diff --git a/changelog b/changelog index 355b823..74613d0 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100606 tpd src/axiom-website/patches.html 20100606.01.tpd.patch +20100606 tpd src/input/Makefile rule-based algebraic integration +20100606 tpd src/input/richalgebraic300-399.input rule-based algebraic int. 20100605 tpd src/axiom-website/patches.html 20100605.02.tpd.patch 20100605 tpd src/input/Makefile rule-based algebraic integration 20100605 tpd src/input/richalgebraic200-299.input rule-based algebraic int. diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index f82b035..43cd8c2 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2854,6 +2854,8 @@ books/bookvol10.4 add GnuDraw package
books/bookvol8 add 3D graphic file format table
20100605.02.tpd.patch src/input/richalgebraic200-299.input rule-based algebraic integration.
+20100606.01.tpd.patch +src/input/richalgebraic300-399.input rule-based algebraic integration.
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 29c3a26..332efce 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -372,6 +372,7 @@ REGRES= ackermann.regress \ richalgebraic000-099.regress \ richalgebraic100-199.regress \ richalgebraic200-299.regress \ + richalgebraic300-399.regress \ richrational.regress robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ @@ -687,6 +688,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richalgebraic000-099.input \ ${OUT}/richalgebraic100-199.input \ ${OUT}/richalgebraic200-299.input \ + ${OUT}/richalgebraic300-399.input \ ${OUT}/richrational.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ @@ -1032,6 +1034,7 @@ DOCFILES= \ ${DOC}/richalgebraic000-099.input.dvi \ ${DOC}/richalgebraic100-199.input.dvi \ ${DOC}/richalgebraic200-299.input.dvi \ + ${DOC}/richalgebraic300-399.input.dvi \ ${DOC}/richrational.input.dvi \ ${DOC}/rk4draw.input.dvi \ ${DOC}/robidoux.input.dvi ${DOC}/roman.input.dvi \ diff --git a/src/input/richalgebraic300-399.input.pamphlet b/src/input/richalgebraic300-399.input.pamphlet new file mode 100644 index 0000000..d90afda --- /dev/null +++ b/src/input/richalgebraic300-399.input.pamphlet @@ -0,0 +1,15061 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richalgebraic300-399.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richalgebraic300-399.output +)spool richalgebraic300-399.output +)set message test on +)set message auto off +)clear all + +--S 1 of 486 +t0300:= 1/(a+b/x^4)^(1/2)/x^3 +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 4 +--R 3 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R Type: Expression Integer +--E 1 + +--S 2 of 486 +r0300:= -1/2*atanh((a+b/x^4)^(1/2)*x^2/b^(1/2))/b^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R atanh(-------------) +--R +-+ +--R \|b +--R (2) - -------------------- +--R +-+ +--R 2\|b +--R Type: Expression Integer +--E 2 + +--S 3 of 486 +a0300:= integrate(t0300,x) +--R +--R +--R +--------+ +--R | 4 4 +-+ +--------+ +--R - 2b\|a x + b + (a x + 2b)\|b +---+ | 4 +--R log(---------------------------------) \|- b \|a x + b +--R 4 atan(-----------------) +--R x b +--R (3) [--------------------------------------,- -----------------------] +--R +-+ +---+ +--R 4\|b 2\|- b +--R Type: Union(List Expression Integer,...) +--E 3 + +--S 4 of 486 +m0300a:= a0300.1-r0300 +--R +--R +--R +--------+ +--R | 4 +--R 2 |a x + b +--R +--------+ x |-------- +--R | 4 4 +-+ | 4 +--R - 2b\|a x + b + (a x + 2b)\|b \| x +--R log(---------------------------------) + 2atanh(-------------) +--R 4 +-+ +--R x \|b +--R (4) -------------------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression Integer +--E 4 + +--S 5 of 486 +d0300a:= D(m0300a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--------+ +--R 4 +-+ 2 |a x + b | 4 +--R ((- a x - 2b)\|b - 2b x |-------- )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 |a x + b +-+ 4 2 +--R (a x + 2b x ) |-------- \|b + 2a b x + 2b +--R | 4 +--R \| x +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 7 3 |a x + b +-+ | 4 7 2 3 |a x + b +--R (a x + 2b x ) |-------- \|b \|a x + b + (- 2a b x - 2b x ) |-------- +--R | 4 | 4 +--R \| x \| x +--R Type: Expression Integer +--E 5 + +--S 6 of 486 +m0300b:= a0300.2-r0300 +--R +--R +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--------+ +--R | 4 +---+ | 4 +--R +---+ \| x +-+ \|- b \|a x + b +--R \|- b atanh(-------------) - \|b atan(-----------------) +--R +-+ b +--R \|b +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression Integer +--E 6 + +--S 7 of 486 +d0300b:= D(m0300b,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R - \|a x + b + x |-------- +--R | 4 +--R \| x +--R (7) ----------------------------- +--R +--------+ +--R | 4 +--------+ +--R 3 |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression Integer +--E 7 + +--S 8 of 486 +t0301:= x^m/(a+b*x^(2+2*m))^(1/2) +--R +--R +--R m +--R x +--R (8) ---------------- +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R Type: Expression Integer +--E 8 + +--S 9 of 486 +r0301:= atanh(x^(-1-m)*(a+b*x^(2+2*m))^(1/2)/b^(1/2))/b^(1/2)/(1+m) +--R +--R +--R +-------------+ +--R - m - 1 | 2m + 2 +--R x \|b x + a +--R atanh(------------------------) +--R +-+ +--R \|b +--R (9) ------------------------------- +--R +-+ +--R (m + 1)\|b +--R Type: Expression Integer +--E 9 + +--S 10 of 486 +--a0301:= integrate(t0301,x) +--E 10 + +--S 11 of 486 +--m0301:= a0301-r0301 +--E 11 + +--S 12 of 486 +--d0301:= D(m0301,x) +-- >> Error detected within library code: +-- integrate: implementation incomplete (constant residues) +--E 12 + +--S 13 of 486 +t0302:= 1/(a+b/x^5)^(1/2)/x +--R +--R +--R 1 +--R (10) ------------ +--R +--------+ +--R | 5 +--R |a x + b +--R x |-------- +--R | 5 +--R \| x +--R Type: Expression Integer +--E 13 + +--S 14 of 486 +r0302:= 2/5*atanh((a+b/x^5)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +--------+ +--R | 5 +--R |a x + b +--R |-------- +--R | 5 +--R \| x +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (11) ------------------- +--R +-+ +--R 5\|a +--R Type: Expression Integer +--E 14 + +--S 15 of 486 +a0302:= integrate(t0302,x) +--R +--R +--R +--------+ +--R +-+ +-+ | 5 +--R |1 3 |1 |a x + b 5 +--R |- log(2a x |- |-------- - 2a x - b) +--R \|a \|a \| x +--R (12) - ----------------------------------------- +--R 5 +--R Type: Union(Expression Integer,...) +--E 15 + +--S 16 of 486 +m0302:= a0302-r0302 +--R +--R +--R +--------+ +--R | 5 +--R |a x + b +--R +--------+ |-------- +--R +-+ +-+ | 5 | 5 +--R |1 +-+ 3 |1 |a x + b 5 \| x +--R - |- \|a log(2a x |- |-------- - 2a x - b) - 2atanh(-----------) +--R \|a \|a \| x +-+ +--R \|a +--R (13) --------------------------------------------------------------------- +--R +-+ +--R 5\|a +--R Type: Expression Integer +--E 16 + +--S 17 of 486 +d0302:= D(m0302,x) +--R +--R +--R (14) +--R +--------+ +--------+ +--R +-+ | 5 | 5 +--R 5 |1 |a x + b 5 |a x + b +--R (- 2a x |- |-------- - 2a x - b) |-------- +--R \|a | 5 \| x +--R \| x +--R + +--R +--------+ +--R | 5 +-+ +--R 7 2 |a x + b 2 7 2 |1 +--R (2a x + b x ) |-------- + (2a x + 2a b x ) |- +--R | 5 \|a +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 5 | 5 +-+ | 5 +--R 6 |a x + b |a x + b 2 8 3 |1 |a x + b +--R (2a x + b x) |-------- |-------- + (- 2a x - 2a b x ) |- |-------- +--R | 5 \| x \|a | 5 +--R \| x \| x +--R Type: Expression Integer +--E 17 + +--S 18 of 486 +t0303:= 1/(-a+b/x^5)^(1/2)/x +--R +--R +--R 1 +--R (15) -------------- +--R +----------+ +--R | 5 +--R |- a x + b +--R x |---------- +--R | 5 +--R \| x +--R Type: Expression Integer +--E 18 + +--S 19 of 486 +r0303:= -2/5*atan((-a+b/x^5)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +----------+ +--R | 5 +--R |- a x + b +--R |---------- +--R | 5 +--R \| x +--R 2atan(-------------) +--R +-+ +--R \|a +--R (16) - -------------------- +--R +-+ +--R 5\|a +--R Type: Expression Integer +--E 19 + +--S 20 of 486 +a0303:= integrate(t0303,x) +--R +--R +--R +----------+ +--R +---+ | 5 +---+ +--R | 1 3 |- a x + b | 1 5 +--R |- - log(2a x |---------- |- - - 2a x + b) +--R \| a \| x \| a +--R (17) - ----------------------------------------------- +--R 5 +--R Type: Union(Expression Integer,...) +--E 20 + +--S 21 of 486 +m0303:= a0303-r0303 +--R +--R +--R (18) +--R +----------+ +--R | 5 +--R |- a x + b +--R +----------+ |---------- +--R +---+ | 5 +---+ | 5 +--R | 1 +-+ 3 |- a x + b | 1 5 \| x +--R - |- - \|a log(2a x |---------- |- - - 2a x + b) + 2atan(-------------) +--R \| a \| x \| a +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-+ +--R 5\|a +--R Type: Expression Integer +--E 21 + +--S 22 of 486 +d0303:= D(m0303,x) +--R +--R +--R (19) +--R +----------+ +----------+ +--R | 5 | 5 +---+ +--R 5 |- a x + b |- a x + b 2 7 2 | 1 +--R (- 2a x |---------- |---------- - 2a x + 2a b x ) |- - +--R \| x | 5 \| a +--R \| x +--R + +--R +----------+ +----------+ +--R | 5 | 5 +--R 7 2 |- a x + b 5 |- a x + b +--R (2a x - b x ) |---------- + (- 2a x + b) |---------- +--R | 5 \| x +--R \| x +--R / +--R +----------+ +--R | 5 +---+ +--R 2 8 3 |- a x + b | 1 +--R (2a x - 2a b x ) |---------- |- - +--R | 5 \| a +--R \| x +--R + +--R +----------+ +----------+ +--R | 5 | 5 +--R 6 |- a x + b |- a x + b +--R (2a x - b x) |---------- |---------- +--R \| x | 5 +--R \| x +--R Type: Expression Integer +--E 22 + +--S 23 of 486 +t0304:= x^(1/3)/(1-x^6) +--R +--R +--R 3+-+ +--R \|x +--R (20) - ------ +--R 6 +--R x - 1 +--R Type: Expression Integer +--E 23 + +--S 24 of 486 +r0304:= -1/6*atan(1/3*(1+2*x^(2/3))*3^(1/2))*3^(1/2)-1/3*atan((x^(2/3)+_ + cos(1/9*%pi))*csc(1/9*%pi))*(1-cos(2/9*%pi))*cot(1/9*%pi)-_ + 1/6*log(1-x^(2/3))+1/12*log(1+x^(2/3)+x^(4/3))-_ + 1/6*cos(2/9*%pi)*log(1+x^(4/3)+2*x^(2/3)*cos(1/9*%pi))+_ + 1/6*cos(1/9*%pi)*log(1+x^(4/3)-2*x^(2/3)*sin(1/18*%pi))+_ + 1/3*atan((x^(2/3)-cos(2/9*%pi))*csc(2/9*%pi))*cot(2/9*%pi)*_ + (1-sin(1/18*%pi))-1/6*log(1+x^(4/3)-2*x^(2/3)*cos(2/9*%pi))*_ + sin(1/18*%pi)+1/3*atan(sec(1/18*%pi)*(x^(2/3)-sin(1/18*%pi)))*_ + (1+cos(1/9*%pi))*tan(1/18*%pi) +--R +--R +--R (21) +--R 2%pi %pi 3+-+2 3+-+ 3+-+2 3+-+ +--R - 2cos(----)log(2cos(---)\|x + x\|x + 1) + log(\|x + x\|x + 1) +--R 9 9 +--R + +--R 3+-+2 %pi 2%pi 3+-+2 3+-+ +--R - 2log(- \|x + 1) - 2sin(---)log(- 2cos(----)\|x + x\|x + 1) +--R 18 9 +--R + +--R %pi %pi 3+-+2 3+-+ +--R 2cos(---)log(- 2sin(---)\|x + x\|x + 1) +--R 9 18 +--R + +--R %pi %pi %pi 3+-+2 %pi %pi +--R (4cos(---) + 4)tan(---)atan(sec(---)\|x - sec(---)sin(---)) +--R 9 18 18 18 18 +--R + +--R 2%pi %pi 2%pi +--R (- 4cot(----)sin(---) + 4cot(----)) +--R 9 18 9 +--R * +--R 2%pi 3+-+2 2%pi 2%pi +--R atan(csc(----)\|x - cos(----)csc(----)) +--R 9 9 9 +--R + +--R 2%pi %pi %pi 3+-+2 %pi %pi +--R (4cos(----) - 4)cot(---)atan(csc(---)\|x + cos(---)csc(---)) +--R 9 9 9 9 9 +--R + +--R +-+3+-+2 +-+ +--R +-+ 2\|3 \|x + \|3 +--R - 2\|3 atan(-----------------) +--R 3 +--R / +--R 12 +--R Type: Expression Integer +--E 24 + +--S 25 of 486 +a0304:= integrate(t0304,x) +--R +--R +--R (22) +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +--R (3sin(----------) - \|3 cos(----------)) +--R 3 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) + 2\|x )sin(----------) +--R 3 3 3 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 3+-+2 \|3 3+-+ +--R cos(----------) - 2\|x cos(----------) + x\|x +--R 3 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +--R (- 3sin(----------) - \|3 cos(----------)) +--R 3 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R - 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R (- 2\|3 sin(----------) + 6cos(----------)) +--R 3 3 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) + 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) - 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 4\|3 sin(----------) +--R 3 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) - 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) + 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R (- 2\|3 sin(----------) - 6cos(----------)) +--R 3 3 +--R * +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 +--R 2cos(----------)sin(----------) +--R 3 3 +--R atan(-------------------------------------------) +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 3+-+2 +--R sin(----------) - cos(----------) + \|x +--R 3 3 +--R + +--R +-+ 3+-+2 3+-+ +-+ 3+-+2 +--R \|3 log(\|x + x\|x + 1) - 2\|3 log(\|x - 1) +--R + +--R +-+3+-+2 +-+ +--R 2\|3 \|x + \|3 +--R 3atan(-------------------) +--R 3+-+2 3+-+ +--R 2\|x + 2x\|x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Union(Expression Integer,...) +--E 25 + +--S 26 of 486 +m0304:= a0304-r0304 +--R +--R +--R (23) +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +--R (3sin(----------) - \|3 cos(----------)) +--R 3 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) + 2\|x )sin(----------) +--R 3 3 3 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 3+-+2 \|3 3+-+ +--R cos(----------) - 2\|x cos(----------) + x\|x +--R 3 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +--R (- 3sin(----------) - \|3 cos(----------)) +--R 3 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R - 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R (- 2\|3 sin(----------) + 6cos(----------)) +--R 3 3 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) + 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) - 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 4\|3 sin(----------) +--R 3 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) - 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) + 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R (- 2\|3 sin(----------) - 6cos(----------)) +--R 3 3 +--R * +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 +--R 2cos(----------)sin(----------) +--R 3 3 +--R atan(-------------------------------------------) +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 3+-+2 +--R sin(----------) - cos(----------) + \|x +--R 3 3 +--R + +--R +-+ 2%pi %pi 3+-+2 3+-+ +-+ 3+-+2 +--R 2\|3 cos(----)log(2cos(---)\|x + x\|x + 1) - 2\|3 log(\|x - 1) +--R 9 9 +--R + +--R +-+ 3+-+2 +-+ %pi 2%pi 3+-+2 3+-+ +--R 2\|3 log(- \|x + 1) + 2\|3 sin(---)log(- 2cos(----)\|x + x\|x + 1) +--R 18 9 +--R + +--R +-+ %pi %pi 3+-+2 3+-+ +--R - 2\|3 cos(---)log(- 2sin(---)\|x + x\|x + 1) +--R 9 18 +--R + +--R +-+ %pi +-+ %pi %pi 3+-+2 %pi %pi +--R (- 4\|3 cos(---) - 4\|3 )tan(---)atan(sec(---)\|x - sec(---)sin(---)) +--R 9 18 18 18 18 +--R + +--R +-+ 2%pi %pi +-+ 2%pi +--R (4\|3 cot(----)sin(---) - 4\|3 cot(----)) +--R 9 18 9 +--R * +--R 2%pi 3+-+2 2%pi 2%pi +--R atan(csc(----)\|x - cos(----)csc(----)) +--R 9 9 9 +--R + +--R +-+ 2%pi +-+ %pi %pi 3+-+2 %pi %pi +--R (- 4\|3 cos(----) + 4\|3 )cot(---)atan(csc(---)\|x + cos(---)csc(---)) +--R 9 9 9 9 9 +--R + +--R +-+3+-+2 +-+ +-+3+-+2 +-+ +--R 2\|3 \|x + \|3 2\|3 \|x + \|3 +--R 6atan(-----------------) + 3atan(-------------------) +--R 3 3+-+2 3+-+ +--R 2\|x + 2x\|x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression Integer +--E 26 + +--S 27 of 486 +--d0304:= D(m0304,x) +--E 27 + +--S 28 of 486 +t0305:= 1/(1+(1/x)^(1/2))^(1/2) +--R +--R +--R 1 +--R (24) ----------- +--R +--------+ +--R | +-+ +--R | |1 +--R | |- + 1 +--R \|\|x +--R Type: Expression Integer +--E 28 + +--S 29 of 486 +r0305:= -3/2*(1+(1/x)^(1/2))^(1/2)/(1/x)^(1/2)+(1+(1/x)^(1/2))^(1/2)*x+_ + 3/2*atanh((1+(1/x)^(1/2))^(1/2)) +--R +--R +--R +--------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R |1 | |1 |1 | |1 +--R 3 |- atanh( | |- + 1 + (2x |- - 3) | |- + 1 +--R \|x \|\|x \|x \|\|x +--R (25) ------------------------------------------------- +--R +-+ +--R |1 +--R 2 |- +--R \|x +--R Type: Expression Integer +--E 29 + +--S 30 of 486 +a0305:= integrate(t0305,x) +--R +--R +--R (26) +--R +--------+ +--------+ +--------+ +--R | +-+ | +-+ +-+ | +-+ +--R | |1 | |1 |1 | |1 +--R 3log( | |- + 1 + 1) - 3log( | |- + 1 - 1) + (- 6x |- + 4x) | |- + 1 +--R \|\|x \|\|x \|x \|\|x +--R -------------------------------------------------------------------------- +--R 4 +--R Type: Union(Expression Integer,...) +--E 30 + +--S 31 of 486 +m0305:= a0305-r0305 +--R +--R +--R +--------+ +--------+ +--------+ +--R | +-+ | +-+ | +-+ +--R | |1 | |1 | |1 +--R 3log( | |- + 1 + 1) - 3log( | |- + 1 - 1) - 6atanh( | |- + 1 ) +--R \|\|x \|\|x \|\|x +--R (27) ------------------------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 31 + +--S 32 of 486 +d0305:= D(m0305,x) +--R +--R +--R (28) 0 +--R Type: Expression Integer +--E 32 + +--S 33 of 486 +t0306:= 1/(1+1/x^(1/2))^(1/2) +--R +--R +--R 1 +--R (29) ----------- +--R +--------+ +--R | +-+ +--R |\|x + 1 +--R |-------- +--R | +-+ +--R \| \|x +--R Type: Expression Integer +--E 33 + +--S 34 of 486 +r0306:= -3/2*(1+1/x^(1/2))^(1/2)*x^(1/2)+(1+1/x^(1/2))^(1/2)*x+_ + 3/2*atanh((1+1/x^(1/2))^(1/2)) +--R +--R +--R +--------+ +--------+ +--R | +-+ | +-+ +--R |\|x + 1 +-+ |\|x + 1 +--R 3atanh( |-------- ) + (- 3\|x + 2x) |-------- +--R | +-+ | +-+ +--R \| \|x \| \|x +--R (30) ----------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 34 + +--S 35 of 486 +a0306:= integrate(t0306,x) +--R +--R +--R (31) +--R +--------+ +--------+ +--R | +-+ | +-+ +--R +-+ |\|x + 1 +-+ |\|x + 1 +--R 3\|x log( |-------- + 1) - 3\|x log( |-------- - 1) +--R | +-+ | +-+ +--R \| \|x \| \|x +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|x + 1 +--R (4x\|x - 6x) |-------- +--R | +-+ +--R \| \|x +--R / +--R +-+ +--R 4\|x +--R Type: Union(Expression Integer,...) +--E 35 + +--S 36 of 486 +m0306:= a0306-r0306 +--R +--R +--R +--------+ +--------+ +--------+ +--R | +-+ | +-+ | +-+ +--R |\|x + 1 |\|x + 1 |\|x + 1 +--R 3log( |-------- + 1) - 3log( |-------- - 1) - 6atanh( |-------- ) +--R | +-+ | +-+ | +-+ +--R \| \|x \| \|x \| \|x +--R (32) ------------------------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 36 + +--S 37 of 486 +d0306:= D(m0306,x) +--R +--R +--R (33) 0 +--R Type: Expression Integer +--E 37 + +--S 38 of 486 +t0307:= (3-1/x^(1/2))^(1/2) +--R +--R +--R +---------+ +--R | +-+ +--R |3\|x - 1 +--R (34) |--------- +--R | +-+ +--R \| \|x +--R Type: Expression Integer +--E 38 + +--S 39 of 486 +r0307:= -1/6*(3-1/x^(1/2))^(1/2)*x^(1/2)+(3-1/x^(1/2))^(1/2)*x-_ + 1/18*atanh(1/3*(3-1/x^(1/2))^(1/2)*3^(1/2))*3^(1/2) +--R +--R +--R +---------+ +--R | +-+ +--R +-+ |3\|x - 1 +--R \|3 |--------- +---------+ +--R | +-+ | +-+ +--R +-+ \| \|x +-+ |3\|x - 1 +--R - \|3 atanh(----------------) + (- 3\|x + 18x) |--------- +--R 3 | +-+ +--R \| \|x +--R (35) ----------------------------------------------------------- +--R 18 +--R Type: Expression Integer +--E 39 + +--S 40 of 486 +a0307:= integrate(t0307,x) +--R +--R +--R (36) +--R +---------+ +--R | +-+ +--R +-+ +-+ |3\|x - 1 +-+ +-+ +-+ +--R \|x log(6\|x |--------- - 6\|3 \|x + \|3 ) +--R | +-+ +--R \| \|x +--R + +--R +---------+ +--R | +-+ +--R +-+ +-+ +-+ |3\|x - 1 +--R (12x\|3 \|x - 2x\|3 ) |--------- +--R | +-+ +--R \| \|x +--R / +--R +-+ +-+ +--R 12\|3 \|x +--R Type: Union(Expression Integer,...) +--E 40 + +--S 41 of 486 +m0307:= a0307-r0307 +--R +--R +--R +---------+ +--R | +-+ +--R +-+ |3\|x - 1 +--R +---------+ \|3 |--------- +--R | +-+ | +-+ +--R +-+ |3\|x - 1 +-+ +-+ +-+ \| \|x +--R log(6\|x |--------- - 6\|3 \|x + \|3 ) + 2atanh(----------------) +--R | +-+ 3 +--R \| \|x +--R (37) -------------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression Integer +--E 41 + +--S 42 of 486 +d0307:= D(m0307,x) +--R +--R +--R (38) 0 +--R Type: Expression Integer +--E 42 + +--S 43 of 486 +t0308:= x^3*(a+b*x+c*x^2)^(1/2) +--R +--R +--R +--------------+ +--R 3 | 2 +--R (39) x \|c x + b x + a +--R Type: Expression Integer +--E 43 + +--S 44 of 486 +r0308:= -7/128*b^3*(b+2*c*x)*(a+b*x+c*x^2)^(1/2)/c^4+3/32*a*b*(b+2*c*x)*_ + (a+b*x+c*x^2)^(1/2)/c^3+7/48*b^2*(a+b*x+c*x^2)^(3/2)/c^3-2/15*a*_ + (a+b*x+c*x^2)^(3/2)/c^2-7/40*b*x*(a+b*x+c*x^2)^(3/2)/c^2+1/5*x^2*_ + (a+b*x+c*x^2)^(3/2)/c+7/256*b^5*atanh(2*c^(1/2)*_ + (a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(9/2)-3/64*a*b*(10/3*b^2-4*a*c)*_ + atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(7/2) +--R +--R +--R (40) +--R +--------------+ +--R +-+ | 2 +--R 2 2 3 5 2\|c \|c x + b x + a +--R (720a b c - 600a b c + 105b )atanh(----------------------) +--R 2c x + b +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R 768c x + 96b c x + (256a c - 112b c )x + (- 464a b c + 140b c)x +--R + +--R 2 2 2 4 +--R - 512a c + 920a b c - 210b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 3840c \|c +--R Type: Expression Integer +--E 44 + +--S 45 of 486 +a0308:= integrate(t0308,x) +--R +--R +--R (41) +--R [ +--R 4 4 3 3 3 2 5 2 7 +--R 23040a b c + 38400a b c - 37440a b c + 2400a b c +--R + +--R 9 +--R 1050b +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (276480a b c - 115200a b c - 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (276480a b c + 253440a b c - 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c - 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R - 307200a b c + 53760a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c + 19200a b c + 14880a b c - 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c - 192000a b c + 187200a b c - 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (- 691200a b c + 288000a b c + 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (- 460800a b c - 422400a b c + 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c + 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R 307200a b c - 53760a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 6 3 5 5 4 9 +--R (- 61440a b c - 30720a b c - 768b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (- 122880a c - 314880a b c - 42240a b c - 96b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (- 773120a b c - 346880a b c - 576a b c + 112b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (- 532480a c - 999680a b c + 960a b c + 464a b c - 140b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (- 1175040a b c + 7680a b c - 7488a b c + 480a b c + 210b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R - 491520a c + 153600a b c - 70400a b c - 25600a b c +--R + +--R 8 +--R 8400a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (215040a b c + 166400a b c - 256640a b c + 50400a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (645120a b c - 537600a b c + 94080a b )x +--R + +--R 6 2 5 3 4 5 +--R (368640a b c - 307200a b c + 53760a b )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 7 2 6 4 5 10 +--R (24576a c + 61440a b c + 7680b c )x +--R + +--R 2 6 3 5 5 4 9 +--R (322560a b c + 192000a b c + 8640b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (327680a c + 929280a b c + 147200a b c - 160b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (1507840a b c + 730240a b c - 1440a b c + 280b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (778240a c + 1514240a b c + 4800a b c + 2320a b c - 700b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (1359360a b c - 87040a b c + 95808a b c - 9920a b c - 1890b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 491520a c - 491520a b c + 236800a b c + 72320a b c +--R + +--R 8 +--R - 25200a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 399360a b c - 289280a b c + 460160a b c - 90720a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (- 829440a b c + 691200a b c - 120960a b )x +--R + +--R 6 2 5 3 4 5 +--R (- 368640a b c + 307200a b c - 53760a b )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 6 2 5 4 4 4 +--R (122880a c + 307200a b c + 38400b c )x +--R + +--R 2 5 3 4 3 3 5 2 2 4 2 +--R (1474560a b c + 614400a b c )x + (1474560a c + 2580480a b c )x +--R + +--R 3 4 4 4 +--R 3932160a b c x + 1966080a c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 6 3 5 5 4 5 +--R (- 307200a b c - 153600a b c - 3840b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 614400a c - 1536000a b c - 192000a b c )x +--R + +--R 3 5 2 3 4 3 +--R (- 3686400a b c - 1536000a b c )x +--R + +--R 4 5 3 2 4 2 4 4 5 4 +--R (- 2457600a c - 4300800a b c )x - 4915200a b c x - 1966080a c +--R * +--R +-+ +--R \|c +--R , +--R +--R 4 4 3 3 3 2 5 2 7 +--R 23040a b c + 38400a b c - 37440a b c + 2400a b c +--R + +--R 9 +--R 1050b +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (276480a b c - 115200a b c - 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (276480a b c + 253440a b c - 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c - 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R - 307200a b c + 53760a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c + 19200a b c + 14880a b c - 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c - 192000a b c + 187200a b c - 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (- 691200a b c + 288000a b c + 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (- 460800a b c - 422400a b c + 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c + 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R 307200a b c - 53760a b +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 6 3 5 5 4 9 +--R (- 30720a b c - 15360a b c - 384b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (- 61440a c - 157440a b c - 21120a b c - 48b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (- 386560a b c - 173440a b c - 288a b c + 56b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (- 266240a c - 499840a b c + 480a b c + 232a b c - 70b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (- 587520a b c + 3840a b c - 3744a b c + 240a b c + 105b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R - 245760a c + 76800a b c - 35200a b c - 12800a b c +--R + +--R 8 +--R 4200a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (107520a b c + 83200a b c - 128320a b c + 25200a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (322560a b c - 268800a b c + 47040a b )x +--R + +--R 6 2 5 3 4 5 +--R (184320a b c - 153600a b c + 26880a b )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 2 7 2 6 4 5 10 +--R (12288a c + 30720a b c + 3840b c )x +--R + +--R 2 6 3 5 5 4 9 +--R (161280a b c + 96000a b c + 4320b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (163840a c + 464640a b c + 73600a b c - 80b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (753920a b c + 365120a b c - 720a b c + 140b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (389120a c + 757120a b c + 2400a b c + 1160a b c - 350b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (679680a b c - 43520a b c + 47904a b c - 4960a b c - 945b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 245760a c - 245760a b c + 118400a b c + 36160a b c +--R + +--R 8 +--R - 12600a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 199680a b c - 144640a b c + 230080a b c - 45360a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (- 414720a b c + 345600a b c - 60480a b )x +--R + +--R 6 2 5 3 4 5 +--R (- 184320a b c + 153600a b c - 26880a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R 2 6 2 5 4 4 4 +--R (61440a c + 153600a b c + 19200b c )x +--R + +--R 2 5 3 4 3 3 5 2 2 4 2 +--R (737280a b c + 307200a b c )x + (737280a c + 1290240a b c )x +--R + +--R 3 4 4 4 +--R 1966080a b c x + 983040a c +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 2 6 3 5 5 4 5 +--R (- 153600a b c - 76800a b c - 1920b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 307200a c - 768000a b c - 96000a b c )x +--R + +--R 3 5 2 3 4 3 +--R (- 1843200a b c - 768000a b c )x +--R + +--R 4 5 3 2 4 2 4 4 5 4 +--R (- 1228800a c - 2150400a b c )x - 2457600a b c x - 983040a c +--R * +--R +---+ +--R \|- c +--R ] +--R Type: Union(List Expression Integer,...) +--E 45 + +--S 46 of 486 +m0308a:= a0308.1-r0308 +--R +--R +--R (42) +--R 4 4 3 3 3 2 5 2 7 9 4 +--R (23040a b c + 38400a b c - 37440a b c + 2400a b c + 1050b )x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (276480a b c - 115200a b c - 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (276480a b c + 253440a b c - 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c - 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R - 307200a b c + 53760a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c + 19200a b c + 14880a b c - 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c - 192000a b c + 187200a b c - 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (- 691200a b c + 288000a b c + 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (- 460800a b c - 422400a b c + 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c + 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R 307200a b c - 53760a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 4 4 3 3 3 2 5 2 7 +--R - 23040a b c - 38400a b c + 37440a b c - 2400a b c +--R + +--R 9 +--R - 1050b +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c + 115200a b c + 55680a b c - 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c - 253440a b c + 362880a b c - 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (- 737280a b c + 614400a b c - 107520a b )x - 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c - 53760a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (57600a b c - 19200a b c - 14880a b c + 3600a b c + 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R 115200a b c + 192000a b c - 187200a b c + 12000a b c +--R + +--R 9 +--R 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c - 288000a b c - 139200a b c + 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c + 422400a b c - 604800a b c + 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (921600a b c - 768000a b c + 134400a b )x + 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c + 53760a b +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R 5 4 4 2 3 3 4 2 2 6 8 4 +--R (- 16384a c - 11520a b c + 61760a b c - 7600a b c - 2100a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 196608a b c + 271360a b c + 66560a b c - 33600a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (- 196608a c + 9216a b c + 537600a b c - 141120a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (- 524288a b c + 942080a b c - 215040a b )x - 262144a c +--R + +--R 6 2 5 4 +--R 471040a b c - 107520a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (40960a b c - 53120a b c - 19488a b c + 7480a b c + 210b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 8 4 +--R (81920a c + 57600a b c - 308800a b c + 38000a b c + 10500a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (491520a b c - 678400a b c - 166400a b c + 84000a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (327680a c - 15360a b c - 896000a b c + 235200a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (655360a b c - 1177600a b c + 268800a b )x + 262144a c +--R + +--R 6 2 5 4 +--R - 471040a b c + 107520a b +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 6 2 5 4 4 4 +--R (122880a c + 307200a b c + 38400b c )x +--R + +--R 2 5 3 4 3 3 5 2 2 4 2 +--R (1474560a b c + 614400a b c )x + (1474560a c + 2580480a b c )x +--R + +--R 3 4 4 4 +--R 3932160a b c x + 1966080a c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 6 3 5 5 4 5 +--R (- 307200a b c - 153600a b c - 3840b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 614400a c - 1536000a b c - 192000a b c )x +--R + +--R 3 5 2 3 4 3 +--R (- 3686400a b c - 1536000a b c )x +--R + +--R 4 5 3 2 4 2 4 4 5 4 +--R (- 2457600a c - 4300800a b c )x - 4915200a b c x - 1966080a c +--R * +--R +-+ +--R \|c +--R Type: Expression Integer +--E 46 + +--S 47 of 486 +d0308a:= D(m0308a,x) +--R +--R +--R (43) 0 +--R Type: Expression Integer +--E 47 + +--S 48 of 486 +m0308b:= a0308.2-r0308 +--R +--R +--R (44) +--R 4 4 3 3 3 2 5 2 7 +--R - 23040a b c - 38400a b c + 37440a b c - 2400a b c +--R + +--R 9 +--R - 1050b +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c + 115200a b c + 55680a b c - 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c - 253440a b c + 362880a b c - 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (- 737280a b c + 614400a b c - 107520a b )x - 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c - 53760a b +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (57600a b c - 19200a b c - 14880a b c + 3600a b c + 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R 115200a b c + 192000a b c - 187200a b c + 12000a b c +--R + +--R 9 +--R 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c - 288000a b c - 139200a b c + 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c + 422400a b c - 604800a b c + 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (921600a b c - 768000a b c + 134400a b )x + 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c + 53760a b +--R * +--R +---+ +--R \|- c +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R 4 4 3 3 3 2 5 2 7 9 4 +--R (46080a b c + 76800a b c - 74880a b c + 4800a b c + 2100b )x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (552960a b c - 230400a b c - 111360a b c + 33600a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (552960a b c + 506880a b c - 725760a b c + 141120a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (1474560a b c - 1228800a b c + 215040a b )x + 737280a b c +--R + +--R 5 3 4 5 +--R - 614400a b c + 107520a b +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 4 2 4 3 4 3 2 6 2 8 +--R - 115200a b c + 38400a b c + 29760a b c - 7200a b c +--R + +--R 10 +--R - 210b +--R * +--R 5 +--R x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 230400a b c - 384000a b c + 374400a b c - 24000a b c +--R + +--R 9 +--R - 10500a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (- 1382400a b c + 576000a b c + 278400a b c - 84000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (- 921600a b c - 844800a b c + 1209600a b c - 235200a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 1843200a b c + 1536000a b c - 268800a b )x - 737280a b c +--R + +--R 6 3 5 5 +--R 614400a b c - 107520a b +--R * +--R +-+ +--R \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 5 4 4 2 3 3 4 2 2 6 8 4 +--R (- 16384a c - 11520a b c + 61760a b c - 7600a b c - 2100a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 196608a b c + 271360a b c + 66560a b c - 33600a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (- 196608a c + 9216a b c + 537600a b c - 141120a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (- 524288a b c + 942080a b c - 215040a b )x - 262144a c +--R + +--R 6 2 5 4 +--R 471040a b c - 107520a b +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|c \|c x + b x + a +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (40960a b c - 53120a b c - 19488a b c + 7480a b c + 210b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 8 4 +--R (81920a c + 57600a b c - 308800a b c + 38000a b c + 10500a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (491520a b c - 678400a b c - 166400a b c + 84000a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (327680a c - 15360a b c - 896000a b c + 235200a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (655360a b c - 1177600a b c + 268800a b )x + 262144a c +--R + +--R 6 2 5 4 +--R - 471040a b c + 107520a b +--R * +--R +---+ +-+ +-+ +--R \|- c \|a \|c +--R / +--R 2 6 2 5 4 4 4 +--R (122880a c + 307200a b c + 38400b c )x +--R + +--R 2 5 3 4 3 3 5 2 2 4 2 +--R (1474560a b c + 614400a b c )x + (1474560a c + 2580480a b c )x +--R + +--R 3 4 4 4 +--R 3932160a b c x + 1966080a c +--R * +--R +--------------+ +--R +---+ +-+ +-+ | 2 +--R \|- c \|a \|c \|c x + b x + a +--R + +--R 2 6 3 5 5 4 5 +--R (- 307200a b c - 153600a b c - 3840b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 614400a c - 1536000a b c - 192000a b c )x +--R + +--R 3 5 2 3 4 3 +--R (- 3686400a b c - 1536000a b c )x +--R + +--R 4 5 3 2 4 2 4 4 5 4 +--R (- 2457600a c - 4300800a b c )x - 4915200a b c x - 1966080a c +--R * +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression Integer +--E 48 + +--S 49 of 486 +d0308b:= D(m0308b,x) +--R +--R +--R (45) 0 +--R Type: Expression Integer +--E 49 + +--S 50 of 486 +t0309:= x^2*(a+b*x+c*x^2)^(1/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (46) x \|c x + b x + a +--R Type: Expression Integer +--E 50 + +--S 51 of 486 +r0309:= 5/64*b^2*(b+2*c*x)*(a+b*x+c*x^2)^(1/2)/c^3-1/16*a*(b+2*c*x)*_ + (a+b*x+c*x^2)^(1/2)/c^2-5/24*b*(a+b*x+c*x^2)^(3/2)/c^2+1/4*x*_ + (a+b*x+c*x^2)^(3/2)/c-5/128*b^4*atanh(2*c^(1/2)*_ + (a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(7/2)+1/32*a*(6*b^2-4*a*c)*_ + atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(5/2) +--R +--R +--R (47) +--R +--------------+ +--R +-+ | 2 +--R 2 2 2 4 2\|c \|c x + b x + a +--R (- 48a c + 72a b c - 15b )atanh(----------------------) +--R 2c x + b +--R + +--R 3 3 2 2 2 2 3 +-+ +--R (96c x + 16b c x + (48a c - 20b c)x - 104a b c + 30b )\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 3 +-+ +--R 384c \|c +--R Type: Expression Integer +--E 51 + +--S 52 of 486 +a0309:= integrate(t0309,x) +--R +--R +--R (48) +--R [ +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 1920a b c - 96a b c + 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c - 768a b c - 4800a b c + 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (9216a b c - 13824a b c + 2880a b )x + 6144a c - 9216a b c +--R + +--R 3 4 +--R 1920a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 4 +--R (- 768a c + 1440a b c - 288a b c - 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 7680a b c + 384a b c - 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c + 1536a b c + 9600a b c - 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (- 12288a b c + 18432a b c - 3840a b )x - 6144a c + 9216a b c +--R + +--R 4 4 +--R - 1920a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 5 2 4 4 3 7 +--R (- 1536a c - 2304a b c - 96b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (- 12544a b c - 3456a b c - 16b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (- 13056a c - 18240a b c - 80a b c + 20b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 31104a b c + 480a b c + 24a b c - 30b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (- 18432a c + 768a b c + 2816a b c - 720a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (- 7680a b c + 11520a b c - 2400a b )x +--R + +--R 5 2 4 2 3 4 +--R (- 6144a c + 9216a b c - 1920a b )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 5 3 4 8 2 5 2 4 4 3 7 +--R (3072a b c + 768b c )x + (6144a c + 11264a b c + 896b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (30208a b c + 9984a b c - 32b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (21504a c + 31488a b c - 320a b c + 80b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (42624a b c - 4896a b c + 152a b c + 210b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (21504a c - 2304a b c - 6464a b c + 1680a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (10752a b c - 16128a b c + 3360a b )x +--R + +--R 5 2 4 2 3 4 +--R (6144a c - 9216a b c + 1920a b )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (12288a b c + 3072b c )x + (24576a c + 30720a b c )x +--R + +--R 2 3 3 3 +--R 73728a b c x + 49152a c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 5 2 4 4 3 4 +--R (- 6144a c - 9216a b c - 384b c )x +--R + +--R 2 4 3 3 3 3 4 2 2 3 2 +--R (- 49152a b c - 12288a b c )x + (- 49152a c - 61440a b c )x +--R + +--R 3 3 4 3 +--R - 98304a b c x - 49152a c +--R * +--R +-+ +--R \|c +--R , +--R +--R 3 3 2 3 2 5 7 3 +--R (- 1536a b c + 1920a b c + 96a b c - 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (- 3072a c + 768a b c + 4800a b c - 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 9216a b c + 13824a b c - 2880a b )x - 6144a c + 9216a b c +--R + +--R 3 4 +--R - 1920a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 4 +--R (768a c - 1440a b c + 288a b c + 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (6144a b c - 7680a b c - 384a b c + 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (6144a c - 1536a b c - 9600a b c + 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (12288a b c - 18432a b c + 3840a b )x + 6144a c - 9216a b c +--R + +--R 4 4 +--R 1920a b +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 5 2 4 4 3 7 +--R (- 768a c - 1152a b c - 48b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (- 6272a b c - 1728a b c - 8b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (- 6528a c - 9120a b c - 40a b c + 10b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 15552a b c + 240a b c + 12a b c - 15b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (- 9216a c + 384a b c + 1408a b c - 360a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (- 3840a b c + 5760a b c - 1200a b )x +--R + +--R 5 2 4 2 3 4 +--R (- 3072a c + 4608a b c - 960a b )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 5 3 4 8 2 5 2 4 4 3 7 +--R (1536a b c + 384b c )x + (3072a c + 5632a b c + 448b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (15104a b c + 4992a b c - 16b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (10752a c + 15744a b c - 160a b c + 40b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (21312a b c - 2448a b c + 76a b c + 105b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (10752a c - 1152a b c - 3232a b c + 840a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (5376a b c - 8064a b c + 1680a b )x +--R + +--R 5 2 4 2 3 4 +--R (3072a c - 4608a b c + 960a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (6144a b c + 1536b c )x + (12288a c + 15360a b c )x +--R + +--R 2 3 3 3 +--R 36864a b c x + 24576a c +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 2 5 2 4 4 3 4 +--R (- 3072a c - 4608a b c - 192b c )x +--R + +--R 2 4 3 3 3 3 4 2 2 3 2 +--R (- 24576a b c - 6144a b c )x + (- 24576a c - 30720a b c )x +--R + +--R 3 3 4 3 +--R - 49152a b c x - 24576a c +--R * +--R +---+ +--R \|- c +--R ] +--R Type: Union(List Expression Integer,...) +--E 52 + +--S 53 of 486 +m0309a:= a0309.1-r0309 +--R +--R +--R (49) +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 1920a b c - 96a b c + 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c - 768a b c - 4800a b c + 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (9216a b c - 13824a b c + 2880a b )x + 6144a c - 9216a b c +--R + +--R 3 4 +--R 1920a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 4 +--R (- 768a c + 1440a b c - 288a b c - 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 7680a b c + 384a b c - 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c + 1536a b c + 9600a b c - 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (- 12288a b c + 18432a b c - 3840a b )x - 6144a c + 9216a b c +--R + +--R 4 4 +--R - 1920a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 1920a b c - 96a b c + 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c - 768a b c - 4800a b c + 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (9216a b c - 13824a b c + 2880a b )x + 6144a c - 9216a b c +--R + +--R 3 4 +--R 1920a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 4 +--R (- 768a c + 1440a b c - 288a b c - 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 7680a b c + 384a b c - 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c + 1536a b c + 9600a b c - 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (- 12288a b c + 18432a b c - 3840a b )x - 6144a c + 9216a b c +--R + +--R 4 4 +--R - 1920a b +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R 3 2 2 2 4 6 3 +--R (- 3328a b c + 128a b c + 240a b )x +--R + +--R 4 2 3 3 2 5 2 4 2 3 4 +--R (- 6656a b c - 6400a b c + 2400a b )x + (- 19968a b c + 5760a b )x +--R + +--R 5 4 3 +--R - 13312a b c + 3840a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 4 +--R (1664a b c + 2016a b c - 616a b c - 30b )x +--R + +--R 3 2 2 2 4 6 3 +--R (13312a b c - 512a b c - 960a b )x +--R + +--R 4 2 3 3 2 5 2 4 2 3 4 +--R (13312a b c + 12800a b c - 4800a b )x + (26624a b c - 7680a b )x +--R + +--R 5 4 3 +--R 13312a b c - 3840a b +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (12288a b c + 3072b c )x + (24576a c + 30720a b c )x +--R + +--R 2 3 3 3 +--R 73728a b c x + 49152a c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 5 2 4 4 3 4 +--R (- 6144a c - 9216a b c - 384b c )x +--R + +--R 2 4 3 3 3 3 4 2 2 3 2 +--R (- 49152a b c - 12288a b c )x + (- 49152a c - 61440a b c )x +--R + +--R 3 3 4 3 +--R - 98304a b c x - 49152a c +--R * +--R +-+ +--R \|c +--R Type: Expression Integer +--E 53 + +--S 54 of 486 +d0309a:= D(m0309a,x) +--R +--R +--R (50) 0 +--R Type: Expression Integer +--E 54 + +--S 55 of 486 +m0309b:= a0309.2-r0309 +--R +--R +--R (51) +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 1920a b c - 96a b c + 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c - 768a b c - 4800a b c + 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (9216a b c - 13824a b c + 2880a b )x + 6144a c - 9216a b c +--R + +--R 3 4 +--R 1920a b +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 4 +--R (- 768a c + 1440a b c - 288a b c - 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 7680a b c + 384a b c - 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c + 1536a b c + 9600a b c - 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (- 12288a b c + 18432a b c - 3840a b )x - 6144a c + 9216a b c +--R + +--R 4 4 +--R - 1920a b +--R * +--R +---+ +--R \|- c +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R 3 3 2 3 2 5 7 3 +--R (- 3072a b c + 3840a b c + 192a b c - 240b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (- 6144a c + 1536a b c + 9600a b c - 2400a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 18432a b c + 27648a b c - 5760a b )x - 12288a c + 18432a b c +--R + +--R 3 4 +--R - 3840a b +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 4 +--R (1536a c - 2880a b c + 576a b c + 30b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (12288a b c - 15360a b c - 768a b c + 960a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (12288a c - 3072a b c - 19200a b c + 4800a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (24576a b c - 36864a b c + 7680a b )x + 12288a c - 18432a b c +--R + +--R 4 4 +--R 3840a b +--R * +--R +-+ +--R \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 2 2 2 4 6 3 +--R (- 3328a b c + 128a b c + 240a b )x +--R + +--R 4 2 3 3 2 5 2 4 2 3 4 +--R (- 6656a b c - 6400a b c + 2400a b )x + (- 19968a b c + 5760a b )x +--R + +--R 5 4 3 +--R - 13312a b c + 3840a b +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 4 +--R (1664a b c + 2016a b c - 616a b c - 30b )x +--R + +--R 3 2 2 2 4 6 3 +--R (13312a b c - 512a b c - 960a b )x +--R + +--R 4 2 3 3 2 5 2 4 2 3 4 +--R (13312a b c + 12800a b c - 4800a b )x + (26624a b c - 7680a b )x +--R + +--R 5 4 3 +--R 13312a b c - 3840a b +--R * +--R +---+ +-+ +-+ +--R \|- c \|a \|c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (12288a b c + 3072b c )x + (24576a c + 30720a b c )x +--R + +--R 2 3 3 3 +--R 73728a b c x + 49152a c +--R * +--R +--------------+ +--R +---+ +-+ +-+ | 2 +--R \|- c \|a \|c \|c x + b x + a +--R + +--R 2 5 2 4 4 3 4 +--R (- 6144a c - 9216a b c - 384b c )x +--R + +--R 2 4 3 3 3 3 4 2 2 3 2 +--R (- 49152a b c - 12288a b c )x + (- 49152a c - 61440a b c )x +--R + +--R 3 3 4 3 +--R - 98304a b c x - 49152a c +--R * +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression Integer +--E 55 + +--S 56 of 486 +d0309b:= D(m0309b,x) +--R +--R +--R (52) 0 +--R Type: Expression Integer +--E 56 + +--S 57 of 486 +t0310:= x*(a+b*x+c*x^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (53) x\|c x + b x + a +--R Type: Expression Integer +--E 57 + +--S 58 of 486 +r0310:= -1/8*b*(b+2*c*x)*(a+b*x+c*x^2)^(1/2)/c^2+1/3*(a+b*x+c*x^2)^(3/2)/c+_ + 1/16*b*(b^2-4*a*c)*atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/_ + (b+2*c*x))/c^(5/2) +--R +--R +--R (54) +--R +--------------+ +--R +-+ | 2 +--R 3 2\|c \|c x + b x + a +--R (- 12a b c + 3b )atanh(----------------------) +--R 2c x + b +--R + +--R +--------------+ +--R 2 2 2 +-+ | 2 +--R (16c x + 4b c x + 16a c - 6b )\|c \|c x + b x + a +--R / +--R 2 +-+ +--R 48c \|c +--R Type: Expression Integer +--E 58 + +--S 59 of 486 +a0310:= integrate(t0310,x) +--R +--R +--R (55) +--R [ +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c + 48a b c - 18b )x + (384a b c - 96a b )x + 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 3 +--R (- 144a b c + 24a b c + 3b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (- 288a b c - 144a b c + 54a b )x + (- 576a b c + 144a b )x +--R + +--R 4 3 3 +--R - 384a b c + 96a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 3 3 2 5 2 3 2 2 4 4 +--R (- 192a b c - 16b c )x + (- 384a c - 336a b c - 4b c)x +--R + +--R 2 2 3 5 3 +--R (- 1056a b c - 16a b c + 6b )x +--R + +--R 3 2 2 2 4 2 3 2 3 +--R (- 768a c - 288a b c + 72a b )x + (- 384a b c + 96a b )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 4 2 3 6 3 3 2 5 +--R (128a c + 96b c )x + (672a b c + 120b c )x +--R + +--R 2 3 2 2 4 4 2 2 3 5 3 +--R (768a c + 816a b c - 12b c)x + (1632a b c + 64a b c - 30b )x +--R + +--R 3 2 2 2 4 2 3 2 3 +--R (768a c + 480a b c - 120a b )x + (384a b c - 96a b )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 2 2 2 2 2 2 +-+ +-+ +--R ((384a c + 288b c )x + 1536a b c x + 1536a c )\|a \|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576a b c - 48b c )x + (- 1152a c - 864a b c )x - 2304a b c x +--R + +--R 3 2 +--R - 1536a c +--R * +--R +-+ +--R \|c +--R , +--R +--R 2 2 3 5 2 2 2 4 +--R (- 96a b c - 48a b c + 18b )x + (- 384a b c + 96a b )x +--R + +--R 3 2 3 +--R - 384a b c + 96a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 3 3 2 2 3 5 2 +--R (144a b c - 24a b c - 3b )x + (288a b c + 144a b c - 54a b )x +--R + +--R 3 2 2 4 4 3 3 +--R (576a b c - 144a b )x + 384a b c - 96a b +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 3 2 5 2 3 2 2 4 4 +--R (- 96a b c - 8b c )x + (- 192a c - 168a b c - 2b c)x +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (- 528a b c - 8a b c + 3b )x + (- 384a c - 144a b c + 36a b )x +--R + +--R 3 2 3 +--R (- 192a b c + 48a b )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 4 2 3 6 3 3 2 5 +--R (64a c + 48b c )x + (336a b c + 60b c )x +--R + +--R 2 3 2 2 4 4 2 2 3 5 3 +--R (384a c + 408a b c - 6b c)x + (816a b c + 32a b c - 15b )x +--R + +--R 3 2 2 2 4 2 3 2 3 +--R (384a c + 240a b c - 60a b )x + (192a b c - 48a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R 3 2 2 2 2 2 2 +---+ +-+ +--R ((192a c + 144b c )x + 768a b c x + 768a c )\|- c \|a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 288a b c - 24b c )x + (- 576a c - 432a b c )x - 1152a b c x +--R + +--R 3 2 +--R - 768a c +--R * +--R +---+ +--R \|- c +--R ] +--R Type: Union(List Expression Integer,...) +--E 59 + +--S 60 of 486 +m0310a:= a0310.1-r0310 +--R +--R +--R (56) +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c + 48a b c - 18b )x + (384a b c - 96a b )x + 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 3 3 2 2 3 5 2 +--R (- 144a b c + 24a b c + 3b )x + (- 288a b c - 144a b c + 54a b )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 576a b c + 144a b )x - 384a b c + 96a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c + 48a b c - 18b )x + (384a b c - 96a b )x + 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 3 3 2 2 3 5 2 +--R (- 144a b c + 24a b c + 3b )x + (- 288a b c - 144a b c + 54a b )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 576a b c + 144a b )x - 384a b c + 96a b +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R 3 2 2 2 4 2 3 2 3 4 +--R (128a c + 48a b c - 36a b )x + (512a b c - 192a b )x + 512a c +--R + +--R 3 2 +--R - 192a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (- 192a b c + 56a b c + 6b )x + (- 384a c - 144a b c + 108a b )x +--R + +--R 3 2 3 4 3 2 +--R (- 768a b c + 288a b )x - 512a c + 192a b +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 2 2 2 2 2 2 +-+ +-+ | 2 +--R ((384a c + 288b c )x + 1536a b c x + 1536a c )\|a \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576a b c - 48b c )x + (- 1152a c - 864a b c )x - 2304a b c x +--R + +--R 3 2 +--R - 1536a c +--R * +--R +-+ +--R \|c +--R Type: Expression Integer +--E 60 + +--S 61 of 486 +d0310a:= D(m0310a,x) +--R +--R +--R (57) 0 +--R Type: Expression Integer +--E 61 + +--S 62 of 486 +m0310b:= a0310.2-r0310 +--R +--R +--R (58) +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c + 48a b c - 18b )x + (384a b c - 96a b )x + 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 3 +--R (- 144a b c + 24a b c + 3b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (- 288a b c - 144a b c + 54a b )x + (- 576a b c + 144a b )x +--R + +--R 4 3 3 +--R - 384a b c + 96a b +--R * +--R +---+ +--R \|- c +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R 2 2 3 5 2 2 2 4 +--R (- 192a b c - 96a b c + 36b )x + (- 768a b c + 192a b )x +--R + +--R 3 2 3 +--R - 768a b c + 192a b +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 2 2 4 6 3 +--R (288a b c - 48a b c - 6b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (576a b c + 288a b c - 108a b )x + (1152a b c - 288a b )x +--R + +--R 4 3 3 +--R 768a b c - 192a b +--R * +--R +-+ +--R \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 2 2 2 4 2 3 2 3 4 +--R (128a c + 48a b c - 36a b )x + (512a b c - 192a b )x + 512a c +--R + +--R 3 2 +--R - 192a b +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|c \|c x + b x + a +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (- 192a b c + 56a b c + 6b )x + (- 384a c - 144a b c + 108a b )x +--R + +--R 3 2 3 4 3 2 +--R (- 768a b c + 288a b )x - 512a c + 192a b +--R * +--R +---+ +-+ +-+ +--R \|- c \|a \|c +--R / +--R 3 2 2 2 2 2 2 +---+ +-+ +-+ +--R ((384a c + 288b c )x + 1536a b c x + 1536a c )\|- c \|a \|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576a b c - 48b c )x + (- 1152a c - 864a b c )x - 2304a b c x +--R + +--R 3 2 +--R - 1536a c +--R * +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression Integer +--E 62 + +--S 63 of 486 +d0310b:= D(m0310b,x) +--R +--R +--R (59) 0 +--R Type: Expression Integer +--E 63 + +--S 64 of 486 +t0311:= (a+b*x+c*x^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (60) \|c x + b x + a +--R Type: Expression Integer +--E 64 + +--S 65 of 486 +r0311:= 1/4*(b+2*c*x)*(a+b*x+c*x^2)^(1/2)/c-1/8*(b^2-4*a*c)*_ + atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(3/2) +--R +--R +--R (61) +--R +--------------+ +--R +-+ | 2 +--------------+ +--R 2 2\|c \|c x + b x + a +-+ | 2 +--R (4a c - b )atanh(----------------------) + (4c x + 2b)\|c \|c x + b x + a +--R 2c x + b +--R --------------------------------------------------------------------------- +--R +-+ +--R 8c\|c +--R Type: Expression Integer +--E 65 + +--S 66 of 486 +a0311:= integrate(t0311,x) +--R +--R +--R (62) +--R [ +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((16a b c - 4b )x + 32a c - 8a b )\|a \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (- 16a c + b )x + (- 32a b c + 8a b )x - 32a c + 8a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 2 3 3 2 2 2 +-+ +--R ((- 16a c - 4b c)x + (- 40a b c - 2b )x + (- 32a c - 8a b )x)\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 4 2 2 3 3 2 +--R 16b c x + (32a c + 24b c)x + (56a b c + 6b )x +--R + +--R 2 2 +--R (32a c + 8a b )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R +-+ +-+ | 2 +--R (32b c x + 64a c)\|a \|c \|c x + b x + a +--R + +--R 2 2 2 2 +-+ +--R ((- 32a c - 8b c)x - 64a b c x - 64a c)\|c +--R , +--R +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((16a b c - 4b )x + 32a c - 8a b )\|a \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (- 16a c + b )x + (- 32a b c + 8a b )x - 32a c + 8a b +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 2 3 3 2 2 2 +---+ +--R ((- 8a c - 2b c)x + (- 20a b c - b )x + (- 16a c - 4a b )x)\|- c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 4 2 2 3 3 2 2 2 +--R (8b c x + (16a c + 12b c)x + (28a b c + 3b )x + (16a c + 4a b )x) +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R +--------------+ +--R +---+ +-+ | 2 +--R (16b c x + 32a c)\|- c \|a \|c x + b x + a +--R + +--R 2 2 2 2 +---+ +--R ((- 16a c - 4b c)x - 32a b c x - 32a c)\|- c +--R ] +--R Type: Union(List Expression Integer,...) +--E 66 + +--S 67 of 486 +m0311a:= a0311.1-r0311 +--R +--R +--R (63) +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((16a b c - 4b )x + 32a c - 8a b )\|a \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (- 16a c + b )x + (- 32a b c + 8a b )x - 32a c + 8a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((- 16a b c + 4b )x - 32a c + 8a b )\|a \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (16a c - b )x + (32a b c - 8a b )x + 32a c - 8a b +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R +--------------+ +--R 2 2 +-+ | 2 +--R (8a b x + 16a b)\|c \|c x + b x + a +--R + +--R 3 2 2 2 +-+ +-+ +--R ((- 8a b c - 2b )x - 16a b x - 16a b)\|a \|c +--R / +--R +--------------+ +--R +-+ +-+ | 2 +--R (32b c x + 64a c)\|a \|c \|c x + b x + a +--R + +--R 2 2 2 2 +-+ +--R ((- 32a c - 8b c)x - 64a b c x - 64a c)\|c +--R Type: Expression Integer +--E 67 + +--S 68 of 486 +d0311a:= D(m0311a,x) +--R +--R +--R (64) 0 +--R Type: Expression Integer +--E 68 + +--S 69 of 486 +m0311b:= a0311.2-r0311 +--R +--R +--R (65) +--R +--------------+ +--R 3 2 2 +---+ +-+ | 2 +--R ((- 16a b c + 4b )x - 32a c + 8a b )\|- c \|a \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +---+ +--R ((16a c - b )x + (32a b c - 8a b )x + 32a c - 8a b )\|- c +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R +--------------+ +--R 3 2 2 +-+ +-+ | 2 +--R ((32a b c - 8b )x + 64a c - 16a b )\|a \|c \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +-+ +--R ((- 32a c + 2b )x + (- 64a b c + 16a b )x - 64a c + 16a b )\|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R +--------------+ +--R 2 2 +---+ +-+ | 2 +--R (8a b x + 16a b)\|- c \|c \|c x + b x + a +--R + +--R 3 2 2 2 +---+ +-+ +-+ +--R ((- 8a b c - 2b )x - 16a b x - 16a b)\|- c \|a \|c +--R / +--R +--------------+ +--R +---+ +-+ +-+ | 2 +--R (32b c x + 64a c)\|- c \|a \|c \|c x + b x + a +--R + +--R 2 2 2 2 +---+ +-+ +--R ((- 32a c - 8b c)x - 64a b c x - 64a c)\|- c \|c +--R Type: Expression Integer +--E 69 + +--S 70 of 486 +d0311b:= D(m0311b,x) +--R +--R +--R (66) 0 +--R Type: Expression Integer +--E 70 + +--S 71 of 486 +t0312:= x^3*(a+b*x-c*x^2)^(1/2) +--R +--R +--R +----------------+ +--R 3 | 2 +--R (67) x \|- c x + b x + a +--R Type: Expression Integer +--E 71 + +--S 72 of 486 +r0312:= -7/128*b^3*(b-2*c*x)*(a+b*x-c*x^2)^(1/2)/c^4-3/32*a*b*(b-2*c*x)*_ + (a+b*x-c*x^2)^(1/2)/c^3-7/48*b^2*(a+b*x-c*x^2)^(3/2)/c^3-2/15*a*_ + (a+b*x-c*x^2)^(3/2)/c^2-7/40*b*x*(a+b*x-c*x^2)^(3/2)/c^2-1/5*x^2*_ + (a+b*x-c*x^2)^(3/2)/c+7/256*b^5*atan(2*c^(1/2)*_ + (a+b*x-c*x^2)^(1/2)/(b-2*c*x))/c^(9/2)+3/64*a*b*(10/3*b^2+4*a*c)*_ + atan(2*c^(1/2)*(a+b*x-c*x^2)^(1/2)/(b-2*c*x))/c^(7/2) +--R +--R +--R (68) +--R +----------------+ +--R | 2 +-+ +--R 2 2 3 5 2\|- c x + b x + a \|c +--R (- 720a b c - 600a b c - 105b )atan(------------------------) +--R 2c x - b +--R + +--R 4 4 3 3 3 2 2 2 +--R 768c x - 96b c x + (- 256a c - 112b c )x +--R + +--R 2 3 2 2 2 4 +--R (- 464a b c - 140b c)x - 512a c - 920a b c - 210b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|c +--R / +--R 4 +-+ +--R 3840c \|c +--R Type: Expression Integer +--E 72 + +--S 73 of 486 +a0312:= integrate(t0312,x) +--R +--R +--R (69) +--R [ +--R 4 4 3 3 3 2 5 2 7 +--R 23040a b c - 38400a b c - 37440a b c - 2400a b c +--R + +--R 9 +--R 1050b +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c - 115200a b c + 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c + 253440a b c + 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c + 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c + 53760a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c - 19200a b c + 14880a b c + 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c + 192000a b c + 187200a b c + 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c + 288000a b c - 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c - 422400a b c - 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c - 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c - 53760a b +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 2 7 2 6 4 5 10 +--R (- 24576a c + 61440a b c - 7680b c )x +--R + +--R 2 6 3 5 5 4 9 +--R (322560a b c - 192000a b c + 8640b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (327680a c - 929280a b c + 147200a b c + 160b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (- 1507840a b c + 730240a b c + 1440a b c + 280b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (- 778240a c + 1514240a b c - 4800a b c + 2320a b c + 700b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (1359360a b c + 87040a b c + 95808a b c + 9920a b c - 1890b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 491520a c + 491520a b c + 236800a b c - 72320a b c +--R + +--R 8 +--R - 25200a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (399360a b c - 289280a b c - 460160a b c - 90720a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (- 829440a b c - 691200a b c - 120960a b )x +--R + +--R 6 2 5 3 4 5 +--R (- 368640a b c - 307200a b c - 53760a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 2 6 3 5 5 4 9 +--R (- 61440a b c + 30720a b c - 768b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (- 122880a c + 314880a b c - 42240a b c + 96b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (773120a b c - 346880a b c + 576a b c + 112b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (532480a c - 999680a b c - 960a b c + 464a b c + 140b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (- 1175040a b c - 7680a b c - 7488a b c - 480a b c + 210b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R - 491520a c - 153600a b c - 70400a b c + 25600a b c +--R + +--R 8 +--R 8400a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 215040a b c + 166400a b c + 256640a b c + 50400a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (645120a b c + 537600a b c + 94080a b )x +--R + +--R 6 2 5 3 4 5 +--R (368640a b c + 307200a b c + 53760a b )x +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R / +--R 2 6 2 5 4 4 4 +--R (122880a c - 307200a b c + 38400b c )x +--R + +--R 2 5 3 4 3 +--R (- 1474560a b c + 614400a b c )x +--R + +--R 3 5 2 2 4 2 3 4 4 4 +--R (- 1474560a c + 2580480a b c )x + 3932160a b c x + 1966080a c +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 2 6 3 5 5 4 5 +--R (- 307200a b c + 153600a b c - 3840b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 614400a c + 1536000a b c - 192000a b c )x +--R + +--R 3 5 2 3 4 3 4 5 3 2 4 2 +--R (3686400a b c - 1536000a b c )x + (2457600a c - 4300800a b c )x +--R + +--R 4 4 5 4 +--R - 4915200a b c x - 1966080a c +--R * +--R +---+ +--R \|- c +--R , +--R +--R 4 4 3 3 3 2 5 2 7 +--R 23040a b c - 38400a b c - 37440a b c - 2400a b c +--R + +--R 9 +--R 1050b +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c - 115200a b c + 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c + 253440a b c + 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c + 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c + 53760a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c - 19200a b c + 14880a b c + 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c + 192000a b c + 187200a b c + 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c + 288000a b c - 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c - 422400a b c - 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c - 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c - 53760a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 2 7 2 6 4 5 10 +--R (- 12288a c + 30720a b c - 3840b c )x +--R + +--R 2 6 3 5 5 4 9 +--R (161280a b c - 96000a b c + 4320b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (163840a c - 464640a b c + 73600a b c + 80b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (- 753920a b c + 365120a b c + 720a b c + 140b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 +--R - 389120a c + 757120a b c - 2400a b c + 1160a b c +--R + +--R 8 +--R 350b c +--R * +--R 6 +--R x +--R + +--R 4 4 3 3 3 2 5 2 7 +--R 679680a b c + 43520a b c + 47904a b c + 4960a b c +--R + +--R 9 +--R - 945b +--R * +--R 5 +--R x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 245760a c + 245760a b c + 118400a b c - 36160a b c +--R + +--R 8 +--R - 12600a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (199680a b c - 144640a b c - 230080a b c - 45360a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (- 414720a b c - 345600a b c - 60480a b )x +--R + +--R 6 2 5 3 4 5 +--R (- 184320a b c - 153600a b c - 26880a b )x +--R * +--R +-+ +--R \|a +--R + +--R 2 6 3 5 5 4 9 +--R (- 30720a b c + 15360a b c - 384b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (- 61440a c + 157440a b c - 21120a b c + 48b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (386560a b c - 173440a b c + 288a b c + 56b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (266240a c - 499840a b c - 480a b c + 232a b c + 70b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (- 587520a b c - 3840a b c - 3744a b c - 240a b c + 105b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R - 245760a c - 76800a b c - 35200a b c + 12800a b c +--R + +--R 8 +--R 4200a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 107520a b c + 83200a b c + 128320a b c + 25200a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (322560a b c + 268800a b c + 47040a b )x +--R + +--R 6 2 5 3 4 5 +--R (184320a b c + 153600a b c + 26880a b )x +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R 2 6 2 5 4 4 4 +--R (61440a c - 153600a b c + 19200b c )x +--R + +--R 2 5 3 4 3 +--R (- 737280a b c + 307200a b c )x +--R + +--R 3 5 2 2 4 2 3 4 4 4 +--R (- 737280a c + 1290240a b c )x + 1966080a b c x + 983040a c +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 6 3 5 5 4 5 +--R (- 153600a b c + 76800a b c - 1920b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 307200a c + 768000a b c - 96000a b c )x +--R + +--R 3 5 2 3 4 3 4 5 3 2 4 2 +--R (1843200a b c - 768000a b c )x + (1228800a c - 2150400a b c )x +--R + +--R 4 4 5 4 +--R - 2457600a b c x - 983040a c +--R * +--R +-+ +--R \|c +--R ] +--R Type: Union(List Expression Integer,...) +--E 73 + +--S 74 of 486 +m0312a:= a0312.1-r0312 +--R +--R +--R (70) +--R 4 4 3 3 3 2 5 2 7 9 4 +--R (23040a b c - 38400a b c - 37440a b c - 2400a b c + 1050b )x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c - 115200a b c + 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c + 253440a b c + 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c + 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c + 53760a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c - 19200a b c + 14880a b c + 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c + 192000a b c + 187200a b c + 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c + 288000a b c - 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c - 422400a b c - 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c - 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c - 53760a b +--R * +--R +-+ +--R \|c +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 4 4 3 3 3 2 5 2 7 9 4 +--R (23040a b c - 38400a b c - 37440a b c - 2400a b c + 1050b )x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c - 115200a b c + 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c + 253440a b c + 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c + 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c + 53760a b +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 4 2 4 3 4 3 2 6 2 8 +--R - 57600a b c - 19200a b c + 14880a b c + 3600a b c +--R + +--R 10 +--R - 105b +--R * +--R 5 +--R x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c + 192000a b c + 187200a b c + 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c + 288000a b c - 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c - 422400a b c - 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c - 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c - 53760a b +--R * +--R +---+ +--R \|- c +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (40960a b c + 53120a b c - 19488a b c - 7480a b c + 210b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 81920a c - 57600a b c - 308800a b c - 38000a b c +--R + +--R 8 +--R 10500a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 491520a b c - 678400a b c + 166400a b c + 84000a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (- 327680a c - 15360a b c + 896000a b c + 235200a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (655360a b c + 1177600a b c + 268800a b )x + 262144a c +--R + +--R 6 2 5 4 +--R 471040a b c + 107520a b +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R - 16384a c + 11520a b c + 61760a b c + 7600a b c +--R + +--R 8 +--R - 2100a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (196608a b c + 271360a b c - 66560a b c - 33600a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (196608a c + 9216a b c - 537600a b c - 141120a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (- 524288a b c - 942080a b c - 215040a b )x - 262144a c +--R + +--R 6 2 5 4 +--R - 471040a b c - 107520a b +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R * +--R +-+ +--R \|c +--R / +--R 2 6 2 5 4 4 4 +--R (122880a c - 307200a b c + 38400b c )x +--R + +--R 2 5 3 4 3 +--R (- 1474560a b c + 614400a b c )x +--R + +--R 3 5 2 2 4 2 3 4 4 4 +--R (- 1474560a c + 2580480a b c )x + 3932160a b c x + 1966080a c +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 2 6 3 5 5 4 5 +--R (- 307200a b c + 153600a b c - 3840b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 614400a c + 1536000a b c - 192000a b c )x +--R + +--R 3 5 2 3 4 3 4 5 3 2 4 2 +--R (3686400a b c - 1536000a b c )x + (2457600a c - 4300800a b c )x +--R + +--R 4 4 5 4 +--R - 4915200a b c x - 1966080a c +--R * +--R +---+ +--R \|- c +--R * +--R +-+ +--R \|c +--R Type: Expression Integer +--E 74 + +--S 75 of 486 +d0312a:= D(m0312a,x) +--R +--R +--R (71) 0 +--R Type: Expression Integer +--E 75 + +--S 76 of 486 +m0312b:= a0312.2-r0312 +--R +--R +--R (72) +--R 4 4 3 3 3 2 5 2 7 9 4 +--R (46080a b c - 76800a b c - 74880a b c - 4800a b c + 2100b )x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 552960a b c - 230400a b c + 111360a b c + 33600a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 552960a b c + 506880a b c + 725760a b c + 141120a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (1474560a b c + 1228800a b c + 215040a b )x + 737280a b c +--R + +--R 5 3 4 5 +--R 614400a b c + 107520a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 115200a b c - 38400a b c + 29760a b c + 7200a b c - 210b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 230400a b c + 384000a b c + 374400a b c + 24000a b c +--R + +--R 9 +--R - 10500a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (1382400a b c + 576000a b c - 278400a b c - 84000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (921600a b c - 844800a b c - 1209600a b c - 235200a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 1843200a b c - 1536000a b c - 268800a b )x - 737280a b c +--R + +--R 6 3 5 5 +--R - 614400a b c - 107520a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 4 4 3 3 3 2 5 2 7 9 4 +--R (23040a b c - 38400a b c - 37440a b c - 2400a b c + 1050b )x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c - 115200a b c + 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c + 253440a b c + 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c + 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c + 53760a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c - 19200a b c + 14880a b c + 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c + 192000a b c + 187200a b c + 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c + 288000a b c - 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c - 422400a b c - 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c - 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c - 53760a b +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (40960a b c + 53120a b c - 19488a b c - 7480a b c + 210b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 81920a c - 57600a b c - 308800a b c - 38000a b c +--R + +--R 8 +--R 10500a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 491520a b c - 678400a b c + 166400a b c + 84000a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (- 327680a c - 15360a b c + 896000a b c + 235200a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (655360a b c + 1177600a b c + 268800a b )x + 262144a c +--R + +--R 6 2 5 4 +--R 471040a b c + 107520a b +--R * +--R +-+ +--R \|a +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R - 16384a c + 11520a b c + 61760a b c + 7600a b c +--R + +--R 8 +--R - 2100a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (196608a b c + 271360a b c - 66560a b c - 33600a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (196608a c + 9216a b c - 537600a b c - 141120a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (- 524288a b c - 942080a b c - 215040a b )x - 262144a c +--R + +--R 6 2 5 4 +--R - 471040a b c - 107520a b +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R 2 6 2 5 4 4 4 +--R (122880a c - 307200a b c + 38400b c )x +--R + +--R 2 5 3 4 3 +--R (- 1474560a b c + 614400a b c )x +--R + +--R 3 5 2 2 4 2 3 4 4 4 +--R (- 1474560a c + 2580480a b c )x + 3932160a b c x + 1966080a c +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 6 3 5 5 4 5 +--R (- 307200a b c + 153600a b c - 3840b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 614400a c + 1536000a b c - 192000a b c )x +--R + +--R 3 5 2 3 4 3 4 5 3 2 4 2 +--R (3686400a b c - 1536000a b c )x + (2457600a c - 4300800a b c )x +--R + +--R 4 4 5 4 +--R - 4915200a b c x - 1966080a c +--R * +--R +-+ +--R \|c +--R Type: Expression Integer +--E 76 + +--S 77 of 486 +d0312b:= D(m0312b,x) +--R +--R +--R (73) 0 +--R Type: Expression Integer +--E 77 + +--S 78 of 486 +t0313:= x^2*(a+b*x-c*x^2)^(1/2) +--R +--R +--R +----------------+ +--R 2 | 2 +--R (74) x \|- c x + b x + a +--R Type: Expression Integer +--E 78 + +--S 79 of 486 +r0313:= -5/64*b^2*(b-2*c*x)*(a+b*x-c*x^2)^(1/2)/c^3-1/16*a*(b-2*c*x)*_ + (a+b*x-c*x^2)^(1/2)/c^2-5/24*b*(a+b*x-c*x^2)^(3/2)/c^2-1/4*x*_ + (a+b*x-c*x^2)^(3/2)/c+5/128*b^4*atan(2*c^(1/2)*_ + (a+b*x-c*x^2)^(1/2)/(b-2*c*x))/c^(7/2)+1/32*a*(6*b^2+4*a*c)*_ + atan(2*c^(1/2)*(a+b*x-c*x^2)^(1/2)/(b-2*c*x))/c^(5/2) +--R +--R +--R (75) +--R +----------------+ +--R | 2 +-+ +--R 2 2 2 4 2\|- c x + b x + a \|c +--R (- 48a c - 72a b c - 15b )atan(------------------------) +--R 2c x - b +--R + +--R 3 3 2 2 2 2 3 +--R (96c x - 16b c x + (- 48a c - 20b c)x - 104a b c - 30b ) +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|c +--R / +--R 3 +-+ +--R 384c \|c +--R Type: Expression Integer +--E 79 + +--S 80 of 486 +a0313:= integrate(t0313,x) +--R +--R +--R (76) +--R [ +--R 3 3 2 3 2 5 7 3 +--R (1536a b c + 1920a b c - 96a b c - 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 768a b c - 4800a b c - 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 9216a b c - 13824a b c - 2880a b )x - 6144a c - 9216a b c +--R + +--R 3 4 +--R - 1920a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 4 2 4 2 6 8 4 +--R (768a c - 1440a b c - 288a b c + 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c - 7680a b c + 384a b c + 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 1536a b c + 9600a b c + 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (12288a b c + 18432a b c + 3840a b )x + 6144a c + 9216a b c +--R + +--R 4 4 +--R 1920a b +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 5 3 4 8 2 5 2 4 4 3 7 +--R (- 3072a b c + 768b c )x + (- 6144a c + 11264a b c - 896b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (30208a b c - 9984a b c - 32b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (21504a c - 31488a b c - 320a b c - 80b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 42624a b c - 4896a b c - 152a b c + 210b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (- 21504a c - 2304a b c + 6464a b c + 1680a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (10752a b c + 16128a b c + 3360a b )x +--R + +--R 5 2 4 2 3 4 +--R (6144a c + 9216a b c + 1920a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 2 5 2 4 4 3 7 +--R (1536a c - 2304a b c + 96b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (- 12544a b c + 3456a b c - 16b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (- 13056a c + 18240a b c - 80a b c - 20b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (31104a b c + 480a b c - 24a b c - 30b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (18432a c + 768a b c - 2816a b c - 720a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (- 7680a b c - 11520a b c - 2400a b )x +--R + +--R 5 2 4 2 3 4 +--R (- 6144a c - 9216a b c - 1920a b )x +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (12288a b c - 3072b c )x + (24576a c - 30720a b c )x +--R + +--R 2 3 3 3 +--R - 73728a b c x - 49152a c +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 2 5 2 4 4 3 4 +--R (6144a c - 9216a b c + 384b c )x +--R + +--R 2 4 3 3 3 3 4 2 2 3 2 +--R (- 49152a b c + 12288a b c )x + (- 49152a c + 61440a b c )x +--R + +--R 3 3 4 3 +--R 98304a b c x + 49152a c +--R * +--R +---+ +--R \|- c +--R , +--R +--R 3 3 2 3 2 5 7 3 +--R (1536a b c + 1920a b c - 96a b c - 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 768a b c - 4800a b c - 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 9216a b c - 13824a b c - 2880a b )x - 6144a c - 9216a b c +--R + +--R 3 4 +--R - 1920a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 4 2 4 2 6 8 4 +--R (768a c - 1440a b c - 288a b c + 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c - 7680a b c + 384a b c + 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 1536a b c + 9600a b c + 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (12288a b c + 18432a b c + 3840a b )x + 6144a c + 9216a b c +--R + +--R 4 4 +--R 1920a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 5 3 4 8 +--R (- 1536a b c + 384b c )x +--R + +--R 2 5 2 4 4 3 7 +--R (- 3072a c + 5632a b c - 448b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (15104a b c - 4992a b c - 16b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (10752a c - 15744a b c - 160a b c - 40b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 21312a b c - 2448a b c - 76a b c + 105b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (- 10752a c - 1152a b c + 3232a b c + 840a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (5376a b c + 8064a b c + 1680a b )x +--R + +--R 5 2 4 2 3 4 +--R (3072a c + 4608a b c + 960a b )x +--R * +--R +-+ +--R \|a +--R + +--R 2 5 2 4 4 3 7 +--R (768a c - 1152a b c + 48b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (- 6272a b c + 1728a b c - 8b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (- 6528a c + 9120a b c - 40a b c - 10b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (15552a b c + 240a b c - 12a b c - 15b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (9216a c + 384a b c - 1408a b c - 360a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (- 3840a b c - 5760a b c - 1200a b )x +--R + +--R 5 2 4 2 3 4 +--R (- 3072a c - 4608a b c - 960a b )x +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (6144a b c - 1536b c )x + (12288a c - 15360a b c )x +--R + +--R 2 3 3 3 +--R - 36864a b c x - 24576a c +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 5 2 4 4 3 4 2 4 3 3 3 +--R (3072a c - 4608a b c + 192b c )x + (- 24576a b c + 6144a b c )x +--R + +--R 3 4 2 2 3 2 3 3 4 3 +--R (- 24576a c + 30720a b c )x + 49152a b c x + 24576a c +--R * +--R +-+ +--R \|c +--R ] +--R Type: Union(List Expression Integer,...) +--E 80 + +--S 81 of 486 +m0313a:= a0313.1-r0313 +--R +--R +--R (77) +--R 3 3 2 3 2 5 7 3 +--R (1536a b c + 1920a b c - 96a b c - 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 768a b c - 4800a b c - 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 9216a b c - 13824a b c - 2880a b )x - 6144a c - 9216a b c +--R + +--R 3 4 +--R - 1920a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 4 2 4 2 6 8 4 +--R (768a c - 1440a b c - 288a b c + 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c - 7680a b c + 384a b c + 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 1536a b c + 9600a b c + 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (12288a b c + 18432a b c + 3840a b )x + 6144a c + 9216a b c +--R + +--R 4 4 +--R 1920a b +--R * +--R +-+ +--R \|c +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 3 3 2 3 2 5 7 3 +--R (1536a b c + 1920a b c - 96a b c - 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 768a b c - 4800a b c - 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 9216a b c - 13824a b c - 2880a b )x - 6144a c - 9216a b c +--R + +--R 3 4 +--R - 1920a b +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 4 4 2 4 2 6 8 4 +--R (768a c - 1440a b c - 288a b c + 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c - 7680a b c + 384a b c + 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 1536a b c + 9600a b c + 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (12288a b c + 18432a b c + 3840a b )x + 6144a c + 9216a b c +--R + +--R 4 4 +--R 1920a b +--R * +--R +---+ +--R \|- c +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 1664a b c + 2016a b c + 616a b c - 30b )x +--R + +--R 3 2 2 2 4 6 3 +--R (13312a b c + 512a b c - 960a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (13312a b c - 12800a b c - 4800a b )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 26624a b c - 7680a b )x - 13312a b c - 3840a b +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 3 2 2 2 4 6 3 +--R (- 3328a b c - 128a b c + 240a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (- 6656a b c + 6400a b c + 2400a b )x +--R + +--R 4 2 3 4 5 4 3 +--R (19968a b c + 5760a b )x + 13312a b c + 3840a b +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R * +--R +-+ +--R \|c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (12288a b c - 3072b c )x + (24576a c - 30720a b c )x +--R + +--R 2 3 3 3 +--R - 73728a b c x - 49152a c +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 2 5 2 4 4 3 4 +--R (6144a c - 9216a b c + 384b c )x +--R + +--R 2 4 3 3 3 3 4 2 2 3 2 +--R (- 49152a b c + 12288a b c )x + (- 49152a c + 61440a b c )x +--R + +--R 3 3 4 3 +--R 98304a b c x + 49152a c +--R * +--R +---+ +--R \|- c +--R * +--R +-+ +--R \|c +--R Type: Expression Integer +--E 81 + +--S 82 of 486 +d0313a:= D(m0313a,x) +--R +--R +--R (78) 0 +--R Type: Expression Integer +--E 82 + +--S 83 of 486 +m0313b:= a0313.2-r0313 +--R +--R +--R (79) +--R 3 3 2 3 2 5 7 3 +--R (3072a b c + 3840a b c - 192a b c - 240b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (6144a c + 1536a b c - 9600a b c - 2400a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 18432a b c - 27648a b c - 5760a b )x - 12288a c - 18432a b c +--R + +--R 3 4 +--R - 3840a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 4 2 4 2 6 8 4 +--R (1536a c - 2880a b c - 576a b c + 30b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 12288a b c - 15360a b c + 768a b c + 960a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 12288a c - 3072a b c + 19200a b c + 4800a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (24576a b c + 36864a b c + 7680a b )x + 12288a c + 18432a b c +--R + +--R 4 4 +--R 3840a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 3 3 2 3 2 5 7 3 +--R (1536a b c + 1920a b c - 96a b c - 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 768a b c - 4800a b c - 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 9216a b c - 13824a b c - 2880a b )x - 6144a c - 9216a b c +--R + +--R 3 4 +--R - 1920a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 4 2 4 2 6 8 4 +--R (768a c - 1440a b c - 288a b c + 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c - 7680a b c + 384a b c + 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 1536a b c + 9600a b c + 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (12288a b c + 18432a b c + 3840a b )x + 6144a c + 9216a b c +--R + +--R 4 4 +--R 1920a b +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 1664a b c + 2016a b c + 616a b c - 30b )x +--R + +--R 3 2 2 2 4 6 3 +--R (13312a b c + 512a b c - 960a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (13312a b c - 12800a b c - 4800a b )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 26624a b c - 7680a b )x - 13312a b c - 3840a b +--R * +--R +-+ +--R \|a +--R + +--R 3 2 2 2 4 6 3 +--R (- 3328a b c - 128a b c + 240a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (- 6656a b c + 6400a b c + 2400a b )x +--R + +--R 4 2 3 4 5 4 3 +--R (19968a b c + 5760a b )x + 13312a b c + 3840a b +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (12288a b c - 3072b c )x + (24576a c - 30720a b c )x +--R + +--R 2 3 3 3 +--R - 73728a b c x - 49152a c +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 5 2 4 4 3 4 2 4 3 3 3 +--R (6144a c - 9216a b c + 384b c )x + (- 49152a b c + 12288a b c )x +--R + +--R 3 4 2 2 3 2 3 3 4 3 +--R (- 49152a c + 61440a b c )x + 98304a b c x + 49152a c +--R * +--R +-+ +--R \|c +--R Type: Expression Integer +--E 83 + +--S 84 of 486 +d0313b:= D(m0313b,x) +--R +--R +--R (80) 0 +--R Type: Expression Integer +--E 84 + +--S 85 of 486 +t0314:= x*(a+b*x-c*x^2)^(1/2) +--R +--R +--R +----------------+ +--R | 2 +--R (81) x\|- c x + b x + a +--R Type: Expression Integer +--E 85 + +--S 86 of 486 +r0314:= -1/8*b*(b-2*c*x)*(a+b*x-c*x^2)^(1/2)/c^2-1/3*(a+b*x-c*x^2)^(3/2)/c+_ + 1/16*b*(b^2+4*a*c)*atan(2*c^(1/2)*(a+b*x-c*x^2)^(1/2)/_ + (b-2*c*x))/c^(5/2) +--R +--R +--R (82) +--R +----------------+ +--R | 2 +-+ +--R 3 2\|- c x + b x + a \|c +--R (- 12a b c - 3b )atan(------------------------) +--R 2c x - b +--R + +--R +----------------+ +--R 2 2 2 | 2 +-+ +--R (16c x - 4b c x - 16a c - 6b )\|- c x + b x + a \|c +--R / +--R 2 +-+ +--R 48c \|c +--R Type: Expression Integer +--E 86 + +--S 87 of 486 +a0314:= integrate(t0314,x) +--R +--R +--R (83) +--R [ +--R 2 2 3 5 2 2 2 4 +--R (96a b c - 48a b c - 18b )x + (- 384a b c - 96a b )x +--R + +--R 3 2 3 +--R - 384a b c - 96a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 2 2 4 6 3 +--R (- 144a b c - 24a b c + 3b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (- 288a b c + 144a b c + 54a b )x + (576a b c + 144a b )x +--R + +--R 4 3 3 +--R 384a b c + 96a b +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 4 2 3 6 3 3 2 5 +--R (- 128a c + 96b c )x + (672a b c - 120b c )x +--R + +--R 2 3 2 2 4 4 2 2 3 5 3 +--R (768a c - 816a b c - 12b c)x + (- 1632a b c + 64a b c + 30b )x +--R + +--R 3 2 2 2 4 2 3 2 3 +--R (- 768a c + 480a b c + 120a b )x + (384a b c + 96a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 3 3 2 5 2 3 2 2 4 4 +--R (- 192a b c + 16b c )x + (- 384a c + 336a b c - 4b c)x +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (1056a b c - 16a b c - 6b )x + (768a c - 288a b c - 72a b )x +--R + +--R 3 2 3 +--R (- 384a b c - 96a b )x +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R / +--R +----------------+ +--R 3 2 2 2 2 2 2 | 2 +--R ((384a c - 288b c )x - 1536a b c x - 1536a c )\|- c x + b x + a +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576a b c + 48b c )x + (- 1152a c + 864a b c )x + 2304a b c x +--R + +--R 3 2 +--R 1536a c +--R * +--R +---+ +--R \|- c +--R , +--R +--R 2 2 3 5 2 2 2 4 +--R (96a b c - 48a b c - 18b )x + (- 384a b c - 96a b )x +--R + +--R 3 2 3 +--R - 384a b c - 96a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 2 2 4 6 3 +--R (- 144a b c - 24a b c + 3b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (- 288a b c + 144a b c + 54a b )x + (576a b c + 144a b )x +--R + +--R 4 3 3 +--R 384a b c + 96a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 4 2 3 6 3 3 2 5 +--R (- 64a c + 48b c )x + (336a b c - 60b c )x +--R + +--R 2 3 2 2 4 4 +--R (384a c - 408a b c - 6b c)x +--R + +--R 2 2 3 5 3 +--R (- 816a b c + 32a b c + 15b )x +--R + +--R 3 2 2 2 4 2 3 2 3 +--R (- 384a c + 240a b c + 60a b )x + (192a b c + 48a b )x +--R * +--R +-+ +--R \|a +--R + +--R 3 3 2 5 2 3 2 2 4 4 +--R (- 96a b c + 8b c )x + (- 192a c + 168a b c - 2b c)x +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (528a b c - 8a b c - 3b )x + (384a c - 144a b c - 36a b )x +--R + +--R 3 2 3 +--R (- 192a b c - 48a b )x +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R +----------------+ +--R 3 2 2 2 2 2 2 | 2 +-+ +--R ((192a c - 144b c )x - 768a b c x - 768a c )\|- c x + b x + a \|a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 288a b c + 24b c )x + (- 576a c + 432a b c )x + 1152a b c x +--R + +--R 3 2 +--R 768a c +--R * +--R +-+ +--R \|c +--R ] +--R Type: Union(List Expression Integer,...) +--E 87 + +--S 88 of 486 +m0314a:= a0314.1-r0314 +--R +--R +--R (84) +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c - 48a b c - 18b )x + (- 384a b c - 96a b )x - 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 2 2 4 6 3 3 2 2 3 5 2 +--R (- 144a b c - 24a b c + 3b )x + (- 288a b c + 144a b c + 54a b )x +--R + +--R 3 2 2 4 4 3 3 +--R (576a b c + 144a b )x + 384a b c + 96a b +--R * +--R +-+ +--R \|c +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c - 48a b c - 18b )x + (- 384a b c - 96a b )x - 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 2 2 2 4 6 3 +--R (- 144a b c - 24a b c + 3b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (- 288a b c + 144a b c + 54a b )x + (576a b c + 144a b )x +--R + +--R 4 3 3 +--R 384a b c + 96a b +--R * +--R +---+ +--R \|- c +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (192a b c + 56a b c - 6b )x + (384a c - 144a b c - 108a b )x +--R + +--R 3 2 3 4 3 2 +--R (- 768a b c - 288a b )x - 512a c - 192a b +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 3 2 2 2 4 2 3 2 3 4 +--R (- 128a c + 48a b c + 36a b )x + (512a b c + 192a b )x + 512a c +--R + +--R 3 2 +--R 192a b +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R * +--R +-+ +--R \|c +--R / +--R +----------------+ +--R 3 2 2 2 2 2 2 | 2 +--R ((384a c - 288b c )x - 1536a b c x - 1536a c )\|- c x + b x + a +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576a b c + 48b c )x + (- 1152a c + 864a b c )x + 2304a b c x +--R + +--R 3 2 +--R 1536a c +--R * +--R +---+ +--R \|- c +--R * +--R +-+ +--R \|c +--R Type: Expression Integer +--E 88 + +--S 89 of 486 +d0314a:= D(m0314a,x) +--R +--R +--R (85) 0 +--R Type: Expression Integer +--E 89 + +--S 90 of 486 +m0314b:= a0314.2-r0314 +--R +--R +--R (86) +--R 2 2 3 5 2 2 2 4 +--R (192a b c - 96a b c - 36b )x + (- 768a b c - 192a b )x +--R + +--R 3 2 3 +--R - 768a b c - 192a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 2 2 4 6 3 +--R (- 288a b c - 48a b c + 6b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (- 576a b c + 288a b c + 108a b )x + (1152a b c + 288a b )x +--R + +--R 4 3 3 +--R 768a b c + 192a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c - 48a b c - 18b )x + (- 384a b c - 96a b )x - 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 2 2 4 6 3 3 2 2 3 5 2 +--R (- 144a b c - 24a b c + 3b )x + (- 288a b c + 144a b c + 54a b )x +--R + +--R 3 2 2 4 4 3 3 +--R (576a b c + 144a b )x + 384a b c + 96a b +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (192a b c + 56a b c - 6b )x + (384a c - 144a b c - 108a b )x +--R + +--R 3 2 3 4 3 2 +--R (- 768a b c - 288a b )x - 512a c - 192a b +--R * +--R +-+ +--R \|a +--R + +--R 3 2 2 2 4 2 3 2 3 4 +--R (- 128a c + 48a b c + 36a b )x + (512a b c + 192a b )x + 512a c +--R + +--R 3 2 +--R 192a b +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R +----------------+ +--R 3 2 2 2 2 2 2 | 2 +-+ +--R ((384a c - 288b c )x - 1536a b c x - 1536a c )\|- c x + b x + a \|a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576a b c + 48b c )x + (- 1152a c + 864a b c )x + 2304a b c x +--R + +--R 3 2 +--R 1536a c +--R * +--R +-+ +--R \|c +--R Type: Expression Integer +--E 90 + +--S 91 of 486 +d0314b:= D(m0314b,x) +--R +--R +--R (87) 0 +--R Type: Expression Integer +--E 91 + +--S 92 of 486 +t0315:= (a+b*x-c*x^2)^(1/2) +--R +--R +--R +----------------+ +--R | 2 +--R (88) \|- c x + b x + a +--R Type: Expression Integer +--E 92 + +--S 93 of 486 +r0315:= -1/4*(b-2*c*x)*(a+b*x-c*x^2)^(1/2)/c+1/8*(b^2+4*a*c)*_ + atan(2*c^(1/2)*(a+b*x-c*x^2)^(1/2)/(b-2*c*x))/c^(3/2) +--R +--R +--R (89) +--R +----------------+ +--R | 2 +-+ +--R 2 2\|- c x + b x + a \|c +--R (- 4a c - b )atan(------------------------) +--R 2c x - b +--R + +--R +----------------+ +--R | 2 +-+ +--R (4c x - 2b)\|- c x + b x + a \|c +--R / +--R +-+ +--R 8c\|c +--R Type: Expression Integer +--E 93 + +--S 94 of 486 +a0315:= integrate(t0315,x) +--R +--R +--R (90) +--R [ +--R +----------------+ +--R 3 2 2 | 2 +-+ +--R ((16a b c + 4b )x + 32a c + 8a b )\|- c x + b x + a \|a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (16a c - b )x + (- 32a b c - 8a b )x - 32a c - 8a b +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 2 4 2 2 3 3 2 +--R - 16b c x + (- 32a c + 24b c)x + (56a b c - 6b )x +--R + +--R 2 2 +--R (32a c - 8a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 2 2 3 3 2 2 2 +--R ((16a c - 4b c)x + (- 40a b c + 2b )x + (- 32a c + 8a b )x) +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R / +--R +----------------+ +--R | 2 +---+ +-+ +--R (32b c x + 64a c)\|- c x + b x + a \|- c \|a +--R + +--R 2 2 2 2 +---+ +--R ((32a c - 8b c)x - 64a b c x - 64a c)\|- c +--R , +--R +--R +----------------+ +--R 3 2 2 | 2 +-+ +--R ((16a b c + 4b )x + 32a c + 8a b )\|- c x + b x + a \|a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (16a c - b )x + (- 32a b c - 8a b )x - 32a c - 8a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 2 4 2 2 3 3 2 +--R - 8b c x + (- 16a c + 12b c)x + (28a b c - 3b )x +--R + +--R 2 2 +--R (16a c - 4a b )x +--R * +--R +-+ +--R \|a +--R + +--R 2 2 3 3 2 2 2 +--R ((8a c - 2b c)x + (- 20a b c + b )x + (- 16a c + 4a b )x) +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R +----------------+ +--R | 2 +-+ 2 2 2 +--R (16b c x + 32a c)\|- c x + b x + a \|a + (16a c - 4b c)x +--R + +--R 2 +--R - 32a b c x - 32a c +--R * +--R +-+ +--R \|c +--R ] +--R Type: Union(List Expression Integer,...) +--E 94 + +--S 95 of 486 +m0315a:= a0315.1-r0315 +--R +--R +--R (91) +--R +----------------+ +--R 3 2 2 | 2 +-+ +--R ((16a b c + 4b )x + 32a c + 8a b )\|- c x + b x + a \|a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (16a c - b )x + (- 32a b c - 8a b )x - 32a c - 8a b +--R * +--R +-+ +--R \|c +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R +----------------+ +--R 3 2 2 | 2 +---+ +-+ +--R ((16a b c + 4b )x + 32a c + 8a b )\|- c x + b x + a \|- c \|a +--R + +--R 2 2 4 2 2 3 3 2 2 +---+ +--R ((16a c - b )x + (- 32a b c - 8a b )x - 32a c - 8a b )\|- c +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 3 2 2 2 +---+ +-+ +--R ((- 8a b c + 2b )x + 16a b x + 16a b)\|- c \|a +--R + +--R +----------------+ +--R 2 2 | 2 +---+ +--R (- 8a b x - 16a b)\|- c x + b x + a \|- c +--R * +--R +-+ +--R \|c +--R / +--R +----------------+ +--R | 2 +---+ +-+ +--R (32b c x + 64a c)\|- c x + b x + a \|- c \|a +--R + +--R 2 2 2 2 +---+ +--R ((32a c - 8b c)x - 64a b c x - 64a c)\|- c +--R * +--R +-+ +--R \|c +--R Type: Expression Integer +--E 95 + +--S 96 of 486 +d0315a:= D(m0315a,x) +--R +--R +--R (92) 0 +--R Type: Expression Integer +--E 96 + +--S 97 of 486 +m0315b:= a0315.2-r0315 +--R +--R +--R (93) +--R +----------------+ +--R 3 2 2 | 2 +-+ +--R ((32a b c + 8b )x + 64a c + 16a b )\|- c x + b x + a \|a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (32a c - 2b )x + (- 64a b c - 16a b )x - 64a c - 16a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R +----------------+ +--R 3 2 2 | 2 +-+ +--R ((16a b c + 4b )x + 32a c + 8a b )\|- c x + b x + a \|a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (16a c - b )x + (- 32a b c - 8a b )x - 32a c - 8a b +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 3 2 2 2 +-+ +--R ((- 8a b c + 2b )x + 16a b x + 16a b)\|a +--R + +--R +----------------+ +--R 2 2 | 2 +--R (- 8a b x - 16a b)\|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R +----------------+ +--R | 2 +-+ 2 2 2 +--R (32b c x + 64a c)\|- c x + b x + a \|a + (32a c - 8b c)x +--R + +--R 2 +--R - 64a b c x - 64a c +--R * +--R +-+ +--R \|c +--R Type: Expression Integer +--E 97 + +--S 98 of 486 +d0315b:= D(m0315b,x) +--R +--R +--R (94) 0 +--R Type: Expression Integer +--E 98 + +--S 99 of 486 +t0316:= 1/(b*x-b^2*x^2)^(1/2) +--R +--R +--R 1 +--R (95) --------------- +--R +------------+ +--R | 2 2 +--R \|- b x + b x +--R Type: Expression Integer +--E 99 + +--S 100 of 486 +r0316:= asin(-1+2*b*x)/b +--R +--R +--R asin(2b x - 1) +--R (96) -------------- +--R b +--R Type: Expression Integer +--E 100 + +--S 101 of 486 +a0316:= integrate(t0316,x) +--R +--R +--R +------------+ +--R | 2 2 +--R \|- b x + b x +--R 2atan(---------------) +--R b x +--R (97) - ---------------------- +--R b +--R Type: Union(Expression Integer,...) +--E 101 + +--S 102 of 486 +m0316:= a0316-r0316 +--R +--R +--R +------------+ +--R | 2 2 +--R \|- b x + b x +--R - 2atan(---------------) - asin(2b x - 1) +--R b x +--R (98) ----------------------------------------- +--R b +--R Type: Expression Integer +--E 102 + +--S 103 of 486 +d0316:= D(m0316,x) +--R +--R +--R +------------+ +--------------+ +--R | 2 2 | 2 2 +--R - 2\|- b x + b x + \|- 4b x + 4b x +--R (99) -------------------------------------- +--R +--------------+ +------------+ +--R | 2 2 | 2 2 +--R \|- 4b x + 4b x \|- b x + b x +--R Type: Expression Integer +--E 103 + +--S 104 of 486 +t0317:= 1/(b*x+b^2*x^2)^(1/2) +--R +--R +--R 1 +--R (100) ------------- +--R +----------+ +--R | 2 2 +--R \|b x + b x +--R Type: Expression Integer +--E 104 + +--S 105 of 486 +r0317:= atanh(2*(b*x*(1+b*x))^(1/2)/(1+2*b*x))/b +--R +--R +--R +----------+ +--R | 2 2 +--R 2\|b x + b x +--R atanh(--------------) +--R 2b x + 1 +--R (101) --------------------- +--R b +--R Type: Expression Integer +--E 105 + +--S 106 of 486 +a0317:= integrate(t0317,x) +--R +--R +--R +----------+ +--R | 2 2 +--R log(2\|b x + b x - 2b x - 1) +--R (102) - ------------------------------ +--R b +--R Type: Union(Expression Integer,...) +--E 106 + +--S 107 of 486 +m0317:= a0317-r0317 +--R +--R +--R +----------+ +--R +----------+ | 2 2 +--R | 2 2 2\|b x + b x +--R - log(2\|b x + b x - 2b x - 1) - atanh(--------------) +--R 2b x + 1 +--R (103) -------------------------------------------------------- +--R b +--R Type: Expression Integer +--E 107 + +--S 108 of 486 +d0317:= D(m0317,x) +--R +--R +--R (104) 0 +--R Type: Expression Integer +--E 108 + +--S 109 of 486 +t0318:= 2/((4*c+b^2)/c+4*b*x+4*c*x^2)^(1/2) +--R +--R +--R 2 +--R (105) --------------------------- +--R +------------------------+ +--R | 2 2 2 +--R |4c x + 4b c x + 4c + b +--R |------------------------ +--R \| c +--R Type: Expression Integer +--E 109 + +--S 110 of 486 +r0318:= asinh(1/2*(b+2*c*x)/c^(1/2))/c^(1/2) +--R +--R +--R 2c x + b +--R asinh(--------) +--R +-+ +--R 2\|c +--R (106) --------------- +--R +-+ +--R \|c +--R Type: Expression Integer +--E 110 + +--S 111 of 486 +a0318:= integrate(t0318,x) +--R +--R +--R (107) +--R [ +--R log +--R +-------+ +------------------------+ +--R | 2 | 2 2 2 +--R |4c + b +-+ 2 |4c x + 4b c x + 4c + b +--R (c |------- \|c - 2c x) |------------------------ +--R \| c \| c +--R + +--R +-------+ +--R | 2 +--R 2 2 2 +-+ 2 |4c + b +--R (- 4c x - 2b c x - 4c - b )\|c + 2c x |------- +--R \| c +--R / +--R +-------+ +------------------------+ +--R | 2 | 2 2 2 +--R |4c + b |4c x + 4b c x + 4c + b 2 +--R c |------- |------------------------ - 2b c x - 4c - b +--R \| c \| c +--R / +--R +-+ +--R \|c +--R , +--R +------------------------+ +-------+ +--R | 2 2 2 | 2 +--R +---+ |4c x + 4b c x + 4c + b +---+ |4c + b +--R \|- c |------------------------ - \|- c |------- +--R \| c \| c +--R 2atan(----------------------------------------------------) +--R 2c x +--R -----------------------------------------------------------] +--R +---+ +--R \|- c +--R Type: Union(List Expression Integer,...) +--E 111 + +--S 112 of 486 +m0318a:= a0318.1-r0318 +--R +--R +--R (108) +--R log +--R +-------+ +------------------------+ +--R | 2 | 2 2 2 +--R |4c + b +-+ 2 |4c x + 4b c x + 4c + b +--R (c |------- \|c - 2c x) |------------------------ +--R \| c \| c +--R + +--R +-------+ +--R | 2 +--R 2 2 2 +-+ 2 |4c + b +--R (- 4c x - 2b c x - 4c - b )\|c + 2c x |------- +--R \| c +--R / +--R +-------+ +------------------------+ +--R | 2 | 2 2 2 +--R |4c + b |4c x + 4b c x + 4c + b 2 +--R c |------- |------------------------ - 2b c x - 4c - b +--R \| c \| c +--R + +--R 2c x + b +--R - asinh(--------) +--R +-+ +--R 2\|c +--R / +--R +-+ +--R \|c +--R Type: Expression Integer +--E 112 + +--S 113 of 486 +d0318a:= D(m0318a,x) +--R +--R +--R (109) +--R 4 3 4 2 3 2 3 3 2 3 +--R - 8b c x + (- 24c - 12b c )x + (- 32b c - 8b c )x - 32c +--R + +--R 2 2 4 +--R - 16b c - 2b c +--R * +--R +-------+ +--R | 2 +--R |4c + b +-+ +--R |------- \|c +--R \| c +--R + +--R 5 2 4 3 4 3 3 2 4 2 3 4 2 +--R (16c + 8b c )x + (48b c + 12b c )x + (64c + 32b c + 4b c )x +--R * +--R +------------------------+ +--R | 2 2 2 +--R |4c x + 4b c x + 4c + b +--R |------------------------ +--R \| 4c +--R + +--R 5 2 4 4 4 3 3 3 +--R (- 16c - 8b c )x + (- 56b c - 16b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 3 +--R (- 80c - 76b c - 14b c )x + (- 96b c - 48b c - 6b c)x - 64c +--R + +--R 2 2 4 6 +--R - 48b c - 12b c - b +--R * +--R +-+ +--R \|c +--R + +--R 5 4 5 2 4 3 4 3 3 2 +--R 8b c x + (24c + 16b c )x + (40b c + 10b c )x +--R + +--R 4 2 3 4 2 +--R (32c + 16b c + 2b c )x +--R * +--R +-------+ +--R | 2 +--R |4c + b +--R |------- +--R \| c +--R * +--R +------------------------+ +--R | 2 2 2 +--R |4c x + 4b c x + 4c + b +--R |------------------------ +--R \| c +--R + +--R 5 2 4 4 4 3 3 3 +--R (32c + 16b c )x + (112b c + 32b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 +--R (160c + 152b c + 28b c )x + (192b c + 96b c + 12b c)x +--R + +--R 3 2 2 4 6 +--R 128c + 96b c + 24b c + 2b +--R * +--R +-+ +--R \|c +--R + +--R 5 4 5 2 4 3 4 3 3 2 +--R - 16b c x + (- 48c - 32b c )x + (- 80b c - 20b c )x +--R + +--R 4 2 3 4 2 +--R (- 64c - 32b c - 4b c )x +--R * +--R +-------+ +--R | 2 +--R |4c + b +--R |------- +--R \| c +--R * +--R +------------------------+ +--R | 2 2 2 +--R |4c x + 4b c x + 4c + b +--R |------------------------ +--R \| 4c +--R + +--R 5 5 5 2 4 4 4 3 3 3 +--R 16b c x + (48c + 40b c )x + (128b c + 44b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 3 +--R (112c + 132b c + 26b c )x + (128b c + 64b c + 8b c)x + 64c +--R + +--R 2 2 4 6 +--R 48b c + 12b c + b +--R * +--R +-------+ +--R | 2 +--R |4c + b +-+ +--R |------- \|c +--R \| c +--R + +--R 6 2 5 5 5 3 4 4 +--R (- 32c - 16b c )x + (- 128b c - 40b c )x +--R + +--R 5 2 4 4 3 3 4 3 3 5 2 2 +--R (- 160c - 184b c - 36b c )x + (- 224b c - 112b c - 14b c )x +--R + +--R 4 2 3 4 2 6 +--R (- 128c - 96b c - 24b c - 2b c)x +--R / +--R 5 2 4 4 4 3 3 3 +--R (16c + 8b c )x + (56b c + 16b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 3 +--R (80c + 76b c + 14b c )x + (96b c + 48b c + 6b c)x + 64c +--R + +--R 2 2 4 6 +--R 48b c + 12b c + b +--R * +--R +-+ +--R \|c +--R + +--R 5 4 5 2 4 3 4 3 3 2 +--R - 8b c x + (- 24c - 16b c )x + (- 40b c - 10b c )x +--R + +--R 4 2 3 4 2 +--R (- 32c - 16b c - 2b c )x +--R * +--R +-------+ +--R | 2 +--R |4c + b +--R |------- +--R \| c +--R * +--R +------------------------+ +------------------------+ +--R | 2 2 2 | 2 2 2 +--R |4c x + 4b c x + 4c + b |4c x + 4b c x + 4c + b +--R |------------------------ |------------------------ +--R \| 4c \| c +--R + +--R 5 5 5 2 4 4 4 3 3 3 +--R - 16b c x + (- 48c - 40b c )x + (- 128b c - 44b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 +--R (- 112c - 132b c - 26b c )x + (- 128b c - 64b c - 8b c)x +--R + +--R 3 2 2 4 6 +--R - 64c - 48b c - 12b c - b +--R * +--R +-------+ +--R | 2 +--R |4c + b +-+ +--R |------- \|c +--R \| c +--R + +--R 6 2 5 5 5 3 4 4 +--R (32c + 16b c )x + (128b c + 40b c )x +--R + +--R 5 2 4 4 3 3 4 3 3 5 2 2 +--R (160c + 184b c + 36b c )x + (224b c + 112b c + 14b c )x +--R + +--R 4 2 3 4 2 6 +--R (128c + 96b c + 24b c + 2b c)x +--R * +--R +------------------------+ +--R | 2 2 2 +--R |4c x + 4b c x + 4c + b +--R |------------------------ +--R \| 4c +--R Type: Expression Integer +--E 113 + +--S 114 of 486 +m0318b:= a0318.2-r0318 +--R +--R +--R (110) +--R +------------------------+ +-------+ +--R | 2 2 2 | 2 +--R +---+ |4c x + 4b c x + 4c + b +---+ |4c + b +--R \|- c |------------------------ - \|- c |------- +--R +-+ \| c \| c +--R 2\|c atan(----------------------------------------------------) +--R 2c x +--R + +--R +---+ 2c x + b +--R - \|- c asinh(--------) +--R +-+ +--R 2\|c +--R / +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression Integer +--E 114 + +--S 115 of 486 +d0318b:= D(m0318b,x) +--R +--R +--R +------------------------+ +------------------------+ +--R | 2 2 2 | 2 2 2 +--R |4c x + 4b c x + 4c + b |4c x + 4b c x + 4c + b +--R - |------------------------ + 2 |------------------------ +--R \| c \| 4c +--R (111) ------------------------------------------------------------ +--R +------------------------+ +------------------------+ +--R | 2 2 2 | 2 2 2 +--R |4c x + 4b c x + 4c + b |4c x + 4b c x + 4c + b +--R |------------------------ |------------------------ +--R \| 4c \| c +--R Type: Expression Integer +--E 115 + +--S 116 of 486 +t0319:= 2/((4*c-b^2)/c+4*b*x-4*c*x^2)^(1/2) +--R +--R +--R 2 +--R (112) ----------------------------- +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +--R |-------------------------- +--R \| c +--R Type: Expression Integer +--E 116 + +--S 117 of 486 +r0319:= -asin(1/2*(b-2*c*x)/c^(1/2))/c^(1/2) +--R +--R +--R 2c x - b +--R asin(--------) +--R +-+ +--R 2\|c +--R (113) -------------- +--R +-+ +--R \|c +--R Type: Expression Integer +--E 117 + +--S 118 of 486 +a0319:= integrate(t0319,x) +--R +--R +--R (114) +--R [ +--R log +--R +--------------------------+ +-------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + 4c - b +---+ 2 |4c - b +--R (c |-------------------------- \|- c - 2c x) |------- +--R \| c \| c +--R + +--R +--------------------------+ +--R | 2 2 2 +--R 2 2 2 +---+ 2 |- 4c x + 4b c x + 4c - b +--R (4c x - 2b c x - 4c + b )\|- c + 2c x |-------------------------- +--R \| c +--R / +--R +--------------------------+ +-------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + 4c - b |4c - b 2 +--R c |-------------------------- |------- - 2b c x - 4c + b +--R \| c \| c +--R / +--R +---+ +--R \|- c +--R , +--R +-------+ +--------------------------+ +--R | 2 | 2 2 2 +--R |4c - b |- 4c x + 4b c x + 4c - b +-+ +--R ( |------- - |-------------------------- )\|c +--R \| c \| c +--R 2atan(------------------------------------------------) +--R 2c x +--R -------------------------------------------------------] +--R +-+ +--R \|c +--R Type: Union(List Expression Integer,...) +--E 118 + +--S 119 of 486 +m0319a:= a0319.1-r0319 +--R +--R +--R (115) +--R +-+ +--R \|c +--R * +--R log +--R +--------------------------+ +-------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + 4c - b +---+ 2 |4c - b +--R (c |-------------------------- \|- c - 2c x) |------- +--R \| c \| c +--R + +--R 2 2 2 +---+ +--R (4c x - 2b c x - 4c + b )\|- c +--R + +--R +--------------------------+ +--R | 2 2 2 +--R 2 |- 4c x + 4b c x + 4c - b +--R 2c x |-------------------------- +--R \| c +--R / +--R +--------------------------+ +-------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + 4c - b |4c - b 2 +--R c |-------------------------- |------- - 2b c x - 4c + b +--R \| c \| c +--R + +--R +---+ 2c x - b +--R - \|- c asin(--------) +--R +-+ +--R 2\|c +--R / +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression Integer +--E 119 + +--S 120 of 486 +d0319a:= D(m0319a,x) +--R +--R +--R (116) +--R 4 3 4 2 3 2 3 3 2 3 +--R - 8b c x + (- 24c + 12b c )x + (32b c - 8b c )x + 32c +--R + +--R 2 2 4 +--R - 16b c + 2b c +--R * +--R +--------------------------+ +--------------------------+ +--R | 2 2 2 | 2 2 2 +--R |- 4c x + 4b c x + 4c - b |- 4c x + 4b c x + 4c - b +--R |-------------------------- |-------------------------- +--R \| c \| 4c +--R + +--R 5 5 5 2 4 4 4 3 3 3 +--R - 16b c x + (- 48c + 40b c )x + (128b c - 44b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 +--R (112c - 132b c + 26b c )x + (- 128b c + 64b c - 8b c)x +--R + +--R 3 2 2 4 6 +--R - 64c + 48b c - 12b c + b +--R * +--R +---+ +--R \|- c +--R + +--R 5 4 5 2 4 3 4 3 3 2 +--R 16b c x + (48c - 32b c )x + (- 80b c + 20b c )x +--R + +--R 4 2 3 4 2 +--R (- 64c + 32b c - 4b c )x +--R * +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +--R |-------------------------- +--R \| 4c +--R + +--R 5 4 5 2 4 3 4 3 3 2 +--R - 8b c x + (- 24c + 16b c )x + (40b c - 10b c )x +--R + +--R 4 2 3 4 2 +--R (32c - 16b c + 2b c )x +--R * +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +--R |-------------------------- +--R \| c +--R * +--R +-------+ +--R | 2 +--R |4c - b +--R |------- +--R \| c +--R + +--R 5 2 4 4 4 3 3 3 +--R (- 32c + 16b c )x + (112b c - 32b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 +--R (160c - 152b c + 28b c )x + (- 192b c + 96b c - 12b c)x +--R + +--R 3 2 2 4 6 +--R - 128c + 96b c - 24b c + 2b +--R * +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +--R |-------------------------- +--R \| 4c +--R + +--R 5 2 4 4 4 3 3 3 +--R (16c - 8b c )x + (- 56b c + 16b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 3 +--R (- 80c + 76b c - 14b c )x + (96b c - 48b c + 6b c)x + 64c +--R + +--R 2 2 4 6 +--R - 48b c + 12b c - b +--R * +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +--R |-------------------------- +--R \| c +--R * +--R +---+ +--R \|- c +--R + +--R 5 2 4 3 4 3 3 2 4 2 3 4 2 +--R ((- 16c + 8b c )x + (48b c - 12b c )x + (64c - 32b c + 4b c )x) +--R * +--R +--------------------------+ +--------------------------+ +--R | 2 2 2 | 2 2 2 +--R |- 4c x + 4b c x + 4c - b |- 4c x + 4b c x + 4c - b +--R |-------------------------- |-------------------------- +--R \| c \| 4c +--R + +--R 6 2 5 5 5 3 4 4 5 2 4 4 3 3 +--R (- 32c + 16b c )x + (128b c - 40b c )x + (160c - 184b c + 36b c )x +--R + +--R 4 3 3 5 2 2 4 2 3 4 2 6 +--R (- 224b c + 112b c - 14b c )x + (- 128c + 96b c - 24b c + 2b c)x +--R / +--R 5 5 5 2 4 4 4 3 3 3 +--R 16b c x + (48c - 40b c )x + (- 128b c + 44b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 +--R (- 112c + 132b c - 26b c )x + (128b c - 64b c + 8b c)x +--R + +--R 3 2 2 4 6 +--R 64c - 48b c + 12b c - b +--R * +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +---+ +--R |-------------------------- \|- c +--R \| 4c +--R + +--R 5 4 5 2 4 3 4 3 3 2 +--R 8b c x + (24c - 16b c )x + (- 40b c + 10b c )x +--R + +--R 4 2 3 4 2 +--R (- 32c + 16b c - 2b c )x +--R * +--R +--------------------------+ +--------------------------+ +--R | 2 2 2 | 2 2 2 +--R |- 4c x + 4b c x + 4c - b |- 4c x + 4b c x + 4c - b +--R |-------------------------- |-------------------------- +--R \| c \| 4c +--R * +--R +-------+ +--R | 2 +--R |4c - b +--R |------- +--R \| c +--R + +--R 5 2 4 4 4 3 3 3 4 2 3 4 2 2 +--R (- 16c + 8b c )x + (56b c - 16b c )x + (80c - 76b c + 14b c )x +--R + +--R 3 3 2 5 3 2 2 4 6 +--R (- 96b c + 48b c - 6b c)x - 64c + 48b c - 12b c + b +--R * +--R +--------------------------+ +--------------------------+ +--R | 2 2 2 | 2 2 2 +--R |- 4c x + 4b c x + 4c - b |- 4c x + 4b c x + 4c - b +---+ +--R |-------------------------- |-------------------------- \|- c +--R \| c \| 4c +--R + +--R 6 2 5 5 5 3 4 4 +--R (32c - 16b c )x + (- 128b c + 40b c )x +--R + +--R 5 2 4 4 3 3 4 3 3 5 2 2 +--R (- 160c + 184b c - 36b c )x + (224b c - 112b c + 14b c )x +--R + +--R 4 2 3 4 2 6 +--R (128c - 96b c + 24b c - 2b c)x +--R * +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +--R |-------------------------- +--R \| 4c +--R Type: Expression Integer +--E 120 + +--S 121 of 486 +m0319b:= a0319.2-r0319 +--R +--R +--R (117) +--R +-------+ +--------------------------+ +--R | 2 | 2 2 2 +--R |4c - b |- 4c x + 4b c x + 4c - b +-+ +--R ( |------- - |-------------------------- )\|c +--R \| c \| c 2c x - b +--R 2atan(------------------------------------------------) - asin(--------) +--R 2c x +-+ +--R 2\|c +--R ------------------------------------------------------------------------ +--R +-+ +--R \|c +--R Type: Expression Integer +--E 121 + +--S 122 of 486 +d0319b:= D(m0319b,x) +--R +--R +--R +--------------------------+ +--------------------------+ +--R | 2 2 2 | 2 2 2 +--R |- 4c x + 4b c x + 4c - b |- 4c x + 4b c x + 4c - b +--R 2 |-------------------------- - |-------------------------- +--R \| 4c \| c +--R (118) -------------------------------------------------------------- +--R +--------------------------+ +--------------------------+ +--R | 2 2 2 | 2 2 2 +--R |- 4c x + 4b c x + 4c - b |- 4c x + 4b c x + 4c - b +--R |-------------------------- |-------------------------- +--R \| c \| 4c +--R Type: Expression Integer +--E 122 + +--S 123 of 486 +t0320:= 2/((c-b^2)/c+4*b*x-4*c*x^2)^(1/2) +--R +--R +--R 2 +--R (119) ---------------------------- +--R +-------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + c - b +--R |------------------------- +--R \| c +--R Type: Expression Integer +--E 123 + +--S 124 of 486 +r0320:= -asin((b-2*c*x)/c^(1/2))/c^(1/2) +--R +--R +--R 2c x - b +--R asin(--------) +--R +-+ +--R \|c +--R (120) -------------- +--R +-+ +--R \|c +--R Type: Expression Integer +--E 124 + +--S 125 of 486 +a0320:= integrate(t0320,x) +--R +--R +--R (121) +--R [ +--R log +--R +-------------------------+ +------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + c - b +---+ 2 |c - b +--R (c |------------------------- \|- c - 2c x) |------ +--R \| c \| c +--R + +--R +-------------------------+ +--R | 2 2 2 +--R 2 2 2 +---+ 2 |- 4c x + 4b c x + c - b +--R (4c x - 2b c x - c + b )\|- c + 2c x |------------------------- +--R \| c +--R / +--R +-------------------------+ +------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + c - b |c - b 2 +--R c |------------------------- |------ - 2b c x - c + b +--R \| c \| c +--R / +--R +---+ +--R \|- c +--R , +--R +------+ +-------------------------+ +--R | 2 | 2 2 2 +--R |c - b |- 4c x + 4b c x + c - b +-+ +--R ( |------ - |------------------------- )\|c +--R \| c \| c +--R 2atan(----------------------------------------------) +--R 2c x +--R -----------------------------------------------------] +--R +-+ +--R \|c +--R Type: Union(List Expression Integer,...) +--E 125 + +--S 126 of 486 +m0320a:= a0320.1-r0320 +--R +--R +--R (122) +--R +-+ +--R \|c +--R * +--R log +--R +-------------------------+ +------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + c - b +---+ 2 |c - b +--R (c |------------------------- \|- c - 2c x) |------ +--R \| c \| c +--R + +--R +-------------------------+ +--R | 2 2 2 +--R 2 2 2 +---+ 2 |- 4c x + 4b c x + c - b +--R (4c x - 2b c x - c + b )\|- c + 2c x |------------------------- +--R \| c +--R / +--R +-------------------------+ +------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + c - b |c - b 2 +--R c |------------------------- |------ - 2b c x - c + b +--R \| c \| c +--R + +--R +---+ 2c x - b +--R - \|- c asin(--------) +--R +-+ +--R \|c +--R / +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression Integer +--E 126 + +--S 127 of 486 +d0320a:= D(m0320a,x) +--R +--R +--R (123) 0 +--R Type: Expression Integer +--E 127 + +--S 128 of 486 +m0320b:= a0320.2-r0320 +--R +--R +--R (124) +--R +------+ +-------------------------+ +--R | 2 | 2 2 2 +--R |c - b |- 4c x + 4b c x + c - b +-+ +--R ( |------ - |------------------------- )\|c +--R \| c \| c 2c x - b +--R 2atan(----------------------------------------------) - asin(--------) +--R 2c x +-+ +--R \|c +--R ---------------------------------------------------------------------- +--R +-+ +--R \|c +--R Type: Expression Integer +--E 128 + +--S 129 of 486 +d0320b:= D(m0320b,x) +--R +--R +--R (125) 0 +--R Type: Expression Integer +--E 129 + +--S 130 of 486 +t0321:= (-(-2+3*x)^2)^(1/2) +--R +--R +--R +---------------+ +--R | 2 +--R (126) \|- 9x + 12x - 4 +--R Type: Expression Integer +--E 130 + +--S 131 of 486 +r0321:= -1/6*(2-3*x)*(-(2-3*x)^2)^(1/2) +--R +--R +--R +---------------+ +--R | 2 +--R (3x - 2)\|- 9x + 12x - 4 +--R (127) -------------------------- +--R 6 +--R Type: Expression Integer +--E 131 + +--S 132 of 486 +a0321:= integrate(t0321,x) +--R +--R +--R 2 +---+ +--R (3x - 4x)\|- 1 +--R (128) ---------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 132 + +--S 133 of 486 +m0321:= a0321-r0321 +--R +--R +--R +---------------+ +--R | 2 2 +---+ +--R (- 3x + 2)\|- 9x + 12x - 4 + (9x - 12x)\|- 1 +--R (129) ------------------------------------------------ +--R 6 +--R Type: Expression Integer +--E 133 + +--S 134 of 486 +d0321:= D(m0321,x) +--R +--R +--R +---------------+ +--R +---+ | 2 2 +--R (3x - 2)\|- 1 \|- 9x + 12x - 4 + 9x - 12x + 4 +--R (130) ------------------------------------------------ +--R +---------------+ +--R | 2 +--R \|- 9x + 12x - 4 +--R Type: Expression Integer +--E 134 + +--S 135 of 486 +t0322:= (-(2+3*x)^2)^(1/2) +--R +--R +--R +---------------+ +--R | 2 +--R (131) \|- 9x - 12x - 4 +--R Type: Expression Integer +--E 135 + +--S 136 of 486 +r0322:= 1/6*(2+3*x)*(-(2+3*x)^2)^(1/2) +--R +--R +--R +---------------+ +--R | 2 +--R (3x + 2)\|- 9x - 12x - 4 +--R (132) -------------------------- +--R 6 +--R Type: Expression Integer +--E 136 + +--S 137 of 486 +a0322:= integrate(t0322,x) +--R +--R +--R 2 +---+ +--R (3x + 4x)\|- 1 +--R (133) ---------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 137 + +--S 138 of 486 +m0322:= a0322-r0322 +--R +--R +--R +---------------+ +--R | 2 2 +---+ +--R (- 3x - 2)\|- 9x - 12x - 4 + (9x + 12x)\|- 1 +--R (134) ------------------------------------------------ +--R 6 +--R Type: Expression Integer +--E 138 + +--S 139 of 486 +d0322:= D(m0322,x) +--R +--R +--R +---------------+ +--R +---+ | 2 2 +--R (3x + 2)\|- 1 \|- 9x - 12x - 4 + 9x + 12x + 4 +--R (135) ------------------------------------------------ +--R +---------------+ +--R | 2 +--R \|- 9x - 12x - 4 +--R Type: Expression Integer +--E 139 + +--S 140 of 486 +t0323:= x/(-(-a+b*x)^2)^(1/2) +--R +--R +--R x +--R (136) ----------------------- +--R +--------------------+ +--R | 2 2 2 +--R \|- b x + 2a b x - a +--R Type: Expression Integer +--E 140 + +--S 141 of 486 +r0323:= -(-(-a+b*x)^2)^(1/2)/b^2-a*(a-b*x)*log(a-b*x)/b^2/(-(a-b*x)^2)^(1/2) +--R +--R +--R 2 2 2 2 +--R (a b x - a )log(- b x + a) + b x - 2a b x + a +--R (137) ----------------------------------------------- +--R +--------------------+ +--R 2 | 2 2 2 +--R b \|- b x + 2a b x - a +--R Type: Expression Integer +--E 141 + +--S 142 of 486 +a0323:= integrate(t0323,x) +--R +--R +--R b x - a +--R a log(-------) + b x +--R b +--R (138) -------------------- +--R 2 +---+ +--R b \|- 1 +--R Type: Union(Expression Integer,...) +--E 142 + +--S 143 of 486 +m0323:= a0323-r0323 +--R +--R +--R (139) +--R +--------------------+ +--R b x - a | 2 2 2 +--R (a log(-------) + b x)\|- b x + 2a b x - a +--R b +--R + +--R 2 +---+ 2 2 2 +---+ +--R (- a b x + a )\|- 1 log(- b x + a) + (- b x + 2a b x - a )\|- 1 +--R / +--R +--------------------+ +--R 2 +---+ | 2 2 2 +--R b \|- 1 \|- b x + 2a b x - a +--R Type: Expression Integer +--E 143 + +--S 144 of 486 +d0323:= D(m0323,x) +--R +--R +--R +--------------------+ +--R +---+ | 2 2 2 2 +--R - x\|- 1 \|- b x + 2a b x - a - b x + a x +--R (140) --------------------------------------------- +--R +--------------------+ +--R | 2 2 2 +--R (b x - a)\|- b x + 2a b x - a +--R Type: Expression Integer +--E 144 + +--S 145 of 486 +t0324:= x/(-(a+b*x)^2)^(1/2) +--R +--R +--R x +--R (141) ----------------------- +--R +--------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a +--R Type: Expression Integer +--E 145 + +--S 146 of 486 +r0324:= -(-(a+b*x)^2)^(1/2)/b^2-a*(a+b*x)*log(a+b*x)/b^2/(-(a+b*x)^2)^(1/2) +--R +--R +--R 2 2 2 2 +--R (- a b x - a )log(b x + a) + b x + 2a b x + a +--R (142) ----------------------------------------------- +--R +--------------------+ +--R 2 | 2 2 2 +--R b \|- b x - 2a b x - a +--R Type: Expression Integer +--E 146 + +--S 147 of 486 +a0324:= integrate(t0324,x) +--R +--R +--R b x + a +--R - a log(-------) + b x +--R b +--R (143) ---------------------- +--R 2 +---+ +--R b \|- 1 +--R Type: Union(Expression Integer,...) +--E 147 + +--S 148 of 486 +m0324:= a0324-r0324 +--R +--R +--R (144) +--R +--------------------+ +--R b x + a | 2 2 2 +--R (- a log(-------) + b x)\|- b x - 2a b x - a +--R b +--R + +--R 2 +---+ 2 2 2 +---+ +--R (a b x + a )\|- 1 log(b x + a) + (- b x - 2a b x - a )\|- 1 +--R / +--R +--------------------+ +--R 2 +---+ | 2 2 2 +--R b \|- 1 \|- b x - 2a b x - a +--R Type: Expression Integer +--E 148 + +--S 149 of 486 +d0324:= D(m0324,x) +--R +--R +--R +--------------------+ +--R +---+ | 2 2 2 2 +--R - x\|- 1 \|- b x - 2a b x - a - b x - a x +--R (145) --------------------------------------------- +--R +--------------------+ +--R | 2 2 2 +--R (b x + a)\|- b x - 2a b x - a +--R Type: Expression Integer +--E 149 + +--S 150 of 486 +t0325:= 1/x/((2+3*x)^2)^(1/2) +--R +--R +--R 1 +--R (146) ----------------- +--R +-------------+ +--R | 2 +--R x\|9x + 12x + 4 +--R Type: Expression Integer +--E 150 + +--S 151 of 486 +r0325:= -atanh(1+3*x)*cos(2+3*x) +--R +--R +--R (147) - atanh(3x + 1)cos(3x + 2) +--R Type: Expression Integer +--E 151 + +--S 152 of 486 +a0325:= integrate(t0325,x) +--R +--R +--R - log(3x + 2) + log(x) +--R (148) ---------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 152 + +--S 153 of 486 +m0325:= a0325-r0325 +--R +--R +--R - log(3x + 2) + log(x) + 2atanh(3x + 1)cos(3x + 2) +--R (149) -------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 153 + +--S 154 of 486 +d0325:= D(m0325,x) +--R +--R +--R 2 +--R (- 9x - 6x)atanh(3x + 1)sin(3x + 2) - cos(3x + 2) + 1 +--R (150) ------------------------------------------------------ +--R 2 +--R 3x + 2x +--R Type: Expression Integer +--E 154 + +--S 155 of 486 +t0326:= 1/x/((-2+3*x)^2)^(1/2) +--R +--R +--R 1 +--R (151) ----------------- +--R +-------------+ +--R | 2 +--R x\|9x - 12x + 4 +--R Type: Expression Integer +--E 155 + +--S 156 of 486 +r0326:= -cos(-2+3*x)*atanh(-1+3*x) +--R +--R +--R (152) - atanh(3x - 1)cos(3x - 2) +--R Type: Expression Integer +--E 156 + +--S 157 of 486 +a0326:= integrate(t0326,x) +--R +--R +--R log(3x - 2) - log(x) +--R (153) -------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 157 + +--S 158 of 486 +m0326:= a0326-r0326 +--R +--R +--R log(3x - 2) - log(x) + 2atanh(3x - 1)cos(3x - 2) +--R (154) ------------------------------------------------ +--R 2 +--R Type: Expression Integer +--E 158 + +--S 159 of 486 +d0326:= D(m0326,x) +--R +--R +--R 2 +--R (- 9x + 6x)atanh(3x - 1)sin(3x - 2) - cos(3x - 2) + 1 +--R (155) ------------------------------------------------------ +--R 2 +--R 3x - 2x +--R Type: Expression Integer +--E 159 + +--S 160 of 486 +t0327:= 1/x/(-(-2+3*x)^2)^(1/2) +--R +--R +--R 1 +--R (156) ------------------- +--R +---------------+ +--R | 2 +--R x\|- 9x + 12x - 4 +--R Type: Expression Integer +--E 160 + +--S 161 of 486 +r0327:= (2-3*x)*atanh(-1+3*x)/(-(2-3*x)^2)^(1/2) +--R +--R +--R (- 3x + 2)atanh(3x - 1) +--R (157) ----------------------- +--R +---------------+ +--R | 2 +--R \|- 9x + 12x - 4 +--R Type: Expression Integer +--E 161 + +--S 162 of 486 +a0327:= integrate(t0327,x) +--R +--R +--R +---+ +---+ 3x - 2 +--R \|- 1 log(x) - \|- 1 log(------) +--R 3 +--R (158) -------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 162 + +--S 163 of 486 +m0327:= a0327-r0327 +--R +--R +--R (159) +--R +---------------+ +--R +---+ +---+ 3x - 2 | 2 +--R (\|- 1 log(x) - \|- 1 log(------))\|- 9x + 12x - 4 + (6x - 4)atanh(3x - 1) +--R 3 +--R ---------------------------------------------------------------------------- +--R +---------------+ +--R | 2 +--R 2\|- 9x + 12x - 4 +--R Type: Expression Integer +--E 163 + +--S 164 of 486 +d0327:= D(m0327,x) +--R +--R +--R +---------------+ +--R +---+ | 2 +--R - \|- 1 \|- 9x + 12x - 4 - 3x + 2 +--R (160) ----------------------------------- +--R +---------------+ +--R 2 | 2 +--R (3x - 2x)\|- 9x + 12x - 4 +--R Type: Expression Integer +--E 164 + +--S 165 of 486 +t0328:= (a+b*x)*(c+d*x+e*x^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (161) (b x + a)\|e x + d x + c +--R Type: Expression Integer +--E 165 + +--S 166 of 486 +r0328:= -1/8*(b*d-2*a*e)*(d+2*e*x)*(c+d*x+e*x^2)^(1/2)/e^2+1/3*b*_ + (c+d*x+e*x^2)^(3/2)/e+1/16*(b*d-2*a*e)*(d^2-4*c*e)*_ + atanh(2*e^(1/2)*(c+d*x+e*x^2)^(1/2)/(d+2*e*x))/e^(5/2) +--R +--R +--R (162) +--R +--------------+ +--R +-+ | 2 +--R 2 2 3 2\|e \|e x + d x + c +--R (24a c e + (- 6a d - 12b c d)e + 3b d )atanh(----------------------) +--R 2e x + d +--R + +--R 2 2 2 2 +-+ +--R (16b e x + (24a e + 4b d e)x + (12a d + 16b c)e - 6b d )\|e +--R * +--R +--------------+ +--R | 2 +--R \|e x + d x + c +--R / +--R 2 +-+ +--R 48e \|e +--R Type: Expression Integer +--E 166 + +--S 167 of 486 +a0328:= integrate(t0328,x) +--R +--R +--R (163) +--R [ +--R 2 3 2 2 2 4 3 +--R 192a c e + (96a c d - 96b c d)e + (- 36a d - 48b c d )e +--R + +--R 5 +--R 18b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 4 +--R (768a c d e + (- 192a c d - 384b c d )e + 96b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R 768a c e + (- 192a c d - 384b c d)e + 96b c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|e x + d x + c +--R + +--R 2 3 3 2 2 2 5 4 +--R - 288a c d e + (48a c d + 144b c d )e + (6a d - 24b c d )e +--R + +--R 6 +--R - 3b d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 2 +--R - 576a c e + (- 288a c d + 288b c d)e +--R + +--R 4 2 3 5 +--R (108a c d + 144b c d )e - 54b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 3 2 2 4 +--R (- 1152a c d e + (288a c d + 576b c d )e - 144b c d )x +--R + +--R 4 2 3 2 4 3 3 +--R - 768a c e + (192a c d + 384b c d)e - 96b c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|c \|e - 2e x)\|e x + d x + c + (- 2e x - d x - 2c)\|e +--R + +--R +-+ +--R 2e x\|c +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|e x + d x + c - d x - 2c +--R + +--R 3 3 2 5 +--R (- 192b c d e - 16b d e )x +--R + +--R 2 3 3 2 2 4 4 +--R ((- 288a c d - 384b c )e + (- 24a d - 336b c d )e - 4b d e)x +--R + +--R 2 3 2 2 2 +--R - 576a c e + (- 576a c d - 1056b c d)e +--R + +--R 4 3 5 +--R (- 12a d - 16b c d )e + 6b d +--R * +--R 3 +--R x +--R + +--R 2 3 2 3 2 2 +--R (- 1344a c d - 768b c )e + (- 144a c d - 288b c d )e +--R + +--R 4 +--R 72b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 2 3 +--R (- 768a c e + (- 192a c d - 384b c d)e + 96b c d )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|e \|e x + d x + c +--R + +--R 4 2 3 6 +--R (128b c e + 96b d e )x +--R + +--R 4 2 3 3 2 5 +--R (192a c e + (144a d + 672b c d)e + 120b d e )x +--R + +--R 2 3 3 2 2 4 4 +--R ((1056a c d + 768b c )e + (216a d + 816b c d )e - 12b d e)x +--R + +--R 2 3 2 2 2 4 3 +--R 960a c e + (1248a c d + 1632b c d)e + (60a d + 64b c d )e +--R + +--R 5 +--R - 30b d +--R * +--R 3 +--R x +--R + +--R 2 3 2 3 2 2 4 2 +--R ((1728a c d + 768b c )e + (240a c d + 480b c d )e - 120b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (768a c e + (192a c d + 384b c d)e - 96b c d )x +--R * +--R +-+ +-+ +--R \|c \|e +--R / +--R 3 2 2 2 2 2 2 +-+ +-+ +--R ((384c e + 288d e )x + 1536c d e x + 1536c e )\|c \|e +--R * +--R +--------------+ +--R | 2 +--R \|e x + d x + c +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576c d e - 48d e )x + (- 1152c e - 864c d e )x - 2304c d e x +--R + +--R 3 2 +--R - 1536c e +--R * +--R +-+ +--R \|e +--R , +--R +--R 2 3 2 2 2 4 3 +--R 192a c e + (96a c d - 96b c d)e + (- 36a d - 48b c d )e +--R + +--R 5 +--R 18b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 4 +--R (768a c d e + (- 192a c d - 384b c d )e + 96b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R 768a c e + (- 192a c d - 384b c d)e + 96b c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|e x + d x + c +--R + +--R 2 3 3 2 2 2 5 4 +--R - 288a c d e + (48a c d + 144b c d )e + (6a d - 24b c d )e +--R + +--R 6 +--R - 3b d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 2 +--R - 576a c e + (- 288a c d + 288b c d)e +--R + +--R 4 2 3 5 +--R (108a c d + 144b c d )e - 54b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 3 2 2 4 +--R (- 1152a c d e + (288a c d + 576b c d )e - 144b c d )x +--R + +--R 4 2 3 2 4 3 3 +--R - 768a c e + (192a c d + 384b c d)e - 96b c d +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- e \|e x + d x + c - \|- e \|c +--R atan(------------------------------------) +--R e x +--R + +--R 3 3 2 5 +--R (- 96b c d e - 8b d e )x +--R + +--R 2 3 3 2 2 4 4 +--R ((- 144a c d - 192b c )e + (- 12a d - 168b c d )e - 2b d e)x +--R + +--R 2 3 2 2 2 4 3 +--R - 288a c e + (- 288a c d - 528b c d)e + (- 6a d - 8b c d )e +--R + +--R 5 +--R 3b d +--R * +--R 3 +--R x +--R + +--R 2 3 2 3 2 2 4 2 +--R ((- 672a c d - 384b c )e + (- 72a c d - 144b c d )e + 36b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 384a c e + (- 96a c d - 192b c d)e + 48b c d )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- e \|e x + d x + c +--R + +--R 4 2 3 6 +--R (64b c e + 48b d e )x +--R + +--R 4 2 3 3 2 5 +--R (96a c e + (72a d + 336b c d)e + 60b d e )x +--R + +--R 2 3 3 2 2 4 4 +--R ((528a c d + 384b c )e + (108a d + 408b c d )e - 6b d e)x +--R + +--R 2 3 2 2 2 4 3 +--R 480a c e + (624a c d + 816b c d)e + (30a d + 32b c d )e +--R + +--R 5 +--R - 15b d +--R * +--R 3 +--R x +--R + +--R 2 3 2 3 2 2 4 2 +--R ((864a c d + 384b c )e + (120a c d + 240b c d )e - 60b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (384a c e + (96a c d + 192b c d)e - 48b c d )x +--R * +--R +---+ +-+ +--R \|- e \|c +--R / +--R 3 2 2 2 2 2 2 +---+ +-+ +--R ((192c e + 144d e )x + 768c d e x + 768c e )\|- e \|c +--R * +--R +--------------+ +--R | 2 +--R \|e x + d x + c +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 288c d e - 24d e )x + (- 576c e - 432c d e )x - 1152c d e x +--R + +--R 3 2 +--R - 768c e +--R * +--R +---+ +--R \|- e +--R ] +--R Type: Union(List Expression Integer,...) +--E 167 + +--S 168 of 486 +m0328a:= a0328.1-r0328 +--R +--R +--R (164) +--R 2 3 2 2 2 4 3 +--R 192a c e + (96a c d - 96b c d)e + (- 36a d - 48b c d )e +--R + +--R 5 +--R 18b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 4 +--R (768a c d e + (- 192a c d - 384b c d )e + 96b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R 768a c e + (- 192a c d - 384b c d)e + 96b c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|e x + d x + c +--R + +--R 2 3 3 2 2 2 5 4 +--R - 288a c d e + (48a c d + 144b c d )e + (6a d - 24b c d )e +--R + +--R 6 +--R - 3b d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 2 +--R - 576a c e + (- 288a c d + 288b c d)e +--R + +--R 4 2 3 5 +--R (108a c d + 144b c d )e - 54b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 3 2 2 4 4 2 +--R (- 1152a c d e + (288a c d + 576b c d )e - 144b c d )x - 768a c e +--R + +--R 3 2 4 3 3 +--R (192a c d + 384b c d)e - 96b c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|c \|e - 2e x)\|e x + d x + c + (- 2e x - d x - 2c)\|e +--R + +--R +-+ +--R 2e x\|c +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|e x + d x + c - d x - 2c +--R + +--R 2 3 2 2 2 4 3 +--R - 192a c e + (- 96a c d + 96b c d)e + (36a d + 48b c d )e +--R + +--R 5 +--R - 18b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 4 +--R (- 768a c d e + (192a c d + 384b c d )e - 96b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R - 768a c e + (192a c d + 384b c d)e - 96b c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|e x + d x + c +--R + +--R 2 3 3 2 2 2 5 4 +--R 288a c d e + (- 48a c d - 144b c d )e + (- 6a d + 24b c d )e +--R + +--R 6 +--R 3b d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 2 4 2 3 +--R 576a c e + (288a c d - 288b c d)e + (- 108a c d - 144b c d )e +--R + +--R 5 +--R 54b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 3 2 2 4 4 2 +--R (1152a c d e + (- 288a c d - 576b c d )e + 144b c d )x + 768a c e +--R + +--R 3 2 4 3 3 +--R (- 192a c d - 384b c d)e + 96b c d +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|e \|e x + d x + c +--R atanh(----------------------) +--R 2e x + d +--R + +--R 2 3 2 3 2 2 4 2 +--R ((96a c d + 128b c )e + (72a c d + 48b c d )e - 36b c d )x +--R + +--R 2 2 3 2 3 3 4 +--R ((384a c d + 512b c d)e - 192b c d )x + (384a c d + 512b c )e +--R + +--R 3 2 +--R - 192b c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|e \|e x + d x + c +--R + +--R 2 2 2 4 3 5 3 +--R ((- 144a c d - 192b c d)e + (- 12a d + 56b c d )e + 6b d )x +--R + +--R 2 3 2 3 2 2 4 2 +--R ((- 288a c d - 384b c )e + (- 216a c d - 144b c d )e + 108b c d )x +--R + +--R 2 2 3 2 3 3 4 +--R ((- 576a c d - 768b c d)e + 288b c d )x + (- 384a c d - 512b c )e +--R + +--R 3 2 +--R 192b c d +--R * +--R +-+ +-+ +--R \|c \|e +--R / +--R +--------------+ +--R 3 2 2 2 2 2 2 +-+ +-+ | 2 +--R ((384c e + 288d e )x + 1536c d e x + 1536c e )\|c \|e \|e x + d x + c +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576c d e - 48d e )x + (- 1152c e - 864c d e )x - 2304c d e x +--R + +--R 3 2 +--R - 1536c e +--R * +--R +-+ +--R \|e +--R Type: Expression Integer +--E 168 + +--S 169 of 486 +d0328a:= D(m0328a,x) +--R +--R +--R (165) 0 +--R Type: Expression Integer +--E 169 + +--S 170 of 486 +m0328b:= a0328.2-r0328 +--R +--R +--R (166) +--R 2 3 2 2 2 4 3 +--R - 192a c e + (- 96a c d + 96b c d)e + (36a d + 48b c d )e +--R + +--R 5 +--R - 18b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 4 +--R (- 768a c d e + (192a c d + 384b c d )e - 96b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R - 768a c e + (192a c d + 384b c d)e - 96b c d +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- e \|c \|e x + d x + c +--R + +--R 2 3 3 2 2 2 +--R 288a c d e + (- 48a c d - 144b c d )e +--R + +--R 5 4 6 +--R (- 6a d + 24b c d )e + 3b d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 2 +--R 576a c e + (288a c d - 288b c d)e +--R + +--R 4 2 3 5 +--R (- 108a c d - 144b c d )e + 54b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 3 2 2 4 +--R (1152a c d e + (- 288a c d - 576b c d )e + 144b c d )x +--R + +--R 4 2 3 2 4 3 3 +--R 768a c e + (- 192a c d - 384b c d)e + 96b c d +--R * +--R +---+ +--R \|- e +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|e \|e x + d x + c +--R atanh(----------------------) +--R 2e x + d +--R + +--R 2 3 2 2 2 4 3 +--R 384a c e + (192a c d - 192b c d)e + (- 72a d - 96b c d )e +--R + +--R 5 +--R 36b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 4 +--R (1536a c d e + (- 384a c d - 768b c d )e + 192b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R 1536a c e + (- 384a c d - 768b c d)e + 192b c d +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|c \|e \|e x + d x + c +--R + +--R 2 3 3 2 2 2 +--R - 576a c d e + (96a c d + 288b c d )e +--R + +--R 5 4 6 +--R (12a d - 48b c d )e - 6b d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 2 +--R - 1152a c e + (- 576a c d + 576b c d)e +--R + +--R 4 2 3 5 +--R (216a c d + 288b c d )e - 108b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 3 2 2 4 +--R (- 2304a c d e + (576a c d + 1152b c d )e - 288b c d )x +--R + +--R 4 2 3 2 4 3 3 +--R - 1536a c e + (384a c d + 768b c d)e - 192b c d +--R * +--R +-+ +--R \|e +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- e \|e x + d x + c - \|- e \|c +--R atan(------------------------------------) +--R e x +--R + +--R 2 3 2 3 2 2 4 2 +--R ((96a c d + 128b c )e + (72a c d + 48b c d )e - 36b c d )x +--R + +--R 2 2 3 2 3 3 4 +--R ((384a c d + 512b c d)e - 192b c d )x + (384a c d + 512b c )e +--R + +--R 3 2 +--R - 192b c d +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- e \|e \|e x + d x + c +--R + +--R 2 2 2 4 3 5 3 +--R ((- 144a c d - 192b c d)e + (- 12a d + 56b c d )e + 6b d )x +--R + +--R 2 3 2 3 2 2 4 2 +--R ((- 288a c d - 384b c )e + (- 216a c d - 144b c d )e + 108b c d )x +--R + +--R 2 2 3 2 3 3 4 +--R ((- 576a c d - 768b c d)e + 288b c d )x + (- 384a c d - 512b c )e +--R + +--R 3 2 +--R 192b c d +--R * +--R +---+ +-+ +-+ +--R \|- e \|c \|e +--R / +--R 3 2 2 2 2 2 2 +---+ +-+ +-+ +--R ((384c e + 288d e )x + 1536c d e x + 1536c e )\|- e \|c \|e +--R * +--R +--------------+ +--R | 2 +--R \|e x + d x + c +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576c d e - 48d e )x + (- 1152c e - 864c d e )x - 2304c d e x +--R + +--R 3 2 +--R - 1536c e +--R * +--R +---+ +-+ +--R \|- e \|e +--R Type: Expression Integer +--E 170 + +--S 171 of 486 +d0328b:= D(m0328b,x) +--R +--R +--R (167) 0 +--R Type: Expression Integer +--E 171 + +--S 172 of 486 +t0329:= 1/(x+(-3-4*x-x^2)^(1/2)) +--R +--R +--R 1 +--R (168) -------------------- +--R +-------------+ +--R | 2 +--R \|- x - 4x - 3 + x +--R Type: Expression Integer +--E 172 + +--S 173 of 486 +r0329:= -atan((-1-x)^(1/2)/(3+x)^(1/2))-2^(1/2)*atan(1/2*(1-3*(-1-x)^(1/2)/_ + (3+x)^(1/2))*2^(1/2))-1/2*log(2/(3+x))+1/2*log(1-3*(1+x)/_ + (3+x)-2*(-1-x)^(1/2)/(3+x)^(1/2)) +--R +--R +--R (169) +--R +-----+ +-------+ +--R - 2x\|x + 3 + (- 2x - 6)\|- x - 1 +--R log(-----------------------------------) +--R +-----+ +--R (x + 3)\|x + 3 +--R + +--R +-+ +-----+ +-+ +-------+ +-------+ +--R +-+ \|2 \|x + 3 - 3\|2 \|- x - 1 \|- x - 1 +--R - 2\|2 atan(------------------------------) - 2atan(----------) +--R +-----+ +-----+ +--R 2\|x + 3 \|x + 3 +--R + +--R 2 +--R - log(-----) +--R x + 3 +--R / +--R 2 +--R Type: Expression Integer +--E 173 + +--S 174 of 486 +a0329:= integrate(t0329,x) +--R +--R +--R (170) +--R +-------------+ +--R | 2 +--R +-+ 2x\|- x - 4x - 3 - 4x - 3 +--R \|2 log(---------------------------) +--R 2 +--R x +--R + +--R +-------------+ +-------------+ +--R | 2 | 2 +--R +-+ - 2x\|- x - 4x - 3 - 4x - 3 +-+ \|- x - 4x - 3 +--R - \|2 log(-----------------------------) - 4\|2 atan(----------------) +--R 2 x + 2 +--R x +--R + +--R +-+ +-+ +--R (2x + 3)\|2 (2x + 3)\|2 +--R - 4atan(---------------------) - 4atan(---------------------) +--R +-------------+ +-------------+ +--R | 2 | 2 +--R 3\|- x - 4x - 3 - x 3\|- x - 4x - 3 + x +--R + +--R +-+ +--R +-+ 2 (2x + 2)\|2 +--R 2\|2 log(2x + 4x + 3) + 4atan(------------) +--R 2 +--R 2x + 4x + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression Integer,...) +--E 174 + +--S 175 of 486 +m0329:= a0329-r0329 +--R +--R +--R (171) +--R +-------------+ +--R | 2 +--R +-+ 2x\|- x - 4x - 3 - 4x - 3 +--R \|2 log(---------------------------) +--R 2 +--R x +--R + +--R +-----+ +-------+ +--R +-+ - 2x\|x + 3 + (- 2x - 6)\|- x - 1 +--R - 4\|2 log(-----------------------------------) +--R +-----+ +--R (x + 3)\|x + 3 +--R + +--R +-------------+ +-------------+ +--R | 2 | 2 +--R +-+ - 2x\|- x - 4x - 3 - 4x - 3 +-+ \|- x - 4x - 3 +--R - \|2 log(-----------------------------) - 4\|2 atan(----------------) +--R 2 x + 2 +--R x +--R + +--R +-+ +-----+ +-+ +-------+ +-+ +--R \|2 \|x + 3 - 3\|2 \|- x - 1 (2x + 3)\|2 +--R 16atan(------------------------------) - 4atan(---------------------) +--R +-----+ +-------------+ +--R 2\|x + 3 | 2 +--R 3\|- x - 4x - 3 - x +--R + +--R +-+ +-------+ +--R (2x + 3)\|2 +-+ \|- x - 1 +--R - 4atan(---------------------) + 8\|2 atan(----------) +--R +-------------+ +-----+ +--R | 2 \|x + 3 +--R 3\|- x - 4x - 3 + x +--R + +--R +-+ +--R +-+ 2 +-+ 2 (2x + 2)\|2 +--R 2\|2 log(2x + 4x + 3) + 4\|2 log(-----) + 4atan(------------) +--R x + 3 2 +--R 2x + 4x + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression Integer +--E 175 + +--S 176 of 486 +d0329:= D(m0329,x) +--R +--R +--R (172) +--R +-------------+ +--R | 2 2 +-------+ +-----+ +--R (x\|- x - 4x - 3 + x + 4x + 3)\|- x - 1 \|x + 3 +--R + +--R +-------------+ +--R 2 | 2 3 2 +--R (- x - 4x - 3)\|- x - 4x - 3 + x + 4x + 3x +--R / +--R +-------------+ +--R 2 | 2 +-------+ +-----+ +--R (2x + 4x + 3)\|- x - 4x - 3 \|- x - 1 \|x + 3 +--R + +--R +-------------+ +--R 3 2 | 2 +--R (2x + 4x + 3x)\|- x - 4x - 3 +--R Type: Expression Integer +--E 176 + +--S 177 of 486 +t0330:= 1/(x+(3-2*x-x^2)^(1/2)) +--R +--R +--R 1 +--R (173) -------------------- +--R +-------------+ +--R | 2 +--R \|- x - 2x + 3 + x +--R Type: Expression Integer +--E 177 + +--S 178 of 486 +r0330:= atan((3^(1/2)-(3-2*x-x^2)^(1/2))/x)-1/7*atanh(1/7*(1+3^(1/2)-_ + 3^(1/2)*(3^(1/2)-(3-2*x-x^2)^(1/2))/x)*7^(1/2))*7^(1/2)-_ + 1/2*log(1+(3^(1/2)-(3-2*x-x^2)^(1/2))^2/x^2)+1/2*log(2-3^(1/2)-_ + 2*(1+3^(1/2))*(3^(1/2)-(3-2*x-x^2)^(1/2))/x+3^(1/2)*(3^(1/2)-_ + (3-2*x-x^2)^(1/2))^2/x^2) +--R +--R +--R (174) +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R (2x\|3 + 2x - 6)\|- x - 2x + 3 + (- 2x - 4x + 6)\|3 + 2x - 6x +--R 7log(-------------------------------------------------------------------) +--R 2 +--R x +--R + +--R +-------------+ +--R +-+ | 2 +--R - 2\|3 \|- x - 2x + 3 - 2x + 6 +--R - 7log(--------------------------------) +--R 2 +--R x +--R + +--R +-------------+ +--R +-+ +-+ | 2 +-+ +-+ +--R +-+ \|3 \|7 \|- x - 2x + 3 + (x\|3 + x - 3)\|7 +--R - 2\|7 atanh(----------------------------------------------) +--R 7x +--R + +--R +-------------+ +--R | 2 +-+ +--R \|- x - 2x + 3 - \|3 +--R - 14atan(-----------------------) +--R x +--R / +--R 14 +--R Type: Expression Integer +--E 178 + +--S 179 of 486 +a0330:= integrate(t0330,x) +--R +--R +--R (175) +--R +-+ +--R \|7 +--R * +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 + 3x)\|- x - 2x + 3 + (x - 3x)\|3 - 3x - 6x + 9 +--R log(-----------------------------------------------------------------) +--R 2 +--R x +--R + +--R - +--R +-+ +--R \|7 +--R * +--R log +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 - 3x)\|- x - 2x + 3 + (- x + 3x)\|3 - 3x +--R + +--R - 6x + 9 +--R / +--R 2 +--R x +--R + +--R log +--R +-------------+ +--R +-+ +-+ +-+ | 2 +--R (((x - 3)\|3 - 3x)\|7 + 7x\|3 )\|- x - 2x + 3 +--R + +--R 2 +-+ 2 +-+ 2 +-+ 2 +--R ((- x + 3x)\|3 + 4x - 6x + 9)\|7 - 7x \|3 + 7x - 21x +--R / +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 - 3x)\|- x - 2x + 3 + (- x + 3x)\|3 - 3x - 6x + 9 +--R + +--R log +--R +-------------+ +--R +-+ +-+ +-+ | 2 +--R (((x - 3)\|3 + 3x)\|7 - 7x\|3 )\|- x - 2x + 3 +--R + +--R 2 +-+ 2 +-+ 2 +-+ 2 +--R ((x - 3x)\|3 + 4x - 6x + 9)\|7 - 7x \|3 - 7x + 21x +--R / +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 + 3x)\|- x - 2x + 3 + (x - 3x)\|3 - 3x - 6x + 9 +--R + +--R +-------------+ +--R | 2 +-+ 2 +-+ +--R +-+ \|- x - 2x + 3 - \|3 (2x + 2x + 4)\|7 + 14x + 7 +--R - 4\|7 atan(-----------------------) + log(----------------------------) +--R x 2 +--R 2x + 2x - 3 +--R + +--R +-+ 2 +--R \|7 log(2x + 2x - 3) +--R / +--R +-+ +--R 4\|7 +--R Type: Union(Expression Integer,...) +--E 179 + +--S 180 of 486 +m0330:= a0330-r0330 +--R +--R +--R (176) +--R - +--R +-+ +--R 2\|7 +--R * +--R log +--R +-------------+ +--R +-+ | 2 2 +-+ +--R (2x\|3 + 2x - 6)\|- x - 2x + 3 + (- 2x - 4x + 6)\|3 +--R + +--R 2 +--R 2x - 6x +--R / +--R 2 +--R x +--R + +--R +-+ +--R \|7 +--R * +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 + 3x)\|- x - 2x + 3 + (x - 3x)\|3 - 3x - 6x + 9 +--R log(-----------------------------------------------------------------) +--R 2 +--R x +--R + +--R - +--R +-+ +--R \|7 +--R * +--R log +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 - 3x)\|- x - 2x + 3 + (- x + 3x)\|3 - 3x +--R + +--R - 6x + 9 +--R / +--R 2 +--R x +--R + +--R log +--R +-------------+ +--R +-+ +-+ +-+ | 2 +--R (((x - 3)\|3 - 3x)\|7 + 7x\|3 )\|- x - 2x + 3 +--R + +--R 2 +-+ 2 +-+ 2 +-+ 2 +--R ((- x + 3x)\|3 + 4x - 6x + 9)\|7 - 7x \|3 + 7x - 21x +--R / +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 - 3x)\|- x - 2x + 3 + (- x + 3x)\|3 - 3x - 6x + 9 +--R + +--R log +--R +-------------+ +--R +-+ +-+ +-+ | 2 +--R (((x - 3)\|3 + 3x)\|7 - 7x\|3 )\|- x - 2x + 3 +--R + +--R 2 +-+ 2 +-+ 2 +-+ 2 +--R ((x - 3x)\|3 + 4x - 6x + 9)\|7 - 7x \|3 - 7x + 21x +--R / +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 + 3x)\|- x - 2x + 3 + (x - 3x)\|3 - 3x - 6x + 9 +--R + +--R +-------------+ +--R +-+ | 2 +--R +-+ - 2\|3 \|- x - 2x + 3 - 2x + 6 +--R 2\|7 log(--------------------------------) +--R 2 +--R x +--R + +--R +-------------+ +--R +-+ +-+ | 2 +-+ +-+ +--R \|3 \|7 \|- x - 2x + 3 + (x\|3 + x - 3)\|7 +--R 4atanh(----------------------------------------------) +--R 7x +--R + +--R 2 +-+ +--R (2x + 2x + 4)\|7 + 14x + 7 +-+ 2 +--R log(----------------------------) + \|7 log(2x + 2x - 3) +--R 2 +--R 2x + 2x - 3 +--R / +--R +-+ +--R 4\|7 +--R Type: Expression Integer +--E 180 + +--S 181 of 486 +d0330:= D(m0330,x) +--R +--R +--R (177) 0 +--R Type: Expression Integer +--E 181 + +--S 182 of 486 +t0331:= (a+b*x+c*x^2)^(1/2)/(d+e*x^2) +--R +--R +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R (178) ----------------- +--R 2 +--R e x + d +--R Type: Expression Integer +--E 182 + +--S 183 of 486 +r0331:= -1/2*(-2*c^(1/2)*atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/_ + (b+2*c*x))*d^(1/2)+(c*d-b*d^(1/2)*(-e)^(1/2)-a*e)^(1/2)*_ + atanh(2*(c*d-b*d^(1/2)*(-e)^(1/2)-a*e)^(1/2)*(a+b*x+c*x^2)^(1/2)/_ + (b*d^(1/2)-2*a*(-e)^(1/2)+2*x*c*d^(1/2)-x*b*(-e)^(1/2)))+_ + (c*d+b*d^(1/2)*(-e)^(1/2)-a*e)^(1/2)*atanh(2*(c*d+b*d^(1/2)*_ + (-e)^(1/2)-a*e)^(1/2)*(a+b*x+c*x^2)^(1/2)/(b*d^(1/2)+2*a*_ + (-e)^(1/2)+2*x*c*d^(1/2)+x*b*(-e)^(1/2))))/d^(1/2)/e +--R +--R +--R (179) +--R - +--R +-----------------------+ +--R | +---+ +-+ +--R \|b\|- e \|d - a e + c d +--R * +--R +--------------+ +-----------------------+ +--R | 2 | +---+ +-+ +--R 2\|c x + b x + a \|b\|- e \|d - a e + c d +--R atanh(--------------------------------------------) +--R +-+ +---+ +--R (2c x + b)\|d + (b x + 2a)\|- e +--R + +--R - +--R +-------------------------+ +--R | +---+ +-+ +--R \|- b\|- e \|d - a e + c d +--R * +--R +--------------+ +-------------------------+ +--R | 2 | +---+ +-+ +--R 2\|c x + b x + a \|- b\|- e \|d - a e + c d +--R atanh(----------------------------------------------) +--R +-+ +---+ +--R (2c x + b)\|d + (- b x - 2a)\|- e +--R + +--R +--------------+ +--R +-+ | 2 +--R +-+ +-+ 2\|c \|c x + b x + a +--R 2\|c \|d atanh(----------------------) +--R 2c x + b +--R / +--R +-+ +--R 2e\|d +--R Type: Expression Integer +--E 183 + +--S 184 of 486 too expensive to compute during test +--a0331:= integrate(t0331,x) +-- +-- +-- (180) +-- [ +-- - +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- - +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-+ +-- 2\|c +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-+ 2 +-- (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x +-- + +-- - 2a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- / +-- 2e +-- , +-- +-- - +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- - +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +--------------+ +-- | 2 +-+ +-- +---+ \|c x + b x + a - \|a +-- 4\|- c atan(------------------------) +-- +---+ +-- x\|- c +-- / +-- 2e +-- ] +-- Type: Union(List Expression Integer,...) +--E 184 + +--S 185 of 486 +--m0331a:= a0331.1-r0331 +-- +-- +-- (181) +-- - +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- - +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-----------------------+ +-- | +---+ +-+ +-- \|b\|- e \|d - a e + c d +-- * +-- +--------------+ +-----------------------+ +-- | 2 | +---+ +-+ +-- 2\|c x + b x + a \|b\|- e \|d - a e + c d +-- atanh(--------------------------------------------) +-- +-+ +---+ +-- (2c x + b)\|d + (b x + 2a)\|- e +-- + +-- +-------------------------+ +-- | +---+ +-+ +-- \|- b\|- e \|d - a e + c d +-- * +-- +--------------+ +-------------------------+ +-- | 2 | +---+ +-+ +-- 2\|c x + b x + a \|- b\|- e \|d - a e + c d +-- atanh(----------------------------------------------) +-- +-+ +---+ +-- (2c x + b)\|d + (- b x - 2a)\|- e +-- + +-- +-+ +-+ +-- 2\|c \|d +-- * +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-+ 2 +-- (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x - 2a +-- log(-------------------------------------------------------------------) +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- +--------------+ +-- +-+ | 2 +-- +-+ +-+ 2\|c \|c x + b x + a +-- - 2\|c \|d atanh(----------------------) +-- 2c x + b +-- / +-- +-+ +-- 2e\|d +-- Type: Expression Integer +--E 185 + +--S 186 of 486 +--d0331a:= D(m0331a,x) +-- +-- +-- (182) 0 +-- Type: Expression Integer +--E 186 + +--S 187 of 486 +--m0331b:= a0331.2-r0331 +-- +-- +-- (183) +-- - +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- - +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-----------------------+ +-- | +---+ +-+ +-- \|b\|- e \|d - a e + c d +-- * +-- +--------------+ +-----------------------+ +-- | 2 | +---+ +-+ +-- 2\|c x + b x + a \|b\|- e \|d - a e + c d +-- atanh(--------------------------------------------) +-- +-+ +---+ +-- (2c x + b)\|d + (b x + 2a)\|- e +-- + +-- +-------------------------+ +-- | +---+ +-+ +-- \|- b\|- e \|d - a e + c d +-- * +-- +--------------+ +-------------------------+ +-- | 2 | +---+ +-+ +-- 2\|c x + b x + a \|- b\|- e \|d - a e + c d +-- atanh(----------------------------------------------) +-- +-+ +---+ +-- (2c x + b)\|d + (- b x - 2a)\|- e +-- + +-- +--------------+ +-- +-+ | 2 +-- +-+ +-+ 2\|c \|c x + b x + a +-- - 2\|c \|d atanh(----------------------) +-- 2c x + b +-- + +-- +--------------+ +-- | 2 +-+ +-- +---+ +-+ \|c x + b x + a - \|a +-- 4\|- c \|d atan(------------------------) +-- +---+ +-- x\|- c +-- / +-- +-+ +-- 2e\|d +-- Type: Expression Integer +--E 187 + +--S 188 of 486 +--d0331b:= D(m0331b,x) +-- +-- +-- (184) 0 +-- Type: Expression Integer +--E 188 + +--S 189 of 486 +t0332:= x*(a+b*x+c*x^2)^(1/2)/(d+e*x^2) +--R +--R +--R +--------------+ +--R | 2 +--R x\|c x + b x + a +--R (180) ------------------ +--R 2 +--R e x + d +--R Type: Expression Integer +--E 189 + +--S 190 of 486 +r0332:= (a+b*x+c*x^2)^(1/2)/e+1/2*b*atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/_ + (b+2*c*x))/c^(1/2)/e+1/2*(-c*d-b*d^(1/2)*(-e)^(1/2)+a*e)^(1/2)*_ + atanh(2*e^(1/2)*(-c*d-b*d^(1/2)*(-e)^(1/2)+a*e)^(1/2)*_ + (a+b*x+c*x^2)^(1/2)/(b*d^(1/2)*(-e)^(1/2)-2*a*e+(2*c*d^(1/2)*_ + (-e)^(1/2)-b*e)*x))/e^(3/2)-1/2*(-c*d+b*d^(1/2)*(-e)^(1/2)+_ + a*e)^(1/2)*atanh(2*e^(1/2)*(-c*d+b*d^(1/2)*(-e)^(1/2)+a*e)^(1/2)_ + *(a+b*x+c*x^2)^(1/2)/(b*d^(1/2)*(-e)^(1/2)+2*a*e+_ + (2*c*d^(1/2)*(-e)^(1/2)+b*e)*x))/e^(3/2) +--R +--R +--R (181) +--R - +--R +-----------------------+ +--R +-+ | +---+ +-+ +--R \|c \|b\|- e \|d + a e - c d +--R * +--R +--------------+ +-----------------------+ +--R +-+ | 2 | +---+ +-+ +--R 2\|e \|c x + b x + a \|b\|- e \|d + a e - c d +--R atanh(------------------------------------------------) +--R +---+ +-+ +--R (2c x + b)\|- e \|d + b e x + 2a e +--R + +--R +-------------------------+ +--R +-+ | +---+ +-+ +--R \|c \|- b\|- e \|d + a e - c d +--R * +--R +--------------+ +-------------------------+ +--R +-+ | 2 | +---+ +-+ +--R 2\|e \|c x + b x + a \|- b\|- e \|d + a e - c d +--R atanh(--------------------------------------------------) +--R +---+ +-+ +--R (2c x + b)\|- e \|d - b e x - 2a e +--R + +--R +--------------+ +--R +-+ | 2 +--------------+ +--R +-+ 2\|c \|c x + b x + a +-+ +-+ | 2 +--R b\|e atanh(----------------------) + 2\|c \|e \|c x + b x + a +--R 2c x + b +--R / +--R +-+ +-+ +--R 2e\|c \|e +--R Type: Expression Integer +--E 190 + +--S 191 of 486 too expensive to compute during test +--a0332:= integrate(t0332,x) +-- +-- +-- (187) +-- [ +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- (2e\|a \|c \|c x + b x + a + (- b e x - 2a e)\|c ) +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- 2e x |- --- |----------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- (- 2e\|a \|c \|c x + b x + a + (b e x + 2a e)\|c ) +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- 2e x |- --- |------------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- (2e\|a \|c \|c x + b x + a + (- b e x - 2a e)\|c ) +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- - 2e x |- --- |------------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- (- 2e\|a \|c \|c x + b x + a + (b e x + 2a e)\|c ) +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- - 2e x |- --- |----------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ | 2 2 +-- (2b\|a \|c x + b x + a - b x - 2a b) +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- +--------------+ +-- +-+ | 2 2 +-+ +-+ +-- - 2b x\|c \|c x + b x + a + (4c x + 2b x)\|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- 4e\|a \|c \|c x + b x + a + (- 2b e x - 4a e)\|c +-- , +-- +-- +--------------+ +-- +---+ +-+ | 2 +---+ +-- (2e\|- c \|a \|c x + b x + a + (- b e x - 2a e)\|- c ) +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- 2e x |- --- |----------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ | 2 +---+ +-- (- 2e\|- c \|a \|c x + b x + a + (b e x + 2a e)\|- c ) +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- 2e x |- --- |------------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ | 2 +---+ +-- (2e\|- c \|a \|c x + b x + a + (- b e x - 2a e)\|- c ) +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- - 2e x |- --- |------------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ | 2 +---+ +-- (- 2e\|- c \|a \|c x + b x + a + (b e x + 2a e)\|- c ) +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- - 2e x |- --- |----------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ | 2 2 +-- (4b\|a \|c x + b x + a - 2b x - 4a b) +-- * +-- +--------------+ +-- +---+ | 2 +---+ +-+ +-- \|- c \|c x + b x + a - \|- c \|a +-- atan(------------------------------------) +-- c x +-- + +-- +--------------+ +-- +---+ | 2 2 +---+ +-+ +-- - 2b x\|- c \|c x + b x + a + (4c x + 2b x)\|- c \|a +-- / +-- +--------------+ +-- +---+ +-+ | 2 +---+ +-- 4e\|- c \|a \|c x + b x + a + (- 2b e x - 4a e)\|- c +-- ] +-- Type: Union(List Expression Integer,...) +--E 191 + +--S 192 of 486 +--m0332a:= a0332.1-r0332 +-- +-- +-- (188) +-- +--------------+ +-- +-+ +-+ +-+ | 2 +-+ +-+ +-- (2e\|a \|c \|e \|c x + b x + a + (- b e x - 2a e)\|c \|e ) +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- 2e x |- --- |----------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ +-+ | 2 +-+ +-+ +-- (- 2e\|a \|c \|e \|c x + b x + a + (b e x + 2a e)\|c \|e ) +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- 2e x |- --- |------------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ +-+ | 2 +-+ +-+ +-- (2e\|a \|c \|e \|c x + b x + a + (- b e x - 2a e)\|c \|e ) +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- - 2e x |- --- |------------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ +-+ | 2 +-+ +-+ +-- (- 2e\|a \|c \|e \|c x + b x + a + (b e x + 2a e)\|c \|e ) +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- - 2e x |- --- |----------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- (2\|a \|c \|c x + b x + a + (- b x - 2a)\|c ) +-- * +-- +-----------------------+ +-- | +---+ +-+ +-- \|b\|- e \|d + a e - c d +-- * +-- +--------------+ +-----------------------+ +-- +-+ | 2 | +---+ +-+ +-- 2\|e \|c x + b x + a \|b\|- e \|d + a e - c d +-- atanh(------------------------------------------------) +-- +---+ +-+ +-- (2c x + b)\|- e \|d + b e x + 2a e +-- + +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- (- 2\|a \|c \|c x + b x + a + (b x + 2a)\|c ) +-- * +-- +-------------------------+ +-- | +---+ +-+ +-- \|- b\|- e \|d + a e - c d +-- * +-- +--------------+ +-------------------------+ +-- +-+ | 2 | +---+ +-+ +-- 2\|e \|c x + b x + a \|- b\|- e \|d + a e - c d +-- atanh(--------------------------------------------------) +-- +---+ +-+ +-- (2c x + b)\|- e \|d - b e x - 2a e +-- + +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2b\|a \|e \|c x + b x + a + (- b x - 2a b)\|e ) +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (- 2b\|a \|e \|c x + b x + a + (b x + 2a b)\|e ) +-- * +-- +--------------+ +-- +-+ | 2 +-- 2\|c \|c x + b x + a +-- atanh(----------------------) +-- 2c x + b +-- + +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-+ +-+ +-- 4a\|c \|e \|c x + b x + a + (- 2b x - 4a)\|a \|c \|e +-- / +-- +--------------+ +-- +-+ +-+ +-+ | 2 +-+ +-+ +-- 4e\|a \|c \|e \|c x + b x + a + (- 2b e x - 4a e)\|c \|e +-- Type: Expression Integer +--E 192 + +--S 193 of 486 +--d0332a:= D(m0332a,x) +-- +-- +-- (189) 0 +-- Type: Expression Integer +--E 193 + +--S 194 of 486 +--m0332b:= a0332.2-r0332 +-- +-- +-- (190) +-- +--------------+ +-- +---+ +-+ +-+ +-+ | 2 +-- 2e\|- c \|a \|c \|e \|c x + b x + a +-- + +-- +---+ +-+ +-+ +-- (- b e x - 2a e)\|- c \|c \|e +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- 2e x |- --- |----------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ +-+ +-+ | 2 +-- - 2e\|- c \|a \|c \|e \|c x + b x + a +-- + +-- +---+ +-+ +-+ +-- (b e x + 2a e)\|- c \|c \|e +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- 2e x |- --- |------------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ +-+ +-+ | 2 +-- 2e\|- c \|a \|c \|e \|c x + b x + a +-- + +-- +---+ +-+ +-+ +-- (- b e x - 2a e)\|- c \|c \|e +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- - 2e x |- --- |------------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ +-+ +-+ | 2 +-- - 2e\|- c \|a \|c \|e \|c x + b x + a +-- + +-- +---+ +-+ +-+ +-- (b e x + 2a e)\|- c \|c \|e +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- - 2e x |- --- |----------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ +-+ | 2 +---+ +-+ +-- (2\|- c \|a \|c \|c x + b x + a + (- b x - 2a)\|- c \|c ) +-- * +-- +-----------------------+ +-- | +---+ +-+ +-- \|b\|- e \|d + a e - c d +-- * +-- +--------------+ +-----------------------+ +-- +-+ | 2 | +---+ +-+ +-- 2\|e \|c x + b x + a \|b\|- e \|d + a e - c d +-- atanh(------------------------------------------------) +-- +---+ +-+ +-- (2c x + b)\|- e \|d + b e x + 2a e +-- + +-- +--------------+ +-- +---+ +-+ +-+ | 2 +---+ +-+ +-- (- 2\|- c \|a \|c \|c x + b x + a + (b x + 2a)\|- c \|c ) +-- * +-- +-------------------------+ +-- | +---+ +-+ +-- \|- b\|- e \|d + a e - c d +-- * +-- +--------------+ +-------------------------+ +-- +-+ | 2 | +---+ +-+ +-- 2\|e \|c x + b x + a \|- b\|- e \|d + a e - c d +-- atanh(--------------------------------------------------) +-- +---+ +-+ +-- (2c x + b)\|- e \|d - b e x - 2a e +-- + +-- +--------------+ +-- +---+ +-+ +-+ | 2 2 +---+ +-+ +-- (- 2b\|- c \|a \|e \|c x + b x + a + (b x + 2a b)\|- c \|e ) +-- * +-- +--------------+ +-- +-+ | 2 +-- 2\|c \|c x + b x + a +-- atanh(----------------------) +-- 2c x + b +-- + +-- +--------------+ +-- +-+ +-+ +-+ | 2 2 +-+ +-+ +-- (4b\|a \|c \|e \|c x + b x + a + (- 2b x - 4a b)\|c \|e ) +-- * +-- +--------------+ +-- +---+ | 2 +---+ +-+ +-- \|- c \|c x + b x + a - \|- c \|a +-- atan(------------------------------------) +-- c x +-- + +-- +--------------+ +-- +---+ +-+ +-+ | 2 +---+ +-+ +-+ +-+ +-- 4a\|- c \|c \|e \|c x + b x + a + (- 2b x - 4a)\|- c \|a \|c \|e +-- / +-- +--------------+ +-- +---+ +-+ +-+ +-+ | 2 +---+ +-+ +-+ +-- 4e\|- c \|a \|c \|e \|c x + b x + a + (- 2b e x - 4a e)\|- c \|c \|e +-- Type: Expression Integer +--E 194 + +--S 195 of 486 +--d0332b:= D(m0332b,x) +-- +-- +-- (191) 0 +-- Type: Expression Integer +--E 195 + +--S 196 of 486 +t0333:= (a+b*x+c*x^2)^(3/2)/(1-x^2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (- c x - b x - a)\|c x + b x + a +--R (182) ----------------------------------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 196 + +--S 197 of 486 +r0333:= -5/4*b*(a+b*x+c*x^2)^(1/2)-1/2*c*x*(a+b*x+c*x^2)^(1/2)-_ + 1/2*(a-b+c)^(3/2)*atanh(2*(a-b+c)^(1/2)*(a+b*x+c*x^2)^(1/2)/_ + (2*a-b+(b-2*c)*x))+1/4*(b-2*c)*(-b+c)*atanh(2*c^(1/2)*_ + (a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(1/2)-1/4*(b+c)*(b+2*c)*_ + atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(1/2)+_ + 1/8*(b^2-12*a*c)*atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/_ + (b+2*c*x))/c^(1/2)+1/2*(a+b+c)^(3/2)*atanh(2*(a+b+c)^(1/2)*_ + (a+b*x+c*x^2)^(1/2)/(2*a+b+(b+2*c)*x)) +--R +--R +--R (183) +--R +--------------+ +--R +---------+ | 2 +--R +-+ +---------+ 2\|c + b + a \|c x + b x + a +--R (4c + 4b + 4a)\|c \|c + b + a atanh(------------------------------) +--R (2c + b)x + b + 2a +--R + +--R +--------------+ +--R +-+ | 2 +--R 2 2 2\|c \|c x + b x + a +--R (- 8c - 12a c - 3b )atanh(----------------------) +--R 2c x + b +--R + +--R +--------------+ +--R +---------+ | 2 +--R +---------+ +-+ 2\|c - b + a \|c x + b x + a +--R (4c - 4b + 4a)\|c - b + a \|c atanh(------------------------------) +--R (2c - b)x + b - 2a +--R + +--R +--------------+ +--R +-+ | 2 +--R (- 4c x - 10b)\|c \|c x + b x + a +--R / +--R +-+ +--R 8\|c +--R Type: Expression Integer +--E 197 + +--S 198 of 486 too expensive to compute during test +--a0333:= integrate(t0333,x) +-- +-- +-- (194) +-- [ +-- 2 2 +-+ +-+ +-- ((16b c + 16b + 16a b)x + 32a c + 32a b + 32a )\|a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b - 16a b - 16a )c - 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c - 32a b - 32a b)x - 32a c - 32a b - 32a +-- * +-- +-+ +---------+ +-- \|c \|c + b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (2x\|c + b + a + (2x - 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x - 2x)\|a \|c + b + a + (2c + b + 2a)x + (b - 2a)x + 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x - 2)\|a \|c x + b x + a - b x + (b - 2a)x + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- - 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- 2 2 +-+ +---------+ +-- ((16b c - 16b + 16a b)x + 32a c - 32a b + 32a )\|a \|c - b + a +-- * +-- +--------------+ +-- +-+ | 2 +-- \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b + 16a b - 16a )c + 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c + 32a b - 32a b)x - 32a c + 32a b - 32a +-- * +-- +---------+ +-+ +-- \|c - b + a \|c +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (- 2x\|c - b + a + (2x + 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x + 2x)\|a \|c - b + a + (- 2c + b - 2a)x + (- b - 2a)x +-- + +-- - 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x + 2)\|a \|c x + b x + a - b x + (- b - 2a)x - 2a +-- + +-- 2 2 3 3 2 2 2 +-+ +-- ((16a c + 4b c)x + (72a b c + 10b )x + (32a c + 40a b )x)\|c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 16b c x + (- 32a c - 56b c)x + (- 88a b c - 30b )x +-- + +-- 2 2 +-- (- 32a c - 40a b )x +-- * +-- +-+ +-+ +-- \|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-- (32b x + 64a)\|a \|c \|c x + b x + a +-- + +-- 2 2 2 +-+ +-- ((- 32a c - 8b )x - 64a b x - 64a )\|c +-- , +-- +-- 2 2 +-+ +-+ +-- ((16b c + 16b + 16a b)x + 32a c + 32a b + 32a )\|a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b - 16a b - 16a )c - 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c - 32a b - 32a b)x - 32a c - 32a b - 32a +-- * +-- +-+ +---------+ +-- \|c \|c + b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (2x\|c + b + a + (2x - 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x - 2x)\|a \|c + b + a + (2c + b + 2a)x + (b - 2a)x + 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x - 2)\|a \|c x + b x + a - b x + (b - 2a)x + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- - 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- 2 2 +-----------+ +-- ((32b c - 32b + 32a b)x + 64a c - 64a b + 64a )\|- c + b - a +-- * +-- +--------------+ +-- +-+ +-+ | 2 +-- \|a \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 32a c + (- 8b + 32a b - 32a )c + 8b - 8a b )x +-- + +-- 2 2 2 2 3 +-- (- 64a b c + 64a b - 64a b)x - 64a c + 64a b - 64a +-- * +-- +-----------+ +-+ +-- \|- c + b - a \|c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (- x - 1)\|a +-- atan(---------------------------------) +-- +-----------+ +-- x\|- c + b - a +-- + +-- 2 2 3 3 2 2 2 +-+ +-- ((16a c + 4b c)x + (72a b c + 10b )x + (32a c + 40a b )x)\|c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 16b c x + (- 32a c - 56b c)x + (- 88a b c - 30b )x +-- + +-- 2 2 +-- (- 32a c - 40a b )x +-- * +-- +-+ +-+ +-- \|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-- (32b x + 64a)\|a \|c \|c x + b x + a +-- + +-- 2 2 2 +-+ +-- ((- 32a c - 8b )x - 64a b x - 64a )\|c +-- , +-- +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- - 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- 2 2 +-+ +---------+ +-- ((16b c - 16b + 16a b)x + 32a c - 32a b + 32a )\|a \|c - b + a +-- * +-- +--------------+ +-- +-+ | 2 +-- \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b + 16a b - 16a )c + 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c + 32a b - 32a b)x - 32a c + 32a b - 32a +-- * +-- +---------+ +-+ +-- \|c - b + a \|c +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (- 2x\|c - b + a + (2x + 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x + 2x)\|a \|c - b + a + (- 2c + b - 2a)x + (- b - 2a)x +-- + +-- - 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x + 2)\|a \|c x + b x + a - b x + (- b - 2a)x - 2a +-- + +-- 2 2 +-----------+ +-- ((32b c + 32b + 32a b)x + 64a c + 64a b + 64a )\|- c - b - a +-- * +-- +--------------+ +-- +-+ +-+ | 2 +-- \|a \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 32a c + (- 8b - 32a b - 32a )c - 8b - 8a b )x +-- + +-- 2 2 2 2 3 +-- (- 64a b c - 64a b - 64a b)x - 64a c - 64a b - 64a +-- * +-- +-----------+ +-+ +-- \|- c - b - a \|c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (x - 1)\|a +-- atan(-------------------------------) +-- +-----------+ +-- x\|- c - b - a +-- + +-- 2 2 3 3 2 2 2 +-+ +-- ((16a c + 4b c)x + (72a b c + 10b )x + (32a c + 40a b )x)\|c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 16b c x + (- 32a c - 56b c)x + (- 88a b c - 30b )x +-- + +-- 2 2 +-- (- 32a c - 40a b )x +-- * +-- +-+ +-+ +-- \|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-- (32b x + 64a)\|a \|c \|c x + b x + a +-- + +-- 2 2 2 +-+ +-- ((- 32a c - 8b )x - 64a b x - 64a )\|c +-- , +-- +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- - 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- 2 2 +-----------+ +-- ((32b c + 32b + 32a b)x + 64a c + 64a b + 64a )\|- c - b - a +-- * +-- +--------------+ +-- +-+ +-+ | 2 +-- \|a \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 32a c + (- 8b - 32a b - 32a )c - 8b - 8a b )x +-- + +-- 2 2 2 2 3 +-- (- 64a b c - 64a b - 64a b)x - 64a c - 64a b - 64a +-- * +-- +-----------+ +-+ +-- \|- c - b - a \|c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (x - 1)\|a +-- atan(-------------------------------) +-- +-----------+ +-- x\|- c - b - a +-- + +-- 2 2 +-----------+ +-- ((32b c - 32b + 32a b)x + 64a c - 64a b + 64a )\|- c + b - a +-- * +-- +--------------+ +-- +-+ +-+ | 2 +-- \|a \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 32a c + (- 8b + 32a b - 32a )c + 8b - 8a b )x +-- + +-- 2 2 2 2 3 +-- (- 64a b c + 64a b - 64a b)x - 64a c + 64a b - 64a +-- * +-- +-----------+ +-+ +-- \|- c + b - a \|c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (- x - 1)\|a +-- atan(---------------------------------) +-- +-----------+ +-- x\|- c + b - a +-- + +-- 2 2 3 3 2 2 2 +-+ +-- ((16a c + 4b c)x + (72a b c + 10b )x + (32a c + 40a b )x)\|c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 16b c x + (- 32a c - 56b c)x + (- 88a b c - 30b )x +-- + +-- 2 2 +-- (- 32a c - 40a b )x +-- * +-- +-+ +-+ +-- \|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-- (32b x + 64a)\|a \|c \|c x + b x + a +-- + +-- 2 2 2 +-+ +-- ((- 32a c - 8b )x - 64a b x - 64a )\|c +-- , +-- +-- 2 2 +---+ +-+ +-- ((8b c + 8b + 8a b)x + 16a c + 16a b + 16a )\|- c \|a +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 8a c + (- 2b - 8a b - 8a )c - 2b - 2a b )x +-- + +-- 2 2 2 2 3 +-- (- 16a b c - 16a b - 16a b)x - 16a c - 16a b - 16a +-- * +-- +---+ +---------+ +-- \|- c \|c + b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (2x\|c + b + a + (2x - 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x - 2x)\|a \|c + b + a + (2c + b + 2a)x + (b - 2a)x + 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x - 2)\|a \|c x + b x + a - b x + (b - 2a)x + 2a +-- + +-- 2 2 +---+ +-+ +-- ((8b c - 8b + 8a b)x + 16a c - 16a b + 16a )\|- c \|a +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c - b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 8a c + (- 2b + 8a b - 8a )c + 2b - 2a b )x +-- + +-- 2 2 2 2 3 +-- (- 16a b c + 16a b - 16a b)x - 16a c + 16a b - 16a +-- * +-- +---+ +---------+ +-- \|- c \|c - b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (- 2x\|c - b + a + (2x + 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x + 2x)\|a \|c - b + a + (- 2c + b - 2a)x + (- b - 2a)x +-- + +-- - 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x + 2)\|a \|c x + b x + a - b x + (- b - 2a)x - 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((- 32b c - 48a b c - 12b )x - 64a c - 96a c - 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (32a c + (8b + 48a )c + 24a b c + 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (64a b c + 96a b c + 24a b )x + 64a c + 96a c + 24a b +-- * +-- +--------------+ +-- +---+ | 2 +---+ +-+ +-- \|- c \|c x + b x + a - \|- c \|a +-- atan(------------------------------------) +-- c x +-- + +-- 2 2 3 3 2 2 2 +---+ +-- ((8a c + 2b c)x + (36a b c + 5b )x + (16a c + 20a b )x)\|- c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 8b c x + (- 16a c - 28b c)x + (- 44a b c - 15b )x +-- + +-- 2 2 +-- (- 16a c - 20a b )x +-- * +-- +---+ +-+ +-- \|- c \|a +-- / +-- +--------------+ +-- +---+ +-+ | 2 +-- (16b x + 32a)\|- c \|a \|c x + b x + a +-- + +-- 2 2 2 +---+ +-- ((- 16a c - 4b )x - 32a b x - 32a )\|- c +-- , +-- +-- 2 2 +---+ +-+ +-- ((8b c + 8b + 8a b)x + 16a c + 16a b + 16a )\|- c \|a +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 8a c + (- 2b - 8a b - 8a )c - 2b - 2a b )x +-- + +-- 2 2 2 2 3 +-- (- 16a b c - 16a b - 16a b)x - 16a c - 16a b - 16a +-- * +-- +---+ +---------+ +-- \|- c \|c + b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (2x\|c + b + a + (2x - 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x - 2x)\|a \|c + b + a + (2c + b + 2a)x + (b - 2a)x + 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x - 2)\|a \|c x + b x + a - b x + (b - 2a)x + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((- 32b c - 48a b c - 12b )x - 64a c - 96a c - 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (32a c + (8b + 48a )c + 24a b c + 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (64a b c + 96a b c + 24a b )x + 64a c + 96a c + 24a b +-- * +-- +--------------+ +-- +---+ | 2 +---+ +-+ +-- \|- c \|c x + b x + a - \|- c \|a +-- atan(------------------------------------) +-- c x +-- + +-- 2 2 +---+ +-- ((16b c - 16b + 16a b)x + 32a c - 32a b + 32a )\|- c +-- * +-- +--------------+ +-- +-----------+ +-+ | 2 +-- \|- c + b - a \|a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b + 16a b - 16a )c + 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c + 32a b - 32a b)x - 32a c + 32a b - 32a +-- * +-- +---+ +-----------+ +-- \|- c \|- c + b - a +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (- x - 1)\|a +-- atan(---------------------------------) +-- +-----------+ +-- x\|- c + b - a +-- + +-- 2 2 3 3 2 2 2 +---+ +-- ((8a c + 2b c)x + (36a b c + 5b )x + (16a c + 20a b )x)\|- c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 8b c x + (- 16a c - 28b c)x + (- 44a b c - 15b )x +-- + +-- 2 2 +-- (- 16a c - 20a b )x +-- * +-- +---+ +-+ +-- \|- c \|a +-- / +-- +--------------+ +-- +---+ +-+ | 2 +-- (16b x + 32a)\|- c \|a \|c x + b x + a +-- + +-- 2 2 2 +---+ +-- ((- 16a c - 4b )x - 32a b x - 32a )\|- c +-- , +-- +-- 2 2 +---+ +-+ +-- ((8b c - 8b + 8a b)x + 16a c - 16a b + 16a )\|- c \|a +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c - b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 8a c + (- 2b + 8a b - 8a )c + 2b - 2a b )x +-- + +-- 2 2 2 2 3 +-- (- 16a b c + 16a b - 16a b)x - 16a c + 16a b - 16a +-- * +-- +---+ +---------+ +-- \|- c \|c - b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (- 2x\|c - b + a + (2x + 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x + 2x)\|a \|c - b + a + (- 2c + b - 2a)x + (- b - 2a)x +-- + +-- - 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x + 2)\|a \|c x + b x + a - b x + (- b - 2a)x - 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((- 32b c - 48a b c - 12b )x - 64a c - 96a c - 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (32a c + (8b + 48a )c + 24a b c + 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (64a b c + 96a b c + 24a b )x + 64a c + 96a c + 24a b +-- * +-- +--------------+ +-- +---+ | 2 +---+ +-+ +-- \|- c \|c x + b x + a - \|- c \|a +-- atan(------------------------------------) +-- c x +-- + +-- 2 2 +-----------+ +-- ((16b c + 16b + 16a b)x + 32a c + 32a b + 32a )\|- c - b - a +-- * +-- +--------------+ +-- +---+ +-+ | 2 +-- \|- c \|a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b - 16a b - 16a )c - 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c - 32a b - 32a b)x - 32a c - 32a b - 32a +-- * +-- +-----------+ +---+ +-- \|- c - b - a \|- c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (x - 1)\|a +-- atan(-------------------------------) +-- +-----------+ +-- x\|- c - b - a +-- + +-- 2 2 3 3 2 2 2 +---+ +-- ((8a c + 2b c)x + (36a b c + 5b )x + (16a c + 20a b )x)\|- c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 8b c x + (- 16a c - 28b c)x + (- 44a b c - 15b )x +-- + +-- 2 2 +-- (- 16a c - 20a b )x +-- * +-- +---+ +-+ +-- \|- c \|a +-- / +-- +--------------+ +-- +---+ +-+ | 2 +-- (16b x + 32a)\|- c \|a \|c x + b x + a +-- + +-- 2 2 2 +---+ +-- ((- 16a c - 4b )x - 32a b x - 32a )\|- c +-- , +-- +-- 2 3 2 2 2 +-+ +-- ((- 32b c - 48a b c - 12b )x - 64a c - 96a c - 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (32a c + (8b + 48a )c + 24a b c + 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (64a b c + 96a b c + 24a b )x + 64a c + 96a c + 24a b +-- * +-- +--------------+ +-- +---+ | 2 +---+ +-+ +-- \|- c \|c x + b x + a - \|- c \|a +-- atan(------------------------------------) +-- c x +-- + +-- 2 2 +-----------+ +-- ((16b c + 16b + 16a b)x + 32a c + 32a b + 32a )\|- c - b - a +-- * +-- +--------------+ +-- +---+ +-+ | 2 +-- \|- c \|a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b - 16a b - 16a )c - 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c - 32a b - 32a b)x - 32a c - 32a b - 32a +-- * +-- +-----------+ +---+ +-- \|- c - b - a \|- c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (x - 1)\|a +-- atan(-------------------------------) +-- +-----------+ +-- x\|- c - b - a +-- + +-- 2 2 +---+ +-- ((16b c - 16b + 16a b)x + 32a c - 32a b + 32a )\|- c +-- * +-- +--------------+ +-- +-----------+ +-+ | 2 +-- \|- c + b - a \|a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b + 16a b - 16a )c + 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c + 32a b - 32a b)x - 32a c + 32a b - 32a +-- * +-- +---+ +-----------+ +-- \|- c \|- c + b - a +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (- x - 1)\|a +-- atan(---------------------------------) +-- +-----------+ +-- x\|- c + b - a +-- + +-- 2 2 3 3 2 2 2 +---+ +-- ((8a c + 2b c)x + (36a b c + 5b )x + (16a c + 20a b )x)\|- c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 8b c x + (- 16a c - 28b c)x + (- 44a b c - 15b )x +-- + +-- 2 2 +-- (- 16a c - 20a b )x +-- * +-- +---+ +-+ +-- \|- c \|a +-- / +-- +--------------+ +-- +---+ +-+ | 2 +-- (16b x + 32a)\|- c \|a \|c x + b x + a +-- + +-- 2 2 2 +---+ +-- ((- 16a c - 4b )x - 32a b x - 32a )\|- c +-- ] +-- Type: Union(List Expression Integer,...) +--E 198 + +--S 199 of 486 +-m0333a:= a0333.1-r0333 +-- +-- +-- (195) +-- 2 2 +-+ +-+ +-- ((16b c + 16b + 16a b)x + 32a c + 32a b + 32a )\|a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b - 16a b - 16a )c - 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c - 32a b - 32a b)x - 32a c - 32a b - 32a +-- * +-- +-+ +---------+ +-- \|c \|c + b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (2x\|c + b + a + (2x - 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x - 2x)\|a \|c + b + a + (2c + b + 2a)x + (b - 2a)x + 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x - 2)\|a \|c x + b x + a - b x + (b - 2a)x + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- - 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- 2 2 +-+ +---------+ +-- ((16b c - 16b + 16a b)x + 32a c - 32a b + 32a )\|a \|c - b + a +-- * +-- +--------------+ +-- +-+ | 2 +-- \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b + 16a b - 16a )c + 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c + 32a b - 32a b)x - 32a c + 32a b - 32a +-- * +-- +---------+ +-+ +-- \|c - b + a \|c +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (- 2x\|c - b + a + (2x + 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x + 2x)\|a \|c - b + a + (- 2c + b - 2a)x + (- b - 2a)x - 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x + 2)\|a \|c x + b x + a - b x + (- b - 2a)x - 2a +-- + +-- 2 2 +-+ +-+ +-- ((- 16b c - 16b - 16a b)x - 32a c - 32a b - 32a )\|a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (16a c + (4b + 16a b + 16a )c + 4b + 4a b )x +-- + +-- 2 2 2 2 3 +-- (32a b c + 32a b + 32a b)x + 32a c + 32a b + 32a +-- * +-- +-+ +---------+ +-- \|c \|c + b + a +-- * +-- +--------------+ +-- +---------+ | 2 +-- 2\|c + b + a \|c x + b x + a +-- atanh(------------------------------) +-- (2c + b)x + b + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- +--------------+ +-- +-+ | 2 +-- 2\|c \|c x + b x + a +-- atanh(----------------------) +-- 2c x + b +-- + +-- 2 2 +-+ +---------+ +-- ((- 16b c + 16b - 16a b)x - 32a c + 32a b - 32a )\|a \|c - b + a +-- * +-- +--------------+ +-- +-+ | 2 +-- \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (16a c + (4b - 16a b + 16a )c - 4b + 4a b )x +-- + +-- 2 2 2 2 3 +-- (32a b c - 32a b + 32a b)x + 32a c - 32a b + 32a +-- * +-- +---------+ +-+ +-- \|c - b + a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- 2\|c - b + a \|c x + b x + a +-- atanh(------------------------------) +-- (2c - b)x + b - 2a +-- + +-- +--------------+ +-- 2 2 +-+ | 2 +-- (- 40a b x - 80a b)\|c \|c x + b x + a +-- + +-- 3 2 2 2 +-+ +-+ +-- ((40a b c + 10b )x + 80a b x + 80a b)\|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-- (32b x + 64a)\|a \|c \|c x + b x + a +-- + +-- 2 2 2 +-+ +-- ((- 32a c - 8b )x - 64a b x - 64a )\|c +-- Type: Expression Integer +--E 199 + +--S 200 of 486 +--d0333a:= D(m0333a,x) +-- +-- +-- (196) 0 +-- Type: Expression Integer +--E 200 + +--S 201 of 486 +--m0333b:= a0333.2-r0333 +-- +-- +-- (197) +-- 2 2 +-+ +-+ +-- ((16b c + 16b + 16a b)x + 32a c + 32a b + 32a )\|a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b - 16a b - 16a )c - 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c - 32a b - 32a b)x - 32a c - 32a b - 32a +-- * +-- +-+ +---------+ +-- \|c \|c + b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (2x\|c + b + a + (2x - 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x - 2x)\|a \|c + b + a + (2c + b + 2a)x + (b - 2a)x + 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x - 2)\|a \|c x + b x + a - b x + (b - 2a)x + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- - 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- 2 2 +-+ +-+ +-- ((- 16b c - 16b - 16a b)x - 32a c - 32a b - 32a )\|a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (16a c + (4b + 16a b + 16a )c + 4b + 4a b )x +-- + +-- 2 2 2 2 3 +-- (32a b c + 32a b + 32a b)x + 32a c + 32a b + 32a +-- * +-- +-+ +---------+ +-- \|c \|c + b + a +-- * +-- +--------------+ +-- +---------+ | 2 +-- 2\|c + b + a \|c x + b x + a +-- atanh(------------------------------) +-- (2c + b)x + b + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- +--------------+ +-- +-+ | 2 +-- 2\|c \|c x + b x + a +-- atanh(----------------------) +-- 2c x + b +-- + +-- 2 2 +-+ +---------+ +-- ((- 16b c + 16b - 16a b)x - 32a c + 32a b - 32a )\|a \|c - b + a +-- * +-- +--------------+ +-- +-+ | 2 +-- \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (16a c + (4b - 16a b + 16a )c - 4b + 4a b )x +-- + +-- 2 2 2 2 3 +-- (32a b c - 32a b + 32a b)x + 32a c - 32a b + 32a +-- * +-- +---------+ +-+ +-- \|c - b + a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- 2\|c - b + a \|c x + b x + a +-- atanh(------------------------------) +-- (2c - b)x + b - 2a +-- + +-- 2 2 +-----------+ +-+ +-- ((32b c - 32b + 32a b)x + 64a c - 64a b + 64a )\|- c + b - a \|a +-- * +-- +--------------+ +-- +-+ | 2 +-- \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 32a c + (- 8b + 32a b - 32a )c + 8b - 8a b )x +-- + +-- 2 2 2 2 3 +-- (- 64a b c + 64a b - 64a b)x - 64a c + 64a b - 64a +-- * +-- +-----------+ +-+ +-- \|- c + b - a \|c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (- x - 1)\|a +-- atan(---------------------------------) +-- +-----------+ +-- x\|- c + b - a +-- + +-- +--------------+ +-- 2 2 +-+ | 2 +-- (- 40a b x - 80a b)\|c \|c x + b x + a +-- + +-- 3 2 2 2 +-+ +-+ +-- ((40a b c + 10b )x + 80a b x + 80a b)\|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-- (32b x + 64a)\|a \|c \|c x + b x + a +-- + +-- 2 2 2 +-+ +-- ((- 32a c - 8b )x - 64a b x - 64a )\|c +-- Type: Expression Integer +--E 201 + +--S 202 of 486 +--d0333b:= D(m0333b,x) +-- +-- +-- (198) 0 +-- Type: Expression Integer +--E 202 + +--S 203 of 486 +t0334:= x^(-1-n*q-p*(1+q))*(x^n*(a+b*x^p))^q +--R +--R +--R (- p - n)q - p - 1 n p n q +--R (184) x (b x x + a x ) +--R Type: Expression Integer +--E 203 + +--S 204 of 486 +r0334:= -x^(-n-n*q-p*(1+q))*(x^n*(a+b*x^p))^(1+q)/a/p/(1+q) +--R +--R +--R (- p - n)q - p - n n p n q + 1 +--R x (b x x + a x ) +--R (185) - --------------------------------------- +--R a p q + a p +--R Type: Expression Integer +--E 204 + +--S 205 of 486 +a0334:= integrate(t0334,x) +--R +--R +--R x +--R ++ (- p - n)q - p - 1 n p n q +--R (186) | %V (b %V %V + a %V ) d%V +--R ++ +--R Type: Union(Expression Integer,...) +--E 205 + +--S 206 of 486 +m0334:= a0334-r0334 +--R +--R +--R (187) +--R x +--R ++ (- p - n)q - p - 1 n p n q +--R (a p q + a p) | %V (b %V %V + a %V ) d%V +--R ++ +--R + +--R (- p - n)q - p - n n p n q + 1 +--R x (b x x + a x ) +--R / +--R a p q + a p +--R Type: Expression Integer +--E 206 + +--S 207 of 486 +d0334:= D(m0334,x) +--R +--R +--R (188) +--R (- p - n)q - p - n - 1 n p n q + 1 +--R (- p - n)x (b x x + a x ) +--R + +--R (- p - n)q - p - n n - 1 p (- p - n)q - p - n n p - 1 +--R b n x x x + b p x x x +--R + +--R (- p - n)q - p - n n - 1 (- p - n)q - p - 1 +--R a n x x + a p x +--R * +--R n p n q +--R (b x x + a x ) +--R / +--R a p +--R Type: Expression Integer +--E 207 + +--S 208 of 486 +t0335:= x^(-1+n-p*(1+q))*(a*x^n+b*x^p)^q +--R +--R +--R - p q - p + n - 1 p n q +--R (189) x (b x + a x ) +--R Type: Expression Integer +--E 208 + +--S 209 of 486 +r0335:= (x^n*(a+b*x^(-n+p)))^(1+q)/(x^(p*(1+q)))/a/(n-p)/(1+q) +--R +--R +--R n p - n n q + 1 +--R (b x x + a x ) +--R (190) - ---------------------------------- +--R p q + p +--R ((a p - a n)q + a p - a n)x +--R Type: Expression Integer +--E 209 + +--S 210 of 486 +a0335:= integrate(t0335,x) +--R +--R +--R x +--R ++ - p q - p + n - 1 p n q +--R (191) | %V (b %V + a %V ) d%V +--R ++ +--R Type: Union(Expression Integer,...) +--E 210 + +--S 211 of 486 +m0335:= a0335-r0335 +--R +--R +--R (192) +--R p q + p +--R ((a p - a n)q + a p - a n)x +--R * +--R x +--R ++ - p q - p + n - 1 p n q +--R | %V (b %V + a %V ) d%V +--R ++ +--R + +--R n p - n n q + 1 +--R (b x x + a x ) +--R / +--R p q + p +--R ((a p - a n)q + a p - a n)x +--R Type: Expression Integer +--E 211 + +--S 212 of 486 +d0335:= D(m0335,x) +--R +--R +--R (193) +--R - p q - p + n - 1 p q + p 2 p n q +--R (a p - a n)x (x ) (b x + a x ) +--R + +--R p q + p - 1 n p - n n q + 1 +--R - p x (b x x + a x ) +--R + +--R n - 1 p - n n p - n - 1 n - 1 p q + p +--R (b n x x + (b p - b n)x x + a n x )x +--R * +--R n p - n n q +--R (b x x + a x ) +--R / +--R p q + p 2 +--R (a p - a n)(x ) +--R Type: Expression Integer +--E 212 + +--S 213 of 486 +t0336:= 1/2*x^(-1+m)*(2*a*m+b*(2*m-n)*x^n)/(a+b*x^n)^(3/2) +--R +--R +--R m - 1 n m - 1 +--R (- b n + 2b m)x x + 2a m x +--R (194) ------------------------------------ +--R +--------+ +--R n | n +--R (2b x + 2a)\|b x + a +--R Type: Expression Integer +--E 213 + +--S 214 of 486 +r0336:= x^m/(a+b*x^n)^(1/2) +--R +--R +--R m +--R x +--R (195) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression Integer +--E 214 + +--S 215 of 486 +a0336:= integrate(t0336,x) +--R +--R +--R +----------------+ +--R (m - 1)log(x) | n log(x) +--R x %e \|b %e + a +--R (196) ------------------------------------ +--R n log(x) +--R b %e + a +--R Type: Union(Expression Integer,...) +--E 215 + +--S 216 of 486 +m0336:= a0336-r0336 +--R +--R +--R (197) +--R +--------+ +----------------+ +--R (m - 1)log(x) | n | n log(x) m n log(x) m +--R x %e \|b x + a \|b %e + a - b x %e - a x +--R ----------------------------------------------------------------------- +--R +--------+ +--R n log(x) | n +--R (b %e + a)\|b x + a +--R Type: Expression Integer +--E 216 + +--S 217 of 486 +d0336:= D(m0336,x) +--R +--R +--R (198) +--R 2 m - 1 n 2 m n - 1 m - 1 n log(x) +--R (- 2b m x x + b n x x - 2a b m x )%e +--R + +--R m - 1 n m n - 1 2 m - 1 +--R - 2a b m x x + a b n x x - 2a m x +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R 2 2 n (m - 1)log(x) n log(x) +--R ((- b n + 2b m)x - a b n + 2a b m)%e %e +--R + +--R n 2 (m - 1)log(x) +--R (2a b m x + 2a m)%e +--R * +--R +--------+ +--R | n +--R \|b x + a +--R / +--R +--------+ +----------------+ +--R 2 n n log(x) n 2 | n | n log(x) +--R ((2b x + 2a b)%e + 2a b x + 2a )\|b x + a \|b %e + a +--R Type: Expression Integer +--E 217 + +--S 218 of 486 +t0337:= -1/2*b*n*x^(-1+m+n)/(a+b*x^n)^(3/2)+m*x^(-1+m)/(a+b*x^n)^(1/2) +--R +--R +--R n + m - 1 m - 1 n m - 1 +--R - b n x + 2b m x x + 2a m x +--R (199) ---------------------------------------------- +--R +--------+ +--R n | n +--R (2b x + 2a)\|b x + a +--R Type: Expression Integer +--E 218 + +--S 219 of 486 +r0337:= x^m/(a+b*x^n)^(1/2) +--R +--R +--R m +--R x +--R (200) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression Integer +--E 219 + +--S 220 of 486 +--a0337:= integrate(t0337,x) +--E 220 + +--S 221 of 486 +--m0337:= a0337-r0337 +--E 221 + +--S 222 of 486 +--d0337:= D(m0337,x) +-- 2 >> Error detected within library code: +-- integrate: implementation incomplete (constant residues) +--E 222 + +--S 223 of 486 +t0338:= a*(2+m)*x^(1+m)/(a+b*x^2)^(1/2)+b*(3+m)*x^(3+m)/(a+b*x^2)^(1/2) +--R +--R +--R m + 3 m + 1 +--R (b m + 3b)x + (a m + 2a)x +--R (201) ----------------------------------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression Integer +--E 223 + +--S 224 of 486 +r0338:= x^(2+m)*(a+b*x^2)^(1/2) +--R +--R +--R +--------+ +--R m + 2 | 2 +--R (202) x \|b x + a +--R Type: Expression Integer +--E 224 + +--S 225 of 486 +a0338:= integrate(t0338,x) +--R +--R +--R +--------+ +--R 3 | 2 3 +-+ (m + 1)log(x) +--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e +--R (203) ---------------------------------------------------------------- +--R +--------+ +--R +-+ | 2 2 +--R 2\|a \|b x + a - b x - 2a +--R Type: Union(Expression Integer,...) +--E 225 + +--S 226 of 486 +m0338:= a0338-r0338 +--R +--R +--R (204) +--R +--------+ +--R 3 | 2 3 +-+ (m + 1)log(x) +--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e +--R + +--R +--------+ +--R 2 m + 2 | 2 2 m + 2 +-+ +--R (b x + 2a)x \|b x + a + (- 2b x - 2a)x \|a +--R / +--R +--------+ +--R +-+ | 2 2 +--R 2\|a \|b x + a - b x - 2a +--R Type: Expression Integer +--E 226 + +--S 227 of 486 +d0338:= D(m0338,x) +--R +--R +--R (205) +--R 2 (m + 1)log(x) m + 2 +--R ((b m + 3b)x + a m + 2a)%e - b x x +--R + +--R 2 m + 1 +--R ((- b m - 2b)x - a m - 2a)x +--R / +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression Integer +--E 227 + +--S 228 of 486 +t0339:= 1/2/(a+b*x^n)^(3/2)/x*(2*x^m*a*m+2*x^(m+n)*m*b-x^(m+n)*b*n) +--R +--R +--R n + m m +--R (- b n + 2b m)x + 2a m x +--R (206) ------------------------------ +--R +--------+ +--R n | n +--R (2b x x + 2a x)\|b x + a +--R Type: Expression Integer +--E 228 + +--S 229 of 486 +r0339:= x^m/(a+b*x^n)^(1/2) +--R +--R +--R m +--R x +--R (207) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression Integer +--E 229 + +--S 230 of 486 +--a0339:= integrate(t0339,x) +--E 230 + +--S 231 of 486 +--m0339:= a0339-r0339 +--E 231 + +--S 232 of 486 +--d0339:= D(m0339,x) +-- 2 >> Error detected within library code: +-- integrate: implementation incomplete (constant residues) +--E 232 + +--S 233 of 486 +t0340:= x^m*m/x/(a+b*x^n)^(1/2)-1/2*x^m/(a+b*x^n)^(3/2)*b*x^n*n/x +--R +--R +--R m n m +--R (- b n + 2b m)x x + 2a m x +--R (208) ---------------------------- +--R +--------+ +--R n | n +--R (2b x x + 2a x)\|b x + a +--R Type: Expression Integer +--E 233 + +--S 234 of 486 +r0340:= x^m/(a+b*x^n)^(1/2) +--R +--R +--R m +--R x +--R (209) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression Integer +--E 234 + +--S 235 of 486 +a0340:= integrate(t0340,x) +--R +--R +--R +----------------+ +--R m log(x) | n log(x) +--R %e \|b %e + a +--R (210) ----------------------------- +--R n log(x) +--R b %e + a +--R Type: Union(Expression Integer,...) +--E 235 + +--S 236 of 486 +m0340:= a0340-r0340 +--R +--R +--R +--------+ +----------------+ +--R m log(x) | n | n log(x) m n log(x) m +--R %e \|b x + a \|b %e + a - b x %e - a x +--R (211) ---------------------------------------------------------------- +--R +--------+ +--R n log(x) | n +--R (b %e + a)\|b x + a +--R Type: Expression Integer +--E 236 + +--S 237 of 486 +d0340:= D(m0340,x) +--R +--R +--R (212) +--R 2 m - 1 n 2 m n - 1 m - 1 n log(x) +--R (- 2b m x x x + b n x x x - 2a b m x x )%e +--R + +--R m - 1 n m n - 1 2 m - 1 +--R - 2a b m x x x + a b n x x x - 2a m x x +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R 2 2 n m log(x) n log(x) +--R ((- b n + 2b m)x - a b n + 2a b m)%e %e +--R + +--R n 2 m log(x) +--R (2a b m x + 2a m)%e +--R * +--R +--------+ +--R | n +--R \|b x + a +--R / +--R +--------+ +--R 2 n n log(x) n 2 | n +--R ((2b x x + 2a b x)%e + 2a b x x + 2a x)\|b x + a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R Type: Expression Integer +--E 237 + +--S 238 of 486 +t0341:= (x^(-2+2*n)*(a+b*x^n))^(1/2) +--R +--R +--R +-----------------+ +--R | n 2n - 2 +--R (213) \|(b x + a)x +--R Type: Expression Integer +--E 238 + +--S 239 of 486 +r0341:= 2/3*x^(3-3*n)*((a+b*x^n)/(x^(2-2*n)))^(3/2)/b/n +--R +--R +--R +---------+ +--R | n +--R - 3n + 3 n - 3n + 3 | b x + a +--R (2b x x + 2a x ) |--------- +--R | - 2n + 2 +--R \|x +--R (214) ------------------------------------------- +--R - 2n + 2 +--R 3b n x +--R Type: Expression Integer +--E 239 + +--S 240 of 486 +a0341:= integrate(t0341,x) +--R +--R +--R +----------------+ +--R n log(x) | n log(x) +--R (2b %e + 2a)\|b %e + a +--R (215) --------------------------------------- +--R 3b n +--R Type: Union(Expression Integer,...) +--E 240 + +--S 241 of 486 +m0341:= a0341-r0341 +--R +--R +--R (216) +--R +----------------+ +--R - 2n + 2 n log(x) - 2n + 2 | n log(x) +--R (2b x %e + 2a x )\|b %e + a +--R + +--R +---------+ +--R | n +--R - 3n + 3 n - 3n + 3 | b x + a +--R (- 2b x x - 2a x ) |--------- +--R | - 2n + 2 +--R \|x +--R / +--R - 2n + 2 +--R 3b n x +--R Type: Expression Integer +--E 241 + +--S 242 of 486 +d0341:= D(m0341,x) +--R +--R +--R (217) +--R 2 2 - 3n + 3 - 2n + 1 - 2n + 2 2 +--R (- 2b n + 2b )x x x (x ) +--R + +--R 2 2 - 4n + 4 - 3n + 2 - 2n + 2 +--R (6b n - 6b )x x x x +--R + +--R 2 2 - 4n + 4 - 3n + 3 - 2n + 1 +--R (- 4b n + 4b )x x x x +--R * +--R n 2 +--R (x ) +--R + +--R 2 - 3n + 3 - 2n + 2 3 +--R - b n x x (x ) +--R + +--R 2 - 4n + 4 - 3n + 3 - 2n + 2 +--R - 2b n x x x x +--R * +--R n - 1 +--R x +--R + +--R - 3n + 3 - 2n + 1 - 2n + 2 2 +--R (- 4a b n + 4a b)x x x (x ) +--R + +--R - 4n + 4 - 3n + 2 - 2n + 2 +--R (12a b n - 12a b)x x x x +--R + +--R - 4n + 4 - 3n + 3 - 2n + 1 +--R (- 8a b n + 8a b)x x x x +--R * +--R n +--R x +--R + +--R - 3n + 3 - 2n + 2 3 +--R - a b n x x (x ) +--R + +--R - 4n + 4 - 3n + 3 - 2n + 2 +--R - 2a b n x x x x +--R * +--R n - 1 +--R x +--R + +--R 2 2 - 3n + 3 - 2n + 1 - 2n + 2 2 +--R (- 2a n + 2a )x x x (x ) +--R + +--R 2 2 - 4n + 4 - 3n + 2 - 2n + 2 +--R (6a n - 6a )x x x x +--R + +--R 2 2 - 4n + 4 - 3n + 3 - 2n + 1 +--R (- 4a n + 4a )x x x x +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R 2 - 4n + 4 - 2n + 2 3 n log(x) 2 +--R 3b n x (x ) (%e ) +--R + +--R - 4n + 4 - 2n + 2 3 n log(x) +--R 3a b n x (x ) %e +--R * +--R +---------+ +--R | n +--R | b x + a +--R |--------- +--R | - 2n + 2 +--R \|x +--R / +--R +---------+ +--R | n +----------------+ +--R - 4n + 4 - 2n + 2 3 | b x + a | n log(x) +--R 3b n x x (x ) |--------- \|b %e + a +--R | - 2n + 2 +--R \|x +--R Type: Expression Integer +--E 242 + +--S 243 of 486 +t0342:= (x^(-3+3*n)*(a+b*x^n))^(1/3) +--R +--R +--R +-----------------+ +--R 3| n 3n - 3 +--R (218) \|(b x + a)x +--R Type: Expression Integer +--E 243 + +--S 244 of 486 +r0342:= 3/4*x^(4-4*n)*((a+b*x^n)/(x^(3-3*n)))^(4/3)/b/n +--R +--R +--R +---------+ +--R | n +--R - 4n + 4 n - 4n + 4 | b x + a +--R (3b x x + 3a x ) |--------- +--R 3| - 3n + 3 +--R \|x +--R (219) ------------------------------------------- +--R - 3n + 3 +--R 4b n x +--R Type: Expression Integer +--E 244 + +--S 245 of 486 +a0342:= integrate(t0342,x) +--R +--R +--R +----------------+ +--R n log(x) 3| n log(x) +--R (3b %e + 3a)\|b %e + a +--R (220) --------------------------------------- +--R 4b n +--R Type: Union(Expression Integer,...) +--E 245 + +--S 246 of 486 +m0342:= a0342-r0342 +--R +--R +--R (221) +--R +----------------+ +--R - 3n + 3 n log(x) - 3n + 3 3| n log(x) +--R (3b x %e + 3a x )\|b %e + a +--R + +--R +---------+ +--R | n +--R - 4n + 4 n - 4n + 4 | b x + a +--R (- 3b x x - 3a x ) |--------- +--R 3| - 3n + 3 +--R \|x +--R / +--R - 3n + 3 +--R 4b n x +--R Type: Expression Integer +--E 246 + +--S 247 of 486 +d0342:= D(m0342,x) +--R +--R +--R (222) +--R 2 2 - 4n + 4 - 3n + 2 - 3n + 3 2 +--R (- 3b n + 3b )x x x (x ) +--R + +--R 2 2 - 6n + 6 - 4n + 3 - 3n + 3 +--R (12b n - 12b )x x x x +--R + +--R 2 2 - 6n + 6 - 4n + 4 - 3n + 2 +--R (- 9b n + 9b )x x x x +--R * +--R n 2 +--R (x ) +--R + +--R 2 - 4n + 4 - 3n + 3 3 +--R - b n x x (x ) +--R + +--R 2 - 6n + 6 - 4n + 4 - 3n + 3 +--R - 3b n x x x x +--R * +--R n - 1 +--R x +--R + +--R - 4n + 4 - 3n + 2 - 3n + 3 2 +--R (- 6a b n + 6a b)x x x (x ) +--R + +--R - 6n + 6 - 4n + 3 - 3n + 3 +--R (24a b n - 24a b)x x x x +--R + +--R - 6n + 6 - 4n + 4 - 3n + 2 +--R (- 18a b n + 18a b)x x x x +--R * +--R n +--R x +--R + +--R - 4n + 4 - 3n + 3 3 +--R - a b n x x (x ) +--R + +--R - 6n + 6 - 4n + 4 - 3n + 3 +--R - 3a b n x x x x +--R * +--R n - 1 +--R x +--R + +--R 2 2 - 4n + 4 - 3n + 2 - 3n + 3 2 +--R (- 3a n + 3a )x x x (x ) +--R + +--R 2 2 - 6n + 6 - 4n + 3 - 3n + 3 +--R (12a n - 12a )x x x x +--R + +--R 2 2 - 6n + 6 - 4n + 4 - 3n + 2 +--R (- 9a n + 9a )x x x x +--R * +--R +----------------+2 +--R 3| n log(x) +--R \|b %e + a +--R + +--R 2 - 6n + 6 - 3n + 3 3 n log(x) 2 +--R 4b n x (x ) (%e ) +--R + +--R - 6n + 6 - 3n + 3 3 n log(x) +--R 4a b n x (x ) %e +--R * +--R +---------+2 +--R | n +--R | b x + a +--R |--------- +--R 3| - 3n + 3 +--R \|x +--R / +--R +---------+2 +--R | n +----------------+2 +--R - 6n + 6 - 3n + 3 3 | b x + a 3| n log(x) +--R 4b n x x (x ) |--------- \|b %e + a +--R 3| - 3n + 3 +--R \|x +--R Type: Expression Integer +--E 247 + +--S 248 of 486 +t0343:= (x^(-4+4*n)*(a+b*x^n))^(1/4) +--R +--R +--R +-----------------+ +--R 4| n 4n - 4 +--R (223) \|(b x + a)x +--R Type: Expression Integer +--E 248 + +--S 249 of 486 +r0343:= 4/5*x^(5-5*n)*((a+b*x^n)/(x^(4-4*n)))^(5/4)/b/n +--R +--R +--R +---------+ +--R | n +--R - 5n + 5 n - 5n + 5 | b x + a +--R (4b x x + 4a x ) |--------- +--R 4| - 4n + 4 +--R \|x +--R (224) ------------------------------------------- +--R - 4n + 4 +--R 5b n x +--R Type: Expression Integer +--E 249 + +--S 250 of 486 +a0343:= integrate(t0343,x) +--R +--R +--R +----------------+ +--R n log(x) 4| n log(x) +--R (4b %e + 4a)\|b %e + a +--R (225) --------------------------------------- +--R 5b n +--R Type: Union(Expression Integer,...) +--E 250 + +--S 251 of 486 +m0343:= a0343-r0343 +--R +--R +--R (226) +--R +----------------+ +--R - 4n + 4 n log(x) - 4n + 4 4| n log(x) +--R (4b x %e + 4a x )\|b %e + a +--R + +--R +---------+ +--R | n +--R - 5n + 5 n - 5n + 5 | b x + a +--R (- 4b x x - 4a x ) |--------- +--R 4| - 4n + 4 +--R \|x +--R / +--R - 4n + 4 +--R 5b n x +--R Type: Expression Integer +--E 251 + +--S 252 of 486 +d0343:= D(m0343,x) +--R +--R +--R (227) +--R 2 2 - 5n + 5 - 4n + 3 - 4n + 4 2 +--R (- 4b n + 4b )x x x (x ) +--R + +--R 2 2 - 8n + 8 - 5n + 4 - 4n + 4 +--R (20b n - 20b )x x x x +--R + +--R 2 2 - 8n + 8 - 5n + 5 - 4n + 3 +--R (- 16b n + 16b )x x x x +--R * +--R n 2 +--R (x ) +--R + +--R 2 - 5n + 5 - 4n + 4 3 +--R - b n x x (x ) +--R + +--R 2 - 8n + 8 - 5n + 5 - 4n + 4 +--R - 4b n x x x x +--R * +--R n - 1 +--R x +--R + +--R - 5n + 5 - 4n + 3 - 4n + 4 2 +--R (- 8a b n + 8a b)x x x (x ) +--R + +--R - 8n + 8 - 5n + 4 - 4n + 4 +--R (40a b n - 40a b)x x x x +--R + +--R - 8n + 8 - 5n + 5 - 4n + 3 +--R (- 32a b n + 32a b)x x x x +--R * +--R n +--R x +--R + +--R - 5n + 5 - 4n + 4 3 +--R - a b n x x (x ) +--R + +--R - 8n + 8 - 5n + 5 - 4n + 4 +--R - 4a b n x x x x +--R * +--R n - 1 +--R x +--R + +--R 2 2 - 5n + 5 - 4n + 3 - 4n + 4 2 +--R (- 4a n + 4a )x x x (x ) +--R + +--R 2 2 - 8n + 8 - 5n + 4 - 4n + 4 +--R (20a n - 20a )x x x x +--R + +--R 2 2 - 8n + 8 - 5n + 5 - 4n + 3 +--R (- 16a n + 16a )x x x x +--R * +--R +----------------+3 +--R 4| n log(x) +--R \|b %e + a +--R + +--R 2 - 8n + 8 - 4n + 4 3 n log(x) 2 +--R 5b n x (x ) (%e ) +--R + +--R - 8n + 8 - 4n + 4 3 n log(x) +--R 5a b n x (x ) %e +--R * +--R +---------+3 +--R | n +--R | b x + a +--R |--------- +--R 4| - 4n + 4 +--R \|x +--R / +--R +---------+3 +--R | n +----------------+3 +--R - 8n + 8 - 4n + 4 3 | b x + a 4| n log(x) +--R 5b n x x (x ) |--------- \|b %e + a +--R 4| - 4n + 4 +--R \|x +--R Type: Expression Integer +--E 252 + +--S 253 of 486 +t0344:= (x^(p*(-1+n))*(a+b*x^n))^(1/p) +--R +--R +--R 1 +--R - +--R n (n - 1)p p +--R (228) ((b x + a)x ) +--R Type: Expression Integer +--E 253 + +--S 254 of 486 +r0344:= x^((1-n)*(p+1))*((a+b*x^n)/(x^((1-n)*p)))^(1+1/p)/b/n/(1+1/p) +--R +--R +--R p + 1 +--R ----- +--R n p +--R (- n + 1)p - n + 1 b x + a +--R p x (-----------) +--R (- n + 1)p +--R x +--R (229) --------------------------------------- +--R b n p + b n +--R Type: Expression Integer +--E 254 + +--S 255 of 486 +a0344:= integrate(t0344,x) +--R +--R +--R 1 +--R x - +--R ++ n (n - 1)p p +--R (230) | ((b %V + a)%V ) d%V +--R ++ +--R Type: Union(Expression Integer,...) +--E 255 + +--S 256 of 486 +m0344:= a0344-r0344 +--R +--R +--R (231) +--R 1 +--R x - +--R ++ n (n - 1)p p +--R (b n p + b n) | ((b %V + a)%V ) d%V +--R ++ +--R + +--R p + 1 +--R ----- +--R n p +--R (- n + 1)p - n + 1 b x + a +--R - p x (-----------) +--R (- n + 1)p +--R x +--R / +--R b n p + b n +--R Type: Expression Integer +--E 256 + +--S 257 of 486 +d0344:= D(m0344,x) +--R +--R +--R (232) +--R 1 +--R - +--R (- 2n + 2)p n (n - 1)p p +--R b n x ((b x + a)x ) +--R + +--R p + 1 +--R ----- +--R n p +--R (- 2n + 2)p (- n + 1)p - n b x + a +--R (n - 1)p x x (-----------) +--R (- n + 1)p +--R x +--R + +--R (- n + 1)p - n + 1 (- n + 1)p - 1 n +--R (- b n + b)p x x x +--R + +--R (- n + 1)p - n + 1 (- n + 1)p n - 1 +--R - b n x x x +--R + +--R (- n + 1)p - n + 1 (- n + 1)p - 1 +--R (- a n + a)p x x +--R * +--R 1 +--R - +--R n p +--R b x + a +--R (-----------) +--R (- n + 1)p +--R x +--R / +--R (- 2n + 2)p +--R b n x +--R Type: Expression Integer +--E 257 + +--S 258 of 486 +t0345:= (x^((-1+n)/p)*(a+b*x^n))^p +--R +--R +--R n - 1 n - 1 p +--R ----- ----- +--R p n p +--R (233) (b x x + a x ) +--R Type: Expression Integer +--E 258 + +--S 259 of 486 +r0345:= 1/b/n/(p+1)*(x^((-1+n)/p)*(a+b*x^n))^p*(a*x^(1-n)+b*x) +--R +--R +--R n - 1 n - 1 p +--R ----- ----- +--R - n + 1 p n p +--R (a x + b x)(b x x + a x ) +--R (234) ------------------------------------------ +--R b n p + b n +--R Type: Expression Integer +--E 259 + +--S 260 of 486 +a0345:= integrate(t0345,x) +--R +--R +--R n - 1 n - 1 p +--R x ----- ----- +--R ++ p n p +--R (235) | (b %V %V + a %V ) d%V +--R ++ +--R Type: Union(Expression Integer,...) +--E 260 + +--S 261 of 486 +m0345:= a0345-r0345 +--R +--R +--R (236) +--R n - 1 n - 1 p +--R x ----- ----- +--R ++ p n p +--R (b n p + b n) | (b %V %V + a %V ) d%V +--R ++ +--R + +--R n - 1 n - 1 p +--R ----- ----- +--R - n + 1 p n p +--R (- a x - b x)(b x x + a x ) +--R / +--R b n p + b n +--R Type: Expression Integer +--E 261 + +--S 262 of 486 +d0345:= D(m0345,x) +--R +--R +--R (237) +--R n - 1 n - 1 p +--R ----- ----- +--R - n p n p +--R ((a n - a)x + b n p + b n - b)(b x x + a x ) +--R + +--R - p + n - 1 +--R ----------- +--R - n + 1 2 2 p n +--R ((- a b n + a b)x + (- b n + b )x)x x +--R + +--R n - 1 +--R ----- +--R - n + 1 2 p n - 1 +--R (- a b n p x - b n p x)x x +--R + +--R - p + n - 1 +--R ----------- +--R 2 2 - n + 1 p +--R ((- a n + a )x + (- a b n + a b)x)x +--R * +--R n - 1 n - 1 p - 1 +--R ----- ----- +--R p n p +--R (b x x + a x ) +--R / +--R b n p + b n +--R Type: Expression Integer +--E 262 + +--S 263 of 486 +t0346:= 1/(a+b/x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R 1 +--R (238) ---------------------- +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|d x + c +--R | 2 +--R \| x +--R Type: Expression Integer +--E 263 + +--S 264 of 486 +r0346:= (b+a*x^2)^(1/2)*atanh(d^(1/2)*(b+a*x^2)^(1/2)/a^(1/2)/_ + (c+d*x^2)^(1/2))/a^(1/2)/d^(1/2)/(a+b/x^2)^(1/2)/x +--R +--R +--R +--------+ +--R +--------+ +-+ | 2 +--R | 2 \|d \|a x + b +--R \|a x + b atanh(---------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|d x + c +--R (239) --------------------------------- +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R x\|a |-------- \|d +--R | 2 +--R \| x +--R Type: Expression Integer +--E 264 + +--S 265 of 486 +--a0346:= integrate(t0346,x) +--E 265 + +--S 266 of 486 +--m0346:= a0346-r0346 +--E 266 + +--S 267 of 486 +--d0346:= D(m0346,x) +--E 267 + +--S 268 of 486 +t0347:= x^m/(a+b*x^(2+2*m)) +--R +--R +--R m +--R x +--R (240) ------------- +--R 2m + 2 +--R b x + a +--R Type: Expression Integer +--E 268 + +--S 269 of 486 +r0347:= atan(b^(1/2)*x^(1+m)/a^(1/2))/a^(1/2)/b^(1/2)/(1+m) +--R +--R +--R m + 1 +-+ +--R x \|b +--R atan(----------) +--R +-+ +--R \|a +--R (241) ---------------- +--R +-+ +-+ +--R (m + 1)\|a \|b +--R Type: Expression Integer +--E 269 + +--S 270 of 486 +a0347:= integrate(t0347,x) +--R +--R +--R (242) +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R [--------------------------------------------------------------, +--R +-----+ +--R (2m + 2)\|- a b +--R +---+ m log(x) +--R x\|a b %e +--R atan(-----------------) +--R a +--R -----------------------] +--R +---+ +--R (m + 1)\|a b +--R Type: Union(List Expression Integer,...) +--E 270 + +--S 271 of 486 +m0347a:= a0347.1-r0347 +--R +--R +--R (243) +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R +-+ +-+ b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R \|a \|b log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R m + 1 +-+ +--R +-----+ x \|b +--R - 2\|- a b atan(----------) +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R (2m + 2)\|- a b \|a \|b +--R Type: Expression Integer +--E 271 + +--S 272 of 486 +d0347a:= D(m0347a,x) +--R +--R +--R 2 m m log(x) 2 m + 1 2 m log(x) m +--R - b x x (%e ) + (b (x ) + a)%e - a x +--R (244) ---------------------------------------------------------- +--R 2 2 m + 1 2 2 m log(x) 2 m + 1 2 2 +--R (b x (x ) + a b x )(%e ) + a b (x ) + a +--R Type: Expression Integer +--E 272 + +--S 273 of 486 +m0347b:= a0347.2-r0347 +--R +--R +--R +---+ m log(x) m + 1 +-+ +--R +-+ +-+ x\|a b %e +---+ x \|b +--R \|a \|b atan(-----------------) - \|a b atan(----------) +--R a +-+ +--R \|a +--R (245) -------------------------------------------------------- +--R +-+ +-+ +---+ +--R (m + 1)\|a \|b \|a b +--R Type: Expression Integer +--E 273 + +--S 274 of 486 +d0347b:= D(m0347b,x) +--R +--R +--R 2 m m log(x) 2 m + 1 2 m log(x) m +--R - b x x (%e ) + (b (x ) + a)%e - a x +--R (246) ---------------------------------------------------------- +--R 2 2 m + 1 2 2 m log(x) 2 m + 1 2 2 +--R (b x (x ) + a b x )(%e ) + a b (x ) + a +--R Type: Expression Integer +--E 274 + +--S 275 of 486 +t0348:= x^m/(a+b*x^(2+2*m))^2 +--R +--R +--R m +--R x +--R (247) -------------------------------- +--R 2 2m + 2 2 2m + 2 2 +--R b (x ) + 2a b x + a +--R Type: Expression Integer +--E 275 + +--S 276 of 486 +r0348:= 1/2*x^(1+m)/a/(1+m)/(a+b*x^(2+2*m))+1/2*atan(b^(1/2)*x^(1+m)/_ + a^(1/2))/a^(3/2)/b^(1/2)/(1+m) +--R +--R +--R m + 1 +-+ +--R 2m + 2 x \|b m + 1 +-+ +-+ +--R (b x + a)atan(----------) + x \|a \|b +--R +-+ +--R \|a +--R (248) ------------------------------------------------ +--R 2m + 2 2 2 +-+ +-+ +--R ((2a b m + 2a b)x + 2a m + 2a )\|a \|b +--R Type: Expression Integer +--E 276 + +--S 277 of 486 +a0348:= integrate(t0348,x) +--R +--R +--R (249) +--R [ +--R 2 m log(x) 2 +--R (b x (%e ) + a) +--R * +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R +-----+ m log(x) +--R 2x\|- a b %e +--R / +--R 2 +-----+ m log(x) 2 2 2 +-----+ +--R (4a b m + 4a b)x \|- a b (%e ) + (4a m + 4a )\|- a b +--R , +--R +---+ m log(x) +--R 2 m log(x) 2 x\|a b %e +---+ m log(x) +--R (b x (%e ) + a)atan(-----------------) + x\|a b %e +--R a +--R ------------------------------------------------------------------] +--R 2 +---+ m log(x) 2 2 2 +---+ +--R (2a b m + 2a b)x \|a b (%e ) + (2a m + 2a )\|a b +--R Type: Union(List Expression Integer,...) +--E 277 + +--S 278 of 486 +m0348a:= a0348.1-r0348 +--R +--R +--R (250) +--R 2 2 2m + 2 2 +-+ +-+ m log(x) 2 +--R (b x x + a b x )\|a \|b (%e ) +--R + +--R 2m + 2 2 +-+ +-+ +--R (a b x + a )\|a \|b +--R * +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R m + 1 +-+ +--R 2 2 2m + 2 2 +-----+ x \|b +--R (- 2b x x - 2a b x )\|- a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 m + 1 +-----+ +-+ +-+ +--R - 2b x x \|- a b \|a \|b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2m + 2 +-----+ +-+ +-+ m log(x) +--R (2b x x + 2a x)\|- a b \|a \|b %e +--R + +--R m + 1 +-+ +--R 2m + 2 2 +-----+ x \|b m + 1 +-----+ +-+ +-+ +--R (- 2a b x - 2a )\|- a b atan(----------) - 2a x \|- a b \|a \|b +--R +-+ +--R \|a +--R / +--R 2 2 2 2m + 2 2 2 2 +-----+ +-+ +-+ +--R ((4a b m + 4a b )x x + (4a b m + 4a b)x )\|- a b \|a \|b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2 2 2m + 2 3 3 +-----+ +-+ +-+ +--R ((4a b m + 4a b)x + 4a m + 4a )\|- a b \|a \|b +--R Type: Expression Integer +--E 278 + +--S 279 of 486 +d0348a:= D(m0348a,x) +--R +--R +--R (251) +--R 4 4 m 2m + 2 2 4 4 m m + 1 2 3 4 m 2m + 2 +--R - b x x (x ) + (- b x x (x ) - 3a b x x )x +--R + +--R 4 4 m + 1 3 3 4 m + 1 2m + 1 3 4 m m + 1 2 2 2 4 m +--R (2b x (x ) + 2a b x x )x - a b x x (x ) - 2a b x x +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 3 2 m 2m + 2 2 3 2 m m + 1 2 2 2 2 m 2m + 2 +--R - 2a b x x (x ) + (- 2a b x x (x ) - 6a b x x )x +--R + +--R 3 2 m + 1 3 2 2 2 m + 1 2m + 1 2 2 2 m m + 1 2 +--R (4a b x (x ) + 4a b x x )x - 2a b x x (x ) +--R + +--R 3 2 m +--R - 4a b x x +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 3 m + 1 2 2 2 2m + 2 2 2 2 m + 1 2 3 2m + 2 +--R (2a b (x ) + 2a b )(x ) + (4a b (x ) + 4a b)x +--R + +--R 3 m + 1 2 4 +--R 2a b (x ) + 2a +--R * +--R m log(x) +--R %e +--R + +--R 2 2 m 2m + 2 2 2 2 m m + 1 2 3 m 2m + 2 +--R - a b x (x ) + (- a b x (x ) - 3a b x )x +--R + +--R 2 2 m + 1 3 3 m + 1 2m + 1 3 m m + 1 2 4 m +--R (2a b (x ) + 2a b x )x - a b x (x ) - 2a x +--R / +--R 5 4 m + 1 2 2 4 4 2m + 2 2 +--R (2a b x (x ) + 2a b x )(x ) +--R + +--R 2 4 4 m + 1 2 3 3 4 2m + 2 3 3 4 m + 1 2 4 2 4 +--R (4a b x (x ) + 4a b x )x + 2a b x (x ) + 2a b x +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 2 4 2 m + 1 2 3 3 2 2m + 2 2 +--R (4a b x (x ) + 4a b x )(x ) +--R + +--R 3 3 2 m + 1 2 4 2 2 2m + 2 4 2 2 m + 1 2 5 2 +--R (8a b x (x ) + 8a b x )x + 4a b x (x ) + 4a b x +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 3 3 m + 1 2 4 2 2m + 2 2 4 2 m + 1 2 5 2m + 2 +--R (2a b (x ) + 2a b )(x ) + (4a b (x ) + 4a b)x +--R + +--R 5 m + 1 2 6 +--R 2a b (x ) + 2a +--R Type: Expression Integer +--E 279 + +--S 280 of 486 +m0348b:= a0348.2-r0348 +--R +--R +--R (252) +--R 2 2 2m + 2 2 +-+ +-+ m log(x) 2 +--R (b x x + a b x )\|a \|b (%e ) +--R + +--R 2m + 2 2 +-+ +-+ +--R (a b x + a )\|a \|b +--R * +--R +---+ m log(x) +--R x\|a b %e +--R atan(-----------------) +--R a +--R + +--R m + 1 +-+ +--R 2 2 2m + 2 2 +---+ x \|b +--R (- b x x - a b x )\|a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 m + 1 +-+ +-+ +---+ +--R - b x x \|a \|b \|a b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2m + 2 +-+ +-+ +---+ m log(x) +--R (b x x + a x)\|a \|b \|a b %e +--R + +--R m + 1 +-+ +--R 2m + 2 2 +---+ x \|b m + 1 +-+ +-+ +---+ +--R (- a b x - a )\|a b atan(----------) - a x \|a \|b \|a b +--R +-+ +--R \|a +--R / +--R 2 2 2 2m + 2 2 2 2 +-+ +-+ +---+ +--R ((2a b m + 2a b )x x + (2a b m + 2a b)x )\|a \|b \|a b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2 2 2m + 2 3 3 +-+ +-+ +---+ +--R ((2a b m + 2a b)x + 2a m + 2a )\|a \|b \|a b +--R Type: Expression Integer +--E 280 + +--S 281 of 486 +d0348b:= D(m0348b,x) +--R +--R +--R (253) +--R 4 4 m 2m + 2 2 4 4 m m + 1 2 3 4 m 2m + 2 +--R - b x x (x ) + (- b x x (x ) - 3a b x x )x +--R + +--R 4 4 m + 1 3 3 4 m + 1 2m + 1 3 4 m m + 1 2 2 2 4 m +--R (2b x (x ) + 2a b x x )x - a b x x (x ) - 2a b x x +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 3 2 m 2m + 2 2 3 2 m m + 1 2 2 2 2 m 2m + 2 +--R - 2a b x x (x ) + (- 2a b x x (x ) - 6a b x x )x +--R + +--R 3 2 m + 1 3 2 2 2 m + 1 2m + 1 2 2 2 m m + 1 2 +--R (4a b x (x ) + 4a b x x )x - 2a b x x (x ) +--R + +--R 3 2 m +--R - 4a b x x +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 3 m + 1 2 2 2 2m + 2 2 2 2 m + 1 2 3 2m + 2 +--R (2a b (x ) + 2a b )(x ) + (4a b (x ) + 4a b)x +--R + +--R 3 m + 1 2 4 +--R 2a b (x ) + 2a +--R * +--R m log(x) +--R %e +--R + +--R 2 2 m 2m + 2 2 2 2 m m + 1 2 3 m 2m + 2 +--R - a b x (x ) + (- a b x (x ) - 3a b x )x +--R + +--R 2 2 m + 1 3 3 m + 1 2m + 1 3 m m + 1 2 4 m +--R (2a b (x ) + 2a b x )x - a b x (x ) - 2a x +--R / +--R 5 4 m + 1 2 2 4 4 2m + 2 2 +--R (2a b x (x ) + 2a b x )(x ) +--R + +--R 2 4 4 m + 1 2 3 3 4 2m + 2 3 3 4 m + 1 2 4 2 4 +--R (4a b x (x ) + 4a b x )x + 2a b x (x ) + 2a b x +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 2 4 2 m + 1 2 3 3 2 2m + 2 2 +--R (4a b x (x ) + 4a b x )(x ) +--R + +--R 3 3 2 m + 1 2 4 2 2 2m + 2 4 2 2 m + 1 2 5 2 +--R (8a b x (x ) + 8a b x )x + 4a b x (x ) + 4a b x +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 3 3 m + 1 2 4 2 2m + 2 2 4 2 m + 1 2 5 2m + 2 +--R (2a b (x ) + 2a b )(x ) + (4a b (x ) + 4a b)x +--R + +--R 5 m + 1 2 6 +--R 2a b (x ) + 2a +--R Type: Expression Integer +--E 281 + +--S 282 of 486 +t0349:= x^n*(1+x^(1+n))^(1/2) +--R +--R +--R +----------+ +--R n | n + 1 +--R (254) x \|x + 1 +--R Type: Expression Integer +--E 282 + +--S 283 of 486 +r0349:= 2*(1+x^(1+n))^(3/2)/(3+3*n) +--R +--R +--R +----------+ +--R n + 1 | n + 1 +--R (2x + 2)\|x + 1 +--R (255) -------------------------- +--R 3n + 3 +--R Type: Expression Integer +--E 283 + +--S 284 of 486 +a0349:= integrate(t0349,x) +--R +--R +--R +-------------------+ +--R (n + 1)log(x) | (n + 1)log(x) +--R (2%e + 2)\|%e + 1 +--R (256) -------------------------------------------- +--R 3n + 3 +--R Type: Union(Expression Integer,...) +--E 284 + +--S 285 of 486 +m0349:= a0349-r0349 +--R +--R +--R (257) +--R +-------------------+ +----------+ +--R (n + 1)log(x) | (n + 1)log(x) n + 1 | n + 1 +--R (2%e + 2)\|%e + 1 + (- 2x - 2)\|x + 1 +--R --------------------------------------------------------------------------- +--R 3n + 3 +--R Type: Expression Integer +--E 285 + +--S 286 of 486 +d0349:= D(m0349,x) +--R +--R +--R (258) +--R +-------------------+ +--R n n + 1 n | (n + 1)log(x) +--R (- x x x - x x )\|%e + 1 +--R + +--R +----------+ +--R (n + 1)log(x) 2 (n + 1)log(x) | n + 1 +--R ((%e ) + %e )\|x + 1 +--R / +--R +----------+ +-------------------+ +--R | n + 1 | (n + 1)log(x) +--R x\|x + 1 \|%e + 1 +--R Type: Expression Integer +--E 286 + +--S 287 of 486 +t0350:= x^n*(a^2+x^(1+n))^(1/2) +--R +--R +--R +-----------+ +--R n | n + 1 2 +--R (259) x \|x + a +--R Type: Expression Integer +--E 287 + +--S 288 of 486 +r0350:= 2*(a^2+x^(1+n))^(3/2)/(3+3*n) +--R +--R +--R +-----------+ +--R n + 1 2 | n + 1 2 +--R (2x + 2a )\|x + a +--R (260) ----------------------------- +--R 3n + 3 +--R Type: Expression Integer +--E 288 + +--S 289 of 486 +a0350:= integrate(t0350,x) +--R +--R +--R +--------------------+ +--R (n + 1)log(x) 2 | (n + 1)log(x) 2 +--R (2%e + 2a )\|%e + a +--R (261) ----------------------------------------------- +--R 3n + 3 +--R Type: Union(Expression Integer,...) +--E 289 + +--S 290 of 486 +m0350:= a0350-r0350 +--R +--R +--R (262) +--R +--------------------+ +--R (n + 1)log(x) 2 | (n + 1)log(x) 2 +--R (2%e + 2a )\|%e + a +--R + +--R +-----------+ +--R n + 1 2 | n + 1 2 +--R (- 2x - 2a )\|x + a +--R / +--R 3n + 3 +--R Type: Expression Integer +--E 290 + +--S 291 of 486 +d0350:= D(m0350,x) +--R +--R +--R (263) +--R +--------------------+ +--R n n + 1 2 n | (n + 1)log(x) 2 +--R (- x x x - a x x )\|%e + a +--R + +--R +-----------+ +--R (n + 1)log(x) 2 2 (n + 1)log(x) | n + 1 2 +--R ((%e ) + a %e )\|x + a +--R / +--R +-----------+ +--------------------+ +--R | n + 1 2 | (n + 1)log(x) 2 +--R x\|x + a \|%e + a +--R Type: Expression Integer +--E 291 + +--S 292 of 486 +t0351:= x/(4-x^2+(4-x^2)^(1/2)) +--R +--R +--R x +--R (264) -------------------- +--R +--------+ +--R | 2 2 +--R \|- x + 4 - x + 4 +--R Type: Expression Integer +--E 292 + +--S 293 of 486 +r0351:= -log(1+(4-x^2)^(1/2)) +--R +--R +--R +--------+ +--R | 2 +--R (265) - log(\|- x + 4 + 1) +--R Type: Expression Integer +--E 293 + +--S 294 of 486 +a0351:94= integrate(t0351,x) +--R +--R +--RDaly Bug +--R Category, domain or package constructor = is not available. +--E 294 + +--S 295 of 486 +m0351:= a0351-r0351 +--R +--R +--R +--------+ +--R | 2 +--R (266) log(\|- x + 4 + 1) + a0351 +--R Type: Expression Integer +--E 295 + +--S 296 of 486 +d0351:= D(m0351,x) +--R +--R +--R x +--R (267) - -------------------- +--R +--------+ +--R | 2 2 +--R \|- x + 4 - x + 4 +--R Type: Expression Integer +--E 296 + +--S 297 of 486 +t0352:= ((b-x)*(-a+x))^(1/2) +--R +--R +--R +---------------------+ +--R | 2 +--R (268) \|- x + (b + a)x - a b +--R Type: Expression Integer +--E 297 + +--S 298 of 486 +r0352:= -1/4*(a+b-2*x)*(-a*b+a*x+b*x-x^2)^(1/2)-1/8*(4*a*b-(a+b)^2)*_ + atan(2*(-a*b+a*x+b*x-x^2)^(1/2)/(a+b-2*x)) +--R +--R +--R (269) +--R +---------------------+ +--R | 2 +--R 2 2 2\|- x + (b + a)x - a b +--R (- b + 2a b - a )atan(-------------------------) +--R 2x - b - a +--R + +--R +---------------------+ +--R | 2 +--R (4x - 2b - 2a)\|- x + (b + a)x - a b +--R / +--R 8 +--R Type: Expression Integer +--E 298 + +--S 299 of 486 +a0352:= integrate(t0352,x) +--R +--R +--R (270) +--R 3 2 2 3 3 2 2 3 +--R ((4b - 4a b - 4a b + 4a )x - 8a b + 16a b - 8a b) +--R * +--R +---------------------+ +--R | 2 +-----+ +--R \|- x + (b + a)x - a b \|- a b +--R + +--R 4 3 2 2 3 4 2 +--R (- b - 4a b + 10a b - 4a b - a )x +--R + +--R 4 2 3 3 2 4 2 4 3 3 4 2 +--R (8a b - 8a b - 8a b + 8a b)x - 8a b + 16a b - 8a b +--R * +--R +---------------------+ +--R +-----+ | 2 +--R \|- a b - \|- x + (b + a)x - a b +--R atan(-----------------------------------) +--R x +--R + +--R 4 2 2 3 +--R (- 8b - 8a)x + (12b + 40a b + 12a )x +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 3b - 37a b - 37a b - 3a )x + (4a b + 24a b + 4a b)x +--R * +--R +-----+ +--R \|- a b +--R + +--R 2 2 3 3 2 2 3 2 +--R (- 2b - 12a b - 2a )x + (b + 23a b + 23a b + a )x +--R + +--R 3 2 2 3 +--R (- 4a b - 24a b - 4a b)x +--R * +--R +---------------------+ +--R | 2 +--R \|- x + (b + a)x - a b +--R / +--R +---------------------+ +--R | 2 +-----+ +--R ((16b + 16a)x - 32a b)\|- x + (b + a)x - a b \|- a b +--R + +--R 2 2 2 2 2 2 2 +--R (- 4b - 24a b - 4a )x + (32a b + 32a b)x - 32a b +--R Type: Union(Expression Integer,...) +--E 299 + +--S 300 of 486 +m0352:= a0352-r0352 +--R +--R +--R (271) +--R 3 2 2 3 3 2 2 3 +--R ((8b - 8a b - 8a b + 8a )x - 16a b + 32a b - 16a b) +--R * +--R +---------------------+ +--R | 2 +-----+ +--R \|- x + (b + a)x - a b \|- a b +--R + +--R 4 3 2 2 3 4 2 +--R (- 2b - 8a b + 20a b - 8a b - 2a )x +--R + +--R 4 2 3 3 2 4 2 4 3 3 4 2 +--R (16a b - 16a b - 16a b + 16a b)x - 16a b + 32a b - 16a b +--R * +--R +---------------------+ +--R +-----+ | 2 +--R \|- a b - \|- x + (b + a)x - a b +--R atan(-----------------------------------) +--R x +--R + +--R 3 2 2 3 3 2 2 3 +--R ((4b - 4a b - 4a b + 4a )x - 8a b + 16a b - 8a b) +--R * +--R +---------------------+ +--R | 2 +-----+ +--R \|- x + (b + a)x - a b \|- a b +--R + +--R 4 3 2 2 3 4 2 +--R (- b - 4a b + 10a b - 4a b - a )x +--R + +--R 4 2 3 3 2 4 2 4 3 3 4 2 +--R (8a b - 8a b - 8a b + 8a b)x - 8a b + 16a b - 8a b +--R * +--R +---------------------+ +--R | 2 +--R 2\|- x + (b + a)x - a b +--R atan(-------------------------) +--R 2x - b - a +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (2b + 14a b + 14a b + 2a )x + (- 16a b - 32a b - 16a b)x +--R + +--R 2 3 3 2 +--R 16a b + 16a b +--R * +--R +-----+ +--R \|- a b +--R + +--R +---------------------+ +--R 3 2 2 3 2 3 3 2 | 2 +--R ((8a b + 16a b + 8a b)x - 16a b - 16a b )\|- x + (b + a)x - a b +--R / +--R +---------------------+ +--R | 2 +-----+ +--R ((32b + 32a)x - 64a b)\|- x + (b + a)x - a b \|- a b +--R + +--R 2 2 2 2 2 2 2 +--R (- 8b - 48a b - 8a )x + (64a b + 64a b)x - 64a b +--R Type: Expression Integer +--E 300 + +--S 301 of 486 +d0352:= D(m0352,x) +--R +--R +--R (272) 0 +--R Type: Expression Integer +--E 301 + +--S 302 of 486 +t0353:= 1/((1+x)^(1/4)+(1+x)^(1/2)) +--R +--R +--R 1 +--R (273) ------------------- +--R 4+-----+ +-----+ +--R \|x + 1 + \|x + 1 +--R Type: Expression Integer +--E 302 + +--S 303 of 486 +r0353:= -4*(1+x)^(1/4)+2*(1+x)^(1/2)+4*log(1+(1+x)^(1/4)) +--R +--R +--R 4+-----+ 4+-----+ +-----+ +--R (274) 4log(\|x + 1 + 1) - 4\|x + 1 + 2\|x + 1 +--R Type: Expression Integer +--E 303 + +--S 304 of 486 +a0353:= integrate(t0353,x) +--R +--R +--R 4+-----+ 4+-----+2 4+-----+ +--R (275) 4log(\|x + 1 + 1) + 2\|x + 1 - 4\|x + 1 +--R Type: Union(Expression Integer,...) +--E 304 + +--S 305 of 486 +m0353:= a0353-r0353 +--R +--R +--R 4+-----+2 +-----+ +--R (276) 2\|x + 1 - 2\|x + 1 +--R Type: Expression Integer +--E 305 + +--S 306 of 486 +d0353:= D(m0353,x) +--R +--R +--R 4+-----+2 +-----+ +--R - \|x + 1 + \|x + 1 +--R (277) ---------------------- +--R +-----+4+-----+2 +--R \|x + 1 \|x + 1 +--R Type: Expression Integer +--E 306 + +--S 307 of 486 +t0354:= 1/(1+x^(2/3)) +--R +--R +--R 1 +--R (278) --------- +--R 3+-+2 +--R \|x + 1 +--R Type: Expression Integer +--E 307 + +--S 308 of 486 +r0354:= 3*x^(1/3)-3*atan(x^(1/3)) +--R +--R +--R 3+-+ 3+-+ +--R (279) - 3atan(\|x ) + 3\|x +--R Type: Expression Integer +--E 308 + +--S 309 of 486 +a0354:= integrate(t0354,x) +--R +--R +--R 3+-+ 3+-+ +--R (280) - 3atan(\|x ) + 3\|x +--R Type: Union(Expression Integer,...) +--E 309 + +--S 310 of 486 +m0354:= a0354-r0354 +--R +--R +--R (281) 0 +--R Type: Expression Integer +--E 310 + +--S 311 of 486 +d0354:= D(m0354,x) +--R +--R +--R (282) 0 +--R Type: Expression Integer +--E 311 + +--S 312 of 486 +t0355:= 1/(1+x^(1/5)) +--R +--R +--R 1 +--R (283) -------- +--R 5+-+ +--R \|x + 1 +--R Type: Expression Integer +--E 312 + +--S 313 of 486 +r0355:= -5*x^(1/5)+5/2*x^(2/5)-5/3*x^(3/5)+5/4*x^(4/5)+5*log(1+x^(1/5)) +--R +--R +--R 5+-+ 5+-+4 5+-+3 5+-+2 5+-+ +--R 60log(\|x + 1) + 15\|x - 20\|x + 30\|x - 60\|x +--R (284) ------------------------------------------------------ +--R 12 +--R Type: Expression Integer +--E 313 + +--S 314 of 486 +a0355:= integrate(t0355,x) +--R +--R +--R 5+-+ 5+-+4 5+-+3 5+-+2 5+-+ +--R 60log(\|x + 1) + 15\|x - 20\|x + 30\|x - 60\|x +--R (285) ------------------------------------------------------ +--R 12 +--R Type: Union(Expression Integer,...) +--E 314 + +--S 315 of 486 +m0355:= a0355-r0355 +--R +--R +--R (286) 0 +--R Type: Expression Integer +--E 315 + +--S 316 of 486 +d0355:= D(m0355,x) +--R +--R +--R (287) 0 +--R Type: Expression Integer +--E 316 + +--S 317 of 486 +t0356:= (1+x^(1/2))/(1+x^(1/3))/x^(1/2) +--R +--R +--R +-+ +--R \|x + 1 +--R (288) --------------- +--R +-+3+-+ +-+ +--R \|x \|x + \|x +--R Type: Expression Integer +--E 317 + +--S 318 of 486 +r0356:= 6*x^(1/6)-3*x^(1/3)+3/2*x^(2/3)-6*atan(x^(1/6))+3*log(1+x^(1/3)) +--R +--R +--R 3+-+ 6+-+ 6+-+ 3+-+2 3+-+ +--R 6log(\|x + 1) - 12atan(\|x ) + 12\|x + 3\|x - 6\|x +--R (289) ------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 318 + +--S 319 of 486 +a0356:= integrate(t0356,x) +--R +--R +--R 6+-+2 6+-+ 6+-+4 6+-+2 6+-+ +--R 6log(\|x + 1) - 12atan(\|x ) + 3\|x - 6\|x + 12\|x +--R (290) --------------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 319 + +--S 320 of 486 +m0356:= a0356-r0356 +--R +--R +--R 6+-+2 3+-+ 6+-+4 6+-+2 3+-+2 3+-+ +--R 6log(\|x + 1) - 6log(\|x + 1) + 3\|x - 6\|x - 3\|x + 6\|x +--R (291) ------------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 320 + +--S 321 of 486 +d0356:= D(m0356,x) +--R +--R +--R 6+-+2 3+-+ +--R - \|x + \|x +--R (292) -------------------------- +--R 3+-+ 6+-+2 3+-+ +--R (\|x + 1)\|x + \|x + 1 +--R Type: Expression Integer +--E 321 + +--S 322 of 486 +t0357:= 1/(1+x^(1/3)) +--R +--R +--R 1 +--R (293) -------- +--R 3+-+ +--R \|x + 1 +--R Type: Expression Integer +--E 322 + +--S 323 of 486 +r0357:= -3*x^(1/3)+3/2*x^(2/3)+3*log(1+x^(1/3)) +--R +--R +--R 3+-+ 3+-+2 3+-+ +--R 6log(\|x + 1) + 3\|x - 6\|x +--R (294) ------------------------------- +--R 2 +--R Type: Expression Integer +--E 323 + +--S 324 of 486 +a0357:= integrate(t0357,x) +--R +--R +--R 3+-+ 3+-+2 3+-+ +--R 6log(\|x + 1) + 3\|x - 6\|x +--R (295) ------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 324 + +--S 325 of 486 +m0357:= a0357-r0357 +--R +--R +--R (296) 0 +--R Type: Expression Integer +--E 325 + +--S 326 of 486 +d0357:= D(m0357,x) +--R +--R +--R (297) 0 +--R Type: Expression Integer +--E 326 + +--S 327 of 486 +t0358:= 1/(-7+2*x+5*x^2)^(1/2)/(8+12*x+5*x^2) +--R +--R +--R 1 +--R (298) ------------------------------ +--R +------------+ +--R 2 | 2 +--R (5x + 12x + 8)\|5x + 2x - 7 +--R Type: Expression Integer +--E 327 + +--S 328 of 486 +r0358:= (1/20+1/10*%i)*atan((40+20*%i)*(-7+2*x+5*x^2)^(1/2)/(-164+8*%i+_ + (-100+40*%i)*x))-(1/10+1/20*%i)*atanh((20+40*%i)*(-7+2*x+_ + 5*x^2)^(1/2)/(-164-8*%i-(100+40*%i)*x)) +--R +--R +--R (299) +--R +------------+ +--R 9 8 | 2 +--R (-- + -- %i)\|5x + 2x - 7 +--R 1 1 29 29 +--R (-- + -- %i)atanh(---------------------------) +--R 10 20 209 72 +--R x + --- - --- %i +--R 145 145 +--R + +--R +------------+ +--R 8 9 | 2 +--R (-- + -- %i)\|5x + 2x - 7 +--R 1 1 29 29 +--R (- -- - -- %i)atan(---------------------------) +--R 20 10 209 72 +--R x + --- + --- %i +--R 145 145 +--R Type: Expression Complex Fraction Integer +--E 328 + +--S 329 of 486 +a0358:= integrate(t0358,x) +--R +--R +--R (300) +--R +------------+ +--R | 2 2 +--R (5x + 5)\|5x + 2x - 7 + 15x + 26x + 9 +--R log(----------------------------------------) +--R 2 +--R x +--R + +--R +------------+ +--R | 2 2 +--R (- 5x - 5)\|5x + 2x - 7 + 15x + 26x + 9 +--R - log(------------------------------------------) +--R 2 +--R x +--R + +--R +------------+ +------------+ +--R | 2 | 2 +--R 5\|5x + 2x - 7 - x + 7 5\|5x + 2x - 7 + x - 7 +--R atan(---------------------------) - atan(---------------------------) +--R +------------+ +------------+ +--R | 2 | 2 +--R 5\|5x + 2x - 7 - 17x - 25 5\|5x + 2x - 7 + 17x + 25 +--R / +--R 20 +--R Type: Union(Expression Integer,...) +--E 329 + +--S 330 of 486 +m0358:= a0358-r0358 +--R +--R +--R (301) +--R +------------+ +--R | 2 2 +--R 1 (5x + 5)\|5x + 2x - 7 + 15x + 26x + 9 +--R -- log(----------------------------------------) +--R 20 2 +--R x +--R + +--R +------------+ +--R | 2 2 +--R 1 (- 5x - 5)\|5x + 2x - 7 + 15x + 26x + 9 +--R - -- log(------------------------------------------) +--R 20 2 +--R x +--R + +--R +------------+ +--R 9 8 | 2 +--R (-- + -- %i)\|5x + 2x - 7 +--R 1 1 29 29 +--R (- -- - -- %i)atanh(---------------------------) +--R 10 20 209 72 +--R x + --- - --- %i +--R 145 145 +--R + +--R +------------+ +--R 8 9 | 2 +--R (-- + -- %i)\|5x + 2x - 7 +--R 1 1 29 29 +--R (-- + -- %i)atan(---------------------------) +--R 20 10 209 72 +--R x + --- + --- %i +--R 145 145 +--R + +--R +------------+ +------------+ +--R | 2 1 7 | 2 1 7 +--R \|5x + 2x - 7 - - x + - \|5x + 2x - 7 + - x - - +--R 1 5 5 1 5 5 +--R -- atan(--------------------------) - -- atan(--------------------------) +--R 20 +------------+ 20 +------------+ +--R | 2 17 | 2 17 +--R \|5x + 2x - 7 - -- x - 5 \|5x + 2x - 7 + -- x + 5 +--R 5 5 +--R Type: Expression Complex Fraction Integer +--E 330 + +--S 331 of 486 +d0358:= D(m0358,x) +--R +--R +--R (302) 0 +--R Type: Expression Complex Fraction Integer +--E 331 + +--S 332 of 486 +t0359:= (x^(1/6)+(x^3)^(1/5))/x^(1/2) +--R +--R +--R +--+ +--R 5| 3 6+-+ +--R \|x + \|x +--R (303) ------------ +--R +-+ +--R \|x +--R Type: Expression Integer +--E 332 + +--S 333 of 486 +r0359:= 3/2*x^(2/3)+10/11*x^(1/2)*(x^3)^(1/5) +--R +--R +--R +--+ +--R +-+5| 3 3+-+2 +--R 20\|x \|x + 33\|x +--R (304) --------------------- +--R 22 +--R Type: Expression Integer +--E 333 + +--S 334 of 486 +--a0359:= integrate(t0359,x) +--E 334 + +--S 335 of 486 +--m0359:= a0359-r0359 +--E 335 + +--S 336 of 486 +--d0359:= D(m0359,x) +--E 336 + +--S 337 of 486 +t0360:= 1/(4+x+(1+x)^(1/2)) +--R +--R +--R 1 +--R (305) ---------------- +--R +-----+ +--R \|x + 1 + x + 4 +--R Type: Expression Integer +--E 337 + +--S 338 of 486 +r0360:= -2/11*atan(1/11*(1+2*(1+x)^(1/2))*11^(1/2))*11^(1/2)+_ + log(4+x+(1+x)^(1/2)) +--R +--R +--R +--+ +-----+ +--+ +--R +-----+ +--+ 2\|11 \|x + 1 + \|11 +--R 11log(\|x + 1 + x + 4) - 2\|11 atan(----------------------) +--R 11 +--R (306) ------------------------------------------------------------ +--R 11 +--R Type: Expression Integer +--E 338 + +--S 339 of 486 +a0360:= integrate(t0360,x) +--R +--R +--R +--+ +-----+ +--+ +--R +--+ +-----+ 2\|11 \|x + 1 + \|11 +--R \|11 log(\|x + 1 + x + 4) - 2atan(----------------------) +--R 11 +--R (307) ---------------------------------------------------------- +--R +--+ +--R \|11 +--R Type: Union(Expression Integer,...) +--E 339 + +--S 340 of 486 +m0360:= a0360-r0360 +--R +--R +--R (308) 0 +--R Type: Expression Integer +--E 340 + +--S 341 of 486 +d0360:= D(m0360,x) +--R +--R +--R (309) 0 +--R Type: Expression Integer +--E 341 + +--S 342 of 486 +t0361:= 1/(-1/x^(1/3)+x^(1/2)) +--R +--R +--R 3+-+ +--R \|x +--R (310) ------------ +--R +-+3+-+ +--R \|x \|x - 1 +--R Type: Expression Integer +--E 342 + +--S 343 of 486 +r0361:= 2*x^(1/2)+6*2^(1/2)/(25+5*5^(1/2))^(1/2)*atan((1-5^(1/2)+_ + 4*x^(1/6))/(10+2*5^(1/2))^(1/2))-6*2^(1/2)/(25-5*5^(1/2))^(1/2)*_ + atan((1+5^(1/2)+4*x^(1/6))/(10-2*5^(1/2))^(1/2))+6/5*log(1-x^(1/6))-_ + 3/10*(5^(1/2)+1)*log(2+(1-5^(1/2))*x^(1/6)+2*x^(1/3))-_ + 3/10*(1-5^(1/2))*log(2+(5^(1/2)+1)*x^(1/6)+2*x^(1/3)) +--R +--R +--R (311) +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (15\|5 - 15)log((\|5 + 1)\|x + 2\|x + 2) + 60log(- \|x + 1) +--R + +--R +-+ +-+ 6+-+ 3+-+ +--R (- 15\|5 - 15)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +------------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x + \|5 + 1 +--R (- 3\|2 \|5 - 15\|2 )\|- 5\|5 + 25 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +----------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x - \|5 + 1 +-+ +--R (- 3\|2 \|5 + 15\|2 )\|5\|5 + 25 atan(----------------) + 100\|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R 50 +--R Type: Expression Integer +--E 343 + +--S 344 of 486 +a0361:= integrate(t0361,x) +--R +--R +--R (312) +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--I - 5%%KV1 - 5%%KV0 - 6 +--R * +--R log +--I (5%%KV1 + 5%%KV0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%KV1 + 25%%KV0 + 72\|x + 36 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--I - 5%%KV1 - 5%%KV0 - 6 +--R * +--R log +--I (- 5%%KV1 - 5%%KV0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%KV1 + 25%%KV0 + 72\|x + 36 +--R + +--R 2 6+-+ 6+-+ +--I 10%%KV1 log(- 25%%KV1 + 36\|x ) + 12log(\|x - 1) +--R + +--R 2 6+-+ 6+-+3 +--I 10%%KV0 log(- 25%%KV0 + 36\|x ) + 20\|x +--R / +--R 10 +--R Type: Union(Expression Integer,...) +--E 344 + +--S 345 of 486 +m0361:= a0361-r0361 +--R +--R +--R (313) +--R +-------------------------------------------------------------+ +--R | 2 2 +--I 5\|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--I - 25%%KV1 - 25%%KV0 - 30 +--R * +--R log +--I (5%%KV1 + 5%%KV0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%KV1 + 25%%KV0 + 72\|x + 36 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - 5\|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--I - 25%%KV1 - 25%%KV0 - 30 +--R * +--R log +--I (- 5%%KV1 - 5%%KV0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%KV1 + 25%%KV0 + 72\|x + 36 +--R + +--R 2 6+-+ +--I 50%%KV1 log(- 25%%KV1 + 36\|x ) +--R + +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (- 15\|5 + 15)log((\|5 + 1)\|x + 2\|x + 2) + 60log(\|x - 1) +--R + +--R 6+-+ +-+ +-+ 6+-+ 3+-+ +--R - 60log(- \|x + 1) + (15\|5 + 15)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R 2 6+-+ +--I 50%%KV0 log(- 25%%KV0 + 36\|x ) +--R + +--R +------------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x + \|5 + 1 +--R (3\|2 \|5 + 15\|2 )\|- 5\|5 + 25 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +----------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x - \|5 + 1 6+-+3 +--R (3\|2 \|5 - 15\|2 )\|5\|5 + 25 atan(----------------) + 100\|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R + +--R +-+ +--R - 100\|x +--R / +--R 50 +--R Type: Expression Integer +--E 345 + +--S 346 of 486 +d0361:= D(m0361,x) +--R +--R +--R (314) +--R +-+ +-+ +-+ +-+3+-+2 2 +-+ +-+ 2 +-+ +-+ 6+-+5 +--R ((2x\|2 \|5 - 10x\|2 )\|x \|x + (x \|2 \|5 - 5x \|2 )\|x )\|x +--R + +--R +-+ +-+ +-+ +-+3+-+2 +--R (x\|2 \|5 - 5x\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((x + 4x)\|2 \|5 + (- 5x - 10x)\|2 )\|x \|x +--R * +--R 6+-+4 +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((- x - x)\|2 \|5 + (5x - 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((- 4x - 5x)\|2 \|5 + (10x + 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +--R (x \|2 \|5 - 5x \|2 )\|x +--R * +--R 6+-+3 +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((x - 3x)\|2 \|5 + (5x + 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((5x + x)\|2 \|5 + (- 5x - 5x)\|2 )\|x \|x +--R + +--R 3 2 +-+ +-+ 3 2 +-+ +-+ +--R ((- x - 3x )\|2 \|5 + (5x + 5x )\|2 )\|x +--R * +--R 6+-+2 +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((3x + 5x)\|2 \|5 + (- 5x - 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((- x + 2x)\|2 \|5 + 5x \|2 )\|x \|x +--R + +--R 3 2 +-+ +-+ 3 2 +-+ +-+ +--R ((3x + 3x )\|2 \|5 + (- 5x - 5x )\|2 )\|x +--R * +--R 6+-+ +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((- 5x - 2x)\|2 \|5 + (5x + 10x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ +-+ +-+3+-+ +--R ((- 2x - x)\|2 \|5 + 5x\|2 )\|x \|x +--R + +--R 3 2 +-+ +-+ 3 2 +-+ +-+ +--R ((- 3x - x )\|2 \|5 + (5x + 5x )\|2 )\|x +--R * +--R +----------+ +----------+ +--R | +-+ | +-+ +--R \|2\|5 + 10 \|5\|5 + 25 +--R + +--R +------------+ +------------+ +--R +-+ +-+ +-+ | +-+ | +-+ +--R (2x\|2 \|5 + 10x\|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 + 400x +--R + +--R - 80 +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R - 800x + 800x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 +-+ 3 2 3+-+ +--R ((- 40x - 80x)\|x - 400x - 800x + 400x)\|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ | +-+ 2 +--R ((x \|2 \|5 + 5x \|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 + 80x - 80x) +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R 400x +--R * +--R 6+-+5 +--R \|x +--R + +--R +------------+ +------------+ +--R +-+ +-+ +-+ | +-+ | +-+ 2 +--R (x\|2 \|5 + 5x\|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 - 80x +--R + +--R - 80x +--R * +--R +-+ +--R \|x +--R + +--R 3 2 +--R 400x - 1600x +--R * +--R 3+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((x + 4x)\|2 \|5 + (5x + 10x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R 80x - 80x +--R * +--R +-+ +--R \|x +--R + +--R 3 2 +--R 400x - 800x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 +-+ 3 +--R 80x \|x - 800x +--R * +--R 6+-+4 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((- x - x)\|2 \|5 + (- 5x + 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R 160x - 240x +--R * +--R +-+ +--R \|x +--R + +--R 3 +--R 800x +--R * +--R 3+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((- 4x - 5x)\|2 \|5 + (- 10x - 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R - 320x - 80x +--R * +--R +-+ +--R \|x +--R + +--R 3 +--R 400x +--R * +--R 3+-+ +--R \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ | +-+ 2 +-+ +--R ((x \|2 \|5 + 5x \|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 - 80x )\|x +--R + +--R 4 +--R 400x +--R * +--R 6+-+3 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((x - 3x)\|2 \|5 + (- 5x - 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R 640x - 240x +--R * +--R +-+3+-+2 +--R \|x \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((5x + x)\|2 \|5 + (5x + 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R 400x + 480x - 80x +--R * +--R +-+3+-+ +--R \|x \|x +--R + +--R +------------+ +--R 3 2 +-+ +-+ 3 2 +-+ | +-+ +--R ((- x - 3x )\|2 \|5 + (- 5x - 5x )\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R 80x - 80x +--R * +--R +-+ +--R \|x +--R * +--R 6+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((3x + 5x)\|2 \|5 + (5x + 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 400x + 1040x - 240x +--R * +--R +-+3+-+2 +--R \|x \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ | +-+ +--R ((- x + 2x)\|2 \|5 - 5x \|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 400x + 480x - 120x +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R - 400x +--R * +--R 3+-+ +--R \|x +--R + +--R +------------+ +--R 3 2 +-+ +-+ 3 2 +-+ | +-+ +--R ((3x + 3x )\|2 \|5 + (5x + 5x )\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R 480x - 80x +--R * +--R +-+ +--R \|x +--R * +--R 6+-+ +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((- 5x - 2x)\|2 \|5 + (- 5x - 10x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 800x + 240x - 320x +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R 400x +--R * +--R 3+-+2 +--R \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ +-+ | +-+ | +-+ +--R ((- 2x - x)\|2 \|5 - 5x\|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 400x + 160x +--R * +--R +-+ +--R \|x +--R + +--R 3 2 +--R 800x + 400x +--R * +--R 3+-+ +--R \|x +--R + +--R +------------+ +--R 3 2 +-+ +-+ 3 2 +-+ | +-+ +--R ((- 3x - x )\|2 \|5 + (- 5x - 5x )\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 4 3 2 +--R - 400x + 80x - 80x +--R * +--R +-+ +--R \|x +--R / +--R 2 +-+3+-+2 3 2 +-+3+-+ 2 +-+ +--R ((800x - 800x)\|x \|x + (400x + 800x - 400x)\|x \|x - 400x \|x ) +--R * +--R 6+-+5 +--R \|x +--R + +--R 3 2 +-+3+-+2 3 2 +-+3+-+ 3 +-+ +--R ((- 400x + 1600x )\|x \|x + (- 400x + 800x )\|x \|x + 800x \|x ) +--R * +--R 6+-+4 +--R \|x +--R + +--R 3 +-+3+-+2 3 +-+3+-+ 4 +-+ 6+-+3 2 +-+3+-+6+-+ +--R (- 800x \|x \|x - 400x \|x \|x - 400x \|x )\|x + 400x \|x \|x \|x +--R + +--R 2 +-+3+-+2 3 2 +-+3+-+ +--R - 400x \|x \|x + (- 800x - 400x )\|x \|x +--R Type: Expression Integer +--E 346 + +--S 347 of 486 +t0362:= x^(1/2)/(-1/x^(1/3)+x^(1/2)) +--R +--R +--R +-+3+-+ +--R \|x \|x +--R (315) ------------ +--R +-+3+-+ +--R \|x \|x - 1 +--R Type: Expression Integer +--E 347 + +--S 348 of 486 +r0362:= 6*x^(1/6)+x-3/5*(10+2*5^(1/2))^(1/2)*atan((1-5^(1/2)+_ + 4*x^(1/6))/(10+2*5^(1/2))^(1/2))-3/5*(10-2*5^(1/2))^(1/2)*_ + atan((1+5^(1/2)+4*x^(1/6))/(10-2*5^(1/2))^(1/2))+_ + 6/5*log(1-x^(1/6))-3/10*(1-5^(1/2))*log(2+(1-5^(1/2))*x^(1/6)+_ + 2*x^(1/3))-3/10*(5^(1/2)+1)*log(2+(5^(1/2)+1)*x^(1/6)+2*x^(1/3)) +--R +--R +--R (316) +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (- 3\|5 - 3)log((\|5 + 1)\|x + 2\|x + 2) + 12log(- \|x + 1) +--R + +--R +-+ +-+ 6+-+ 3+-+ +--R (3\|5 - 3)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +------------+ 6+-+ +-+ +--R | +-+ 4\|x + \|5 + 1 +--R - 6\|- 2\|5 + 10 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +----------+ 6+-+ +-+ +--R | +-+ 4\|x - \|5 + 1 6+-+ +--R - 6\|2\|5 + 10 atan(----------------) + 60\|x + 10x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R 10 +--R Type: Expression Integer +--E 348 + +--S 349 of 486 +a0362:= integrate(t0362,x) +--R +--R +--R (317) +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--I - 5%%KW1 - 5%%KW0 - 6 +--R * +--R log +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--R 6+-+ +--I 5%%KW1 + 5%%KW0 + 12\|x + 6 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--I - 5%%KW1 - 5%%KW0 - 6 +--R * +--R log +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--R 6+-+ +--I 5%%KW1 + 5%%KW0 + 12\|x + 6 +--R + +--R 6+-+ 6+-+ +--I 10%%KW1 log(- 5%%KW1 + 6\|x ) + 12log(\|x - 1) +--R + +--R 6+-+ 6+-+ +--I 10%%KW0 log(- 5%%KW0 + 6\|x ) + 60\|x + 10x +--R / +--R 10 +--R Type: Union(Expression Integer,...) +--E 349 + +--S 350 of 486 +m0362:= a0362-r0362 +--R +--R +--R (318) +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--I - 5%%KW1 - 5%%KW0 - 6 +--R * +--R log +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--R 6+-+ +--I 5%%KW1 + 5%%KW0 + 12\|x + 6 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--I - 5%%KW1 - 5%%KW0 - 6 +--R * +--R log +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--R 6+-+ +--I 5%%KW1 + 5%%KW0 + 12\|x + 6 +--R + +--R 6+-+ +--I 10%%KW1 log(- 5%%KW1 + 6\|x ) +--R + +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (3\|5 + 3)log((\|5 + 1)\|x + 2\|x + 2) + 12log(\|x - 1) +--R + +--R 6+-+ +-+ +-+ 6+-+ 3+-+ +--R - 12log(- \|x + 1) + (- 3\|5 + 3)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +------------+ 6+-+ +-+ +--R 6+-+ | +-+ 4\|x + \|5 + 1 +--I 10%%KW0 log(- 5%%KW0 + 6\|x ) + 6\|- 2\|5 + 10 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +----------+ 6+-+ +-+ +--R | +-+ 4\|x - \|5 + 1 +--R 6\|2\|5 + 10 atan(----------------) +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R 10 +--R Type: Expression Integer +--E 350 + +--S 351 of 486 +d0362:= D(m0362,x) +--R +--R +--R (319) +--R 3+-+2 3+-+ 2 6+-+5 +--R ((- 4x - 6)\|x + (- 3x - 7)\|x - 3x - 2x)\|x +--R + +--R 3+-+2 3+-+ 2 6+-+4 +--R ((6x - 1)\|x + (7x + 2)\|x + 2x - 2x)\|x +--R + +--R 3+-+2 3+-+ 2 6+-+3 +--R ((x + 7)\|x - x\|x + 2x + 3x)\|x +--R + +--R 3+-+2 2 3+-+ 2 6+-+2 +--R ((- 10x - 2)\|x + (- x - 2x)\|x - 3x - 2x)\|x +--R + +--R 2 3+-+2 2 3+-+ 2 6+-+ 2 3+-+2 +--R ((3x + 3x)\|x + (2x + 3x)\|x + 2x )\|x + (- x + 4x)\|x +--R + +--R 2 3+-+ 2 +--R (- 3x + 3x)\|x + 3x +--R / +--R 3+-+6+-+4 3+-+2 2 3+-+ 6+-+3 +--R 10x\|x \|x + (- 10x \|x + (- 20x - 10x)\|x )\|x +--R + +--R 2 3+-+2 3 2 3+-+ 2 6+-+2 +--R ((20x - 20x)\|x + (10x + 20x - 10x)\|x - 10x )\|x +--R + +--R 3 2 3+-+2 3 2 3+-+ 3 6+-+ 3 3+-+2 +--R ((- 10x + 40x )\|x + (- 10x + 20x )\|x + 20x )\|x - 20x \|x +--R + +--R 3 3+-+ 4 +--R - 10x \|x - 10x +--R Type: Expression Integer +--E 351 + +--S 352 of 486 +t0363:= 1/(1+2*x)/(x+x^2)^(1/2) +--R +--R +--R 1 +--R (320) ----------------- +--R +------+ +--R | 2 +--R (2x + 1)\|x + x +--R Type: Expression Integer +--E 352 + +--S 353 of 486 +r0363:= atan(2*(x+x^2)^(1/2)) +--R +--R +--R +------+ +--R | 2 +--R (321) atan(2\|x + x ) +--R Type: Expression Integer +--E 353 + +--S 354 of 486 +a0363:= integrate(t0363,x) +--R +--R +--R +------+ +--R | 2 +--R (322) 2atan(2\|x + x - 2x - 1) +--R Type: Union(Expression Integer,...) +--E 354 + +--S 355 of 486 +m0363:= a0363-r0363 +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (323) - atan(2\|x + x ) + 2atan(2\|x + x - 2x - 1) +--R Type: Expression Integer +--E 355 + +--S 356 of 486 +d0363:= D(m0363,x) +--R +--R +--R (324) 0 +--R Type: Expression Integer +--E 356 + +--S 357 of 486 +t0364:= 1/(2+(1+x^(1/2))^(1/2))^(1/2) +--R +--R +--R 1 +--R (325) ------------------ +--R +---------------+ +--R | +--------+ +--R | | +-+ +--R \|\|\|x + 1 + 2 +--R Type: Expression Integer +--E 357 + +--S 358 of 486 +r0364:= -48*(2+(1+x^(1/2))^(1/2))^(1/2)+88/3*(2+(1+x^(1/2))^(1/2))^(3/2)-_ + 48/5*(2+(1+x^(1/2))^(1/2))^(5/2)+8/7*(2+(1+x^(1/2))^(1/2))^(7/2) +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R +-+ | +-+ +-+ | | +-+ +--R ((120\|x + 608)\|\|x + 1 - 288\|x - 2240)\|\|\|x + 1 + 2 +--R (326) --------------------------------------------------------------- +--R 105 +--R Type: Expression Integer +--E 358 + +--S 359 of 486 +a0364:= integrate(t0364,x) +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R +-+ | +-+ +-+ | | +-+ +--R ((120\|x + 608)\|\|x + 1 - 288\|x - 2240)\|\|\|x + 1 + 2 +--R (327) --------------------------------------------------------------- +--R 105 +--R Type: Union(Expression Integer,...) +--E 359 + +--S 360 of 486 +m0364:= a0364-r0364 +--R +--R +--R (328) 0 +--R Type: Expression Integer +--E 360 + +--S 361 of 486 +d0364:= D(m0364,x) +--R +--R +--R (329) 0 +--R Type: Expression Integer +--E 361 + +--S 362 of 486 +t0365:= x^(1/2)/(-1+x) +--R +--R +--R +-+ +--R \|x +--R (330) ----- +--R x - 1 +--R Type: Expression Integer +--E 362 + +--S 363 of 486 +r0365:= 2*x^(1/2)-2*atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (331) - 2atanh(\|x ) + 2\|x +--R Type: Expression Integer +--E 363 + +--S 364 of 486 +a0365:= integrate(t0365,x) +--R +--R +--R +-+ +-+ +-+ +--R (332) - log(\|x + 1) + log(\|x - 1) + 2\|x +--R Type: Union(Expression Integer,...) +--E 364 + +--S 365 of 486 +m0365:= a0365-r0365 +--R +--R +--R +-+ +-+ +-+ +--R (333) - log(\|x + 1) + log(\|x - 1) + 2atanh(\|x ) +--R Type: Expression Integer +--E 365 + +--S 366 of 486 +d0365:= D(m0365,x) +--R +--R +--R (334) 0 +--R Type: Expression Integer +--E 366 + +--S 367 of 486 +t0366:= 3/(4+x^(1/3)) +--R +--R +--R 3 +--R (335) -------- +--R 3+-+ +--R \|x + 4 +--R Type: Expression Integer +--E 367 + +--S 368 of 486 +r0366:= -36*x^(1/3)+9/2*x^(2/3)+144*log(4+x^(1/3)) +--R +--R +--R 3+-+ 3+-+2 3+-+ +--R 288log(\|x + 4) + 9\|x - 72\|x +--R (336) ---------------------------------- +--R 2 +--R Type: Expression Integer +--E 368 + +--S 369 of 486 +a0366:= integrate(t0366,x) +--R +--R +--R 3+-+ 3+-+2 3+-+ +--R 288log(\|x + 4) + 9\|x - 72\|x +--R (337) ---------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 369 + +--S 370 of 486 +m0366:= a0366-r0366 +--R +--R +--R (338) 0 +--R Type: Expression Integer +--E 370 + +--S 371 of 486 +d0366:= D(m0366,x) +--R +--R +--R (339) 0 +--R Type: Expression Integer +--E 371 + +--S 372 of 486 +t0367:= (1+(-3+x)^(1/2))^(1/3) +--R +--R +--R +------------+ +--R 3| +-----+ +--R (340) \|\|x - 3 + 1 +--R Type: Expression Integer +--E 372 + +--S 373 of 486 +r0367:= -9/14*(1+(-3+x)^(1/2))^(4/3)+6/7*(1+(-3+x)^(1/2))^(4/3)*(-3+x)^(1/2) +--R +--R +--R +------------+ +--R +-----+ 3| +-----+ +--R (3\|x - 3 + 12x - 45)\|\|x - 3 + 1 +--R (341) ------------------------------------- +--R 14 +--R Type: Expression Integer +--E 373 + +--S 374 of 486 +a0367:= integrate(t0367,x) +--R +--R +--R +------------+ +--R +-----+ 3| +-----+ +--R (3\|x - 3 + 12x - 45)\|\|x - 3 + 1 +--R (342) ------------------------------------- +--R 14 +--R Type: Union(Expression Integer,...) +--E 374 + +--S 375 of 486 +m0367:= a0367-r0367 +--R +--R +--R (343) 0 +--R Type: Expression Integer +--E 375 + +--S 376 of 486 +d0367:= D(m0367,x) +--R +--R +--R (344) 0 +--R Type: Expression Integer +--E 376 + +--S 377 of 486 +t0368:= (1+x^(1/2)+x)^(1/2) +--R +--R +--R +------------+ +--R | +-+ +--R (345) \|\|x + x + 1 +--R Type: Expression Integer +--E 377 + +--S 378 of 486 +r0368:= -1/4*(1+2*x^(1/2))*(1+x^(1/2)+x)^(1/2)+2/3*(1+x^(1/2)+x)^(3/2)-3/8*_ + asinh(1/3*(1+2*x^(1/2))*3^(1/2)) +--R +--R +--R +------------+ +-+ +-+ +-+ +--R +-+ | +-+ 2\|3 \|x + \|3 +--R (4\|x + 16x + 10)\|\|x + x + 1 - 9asinh(----------------) +--R 3 +--R (346) ------------------------------------------------------------ +--R 24 +--R Type: Expression Integer +--E 378 + +--S 379 of 486 +a0368:= integrate(t0368,x) +--R +--R +--R (347) +--R +------------+ +--R +-+ | +-+ +-+ +--R - 9log((8\|x + 4)\|\|x + x + 1 + 8\|x + 8x + 5) +--R + +--R +------------+ +--R +-+ | +-+ +--R (8\|x + 32x + 20)\|\|x + x + 1 +--R / +--R 48 +--R Type: Union(Expression Integer,...) +--E 379 + +--S 380 of 486 +m0368:= a0368-r0368 +--R +--R +--R (348) +--R +------------+ +--R +-+ | +-+ +-+ +--R - 3log((8\|x + 4)\|\|x + x + 1 + 8\|x + 8x + 5) +--R + +--R +-+ +-+ +-+ +--R 2\|3 \|x + \|3 +--R 6asinh(----------------) +--R 3 +--R / +--R 16 +--R Type: Expression Integer +--E 380 + +--S 381 of 486 +d0368:= D(m0368,x) +--R +--R +--R +--------------+ +------------+ +--R | +-+ | +-+ +--R - 3\|4\|x + 4x + 4 + 6\|\|x + x + 1 +--R (349) --------------------------------------- +--R +------------+ +--------------+ +--R +-+ | +-+ | +-+ +--R 16\|x \|\|x + x + 1 \|4\|x + 4x + 4 +--R Type: Expression Integer +--E 381 + +--S 382 of 486 +t0369:= (1+x+(1+x)^(1/2))^(1/2) +--R +--R +--R +----------------+ +--R | +-----+ +--R (350) \|\|x + 1 + x + 1 +--R Type: Expression Integer +--E 382 + +--S 383 of 486 +r0369:= 2/3*(1+x+(1+x)^(1/2))^(3/2)-1/4*(1+x+(1+x)^(1/2))^(1/2)*_ + (1+2*(1+x)^(1/2))+1/8*atanh(2*(1+x+(1+x)^(1/2))^(1/2)/_ + (1+2*(1+x)^(1/2))) +--R +--R +--R (351) +--R +----------------+ +--R | +-----+ +----------------+ +--R 2\|\|x + 1 + x + 1 +-----+ | +-----+ +--R 3atanh(--------------------) + (4\|x + 1 + 16x + 10)\|\|x + 1 + x + 1 +--R +-----+ +--R 2\|x + 1 + 1 +--R ------------------------------------------------------------------------ +--R 24 +--R Type: Expression Integer +--E 383 + +--S 384 of 486 +a0369:= integrate(t0369,x) +--R +--R +--R (352) +--R +----------------+ +--R +-----+ | +-----+ +-----+ +--R - 3log((- 8\|x + 1 - 4)\|\|x + 1 + x + 1 + 8\|x + 1 + 8x + 9) +--R + +--R +----------------+ +--R +-----+ | +-----+ +--R (8\|x + 1 + 32x + 20)\|\|x + 1 + x + 1 +--R / +--R 48 +--R Type: Union(Expression Integer,...) +--E 384 + +--S 385 of 486 +m0369:= a0369-r0369 +--R +--R +--R (353) +--R +----------------+ +--R +-----+ | +-----+ +-----+ +--R - log((- 8\|x + 1 - 4)\|\|x + 1 + x + 1 + 8\|x + 1 + 8x + 9) +--R + +--R +----------------+ +--R | +-----+ +--R 2\|\|x + 1 + x + 1 +--R - 2atanh(--------------------) +--R +-----+ +--R 2\|x + 1 + 1 +--R / +--R 16 +--R Type: Expression Integer +--E 385 + +--S 386 of 486 +d0369:= D(m0369,x) +--R +--R +--R (354) 0 +--R Type: Expression Integer +--E 386 + +--S 387 of 486 +t0370:= (2*x+(-1+2*x)^(1/2))^(1/2) +--R +--R +--R +--------------+ +--R | +------+ +--R (355) \|\|2x - 1 + 2x +--R Type: Expression Integer +--E 387 + +--S 388 of 486 +r0370:= 1/3*(2*x+(-1+2*x)^(1/2))^(3/2)-1/8*(2*x+(-1+2*x)^(1/2))^(1/2)*_ + (1+2*(-1+2*x)^(1/2))-3/16*asinh(1/3*(1+2*(-1+2*x)^(1/2))*3^(1/2)) +--R +--R +--R (356) +--R +--------------+ +-+ +------+ +-+ +--R +------+ | +------+ 2\|3 \|2x - 1 + \|3 +--R (4\|2x - 1 + 32x - 6)\|\|2x - 1 + 2x - 9asinh(---------------------) +--R 3 +--R ----------------------------------------------------------------------- +--R 48 +--R Type: Expression Integer +--E 388 + +--S 389 of 486 +a0370:= integrate(t0370,x) +--R +--R +--R (357) +--R +--------------+ +--R +------+ | +------+ +------+ +--R - 9log((- 8\|2x - 1 - 4)\|\|2x - 1 + 2x - 8\|2x - 1 - 16x + 3) +--R + +--R +--------------+ +--R +------+ | +------+ +--R (8\|2x - 1 + 64x - 12)\|\|2x - 1 + 2x +--R / +--R 96 +--R Type: Union(Expression Integer,...) +--E 389 + +--S 390 of 486 +m0370:= a0370-r0370 +--R +--R +--R (358) +--R +--------------+ +--R +------+ | +------+ +------+ +--R - 3log((- 8\|2x - 1 - 4)\|\|2x - 1 + 2x - 8\|2x - 1 - 16x + 3) +--R + +--R +-+ +------+ +-+ +--R 2\|3 \|2x - 1 + \|3 +--R 6asinh(---------------------) +--R 3 +--R / +--R 32 +--R Type: Expression Integer +--E 390 + +--S 391 of 486 +d0370:= D(m0370,x) +--R +--R +--R +---------------+ +--------------+ +--R | +------+ | +------+ +--R - 3\|4\|2x - 1 + 8x + 6\|\|2x - 1 + 2x +--R (359) ---------------------------------------------- +--R +--------------+ +---------------+ +--R +------+ | +------+ | +------+ +--R 16\|2x - 1 \|\|2x - 1 + 2x \|4\|2x - 1 + 8x +--R Type: Expression Integer +--E 391 + +--S 392 of 486 +t0371:= ((-1+x)^(1/2)+x)^(1/2) +--R +--R +--R +------------+ +--R | +-----+ +--R (360) \|\|x - 1 + x +--R Type: Expression Integer +--E 392 + +--S 393 of 486 +r0371:= -1/4*(1+2*(-1+x)^(1/2))*((-1+x)^(1/2)+x)^(1/2)+_ + 2/3*((-1+x)^(1/2)+x)^(3/2)-3/8*asinh(1/3*(1+2*(-1+x)^(1/2))*3^(1/2)) +--R +--R +--R +------------+ +-+ +-----+ +-+ +--R +-----+ | +-----+ 2\|3 \|x - 1 + \|3 +--R (4\|x - 1 + 16x - 6)\|\|x - 1 + x - 9asinh(--------------------) +--R 3 +--R (361) ------------------------------------------------------------------- +--R 24 +--R Type: Expression Integer +--E 393 + +--S 394 of 486 +a0371:= integrate(t0371,x) +--R +--R +--R (362) +--R +------------+ +--R +-----+ | +-----+ +-----+ +--R - 9log((- 8\|x - 1 - 4)\|\|x - 1 + x - 8\|x - 1 - 8x + 3) +--R + +--R +------------+ +--R +-----+ | +-----+ +--R (8\|x - 1 + 32x - 12)\|\|x - 1 + x +--R / +--R 48 +--R Type: Union(Expression Integer,...) +--E 394 + +--S 395 of 486 +m0371:= a0371-r0371 +--R +--R +--R (363) +--R +------------+ +--R +-----+ | +-----+ +-----+ +--R - 3log((- 8\|x - 1 - 4)\|\|x - 1 + x - 8\|x - 1 - 8x + 3) +--R + +--R +-+ +-----+ +-+ +--R 2\|3 \|x - 1 + \|3 +--R 6asinh(--------------------) +--R 3 +--R / +--R 16 +--R Type: Expression Integer +--E 395 + +--S 396 of 486 +d0371:= D(m0371,x) +--R +--R +--R +--------------+ +------------+ +--R | +-----+ | +-----+ +--R - 3\|4\|x - 1 + 4x + 6\|\|x - 1 + x +--R (364) ------------------------------------------ +--R +------------+ +--------------+ +--R +-----+ | +-----+ | +-----+ +--R 16\|x - 1 \|\|x - 1 + x \|4\|x - 1 + 4x +--R Type: Expression Integer +--E 396 + +--S 397 of 486 +t0372:= 1/(3+(-1+2*x)^(1/2))^(1/2) +--R +--R +--R 1 +--R (365) ---------------- +--R +-------------+ +--R | +------+ +--R \|\|2x - 1 + 3 +--R Type: Expression Integer +--E 397 + +--S 398 of 486 +r0372:= -4*(3+(-1+2*x)^(1/2))^(1/2)+2/3*(-1+2*x)^(1/2)*(3+(-1+2*x)^(1/2))^(1/2) +--R +--R +--R +-------------+ +--R +------+ | +------+ +--R (2\|2x - 1 - 12)\|\|2x - 1 + 3 +--R (366) --------------------------------- +--R 3 +--R Type: Expression Integer +--E 398 + +--S 399 of 486 +a0372:= integrate(t0372,x) +--R +--R +--R +-------------+ +--R +------+ | +------+ +--R (2\|2x - 1 - 12)\|\|2x - 1 + 3 +--R (367) --------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 399 + +--S 400 of 486 +m0372:= a0372-r0372 +--R +--R +--R (368) 0 +--R Type: Expression Integer +--E 400 + +--S 401 of 486 +d0372:= D(m0372,x) +--R +--R +--R (369) 0 +--R Type: Expression Integer +--E 401 + +--S 402 of 486 +t0373:= 1/(x+(1+x)^(1/2))^(1/2) +--R +--R +--R 1 +--R (370) --------------- +--R +------------+ +--R | +-----+ +--R \|\|x + 1 + x +--R Type: Expression Integer +--E 402 + +--S 403 of 486 +r0373:= 2*(x+(1+x)^(1/2))^(1/2)-_ + atanh(2*(x+(1+x)^(1/2))^(1/2)/(1+2*(1+x)^(1/2))) +--R +--R +--R +------------+ +--R | +-----+ +------------+ +--R 2\|\|x + 1 + x | +-----+ +--R (371) - atanh(----------------) + 2\|\|x + 1 + x +--R +-----+ +--R 2\|x + 1 + 1 +--R Type: Expression Integer +--E 403 + +--S 404 of 486 +a0373:= integrate(t0373,x) +--R +--R +--R (372) +--R +------------+ +------------+ +--R +-----+ | +-----+ +-----+ | +-----+ +--R - log((8\|x + 1 + 4)\|\|x + 1 + x + 8\|x + 1 + 8x + 5) + 4\|\|x + 1 + x +--R ----------------------------------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 404 + +--S 405 of 486 +m0373:= a0373-r0373 +--R +--R +--R (373) +--R +------------+ +--R +-----+ | +-----+ +-----+ +--R - log((8\|x + 1 + 4)\|\|x + 1 + x + 8\|x + 1 + 8x + 5) +--R + +--R +------------+ +--R | +-----+ +--R 2\|\|x + 1 + x +--R 2atanh(----------------) +--R +-----+ +--R 2\|x + 1 + 1 +--R / +--R 2 +--R Type: Expression Integer +--E 405 + +--S 406 of 486 +d0373:= D(m0373,x) +--R +--R +--R (374) 0 +--R Type: Expression Integer +--E 406 + +--S 407 of 486 +t0374:= 1/(1+x+(-1+2*x)^(1/2))^(1/2) +--R +--R +--R 1 +--R (375) -------------------- +--R +-----------------+ +--R | +------+ +--R \|\|2x - 1 + x + 1 +--R Type: Expression Integer +--E 407 + +--S 408 of 486 +r0374:= 2*(1+x+(-1+2*x)^(1/2))^(1/2)-2^(1/2)*_ + asinh(1/2*(1+(-1+2*x)^(1/2))*2^(1/2)) +--R +--R +--R +-----------------+ +-+ +------+ +-+ +--R | +------+ +-+ \|2 \|2x - 1 + \|2 +--R (376) 2\|\|2x - 1 + x + 1 - \|2 asinh(--------------------) +--R 2 +--R Type: Expression Integer +--E 408 + +--S 409 of 486 +a0374:= integrate(t0374,x) +--R +--R +--R (377) +--R - +--R +-+ +--R \|2 +--R * +--R +-----------------+ +--R +-+ +------+ +-+ | +------+ +------+ +--R log((\|2 \|2x - 1 + \|2 )\|\|2x - 1 + x + 1 + 2\|2x - 1 + 2x + 1) +--R + +--R +-----------------+ +--R | +------+ +--R 4\|\|2x - 1 + x + 1 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 409 + +--S 410 of 486 +m0374:= a0374-r0374 +--R +--R +--R (378) +--R - +--R +-+ +--R \|2 +--R * +--R +-----------------+ +--R +-+ +------+ +-+ | +------+ +------+ +--R log((\|2 \|2x - 1 + \|2 )\|\|2x - 1 + x + 1 + 2\|2x - 1 + 2x + 1) +--R + +--R +-+ +------+ +-+ +--R +-+ \|2 \|2x - 1 + \|2 +--R 2\|2 asinh(--------------------) +--R 2 +--R / +--R 2 +--R Type: Expression Integer +--E 410 + +--S 411 of 486 +d0374:= D(m0374,x) +--R +--R +--R (379) 0 +--R Type: Expression Integer +--E 411 + +--S 412 of 486 +t0375:= (3*x+(-7+8*x)^(1/2))^(1/2) +--R +--R +--R +--------------+ +--R | +------+ +--R (380) \|\|8x - 7 + 3x +--R Type: Expression Integer +--E 412 + +--S 413 of 486 +r0375:= 2/9*(3*x+(-7+8*x)^(1/2))^(3/2)-1/18*(3*x+(-7+8*x)^(1/2))^(1/2)*_ + (4+3*(-7+8*x)^(1/2))-47/216*asinh(1/47*(4+3*(-7+8*x)^(1/2))*_ + 47^(1/2))*6^(1/2) +--R +--R +--R (381) +--R +--------------+ +--R +------+ | +------+ +--R (12\|8x - 7 + 144x - 48)\|\|8x - 7 + 3x +--R + +--R +--+ +------+ +--+ +--R +-+ 3\|47 \|8x - 7 + 4\|47 +--R - 47\|6 asinh(------------------------) +--R 47 +--R / +--R 216 +--R Type: Expression Integer +--E 413 + +--S 414 of 486 +a0375:= integrate(t0375,x) +--R +--R +--R (382) +--R - +--R +-+ +--R 47\|6 +--R * +--R log +--R +--------------+ +--R +-+ +------+ +-+ | +------+ +------+ +--R (- 12\|6 \|8x - 7 - 16\|6 )\|\|8x - 7 + 3x - 48\|8x - 7 +--R + +--R - 144x + 47 +--R + +--R +--------------+ +--R +------+ | +------+ +--R (24\|8x - 7 + 288x - 96)\|\|8x - 7 + 3x +--R / +--R 432 +--R Type: Union(Expression Integer,...) +--E 414 + +--S 415 of 486 +m0375:= a0375-r0375 +--R +--R +--R (383) +--R - +--R +-+ +--R 47\|6 +--R * +--R log +--R +--------------+ +--R +-+ +------+ +-+ | +------+ +------+ +--R (- 12\|6 \|8x - 7 - 16\|6 )\|\|8x - 7 + 3x - 48\|8x - 7 +--R + +--R - 144x + 47 +--R + +--R +--+ +------+ +--+ +--R +-+ 3\|47 \|8x - 7 + 4\|47 +--R 94\|6 asinh(------------------------) +--R 47 +--R / +--R 432 +--R Type: Expression Integer +--E 415 + +--S 416 of 486 +d0375:= D(m0375,x) +--R +--R +--R (384) +--R +--------------+ +--R +-+ +------+ +-+ | +------+ +--R (- 752\|6 \|8x - 7 + (- 4512x + 3948)\|6 )\|\|8x - 7 + 3x +--R + +--R +------+ +--R (- 6768x + 2209)\|8x - 7 - 18048x + 15792 +--R * +--R +-----------------+ +--R | +------+ +--R \|24\|8x - 7 + 72x +--R + +--R +--------------+ +--R +-+ +------+ +-+ | +------+ +--R ((13536x - 4418)\|6 \|8x - 7 + (36096x - 31584)\|6 )\|\|8x - 7 + 3x +--R + +--R +------+ 2 +--R (81216x - 47376)\|8x - 7 + 162432x - 69936x - 63168 +--R / +--R +--------------+ +--R +------+ 2 | +------+ +--R ((13824x - 12096)\|8x - 7 + 41472x - 49824x + 11844)\|\|8x - 7 + 3x +--R + +--R 2 +-+ +------+ 2 +-+ +--R (10368x - 4464x - 4032)\|6 \|8x - 7 + (41472x - 60480x + 21168)\|6 +--R * +--R +-----------------+ +--R | +------+ +--R \|24\|8x - 7 + 72x +--R Type: Expression Integer +--E 416 + +--S 417 of 486 +t0376:= (1+(1+x^2)^(1/2))^(1/2) +--R +--R +--R +-------------+ +--R | +------+ +--R | | 2 +--R (385) \|\|x + 1 + 1 +--R Type: Expression Integer +--E 417 + +--S 418 of 486 +r0376:= 2/3*(-1+x^2+(1+x^2)^(1/2))*(1+(1+x^2)^(1/2))^(1/2)/x +--R +--R +--R +-------------+ +--R +------+ | +------+ +--R | 2 2 | | 2 +--R (2\|x + 1 + 2x - 2)\|\|x + 1 + 1 +--R (386) -------------------------------------- +--R 3x +--R Type: Expression Integer +--E 418 + +--S 419 of 486 +a0376:= integrate(t0376,x) +--R +--R +--R +-------------+ +--R +------+ | +------+ +--R | 2 2 | | 2 +--R (2\|x + 1 + 2x - 2)\|\|x + 1 + 1 +--R (387) -------------------------------------- +--R 3x +--R Type: Union(Expression Integer,...) +--E 419 + +--S 420 of 486 +m0376:= a0376-r0376 +--R +--R +--R (388) 0 +--R Type: Expression Integer +--E 420 + +--S 421 of 486 +d0376:= D(m0376,x) +--R +--R +--R (389) 0 +--R Type: Expression Integer +--E 421 + +--S 422 of 486 +t0377:= (5+(25+x^2)^(1/2))^(1/2) +--R +--R +--R +--------------+ +--R | +-------+ +--R | | 2 +--R (390) \|\|x + 25 + 5 +--R Type: Expression Integer +--E 422 + +--S 423 of 486 +r0377:= 2/3*(-25+x^2+5*(25+x^2)^(1/2))*(5+(25+x^2)^(1/2))^(1/2)/x +--R +--R +--R +--------------+ +--R +-------+ | +-------+ +--R | 2 2 | | 2 +--R (10\|x + 25 + 2x - 50)\|\|x + 25 + 5 +--R (391) ------------------------------------------ +--R 3x +--R Type: Expression Integer +--E 423 + +--S 424 of 486 +a0377:= integrate(t0377,x) +--R +--R +--R +--------------+ +--R +-------+ | +-------+ +--R | 2 2 | | 2 +--R (10\|x + 25 + 2x - 50)\|\|x + 25 + 5 +--R (392) ------------------------------------------ +--R 3x +--R Type: Union(Expression Integer,...) +--E 424 + +--S 425 of 486 +m0377:= a0377-r0377 +--R +--R +--R (393) 0 +--R Type: Expression Integer +--E 425 + +--S 426 of 486 +d0377:= D(m0377,x) +--R +--R +--R (394) 0 +--R Type: Expression Integer +--E 426 + +--S 427 of 486 +t0378:= x^2*((1-x^3)/(1+x^3))^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R 2 |- x + 1 +--R (395) x |-------- +--R | 3 +--R \| x + 1 +--R Type: Expression Integer +--E 427 + +--S 428 of 486 +r0378:= 1/3*((1-x^3)/(1+x^3))^(1/2)*(1+x^3)-2/3*atan(((1-x^3)/(1+x^3))^(1/2)) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R |- x + 1 3 |- x + 1 +--R - 2atan( |-------- ) + (x + 1) |-------- +--R | 3 | 3 +--R \| x + 1 \| x + 1 +--R (396) ------------------------------------------ +--R 3 +--R Type: Expression Integer +--E 428 + +--S 429 of 486 +a0378:= integrate(t0378,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 |- x + 1 +--R +--------+ (x + 1) |-------- - 1 +--R | 3 | 3 +--R 3 |- x + 1 \| x + 1 6 +--R ((- 2x - 2) |-------- + 2)atan(-----------------------) - x +--R | 3 3 +--R \| x + 1 x +--R (397) -------------------------------------------------------------- +--R +--------+ +--R | 3 +--R 3 |- x + 1 +--R (3x + 3) |-------- - 3 +--R | 3 +--R \| x + 1 +--R Type: Union(Expression Integer,...) +--E 429 + +--S 430 of 486 +m0378:= a0378-r0378 +--R +--R +--R +--------+ +--R | 3 +--R 3 |- x + 1 +--R (x + 1) |-------- - 1 +--------+ +--R | 3 | 3 +--R \| x + 1 |- x + 1 +--R - 2atan(-----------------------) + 2atan( |-------- ) + 1 +--R 3 | 3 +--R x \| x + 1 +--R (398) --------------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 430 + +--S 431 of 486 +d0378:= D(m0378,x) +--R +--R +--R (399) 0 +--R Type: Expression Integer +--E 431 + +--S 432 of 486 +t0379:= x^8*((1-x^3)/(1+x^3))^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R 8 |- x + 1 +--R (400) x |-------- +--R | 3 +--R \| x + 1 +--R Type: Expression Integer +--E 432 + +--S 433 of 486 +r0379:= 2/9*(-(-1+x^3)/(1+x^3))^(1/2)+1/18*(-(-1+x^3)/(1+x^3))^(1/2)*x^3-_ + 1/18*(-(-1+x^3)/(1+x^3))^(1/2)*x^6+1/9*(-(-1+x^3)/_ + (1+x^3))^(1/2)*x^9-1/3*atan((-(-1+x^3)/(1+x^3))^(1/2)) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R |- x + 1 9 6 3 |- x + 1 +--R - 6atan( |-------- ) + (2x - x + x + 4) |-------- +--R | 3 | 3 +--R \| x + 1 \| x + 1 +--R (401) ----------------------------------------------------- +--R 18 +--R Type: Expression Integer +--E 433 + +--S 434 of 486 +a0379:= integrate(t0379,x) +--R +--R +--R (402) +--R +--------+ +--R | 3 +--R 9 6 3 |- x + 1 6 +--R ((- 6x - 6x + 24x + 24) |-------- + 18x - 24) +--R | 3 +--R \| x + 1 +--R * +--R +--------+ +--R | 3 +--R 3 |- x + 1 +--R (x + 1) |-------- - 1 +--R | 3 +--R \| x + 1 +--R atan(-----------------------) +--R 3 +--R x +--R + +--R +--------+ +--R | 3 +--R 15 12 9 6 3 |- x + 1 18 15 12 +--R (- 6x + 3x + 9x - 12x - 12x ) |-------- - 2x + 3x + 6x +--R | 3 +--R \| x + 1 +--R + +--R 9 3 +--R - 15x + 12x +--R / +--R +--------+ +--R | 3 +--R 9 6 3 |- x + 1 6 +--R (18x + 18x - 72x - 72) |-------- - 54x + 72 +--R | 3 +--R \| x + 1 +--R Type: Union(Expression Integer,...) +--E 434 + +--S 435 of 486 +m0379:= a0379-r0379 +--R +--R +--R +--------+ +--R | 3 +--R 3 |- x + 1 +--R (x + 1) |-------- - 1 +--------+ +--R | 3 | 3 +--R \| x + 1 |- x + 1 +--R - 3atan(-----------------------) + 3atan( |-------- ) + 2 +--R 3 | 3 +--R x \| x + 1 +--R (403) --------------------------------------------------------- +--R 9 +--R Type: Expression Integer +--E 435 + +--S 436 of 486 +d0379:= D(m0379,x) +--R +--R +--R (404) 0 +--R Type: Expression Integer +--E 436 + +--S 437 of 486 +t0380:= x^9*((5-7*x^5)/(7+5*x^5))^(1/2) +--R +--R +--R +---------+ +--R | 5 +--R 9 |- 7x + 5 +--R (405) x |--------- +--R | 5 +--R \| 5x + 7 +--R Type: Expression Integer +--E 437 + +--S 438 of 486 +r0380:= -43/125*(-(-5+7*x^5)/(7+5*x^5))^(1/2)-37/350*(-(-5+7*x^5)/_ + (7+5*x^5))^(1/2)*x^5+1/10*(-(-5+7*x^5)/(7+5*x^5))^(1/2)*x^10+_ + 2257/30625*atan(1/7*35^(1/2)*(-(-5+7*x^5)/(7+5*x^5))^(1/2))*35^(1/2) +--R +--R +--R (406) +--R +---------+ +--R | 5 +--R +--+ |- 7x + 5 +--R \|35 |--------- +---------+ +--R | 5 | 5 +--R +--+ \| 5x + 7 10 5 |- 7x + 5 +--R 4514\|35 atan(-----------------) + (6125x - 6475x - 21070) |--------- +--R 7 | 5 +--R \| 5x + 7 +--R ------------------------------------------------------------------------- +--R 61250 +--R Type: Expression Integer +--E 438 + +--S 439 of 486 +a0380:= integrate(t0380,x) +--R +--R +--R (407) +--R +---------+ +--R | 5 +--R 10 5 |- 7x + 5 +--R (18958800x - 28754180x - 77415100) |--------- +--R | 5 +--R \| 5x + 7 +--R + +--R 10 5 +--+ +--R (- 4879634x - 7583520x + 11059300)\|35 +--R * +--R +---------+ +--R | 5 +--R 5 +--+ |- 7x + 5 +--R (5x + 7)\|35 |--------- - 35 +--R | 5 +--R \| 5x + 7 +--R atan(-------------------------------) +--R 5 +--R 35x +--R + +--R +---------+ +--R | 5 +--R 20 15 10 5 |- 7x + 5 +--R (- 6621125x - 3290525x + 36018920x + 38707550x ) |--------- +--R | 5 +--R \| 5x + 7 +--R + +--R 20 15 10 5 +--+ +--R (- 1029000x + 4824050x + 700070x - 5529650x )\|35 +--R / +--R +---------+ +--R | 5 +--R 10 5 +--+ |- 7x + 5 10 +--R (7350000x - 11147500x - 30012500)\|35 |--------- - 66211250x +--R | 5 +--R \| 5x + 7 +--R + +--R 5 +--R - 102900000x + 150062500 +--R Type: Union(Expression Integer,...) +--E 439 + +--S 440 of 486 +m0380:= a0380-r0380 +--R +--R +--R (408) +--R +---------+ +--R | 5 +--R 10 5 |- 7x + 5 +--R (9479400x - 14377090x - 38707550) |--------- +--R | 5 +--R \| 5x + 7 +--R + +--R 10 5 +--+ +--R (- 2439817x - 3791760x + 5529650)\|35 +--R * +--R +---------+ +--R | 5 +--R 5 +--+ |- 7x + 5 +--R (5x + 7)\|35 |--------- - 35 +--R | 5 +--R \| 5x + 7 +--R atan(-------------------------------) +--R 5 +--R 35x +--R + +--R +---------+ +--R | 5 +--R 10 5 |- 7x + 5 +--R (- 9479400x + 14377090x + 38707550) |--------- +--R | 5 +--R \| 5x + 7 +--R + +--R 10 5 +--+ +--R (2439817x + 3791760x - 5529650)\|35 +--R * +--R +---------+ +--R | 5 +--R +--+ |- 7x + 5 +--R \|35 |--------- +--R | 5 +--R \| 5x + 7 +--R atan(-----------------) +--R 7 +--R + +--R +---------+ +--R | 5 +--R 10 5 |- 7x + 5 +--R (- 6321000x + 9586850x + 25810750) |--------- +--R | 5 +--R \| 5x + 7 +--R + +--R 10 5 +--+ +--R (1626905x + 2528400x - 3687250)\|35 +--R / +--R +---------+ +--R | 5 +--R 10 5 +--+ |- 7x + 5 10 +--R (3675000x - 5573750x - 15006250)\|35 |--------- - 33105625x +--R | 5 +--R \| 5x + 7 +--R + +--R 5 +--R - 51450000x + 75031250 +--R Type: Expression Integer +--E 440 + +--S 441 of 486 +d0380:= D(m0380,x) +--R +--R +--R (409) 0 +--R Type: Expression Integer +--E 441 + +--S 442 of 486 +t0381:= (-1+x^3)/x^(1/2)/(1+x^2) +--R +--R +--R 3 +--R x - 1 +--R (410) ------------ +--R 2 +-+ +--R (x + 1)\|x +--R Type: Expression Integer +--E 442 + +--S 443 of 486 +r0381:= 2/3*x^(3/2)-atan(-1+2^(1/2)*x^(1/2))*2^(1/2)-_ + atan(1+2^(1/2)*x^(1/2))*2^(1/2) +--R +--R +--R +-+ +-+ +-+ +-+ +-+ +-+ +-+ +--R - 3\|2 atan(\|2 \|x + 1) - 3\|2 atan(\|2 \|x - 1) + 2x\|x +--R (411) ------------------------------------------------------------ +--R 3 +--R Type: Expression Integer +--E 443 + +--S 444 of 486 +a0381:= integrate(t0381,x) +--R +--R +--R +-+ +-+ +--R +-+ \|2 \|x +-+ +--R 3\|2 atan(--------) + 2x\|x +--R x - 1 +--R (412) ---------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 444 + +--S 445 of 486 +m0381:= a0381-r0381 +--R +--R +--R +-+ +-+ +--R +-+ +-+ +-+ +-+ +-+ +-+ +-+ \|2 \|x +--R (413) \|2 atan(\|2 \|x + 1) + \|2 atan(\|2 \|x - 1) + \|2 atan(--------) +--R x - 1 +--R Type: Expression Integer +--E 445 + +--S 446 of 486 +d0381:= D(m0381,x) +--R +--R +--R (414) 0 +--R Type: Expression Integer +--E 446 + +--S 447 of 486 +t0382:= 1/(1+x^4)/(-x^2+(1+x^4)^(1/2))^(1/2) +--R +--R +--R 1 +--R (415) ------------------------- +--R +--------------+ +--R | +------+ +--R 4 | | 4 2 +--R (x + 1)\|\|x + 1 - x +--R Type: Expression Integer +--E 447 + +--S 448 of 486 +r0382:= acot((-x^2+(1+x^4)^(1/2))^(1/2)/x) +--R +--R +--R +--------------+ +--R | +------+ +--R | | 4 2 +--R \|\|x + 1 - x +--R (416) acot(-----------------) +--R x +--R Type: Expression Integer +--E 448 + +--S 449 of 486 +a0382:= integrate(t0382,x) +--R +--R +--R +------+ +--R 2 | 4 4 +--R 8x \|x + 1 - 9x - 1 +--R atan(------------------------------------) +--R +--------------+ +--R +------+ | +------+ +--R | 4 3 | | 4 2 +--R (4x\|x + 1 - 8x )\|\|x + 1 - x +--R (417) ------------------------------------------ +--R 4 +--R Type: Union(Expression Integer,...) +--E 449 + +--S 450 of 486 +m0382:= a0382-r0382 +--R +--R +--R (418) +--R +--------------+ +--R +------+ | +------+ +--R 2 | 4 4 | | 4 2 +--R 8x \|x + 1 - 9x - 1 \|\|x + 1 - x +--R atan(------------------------------------) - 4acot(-----------------) +--R +--------------+ x +--R +------+ | +------+ +--R | 4 3 | | 4 2 +--R (4x\|x + 1 - 8x )\|\|x + 1 - x +--R --------------------------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 450 + +--S 451 of 486 +d0382:= D(m0382,x) +--R +--R +--R (419) 0 +--R Type: Expression Integer +--E 451 + +--S 452 of 486 +t0383:= (1+x^(7/2))/(1-x^2) +--R +--R +--R 3 +-+ +--R - x \|x - 1 +--R (420) ------------ +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 452 + +--S 453 of 486 +r0383:= -2*x^(1/2)-2/5*x^(5/2)+atan(x^(1/2))+atanh(x^(1/2))+atanh(x) +--R +--R +--R +-+ +-+ 2 +-+ +--R 5atanh(\|x ) + 5atan(\|x ) + (- 2x - 10)\|x + 5atanh(x) +--R (421) --------------------------------------------------------- +--R 5 +--R Type: Expression Integer +--E 453 + +--S 454 of 486 +a0383:= integrate(t0383,x) +--R +--R +--R +-+ +-+ 2 +-+ +--R - 10log(\|x - 1) + 10atan(\|x ) + (- 4x - 20)\|x + 5log(x + 1) +--R (422) ----------------------------------------------------------------- +--R 10 +--R Type: Union(Expression Integer,...) +--E 454 + +--S 455 of 486 +m0383:= a0383-r0383 +--R +--R +--R +-+ +-+ +--R - 2log(\|x - 1) - 2atanh(\|x ) + log(x + 1) - 2atanh(x) +--R (423) -------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 455 + +--S 456 of 486 +d0383:= D(m0383,x) +--R +--R +--R (424) 0 +--R Type: Expression Integer +--E 456 + +--S 457 of 486 +t0384:= 1/(1+3*x^(1/2))/x +--R +--R +--R 1 +--R (425) ---------- +--R +-+ +--R 3x\|x + x +--R Type: Expression Integer +--E 457 + +--S 458 of 486 +r0384:= -2*log(3+1/x^(1/2)) +--R +--R +--R +-+ +--R 3\|x + 1 +--R (426) - 2log(---------) +--R +-+ +--R \|x +--R Type: Expression Integer +--E 458 + +--S 459 of 486 +a0384:= integrate(t0384,x) +--R +--R +--R +-+ +-+ +--R (427) - 2log(3\|x + 1) + 2log(\|x ) +--R Type: Union(Expression Integer,...) +--E 459 + +--S 460 of 486 +m0384:= a0384-r0384 +--R +--R +--R +-+ +--R +-+ +-+ 3\|x + 1 +--R (428) - 2log(3\|x + 1) + 2log(\|x ) + 2log(---------) +--R +-+ +--R \|x +--R Type: Expression Integer +--E 460 + +--S 461 of 486 +d0384:= D(m0384,x) +--R +--R +--R (429) 0 +--R Type: Expression Integer +--E 461 + +--S 462 of 486 +t0385:= (x+x^(5/2))^(1/2) +--R +--R +--R +----------+ +--R | 2 +-+ +--R (430) \|x \|x + x +--R Type: Expression Integer +--E 462 + +--S 463 of 486 +r0385:= 4/9*(x*(1+x^(3/2)))^(3/2)/x^(3/2) +--R +--R +--R +----------+ +--R +-+ | 2 +-+ +--R (4x\|x + 4)\|x \|x + x +--R (431) ------------------------- +--R +-+ +--R 9\|x +--R Type: Expression Integer +--E 463 + +--S 464 of 486 +a0385:= integrate(t0385,x) +--R +--R +--R +----------+ +--R +-+ 2 | 2 +-+ +--R (4\|x + 4x )\|x \|x + x +--R (432) -------------------------- +--R 9x +--R Type: Union(Expression Integer,...) +--E 464 + +--S 465 of 486 +m0385:= a0385-r0385 +--R +--R +--R (433) 0 +--R Type: Expression Integer +--E 465 + +--S 466 of 486 +d0385:= D(m0385,x) +--R +--R +--R (434) 0 +--R Type: Expression Integer +--E 466 + +--S 467 of 486 +t0386:= (x^(1/4)+x)^(1/2) +--R +--R +--R +--------+ +--R |4+-+ +--R (435) \|\|x + x +--R Type: Expression Integer +--E 467 + +--S 468 of 486 +r0386:= 1/3*((1+x^(3/4))*x^(1/4))^(1/2)*((1+x^(3/4))^(1/2)*x^(3/8)+_ + 2*(1+x^(3/4))^(1/2)*x^(9/8)-asinh(x^(3/8)))/(1+x^(3/4))^(1/2)/x^(1/8) +--R +--R +--R +--------+ +---------+ +--------+ +--R 8+-+3 8+-+ |4+-+ |4+-+3 8+-+3 |4+-+ +--R (\|x + 2x\|x )\|\|x + x \|\|x + 1 - asinh(\|x )\|\|x + x +--R (436) ----------------------------------------------------------------- +--R +---------+ +--R 8+-+ |4+-+3 +--R 3\|x \|\|x + 1 +--R Type: Expression Integer +--E 468 + +--S 469 of 486 +--a0386:= integrate(t0386,x) +--E 469 + +--S 470 of 486 +--m0386:= a0386-r0386 +--E 470 + +--S 471 of 486 +--d0386:= D(m0386,x) +--E 471 + +--S 472 of 486 +t0387:= (a*x^m+b*x^(6*m+1))^5 +--R +--R +--R (437) +--R 5 6m + 1 5 4 m 6m + 1 4 2 3 m 2 6m + 1 3 +--R b (x ) + 5a b x (x ) + 10a b (x ) (x ) +--R + +--R 3 2 m 3 6m + 1 2 4 m 4 6m + 1 5 m 5 +--R 10a b (x ) (x ) + 5a b (x ) x + a (x ) +--R Type: Expression Integer +--E 472 + +--S 473 of 486 +r0387:= 1/6*(a+b*x^(1+5*m))^6/b/(1+5*m) +--R +--R +--R (438) +--R 6 5m + 1 6 5 5m + 1 5 2 4 5m + 1 4 3 3 5m + 1 3 +--R b (x ) + 6a b (x ) + 15a b (x ) + 20a b (x ) +--R + +--R 4 2 5m + 1 2 5 5m + 1 6 +--R 15a b (x ) + 6a b x + a +--R / +--R 30b m + 6b +--R Type: Expression Integer +--E 473 + +--S 474 of 486 +a0387:= integrate(t0387,x) +--R +--R +--R (439) +--R 5 6 m log(x) 30 4 5 m log(x) 25 2 3 4 m log(x) 20 +--R b x (%e ) + 6a b x (%e ) + 15a b x (%e ) +--R + +--R 3 2 3 m log(x) 15 4 2 m log(x) 10 5 m log(x) 5 +--R 20a b x (%e ) + 15a b x (%e ) + 6a x (%e ) +--R / +--R 30m + 6 +--R Type: Union(Expression Integer,...) +--E 474 + +--S 475 of 486 +m0387:= a0387-r0387 +--R +--R +--R (440) +--R 6 6 m log(x) 30 5 5 m log(x) 25 2 4 4 m log(x) 20 +--R b x (%e ) + 6a b x (%e ) + 15a b x (%e ) +--R + +--R 3 3 3 m log(x) 15 4 2 2 m log(x) 10 5 m log(x) 5 +--R 20a b x (%e ) + 15a b x (%e ) + 6a b x (%e ) +--R + +--R 6 5m + 1 6 5 5m + 1 5 2 4 5m + 1 4 3 3 5m + 1 3 +--R - b (x ) - 6a b (x ) - 15a b (x ) - 20a b (x ) +--R + +--R 4 2 5m + 1 2 5 5m + 1 6 +--R - 15a b (x ) - 6a b x - a +--R / +--R 30b m + 6b +--R Type: Expression Integer +--E 475 + +--S 476 of 486 +d0387:= D(m0387,x) +--R +--R +--R (441) +--R 5 5 m log(x) 30 4 4 m log(x) 25 2 3 3 m log(x) 20 +--R b x (%e ) + 5a b x (%e ) + 10a b x (%e ) +--R + +--R 3 2 2 m log(x) 15 4 m log(x) 10 5 m log(x) 5 +--R 10a b x (%e ) + 5a b x (%e ) + a (%e ) +--R + +--R 5 5m 5m + 1 5 4 5m 5m + 1 4 2 3 5m 5m + 1 3 +--R - b x (x ) - 5a b x (x ) - 10a b x (x ) +--R + +--R 3 2 5m 5m + 1 2 4 5m 5m + 1 5 5m +--R - 10a b x (x ) - 5a b x x - a x +--R Type: Expression Integer +--E 476 + +--S 477 of 486 +t0388:= 1/(a*x^m+b*x^(1-2*m))^3 +--R +--R +--R 1 +--R (442) -------------------------------------------------------------------- +--R 3 m 3 2 - 2m + 1 m 2 2 - 2m + 1 2 m 3 - 2m + 1 3 +--R a (x ) + 3a b x (x ) + 3a b (x ) x + b (x ) +--R Type: Expression Integer +--E 477 + +--S 478 of 486 +r0388:= -1/2/b/(1-3*m)/(a+b*x^(1-3*m))^2 +--R +--R +--R (443) +--R 1 +--R --------------------------------------------------------------------- +--R 3 3 - 3m + 1 2 2 2 - 3m + 1 2 2 +--R (6b m - 2b )(x ) + (12a b m - 4a b )x + 6a b m - 2a b +--R Type: Expression Integer +--E 478 + +--S 479 of 486 +a0388:= integrate(t0388,x) +--R +--R +--R (444) +--R m log(x) 3 2 +--R - 2a x (%e ) - b x +--R / +--R 4 4 m log(x) 6 3 3 m log(x) 3 +--R (6a m - 2a )(%e ) + (12a b m - 4a b)x (%e ) +--R + +--R 2 2 2 2 2 +--R (6a b m - 2a b )x +--R Type: Union(Expression Integer,...) +--E 479 + +--S 480 of 486 +m0388:= a0388-r0388 +--R +--R +--R (445) +--R 4 m log(x) 6 +--R - a (%e ) +--R + +--R 3 - 3m + 1 2 2 2 - 3m + 1 3 m log(x) 3 +--R (- 2a b x (x ) - 4a b x x - 4a b x)(%e ) +--R + +--R 4 2 - 3m + 1 2 3 2 - 3m + 1 2 2 2 +--R - b x (x ) - 2a b x x - 2a b x +--R / +--R 4 3 4 3 - 3m + 1 2 5 2 5 2 - 3m + 1 6 +--R (6a b m - 2a b )(x ) + (12a b m - 4a b )x + 6a b m +--R + +--R 6 +--R - 2a b +--R * +--R m log(x) 6 +--R (%e ) +--R + +--R 3 4 3 4 - 3m + 1 2 4 3 4 3 - 3m + 1 +--R (12a b m - 4a b )x (x ) + (24a b m - 8a b )x x +--R + +--R 5 2 5 2 +--R (12a b m - 4a b )x +--R * +--R m log(x) 3 +--R (%e ) +--R + +--R 2 5 2 5 2 - 3m + 1 2 3 4 3 4 2 - 3m + 1 +--R (6a b m - 2a b )x (x ) + (12a b m - 4a b )x x +--R + +--R 4 3 4 3 2 +--R (6a b m - 2a b )x +--R Type: Expression Integer +--E 480 + +--S 481 of 486 +d0388:= D(m0388,x) +--R +--R +--R (446) +--R 3 - 3m m log(x) 9 +--R - a x (%e ) +--R + +--R 3 - 3m + 1 3 2 - 3m + 1 2 2 - 3m + 1 2 - 3m +--R b (x ) + 3a b (x ) + 3a b x - 3a b x x +--R + +--R 3 +--R a +--R * +--R m log(x) 6 +--R (%e ) +--R + +--R 2 2 - 3m m log(x) 3 3 3 - 3m +--R - 3a b x x (%e ) - b x x +--R / +--R 3 3 - 3m + 1 3 4 2 - 3m + 1 2 5 - 3m + 1 6 m log(x) 9 +--R (a b (x ) + 3a b (x ) + 3a b x + a )(%e ) +--R + +--R 2 4 - 3m + 1 3 3 3 - 3m + 1 2 4 2 - 3m + 1 5 +--R (3a b x (x ) + 9a b x (x ) + 9a b x x + 3a b x) +--R * +--R m log(x) 6 +--R (%e ) +--R + +--R 5 2 - 3m + 1 3 2 4 2 - 3m + 1 2 3 3 2 - 3m + 1 +--R 3a b x (x ) + 9a b x (x ) + 9a b x x +--R + +--R 4 2 2 +--R 3a b x +--R * +--R m log(x) 3 +--R (%e ) +--R + +--R 6 3 - 3m + 1 3 5 3 - 3m + 1 2 2 4 3 - 3m + 1 3 3 3 +--R b x (x ) + 3a b x (x ) + 3a b x x + a b x +--R Type: Expression Integer +--E 481 + +--S 482 of 486 +t0389:= (1/x^3)^(1/3) +--R +--R +--R +--+ +--R | 1 +--R (447) |-- +--R 3| 3 +--R \|x +--R Type: Expression Integer +--E 482 + +--S 483 of 486 +r0389:= (1/x^3)^(1/3)*x*log(x) +--R +--R +--R +--+ +--R | 1 +--R (448) x log(x) |-- +--R 3| 3 +--R \|x +--R Type: Expression Integer +--E 483 + +--S 484 of 486 +a0389:= integrate(t0389,x) +--R +--R +--R (449) log(x) +--R Type: Union(Expression Integer,...) +--E 484 + +--S 485 of 486 +m0389:= a0389-r0389 +--R +--R +--R +--+ +--R | 1 +--R (450) - x log(x) |-- + log(x) +--R 3| 3 +--R \|x +--R Type: Expression Integer +--E 485 + +--S 486 of 486 +d0389:= D(m0389,x) +--R +--R +--R +--+2 +--R 2 | 1 +--R x |-- - 1 +--R 3| 3 +--R \|x +--R (451) ------------ +--R +--+2 +--R 3 | 1 +--R x |-- +--R 3| 3 +--R \|x +--R Type: Expression Integer +--E 486 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}