b c d + 256b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 1386a d - 4620a b c d + 7392a b c d - 6336a b c d + 2816a b c d +--R + +--R 5 5 +--R - 512b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 +--R 693d +--R Type: Union(Expression(Integer),...) +--E 1354 + +--S 1355 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1355 + +--S 1356 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1356 + +)clear all + +--S 1357 of 2952 +t0000:=(a+b*x)^4/(c+d*x)^(1/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (1) -------------------------------------- +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1357 + +--S 1358 of 2952 +r0000:=-8/3*b*(b*c-a*d)^3*(c+d*x)^(3/2)/d^5+_ + 12/5*b^2*(b*c-a*d)^2*(c+d*x)^(5/2)/d^5-_ + 8/7*b^3*(b*c-a*d)*(c+d*x)^(7/2)/d^5+_ + 2/9*b^4*(c+d*x)^(9/2)/d^5+2*(b*c-a*d)^4*sqrt(c+d*x)/d^5 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 70b d x + (360a b d - 80b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (756a b d - 432a b c d + 96b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (840a b d - 1008a b c d + 576a b c d - 128b c d)x + 630a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1680a b c d + 2016a b c d - 1152a b c d + 256b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 +--R 315d +--R Type: Expression(Integer) +--E 1358 + +--S 1359 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 70b d x + (360a b d - 80b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (756a b d - 432a b c d + 96b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (840a b d - 1008a b c d + 576a b c d - 128b c d)x + 630a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1680a b c d + 2016a b c d - 1152a b c d + 256b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 +--R 315d +--R Type: Union(Expression(Integer),...) +--E 1359 + +--S 1360 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1360 + +--S 1361 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1361 + +)clear all + +--S 1362 of 2952 +t0000:=(a+b*x)^3/(c+d*x)^(1/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1362 + +--S 1363 of 2952 +r0000:=2*b*(b*c-a*d)^2*(c+d*x)^(3/2)/d^4-6/5*b^2*(b*c-a*d)*(c+d*x)^(5/2)/d^4+_ + 2/7*b^3*(c+d*x)^(7/2)/d^4-2*(b*c-a*d)^3*sqrt(c+d*x)/d^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 10b d x + (42a b d - 12b c d )x + (70a b d - 56a b c d + 16b c d)x +--R + +--R 3 3 2 2 2 2 3 3 +--R 70a d - 140a b c d + 112a b c d - 32b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 +--R 35d +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 10b d x + (42a b d - 12b c d )x + (70a b d - 56a b c d + 16b c d)x +--R + +--R 3 3 2 2 2 2 3 3 +--R 70a d - 140a b c d + 112a b c d - 32b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 +--R 35d +--R Type: Union(Expression(Integer),...) +--E 1364 + +--S 1365 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1365 + +--S 1366 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1366 + +)clear all + +--S 1367 of 2952 +t0000:=(a+b*x)^2/(c+d*x)^(1/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1367 + +--S 1368 of 2952 +r0000:=-4/3*b*(b*c-a*d)*(c+d*x)^(3/2)/d^3+2/5*b^2*(c+d*x)^(5/2)/d^3+_ + 2*(b*c-a*d)^2*sqrt(c+d*x)/d^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (6b d x + (20a b d - 8b c d)x + 30a d - 40a b c d + 16b c )\|d x + c +--R ------------------------------------------------------------------------ +--R 3 +--R 15d +--R Type: Expression(Integer) +--E 1368 + +--S 1369 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (6b d x + (20a b d - 8b c d)x + 30a d - 40a b c d + 16b c )\|d x + c +--R ------------------------------------------------------------------------ +--R 3 +--R 15d +--R Type: Union(Expression(Integer),...) +--E 1369 + +--S 1370 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1370 + +--S 1371 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1371 + +)clear all + +--S 1372 of 2952 +t0000:=(a+b*x)/(c+d*x)^(1/2) +--R +--R +--R b x + a +--R (1) ---------- +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1372 + +--S 1373 of 2952 +r0000:=2/3*b*(c+d*x)^(3/2)/d^2-2*(b*c-a*d)*sqrt(c+d*x)/d^2 +--R +--R +--R +-------+ +--R (2b d x + 6a d - 4b c)\|d x + c +--R (2) -------------------------------- +--R 2 +--R 3d +--R Type: Expression(Integer) +--E 1373 + +--S 1374 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +--R (2b d x + 6a d - 4b c)\|d x + c +--R (3) -------------------------------- +--R 2 +--R 3d +--R Type: Union(Expression(Integer),...) +--E 1374 + +--S 1375 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1375 + +--S 1376 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1376 + +)clear all + +--S 1377 of 2952 +t0000:=1/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (1) ---------- +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1377 + +--S 1378 of 2952 +r0000:=2*sqrt(c+d*x)/d +--R +--R +--R +-------+ +--R 2\|d x + c +--R (2) ----------- +--R d +--R Type: Expression(Integer) +--E 1378 + +--S 1379 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +--R 2\|d x + c +--R (3) ----------- +--R d +--R Type: Union(Expression(Integer),...) +--E 1379 + +--S 1380 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1380 + +--S 1381 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1381 + +)clear all + +--S 1382 of 2952 +t0000:=1/((a+b*x)*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|d x + c +--R Type: Expression(Integer) +--E 1382 + +--S 1383 of 2952 +r0000:=-2*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(sqrt(b)*sqrt(b*c-a*d)) +--R +--R +--R +-+ +-------+ +--R \|b \|d x + c +--R 2atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R (2) - ---------------------- +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1383 + +--S 1384 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R [---------------------------------------------------------------------, +--R +-------------+ +--R | 2 +--R \|- a b d + b c +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R 2atan(------------------------) +--R a d - b c +--R -------------------------------] +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R Type: Union(List(Expression(Integer)),...) +--E 1384 + +--S 1385 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--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 \|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1385 + +--S 1386 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1386 + +--S 1387 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--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 +-----------+ +-+ \|a b d - b c \|d x + c +--R 2\|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R +-----------+ +--R +-----------+ +-+ | 2 +--R \|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1387 + +--S 1388 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1388 + +)clear all + +--S 1389 of 2952 +t0000:=1/((a+b*x)^2*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|d x + c +--R Type: Expression(Integer) +--E 1389 + +--S 1390 of 2952 +r0000:=d*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + ((b*c-a*d)^(3/2)*sqrt(b))-sqrt(c+d*x)/((b*c-a*d)*(a+b*x)) +--R +--R +--R +-+ +-------+ +--R \|b \|d x + c +-----------+ +-+ +-------+ +--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 ((a b d - b c)x + a d - a b c)\|- a d + b c \|b +--R Type: Expression(Integer) +--E 1390 + +--S 1391 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R (b d x + a d) +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R 2\|- a b d + b c \|d x + c +--R / +--R +-------------+ +--R 2 2 | 2 +--R ((2a b d - 2b c)x + 2a d - 2a b c)\|- a b d + b c +--R , +--R +-----------+ +--R | 2 +-------+ +-----------+ +--R \|a b d - b c \|d x + c | 2 +-------+ +--R (b d x + a d)atan(------------------------) + \|a b d - b c \|d x + c +--R a d - b c +--R ----------------------------------------------------------------------] +--R +-----------+ +--R 2 2 | 2 +--R ((a b d - b c)x + a d - a b c)\|a b d - b c +--R Type: Union(List(Expression(Integer)),...) +--E 1391 + +--S 1392 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +-+ +--R d\|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|d x + c +--R 2d\|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R | 2 +-----------+ +-+ +--R (2a d - 2b c)\|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1392 + +--S 1393 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1393 + +--S 1394 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|d x + c +--R d\|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b d - b c \|d x + c +--R d\|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R +-----------+ +--R +-----------+ +-+ | 2 +--R (a d - b c)\|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1394 + +--S 1395 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1395 + +)clear all + +--S 1396 of 2952 +t0000:=1/((a+b*x)^3*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (b x + 3a b x + 3a b x + a )\|d x + c +--R Type: Expression(Integer) +--E 1396 + +--S 1397 of 2952 +r0000:=-3/4*d^2*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + ((b*c-a*d)^(5/2)*sqrt(b))-1/2*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^2)+_ + 3/4*d*sqrt(c+d*x)/((b*c-a*d)^2*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 \|b \|d x + c +--R (- 3b d x - 6a b d x - 3a d )atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +-+ +-------+ +--R (3b d x + 5a d - 2b c)\|- a d + b c \|b \|d x + c +--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 + (8a b d - 16a b c d + 8a b c )x +--R + +--R 4 2 3 2 2 2 +--R 4a d - 8a b c d + 4a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1397 + +--S 1398 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 2 2 +--R (3b d x + 6a b d x + 3a d ) +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (6b d x + 10a d - 4b c)\|- a b d + b c \|d x + c +--R / +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (8a b d - 16a b c d + 8b c )x + (16a b d - 32a b c d + 16a b c )x +--R + +--R 4 2 3 2 2 2 +--R 8a d - 16a b c d + 8a b c +--R * +--R +-------------+ +--R | 2 +--R \|- a b d + b c +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R 2 2 2 2 2 2 \|a b d - b c \|d x + c +--R (3b d x + 6a b d x + 3a d )atan(------------------------) +--R a d - b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R (3b d x + 5a d - 2b c)\|a b d - b c \|d x + c +--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 + (8a b d - 16a b c d + 8a b c )x +--R + +--R 4 2 3 2 2 2 +--R 4a d - 8a b c d + 4a b c +--R * +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1398 + +--S 1399 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R 3d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|d x + c +--R 6d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R 2 2 2 2 | 2 +-----------+ +-+ +--R (8a d - 16a b c d + 8b c )\|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1399 + +--S 1400 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1400 + +--S 1401 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|d x + c +--R 3d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 2 +-----------+ +-+ \|a b d - b c \|d x + c +--R 3d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R +-----------+ +--R 2 2 2 2 +-----------+ +-+ | 2 +--R (4a d - 8a b c d + 4b c )\|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1401 + +--S 1402 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1402 + +)clear all + +--S 1403 of 2952 +t0000:=1/((a+b*x)^4*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|d x + c +--R Type: Expression(Integer) +--E 1403 + +--S 1404 of 2952 +r0000:=5/8*d^3*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + ((b*c-a*d)^(7/2)*sqrt(b))-1/3*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^3)+_ + 5/12*d*sqrt(c+d*x)/((b*c-a*d)^2*(a+b*x)^2)-_ + 5/8*d^2*sqrt(c+d*x)/((b*c-a*d)^3*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 3 2 3 2 2 3 3 3 \|b \|d x + c +--R (- 15b d x - 45a b d x - 45a b d x - 15a d )atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b d x + (40a b d - 10b c d)x + 33a d - 26a b c d + 8b c ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|b \|d x + c +--R / +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (24a b d - 72a b c d + 72a b c d - 24b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (72a b d - 216a b c d + 216a b c d - 72a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 5 2 +--R (72a b d - 216a b c d + 216a b c d - 72a b c )x + 24a d - 72a b c d +--R + +--R 4 2 2 3 3 3 +--R 72a b c d - 24a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1404 + +--S 1405 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 2 3 3 3 +--R (15b d x + 45a b d x + 45a b d x + 15a d ) +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (30b d x + (80a b d - 20b c d)x + 66a d - 52a b c d + 16b c ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b d + b c \|d x + c +--R / +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (48a b d - 144a b c d + 144a b c d - 48b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (144a b d - 432a b c d + 432a b c d - 144a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (144a b d - 432a b c d + 432a b c d - 144a b c )x + 48a d +--R + +--R 5 2 4 2 2 3 3 3 +--R - 144a b c d + 144a b c d - 48a b c +--R * +--R +-------------+ +--R | 2 +--R \|- a b d + b c +--R , +--R +--R 3 3 3 2 3 2 2 3 3 3 +--R (15b d x + 45a b d x + 45a b d x + 15a d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R atan(------------------------) +--R a d - b c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (15b d x + (40a b d - 10b c d)x + 33a d - 26a b c d + 8b c ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R / +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (24a b d - 72a b c d + 72a b c d - 24b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (72a b d - 216a b c d + 216a b c d - 72a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (72a b d - 216a b c d + 216a b c d - 72a b c )x + 24a d +--R + +--R 5 2 4 2 2 3 3 3 +--R - 72a b c d + 72a b c d - 24a b c +--R * +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1405 + +--S 1406 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 3 +-----------+ +-+ +--R 5d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 3 | 2 \|b \|d x + c +--R 10d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-------------+ +--R 3 3 2 2 2 2 3 3 | 2 +-----------+ +--R (16a d - 48a b c d + 48a b c d - 16b c )\|- a b d + b c \|- a d + b c +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1406 + +--S 1407 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1407 + +--S 1408 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 3 | 2 \|b \|d x + c +--R 5d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 3 +-----------+ +-+ \|a b d - b c \|d x + c +--R 5d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R +-----------+ +--R 3 3 2 2 2 2 3 3 +-----------+ +-+ | 2 +--R (8a d - 24a b c d + 24a b c d - 8b c )\|- a d + b c \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1408 + +--S 1409 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1409 + +)clear all + +--S 1410 of 2952 +t0000:=1/((a+b*x)^5*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|d x + c +--R Type: Expression(Integer) +--E 1410 + +--S 1411 of 2952 +r0000:=-35/64*d^4*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + ((b*c-a*d)^(9/2)*sqrt(b))-1/4*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^4)+_ + 7/24*d*sqrt(c+d*x)/((b*c-a*d)^2*(a+b*x)^3)-_ + 35/96*d^2*sqrt(c+d*x)/((b*c-a*d)^3*(a+b*x)^2)+_ + 35/64*d^3*sqrt(c+d*x)/((b*c-a*d)^4*(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (- 105b d x - 420a b d x - 630a b d x - 420a b d x - 105a d ) +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b d x + (385a b d - 70b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (511a b d - 252a b c d + 56b c d)x + 279a d - 326a b c d +--R + +--R 2 2 3 3 +--R 200a b c d - 48b c +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|b \|d x + c +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (192a b d - 768a b c d + 1152a b c d - 768a b c d + 192b c )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (768a b d - 3072a b c d + 4608a b c d - 3072a b c d + 768a b c )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 2 6 4 2 +--R (1152a b d - 4608a b c d + 6912a b c d - 4608a b c d + 1152a b c )x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R (768a b d - 3072a b c d + 4608a b c d - 3072a b c d + 768a b c )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R 192a d - 768a b c d + 1152a b c d - 768a b c d + 192a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1411 + +--S 1412 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (105b d x + 420a b d x + 630a b d x + 420a b d x + 105a d ) +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 210b d x + (770a b d - 140b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (1022a b d - 504a b c d + 112b c d)x + 558a d - 652a b c d +--R + +--R 2 2 3 3 +--R 400a b c d - 96b c +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b d + b c \|d x + c +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (384a b d - 1536a b c d + 2304a b c d - 1536a b c d + 384b c )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 +--R 1536a b d - 6144a b c d + 9216a b c d - 6144a b c d +--R + +--R 7 4 +--R 1536a b c +--R * +--R 3 +--R x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 +--R 2304a b d - 9216a b c d + 13824a b c d - 9216a b c d +--R + +--R 2 6 4 +--R 2304a b c +--R * +--R 2 +--R x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 +--R 1536a b d - 6144a b c d + 9216a b c d - 6144a b c d +--R + +--R 3 5 4 +--R 1536a b c +--R * +--R x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R 384a d - 1536a b c d + 2304a b c d - 1536a b c d + 384a b c +--R * +--R +-------------+ +--R | 2 +--R \|- a b d + b c +--R , +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R (105b d x + 420a b d x + 630a b d x + 420a b d x + 105a d ) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R atan(------------------------) +--R a d - b c +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b d x + (385a b d - 70b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (511a b d - 252a b c d + 56b c d)x + 279a d - 326a b c d +--R + +--R 2 2 3 3 +--R 200a b c d - 48b c +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b d - b c \|d x + c +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (192a b d - 768a b c d + 1152a b c d - 768a b c d + 192b c )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (768a b d - 3072a b c d + 4608a b c d - 3072a b c d + 768a b c )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 +--R 1152a b d - 4608a b c d + 6912a b c d - 4608a b c d +--R + +--R 2 6 4 +--R 1152a b c +--R * +--R 2 +--R x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R (768a b d - 3072a b c d + 4608a b c d - 3072a b c d + 768a b c )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R 192a d - 768a b c d + 1152a b c d - 768a b c d + 192a b c +--R * +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1412 + +--S 1413 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R 35d \|- a d + b c \|b +--R * +--R +-------------+ +--R 2 +-------+ | 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 b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 4 | 2 \|b \|d x + c +--R 70d \|- a b d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (128a d - 512a b c d + 768a b c d - 512a b c d + 128b c ) +--R * +--R +-------------+ +--R | 2 +-----------+ +-+ +--R \|- a b d + b c \|- a d + b c \|b +--R Type: Expression(Integer) +--E 1413 + +--S 1414 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1414 + +--S 1415 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 4 | 2 \|b \|d x + c +--R 35d \|a b d - b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R | 2 +-------+ +--R 4 +-----------+ +-+ \|a b d - b c \|d x + c +--R 35d \|- a d + b c \|b atan(------------------------) +--R a d - b c +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (64a d - 256a b c d + 384a b c d - 256a b c d + 64b c )\|- a d + b c +--R * +--R +-----------+ +--R +-+ | 2 +--R \|b \|a b d - b c +--R Type: Expression(Integer) +--E 1415 + +--S 1416 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1416 + +)clear all + +--S 1417 of 2952 +t0000:=(a+b*x)^5/(c+d*x)^(3/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R +-------+ +--R (d x + c)\|d x + c +--R Type: Expression(Integer) +--E 1417 + +--S 1418 of 2952 +r0000:=-20/3*b^2*(b*c-a*d)^3*(c+d*x)^(3/2)/d^6+_ + 4*b^3*(b*c-a*d)^2*(c+d*x)^(5/2)/d^6-_ + 10/7*b^4*(b*c-a*d)*(c+d*x)^(7/2)/d^6+_ + 2/9*b^5*(c+d*x)^(9/2)/d^6+2*(b*c-a*d)^5/(d^6*sqrt(c+d*x))+_ + 10*b*(b*c-a*d)^4*sqrt(c+d*x)/d^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 14b d x + (90a b d - 20b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (252a b d - 144a b c d + 32b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b d - 504a b c d + 288a b c d - 64b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (630a b d - 1680a b c d + 2016a b c d - 1152a b c d + 256b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 126a d + 1260a b c d - 3360a b c d + 4032a b c d - 2304a b c d +--R + +--R 5 5 +--R 512b c +--R / +--R 6 +-------+ +--R 63d \|d x + c +--R Type: Expression(Integer) +--E 1418 + +--S 1419 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R 14b d x + (90a b d - 20b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (252a b d - 144a b c d + 32b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b d - 504a b c d + 288a b c d - 64b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (630a b d - 1680a b c d + 2016a b c d - 1152a b c d + 256b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 126a d + 1260a b c d - 3360a b c d + 4032a b c d - 2304a b c d +--R + +--R 5 5 +--R 512b c +--R / +--R 6 +-------+ +--R 63d \|d x + c +--R Type: Union(Expression(Integer),...) +--E 1419 + +--S 1420 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1420 + +--S 1421 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1421 + +)clear all + +--S 1422 of 2952 +t0000:=(a+b*x)^4/(c+d*x)^(3/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (1) -------------------------------------- +--R +-------+ +--R (d x + c)\|d x + c +--R Type: Expression(Integer) +--E 1422 + +--S 1423 of 2952 +r0000:=4*b^2*(b*c-a*d)^2*(c+d*x)^(3/2)/d^5-_ + 8/5*b^3*(b*c-a*d)*(c+d*x)^(5/2)/d^5+2/7*b^4*(c+d*x)^(7/2)/d^5-_ + 2*(b*c-a*d)^4/(d^5*sqrt(c+d*x))-8*b*(b*c-a*d)^3*sqrt(c+d*x)/d^5 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 10b d x + (56a b d - 16b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (140a b d - 112a b c d + 32b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (280a b d - 560a b c d + 448a b c d - 128b c d)x - 70a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 560a b c d - 1120a b c d + 896a b c d - 256b c +--R / +--R 5 +-------+ +--R 35d \|d x + c +--R Type: Expression(Integer) +--E 1423 + +--S 1424 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 10b d x + (56a b d - 16b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (140a b d - 112a b c d + 32b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (280a b d - 560a b c d + 448a b c d - 128b c d)x - 70a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 560a b c d - 1120a b c d + 896a b c d - 256b c +--R / +--R 5 +-------+ +--R 35d \|d x + c +--R Type: Union(Expression(Integer),...) +--E 1424 + +--S 1425 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1425 + +--S 1426 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1426 + +)clear all + +--S 1427 of 2952 +t0000:=(a+b*x)^3/(c+d*x)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R +-------+ +--R (d x + c)\|d x + c +--R Type: Expression(Integer) +--E 1427 + +--S 1428 of 2952 +r0000:=-2*b^2*(b*c-a*d)*(c+d*x)^(3/2)/d^4+2/5*b^3*(c+d*x)^(5/2)/d^4+_ + 2*(b*c-a*d)^3/(d^4*sqrt(c+d*x))+6*b*(b*c-a*d)^2*sqrt(c+d*x)/d^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b d x + (10a b d - 4b c d )x + (30a b d - 40a b c d + 16b c d)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 10a d + 60a b c d - 80a b c d + 32b c +--R / +--R 4 +-------+ +--R 5d \|d x + c +--R Type: Expression(Integer) +--E 1428 + +--S 1429 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b d x + (10a b d - 4b c d )x + (30a b d - 40a b c d + 16b c d)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 10a d + 60a b c d - 80a b c d + 32b c +--R / +--R 4 +-------+ +--R 5d \|d x + c +--R Type: Union(Expression(Integer),...) +--E 1429 + +--S 1430 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1430 + +--S 1431 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1431 + +)clear all + +--S 1432 of 2952 +t0000:=(a+b*x)^2/(c+d*x)^(3/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R +-------+ +--R (d x + c)\|d x + c +--R Type: Expression(Integer) +--E 1432 + +--S 1433 of 2952 +r0000:=2/3*b^2*(c+d*x)^(3/2)/d^3-2*(b*c-a*d)^2/(d^3*sqrt(c+d*x))-_ + 4*b*(b*c-a*d)*sqrt(c+d*x)/d^3 +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R 2b d x + (12a b d - 8b c d)x - 6a d + 24a b c d - 16b c +--R (2) ----------------------------------------------------------- +--R 3 +-------+ +--R 3d \|d x + c +--R Type: Expression(Integer) +--E 1433 + +--S 1434 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R 2b d x + (12a b d - 8b c d)x - 6a d + 24a b c d - 16b c +--R (3) ----------------------------------------------------------- +--R 3 +-------+ +--R 3d \|d x + c +--R Type: Union(Expression(Integer),...) +--E 1434 + +--S 1435 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1435 + +--S 1436 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1436 + +)clear all + +--S 1437 of 2952 +t0000:=(a+b*x)/(c+d*x)^(3/2) +--R +--R +--R b x + a +--R (1) ------------------- +--R +-------+ +--R (d x + c)\|d x + c +--R Type: Expression(Integer) +--E 1437 + +--S 1438 of 2952 +r0000:=2*(b*c-a*d)/(d^2*sqrt(c+d*x))+2*b*sqrt(c+d*x)/d^2 +--R +--R +--R 2b d x - 2a d + 4b c +--R (2) -------------------- +--R 2 +-------+ +--R d \|d x + c +--R Type: Expression(Integer) +--E 1438 + +--S 1439 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2b d x - 2a d + 4b c +--R (3) -------------------- +--R 2 +-------+ +--R d \|d x + c +--R Type: Union(Expression(Integer),...) +--E 1439 + +--S 1440 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1440 + +--S 1441 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1441 + +)clear all + +--S 1442 of 2952 +t0000:=1/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (1) ------------------- +--R +-------+ +--R (d x + c)\|d x + c +--R Type: Expression(Integer) +--E 1442 + +--S 1443 of 2952 +r0000:=(-2)/(d*sqrt(c+d*x)) +--R +--R +--R 2 +--R (2) - ----------- +--R +-------+ +--R d\|d x + c +--R Type: Expression(Integer) +--E 1443 + +--S 1444 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) - ----------- +--R +-------+ +--R d\|d x + c +--R Type: Union(Expression(Integer),...) +--E 1444 + +--S 1445 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1445 + +--S 1446 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1446 + +)clear all + +--S 1447 of 2952 +t0000:=1/((a+b*x)*(c+d*x)^(3/2)) +--R +--R +--R 1 +--R (1) --------------------------------------- +--R 2 +-------+ +--R (b d x + (a d + b c)x + a c)\|d x + c +--R Type: Expression(Integer) +--E 1447 + +--S 1448 of 2952 +r0000:=-2*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/(b*c-a*d)^(3/2)+_ + 2/((b*c-a*d)*sqrt(c+d*x)) +--R +--R +--R +-+ +-------+ +--R +-+ +-------+ \|b \|d x + c +-----------+ +--R 2\|b \|d x + c atanh(--------------) - 2\|- a d + b c +--R +-----------+ +--R \|- a d + b c +--R (2) ------------------------------------------------------ +--R +-----------+ +-------+ +--R (a d - b c)\|- a d + b c \|d x + c +--R Type: Expression(Integer) +--E 1448 + +--S 1449 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | b +-------+ +--R |- --------- \|d x + c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R - 2 +--R / +--R +-------+ +--R (a d - b c)\|d x + c +--R , +--R +---------+ +-------+ +--R | b +-------+ b\|d x + c +--R - 2 |--------- \|d x + c atan(----------------------- - 2 +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R ----------------------------------------------------------] +--R +-------+ +--R (a d - b c)\|d x + c +--R Type: Union(List(Expression(Integer)),...) +--E 1449 + +--S 1450 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +--R \|- a d + b c |- --------- +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|d x + c +--R - 2\|b atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R +-----------+ +--R (a d - b c)\|- a d + b c +--R Type: Expression(Integer) +--E 1450 + +--S 1451 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1451 + +--S 1452 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ \|b \|d x + c +--R - 2\|b atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R +-----------+ | b b\|d x + c +--R - 2\|- a d + b c |--------- atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R / +--R +-----------+ +--R (a d - b c)\|- a d + b c +--R Type: Expression(Integer) +--E 1452 + +--S 1453 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1453 + +)clear all + +--S 1454 of 2952 +t0000:=1/((a+b*x)^2*(c+d*x)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------- +--R 2 3 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 1454 + +--S 1455 of 2952 +r0000:=3*d*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/(b*c-a*d)^(5/2)-_ + 3*d/((b*c-a*d)^2*sqrt(c+d*x))+(-1)/((b*c-a*d)*(a+b*x)*sqrt(c+d*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|b \|d x + c +--R (3b d x + 3a d)\|b \|d x + c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R (- 3b d x - 2a d - b c)\|- a d + b c +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-----------+ +--R ((a b d - 2a b c d + b c )x + a d - 2a b c d + a b c )\|- a d + b c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1455 + +--S 1456 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | b +-------+ +--R (3b d x + 3a d) |- --------- \|d x + c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R - 6b d x - 4a d - 2b c +--R / +--R 2 2 2 3 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 )\|d x + c +--R , +--R +--R +---------+ +-------+ +--R | b +-------+ b\|d x + c +--R (- 3b d x - 3a d) |--------- \|d x + c atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R - 3b d x - 2a d - b c +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-------+ +--R ((a b d - 2a b c d + b c )x + a d - 2a b c d + a b c )\|d x + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1456 + +--S 1457 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +--R 3d\|- a d + b c |- --------- +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|d x + c +--R - 6d\|b atanh(--------------) +--R +-----------+ +--R \|- a d + b 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 1457 + +--S 1458 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1458 + +--S 1459 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ \|b \|d x + c +--R - 3d\|b atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R +-----------+ | b b\|d x + c +--R - 3d\|- a d + b c |--------- atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b 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 1459 + +--S 1460 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1460 + +)clear all + +--S 1461 of 2952 +t0000:=1/((a+b*x)^3*(c+d*x)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 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 * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1461 + +--S 1462 of 2952 +r0000:=-15/4*d^2*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/_ + (b*c-a*d)^(7/2)+15/4*d^2/((b*c-a*d)^3*sqrt(c+d*x))+_ + (-1/2)/((b*c-a*d)*(a+b*x)^2*sqrt(c+d*x))+_ + 5/4*d/((b*c-a*d)^2*(a+b*x)*sqrt(c+d*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-+ +-------+ \|b \|d x + c +--R (15b d x + 30a b d x + 15a d )\|b \|d x + c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 15b d x + (- 25a b d - 5b c d)x - 8a d - 9a b c d + 2b c ) +--R * +--R +-----------+ +--R \|- a d + b c +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b d - 12a b c d + 12a b c d - 4b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b d - 24a b c d + 24a b c d - 8a b c )x + 4a d - 12a b c d +--R + +--R 3 2 2 2 3 3 +--R 12a b c d - 4a b c +--R * +--R +-----------+ +-------+ +--R \|- a d + b c \|d x + c +--R Type: Expression(Integer) +--E 1462 + +--S 1463 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 2 2 | b +-------+ +--R (15b d x + 30a b d x + 15a d ) |- --------- \|d x + c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R - 30b d x + (- 50a b d - 10b c d)x - 16a d - 18a b c d + 4b c +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (8a b d - 24a b c d + 24a b c d - 8b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 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 3 2 2 2 3 3 +--R 24a b c d - 8a b c +--R * +--R +-------+ +--R \|d x + c +--R , +--R +--R +---------+ +--R 2 2 2 2 2 2 | b +-------+ +--R (- 15b d x - 30a b d x - 15a d ) |--------- \|d x + c +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 2 2 2 2 2 2 2 2 2 +--R - 15b d x + (- 25a b d - 5b c d)x - 8a d - 9a b c d + 2b c +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b d - 12a b c d + 12a b c d - 4b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b d - 24a b c d + 24a b c d - 8a b c )x + 4a d - 12a b c d +--R + +--R 3 2 2 2 3 3 +--R 12a b c d - 4a b c +--R * +--R +-------+ +--R \|d x + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1463 + +--S 1464 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R 2 +-----------+ | b +--R 15d \|- a d + b c |- --------- +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-+ \|b \|d x + c +--R - 30d \|b atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (8a d - 24a b c d + 24a b c d - 8b c )\|- a d + b c +--R Type: Expression(Integer) +--E 1464 + +--S 1465 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1465 + +--S 1466 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ \|b \|d x + c +--R - 15d \|b atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 2 +-----------+ | b b\|d x + c +--R - 15d \|- a d + b c |--------- atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b 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 1466 + +--S 1467 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1467 + +)clear all + +--S 1468 of 2952 +t0000:=1/((a+b*x)^4*(c+d*x)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b d x + (4a b d + b c)x + (6a b d + 4a b c)x + (4a b d + 6a b c)x +--R + +--R 4 3 4 +--R (a d + 4a b c)x + a c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1468 + +--S 1469 of 2952 +r0000:=35/8*d^3*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/_ + (b*c-a*d)^(9/2)-35/8*d^3/((b*c-a*d)^4*sqrt(c+d*x))+(-1/3)/_ + ((b*c-a*d)*(a+b*x)^3*sqrt(c+d*x))+_ + 7/12*d/((b*c-a*d)^2*(a+b*x)^2*sqrt(c+d*x))-_ + 35/24*d^2/((b*c-a*d)^3*(a+b*x)*sqrt(c+d*x)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +-+ +-------+ +--R (105b d x + 315a b d x + 315a b d x + 105a d )\|b \|d x + c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b d x + (- 280a b d - 35b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 231a b d - 98a b c d + 14b c d)x - 48a d - 87a b c d +--R + +--R 2 2 3 3 +--R 38a b c d - 8b c +--R * +--R +-----------+ +--R \|- a d + b c +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (24a b d - 96a b c d + 144a b c d - 96a b c d + 24b c )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (72a b d - 288a b c d + 432a b c d - 288a b c d + 72a b c )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (72a b d - 288a b c d + 432a b c d - 288a b c d + 72a b c )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 24a d - 96a b c d + 144a b c d - 96a b c d + 24a b c +--R * +--R +-----------+ +-------+ +--R \|- a d + b c \|d x + c +--R Type: Expression(Integer) +--E 1469 + +--S 1470 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 3 3 3 2 3 2 2 3 3 3 | b +--R (105b d x + 315a b d x + 315a b d x + 105a d ) |- --------- +--R \| a d - b c +--R * +--R +-------+ +--R \|d x + c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R - 210b d x + (- 560a b d - 70b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 462a b d - 196a b c d + 28b c d)x - 96a d - 174a b c d +--R + +--R 2 2 3 3 +--R 76a b c d - 16b c +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (48a b d - 192a b c d + 288a 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 6 4 2 +--R (144a b d - 576a b c d + 864a b c d - 576a b c d + 144a b c )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (144a b d - 576a b c d + 864a b c d - 576a b c d + 144a b c )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 48a d - 192a b c d + 288a b c d - 192a b c d + 48a b c +--R * +--R +-------+ +--R \|d x + c +--R , +--R +--R +---------+ +--R 3 3 3 2 3 2 2 3 3 3 | b +--R (- 105b d x - 315a b d x - 315a b d x - 105a d ) |--------- +--R \|a d - b c +--R * +--R +-------+ +--R +-------+ b\|d x + c +--R \|d x + c atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 3 3 3 2 3 3 2 2 +--R - 105b d x + (- 280a b d - 35b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 231a b d - 98a b c d + 14b c d)x - 48a d - 87a b c d + 38a b c d +--R + +--R 3 3 +--R - 8b c +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (24a b d - 96a b c d + 144a b c d - 96a b c d + 24b c )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (72a b d - 288a b c d + 432a b c d - 288a b c d + 72a b c )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (72a b d - 288a b c d + 432a b c d - 288a b c d + 72a b c )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 24a d - 96a b c d + 144a b c d - 96a b c d + 24a b c +--R * +--R +-------+ +--R \|d x + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1470 + +--S 1471 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R 3 +-----------+ | b +--R 35d \|- a d + b c |- --------- +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 +-+ \|b \|d x + c +--R - 70d \|b atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--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 )\|- a d + b c +--R Type: Expression(Integer) +--E 1471 + +--S 1472 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1472 + +--S 1473 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 +-+ \|b \|d x + c +--R - 35d \|b atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 3 +-----------+ | b b\|d x + c +--R - 35d \|- a d + b c |--------- atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--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 )\|- a d + b c +--R Type: Expression(Integer) +--E 1473 + +--S 1474 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1474 + +)clear all + +--S 1475 of 2952 +t0000:=(a+b*x)^5/(c+d*x)^(5/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R Type: Expression(Integer) +--E 1475 + +--S 1476 of 2952 +r0000:=2/3*(b*c-a*d)^5/(d^6*(c+d*x)^(3/2))+20/3*b^3*(b*c-a*d)^2*_ + (c+d*x)^(3/2)/d^6-2*b^4*(b*c-a*d)*(c+d*x)^(5/2)/d^6+_ + 2/7*b^5*(c+d*x)^(7/2)/d^6-10*b*(b*c-a*d)^4/(d^6*sqrt(c+d*x))-_ + 20*b^2*(b*c-a*d)^3*sqrt(c+d*x)/d^6 +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 6b d x + (42a b d - 12b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (140a b d - 112a b c d + 32b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b d - 840a b c d + 672a b c d - 192b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 210a b d + 1680a b c d - 3360a b c d + 2688a b c d - 768b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 14a d - 140a b c d + 1120a b c d - 2240a b c d + 1792a b c d +--R + +--R 5 5 +--R - 512b c +--R / +--R 7 6 +-------+ +--R (21d x + 21c d )\|d x + c +--R Type: Expression(Integer) +--E 1476 + +--S 1477 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 5 4 5 5 4 4 +--R 6b d x + (42a b d - 12b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (140a b d - 112a b c d + 32b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (420a b d - 840a b c d + 672a b c d - 192b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 210a b d + 1680a b c d - 3360a b c d + 2688a b c d - 768b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 14a d - 140a b c d + 1120a b c d - 2240a b c d + 1792a b c d +--R + +--R 5 5 +--R - 512b c +--R / +--R 7 6 +-------+ +--R (21d x + 21c d )\|d x + c +--R Type: Union(Expression(Integer),...) +--E 1477 + +--S 1478 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1478 + +--S 1479 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1479 + +)clear all + +--S 1480 of 2952 +t0000:=(a+b*x)^4/(c+d*x)^(5/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (1) -------------------------------------- +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R Type: Expression(Integer) +--E 1480 + +--S 1481 of 2952 +r0000:=-2/3*(b*c-a*d)^4/(d^5*(c+d*x)^(3/2))-_ + 8/3*b^3*(b*c-a*d)*(c+d*x)^(3/2)/d^5+_ + 2/5*b^4*(c+d*x)^(5/2)/d^5+8*b*(b*c-a*d)^3/(d^5*sqrt(c+d*x))+_ + 12*b^2*(b*c-a*d)^2*sqrt(c+d*x)/d^5 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 6b d x + (40a b d - 16b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (180a b d - 240a b c d + 96b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 120a b d + 720a b c d - 960a b c d + 384b c d)x - 10a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b c d + 480a b c d - 640a b c d + 256b c +--R / +--R 6 5 +-------+ +--R (15d x + 15c d )\|d x + c +--R Type: Expression(Integer) +--E 1481 + +--S 1482 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 6b d x + (40a b d - 16b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (180a b d - 240a b c d + 96b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 120a b d + 720a b c d - 960a b c d + 384b c d)x - 10a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 80a b c d + 480a b c d - 640a b c d + 256b c +--R / +--R 6 5 +-------+ +--R (15d x + 15c d )\|d x + c +--R Type: Union(Expression(Integer),...) +--E 1482 + +--S 1483 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1483 + +--S 1484 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1484 + +)clear all + +--S 1485 of 2952 +t0000:=(a+b*x)^3/(c+d*x)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R Type: Expression(Integer) +--E 1485 + +--S 1486 of 2952 +r0000:=2/3*(b*c-a*d)^3/(d^4*(c+d*x)^(3/2))+2/3*b^3*(c+d*x)^(3/2)/d^4-_ + 6*b*(b*c-a*d)^2/(d^4*sqrt(c+d*x))-6*b^2*(b*c-a*d)*sqrt(c+d*x)/d^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b d x + (18a b d - 12b c d )x + (- 18a b d + 72a b c d - 48b c d)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 2a d - 12a b c d + 48a b c d - 32b c +--R / +--R 5 4 +-------+ +--R (3d x + 3c d )\|d x + c +--R Type: Expression(Integer) +--E 1486 + +--S 1487 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 2b d x + (18a b d - 12b c d )x + (- 18a b d + 72a b c d - 48b c d)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 2a d - 12a b c d + 48a b c d - 32b c +--R / +--R 5 4 +-------+ +--R (3d x + 3c d )\|d x + c +--R Type: Union(Expression(Integer),...) +--E 1487 + +--S 1488 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1488 + +--S 1489 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1489 + +)clear all + +--S 1490 of 2952 +t0000:=(a+b*x)^2/(c+d*x)^(5/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R Type: Expression(Integer) +--E 1490 + +--S 1491 of 2952 +r0000:=-2/3*(b*c-a*d)^2/(d^3*(c+d*x)^(3/2))+4*b*(b*c-a*d)/(d^3*sqrt(c+d*x))+_ + 2*b^2*sqrt(c+d*x)/d^3 +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R 6b d x + (- 12a b d + 24b c d)x - 2a d - 8a b c d + 16b c +--R (2) ------------------------------------------------------------- +--R 4 3 +-------+ +--R (3d x + 3c d )\|d x + c +--R Type: Expression(Integer) +--E 1491 + +--S 1492 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 2 2 2 2 2 2 +--R 6b d x + (- 12a b d + 24b c d)x - 2a d - 8a b c d + 16b c +--R (3) ------------------------------------------------------------- +--R 4 3 +-------+ +--R (3d x + 3c d )\|d x + c +--R Type: Union(Expression(Integer),...) +--E 1492 + +--S 1493 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1493 + +--S 1494 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1494 + +)clear all + +--S 1495 of 2952 +t0000:=(a+b*x)/(c+d*x)^(5/2) +--R +--R +--R b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R Type: Expression(Integer) +--E 1495 + +--S 1496 of 2952 +r0000:=2/3*(b*c-a*d)/(d^2*(c+d*x)^(3/2))-2*b/(d^2*sqrt(c+d*x)) +--R +--R +--R - 6b d x - 2a d - 4b c +--R (2) ------------------------ +--R 3 2 +-------+ +--R (3d x + 3c d )\|d x + c +--R Type: Expression(Integer) +--E 1496 + +--S 1497 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R - 6b d x - 2a d - 4b c +--R (3) ------------------------ +--R 3 2 +-------+ +--R (3d x + 3c d )\|d x + c +--R Type: Union(Expression(Integer),...) +--E 1497 + +--S 1498 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1498 + +--S 1499 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1499 + +)clear all + +--S 1500 of 2952 +t0000:=1/(c+d*x)^(5/2) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R Type: Expression(Integer) +--E 1500 + +--S 1501 of 2952 +r0000:=(-2/3)/(d*(c+d*x)^(3/2)) +--R +--R +--R 2 +--R (2) - ----------------------- +--R 2 +-------+ +--R (3d x + 3c d)\|d x + c +--R Type: Expression(Integer) +--E 1501 + +--S 1502 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) - ----------------------- +--R 2 +-------+ +--R (3d x + 3c d)\|d x + c +--R Type: Union(Expression(Integer),...) +--E 1502 + +--S 1503 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1503 + +--S 1504 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1504 + +)clear all + +--S 1505 of 2952 +t0000:=1/((a+b*x)*(c+d*x)^(5/2)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------------- +--R 2 3 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 1505 + +--S 1506 of 2952 +r0000:=2/3/((b*c-a*d)*(c+d*x)^(3/2))-2*b^(3/2)*atanh(sqrt(b)*sqrt(c+d*x)/_ + sqrt(b*c-a*d))/(b*c-a*d)^(5/2)+2*b/((b*c-a*d)^2*sqrt(c+d*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|b \|d x + c +--R (- 6b d x - 6b c)\|b \|d x + c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-----------+ +--R (6b d x - 2a d + 8b c)\|- a d + b c +--R / +--R 2 3 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 \|- a d + b c \|d x + c +--R Type: Expression(Integer) +--E 1506 + +--S 1507 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | b +-------+ +--R (3b d x + 3b c) |- --------- \|d x + c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 6b d x - 2a d + 8b c +--R / +--R 2 3 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 )\|d x + c +--R , +--R +--R +---------+ +-------+ +--R | b +-------+ b\|d x + c +--R (6b d x + 6b c) |--------- \|d x + c atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 6b d x - 2a d + 8b c +--R / +--R 2 3 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 )\|d x + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1507 + +--S 1508 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +--R b\|- a d + b c |- --------- +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|d x + c +--R 2b\|b atanh(--------------) +--R +-----------+ +--R \|- a d + b 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 1508 + +--S 1509 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1509 + +--S 1510 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ \|b \|d x + c +--R 2b\|b atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R +-----------+ | b b\|d x + c +--R 2b\|- a d + b c |--------- atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b 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 1510 + +--S 1511 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1511 + +)clear all + +--S 1512 of 2952 +t0000:=1/((a+b*x)^2*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--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 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1512 + +--S 1513 of 2952 +r0000:=-5/3*d/((b*c-a*d)^2*(c+d*x)^(3/2))+(-1)/((b*c-a*d)*_ + (a+b*x)*(c+d*x)^(3/2))+5*b^(3/2)*d*atanh(sqrt(b)*sqrt(c+d*x)/_ + sqrt(b*c-a*d))/(b*c-a*d)^(7/2)-5*b*d/((b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 2 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 \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 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 2 +--R (3a b d - 9a b c d + 9a b c d - 3b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a d - 6a b c d + 6a b c d - 3b c )x + 3a c d - 9a b c d +--R + +--R 2 2 3 3 4 +--R 9a b c d - 3a b c +--R * +--R +-----------+ +-------+ +--R \|- a d + b c \|d x + c +--R Type: Expression(Integer) +--E 1513 + +--S 1514 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 2 | b +--R (15b d x + (15a b d + 15b c d)x + 15a b c d) |- --------- +--R \| a d - b c +--R * +--R +-------+ +--R \|d x + c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R 30b d x + (20a b d + 40b c d)x - 4a d + 28a b c d + 6b c +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--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 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 \|d x + c +--R , +--R +--R +---------+ +--R 2 2 2 2 2 | b +-------+ +--R (15b d x + (15a b d + 15b c d)x + 15a b c d) |--------- \|d x + c +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 2 2 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 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b d - 9a b c d + 9a b c d - 3b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a d - 6a b c d + 6a b c d - 3b c )x + 3a c d - 9a b c d +--R + +--R 2 2 3 3 4 +--R 9a b c d - 3a b c +--R * +--R +-------+ +--R \|d x + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1514 + +--S 1515 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +--R 5b d\|- a d + b c |- --------- +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|d x + c +--R 10b d\|b atanh(--------------) +--R +-----------+ +--R \|- a d + b 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 1515 + +--S 1516 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1516 + +--S 1517 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ \|b \|d x + c +--R 5b d\|b atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R +-----------+ | b b\|d x + c +--R 5b d\|- a d + b c |--------- atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (a d - 3a b c d + 3a b c d - b c )\|- a d + b c +--R Type: Expression(Integer) +--E 1517 + +--S 1518 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1518 + +)clear all + +--S 1519 of 2952 +t0000:=1/((a+b*x)^3*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--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 2 3 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 * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1519 + +--S 1520 of 2952 +r0000:=35/12*d^2/((b*c-a*d)^3*(c+d*x)^(3/2))+(-1/2)/((b*c-a*d)*(a+b*x)^2*_ + (c+d*x)^(3/2))+7/4*d/((b*c-a*d)^2*(a+b*x)*(c+d*x)^(3/2))-_ + 35/4*b^(3/2)*d^2*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (b*c-a*d)^(9/2)+35/4*b*d^2/((b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 +--R - 105b d x + (- 210a b d - 105b c d )x +--R + +--R 2 3 2 2 2 2 +--R (- 105a b d - 210a b c d )x - 105a b c d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|d x + c +--R \|b \|d x + c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b d x + (175a b d + 140b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (56a b d + 238a b c d + 21b c d)x - 8a d + 80a b c d + 39a b c d +--R + +--R 3 3 +--R - 6b c +--R * +--R +-----------+ +--R \|- a d + b c +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b d - 48a b c d + 72a b c d - 48a b c d + 12b c d)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b d - 84a b c d + 96a b c d - 24a b c d - 24a b c d +--R + +--R 6 5 +--R 12b c +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (12a d - 24a b c d - 24a b c d + 96a b c d - 84a b c d + 24a b c )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a c d - 48a b c d + 72a b c d - 48a b c d + 12a b c +--R * +--R +-----------+ +-------+ +--R \|- a d + b c \|d x + c +--R Type: Expression(Integer) +--E 1520 + +--S 1521 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 105b d x + (210a b d + 105b c d )x + (105a b d + 210a b c d )x +--R + +--R 2 2 +--R 105a b c d +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|d x + c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 210b d x + (350a b d + 280b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (112a b d + 476a b c d + 42b c d)x - 16a d + 160a b c d + 78a b c d +--R + +--R 3 3 +--R - 12b c +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (24a b d - 96a b c d + 144a b c d - 96a b c d + 24b c d)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 48a b d - 168a b c d + 192a b c d - 48a b c d - 48a b c d +--R + +--R 6 5 +--R 24b c +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 24a d - 48a b c d - 48a b c d + 192a b c d - 168a b c d +--R + +--R 5 5 +--R 48a b c +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 24a c d - 96a b c d + 144a b c d - 96a b c d + 24a b c +--R * +--R +-------+ +--R \|d x + c +--R , +--R +--R 3 3 3 2 3 3 2 2 2 3 2 2 +--R 105b d x + (210a b d + 105b c d )x + (105a b d + 210a b c d )x +--R + +--R 2 2 +--R 105a b c d +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|d x + c +--R |--------- \|d x + c atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 3 3 3 2 3 3 2 2 +--R 105b d x + (175a b d + 140b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (56a b d + 238a b c d + 21b c d)x - 8a d + 80a b c d + 39a b c d +--R + +--R 3 3 +--R - 6b c +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b d - 48a b c d + 72a b c d - 48a b c d + 12b c d)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b d - 84a b c d + 96a b c d - 24a b c d - 24a b c d +--R + +--R 6 5 +--R 12b c +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 12a d - 24a b c d - 24a b c d + 96a b c d - 84a b c d +--R + +--R 5 5 +--R 24a b c +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a c d - 48a b c d + 72a b c d - 48a b c d + 12a b c +--R * +--R +-------+ +--R \|d x + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1521 + +--S 1522 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R 2 +-----------+ | b +--R 35b d \|- a d + b c |- --------- +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-+ \|b \|d x + c +--R 70b d \|b atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--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 )\|- a d + b c +--R Type: Expression(Integer) +--E 1522 + +--S 1523 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1523 + +--S 1524 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ \|b \|d x + c +--R 35b d \|b atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 2 +-----------+ | b b\|d x + c +--R 35b d \|- a d + b c |--------- atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (4a d - 16a b c d + 24a b c d - 16a b c d + 4b c )\|- a d + b c +--R Type: Expression(Integer) +--E 1524 + +--S 1525 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1525 + +)clear all + +--S 1526 of 2952 +t0000:=1/((a+b*x)^4*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b d x + (4a b d + 2b c d)x + (6a b d + 8a b c d + b c )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b d + 12a b c d + 4a b c )x + (a d + 8a b c d + 6a b c )x +--R + +--R 4 3 2 4 2 +--R (2a c d + 4a b c )x + a c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1526 + +--S 1527 of 2952 +r0000:=-35/8*d^3/((b*c-a*d)^4*(c+d*x)^(3/2))+(-1/3)/((b*c-a*d)*(a+b*x)^3*_ + (c+d*x)^(3/2))+3/4*d/((b*c-a*d)^2*(a+b*x)^2*(c+d*x)^(3/2))-_ + 21/8*d^2/((b*c-a*d)^3*(a+b*x)*(c+d*x)^(3/2))+_ + 105/8*b^(3/2)*d^3*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (b*c-a*d)^(11/2)-105/8*b*d^3/((b*c-a*d)^5*sqrt(c+d*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 315b d x + (- 945a b d - 315b c d )x +--R + +--R 2 2 4 3 3 2 3 4 2 2 3 +--R (- 945a b d - 945a b c d )x + (- 315a b d - 945a b c d )x +--R + +--R 3 3 +--R - 315a b c d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|d x + c +--R \|b \|d x + c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 4 4 3 4 4 3 3 +--R 315b d x + (840a b d + 420b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (693a b d + 1134a b c d + 63b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (144a b d + 954a b c d + 180a b c d - 18b c d)x - 16a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 208a b c d + 165a b c d - 50a b c d + 8b c +--R * +--R +-----------+ +--R \|- a d + b c +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 24a b d - 120a b c d + 240a b c d - 240a b c d + 120a b c d +--R + +--R 8 5 +--R - 24b c d +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 72a b d - 336a b c d + 600a b c d - 480a b c d + 120a b c d +--R + +--R 7 5 8 6 +--R 48a b c d - 24b c +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 72a b d - 288a b c d + 360a b c d - 360a b c d + 288a b c d +--R + +--R 7 6 +--R - 72a b c +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 24a d - 48a b c d - 120a b c d + 480a b c d - 600a b c d +--R + +--R 3 5 5 2 6 6 +--R 336a b c d - 72a b c +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 24a c d - 120a b c d + 240a b c d - 240a b c d + 120a b c d +--R + +--R 3 5 6 +--R - 24a b c +--R * +--R +-----------+ +-------+ +--R \|- a d + b c \|d x + c +--R Type: Expression(Integer) +--E 1527 + +--S 1528 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R [ +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 315b d x + (945a b d + 315b c d )x + (945a b d + 945a b c d )x +--R + +--R 3 4 2 2 3 3 3 +--R (315a b d + 945a b c d )x + 315a b c d +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|d x + c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R 630b d x + (1680a b d + 840b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (1386a b d + 2268a b c d + 126b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (288a b d + 1908a b c d + 360a b c d - 36b c d)x - 32a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 416a b c d + 330a b c d - 100a b c d + 16b c +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 48a b d - 240a b c d + 480a b c d - 480a b c d + 240a b c d +--R + +--R 8 5 +--R - 48b c d +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 +--R 144a b d - 672a b c d + 1200a b c d - 960a b c d +--R + +--R 2 6 4 2 7 5 8 6 +--R 240a b c d + 96a b c d - 48b c +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 144a b d - 576a b c d + 720a b c d - 720a b c d + 576a b c d +--R + +--R 7 6 +--R - 144a b c +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 48a d - 96a b c d - 240a b c d + 960a b c d - 1200a b c d +--R + +--R 3 5 5 2 6 6 +--R 672a b c d - 144a b c +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 48a c d - 240a b c d + 480a b c d - 480a b c d + 240a b c d +--R + +--R 3 5 6 +--R - 48a b c +--R * +--R +-------+ +--R \|d x + c +--R , +--R +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 2 +--R 315b d x + (945a b d + 315b c d )x + (945a b d + 945a b c d )x +--R + +--R 3 4 2 2 3 3 3 +--R (315a b d + 945a b c d )x + 315a b c d +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|d x + c +--R |--------- \|d x + c atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 4 4 4 3 4 4 3 3 +--R 315b d x + (840a b d + 420b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (693a b d + 1134a b c d + 63b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (144a b d + 954a b c d + 180a b c d - 18b c d)x - 16a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 208a b c d + 165a b c d - 50a b c d + 8b c +--R / +--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 7 4 2 +--R 24a b d - 120a b c d + 240a b c d - 240a b c d + 120a b c d +--R + +--R 8 5 +--R - 24b c d +--R * +--R 4 +--R x +--R + +--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3 2 6 4 2 +--R 72a b d - 336a b c d + 600a b c d - 480a b c d + 120a b c d +--R + +--R 7 5 8 6 +--R 48a b c d - 24b c +--R * +--R 3 +--R x +--R + +--R 7 6 6 2 5 5 3 2 4 3 5 4 2 2 6 5 +--R 72a b d - 288a b c d + 360a b c d - 360a b c d + 288a b c d +--R + +--R 7 6 +--R - 72a b c +--R * +--R 2 +--R x +--R + +--R 8 6 7 5 6 2 2 4 5 3 3 3 4 4 4 2 +--R 24a d - 48a b c d - 120a b c d + 480a b c d - 600a b c d +--R + +--R 3 5 5 2 6 6 +--R 336a b c d - 72a b c +--R * +--R x +--R + +--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5 +--R 24a c d - 120a b c d + 240a b c d - 240a b c d + 120a b c d +--R + +--R 3 5 6 +--R - 24a b c +--R * +--R +-------+ +--R \|d x + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1528 + +--S 1529 of 2952 +m0000:=a0000.1 - r0000 +--R +--R +--R (4) +--R +-----------+ +--R 3 +-----------+ | b +--R 105b d \|- a d + b c |- --------- +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 +-+ \|b \|d x + c +--R 210b d \|b atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (16a d - 80a b c d + 160a b c d - 160a b c d + 80a b c d - 16b c ) +--R * +--R +-----------+ +--R \|- a d + b c +--R Type: Expression(Integer) +--E 1529 + +--S 1530 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1530 + +--S 1531 of 2952 +m0000:=a0000.2 - r0000 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 +-+ \|b \|d x + c +--R 105b d \|b atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 3 +-----------+ | b b\|d x + c +--R 105b d \|- a d + b c |--------- atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (8a d - 40a b c d + 80a b c d - 80a b c d + 40a b c d - 8b c ) +--R * +--R +-----------+ +--R \|- a d + b c +--R Type: Expression(Integer) +--E 1531 + +--S 1532 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1532 + +)clear all + +--S 1533 of 2952 +t0000:=(a+b*x)^5*(a*c+b*c*x)^(3/2) +--R +--R +--R (1) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x +--R + +--R 6 +--R a c +--R * +--R +-----------+ +--R \|b c x + a c +--R Type: Expression(Integer) +--E 1533 + +--S 1534 of 2952 +r0000:=2/15*(a*c+b*c*x)^(15/2)/(b*c^6) +--R +--R +--R (2) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 2b c x + 14a b c x + 42a b c x + 70a b c x + 70a b c x +--R + +--R 5 2 2 6 7 +--R 42a b c x + 14a b c x + 2a c +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R 15b +--R Type: Expression(Integer) +--E 1534 + +--S 1535 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R 2b c x + 14a b c x + 42a b c x + 70a b c x + 70a b c x +--R + +--R 5 2 2 6 7 +--R 42a b c x + 14a b c x + 2a c +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R 15b +--R Type: Union(Expression(Integer),...) +--E 1535 + +--S 1536 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1536 + +--S 1537 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1537 + +)clear all + +--S 1538 of 2952 +t0000:=(a+b*x)^5*(a*c+b*c*x)^(1/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-----------+ +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b c x + a c +--R Type: Expression(Integer) +--E 1538 + +--S 1539 of 2952 +r0000:=2/13*(a*c+b*c*x)^(13/2)/(b*c^6) +--R +--R +--R (2) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (2b x + 12a b x + 30a b x + 40a b x + 30a b x + 12a b x + 2a ) +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R 13b +--R Type: Expression(Integer) +--E 1539 + +--S 1540 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (2b x + 12a b x + 30a b x + 40a b x + 30a b x + 12a b x + 2a ) +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R 13b +--R Type: Union(Expression(Integer),...) +--E 1540 + +--S 1541 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1541 + +--S 1542 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1542 + +)clear all + +--S 1543 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^(1/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) -------------------------------------------------- +--R +-----------+ +--R \|b c x + a c +--R Type: Expression(Integer) +--E 1543 + +--S 1544 of 2952 +r0000:=2/11*(a*c+b*c*x)^(11/2)/(b*c^6) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-----------+ +--R (2b x + 10a b x + 20a b x + 20a b x + 10a b x + 2a )\|b c x + a c +--R (2) ---------------------------------------------------------------------- +--R 11b c +--R Type: Expression(Integer) +--E 1544 + +--S 1545 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-----------+ +--R (2b x + 10a b x + 20a b x + 20a b x + 10a b x + 2a )\|b c x + a c +--R (3) ---------------------------------------------------------------------- +--R 11b c +--R Type: Union(Expression(Integer),...) +--E 1545 + +--S 1546 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1546 + +--S 1547 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1547 + +)clear all + +--S 1548 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^(3/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (1) -------------------------------------- +--R +-----------+ +--R c\|b c x + a c +--R Type: Expression(Integer) +--E 1548 + +--S 1549 of 2952 +r0000:=2/9*(a*c+b*c*x)^(9/2)/(b*c^6) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-----------+ +--R (2b x + 8a b x + 12a b x + 8a b x + 2a )\|b c x + a c +--R (2) --------------------------------------------------------- +--R 2 +--R 9b c +--R Type: Expression(Integer) +--E 1549 + +--S 1550 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-----------+ +--R (2b x + 8a b x + 12a b x + 8a b x + 2a )\|b c x + a c +--R (3) --------------------------------------------------------- +--R 2 +--R 9b c +--R Type: Union(Expression(Integer),...) +--E 1550 + +--S 1551 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1551 + +--S 1552 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1552 + +)clear all + +--S 1553 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 2 +-----------+ +--R c \|b c x + a c +--R Type: Expression(Integer) +--E 1553 + +--S 1554 of 2952 +r0000:=2/7*(a*c+b*c*x)^(7/2)/(b*c^6) +--R +--R +--R 3 3 2 2 2 3 +-----------+ +--R (2b x + 6a b x + 6a b x + 2a )\|b c x + a c +--R (2) ---------------------------------------------- +--R 3 +--R 7b c +--R Type: Expression(Integer) +--E 1554 + +--S 1555 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 3 2 2 2 3 +-----------+ +--R (2b x + 6a b x + 6a b x + 2a )\|b c x + a c +--R (3) ---------------------------------------------- +--R 3 +--R 7b c +--R Type: Union(Expression(Integer),...) +--E 1555 + +--S 1556 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1556 + +--S 1557 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1557 + +)clear all + +--S 1558 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^(7/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 3 +-----------+ +--R c \|b c x + a c +--R Type: Expression(Integer) +--E 1558 + +--S 1559 of 2952 +r0000:=2/5*(a*c+b*c*x)^(5/2)/(b*c^6) +--R +--R +--R 2 2 2 +-----------+ +--R (2b x + 4a b x + 2a )\|b c x + a c +--R (2) ------------------------------------ +--R 4 +--R 5b c +--R Type: Expression(Integer) +--E 1559 + +--S 1560 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 2 2 +-----------+ +--R (2b x + 4a b x + 2a )\|b c x + a c +--R (3) ------------------------------------ +--R 4 +--R 5b c +--R Type: Union(Expression(Integer),...) +--E 1560 + +--S 1561 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1561 + +--S 1562 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1562 + +)clear all + +--S 1563 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^(9/2) +--R +--R +--R b x + a +--R (1) ---------------- +--R 4 +-----------+ +--R c \|b c x + a c +--R Type: Expression(Integer) +--E 1563 + +--S 1564 of 2952 +r0000:=2/3*(a*c+b*c*x)^(3/2)/(b*c^6) +--R +--R +--R +-----------+ +--R (2b x + 2a)\|b c x + a c +--R (2) ------------------------- +--R 5 +--R 3b c +--R Type: Expression(Integer) +--E 1564 + +--S 1565 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +-----------+ +--R (2b x + 2a)\|b c x + a c +--R (3) ------------------------- +--R 5 +--R 3b c +--R Type: Union(Expression(Integer),...) +--E 1565 + +--S 1566 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1566 + +--S 1567 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1567 + +)clear all + +--S 1568 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^(11/2) +--R +--R +--R 1 +--R (1) ---------------- +--R 5 +-----------+ +--R c \|b c x + a c +--R Type: Expression(Integer) +--E 1568 + +--S 1569 of 2952 +r0000:=2*sqrt(a*c+b*c*x)/(b*c^6) +--R +--R +--R +-----------+ +--R 2\|b c x + a c +--R (2) --------------- +--R 6 +--R b c +--R Type: Expression(Integer) +--E 1569 + +--S 1570 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +-----------+ +--R 2\|b c x + a c +--R (3) --------------- +--R 6 +--R b c +--R Type: Union(Expression(Integer),...) +--E 1570 + +--S 1571 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1571 + +--S 1572 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1572 + +)clear all + +--S 1573 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^(13/2) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 6 6 +-----------+ +--R (b c x + a c )\|b c x + a c +--R Type: Expression(Integer) +--E 1573 + +--S 1574 of 2952 +r0000:=(-2)/(b*c^6*sqrt(a*c+b*c*x)) +--R +--R +--R 2 +--R (2) - ------------------ +--R 6 +-----------+ +--R b c \|b c x + a c +--R Type: Expression(Integer) +--E 1574 + +--S 1575 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) - ------------------ +--R 6 +-----------+ +--R b c \|b c x + a c +--R Type: Union(Expression(Integer),...) +--E 1575 + +--S 1576 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1576 + +--S 1577 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1577 + +)clear all + +--S 1578 of 2952 +t0000:=1/((-2+x)*sqrt(2+x)) +--R +--R +--R 1 +--R (1) --------------- +--R +-----+ +--R (x - 2)\|x + 2 +--R Type: Expression(Integer) +--E 1578 + +--S 1579 of 2952 +r0000:=-atanh(1/2*sqrt(2+x)) +--R +--R +--R +-----+ +--R \|x + 2 +--R (2) - atanh(--------) +--R 2 +--R Type: Expression(Integer) +--E 1579 + +--S 1580 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +-----+ +-----+ +--R - log(\|x + 2 + 2) + log(\|x + 2 - 2) +--R (3) --------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1580 + +--S 1581 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +-----+ +--R +-----+ +-----+ \|x + 2 +--R - log(\|x + 2 + 2) + log(\|x + 2 - 2) + 2atanh(--------) +--R 2 +--R (4) ---------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1581 + +--S 1582 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1582 + +)clear all + +--S 1583 of 2952 +t0000:=1/((2+3*x)*sqrt(1+5*x)) +--R +--R +--R 1 +--R (1) ----------------- +--R +------+ +--R (3x + 2)\|5x + 1 +--R Type: Expression(Integer) +--E 1583 + +--S 1584 of 2952 +r0000:=2*atan(sqrt(3/7)*sqrt(1+5*x))/sqrt(21) +--R +--R +--R +-+ +------+ +--R \|3 \|5x + 1 +--R 2atan(-------------) +--R +-+ +--R \|7 +--R (2) -------------------- +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 1584 + +--S 1585 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +--+ +------+ +--R \|21 \|5x + 1 +--R 2atan(--------------) +--R 7 +--R (3) --------------------- +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 1585 + +--S 1586 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +--+ +------+ +-+ +------+ +--R \|21 \|5x + 1 \|3 \|5x + 1 +--R 2atan(--------------) - 2atan(-------------) +--R 7 +-+ +--R \|7 +--R (4) -------------------------------------------- +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 1586 + +--S 1587 of 2952 +d0000:=D(m0000,x) +--R +--R +--R +-+ +-+ +--+ +--R - \|3 \|7 \|21 + 21 +--R (5) -------------------- +--R +------+ +--R (63x + 42)\|5x + 1 +--R Type: Expression(Integer) +--E 1587 + +)clear all + +--S 1588 of 2952 +t0000:=(1-x)^(1/3)/(1+x) +--R +--R +--R 3+-------+ +--R \|- x + 1 +--R (1) ---------- +--R x + 1 +--R Type: Expression(Integer) +--E 1588 + +--S 1589 of 2952 +r0000:=3*(1-x)^(1/3)+2^(1/3)*log(2^(1/3)-(1-x)^(1/3))-_ + log(2^(2/3)+2^(1/3)*(1-x)^(1/3)+(1-x)^(2/3))/2^(2/3)-_ + 2^(1/3)*atan((1+2^(2/3)*(1-x)^(1/3))/sqrt(3))*sqrt(3) +--R +--R +--R (2) +--R 3+-------+2 3+-+3+-------+ 3+-+2 3+-------+ 3+-+ +--R - log(\|- x + 1 + \|2 \|- x + 1 + \|2 ) + 2log(- \|- x + 1 + \|2 ) +--R + +--R 3+-+2 3+-------+ +--R +-+ \|2 \|- x + 1 + 1 3+-+2 3+-------+ +--R - 2\|3 atan(-------------------) + 3\|2 \|- x + 1 +--R +-+ +--R \|3 +--R / +--R 3+-+2 +--R \|2 +--R Type: Expression(Integer) +--E 1589 + +--S 1590 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3+-+ 3+-------+2 3+-+3+-------+ 3+-+2 +--R - \|2 log(\|- x + 1 + \|2 \|- x + 1 + \|2 ) +--R + +--R 3+-------+ 3+-+ +--R 3+-+ 3+-------+ 3+-+ 3+-+ +-+ 2\|- x + 1 + \|2 +--R 2\|2 log(\|- x + 1 - \|2 ) - 2\|2 \|3 atan(------------------) +--R 3+-+ +-+ +--R \|2 \|3 +--R + +--R 3+-------+ +--R 6\|- x + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1590 + +--S 1591 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3+-------+ 3+-+ 3+-------+ 3+-+ +--R 2log(\|- x + 1 - \|2 ) - 2log(- \|- x + 1 + \|2 ) +--R + +--R 3+-+2 3+-------+ 3+-------+ 3+-+ +--R +-+ \|2 \|- x + 1 + 1 +-+ 2\|- x + 1 + \|2 +--R 2\|3 atan(-------------------) - 2\|3 atan(------------------) +--R +-+ 3+-+ +-+ +--R \|3 \|2 \|3 +--R / +--R 3+-+2 +--R \|2 +--R Type: Expression(Integer) +--E 1591 + +--S 1592 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1592 + +)clear all + +--S 1593 of 2952 +t0000:=(3-2*x)^(1/3)*(7+x) +--R +--R +--R 3+--------+ +--R (1) (x + 7)\|- 2x + 3 +--R Type: Expression(Integer) +--E 1593 + +--S 1594 of 2952 +r0000:=-51/16*(3-2*x)^(4/3)+3/28*(3-2*x)^(7/3) +--R +--R +--R 2 3+--------+ +--R (48x + 570x - 963)\|- 2x + 3 +--R (2) ------------------------------ +--R 112 +--R Type: Expression(Integer) +--E 1594 + +--S 1595 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3+--------+ +--R (48x + 570x - 963)\|- 2x + 3 +--R (3) ------------------------------ +--R 112 +--R Type: Union(Expression(Integer),...) +--E 1595 + +--S 1596 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1596 + +--S 1597 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1597 + +)clear all + +--S 1598 of 2952 +t0000:=(1-x)^(1/3)*(1+x)^2 +--R +--R +--R 2 3+-------+ +--R (1) (x + 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 1598 + +--S 1599 of 2952 +r0000:=-3*(1-x)^(4/3)+12/7*(1-x)^(7/3)-3/10*(1-x)^(10/3) +--R +--R +--R 3 2 3+-------+ +--R (21x + 57x + 33x - 111)\|- x + 1 +--R (2) ----------------------------------- +--R 70 +--R Type: Expression(Integer) +--E 1599 + +--S 1600 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 2 3+-------+ +--R (21x + 57x + 33x - 111)\|- x + 1 +--R (3) ----------------------------------- +--R 70 +--R Type: Union(Expression(Integer),...) +--E 1600 + +--S 1601 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1601 + +--S 1602 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1602 + +)clear all + +--S 1603 of 2952 +t0000:=(a+b*x)^(7/2)*(c+d*x)^(1/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +-------+ +--R (1) (b x + 3a b x + 3a b x + a )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1603 + +--S 1604 of 2952 +r0000:=7/128*(b*c-a*d)^5*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(3/2)*d^(9/2))+7/192*(b*c-a*d)^3*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d^3)-_ + 7/240*(b*c-a*d)^2*(a+b*x)^(5/2)*sqrt(c+d*x)/(b*d^2)+_ + 1/40*(b*c-a*d)*(a+b*x)^(7/2)*sqrt(c+d*x)/(b*d)+_ + 1/5*(a+b*x)^(9/2)*sqrt(c+d*x)/b-_ + 7/128*(b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^4) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 105a d + 525a b c d - 1050a b c d + 1050a b c d - 525a b c d +--R + +--R 5 5 +--R 105b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 4 4 3 4 4 3 3 +--R 384b d x + (1488a b d + 48b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (2104a b d + 256a b c d - 56b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (1210a b d + 578a b c d - 322a b c d + 70b c d)x + 105a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 790a b c d - 896a b c d + 490a b c d - 105b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 4 +-+ +-+ +--R 1920b d \|b \|d +--R Type: Expression(Integer) +--E 1604 + +--S 1605 of 2952 +--a0000:=integrate(t0000,x) +--E 1605 + +--S 1606 of 2952 +--m0000:=a0000 - r0000 +--E 1606 + +--S 1607 of 2952 +--d0000:=D(m0000,x) +--E 1607 + +)clear all + +--S 1608 of 2952 +t0000:=(a+b*x)^(5/2)*(c+d*x)^(1/2) +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (1) (b x + 2a b x + a )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1608 + +--S 1609 of 2952 +r0000:=-5/64*(b*c-a*d)^4*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(3/2)*d^(7/2))-5/96*(b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d^2)+_ + 1/24*(b*c-a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/(b*d)+_ + 1/4*(a+b*x)^(7/2)*sqrt(c+d*x)/b+_ + 5/64*(b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x)/(b*d^3) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 15a d + 60a b c d - 90a b c d + 60a b c d - 15b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b d x + (136a b d + 8b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (118a b d + 36a b c d - 10b c d)x + 15a d + 73a b c d - 55a b c d +--R + +--R 3 3 +--R 15b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 +-+ +-+ +--R 192b d \|b \|d +--R Type: Expression(Integer) +--E 1609 + +--S 1610 of 2952 +--a0000:=integrate(t0000,x) +--E 1610 + +--S 1611 of 2952 +--m0000:=a0000 - r0000 +--E 1611 + +--S 1612 of 2952 +--d0000:=D(m0000,x) +--E 1612 + +)clear all + +--S 1613 of 2952 +t0000:=(a+b*x)^(3/2)*(c+d*x)^(1/2) +--R +--R +--R +-------+ +-------+ +--R (1) (b x + a)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1613 + +--S 1614 of 2952 +r0000:=1/8*(b*c-a*d)^3*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(3/2)*d^(5/2))+1/12*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b*d)+_ + 1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/b-1/8*(b*c-a*d)^2*_ + sqrt(a+b*x)*sqrt(c+d*x)/(b*d^2) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (- 3a d + 9a b c d - 9a b c d + 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (14a b d + 2b c d)x + 3a d + 8a b c d - 3b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 24b d \|b \|d +--R Type: Expression(Integer) +--E 1614 + +--S 1615 of 2952 +--a0000:=integrate(t0000,x) +--E 1615 + +--S 1616 of 2952 +--m0000:=a0000 - r0000 +--E 1616 + +--S 1617 of 2952 +--d0000:=D(m0000,x) +--E 1617 + +)clear all + +--S 1618 of 2952 +t0000:=(a+b*x)^(1/2)*(c+d*x)^(1/2) +--R +--R +--R +-------+ +-------+ +--R (1) \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1618 + +--S 1619 of 2952 +r0000:=-1/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(3/2)*d^(3/2))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/b+_ + 1/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b*d) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 \|d \|b x + a +--R (- a d + 2a b c d - b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2b d x + a d + b c)\|b \|d \|b x + a \|d x + c +--R / +--R +-+ +-+ +--R 4b d\|b \|d +--R Type: Expression(Integer) +--E 1619 + +--S 1620 of 2952 +--a0000:=integrate(t0000,x) +--E 1620 + +--S 1621 of 2952 +--m0000:=a0000 - r0000 +--E 1621 + +--S 1622 of 2952 +--d0000:=D(m0000,x) +--E 1622 + +)clear all + +--S 1623 of 2952 +t0000:=(c+d*x)^(1/2)/(a+b*x)^(1/2) +--R +--R +--R +-------+ +--R \|d x + c +--R (1) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1623 + +--S 1624 of 2952 +r0000:=(b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(3/2)*sqrt(d))+sqrt(a+b*x)*sqrt(c+d*x)/b +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +-+ +-+ +-------+ +-------+ +--R (- a d + b c)atanh(--------------) + \|b \|d \|b x + a \|d x + c +--R +-+ +-------+ +--R \|b \|d x + c +--R (2) ----------------------------------------------------------------- +--R +-+ +-+ +--R b\|b \|d +--R Type: Expression(Integer) +--E 1624 + +--S 1625 of 2952 +--a0000:=integrate(t0000,x) +--E 1625 + +--S 1626 of 2952 +--m0000:=a0000 - r0000 +--E 1626 + +--S 1627 of 2952 +--d0000:=D(m0000,x) +--E 1627 + +)clear all + +--S 1628 of 2952 +t0000:=(c+d*x)^(1/2)/(a+b*x)^(3/2) +--R +--R +--R +-------+ +--R \|d x + c +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1628 + +--S 1629 of 2952 +r0000:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(3/2)-_ + 2*sqrt(c+d*x)/(b*sqrt(a+b*x)) +--R +--R +--R +-+ +-------+ +--R +-+ +-------+ \|d \|b x + a +-+ +-------+ +--R 2\|d \|b x + a atanh(--------------) - 2\|b \|d x + c +--R +-+ +-------+ +--R \|b \|d x + c +--R (2) ------------------------------------------------------ +--R +-+ +-------+ +--R b\|b \|b x + a +--R Type: Expression(Integer) +--E 1629 + +--S 1630 of 2952 +--a0000:=integrate(t0000,x) +--E 1630 + +--S 1631 of 2952 +--m0000:=a0000 - r0000 +--E 1631 + +--S 1632 of 2952 +--d0000:=D(m0000,x) +--E 1632 + +)clear all + +--S 1633 of 2952 +t0000:=(c+d*x)^(1/2)/(a+b*x)^(5/2) +--R +--R +--R +-------+ +--R \|d x + c +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1633 + +--S 1634 of 2952 +r0000:=-2/3*(c+d*x)^(3/2)/((b*c-a*d)*(a+b*x)^(3/2)) +--R +--R +--R +-------+ +--R (2d x + 2c)\|d x + c +--R (2) -------------------------------------------- +--R 2 2 +-------+ +--R ((3a b d - 3b c)x + 3a d - 3a b c)\|b x + a +--R Type: Expression(Integer) +--E 1634 + +--S 1635 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +-------+ +-------+ 2 2 2 2 +--R (4a d x + 4a c)\|b x + a \|d x + c + (b c + 4a b c)x +--R + +--R 2 2 2 2 3 +--R (2a b c + 8a b c)x + a c + 4a c +--R / +--R 3 2 2 3 2 4 3 2 5 4 +--R (6a b d - 6a b c)x + (12a b d - 12a b c)x + 6a d - 6a b c +--R Type: Union(Expression(Integer),...) +--E 1635 + +--S 1636 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R c + 4a c +--R (4) ------------- +--R 3 2 +--R 6a d - 6a b c +--R Type: Expression(Integer) +--E 1636 + +--S 1637 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1637 + +)clear all + +--S 1638 of 2952 +t0000:=(c+d*x)^(1/2)/(a+b*x)^(7/2) +--R +--R +--R +-------+ +--R \|d x + c +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1638 + +--S 1639 of 2952 +r0000:=-2/5*(c+d*x)^(3/2)/((b*c-a*d)*(a+b*x)^(5/2))+_ + 4/15*d*(c+d*x)^(3/2)/((b*c-a*d)^2*(a+b*x)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 2 +-------+ +--R (4b d x + (10a d - 2b c d)x + 10a c d - 6b c )\|d x + c +--R / +--R 2 2 2 3 4 2 2 3 2 2 2 3 2 +--R (15a b d - 30a b c d + 15b c )x + (30a b d - 60a b c d + 30a b c )x +--R + +--R 4 2 3 2 2 2 +--R 15a d - 30a b c d + 15a b c +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1639 + +--S 1640 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 4 2 3 4 3 2 +-------+ +--R (12a b d x + (30a d - 6a b c d)x + 30a c d - 18a b c )\|b x + a +--R * +--R +-------+ +--R \|d x + c +--R + +--R 3 2 2 3 4 3 4 2 3 +--R ((- 5a b c - 45a b c)d + 3b c + 27a b c )x +--R + +--R 2 2 2 3 2 3 3 2 3 2 2 +--R ((- 15a b c - 135a b c)d + 9a b c + 81a b c )x +--R + +--R 3 2 4 2 2 3 3 2 2 4 2 5 +--R ((- 15a b c - 135a b c)d + 9a b c + 81a b c )x + (- 5a c - 45a c)d +--R + +--R 3 3 4 2 +--R 3a b c + 27a b c +--R / +--R 5 3 2 4 4 3 5 2 3 +--R (45a b d - 90a b c d + 45a b c )x +--R + +--R 6 2 2 5 3 4 4 2 2 +--R (135a b d - 270a b c d + 135a b c )x +--R + +--R 7 2 6 2 5 3 2 8 2 7 6 2 2 +--R (135a b d - 270a b c d + 135a b c )x + 45a d - 90a b c d + 45a b c +--R Type: Union(Expression(Integer),...) +--E 1640 + +--S 1641 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 3 2 +--R (- 5a c - 45a c)d + 3b c + 27a b c +--R (4) ------------------------------------- +--R 5 2 4 3 2 2 +--R 45a d - 90a b c d + 45a b c +--R Type: Expression(Integer) +--E 1641 + +--S 1642 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1642 + +)clear all + +--S 1643 of 2952 +t0000:=(c+d*x)^(1/2)/(a+b*x)^(9/2) +--R +--R +--R +-------+ +--R \|d x + c +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1643 + +--S 1644 of 2952 +r0000:=-2/7*(c+d*x)^(3/2)/((b*c-a*d)*(a+b*x)^(7/2))+_ + 8/35*d*(c+d*x)^(3/2)/((b*c-a*d)^2*(a+b*x)^(5/2))-_ + 16/105*d^2*(c+d*x)^(3/2)/((b*c-a*d)^3*(a+b*x)^(3/2)) +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 2 3 2 2 2 +--R 16b d x + (56a b d - 8b c d )x + (70a d - 28a b c d + 6b c d)x +--R + +--R 2 2 2 2 3 +--R 70a c d - 84a b c d + 30b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (105a b d - 315a b c d + 315a b c d - 105b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (315a b d - 945a b c d + 945a b c d - 315a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (315a b d - 945a b c d + 945a b c d - 315a b c )x + 105a d +--R + +--R 5 2 4 2 2 3 3 3 +--R - 315a b c d + 315a b c d - 105a b c +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1644 + +--S 1645 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 2 3 3 5 3 4 2 2 2 +--R 64a b d x + (224a b d - 32a b c d )x +--R + +--R 6 3 5 2 4 2 2 6 2 5 2 +--R (280a d - 112a b c d + 24a b c d)x + 280a c d - 336a b c d +--R + +--R 4 2 3 +--R 120a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 4 2 3 4 2 5 3 2 5 2 6 4 +--R (35a b c + 560a b c)d + (- 42a b c - 672a b c )d + 15b c +--R + +--R 6 3 +--R 240a b c +--R * +--R 4 +--R x +--R + +--R 3 3 2 4 3 2 2 4 3 3 4 2 5 4 +--R (140a b c + 2240a b c)d + (- 168a b c - 2688a b c )d + 60a b c +--R + +--R 2 5 3 +--R 960a b c +--R * +--R 3 +--R x +--R + +--R 4 2 2 5 2 2 3 3 3 4 3 2 2 4 4 +--R (210a b c + 3360a b c)d + (- 252a b c - 4032a b c )d + 90a b c +--R + +--R 3 4 3 +--R 1440a b c +--R * +--R 2 +--R x +--R + +--R 5 2 6 2 4 2 3 5 2 2 3 3 4 +--R (140a b c + 2240a b c)d + (- 168a b c - 2688a b c )d + 60a b c +--R + +--R 4 3 3 +--R 960a b c +--R * +--R x +--R + +--R 6 2 7 2 5 3 6 2 4 2 4 5 2 3 +--R (35a c + 560a c)d + (- 42a b c - 672a b c )d + 15a b c + 240a b c +--R / +--R 7 4 3 6 5 2 5 6 2 4 7 3 4 +--R (420a b d - 1260a b c d + 1260a b c d - 420a b c )x +--R + +--R 8 3 3 7 4 2 6 5 2 5 6 3 3 +--R (1680a b d - 5040a b c d + 5040a b c d - 1680a b c )x +--R + +--R 9 2 3 8 3 2 7 4 2 6 5 3 2 +--R (2520a b d - 7560a b c d + 7560a b c d - 2520a b c )x +--R + +--R 10 3 9 2 2 8 3 2 7 4 3 11 3 +--R (1680a b d - 5040a b c d + 5040a b c d - 1680a b c )x + 420a d +--R + +--R 10 2 9 2 2 8 3 3 +--R - 1260a b c d + 1260a b c d - 420a b c +--R Type: Union(Expression(Integer),...) +--E 1645 + +--S 1646 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 3 2 3 2 2 2 4 2 3 +--R (35a c + 560a c)d + (- 42a b c - 672a b c )d + 15b c + 240a b c +--R (4) -------------------------------------------------------------------- +--R 7 3 6 2 5 2 2 4 3 3 +--R 420a d - 1260a b c d + 1260a b c d - 420a b c +--R Type: Expression(Integer) +--E 1646 + +--S 1647 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1647 + +)clear all + +--S 1648 of 2952 +t0000:=(c+d*x)^(1/2)/(a+b*x)^(11/2) +--R +--R +--R +-------+ +--R \|d x + c +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1648 + +--S 1649 of 2952 +r0000:=-2/9*(c+d*x)^(3/2)/((b*c-a*d)*(a+b*x)^(9/2))+_ + 4/21*d*(c+d*x)^(3/2)/((b*c-a*d)^2*(a+b*x)^(7/2))-_ + 16/105*d^2*(c+d*x)^(3/2)/((b*c-a*d)^3*(a+b*x)^(5/2))+_ + 32/315*d^3*(c+d*x)^(3/2)/((b*c-a*d)^4*(a+b*x)^(3/2)) +--R +--R +--R (2) +--R 3 4 4 2 4 3 3 3 +--R 32b d x + (144a b d - 16b c d )x +--R + +--R 2 4 2 3 3 2 2 2 +--R (252a b d - 72a b c d + 12b c d )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 +--R (210a d - 126a b c d + 54a b c d - 10b c d)x + 210a c d +--R + +--R 2 2 2 2 3 3 4 +--R - 378a b c d + 270a b c d - 70b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 4 4 3 5 3 2 6 2 2 7 3 8 4 4 +--R (315a b d - 1260a b c d + 1890a b c d - 1260a b c d + 315b c )x +--R + +--R 5 3 4 4 4 3 3 5 2 2 2 6 3 7 4 3 +--R (1260a b d - 5040a b c d + 7560a b c d - 5040a b c d + 1260a b c )x +--R + +--R 6 2 4 5 3 3 4 4 2 2 3 5 3 +--R 1890a b d - 7560a b c d + 11340a b c d - 7560a b c d +--R + +--R 2 6 4 +--R 1890a b c +--R * +--R 2 +--R x +--R + +--R 7 4 6 2 3 5 3 2 2 4 4 3 3 5 4 +--R (1260a b d - 5040a b c d + 7560a b c d - 5040a b c d + 1260a b c )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 4 4 4 +--R 315a d - 1260a b c d + 1890a b c d - 1260a b c d + 315a b c +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1649 + +--S 1650 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 3 4 4 6 2 4 5 3 3 3 +--R 32a b d x + (144a b d - 16a b c d )x +--R + +--R 7 4 6 2 3 5 3 2 2 2 +--R (252a b d - 72a b c d + 12a b c d )x +--R + +--R 8 4 7 3 6 2 2 2 5 3 3 8 3 +--R (210a d - 126a b c d + 54a b c d - 10a b c d)x + 210a c d +--R + +--R 7 2 2 6 2 3 5 3 4 +--R - 378a b c d + 270a b c d - 70a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 3 5 2 4 5 3 2 6 3 3 6 2 2 +--R (105a b c + 105a b c)d + (- 189a b c - 189a b c )d +--R + +--R 7 4 2 7 3 8 5 8 4 +--R (135a b c + 135a b c )d - 35b c - 35a b c +--R * +--R 5 +--R x +--R + +--R 4 4 2 5 4 3 3 5 3 4 5 2 2 +--R (525a b c + 525a b c)d + (- 945a b c - 945a b c )d +--R + +--R 2 6 4 3 6 3 7 5 2 7 4 +--R (675a b c + 675a b c )d - 175a b c - 175a b c +--R * +--R 4 +--R x +--R + +--R 5 3 2 6 3 3 4 4 3 5 4 2 2 +--R (1050a b c + 1050a b c)d + (- 1890a b c - 1890a b c )d +--R + +--R 3 5 4 4 5 3 2 6 5 3 6 4 +--R (1350a b c + 1350a b c )d - 350a b c - 350a b c +--R * +--R 3 +--R x +--R + +--R 6 2 2 7 2 3 5 3 3 6 3 2 2 +--R (1050a b c + 1050a b c)d + (- 1890a b c - 1890a b c )d +--R + +--R 4 4 4 5 4 3 3 5 5 4 5 4 +--R (1350a b c + 1350a b c )d - 350a b c - 350a b c +--R * +--R 2 +--R x +--R + +--R 7 2 8 3 6 2 3 7 2 2 2 +--R (525a b c + 525a b c)d + (- 945a b c - 945a b c )d +--R + +--R 5 3 4 6 3 3 4 4 5 5 4 4 +--R (675a b c + 675a b c )d - 175a b c - 175a b c +--R * +--R x +--R + +--R 8 2 9 3 7 3 8 2 2 +--R (105a c + 105a c)d + (- 189a b c - 189a b c )d +--R + +--R 6 2 4 7 2 3 5 3 5 6 3 4 +--R (135a b c + 135a b c )d - 35a b c - 35a b c +--R / +--R 9 5 4 8 6 3 7 7 2 2 6 8 3 5 9 4 5 +--R (315a b d - 1260a b c d + 1890a b c d - 1260a b c d + 315a b c )x +--R + +--R 10 4 4 9 5 3 8 6 2 2 7 7 3 6 8 4 4 +--R (1575a b d - 6300a b c d + 9450a b c d - 6300a b c d + 1575a b c )x +--R + +--R 11 3 4 10 4 3 9 5 2 2 8 6 3 +--R 3150a b d - 12600a b c d + 18900a b c d - 12600a b c d +--R + +--R 7 7 4 +--R 3150a b c +--R * +--R 3 +--R x +--R + +--R 12 2 4 11 3 3 10 4 2 2 9 5 3 +--R 3150a b d - 12600a b c d + 18900a b c d - 12600a b c d +--R + +--R 8 6 4 +--R 3150a b c +--R * +--R 2 +--R x +--R + +--R 13 4 12 2 3 11 3 2 2 10 4 3 +--R 1575a b d - 6300a b c d + 9450a b c d - 6300a b c d +--R + +--R 9 5 4 +--R 1575a b c +--R * +--R x +--R + +--R 14 4 13 3 12 2 2 2 11 3 3 10 4 4 +--R 315a d - 1260a b c d + 1890a b c d - 1260a b c d + 315a b c +--R Type: Union(Expression(Integer),...) +--E 1650 + +--S 1651 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 2 4 3 2 3 3 2 2 +--R (105a c + 105a c)d + (- 189a b c - 189a b c )d +--R + +--R 2 4 2 2 3 3 5 3 4 +--R (135a b c + 135a b c )d - 35b c - 35a b c +--R / +--R 9 4 8 3 7 2 2 2 6 3 3 5 4 4 +--R 315a d - 1260a b c d + 1890a b c d - 1260a b c d + 315a b c +--R Type: Expression(Integer) +--E 1651 + +--S 1652 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1652 + +)clear all + +--S 1653 of 2952 +t0000:=(c+d*x)^(1/2)/(a+b*x)^(13/2) +--R +--R +--R (1) +--R +-------+ +--R \|d x + c +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1653 + +--S 1654 of 2952 +r0000:=-2/11*(c+d*x)^(3/2)/((b*c-a*d)*(a+b*x)^(11/2))+_ + 16/99*d*(c+d*x)^(3/2)/((b*c-a*d)^2*(a+b*x)^(9/2))-_ + 32/231*d^2*(c+d*x)^(3/2)/((b*c-a*d)^3*(a+b*x)^(7/2))+_ + 128/1155*d^3*(c+d*x)^(3/2)/((b*c-a*d)^4*(a+b*x)^(5/2))-_ + 256/3465*d^4*(c+d*x)^(3/2)/((b*c-a*d)^5*(a+b*x)^(3/2)) +--R +--R +--R (2) +--R 4 5 5 3 5 4 4 4 +--R 256b d x + (1408a b d - 128b c d )x +--R + +--R 2 2 5 3 4 4 2 3 3 +--R (3168a b d - 704a b c d + 96b c d )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (3696a b d - 1584a b c d + 528a b c d - 80b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (2310a d - 1848a b c d + 1188a b c d - 440a b c d + 70b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R 2310a c d - 5544a b c d + 5940a b c d - 3080a b c d + 630b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 5 5 4 6 4 3 7 2 3 2 8 3 2 +--R 3465a b d - 17325a b c d + 34650a b c d - 34650a b c d +--R + +--R 9 4 10 5 +--R 17325a b c d - 3465b c +--R * +--R 5 +--R x +--R + +--R 6 4 5 5 5 4 4 6 2 3 3 7 3 2 +--R 17325a b d - 86625a b c d + 173250a b c d - 173250a b c d +--R + +--R 2 8 4 9 5 +--R 86625a b c d - 17325a b c +--R * +--R 4 +--R x +--R + +--R 7 3 5 6 4 4 5 5 2 3 4 6 3 2 +--R 34650a b d - 173250a b c d + 346500a b c d - 346500a b c d +--R + +--R 3 7 4 2 8 5 +--R 173250a b c d - 34650a b c +--R * +--R 3 +--R x +--R + +--R 8 2 5 7 3 4 6 4 2 3 5 5 3 2 +--R 34650a b d - 173250a b c d + 346500a b c d - 346500a b c d +--R + +--R 4 6 4 3 7 5 +--R 173250a b c d - 34650a b c +--R * +--R 2 +--R x +--R + +--R 9 5 8 2 4 7 3 2 3 6 4 3 2 +--R 17325a b d - 86625a b c d + 173250a b c d - 173250a b c d +--R + +--R 5 5 4 4 6 5 +--R 86625a b c d - 17325a b c +--R * +--R x +--R + +--R 10 5 9 4 8 2 2 3 7 3 3 2 +--R 3465a d - 17325a b c d + 34650a b c d - 34650a b c d +--R + +--R 6 4 4 5 5 5 +--R 17325a b c d - 3465a b c +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1654 + +--S 1655 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 4 5 5 7 3 5 6 4 4 4 +--R 256a b d x + (1408a b d - 128a b c d )x +--R + +--R 8 2 5 7 3 4 6 4 2 3 3 +--R (3168a b d - 704a b c d + 96a b c d )x +--R + +--R 9 5 8 2 4 7 3 2 3 6 4 3 2 2 +--R (3696a b d - 1584a b c d + 528a b c d - 80a b c d )x +--R + +--R 10 5 9 4 8 2 2 3 7 3 3 2 6 4 4 +--R (2310a d - 1848a b c d + 1188a b c d - 440a b c d + 70a b c d)x +--R + +--R 10 4 9 2 3 8 2 3 2 7 3 4 6 4 5 +--R 2310a c d - 5544a b c d + 5940a b c d - 3080a b c d + 630a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 4 6 2 5 6 4 3 7 3 4 7 2 3 +--R (- 1155a b c - 1155a b c)d + (2772a b c + 2772a b c )d +--R + +--R 2 8 4 3 8 3 2 9 5 2 9 4 10 6 +--R (- 2970a b c - 2970a b c )d + (1540a b c + 1540a b c )d - 315b c +--R + +--R 10 5 +--R - 315a b c +--R * +--R 6 +--R x +--R + +--R 5 5 2 6 5 4 4 6 3 5 6 2 3 +--R (- 6930a b c - 6930a b c)d + (16632a b c + 16632a b c )d +--R + +--R 3 7 4 4 7 3 2 2 8 5 3 8 4 +--R (- 17820a b c - 17820a b c )d + (9240a b c + 9240a b c )d +--R + +--R 9 6 2 9 5 +--R - 1890a b c - 1890a b c +--R * +--R 5 +--R x +--R + +--R 6 4 2 7 4 4 5 5 3 6 5 2 3 +--R (- 17325a b c - 17325a b c)d + (41580a b c + 41580a b c )d +--R + +--R 4 6 4 5 6 3 2 3 7 5 4 7 4 +--R (- 44550a b c - 44550a b c )d + (23100a b c + 23100a b c )d +--R + +--R 2 8 6 3 8 5 +--R - 4725a b c - 4725a b c +--R * +--R 4 +--R x +--R + +--R 7 3 2 8 3 4 6 4 3 7 4 2 3 +--R (- 23100a b c - 23100a b c)d + (55440a b c + 55440a b c )d +--R + +--R 5 5 4 6 5 3 2 4 6 5 5 6 4 +--R (- 59400a b c - 59400a b c )d + (30800a b c + 30800a b c )d +--R + +--R 3 7 6 4 7 5 +--R - 6300a b c - 6300a b c +--R * +--R 3 +--R x +--R + +--R 8 2 2 9 2 4 7 3 3 8 3 2 3 +--R (- 17325a b c - 17325a b c)d + (41580a b c + 41580a b c )d +--R + +--R 6 4 4 7 4 3 2 5 5 5 6 5 4 +--R (- 44550a b c - 44550a b c )d + (23100a b c + 23100a b c )d +--R + +--R 4 6 6 5 6 5 +--R - 4725a b c - 4725a b c +--R * +--R 2 +--R x +--R + +--R 9 2 10 4 8 2 3 9 2 2 3 +--R (- 6930a b c - 6930a b c)d + (16632a b c + 16632a b c )d +--R + +--R 7 3 4 8 3 3 2 6 4 5 7 4 4 +--R (- 17820a b c - 17820a b c )d + (9240a b c + 9240a b c )d +--R + +--R 5 5 6 6 5 5 +--R - 1890a b c - 1890a b c +--R * +--R x +--R + +--R 10 2 11 4 9 3 10 2 3 +--R (- 1155a c - 1155a c)d + (2772a b c + 2772a b c )d +--R + +--R 8 2 4 9 2 3 2 7 3 5 8 3 4 6 4 6 +--R (- 2970a b c - 2970a b c )d + (1540a b c + 1540a b c )d - 315a b c +--R + +--R 7 4 5 +--R - 315a b c +--R / +--R 11 6 5 10 7 4 9 8 2 3 8 9 3 2 +--R 3465a b d - 17325a b c d + 34650a b c d - 34650a b c d +--R + +--R 7 10 4 6 11 5 +--R 17325a b c d - 3465a b c +--R * +--R 6 +--R x +--R + +--R 12 5 5 11 6 4 10 7 2 3 9 8 3 2 +--R 20790a b d - 103950a b c d + 207900a b c d - 207900a b c d +--R + +--R 8 9 4 7 10 5 +--R 103950a b c d - 20790a b c +--R * +--R 5 +--R x +--R + +--R 13 4 5 12 5 4 11 6 2 3 10 7 3 2 +--R 51975a b d - 259875a b c d + 519750a b c d - 519750a b c d +--R + +--R 9 8 4 8 9 5 +--R 259875a b c d - 51975a b c +--R * +--R 4 +--R x +--R + +--R 14 3 5 13 4 4 12 5 2 3 11 6 3 2 +--R 69300a b d - 346500a b c d + 693000a b c d - 693000a b c d +--R + +--R 10 7 4 9 8 5 +--R 346500a b c d - 69300a b c +--R * +--R 3 +--R x +--R + +--R 15 2 5 14 3 4 13 4 2 3 12 5 3 2 +--R 51975a b d - 259875a b c d + 519750a b c d - 519750a b c d +--R + +--R 11 6 4 10 7 5 +--R 259875a b c d - 51975a b c +--R * +--R 2 +--R x +--R + +--R 16 5 15 2 4 14 3 2 3 13 4 3 2 +--R 20790a b d - 103950a b c d + 207900a b c d - 207900a b c d +--R + +--R 12 5 4 11 6 5 +--R 103950a b c d - 20790a b c +--R * +--R x +--R + +--R 17 5 16 4 15 2 2 3 14 3 3 2 +--R 3465a d - 17325a b c d + 34650a b c d - 34650a b c d +--R + +--R 13 4 4 12 5 5 +--R 17325a b c d - 3465a b c +--R Type: Union(Expression(Integer),...) +--E 1655 + +--S 1656 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 4 2 5 4 3 3 4 2 3 +--R (- 1155a c - 1155a c)d + (2772a b c + 2772a b c )d +--R + +--R 2 2 4 3 2 3 2 3 5 2 3 4 4 6 +--R (- 2970a b c - 2970a b c )d + (1540a b c + 1540a b c )d - 315b c +--R + +--R 4 5 +--R - 315a b c +--R / +--R 11 5 10 4 9 2 2 3 8 3 3 2 7 4 4 +--R 3465a d - 17325a b c d + 34650a b c d - 34650a b c d + 17325a b c d +--R + +--R 6 5 5 +--R - 3465a b c +--R Type: Expression(Integer) +--E 1656 + +--S 1657 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1657 + +)clear all + +--S 1658 of 2952 +t0000:=(a+b*x)^(5/2)*(c+d*x)^(3/2) +--R +--R +--R (1) +--R 2 3 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 1658 + +--S 1659 of 2952 +r0000:=1/5*(a+b*x)^(7/2)*(c+d*x)^(3/2)/b-_ + 3/128*(b*c-a*d)^5*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(5/2)*d^(7/2))-1/64*(b*c-a*d)^3*(a+b*x)^(3/2)*sqrt(c+d*x)/_ + (b^2*d^2)+1/80*(b*c-a*d)^2*(a+b*x)^(5/2)*sqrt(c+d*x)/(b^2*d)+_ + 3/40*(b*c-a*d)*(a+b*x)^(7/2)*sqrt(c+d*x)/b^2+_ + 3/128*(b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^3) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (15a d - 75a b c d + 150a b c d - 150a b c d + 75a b c d - 15b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 4 4 3 4 4 3 3 +--R 128b d x + (336a b d + 176b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (248a b d + 512a b c d + 8b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (10a b d + 466a b c d + 46a b c d - 10b c d)x - 15a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 70a b c d + 128a b c d - 70a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 2 3 +-+ +-+ +--R 640b d \|b \|d +--R Type: Expression(Integer) +--E 1659 + +--S 1660 of 2952 +--a0000:=integrate(t0000,x) +--E 1660 + +--S 1661 of 2952 +--m0000:=a0000 - r0000 +--E 1661 + +--S 1662 of 2952 +--d0000:=D(m0000,x) +--E 1662 + +)clear all + +--S 1663 of 2952 +t0000:=(a+b*x)^(3/2)*(c+d*x)^(3/2) +--R +--R +--R 2 +-------+ +-------+ +--R (1) (b d x + (a d + b c)x + a c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1663 + +--S 1664 of 2952 +r0000:=1/4*(a+b*x)^(5/2)*(c+d*x)^(3/2)/b+_ + 3/64*(b*c-a*d)^4*atanh(sqrt(d)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))+_ + 1/32*(b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d)+_ + 1/8*(b*c-a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/b^2-_ + 3/64*(b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d^2) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (3a d - 12a b c d + 18a b c d - 12a b c d + 3b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 16b d x + (24a b d + 24b c d )x + (2a b d + 44a b c d + 2b c d)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 3a d + 11a b c d + 11a b c d - 3b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 2 2 +-+ +-+ +--R 64b d \|b \|d +--R Type: Expression(Integer) +--E 1664 + +--S 1665 of 2952 +--a0000:=integrate(t0000,x) +--E 1665 + +--S 1666 of 2952 +--m0000:=a0000 - r0000 +--E 1666 + +--S 1667 of 2952 +--d0000:=D(m0000,x) +--E 1667 + +)clear all + +--S 1668 of 2952 +t0000:=(a+b*x)^(1/2)*(c+d*x)^(3/2) +--R +--R +--R +-------+ +-------+ +--R (1) (d x + c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1668 + +--S 1669 of 2952 +r0000:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b-1/8*(b*c-a*d)^3*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(3/2))+_ + 1/4*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/b^2+_ + 1/8*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/(b^2*d) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (3a d - 9a b c d + 9a b c d - 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (2a b d + 14b c d)x - 3a d + 8a b c d + 3b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 24b d\|b \|d +--R Type: Expression(Integer) +--E 1669 + +--S 1670 of 2952 +--a0000:=integrate(t0000,x) +--E 1670 + +--S 1671 of 2952 +--m0000:=a0000 - r0000 +--E 1671 + +--S 1672 of 2952 +--d0000:=D(m0000,x) +--E 1672 + +)clear all + +--S 1673 of 2952 +t0000:=(c+d*x)^(3/2)/(a+b*x)^(1/2) +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) ------------------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1673 + +--S 1674 of 2952 +r0000:=3/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(5/2)*sqrt(d))+1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/b+_ + 3/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 \|d \|b x + a +--R (3a d - 6a b c d + 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2b d x - 3a d + 5b c)\|b \|d \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 4b \|b \|d +--R Type: Expression(Integer) +--E 1674 + +--S 1675 of 2952 +--a0000:=integrate(t0000,x) +--E 1675 + +--S 1676 of 2952 +--m0000:=a0000 - r0000 +--E 1676 + +--S 1677 of 2952 +--d0000:=D(m0000,x) +--E 1677 + +)clear all + +--S 1678 of 2952 +t0000:=(c+d*x)^(3/2)/(a+b*x)^(3/2) +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1678 + +--S 1679 of 2952 +r0000:=3*(b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_ + sqrt(d)/b^(5/2)-2*(c+d*x)^(3/2)/(b*sqrt(a+b*x))+_ + 3*d*sqrt(a+b*x)*sqrt(c+d*x)/b^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|d \|b x + a +--R (- 3a d + 3b c)\|d \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R (b d x + 3a d - 2b c)\|b \|d x + c +--R / +--R 2 +-+ +-------+ +--R b \|b \|b x + a +--R Type: Expression(Integer) +--E 1679 + +--S 1680 of 2952 +--a0000:=integrate(t0000,x) +--E 1680 + +--S 1681 of 2952 +--m0000:=a0000 - r0000 +--E 1681 + +--S 1682 of 2952 +--d0000:=D(m0000,x) +--E 1682 + +)clear all + +--S 1683 of 2952 +t0000:=(c+d*x)^(3/2)/(a+b*x)^(5/2) +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1683 + +--S 1684 of 2952 +r0000:=-2/3*(c+d*x)^(3/2)/(b*(a+b*x)^(3/2))+_ + 2*d^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(5/2)-_ + 2*d*sqrt(c+d*x)/(b^2*sqrt(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|d \|b x + a +--R (6b d x + 6a d)\|d \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R (- 8b d x - 6a d - 2b c)\|b \|d x + c +--R / +--R 3 2 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 1684 + +--S 1685 of 2952 +--a0000:=integrate(t0000,x) +--E 1685 + +--S 1686 of 2952 +--m0000:=a0000 - r0000 +--E 1686 + +--S 1687 of 2952 +--d0000:=D(m0000,x) +--E 1687 + +)clear all + +--S 1688 of 2952 +t0000:=(c+d*x)^(3/2)/(a+b*x)^(7/2) +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1688 + +--S 1689 of 2952 +r0000:=-2/5*(c+d*x)^(5/2)/((b*c-a*d)*(a+b*x)^(5/2)) +--R +--R +--R 2 2 2 +-------+ +--R (2d x + 4c d x + 2c )\|d x + c +--R (2) -------------------------------------------------------------------- +--R 2 3 2 2 2 3 2 +-------+ +--R ((5a b d - 5b c)x + (10a b d - 10a b c)x + 5a d - 5a b c)\|b x + a +--R Type: Expression(Integer) +--E 1689 + +--S 1690 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 3 3 2 +-------+ +-------+ 3 3 3 2 3 +--R (4a d x + 8a c d x + 4a c )\|b x + a \|d x + c + (b c + 4a b c )x +--R + +--R 2 3 2 2 2 2 2 3 3 2 3 3 4 2 +--R (3a b c + 12a b c )x + (3a b c + 12a b c )x + a c + 4a c +--R / +--R 4 3 3 4 3 5 2 4 3 2 6 5 2 +--R (10a b d - 10a b c)x + (30a b d - 30a b c)x + (30a b d - 30a b c)x +--R + +--R 7 6 +--R 10a d - 10a b c +--R Type: Union(Expression(Integer),...) +--E 1690 + +--S 1691 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 +--R c + 4a c +--R (4) --------------- +--R 4 3 +--R 10a d - 10a b c +--R Type: Expression(Integer) +--E 1691 + +--S 1692 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1692 + +)clear all + +--S 1693 of 2952 +t0000:=(c+d*x)^(3/2)/(a+b*x)^(9/2) +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1693 + +--S 1694 of 2952 +r0000:=-2/7*(c+d*x)^(5/2)/((b*c-a*d)*(a+b*x)^(7/2))+_ + 4/35*d*(c+d*x)^(5/2)/((b*c-a*d)^2*(a+b*x)^(5/2)) +--R +--R +--R (2) +--R 3 3 3 2 2 2 2 2 +--R 4b d x + (14a d - 2b c d )x + (28a c d - 16b c d)x + 14a c d +--R + +--R 3 +--R - 10b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 2 3 2 4 5 2 3 +--R (35a b d - 70a b c d + 35b c )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (105a b d - 210a b c d + 105a b c )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (105a b d - 210a b c d + 105a b c )x + 35a d - 70a b c d + 35a b c +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1694 + +--S 1695 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 3 5 3 4 2 2 5 2 4 2 +--R 16a b d x + (56a d - 8a b c d )x + (112a c d - 64a b c d)x +--R + +--R 5 2 4 3 +--R 56a c d - 40a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 4 3 2 4 2 5 4 5 3 4 +--R ((7a b c + 112a b c )d - 5b c - 80a b c )x +--R + +--R 2 3 3 3 3 2 4 4 2 4 3 3 +--R ((28a b c + 448a b c )d - 20a b c - 320a b c )x +--R + +--R 3 2 3 4 2 2 2 3 4 3 3 3 2 +--R ((42a b c + 672a b c )d - 30a b c - 480a b c )x +--R + +--R 4 3 5 2 3 2 4 4 2 3 5 3 6 2 +--R ((28a b c + 448a b c )d - 20a b c - 320a b c )x + (7a c + 112a c )d +--R + +--R 4 4 5 3 +--R - 5a b c - 80a b c +--R / +--R 6 4 2 5 5 4 6 2 4 +--R (140a b d - 280a b c d + 140a b c )x +--R + +--R 7 3 2 6 4 5 5 2 3 +--R (560a b d - 1120a b c d + 560a b c )x +--R + +--R 8 2 2 7 3 6 4 2 2 +--R (840a b d - 1680a b c d + 840a b c )x +--R + +--R 9 2 8 2 7 3 2 10 2 9 8 2 2 +--R (560a b d - 1120a b c d + 560a b c )x + 140a d - 280a b c d + 140a b c +--R Type: Union(Expression(Integer),...) +--E 1695 + +--S 1696 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 2 2 4 3 +--R (7a c + 112a c )d - 5b c - 80a b c +--R (4) ------------------------------------- +--R 6 2 5 4 2 2 +--R 140a d - 280a b c d + 140a b c +--R Type: Expression(Integer) +--E 1696 + +--S 1697 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1697 + +)clear all + +--S 1698 of 2952 +t0000:=(c+d*x)^(3/2)/(a+b*x)^(11/2) +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1698 + +--S 1699 of 2952 +r0000:=-2/9*(c+d*x)^(5/2)/((b*c-a*d)*(a+b*x)^(9/2))+_ + 8/63*d*(c+d*x)^(5/2)/((b*c-a*d)^2*(a+b*x)^(7/2))-_ + 16/315*d^2*(c+d*x)^(5/2)/((b*c-a*d)^3*(a+b*x)^(5/2)) +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 2 4 3 2 2 2 2 +--R 16b d x + (72a b d - 8b c d )x + (126a d - 36a b c d + 6b c d )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (252a c d - 288a b c d + 100b c d)x + 126a c d - 180a b c d + 70b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (315a b d - 945a b c d + 945a b c d - 315b c )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (1260a b d - 3780a b c d + 3780a b c d - 1260a b c )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (1890a b d - 5670a b c d + 5670a b c d - 1890a b c )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 +--R (1260a b d - 3780a b c d + 3780a b c d - 1260a b c )x + 315a d +--R + +--R 6 2 5 2 2 4 3 3 +--R - 945a b c d + 945a b c d - 315a b c +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1699 + +--S 1700 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 2 4 4 6 4 5 2 3 3 +--R 64a b d x + (288a b d - 32a b c d )x +--R + +--R 7 4 6 3 5 2 2 2 2 +--R (504a d - 144a b c d + 24a b c d )x +--R + +--R 7 3 6 2 2 5 2 3 7 2 2 6 3 +--R (1008a c d - 1152a b c d + 400a b c d)x + 504a c d - 720a b c d +--R + +--R 5 2 4 +--R 280a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 5 3 3 5 2 2 6 4 2 6 3 7 5 +--R (63a b c + 1008a b c )d + (- 90a b c - 1440a b c )d + 35b c +--R + +--R 7 4 +--R 560a b c +--R * +--R 5 +--R x +--R + +--R 3 4 3 4 4 2 2 2 5 4 3 5 3 6 5 +--R (315a b c + 5040a b c )d + (- 450a b c - 7200a b c )d + 175a b c +--R + +--R 2 6 4 +--R 2800a b c +--R * +--R 4 +--R x +--R + +--R 4 3 3 5 3 2 2 3 4 4 4 4 3 +--R (630a b c + 10080a b c )d + (- 900a b c - 14400a b c )d +--R + +--R 2 5 5 3 5 4 +--R 350a b c + 5600a b c +--R * +--R 3 +--R x +--R + +--R 5 2 3 6 2 2 2 4 3 4 5 3 3 +--R (630a b c + 10080a b c )d + (- 900a b c - 14400a b c )d +--R + +--R 3 4 5 4 4 4 +--R 350a b c + 5600a b c +--R * +--R 2 +--R x +--R + +--R 6 3 7 2 2 5 2 4 6 2 3 4 3 5 +--R (315a b c + 5040a b c )d + (- 450a b c - 7200a b c )d + 175a b c +--R + +--R 5 3 4 +--R 2800a b c +--R * +--R x +--R + +--R 7 3 8 2 2 6 4 7 3 5 2 5 6 2 4 +--R (63a c + 1008a c )d + (- 90a b c - 1440a b c )d + 35a b c + 560a b c +--R / +--R 8 5 3 7 6 2 6 7 2 5 8 3 5 +--R (1260a b d - 3780a b c d + 3780a b c d - 1260a b c )x +--R + +--R 9 4 3 8 5 2 7 6 2 6 7 3 4 +--R (6300a b d - 18900a b c d + 18900a b c d - 6300a b c )x +--R + +--R 10 3 3 9 4 2 8 5 2 7 6 3 3 +--R (12600a b d - 37800a b c d + 37800a b c d - 12600a b c )x +--R + +--R 11 2 3 10 3 2 9 4 2 8 5 3 2 +--R (12600a b d - 37800a b c d + 37800a b c d - 12600a b c )x +--R + +--R 12 3 11 2 2 10 3 2 9 4 3 13 3 +--R (6300a b d - 18900a b c d + 18900a b c d - 6300a b c )x + 1260a d +--R + +--R 12 2 11 2 2 10 3 3 +--R - 3780a b c d + 3780a b c d - 1260a b c +--R Type: Union(Expression(Integer),...) +--E 1700 + +--S 1701 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 3 3 2 2 4 2 3 2 5 2 4 +--R (63a c + 1008a c )d + (- 90a b c - 1440a b c )d + 35b c + 560a b c +--R ----------------------------------------------------------------------- +--R 8 3 7 2 6 2 2 5 3 3 +--R 1260a d - 3780a b c d + 3780a b c d - 1260a b c +--R Type: Expression(Integer) +--E 1701 + +--S 1702 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1702 + +)clear all + +--S 1703 of 2952 +t0000:=(c+d*x)^(3/2)/(a+b*x)^(13/2) +--R +--R +--R (1) +--R +-------+ +--R (d x + c)\|d x + c +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1703 + +--S 1704 of 2952 +r0000:=-2/11*(c+d*x)^(5/2)/((b*c-a*d)*(a+b*x)^(11/2))+_ + 4/33*d*(c+d*x)^(5/2)/((b*c-a*d)^2*(a+b*x)^(9/2))-_ + 16/231*d^2*(c+d*x)^(5/2)/((b*c-a*d)^3*(a+b*x)^(7/2))+_ + 32/1155*d^3*(c+d*x)^(5/2)/((b*c-a*d)^4*(a+b*x)^(5/2)) +--R +--R +--R (2) +--R 3 5 5 2 5 3 4 4 +--R 32b d x + (176a b d - 16b c d )x +--R + +--R 2 5 2 4 3 2 3 3 +--R (396a b d - 88a b c d + 12b c d )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (462a d - 198a b c d + 66a b c d - 10b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (924a c d - 1584a b c d + 1100a b c d - 280b c d)x + 462a c d +--R + +--R 2 3 2 2 4 3 5 +--R - 990a b c d + 770a b c d - 210b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 5 4 3 6 3 2 7 2 2 8 3 9 4 5 +--R (1155a b d - 4620a b c d + 6930a b c d - 4620a b c d + 1155b c )x +--R + +--R 5 4 4 4 5 3 3 6 2 2 2 7 3 +--R 5775a b d - 23100a b c d + 34650a b c d - 23100a b c d +--R + +--R 8 4 +--R 5775a b c +--R * +--R 4 +--R x +--R + +--R 6 3 4 5 4 3 4 5 2 2 3 6 3 +--R 11550a b d - 46200a b c d + 69300a b c d - 46200a b c d +--R + +--R 2 7 4 +--R 11550a b c +--R * +--R 3 +--R x +--R + +--R 7 2 4 6 3 3 5 4 2 2 4 5 3 +--R 11550a b d - 46200a b c d + 69300a b c d - 46200a b c d +--R + +--R 3 6 4 +--R 11550a b c +--R * +--R 2 +--R x +--R + +--R 8 4 7 2 3 6 3 2 2 5 4 3 +--R 5775a b d - 23100a b c d + 34650a b c d - 23100a b c d +--R + +--R 4 5 4 +--R 5775a b c +--R * +--R x +--R + +--R 9 4 8 3 7 2 2 2 6 3 3 5 4 4 +--R 1155a d - 4620a b c d + 6930a b c d - 4620a b c d + 1155a b c +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1704 + +--S 1705 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 3 5 5 7 2 5 6 3 4 4 +--R 96a b d x + (528a b d - 48a b c d )x +--R + +--R 8 5 7 2 4 6 3 2 3 3 +--R (1188a b d - 264a b c d + 36a b c d )x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 2 +--R (1386a d - 594a b c d + 198a b c d - 30a b c d )x +--R + +--R 9 4 8 2 3 7 2 3 2 6 3 4 9 2 3 +--R (2772a c d - 4752a b c d + 3300a b c d - 840a b c d)x + 1386a c d +--R + +--R 8 3 2 7 2 4 6 3 5 +--R - 2970a b c d + 2310a b c d - 630a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 3 6 3 4 6 2 3 2 7 4 3 7 3 2 +--R (231a b c + 2079a b c )d + (- 495a b c - 4455a b c )d +--R + +--R 8 5 2 8 4 9 6 9 5 +--R (385a b c + 3465a b c )d - 105b c - 945a b c +--R * +--R 6 +--R x +--R + +--R 4 5 3 5 5 2 3 3 6 4 4 6 3 2 +--R (1386a b c + 12474a b c )d + (- 2970a b c - 26730a b c )d +--R + +--R 2 7 5 3 7 4 8 6 2 8 5 +--R (2310a b c + 20790a b c )d - 630a b c - 5670a b c +--R * +--R 5 +--R x +--R + +--R 5 4 3 6 4 2 3 4 5 4 5 5 3 2 +--R (3465a b c + 31185a b c )d + (- 7425a b c - 66825a b c )d +--R + +--R 3 6 5 4 6 4 2 7 6 3 7 5 +--R (5775a b c + 51975a b c )d - 1575a b c - 14175a b c +--R * +--R 4 +--R x +--R + +--R 6 3 3 7 3 2 3 5 4 4 6 4 3 2 +--R (4620a b c + 41580a b c )d + (- 9900a b c - 89100a b c )d +--R + +--R 4 5 5 5 5 4 3 6 6 4 6 5 +--R (7700a b c + 69300a b c )d - 2100a b c - 18900a b c +--R * +--R 3 +--R x +--R + +--R 7 2 3 8 2 2 3 6 3 4 7 3 3 2 +--R (3465a b c + 31185a b c )d + (- 7425a b c - 66825a b c )d +--R + +--R 5 4 5 6 4 4 4 5 6 5 5 5 +--R (5775a b c + 51975a b c )d - 1575a b c - 14175a b c +--R * +--R 2 +--R x +--R + +--R 8 3 9 2 3 7 2 4 8 2 3 2 +--R (1386a b c + 12474a b c )d + (- 2970a b c - 26730a b c )d +--R + +--R 6 3 5 7 3 4 5 4 6 6 4 5 +--R (2310a b c + 20790a b c )d - 630a b c - 5670a b c +--R * +--R x +--R + +--R 9 3 10 2 3 8 4 9 3 2 +--R (231a c + 2079a c )d + (- 495a b c - 4455a b c )d +--R + +--R 7 2 5 8 2 4 6 3 6 7 3 5 +--R (385a b c + 3465a b c )d - 105a b c - 945a b c +--R / +--R 10 6 4 9 7 3 8 8 2 2 7 9 3 +--R 3465a b d - 13860a b c d + 20790a b c d - 13860a b c d +--R + +--R 6 10 4 +--R 3465a b c +--R * +--R 6 +--R x +--R + +--R 11 5 4 10 6 3 9 7 2 2 8 8 3 +--R 20790a b d - 83160a b c d + 124740a b c d - 83160a b c d +--R + +--R 7 9 4 +--R 20790a b c +--R * +--R 5 +--R x +--R + +--R 12 4 4 11 5 3 10 6 2 2 9 7 3 +--R 51975a b d - 207900a b c d + 311850a b c d - 207900a b c d +--R + +--R 8 8 4 +--R 51975a b c +--R * +--R 4 +--R x +--R + +--R 13 3 4 12 4 3 11 5 2 2 10 6 3 +--R 69300a b d - 277200a b c d + 415800a b c d - 277200a b c d +--R + +--R 9 7 4 +--R 69300a b c +--R * +--R 3 +--R x +--R + +--R 14 2 4 13 3 3 12 4 2 2 11 5 3 +--R 51975a b d - 207900a b c d + 311850a b c d - 207900a b c d +--R + +--R 10 6 4 +--R 51975a b c +--R * +--R 2 +--R x +--R + +--R 15 4 14 2 3 13 3 2 2 12 4 3 +--R 20790a b d - 83160a b c d + 124740a b c d - 83160a b c d +--R + +--R 11 5 4 +--R 20790a b c +--R * +--R x +--R + +--R 16 4 15 3 14 2 2 2 13 3 3 12 4 4 +--R 3465a d - 13860a b c d + 20790a b c d - 13860a b c d + 3465a b c +--R Type: Union(Expression(Integer),...) +--E 1705 + +--S 1706 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 3 4 2 3 2 4 3 3 2 +--R (231a c + 2079a c )d + (- 495a b c - 4455a b c )d +--R + +--R 2 5 2 2 4 3 6 3 5 +--R (385a b c + 3465a b c )d - 105b c - 945a b c +--R / +--R 10 4 9 3 8 2 2 2 7 3 3 6 4 4 +--R 3465a d - 13860a b c d + 20790a b c d - 13860a b c d + 3465a b c +--R Type: Expression(Integer) +--E 1706 + +--S 1707 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1707 + +)clear all + +--S 1708 of 2952 +t0000:=(a+b*x)^(5/2)*(c+d*x)^(5/2) +--R +--R +--R (1) +--R 2 2 4 2 2 3 2 2 2 2 2 +--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 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1708 + +--S 1709 of 2952 +r0000:=1/12*(b*c-a*d)*(a+b*x)^(7/2)*(c+d*x)^(3/2)/b^2+_ + 1/6*(a+b*x)^(7/2)*(c+d*x)^(5/2)/b-_ + 5/512*(b*c-a*d)^6*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(7/2)*d^(7/2))-5/768*(b*c-a*d)^4*(a+b*x)^(3/2)*_ + sqrt(c+d*x)/(b^3*d^2)+1/192*(b*c-a*d)^3*(a+b*x)^(5/2)*_ + sqrt(c+d*x)/(b^3*d)+1/32*(b*c-a*d)^2*(a+b*x)^(7/2)*_ + sqrt(c+d*x)/b^3+5/512*(b*c-a*d)^5*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^3) +--R +--R +--R (2) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 15a d + 90a b c d - 225a b c d + 300a b c d - 225a b c d +--R + +--R 5 5 6 6 +--R 90a b c d - 15b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 5 5 5 4 5 5 4 4 +--R 256b d x + (640a b d + 640b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (432a b d + 1696a b c d + 432b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (8a b d + 1272a b c d + 1272a b c d + 8b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 10a b d + 56a b c d + 1188a b c d + 56a b c d - 10b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 15a d - 85a b c d + 198a b c d + 198a b c d - 85a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 3 +-+ +-+ +--R 1536b d \|b \|d +--R Type: Expression(Integer) +--E 1709 + +--S 1710 of 2952 +--a0000:=integrate(t0000,x) +--E 1710 + +--S 1711 of 2952 +--m0000:=a0000 - r0000 +--E 1711 + +--S 1712 of 2952 +--d0000:=D(m0000,x) +--E 1712 + +)clear all + +--S 1713 of 2952 +t0000:=(a+b*x)^(3/2)*(c+d*x)^(5/2) +--R +--R +--R (1) +--R 2 3 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 \|d x + c +--R Type: Expression(Integer) +--E 1713 + +--S 1714 of 2952 +r0000:=1/8*(b*c-a*d)*(a+b*x)^(5/2)*(c+d*x)^(3/2)/b^2+_ + 1/5*(a+b*x)^(5/2)*(c+d*x)^(5/2)/b+_ + 3/128*(b*c-a*d)^5*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(7/2)*d^(5/2))+1/64*(b*c-a*d)^3*(a+b*x)^(3/2)*sqrt(c+d*x)/_ + (b^3*d)+1/16*(b*c-a*d)^2*(a+b*x)^(5/2)*sqrt(c+d*x)/b^3-_ + 3/128*(b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^2) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 15a d + 75a b c d - 150a b c d + 150a b c d - 75a b c d +--R + +--R 5 5 +--R 15b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 4 4 3 4 4 3 3 +--R 128b d x + (176a b d + 336b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (8a b d + 512a b c d + 248b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 10a b d + 46a b c d + 466a b c d + 10b c d)x + 15a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 70a b c d + 128a b c d + 70a b c d - 15b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 2 +-+ +-+ +--R 640b d \|b \|d +--R Type: Expression(Integer) +--E 1714 + +--S 1715 of 2952 +--a0000:=integrate(t0000,x) +--E 1715 + +--S 1716 of 2952 +--m0000:=a0000 - r0000 +--E 1716 + +--S 1717 of 2952 +--d0000:=D(m0000,x) +--E 1717 + +)clear all + +--S 1718 of 2952 +t0000:=(a+b*x)^(1/2)*(c+d*x)^(5/2) +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (1) (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1718 + +--S 1719 of 2952 +r0000:=5/24*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b^2+_ + 1/4*(a+b*x)^(3/2)*(c+d*x)^(5/2)/b-_ + 5/64*(b*c-a*d)^4*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(7/2)*d^(3/2))+5/32*(b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x)/b^3+_ + 5/64*(b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 15a d + 60a b c d - 90a b c d + 60a b c d - 15b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b d x + (8a b d + 136b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 10a b d + 36a b c d + 118b c d)x + 15a d - 55a b c d +--R + +--R 2 2 3 3 +--R 73a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 +-+ +-+ +--R 192b d\|b \|d +--R Type: Expression(Integer) +--E 1719 + +--S 1720 of 2952 +--a0000:=integrate(t0000,x) +--E 1720 + +--S 1721 of 2952 +--m0000:=a0000 - r0000 +--E 1721 + +--S 1722 of 2952 +--d0000:=D(m0000,x) +--E 1722 + +)clear all + +--S 1723 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x)^(1/2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1723 + +--S 1724 of 2952 +r0000:=5/8*(b*c-a*d)^3*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(7/2)*sqrt(d))+5/12*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/b^2+_ + 1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/b+_ + 5/8*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (- 15a d + 45a b c d - 45a b c d + 15b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (8b d x + (- 10a b d + 26b c d)x + 15a d - 40a b c d + 33b c )\|b +--R * +--R +-+ +-------+ +-------+ +--R \|d \|b x + a \|d x + c +--R / +--R 3 +-+ +-+ +--R 24b \|b \|d +--R Type: Expression(Integer) +--E 1724 + +--S 1725 of 2952 +--a0000:=integrate(t0000,x) +--E 1725 + +--S 1726 of 2952 +--m0000:=a0000 - r0000 +--E 1726 + +--S 1727 of 2952 +--d0000:=D(m0000,x) +--E 1727 + +)clear all + +--S 1728 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x)^(3/2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1728 + +--S 1729 of 2952 +r0000:=15/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_ + sqrt(d)/b^(7/2)-2*(c+d*x)^(5/2)/(b*sqrt(a+b*x))+_ + 5/2*d*(c+d*x)^(3/2)*sqrt(a+b*x)/b^2+_ + 15/4*d*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-------+ \|d \|b x + a +--R (15a d - 30a b c d + 15b c )\|d \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (2b d x + (- 5a b d + 9b c d)x - 15a d + 25a b c d - 8b c )\|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +-+ +-------+ +--R 4b \|b \|b x + a +--R Type: Expression(Integer) +--E 1729 + +--S 1730 of 2952 +--a0000:=integrate(t0000,x) +--E 1730 + +--S 1731 of 2952 +--m0000:=a0000 - r0000 +--E 1731 + +--S 1732 of 2952 +--d0000:=D(m0000,x) +--E 1732 + +)clear all + +--S 1733 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1733 + +--S 1734 of 2952 +r0000:=-2/3*(c+d*x)^(5/2)/(b*(a+b*x)^(3/2))+_ + 5*d^(3/2)*(b*c-a*d)*atanh(sqrt(d)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(7/2)-_ + 10/3*d*(c+d*x)^(3/2)/(b^2*sqrt(a+b*x))+_ + 5*d^2*sqrt(a+b*x)*sqrt(c+d*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 +-+ +-------+ +--R ((- 15a b d + 15b c d)x - 15a d + 15a b c d)\|d \|b x + a +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (3b d x + (20a b d - 14b c d)x + 15a d - 10a b c d - 2b c )\|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 1734 + +--S 1735 of 2952 +--a0000:=integrate(t0000,x) +--E 1735 + +--S 1736 of 2952 +--m0000:=a0000 - r0000 +--E 1736 + +--S 1737 of 2952 +--d0000:=D(m0000,x) +--E 1737 + +)clear all + +--S 1738 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x)^(7/2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1738 + +--S 1739 of 2952 +r0000:=-2/3*d*(c+d*x)^(3/2)/(b^2*(a+b*x)^(3/2))-_ + 2/5*(c+d*x)^(5/2)/(b*(a+b*x)^(5/2))+_ + 2*d^(5/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/b^(7/2)-_ + 2*d^2*sqrt(c+d*x)/(b^3*sqrt(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 2 +-+ +-------+ \|d \|b x + a +--R (30b d x + 60a b d x + 30a d )\|d \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (- 46b d x + (- 70a b d - 22b c d)x - 30a d - 10a b c d - 6b c )\|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 2 4 2 3 +-+ +-------+ +--R (15b x + 30a b x + 15a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 1739 + +--S 1740 of 2952 +--a0000:=integrate(t0000,x) +--E 1740 + +--S 1741 of 2952 +--m0000:=a0000 - r0000 +--E 1741 + +--S 1742 of 2952 +--d0000:=D(m0000,x) +--E 1742 + +)clear all + +--S 1743 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x)^(9/2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1743 + +--S 1744 of 2952 +r0000:=-2/7*(c+d*x)^(7/2)/((b*c-a*d)*(a+b*x)^(7/2)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +-------+ +--R (2d x + 6c d x + 6c d x + 2c )\|d x + c +--R / +--R 3 4 3 2 2 3 2 3 2 2 4 +--R (7a b d - 7b c)x + (21a b d - 21a b c)x + (21a b d - 21a b c)x + 7a d +--R + +--R 3 +--R - 7a b c +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1744 + +--S 1745 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 3 4 2 2 4 2 4 3 +-------+ +-------+ +--R (4a d x + 12a c d x + 12a c d x + 4a c )\|b x + a \|d x + c +--R + +--R 4 4 4 3 4 3 4 2 3 3 3 2 2 4 3 2 3 2 +--R (b c + 4a b c )x + (4a b c + 16a b c )x + (6a b c + 24a b c )x +--R + +--R 3 4 4 3 4 4 5 3 +--R (4a b c + 16a b c )x + a c + 4a c +--R / +--R 5 4 4 5 4 6 3 5 4 3 7 2 6 3 2 +--R (14a b d - 14a b c)x + (56a b d - 56a b c)x + (84a b d - 84a b c)x +--R + +--R 8 7 2 9 8 +--R (56a b d - 56a b c)x + 14a d - 14a b c +--R Type: Union(Expression(Integer),...) +--E 1745 + +--S 1746 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 4 3 +--R c + 4a c +--R (4) --------------- +--R 5 4 +--R 14a d - 14a b c +--R Type: Expression(Integer) +--E 1746 + +--S 1747 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1747 + +)clear all + +--S 1748 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x)^(11/2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1748 + +--S 1749 of 2952 +r0000:=-2/9*(c+d*x)^(7/2)/((b*c-a*d)*(a+b*x)^(9/2))+_ + 4/63*d*(c+d*x)^(7/2)/((b*c-a*d)^2*(a+b*x)^(7/2)) +--R +--R +--R (2) +--R 4 4 4 3 3 3 2 2 2 +--R 4b d x + (18a d - 2b c d )x + (54a c d - 30b c d )x +--R + +--R 2 2 3 3 4 +--R (54a c d - 38b c d)x + 18a c d - 14b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 2 4 2 5 6 2 4 +--R (63a b d - 126a b c d + 63b c )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (252a b d - 504a b c d + 252a b c )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (378a b d - 756a b c d + 378a b c )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (252a b d - 504a b c d + 252a b c )x + 63a d - 126a b c d + 63a b c +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1749 + +--S 1750 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 4 6 4 5 3 3 6 3 5 2 2 2 +--R 4a b d x + (18a d - 2a b c d )x + (54a c d - 30a b c d )x +--R + +--R 6 2 2 5 3 6 3 5 4 +--R (54a c d - 38a b c d)x + 18a c d - 14a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 5 4 2 5 3 6 5 6 4 5 +--R ((- 9a b c - 9a b c )d + 7b c + 7a b c )x +--R + +--R 2 4 4 3 4 3 5 5 2 5 4 4 +--R ((- 45a b c - 45a b c )d + 35a b c + 35a b c )x +--R + +--R 3 3 4 4 3 3 2 4 5 3 4 4 3 +--R ((- 90a b c - 90a b c )d + 70a b c + 70a b c )x +--R + +--R 4 2 4 5 2 3 3 3 5 4 3 4 2 +--R ((- 90a b c - 90a b c )d + 70a b c + 70a b c )x +--R + +--R 5 4 6 3 4 2 5 5 2 4 6 4 7 3 +--R ((- 45a b c - 45a b c )d + 35a b c + 35a b c )x + (- 9a c - 9a c )d +--R + +--R 5 5 6 4 +--R 7a b c + 7a b c +--R / +--R 7 5 2 6 6 5 7 2 5 +--R (63a b d - 126a b c d + 63a b c )x +--R + +--R 8 4 2 7 5 6 6 2 4 +--R (315a b d - 630a b c d + 315a b c )x +--R + +--R 9 3 2 8 4 7 5 2 3 +--R (630a b d - 1260a b c d + 630a b c )x +--R + +--R 10 2 2 9 3 8 4 2 2 +--R (630a b d - 1260a b c d + 630a b c )x +--R + +--R 11 2 10 2 9 3 2 12 2 11 10 2 2 +--R (315a b d - 630a b c d + 315a b c )x + 63a d - 126a b c d + 63a b c +--R Type: Union(Expression(Integer),...) +--E 1750 + +--S 1751 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 4 2 3 5 4 +--R (- 9a c - 9a c )d + 7b c + 7a b c +--R (4) ------------------------------------ +--R 7 2 6 5 2 2 +--R 63a d - 126a b c d + 63a b c +--R Type: Expression(Integer) +--E 1751 + +--S 1752 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1752 + +)clear all + +--S 1753 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x)^(13/2) +--R +--R +--R (1) +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1753 + +--S 1754 of 2952 +r0000:=-2/11*(c+d*x)^(7/2)/((b*c-a*d)*(a+b*x)^(11/2))+_ + 8/99*d*(c+d*x)^(7/2)/((b*c-a*d)^2*(a+b*x)^(9/2))-_ + 16/693*d^2*(c+d*x)^(7/2)/((b*c-a*d)^3*(a+b*x)^(7/2)) +--R +--R +--R (2) +--R 2 5 5 5 2 4 4 2 5 4 2 2 3 3 +--R 16b d x + (88a b d - 8b c d )x + (198a d - 44a b c d + 6b c d )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (594a c d - 660a b c d + 226b c d )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (594a c d - 836a b c d + 322b c d)x + 198a c d - 308a b c d + 126b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 5 3 2 6 2 7 2 8 3 5 +--R (693a b d - 2079a b c d + 2079a b c d - 693b c )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 4 +--R (3465a b d - 10395a b c d + 10395a b c d - 3465a b c )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 3 +--R (6930a b d - 20790a b c d + 20790a b c d - 6930a b c )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 2 +--R (6930a b d - 20790a b c d + 20790a b c d - 6930a b c )x +--R + +--R 7 3 6 2 2 5 3 2 4 4 3 8 3 +--R (3465a b d - 10395a b c d + 10395a b c d - 3465a b c )x + 693a d +--R + +--R 7 2 6 2 2 5 3 3 +--R - 2079a b c d + 2079a b c d - 693a b c +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1754 + +--S 1755 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 2 5 5 7 5 6 2 4 4 +--R 48a b d x + (264a b d - 24a b c d )x +--R + +--R 8 5 7 4 6 2 2 3 3 +--R (594a d - 132a b c d + 18a b c d )x +--R + +--R 8 4 7 2 3 6 2 3 2 2 +--R (1782a c d - 1980a b c d + 678a b c d )x +--R + +--R 8 2 3 7 3 2 6 2 4 8 3 2 7 4 +--R (1782a c d - 2508a b c d + 966a b c d)x + 594a c d - 924a b c d +--R + +--R 6 2 5 +--R 378a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 6 4 3 6 3 2 7 5 2 7 4 8 6 +--R (- 99a b c - 891a b c )d + (154a b c + 1386a b c )d - 63b c +--R + +--R 8 5 +--R - 567a b c +--R * +--R 6 +--R x +--R + +--R 3 5 4 4 5 3 2 2 6 5 3 6 4 7 6 +--R (- 594a b c - 5346a b c )d + (924a b c + 8316a b c )d - 378a b c +--R + +--R 2 7 5 +--R - 3402a b c +--R * +--R 5 +--R x +--R + +--R 4 4 4 5 4 3 2 3 5 5 4 5 4 +--R (- 1485a b c - 13365a b c )d + (2310a b c + 20790a b c )d +--R + +--R 2 6 6 3 6 5 +--R - 945a b c - 8505a b c +--R * +--R 4 +--R x +--R + +--R 5 3 4 6 3 3 2 4 4 5 5 4 4 +--R (- 1980a b c - 17820a b c )d + (3080a b c + 27720a b c )d +--R + +--R 3 5 6 4 5 5 +--R - 1260a b c - 11340a b c +--R * +--R 3 +--R x +--R + +--R 6 2 4 7 2 3 2 5 3 5 6 3 4 +--R (- 1485a b c - 13365a b c )d + (2310a b c + 20790a b c )d +--R + +--R 4 4 6 5 4 5 +--R - 945a b c - 8505a b c +--R * +--R 2 +--R x +--R + +--R 7 4 8 3 2 6 2 5 7 2 4 5 3 6 +--R (- 594a b c - 5346a b c )d + (924a b c + 8316a b c )d - 378a b c +--R + +--R 6 3 5 +--R - 3402a b c +--R * +--R x +--R + +--R 8 4 9 3 2 7 5 8 4 6 2 6 7 2 5 +--R (- 99a c - 891a c )d + (154a b c + 1386a b c )d - 63a b c - 567a b c +--R / +--R 9 6 3 8 7 2 7 8 2 6 9 3 6 +--R (2079a b d - 6237a b c d + 6237a b c d - 2079a b c )x +--R + +--R 10 5 3 9 6 2 8 7 2 7 8 3 5 +--R (12474a b d - 37422a b c d + 37422a b c d - 12474a b c )x +--R + +--R 11 4 3 10 5 2 9 6 2 8 7 3 4 +--R (31185a b d - 93555a b c d + 93555a b c d - 31185a b c )x +--R + +--R 12 3 3 11 4 2 10 5 2 9 6 3 3 +--R (41580a b d - 124740a b c d + 124740a b c d - 41580a b c )x +--R + +--R 13 2 3 12 3 2 11 4 2 10 5 3 2 +--R (31185a b d - 93555a b c d + 93555a b c d - 31185a b c )x +--R + +--R 14 3 13 2 2 12 3 2 11 4 3 +--R (12474a b d - 37422a b c d + 37422a b c d - 12474a b c )x +--R + +--R 15 3 14 2 13 2 2 12 3 3 +--R 2079a d - 6237a b c d + 6237a b c d - 2079a b c +--R Type: Union(Expression(Integer),...) +--E 1755 + +--S 1756 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 4 3 3 2 5 2 4 2 6 2 5 +--R (- 99a c - 891a c )d + (154a b c + 1386a b c )d - 63b c - 567a b c +--R ----------------------------------------------------------------------- +--R 9 3 8 2 7 2 2 6 3 3 +--R 2079a d - 6237a b c d + 6237a b c d - 2079a b c +--R Type: Expression(Integer) +--E 1756 + +--S 1757 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1757 + +)clear all + +--S 1758 of 2952 +t0000:=(c+d*x)^(5/2)/(a+b*x)^(15/2) +--R +--R +--R (1) +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x +--R + +--R 7 +--R a +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1758 + +--S 1759 of 2952 +r0000:=-2/13*(c+d*x)^(7/2)/((b*c-a*d)*(a+b*x)^(13/2))+_ + 12/143*d*(c+d*x)^(7/2)/((b*c-a*d)^2*(a+b*x)^(11/2))-_ + 16/429*d^2*(c+d*x)^(7/2)/((b*c-a*d)^3*(a+b*x)^(9/2))+_ + 32/3003*d^3*(c+d*x)^(7/2)/((b*c-a*d)^4*(a+b*x)^(7/2)) +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 32b d x + (208a b d - 16b c d )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (572a b d - 104a b c d + 12b c d )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (858a d - 286a b c d + 78a b c d - 10b c d )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (2574a c d - 4290a b c d + 2938a b c d - 742b c d )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (2574a c d - 5434a b c d + 4186a b c d - 1134b c d)x + 858a c d +--R + +--R 2 4 2 2 5 3 6 +--R - 2002a b c d + 1638a b c d - 462b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 6 4 3 7 3 2 8 2 2 9 3 +--R 3003a b d - 12012a b c d + 18018a b c d - 12012a b c d +--R + +--R 10 4 +--R 3003b c +--R * +--R 6 +--R x +--R + +--R 5 5 4 4 6 3 3 7 2 2 2 8 3 +--R 18018a b d - 72072a b c d + 108108a b c d - 72072a b c d +--R + +--R 9 4 +--R 18018a b c +--R * +--R 5 +--R x +--R + +--R 6 4 4 5 5 3 4 6 2 2 3 7 3 +--R 45045a b d - 180180a b c d + 270270a b c d - 180180a b c d +--R + +--R 2 8 4 +--R 45045a b c +--R * +--R 4 +--R x +--R + +--R 7 3 4 6 4 3 5 5 2 2 4 6 3 +--R 60060a b d - 240240a b c d + 360360a b c d - 240240a b c d +--R + +--R 3 7 4 +--R 60060a b c +--R * +--R 3 +--R x +--R + +--R 8 2 4 7 3 3 6 4 2 2 5 5 3 +--R 45045a b d - 180180a b c d + 270270a b c d - 180180a b c d +--R + +--R 4 6 4 +--R 45045a b c +--R * +--R 2 +--R x +--R + +--R 9 4 8 2 3 7 3 2 2 6 4 3 +--R 18018a b d - 72072a b c d + 108108a b c d - 72072a b c d +--R + +--R 5 5 4 +--R 18018a b c +--R * +--R x +--R + +--R 10 4 9 3 8 2 2 2 7 3 3 6 4 4 +--R 3003a d - 12012a b c d + 18018a b c d - 12012a b c d + 3003a b c +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1759 + +--S 1760 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 3 6 6 8 2 6 7 3 5 5 +--R 160a b d x + (1040a b d - 80a b c d )x +--R + +--R 9 6 8 2 5 7 3 2 4 4 +--R (2860a b d - 520a b c d + 60a b c d )x +--R + +--R 10 6 9 5 8 2 2 4 7 3 3 3 3 +--R (4290a d - 1430a b c d + 390a b c d - 50a b c d )x +--R + +--R 10 5 9 2 4 8 2 3 3 7 3 4 2 2 +--R (12870a c d - 21450a b c d + 14690a b c d - 3710a b c d )x +--R + +--R 10 2 4 9 3 3 8 2 4 2 7 3 5 +--R (12870a c d - 27170a b c d + 20930a b c d - 5670a b c d)x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 +--R 4290a c d - 10010a b c d + 8190a b c d - 2310a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 3 7 4 4 7 3 3 2 8 5 3 8 4 2 +--R (429a b c + 10725a b c )d + (- 1001a b c - 25025a b c )d +--R + +--R 9 6 2 9 5 10 7 10 6 +--R (819a b c + 20475a b c )d - 231b c - 5775a b c +--R * +--R 7 +--R x +--R + +--R 4 6 4 5 6 3 3 3 7 5 4 7 4 2 +--R (3003a b c + 75075a b c )d + (- 7007a b c - 175175a b c )d +--R + +--R 2 8 6 3 8 5 9 7 2 9 6 +--R (5733a b c + 143325a b c )d - 1617a b c - 40425a b c +--R * +--R 6 +--R x +--R + +--R 5 5 4 6 5 3 3 4 6 5 5 6 4 2 +--R (9009a b c + 225225a b c )d + (- 21021a b c - 525525a b c )d +--R + +--R 3 7 6 4 7 5 2 8 7 3 8 6 +--R (17199a b c + 429975a b c )d - 4851a b c - 121275a b c +--R * +--R 5 +--R x +--R + +--R 6 4 4 7 4 3 3 5 5 5 6 5 4 2 +--R (15015a b c + 375375a b c )d + (- 35035a b c - 875875a b c )d +--R + +--R 4 6 6 5 6 5 3 7 7 4 7 6 +--R (28665a b c + 716625a b c )d - 8085a b c - 202125a b c +--R * +--R 4 +--R x +--R + +--R 7 3 4 8 3 3 3 6 4 5 7 4 4 2 +--R (15015a b c + 375375a b c )d + (- 35035a b c - 875875a b c )d +--R + +--R 5 5 6 6 5 5 4 6 7 5 6 6 +--R (28665a b c + 716625a b c )d - 8085a b c - 202125a b c +--R * +--R 3 +--R x +--R + +--R 8 2 4 9 2 3 3 7 3 5 8 3 4 2 +--R (9009a b c + 225225a b c )d + (- 21021a b c - 525525a b c )d +--R + +--R 6 4 6 7 4 5 5 5 7 6 5 6 +--R (17199a b c + 429975a b c )d - 4851a b c - 121275a b c +--R * +--R 2 +--R x +--R + +--R 9 4 10 3 3 8 2 5 9 2 4 2 +--R (3003a b c + 75075a b c )d + (- 7007a b c - 175175a b c )d +--R + +--R 7 3 6 8 3 5 6 4 7 7 4 6 +--R (5733a b c + 143325a b c )d - 1617a b c - 40425a b c +--R * +--R x +--R + +--R 10 4 11 3 3 9 5 10 4 2 +--R (429a c + 10725a c )d + (- 1001a b c - 25025a b c )d +--R + +--R 8 2 6 9 2 5 7 3 7 8 3 6 +--R (819a b c + 20475a b c )d - 231a b c - 5775a b c +--R / +--R 11 7 4 10 8 3 9 9 2 2 8 10 3 +--R 15015a b d - 60060a b c d + 90090a b c d - 60060a b c d +--R + +--R 7 11 4 +--R 15015a b c +--R * +--R 7 +--R x +--R + +--R 12 6 4 11 7 3 10 8 2 2 9 9 3 +--R 105105a b d - 420420a b c d + 630630a b c d - 420420a b c d +--R + +--R 8 10 4 +--R 105105a b c +--R * +--R 6 +--R x +--R + +--R 13 5 4 12 6 3 11 7 2 2 10 8 3 +--R 315315a b d - 1261260a b c d + 1891890a b c d - 1261260a b c d +--R + +--R 9 9 4 +--R 315315a b c +--R * +--R 5 +--R x +--R + +--R 14 4 4 13 5 3 12 6 2 2 11 7 3 +--R 525525a b d - 2102100a b c d + 3153150a b c d - 2102100a b c d +--R + +--R 10 8 4 +--R 525525a b c +--R * +--R 4 +--R x +--R + +--R 15 3 4 14 4 3 13 5 2 2 12 6 3 +--R 525525a b d - 2102100a b c d + 3153150a b c d - 2102100a b c d +--R + +--R 11 7 4 +--R 525525a b c +--R * +--R 3 +--R x +--R + +--R 16 2 4 15 3 3 14 4 2 2 13 5 3 +--R 315315a b d - 1261260a b c d + 1891890a b c d - 1261260a b c d +--R + +--R 12 6 4 +--R 315315a b c +--R * +--R 2 +--R x +--R + +--R 17 4 16 2 3 15 3 2 2 14 4 3 +--R 105105a b d - 420420a b c d + 630630a b c d - 420420a b c d +--R + +--R 13 5 4 +--R 105105a b c +--R * +--R x +--R + +--R 18 4 17 3 16 2 2 2 15 3 3 14 4 4 +--R 15015a d - 60060a b c d + 90090a b c d - 60060a b c d + 15015a b c +--R Type: Union(Expression(Integer),...) +--E 1760 + +--S 1761 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 4 4 3 3 2 5 3 4 2 +--R (429a c + 10725a c )d + (- 1001a b c - 25025a b c )d +--R + +--R 2 6 2 2 5 3 7 3 6 +--R (819a b c + 20475a b c )d - 231b c - 5775a b c +--R / +--R 11 4 10 3 9 2 2 2 8 3 3 7 4 4 +--R 15015a d - 60060a b c d + 90090a b c d - 60060a b c d + 15015a b c +--R Type: Expression(Integer) +--E 1761 + +--S 1762 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1762 + +)clear all + +--S 1763 of 2952 +t0000:=(a+b*x)^(7/2)/(c+d*x)^(1/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R (1) ---------------------------------------- +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1763 + +--S 1764 of 2952 +r0000:=35/64*(b*c-a*d)^4*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (d^(9/2)*sqrt(b))+35/96*(b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x)/d^3-_ + 7/24*(b*c-a*d)*(a+b*x)^(5/2)*sqrt(c+d*x)/d^2+_ + 1/4*(a+b*x)^(7/2)*sqrt(c+d*x)/d-_ + 35/64*(b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x)/d^4 +--R +--R +--R (2) +--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 \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b d x + (200a b d - 56b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (326a b d - 252a b c d + 70b c d)x + 279a d - 511a b c d +--R + +--R 2 2 3 3 +--R 385a b c d - 105b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 4 +-+ +-+ +--R 192d \|b \|d +--R Type: Expression(Integer) +--E 1764 + +--S 1765 of 2952 +--a0000:=integrate(t0000,x) +--E 1765 + +--S 1766 of 2952 +--m0000:=a0000 - r0000 +--E 1766 + +--S 1767 of 2952 +--d0000:=D(m0000,x) +--E 1767 + +)clear all + +--S 1768 of 2952 +t0000:=(a+b*x)^(5/2)/(c+d*x)^(1/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1768 + +--S 1769 of 2952 +r0000:=-5/8*(b*c-a*d)^3*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (d^(7/2)*sqrt(b))-5/12*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/d^2+_ + 1/3*(a+b*x)^(5/2)*sqrt(c+d*x)/d+_ + 5/8*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/d^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (15a d - 45a b c d + 45a b c d - 15b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (26a b d - 10b c d)x + 33a d - 40a b c d + 15b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 3 +-+ +-+ +--R 24d \|b \|d +--R Type: Expression(Integer) +--E 1769 + +--S 1770 of 2952 +--a0000:=integrate(t0000,x) +--E 1770 + +--S 1771 of 2952 +--m0000:=a0000 - r0000 +--E 1771 + +--S 1772 of 2952 +--d0000:=D(m0000,x) +--E 1772 + +)clear all + +--S 1773 of 2952 +t0000:=(a+b*x)^(3/2)/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1773 + +--S 1774 of 2952 +r0000:=3/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (d^(5/2)*sqrt(b))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/d-_ + 3/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 \|d \|b x + a +--R (3a d - 6a b c d + 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2b d x + 5a d - 3b c)\|b \|d \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 4d \|b \|d +--R Type: Expression(Integer) +--E 1774 + +--S 1775 of 2952 +--a0000:=integrate(t0000,x) +--E 1775 + +--S 1776 of 2952 +--m0000:=a0000 - r0000 +--E 1776 + +--S 1777 of 2952 +--d0000:=D(m0000,x) +--E 1777 + +)clear all + +--S 1778 of 2952 +t0000:=(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ---------- +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 1778 + +--S 1779 of 2952 +r0000:=-(b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (d^(3/2)*sqrt(b))+sqrt(a+b*x)*sqrt(c+d*x)/d +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +-+ +-+ +-------+ +-------+ +--R (a d - b c)atanh(--------------) + \|b \|d \|b x + a \|d x + c +--R +-+ +-------+ +--R \|b \|d x + c +--R (2) --------------------------------------------------------------- +--R +-+ +-+ +--R d\|b \|d +--R Type: Expression(Integer) +--E 1779 + +--S 1780 of 2952 +--a0000:=integrate(t0000,x) +--E 1780 + +--S 1781 of 2952 +--m0000:=a0000 - r0000 +--E 1781 + +--S 1782 of 2952 +--d0000:=D(m0000,x) +--E 1782 + +)clear all + +--S 1783 of 2952 +t0000:=1/((a+b*x)^(1/2)*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1783 + +--S 1784 of 2952 +r0000:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(sqrt(b)*sqrt(d)) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +--R 2atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R (2) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 1784 + +--S 1785 of 2952 +--a0000:=integrate(t0000,x) +--E 1785 + +--S 1786 of 2952 +--m0000:=a0000 - r0000 +--E 1786 + +--S 1787 of 2952 +--d0000:=D(m0000,x) +--E 1787 + +)clear all + +--S 1788 of 2952 +t0000:=1/((a+b*x)^(3/2)*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (1) ----------------------------- +--R +-------+ +-------+ +--R (b x + a)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1788 + +--S 1789 of 2952 +r0000:=-2*sqrt(c+d*x)/((b*c-a*d)*sqrt(a+b*x)) +--R +--R +--R +-------+ +--R 2\|d x + c +--R (2) --------------------- +--R +-------+ +--R (a d - b c)\|b x + a +--R Type: Expression(Integer) +--E 1789 + +--S 1790 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-------+ 2 +--R 6a\|b x + a \|d x + c + (- b c - 9a b)x - a c - 9a +--R (3) ---------------------------------------------------- +--R 2 2 3 2 +--R (3a b d - 3a b c)x + 3a d - 3a b c +--R Type: Union(Expression(Integer),...) +--E 1790 + +--S 1791 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R - c - 9a +--R (4) ------------- +--R 2 +--R 3a d - 3a b c +--R Type: Expression(Integer) +--E 1791 + +--S 1792 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1792 + +)clear all + +--S 1793 of 2952 +t0000:=1/((a+b*x)^(5/2)*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (b x + 2a b x + a )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1793 + +--S 1794 of 2952 +r0000:=-2/3*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^(3/2))+_ + 4/3*d*sqrt(c+d*x)/((b*c-a*d)^2*sqrt(a+b*x)) +--R +--R +--R +-------+ +--R (4b d x + 6a d - 2b c)\|d x + c +--R (2) ---------------------------------------------------------------------- +--R 2 2 2 3 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 )\|b x + a +--R Type: Expression(Integer) +--E 1794 + +--S 1795 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 3 2 +-------+ +-------+ +--R (12a b d x + 18a d - 6a b c)\|b x + a \|d x + c +--R + +--R 2 2 2 3 2 3 2 +--R ((- 3a b c - 27a b )d + b c + 9a b c)x +--R + +--R 2 3 2 2 2 2 3 4 2 2 +--R ((- 6a b c - 54a b)d + 2a b c + 18a b c)x + (- 3a c - 27a )d + a b c +--R + +--R 3 +--R 9a b c +--R / +--R 4 2 2 3 3 2 4 2 2 5 2 4 2 3 3 2 +--R (9a b d - 18a b c d + 9a b c )x + (18a b d - 36a b c d + 18a b c )x +--R + +--R 6 2 5 4 2 2 +--R 9a d - 18a b c d + 9a b c +--R Type: Union(Expression(Integer),...) +--E 1795 + +--S 1796 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R (- 3a c - 27a )d + b c + 9a b c +--R (4) -------------------------------- +--R 4 2 3 2 2 2 +--R 9a d - 18a b c d + 9a b c +--R Type: Expression(Integer) +--E 1796 + +--S 1797 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1797 + +)clear all + +--S 1798 of 2952 +t0000:=1/((a+b*x)^(7/2)*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +-------+ +--R (b x + 3a b x + 3a b x + a )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1798 + +--S 1799 of 2952 +r0000:=-2/5*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^(5/2))+_ + 8/15*d*sqrt(c+d*x)/((b*c-a*d)^2*(a+b*x)^(3/2))-_ + 16/15*d^2*sqrt(c+d*x)/((b*c-a*d)^3*sqrt(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +-------+ +--R (16b d x + (40a b d - 8b c d)x + 30a d - 20a b c d + 6b c )\|d x + c +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--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 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 \|b x + a +--R Type: Expression(Integer) +--E 1799 + +--S 1800 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 2 2 4 2 3 2 5 2 4 3 2 2 +--R (16a b d x + (40a b d - 8a b c d)x + 30a d - 20a b c d + 6a b c ) +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 3 3 3 2 4 2 2 4 5 3 5 2 3 +--R ((15a b c + 15a b )d + (- 10a b c - 10a b c)d + 3b c + 3a b c )x +--R + +--R 3 2 4 2 2 2 3 2 3 3 4 3 2 4 2 2 +--R ((45a b c + 45a b )d + (- 30a b c - 30a b c)d + 9a b c + 9a b c )x +--R + +--R 4 5 2 3 2 2 4 2 2 3 3 3 3 2 +--R ((45a b c + 45a b)d + (- 30a b c - 30a b c)d + 9a b c + 9a b c )x +--R + +--R 5 6 2 4 2 5 3 2 3 4 2 2 +--R (15a c + 15a )d + (- 10a b c - 10a b c)d + 3a b c + 3a b c +--R / +--R 6 3 3 5 4 2 4 5 2 3 6 3 3 +--R (15a b d - 45a b c d + 45a b c d - 15a b c )x +--R + +--R 7 2 3 6 3 2 5 4 2 4 5 3 2 +--R (45a b d - 135a b c d + 135a b c d - 45a b c )x +--R + +--R 8 3 7 2 2 6 3 2 5 4 3 9 3 8 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 7 2 2 6 3 3 +--R 45a b c d - 15a b c +--R Type: Union(Expression(Integer),...) +--E 1800 + +--S 1801 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 3 2 2 2 2 3 2 2 +--R (15a c + 15a )d + (- 10a b c - 10a b c)d + 3b c + 3a b c +--R (4) ------------------------------------------------------------ +--R 6 3 5 2 4 2 2 3 3 3 +--R 15a d - 45a b c d + 45a b c d - 15a b c +--R Type: Expression(Integer) +--E 1801 + +--S 1802 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1802 + +)clear all + +--S 1803 of 2952 +t0000:=1/((a+b*x)^(9/2)*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +-------+ +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1803 + +--S 1804 of 2952 +r0000:=-2/7*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^(7/2))+_ + 12/35*d*sqrt(c+d*x)/((b*c-a*d)^2*(a+b*x)^(5/2))-_ + 16/35*d^2*sqrt(c+d*x)/((b*c-a*d)^3*(a+b*x)^(3/2))+_ + 32/35*d^3*sqrt(c+d*x)/((b*c-a*d)^4*sqrt(a+b*x)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 +--R 32b d x + (112a b d - 16b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (140a b d - 56a b c d + 12b c d)x + 70a d - 70a b c d + 42a b c d +--R + +--R 3 3 +--R - 10b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 3 +--R (35a b d - 140a b c d + 210a b c d - 140a b c d + 35b c )x +--R + +--R 5 2 4 4 3 3 3 4 2 2 2 5 3 6 4 2 +--R (105a b d - 420a b c d + 630a b c d - 420a b c d + 105a b c )x +--R + +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R (105a b d - 420a b c d + 630a b c d - 420a b c d + 105a b c )x +--R + +--R 7 4 6 3 5 2 2 2 4 3 3 3 4 4 +--R 35a d - 140a b c d + 210a b c d - 140a b c d + 35a b c +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1804 + +--S 1805 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 3 3 5 2 3 4 3 2 2 +--R 96a b d x + (336a b d - 48a b c d )x +--R + +--R 6 3 5 2 2 4 3 2 7 3 6 2 +--R (420a b d - 168a b c d + 36a b c d)x + 210a d - 210a b c d +--R + +--R 5 2 2 4 3 3 +--R 126a b c d - 30a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 3 4 4 4 3 2 5 2 3 5 2 +--R (35a b c + 315a b )d + (- 35a b c - 315a b c)d +--R + +--R 6 3 2 6 2 7 4 7 3 +--R (21a b c + 189a b c )d - 5b c - 45a b c +--R * +--R 4 +--R x +--R + +--R 4 3 5 3 3 3 4 2 4 4 2 +--R (140a b c + 1260a b )d + (- 140a b c - 1260a b c)d +--R + +--R 2 5 3 3 5 2 6 4 2 6 3 +--R (84a b c + 756a b c )d - 20a b c - 180a b c +--R * +--R 3 +--R x +--R + +--R 5 2 6 2 3 4 3 2 5 3 2 +--R (210a b c + 1890a b )d + (- 210a b c - 1890a b c)d +--R + +--R 3 4 3 4 4 2 2 5 4 3 5 3 +--R (126a b c + 1134a b c )d - 30a b c - 270a b c +--R * +--R 2 +--R x +--R + +--R 6 7 3 5 2 2 6 2 2 +--R (140a b c + 1260a b)d + (- 140a b c - 1260a b c)d +--R + +--R 4 3 3 5 3 2 3 4 4 4 4 3 +--R (84a b c + 756a b c )d - 20a b c - 180a b c +--R * +--R x +--R + +--R 7 8 3 6 2 7 2 5 2 3 6 2 2 +--R (35a c + 315a )d + (- 35a b c - 315a b c)d + (21a b c + 189a b c )d +--R + +--R 4 3 4 5 3 3 +--R - 5a b c - 45a b c +--R / +--R 8 4 4 7 5 3 6 6 2 2 5 7 3 4 8 4 4 +--R (105a b d - 420a b c d + 630a b c d - 420a b c d + 105a b c )x +--R + +--R 9 3 4 8 4 3 7 5 2 2 6 6 3 5 7 4 3 +--R (420a b d - 1680a b c d + 2520a b c d - 1680a b c d + 420a b c )x +--R + +--R 10 2 4 9 3 3 8 4 2 2 7 5 3 6 6 4 2 +--R (630a b d - 2520a b c d + 3780a b c d - 2520a b c d + 630a b c )x +--R + +--R 11 4 10 2 3 9 3 2 2 8 4 3 7 5 4 +--R (420a b d - 1680a b c d + 2520a b c d - 1680a b c d + 420a b c )x +--R + +--R 12 4 11 3 10 2 2 2 9 3 3 8 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 1805 + +--S 1806 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 2 3 2 2 2 +--R (35a c + 315a )d + (- 35a b c - 315a b c)d + (21a b c + 189a b c )d +--R + +--R 3 4 3 3 +--R - 5b c - 45a b c +--R / +--R 8 4 7 3 6 2 2 2 5 3 3 4 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 1806 + +--S 1807 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1807 + +)clear all + +--S 1808 of 2952 +t0000:=1/((a+b*x)^(11/2)*(c+d*x)^(1/2)) +--R +--R +--R (1) +--R 1 +--R ------------------------------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +-------+ +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1808 + +--S 1809 of 2952 +r0000:=-2/9*sqrt(c+d*x)/((b*c-a*d)*(a+b*x)^(9/2))+_ + 16/63*d*sqrt(c+d*x)/((b*c-a*d)^2*(a+b*x)^(7/2))-_ + 32/105*d^2*sqrt(c+d*x)/((b*c-a*d)^3*(a+b*x)^(5/2))+_ + 128/315*d^3*sqrt(c+d*x)/((b*c-a*d)^4*(a+b*x)^(3/2))-_ + 256/315*d^4*sqrt(c+d*x)/((b*c-a*d)^5*sqrt(a+b*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 256b d x + (1152a b d - 128b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (2016a b d - 576a b c d + 96b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (1680a b d - 1008a b c d + 432a b c d - 80b c d)x + 630a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 840a b c d + 756a b c d - 360a b c d + 70b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 4 5 4 5 4 3 6 2 3 2 7 3 2 +--R 315a b d - 1575a b c d + 3150a b c d - 3150a b c d +--R + +--R 8 4 9 5 +--R 1575a b c d - 315b c +--R * +--R 4 +--R x +--R + +--R 6 3 5 5 4 4 4 5 2 3 3 6 3 2 +--R 1260a b d - 6300a b c d + 12600a b c d - 12600a b c d +--R + +--R 2 7 4 8 5 +--R 6300a b c d - 1260a b c +--R * +--R 3 +--R x +--R + +--R 7 2 5 6 3 4 5 4 2 3 4 5 3 2 +--R 1890a b d - 9450a b c d + 18900a b c d - 18900a b c d +--R + +--R 3 6 4 2 7 5 +--R 9450a b c d - 1890a b c +--R * +--R 2 +--R x +--R + +--R 8 5 7 2 4 6 3 2 3 5 4 3 2 +--R 1260a b d - 6300a b c d + 12600a b c d - 12600a b c d +--R + +--R 4 5 4 3 6 5 +--R 6300a b c d - 1260a b c +--R * +--R x +--R + +--R 9 5 8 4 7 2 2 3 6 3 3 2 5 4 4 +--R 315a d - 1575a b c d + 3150a b c d - 3150a b c d + 1575a b c d +--R + +--R 4 5 5 +--R - 315a b c +--R * +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1809 + +--S 1810 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 4 4 6 3 4 5 4 3 3 +--R 256a b d x + (1152a b d - 128a b c d )x +--R + +--R 7 2 4 6 3 3 5 4 2 2 2 +--R (2016a b d - 576a b c d + 96a b c d )x +--R + +--R 8 4 7 2 3 6 3 2 2 5 4 3 9 4 +--R (1680a b d - 1008a b c d + 432a b c d - 80a b c d)x + 630a d +--R + +--R 8 3 7 2 2 2 6 3 3 5 4 4 +--R - 840a b c d + 756a b c d - 360a b c d + 70a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 4 5 5 5 4 3 6 2 4 6 3 +--R (315a b c + 315a b )d + (- 420a b c - 420a b c)d +--R + +--R 2 7 3 3 7 2 2 8 4 2 8 3 9 5 +--R (378a b c + 378a b c )d + (- 180a b c - 180a b c )d + 35b c +--R + +--R 9 4 +--R 35a b c +--R * +--R 5 +--R x +--R + +--R 5 4 6 4 4 4 5 2 5 5 3 +--R (1575a b c + 1575a b )d + (- 2100a b c - 2100a b c)d +--R + +--R 3 6 3 4 6 2 2 2 7 4 3 7 3 8 5 +--R (1890a b c + 1890a b c )d + (- 900a b c - 900a b c )d + 175a b c +--R + +--R 2 8 4 +--R 175a b c +--R * +--R 4 +--R x +--R + +--R 6 3 7 3 4 5 4 2 6 4 3 +--R (3150a b c + 3150a b )d + (- 4200a b c - 4200a b c)d +--R + +--R 4 5 3 5 5 2 2 3 6 4 4 6 3 +--R (3780a b c + 3780a b c )d + (- 1800a b c - 1800a b c )d +--R + +--R 2 7 5 3 7 4 +--R 350a b c + 350a b c +--R * +--R 3 +--R x +--R + +--R 7 2 8 2 4 6 3 2 7 3 3 +--R (3150a b c + 3150a b )d + (- 4200a b c - 4200a b c)d +--R + +--R 5 4 3 6 4 2 2 4 5 4 5 5 3 +--R (3780a b c + 3780a b c )d + (- 1800a b c - 1800a b c )d +--R + +--R 3 6 5 4 6 4 +--R 350a b c + 350a b c +--R * +--R 2 +--R x +--R + +--R 8 9 4 7 2 2 8 2 3 +--R (1575a b c + 1575a b)d + (- 2100a b c - 2100a b c)d +--R + +--R 6 3 3 7 3 2 2 5 4 4 6 4 3 4 5 5 +--R (1890a b c + 1890a b c )d + (- 900a b c - 900a b c )d + 175a b c +--R + +--R 5 5 4 +--R 175a b c +--R * +--R x +--R + +--R 9 10 4 8 2 9 3 +--R (315a c + 315a )d + (- 420a b c - 420a b c)d +--R + +--R 7 2 3 8 2 2 2 6 3 4 7 3 3 5 4 5 +--R (378a b c + 378a b c )d + (- 180a b c - 180a b c )d + 35a b c +--R + +--R 6 4 4 +--R 35a b c +--R / +--R 10 5 5 9 6 4 8 7 2 3 7 8 3 2 6 9 4 +--R 315a b d - 1575a b c d + 3150a b c d - 3150a b c d + 1575a b c d +--R + +--R 5 10 5 +--R - 315a b c +--R * +--R 5 +--R x +--R + +--R 11 4 5 10 5 4 9 6 2 3 8 7 3 2 +--R 1575a b d - 7875a b c d + 15750a b c d - 15750a b c d +--R + +--R 7 8 4 6 9 5 +--R 7875a b c d - 1575a b c +--R * +--R 4 +--R x +--R + +--R 12 3 5 11 4 4 10 5 2 3 9 6 3 2 +--R 3150a b d - 15750a b c d + 31500a b c d - 31500a b c d +--R + +--R 8 7 4 7 8 5 +--R 15750a b c d - 3150a b c +--R * +--R 3 +--R x +--R + +--R 13 2 5 12 3 4 11 4 2 3 10 5 3 2 +--R 3150a b d - 15750a b c d + 31500a b c d - 31500a b c d +--R + +--R 9 6 4 8 7 5 +--R 15750a b c d - 3150a b c +--R * +--R 2 +--R x +--R + +--R 14 5 13 2 4 12 3 2 3 11 4 3 2 +--R 1575a b d - 7875a b c d + 15750a b c d - 15750a b c d +--R + +--R 10 5 4 9 6 5 +--R 7875a b c d - 1575a b c +--R * +--R x +--R + +--R 15 5 14 4 13 2 2 3 12 3 3 2 11 4 4 +--R 315a d - 1575a b c d + 3150a b c d - 3150a b c d + 1575a b c d +--R + +--R 10 5 5 +--R - 315a b c +--R Type: Union(Expression(Integer),...) +--E 1810 + +--S 1811 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 4 5 4 3 2 4 3 +--R (315a c + 315a )d + (- 420a b c - 420a b c)d +--R + +--R 2 2 3 3 2 2 2 3 4 2 3 3 4 5 4 4 +--R (378a b c + 378a b c )d + (- 180a b c - 180a b c )d + 35b c + 35a b c +--R / +--R 10 5 9 4 8 2 2 3 7 3 3 2 6 4 4 +--R 315a d - 1575a b c d + 3150a b c d - 3150a b c d + 1575a b c d +--R + +--R 5 5 5 +--R - 315a b c +--R Type: Expression(Integer) +--E 1811 + +--S 1812 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1812 + +)clear all + +--S 1813 of 2952 +t0000:=(a+b*x)^(7/2)/(c+d*x)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R (1) ---------------------------------------- +--R +-------+ +--R (d x + c)\|d x + c +--R Type: Expression(Integer) +--E 1813 + +--S 1814 of 2952 +r0000:=-35/8*(b*c-a*d)^3*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_ + sqrt(b)/d^(9/2)-2*(a+b*x)^(7/2)/(d*sqrt(c+d*x))-_ + 35/12*b*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/d^3+_ + 7/3*b*(a+b*x)^(5/2)*sqrt(c+d*x)/d^2+_ + 35/8*b*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/d^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 +-+ +-------+ +--R (105a d - 315a b c d + 315a b c d - 105b c )\|b \|d x + c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 8b d x + (38a b d - 14b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (87a b d - 98a b c d + 35b c d)x - 48a d + 231a b c d +--R + +--R 2 2 3 3 +--R - 280a b c d + 105b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R / +--R 4 +-+ +-------+ +--R 24d \|d \|d x + c +--R Type: Expression(Integer) +--E 1814 + +--S 1815 of 2952 +--a0000:=integrate(t0000,x) +--E 1815 + +--S 1816 of 2952 +--m0000:=a0000 - r0000 +--E 1816 + +--S 1817 of 2952 +--d0000:=D(m0000,x) +--E 1817 + +)clear all + +--S 1818 of 2952 +t0000:=(a+b*x)^(5/2)/(c+d*x)^(3/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R +-------+ +--R (d x + c)\|d x + c +--R Type: Expression(Integer) +--E 1818 + +--S 1819 of 2952 +r0000:=15/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_ + sqrt(b)/d^(7/2)-2*(a+b*x)^(5/2)/(d*sqrt(c+d*x))+_ + 5/2*b*(a+b*x)^(3/2)*sqrt(c+d*x)/d^2-_ + 15/4*b*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-------+ \|d \|b x + a +--R (15a d - 30a b c d + 15b c )\|b \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-------+ +--R (2b d x + (9a b d - 5b c d)x - 8a d + 25a b c d - 15b c )\|d \|b x + a +--R / +--R 3 +-+ +-------+ +--R 4d \|d \|d x + c +--R Type: Expression(Integer) +--E 1819 + +--S 1820 of 2952 +--a0000:=integrate(t0000,x) +--E 1820 + +--S 1821 of 2952 +--m0000:=a0000 - r0000 +--E 1821 + +--S 1822 of 2952 +--d0000:=D(m0000,x) +--E 1822 + +)clear all + +--S 1823 of 2952 +t0000:=(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------- +--R +-------+ +--R (d x + c)\|d x + c +--R Type: Expression(Integer) +--E 1823 + +--S 1824 of 2952 +r0000:=-3*(b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_ + sqrt(b)/d^(5/2)-2*(a+b*x)^(3/2)/(d*sqrt(c+d*x))+_ + 3*b*sqrt(a+b*x)*sqrt(c+d*x)/d^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|d \|b x + a +--R (3a d - 3b c)\|b \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R (b d x - 2a d + 3b c)\|d \|b x + a +--R / +--R 2 +-+ +-------+ +--R d \|d \|d x + c +--R Type: Expression(Integer) +--E 1824 + +--S 1825 of 2952 +--a0000:=integrate(t0000,x) +--E 1825 + +--S 1826 of 2952 +--m0000:=a0000 - r0000 +--E 1826 + +--S 1827 of 2952 +--d0000:=D(m0000,x) +--E 1827 + +)clear all + +--S 1828 of 2952 +t0000:=(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ------------------- +--R +-------+ +--R (d x + c)\|d x + c +--R Type: Expression(Integer) +--E 1828 + +--S 1829 of 2952 +r0000:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)/d^(3/2)-_ + 2*sqrt(a+b*x)/(d*sqrt(c+d*x)) +--R +--R +--R +-+ +-------+ +--R +-+ +-------+ \|d \|b x + a +-+ +-------+ +--R 2\|b \|d x + c atanh(--------------) - 2\|d \|b x + a +--R +-+ +-------+ +--R \|b \|d x + c +--R (2) ------------------------------------------------------ +--R +-+ +-------+ +--R d\|d \|d x + c +--R Type: Expression(Integer) +--E 1829 + +--S 1830 of 2952 +--a0000:=integrate(t0000,x) +--E 1830 + +--S 1831 of 2952 +--m0000:=a0000 - r0000 +--E 1831 + +--S 1832 of 2952 +--d0000:=D(m0000,x) +--E 1832 + +)clear all + +--S 1833 of 2952 +t0000:=1/((a+b*x)^(1/2)*(c+d*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------------- +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1833 + +--S 1834 of 2952 +r0000:=2*sqrt(a+b*x)/((b*c-a*d)*sqrt(c+d*x)) +--R +--R +--R +-------+ +--R 2\|b x + a +--R (2) - --------------------- +--R +-------+ +--R (a d - b c)\|d x + c +--R Type: Expression(Integer) +--E 1834 + +--S 1835 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-------+ 2 +--R - 8c\|b x + a \|d x + c + (- c - 16a)d x - c - 16a c +--R (3) ------------------------------------------------------ +--R 2 2 2 3 +--R (4a c d - 4b c d)x + 4a c d - 4b c +--R Type: Union(Expression(Integer),...) +--E 1835 + +--S 1836 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R - c - 16a +--R (4) -------------- +--R 2 +--R 4a c d - 4b c +--R Type: Expression(Integer) +--E 1836 + +--S 1837 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1837 + +)clear all + +--S 1838 of 2952 +t0000:=1/((a+b*x)^(3/2)*(c+d*x)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------- +--R 2 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1838 + +--S 1839 of 2952 +r0000:=(-2)/((b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x))-_ + 4*d*sqrt(a+b*x)/((b*c-a*d)^2*sqrt(c+d*x)) +--R +--R +--R - 4b d x - 2a d - 2b c +--R (2) -------------------------------------------- +--R 2 2 2 2 +-------+ +-------+ +--R (a d - 2a b c d + b c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1839 + +--S 1840 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +-------+ +-------+ +--R (- 16a b c d x - 8a c d - 8a b c )\|b x + a \|d x + c +--R + +--R 2 2 2 2 2 2 +--R ((- a b c - 16a b)d + (- b c - 16a b c)d)x +--R + +--R 2 3 2 2 2 2 3 2 2 +--R ((- a c - 16a )d + (- 2a b c - 32a b c)d - b c - 16a b c )x +--R + +--R 2 2 3 3 2 2 +--R (- a c - 16a c)d - a b c - 16a b c +--R / +--R 3 3 2 2 2 2 3 3 2 +--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 2 2 3 3 2 2 4 +--R (4a c d - 4a b c d - 4a b c d + 4a b c )x + 4a c d - 8a b c d + 4a b c +--R Type: Union(Expression(Integer),...) +--E 1840 + +--S 1841 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R (- a c - 16a )d - b c - 16a b c +--R (4) -------------------------------- +--R 3 2 2 2 2 3 +--R 4a c d - 8a b c d + 4a b c +--R Type: Expression(Integer) +--E 1841 + +--S 1842 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1842 + +)clear all + +--S 1843 of 2952 +t0000:=1/((a+b*x)^(5/2)*(c+d*x)^(3/2)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 2 3 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 1843 + +--S 1844 of 2952 +r0000:=(-2/3)/((b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x))+_ + 8/3*d/((b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x))+_ + 16/3*d^2*sqrt(a+b*x)/((b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R - 16b d x + (- 24a b d - 8b c d)x - 6a d - 12a b c d + 2b c +--R / +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (3a b d - 9a b c d + 9a b c d - 3b c )x + 3a d - 9a b c d +--R + +--R 2 2 2 3 3 +--R 9a b c d - 3a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1844 + +--S 1845 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 3 2 2 2 2 4 2 3 2 +--R - 64a b c d x + (- 96a b c d - 32a b c d)x - 24a c d - 48a b c d +--R + +--R 2 2 3 +--R 8a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 2 3 2 3 3 2 2 3 2 4 3 4 2 3 +--R ((3a b c + 48a b )d + (6a b c + 96a b c)d + (- b c - 16a b c )d)x +--R + +--R 3 4 3 2 2 2 3 2 2 3 3 2 3 2 +--R (6a b c + 96a b)d + (15a b c + 240a b c)d + (4a b c + 64a b c )d +--R + +--R 4 4 4 3 +--R - b c - 16a b c +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 2 2 3 3 2 2 +--R (3a c + 48a )d + (12a b c + 192a b c)d + (11a b c + 176a b c )d +--R + +--R 3 4 2 3 3 +--R - 2a b c - 32a b c +--R * +--R x +--R + +--R 4 2 5 2 3 3 4 2 2 2 4 3 2 3 +--R (3a c + 48a c)d + (6a b c + 96a b c )d - a b c - 16a b c +--R / +--R 5 2 4 4 3 2 3 3 4 3 2 2 5 4 3 +--R (12a b c d - 36a b c d + 36a b c d - 12a b c d)x +--R + +--R 6 4 5 2 2 3 4 3 3 2 3 4 4 2 5 5 2 +--R (24a b c d - 60a b c d + 36a b c d + 12a b c d - 12a b c )x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 7 2 3 +--R (12a c d - 12a b c d - 36a b c d + 60a b c d - 24a b c )x + 12a c d +--R + +--R 6 3 2 5 2 4 4 3 5 +--R - 36a b c d + 36a b c d - 12a b c +--R Type: Union(Expression(Integer),...) +--E 1845 + +--S 1846 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 3 2 2 2 2 3 2 2 +--R (3a c + 48a )d + (6a b c + 96a b c)d - b c - 16a b c +--R (4) -------------------------------------------------------- +--R 5 3 4 2 2 3 2 3 2 3 4 +--R 12a c d - 36a b c d + 36a b c d - 12a b c +--R Type: Expression(Integer) +--E 1846 + +--S 1847 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1847 + +)clear all + +--S 1848 of 2952 +t0000:=1/((a+b*x)^(7/2)*(c+d*x)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 4 2 3 3 2 2 2 3 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 * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1848 + +--S 1849 of 2952 +r0000:=(-2/5)/((b*c-a*d)*(a+b*x)^(5/2)*sqrt(c+d*x))+_ + 4/5*d/((b*c-a*d)^2*(a+b*x)^(3/2)*sqrt(c+d*x))-_ + 16/5*d^2/((b*c-a*d)^3*sqrt(a+b*x)*sqrt(c+d*x))-_ + 32/5*d^3*sqrt(a+b*x)/((b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 +--R - 32b d x + (- 80a b d - 16b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 60a b d - 40a b c d + 4b c d)x - 10a d - 30a b c d + 10a b c d +--R + +--R 3 3 +--R - 2b c +--R / +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2 +--R (5a b d - 20a b c d + 30a b c d - 20a b c d + 5b c )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 6 4 +--R (10a b d - 40a b c d + 60a b c d - 40a b c d + 10a b c )x + 5a d +--R + +--R 5 3 4 2 2 2 3 3 3 2 4 4 +--R - 20a b c d + 30a b c d - 20a b c d + 5a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1849 + +--S 1850 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 3 3 4 2 3 3 3 2 2 2 +--R - 128a b c d x + (- 320a b c d - 64a b c d )x +--R + +--R 5 3 4 2 2 2 3 3 3 6 3 5 2 2 +--R (- 240a b c d - 160a b c d + 16a b c d)x - 40a c d - 120a b c d +--R + +--R 4 2 3 3 3 4 +--R 40a b c d - 8a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 3 3 4 3 4 2 4 2 3 4 3 +--R (5a b c + 80a b )d + (15a b c + 240a b c)d +--R + +--R 5 3 2 5 2 2 6 4 6 3 +--R (- 5a b c - 80a b c )d + (b c + 16a b c )d +--R * +--R 4 +--R x +--R + +--R 4 2 5 2 4 3 3 2 4 3 3 +--R (15a b c + 240a b )d + (50a b c + 800a b c)d +--R + +--R 5 4 2 5 3 6 5 6 4 +--R (- 2a b c - 32a b c )d + b c + 16a b c +--R * +--R 3 +--R x +--R + +--R 5 6 4 4 2 2 5 2 3 +--R (15a b c + 240a b)d + (60a b c + 960a b c)d +--R + +--R 3 3 3 4 3 2 2 2 4 4 3 4 3 5 5 +--R (30a b c + 480a b c )d + (- 12a b c - 192a b c )d + 3a b c +--R + +--R 2 5 4 +--R 48a b c +--R * +--R 2 +--R x +--R + +--R 6 7 4 5 2 6 3 4 2 3 5 2 2 2 +--R (5a c + 80a )d + (30a b c + 480a b c)d + (40a b c + 640a b c )d +--R + +--R 3 3 4 4 3 3 2 4 5 3 4 4 +--R (- 14a b c - 224a b c )d + 3a b c + 48a b c +--R * +--R x +--R + +--R 6 2 7 3 5 3 6 2 2 4 2 4 5 2 3 +--R (5a c + 80a c)d + (15a b c + 240a b c )d + (- 5a b c - 80a b c )d +--R + +--R 3 3 5 4 3 4 +--R a b c + 16a b c +--R / +--R 7 3 5 6 4 2 4 5 5 3 3 4 6 4 2 3 7 5 4 +--R (20a b c d - 80a b c d + 120a b c d - 80a b c d + 20a b c d)x +--R + +--R 8 2 5 7 3 2 4 6 4 3 3 5 5 4 2 4 6 5 +--R 60a b c d - 220a b c d + 280a b c d - 120a b c d - 20a b c d +--R + +--R 3 7 6 +--R 20a b c +--R * +--R 3 +--R x +--R + +--R 9 5 8 2 2 4 7 3 3 3 6 4 4 2 5 5 5 +--R 60a b c d - 180a b c d + 120a b c d + 120a b c d - 180a b c d +--R + +--R 4 6 6 +--R 60a b c +--R * +--R 2 +--R x +--R + +--R 10 5 9 2 4 8 2 3 3 7 3 4 2 6 4 5 +--R 20a c d - 20a b c d - 120a b c d + 280a b c d - 220a b c d +--R + +--R 5 5 6 +--R 60a b c +--R * +--R x +--R + +--R 10 2 4 9 3 3 8 2 4 2 7 3 5 6 4 6 +--R 20a c d - 80a b c d + 120a b c d - 80a b c d + 20a b c +--R Type: Union(Expression(Integer),...) +--E 1850 + +--S 1851 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 2 3 2 2 2 +--R (5a c + 80a )d + (15a b c + 240a b c)d + (- 5a b c - 80a b c )d +--R + +--R 3 4 3 3 +--R b c + 16a b c +--R / +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 +--R 20a c d - 80a b c d + 120a b c d - 80a b c d + 20a b c +--R Type: Expression(Integer) +--E 1851 + +--S 1852 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1852 + +)clear all + +--S 1853 of 2952 +t0000:=1/((a+b*x)^(9/2)*(c+d*x)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b d x + (4a b d + b c)x + (6a b d + 4a b c)x + (4a b d + 6a b c)x +--R + +--R 4 3 4 +--R (a d + 4a b c)x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1853 + +--S 1854 of 2952 +r0000:=(-2/7)/((b*c-a*d)*(a+b*x)^(7/2)*sqrt(c+d*x))+_ + 16/35*d/((b*c-a*d)^2*(a+b*x)^(5/2)*sqrt(c+d*x))-_ + 32/35*d^2/((b*c-a*d)^3*(a+b*x)^(3/2)*sqrt(c+d*x))+_ + 128/35*d^3/((b*c-a*d)^4*sqrt(a+b*x)*sqrt(c+d*x))+_ + 256/35*d^4*sqrt(a+b*x)/((b*c-a*d)^5*sqrt(c+d*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R - 256b d x + (- 896a b d - 128b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 1120a b d - 448a b c d + 32b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 560a b d - 560a b c d + 112a b c d - 16b c d)x - 70a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 280a b c d + 140a b c d - 56a b c d + 10b c +--R / +--R 5 3 5 4 4 4 3 5 2 3 2 6 3 2 7 4 +--R 35a b d - 175a b c d + 350a b c d - 350a b c d + 175a b c d +--R + +--R 8 5 +--R - 35b c +--R * +--R 3 +--R x +--R + +--R 6 2 5 5 3 4 4 4 2 3 3 5 3 2 2 6 4 +--R 105a b d - 525a b c d + 1050a b c d - 1050a b c d + 525a b c d +--R + +--R 7 5 +--R - 105a b c +--R * +--R 2 +--R x +--R + +--R 7 5 6 2 4 5 3 2 3 4 4 3 2 3 5 4 +--R 105a b d - 525a b c d + 1050a b c d - 1050a b c d + 525a b c d +--R + +--R 2 6 5 +--R - 105a b c +--R * +--R x +--R + +--R 8 5 7 4 6 2 2 3 5 3 3 2 4 4 4 3 5 5 +--R 35a d - 175a b c d + 350a b c d - 350a b c d + 175a b c d - 35a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1854 + +--S 1855 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 4 4 5 3 4 4 4 2 3 3 +--R - 1280a b c d x + (- 4480a b c d - 640a b c d )x +--R + +--R 6 2 4 5 3 2 3 4 4 3 2 2 +--R (- 5600a b c d - 2240a b c d + 160a b c d )x +--R + +--R 7 4 6 2 2 3 5 3 3 2 4 4 4 +--R (- 2800a b c d - 2800a b c d + 560a b c d - 80a b c d)x +--R + +--R 8 4 7 2 3 6 2 3 2 5 3 4 4 4 5 +--R - 350a c d - 1400a b c d + 700a b c d - 280a b c d + 50a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 4 4 5 4 5 3 5 2 4 5 4 +--R (- 35a b c - 875a b )d + (- 140a b c - 3500a b c)d +--R + +--R 2 6 3 3 6 2 3 7 4 2 7 3 2 +--R (70a b c + 1750a b c )d + (- 28a b c - 700a b c )d +--R + +--R 8 5 8 4 +--R (5b c + 125a b c )d +--R * +--R 5 +--R x +--R + +--R 5 3 6 3 5 4 4 2 5 4 4 +--R (- 140a b c - 3500a b )d + (- 595a b c - 14875a b c)d +--R + +--R 3 5 3 4 5 2 3 2 6 4 3 6 3 2 +--R (140a b c + 3500a b c )d + (- 42a b c - 1050a b c )d +--R + +--R 7 5 2 7 4 8 6 8 5 +--R (- 8a b c - 200a b c )d + 5b c + 125a b c +--R * +--R 4 +--R x +--R + +--R 6 2 7 2 5 5 3 2 6 3 4 +--R (- 210a b c - 5250a b )d + (- 980a b c - 24500a b c)d +--R + +--R 4 4 3 5 4 2 3 3 5 4 4 5 3 2 +--R (- 140a b c - 3500a b c )d + (112a b c + 2800a b c )d +--R + +--R 2 6 5 3 6 4 7 6 2 7 5 +--R (- 82a b c - 2050a b c )d + 20a b c + 500a b c +--R * +--R 3 +--R x +--R + +--R 7 8 5 6 2 2 7 2 4 +--R (- 140a b c - 3500a b)d + (- 770a b c - 19250a b c)d +--R + +--R 5 3 3 6 3 2 3 4 4 4 5 4 3 2 +--R (- 560a b c - 14000a b c )d + (308a b c + 7700a b c )d +--R + +--R 3 5 5 4 5 4 2 6 6 3 6 5 +--R (- 148a b c - 3700a b c )d + 30a b c + 750a b c +--R * +--R 2 +--R x +--R + +--R 8 9 5 7 2 8 4 +--R (- 35a c - 875a )d + (- 280a b c - 7000a b c)d +--R + +--R 6 2 3 7 2 2 3 5 3 4 6 3 3 2 +--R (- 490a b c - 12250a b c )d + (252a b c + 6300a b c )d +--R + +--R 4 4 5 5 4 4 3 5 6 4 5 5 +--R (- 107a b c - 2675a b c )d + 20a b c + 500a b c +--R * +--R x +--R + +--R 8 2 9 4 7 3 8 2 3 +--R (- 35a c - 875a c)d + (- 140a b c - 3500a b c )d +--R + +--R 6 2 4 7 2 3 2 5 3 5 6 3 4 4 4 6 5 4 5 +--R (70a b c + 1750a b c )d + (- 28a b c - 700a b c )d + 5a b c + 125a b c +--R / +--R 9 4 6 8 5 2 5 7 6 3 4 6 7 4 3 5 8 5 2 +--R 175a b c d - 875a b c d + 1750a b c d - 1750a b c d + 875a b c d +--R + +--R 4 9 6 +--R - 175a b c d +--R * +--R 5 +--R x +--R + +--R 10 3 6 9 4 2 5 8 5 3 4 7 6 4 3 +--R 700a b c d - 3325a b c d + 6125a b c d - 5250a b c d +--R + +--R 6 7 5 2 5 8 6 4 9 7 +--R 1750a b c d + 175a b c d - 175a b c +--R * +--R 4 +--R x +--R + +--R 11 2 6 10 3 2 5 9 4 3 4 8 5 4 3 +--R 1050a b c d - 4550a b c d + 7000a b c d - 3500a b c d +--R + +--R 7 6 5 2 6 7 6 5 8 7 +--R - 1750a b c d + 2450a b c d - 700a b c +--R * +--R 3 +--R x +--R + +--R 12 6 11 2 2 5 10 3 3 4 9 4 4 3 +--R 700a b c d - 2450a b c d + 1750a b c d + 3500a b c d +--R + +--R 8 5 5 2 7 6 6 6 7 7 +--R - 7000a b c d + 4550a b c d - 1050a b c +--R * +--R 2 +--R x +--R + +--R 13 6 12 2 5 11 2 3 4 10 3 4 3 +--R 175a c d - 175a b c d - 1750a b c d + 5250a b c d +--R + +--R 9 4 5 2 8 5 6 7 6 7 +--R - 6125a b c d + 3325a b c d - 700a b c +--R * +--R x +--R + +--R 13 2 5 12 3 4 11 2 4 3 10 3 5 2 9 4 6 +--R 175a c d - 875a b c d + 1750a b c d - 1750a b c d + 875a b c d +--R + +--R 8 5 7 +--R - 175a b c +--R Type: Union(Expression(Integer),...) +--E 1855 + +--S 1856 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 4 5 4 3 2 4 3 +--R (- 35a c - 875a )d + (- 140a b c - 3500a b c)d +--R + +--R 2 2 3 3 2 2 2 3 4 2 3 3 4 5 4 4 +--R (70a b c + 1750a b c )d + (- 28a b c - 700a b c )d + 5b c + 125a b c +--R / +--R 9 5 8 2 4 7 2 3 3 6 3 4 2 5 4 5 +--R 175a c d - 875a b c d + 1750a b c d - 1750a b c d + 875a b c d +--R + +--R 4 5 6 +--R - 175a b c +--R Type: Expression(Integer) +--E 1856 + +--S 1857 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1857 + +)clear all + +--S 1858 of 2952 +t0000:=1/((a+b*x)^(11/2)*(c+d*x)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 5 6 4 5 5 2 3 4 4 +--R b d x + (5a b d + b c)x + (10a b d + 5a b c)x +--R + +--R 3 2 2 3 3 4 3 2 2 5 4 5 +--R (10a b d + 10a b c)x + (5a b d + 10a b c)x + (a d + 5a b c)x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1858 + +--S 1859 of 2952 +r0000:=(-2/9)/((b*c-a*d)*(a+b*x)^(9/2)*sqrt(c+d*x))+_ + 20/63*d/((b*c-a*d)^2*(a+b*x)^(7/2)*sqrt(c+d*x))-_ + 32/63*d^2/((b*c-a*d)^3*(a+b*x)^(5/2)*sqrt(c+d*x))+_ + 64/63*d^3/((b*c-a*d)^4*(a+b*x)^(3/2)*sqrt(c+d*x))-_ + 256/63*d^4/((b*c-a*d)^5*sqrt(a+b*x)*sqrt(c+d*x))-_ + 512/63*d^5*sqrt(a+b*x)/((b*c-a*d)^6*sqrt(c+d*x)) +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R - 512b d x + (- 2304a b d - 256b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 4032a b d - 1152a b c d + 64b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 3360a b d - 2016a b c d + 288a b c d - 32b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 1260a b d - 1680a b c d + 504a b c d - 144a b c d + 20b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 126a d - 630a b c d + 420a b c d - 252a b c d + 90a b c d - 14b c +--R / +--R 6 4 6 5 5 5 4 6 2 4 3 7 3 3 2 8 4 2 +--R 63a b d - 378a b c d + 945a b c d - 1260a b c d + 945a b c d +--R + +--R 9 5 10 6 +--R - 378a b c d + 63b c +--R * +--R 4 +--R x +--R + +--R 7 3 6 6 4 5 5 5 2 4 4 6 3 3 +--R 252a b d - 1512a b c d + 3780a b c d - 5040a b c d +--R + +--R 3 7 4 2 2 8 5 9 6 +--R 3780a b c d - 1512a b c d + 252a b c +--R * +--R 3 +--R x +--R + +--R 8 2 6 7 3 5 6 4 2 4 5 5 3 3 +--R 378a b d - 2268a b c d + 5670a b c d - 7560a b c d +--R + +--R 4 6 4 2 3 7 5 2 8 6 +--R 5670a b c d - 2268a b c d + 378a b c +--R * +--R 2 +--R x +--R + +--R 9 6 8 2 5 7 3 2 4 6 4 3 3 +--R 252a b d - 1512a b c d + 3780a b c d - 5040a b c d +--R + +--R 5 5 4 2 4 6 5 3 7 6 +--R 3780a b c d - 1512a b c d + 252a b c +--R * +--R x +--R + +--R 10 6 9 5 8 2 2 4 7 3 3 3 6 4 4 2 +--R 63a d - 378a b c d + 945a b c d - 1260a b c d + 945a b c d +--R + +--R 5 5 5 4 6 6 +--R - 378a b c d + 63a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1859 + +--S 1860 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 5 5 5 6 4 5 5 5 2 4 4 +--R - 1536a b c d x + (- 6912a b c d - 768a b c d )x +--R + +--R 7 3 5 6 4 2 4 5 5 3 3 3 +--R (- 12096a b c d - 3456a b c d + 192a b c d )x +--R + +--R 8 2 5 7 3 2 4 6 4 3 3 5 5 4 2 2 +--R (- 10080a b c d - 6048a b c d + 864a b c d - 96a b c d )x +--R + +--R 9 5 8 2 2 4 7 3 3 3 6 4 4 2 +--R - 3780a b c d - 5040a b c d + 1512a b c d - 432a b c d +--R + +--R 5 5 5 +--R 60a b c d +--R * +--R x +--R + +--R 10 5 9 2 4 8 2 3 3 7 3 4 2 6 4 5 +--R - 378a c d - 1890a b c d + 1260a b c d - 756a b c d + 270a b c d +--R + +--R 5 5 6 +--R - 42a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 5 5 6 5 6 4 6 2 5 6 5 +--R (- 63a b c - 567a b )d + (- 315a b c - 2835a b c)d +--R + +--R 3 7 3 4 7 2 4 2 8 4 3 8 3 3 +--R (210a b c + 1890a b c )d + (- 126a b c - 1134a b c )d +--R + +--R 9 5 2 9 4 2 10 6 10 5 +--R (45a b c + 405a b c )d + (- 7b c - 63a b c )d +--R * +--R 6 +--R x +--R + +--R 6 4 7 4 6 5 5 2 6 5 5 +--R (- 315a b c - 2835a b )d + (- 1638a b c - 14742a b c)d +--R + +--R 4 6 3 5 6 2 4 3 7 4 4 7 3 3 +--R (735a b c + 6615a b c )d + (- 420a b c - 3780a b c )d +--R + +--R 2 8 5 3 8 4 2 9 6 2 9 5 10 7 10 6 +--R (99a b c + 891a b c )d + (10a b c + 90a b c )d - 7b c - 63a b c +--R * +--R 5 +--R x +--R + +--R 7 3 8 3 6 6 4 2 7 4 5 +--R (- 630a b c - 5670a b )d + (- 3465a b c - 31185a b c)d +--R + +--R 5 5 3 6 5 2 4 4 6 4 5 6 3 3 +--R (525a b c + 4725a b c )d + (- 210a b c - 1890a b c )d +--R + +--R 3 7 5 4 7 4 2 2 8 6 3 8 5 9 7 +--R (- 180a b c - 1620a b c )d + (155a b c + 1395a b c )d - 35a b c +--R + +--R 2 9 6 +--R - 315a b c +--R * +--R 4 +--R x +--R + +--R 8 2 9 2 6 7 3 2 8 3 5 +--R (- 630a b c - 5670a b )d + (- 3780a b c - 34020a b c)d +--R + +--R 6 4 3 7 4 2 4 5 5 4 6 5 3 3 +--R (- 1050a b c - 9450a b c )d + (840a b c + 7560a b c )d +--R + +--R 4 6 5 5 6 4 2 3 7 6 4 7 5 2 8 7 +--R (- 810a b c - 7290a b c )d + (380a b c + 3420a b c )d - 70a b c +--R + +--R 3 8 6 +--R - 630a b c +--R * +--R 3 +--R x +--R + +--R 9 10 6 8 2 2 9 2 5 +--R (- 315a b c - 2835a b)d + (- 2205a b c - 19845a b c)d +--R + +--R 7 3 3 8 3 2 4 6 4 4 7 4 3 3 +--R (- 2100a b c - 18900a b c )d + (1470a b c + 13230a b c )d +--R + +--R 5 5 5 6 5 4 2 4 6 6 5 6 5 3 7 7 +--R (- 1035a b c - 9315a b c )d + (415a b c + 3735a b c )d - 70a b c +--R + +--R 4 7 6 +--R - 630a b c +--R * +--R 2 +--R x +--R + +--R 10 11 6 9 2 10 5 +--R (- 63a c - 567a )d + (- 630a b c - 5670a b c)d +--R + +--R 8 2 3 9 2 2 4 7 3 4 8 3 3 3 +--R (- 1365a b c - 12285a b c )d + (924a b c + 8316a b c )d +--R + +--R 6 4 5 7 4 4 2 5 5 6 6 5 5 4 6 7 +--R (- 585a b c - 5265a b c )d + (218a b c + 1962a b c )d - 35a b c +--R + +--R 5 6 6 +--R - 315a b c +--R * +--R x +--R + +--R 10 2 11 5 9 3 10 2 4 +--R (- 63a c - 567a c)d + (- 315a b c - 2835a b c )d +--R + +--R 8 2 4 9 2 3 3 7 3 5 8 3 4 2 +--R (210a b c + 1890a b c )d + (- 126a b c - 1134a b c )d +--R + +--R 6 4 6 7 4 5 5 5 7 6 5 6 +--R (45a b c + 405a b c )d - 7a b c - 63a b c +--R / +--R 11 5 7 10 6 2 6 9 7 3 5 8 8 4 4 +--R 189a b c d - 1134a b c d + 2835a b c d - 3780a b c d +--R + +--R 7 9 5 3 6 10 6 2 5 11 7 +--R 2835a b c d - 1134a b c d + 189a b c d +--R * +--R 6 +--R x +--R + +--R 12 4 7 11 5 2 6 10 6 3 5 9 7 4 4 +--R 945a b c d - 5481a b c d + 13041a b c d - 16065a b c d +--R + +--R 8 8 5 3 7 9 6 2 6 10 7 5 11 8 +--R 10395a b c d - 2835a b c d - 189a b c d + 189a b c +--R * +--R 5 +--R x +--R + +--R 13 3 7 12 4 2 6 11 5 3 5 10 6 4 4 +--R 1890a b c d - 10395a b c d + 22680a b c d - 23625a b c d +--R + +--R 9 7 5 3 8 8 6 2 7 9 7 6 10 8 +--R 9450a b c d + 2835a b c d - 3780a b c d + 945a b c +--R * +--R 4 +--R x +--R + +--R 14 2 7 13 3 2 6 12 4 3 5 11 5 4 4 +--R 1890a b c d - 9450a b c d + 17010a b c d - 9450a b c d +--R + +--R 10 6 5 3 9 7 6 2 8 8 7 7 9 8 +--R - 9450a b c d + 17010a b c d - 9450a b c d + 1890a b c +--R * +--R 3 +--R x +--R + +--R 15 7 14 2 2 6 13 3 3 5 12 4 4 4 +--R 945a b c d - 3780a b c d + 2835a b c d + 9450a b c d +--R + +--R 11 5 5 3 10 6 6 2 9 7 7 8 8 8 +--R - 23625a b c d + 22680a b c d - 10395a b c d + 1890a b c +--R * +--R 2 +--R x +--R + +--R 16 7 15 2 6 14 2 3 5 13 3 4 4 +--R 189a c d - 189a b c d - 2835a b c d + 10395a b c d +--R + +--R 12 4 5 3 11 5 6 2 10 6 7 9 7 8 +--R - 16065a b c d + 13041a b c d - 5481a b c d + 945a b c +--R * +--R x +--R + +--R 16 2 6 15 3 5 14 2 4 4 13 3 5 3 +--R 189a c d - 1134a b c d + 2835a b c d - 3780a b c d +--R + +--R 12 4 6 2 11 5 7 10 6 8 +--R 2835a b c d - 1134a b c d + 189a b c +--R Type: Union(Expression(Integer),...) +--E 1860 + +--S 1861 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 5 6 5 4 2 5 4 +--R (- 63a c - 567a )d + (- 315a b c - 2835a b c)d +--R + +--R 3 2 3 4 2 2 3 2 3 4 3 3 3 2 +--R (210a b c + 1890a b c )d + (- 126a b c - 1134a b c )d +--R + +--R 4 5 2 4 4 5 6 5 5 +--R (45a b c + 405a b c )d - 7b c - 63a b c +--R / +--R 11 6 10 2 5 9 2 3 4 8 3 4 3 7 4 5 2 +--R 189a c d - 1134a b c d + 2835a b c d - 3780a b c d + 2835a b c d +--R + +--R 6 5 6 5 6 7 +--R - 1134a b c d + 189a b c +--R Type: Expression(Integer) +--E 1861 + +--S 1862 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1862 + +)clear all + +--S 1863 of 2952 +t0000:=(a+b*x)^(9/2)/(c+d*x)^(5/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) -------------------------------------------------- +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R Type: Expression(Integer) +--E 1863 + +--S 1864 of 2952 +r0000:=-2/3*(a+b*x)^(9/2)/(d*(c+d*x)^(3/2))-_ + 105/8*b^(3/2)*(b*c-a*d)^3*atanh(sqrt(d)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(c+d*x)))/d^(11/2)-6*b*(a+b*x)^(7/2)/(d^2*sqrt(c+d*x))-_ + 35/4*b^2*(b*c-a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/d^4+_ + 7*b^2*(a+b*x)^(5/2)*sqrt(c+d*x)/d^3+_ + 105/8*b^2*(b*c-a*d)^2*sqrt(a+b*x)*sqrt(c+d*x)/d^5 +--R +--R +--R (2) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (315a b d - 945a b c d + 945a b c d - 315b c d)x + 315a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R - 945a b c d + 945a b c d - 315b c +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|d \|b x + a +--R \|b \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 4 4 3 4 4 3 3 +--R 8b d x + (50a b d - 18b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (165a b d - 180a b c d + 63b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 208a b d + 954a b c d - 1134a b c d + 420b c d)x - 16a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 144a b c d + 693a b c d - 840a b c d + 315b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R / +--R 6 5 +-+ +-------+ +--R (24d x + 24c d )\|d \|d x + c +--R Type: Expression(Integer) +--E 1864 + +--S 1865 of 2952 +--a0000:=integrate(t0000,x) +--E 1865 + +--S 1866 of 2952 +--m0000:=a0000 - r0000 +--E 1866 + +--S 1867 of 2952 +--d0000:=D(m0000,x) +--E 1867 + +)clear all + +--S 1868 of 2952 +t0000:=(a+b*x)^(7/2)/(c+d*x)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R (1) ---------------------------------------- +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R Type: Expression(Integer) +--E 1868 + +--S 1869 of 2952 +r0000:=-2/3*(a+b*x)^(7/2)/(d*(c+d*x)^(3/2))+_ + 35/4*b^(3/2)*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(c+d*x)))/d^(9/2)-_ + 14/3*b*(a+b*x)^(5/2)/(d^2*sqrt(c+d*x))+_ + 35/6*b^2*(a+b*x)^(3/2)*sqrt(c+d*x)/d^3-_ + 35/4*b^2*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/d^4 +--R +--R +--R (2) +--R 2 3 2 2 3 2 2 2 2 2 +--R (105a b d - 210a b c d + 105b c d)x + 105a b c d - 210a b c d +--R + +--R 3 3 +--R 105b c +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|d \|b x + a +--R \|b \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 6b d x + (39a b d - 21b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 80a b d + 238a b c d - 140b c d)x - 8a d - 56a b c d +--R + +--R 2 2 3 3 +--R 175a b c d - 105b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R / +--R 5 4 +-+ +-------+ +--R (12d x + 12c d )\|d \|d x + c +--R Type: Expression(Integer) +--E 1869 + +--S 1870 of 2952 +--a0000:=integrate(t0000,x) +--E 1870 + +--S 1871 of 2952 +--m0000:=a0000 - r0000 +--E 1871 + +--S 1872 of 2952 +--d0000:=D(m0000,x) +--E 1872 + +)clear all + +--S 1873 of 2952 +t0000:=(a+b*x)^(5/2)/(c+d*x)^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R Type: Expression(Integer) +--E 1873 + +--S 1874 of 2952 +r0000:=-2/3*(a+b*x)^(5/2)/(d*(c+d*x)^(3/2))-_ + 5*b^(3/2)*(b*c-a*d)*atanh(sqrt(d)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(c+d*x)))/d^(7/2)-_ + 10/3*b*(a+b*x)^(3/2)/(d^2*sqrt(c+d*x))+_ + 5*b^2*sqrt(a+b*x)*sqrt(c+d*x)/d^3 +--R +--R +--R (2) +--R 2 2 2 2 +-+ +-------+ +--R ((15a b d - 15b c d)x + 15a b c d - 15b c )\|b \|d x + c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (3b d x + (- 14a b d + 20b c d)x - 2a d - 10a b c d + 15b c )\|d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 3 +-+ +-------+ +--R (3d x + 3c d )\|d \|d x + c +--R Type: Expression(Integer) +--E 1874 + +--S 1875 of 2952 +--a0000:=integrate(t0000,x) +--E 1875 + +--S 1876 of 2952 +--m0000:=a0000 - r0000 +--E 1876 + +--S 1877 of 2952 +--d0000:=D(m0000,x) +--E 1877 + +)clear all + +--S 1878 of 2952 +t0000:=(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R Type: Expression(Integer) +--E 1878 + +--S 1879 of 2952 +r0000:=-2/3*(a+b*x)^(3/2)/(d*(c+d*x)^(3/2))+_ + 2*b^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + d^(5/2)-2*b*sqrt(a+b*x)/(d^2*sqrt(c+d*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-------+ \|d \|b x + a +--R (6b d x + 6b c)\|b \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R (- 8b d x - 2a d - 6b c)\|d \|b x + a +--R / +--R 3 2 +-+ +-------+ +--R (3d x + 3c d )\|d \|d x + c +--R Type: Expression(Integer) +--E 1879 + +--S 1880 of 2952 +--a0000:=integrate(t0000,x) +--E 1880 + +--S 1881 of 2952 +--m0000:=a0000 - r0000 +--E 1881 + +--S 1882 of 2952 +--d0000:=D(m0000,x) +--E 1882 + +)clear all + +--S 1883 of 2952 +t0000:=(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R Type: Expression(Integer) +--E 1883 + +--S 1884 of 2952 +r0000:=2/3*(a+b*x)^(3/2)/((b*c-a*d)*(c+d*x)^(3/2)) +--R +--R +--R +-------+ +--R (- 2b x - 2a)\|b x + a +--R (2) ---------------------------------------------- +--R 2 2 +-------+ +--R ((3a d - 3b c d)x + 3a c d - 3b c )\|d x + c +--R Type: Expression(Integer) +--E 1884 + +--S 1885 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 +-------+ +-------+ 2 2 2 +--R (- 2b c x - 2a c )\|b x + a \|d x + c + (- a c - a )d x +--R + +--R 2 2 3 2 2 +--R (- 2a c - 2a c)d x - a c - a c +--R / +--R 2 3 3 2 2 3 2 4 4 5 +--R (3a c d - 3b c d )x + (6a c d - 6b c d)x + 3a c d - 3b c +--R Type: Union(Expression(Integer),...) +--E 1885 + +--S 1886 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R - a c - a +--R (4) -------------- +--R 2 3 +--R 3a c d - 3b c +--R Type: Expression(Integer) +--E 1886 + +--S 1887 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1887 + +)clear all + +--S 1888 of 2952 +t0000:=1/((a+b*x)^(1/2)*(c+d*x)^(5/2)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1888 + +--S 1889 of 2952 +r0000:=2/3*sqrt(a+b*x)/((b*c-a*d)*(c+d*x)^(3/2))+_ + 4/3*b*sqrt(a+b*x)/((b*c-a*d)^2*sqrt(c+d*x)) +--R +--R +--R +-------+ +--R (4b d x - 2a d + 6b c)\|b x + a +--R (2) ---------------------------------------------------------------------- +--R 2 3 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 )\|d x + c +--R Type: Expression(Integer) +--E 1889 + +--S 1890 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 3 +-------+ +-------+ +--R (20b c d x - 10a c d + 30b c )\|b x + a \|d x + c +--R + +--R 2 3 2 2 2 +--R ((- a c - 25a )d + (3b c + 75a b c)d )x +--R + +--R 2 2 2 3 2 3 2 2 +--R ((- 2a c - 50a c)d + (6b c + 150a b c )d)x + (- a c - 25a c )d +--R + +--R 4 3 +--R 3b c + 75a b c +--R / +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (15a c d - 30a b c d + 15b c d )x + (30a c d - 60a b c d + 30b c d)x +--R + +--R 2 4 2 5 2 6 +--R 15a c d - 30a b c d + 15b c +--R Type: Union(Expression(Integer),...) +--E 1890 + +--S 1891 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 2 +--R (- a c - 25a )d + 3b c + 75a b c +--R (4) --------------------------------- +--R 2 2 2 3 2 4 +--R 15a c d - 30a b c d + 15b c +--R Type: Expression(Integer) +--E 1891 + +--S 1892 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1892 + +)clear all + +--S 1893 of 2952 +t0000:=1/((a+b*x)^(3/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R -------------------------------------------------------------------------- +--R 2 3 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 \|d x + c +--R Type: Expression(Integer) +--E 1893 + +--S 1894 of 2952 +r0000:=(-2)/((b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x))-_ + 8/3*d*sqrt(a+b*x)/((b*c-a*d)^2*(c+d*x)^(3/2))-_ + 16/3*b*d*sqrt(a+b*x)/((b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R 16b d x + (8a b d + 24b c d)x - 2a d + 12a b c d + 6b c +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (3a d - 9a b c d + 9a b c d - 3b c d)x + 3a c d - 9a b c d +--R + +--R 2 3 3 4 +--R 9a b c d - 3b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1894 + +--S 1895 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 3 3 2 2 2 3 +--R 64a b c d x + (32a b c d + 96a b c d)x - 8a c d + 48a b c d +--R + +--R 2 4 +--R 24a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 2 3 4 2 2 2 2 3 3 3 3 2 2 3 +--R ((a b c + 16a b)d + (- 6a b c - 96a b c)d + (- 3b c - 48a b c )d )x +--R + +--R 3 4 4 2 2 3 3 2 3 2 2 2 2 +--R (a c + 16a )d + (- 4a b c - 64a b c)d + (- 15a b c - 240a b c )d +--R + +--R 3 4 3 3 +--R (- 6b c - 96a b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2a c + 32a c)d + (- 11a b c - 176a b c )d +--R + +--R 2 4 2 2 3 3 5 3 4 +--R (- 12a b c - 192a b c )d - 3b c - 48a b c +--R * +--R x +--R + +--R 3 3 4 2 2 2 4 3 3 2 5 2 2 4 +--R (a c + 16a c )d + (- 6a b c - 96a b c )d - 3a b c - 48a b c +--R / +--R 4 2 5 3 2 3 4 2 3 4 3 4 5 2 3 +--R (12a b c d - 36a b c d + 36a b c d - 12a b c d )x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 2 +--R (12a c d - 12a b c d - 36a b c d + 60a b c d - 24a b c d)x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 5 4 3 +--R (24a c d - 60a b c d + 36a b c d + 12a b c d - 12a b c )x + 12a c d +--R + +--R 4 5 2 3 2 6 2 3 7 +--R - 36a b c d + 36a b c d - 12a b c +--R Type: Union(Expression(Integer),...) +--E 1895 + +--S 1896 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 3 2 2 2 2 3 2 2 +--R (a c + 16a )d + (- 6a b c - 96a b c)d - 3b c - 48a b c +--R (4) ---------------------------------------------------------- +--R 4 2 3 3 3 2 2 2 4 3 5 +--R 12a c d - 36a b c d + 36a b c d - 12a b c +--R Type: Expression(Integer) +--E 1896 + +--S 1897 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1897 + +)clear all + +--S 1898 of 2952 +t0000:=1/((a+b*x)^(5/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--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 +--R (2a c d + 2a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1898 + +--S 1899 of 2952 +r0000:=(-2/3)/((b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2))+_ + 4*d/((b*c-a*d)^2*(c+d*x)^(3/2)*sqrt(a+b*x))+_ + 16/3*d^2*sqrt(a+b*x)/((b*c-a*d)^3*(c+d*x)^(3/2))+_ + 32/3*b*d^2*sqrt(a+b*x)/((b*c-a*d)^4*sqrt(c+d*x)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 +--R 32b d x + (48a b d + 48b c d )x + (12a b d + 72a b c d + 12b c d)x +--R + +--R 3 3 2 2 2 2 3 3 +--R - 2a d + 18a b c d + 18a b c d - 2b c +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (3a b d - 12a b c d + 18a b c d - 12a b c d + 3b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (3a d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1899 + +--S 1900 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 3 2 3 3 3 2 2 3 2 3 3 2 2 +--R 160a b c d x + (240a b c d + 240a b c d )x +--R + +--R 4 2 3 3 2 3 2 2 3 4 5 2 3 4 3 2 +--R (60a b c d + 360a b c d + 60a b c d)x - 10a c d + 90a b c d +--R + +--R 3 2 4 2 3 5 +--R 90a b c d - 10a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 3 2 4 2 5 2 3 2 3 3 4 +--R (- a b c - 25a b )d + (9a b c + 225a b c)d +--R + +--R 4 3 2 4 2 3 5 4 5 3 2 +--R (9a b c + 225a b c )d + (- b c - 25a b c )d +--R * +--R 4 +--R x +--R + +--R 4 5 5 3 2 2 4 2 4 +--R (- 2a b c - 50a b)d + (16a b c + 400a b c)d +--R + +--R 2 3 3 3 3 2 3 4 4 2 4 3 2 +--R (36a b c + 900a b c )d + (16a b c + 400a b c )d +--R + +--R 5 5 5 4 +--R (- 2b c - 50a b c )d +--R * +--R 3 +--R x +--R + +--R 5 6 5 4 2 5 4 3 2 3 4 2 2 3 +--R (- a c - 25a )d + (5a b c + 125a b c)d + (44a b c + 1100a b c )d +--R + +--R 2 3 4 3 3 3 2 4 5 2 4 4 5 6 5 5 +--R (44a b c + 1100a b c )d + (5a b c + 125a b c )d - b c - 25a b c +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 4 3 5 2 3 +--R (- 2a c - 50a c)d + (16a b c + 400a b c )d +--R + +--R 3 2 4 4 2 3 2 2 3 5 3 3 4 4 6 2 4 5 +--R (36a b c + 900a b c )d + (16a b c + 400a b c )d - 2a b c - 50a b c +--R * +--R x +--R + +--R 5 3 6 2 3 4 4 5 3 2 3 2 5 4 2 4 +--R (- a c - 25a c )d + (9a b c + 225a b c )d + (9a b c + 225a b c )d +--R + +--R 2 3 6 3 3 5 +--R - a b c - 25a b c +--R / +--R 6 2 2 6 5 3 3 5 4 4 4 4 3 5 5 3 2 6 6 2 4 +--R (15a b c d - 60a b c d + 90a b c d - 60a b c d + 15a b c d )x +--R + +--R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 +--R 30a b c d - 90a b c d + 60a b c d + 60a b c d - 90a b c d +--R + +--R 2 6 7 +--R 30a b c d +--R * +--R 3 +--R x +--R + +--R 8 2 6 6 2 4 4 5 3 5 3 4 4 6 2 2 6 8 2 +--R (15a c d - 135a b c d + 240a b c d - 135a b c d + 15a b c )x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 +--R (30a c d - 90a b c d + 60a b c d + 60a b c d - 90a b c d + 30a b c )x +--R + +--R 8 4 4 7 5 3 6 2 6 2 5 3 7 4 4 8 +--R 15a c d - 60a b c d + 90a b c d - 60a b c d + 15a b c +--R Type: Union(Expression(Integer),...) +--E 1900 + +--S 1901 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 2 3 2 2 2 3 4 +--R (- a c - 25a )d + (9a b c + 225a b c)d + (9a b c + 225a b c )d - b c +--R + +--R 3 3 +--R - 25a b c +--R / +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R 15a c d - 60a b c d + 90a b c d - 60a b c d + 15a b c +--R Type: Expression(Integer) +--E 1901 + +--S 1902 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1902 + +)clear all + +--S 1903 of 2952 +t0000:=1/((a+b*x)^(7/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--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 2 3 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 * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1903 + +--S 1904 of 2952 +r0000:=(-2/5)/((b*c-a*d)*(a+b*x)^(5/2)*(c+d*x)^(3/2))+_ + 16/15*d/((b*c-a*d)^2*(a+b*x)^(3/2)*(c+d*x)^(3/2))-_ + 32/5*d^2/((b*c-a*d)^3*(c+d*x)^(3/2)*sqrt(a+b*x))-_ + 128/15*d^3*sqrt(a+b*x)/((b*c-a*d)^4*(c+d*x)^(3/2))-_ + 256/15*b*d^3*sqrt(a+b*x)/((b*c-a*d)^5*sqrt(c+d*x)) +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 256b d x + (640a b d + 384b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (480a b d + 960a b c d + 96b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (80a b d + 720a b c d + 240a b c d - 16b c d)x - 10a d + 120a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R 180a b c d - 40a b c d + 6b c +--R / +--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 6 4 2 +--R 15a b d - 75a b c d + 150a b c d - 150a b c d + 75a b c d +--R + +--R 7 5 +--R - 15b c d +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 3 2 4 3 4 3 3 6 5 +--R 30a b d - 135a b c d + 225a b c d - 150a b c d + 45a b c d +--R + +--R 7 6 +--R - 15b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 5 4 3 3 3 3 4 4 2 2 5 5 +--R 15a d - 45a b c d + 150a b c d - 225a b c d + 135a b c d +--R + +--R 6 6 +--R - 30a b c +--R * +--R x +--R + +--R 7 5 6 2 4 5 2 3 3 4 3 4 2 3 4 5 2 5 6 +--R 15a c d - 75a b c d + 150a b c d - 150a b c d + 75a b c d - 15a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1904 + +--S 1905 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 4 2 4 4 4 3 2 4 3 4 3 3 3 +--R 256a b c d x + (640a b c d + 384a b c d )x +--R + +--R 5 2 2 4 4 3 3 3 3 4 4 2 2 +--R (480a b c d + 960a b c d + 96a b c d )x +--R + +--R 6 2 4 5 2 3 3 4 3 4 2 3 4 5 7 2 4 +--R (80a b c d + 720a b c d + 240a b c d - 16a b c d)x - 10a c d +--R + +--R 6 3 3 5 2 4 2 4 3 5 3 4 6 +--R 120a b c d + 180a b c d - 40a b c d + 6a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 4 3 5 3 6 3 4 2 4 4 5 +--R (5a b c + 5a b )d + (- 60a b c - 60a b c)d +--R + +--R 2 5 3 3 5 2 4 6 4 2 6 3 3 +--R (- 90a b c - 90a b c )d + (20a b c + 20a b c )d +--R + +--R 7 5 7 4 2 +--R (- 3b c - 3a b c )d +--R * +--R 5 +--R x +--R + +--R 5 2 6 2 6 4 3 2 5 3 5 +--R (15a b c + 15a b )d + (- 170a b c - 170a b c)d +--R + +--R 3 4 3 4 4 2 4 2 5 4 3 5 3 3 +--R (- 390a b c - 390a b c )d + (- 120a b c - 120a b c )d +--R + +--R 6 5 2 6 4 2 7 6 7 5 +--R (31a b c + 31a b c )d + (- 6b c - 6a b c )d +--R * +--R 4 +--R x +--R + +--R 6 7 6 5 2 2 6 2 5 +--R (15a b c + 15a b)d + (- 150a b c - 150a b c)d +--R + +--R 4 3 3 5 3 2 4 3 4 4 4 4 3 3 +--R (- 625a b c - 625a b c )d + (- 540a b c - 540a b c )d +--R + +--R 2 5 5 3 5 4 2 6 6 2 6 5 7 7 7 6 +--R (21a b c + 21a b c )d + (2a b c + 2a b c )d - 3b c - 3a b c +--R * +--R 3 +--R x +--R + +--R 7 8 6 6 2 7 5 +--R (5a c + 5a )d + (- 30a b c - 30a b c)d +--R + +--R 5 2 3 6 2 2 4 4 3 4 5 3 3 3 +--R (- 435a b c - 435a b c )d + (- 700a b c - 700a b c )d +--R + +--R 3 4 5 4 4 4 2 2 5 6 3 5 5 6 7 +--R (- 153a b c - 153a b c )d + (42a b c + 42a b c )d - 9a b c +--R + +--R 2 6 6 +--R - 9a b c +--R * +--R 2 +--R x +--R + +--R 7 2 8 5 6 3 7 2 4 +--R (10a c + 10a c)d + (- 105a b c - 105a b c )d +--R + +--R 5 2 4 6 2 3 3 4 3 5 5 3 4 2 +--R (- 360a b c - 360a b c )d + (- 230a b c - 230a b c )d +--R + +--R 3 4 6 4 4 5 2 5 7 3 5 6 +--R (54a b c + 54a b c )d - 9a b c - 9a b c +--R * +--R x +--R + +--R 7 3 8 2 4 6 4 7 3 3 5 2 5 6 2 4 2 +--R (5a c + 5a c )d + (- 60a b c - 60a b c )d + (- 90a b c - 90a b c )d +--R + +--R 4 3 6 5 3 5 3 4 7 4 4 6 +--R (20a b c + 20a b c )d - 3a b c - 3a b c +--R / +--R 8 3 2 7 7 4 3 6 6 5 4 5 5 6 5 4 4 7 6 3 +--R 15a b c d - 75a b c d + 150a b c d - 150a b c d + 75a b c d +--R + +--R 3 8 7 2 +--R - 15a b c d +--R * +--R 5 +--R x +--R + +--R 9 2 2 7 8 3 3 6 7 4 4 5 6 5 5 4 5 6 6 3 +--R 45a b c d - 195a b c d + 300a b c d - 150a b c d - 75a b c d +--R + +--R 4 7 7 2 3 8 8 +--R 105a b c d - 30a b c d +--R * +--R 4 +--R x +--R + +--R 10 2 7 9 2 3 6 8 3 4 5 7 4 5 4 6 5 6 3 +--R 45a b c d - 135a b c d + 15a b c d + 375a b c d - 525a b c d +--R + +--R 5 6 7 2 4 7 8 3 8 9 +--R 255a b c d - 15a b c d - 15a b c +--R * +--R 3 +--R x +--R + +--R 11 2 7 10 3 6 9 2 4 5 8 3 5 4 7 4 6 3 +--R 15a c d + 15a b c d - 255a b c d + 525a b c d - 375a b c d +--R + +--R 6 5 7 2 5 6 8 4 7 9 +--R - 15a b c d + 135a b c d - 45a b c +--R * +--R 2 +--R x +--R + +--R 11 3 6 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 +--R 30a c d - 105a b c d + 75a b c d + 150a b c d - 300a b c d +--R + +--R 6 5 8 5 6 9 +--R 195a b c d - 45a b c +--R * +--R x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 6 5 9 +--R 15a c d - 75a b c d + 150a b c d - 150a b c d + 75a b c d - 15a b c +--R Type: Union(Expression(Integer),...) +--E 1905 + +--S 1906 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 4 5 4 3 2 4 3 2 2 3 3 2 2 2 +--R (5a c + 5a )d + (- 60a b c - 60a b c)d + (- 90a b c - 90a b c )d +--R + +--R 3 4 2 3 3 4 5 4 4 +--R (20a b c + 20a b c )d - 3b c - 3a b c +--R / +--R 8 2 5 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 5 7 +--R 15a c d - 75a b c d + 150a b c d - 150a b c d + 75a b c d - 15a b c +--R Type: Expression(Integer) +--E 1906 + +--S 1907 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1907 + +)clear all + +--S 1908 of 2952 +t0000:=1/((a+b*x)^(9/2)*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b d x + (4a b d + 2b c d)x + (6a b d + 8a b c d + b c )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b d + 12a b c d + 4a b c )x + (a d + 8a b c d + 6a b c )x +--R + +--R 4 3 2 4 2 +--R (2a c d + 4a b c )x + a c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1908 + +--S 1909 of 2952 +r0000:=(-2/7)/((b*c-a*d)*(a+b*x)^(7/2)*(c+d*x)^(3/2))+_ + 4/7*d/((b*c-a*d)^2*(a+b*x)^(5/2)*(c+d*x)^(3/2))-_ + 32/21*d^2/((b*c-a*d)^3*(a+b*x)^(3/2)*(c+d*x)^(3/2))+_ + 64/7*d^3/((b*c-a*d)^4*(c+d*x)^(3/2)*sqrt(a+b*x))+_ + 256/21*d^4*sqrt(a+b*x)/((b*c-a*d)^5*(c+d*x)^(3/2))+_ + 512/21*b*d^4*sqrt(a+b*x)/((b*c-a*d)^6*sqrt(c+d*x)) +--R +--R +--R (2) +--R 5 5 5 4 5 5 4 4 +--R 512b d x + (1792a b d + 768b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (2240a b d + 2688a b c d + 192b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (1120a b d + 3360a b c d + 672a b c d - 32b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (140a b d + 1680a b c d + 840a b c d - 112a b c d + 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 14a d + 210a b c d + 420a b c d - 140a b c d + 42a b c d - 6b c +--R / +--R 6 3 7 5 4 6 4 5 2 5 3 6 3 4 2 7 4 3 +--R 21a b d - 126a b c d + 315a b c d - 420a b c d + 315a b c d +--R + +--R 8 5 2 9 6 +--R - 126a b c d + 21b c d +--R * +--R 4 +--R x +--R + +--R 7 2 7 6 3 6 5 4 2 5 4 5 3 4 3 6 4 3 +--R 63a b d - 357a b c d + 819a b c d - 945a b c d + 525a b c d +--R + +--R 2 7 5 2 8 6 9 7 +--R - 63a b c d - 63a b c d + 21b c +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 3 2 5 5 4 3 4 4 5 4 3 +--R 63a b d - 315a b c d + 567a b c d - 315a b c d - 315a b c d +--R + +--R 3 6 5 2 2 7 6 8 7 +--R 567a b c d - 315a b c d + 63a b c +--R * +--R 2 +--R x +--R + +--R 9 7 8 6 7 2 2 5 6 3 3 4 5 4 4 3 +--R 21a d - 63a b c d - 63a b c d + 525a b c d - 945a b c d +--R + +--R 4 5 5 2 3 6 6 2 7 7 +--R 819a b c d - 357a b c d + 63a b c +--R * +--R x +--R + +--R 9 6 8 2 5 7 2 3 4 6 3 4 3 5 4 5 2 +--R 21a c d - 126a b c d + 315a b c d - 420a b c d + 315a b c d +--R + +--R 4 5 6 3 6 7 +--R - 126a b c d + 21a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1909 + +--S 1910 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 5 2 5 5 5 4 2 5 4 5 3 4 4 +--R 1024a b c d x + (3584a b c d + 1536a b c d )x +--R + +--R 6 3 2 5 5 4 3 4 4 5 4 3 3 +--R (4480a b c d + 5376a b c d + 384a b c d )x +--R + +--R 7 2 2 5 6 3 3 4 5 4 4 3 4 5 5 2 2 +--R (2240a b c d + 6720a b c d + 1344a b c d - 64a b c d )x +--R + +--R 8 2 5 7 2 3 4 6 3 4 3 5 4 5 2 +--R 280a b c d + 3360a b c d + 1680a b c d - 224a b c d +--R + +--R 4 5 6 +--R 24a b c d +--R * +--R x +--R + +--R 9 2 5 8 3 4 7 2 4 3 6 3 5 2 5 4 6 +--R - 28a c d + 420a b c d + 840a b c d - 280a b c d + 84a b c d +--R + +--R 4 5 7 +--R - 12a b c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R + +--R 5 4 6 4 7 4 5 2 5 5 6 +--R (7a b c + 28a b )d + (- 105a b c - 420a b c)d +--R + +--R 3 6 3 4 6 2 5 2 7 4 3 7 3 4 +--R (- 210a b c - 840a b c )d + (70a b c + 280a b c )d +--R + +--R 8 5 2 8 4 3 9 6 9 5 2 +--R (- 21a b c - 84a b c )d + (3b c + 12a b c )d +--R * +--R 6 +--R x +--R + +--R 6 3 7 3 7 5 4 2 6 4 6 +--R (28a b c + 112a b )d + (- 406a b c - 1624a b c)d +--R + +--R 4 5 3 5 5 2 5 3 6 4 4 6 3 4 +--R (- 1050a b c - 4200a b c )d + (- 140a b c - 560a b c )d +--R + +--R 2 7 5 3 7 4 3 8 6 2 8 5 2 +--R (56a b c + 224a b c )d + (- 30a b c - 120a b c )d +--R + +--R 9 7 9 6 +--R (6b c + 24a b c )d +--R * +--R 5 +--R x +--R + +--R 7 2 8 2 7 6 3 2 7 3 6 +--R (42a b c + 168a b )d + (- 574a b c - 2296a b c)d +--R + +--R 5 4 3 6 4 2 5 4 5 4 5 5 3 4 +--R (- 2093a b c - 8372a b c )d + (- 1365a b c - 5460a b c )d +--R + +--R 3 6 5 4 6 4 3 2 7 6 3 7 5 2 +--R (224a b c + 896a b c )d + (- 80a b c - 320a b c )d +--R + +--R 8 7 2 8 6 9 8 9 7 +--R (3a b c + 12a b c )d + 3b c + 12a b c +--R * +--R 4 +--R x +--R + +--R 8 9 7 7 2 2 8 2 6 +--R (28a b c + 112a b)d + (- 336a b c - 1344a b c)d +--R + +--R 6 3 3 7 3 2 5 5 4 4 6 4 3 4 +--R (- 2072a b c - 8288a b c )d + (- 2660a b c - 10640a b c )d +--R + +--R 4 5 5 5 5 4 3 3 6 6 4 6 5 2 +--R (- 84a b c - 336a b c )d + (40a b c + 160a b c )d +--R + +--R 2 7 7 3 7 6 8 8 2 8 7 +--R (- 48a b c - 192a b c )d + 12a b c + 48a b c +--R * +--R 3 +--R x +--R + +--R 9 10 7 8 2 9 6 +--R (7a c + 28a )d + (- 49a b c - 196a b c)d +--R + +--R 7 2 3 8 2 2 5 6 3 4 7 3 3 4 +--R (- 1008a b c - 4032a b c )d + (- 2240a b c - 8960a b c )d +--R + +--R 5 4 5 6 4 4 3 4 5 6 5 5 5 2 +--R (- 721a b c - 2884a b c )d + (255a b c + 1020a b c )d +--R + +--R 3 6 7 4 6 6 2 7 8 3 7 7 +--R (- 102a b c - 408a b c )d + 18a b c + 72a b c +--R * +--R 2 +--R x +--R + +--R 9 2 10 6 8 3 9 2 5 +--R (14a c + 56a c)d + (- 182a b c - 728a b c )d +--R + +--R 7 2 4 8 2 3 4 6 3 5 7 3 4 3 +--R (- 840a b c - 3360a b c )d + (- 700a b c - 2800a b c )d +--R + +--R 5 4 6 6 4 5 2 4 5 7 5 5 6 3 6 8 +--R (238a b c + 952a b c )d + (- 78a b c - 312a b c )d + 12a b c +--R + +--R 4 6 7 +--R 48a b c +--R * +--R x +--R + +--R 9 3 10 2 5 8 4 9 3 4 +--R (7a c + 28a c )d + (- 105a b c - 420a b c )d +--R + +--R 7 2 5 8 2 4 3 6 3 6 7 3 5 2 +--R (- 210a b c - 840a b c )d + (70a b c + 280a b c )d +--R + +--R 5 4 7 6 4 6 4 5 8 5 5 7 +--R (- 21a b c - 84a b c )d + 3a b c + 12a b c +--R / +--R 10 4 2 8 9 5 3 7 8 6 4 6 7 7 5 5 6 8 6 4 +--R 42a b c d - 252a b c d + 630a b c d - 840a b c d + 630a b c d +--R + +--R 5 9 7 3 4 10 8 2 +--R - 252a b c d + 42a b c d +--R * +--R 6 +--R x +--R + +--R 11 3 2 8 10 4 3 7 9 5 4 6 8 6 5 5 +--R 168a b c d - 924a b c d + 2016a b c d - 2100a b c d +--R + +--R 7 7 6 4 6 8 7 3 5 9 8 2 4 10 9 +--R 840a b c d + 252a b c d - 336a b c d + 84a b c d +--R * +--R 5 +--R x +--R + +--R 12 2 2 8 11 3 3 7 10 4 4 6 9 5 5 5 +--R 252a b c d - 1176a b c d + 1806a b c d - 252a b c d +--R + +--R 8 6 6 4 7 7 7 3 6 8 8 2 5 9 9 4 10 10 +--R - 2310a b c d + 2688a b c d - 1134a b c d + 84a b c d + 42a b c +--R * +--R 4 +--R x +--R + +--R 13 2 8 12 2 3 7 11 3 4 6 10 4 5 5 +--R 168a b c d - 504a b c d - 336a b c d + 3192a b c d +--R + +--R 9 5 6 4 8 6 7 3 7 7 8 2 6 8 9 5 9 10 +--R - 5040a b c d + 3192a b c d - 336a b c d - 504a b c d + 168a b c +--R * +--R 3 +--R x +--R + +--R 14 2 8 13 3 7 12 2 4 6 11 3 5 5 +--R 42a c d + 84a b c d - 1134a b c d + 2688a b c d +--R + +--R 10 4 6 4 9 5 7 3 8 6 8 2 7 7 9 6 8 10 +--R - 2310a b c d - 252a b c d + 1806a b c d - 1176a b c d + 252a b c +--R * +--R 2 +--R x +--R + +--R 14 3 7 13 4 6 12 2 5 5 11 3 6 4 +--R 84a c d - 336a b c d + 252a b c d + 840a b c d +--R + +--R 10 4 7 3 9 5 8 2 8 6 9 7 7 10 +--R - 2100a b c d + 2016a b c d - 924a b c d + 168a b c +--R * +--R x +--R + +--R 14 4 6 13 5 5 12 2 6 4 11 3 7 3 10 4 8 2 +--R 42a c d - 252a b c d + 630a b c d - 840a b c d + 630a b c d +--R + +--R 9 5 9 8 6 10 +--R - 252a b c d + 42a b c +--R Type: Union(Expression(Integer),...) +--E 1910 + +--S 1911 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 5 6 5 4 2 5 4 +--R (7a c + 28a )d + (- 105a b c - 420a b c)d +--R + +--R 3 2 3 4 2 2 3 2 3 4 3 3 3 2 +--R (- 210a b c - 840a b c )d + (70a b c + 280a b c )d +--R + +--R 4 5 2 4 4 5 6 5 5 +--R (- 21a b c - 84a b c )d + 3b c + 12a b c +--R / +--R 10 2 6 9 3 5 8 2 4 4 7 3 5 3 6 4 6 2 +--R 42a c d - 252a b c d + 630a b c d - 840a b c d + 630a b c d +--R + +--R 5 5 7 4 6 8 +--R - 252a b c d + 42a b c +--R Type: Expression(Integer) +--E 1911 + +--S 1912 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1912 + +)clear all + +--S 1913 of 2952 +t0000:=1/(sqrt(a+b*x)*sqrt(4+a+b*x)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +-------+ +-----------+ +--R \|b x + a \|b x + a + 4 +--R Type: Expression(Integer) +--E 1913 + +--S 1914 of 2952 +r0000:=2*asinh(1/2*sqrt(a+b*x))/b +--R +--R +--R +-------+ +--R \|b x + a +--R 2asinh(----------) +--R 2 +--R (2) ------------------ +--R b +--R Type: Expression(Integer) +--E 1914 + +--S 1915 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-----------+ +-------+ +--R 2log(\|b x + a + 4 + \|b x + a ) +--R (3) --------------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1915 + +--S 1916 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R +-------+ +--R +-----------+ +-------+ \|b x + a +--R 2log(\|b x + a + 4 + \|b x + a ) - 2asinh(----------) +--R 2 +--R (4) ------------------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 1916 + +--S 1917 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1917 + +)clear all + +--S 1918 of 2952 +t0000:=1/(sqrt(2+b*x)*sqrt(6+b*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x + 2 \|b x + 6 +--R Type: Expression(Integer) +--E 1918 + +--S 1919 of 2952 +r0000:=2*asinh(1/2*sqrt(2+b*x))/b +--R +--R +--R +-------+ +--R \|b x + 2 +--R 2asinh(----------) +--R 2 +--R (2) ------------------ +--R b +--R Type: Expression(Integer) +--E 1919 + +--S 1920 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 1920 + +--S 1921 of 2952 +--m0000:=a0000 - r0000 +--E 1921 + +--S 1922 of 2952 +--d0000:=D(m0000,x) +--E 1922 + +)clear all + +--S 1923 of 2952 +t0000:=1/(sqrt(1+b*x)*sqrt(5+b*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x + 1 \|b x + 5 +--R Type: Expression(Integer) +--E 1923 + +--S 1924 of 2952 +r0000:=2*asinh(1/2*sqrt(1+b*x))/b +--R +--R +--R +-------+ +--R \|b x + 1 +--R 2asinh(----------) +--R 2 +--R (2) ------------------ +--R b +--R Type: Expression(Integer) +--E 1924 + +--S 1925 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-------+ +--R 2log(\|b x + 5 - \|b x + 1 ) +--R (3) - ----------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1925 + +--S 1926 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R +-------+ +--R +-------+ +-------+ \|b x + 1 +--R - 2log(\|b x + 5 - \|b x + 1 ) - 2asinh(----------) +--R 2 +--R (4) ---------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 1926 + +--S 1927 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1927 + +)clear all + +--S 1928 of 2952 +t0000:=1/(sqrt(b*x)*sqrt(4+b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R +---+ +-------+ +--R \|b x \|b x + 4 +--R Type: Expression(Integer) +--E 1928 + +--S 1929 of 2952 +r0000:=2*asinh(1/2*sqrt(b*x))/b +--R +--R +--R +---+ +--R \|b x +--R 2asinh(------) +--R 2 +--R (2) -------------- +--R b +--R Type: Expression(Integer) +--E 1929 + +--S 1930 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 1930 + +--S 1931 of 2952 +--m0000:=a0000 - r0000 +--E 1931 + +--S 1932 of 2952 +--d0000:=D(m0000,x) +--E 1932 + +)clear all + +--S 1933 of 2952 +t0000:=1/(sqrt(-1+b*x)*sqrt(3+b*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x - 1 \|b x + 3 +--R Type: Expression(Integer) +--E 1933 + +--S 1934 of 2952 +r0000:=2*asinh(1/2*sqrt(-1+b*x))/b +--R +--R +--R +-------+ +--R \|b x - 1 +--R 2asinh(----------) +--R 2 +--R (2) ------------------ +--R b +--R Type: Expression(Integer) +--E 1934 + +--S 1935 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-------+ +--R 2log(\|b x + 3 + \|b x - 1 ) +--R (3) ----------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1935 + +--S 1936 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R +-------+ +--R +-------+ +-------+ \|b x - 1 +--R 2log(\|b x + 3 + \|b x - 1 ) - 2asinh(----------) +--R 2 +--R (4) -------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 1936 + +--S 1937 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1937 + +)clear all + +--S 1938 of 2952 +t0000:=1/(sqrt(-2+b*x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x - 2 \|b x + 2 +--R Type: Expression(Integer) +--E 1938 + +--S 1939 of 2952 +r0000:=acosh(1/2*b*x)/b +--R +--R +--R b x +--R acosh(---) +--R 2 +--R (2) ---------- +--R b +--R Type: Expression(Integer) +--E 1939 + +--S 1940 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 1940 + +--S 1941 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R b x +--R - acosh(---) + a0000 b +--R 2 +--R (3) ---------------------- +--R b +--R Type: Expression(Integer) +--E 1941 + +--S 1942 of 2952 +d0000:=D(m0000,x) +--R +--R +--R 1 +--R (4) - ----------- +--R +--------+ +--R | 2 2 +--R \|b x - 4 +--R Type: Expression(Integer) +--E 1942 + +)clear all + +--S 1943 of 2952 +t0000:=1/(sqrt(-3+b*x)*sqrt(1+b*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x - 3 \|b x + 1 +--R Type: Expression(Integer) +--E 1943 + +--S 1944 of 2952 +r0000:=2*asinh(1/2*sqrt(-3+b*x))/b +--R +--R +--R +-------+ +--R \|b x - 3 +--R 2asinh(----------) +--R 2 +--R (2) ------------------ +--R b +--R Type: Expression(Integer) +--E 1944 + +--S 1945 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 1945 + +--S 1946 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +-------+ +--R \|b x - 3 +--R - 2asinh(----------) + a0000 b +--R 2 +--R (3) ------------------------------ +--R b +--R Type: Expression(Integer) +--E 1946 + +--S 1947 of 2952 +d0000:=D(m0000,x) +--R +--R +--R 1 +--R (4) - -------------------- +--R +-------+ +-------+ +--R \|b x - 3 \|b x + 1 +--R Type: Expression(Integer) +--E 1947 + +)clear all + +--S 1948 of 2952 +t0000:=1/(sqrt(2+b*x)*sqrt(3+b*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x + 2 \|b x + 3 +--R Type: Expression(Integer) +--E 1948 + +--S 1949 of 2952 +r0000:=2*asinh(sqrt(2+b*x))/b +--R +--R +--R +-------+ +--R 2asinh(\|b x + 2 ) +--R (2) ------------------ +--R b +--R Type: Expression(Integer) +--E 1949 + +--S 1950 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-------+ +--R 2log(\|b x + 3 + \|b x + 2 ) +--R (3) ----------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1950 + +--S 1951 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R +-------+ +-------+ +-------+ +--R 2log(\|b x + 3 + \|b x + 2 ) - 2asinh(\|b x + 2 ) +--R (4) -------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 1951 + +--S 1952 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1952 + +)clear all + +--S 1953 of 2952 +t0000:=1/sqrt(2+b*x)^2 +--R +--R +--R 1 +--R (1) ------- +--R b x + 2 +--R Type: Expression(Integer) +--E 1953 + +--S 1954 of 2952 +r0000:=log(2+b*x)/b +--R +--R +--R log(b x + 2) +--R (2) ------------ +--R b +--R Type: Expression(Integer) +--E 1954 + +--S 1955 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R log(b x + 2) +--R (3) ------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 1955 + +--S 1956 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1956 + +--S 1957 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1957 + +)clear all + +--S 1958 of 2952 +t0000:=1/(sqrt(1+b*x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x + 1 \|b x + 2 +--R Type: Expression(Integer) +--E 1958 + +--S 1959 of 2952 +r0000:=2*asinh(sqrt(1+b*x))/b +--R +--R +--R +-------+ +--R 2asinh(\|b x + 1 ) +--R (2) ------------------ +--R b +--R Type: Expression(Integer) +--E 1959 + +--S 1960 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-------+ +--R 2log(\|b x + 2 + \|b x + 1 ) +--R (3) ----------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1960 + +--S 1961 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R +-------+ +-------+ +-------+ +--R 2log(\|b x + 2 + \|b x + 1 ) - 2asinh(\|b x + 1 ) +--R (4) -------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 1961 + +--S 1962 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1962 + +)clear all + +--S 1963 of 2952 +t0000:=1/(sqrt(b*x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) ---------------- +--R +---+ +-------+ +--R \|b x \|b x + 2 +--R Type: Expression(Integer) +--E 1963 + +--S 1964 of 2952 +r0000:=2*asinh(sqrt(b*x)/sqrt(2))/b +--R +--R +--R +---+ +--R \|b x +--R 2asinh(------) +--R +-+ +--R \|2 +--R (2) -------------- +--R b +--R Type: Expression(Integer) +--E 1964 + +--S 1965 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 1965 + +--S 1966 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +---+ +--R \|b x +--R - 2asinh(------) + a0000 b +--R +-+ +--R \|2 +--R (3) -------------------------- +--R b +--R Type: Expression(Integer) +--E 1966 + +--S 1967 of 2952 +d0000:=D(m0000,x) +--R +--R +--R 1 +--R (4) - ---------------- +--R +---+ +-------+ +--R \|b x \|b x + 2 +--R Type: Expression(Integer) +--E 1967 + +)clear all + +--S 1968 of 2952 +t0000:=1/(sqrt(-1+b*x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x - 1 \|b x + 2 +--R Type: Expression(Integer) +--E 1968 + +--S 1969 of 2952 +r0000:=2*asinh(sqrt(-1+b*x)/sqrt(3))/b +--R +--R +--R +-------+ +--R \|b x - 1 +--R 2asinh(----------) +--R +-+ +--R \|3 +--R (2) ------------------ +--R b +--R Type: Expression(Integer) +--E 1969 + +--S 1970 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-------+ +--R 2log(\|b x + 2 + \|b x - 1 ) +--R (3) ----------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1970 + +--S 1971 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R +-------+ +--R +-------+ +-------+ \|b x - 1 +--R 2log(\|b x + 2 + \|b x - 1 ) - 2asinh(----------) +--R +-+ +--R \|3 +--R (4) -------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 1971 + +--S 1972 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1972 + +)clear all + +--S 1973 of 2952 +t0000:=1/(sqrt(-2+b*x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x - 2 \|b x + 2 +--R Type: Expression(Integer) +--E 1973 + +--S 1974 of 2952 +r0000:=acosh(1/2*b*x)/b +--R +--R +--R b x +--R acosh(---) +--R 2 +--R (2) ---------- +--R b +--R Type: Expression(Integer) +--E 1974 + +--S 1975 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-------+ +--R 2log(\|b x + 2 + \|b x - 2 ) +--R (3) ----------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1975 + +--S 1976 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +-------+ +-------+ b x +--R 2log(\|b x + 2 + \|b x - 2 ) - acosh(---) +--R 2 +--R (4) ------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 1976 + +--S 1977 of 2952 +d0000:=D(m0000,x) +--R +--R +--R +--------+ +--R | 2 2 +-------+ +-------+ +--R \|b x - 4 - \|b x - 2 \|b x + 2 +--R (5) ---------------------------------- +--R +--------+ +--R +-------+ +-------+ | 2 2 +--R \|b x - 2 \|b x + 2 \|b x - 4 +--R Type: Expression(Integer) +--E 1977 + +)clear all + +--S 1978 of 2952 +t0000:=1/(sqrt(-3+b*x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x - 3 \|b x + 2 +--R Type: Expression(Integer) +--E 1978 + +--S 1979 of 2952 +r0000:=2*asinh(sqrt(-3+b*x)/sqrt(5))/b +--R +--R +--R +-------+ +--R \|b x - 3 +--R 2asinh(----------) +--R +-+ +--R \|5 +--R (2) ------------------ +--R b +--R Type: Expression(Integer) +--E 1979 + +--S 1980 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 1980 + +--S 1981 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +-------+ +--R \|b x - 3 +--R - 2asinh(----------) + a0000 b +--R +-+ +--R \|5 +--R (3) ------------------------------ +--R b +--R Type: Expression(Integer) +--E 1981 + +-- TPDHERE +--S 1982 of 2952 +d0000:=D(m0000,x) +--R +--R +--R 1 +--R (4) - -------------------- +--R +-------+ +-------+ +--R \|b x - 3 \|b x + 2 +--R Type: Expression(Integer) +--E 1982 + +)clear all + +--S 1983 of 2952 +t0000:=1/(sqrt(3-b*x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) ---------------------- +--R +---------+ +-------+ +--R \|- b x + 3 \|b x + 2 +--R Type: Expression(Integer) +--E 1983 + +--S 1984 of 2952 +r0000:=-asin(1/5*(1-2*b*x))/b +--R +--R +--R 2b x - 1 +--R asin(--------) +--R 5 +--R (2) -------------- +--R b +--R Type: Expression(Integer) +--E 1984 + +--S 1985 of 2952 +--a0000:=integrate(t0000,x) +--E 1985 + +--S 1986 of 2952 +--m0000:=a0000 - r0000 +--E 1986 + +--S 1987 of 2952 +--d0000:=D(m0000,x) +--E 1987 + +)clear all + +--S 1988 of 2952 +t0000:=1/(sqrt(2-b*x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) ---------------------- +--R +---------+ +-------+ +--R \|- b x + 2 \|b x + 2 +--R Type: Expression(Integer) +--E 1988 + +--S 1989 of 2952 +r0000:=asin(1/2*b*x)/b +--R +--R +--R b x +--R asin(---) +--R 2 +--R (2) --------- +--R b +--R Type: Expression(Integer) +--E 1989 + +--S 1990 of 2952 +--a0000:=integrate(t0000,x) +--E 1990 + +--S 1991 of 2952 +--m0000:=a0000 - r0000 +--E 1991 + +--S 1992 of 2952 +--d0000:=D(m0000,x) +--E 1992 + +)clear all + +--S 1993 of 2952 +t0000:=1/(sqrt(1-b*x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) ---------------------- +--R +---------+ +-------+ +--R \|- b x + 1 \|b x + 2 +--R Type: Expression(Integer) +--E 1993 + +--S 1994 of 2952 +r0000:=-asin(1/3*(-1-2*b*x))/b +--R +--R +--R 2b x + 1 +--R asin(--------) +--R 3 +--R (2) -------------- +--R b +--R Type: Expression(Integer) +--E 1994 + +--S 1995 of 2952 +--a0000:=integrate(t0000,x) +--E 1995 + +--S 1996 of 2952 +--m0000:=a0000 - r0000 +--E 1996 + +--S 1997 of 2952 +--d0000:=D(m0000,x) +--E 1997 + +)clear all + +--S 1998 of 2952 +t0000:=1/(sqrt(-b*x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) ------------------ +--R +-----+ +-------+ +--R \|- b x \|b x + 2 +--R Type: Expression(Integer) +--E 1998 + +--S 1999 of 2952 +r0000:=asin(1+b*x)/b +--R +--R +--R asin(b x + 1) +--R (2) ------------- +--R b +--R Type: Expression(Integer) +--E 1999 + +--S 2000 of 2952 +--a0000:=integrate(t0000,x) +--E 2000 + +--S 2001 of 2952 +--m0000:=a0000 - r0000 +--E 2001 + +--S 2002 of 2952 +--d0000:=D(m0000,x) +--E 2002 + +)clear all + +--S 2003 of 2952 +t0000:=1/(sqrt(-1-b*x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) ---------------------- +--R +---------+ +-------+ +--R \|- b x - 1 \|b x + 2 +--R Type: Expression(Integer) +--E 2003 + +--S 2004 of 2952 +r0000:=asin(3+2*b*x)/b +--R +--R +--R asin(2b x + 3) +--R (2) -------------- +--R b +--R Type: Expression(Integer) +--E 2004 + +--S 2005 of 2952 +--a0000:=integrate(t0000,x) +--E 2005 + +--S 2006 of 2952 +--m0000:=a0000 - r0000 +--E 2006 + +--S 2007 of 2952 +--d0000:=D(m0000,x) +--E 2007 + +)clear all + +--S 2008 of 2952 +t0000:=1/(sqrt(-2-b*x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) ---------------------- +--R +---------+ +-------+ +--R \|- b x - 2 \|b x + 2 +--R Type: Expression(Integer) +--E 2008 + +--S 2009 of 2952 +r0000:=log(2+b*x)*sqrt(2+b*x)/(b*sqrt(-2-b*x)) +--R +--R +--R +-------+ +--R log(b x + 2)\|b x + 2 +--R (2) ---------------------- +--R +---------+ +--R b\|- b x - 2 +--R Type: Expression(Integer) +--E 2009 + +--S 2010 of 2952 +--a0000:=integrate(t0000,x) +--E 2010 + +--S 2011 of 2952 +--m0000:=a0000 - r0000 +--E 2011 + +--S 2012 of 2952 +--d0000:=D(m0000,x) +--E 2012 + +)clear all + +--S 2013 of 2952 +t0000:=1/(sqrt(-3-b*x)*sqrt(2+b*x)) +--R +--R +--R 1 +--R (1) ---------------------- +--R +---------+ +-------+ +--R \|- b x - 3 \|b x + 2 +--R Type: Expression(Integer) +--E 2013 + +--S 2014 of 2952 +r0000:=-2*atan(sqrt(-3-b*x)/sqrt(2+b*x))/b +--R +--R +--R +---------+ +--R \|- b x - 3 +--R 2atan(------------) +--R +-------+ +--R \|b x + 2 +--R (2) - ------------------- +--R b +--R Type: Expression(Integer) +--E 2014 + +--S 2015 of 2952 +--a0000:=integrate(t0000,x) +--E 2015 + +--S 2016 of 2952 +--m0000:=a0000 - r0000 +--E 2016 + +--S 2017 of 2952 +--d0000:=D(m0000,x) +--E 2017 + +)clear all + +--S 2018 of 2952 +t0000:=1/(sqrt(2-b*x)*sqrt(3-b*x)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +---------+ +---------+ +--R \|- b x + 2 \|- b x + 3 +--R Type: Expression(Integer) +--E 2018 + +--S 2019 of 2952 +r0000:=-2*asinh(sqrt(2-b*x))/b +--R +--R +--R +---------+ +--R 2asinh(\|- b x + 2 ) +--R (2) - -------------------- +--R b +--R Type: Expression(Integer) +--E 2019 + +--S 2020 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +---------+ +---------+ +--R 2log(\|- b x + 3 - \|- b x + 2 ) +--R (3) --------------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 2020 + +--S 2021 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R +---------+ +---------+ +---------+ +--R 2log(\|- b x + 3 - \|- b x + 2 ) + 2asinh(\|- b x + 2 ) +--R (4) -------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 2021 + +--S 2022 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2022 + +)clear all + +--S 2023 of 2952 +t0000:=1/sqrt(2-b*x)^2 +--R +--R +--R 1 +--R (1) - ------- +--R b x - 2 +--R Type: Expression(Integer) +--E 2023 + +--S 2024 of 2952 +r0000:=-log(2-b*x)/b +--R +--R +--R log(- b x + 2) +--R (2) - -------------- +--R b +--R Type: Expression(Integer) +--E 2024 + +--S 2025 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R log(b x - 2) +--R (3) - ------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 2025 + +--S 2026 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R - log(b x - 2) + log(- b x + 2) +--R (4) ------------------------------- +--R b +--R Type: Expression(Integer) +--E 2026 + +--S 2027 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2027 + +)clear all + +--S 2028 of 2952 +t0000:=1/(sqrt(1-b*x)*sqrt(2-b*x)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +---------+ +---------+ +--R \|- b x + 1 \|- b x + 2 +--R Type: Expression(Integer) +--E 2028 + +--S 2029 of 2952 +r0000:=-2*asinh(sqrt(1-b*x))/b +--R +--R +--R +---------+ +--R 2asinh(\|- b x + 1 ) +--R (2) - -------------------- +--R b +--R Type: Expression(Integer) +--E 2029 + +--S 2030 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +---------+ +---------+ +--R 2log(\|- b x + 2 + \|- b x + 1 ) +--R (3) - --------------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 2030 + +--S 2031 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R +---------+ +---------+ +---------+ +--R - 2log(\|- b x + 2 + \|- b x + 1 ) + 2asinh(\|- b x + 1 ) +--R (4) ---------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 2031 + +--S 2032 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2032 + +)clear all + +--S 2033 of 2952 +t0000:=1/(sqrt(-b*x)*sqrt(2-b*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-----+ +---------+ +--R \|- b x \|- b x + 2 +--R Type: Expression(Integer) +--E 2033 + +--S 2034 of 2952 +r0000:=-2*asinh(sqrt(-b*x)/sqrt(2))/b +--R +--R +--R +-----+ +--R \|- b x +--R 2asinh(--------) +--R +-+ +--R \|2 +--R (2) - ---------------- +--R b +--R Type: Expression(Integer) +--E 2034 + +--S 2035 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 2035 + +--S 2036 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +-----+ +--R \|- b x +--R 2asinh(--------) + a0000 b +--R +-+ +--R \|2 +--R (3) -------------------------- +--R b +--R Type: Expression(Integer) +--E 2036 + +--S 2037 of 2952 +d0000:=D(m0000,x) +--R +--R +--R 1 +--R (4) - -------------------- +--R +-----+ +---------+ +--R \|- b x \|- b x + 2 +--R Type: Expression(Integer) +--E 2037 + +)clear all + +--S 2038 of 2952 +t0000:=1/(sqrt(-1-b*x)*sqrt(2-b*x)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +---------+ +---------+ +--R \|- b x - 1 \|- b x + 2 +--R Type: Expression(Integer) +--E 2038 + +--S 2039 of 2952 +r0000:=-2*asinh(sqrt(-1-b*x)/sqrt(3))/b +--R +--R +--R +---------+ +--R \|- b x - 1 +--R 2asinh(------------) +--R +-+ +--R \|3 +--R (2) - -------------------- +--R b +--R Type: Expression(Integer) +--E 2039 + +--S 2040 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 2040 + +--S 2041 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +---------+ +--R \|- b x - 1 +--R 2asinh(------------) + a0000 b +--R +-+ +--R \|3 +--R (3) ------------------------------ +--R b +--R Type: Expression(Integer) +--E 2041 + +-- TPDHERE +--S 2042 of 2952 +d0000:=D(m0000,x) +--R +--R +--R 1 +--R (4) - ------------------------ +--R +---------+ +---------+ +--R \|- b x - 1 \|- b x + 2 +--R Type: Expression(Integer) +--E 2042 + +)clear all + +--S 2043 of 2952 +t0000:=1/(sqrt(-2-b*x)*sqrt(2-b*x)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +---------+ +---------+ +--R \|- b x - 2 \|- b x + 2 +--R Type: Expression(Integer) +--E 2043 + +--S 2044 of 2952 +r0000:=-acosh(-1/2*b*x)/b +--R +--R +--R b x +--R acosh(- ---) +--R 2 +--R (2) - ------------ +--R b +--R Type: Expression(Integer) +--E 2044 + +--S 2045 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 2045 + +--S 2046 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R b x +--R acosh(- ---) + a0000 b +--R 2 +--R (3) ---------------------- +--R b +--R Type: Expression(Integer) +--E 2046 + +--S 2047 of 2952 +d0000:=D(m0000,x) +--R +--R +--R 1 +--R (4) - ----------- +--R +--------+ +--R | 2 2 +--R \|b x - 4 +--R Type: Expression(Integer) +--E 2047 + +)clear all + +--S 2048 of 2952 +t0000:=1/(sqrt(-3-b*x)*sqrt(2-b*x)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +---------+ +---------+ +--R \|- b x - 3 \|- b x + 2 +--R Type: Expression(Integer) +--E 2048 + +--S 2049 of 2952 +r0000:=-2*asinh(sqrt(-3-b*x)/sqrt(5))/b +--R +--R +--R +---------+ +--R \|- b x - 3 +--R 2asinh(------------) +--R +-+ +--R \|5 +--R (2) - -------------------- +--R b +--R Type: Expression(Integer) +--E 2049 + +--S 2050 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 2050 + +--S 2051 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +---------+ +--R \|- b x - 3 +--R 2asinh(------------) + a0000 b +--R +-+ +--R \|5 +--R (3) ------------------------------ +--R b +--R Type: Expression(Integer) +--E 2051 + +--S 2052 of 2952 +d0000:=D(m0000,x) +--R +--R +--R 1 +--R (4) - ------------------------ +--R +---------+ +---------+ +--R \|- b x - 3 \|- b x + 2 +--R Type: Expression(Integer) +--E 2052 + +)clear all + +--S 2053 of 2952 +t0000:=1/(sqrt(-4+b*x)*sqrt(4+b*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x - 4 \|b x + 4 +--R Type: Expression(Integer) +--E 2053 + +--S 2054 of 2952 +r0000:=acosh(1/4*b*x)/b +--R +--R +--R b x +--R acosh(---) +--R 4 +--R (2) ---------- +--R b +--R Type: Expression(Integer) +--E 2054 + +--S 2055 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 2055 + +--S 2056 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R b x +--R - acosh(---) + a0000 b +--R 4 +--R (3) ---------------------- +--R b +--R Type: Expression(Integer) +--E 2056 + +--S 2057 of 2952 +d0000:=D(m0000,x) +--R +--R +--R 1 +--R (4) - ------------ +--R +---------+ +--R | 2 2 +--R \|b x - 16 +--R Type: Expression(Integer) +--E 2057 + +)clear all + +--S 2058 of 2952 +t0000:=1/(sqrt((-b+b*c)/d+b*x)*sqrt(c+d*x)) +--R +--R +--R 1 +--R (1) ---------------------------- +--R +---------------+ +--R |b d x + b c - b +-------+ +--R |--------------- \|d x + c +--R \| d +--R Type: Expression(Integer) +--E 2058 + +--S 2059 of 2952 +r0000:=2*atanh(sqrt(d)*sqrt(-b*(1-c)/d+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (sqrt(b)*sqrt(d)) +--R +--R +--R +---------------+ +--R +-+ |b d x + b c - b +--R \|d |--------------- +--R \| d +--R 2atanh(----------------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R (2) ------------------------------ +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 2059 + +--S 2060 of 2952 +--a0000:=integrate(t0000,x) +--E 2060 + +--S 2061 of 2952 +--m0000:=a0000 - r0000 +--E 2061 + +--S 2062 of 2952 +--d0000:=D(m0000,x) +--E 2062 + +)clear all + +--S 2063 of 2952 +t0000:=1/(sqrt(x)*sqrt(-3+2*x)) +--R +--R +--R 1 +--R (1) ------------- +--R +-+ +------+ +--R \|x \|2x - 3 +--R Type: Expression(Integer) +--E 2063 + +--S 2064 of 2952 +r0000:=asinh(sqrt(-3+2*x)/sqrt(3))*sqrt(2) +--R +--R +--R +------+ +--R +-+ \|2x - 3 +--R (2) \|2 asinh(---------) +--R +-+ +--R \|3 +--R Type: Expression(Integer) +--E 2064 + +--S 2065 of 2952 +--a0000:=integrate(t0000,x) +--E 2065 + +--S 2066 of 2952 +--m0000:=a0000 - r0000 +--E 2066 + +--S 2067 of 2952 +--d0000:=D(m0000,x) +--E 2067 + +)clear all + +--S 2068 of 2952 +t0000:=1/(sqrt(-3+2*x)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) ------------------ +--R +------+ +------+ +--R \|2x - 3 \|3x + 2 +--R Type: Expression(Integer) +--E 2068 + +--S 2069 of 2952 +r0000:=asinh(sqrt(3/13)*sqrt(-3+2*x))*sqrt(2/3) +--R +--R +--R +-+ +------+ +--R +-+ \|3 \|2x - 3 +--R \|2 asinh(-------------) +--R +--+ +--R \|13 +--R (2) ------------------------ +--R +-+ +--R \|3 +--R Type: Expression(Integer) +--E 2069 + +--S 2070 of 2952 +--a0000:=integrate(t0000,x) +--E 2070 + +--S 2071 of 2952 +--m0000:=a0000 - r0000 +--E 2071 + +--S 2072 of 2952 +--d0000:=D(m0000,x) +--E 2072 + +)clear all + +--S 2073 of 2952 +t0000:=1/(sqrt(a+b*x)*sqrt(c+d*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 2073 + +--S 2074 of 2952 +r0000:=2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(sqrt(b)*sqrt(d)) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +--R 2atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R (2) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 2074 + +--S 2075 of 2952 +--a0000:=integrate(t0000,x) +--E 2075 + +--S 2076 of 2952 +--m0000:=a0000 - r0000 +--E 2076 + +--S 2077 of 2952 +--d0000:=D(m0000,x) +--E 2077 + +)clear all + +--S 2078 of 2952 +t0000:=1/(sqrt((b-b*c)/d+b*x)*sqrt(c-d*x)) +--R +--R +--R 1 +--R (1) ------------------------------ +--R +---------------+ +--R +---------+ |b d x - b c + b +--R \|- d x + c |--------------- +--R \| d +--R Type: Expression(Integer) +--E 2078 + +--S 2079 of 2952 +r0000:=2*atan(sqrt(d)*sqrt(b*(1-c)/d+b*x)/(sqrt(b)*sqrt(c-d*x)))/_ + (sqrt(b)*sqrt(d)) +--R +--R +--R +---------------+ +--R +-+ |b d x - b c + b +--R \|d |--------------- +--R \| d +--R 2atan(----------------------) +--R +---------+ +-+ +--R \|- d x + c \|b +--R (2) ----------------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 2079 + +--S 2080 of 2952 +--a0000:=integrate(t0000,x) +--E 2080 + +--S 2081 of 2952 +--m0000:=a0000 - r0000 +--E 2081 + +--S 2082 of 2952 +--d0000:=D(m0000,x) +--E 2082 + +)clear all + +--S 2083 of 2952 +t0000:=1/(sqrt(4-x)*sqrt(x)) +--R +--R +--R 1 +--R (1) -------------- +--R +-------+ +-+ +--R \|- x + 4 \|x +--R Type: Expression(Integer) +--E 2083 + +--S 2084 of 2952 +r0000:=-asin(1/2*(2-x)) +--R +--R +--R x - 2 +--R (2) asin(-----) +--R 2 +--R Type: Expression(Integer) +--E 2084 + +--S 2085 of 2952 +--a0000:=integrate(t0000,x) +--E 2085 + +--S 2086 of 2952 +--m0000:=a0000 - r0000 +--E 2086 + +--S 2087 of 2952 +--d0000:=D(m0000,x) +--E 2087 + +)clear all + +--S 2088 of 2952 +t0000:=1/(sqrt(3-2*x)*sqrt(x)) +--R +--R +--R 1 +--R (1) --------------- +--R +--------+ +-+ +--R \|- 2x + 3 \|x +--R Type: Expression(Integer) +--E 2088 + +--S 2089 of 2952 +r0000:=asin(sqrt(2/3)*sqrt(x))*sqrt(2) +--R +--R +--R +-+ +-+ +--R +-+ \|2 \|x +--R (2) \|2 asin(--------) +--R +-+ +--R \|3 +--R Type: Expression(Integer) +--E 2089 + +--S 2090 of 2952 +--a0000:=integrate(t0000,x) +--E 2090 + +--S 2091 of 2952 +--m0000:=a0000 - r0000 +--E 2091 + +--S 2092 of 2952 +--d0000:=D(m0000,x) +--E 2092 + +)clear all + +--S 2093 of 2952 +t0000:=1/(sqrt(3-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 3 \|5x + 3 +--R Type: Expression(Integer) +--E 2093 + +--S 2094 of 2952 +r0000:=asin(sqrt(2/21)*sqrt(3+5*x))*sqrt(2/5) +--R +--R +--R +-+ +------+ +--R +-+ \|2 \|5x + 3 +--R \|2 asin(-------------) +--R +--+ +--R \|21 +--R (2) ----------------------- +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 2094 + +--S 2095 of 2952 +--a0000:=integrate(t0000,x) +--E 2095 + +--S 2096 of 2952 +--m0000:=a0000 - r0000 +--E 2096 + +--S 2097 of 2952 +--d0000:=D(m0000,x) +--E 2097 + +)clear all + +--S 2098 of 2952 +t0000:=1/(sqrt(a-b*x)*sqrt(c+d*x)) +--R +--R +--R 1 +--R (1) ---------------------- +--R +---------+ +-------+ +--R \|- b x + a \|d x + c +--R Type: Expression(Integer) +--E 2098 + +--S 2099 of 2952 +r0000:=-2*atan(sqrt(d)*sqrt(a-b*x)/(sqrt(b)*sqrt(c+d*x)))/(sqrt(b)*sqrt(d)) +--R +--R +--R +---------+ +-+ +--R \|- b x + a \|d +--R 2atan(----------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R (2) - ----------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 2099 + +--S 2100 of 2952 +--a0000:=integrate(t0000,x) +--E 2100 + +--S 2101 of 2952 +--m0000:=a0000 - r0000 +--E 2101 + +--S 2102 of 2952 +--d0000:=D(m0000,x) +--E 2102 + +)clear all + +--S 2103 of 2952 +t0000:=(-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 2103 + +--S 2104 of 2952 +r0000:=(-1+x)^(1/3)*(1+x)^(2/3)+2/3*log(1-(-1+x)^(1/3)/(1+x)^(1/3))-_ + 1/3*log(1+(-1+x)^(2/3)/(1+x)^(2/3)+(-1+x)^(1/3)/(1+x)^(1/3))-_ + 2*atan((1+2*(-1+x)^(1/3)/(1+x)^(1/3))/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 3+-----+2 3+-----+3+-----+ 3+-----+2 +--R +-+ \|x + 1 + \|x - 1 \|x + 1 + \|x - 1 +--R - \|3 log(----------------------------------------) +--R 3+-----+2 +--R \|x + 1 +--R + +--R 3+-----+ 3+-----+ 3+-----+ 3+-----+ +--R +-+ \|x + 1 - \|x - 1 \|x + 1 + 2\|x - 1 +--R 2\|3 log(-------------------) - 6atan(--------------------) +--R 3+-----+ +-+3+-----+ +--R \|x + 1 \|3 \|x + 1 +--R + +--R +-+3+-----+3+-----+2 +--R 3\|3 \|x - 1 \|x + 1 +--R / +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 2104 + +--S 2105 of 2952 +--a0000:=integrate(t0000,x) +--E 2105 + +--S 2106 of 2952 +--m0000:=a0000 - r0000 +--E 2106 + +--S 2107 of 2952 +--d0000:=D(m0000,x) +--E 2107 + +)clear all + +--S 2108 of 2952 +t0000:=(1-x)^(9/2)*(1+x)^(1/2) +--R +--R +--R 4 3 2 +-------+ +-----+ +--R (1) (x - 4x + 6x - 4x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2108 + +--S 2109 of 2952 +r0000:=21/16*asin(x)+7/16*(1-x)^(3/2)*sqrt(1+x)+7/40*(1-x)^(5/2)*sqrt(1+x)+_ + 3/40*(1-x)^(7/2)*sqrt(1+x)+1/30*(1-x)^(9/2)*sqrt(1+x)-_ + 1/6*(1-x)^(11/2)*sqrt(1+x)+21/16*sqrt(1-x)*sqrt(1+x) +--R +--R +--R (2) +--R 5 4 3 2 +-------+ +-----+ +--R (40x - 192x + 350x - 256x - 75x + 448)\|- x + 1 \|x + 1 + 315asin(x) +--R ------------------------------------------------------------------------- +--R 240 +--R Type: Expression(Integer) +--E 2109 + +--S 2110 of 2952 +--a0000:=integrate(t0000,x) +--E 2110 + +--S 2111 of 2952 +--m0000:=a0000 - r0000 +--E 2111 + +--S 2112 of 2952 +--d0000:=D(m0000,x) +--E 2112 + +)clear all + +--S 2113 of 2952 +t0000:=(1-x)^(7/2)*(1+x)^(1/2) +--R +--R +--R 3 2 +-------+ +-----+ +--R (1) (- x + 3x - 3x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2113 + +--S 2114 of 2952 +r0000:=7/8*asin(x)+7/24*(1-x)^(3/2)*sqrt(1+x)+7/60*(1-x)^(5/2)*sqrt(1+x)+_ + 1/20*(1-x)^(7/2)*sqrt(1+x)-1/5*(1-x)^(9/2)*sqrt(1+x)+_ + 7/8*sqrt(1-x)*sqrt(1+x) +--R +--R +--R 4 3 2 +-------+ +-----+ +--R (- 24x + 90x - 112x + 15x + 136)\|- x + 1 \|x + 1 + 105asin(x) +--R (2) ------------------------------------------------------------------ +--R 120 +--R Type: Expression(Integer) +--E 2114 + +--S 2115 of 2952 +--a0000:=integrate(t0000,x) +--E 2115 + +--S 2116 of 2952 +--m0000:=a0000 - r0000 +--E 2116 + +--S 2117 of 2952 +--d0000:=D(m0000,x) +--E 2117 + +)clear all + +--S 2118 of 2952 +t0000:=(1-x)^(5/2)*(1+x)^(1/2) +--R +--R +--R 2 +-------+ +-----+ +--R (1) (x - 2x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2118 + +--S 2119 of 2952 +r0000:=5/8*asin(x)+5/24*(1-x)^(3/2)*sqrt(1+x)+1/12*(1-x)^(5/2)*sqrt(1+x)-_ + 1/4*(1-x)^(7/2)*sqrt(1+x)+5/8*sqrt(1-x)*sqrt(1+x) +--R +--R +--R 3 2 +-------+ +-----+ +--R (6x - 16x + 9x + 16)\|- x + 1 \|x + 1 + 15asin(x) +--R (2) ---------------------------------------------------- +--R 24 +--R Type: Expression(Integer) +--E 2119 + +--S 2120 of 2952 +--a0000:=integrate(t0000,x) +--E 2120 + +--S 2121 of 2952 +--m0000:=a0000 - r0000 +--E 2121 + +--S 2122 of 2952 +--d0000:=D(m0000,x) +--E 2122 + +)clear all + +--S 2123 of 2952 +t0000:=(1-x)^(3/2)*(1+x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (1) (- x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2123 + +--S 2124 of 2952 +r0000:=1/2*asin(x)+1/6*(1-x)^(3/2)*sqrt(1+x)-1/3*(1-x)^(5/2)*sqrt(1+x)+_ + 1/2*sqrt(1-x)*sqrt(1+x) +--R +--R +--R 2 +-------+ +-----+ +--R (- 2x + 3x + 2)\|- x + 1 \|x + 1 + 3asin(x) +--R (2) --------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 2124 + +--S 2125 of 2952 +--a0000:=integrate(t0000,x) +--E 2125 + +--S 2126 of 2952 +--m0000:=a0000 - r0000 +--E 2126 + +--S 2127 of 2952 +--d0000:=D(m0000,x) +--E 2127 + +)clear all + +--S 2128 of 2952 +t0000:=(1-x)^(1/2)*(1+x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (1) \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2128 + +--S 2129 of 2952 +r0000:=1/2*asin(x)+1/2*x*sqrt(1-x^2) +--R +--R +--R +--------+ +--R | 2 +--R x\|- x + 1 + asin(x) +--R (2) ---------------------- +--R 2 +--R Type: Expression(Integer) +--E 2129 + +--S 2130 of 2952 +--a0000:=integrate(t0000,x) +--E 2130 + +--S 2131 of 2952 +--m0000:=a0000 - r0000 +--E 2131 + +--S 2132 of 2952 +--d0000:=D(m0000,x) +--E 2132 + +)clear all + +--S 2133 of 2952 +t0000:=(1+x)^(1/2)/(1-x)^(1/2) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) ---------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 2133 + +--S 2134 of 2952 +r0000:=asin(x)-sqrt(1-x)*sqrt(1+x) +--R +--R +--R +-------+ +-----+ +--R (2) - \|- x + 1 \|x + 1 + asin(x) +--R Type: Expression(Integer) +--E 2134 + +--S 2135 of 2952 +--a0000:=integrate(t0000,x) +--E 2135 + +--S 2136 of 2952 +--m0000:=a0000 - r0000 +--E 2136 + +--S 2137 of 2952 +--d0000:=D(m0000,x) +--E 2137 + +)clear all + +--S 2138 of 2952 +t0000:=(1+x)^(1/2)/(1-x)^(3/2) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) - ----------------- +--R +-------+ +--R (x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2138 + +--S 2139 of 2952 +r0000:=-asin(x)+2*sqrt(1+x)/sqrt(1-x) +--R +--R +--R +-----+ +-------+ +--R 2\|x + 1 - asin(x)\|- x + 1 +--R (2) ----------------------------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 2139 + +--S 2140 of 2952 +--a0000:=integrate(t0000,x) +--E 2140 + +--S 2141 of 2952 +--m0000:=a0000 - r0000 +--E 2141 + +--S 2142 of 2952 +--d0000:=D(m0000,x) +--E 2142 + +)clear all + +--S 2143 of 2952 +t0000:=(1+x)^(1/2)/(1-x)^(5/2) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2143 + +--S 2144 of 2952 +r0000:=1/3*(1+x)^(3/2)/(1-x)^(3/2) +--R +--R +--R +-----+ +--R (- x - 1)\|x + 1 +--R (2) ------------------ +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 2144 + +--S 2145 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-----+ 2 +--R (3x + 3)\|- x + 1 \|x + 1 + 5x - 10x + 5 +--R (3) ------------------------------------------ +--R 2 +--R 9x - 18x + 9 +--R Type: Union(Expression(Integer),...) +--E 2145 + +--S 2146 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 5 +--R (4) - +--R 9 +--R Type: Expression(Integer) +--E 2146 + +--S 2147 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2147 + +)clear all + +--S 2148 of 2952 +t0000:=(1+x)^(1/2)/(1-x)^(7/2) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) - ----------------------------- +--R 3 2 +-------+ +--R (x - 3x + 3x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2148 + +--S 2149 of 2952 +r0000:=1/5*(1+x)^(3/2)/(1-x)^(5/2)+1/15*(1+x)^(3/2)/(1-x)^(3/2) +--R +--R +--R 2 +-----+ +--R (- x + 3x + 4)\|x + 1 +--R (2) --------------------------- +--R 2 +-------+ +--R (15x - 30x + 15)\|- x + 1 +--R Type: Expression(Integer) +--E 2149 + +--S 2150 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R 2 +-------+ +-----+ 3 2 +--R (x - 3x - 4)\|- x + 1 \|x + 1 + 6x - 18x + 18x - 6 +--R (3) ------------------------------------------------------ +--R 3 2 +--R 15x - 45x + 45x - 15 +--R Type: Union(Expression(Integer),...) +--E 2150 + +--S 2151 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 2 +--R (4) - +--R 5 +--R Type: Expression(Integer) +--E 2151 + +--S 2152 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2152 + +)clear all + +--S 2153 of 2952 +t0000:=(1+x)^(1/2)/(1-x)^(9/2) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) ----------------------------------- +--R 4 3 2 +-------+ +--R (x - 4x + 6x - 4x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2153 + +--S 2154 of 2952 +r0000:=1/7*(1+x)^(3/2)/(1-x)^(7/2)+2/35*(1+x)^(3/2)/(1-x)^(5/2)+_ + 2/105*(1+x)^(3/2)/(1-x)^(3/2) +--R +--R +--R 3 2 +-----+ +--R (- 2x + 8x - 13x - 23)\|x + 1 +--R (2) -------------------------------------- +--R 3 2 +-------+ +--R (105x - 315x + 315x - 105)\|- x + 1 +--R Type: Expression(Integer) +--E 2154 + +--S 2155 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 +-------+ +-----+ 4 3 2 +--R (16x - 64x + 104x + 184)\|- x + 1 \|x + 1 - 391x + 1564x - 2346x +--R + +--R 1564x - 391 +--R / +--R 4 3 2 +--R 840x - 3360x + 5040x - 3360x + 840 +--R Type: Union(Expression(Integer),...) +--E 2155 + +--S 2156 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 391 +--R (4) - --- +--R 840 +--R Type: Expression(Integer) +--E 2156 + +--S 2157 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2157 + +)clear all + +--S 2158 of 2952 +t0000:=(1+x)^(1/2)/(1-x)^(11/2) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) - ------------------------------------------- +--R 5 4 3 2 +-------+ +--R (x - 5x + 10x - 10x + 5x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2158 + +--S 2159 of 2952 +r0000:=1/9*(1+x)^(3/2)/(1-x)^(9/2)+1/21*(1+x)^(3/2)/(1-x)^(7/2)+_ + 2/105*(1+x)^(3/2)/(1-x)^(5/2)+2/315*(1+x)^(3/2)/(1-x)^(3/2) +--R +--R +--R 4 3 2 +-----+ +--R (- 2x + 10x - 21x + 25x + 58)\|x + 1 +--R (2) ------------------------------------------------- +--R 4 3 2 +-------+ +--R (315x - 1260x + 1890x - 1260x + 315)\|- x + 1 +--R Type: Expression(Integer) +--E 2159 + +--S 2160 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 2 +-------+ +-----+ 5 4 3 +--R (2x - 10x + 21x - 25x - 58)\|- x + 1 \|x + 1 - 72x + 360x - 720x +--R + +--R 2 +--R 720x - 360x + 72 +--R / +--R 5 4 3 2 +--R 315x - 1575x + 3150x - 3150x + 1575x - 315 +--R Type: Union(Expression(Integer),...) +--E 2160 + +--S 2161 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 8 +--R (4) - -- +--R 35 +--R Type: Expression(Integer) +--E 2161 + +--S 2162 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2162 + +)clear all + +--S 2163 of 2952 +t0000:=(1+x)^(1/2)/(1-x)^(13/2) +--R +--R +--R +-----+ +--R \|x + 1 +--R (1) -------------------------------------------------- +--R 6 5 4 3 2 +-------+ +--R (x - 6x + 15x - 20x + 15x - 6x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2163 + +--S 2164 of 2952 +r0000:=1/11*(1+x)^(3/2)/(1-x)^(11/2)+4/99*(1+x)^(3/2)/(1-x)^(9/2)+_ + 4/231*(1+x)^(3/2)/(1-x)^(7/2)+8/1155*(1+x)^(3/2)/(1-x)^(5/2)+_ + 8/3465*(1+x)^(3/2)/(1-x)^(3/2) +--R +--R +--R 5 4 3 2 +-----+ +--R (- 8x + 48x - 124x + 184x - 183x - 547)\|x + 1 +--R (2) ---------------------------------------------------------------- +--R 5 4 3 2 +-------+ +--R (3465x - 17325x + 34650x - 34650x + 17325x - 3465)\|- x + 1 +--R Type: Expression(Integer) +--E 2164 + +--S 2165 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 3 2 +-------+ +-----+ 6 +--R (32x - 192x + 496x - 736x + 732x + 2188)\|- x + 1 \|x + 1 - 2735x +--R + +--R 5 4 3 2 +--R 16410x - 41025x + 54700x - 41025x + 16410x - 2735 +--R / +--R 6 5 4 3 2 +--R 13860x - 83160x + 207900x - 277200x + 207900x - 83160x + 13860 +--R Type: Union(Expression(Integer),...) +--E 2165 + +--S 2166 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 547 +--R (4) - ---- +--R 2772 +--R Type: Expression(Integer) +--E 2166 + +--S 2167 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2167 + +)clear all + +--S 2168 of 2952 +t0000:=(1-x)^(11/2)*(1+x)^(3/2) +--R +--R +--R 6 5 4 2 +-------+ +-----+ +--R (1) (- x + 4x - 5x + 5x - 4x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2168 + +--S 2169 of 2952 +r0000:=-1/8*(1-x)^(13/2)*(1+x)^(3/2)+99/128*asin(x)+_ + 33/128*(1-x)^(3/2)*sqrt(1+x)+33/320*(1-x)^(5/2)*sqrt(1+x)+_ + 99/2240*(1-x)^(7/2)*sqrt(1+x)+11/560*(1-x)^(9/2)*sqrt(1+x)+_ + 1/112*(1-x)^(11/2)*sqrt(1+x)-3/56*(1-x)^(13/2)*sqrt(1+x)+_ + 99/128*sqrt(1-x)*sqrt(1+x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R (- 560x + 2560x - 3640x - 512x + 6650x - 6656x + 1015x + 4608) +--R * +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R + +--R 3465asin(x) +--R / +--R 4480 +--R Type: Expression(Integer) +--E 2169 + +--S 2170 of 2952 +--a0000:=integrate(t0000,x) +--E 2170 + +--S 2171 of 2952 +--m0000:=a0000 - r0000 +--E 2171 + +--S 2172 of 2952 +--d0000:=D(m0000,x) +--E 2172 + +)clear all + +--S 2173 of 2952 +t0000:=(1-x)^(9/2)*(1+x)^(3/2) +--R +--R +--R 5 4 3 2 +-------+ +-----+ +--R (1) (x - 3x + 2x + 2x - 3x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2173 + +--S 2174 of 2952 +r0000:=-1/7*(1-x)^(11/2)*(1+x)^(3/2)+9/16*asin(x)+_ + 3/16*(1-x)^(3/2)*sqrt(1+x)+3/40*(1-x)^(5/2)*sqrt(1+x)+_ + 9/280*(1-x)^(7/2)*sqrt(1+x)+1/70*(1-x)^(9/2)*sqrt(1+x)-_ + 1/14*(1-x)^(11/2)*sqrt(1+x)+9/16*sqrt(1-x)*sqrt(1+x) +--R +--R +--R (2) +--R 6 5 4 3 2 +-------+ +-----+ +--R (80x - 280x + 208x + 350x - 656x + 245x + 368)\|- x + 1 \|x + 1 +--R + +--R 315asin(x) +--R / +--R 560 +--R Type: Expression(Integer) +--E 2174 + +--S 2175 of 2952 +--a0000:=integrate(t0000,x) +--E 2175 + +--S 2176 of 2952 +--m0000:=a0000 - r0000 +--E 2176 + +--S 2177 of 2952 +--d0000:=D(m0000,x) +--E 2177 + +)clear all + +--S 2178 of 2952 +t0000:=(1-x)^(7/2)*(1+x)^(3/2) +--R +--R +--R 4 3 +-------+ +-----+ +--R (1) (- x + 2x - 2x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2178 + +--S 2179 of 2952 +r0000:=-1/6*(1-x)^(9/2)*(1+x)^(3/2)+7/16*asin(x)+7/48*(1-x)^(3/2)*sqrt(1+x)+_ + 7/120*(1-x)^(5/2)*sqrt(1+x)+1/40*(1-x)^(7/2)*sqrt(1+x)-_ + 1/10*(1-x)^(9/2)*sqrt(1+x)+7/16*sqrt(1-x)*sqrt(1+x) +--R +--R +--R (2) +--R 5 4 3 2 +-------+ +-----+ +--R (- 40x + 96x + 10x - 192x + 135x + 96)\|- x + 1 \|x + 1 + 105asin(x) +--R ------------------------------------------------------------------------- +--R 240 +--R Type: Expression(Integer) +--E 2179 + +--S 2180 of 2952 +--a0000:=integrate(t0000,x) +--E 2180 + +--S 2181 of 2952 +--m0000:=a0000 - r0000 +--E 2181 + +--S 2182 of 2952 +--d0000:=D(m0000,x) +--E 2182 + +)clear all + +--S 2183 of 2952 +t0000:=(1-x)^(5/2)*(1+x)^(3/2) +--R +--R +--R 3 2 +-------+ +-----+ +--R (1) (x - x - x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2183 + +--S 2184 of 2952 +r0000:=-1/5*(1-x)^(7/2)*(1+x)^(3/2)+3/8*asin(x)+1/8*(1-x)^(3/2)*sqrt(1+x)+_ + 1/20*(1-x)^(5/2)*sqrt(1+x)-3/20*(1-x)^(7/2)*sqrt(1+x)+_ + 3/8*sqrt(1-x)*sqrt(1+x) +--R +--R +--R 4 3 2 +-------+ +-----+ +--R (8x - 10x - 16x + 25x + 8)\|- x + 1 \|x + 1 + 15asin(x) +--R (2) ----------------------------------------------------------- +--R 40 +--R Type: Expression(Integer) +--E 2184 + +--S 2185 of 2952 +--a0000:=integrate(t0000,x) +--E 2185 + +--S 2186 of 2952 +--m0000:=a0000 - r0000 +--E 2186 + +--S 2187 of 2952 +--d0000:=D(m0000,x) +--E 2187 + +)clear all + +--S 2188 of 2952 +t0000:=(1-x)^(3/2)*(1+x)^(3/2) +--R +--R +--R 2 +-------+ +-----+ +--R (1) (- x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2188 + +--S 2189 of 2952 +r0000:=1/4*x*(1-x^2)^(3/2)+3/8*asin(x)+3/8*x*sqrt(1-x^2) +--R +--R +--R +--------+ +--R 3 | 2 +--R (- 2x + 5x)\|- x + 1 + 3asin(x) +--R (2) ---------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 2189 + +--S 2190 of 2952 +--a0000:=integrate(t0000,x) +--E 2190 + +--S 2191 of 2952 +--m0000:=a0000 - r0000 +--E 2191 + +--S 2192 of 2952 +--d0000:=D(m0000,x) +--E 2192 + +)clear all + +--S 2193 of 2952 +t0000:=(1-x)^(1/2)*(1+x)^(3/2) +--R +--R +--R +-------+ +-----+ +--R (1) (x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2193 + +--S 2194 of 2952 +r0000:=-1/3*(1-x)^(3/2)*(1+x)^(3/2)+1/2*asin(x)+1/2*x*sqrt(1-x^2) +--R +--R +--R +--------+ +--R 2 +-------+ +-----+ | 2 +--R (2x - 2)\|- x + 1 \|x + 1 + 3x\|- x + 1 + 3asin(x) +--R (2) ------------------------------------------------------ +--R 6 +--R Type: Expression(Integer) +--E 2194 + +--S 2195 of 2952 +--a0000:=integrate(t0000,x) +--E 2195 + +--S 2196 of 2952 +--m0000:=a0000 - r0000 +--E 2196 + +--S 2197 of 2952 +--d0000:=D(m0000,x) +--E 2197 + +)clear all + +--S 2198 of 2952 +t0000:=(1+x)^(3/2)/(1-x)^(1/2) +--R +--R +--R +-----+ +--R (x + 1)\|x + 1 +--R (1) --------------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 2198 + +--S 2199 of 2952 +r0000:=3/2*asin(x)-1/2*(1+x)^(3/2)*sqrt(1-x)-3/2*sqrt(1-x)*sqrt(1+x) +--R +--R +--R +-------+ +-----+ +--R (- x - 4)\|- x + 1 \|x + 1 + 3asin(x) +--R (2) -------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 2199 + +--S 2200 of 2952 +--a0000:=integrate(t0000,x) +--E 2200 + +--S 2201 of 2952 +--m0000:=a0000 - r0000 +--E 2201 + +--S 2202 of 2952 +--d0000:=D(m0000,x) +--E 2202 + +)clear all + +--S 2203 of 2952 +t0000:=(1+x)^(3/2)/(1-x)^(3/2) +--R +--R +--R +-----+ +--R (- x - 1)\|x + 1 +--R (1) ----------------- +--R +-------+ +--R (x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2203 + +--S 2204 of 2952 +r0000:=-3*asin(x)+2*(1+x)^(3/2)/sqrt(1-x)+3*sqrt(1-x)*sqrt(1+x) +--R +--R +--R +-----+ +-------+ +--R (- x + 5)\|x + 1 - 3asin(x)\|- x + 1 +--R (2) -------------------------------------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 2204 + +--S 2205 of 2952 +--a0000:=integrate(t0000,x) +--E 2205 + +--S 2206 of 2952 +--m0000:=a0000 - r0000 +--E 2206 + +--S 2207 of 2952 +--d0000:=D(m0000,x) +--E 2207 + +)clear all + +--S 2208 of 2952 +t0000:=(1+x)^(3/2)/(1-x)^(5/2) +--R +--R +--R +-----+ +--R (x + 1)\|x + 1 +--R (1) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2208 + +--S 2209 of 2952 +r0000:=2/3*(1+x)^(3/2)/(1-x)^(3/2)+asin(x)-2*sqrt(1+x)/sqrt(1-x) +--R +--R +--R +-----+ +-------+ +--R (- 8x + 4)\|x + 1 + (3x - 3)asin(x)\|- x + 1 +--R (2) ---------------------------------------------- +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 2209 + +--S 2210 of 2952 +--a0000:=integrate(t0000,x) +--E 2210 + +--S 2211 of 2952 +--m0000:=a0000 - r0000 +--E 2211 + +--S 2212 of 2952 +--d0000:=D(m0000,x) +--E 2212 + +)clear all + +--S 2213 of 2952 +t0000:=(1+x)^(3/2)/(1-x)^(7/2) +--R +--R +--R +-----+ +--R (- x - 1)\|x + 1 +--R (1) ----------------------------- +--R 3 2 +-------+ +--R (x - 3x + 3x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2213 + +--S 2214 of 2952 +r0000:=1/5*(1+x)^(5/2)/(1-x)^(5/2) +--R +--R +--R 2 +-----+ +--R (x + 2x + 1)\|x + 1 +--R (2) ------------------------- +--R 2 +-------+ +--R (5x - 10x + 5)\|- x + 1 +--R Type: Expression(Integer) +--E 2214 + +--S 2215 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R 2 +-------+ +-----+ 3 2 +--R (- 4x - 8x - 4)\|- x + 1 \|x + 1 + 5x - 15x + 15x - 5 +--R (3) --------------------------------------------------------- +--R 3 2 +--R 20x - 60x + 60x - 20 +--R Type: Union(Expression(Integer),...) +--E 2215 + +--S 2216 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 1 +--R (4) - +--R 4 +--R Type: Expression(Integer) +--E 2216 + +--S 2217 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2217 + +)clear all + +--S 2218 of 2952 +t0000:=(1+x)^(3/2)/(1-x)^(9/2) +--R +--R +--R +-----+ +--R (x + 1)\|x + 1 +--R (1) ----------------------------------- +--R 4 3 2 +-------+ +--R (x - 4x + 6x - 4x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2218 + +--S 2219 of 2952 +r0000:=1/7*(1+x)^(5/2)/(1-x)^(7/2)+1/35*(1+x)^(5/2)/(1-x)^(5/2) +--R +--R +--R 3 2 +-----+ +--R (x - 4x - 11x - 6)\|x + 1 +--R (2) ------------------------------------ +--R 3 2 +-------+ +--R (35x - 105x + 105x - 35)\|- x + 1 +--R Type: Expression(Integer) +--E 2219 + +--S 2220 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 +-------+ +-----+ 4 3 2 +--R (- x + 4x + 11x + 6)\|- x + 1 \|x + 1 + 36x - 144x + 216x - 144x + 36 +--R --------------------------------------------------------------------------- +--R 4 3 2 +--R 35x - 140x + 210x - 140x + 35 +--R Type: Union(Expression(Integer),...) +--E 2220 + +--S 2221 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 36 +--R (4) -- +--R 35 +--R Type: Expression(Integer) +--E 2221 + +--S 2222 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2222 + +)clear all + +--S 2223 of 2952 +t0000:=(1+x)^(3/2)/(1-x)^(11/2) +--R +--R +--R +-----+ +--R (- x - 1)\|x + 1 +--R (1) ------------------------------------------- +--R 5 4 3 2 +-------+ +--R (x - 5x + 10x - 10x + 5x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2223 + +--S 2224 of 2952 +r0000:=1/9*(1+x)^(5/2)/(1-x)^(9/2)+2/63*(1+x)^(5/2)/(1-x)^(7/2)+_ + 2/315*(1+x)^(5/2)/(1-x)^(5/2) +--R +--R +--R 4 3 2 +-----+ +--R (2x - 10x + 21x + 80x + 47)\|x + 1 +--R (2) ------------------------------------------------- +--R 4 3 2 +-------+ +--R (315x - 1260x + 1890x - 1260x + 315)\|- x + 1 +--R Type: Expression(Integer) +--E 2224 + +--S 2225 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 2 +-------+ +-----+ 5 4 +--R (- 2x + 10x - 21x - 80x - 47)\|- x + 1 \|x + 1 + 243x - 1215x +--R + +--R 3 2 +--R 2430x - 2430x + 1215x - 243 +--R / +--R 5 4 3 2 +--R 315x - 1575x + 3150x - 3150x + 1575x - 315 +--R Type: Union(Expression(Integer),...) +--E 2225 + +--S 2226 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 27 +--R (4) -- +--R 35 +--R Type: Expression(Integer) +--E 2226 + +--S 2227 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2227 + +)clear all + +--S 2228 of 2952 +t0000:=(1+x)^(3/2)/(1-x)^(13/2) +--R +--R +--R +-----+ +--R (x + 1)\|x + 1 +--R (1) -------------------------------------------------- +--R 6 5 4 3 2 +-------+ +--R (x - 6x + 15x - 20x + 15x - 6x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2228 + +--S 2229 of 2952 +r0000:=1/11*(1+x)^(5/2)/(1-x)^(11/2)+1/33*(1+x)^(5/2)/(1-x)^(9/2)+_ + 2/231*(1+x)^(5/2)/(1-x)^(7/2)+2/1155*(1+x)^(5/2)/(1-x)^(5/2) +--R +--R +--R 5 4 3 2 +-----+ +--R (2x - 12x + 31x - 46x - 243x - 152)\|x + 1 +--R (2) -------------------------------------------------------------- +--R 5 4 3 2 +-------+ +--R (1155x - 5775x + 11550x - 11550x + 5775x - 1155)\|- x + 1 +--R Type: Expression(Integer) +--E 2229 + +--S 2230 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 3 2 +-------+ +-----+ 6 +--R (- 6x + 36x - 93x + 138x + 729x + 456)\|- x + 1 \|x + 1 + 760x +--R + +--R 5 4 3 2 +--R - 4560x + 11400x - 15200x + 11400x - 4560x + 760 +--R / +--R 6 5 4 3 2 +--R 3465x - 20790x + 51975x - 69300x + 51975x - 20790x + 3465 +--R Type: Union(Expression(Integer),...) +--E 2230 + +--S 2231 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 152 +--R (4) --- +--R 693 +--R Type: Expression(Integer) +--E 2231 + +--S 2232 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2232 + +)clear all + +--S 2233 of 2952 +t0000:=(1+x)^(3/2)/(1-x)^(15/2) +--R +--R +--R +-----+ +--R (- x - 1)\|x + 1 +--R (1) --------------------------------------------------------- +--R 7 6 5 4 3 2 +-------+ +--R (x - 7x + 21x - 35x + 35x - 21x + 7x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2233 + +--S 2234 of 2952 +r0000:=1/13*(1+x)^(5/2)/(1-x)^(13/2)+4/143*(1+x)^(5/2)/(1-x)^(11/2)+_ + 4/429*(1+x)^(5/2)/(1-x)^(9/2)+8/3003*(1+x)^(5/2)/(1-x)^(7/2)+_ + 8/15015*(1+x)^(5/2)/(1-x)^(5/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +-----+ +--R (8x - 56x + 172x - 308x + 367x + 2674x + 1763)\|x + 1 +--R / +--R 6 5 4 3 2 +--R (15015x - 90090x + 225225x - 300300x + 225225x - 90090x + 15015) +--R * +--R +-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 2234 + +--S 2235 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +-------+ +--R (- 40x + 280x - 860x + 1540x - 1835x - 13370x - 8815)\|- x + 1 +--R * +--R +-----+ +--R \|x + 1 +--R + +--R 7 6 5 4 3 2 +--R 22919x - 160433x + 481299x - 802165x + 802165x - 481299x + 160433x +--R + +--R - 22919 +--R / +--R 7 6 5 4 3 2 +--R 75075x - 525525x + 1576575x - 2627625x + 2627625x - 1576575x +--R + +--R 525525x - 75075 +--R Type: Union(Expression(Integer),...) +--E 2235 + +--S 2236 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 1763 +--R (4) ---- +--R 5775 +--R Type: Expression(Integer) +--E 2236 + +--S 2237 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2237 + +)clear all + +--S 2238 of 2952 +t0000:=(1-x)^(13/2)*(1+x)^(5/2) +--R +--R +--R 8 7 6 5 4 3 2 +-------+ +-----+ +--R (1) (x - 4x + 4x + 4x - 10x + 4x + 4x - 4x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2238 + +--S 2239 of 2952 +r0000:=-1/18*(1-x)^(15/2)*(1+x)^(3/2)-1/10*(1-x)^(15/2)*(1+x)^(5/2)+_ + 143/256*asin(x)+143/768*(1-x)^(3/2)*sqrt(1+x)+_ + 143/1920*(1-x)^(5/2)*sqrt(1+x)+143/4480*(1-x)^(7/2)*sqrt(1+x)+_ + 143/10080*(1-x)^(9/2)*sqrt(1+x)+13/2016*(1-x)^(11/2)*sqrt(1+x)+_ + 1/336*(1-x)^(13/2)*sqrt(1+x)-1/48*(1-x)^(15/2)*sqrt(1+x)+_ + 143/256*sqrt(1-x)*sqrt(1+x) +--R +--R +--R (2) +--R 9 8 7 6 5 4 3 +--R 8064x - 35840x + 39312x + 51200x - 142296x + 61440x + 104370x +--R + +--R 2 +--R - 133120x + 35595x + 56320 +--R * +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R + +--R 45045asin(x) +--R / +--R 80640 +--R Type: Expression(Integer) +--E 2239 + +--S 2240 of 2952 +--a0000:=integrate(t0000,x) +--E 2240 + +--S 2241 of 2952 +--m0000:=a0000 - r0000 +--E 2241 + +--S 2242 of 2952 +--d0000:=D(m0000,x) +--E 2242 + +)clear all + +--S 2243 of 2952 +t0000:=(1-x)^(11/2)*(1+x)^(5/2) +--R +--R +--R 7 6 5 4 3 2 +-------+ +-----+ +--R (1) (- x + 3x - x - 5x + 5x + x - 3x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2243 + +--S 2244 of 2952 +r0000:=-5/72*(1-x)^(13/2)*(1+x)^(3/2)-1/9*(1-x)^(13/2)*(1+x)^(5/2)+_ + 55/128*asin(x)+55/384*(1-x)^(3/2)*sqrt(1+x)+_ + 11/192*(1-x)^(5/2)*sqrt(1+x)+11/448*(1-x)^(7/2)*sqrt(1+x)+_ + 11/1008*(1-x)^(9/2)*sqrt(1+x)+5/1008*(1-x)^(11/2)*sqrt(1+x)-_ + 5/168*(1-x)^(13/2)*sqrt(1+x)+55/128*sqrt(1-x)*sqrt(1+x) +--R +--R +--R (2) +--R 8 7 6 5 4 3 2 +--R - 896x + 3024x - 1024x - 7224x + 8448x + 3066x - 10240x +--R + +--R 4599x + 3712 +--R * +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R + +--R 3465asin(x) +--R / +--R 8064 +--R Type: Expression(Integer) +--E 2244 + +--S 2245 of 2952 +--a0000:=integrate(t0000,x) +--E 2245 + +--S 2246 of 2952 +--m0000:=a0000 - r0000 +--E 2246 + +--S 2247 of 2952 +--d0000:=D(m0000,x) +--E 2247 + +)clear all + +--S 2248 of 2952 +t0000:=(1-x)^(9/2)*(1+x)^(5/2) +--R +--R +--R 6 5 4 3 2 +-------+ +-----+ +--R (1) (x - 2x - x + 4x - x - 2x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2248 + +--S 2249 of 2952 +r0000:=-5/56*(1-x)^(11/2)*(1+x)^(3/2)-1/8*(1-x)^(11/2)*(1+x)^(5/2)+_ + 45/128*asin(x)+15/128*(1-x)^(3/2)*sqrt(1+x)+_ + 3/64*(1-x)^(5/2)*sqrt(1+x)+9/448*(1-x)^(7/2)*sqrt(1+x)+_ + 1/112*(1-x)^(9/2)*sqrt(1+x)-_ + 5/112*(1-x)^(11/2)*sqrt(1+x)+45/128*sqrt(1-x)*sqrt(1+x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +-------+ +--R (112x - 256x - 168x + 768x - 210x - 768x + 581x + 256)\|- x + 1 +--R * +--R +-----+ +--R \|x + 1 +--R + +--R 315asin(x) +--R / +--R 896 +--R Type: Expression(Integer) +--E 2249 + +--S 2250 of 2952 +--a0000:=integrate(t0000,x) +--E 2250 + +--S 2251 of 2952 +--m0000:=a0000 - r0000 +--E 2251 + +--S 2252 of 2952 +--d0000:=D(m0000,x) +--E 2252 + +)clear all + +--S 2253 of 2952 +t0000:=(1-x)^(7/2)*(1+x)^(5/2) +--R +--R +--R 5 4 3 2 +-------+ +-----+ +--R (1) (- x + x + 2x - 2x - x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2253 + +--S 2254 of 2952 +r0000:=-5/42*(1-x)^(9/2)*(1+x)^(3/2)-1/7*(1-x)^(9/2)*(1+x)^(5/2)+_ + 5/16*asin(x)+5/48*(1-x)^(3/2)*sqrt(1+x)+1/24*(1-x)^(5/2)*sqrt(1+x)+_ + 1/56*(1-x)^(7/2)*sqrt(1+x)-1/14*(1-x)^(9/2)*sqrt(1+x)+_ + 5/16*sqrt(1-x)*sqrt(1+x) +--R +--R +--R (2) +--R 6 5 4 3 2 +-------+ +-----+ +--R (- 48x + 56x + 144x - 182x - 144x + 231x + 48)\|- x + 1 \|x + 1 +--R + +--R 105asin(x) +--R / +--R 336 +--R Type: Expression(Integer) +--E 2254 + +--S 2255 of 2952 +--a0000:=integrate(t0000,x) +--E 2255 + +--S 2256 of 2952 +--m0000:=a0000 - r0000 +--E 2256 + +--S 2257 of 2952 +--d0000:=D(m0000,x) +--E 2257 + +)clear all + +--S 2258 of 2952 +t0000:=(1-x)^(5/2)*(1+x)^(5/2) +--R +--R +--R 4 2 +-------+ +-----+ +--R (1) (x - 2x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2258 + +--S 2259 of 2952 +r0000:=5/24*x*(1-x^2)^(3/2)+1/6*x*(1-x^2)^(5/2)+5/16*asin(x)+5/16*x*sqrt(1-x^2) +--R +--R +--R +--------+ +--R 5 3 | 2 +--R (8x - 26x + 33x)\|- x + 1 + 15asin(x) +--R (2) ----------------------------------------- +--R 48 +--R Type: Expression(Integer) +--E 2259 + +--S 2260 of 2952 +--a0000:=integrate(t0000,x) +--E 2260 + +--S 2261 of 2952 +--m0000:=a0000 - r0000 +--E 2261 + +--S 2262 of 2952 +--d0000:=D(m0000,x) +--E 2262 + +)clear all + +--S 2263 of 2952 +t0000:=(1-x)^(3/2)*(1+x)^(5/2) +--R +--R +--R 3 2 +-------+ +-----+ +--R (1) (- x - x + x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2263 + +--S 2264 of 2952 +r0000:=-1/5*(1-x)^(5/2)*(1+x)^(5/2)+1/4*x*(1-x^2)^(3/2)+3/8*asin(x)+_ + 3/8*x*sqrt(1-x^2) +--R +--R +--R (2) +--R +--------+ +--R 4 2 +-------+ +-----+ 3 | 2 +--R (- 8x + 16x - 8)\|- x + 1 \|x + 1 + (- 10x + 25x)\|- x + 1 + 15asin(x) +--R ---------------------------------------------------------------------------- +--R 40 +--R Type: Expression(Integer) +--E 2264 + +--S 2265 of 2952 +--a0000:=integrate(t0000,x) +--E 2265 + +--S 2266 of 2952 +--m0000:=a0000 - r0000 +--E 2266 + +--S 2267 of 2952 +--d0000:=D(m0000,x) +--E 2267 + +)clear all + +--S 2268 of 2952 +t0000:=(1-x)^(1/2)*(1+x)^(5/2) +--R +--R +--R 2 +-------+ +-----+ +--R (1) (x + 2x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2268 + +--S 2269 of 2952 +r0000:=-5/12*(1-x)^(3/2)*(1+x)^(3/2)-1/4*(1-x)^(3/2)*(1+x)^(5/2)+_ + 5/8*asin(x)+5/8*x*sqrt(1-x^2) +--R +--R +--R +--------+ +--R 3 2 +-------+ +-----+ | 2 +--R (6x + 16x - 6x - 16)\|- x + 1 \|x + 1 + 15x\|- x + 1 + 15asin(x) +--R (2) --------------------------------------------------------------------- +--R 24 +--R Type: Expression(Integer) +--E 2269 + +--S 2270 of 2952 +--a0000:=integrate(t0000,x) +--E 2270 + +--S 2271 of 2952 +--m0000:=a0000 - r0000 +--E 2271 + +--S 2272 of 2952 +--d0000:=D(m0000,x) +--E 2272 + +)clear all + +--S 2273 of 2952 +t0000:=(1+x)^(5/2)/(1-x)^(1/2) +--R +--R +--R 2 +-----+ +--R (x + 2x + 1)\|x + 1 +--R (1) --------------------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 2273 + +--S 2274 of 2952 +r0000:=5/2*asin(x)-5/6*(1+x)^(3/2)*sqrt(1-x)-1/3*(1+x)^(5/2)*sqrt(1-x)-_ + 5/2*sqrt(1-x)*sqrt(1+x) +--R +--R +--R 2 +-------+ +-----+ +--R (- 2x - 9x - 22)\|- x + 1 \|x + 1 + 15asin(x) +--R (2) ----------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 2274 + +--S 2275 of 2952 +--a0000:=integrate(t0000,x) +--E 2275 + +--S 2276 of 2952 +--m0000:=a0000 - r0000 +--E 2276 + +--S 2277 of 2952 +--d0000:=D(m0000,x) +--E 2277 + +)clear all + +--S 2278 of 2952 +t0000:=(1+x)^(5/2)/(1-x)^(3/2) +--R +--R +--R 2 +-----+ +--R (- x - 2x - 1)\|x + 1 +--R (1) ----------------------- +--R +-------+ +--R (x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2278 + +--S 2279 of 2952 +r0000:=-15/2*asin(x)+2*(1+x)^(5/2)/sqrt(1-x)+5/2*(1+x)^(3/2)*sqrt(1-x)+_ + 15/2*sqrt(1-x)*sqrt(1+x) +--R +--R +--R 2 +-----+ +-------+ +--R (- x - 7x + 24)\|x + 1 - 15asin(x)\|- x + 1 +--R (2) ---------------------------------------------- +--R +-------+ +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 2279 + +--S 2280 of 2952 +--a0000:=integrate(t0000,x) +--E 2280 + +--S 2281 of 2952 +--m0000:=a0000 - r0000 +--E 2281 + +--S 2282 of 2952 +--d0000:=D(m0000,x) +--E 2282 + +)clear all + +--S 2283 of 2952 +t0000:=(1+x)^(5/2)/(1-x)^(5/2) +--R +--R +--R 2 +-----+ +--R (x + 2x + 1)\|x + 1 +--R (1) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2283 + +--S 2284 of 2952 +r0000:=2/3*(1+x)^(5/2)/(1-x)^(3/2)+5*asin(x)-10/3*(1+x)^(3/2)/sqrt(1-x)-_ + 5*sqrt(1-x)*sqrt(1+x) +--R +--R +--R 2 +-----+ +-------+ +--R (3x - 34x + 23)\|x + 1 + (15x - 15)asin(x)\|- x + 1 +--R (2) ------------------------------------------------------ +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 2284 + +--S 2285 of 2952 +--a0000:=integrate(t0000,x) +--E 2285 + +--S 2286 of 2952 +--m0000:=a0000 - r0000 +--E 2286 + +--S 2287 of 2952 +--d0000:=D(m0000,x) +--E 2287 + +)clear all + +--S 2288 of 2952 +t0000:=(1+x)^(5/2)/(1-x)^(7/2) +--R +--R +--R 2 +-----+ +--R (- x - 2x - 1)\|x + 1 +--R (1) ----------------------------- +--R 3 2 +-------+ +--R (x - 3x + 3x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2288 + +--S 2289 of 2952 +r0000:=-2/3*(1+x)^(3/2)/(1-x)^(3/2)+2/5*(1+x)^(5/2)/(1-x)^(5/2)-_ + asin(x)+2*sqrt(1+x)/sqrt(1-x) +--R +--R +--R 2 +-----+ 2 +-------+ +--R (46x - 48x + 26)\|x + 1 + (- 15x + 30x - 15)asin(x)\|- x + 1 +--R (2) ---------------------------------------------------------------- +--R 2 +-------+ +--R (15x - 30x + 15)\|- x + 1 +--R Type: Expression(Integer) +--E 2289 + +--S 2290 of 2952 +--a0000:=integrate(t0000,x) +--E 2290 + +--S 2291 of 2952 +--m0000:=a0000 - r0000 +--E 2291 + +--S 2292 of 2952 +--d0000:=D(m0000,x) +--E 2292 + +)clear all + +--S 2293 of 2952 +t0000:=(1+x)^(5/2)/(1-x)^(9/2) +--R +--R +--R 2 +-----+ +--R (x + 2x + 1)\|x + 1 +--R (1) ----------------------------------- +--R 4 3 2 +-------+ +--R (x - 4x + 6x - 4x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2293 + +--S 2294 of 2952 +r0000:=1/7*(1+x)^(7/2)/(1-x)^(7/2) +--R +--R +--R 3 2 +-----+ +--R (- x - 3x - 3x - 1)\|x + 1 +--R (2) -------------------------------- +--R 3 2 +-------+ +--R (7x - 21x + 21x - 7)\|- x + 1 +--R Type: Expression(Integer) +--E 2294 + +--S 2295 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R 3 2 +-------+ +-----+ 4 3 2 +--R (4x + 12x + 12x + 4)\|- x + 1 \|x + 1 - 5x + 20x - 30x + 20x - 5 +--R (3) ---------------------------------------------------------------------- +--R 4 3 2 +--R 28x - 112x + 168x - 112x + 28 +--R Type: Union(Expression(Integer),...) +--E 2295 + +--S 2296 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 5 +--R (4) - -- +--R 28 +--R Type: Expression(Integer) +--E 2296 + +--S 2297 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2297 + +)clear all + +--S 2298 of 2952 +t0000:=(1+x)^(5/2)/(1-x)^(11/2) +--R +--R +--R 2 +-----+ +--R (- x - 2x - 1)\|x + 1 +--R (1) ------------------------------------------- +--R 5 4 3 2 +-------+ +--R (x - 5x + 10x - 10x + 5x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2298 + +--S 2299 of 2952 +r0000:=1/9*(1+x)^(7/2)/(1-x)^(9/2)+1/63*(1+x)^(7/2)/(1-x)^(7/2) +--R +--R +--R 4 3 2 +-----+ +--R (- x + 5x + 21x + 23x + 8)\|x + 1 +--R (2) -------------------------------------------- +--R 4 3 2 +-------+ +--R (63x - 252x + 378x - 252x + 63)\|- x + 1 +--R Type: Expression(Integer) +--E 2299 + +--S 2300 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 2 +-------+ +-----+ 5 4 3 +--R (x - 5x - 21x - 23x - 8)\|- x + 1 \|x + 1 - 17x + 85x - 170x +--R + +--R 2 +--R 170x - 85x + 17 +--R / +--R 5 4 3 2 +--R 63x - 315x + 630x - 630x + 315x - 63 +--R Type: Union(Expression(Integer),...) +--E 2300 + +--S 2301 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 17 +--R (4) - -- +--R 63 +--R Type: Expression(Integer) +--E 2301 + +--S 2302 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2302 + +)clear all + +--S 2303 of 2952 +t0000:=(1+x)^(5/2)/(1-x)^(13/2) +--R +--R +--R 2 +-----+ +--R (x + 2x + 1)\|x + 1 +--R (1) -------------------------------------------------- +--R 6 5 4 3 2 +-------+ +--R (x - 6x + 15x - 20x + 15x - 6x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2303 + +--S 2304 of 2952 +r0000:=1/11*(1+x)^(7/2)/(1-x)^(11/2)+2/99*(1+x)^(7/2)/(1-x)^(9/2)+_ + 2/693*(1+x)^(7/2)/(1-x)^(7/2) +--R +--R +--R 5 4 3 2 +-----+ +--R (- 2x + 12x - 31x - 185x - 219x - 79)\|x + 1 +--R (2) ---------------------------------------------------------- +--R 5 4 3 2 +-------+ +--R (693x - 3465x + 6930x - 6930x + 3465x - 693)\|- x + 1 +--R Type: Expression(Integer) +--E 2304 + +--S 2305 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 3 2 +-------+ +-----+ 6 +--R (10x - 60x + 155x + 925x + 1095x + 395)\|- x + 1 \|x + 1 + 1027x +--R + +--R 5 4 3 2 +--R - 6162x + 15405x - 20540x + 15405x - 6162x + 1027 +--R / +--R 6 5 4 3 2 +--R 3465x - 20790x + 51975x - 69300x + 51975x - 20790x + 3465 +--R Type: Union(Expression(Integer),...) +--E 2305 + +--S 2306 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 1027 +--R (4) ---- +--R 3465 +--R Type: Expression(Integer) +--E 2306 + +--S 2307 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2307 + +)clear all + +--S 2308 of 2952 +t0000:=(1+x)^(5/2)/(1-x)^(15/2) +--R +--R +--R 2 +-----+ +--R (- x - 2x - 1)\|x + 1 +--R (1) --------------------------------------------------------- +--R 7 6 5 4 3 2 +-------+ +--R (x - 7x + 21x - 35x + 35x - 21x + 7x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2308 + +--S 2309 of 2952 +r0000:=1/13*(1+x)^(7/2)/(1-x)^(13/2)+3/143*(1+x)^(7/2)/(1-x)^(11/2)+_ + 2/429*(1+x)^(7/2)/(1-x)^(9/2)+2/3003*(1+x)^(7/2)/(1-x)^(7/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +-----+ +--R (- 2x + 14x - 43x + 77x + 659x + 833x + 310)\|x + 1 +--R -------------------------------------------------------------------------- +--R 6 5 4 3 2 +-------+ +--R (3003x - 18018x + 45045x - 60060x + 45045x - 18018x + 3003)\|- x + 1 +--R Type: Expression(Integer) +--E 2309 + +--S 2310 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +-------+ +-----+ +--R (2x - 14x + 43x - 77x - 659x - 833x - 310)\|- x + 1 \|x + 1 +--R + +--R 7 6 5 4 3 2 +--R - 4860x + 34020x - 102060x + 170100x - 170100x + 102060x - 34020x +--R + +--R 4860 +--R / +--R 7 6 5 4 3 2 +--R 3003x - 21021x + 63063x - 105105x + 105105x - 63063x + 21021x - 3003 +--R Type: Union(Expression(Integer),...) +--E 2310 + +--S 2311 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 1620 +--R (4) - ---- +--R 1001 +--R Type: Expression(Integer) +--E 2311 + +--S 2312 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2312 + +)clear all + +--S 2313 of 2952 +t0000:=(1+x)^(5/2)/(1-x)^(17/2) +--R +--R +--R 2 +-----+ +--R (x + 2x + 1)\|x + 1 +--R (1) ---------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +-------+ +--R (x - 8x + 28x - 56x + 70x - 56x + 28x - 8x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2313 + +--S 2314 of 2952 +r0000:=1/15*(1+x)^(7/2)/(1-x)^(15/2)+4/195*(1+x)^(7/2)/(1-x)^(13/2)+_ + 4/715*(1+x)^(7/2)/(1-x)^(11/2)+8/6435*(1+x)^(7/2)/(1-x)^(9/2)+_ + 8/45045*(1+x)^(7/2)/(1-x)^(7/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +-----+ +--R (- 8x + 64x - 228x + 480x - 675x - 8313x - 11101x - 4243)\|x + 1 +--R / +--R 7 6 5 4 3 2 +--R 45045x - 315315x + 945945x - 1576575x + 1576575x - 945945x +--R + +--R 315315x - 45045 +--R * +--R +-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 2314 + +--S 2315 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R (64x - 512x + 1824x - 3840x + 5400x + 66504x + 88808x + 33944) +--R * +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R + +--R 8 7 6 5 4 3 +--R 72131x - 577048x + 2019668x - 4039336x + 5049170x - 4039336x +--R + +--R 2 +--R 2019668x - 577048x + 72131 +--R / +--R 8 7 6 5 4 3 +--R 360360x - 2882880x + 10090080x - 20180160x + 25225200x - 20180160x +--R + +--R 2 +--R 10090080x - 2882880x + 360360 +--R Type: Union(Expression(Integer),...) +--E 2315 + +--S 2316 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 72131 +--R (4) ------ +--R 360360 +--R Type: Expression(Integer) +--E 2316 + +--S 2317 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2317 + +)clear all + +--S 2318 of 2952 +t0000:=(1+x)^(5/2)/(1-x)^(19/2) +--R +--R +--R (1) +--R 2 +-----+ +--R (- x - 2x - 1)\|x + 1 +--R ------------------------------------------------------------------------- +--R 9 8 7 6 5 4 3 2 +-------+ +--R (x - 9x + 36x - 84x + 126x - 126x + 84x - 36x + 9x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 2318 + +--S 2319 of 2952 +r0000:=1/17*(1+x)^(7/2)/(1-x)^(17/2)+1/51*(1+x)^(7/2)/(1-x)^(15/2)+_ + 4/663*(1+x)^(7/2)/(1-x)^(13/2)+4/2431*(1+x)^(7/2)/(1-x)^(11/2)+_ + 8/21879*(1+x)^(7/2)/(1-x)^(9/2)+8/153153*(1+x)^(7/2)/(1-x)^(7/2) +--R +--R +--R (2) +--R 8 7 6 5 4 3 2 +--R - 8x + 72x - 292x + 708x - 1155x + 1371x + 24239x + 33885x +--R + +--R 13252 +--R * +--R +-----+ +--R \|x + 1 +--R / +--R 8 7 6 5 4 3 +--R 153153x - 1225224x + 4288284x - 8576568x + 10720710x - 8576568x +--R + +--R 2 +--R 4288284x - 1225224x + 153153 +--R * +--R +-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 2319 + +--S 2320 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 8 7 6 5 4 3 2 +--R 24x - 216x + 876x - 2124x + 3465x - 4113x - 72717x - 101655x +--R + +--R - 39756 +--R * +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R + +--R 9 8 7 6 5 4 +--R 66260x - 596340x + 2385360x - 5565840x + 8348760x - 8348760x +--R + +--R 3 2 +--R 5565840x - 2385360x + 596340x - 66260 +--R / +--R 9 8 7 6 5 4 +--R 459459x - 4135131x + 16540524x - 38594556x + 57891834x - 57891834x +--R + +--R 3 2 +--R 38594556x - 16540524x + 4135131x - 459459 +--R Type: Union(Expression(Integer),...) +--E 2320 + +--S 2321 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 66260 +--R (4) ------ +--R 459459 +--R Type: Expression(Integer) +--E 2321 + +--S 2322 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2322 + +)clear all + +--S 2323 of 2952 +t0000:=(1-x)^(7/2)/(1+x)^(1/2) +--R +--R +--R 3 2 +-------+ +--R (- x + 3x - 3x + 1)\|- x + 1 +--R (1) ------------------------------- +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 2323 + +--S 2324 of 2952 +r0000:=35/8*asin(x)+35/24*(1-x)^(3/2)*sqrt(1+x)+7/12*(1-x)^(5/2)*sqrt(1+x)+_ + 1/4*(1-x)^(7/2)*sqrt(1+x)+35/8*sqrt(1-x)*sqrt(1+x) +--R +--R +--R 3 2 +-------+ +-----+ +--R (- 6x + 32x - 81x + 160)\|- x + 1 \|x + 1 + 105asin(x) +--R (2) --------------------------------------------------------- +--R 24 +--R Type: Expression(Integer) +--E 2324 + +--S 2325 of 2952 +--a0000:=integrate(t0000,x) +--E 2325 + +--S 2326 of 2952 +--m0000:=a0000 - r0000 +--E 2326 + +--S 2327 of 2952 +--d0000:=D(m0000,x) +--E 2327 + +)clear all + +--S 2328 of 2952 +t0000:=(1-x)^(5/2)/(1+x)^(1/2) +--R +--R +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R (1) ----------------------- +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 2328 + +--S 2329 of 2952 +r0000:=5/2*asin(x)+5/6*(1-x)^(3/2)*sqrt(1+x)+1/3*(1-x)^(5/2)*sqrt(1+x)+_ + 5/2*sqrt(1-x)*sqrt(1+x) +--R +--R +--R 2 +-------+ +-----+ +--R (2x - 9x + 22)\|- x + 1 \|x + 1 + 15asin(x) +--R (2) --------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 2329 + +--S 2330 of 2952 +--a0000:=integrate(t0000,x) +--E 2330 + +--S 2331 of 2952 +--m0000:=a0000 - r0000 +--E 2331 + +--S 2332 of 2952 +--d0000:=D(m0000,x) +--E 2332 + +)clear all + +--S 2333 of 2952 +t0000:=(1-x)^(3/2)/(1+x)^(1/2) +--R +--R +--R +-------+ +--R (- x + 1)\|- x + 1 +--R (1) ------------------- +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 2333 + +--S 2334 of 2952 +r0000:=3/2*asin(x)+1/2*(1-x)^(3/2)*sqrt(1+x)+3/2*sqrt(1-x)*sqrt(1+x) +--R +--R +--R +-------+ +-----+ +--R (- x + 4)\|- x + 1 \|x + 1 + 3asin(x) +--R (2) -------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 2334 + +--S 2335 of 2952 +--a0000:=integrate(t0000,x) +--E 2335 + +--S 2336 of 2952 +--m0000:=a0000 - r0000 +--E 2336 + +--S 2337 of 2952 +--d0000:=D(m0000,x) +--E 2337 + +)clear all + +--S 2338 of 2952 +t0000:=(1-x)^(1/2)/(1+x)^(1/2) +--R +--R +--R +-------+ +--R \|- x + 1 +--R (1) ---------- +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 2338 + +--S 2339 of 2952 +r0000:=asin(x)+sqrt(1-x)*sqrt(1+x) +--R +--R +--R +-------+ +-----+ +--R (2) \|- x + 1 \|x + 1 + asin(x) +--R Type: Expression(Integer) +--E 2339 + +--S 2340 of 2952 +--a0000:=integrate(t0000,x) +--E 2340 + +--S 2341 of 2952 +--m0000:=a0000 - r0000 +--E 2341 + +--S 2342 of 2952 +--d0000:=D(m0000,x) +--E 2342 + +)clear all + +--S 2343 of 2952 +t0000:=1/((1-x)^(1/2)*(1+x)^(1/2)) +--R +--R +--R 1 +--R (1) ------------------ +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2343 + +--S 2344 of 2952 +r0000:=asin(x) +--R +--R +--R (2) asin(x) +--R Type: Expression(Integer) +--E 2344 + +--S 2345 of 2952 +--a0000:=integrate(t0000,x) +--E 2345 + +--S 2346 of 2952 +--m0000:=a0000 - r0000 +--E 2346 + +--S 2347 of 2952 +--d0000:=D(m0000,x) +--E 2347 + +)clear all + +--S 2348 of 2952 +t0000:=1/((1-x)^(3/2)*(1+x)^(1/2)) +--R +--R +--R 1 +--R (1) - ------------------------- +--R +-------+ +-----+ +--R (x - 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2348 + +--S 2349 of 2952 +r0000:=sqrt(1+x)/sqrt(1-x) +--R +--R +--R +-----+ +--R \|x + 1 +--R (2) ---------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 2349 + +--S 2350 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-----+ +--R - \|- x + 1 \|x + 1 - x + 1 +--R (3) ---------------------------- +--R x - 1 +--R Type: Union(Expression(Integer),...) +--E 2350 + +--S 2351 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) - 1 +--R Type: Expression(Integer) +--E 2351 + +--S 2352 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2352 + +)clear all + +--S 2353 of 2952 +t0000:=1/((1-x)^(5/2)*(1+x)^(1/2)) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 2 +-------+ +-----+ +--R (x - 2x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2353 + +--S 2354 of 2952 +r0000:=1/3*sqrt(1+x)/(1-x)^(3/2)+1/3*sqrt(1+x)/sqrt(1-x) +--R +--R +--R +-----+ +--R (x - 2)\|x + 1 +--R (2) ------------------ +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 2354 + +--S 2355 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-----+ +--R (- x + 2)\|- x + 1 \|x + 1 +--R (3) --------------------------- +--R 2 +--R 3x - 6x + 3 +--R Type: Union(Expression(Integer),...) +--E 2355 + +--S 2356 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2356 + +--S 2357 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2357 + +)clear all + +--S 2358 of 2952 +t0000:=1/((1-x)^(7/2)*(1+x)^(1/2)) +--R +--R +--R 1 +--R (1) - ------------------------------------- +--R 3 2 +-------+ +-----+ +--R (x - 3x + 3x - 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2358 + +--S 2359 of 2952 +r0000:=1/5*sqrt(1+x)/(1-x)^(5/2)+2/15*sqrt(1+x)/(1-x)^(3/2)+_ + 2/15*sqrt(1+x)/sqrt(1-x) +--R +--R +--R 2 +-----+ +--R (2x - 6x + 7)\|x + 1 +--R (2) --------------------------- +--R 2 +-------+ +--R (15x - 30x + 15)\|- x + 1 +--R Type: Expression(Integer) +--E 2359 + +--S 2360 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R 2 +-------+ +-----+ 3 2 +--R (- 8x + 24x - 28)\|- x + 1 \|x + 1 - 35x + 105x - 105x + 35 +--R (3) --------------------------------------------------------------- +--R 3 2 +--R 60x - 180x + 180x - 60 +--R Type: Union(Expression(Integer),...) +--E 2360 + +--S 2361 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 7 +--R (4) - -- +--R 12 +--R Type: Expression(Integer) +--E 2361 + +--S 2362 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2362 + +)clear all + +--S 2363 of 2952 +t0000:=1/((1-x)^(9/2)*(1+x)^(1/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------- +--R 4 3 2 +-------+ +-----+ +--R (x - 4x + 6x - 4x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2363 + +--S 2364 of 2952 +r0000:=1/7*sqrt(1+x)/(1-x)^(7/2)+3/35*sqrt(1+x)/(1-x)^(5/2)+_ + 2/35*sqrt(1+x)/(1-x)^(3/2)+2/35*sqrt(1+x)/sqrt(1-x) +--R +--R +--R 3 2 +-----+ +--R (2x - 8x + 13x - 12)\|x + 1 +--R (2) ------------------------------------ +--R 3 2 +-------+ +--R (35x - 105x + 105x - 35)\|- x + 1 +--R Type: Expression(Integer) +--E 2364 + +--S 2365 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 +-------+ +-----+ 4 3 2 +--R (- 10x + 40x - 65x + 60)\|- x + 1 \|x + 1 + 156x - 624x + 936x +--R + +--R - 624x + 156 +--R / +--R 4 3 2 +--R 175x - 700x + 1050x - 700x + 175 +--R Type: Union(Expression(Integer),...) +--E 2365 + +--S 2366 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 156 +--R (4) --- +--R 175 +--R Type: Expression(Integer) +--E 2366 + +--S 2367 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2367 + +)clear all + +--S 2368 of 2952 +t0000:=1/((1-x)^(11/2)*(1+x)^(1/2)) +--R +--R +--R 1 +--R (1) - --------------------------------------------------- +--R 5 4 3 2 +-------+ +-----+ +--R (x - 5x + 10x - 10x + 5x - 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2368 + +--S 2369 of 2952 +r0000:=1/9*sqrt(1+x)/(1-x)^(9/2)+4/63*sqrt(1+x)/(1-x)^(7/2)+_ + 4/105*sqrt(1+x)/(1-x)^(5/2)+8/315*sqrt(1+x)/(1-x)^(3/2)+_ + 8/315*sqrt(1+x)/sqrt(1-x) +--R +--R +--R 4 3 2 +-----+ +--R (8x - 40x + 84x - 100x + 83)\|x + 1 +--R (2) ------------------------------------------------- +--R 4 3 2 +-------+ +--R (315x - 1260x + 1890x - 1260x + 315)\|- x + 1 +--R Type: Expression(Integer) +--E 2369 + +--S 2370 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 2 +-------+ +-----+ 5 4 +--R (- 8x + 40x - 84x + 100x - 83)\|- x + 1 \|x + 1 - 27x + 135x +--R + +--R 3 2 +--R - 270x + 270x - 135x + 27 +--R / +--R 5 4 3 2 +--R 315x - 1575x + 3150x - 3150x + 1575x - 315 +--R Type: Union(Expression(Integer),...) +--E 2370 + +--S 2371 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 3 +--R (4) - -- +--R 35 +--R Type: Expression(Integer) +--E 2371 + +--S 2372 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2372 + +)clear all + +--S 2373 of 2952 +t0000:=(1-x)^(7/2)/(1+x)^(3/2) +--R +--R +--R 3 2 +-------+ +--R (- x + 3x - 3x + 1)\|- x + 1 +--R (1) ------------------------------- +--R +-----+ +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 2373 + +--S 2374 of 2952 +r0000:=-35/2*asin(x)-2*(1-x)^(7/2)/sqrt(1+x)-_ + 35/6*(1-x)^(3/2)*sqrt(1+x)-7/3*(1-x)^(5/2)*sqrt(1+x)-_ + 35/2*sqrt(1-x)*sqrt(1+x) +--R +--R +--R +-----+ 3 2 +-------+ +--R - 105asin(x)\|x + 1 + (- 2x + 13x - 55x - 166)\|- x + 1 +--R (2) ----------------------------------------------------------- +--R +-----+ +--R 6\|x + 1 +--R Type: Expression(Integer) +--E 2374 + +--S 2375 of 2952 +--a0000:=integrate(t0000,x) +--E 2375 + +--S 2376 of 2952 +--m0000:=a0000 - r0000 +--E 2376 + +--S 2377 of 2952 +--d0000:=D(m0000,x) +--E 2377 + +)clear all + +--S 2378 of 2952 +t0000:=(1-x)^(5/2)/(1+x)^(3/2) +--R +--R +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R (1) ----------------------- +--R +-----+ +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 2378 + +--S 2379 of 2952 +r0000:=-15/2*asin(x)-2*(1-x)^(5/2)/sqrt(1+x)-_ + 5/2*(1-x)^(3/2)*sqrt(1+x)-15/2*sqrt(1-x)*sqrt(1+x) +--R +--R +--R +-----+ 2 +-------+ +--R - 15asin(x)\|x + 1 + (x - 7x - 24)\|- x + 1 +--R (2) ---------------------------------------------- +--R +-----+ +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 2379 + +--S 2380 of 2952 +--a0000:=integrate(t0000,x) +--E 2380 + +--S 2381 of 2952 +--m0000:=a0000 - r0000 +--E 2381 + +--S 2382 of 2952 +--d0000:=D(m0000,x) +--E 2382 + +)clear all + +--S 2383 of 2952 +t0000:=(1-x)^(3/2)/(1+x)^(3/2) +--R +--R +--R +-------+ +--R (- x + 1)\|- x + 1 +--R (1) ------------------- +--R +-----+ +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 2383 + +--S 2384 of 2952 +r0000:=-3*asin(x)-2*(1-x)^(3/2)/sqrt(1+x)-3*sqrt(1-x)*sqrt(1+x) +--R +--R +--R +-----+ +-------+ +--R - 3asin(x)\|x + 1 + (- x - 5)\|- x + 1 +--R (2) ---------------------------------------- +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 2384 + +--S 2385 of 2952 +--a0000:=integrate(t0000,x) +--E 2385 + +--S 2386 of 2952 +--m0000:=a0000 - r0000 +--E 2386 + +--S 2387 of 2952 +--d0000:=D(m0000,x) +--E 2387 + +)clear all + +--S 2388 of 2952 +t0000:=(1-x)^(1/2)/(1+x)^(3/2) +--R +--R +--R +-------+ +--R \|- x + 1 +--R (1) --------------- +--R +-----+ +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 2388 + +--S 2389 of 2952 +r0000:=-asin(x)-2*sqrt(1-x)/sqrt(1+x) +--R +--R +--R +-----+ +-------+ +--R - asin(x)\|x + 1 - 2\|- x + 1 +--R (2) ------------------------------- +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 2389 + +--S 2390 of 2952 +--a0000:=integrate(t0000,x) +--E 2390 + +--S 2391 of 2952 +--m0000:=a0000 - r0000 +--E 2391 + +--S 2392 of 2952 +--d0000:=D(m0000,x) +--E 2392 + +)clear all + +--S 2393 of 2952 +t0000:=1/((1-x)^(1/2)*(1+x)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------- +--R +-------+ +-----+ +--R (x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2393 + +--S 2394 of 2952 +r0000:=-sqrt(1-x)/sqrt(1+x) +--R +--R +--R +-------+ +--R \|- x + 1 +--R (2) - ---------- +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 2394 + +--S 2395 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-----+ +--R - 8\|- x + 1 \|x + 1 - 17x - 17 +--R (3) -------------------------------- +--R 8x + 8 +--R Type: Union(Expression(Integer),...) +--E 2395 + +--S 2396 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 17 +--R (4) - -- +--R 8 +--R Type: Expression(Integer) +--E 2396 + +--S 2397 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2397 + +)clear all + +--S 2398 of 2952 +t0000:=1/((1-x)^(3/2)*(1+x)^(3/2)) +--R +--R +--R 1 +--R (1) - -------------------------- +--R 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2398 + +--S 2399 of 2952 +r0000:=x/sqrt(1-x^2) +--R +--R +--R x +--R (2) ----------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 2399 + +--S 2400 of 2952 +--a0000:=integrate(t0000,x) +--E 2400 + +--S 2401 of 2952 +--m0000:=a0000 - r0000 +--E 2401 + +--S 2402 of 2952 +--d0000:=D(m0000,x) +--E 2402 + +)clear all + +--S 2403 of 2952 +t0000:=1/((1-x)^(5/2)*(1+x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 3 2 +-------+ +-----+ +--R (x - x - x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2403 + +--S 2404 of 2952 +r0000:=1/3/((1-x)^(3/2)*sqrt(1+x))+2/3*x/sqrt(1-x^2) +--R +--R +--R +--------+ +--R 2 +-------+ +-----+ | 2 +--R (2x - 2x)\|- x + 1 \|x + 1 - \|- x + 1 +--R (2) ------------------------------------------ +--R +--------+ +--R | 2 +-------+ +-----+ +--R (3x - 3)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2404 + +--S 2405 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +-------+ +-----+ 3 2 +--R (- 6x + 6x + 3)\|- x + 1 \|x + 1 - 5x + 5x + 5x - 5 +--R (3) ------------------------------------------------------- +--R 3 2 +--R 9x - 9x - 9x + 9 +--R Type: Union(Expression(Integer),...) +--E 2405 + +--S 2406 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ | 2 +--R (- 5\|- x + 1 - 6x)\|- x + 1 \|x + 1 + 6x\|- x + 1 +--R (4) ------------------------------------------------------- +--R +--------+ +--R | 2 +-------+ +-----+ +--R 9\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2406 + +-- TPDHERE +--S 2407 of 2952 +d0000:=D(m0000,x) +--R +--R +--R +--------+ +--R +-------+ +-----+ | 2 +--R 2\|- x + 1 \|x + 1 - 2\|- x + 1 +--R (5) -------------------------------------- +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R (3x - 3)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2407 + +)clear all + +--S 2408 of 2952 +t0000:=1/((1-x)^(7/2)*(1+x)^(3/2)) +--R +--R +--R 1 +--R (1) - ------------------------------------- +--R 4 3 +-------+ +-----+ +--R (x - 2x + 2x - 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2408 + +--S 2409 of 2952 +r0000:=1/5/((1-x)^(5/2)*sqrt(1+x))+1/5/((1-x)^(3/2)*sqrt(1+x))+_ + 2/5*x/sqrt(1-x^2) +--R +--R +--R +--------+ +--R 3 2 +-------+ +-----+ | 2 +--R (2x - 4x + 2x)\|- x + 1 \|x + 1 + (- x + 2)\|- x + 1 +--R (2) --------------------------------------------------------- +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R (5x - 10x + 5)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2409 + +--S 2410 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 2 +-------+ +-----+ 4 3 +--R (- 8x + 16x - 4x - 8)\|- x + 1 \|x + 1 - 17x + 34x - 34x + 17 +--R (3) ------------------------------------------------------------------ +--R 4 3 +--R 20x - 40x + 40x - 20 +--R Type: Union(Expression(Integer),...) +--E 2410 + +--S 2411 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ | 2 +--R (- 17\|- x + 1 - 8x)\|- x + 1 \|x + 1 + 8x\|- x + 1 +--R (4) -------------------------------------------------------- +--R +--------+ +--R | 2 +-------+ +-----+ +--R 20\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2411 + +-- TPDHERE +--S 2412 of 2952 +d0000:=D(m0000,x) +--R +--R +--R +--------+ +--R +-------+ +-----+ | 2 +--R 2\|- x + 1 \|x + 1 - 2\|- x + 1 +--R (5) -------------------------------------- +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R (5x - 5)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2412 + +)clear all + +--S 2413 of 2952 +t0000:=1/((1-x)^(9/2)*(1+x)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +-------+ +-----+ +--R (x - 3x + 2x + 2x - 3x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2413 + +--S 2414 of 2952 +r0000:=1/7/((1-x)^(7/2)*sqrt(1+x))+4/35/((1-x)^(5/2)*sqrt(1+x))+_ + 4/35/((1-x)^(3/2)*sqrt(1+x))+8/35*x/sqrt(1-x^2) +--R +--R +--R (2) +--R +--------+ +--R 4 3 2 +-------+ +-----+ 2 | 2 +--R (8x - 24x + 24x - 8x)\|- x + 1 \|x + 1 + (- 4x + 12x - 13)\|- x + 1 +--R -------------------------------------------------------------------------- +--R +--------+ +--R 3 2 | 2 +-------+ +-----+ +--R (35x - 105x + 105x - 35)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2414 + +--S 2415 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 2 +-------+ +-----+ 5 4 +--R (- 40x + 120x - 100x - 20x + 65)\|- x + 1 \|x + 1 + 169x - 507x +--R + +--R 3 2 +--R 338x + 338x - 507x + 169 +--R / +--R 5 4 3 2 +--R 175x - 525x + 350x + 350x - 525x + 175 +--R Type: Union(Expression(Integer),...) +--E 2415 + +--S 2416 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ | 2 +--R (169\|- x + 1 - 40x)\|- x + 1 \|x + 1 + 40x\|- x + 1 +--R (4) --------------------------------------------------------- +--R +--------+ +--R | 2 +-------+ +-----+ +--R 175\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2416 + +-- TPDHERE +--S 2417 of 2952 +d0000:=D(m0000,x) +--R +--R +--R +--------+ +--R +-------+ +-----+ | 2 +--R 8\|- x + 1 \|x + 1 - 8\|- x + 1 +--R (5) ---------------------------------------- +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R (35x - 35)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2417 + +)clear all + +--S 2418 of 2952 +t0000:=1/((1-x)^(11/2)*(1+x)^(3/2)) +--R +--R +--R 1 +--R (1) - ------------------------------------------------- +--R 6 5 4 2 +-------+ +-----+ +--R (x - 4x + 5x - 5x + 4x - 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2418 + +--S 2419 of 2952 +r0000:=1/9/((1-x)^(9/2)*sqrt(1+x))+5/63/((1-x)^(7/2)*sqrt(1+x))+_ + 4/63/((1-x)^(5/2)*sqrt(1+x))+4/63/((1-x)^(3/2)*sqrt(1+x))+_ + 8/63*x/sqrt(1-x^2) +--R +--R +--R (2) +--R 5 4 3 2 +-------+ +-----+ +--R (8x - 32x + 48x - 32x + 8x)\|- x + 1 \|x + 1 +--R + +--R +--------+ +--R 3 2 | 2 +--R (- 4x + 16x - 25x + 20)\|- x + 1 +--R / +--R +--------+ +--R 4 3 2 | 2 +-------+ +-----+ +--R (63x - 252x + 378x - 252x + 63)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2419 + +--S 2420 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 3 2 +-------+ +-----+ 6 +--R (- 24x + 96x - 132x + 48x + 51x - 60)\|- x + 1 \|x + 1 - 100x +--R + +--R 5 4 2 +--R 400x - 500x + 500x - 400x + 100 +--R / +--R 6 5 4 2 +--R 189x - 756x + 945x - 945x + 756x - 189 +--R Type: Union(Expression(Integer),...) +--E 2420 + +--S 2421 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ | 2 +--R (- 100\|- x + 1 - 24x)\|- x + 1 \|x + 1 + 24x\|- x + 1 +--R (4) ----------------------------------------------------------- +--R +--------+ +--R | 2 +-------+ +-----+ +--R 189\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2421 + +-- TPDHERE +--S 2422 of 2952 +d0000:=D(m0000,x) +--R +--R +--R +--------+ +--R +-------+ +-----+ | 2 +--R 8\|- x + 1 \|x + 1 - 8\|- x + 1 +--R (5) ---------------------------------------- +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R (63x - 63)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2422 + +)clear all + +--S 2423 of 2952 +t0000:=(1-x)^(9/2)/(1+x)^(5/2) +--R +--R +--R 4 3 2 +-------+ +--R (x - 4x + 6x - 4x + 1)\|- x + 1 +--R (1) ----------------------------------- +--R 2 +-----+ +--R (x + 2x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 2423 + +--S 2424 of 2952 +r0000:=-2/3*(1-x)^(9/2)/(1+x)^(3/2)+_ + 105/2*asin(x)+6*(1-x)^(7/2)/sqrt(1+x)+_ + 35/2*(1-x)^(3/2)*sqrt(1+x)+7*(1-x)^(5/2)*sqrt(1+x)+_ + 105/2*sqrt(1-x)*sqrt(1+x) +--R +--R +--R (2) +--R +-----+ 4 3 2 +-------+ +--R (315x + 315)asin(x)\|x + 1 + (2x - 17x + 102x + 679x + 494)\|- x + 1 +--R ------------------------------------------------------------------------- +--R +-----+ +--R (6x + 6)\|x + 1 +--R Type: Expression(Integer) +--E 2424 + +--S 2425 of 2952 +--a0000:=integrate(t0000,x) +--E 2425 + +--S 2426 of 2952 +--m0000:=a0000 - r0000 +--E 2426 + +--S 2427 of 2952 +--d0000:=D(m0000,x) +--E 2427 + +)clear all + +--S 2428 of 2952 +t0000:=(1-x)^(7/2)/(1+x)^(5/2) +--R +--R +--R 3 2 +-------+ +--R (- x + 3x - 3x + 1)\|- x + 1 +--R (1) ------------------------------- +--R 2 +-----+ +--R (x + 2x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 2428 + +--S 2429 of 2952 +r0000:=-2/3*(1-x)^(7/2)/(1+x)^(3/2)+_ + 35/2*asin(x)+14/3*(1-x)^(5/2)/sqrt(1+x)+_ + 35/6*(1-x)^(3/2)*sqrt(1+x)+35/2*sqrt(1-x)*sqrt(1+x) +--R +--R +--R +-----+ 3 2 +-------+ +--R (105x + 105)asin(x)\|x + 1 + (- 3x + 30x + 229x + 164)\|- x + 1 +--R (2) ------------------------------------------------------------------- +--R +-----+ +--R (6x + 6)\|x + 1 +--R Type: Expression(Integer) +--E 2429 + +--S 2430 of 2952 +--a0000:=integrate(t0000,x) +--E 2430 + +--S 2431 of 2952 +--m0000:=a0000 - r0000 +--E 2431 + +--S 2432 of 2952 +--d0000:=D(m0000,x) +--E 2432 + +)clear all + +--S 2433 of 2952 +t0000:=(1-x)^(5/2)/(1+x)^(5/2) +--R +--R +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R (1) ----------------------- +--R 2 +-----+ +--R (x + 2x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 2433 + +--S 2434 of 2952 +r0000:=-2/3*(1-x)^(5/2)/(1+x)^(3/2)+5*asin(x)+_ + 10/3*(1-x)^(3/2)/sqrt(1+x)+5*sqrt(1-x)*sqrt(1+x) +--R +--R +--R +-----+ 2 +-------+ +--R (15x + 15)asin(x)\|x + 1 + (3x + 34x + 23)\|- x + 1 +--R (2) ------------------------------------------------------ +--R +-----+ +--R (3x + 3)\|x + 1 +--R Type: Expression(Integer) +--E 2434 + +--S 2435 of 2952 +--a0000:=integrate(t0000,x) +--E 2435 + +--S 2436 of 2952 +--m0000:=a0000 - r0000 +--E 2436 + +--S 2437 of 2952 +--d0000:=D(m0000,x) +--E 2437 + +)clear all + +--S 2438 of 2952 +t0000:=(1-x)^(3/2)/(1+x)^(5/2) +--R +--R +--R +-------+ +--R (- x + 1)\|- x + 1 +--R (1) --------------------- +--R 2 +-----+ +--R (x + 2x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 2438 + +--S 2439 of 2952 +r0000:=-2/3*(1-x)^(3/2)/(1+x)^(3/2)+asin(x)+2*sqrt(1-x)/sqrt(1+x) +--R +--R +--R +-----+ +-------+ +--R (3x + 3)asin(x)\|x + 1 + (8x + 4)\|- x + 1 +--R (2) -------------------------------------------- +--R +-----+ +--R (3x + 3)\|x + 1 +--R Type: Expression(Integer) +--E 2439 + +--S 2440 of 2952 +--a0000:=integrate(t0000,x) +--E 2440 + +--S 2441 of 2952 +--m0000:=a0000 - r0000 +--E 2441 + +--S 2442 of 2952 +--d0000:=D(m0000,x) +--E 2442 + +)clear all + +--S 2443 of 2952 +t0000:=(1-x)^(1/2)/(1+x)^(5/2) +--R +--R +--R +-------+ +--R \|- x + 1 +--R (1) --------------------- +--R 2 +-----+ +--R (x + 2x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 2443 + +--S 2444 of 2952 +r0000:=-1/3*(1-x)^(3/2)/(1+x)^(3/2) +--R +--R +--R +-------+ +--R (x - 1)\|- x + 1 +--R (2) ----------------- +--R +-----+ +--R (3x + 3)\|x + 1 +--R Type: Expression(Integer) +--E 2444 + +--S 2445 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-----+ 2 +--R (8x - 8)\|- x + 1 \|x + 1 - 17x - 34x - 17 +--R (3) -------------------------------------------- +--R 2 +--R 24x + 48x + 24 +--R Type: Union(Expression(Integer),...) +--E 2445 + +--S 2446 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 17 +--R (4) - -- +--R 24 +--R Type: Expression(Integer) +--E 2446 + +--S 2447 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2447 + +)clear all + +--S 2448 of 2952 +t0000:=1/((1-x)^(1/2)*(1+x)^(5/2)) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 2 +-------+ +-----+ +--R (x + 2x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2448 + +--S 2449 of 2952 +r0000:=-1/3*sqrt(1-x)/(1+x)^(3/2)-1/3*sqrt(1-x)/sqrt(1+x) +--R +--R +--R +-------+ +--R (- x - 2)\|- x + 1 +--R (2) ------------------- +--R +-----+ +--R (3x + 3)\|x + 1 +--R Type: Expression(Integer) +--E 2449 + +--S 2450 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-----+ 2 +--R (- 3x - 6)\|- x + 1 \|x + 1 + 10x + 20x + 10 +--R (3) ---------------------------------------------- +--R 2 +--R 9x + 18x + 9 +--R Type: Union(Expression(Integer),...) +--E 2450 + +--S 2451 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 10 +--R (4) -- +--R 9 +--R Type: Expression(Integer) +--E 2451 + +--S 2452 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2452 + +)clear all + +--S 2453 of 2952 +t0000:=1/((1-x)^(3/2)*(1+x)^(5/2)) +--R +--R +--R 1 +--R (1) - ----------------------------------- +--R 3 2 +-------+ +-----+ +--R (x + x - x - 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2453 + +--S 2454 of 2952 +r0000:=1/((1+x)^(3/2)*sqrt(1-x))-2/3*sqrt(1-x)/(1+x)^(3/2)-_ + 2/3*sqrt(1-x)/sqrt(1+x) +--R +--R +--R 2 +--R 2x + 2x - 1 +--R (2) -------------------------- +--R +-------+ +-----+ +--R (3x + 3)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2454 + +--S 2455 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R 2 +-------+ +-----+ 3 2 +--R (- 18x - 18x + 9)\|- x + 1 \|x + 1 + 11x + 11x - 11x - 11 +--R (3) ------------------------------------------------------------- +--R 3 2 +--R 27x + 27x - 27x - 27 +--R Type: Union(Expression(Integer),...) +--E 2455 + +--S 2456 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R 11 +--R (4) -- +--R 27 +--R Type: Expression(Integer) +--E 2456 + +--S 2457 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2457 + +)clear all + +--S 2458 of 2952 +t0000:=1/((1-x)^(5/2)*(1+x)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 4 2 +-------+ +-----+ +--R (x - 2x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2458 + +--S 2459 of 2952 +r0000:=1/3*x/(1-x^2)^(3/2)+2/3*x/sqrt(1-x^2) +--R +--R +--R 3 +--R 2x - 3x +--R (2) -------------------- +--R +--------+ +--R 2 | 2 +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 2459 + +--S 2460 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 +-------+ +-----+ +--R (- 2x + 3x)\|- x + 1 \|x + 1 +--R (3) ------------------------------ +--R 4 2 +--R 3x - 6x + 3 +--R Type: Union(Expression(Integer),...) +--E 2460 + +--S 2461 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +--------+ +--R 3 | 2 +-------+ +-----+ 5 3 +--R (- 2x + 3x)\|- x + 1 \|- x + 1 \|x + 1 - 2x + 5x - 3x +--R (4) ---------------------------------------------------------- +--R +--------+ +--R 4 2 | 2 +--R (3x - 6x + 3)\|- x + 1 +--R Type: Expression(Integer) +--E 2461 + +-- TPDHERE +--S 2462 of 2952 +d0000:=D(m0000,x) +--R +--R +--R +--------+ +--R +-------+ +-----+ | 2 +--R - \|- x + 1 \|x + 1 + \|- x + 1 +--R (5) ------------------------------------------- +--R +--------+ +--R 4 2 | 2 +-------+ +-----+ +--R (x - 2x + 1)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2462 + +)clear all + +--S 2463 of 2952 +t0000:=1/((1-x)^(7/2)*(1+x)^(5/2)) +--R +--R +--R 1 +--R (1) - ----------------------------------------------- +--R 5 4 3 2 +-------+ +-----+ +--R (x - x - 2x + 2x + x - 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2463 + +--S 2464 of 2952 +r0000:=1/5/((1-x)^(5/2)*(1+x)^(3/2))+4/15*x/(1-x^2)^(3/2)+8/15*x/sqrt(1-x^2) +--R +--R +--R +--------+ +--R 4 3 2 +-------+ +-----+ | 2 +--R (8x - 8x - 12x + 12x)\|- x + 1 \|x + 1 + 3\|- x + 1 +--R (2) --------------------------------------------------------- +--R +--------+ +--R 3 2 | 2 +-------+ +-----+ +--R (15x - 15x - 15x + 15)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2464 + +--S 2465 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 3 2 +-------+ +-----+ 5 4 3 +--R (- 32x + 32x + 48x - 48x - 12)\|- x + 1 \|x + 1 + 15x - 15x - 30x +--R + +--R 2 +--R 30x + 15x - 15 +--R / +--R 5 4 3 2 +--R 60x - 60x - 120x + 120x + 60x - 60 +--R Type: Union(Expression(Integer),...) +--E 2465 + +--S 2466 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +--------+ +--R 2 | 2 3 +-------+ +-----+ +--R ((15x - 15)\|- x + 1 - 32x + 48x)\|- x + 1 \|x + 1 +--R + +--R +--------+ +--R 3 | 2 +--R (32x - 48x)\|- x + 1 +--R / +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R (60x - 60)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2466 + +-- TPDHERE +--S 2467 of 2952 +d0000:=D(m0000,x) +--R +--R +--R +--------+ +--R +-------+ +-----+ | 2 +--R - 4\|- x + 1 \|x + 1 + 4\|- x + 1 +--R (5) --------------------------------------------- +--R +--------+ +--R 4 2 | 2 +-------+ +-----+ +--R (5x - 10x + 5)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2467 + +)clear all + +--S 2468 of 2952 +t0000:=1/((1-x)^(9/2)*(1+x)^(5/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +-------+ +-----+ +--R (x - 2x - x + 4x - x - 2x + 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2468 + +--S 2469 of 2952 +r0000:=1/7/((1-x)^(7/2)*(1+x)^(3/2))+1/7/((1-x)^(5/2)*(1+x)^(3/2))+_ + 4/21*x/(1-x^2)^(3/2)+8/21*x/sqrt(1-x^2) +--R +--R +--R (2) +--R +--------+ +--R 5 4 3 2 +-------+ +-----+ | 2 +--R (8x - 16x - 4x + 24x - 12x)\|- x + 1 \|x + 1 + (3x - 6)\|- x + 1 +--R ----------------------------------------------------------------------- +--R +--------+ +--R 4 3 | 2 +-------+ +-----+ +--R (21x - 42x + 42x - 21)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2469 + +--S 2470 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 5 4 3 2 +-------+ +-----+ 6 5 +--R (- 16x + 32x + 8x - 48x + 18x + 12)\|- x + 1 \|x + 1 + 15x - 30x +--R + +--R 4 3 2 +--R - 15x + 60x - 15x - 30x + 15 +--R / +--R 6 5 4 3 2 +--R 42x - 84x - 42x + 168x - 42x - 84x + 42 +--R Type: Union(Expression(Integer),...) +--E 2470 + +--S 2471 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +--------+ +--R 2 | 2 3 +-------+ +-----+ +--R ((15x - 15)\|- x + 1 - 16x + 24x)\|- x + 1 \|x + 1 +--R + +--R +--------+ +--R 3 | 2 +--R (16x - 24x)\|- x + 1 +--R / +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R (42x - 42)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2471 + +-- TPDHERE +--S 2472 of 2952 +d0000:=D(m0000,x) +--R +--R +--R +--------+ +--R +-------+ +-----+ | 2 +--R - 4\|- x + 1 \|x + 1 + 4\|- x + 1 +--R (5) --------------------------------------------- +--R +--------+ +--R 4 2 | 2 +-------+ +-----+ +--R (7x - 14x + 7)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2472 + +)clear all + +--S 2473 of 2952 +t0000:=1/((1-x)^(11/2)*(1+x)^(5/2)) +--R +--R +--R 1 +--R (1) - ----------------------------------------------------------- +--R 7 6 5 4 3 2 +-------+ +-----+ +--R (x - 3x + x + 5x - 5x - x + 3x - 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2473 + +--S 2474 of 2952 +r0000:=1/9/((1-x)^(9/2)*(1+x)^(3/2))+2/21/((1-x)^(7/2)*(1+x)^(3/2))+_ + 2/21/((1-x)^(5/2)*(1+x)^(3/2))+8/63*x/(1-x^2)^(3/2)+16/63*x/sqrt(1-x^2) +--R +--R +--R (2) +--R 6 5 4 3 2 +-------+ +-----+ +--R (16x - 48x + 24x + 56x - 72x + 24x)\|- x + 1 \|x + 1 +--R + +--R +--------+ +--R 2 | 2 +--R (6x - 18x + 19)\|- x + 1 +--R / +--R +--------+ +--R 5 4 3 2 | 2 +-------+ +-----+ +--R (63x - 189x + 126x + 126x - 189x + 63)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2474 + +--S 2475 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +-------+ +-----+ +--R (- 80x + 240x - 120x - 280x + 330x - 30x - 95)\|- x + 1 \|x + 1 +--R + +--R 7 6 5 4 3 2 +--R 247x - 741x + 247x + 1235x - 1235x - 247x + 741x - 247 +--R / +--R 7 6 5 4 3 2 +--R 315x - 945x + 315x + 1575x - 1575x - 315x + 945x - 315 +--R Type: Union(Expression(Integer),...) +--E 2475 + +--S 2476 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +--------+ +--R 2 | 2 3 +-------+ +-----+ +--R ((247x - 247)\|- x + 1 - 80x + 120x)\|- x + 1 \|x + 1 +--R + +--R +--------+ +--R 3 | 2 +--R (80x - 120x)\|- x + 1 +--R / +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R (315x - 315)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2476 + +-- TPDHERE +--S 2477 of 2952 +d0000:=D(m0000,x) +--R +--R +--R +--------+ +--R +-------+ +-----+ | 2 +--R - 8\|- x + 1 \|x + 1 + 8\|- x + 1 +--R (5) ----------------------------------------------- +--R +--------+ +--R 4 2 | 2 +-------+ +-----+ +--R (21x - 42x + 21)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 2477 + +)clear all + +--S 2478 of 2952 +t0000:=(3-x)^(3/2)*(-2+x)^(3/2) +--R +--R +--R 2 +-------+ +-----+ +--R (1) (- x + 5x - 6)\|- x + 3 \|x - 2 +--R Type: Expression(Integer) +--E 2478 + +--S 2479 of 2952 +r0000:=-1/8*(5-2*x)*(-6+5*x-x^2)^(3/2)-3/128*asin(5-2*x)-_ + 3/64*(5-2*x)*sqrt(-6+5*x-x^2) +--R +--R +--R +-------------+ +--R 3 2 | 2 +--R (- 32x + 240x - 580x + 450)\|- x + 5x - 6 + 3asin(2x - 5) +--R (2) ------------------------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 2479 + +--S 2480 of 2952 +--a0000:=integrate(t0000,x) +--E 2480 + +--S 2481 of 2952 +--m0000:=a0000 - r0000 +--E 2481 + +--S 2482 of 2952 +--d0000:=D(m0000,x) +--E 2482 + +)clear all + +--S 2483 of 2952 +t0000:=sqrt(3-x)*sqrt(-2+x) +--R +--R +--R +-------+ +-----+ +--R (1) \|- x + 3 \|x - 2 +--R Type: Expression(Integer) +--E 2483 + +--S 2484 of 2952 +r0000:=-1/8*asin(5-2*x)-1/4*(5-2*x)*sqrt(-6+5*x-x^2) +--R +--R +--R +-------------+ +--R | 2 +--R (4x - 10)\|- x + 5x - 6 + asin(2x - 5) +--R (2) ---------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 2484 + +--S 2485 of 2952 +--a0000:=integrate(t0000,x) +--E 2485 + +--S 2486 of 2952 +--m0000:=a0000 - r0000 +--E 2486 + +--S 2487 of 2952 +--d0000:=D(m0000,x) +--E 2487 + +)clear all + +--S 2488 of 2952 +t0000:=1/(sqrt(3-x)*sqrt(-2+x)) +--R +--R +--R 1 +--R (1) ------------------ +--R +-------+ +-----+ +--R \|- x + 3 \|x - 2 +--R Type: Expression(Integer) +--E 2488 + +--S 2489 of 2952 +r0000:=-asin(5-2*x) +--R +--R +--R (2) asin(2x - 5) +--R Type: Expression(Integer) +--E 2489 + +--S 2490 of 2952 +--a0000:=integrate(t0000,x) +--E 2490 + +--S 2491 of 2952 +--m0000:=a0000 - r0000 +--E 2491 + +--S 2492 of 2952 +--d0000:=D(m0000,x) +--E 2492 + +)clear all + +--S 2493 of 2952 +t0000:=1/((3-x)^(3/2)*(-2+x)^(3/2)) +--R +--R +--R 1 +--R (1) - ------------------------------- +--R 2 +-------+ +-----+ +--R (x - 5x + 6)\|- x + 3 \|x - 2 +--R Type: Expression(Integer) +--E 2493 + +--S 2494 of 2952 +r0000:=-2*(5-2*x)/sqrt(-6+5*x-x^2) +--R +--R +--R 4x - 10 +--R (2) ---------------- +--R +-------------+ +--R | 2 +--R \|- x + 5x - 6 +--R Type: Expression(Integer) +--E 2494 + +--S 2495 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R +-------+ +-----+ 2 +--R (- 24x + 60)\|- x + 3 \|x - 2 + 5x - 25x + 30 +--R (3) ----------------------------------------------- +--R 2 +--R 6x - 30x + 36 +--R Type: Union(Expression(Integer),...) +--E 2495 + +--S 2496 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-------------+ +--R | 2 +-------+ +-----+ +--R (- 24x + 60)\|- x + 5x - 6 \|- x + 3 \|x - 2 +--R + +--R +-------------+ +--R 2 | 2 3 2 +--R (5x - 25x + 30)\|- x + 5x - 6 - 24x + 180x - 444x + 360 +--R / +--R +-------------+ +--R 2 | 2 +--R (6x - 30x + 36)\|- x + 5x - 6 +--R Type: Expression(Integer) +--E 2496 + +-- TPDHERE +--S 2497 of 2952 +d0000:=D(m0000,x) +--R +--R +--R +-------------+ +--R +-------+ +-----+ | 2 +--R \|- x + 3 \|x - 2 - \|- x + 5x - 6 +--R (5) ----------------------------------------------- +--R +-------------+ +--R 2 | 2 +-------+ +-----+ +--R (x - 5x + 6)\|- x + 5x - 6 \|- x + 3 \|x - 2 +--R Type: Expression(Integer) +--E 2497 + +)clear all + +--S 2498 of 2952 +t0000:=1/((3-x)^(5/2)*(-2+x)^(5/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------------- +--R 4 3 2 +-------+ +-----+ +--R (x - 10x + 37x - 60x + 36)\|- x + 3 \|x - 2 +--R Type: Expression(Integer) +--E 2498 + +--S 2499 of 2952 +r0000:=-2/3*(5-2*x)/(-6+5*x-x^2)^(3/2)-16/3*(5-2*x)/sqrt(-6+5*x-x^2) +--R +--R +--R 3 2 +--R 32x - 240x + 588x - 470 +--R (2) -------------------------------- +--R +-------------+ +--R 2 | 2 +--R (3x - 15x + 18)\|- x + 5x - 6 +--R Type: Expression(Integer) +--E 2499 + +--S 2500 of 2952 ok to fail, differs by a constant +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 2 +-------+ +-----+ 4 3 +--R (- 1152x + 8640x - 21168x + 16920)\|- x + 3 \|x - 2 + 235x - 2350x +--R + +--R 2 +--R 8695x - 14100x + 8460 +--R / +--R 4 3 2 +--R 108x - 1080x + 3996x - 6480x + 3888 +--R Type: Union(Expression(Integer),...) +--E 2500 + +--S 2501 of 2952 ok to fail, differs by a constant +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R +-------------+ +--R 3 2 | 2 +-------+ +-----+ +--R (- 1152x + 8640x - 21168x + 16920)\|- x + 5x - 6 \|- x + 3 \|x - 2 +--R + +--R +-------------+ +--R 4 3 2 | 2 5 +--R (235x - 2350x + 8695x - 14100x + 8460)\|- x + 5x - 6 - 1152x +--R + +--R 4 3 2 +--R 14400x - 71280x + 174600x - 211608x + 101520 +--R / +--R +-------------+ +--R 4 3 2 | 2 +--R (108x - 1080x + 3996x - 6480x + 3888)\|- x + 5x - 6 +--R Type: Expression(Integer) +--E 2501 + +-- TPDHERE +--S 2502 of 2952 +d0000:=D(m0000,x) +--R +--R +--R +-------------+ +--R +-------+ +-----+ | 2 +--R - \|- x + 3 \|x - 2 + \|- x + 5x - 6 +--R (5) --------------------------------------------------------------- +--R +-------------+ +--R 4 3 2 | 2 +-------+ +-----+ +--R (x - 10x + 37x - 60x + 36)\|- x + 5x - 6 \|- x + 3 \|x - 2 +--R Type: Expression(Integer) +--E 2502 + +)clear all + +--S 2503 of 2952 +t0000:=(c+d*x)^(5/4)/(a+b*x)^(1/4) +--R +--R +--R 4+-------+ +--R (d x + c)\|d x + c +--R (1) ------------------- +--R 4+-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 2503 + +--S 2504 of 2952 +r0000:=5/8*(b*c-a*d)*(a+b*x)^(3/4)*(c+d*x)^(1/4)/b^2+_ + 1/2*(a+b*x)^(3/4)*(c+d*x)^(5/4)/b-_ + 5/16*(b*c-a*d)^2*atan(d^(1/4)*(a+b*x)^(1/4)/_ + (b^(1/4)*(c+d*x)^(1/4)))/(b^(9/4)*d^(3/4))+_ + 5/16*(b*c-a*d)^2*atanh(d^(1/4)*(a+b*x)^(1/4)/_ + (b^(1/4)*(c+d*x)^(1/4)))/(b^(9/4)*d^(3/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ +--R 2 2 2 2 \|d \|b x + a +--R (5a d - 10a b c d + 5b c )atanh(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+4+-------+ +--R 2 2 2 2 \|d \|b x + a +--R (- 5a d + 10a b c d - 5b c )atan(--------------) +--R 4+-+4+-------+ +--R \|b \|d x + c +--R + +--R 4+-+4+-+3 4+-------+3 4+-------+ +--R (8b d x - 10a d + 18b c)\|b \|d \|b x + a \|d x + c +--R / +--R 2 4+-+4+-+3 +--R 16b \|b \|d +--R Type: Expression(Integer) +--E 2504 + +--S 2505 of 2952 +--a0000:=integrate(t0000,x) +--E 2505 + +--S 2506 of 2952 +--m0000:=a0000 - r0000 +--E 2506 + +--S 2507 of 2952 +--d0000:=D(m0000,x) +--E 2507 + +)clear all + +--S 2508 of 2952 +t0000:=(c+d*x)^(1/4)/(a+b*x)^(1/4) +--R +--R +--R 4+-------+ +--R \|d x + c +--R (1) ---------- +--R 4+-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 2508 + +--S 2509 of 2952 +r0000:=(a+b*x)^(3/4)*(c+d*x)^(1/4)/b-_ + 1/2*(b*c-a*d)*atan(d^(1/4)*(a+b*x)^(1/4)/_ + (b^(1/4)*(c+d*x)^(1/4)))/(b^(5/4)*d^(3/4))+_ + 1/2*(b*c-a*d)*atanh(d^(1/4)*(a+b*x)^(1/4)/_ + (b^(1/4)*(c+d*x)^(1/4)))/(b^(5/4)*d^(3/4)) +--R +--R +--R (2) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|d \|b x + a \|d \|b x + a +--R (- a d + b c)atanh(--------------) + (a d - b c)atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|b \|d x + c \|b \|d x + c +--R + +--R 4+-+4+-+3 4+-------+3 4+-------+ +--R 2\|b \|d \|b x + a \|d x + c +--R / +--R 4+-+4+-+3 +--R 2b\|b \|d +--R Type: Expression(Integer) +--E 2509 + +--S 2510 of 2952 +--a0000:=integrate(t0000,x) +--E 2510 + +--S 2511 of 2952 +--m0000:=a0000 - r0000 +--E 2511 + +--S 2512 of 2952 +--d0000:=D(m0000,x) +--E 2512 + +)clear all + +--S 2513 of 2952 +t0000:=1/((a+b*x)^(1/4)*(c+d*x)^(3/4)) +--R +--R +--R 1 +--R (1) --------------------- +--R 4+-------+4+-------+3 +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 2513 + +--S 2514 of 2952 +r0000:=-2*atan(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*_ + (c+d*x)^(1/4)))/(b^(1/4)*d^(3/4))+_ + 2*atanh(d^(1/4)*(a+b*x)^(1/4)/(b^(1/4)*(c+d*x)^(1/4)))/(b^(1/4)*d^(3/4)) +--R +--R +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|d \|b x + a \|d \|b x + a +--R 2atanh(--------------) - 2atan(--------------) +--R 4+-+4+-------+ 4+-+4+-------+ +--R \|b \|d x + c \|b \|d x + c +--R (2) ---------------------------------------------- +--R 4+-+4+-+3 +--R \|b \|d +--R Type: Expression(Integer) +--E 2514 + +--S 2515 of 2952 +--a0000:=integrate(t0000,x) +--E 2515 + +--S 2516 of 2952 +--m0000:=a0000 - r0000 +--E 2516 + +--S 2517 of 2952 +--d0000:=D(m0000,x) +--E 2517 + +)clear all + +--S 2518 of 2952 +t0000:=1/((a+b*x)^(1/4)*(c+d*x)^(7/4)) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 4+-------+4+-------+3 +--R (d x + c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 2518 + +--S 2519 of 2952 +r0000:=4/3*(a+b*x)^(3/4)/((b*c-a*d)*(c+d*x)^(3/4)) +--R +--R +--R 4+-------+3 +--R 4\|b x + a +--R (2) - ------------------------ +--R 4+-------+3 +--R (3a d - 3b c)\|d x + c +--R Type: Expression(Integer) +--E 2519 + +--S 2520 of 2952 +--a0000:=integrate(t0000,x) +--E 2520 + +--S 2521 of 2952 +--m0000:=a0000 - r0000 +--E 2521 + +--S 2522 of 2952 +--d0000:=D(m0000,x) +--E 2522 + +)clear all + +--S 2523 of 2952 +t0000:=1/((a+b*x)^(1/4)*(c+d*x)^(11/4)) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 2 2 2 4+-------+4+-------+3 +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 2523 + +--S 2524 of 2952 +r0000:=4/7*(a+b*x)^(3/4)/((b*c-a*d)*(c+d*x)^(7/4))+_ + 16/21*b*(a+b*x)^(3/4)/((b*c-a*d)^2*(c+d*x)^(3/4)) +--R +--R +--R (2) +--R 4+-------+3 +--R (16b d x - 12a d + 28b c)\|b x + a +--R ----------------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 4+-------+3 +--R ((21a d - 42a b c d + 21b c d)x + 21a c d - 42a b c d + 21b c )\|d x + c +--R Type: Expression(Integer) +--E 2524 + +--S 2525 of 2952 +--a0000:=integrate(t0000,x) +--E 2525 + +--S 2526 of 2952 +--m0000:=a0000 - r0000 +--E 2526 + +--S 2527 of 2952 +--d0000:=D(m0000,x) +--E 2527 + +)clear all + +--S 2528 of 2952 +t0000:=1/((a+b*x)^(1/4)*(c+d*x)^(15/4)) +--R +--R +--R 1 +--R (1) --------------------------------------------------- +--R 3 3 2 2 2 3 4+-------+4+-------+3 +--R (d x + 3c d x + 3c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 2528 + +--S 2529 of 2952 +r0000:=4/11*(a+b*x)^(3/4)/((b*c-a*d)*(c+d*x)^(11/4))+_ + 32/77*b*(a+b*x)^(3/4)/((b*c-a*d)^2*(c+d*x)^(7/4))+_ + 128/231*b^2*(a+b*x)^(3/4)/((b*c-a*d)^3*(c+d*x)^(3/4)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 128b d x + (96a b d - 352b c d)x - 84a d + 264a b c d - 308b c ) +--R * +--R 4+-------+3 +--R \|b x + a +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (231a d - 693a b c d + 693a b c d - 231b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (462a c d - 1386a b c d + 1386a b c d - 462b c d)x + 231a c d +--R + +--R 2 3 2 2 4 3 5 +--R - 693a b c d + 693a b c d - 231b c +--R * +--R 4+-------+3 +--R \|d x + c +--R Type: Expression(Integer) +--E 2529 + +--S 2530 of 2952 +--a0000:=integrate(t0000,x) +--E 2530 + +--S 2531 of 2952 +--m0000:=a0000 - r0000 +--E 2531 + +--S 2532 of 2952 +--d0000:=D(m0000,x) +--E 2532 + +)clear all + +--S 2533 of 2952 +t0000:=(a+b*x)^3*(c+d*x)^n +--R +--R +--R 3 3 2 2 2 3 n +--R (1) (b x + 3a b x + 3a b x + a )(d x + c) +--R Type: Expression(Integer) +--E 2533 + +--S 2534 of 2952 +r0000:=-(b*c-a*d)^3*(c+d*x)^(1+n)/(d^4*(1+n))+_ + 3*b*(b*c-a*d)^2*(c+d*x)^(2+n)/(d^4*(2+n))-_ + 3*b^2*(b*c-a*d)*(c+d*x)^(3+n)/(d^4*(3+n))+b^3*(c+d*x)^(4+n)/(d^4*(4+n)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 n + 4 +--R (b n + 6b n + 11b n + 6b )(d x + c) +--R + +--R 2 3 3 2 3 2 2 3 +--R (3a b d - 3b c)n + (21a b d - 21b c)n + (42a b d - 42b c)n +--R + +--R 2 3 +--R 24a b d - 24b c +--R * +--R n + 3 +--R (d x + c) +--R + +--R 2 2 2 3 2 3 2 2 2 3 2 2 +--R (3a b d - 6a b c d + 3b c )n + (24a b d - 48a b c d + 24b c )n +--R + +--R 2 2 2 3 2 2 2 2 3 2 +--R (57a b d - 114a b c d + 57b c )n + 36a b d - 72a b c d + 36b c +--R * +--R n + 2 +--R (d x + c) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (9a d - 27a b c d + 27a b c d - 9b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (26a d - 78a b c d + 78a b c d - 26b c )n + 24a d - 72a b c d +--R + +--R 2 2 3 3 +--R 72a b c d - 24b c +--R * +--R n + 1 +--R (d x + c) +--R / +--R 4 4 4 3 4 2 4 4 +--R d n + 10d n + 35d n + 50d n + 24d +--R Type: Expression(Integer) +--E 2534 + +--S 2535 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 4 3 3 4 2 3 4 3 4 4 +--R (b d n + 6b d n + 11b d n + 6b d )x +--R + +--R 2 4 3 3 3 2 4 3 3 2 +--R (3a b d + b c d )n + (21a b d + 3b c d )n +--R + +--R 2 4 3 3 2 4 +--R (42a b d + 2b c d )n + 24a b d +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 3 2 4 2 3 3 2 2 2 +--R (3a b d + 3a b c d )n + (24a b d + 15a b c d - 3b c d )n +--R + +--R 2 4 2 3 3 2 2 2 4 +--R (57a b d + 12a b c d - 3b c d )n + 36a b d +--R * +--R 2 +--R x +--R + +--R 3 4 2 3 3 3 4 2 3 2 2 2 2 +--R (a d + 3a b c d )n + (9a d + 21a b c d - 6a b c d )n +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 +--R (26a d + 36a b c d - 24a b c d + 6b c d)n + 24a d +--R * +--R x +--R + +--R 3 3 3 3 3 2 2 2 2 +--R a c d n + (9a c d - 3a b c d )n +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (26a c d - 21a b c d + 6a b c d)n + 24a c d - 36a b c d + 24a b c d +--R + +--R 3 4 +--R - 6b c +--R * +--R n log(d x + c) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R d n + 10d n + 35d n + 50d n + 24d +--R Type: Union(Expression(Integer),...) +--E 2535 + +--S 2536 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 4 3 3 4 2 3 4 3 4 4 +--R (b d n + 6b d n + 11b d n + 6b d )x +--R + +--R 2 4 3 3 3 2 4 3 3 2 +--R (3a b d + b c d )n + (21a b d + 3b c d )n +--R + +--R 2 4 3 3 2 4 +--R (42a b d + 2b c d )n + 24a b d +--R * +--R 3 +--R x +--R + +--R 2 4 2 3 3 2 4 2 3 3 2 2 2 +--R (3a b d + 3a b c d )n + (24a b d + 15a b c d - 3b c d )n +--R + +--R 2 4 2 3 3 2 2 2 4 +--R (57a b d + 12a b c d - 3b c d )n + 36a b d +--R * +--R 2 +--R x +--R + +--R 3 4 2 3 3 3 4 2 3 2 2 2 2 +--R (a d + 3a b c d )n + (9a d + 21a b c d - 6a b c d )n +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 +--R (26a d + 36a b c d - 24a b c d + 6b c d)n + 24a d +--R * +--R x +--R + +--R 3 3 3 3 3 2 2 2 2 +--R a c d n + (9a c d - 3a b c d )n +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 +--R (26a c d - 21a b c d + 6a b c d)n + 24a c d - 36a b c d +--R + +--R 2 3 3 4 +--R 24a b c d - 6b c +--R * +--R n log(d x + c) +--R %e +--R + +--R 3 3 3 2 3 3 n + 4 +--R (- b n - 6b n - 11b n - 6b )(d x + c) +--R + +--R 2 3 3 2 3 2 2 3 +--R (- 3a b d + 3b c)n + (- 21a b d + 21b c)n + (- 42a b d + 42b c)n +--R + +--R 2 3 +--R - 24a b d + 24b c +--R * +--R n + 3 +--R (d x + c) +--R + +--R 2 2 2 3 2 3 +--R (- 3a b d + 6a b c d - 3b c )n +--R + +--R 2 2 2 3 2 2 +--R (- 24a b d + 48a b c d - 24b c )n +--R + +--R 2 2 2 3 2 2 2 2 3 2 +--R (- 57a b d + 114a b c d - 57b c )n - 36a b d + 72a b c d - 36b c +--R * +--R n + 2 +--R (d x + c) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a d + 3a b c d - 3a b c d + b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 9a d + 27a b c d - 27a b c d + 9b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (- 26a d + 78a b c d - 78a b c d + 26b c )n - 24a d + 72a b c d +--R + +--R 2 2 3 3 +--R - 72a b c d + 24b c +--R * +--R n + 1 +--R (d x + c) +--R / +--R 4 4 4 3 4 2 4 4 +--R d n + 10d n + 35d n + 50d n + 24d +--R Type: Expression(Integer) +--E 2536 + +--S 2537 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 3 3 3 2 3 2 2 3 3 3 n log(d x + c) 3 n + 3 +--R (b d x + 3a b d x + 3a b d x + a d )%e - b (d x + c) +--R + +--R 2 3 n + 2 +--R (- 3a b d + 3b c)(d x + c) +--R + +--R 2 2 2 3 2 n + 1 +--R (- 3a b d + 6a b c d - 3b c )(d x + c) +--R + +--R 3 3 2 2 2 2 3 3 n +--R (- a d + 3a b c d - 3a b c d + b c )(d x + c) +--R / +--R 3 +--R d +--R Type: Expression(Integer) +--E 2537 + +)clear all + +--S 2538 of 2952 +t0000:=(a+b*x)^2*(c+d*x)^n +--R +--R +--R 2 2 2 n +--R (1) (b x + 2a b x + a )(d x + c) +--R Type: Expression(Integer) +--E 2538 + +--S 2539 of 2952 +r0000:=(b*c-a*d)^2*(c+d*x)^(1+n)/(d^3*(1+n))-_ + 2*b*(b*c-a*d)*(c+d*x)^(2+n)/(d^3*(2+n))+b^2*(c+d*x)^(3+n)/(d^3*(3+n)) +--R +--R +--R (2) +--R 2 2 2 2 n + 3 +--R (b n + 3b n + 2b )(d x + c) +--R + +--R 2 2 2 2 n + 2 +--R ((2a b d - 2b c)n + (8a b d - 8b c)n + 6a b d - 6b c)(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (5a d - 10a b c d + 5b c )n + 6a d +--R + +--R 2 2 +--R - 12a b c d + 6b c +--R * +--R n + 1 +--R (d x + c) +--R / +--R 3 3 3 2 3 3 +--R d n + 6d n + 11d n + 6d +--R Type: Expression(Integer) +--E 2539 + +--S 2540 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 3 2 2 3 2 3 3 +--R (b d n + 3b d n + 2b d )x +--R + +--R 3 2 2 2 3 2 2 3 2 +--R ((2a b d + b c d )n + (8a b d + b c d )n + 6a b d )x +--R + +--R 2 3 2 2 2 3 2 2 2 2 3 +--R ((a d + 2a b c d )n + (5a d + 6a b c d - 2b c d)n + 6a d )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 3 +--R a c d n + (5a c d - 2a b c d)n + 6a c d - 6a b c d + 2b c +--R * +--R n log(d x + c) +--R %e +--R / +--R 3 3 3 2 3 3 +--R d n + 6d n + 11d n + 6d +--R Type: Union(Expression(Integer),...) +--E 2540 + +--S 2541 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 3 2 2 3 2 3 3 +--R (b d n + 3b d n + 2b d )x +--R + +--R 3 2 2 2 3 2 2 3 2 +--R ((2a b d + b c d )n + (8a b d + b c d )n + 6a b d )x +--R + +--R 2 3 2 2 2 3 2 2 2 2 3 +--R ((a d + 2a b c d )n + (5a d + 6a b c d - 2b c d)n + 6a d )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 3 +--R a c d n + (5a c d - 2a b c d)n + 6a c d - 6a b c d + 2b c +--R * +--R n log(d x + c) +--R %e +--R + +--R 2 2 2 2 n + 3 +--R (- b n - 3b n - 2b )(d x + c) +--R + +--R 2 2 2 2 n + 2 +--R ((- 2a b d + 2b c)n + (- 8a b d + 8b c)n - 6a b d + 6b c)(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (- a d + 2a b c d - b c )n + (- 5a d + 10a b c d - 5b c )n - 6a d +--R + +--R 2 2 +--R 12a b c d - 6b c +--R * +--R n + 1 +--R (d x + c) +--R / +--R 3 3 3 2 3 3 +--R d n + 6d n + 11d n + 6d +--R Type: Expression(Integer) +--E 2541 + +--S 2542 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 2 2 2 2 2 2 n log(d x + c) 2 n + 2 +--R (b d x + 2a b d x + a d )%e - b (d x + c) +--R + +--R 2 n + 1 2 2 2 2 n +--R (- 2a b d + 2b c)(d x + c) + (- a d + 2a b c d - b c )(d x + c) +--R / +--R 2 +--R d +--R Type: Expression(Integer) +--E 2542 + +)clear all + +--S 2543 of 2952 +t0000:=(a+b*x)*(c+d*x)^n +--R +--R +--R n +--R (1) (b x + a)(d x + c) +--R Type: Expression(Integer) +--E 2543 + +--S 2544 of 2952 +r0000:=-(b*c-a*d)*(c+d*x)^(1+n)/(d^2*(1+n))+b*(c+d*x)^(2+n)/(d^2*(2+n)) +--R +--R +--R n + 2 n + 1 +--R (b n + b)(d x + c) + ((a d - b c)n + 2a d - 2b c)(d x + c) +--R (2) -------------------------------------------------------------------- +--R 2 2 2 2 +--R d n + 3d n + 2d +--R Type: Expression(Integer) +--E 2544 + +--S 2545 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R ((b d n + b d )x + ((a d + b c d)n + 2a d )x + a c d n + 2a c d - b c ) +--R * +--R n log(d x + c) +--R %e +--R / +--R 2 2 2 2 +--R d n + 3d n + 2d +--R Type: Union(Expression(Integer),...) +--E 2545 + +--S 2546 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 2 2 2 2 +--R (b d n + b d )x + ((a d + b c d)n + 2a d )x + a c d n + 2a c d +--R + +--R 2 +--R - b c +--R * +--R n log(d x + c) +--R %e +--R + +--R n + 2 n + 1 +--R (- b n - b)(d x + c) + ((- a d + b c)n - 2a d + 2b c)(d x + c) +--R / +--R 2 2 2 2 +--R d n + 3d n + 2d +--R Type: Expression(Integer) +--E 2546 + +--S 2547 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R n log(d x + c) n + 1 n +--R (b d x + a d)%e - b (d x + c) + (- a d + b c)(d x + c) +--R -------------------------------------------------------------------------- +--R d +--R Type: Expression(Integer) +--E 2547 + +)clear all + +--S 2548 of 2952 +t0000:=(c+d*x)^n +--R +--R +--R n +--R (1) (d x + c) +--R Type: Expression(Integer) +--E 2548 + +--S 2549 of 2952 +r0000:=(c+d*x)^(1+n)/(d*(1+n)) +--R +--R +--R n + 1 +--R (d x + c) +--R (2) -------------- +--R d n + d +--R Type: Expression(Integer) +--E 2549 + +--S 2550 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R n log(d x + c) +--R (d x + c)%e +--R (3) ------------------------- +--R d n + d +--R Type: Union(Expression(Integer),...) +--E 2550 + +--S 2551 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R n log(d x + c) n + 1 +--R (d x + c)%e - (d x + c) +--R (4) ------------------------------------------ +--R d n + d +--R Type: Expression(Integer) +--E 2551 + +--S 2552 of 2952 +d0000:=D(m0000,x) +--R +--R +--R n log(d x + c) n +--R (5) %e - (d x + c) +--R Type: Expression(Integer) +--E 2552 + +)clear all + +--S 2553 of 2952 +t0000:=(c+d*x)^n/(a+b*x) +--R +--R +--R n +--R (d x + c) +--R (1) ---------- +--R b x + a +--R Type: Expression(Integer) +--E 2553 + +--S 2554 of 2952 +--r0000:=-(c+d*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,b*(c+d*x)/(b*c-a*d))/((b*c-a*d)*(1+n)) +--E 2554 + +--S 2555 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n +--R ++ (%BJ d + c) +--R (2) | ------------ d%BJ +--R ++ %BJ b + a +--R Type: Union(Expression(Integer),...) +--E 2555 + +--S 2556 of 2952 +--m0000:=a0000 - r0000 +--E 2556 + +--S 2557 of 2952 +--d0000:=D(m0000,x) +--E 2557 + +)clear all + +--S 2558 of 2952 +t0000:=(c+d*x)^n/(a+b*x)^2 +--R +--R +--R n +--R (d x + c) +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 2558 + +--S 2559 of 2952 +--r0000:=-(c+d*x)^(1+n)/((b*c-a*d)*(a+b*x))-d*n*(c+d*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,b*(c+d*x)/(b*c-a*d))/((b*c-a*d)^2*(1+n)) +--E 2559 + +--S 2560 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n +--R ++ (%BJ d + c) +--R (2) | ---------------------- d%BJ +--R ++ 2 2 2 +--R %BJ b + 2%BJ a b + a +--R Type: Union(Expression(Integer),...) +--E 2560 + +--S 2561 of 2952 +--m0000:=a0000 - r0000 +--E 2561 + +--S 2562 of 2952 +--d0000:=D(m0000,x) +--E 2562 + +)clear all + +--S 2563 of 2952 +t0000:=(c+d*x)^n/(a+b*x)^3 +--R +--R +--R n +--R (d x + c) +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 2563 + +--S 2564 of 2952 +--r0000:=-1/2*(c+d*x)^(1+n)/((b*c-a*d)*(a+b*x)^2)+_ +-- 1/2*d*(1-n)*(c+d*x)^(1+n)/((b*c-a*d)^2*(a+b*x))+_ +-- 1/2*d^2*(1-n)*n*(c+d*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,b*(c+d*x)/(b*c-a*d))/((b*c-a*d)^3*(1+n)) +--E 2564 + +--S 2565 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n +--R ++ (%BJ d + c) +--R (2) | ---------------------------------- d%BJ +--R ++ 3 3 2 2 2 3 +--R %BJ b + 3%BJ a b + 3%BJ a b + a +--R Type: Union(Expression(Integer),...) +--E 2565 + +--S 2566 of 2952 +--m0000:=a0000 - r0000 +--E 2566 + +--S 2567 of 2952 +--d0000:=D(m0000,x) +--E 2567 + +)clear all + +--S 2568 of 2952 +t0000:=(a+b*x)^(-4+n)/(c+d*x)^n +--R +--R +--R n - 4 +--R (b x + a) +--R (1) -------------- +--R n +--R (d x + c) +--R Type: Expression(Integer) +--E 2568 + +--S 2569 of 2952 +r0000:=-(a+b*x)^(-3+n)*(c+d*x)^(1-n)/((b*c-a*d)*(3-n))+_ + 2*d*(a+b*x)^(-2+n)*(c+d*x)^(1-n)/((b*c-a*d)^2*(2-n)*(3-n))-_ + 2*d^2*(a+b*x)^(-1+n)*(c+d*x)^(1-n)/((b*c-a*d)^3*(1-n)*(2-n)*(3-n)) +--R +--R +--R (2) +--R 2 n - 1 +--R - 2d (b x + a) +--R + +--R 2 2 n - 2 +--R ((2a d - 2b c d)n - 2a d + 2b c d)(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (- a d + 2a b c d - b c )n + (3a d - 6a b c d + 3b c )n - 2a d +--R + +--R 2 2 +--R 4a b c d - 2b c +--R * +--R n - 3 +--R (b x + a) +--R * +--R - n + 1 +--R (d x + c) +--R / +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11a d - 33a b c d + 33a b c d - 11b c )n - 6a d + 18a b c d +--R + +--R 2 2 3 3 +--R - 18a b c d + 6b c +--R Type: Expression(Integer) +--E 2569 + +--S 2570 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 4 2 3 3 2 2 3 3 +--R - 2b d x + ((2a b d - 2b c d )n - 8a b d )x +--R + +--R 2 3 2 2 3 2 2 2 3 2 2 3 2 +--R (- a b d + 2a b c d - b c d)n + (7a b d - 8a b c d + b c d)n +--R + +--R 2 3 +--R - 12a b d +--R * +--R 2 +--R x +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- a d + a b c d + a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (5a d - a b c d - 7a b c d + 3b c )n - 6a d - 6a b c d +--R + +--R 2 2 3 3 +--R 6a b c d - 2b c +--R * +--R x +--R + +--R 3 2 2 2 2 3 2 3 2 2 2 2 3 +--R (- a c d + 2a b c d - a b c )n + (5a c d - 8a b c d + 3a b c )n +--R + +--R 3 2 2 2 2 3 +--R - 6a c d + 6a b c d - 2a b c +--R * +--R (n - 4)log(b x + a) +--R %e +--R / +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11a d - 33a b c d + 33a b c d - 11b c )n - 6a d + 18a b c d +--R + +--R 2 2 3 3 +--R - 18a b c d + 6b c +--R * +--R n log(d x + c) +--R %e +--R Type: Union(Expression(Integer),...) +--E 2570 + +--S 2571 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 n - 1 +--R 2d (b x + a) +--R + +--R 2 2 n - 2 +--R ((- 2a d + 2b c d)n + 2a d - 2b c d)(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (- 3a d + 6a b c d - 3b c )n +--R + +--R 2 2 2 2 +--R 2a d - 4a b c d + 2b c +--R * +--R n - 3 +--R (b x + a) +--R * +--R - n + 1 n log(d x + c) +--R (d x + c) %e +--R + +--R 3 3 4 2 3 3 2 2 3 3 +--R - 2b d x + ((2a b d - 2b c d )n - 8a b d )x +--R + +--R 2 3 2 2 3 2 2 2 3 2 2 3 2 +--R (- a b d + 2a b c d - b c d)n + (7a b d - 8a b c d + b c d)n +--R + +--R 2 3 +--R - 12a b d +--R * +--R 2 +--R x +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- a d + a b c d + a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (5a d - a b c d - 7a b c d + 3b c )n - 6a d - 6a b c d +--R + +--R 2 2 3 3 +--R 6a b c d - 2b c +--R * +--R x +--R + +--R 3 2 2 2 2 3 2 3 2 2 2 2 3 +--R (- a c d + 2a b c d - a b c )n + (5a c d - 8a b c d + 3a b c )n +--R + +--R 3 2 2 2 2 3 +--R - 6a c d + 6a b c d - 2a b c +--R * +--R (n - 4)log(b x + a) +--R %e +--R / +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11a d - 33a b c d + 33a b c d - 11b c )n - 6a d + 18a b c d +--R + +--R 2 2 3 3 +--R - 18a b c d + 6b c +--R * +--R n log(d x + c) +--R %e +--R Type: Expression(Integer) +--E 2571 + +--S 2572 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 2 n - 2 +--R 2b d (b x + a) +--R + +--R 2 2 2 2 n - 3 +--R ((- 2a b d + 2b c d)n + 4a b d - 4b c d)(b x + a) +--R + +--R 2 2 2 3 2 2 +--R (a b d - 2a b c d + b c )n +--R + +--R 2 2 2 3 2 2 2 2 3 2 +--R (- 5a b d + 10a b c d - 5b c )n + 6a b d - 12a b c d + 6b c +--R * +--R n - 4 +--R (b x + a) +--R * +--R - n + 1 +--R (d x + c) +--R + +--R 3 n - 1 +--R - 2d (b x + a) +--R + +--R 3 2 3 2 n - 2 +--R ((2a d - 2b c d )n - 2a d + 2b c d )(b x + a) +--R + +--R 2 3 2 2 2 2 +--R (- a d + 2a b c d - b c d)n +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R (3a d - 6a b c d + 3b c d)n - 2a d + 4a b c d - 2b c d +--R * +--R n - 3 +--R (b x + a) +--R * +--R - n +--R (d x + c) +--R * +--R n log(d x + c) +--R %e +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (- 5a d + 15a b c d - 15a b c d + 5b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R * +--R (n - 4)log(b x + a) +--R %e +--R / +--R 3 3 2 2 2 2 3 3 2 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (- 5a d + 15a b c d - 15a b c d + 5b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R * +--R n log(d x + c) +--R %e +--R Type: Expression(Integer) +--E 2572 + +)clear all + +--S 2573 of 2952 +t0000:=(a+b*x)^(-3+n)/(c+d*x)^n +--R +--R +--R n - 3 +--R (b x + a) +--R (1) -------------- +--R n +--R (d x + c) +--R Type: Expression(Integer) +--E 2573 + +--S 2574 of 2952 +r0000:=-(a+b*x)^(-2+n)*(c+d*x)^(1-n)/((b*c-a*d)*(2-n))+_ + d*(a+b*x)^(-1+n)*(c+d*x)^(1-n)/((b*c-a*d)^2*(1-n)*(2-n)) +--R +--R +--R (2) +--R n - 1 n - 2 +--R (d (b x + a) + ((- a d + b c)n + a d - b c)(b x + a) ) +--R * +--R - n + 1 +--R (d x + c) +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (- 3a d + 6a b c d - 3b c )n + 2a d +--R + +--R 2 2 +--R - 4a b c d + 2b c +--R Type: Expression(Integer) +--E 2574 + +--S 2575 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 3 2 2 2 2 +--R b d x + ((- a b d + b c d)n + 3a b d )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R ((- a d + b c )n + 2a d + 2a b c d - b c )x + (- a c d + a b c )n +--R + +--R 2 2 +--R 2a c d - a b c +--R * +--R (n - 3)log(b x + a) +--R %e +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (- 3a d + 6a b c d - 3b c )n + 2a d +--R + +--R 2 2 +--R - 4a b c d + 2b c +--R * +--R n log(d x + c) +--R %e +--R Type: Union(Expression(Integer),...) +--E 2575 + +--S 2576 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R n - 1 n - 2 +--R (- d (b x + a) + ((a d - b c)n - a d + b c)(b x + a) ) +--R * +--R - n + 1 n log(d x + c) +--R (d x + c) %e +--R + +--R 2 2 3 2 2 2 2 +--R b d x + ((- a b d + b c d)n + 3a b d )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R ((- a d + b c )n + 2a d + 2a b c d - b c )x + (- a c d + a b c )n +--R + +--R 2 2 +--R 2a c d - a b c +--R * +--R (n - 3)log(b x + a) +--R %e +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (- 3a d + 6a b c d - 3b c )n + 2a d +--R + +--R 2 2 +--R - 4a b c d + 2b c +--R * +--R n log(d x + c) +--R %e +--R Type: Expression(Integer) +--E 2576 + +--S 2577 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R n - 2 +--R - b d (b x + a) +--R + +--R 2 2 n - 3 +--R ((a b d - b c)n - 2a b d + 2b c)(b x + a) +--R * +--R - n + 1 +--R (d x + c) +--R + +--R 2 n - 1 +--R d (b x + a) +--R + +--R 2 2 n - 2 +--R ((- a d + b c d)n + a d - b c d)(b x + a) +--R * +--R - n +--R (d x + c) +--R * +--R n log(d x + c) +--R %e +--R + +--R 2 2 2 2 2 2 2 2 (n - 3)log(b x + a) +--R ((a d - 2a b c d + b c )n - 2a d + 4a b c d - 2b c )%e +--R / +--R 2 2 2 2 2 2 2 2 n log(d x + c) +--R ((a d - 2a b c d + b c )n - 2a d + 4a b c d - 2b c )%e +--R Type: Expression(Integer) +--E 2577 + +)clear all + +--S 2578 of 2952 +t0000:=(a+b*x)^(-2+n)/(c+d*x)^n +--R +--R +--R n - 2 +--R (b x + a) +--R (1) -------------- +--R n +--R (d x + c) +--R Type: Expression(Integer) +--E 2578 + +--S 2579 of 2952 +r0000:=-(a+b*x)^(-1+n)*(c+d*x)^(1-n)/((b*c-a*d)*(1-n)) +--R +--R +--R n - 1 - n + 1 +--R (b x + a) (d x + c) +--R (2) - ------------------------------ +--R (a d - b c)n - a d + b c +--R Type: Expression(Integer) +--E 2579 + +--S 2580 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 (n - 2)log(b x + a) +--R (- b d x + (- a d - b c)x - a c)%e +--R (3) ------------------------------------------------------ +--R n log(d x + c) +--R ((a d - b c)n - a d + b c)%e +--R Type: Union(Expression(Integer),...) +--E 2580 + +--S 2581 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R n - 1 - n + 1 n log(d x + c) +--R (b x + a) (d x + c) %e +--R + +--R 2 (n - 2)log(b x + a) +--R (- b d x + (- a d - b c)x - a c)%e +--R / +--R n log(d x + c) +--R ((a d - b c)n - a d + b c)%e +--R Type: Expression(Integer) +--E 2581 + +--S 2582 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R n - 2 - n + 1 n - 1 - n +--R (b (b x + a) (d x + c) - d (b x + a) (d x + c) ) +--R * +--R n log(d x + c) +--R %e +--R + +--R (n - 2)log(b x + a) +--R (a d - b c)%e +--R / +--R n log(d x + c) +--R (a d - b c)%e +--R Type: Expression(Integer) +--E 2582 + +)clear all + +--S 2583 of 2952 +t0000:=(a+b*x)^(-1+n)/(c+d*x)^n +--R +--R +--R n - 1 +--R (b x + a) +--R (1) -------------- +--R n +--R (d x + c) +--R Type: Expression(Integer) +--E 2583 + +--S 2584 of 2952 +--r0000:=(a+b*x)^n*(c+d*x)^(1-n)/((b*c-a*d)*n)-(a+b*x)^n*(c+d*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,b*(c+d*x)/(b*c-a*d))/_ +-- ((b*c-a*d)*(1-n)*n*(-d*(a+b*x)/(b*c-a*d))^n) +--E 2584 + +--S 2585 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n - 1 +--R ++ (%BJ b + a) +--R (2) | ---------------- d%BJ +--R ++ n +--R (%BJ d + c) +--R Type: Union(Expression(Integer),...) +--E 2585 + +--S 2586 of 2952 +--m0000:=a0000 - r0000 +--E 2586 + +--S 2587 of 2952 +--d0000:=D(m0000,x) +--E 2587 + +)clear all + +--S 2588 of 2952 +t0000:=(a+b*x)^n/(c+d*x)^n +--R +--R +--R n +--R (b x + a) +--R (1) ---------- +--R n +--R (d x + c) +--R Type: Expression(Integer) +--E 2588 + +--S 2589 of 2952 +--r0000:=(a+b*x)^n*(c+d*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,b*(c+d*x)/(b*c-a*d))/_ +-- (d*(1-n)*(-d*(a+b*x)/(b*c-a*d))^n) +--E 2589 + +--S 2590 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n +--R ++ (%BJ b + a) +--R (2) | ------------ d%BJ +--R ++ n +--R (%BJ d + c) +--R Type: Union(Expression(Integer),...) +--E 2590 + +--S 2591 of 2952 +--m0000:=a0000 - r0000 +--E 2591 + +--S 2592 of 2952 +--d0000:=D(m0000,x) +--E 2592 + +)clear all + +--S 2593 of 2952 +t0000:=(a+b*x)^(1+n)/(c+d*x)^n +--R +--R +--R n + 1 +--R (b x + a) +--R (1) -------------- +--R n +--R (d x + c) +--R Type: Expression(Integer) +--E 2593 + +--S 2594 of 2952 +--r0000:=1/2*(a+b*x)^(1+n)*(c+d*x)^(1-n)/d-_ +-- 1/2*(b*c-a*d)*(1+n)*(a+b*x)^n*(c+d*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,b*(c+d*x)/(b*c-a*d))/_ +-- (d^2*(1-n)*(-d*(a+b*x)/(b*c-a*d))^n) +--E 2594 + +--S 2595 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n + 1 +--R ++ (%BJ b + a) +--R (2) | ---------------- d%BJ +--R ++ n +--R (%BJ d + c) +--R Type: Union(Expression(Integer),...) +--E 2595 + +--S 2596 of 2952 +--m0000:=a0000 - r0000 +--E 2596 + +--S 2597 of 2952 +--d0000:=D(m0000,x) +--E 2597 + +)clear all + +--S 2598 of 2952 +t0000:=(a+b*x)^(2+n)/(c+d*x)^n +--R +--R +--R n + 2 +--R (b x + a) +--R (1) -------------- +--R n +--R (d x + c) +--R Type: Expression(Integer) +--E 2598 + +--S 2599 of 2952 +--r0000:=-1/6*(b*c-a*d)*(2+n)*(a+b*x)^(1+n)*(c+d*x)^(1-n)/d^2+_ +-- 1/3*(a+b*x)^(2+n)*(c+d*x)^(1-n)/d+_ +-- 1/6*(b*c-a*d)^2*(1+n)*(2+n)*(a+b*x)^n*(c+d*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,b*(c+d*x)/(b*c-a*d))/_ +-- (d^3*(1-n)*(-d*(a+b*x)/(b*c-a*d))^n) +--E 2599 + +--S 2600 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n + 2 +--R ++ (%BJ b + a) +--R (2) | ---------------- d%BJ +--R ++ n +--R (%BJ d + c) +--R Type: Union(Expression(Integer),...) +--E 2600 + +--S 2601 of 2952 +--m0000:=a0000 - r0000 +--E 2601 + +--S 2602 of 2952 +--d0000:=D(m0000,x) +--E 2602 + +)clear all + +--S 2603 of 2952 +t0000:=(c+d*x)^n/(a+b*x)^n +--R +--R +--R n +--R (d x + c) +--R (1) ---------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 2603 + +--S 2604 of 2952 +--r0000:=(-d*(a+b*x)/(b*c-a*d))^n*(c+d*x)^(1+n)*_ +-- hypergeometric(n,1+n,2+n,b*(c+d*x)/(b*c-a*d))/(d*(1+n)*(a+b*x)^n) +--E 2604 + +--S 2605 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n +--R ++ (%BJ d + c) +--R (2) | ------------ d%BJ +--R ++ n +--R (%BJ b + a) +--R Type: Union(Expression(Integer),...) +--E 2605 + +--S 2606 of 2952 +--m0000:=a0000 - r0000 +--E 2606 + +--S 2607 of 2952 +--d0000:=D(m0000,x) +--E 2607 + +)clear all + +--S 2608 of 2952 +t0000:=(a+b*x)^(-1-n)*(c+d*x)^n +--R +--R +--R - n - 1 n +--R (1) (b x + a) (d x + c) +--R Type: Expression(Integer) +--E 2608 + +--S 2609 of 2952 +--r0000:=-(c+d*x)^(1+n)/((b*c-a*d)*n*(a+b*x)^n)+_ +-- (-d*(a+b*x)/(b*c-a*d))^n*(c+d*x)^(1+n)*_ +-- hypergeometric(n,1+n,2+n,b*(c+d*x)/(b*c-a*d))/_ +-- ((b*c-a*d)*n*(1+n)*(a+b*x)^n) +--E 2609 + +--S 2610 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R ++ - n - 1 n +--R (2) | (%BJ b + a) (%BJ d + c) d%BJ +--R ++ +--R Type: Union(Expression(Integer),...) +--E 2610 + +--S 2611 of 2952 +--m0000:=a0000 - r0000 +--E 2611 + +--S 2612 of 2952 +--d0000:=D(m0000,x) +--E 2612 + +)clear all + +--S 2613 of 2952 +t0000:=(a+b*x)^(-2-n)*(c+d*x)^n +--R +--R +--R - n - 2 n +--R (1) (b x + a) (d x + c) +--R Type: Expression(Integer) +--E 2613 + +--S 2614 of 2952 +r0000:=-(a+b*x)^(-1-n)*(c+d*x)^(1+n)/((b*c-a*d)*(1+n)) +--R +--R +--R - n - 1 n + 1 +--R (b x + a) (d x + c) +--R (2) ------------------------------ +--R (a d - b c)n + a d - b c +--R Type: Expression(Integer) +--E 2614 + +--S 2615 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 (- n - 2)log(b x + a) n log(d x + c) +--R (b d x + (a d + b c)x + a c)%e %e +--R (3) -------------------------------------------------------------------- +--R (a d - b c)n + a d - b c +--R Type: Union(Expression(Integer),...) +--E 2615 + +--S 2616 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 (- n - 2)log(b x + a) n log(d x + c) +--R (b d x + (a d + b c)x + a c)%e %e +--R + +--R - n - 1 n + 1 +--R - (b x + a) (d x + c) +--R / +--R (a d - b c)n + a d - b c +--R Type: Expression(Integer) +--E 2616 + +--S 2617 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R (- n - 2)log(b x + a) n log(d x + c) +--R (a d - b c)%e %e +--R + +--R - n - 2 n + 1 - n - 1 n +--R b (b x + a) (d x + c) - d (b x + a) (d x + c) +--R / +--R a d - b c +--R Type: Expression(Integer) +--E 2617 + +)clear all + +--S 2618 of 2952 +t0000:=(a+b*x)^(-3-n)*(c+d*x)^n +--R +--R +--R - n - 3 n +--R (1) (b x + a) (d x + c) +--R Type: Expression(Integer) +--E 2618 + +--S 2619 of 2952 +r0000:=-(a+b*x)^(-2-n)*(c+d*x)^(1+n)/((b*c-a*d)*(2+n))+_ + d*(a+b*x)^(-1-n)*(c+d*x)^(1+n)/((b*c-a*d)^2*(1+n)*(2+n)) +--R +--R +--R (2) +--R - n - 1 - n - 2 +--R (d (b x + a) + ((a d - b c)n + a d - b c)(b x + a) ) +--R * +--R n + 1 +--R (d x + c) +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (3a d - 6a b c d + 3b c )n + 2a d +--R + +--R 2 2 +--R - 4a b c d + 2b c +--R Type: Expression(Integer) +--E 2619 + +--S 2620 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 3 2 2 2 2 +--R b d x + ((a b d - b c d)n + 3a b d )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R ((a d - b c )n + 2a d + 2a b c d - b c )x + (a c d - a b c )n +--R + +--R 2 2 +--R 2a c d - a b c +--R * +--R (- n - 3)log(b x + a) n log(d x + c) +--R %e %e +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (3a d - 6a b c d + 3b c )n + 2a d +--R + +--R 2 2 +--R - 4a b c d + 2b c +--R Type: Union(Expression(Integer),...) +--E 2620 + +--S 2621 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 2 3 2 2 2 2 +--R b d x + ((a b d - b c d)n + 3a b d )x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R ((a d - b c )n + 2a d + 2a b c d - b c )x + (a c d - a b c )n +--R + +--R 2 2 +--R 2a c d - a b c +--R * +--R (- n - 3)log(b x + a) n log(d x + c) +--R %e %e +--R + +--R - n - 1 - n - 2 +--R (- d (b x + a) + ((- a d + b c)n - a d + b c)(b x + a) ) +--R * +--R n + 1 +--R (d x + c) +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (3a d - 6a b c d + 3b c )n + 2a d +--R + +--R 2 2 +--R - 4a b c d + 2b c +--R Type: Expression(Integer) +--E 2621 + +--S 2622 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 2 2 2 2 2 2 2 2 +--R ((a d - 2a b c d + b c )n + 2a d - 4a b c d + 2b c ) +--R * +--R (- n - 3)log(b x + a) n log(d x + c) +--R %e %e +--R + +--R - n - 2 +--R b d (b x + a) +--R + +--R 2 2 - n - 3 +--R ((a b d - b c)n + 2a b d - 2b c)(b x + a) +--R * +--R n + 1 +--R (d x + c) +--R + +--R 2 - n - 1 +--R - d (b x + a) +--R + +--R 2 2 - n - 2 +--R ((- a d + b c d)n - a d + b c d)(b x + a) +--R * +--R n +--R (d x + c) +--R / +--R 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + 2a d - 4a b c d + 2b c +--R Type: Expression(Integer) +--E 2622 + +)clear all + +--S 2623 of 2952 +t0000:=(a+b*x)^(-4-n)*(c+d*x)^n +--R +--R +--R - n - 4 n +--R (1) (b x + a) (d x + c) +--R Type: Expression(Integer) +--E 2623 + +--S 2624 of 2952 +r0000:=-(a+b*x)^(-3-n)*(c+d*x)^(1+n)/((b*c-a*d)*(3+n))+_ + 2*d*(a+b*x)^(-2-n)*(c+d*x)^(1+n)/((b*c-a*d)^2*(2+n)*(3+n))-_ + 2*d^2*(a+b*x)^(-1-n)*(c+d*x)^(1+n)/((b*c-a*d)^3*(1+n)*(2+n)*(3+n)) +--R +--R +--R (2) +--R 2 - n - 1 +--R 2d (b x + a) +--R + +--R 2 2 - n - 2 +--R ((2a d - 2b c d)n + 2a d - 2b c d)(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (3a d - 6a b c d + 3b c )n + 2a d +--R + +--R 2 2 +--R - 4a b c d + 2b c +--R * +--R - n - 3 +--R (b x + a) +--R * +--R n + 1 +--R (d x + c) +--R / +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (6a d - 18a b c d + 18a b c d - 6b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11a d - 33a b c d + 33a b c d - 11b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R Type: Expression(Integer) +--E 2624 + +--S 2625 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 4 2 3 3 2 2 3 3 +--R 2b d x + ((2a b d - 2b c d )n + 8a b d )x +--R + +--R 2 3 2 2 3 2 2 2 3 2 2 3 2 +--R (a b d - 2a b c d + b c d)n + (7a b d - 8a b c d + b c d)n +--R + +--R 2 3 +--R 12a b d +--R * +--R 2 +--R x +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (a d - a b c d - a b c d + b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (5a d - a b c d - 7a b c d + 3b c )n + 6a d + 6a b c d +--R + +--R 2 2 3 3 +--R - 6a b c d + 2b c +--R * +--R x +--R + +--R 3 2 2 2 2 3 2 3 2 2 2 2 3 +--R (a c d - 2a b c d + a b c )n + (5a c d - 8a b c d + 3a b c )n +--R + +--R 3 2 2 2 2 3 +--R 6a c d - 6a b c d + 2a b c +--R * +--R (- n - 4)log(b x + a) n log(d x + c) +--R %e %e +--R / +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (6a d - 18a b c d + 18a b c d - 6b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11a d - 33a b c d + 33a b c d - 11b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R Type: Union(Expression(Integer),...) +--E 2625 + +--S 2626 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 3 4 2 3 3 2 2 3 3 +--R 2b d x + ((2a b d - 2b c d )n + 8a b d )x +--R + +--R 2 3 2 2 3 2 2 2 3 2 2 3 2 +--R (a b d - 2a b c d + b c d)n + (7a b d - 8a b c d + b c d)n +--R + +--R 2 3 +--R 12a b d +--R * +--R 2 +--R x +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (a d - a b c d - a b c d + b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (5a d - a b c d - 7a b c d + 3b c )n + 6a d + 6a b c d +--R + +--R 2 2 3 3 +--R - 6a b c d + 2b c +--R * +--R x +--R + +--R 3 2 2 2 2 3 2 3 2 2 2 2 3 +--R (a c d - 2a b c d + a b c )n + (5a c d - 8a b c d + 3a b c )n +--R + +--R 3 2 2 2 2 3 +--R 6a c d - 6a b c d + 2a b c +--R * +--R (- n - 4)log(b x + a) n log(d x + c) +--R %e %e +--R + +--R 2 - n - 1 +--R - 2d (b x + a) +--R + +--R 2 2 - n - 2 +--R ((- 2a d + 2b c d)n - 2a d + 2b c d)(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- a d + 2a b c d - b c )n + (- 3a d + 6a b c d - 3b c )n +--R + +--R 2 2 2 2 +--R - 2a d + 4a b c d - 2b c +--R * +--R - n - 3 +--R (b x + a) +--R * +--R n + 1 +--R (d x + c) +--R / +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (6a d - 18a b c d + 18a b c d - 6b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11a d - 33a b c d + 33a b c d - 11b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R Type: Expression(Integer) +--E 2626 + +--S 2627 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 3 3 2 2 2 2 3 3 2 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (5a d - 15a b c d + 15a b c d - 5b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R * +--R (- n - 4)log(b x + a) n log(d x + c) +--R %e %e +--R + +--R 2 - n - 2 +--R 2b d (b x + a) +--R + +--R 2 2 2 2 - n - 3 +--R ((2a b d - 2b c d)n + 4a b d - 4b c d)(b x + a) +--R + +--R 2 2 2 3 2 2 2 2 2 3 2 +--R (a b d - 2a b c d + b c )n + (5a b d - 10a b c d + 5b c )n +--R + +--R 2 2 2 3 2 +--R 6a b d - 12a b c d + 6b c +--R * +--R - n - 4 +--R (b x + a) +--R * +--R n + 1 +--R (d x + c) +--R + +--R 3 - n - 1 +--R - 2d (b x + a) +--R + +--R 3 2 3 2 - n - 2 +--R ((- 2a d + 2b c d )n - 2a d + 2b c d )(b x + a) +--R + +--R 2 3 2 2 2 2 2 3 2 2 2 +--R (- a d + 2a b c d - b c d)n + (- 3a d + 6a b c d - 3b c d)n +--R + +--R 2 3 2 2 2 +--R - 2a d + 4a b c d - 2b c d +--R * +--R - n - 3 +--R (b x + a) +--R * +--R n +--R (d x + c) +--R / +--R 3 3 2 2 2 2 3 3 2 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (5a d - 15a b c d + 15a b c d - 5b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R Type: Expression(Integer) +--E 2627 + +)clear all + +--S 2628 of 2952 +t0000:=(a+b*x)^(-5-n)*(c+d*x)^n +--R +--R +--R - n - 5 n +--R (1) (b x + a) (d x + c) +--R Type: Expression(Integer) +--E 2628 + +--S 2629 of 2952 +r0000:=-(a+b*x)^(-4-n)*(c+d*x)^(1+n)/((b*c-a*d)*(4+n))+_ + 3*d*(a+b*x)^(-3-n)*(c+d*x)^(1+n)/((b*c-a*d)^2*(3+n)*(4+n))-_ + 6*d^2*(a+b*x)^(-2-n)*(c+d*x)^(1+n)/((b*c-a*d)^3*(2+n)*(3+n)*(4+n))+_ + 6*d^3*(a+b*x)^(-1-n)*(c+d*x)^(1+n)/((b*c-a*d)^4*(1+n)*(2+n)*(3+n)*(4+n)) +--R +--R +--R (2) +--R 3 - n - 1 +--R 6d (b x + a) +--R + +--R 3 2 3 2 - n - 2 +--R ((6a d - 6b c d )n + 6a d - 6b c d )(b x + a) +--R + +--R 2 3 2 2 2 2 2 3 2 2 2 +--R (3a d - 6a b c d + 3b c d)n + (9a d - 18a b c d + 9b c d)n +--R + +--R 2 3 2 2 2 +--R 6a d - 12a b c d + 6b c d +--R * +--R - n - 3 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (6a d - 18a b c d + 18a b c d - 6b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11a d - 33a b c d + 33a b c d - 11b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R * +--R - n - 4 +--R (b x + a) +--R * +--R n + 1 +--R (d x + c) +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (10a d - 40a b c d + 60a b c d - 40a b c d + 10b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (35a d - 140a b c d + 210a b c d - 140a b c d + 35b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (50a d - 200a b c d + 300a b c d - 200a b c d + 50b c )n + 24a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96a b c d + 144a b c d - 96a b c d + 24b c +--R Type: Expression(Integer) +--E 2629 + +--S 2630 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 5 3 4 4 3 3 4 4 +--R 6b d x + ((6a b d - 6b c d )n + 30a b d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (3a b d - 6a b c d + 3b c d )n +--R + +--R 2 2 4 3 3 4 2 2 2 2 4 +--R (27a b d - 30a b c d + 3b c d )n + 60a b d +--R * +--R 3 +--R x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (a b d - 3a b c d + 3a b c d - b c d)n +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (12a b d - 27a b c d + 18a b c d - 3b c d)n +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 4 +--R (47a b d - 60a b c d + 15a b c d - 2b c d)n + 60a b d +--R * +--R 2 +--R x +--R + +--R 4 4 3 3 3 3 4 4 3 +--R (a d - 2a b c d + 2a b c d - b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (9a d - 12a b c d - 9a b c d + 18a b c d - 6b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (26a d - 10a b c d - 45a b c d + 40a b c d - 11b c )n + 24a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 24a b c d - 36a b c d + 24a b c d - 6b c +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (a c d - 3a b c d + 3a b c d - a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 +--R (9a c d - 24a b c d + 21a b c d - 6a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 3 3 2 2 +--R (26a c d - 57a b c d + 42a b c d - 11a b c )n + 24a c d - 36a b c d +--R + +--R 2 2 3 3 4 +--R 24a b c d - 6a b c +--R * +--R (- n - 5)log(b x + a) n log(d x + c) +--R %e %e +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (10a d - 40a b c d + 60a b c d - 40a b c d + 10b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (35a d - 140a b c d + 210a b c d - 140a b c d + 35b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (50a d - 200a b c d + 300a b c d - 200a b c d + 50b c )n + 24a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96a b c d + 144a b c d - 96a b c d + 24b c +--R Type: Union(Expression(Integer),...) +--E 2630 + +--S 2631 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 4 4 5 3 4 4 3 3 4 4 +--R 6b d x + ((6a b d - 6b c d )n + 30a b d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (3a b d - 6a b c d + 3b c d )n +--R + +--R 2 2 4 3 3 4 2 2 2 2 4 +--R (27a b d - 30a b c d + 3b c d )n + 60a b d +--R * +--R 3 +--R x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (a b d - 3a b c d + 3a b c d - b c d)n +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (12a b d - 27a b c d + 18a b c d - 3b c d)n +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 4 +--R (47a b d - 60a b c d + 15a b c d - 2b c d)n + 60a b d +--R * +--R 2 +--R x +--R + +--R 4 4 3 3 3 3 4 4 3 +--R (a d - 2a b c d + 2a b c d - b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (9a d - 12a b c d - 9a b c d + 18a b c d - 6b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (26a d - 10a b c d - 45a b c d + 40a b c d - 11b c )n + 24a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 24a b c d - 36a b c d + 24a b c d - 6b c +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (a c d - 3a b c d + 3a b c d - a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 +--R (9a c d - 24a b c d + 21a b c d - 6a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 3 +--R (26a c d - 57a b c d + 42a b c d - 11a b c )n + 24a c d +--R + +--R 3 2 2 2 2 3 3 4 +--R - 36a b c d + 24a b c d - 6a b c +--R * +--R (- n - 5)log(b x + a) n log(d x + c) +--R %e %e +--R + +--R 3 - n - 1 +--R - 6d (b x + a) +--R + +--R 3 2 3 2 - n - 2 +--R ((- 6a d + 6b c d )n - 6a d + 6b c d )(b x + a) +--R + +--R 2 3 2 2 2 2 +--R (- 3a d + 6a b c d - 3b c d)n +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R (- 9a d + 18a b c d - 9b c d)n - 6a d + 12a b c d - 6b c d +--R * +--R - n - 3 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a d + 3a b c d - 3a b c d + b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 +--R (- 11a d + 33a b c d - 33a b c d + 11b c )n - 6a d +--R + +--R 2 2 2 2 3 3 +--R 18a b c d - 18a b c d + 6b c +--R * +--R - n - 4 +--R (b x + a) +--R * +--R n + 1 +--R (d x + c) +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (10a d - 40a b c d + 60a b c d - 40a b c d + 10b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (35a d - 140a b c d + 210a b c d - 140a b c d + 35b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (50a d - 200a b c d + 300a b c d - 200a b c d + 50b c )n + 24a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96a b c d + 144a b c d - 96a b c d + 24b c +--R Type: Expression(Integer) +--E 2631 + +--S 2632 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (9a d - 36a b c d + 54a b c d - 36a b c d + 9b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (26a d - 104a b c d + 156a b c d - 104a b c d + 26b c )n + 24a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96a b c d + 144a b c d - 96a b c d + 24b c +--R * +--R (- n - 5)log(b x + a) n log(d x + c) +--R %e %e +--R + +--R 3 - n - 2 +--R 6b d (b x + a) +--R + +--R 3 2 2 3 2 2 - n - 3 +--R ((6a b d - 6b c d )n + 12a b d - 12b c d )(b x + a) +--R + +--R 2 3 2 2 3 2 2 +--R (3a b d - 6a b c d + 3b c d)n +--R + +--R 2 3 2 2 3 2 2 3 2 2 +--R (15a b d - 30a b c d + 15b c d)n + 18a b d - 36a b c d +--R + +--R 3 2 +--R 18b c d +--R * +--R - n - 4 +--R (b x + a) +--R + +--R 3 3 2 2 2 3 2 4 3 3 +--R (a b d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (9a b d - 27a b c d + 27a b c d - 9b c )n +--R + +--R 3 3 2 2 2 3 2 4 3 3 3 +--R (26a b d - 78a b c d + 78a b c d - 26b c )n + 24a b d +--R + +--R 2 2 2 3 2 4 3 +--R - 72a b c d + 72a b c d - 24b c +--R * +--R - n - 5 +--R (b x + a) +--R * +--R n + 1 +--R (d x + c) +--R + +--R 4 - n - 1 +--R - 6d (b x + a) +--R + +--R 4 3 4 3 - n - 2 +--R ((- 6a d + 6b c d )n - 6a d + 6b c d )(b x + a) +--R + +--R 2 4 3 2 2 2 2 +--R (- 3a d + 6a b c d - 3b c d )n +--R + +--R 2 4 3 2 2 2 2 4 3 2 2 2 +--R (- 9a d + 18a b c d - 9b c d )n - 6a d + 12a b c d - 6b c d +--R * +--R - n - 3 +--R (b x + a) +--R + +--R 3 4 2 3 2 2 2 3 3 3 +--R (- a d + 3a b c d - 3a b c d + b c d)n +--R + +--R 3 4 2 3 2 2 2 3 3 2 +--R (- 6a d + 18a b c d - 18a b c d + 6b c d)n +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 +--R (- 11a d + 33a b c d - 33a b c d + 11b c d)n - 6a d +--R + +--R 2 3 2 2 2 3 3 +--R 18a b c d - 18a b c d + 6b c d +--R * +--R - n - 4 +--R (b x + a) +--R * +--R n +--R (d x + c) +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (9a d - 36a b c d + 54a b c d - 36a b c d + 9b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (26a d - 104a b c d + 156a b c d - 104a b c d + 26b c )n + 24a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96a b c d + 144a b c d - 96a b c d + 24b c +--R Type: Expression(Integer) +--E 2632 + +)clear all + +--S 2633 of 2952 +t0000:=(a+b*x)^n/(c+d*x)^n +--R +--R +--R n +--R (b x + a) +--R (1) ---------- +--R n +--R (d x + c) +--R Type: Expression(Integer) +--E 2633 + +--S 2634 of 2952 +--r0000:=(a+b*x)^n*(c+d*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,b*(c+d*x)/(b*c-a*d))/_ +-- (d*(1-n)*(-d*(a+b*x)/(b*c-a*d))^n) +--E 2634 + +--S 2635 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x n +--R ++ (%BJ b + a) +--R (2) | ------------ d%BJ +--R ++ n +--R (%BJ d + c) +--R Type: Union(Expression(Integer),...) +--E 2635 + +--S 2636 of 2952 +--m0000:=a0000 - r0000 +--E 2636 + +--S 2637 of 2952 +--d0000:=D(m0000,x) +--E 2637 + +)clear all + +--S 2638 of 2952 +t0000:=(a+b*x)^n*(c+d*x)^(-1-n) +--R +--R +--R n - n - 1 +--R (1) (b x + a) (d x + c) +--R Type: Expression(Integer) +--E 2638 + +--S 2639 of 2952 +--r0000:=(a+b*x)^(1+n)/((b*c-a*d)*n*(c+d*x)^n)-_ +-- b*(a+b*x)^n*(c+d*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,b*(c+d*x)/(b*c-a*d))/_ +-- (d*(b*c-a*d)*(1-n)*n*(-d*(a+b*x)/(b*c-a*d))^n) +--E 2639 + +--S 2640 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R ++ n - n - 1 +--R (2) | (%BJ b + a) (%BJ d + c) d%BJ +--R ++ +--R Type: Union(Expression(Integer),...) +--E 2640 + +--S 2641 of 2952 +--m0000:=a0000 - r0000 +--E 2641 + +--S 2642 of 2952 +--d0000:=D(m0000,x) +--E 2642 + +)clear all + +--S 2643 of 2952 +t0000:=(a+b*x)^n*(c+d*x)^(-2-n) +--R +--R +--R n - n - 2 +--R (1) (b x + a) (d x + c) +--R Type: Expression(Integer) +--E 2643 + +--S 2644 of 2952 +r0000:=(a+b*x)^(1+n)*(c+d*x)^(-1-n)/((b*c-a*d)*(1+n)) +--R +--R +--R n + 1 - n - 1 +--R (b x + a) (d x + c) +--R (2) - ------------------------------ +--R (a d - b c)n + a d - b c +--R Type: Expression(Integer) +--E 2644 + +--S 2645 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 (- n - 2)log(d x + c) n log(b x + a) +--R (- b d x + (- a d - b c)x - a c)%e %e +--R ------------------------------------------------------------------------ +--R (a d - b c)n + a d - b c +--R Type: Union(Expression(Integer),...) +--E 2645 + +--S 2646 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 (- n - 2)log(d x + c) n log(b x + a) +--R (- b d x + (- a d - b c)x - a c)%e %e +--R + +--R n + 1 - n - 1 +--R (b x + a) (d x + c) +--R / +--R (a d - b c)n + a d - b c +--R Type: Expression(Integer) +--E 2646 + +--S 2647 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R (- n - 2)log(d x + c) n log(b x + a) +--R (a d - b c)%e %e +--R + +--R n - n - 1 n + 1 - n - 2 +--R b (b x + a) (d x + c) - d (b x + a) (d x + c) +--R / +--R a d - b c +--R Type: Expression(Integer) +--E 2647 + +)clear all + +--S 2648 of 2952 +t0000:=(a+b*x)^n*(c+d*x)^(-3-n) +--R +--R +--R n - n - 3 +--R (1) (b x + a) (d x + c) +--R Type: Expression(Integer) +--E 2648 + +--S 2649 of 2952 +r0000:=(a+b*x)^(1+n)*(c+d*x)^(-2-n)/((b*c-a*d)*(2+n))+_ + b*(a+b*x)^(1+n)*(c+d*x)^(-1-n)/((b*c-a*d)^2*(1+n)*(2+n)) +--R +--R +--R (2) +--R n + 1 - n - 1 +--R b (b x + a) (d x + c) +--R + +--R n + 1 - n - 2 +--R ((- a d + b c)n - a d + b c)(b x + a) (d x + c) +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (3a d - 6a b c d + 3b c )n + 2a d +--R + +--R 2 2 +--R - 4a b c d + 2b c +--R Type: Expression(Integer) +--E 2649 + +--S 2650 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 2 2 3 2 2 2 2 +--R b d x + ((- a b d + b c d)n + 3b c d)x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R ((- a d + b c )n - a d + 2a b c d + 2b c )x + (- a c d + a b c )n +--R + +--R 2 2 +--R - a c d + 2a b c +--R * +--R (- n - 3)log(d x + c) n log(b x + a) +--R %e %e +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (3a d - 6a b c d + 3b c )n + 2a d +--R + +--R 2 2 +--R - 4a b c d + 2b c +--R Type: Union(Expression(Integer),...) +--E 2650 + +--S 2651 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 2 2 3 2 2 2 2 +--R b d x + ((- a b d + b c d)n + 3b c d)x +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R ((- a d + b c )n - a d + 2a b c d + 2b c )x + (- a c d + a b c )n +--R + +--R 2 2 +--R - a c d + 2a b c +--R * +--R (- n - 3)log(d x + c) n log(b x + a) +--R %e %e +--R + +--R n + 1 - n - 1 +--R - b (b x + a) (d x + c) +--R + +--R n + 1 - n - 2 +--R ((a d - b c)n + a d - b c)(b x + a) (d x + c) +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (3a d - 6a b c d + 3b c )n + 2a d +--R + +--R 2 2 +--R - 4a b c d + 2b c +--R Type: Expression(Integer) +--E 2651 + +--S 2652 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 2 2 2 2 2 2 2 2 +--R ((a d - 2a b c d + b c )n + 2a d - 4a b c d + 2b c ) +--R * +--R (- n - 3)log(d x + c) n log(b x + a) +--R %e %e +--R + +--R 2 n - n - 1 +--R - b (b x + a) (d x + c) +--R + +--R n + 1 2 2 n +--R (b d (b x + a) + ((a b d - b c)n + a b d - b c)(b x + a) ) +--R * +--R - n - 2 +--R (d x + c) +--R + +--R 2 2 n + 1 - n - 3 +--R ((- a d + b c d)n - 2a d + 2b c d)(b x + a) (d x + c) +--R / +--R 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + 2a d - 4a b c d + 2b c +--R Type: Expression(Integer) +--E 2652 + +)clear all + +--S 2653 of 2952 +t0000:=(a+b*x)^n*(c+d*x)^(-4-n) +--R +--R +--R n - n - 4 +--R (1) (b x + a) (d x + c) +--R Type: Expression(Integer) +--E 2653 + +--S 2654 of 2952 +r0000:=(a+b*x)^(1+n)*(c+d*x)^(-3-n)/((b*c-a*d)*(3+n))+_ + 2*b*(a+b*x)^(1+n)*(c+d*x)^(-2-n)/((b*c-a*d)^2*(2+n)*(3+n))+_ + 2*b^2*(a+b*x)^(1+n)*(c+d*x)^(-1-n)/((b*c-a*d)^3*(1+n)*(2+n)*(3+n)) +--R +--R +--R (2) +--R 2 n + 1 - n - 1 +--R - 2b (b x + a) (d x + c) +--R + +--R 2 2 n + 1 - n - 2 +--R ((2a b d - 2b c)n + 2a b d - 2b c)(b x + a) (d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (- a d + 2a b c d - b c )n + (- 3a d + 6a b c d - 3b c )n - 2a d +--R + +--R 2 2 +--R 4a b c d - 2b c +--R * +--R n + 1 - n - 3 +--R (b x + a) (d x + c) +--R / +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (6a d - 18a b c d + 18a b c d - 6b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11a d - 33a b c d + 33a b c d - 11b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R Type: Expression(Integer) +--E 2654 + +--S 2655 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 3 3 4 2 3 3 2 3 2 3 +--R - 2b d x + ((2a b d - 2b c d )n - 8b c d )x +--R + +--R 2 3 2 2 3 2 2 2 3 2 2 3 2 +--R (- a b d + 2a b c d - b c d)n + (- a b d + 8a b c d - 7b c d)n +--R + +--R 3 2 +--R - 12b c d +--R * +--R 2 +--R x +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- a d + a b c d + a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (- 3a d + 7a b c d + a b c d - 5b c )n - 2a d + 6a b c d +--R + +--R 2 2 3 3 +--R - 6a b c d - 6b c +--R * +--R x +--R + +--R 3 2 2 2 2 3 2 3 2 2 2 2 3 +--R (- a c d + 2a b c d - a b c )n + (- 3a c d + 8a b c d - 5a b c )n +--R + +--R 3 2 2 2 2 3 +--R - 2a c d + 6a b c d - 6a b c +--R * +--R (- n - 4)log(d x + c) n log(b x + a) +--R %e %e +--R / +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (6a d - 18a b c d + 18a b c d - 6b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11a d - 33a b c d + 33a b c d - 11b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R Type: Union(Expression(Integer),...) +--E 2655 + +--S 2656 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 3 3 4 2 3 3 2 3 2 3 +--R - 2b d x + ((2a b d - 2b c d )n - 8b c d )x +--R + +--R 2 3 2 2 3 2 2 +--R (- a b d + 2a b c d - b c d)n +--R + +--R 2 3 2 2 3 2 3 2 +--R (- a b d + 8a b c d - 7b c d)n - 12b c d +--R * +--R 2 +--R x +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- a d + a b c d + a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (- 3a d + 7a b c d + a b c d - 5b c )n - 2a d + 6a b c d +--R + +--R 2 2 3 3 +--R - 6a b c d - 6b c +--R * +--R x +--R + +--R 3 2 2 2 2 3 2 3 2 2 2 2 3 +--R (- a c d + 2a b c d - a b c )n + (- 3a c d + 8a b c d - 5a b c )n +--R + +--R 3 2 2 2 2 3 +--R - 2a c d + 6a b c d - 6a b c +--R * +--R (- n - 4)log(d x + c) n log(b x + a) +--R %e %e +--R + +--R 2 n + 1 - n - 1 +--R 2b (b x + a) (d x + c) +--R + +--R 2 2 n + 1 - n - 2 +--R ((- 2a b d + 2b c)n - 2a b d + 2b c)(b x + a) (d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (3a d - 6a b c d + 3b c )n + 2a d +--R + +--R 2 2 +--R - 4a b c d + 2b c +--R * +--R n + 1 - n - 3 +--R (b x + a) (d x + c) +--R / +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (6a d - 18a b c d + 18a b c d - 6b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11a d - 33a b c d + 33a b c d - 11b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R Type: Expression(Integer) +--E 2656 + +--S 2657 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 3 3 2 2 2 2 3 3 2 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (5a d - 15a b c d + 15a b c d - 5b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R * +--R (- n - 4)log(d x + c) n log(b x + a) +--R %e %e +--R + +--R 3 n - n - 1 +--R 2b (b x + a) (d x + c) +--R + +--R 2 n + 1 +--R - 2b d (b x + a) +--R + +--R 2 3 2 3 n +--R ((- 2a b d + 2b c)n - 2a b d + 2b c)(b x + a) +--R * +--R - n - 2 +--R (d x + c) +--R + +--R 2 2 2 2 n + 1 +--R ((2a b d - 2b c d)n + 4a b d - 4b c d)(b x + a) +--R + +--R 2 2 2 3 2 2 2 2 2 3 2 +--R (a b d - 2a b c d + b c )n + (3a b d - 6a b c d + 3b c )n +--R + +--R 2 2 2 3 2 +--R 2a b d - 4a b c d + 2b c +--R * +--R n +--R (b x + a) +--R * +--R - n - 3 +--R (d x + c) +--R + +--R 2 3 2 2 2 2 2 3 2 2 2 +--R (- a d + 2a b c d - b c d)n + (- 5a d + 10a b c d - 5b c d)n +--R + +--R 2 3 2 2 2 +--R - 6a d + 12a b c d - 6b c d +--R * +--R n + 1 - n - 4 +--R (b x + a) (d x + c) +--R / +--R 3 3 2 2 2 2 3 3 2 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (5a d - 15a b c d + 15a b c d - 5b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R Type: Expression(Integer) +--E 2657 + +)clear all + +--S 2658 of 2952 +t0000:=(a+b*x)^n*(c+d*x)^(-5-n) +--R +--R +--R n - n - 5 +--R (1) (b x + a) (d x + c) +--R Type: Expression(Integer) +--E 2658 + +--S 2659 of 2952 +r0000:=(a+b*x)^(1+n)*(c+d*x)^(-4-n)/((b*c-a*d)*(4+n))+_ + 3*b*(a+b*x)^(1+n)*(c+d*x)^(-3-n)/((b*c-a*d)^2*(3+n)*(4+n))+_ + 6*b^2*(a+b*x)^(1+n)*(c+d*x)^(-2-n)/((b*c-a*d)^3*(2+n)*(3+n)*(4+n))+_ + 6*b^3*(a+b*x)^(1+n)*(c+d*x)^(-1-n)/((b*c-a*d)^4*(1+n)*(2+n)*(3+n)*(4+n)) +--R +--R +--R (2) +--R 3 n + 1 - n - 1 +--R 6b (b x + a) (d x + c) +--R + +--R 2 3 2 3 n + 1 - n - 2 +--R ((- 6a b d + 6b c)n - 6a b d + 6b c)(b x + a) (d x + c) +--R + +--R 2 2 2 3 2 2 2 2 2 3 2 +--R (3a b d - 6a b c d + 3b c )n + (9a b d - 18a b c d + 9b c )n +--R + +--R 2 2 2 3 2 +--R 6a b d - 12a b c d + 6b c +--R * +--R n + 1 - n - 3 +--R (b x + a) (d x + c) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a d + 3a b c d - 3a b c d + b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (- 11a d + 33a b c d - 33a b c d + 11b c )n - 6a d + 18a b c d +--R + +--R 2 2 3 3 +--R - 18a b c d + 6b c +--R * +--R n + 1 - n - 4 +--R (b x + a) (d x + c) +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (10a d - 40a b c d + 60a b c d - 40a b c d + 10b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (35a d - 140a b c d + 210a b c d - 140a b c d + 35b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (50a d - 200a b c d + 300a b c d - 200a b c d + 50b c )n + 24a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96a b c d + 144a b c d - 96a b c d + 24b c +--R Type: Expression(Integer) +--E 2659 + +--S 2660 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 4 4 5 3 4 4 3 4 3 4 +--R 6b d x + ((- 6a b d + 6b c d )n + 30b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (3a b d - 6a b c d + 3b c d )n +--R + +--R 2 2 4 3 3 4 2 2 4 2 2 +--R (3a b d - 30a b c d + 27b c d )n + 60b c d +--R * +--R 3 +--R x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (- a b d + 3a b c d - 3a b c d + b c d)n +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (- 3a b d + 18a b c d - 27a b c d + 12b c d)n +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 3 +--R (- 2a b d + 15a b c d - 60a b c d + 47b c d)n + 60b c d +--R * +--R 2 +--R x +--R + +--R 4 4 3 3 3 3 4 4 3 +--R (- a d + 2a b c d - 2a b c d + b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (- 6a d + 18a b c d - 9a b c d - 12a b c d + 9b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (- 11a d + 40a b c d - 45a b c d - 10a b c d + 26b c )n - 6a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 24a b c d - 36a b c d + 24a b c d + 24b c +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (- a c d + 3a b c d - 3a b c d + a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 +--R (- 6a c d + 21a b c d - 24a b c d + 9a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 3 +--R (- 11a c d + 42a b c d - 57a b c d + 26a b c )n - 6a c d +--R + +--R 3 2 2 2 2 3 3 4 +--R 24a b c d - 36a b c d + 24a b c +--R * +--R (- n - 5)log(d x + c) n log(b x + a) +--R %e %e +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (10a d - 40a b c d + 60a b c d - 40a b c d + 10b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (35a d - 140a b c d + 210a b c d - 140a b c d + 35b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (50a d - 200a b c d + 300a b c d - 200a b c d + 50b c )n + 24a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96a b c d + 144a b c d - 96a b c d + 24b c +--R Type: Union(Expression(Integer),...) +--E 2660 + +--S 2661 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 4 4 5 3 4 4 3 4 3 4 +--R 6b d x + ((- 6a b d + 6b c d )n + 30b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (3a b d - 6a b c d + 3b c d )n +--R + +--R 2 2 4 3 3 4 2 2 4 2 2 +--R (3a b d - 30a b c d + 27b c d )n + 60b c d +--R * +--R 3 +--R x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (- a b d + 3a b c d - 3a b c d + b c d)n +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (- 3a b d + 18a b c d - 27a b c d + 12b c d)n +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 3 +--R (- 2a b d + 15a b c d - 60a b c d + 47b c d)n + 60b c d +--R * +--R 2 +--R x +--R + +--R 4 4 3 3 3 3 4 4 3 +--R (- a d + 2a b c d - 2a b c d + b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (- 6a d + 18a b c d - 9a b c d - 12a b c d + 9b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 11a d + 40a b c d - 45a b c d - 10a b c d + 26b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - 6a d + 24a b c d - 36a b c d + 24a b c d + 24b c +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (- a c d + 3a b c d - 3a b c d + a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 +--R (- 6a c d + 21a b c d - 24a b c d + 9a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 3 +--R (- 11a c d + 42a b c d - 57a b c d + 26a b c )n - 6a c d +--R + +--R 3 2 2 2 2 3 3 4 +--R 24a b c d - 36a b c d + 24a b c +--R * +--R (- n - 5)log(d x + c) n log(b x + a) +--R %e %e +--R + +--R 3 n + 1 - n - 1 +--R - 6b (b x + a) (d x + c) +--R + +--R 2 3 2 3 n + 1 - n - 2 +--R ((6a b d - 6b c)n + 6a b d - 6b c)(b x + a) (d x + c) +--R + +--R 2 2 2 3 2 2 2 2 2 3 2 +--R (- 3a b d + 6a b c d - 3b c )n + (- 9a b d + 18a b c d - 9b c )n +--R + +--R 2 2 2 3 2 +--R - 6a b d + 12a b c d - 6b c +--R * +--R n + 1 - n - 3 +--R (b x + a) (d x + c) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (6a d - 18a b c d + 18a b c d - 6b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11a d - 33a b c d + 33a b c d - 11b c )n + 6a d - 18a b c d +--R + +--R 2 2 3 3 +--R 18a b c d - 6b c +--R * +--R n + 1 - n - 4 +--R (b x + a) (d x + c) +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (10a d - 40a b c d + 60a b c d - 40a b c d + 10b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (35a d - 140a b c d + 210a b c d - 140a b c d + 35b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (50a d - 200a b c d + 300a b c d - 200a b c d + 50b c )n + 24a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96a b c d + 144a b c d - 96a b c d + 24b c +--R Type: Expression(Integer) +--E 2661 + +--S 2662 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (9a d - 36a b c d + 54a b c d - 36a b c d + 9b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (26a d - 104a b c d + 156a b c d - 104a b c d + 26b c )n + 24a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96a b c d + 144a b c d - 96a b c d + 24b c +--R * +--R (- n - 5)log(d x + c) n log(b x + a) +--R %e %e +--R + +--R 4 n - n - 1 +--R - 6b (b x + a) (d x + c) +--R + +--R 3 n + 1 3 4 3 4 n +--R (6b d (b x + a) + ((6a b d - 6b c)n + 6a b d - 6b c)(b x + a) ) +--R * +--R - n - 2 +--R (d x + c) +--R + +--R 2 2 3 2 2 3 n + 1 +--R ((- 6a b d + 6b c d)n - 12a b d + 12b c d)(b x + a) +--R + +--R 2 2 2 3 4 2 2 +--R (- 3a b d + 6a b c d - 3b c )n +--R + +--R 2 2 2 3 4 2 2 2 2 3 4 2 +--R (- 9a b d + 18a b c d - 9b c )n - 6a b d + 12a b c d - 6b c +--R * +--R n +--R (b x + a) +--R * +--R - n - 3 +--R (d x + c) +--R + +--R 2 3 2 2 3 2 2 +--R (3a b d - 6a b c d + 3b c d)n +--R + +--R 2 3 2 2 3 2 2 3 2 2 +--R (15a b d - 30a b c d + 15b c d)n + 18a b d - 36a b c d +--R + +--R 3 2 +--R 18b c d +--R * +--R n + 1 +--R (b x + a) +--R + +--R 3 3 2 2 2 3 2 4 3 3 +--R (a b d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (6a b d - 18a b c d + 18a b c d - 6b c )n +--R + +--R 3 3 2 2 2 3 2 4 3 3 3 +--R (11a b d - 33a b c d + 33a b c d - 11b c )n + 6a b d +--R + +--R 2 2 2 3 2 4 3 +--R - 18a b c d + 18a b c d - 6b c +--R * +--R n +--R (b x + a) +--R * +--R - n - 4 +--R (d x + c) +--R + +--R 3 4 2 3 2 2 2 3 3 3 +--R (- a d + 3a b c d - 3a b c d + b c d)n +--R + +--R 3 4 2 3 2 2 2 3 3 2 +--R (- 9a d + 27a b c d - 27a b c d + 9b c d)n +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 2 3 +--R (- 26a d + 78a b c d - 78a b c d + 26b c d)n - 24a d + 72a b c d +--R + +--R 2 2 2 3 3 +--R - 72a b c d + 24b c d +--R * +--R n + 1 - n - 5 +--R (b x + a) (d x + c) +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (9a d - 36a b c d + 54a b c d - 36a b c d + 9b c )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (26a d - 104a b c d + 156a b c d - 104a b c d + 26b c )n + 24a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96a b c d + 144a b c d - 96a b c d + 24b c +--R Type: Expression(Integer) +--E 2662 + +)clear all + +--S 2663 of 2952 +t0000:=(a+b*x)^(-2+n)*(c+d*x)^(1-n) +--R +--R +--R n - 2 - n + 1 +--R (1) (b x + a) (d x + c) +--R Type: Expression(Integer) +--E 2663 + +--S 2664 of 2952 +--r0000:=d*(a+b*x)^n*(c+d*x)^(1-n)/(b*(b*c-a*d)*(1-n)*n)-_ +-- (a+b*x)^(-1+n)*(c+d*x)^(2-n)/((b*c-a*d)*(1-n))-_ +-- d*(a+b*x)^n*(c+d*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,b*(c+d*x)/(b*c-a*d))/_ +-- (b*(b*c-a*d)*(1-n)*n*(-d*(a+b*x)/(b*c-a*d))^n),_ +-- d*(a+b*x)^n*(c+d*x)^(1-n)/(b*(b*c-a*d)*(1-n))+_ +-- d*(a+b*x)^n*(c+d*x)^(1-n)/(b*(b*c-a*d)*n)-_ +-- (a+b*x)^(-1+n)*(c+d*x)^(2-n)/((b*c-a*d)*(1-n))-_ +-- d*(a+b*x)^n*(c+d*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,b*(c+d*x)/(b*c-a*d))/_ +-- (b*(b*c-a*d)*(1-n)*n*(-d*(a+b*x)/(b*c-a*d))^n) +--E 2664 + +--S 2665 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R ++ n - 2 - n + 1 +--R (2) | (%BJ b + a) (%BJ d + c) d%BJ +--R ++ +--R Type: Union(Expression(Integer),...) +--E 2665 + +--S 2666 of 2952 +--m0000:=a0000 - r0000 +--E 2666 + +--S 2667 of 2952 +--d0000:=D(m0000,x) +--E 2667 + +)clear all + +--S 2668 of 2952 +t0000:=(a+b*x)^(1+n)*(c+d*x)^(-1-n) +--R +--R +--R n + 1 - n - 1 +--R (1) (b x + a) (d x + c) +--R Type: Expression(Integer) +--E 2668 + +--S 2669 of 2952 +--r0000:=-(a+b*x)^(1+n)/(d*n*(c+d*x)^n)+b*(1+n)*(a+b*x)^n*(c+d*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,b*(c+d*x)/(b*c-a*d))/_ +-- (d^2*(1-n)*n*(-d*(a+b*x)/(b*c-a*d))^n),_ +-- (a+b*x)^(1+n)/(d*(c+d*x)^n)-(1+n)*(a+b*x)^(1+n)/(d*n*(c+d*x)^n)+_ +-- b*(1+n)*(a+b*x)^n*(c+d*x)^(1-n)*_ +-- hypergeometric(1-n,-n,2-n,b*(c+d*x)/(b*c-a*d))/_ +-- (d^2*(1-n)*n*(-d*(a+b*x)/(b*c-a*d))^n) +--E 2669 + +--S 2670 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R ++ n + 1 - n - 1 +--R (2) | (%BJ b + a) (%BJ d + c) d%BJ +--R ++ +--R Type: Union(Expression(Integer),...) +--E 2670 + +--S 2671 of 2952 +--m0000:=a0000 - r0000 +--E 2671 + +--S 2672 of 2952 +--d0000:=D(m0000,x) +--E 2672 + +)clear all + +--S 2673 of 2952 +t0000:=(a+b*x)^5/(a*d/b+d*x)^3 +--R +--R +--R 5 2 4 2 3 +--R b x + 2a b x + a b +--R (1) -------------------- +--R 3 +--R d +--R Type: Fraction(Polynomial(Integer)) +--E 2673 + +--S 2674 of 2952 +r0000:=1/3*b^2*(a+b*x)^3/d^3 +--R +--R +--R 1 5 3 4 2 2 3 1 3 2 +--R - b x + a b x + a b x + - a b +--R 3 3 +--R (2) -------------------------------- +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2674 + +--S 2675 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 5 3 4 2 2 3 +--R b x + 3a b x + 3a b x +--R (3) ----------------------- +--R 3 +--R 3d +--R Type: Union(Expression(Integer),...) +--E 2675 + +--S 2676 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 3 2 +--R a b +--R (4) - ---- +--R 3 +--R 3d +--R Type: Expression(Integer) +--E 2676 + +--S 2677 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2677 + +)clear all + +--S 2678 of 2952 +t0000:=(a+b*x)^4/(a*d/b+d*x)^3 +--R +--R +--R 4 3 +--R b x + a b +--R (1) ---------- +--R 3 +--R d +--R Type: Fraction(Polynomial(Integer)) +--E 2678 + +--S 2679 of 2952 +r0000:=a*b^3*x/d^3+1/2*b^4*x^2/d^3 +--R +--R +--R 1 4 2 3 +--R - b x + a b x +--R 2 +--R (2) -------------- +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2679 + +--S 2680 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 4 2 3 +--R b x + 2a b x +--R (3) ------------- +--R 3 +--R 2d +--R Type: Union(Expression(Integer),...) +--E 2680 + +--S 2681 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2681 + +--S 2682 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2682 + +)clear all + +--S 2683 of 2952 +t0000:=(a+b*x)^3/(a*d/b+d*x)^3 +--R +--R +--R 3 +--R b +--R (1) -- +--R 3 +--R d +--R Type: Fraction(Polynomial(Integer)) +--E 2683 + +--S 2684 of 2952 +r0000:=b^3*x/d^3 +--R +--R +--R 3 +--R b x +--R (2) --- +--R 3 +--R d +--R Type: Fraction(Polynomial(Integer)) +--E 2684 + +--S 2685 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 +--R b x +--R (3) --- +--R 3 +--R d +--R Type: Union(Expression(Integer),...) +--E 2685 + +--S 2686 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2686 + +--S 2687 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2687 + +)clear all + +--S 2688 of 2952 +t0000:=(a+b*x)^2/(a*d/b+d*x)^3 +--R +--R +--R 3 +--R b +--R (1) ------------ +--R 3 3 +--R b d x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 2688 + +--S 2689 of 2952 +r0000:=b^2*log(a+b*x)/d^3 +--R +--R +--R 2 +--R b log(b x + a) +--R (2) -------------- +--R 3 +--R d +--R Type: Expression(Integer) +--E 2689 + +--S 2690 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R b log(b x + a) +--R (3) -------------- +--R 3 +--R d +--R Type: Union(Expression(Integer),...) +--E 2690 + +--S 2691 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2691 + +--S 2692 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2692 + +)clear all + +--S 2693 of 2952 +t0000:=(a+b*x)/(a*d/b+d*x)^3 +--R +--R +--R 3 +--R b +--R (1) ------------------------ +--R 2 3 2 3 2 3 +--R b d x + 2a b d x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 2693 + +--S 2694 of 2952 +r0000:=-b^2/(d^3*(a+b*x)) +--R +--R +--R 2 +--R b +--R (2) - ------------ +--R 3 3 +--R b d x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 2694 + +--S 2695 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R b +--R (3) - ------------ +--R 3 3 +--R b d x + a d +--R Type: Union(Expression(Integer),...) +--E 2695 + +--S 2696 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2696 + +--S 2697 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2697 + +)clear all + +--S 2698 of 2952 +t0000:=1/((a+b*x)*(a*d/b+d*x)^3) +--R +--R +--R 3 +--R b +--R (1) ------------------------------------------------ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R b d x + 4a b d x + 6a b d x + 4a b d x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 2698 + +--S 2699 of 2952 +r0000:=-1/3*b^2/(d^3*(a+b*x)^3) +--R +--R +--R 1 2 +--R - b +--R 3 +--R (2) - ------------------------------------ +--R 3 3 3 2 3 2 2 3 3 3 +--R b d x + 3a b d x + 3a b d x + a d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2699 + +--S 2700 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R b +--R (3) - -------------------------------------- +--R 3 3 3 2 3 2 2 3 3 3 +--R 3b d x + 9a b d x + 9a b d x + 3a d +--R Type: Union(Expression(Integer),...) +--E 2700 + +--S 2701 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2701 + +--S 2702 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2702 + +)clear all + +--S 2703 of 2952 +t0000:=1/((a+b*x)^2*(a*d/b+d*x)^3) +--R +--R +--R 3 +--R b +--R (1) -------------------------------------------------------------- +--R 5 3 5 4 3 4 2 3 3 3 3 2 3 2 4 3 5 3 +--R b d x + 5a b d x + 10a b d x + 10a b d x + 5a b d x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 2703 + +--S 2704 of 2952 +r0000:=-1/4*b^2/(d^3*(a+b*x)^4) +--R +--R +--R 1 2 +--R - b +--R 4 +--R (2) - ------------------------------------------------ +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R b d x + 4a b d x + 6a b d x + 4a b d x + a d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2704 + +--S 2705 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R b +--R (3) - ----------------------------------------------------- +--R 4 3 4 3 3 3 2 2 3 2 3 3 4 3 +--R 4b d x + 16a b d x + 24a b d x + 16a b d x + 4a d +--R Type: Union(Expression(Integer),...) +--E 2705 + +--S 2706 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2706 + +--S 2707 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2707 + +)clear all + +--S 2708 of 2952 +t0000:=1/((a+b*x)^3*(a*d/b+d*x)^3) +--R +--R +--R (1) +--R 3 +--R b +--R --------------------------------------------------------------------------- +--R 6 3 6 5 3 5 2 4 3 4 3 3 3 3 4 2 3 2 5 3 6 3 +--R b d x + 6a b d x + 15a b d x + 20a b d x + 15a b d x + 6a b d x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 2708 + +--S 2709 of 2952 +r0000:=-1/5*b^2/(d^3*(a+b*x)^5) +--R +--R +--R 1 2 +--R - b +--R 5 +--R (2) - -------------------------------------------------------------- +--R 5 3 5 4 3 4 2 3 3 3 3 2 3 2 4 3 5 3 +--R b d x + 5a b d x + 10a b d x + 10a b d x + 5a b d x + a d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2709 + +--S 2710 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R b +--R (3) - ------------------------------------------------------------------ +--R 5 3 5 4 3 4 2 3 3 3 3 2 3 2 4 3 5 3 +--R 5b d x + 25a b d x + 50a b d x + 50a b d x + 25a b d x + 5a d +--R Type: Union(Expression(Integer),...) +--E 2710 + +--S 2711 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2711 + +--S 2712 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2712 + +)clear all + +--S 2713 of 2952 +t0000:=(b*c/d+b*x)^5/(c+d*x)^3 +--R +--R +--R 5 2 2 5 5 2 +--R b d x + 2b c d x + b c +--R (1) ------------------------ +--R 5 +--R d +--R Type: Fraction(Polynomial(Integer)) +--E 2713 + +--S 2714 of 2952 +r0000:=1/3*b^5*(c+d*x)^3/d^6 +--R +--R +--R 1 5 3 3 5 2 2 5 2 1 5 3 +--R - b d x + b c d x + b c d x + - b c +--R 3 3 +--R (2) -------------------------------------- +--R 6 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2714 + +--S 2715 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 5 2 3 5 2 5 2 +--R b d x + 3b c d x + 3b c x +--R (3) --------------------------- +--R 5 +--R 3d +--R Type: Union(Expression(Integer),...) +--E 2715 + +--S 2716 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 5 3 +--R b c +--R (4) - ---- +--R 6 +--R 3d +--R Type: Expression(Integer) +--E 2716 + +--S 2717 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2717 + +)clear all + +--S 2718 of 2952 +t0000:=(b*c/d+b*x)^4/(c+d*x)^3 +--R +--R +--R 4 4 +--R b d x + b c +--R (1) ----------- +--R 4 +--R d +--R Type: Fraction(Polynomial(Integer)) +--E 2718 + +--S 2719 of 2952 +r0000:=b^4*c*x/d^4+1/2*b^4*x^2/d^3 +--R +--R +--R 1 4 2 4 +--R - b d x + b c x +--R 2 +--R (2) ---------------- +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2719 + +--S 2720 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 4 2 4 +--R b d x + 2b c x +--R (3) --------------- +--R 4 +--R 2d +--R Type: Union(Expression(Integer),...) +--E 2720 + +--S 2721 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2721 + +--S 2722 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2722 + +)clear all + +--S 2723 of 2952 +t0000:=(b*c/d+b*x)^3/(c+d*x)^3 +--R +--R +--R 3 +--R b +--R (1) -- +--R 3 +--R d +--R Type: Fraction(Polynomial(Integer)) +--E 2723 + +--S 2724 of 2952 +r0000:=b^3*x/d^3 +--R +--R +--R 3 +--R b x +--R (2) --- +--R 3 +--R d +--R Type: Fraction(Polynomial(Integer)) +--E 2724 + +--S 2725 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 +--R b x +--R (3) --- +--R 3 +--R d +--R Type: Union(Expression(Integer),...) +--E 2725 + +--S 2726 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2726 + +--S 2727 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2727 + +)clear all + +--S 2728 of 2952 +t0000:=(b*c/d+b*x)^2/(c+d*x)^3 +--R +--R +--R 2 +--R b +--R (1) ---------- +--R 3 2 +--R d x + c d +--R Type: Fraction(Polynomial(Integer)) +--E 2728 + +--S 2729 of 2952 +r0000:=b^2*log(c+d*x)/d^3 +--R +--R +--R 2 +--R b log(d x + c) +--R (2) -------------- +--R 3 +--R d +--R Type: Expression(Integer) +--E 2729 + +--S 2730 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R b log(d x + c) +--R (3) -------------- +--R 3 +--R d +--R Type: Union(Expression(Integer),...) +--E 2730 + +--S 2731 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2731 + +--S 2732 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2732 + +)clear all + +--S 2733 of 2952 +t0000:=(b*c/d+b*x)/(c+d*x)^3 +--R +--R +--R b +--R (1) ------------------- +--R 3 2 2 2 +--R d x + 2c d x + c d +--R Type: Fraction(Polynomial(Integer)) +--E 2733 + +--S 2734 of 2952 +r0000:=-b/(d^2*(c+d*x)) +--R +--R +--R b +--R (2) - ---------- +--R 3 2 +--R d x + c d +--R Type: Fraction(Polynomial(Integer)) +--E 2734 + +--S 2735 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R b +--R (3) - ---------- +--R 3 2 +--R d x + c d +--R Type: Union(Expression(Integer),...) +--E 2735 + +--S 2736 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2736 + +--S 2737 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2737 + +)clear all + +--S 2738 of 2952 +t0000:=1/((b*c/d+b*x)*(c+d*x)^3) +--R +--R +--R d +--R (1) ------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + b c +--R Type: Fraction(Polynomial(Integer)) +--E 2738 + +--S 2739 of 2952 +r0000:=(-1/3)/(b*(c+d*x)^3) +--R +--R +--R 1 +--R - +--R 3 +--R (2) - ------------------------------------ +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2739 + +--S 2740 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - -------------------------------------- +--R 3 3 2 2 2 3 +--R 3b d x + 9b c d x + 9b c d x + 3b c +--R Type: Union(Expression(Integer),...) +--E 2740 + +--S 2741 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2741 + +--S 2742 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2742 + +)clear all + +--S 2743 of 2952 +t0000:=1/((b*c/d+b*x)^2*(c+d*x)^3) +--R +--R +--R 2 +--R d +--R (1) -------------------------------------------------------------- +--R 2 5 5 2 4 4 2 2 3 3 2 3 2 2 2 4 2 5 +--R b d x + 5b c d x + 10b c d x + 10b c d x + 5b c d x + b c +--R Type: Fraction(Polynomial(Integer)) +--E 2743 + +--S 2744 of 2952 +r0000:=-1/4*d/(b^2*(c+d*x)^4) +--R +--R +--R 1 +--R - d +--R 4 +--R (2) - ------------------------------------------------ +--R 2 4 4 2 3 3 2 2 2 2 2 3 2 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2744 + +--S 2745 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R d +--R (3) - ----------------------------------------------------- +--R 2 4 4 2 3 3 2 2 2 2 2 3 2 4 +--R 4b d x + 16b c d x + 24b c d x + 16b c d x + 4b c +--R Type: Union(Expression(Integer),...) +--E 2745 + +--S 2746 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2746 + +--S 2747 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2747 + +)clear all + +--S 2748 of 2952 +t0000:=1/((b*c/d+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 3 +--R d +--R --------------------------------------------------------------------------- +--R 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 3 5 3 6 +--R b d x + 6b c d x + 15b c d x + 20b c d x + 15b c d x + 6b c d x + b c +--R Type: Fraction(Polynomial(Integer)) +--E 2748 + +--S 2749 of 2952 +r0000:=-1/5*d^2/(b^3*(c+d*x)^5) +--R +--R +--R 1 2 +--R - d +--R 5 +--R (2) - -------------------------------------------------------------- +--R 3 5 5 3 4 4 3 2 3 3 3 3 2 2 3 4 3 5 +--R b d x + 5b c d x + 10b c d x + 10b c d x + 5b c d x + b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2749 + +--S 2750 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R d +--R (3) - ------------------------------------------------------------------ +--R 3 5 5 3 4 4 3 2 3 3 3 3 2 2 3 4 3 5 +--R 5b d x + 25b c d x + 50b c d x + 50b c d x + 25b c d x + 5b c +--R Type: Union(Expression(Integer),...) +--E 2750 + +--S 2751 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2751 + +--S 2752 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2752 + +)clear all + +--S 2753 of 2952 +t0000:=(a+b*x)^5*(a*c+b*c*x)^n +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 n +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )(b c x + a c) +--R Type: Expression(Integer) +--E 2753 + +--S 2754 of 2952 +r0000:=(a*c+b*c*x)^(6+n)/(b*c^6*(6+n)) +--R +--R +--R n + 6 +--R (b c x + a c) +--R (2) ------------------ +--R 6 6 +--R b c n + 6b c +--R Type: Expression(Integer) +--E 2754 + +--S 2755 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R n log(b c x + a c) +--R %e +--R / +--R b n + 6b +--R Type: Union(Expression(Integer),...) +--E 2755 + +--S 2756 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) +--R 6 6 6 5 6 5 2 4 6 4 3 3 6 3 4 2 6 2 5 6 +--R b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x +--R + +--R 6 6 +--R a c +--R * +--R n log(b c x + a c) +--R %e +--R + +--R n + 6 +--R - (b c x + a c) +--R / +--R 6 6 +--R b c n + 6b c +--R Type: Expression(Integer) +--E 2756 + +--S 2757 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) +--R 5 5 5 4 5 4 2 3 5 3 3 2 5 2 4 5 5 5 +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c ) +--R * +--R n log(b c x + a c) +--R %e +--R + +--R n + 5 +--R - (b c x + a c) +--R / +--R 5 +--R c +--R Type: Expression(Integer) +--E 2757 + +)clear all + +--S 2758 of 2952 +t0000:=(a+b*x)^5*(a*c+b*c*x)^3 +--R +--R +--R (1) +--R 8 3 8 7 3 7 2 6 3 6 3 5 3 5 4 4 3 4 5 3 3 3 +--R b c x + 8a b c x + 28a b c x + 56a b c x + 70a b c x + 56a b c x +--R + +--R 6 2 3 2 7 3 8 3 +--R 28a b c x + 8a b c x + a c +--R Type: Polynomial(Integer) +--E 2758 + +--S 2759 of 2952 +r0000:=1/9*c^3*(a+b*x)^9/b +--R +--R +--R (2) +--R 1 9 3 9 8 3 8 2 7 3 7 28 3 6 3 6 4 5 3 5 5 4 3 4 +--R - b c x + a b c x + 4a b c x + -- a b c x + 14a b c x + 14a b c x +--R 9 3 +--R + +--R 28 6 3 3 3 7 2 3 2 8 3 1 9 3 +--R -- a b c x + 4a b c x + a b c x + - a c +--R 3 9 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2759 + +--S 2760 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 8 3 9 7 3 8 2 6 3 7 28 3 5 3 6 4 4 3 5 5 3 3 4 +--R - b c x + a b c x + 4a b c x + -- a b c x + 14a b c x + 14a b c x +--R 9 3 +--R + +--R 28 6 2 3 3 7 3 2 8 3 +--R -- a b c x + 4a b c x + a c x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 2760 + +--S 2761 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 9 3 +--R - a c +--R 9 +--R (4) - ------ +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2761 + +--S 2762 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2762 + +)clear all + +--S 2763 of 2952 +t0000:=(a+b*x)^5*(a*c+b*c*x)^2 +--R +--R +--R (1) +--R 7 2 7 6 2 6 2 5 2 5 3 4 2 4 4 3 2 3 5 2 2 2 +--R b c x + 7a b c x + 21a b c x + 35a b c x + 35a b c x + 21a b c x +--R + +--R 6 2 7 2 +--R 7a b c x + a c +--R Type: Polynomial(Integer) +--E 2763 + +--S 2764 of 2952 +r0000:=1/8*c^2*(a+b*x)^8/b +--R +--R +--R (2) +--R 1 8 2 8 7 2 7 7 2 6 2 6 3 5 2 5 35 4 4 2 4 5 3 2 3 +--R - b c x + a b c x + - a b c x + 7a b c x + -- a b c x + 7a b c x +--R 8 2 4 +--R + +--R 7 6 2 2 2 7 2 1 8 2 +--R - a b c x + a b c x + - a c +--R 2 8 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2764 + +--S 2765 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 7 2 8 6 2 7 7 2 5 2 6 3 4 2 5 35 4 3 2 4 5 2 2 3 +--R - b c x + a b c x + - a b c x + 7a b c x + -- a b c x + 7a b c x +--R 8 2 4 +--R + +--R 7 6 2 2 7 2 +--R - a b c x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 2765 + +--S 2766 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 8 2 +--R - a c +--R 8 +--R (4) - ------ +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2766 + +--S 2767 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2767 + +)clear all + +--S 2768 of 2952 +t0000:=(a+b*x)^5*(a*c+b*c*x) +--R +--R +--R (1) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x + a c +--R Type: Polynomial(Integer) +--E 2768 + +--S 2769 of 2952 +r0000:=1/7*c*(a+b*x)^7/b +--R +--R +--R (2) +--R 1 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - b c x + a b c x + 3a b c x + 5a b c x + 5a b c x + 3a b c x +--R 7 +--R + +--R 6 1 7 +--R a b c x + - a c +--R 7 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2769 + +--S 2770 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 1 6 7 5 6 2 4 5 3 3 4 4 2 3 5 2 6 +--R - b c x + a b c x + 3a b c x + 5a b c x + 5a b c x + 3a b c x + a c x +--R 7 +--R Type: Polynomial(Fraction(Integer)) +--E 2770 + +--S 2771 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 1 7 +--R - a c +--R 7 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2771 + +--S 2772 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2772 + +)clear all + +--S 2773 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (1) -------------------------------------- +--R c +--R Type: Fraction(Polynomial(Integer)) +--E 2773 + +--S 2774 of 2952 +r0000:=1/5*(a+b*x)^5/(b*c) +--R +--R +--R 1 5 5 4 4 2 3 3 3 2 2 4 1 5 +--R - b x + a b x + 2a b x + 2a b x + a b x + - a +--R 5 5 +--R (2) -------------------------------------------------- +--R b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2774 + +--S 2775 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 4 5 3 4 2 2 3 3 2 4 +--R b x + 5a b x + 10a b x + 10a b x + 5a x +--R (3) ------------------------------------------- +--R 5c +--R Type: Union(Expression(Integer),...) +--E 2775 + +--S 2776 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 5 +--R a +--R (4) - ---- +--R 5b c +--R Type: Expression(Integer) +--E 2776 + +--S 2777 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2777 + +)clear all + +--S 2778 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 2 +--R c +--R Type: Fraction(Polynomial(Integer)) +--E 2778 + +--S 2779 of 2952 +r0000:=1/4*(a+b*x)^4/(b*c^2) +--R +--R +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - b x + a b x + - a b x + a b x + - a +--R 4 2 4 +--R (2) ----------------------------------------- +--R 2 +--R b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2779 + +--S 2780 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 4 2 3 2 2 3 +--R b x + 4a b x + 6a b x + 4a x +--R (3) ------------------------------- +--R 2 +--R 4c +--R Type: Union(Expression(Integer),...) +--E 2780 + +--S 2781 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 4 +--R a +--R (4) - ----- +--R 2 +--R 4b c +--R Type: Expression(Integer) +--E 2781 + +--S 2782 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2782 + +)clear all + +--S 2783 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^3 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 3 +--R c +--R Type: Fraction(Polynomial(Integer)) +--E 2783 + +--S 2784 of 2952 +r0000:=1/3*(a+b*x)^3/(b*c^3) +--R +--R +--R 1 3 3 2 2 2 1 3 +--R - b x + a b x + a b x + - a +--R 3 3 +--R (2) ------------------------------ +--R 3 +--R b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2784 + +--S 2785 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 2 2 +--R b x + 3a b x + 3a x +--R (3) --------------------- +--R 3 +--R 3c +--R Type: Union(Expression(Integer),...) +--E 2785 + +--S 2786 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R 3 +--R a +--R (4) - ----- +--R 3 +--R 3b c +--R Type: Expression(Integer) +--E 2786 + +--S 2787 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2787 + +)clear all + +--S 2788 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^4 +--R +--R +--R b x + a +--R (1) ------- +--R 4 +--R c +--R Type: Fraction(Polynomial(Integer)) +--E 2788 + +--S 2789 of 2952 +r0000:=a*x/c^4+1/2*b*x^2/c^4 +--R +--R +--R 1 2 +--R - b x + a x +--R 2 +--R (2) ------------ +--R 4 +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2789 + +--S 2790 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R b x + 2a x +--R (3) ----------- +--R 4 +--R 2c +--R Type: Union(Expression(Integer),...) +--E 2790 + +--S 2791 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2791 + +--S 2792 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2792 + +)clear all + +--S 2793 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^5 +--R +--R +--R 1 +--R (1) -- +--R 5 +--R c +--R Type: Fraction(Polynomial(Integer)) +--E 2793 + +--S 2794 of 2952 +r0000:=x/c^5 +--R +--R +--R x +--R (2) -- +--R 5 +--R c +--R Type: Fraction(Polynomial(Integer)) +--E 2794 + +--S 2795 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R x +--R (3) -- +--R 5 +--R c +--R Type: Union(Expression(Integer),...) +--E 2795 + +--S 2796 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2796 + +--S 2797 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2797 + +)clear all + +--S 2798 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^6 +--R +--R +--R 1 +--R (1) ------------ +--R 6 6 +--R b c x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 2798 + +--S 2799 of 2952 +r0000:=log(a+b*x)/(b*c^6) +--R +--R +--R log(b x + a) +--R (2) ------------ +--R 6 +--R b c +--R Type: Expression(Integer) +--E 2799 + +--S 2800 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R log(b x + a) +--R (3) ------------ +--R 6 +--R b c +--R Type: Union(Expression(Integer),...) +--E 2800 + +--S 2801 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2801 + +--S 2802 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2802 + +)clear all + +--S 2803 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^7 +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 7 2 7 2 7 +--R b c x + 2a b c x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 2803 + +--S 2804 of 2952 +r0000:=(-1)/(b*c^7*(a+b*x)) +--R +--R +--R 1 +--R (2) - -------------- +--R 2 7 7 +--R b c x + a b c +--R Type: Fraction(Polynomial(Integer)) +--E 2804 + +--S 2805 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - -------------- +--R 2 7 7 +--R b c x + a b c +--R Type: Union(Expression(Integer),...) +--E 2805 + +--S 2806 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2806 + +--S 2807 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2807 + +)clear all + +--S 2808 of 2952 +t0000:=(a+b*x)^5/(a*c+b*c*x)^8 +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 8 3 2 8 2 2 8 3 8 +--R b c x + 3a b c x + 3a b c x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 2808 + +--S 2809 of 2952 +r0000:=(-1/2)/(b*c^8*(a+b*x)^2) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - -------------------------- +--R 3 8 2 2 8 2 8 +--R b c x + 2a b c x + a b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2809 + +--S 2810 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 +--R (3) - ---------------------------- +--R 3 8 2 2 8 2 8 +--R 2b c x + 4a b c x + 2a b c +--R Type: Union(Expression(Integer),...) +--E 2810 + +--S 2811 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2811 + +--S 2812 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2812 + +)clear all + +--S 2813 of 2952 +t0000:=1/(sqrt(-2-3*x)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 3x - 2 \|3x + 2 +--R Type: Expression(Integer) +--E 2813 + +--S 2814 of 2952 +r0000:=1/3*log(2+3*x)*sqrt(2+3*x)/sqrt(-2-3*x) +--R +--R +--R +------+ +--R log(3x + 2)\|3x + 2 +--R (2) -------------------- +--R +--------+ +--R 3\|- 3x - 2 +--R Type: Expression(Integer) +--E 2814 + +--S 2815 of 2952 +--a0000:=integrate(t0000,x) +--E 2815 + +--S 2816 of 2952 +--m0000:=a0000 - r0000 +--E 2816 + +--S 2817 of 2952 +--d0000:=D(m0000,x) +--E 2817 + +)clear all + +--S 2818 of 2952 +t0000:=a+b*x+c*x^2+d*x^3 +--R +--R +--R 3 2 +--R (1) d x + c x + b x + a +--R Type: Polynomial(Integer) +--E 2818 + +--S 2819 of 2952 +r0000:=a*x+1/2*b*x^2+1/3*c*x^3+1/4*d*x^4 +--R +--R +--R 1 4 1 3 1 2 +--R (2) - d x + - c x + - b x + a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 2819 + +--S 2820 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 4 1 3 1 2 +--R (3) - d x + - c x + - b x + a x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 2820 + +--S 2821 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2821 + +--S 2822 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2822 + +)clear all + +--S 2823 of 2952 +t0000:=-x^3+x^4 +--R +--R +--R 4 3 +--R (1) x - x +--R Type: Polynomial(Integer) +--E 2823 + +--S 2824 of 2952 +r0000:=-1/4*x^4+1/5*x^5 +--R +--R +--R 1 5 1 4 +--R (2) - x - - x +--R 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 2824 + +--S 2825 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 5 1 4 +--R (3) - x - - x +--R 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 2825 + +--S 2826 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2826 + +--S 2827 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2827 + +)clear all + +--S 2828 of 2952 +t0000:=-1+x^5 +--R +--R +--R 5 +--R (1) x - 1 +--R Type: Polynomial(Integer) +--E 2828 + +--S 2829 of 2952 +r0000:=-x+1/6*x^6 +--R +--R +--R 1 6 +--R (2) - x - x +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 2829 + +--S 2830 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 6 +--R (3) - x - x +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 2830 + +--S 2831 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2831 + +--S 2832 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2832 + +)clear all + +--S 2833 of 2952 +t0000:=7+4*x +--R +--R +--R (1) 4x + 7 +--R Type: Polynomial(Integer) +--E 2833 + +--S 2834 of 2952 +r0000:=7*x+2*x^2 +--R +--R +--R 2 +--R (2) 2x + 7x +--R Type: Polynomial(Integer) +--E 2834 + +--S 2835 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R (3) 2x + 7x +--R Type: Polynomial(Fraction(Integer)) +--E 2835 + +--S 2836 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2836 + +--S 2837 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2837 + +)clear all + +--S 2838 of 2952 +t0000:=4*x+%pi*x^3 +--R +--R +--R 3 +--R (1) %pi x + 4x +--R Type: Expression(Integer) +--E 2838 + +--S 2839 of 2952 +r0000:=2*x^2+1/4*%pi*x^4 +--R +--R +--R 4 2 +--R %pi x + 8x +--R (2) ------------ +--R 4 +--R Type: Expression(Integer) +--E 2839 + +--S 2840 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 4 2 +--R %pi x + 8x +--R (3) ------------ +--R 4 +--R Type: Union(Expression(Integer),...) +--E 2840 + +--S 2841 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2841 + +--S 2842 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2842 + +)clear all + +--S 2843 of 2952 +t0000:=2*x+5*x^2 +--R +--R +--R 2 +--R (1) 5x + 2x +--R Type: Polynomial(Integer) +--E 2843 + +--S 2844 of 2952 +r0000:=x^2+5/3*x^3 +--R +--R +--R 5 3 2 +--R (2) - x + x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 2844 + +--S 2845 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 5 3 2 +--R (3) - x + x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 2845 + +--S 2846 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2846 + +--S 2847 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2847 + +)clear all + +--S 2848 of 2952 +t0000:=1/2*x^2+1/3*x^3 +--R +--R +--R 1 3 1 2 +--R (1) - x + - x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 2848 + +--S 2849 of 2952 +r0000:=1/6*x^3+1/12*x^4 +--R +--R +--R 1 4 1 3 +--R (2) -- x + - x +--R 12 6 +--R Type: Polynomial(Fraction(Integer)) +--E 2849 + +--S 2850 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 4 1 3 +--R (3) -- x + - x +--R 12 6 +--R Type: Polynomial(Fraction(Integer)) +--E 2850 + +--S 2851 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2851 + +--S 2852 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2852 + +)clear all + +--S 2853 of 2952 +t0000:=3-5*x+2*x^2 +--R +--R +--R 2 +--R (1) 2x - 5x + 3 +--R Type: Polynomial(Integer) +--E 2853 + +--S 2854 of 2952 +r0000:=3*x-5/2*x^2+2/3*x^3 +--R +--R +--R 2 3 5 2 +--R (2) - x - - x + 3x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 2854 + +--S 2855 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 5 2 +--R (3) - x - - x + 3x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 2855 + +--S 2856 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2856 + +--S 2857 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2857 + +)clear all + +--S 2858 of 2952 +t0000:=-2*x+x^2+x^3 +--R +--R +--R 3 2 +--R (1) x + x - 2x +--R Type: Polynomial(Integer) +--E 2858 + +--S 2859 of 2952 +r0000:=-x^2+1/3*x^3+1/4*x^4 +--R +--R +--R 1 4 1 3 2 +--R (2) - x + - x - x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 2859 + +--S 2860 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 4 1 3 2 +--R (3) - x + - x - x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 2860 + +--S 2861 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2861 + +--S 2862 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2862 + +)clear all + +--S 2863 of 2952 +t0000:=1-x^2-3*x^5 +--R +--R +--R 5 2 +--R (1) - 3x - x + 1 +--R Type: Polynomial(Integer) +--E 2863 + +--S 2864 of 2952 +r0000:=x-1/3*x^3-1/2*x^6 +--R +--R +--R 1 6 1 3 +--R (2) - - x - - x + x +--R 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 2864 + +--S 2865 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 6 1 3 +--R (3) - - x - - x + x +--R 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 2865 + +--S 2866 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2866 + +--S 2867 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2867 + +)clear all + +--S 2868 of 2952 +t0000:=5+2*x+3*x^2+4*x^3 +--R +--R +--R 3 2 +--R (1) 4x + 3x + 2x + 5 +--R Type: Polynomial(Integer) +--E 2868 + +--S 2869 of 2952 +r0000:=5*x+x^2+x^3+x^4 +--R +--R +--R 4 3 2 +--R (2) x + x + x + 5x +--R Type: Polynomial(Integer) +--E 2869 + +--S 2870 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 4 3 2 +--R (3) x + x + x + 5x +--R Type: Polynomial(Fraction(Integer)) +--E 2870 + +--S 2871 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2871 + +--S 2872 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 2872 + +)clear all + +--S 2873 of 2952 +t0000:=a+d/x^3+c/x^2+b/x +--R +--R +--R 3 2 +--R a x + b x + c x + d +--R (1) --------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 2873 + +--S 2874 of 2952 +r0000:=-1/2*d/x^2-c/x+a*x+b*log(x) +--R +--R +--R 2 3 +--R 2b x log(x) + 2a x - 2c x - d +--R (2) ------------------------------ +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 2874 + +--S 2875 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 3 +--R 2b x log(x) + 2a x - 2c x - d +--R (3) ------------------------------ +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 2875 + +--S 2876 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2876 + +--S 2877 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2877 + +)clear all + +--S 2878 of 2952 +t0000:=1/x^5+x+x^5 +--R +--R +--R 10 6 +--R x + x + 1 +--R (1) ------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 2878 + +--S 2879 of 2952 +r0000:=(-1/4)/x^4+1/2*x^2+1/6*x^6 +--R +--R +--R 1 10 1 6 1 +--R - x + - x - - +--R 6 2 4 +--R (2) ---------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2879 + +--S 2880 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 10 6 +--R 2x + 6x - 3 +--R (3) -------------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 2880 + +--S 2881 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2881 + +--S 2882 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2882 + +)clear all + +--S 2883 of 2952 +t0000:=1/x^3+1/x^2+1/x +--R +--R +--R 2 +--R x + x + 1 +--R (1) ---------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 2883 + +--S 2884 of 2952 +r0000:=(-1/2)/x^2+(-1)/x+log(x) +--R +--R +--R 2 +--R 2x log(x) - 2x - 1 +--R (2) ------------------ +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 2884 + +--S 2885 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R 2x log(x) - 2x - 1 +--R (3) ------------------ +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 2885 + +--S 2886 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2886 + +--S 2887 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2887 + +)clear all + +--S 2888 of 2952 +t0000:=(-2)/x^2+3/x +--R +--R +--R 3x - 2 +--R (1) ------ +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 2888 + +--S 2889 of 2952 +r0000:=2/x+3*log(x) +--R +--R +--R 3x log(x) + 2 +--R (2) ------------- +--R x +--R Type: Expression(Integer) +--E 2889 + +--S 2890 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3x log(x) + 2 +--R (3) ------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 2890 + +--S 2891 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2891 + +--S 2892 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2892 + +)clear all + +--S 2893 of 2952 +t0000:=(-1/7)/x^6+x^6 +--R +--R +--R 12 1 +--R x - - +--R 7 +--R (1) ------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2893 + +--S 2894 of 2952 +r0000:=1/35/x^5+1/7*x^7 +--R +--R +--R 1 12 1 +--R - x + -- +--R 7 35 +--R (2) ---------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2894 + +--S 2895 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 1 12 1 +--R - x + -- +--R 7 35 +--R (3) ---------- +--R 5 +--R x +--R Type: Union(Expression(Fraction(Integer)),...) +--E 2895 + +--S 2896 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Fraction(Integer)) +--E 2896 + +--S 2897 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Fraction(Integer)) +--E 2897 + +)clear all + +--S 2898 of 2952 +t0000:=1+1/x+x +--R +--R +--R 2 +--R x + x + 1 +--R (1) ---------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 2898 + +--S 2899 of 2952 +r0000:=x+1/2*x^2+log(x) +--R +--R +--R 2 +--R 2log(x) + x + 2x +--R (2) ----------------- +--R 2 +--R Type: Expression(Integer) +--E 2899 + +--S 2900 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 2 +--R 2log(x) + x + 2x +--R (3) ----------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 2900 + +--S 2901 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2901 + +--S 2902 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2902 + +)clear all + +--S 2903 of 2952 +t0000:=(-3)/x^3+4/x^2 +--R +--R +--R 4x - 3 +--R (1) ------ +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 2903 + +--S 2904 of 2952 +r0000:=3/2/x^2+(-4)/x +--R +--R +--R 3 +--R - 4x + - +--R 2 +--R (2) -------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2904 + +--S 2905 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R - 8x + 3 +--R (3) -------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 2905 + +--S 2906 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2906 + +--S 2907 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2907 + +)clear all + +--S 2908 of 2952 +t0000:=1/x+2*x+x^2 +--R +--R +--R 3 2 +--R x + 2x + 1 +--R (1) ------------ +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 2908 + +--S 2909 of 2952 +r0000:=x^2+1/3*x^3+log(x) +--R +--R +--R 3 2 +--R 3log(x) + x + 3x +--R (2) ------------------ +--R 3 +--R Type: Expression(Integer) +--E 2909 + +--S 2910 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 2 +--R 3log(x) + x + 3x +--R (3) ------------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 2910 + +--S 2911 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2911 + +--S 2912 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2912 + +)clear all + +--S 2913 of 2952 +t0000:=x^(5/6)-x^3 +--R +--R +--R 6+-+5 3 +--R (1) \|x - x +--R Type: Expression(Integer) +--E 2913 + +--S 2914 of 2952 +r0000:=6/11*x^(11/6)-1/4*x^4 +--R +--R +--R 6+-+5 4 +--R 24x \|x - 11x +--R (2) ---------------- +--R 44 +--R Type: Expression(Integer) +--E 2914 + +--S 2915 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 6+-+5 4 +--R 24x \|x - 11x +--R (3) ---------------- +--R 44 +--R Type: Union(Expression(Integer),...) +--E 2915 + +--S 2916 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2916 + +--S 2917 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2917 + +)clear all + +--S 2918 of 2952 +t0000:=33+x^(1/33) +--R +--R +--R 33+-+ +--R (1) \|x + 33 +--R Type: Expression(Integer) +--E 2918 + +--S 2919 of 2952 +r0000:=33*x+33/34*x^(34/33) +--R +--R +--R 33+-+ +--R 33x \|x + 1122x +--R (2) ---------------- +--R 34 +--R Type: Expression(Integer) +--E 2919 + +--S 2920 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 33+-+ +--R 33x \|x + 1122x +--R (3) ---------------- +--R 34 +--R Type: Union(Expression(Integer),...) +--E 2920 + +--S 2921 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2921 + +--S 2922 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2922 + +)clear all + +--S 2923 of 2952 +t0000:=1/2/sqrt(x)+2*sqrt(x) +--R +--R +--R 4x + 1 +--R (1) ------ +--R +-+ +--R 2\|x +--R Type: Expression(Integer) +--E 2923 + +--S 2924 of 2952 +r0000:=4/3*x^(3/2)+sqrt(x) +--R +--R +--R +-+ +--R (4x + 3)\|x +--R (2) ------------ +--R 3 +--R Type: Expression(Integer) +--E 2924 + +--S 2925 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ +--R (4x + 3)\|x +--R (3) ------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 2925 + +--S 2926 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2926 + +--S 2927 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2927 + +)clear all + +--S 2928 of 2952 +t0000:=(-1)/x^2+10/x+6*sqrt(x) +--R +--R +--R 2 +-+ +--R 6x \|x + 10x - 1 +--R (1) ----------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 2928 + +--S 2929 of 2952 +r0000:=1/x+4*x^(3/2)+10*log(x) +--R +--R +--R 2 +-+ +--R 4x \|x + 10x log(x) + 1 +--R (2) ------------------------ +--R x +--R Type: Expression(Integer) +--E 2929 + +--S 2930 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ 2 +-+ +--R 20x log(\|x ) + 4x \|x + 1 +--R (3) --------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 2930 + +--S 2931 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +-+ +--R (4) 20log(\|x ) - 10log(x) +--R Type: Expression(Integer) +--E 2931 + +--S 2932 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2932 + +)clear all + +--S 2933 of 2952 +t0000:=1/x^(3/2)+x^(3/2) +--R +--R +--R 3 +--R x + 1 +--R (1) ------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 2933 + +--S 2934 of 2952 +r0000:=2/5*x^(5/2)+(-2)/sqrt(x) +--R +--R +--R 3 +--R 2x - 10 +--R (2) -------- +--R +-+ +--R 5\|x +--R Type: Expression(Integer) +--E 2934 + +--S 2935 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 +--R 2x - 10 +--R (3) -------- +--R +-+ +--R 5\|x +--R Type: Union(Expression(Integer),...) +--E 2935 + +--S 2936 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2936 + +--S 2937 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2937 + +)clear all + +--S 2938 of 2952 +t0000:=-5*x^(3/2)+7*x^(5/2) +--R +--R +--R 2 +-+ +--R (1) (7x - 5x)\|x +--R Type: Expression(Integer) +--E 2938 + +--S 2939 of 2952 +r0000:=-2*x^(5/2)+2*x^(7/2) +--R +--R +--R 3 2 +-+ +--R (2) (2x - 2x )\|x +--R Type: Expression(Integer) +--E 2939 + +--S 2940 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R 3 2 +-+ +--R (3) (2x - 2x )\|x +--R Type: Union(Expression(Integer),...) +--E 2940 + +--S 2941 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2941 + +--S 2942 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2942 + +)clear all + +--S 2943 of 2952 +t0000:=-1/2*x+2/sqrt(x)+sqrt(x) +--R +--R +--R +-+ +--R - x\|x + 2x + 4 +--R (1) ---------------- +--R +-+ +--R 2\|x +--R Type: Expression(Integer) +--E 2943 + +--S 2944 of 2952 +r0000:=2/3*x^(3/2)-1/4*x^2+4*sqrt(x) +--R +--R +--R +-+ 2 +--R (8x + 48)\|x - 3x +--R (2) ------------------- +--R 12 +--R Type: Expression(Integer) +--E 2944 + +--S 2945 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ 2 +--R (8x + 48)\|x - 3x +--R (3) ------------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 2945 + +--S 2946 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 2946 + +--S 2947 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2947 + +)clear all + +--S 2948 of 2952 +t0000:=(-2)/x+x^(3/2)+1/5*sqrt(x) +--R +--R +--R 2 +-+ +--R (5x + x)\|x - 10 +--R (1) ------------------ +--R 5x +--R Type: Expression(Integer) +--E 2948 + +--S 2949 of 2952 +r0000:=2/15*x^(3/2)+2/5*x^(5/2)-2*log(x) +--R +--R +--R 2 +-+ +--R (6x + 2x)\|x - 30log(x) +--R (2) ------------------------- +--R 15 +--R Type: Expression(Integer) +--E 2949 + +--S 2950 of 2952 +a0000:=integrate(t0000,x) +--R +--R +--R +-+ 2 +-+ +--R - 60log(\|x ) + (6x + 2x)\|x +--R (3) ------------------------------ +--R 15 +--R Type: Union(Expression(Integer),...) +--E 2950 + +--S 2951 of 2952 +m0000:=a0000 - r0000 +--R +--R +--R +-+ +--R (4) - 4log(\|x ) + 2log(x) +--R Type: Expression(Integer) +--E 2951 + +--S 2952 of 2952 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 2952 + + +)spool + +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} + diff --git a/src/axiom-website/CATS/rich1b.input.pdf b/src/axiom-website/CATS/rich1b.input.pdf new file mode 100644 index 0000000..4a4efb5 Binary files /dev/null and b/src/axiom-website/CATS/rich1b.input.pdf differ diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 1c5dfb2..15bf897 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4235,7 +4235,9 @@ src/input/charlwood.input added 20130715.01.tpd.patch CATS updated with txt, charlwood 20130718.01.tpd.patch -CATS rich1a, rich1b +src/input/rich1a, rich1b +20130719.01.tpd.patch +src/axiom-website/CATS/index.html, rich1a, rich1b