diff --git a/changelog b/changelog index c365e51..7d71ae3 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100604 tpd src/axiom-website/patches.html 20100604.06.tpd.patch +20100604 tpd src/input/Makefile add rule-based algebraic integration +20100604 tpd src/input/richalgebraic100-199.input rule-based algebraic int. 20100604 tpd src/axiom-website/patches.html 20100604.05.tpd.patch 20100604 tpd books/bookvolbib cite Albert D. Rich website 20100604 tpd src/input/unittest1.input add Albert D. Rich to credits diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 4f90f45..6bf4eba 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2844,5 +2844,7 @@ src/input/richrational.input add rule-based rational integration
src/input/richalgebraic000-099.input rule-based algebraic integration
20100605.05.tpd.patch books/bookvol5 add Albert D. Rich to credits
+20100605.06.tpd.patch +src/input/richalgebraic100-199.input rule-based algebraic integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index b76e4b1..9b4d525 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -368,7 +368,9 @@ REGRES= ackermann.regress \ quat1.regress quat.regress r20abugs.regress r20bugs.regress \ r21bugsbig.regress r21bugs.regress radff.regress radix.regress \ realclos.regress reclos.regress reclos2.regress regset.regress \ - repa6.regress richalgebraic000-099.regress \ + repa6.regress \ + richalgebraic000-099.regress \ + richalgebraic100-199.regress \ richrational.regress robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ @@ -682,6 +684,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/radff.input ${OUT}/radix.input ${OUT}/realclos.input \ ${OUT}/reclos.input ${OUT}/reclos2.input ${OUT}/regset.input \ ${OUT}/richalgebraic000-099.input \ + ${OUT}/richalgebraic100-199.input \ ${OUT}/richrational.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ @@ -1025,6 +1028,7 @@ DOCFILES= \ ${DOC}/ribbon.input.dvi ${DOC}/ribbons.input.dvi \ ${DOC}/ribbonsnew.input.dvi \ ${DOC}/richalgebraic000-099.input.dvi \ + ${DOC}/richalgebraic100-199.input.dvi \ ${DOC}/richrational.input.dvi \ ${DOC}/rk4draw.input.dvi \ ${DOC}/robidoux.input.dvi ${DOC}/roman.input.dvi \ diff --git a/src/input/richalgebraic100-199.input.pamphlet b/src/input/richalgebraic100-199.input.pamphlet new file mode 100644 index 0000000..29a4df5 --- /dev/null +++ b/src/input/richalgebraic100-199.input.pamphlet @@ -0,0 +1,13442 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richalgebraic100-199.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richalgebraic100-199.output +)spool richalgebraic100-199.output +)set message test on +)set message auto off +)clear all + +--S 1 of 512 +t0100:= x^3/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 3 +--R x +--R (1) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression Integer +--E 1 + +--S 2 of 512 +r0100:= -2/3*c^3*(a+b*x)^(1/2)/d^3/(b*c-a*d)/(c+d*x)^(3/2)-_ + 4/3*b*c^3*(a+b*x)^(1/2)/d^3/(b*c-a*d)^2/(c+d*x)^(1/2)+_ + 6*c^2*(a+b*x)^(1/2)/d^3/(b*c-a*d)/(c+d*x)^(1/2)+(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/b/d^3-5*c*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(1/2)/d^(7/2)-a*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(3/2)/d^(5/2) +--R +--R +--R (2) +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (- 3a d - 9a b c d + 27a b c d - 15b c d)x - 3a c d - 9a b c d +--R + +--R 2 3 3 4 +--R 27a b c d - 15b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 4 3 2 2 2 2 2 3 2 2 2 3 +--R (3a d - 6a b c d + 3b c d )x + (6a c d - 30a b c d + 20b c d)x +--R + +--R 2 2 2 3 2 4 +--R 3a c d - 22a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|b x + a +--R / +--R 2 6 2 5 3 2 4 2 5 2 2 4 3 3 3 +-+ +--R ((3a b d - 6a b c d + 3b c d )x + 3a b c d - 6a b c d + 3b c d )\|b +--R * +--R +-+ +-------+ +--R \|d \|d x + c +--R Type: Expression Integer +--E 2 + +--S 3 of 512 +--a0100:= integrate(t0100,x) +--E 3 + +--S 4 of 512 +--m0100:= a0100-r0100 +--E 4 + +--S 5 of 512 +--d0100:= D(m0100,x) +--E 5 + +--S 6 of 512 +t0101:= x^2/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 2 +--R x +--R (3) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression Integer +--E 6 + +--S 7 of 512 +r0101:= 2/3*c^2*(a+b*x)^(1/2)/d^2/(b*c-a*d)/(c+d*x)^(3/2)+_ + 4/3*b*c^2*(a+b*x)^(1/2)/d^2/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 4*c*(a+b*x)^(1/2)/d^2/(b*c-a*d)/(c+d*x)^(1/2)+_ + 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(5/2) +--R +--R +--R (4) +--R 2 3 2 2 2 2 2 2 2 3 +--R ((6a d - 12a b c d + 6b c d)x + 6a c d - 12a b c d + 6b c ) +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 3 +-+ +-+ +-------+ +--R ((12a c d - 8b c d)x + 10a c d - 6b c )\|b \|d \|b x + a +--R / +--R 2 5 4 2 2 3 2 4 2 3 2 3 2 +-+ +-+ +--R ((3a d - 6a b c d + 3b c d )x + 3a c d - 6a b c d + 3b c d )\|b \|d +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression Integer +--E 7 + +--S 8 of 512 +--a0101:= integrate(t0101,x) +--E 8 + +--S 9 of 512 +--m0101:= a0101-r0101 +--E 9 + +--S 10 of 512 +--d0101:= D(m0101,x) +--E 10 + +--S 11 of 512 +t0102:= 1/x/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 1 +--R (5) ------------------------------------------ +--R 2 3 2 2 +-------+ +-------+ +--R (d x + 2c d x + c x)\|b x + a \|d x + c +--R Type: Expression Integer +--E 11 + +--S 12 of 512 +r0102:= -2/3*d*(a+b*x)^(1/2)/c/(b*c-a*d)/(c+d*x)^(3/2)-_ + 4/3*b*d*(a+b*x)^(1/2)/c/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 2*d*(a+b*x)^(1/2)/c^2/(b*c-a*d)/(c+d*x)^(1/2)-_ + 2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(5/2) +--R +--R +--R (6) +--R 2 3 2 2 2 2 2 2 2 3 +--R ((- 6a d + 12a b c d - 6b c d)x - 6a c d + 12a b c d - 6b c ) +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 2 2 2 +-+ +-+ +-------+ +--R ((6a d - 10b c d )x + 8a c d - 12b c d)\|a \|c \|b x + a +--R / +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +-+ +-+ +--R ((3a c d - 6a b c d + 3b c d)x + 3a c d - 6a b c d + 3b c )\|a \|c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression Integer +--E 12 + +--S 13 of 512 +--a0102:= integrate(t0102,x) +--E 13 + +--S 14 of 512 +--m0102:= a0102-r0102 +--E 14 + +--S 15 of 512 +--d0102:= D(m0102,x) +--E 15 + +--S 16 of 512 +t0103:= 1/x^2/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 1 +--R (7) ------------------------------------------- +--R 2 4 3 2 2 +-------+ +-------+ +--R (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression Integer +--E 16 + +--S 17 of 512 +r0103:= 2/3*d^2*(a+b*x)^(1/2)/c^2/(b*c-a*d)/(c+d*x)^(3/2)+_ + 4/3*b*d^2*(a+b*x)^(1/2)/c^2/(b*c-a*d)^2/(c+d*x)^(1/2)+_ + 4*d^2*(a+b*x)^(1/2)/c^3/(b*c-a*d)/(c+d*x)^(1/2)-_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^3/x+_ + b*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/c^(5/2)+_ + 5*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(7/2) +--R +--R +--R (8) +--R 3 4 2 3 2 2 2 3 3 2 +--R (15a d - 27a b c d + 9a b c d + 3b c d)x +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (15a c d - 27a b c d + 9a b c d + 3b c )x +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 4 3 2 2 2 2 +--R (- 15a d + 22a b c d - 3b c d )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 20a c d + 30a b c d - 6b c d)x - 3a c d + 6a b c d - 3b c +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|b x + a +--R / +--R 3 3 3 2 4 2 2 5 2 3 4 2 2 5 2 6 +--R ((3a c d - 6a b c d + 3a b c d)x + (3a c d - 6a b c d + 3a b c )x) +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|d x + c +--R Type: Expression Integer +--E 17 + +--S 18 of 512 +--a0103:= integrate(t0103,x) +--E 18 + +--S 19 of 512 +--m0103:= a0103-r0103 +--E 19 + +--S 20 of 512 +--d0103:= D(m0103,x) +--E 20 + +--S 21 of 512 +t0104:= 1/x^3/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 1 +--R (9) ------------------------------------------- +--R 2 5 4 2 3 +-------+ +-------+ +--R (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression Integer +--E 21 + +--S 22 of 512 +r0104:= -2/3*d^3*(a+b*x)^(1/2)/c^3/(b*c-a*d)/(c+d*x)^(3/2)-_ + 4/3*b*d^3*(a+b*x)^(1/2)/c^3/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 6*d^3*(a+b*x)^(1/2)/c^4/(b*c-a*d)/(c+d*x)^(1/2)-_ + 1/2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^3/x^2+3/4*b*(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/a^2/c^3/x+11/4*d*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^4/x-_ + b*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/_ + c^(7/2)-8*d^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/_ + a^(1/2)/c^(9/2)-3/4*(b*c+a*d)^2*atanh(c^(1/2)*(a+b*x)^(1/2)/_ + a^(1/2)/(c+d*x)^(1/2))/a^(5/2)/c^(9/2) +--R +--R +--R (10) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3 +--R (- 105a d + 180a b c d - 54a b c d - 12a b c d - 9b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 2 +--R (- 105a c d + 180a b c d - 54a b c d - 12a b c d - 9b c )x +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 5 2 4 2 2 3 3 3 2 3 +--R (105a d - 145a b c d + 15a b c d + 9b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 2 +--R (140a c d - 198a b c d + 24a b c d + 18b c d)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 3 2 2 4 +--R (21a c d - 33a b c d + 3a b c d + 9b c )x - 6a c d + 12a b c d +--R + +--R 2 5 +--R - 6a b c +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|b x + a +--R / +--R 4 4 3 3 5 2 2 2 6 3 +--R (12a c d - 24a b c d + 12a b c d)x +--R + +--R 4 5 2 3 6 2 2 7 2 +--R (12a c d - 24a b c d + 12a b c )x +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|d x + c +--R Type: Expression Integer +--E 22 + +--S 23 of 512 +--a0104:= integrate(t0104,x) +--E 23 + +--S 24 of 512 +--m0104:= a0104-r0104 +--E 24 + +--S 25 of 512 +--d0104:= D(m0104,x) +--E 25 + +--S 26 of 512 +t0105:= x^3/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 3 +--R x +--R (11) ------------------------------------------------- +--R 2 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c +--R Type: Expression Integer +--E 26 + +--S 27 of 512 +r0105:= 2*a*c/b^2/d^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+_ + 2*a*c*(b*c+a*d)/b^2/d^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + 3/4*(b*c+a*d)^2/b^3/d^3/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + 3/4*(b*c+a*d)^3/b^3/d^3/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+_ + 3/2*(b*c+a*d)*x/b^2/d^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+x^2/b/d/_ + (a+b*x)^(1/2)/(c+d*x)^(1/2)-4*a*c*(b*c+a*d)*(c+d*x)^(1/2)/b/d^2/_ + (b*c-a*d)^2/(a+b*x)^(1/2)+3/2*(b*c+a*d)^3*(c+d*x)^(1/2)/b^2/d^3/_ + (b*c-a*d)^2/(a+b*x)^(1/2)-3*(b*c+a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/d^(5/2) +--R +--R +--R (12) +--R 3 3 2 2 2 2 3 3 +-------+ +-------+ +--R (- 3a d + 3a b c d + 3a b c d - 3b c )\|b x + a \|d x + c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 3 2 2 3 2 2 +--R (a b d - 2a b c d + b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (3a d - a b c d - a b c d + 3b c )x + 3a c d - 2a b c d + 3a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 2 2 4 3 3 4 2 2 +-+ +-+ +-------+ +-------+ +--R (a b d - 2a b c d + b c d )\|b \|d \|b x + a \|d x + c +--R Type: Expression Integer +--E 27 + +--S 28 of 512 +--a0105:= integrate(t0105,x) +--E 28 + +--S 29 of 512 +--m0105:= a0105-r0105 +--E 29 + +--S 30 of 512 +--d0105:= D(m0105,x) +--E 30 + +--S 31 of 512 +t0106:= x^2/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 2 +--R x +--R (13) ------------------------------------------------- +--R 2 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c +--R Type: Expression Integer +--E 31 + +--S 32 of 512 +r0106:= 1/2*(b*c+a*d)/b^2/d^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+_ + 1/2*(b*c+a*d)^2/b^2/d^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + x/b/d/(a+b*x)^(1/2)/(c+d*x)^(1/2)-(b*c+a*d)^2*(c+d*x)^(1/2)/b/d^2/_ + (b*c-a*d)^2/(a+b*x)^(1/2)+2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(3/2)/d^(3/2) +--R +--R +--R (14) +--R +-+ +-------+ +--R 2 2 2 2 +-------+ +-------+ \|d \|b x + a +--R (2a d - 4a b c d + 2b c )\|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 +-+ +-+ +--R ((- 2a d - 2b c )x - 2a c d - 2a b c )\|b \|d +--R / +--R 2 3 2 2 3 2 +-+ +-+ +-------+ +-------+ +--R (a b d - 2a b c d + b c d)\|b \|d \|b x + a \|d x + c +--R Type: Expression Integer +--E 32 + +--S 33 of 512 +--a0106:= integrate(t0106,x) +--E 33 + +--S 34 of 512 +--m0106:= a0106-r0106 +--E 34 + +--S 35 of 512 +--d0106:= D(m0106,x) +--E 35 + +--S 36 of 512 +t0107:= 1/x/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (15) ---------------------------------------------------- +--R 3 2 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c x)\|b x + a \|d x + c +--R Type: Expression Integer +--E 36 + +--S 37 of 512 +r0107:= 1/a/c/(a+b*x)^(1/2)/(c+d*x)^(1/2)-(b*c+a*d)/a/c/(b*c-a*d)/_ + (a+b*x)^(1/2)/(c+d*x)^(1/2)+2*b*(b*c+a*d)*(c+d*x)^(1/2)/a/c/_ + (b*c-a*d)^2/(a+b*x)^(1/2)-2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(3/2)/c^(3/2) +--R +--R +--R (16) +--R +-+ +-------+ +--R 2 2 2 2 +-------+ +-------+ \|c \|b x + a +--R (- 2a d + 4a b c d - 2b c )\|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 +-+ +-+ +--R ((2a b d + 2b c d)x + 2a d + 2b c )\|a \|c +--R / +--R 3 2 2 2 2 3 +-+ +-+ +-------+ +-------+ +--R (a c d - 2a b c d + a b c )\|a \|c \|b x + a \|d x + c +--R Type: Expression Integer +--E 37 + +--S 38 of 512 +--a0107:= integrate(t0107,x) +--E 38 + +--S 39 of 512 +--m0107:= a0107-r0107 +--E 39 + +--S 40 of 512 +--d0107:= D(m0107,x) +--E 40 + +--S 41 of 512 +t0108:= 1/x^2/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (17) ----------------------------------------------------- +--R 4 3 2 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c x )\|b x + a \|d x + c +--R Type: Expression Integer +--E 41 + +--S 42 of 512 +r0108:= -4*b*d/a/c/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-3/2*(b*c+a*d)/_ + a^2/c^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+3/2*(b*c+a*d)^2/a^2/c^2/_ + (b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-1/a/c/x/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)+8*b^2*d*(c+d*x)^(1/2)/a/c/(b*c-a*d)^2/(a+b*x)^(1/2)-_ + 3*b*(b*c+a*d)^2*(c+d*x)^(1/2)/a^2/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)+_ + 3*(b*c+a*d)*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/_ + a^(5/2)/c^(5/2) +--R +--R +--R (18) +--R 3 3 2 2 2 2 3 3 +-------+ +-------+ +--R (3a d - 3a b c d - 3a b c d + 3b c )x\|b x + a \|d x + c +--R * +--R +-+ +-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 3 2 2 3 2 2 +--R (- 3a b d + 2a b c d - 3b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (- 3a d + a b c d + a b c d - 3b c )x - a c d + 2a b c d - a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 2 3 3 2 2 4 +-+ +-+ +-------+ +-------+ +--R (a c d - 2a b c d + a b c )x\|a \|c \|b x + a \|d x + c +--R Type: Expression Integer +--E 42 + +--S 43 of 512 +--a0108:= integrate(t0108,x) +--E 43 + +--S 44 of 512 +--m0108:= a0108-r0108 +--E 44 + +--S 45 of 512 +--d0108:= D(m0108,x) +--E 45 + +--S 46 of 512 +t0109:= 1/x^3/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (19) ----------------------------------------------------- +--R 5 4 3 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c x )\|b x + a \|d x + c +--R Type: Expression Integer +--E 46 + +--S 47 of 512 +r0109:= -3/2*b*d/a^2/c^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+13/2*b*d*(b*c+a*d)/_ + a^2/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+15/8*(b*c+a*d)^2/_ + a^3/c^3/(a+b*x)^(1/2)/(c+d*x)^(1/2)-15/8*(b*c+a*d)^3/a^3/c^3/_ + (b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-1/2/a/c/x^2/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)+5/4*(b*c+a*d)/a^2/c^2/x/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + 13*b^2*d*(b*c+a*d)*(c+d*x)^(1/2)/a^2/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)+_ + 15/4*b*(b*c+a*d)^3*(c+d*x)^(1/2)/a^3/c^3/(b*c-a*d)^2/(a+b*x)^(1/2)+_ + 3*b*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(5/2)/_ + c^(5/2)-15/4*(b*c+a*d)^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(7/2)/c^(7/2) +--R +--R +--R (20) +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +-------+ +--R (- 15a d + 12a b c d + 6a b c d + 12a b c d - 15b c )x \|b x + a +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (15a b d - 7a b c d - 7a b c d + 15b c d)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (15a d - 2a b c d - 10a b c d - 2a b c d + 15b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 +--R (5a c d - 5a b c d - 5a b c d + 5a b c )x - 2a c d + 4a b c d +--R + +--R 2 2 4 +--R - 2a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 5 3 2 4 4 3 2 5 2 +-+ +-+ +-------+ +-------+ +--R (4a c d - 8a b c d + 4a b c )x \|a \|c \|b x + a \|d x + c +--R Type: Expression Integer +--E 47 + +--S 48 of 512 +--a0109:= integrate(t0109,x) +--E 48 + +--S 49 of 512 +--m0109:= a0109-r0109 +--E 49 + +--S 50 of 512 +--d0109:= D(m0109,x) +--E 50 + +--S 51 of 512 +t0110:= x^5/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (21) +--R 5 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression Integer +--E 51 + +--S 52 of 512 +r0110:= 2*a^5/b^5/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)+8/3*a^5*d*_ + (a+b*x)^(1/2)/b^5/(b*c-a*d)^2/(c+d*x)^(3/2)+10/3*a^4*(a+b*x)^(1/2)/_ + b^5/(b*c-a*d)/(c+d*x)^(3/2)-20/3*a^2*(a+b*x)^(3/2)/b^5/d/_ + (c+d*x)^(3/2)-20/3*a^3*(a+b*x)^(3/2)/b^5/(b*c-a*d)/(c+d*x)^(3/2)+_ + 10/3*a*(a+b*x)^(5/2)/b^5/d/(c+d*x)^(3/2)-2/3*(a+b*x)^(7/2)/b^5/d/_ + (c+d*x)^(3/2)-20*a^2*(a+b*x)^(1/2)/b^4/d^2/(c+d*x)^(1/2)+16/3*a^5*_ + d*(a+b*x)^(1/2)/b^4/(b*c-a*d)^3/(c+d*x)^(1/2)+20/3*a^4*_ + (a+b*x)^(1/2)/b^4/(b*c-a*d)^2/(c+d*x)^(1/2)+50/3*a*(a+b*x)^(3/2)/_ + b^4/d^2/(c+d*x)^(1/2)-14/3*(a+b*x)^(5/2)/b^4/d^2/(c+d*x)^(1/2)-_ + 25*a*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^3-35/4*(b*c-a*d)*_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^4+35/6*(a+b*x)^(3/2)*_ + (c+d*x)^(1/2)/b^3/d^3+20*a^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(5/2)+25*a*(b*c-a*d)*atanh(d^(1/2)*_ + (a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(7/2)/d^(7/2)+35/4*_ + (b*c-a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(7/2)/d^(9/2) +--R +--R +--R (22) +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 45a d - 45a b c d - 30a b c d - 90a b c d + 225a b c d +--R + +--R 5 5 +--R - 105b c d +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R 45a c d - 45a b c d - 30a b c d - 90a b c d + 225a b c d - 105b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 4 +--R (6a b d - 18a b c d + 18a b c d - 6b c d )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (- 15a b d + 24a b c d + 18a b c d - 48a b c d + 21b c d )x +--R + +--R 5 6 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (- 45a d + 66a b c d + 12a b c d - 237a b c d + 140b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R - 90a c d + 45a b c d + 84a b c d - 222a b c d - 50a b c d +--R + +--R 5 6 +--R 105b c +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R - 45a c d + 30a b c d + 36a b c d - 190a b c d + 105a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 3 8 2 4 7 5 2 6 6 3 5 3 3 7 +--R (12a b d - 36a b c d + 36a b c d - 12b c d )x + 12a b c d +--R + +--R 2 4 2 6 5 3 5 6 4 4 +--R - 36a b c d + 36a b c d - 12b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression Integer +--E 52 + +--S 53 of 512 +--a0110:= integrate(t0110,x) +--E 53 + +--S 54 of 512 +--m0110:= a0110-r0110 +--E 54 + +--S 55 of 512 +--d0110:= D(m0110,x) +--E 55 + +--S 56 of 512 +t0111:= x^4/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (23) +--R 4 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression Integer +--E 56 + +--S 57 of 512 +r0111:= -2*a^4/b^4/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)-8/3*a^4*d*_ + (a+b*x)^(1/2)/b^4/(b*c-a*d)^2/(c+d*x)^(3/2)-8/3*a^3*(a+b*x)^(1/2)/_ + b^4/(b*c-a*d)/(c+d*x)^(3/2)+8/3*a*(a+b*x)^(3/2)/b^4/d/(c+d*x)^(3/2)+_ + 4*a^2*(a+b*x)^(3/2)/b^4/(b*c-a*d)/(c+d*x)^(3/2)-2/3*(a+b*x)^(5/2)/_ + b^4/d/(c+d*x)^(3/2)+8*a*(a+b*x)^(1/2)/b^3/d^2/(c+d*x)^(1/2)-_ + 16/3*a^4*d*(a+b*x)^(1/2)/b^3/(b*c-a*d)^3/(c+d*x)^(1/2)-_ + 16/3*a^3*(a+b*x)^(1/2)/b^3/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 10/3*(a+b*x)^(3/2)/b^3/d^2/(c+d*x)^(1/2)+5*(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/b^2/d^3-5*c*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(3/2)/d^(7/2)-3*a*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/d^(5/2) +--R +--R +--R (24) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 4 +--R (- 9a d + 12a b c d + 18a b c d - 36a b c d + 15b c d)x - 9a c d +--R + +--R 3 2 3 2 2 3 2 3 4 4 5 +--R 12a b c d + 18a b c d - 36a b c d + 15b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (9a d - 3a b c d - 9a b c d + 39a b c d - 20b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (18a c d - 15a b c d + 33a b c d + 11a b c d - 15b c )x + 9a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R - 9a b c d + 31a b c d - 15a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 2 7 2 3 6 4 2 5 5 3 4 3 2 6 2 3 2 5 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 4 3 4 5 4 3 +--R 9a b c d - 3b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression Integer +--E 57 + +--S 58 of 512 +--a0111:= integrate(t0111,x) +--E 58 + +--S 59 of 512 +--m0111:= a0111-r0111 +--E 59 + +--S 60 of 512 +--d0111:= D(m0111,x) +--E 60 + +--S 61 of 512 +t0112:= x^3/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (25) +--R 3 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression Integer +--E 61 + +--S 62 of 512 +r0112:= 2*a^3/b^3/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)+8/3*a^3*d*_ + (a+b*x)^(1/2)/b^3/(b*c-a*d)^2/(c+d*x)^(3/2)+2*a^2*(a+b*x)^(1/2)/_ + b^3/(b*c-a*d)/(c+d*x)^(3/2)-2/3*(a+b*x)^(3/2)/b^3/d/(c+d*x)^(3/2)-_ + 2*a*(a+b*x)^(3/2)/b^3/(b*c-a*d)/(c+d*x)^(3/2)-2*(a+b*x)^(1/2)/_ + b^2/d^2/(c+d*x)^(1/2)+16/3*a^3*d*(a+b*x)^(1/2)/b^2/(b*c-a*d)^3/_ + (c+d*x)^(1/2)+4*a^2*(a+b*x)^(1/2)/b^2/(b*c-a*d)^2/(c+d*x)^(1/2)+_ + 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(3/2)/d^(5/2) +--R +--R +--R (26) +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (6a d - 18a b c d + 18a b c d - 6b c d)x + 6a c d - 18a b c d +--R + +--R 2 3 3 4 +--R 18a b c d - 6b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 4 2 2 2 3 3 2 +--R (- 6a d - 18a b c d + 8b c d)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 2 2 2 3 +--R (- 12a c d - 18a b c d - 8a b c d + 6b c )x - 6a c d - 16a b c d +--R + +--R 2 4 +--R 6a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 6 2 2 5 3 2 4 4 3 3 3 5 2 2 2 4 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 3 3 3 4 4 2 +--R 9a b c d - 3b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression Integer +--E 62 + +--S 63 of 512 +--a0112:= integrate(t0112,x) +--E 63 + +--S 64 of 512 +--m0112:= a0112-r0112 +--E 64 + +--S 65 of 512 +--d0112:= D(m0112,x) +--E 65 + +--S 66 of 512 +t0113:= 1/x/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (27) +--R 1 +--R ---------------------------------------------------------------------------- +--R 2 4 2 3 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x)\|b x + a \|d x + c +--R Type: Expression Integer +--E 66 + +--S 67 of 512 +r0113:= 2*d/c/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)+8/3*d^2*(a+b*x)^(1/2)/_ + c/(b*c-a*d)^2/(c+d*x)^(3/2)+1/a/c^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + (b*c+a*d)/a/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+16/3*b*d^2*_ + (a+b*x)^(1/2)/c/(b*c-a*d)^3/(c+d*x)^(1/2)+2*b*(b*c+a*d)*_ + (c+d*x)^(1/2)/a/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)-2*atanh(c^(1/2)*_ + (a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/c^(5/2) +--R +--R +--R (28) +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (- 6a d + 18a b c d - 18a b c d + 6b c d)x - 6a c d + 18a b c d +--R + +--R 2 3 3 4 +--R - 18a b c d + 6b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 4 2 3 3 2 2 2 +--R (6a b d - 16a b c d - 6b c d )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (6a d - 8a b c d - 18a b c d - 12b c d)x + 8a c d - 18a b c d +--R + +--R 3 4 +--R - 6b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 3 3 3 4 2 +--R (3a c d - 9a b c d + 9a b c d - 3a b c d)x + 3a c d - 9a b c d +--R + +--R 2 2 5 3 6 +--R 9a b c d - 3a b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression Integer +--E 67 + +--S 68 of 512 +--a0113:= integrate(t0113,x) +--E 68 + +--S 69 of 512 +--m0113:= a0113-r0113 +--E 69 + +--S 70 of 512 +--d0113:= D(m0113,x) +--E 70 + +--S 71 of 512 +t0114:= 1/x^2/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (29) +--R 1 +--R ----------------------------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|b x + a \|d x + c +--R Type: Expression Integer +--E 71 + +--S 72 of 512 +r0114:= -2*d^2/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)-8/3*d^3*_ + (a+b*x)^(1/2)/c^2/(b*c-a*d)^2/(c+d*x)^(3/2)-d/a/c^3/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)-4*b*d/a/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + 3/2*(b*c+a*d)/a^2/c^3/(a+b*x)^(1/2)/(c+d*x)^(1/2)+d*(b*c+a*d)/a/_ + c^3/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+3/2*(b*c+a*d)^2/a^2/_ + c^3/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-1/a/c^2/x/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)-16/3*b*d^3*(a+b*x)^(1/2)/c^2/(b*c-a*d)^3/_ + (c+d*x)^(1/2)+8*b^2*d*(c+d*x)^(1/2)/a/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)-_ + 2*b*d*(b*c+a*d)*(c+d*x)^(1/2)/a/c^3/(b*c-a*d)^2/(a+b*x)^(1/2)-_ + 3*b*(b*c+a*d)^2*(c+d*x)^(1/2)/a^2/c^3/(b*c-a*d)^2/(a+b*x)^(1/2)+_ + 2*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/_ + c^(7/2)+3*(b*c+a*d)*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(5/2)/c^(7/2) +--R +--R +--R (30) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (15a d - 36a b c d + 18a b c d + 12a b c d - 9b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R (15a c d - 36a b c d + 18a b c d + 12a b c d - 9b c )x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (- 15a b d + 31a b c d - 9a b c d + 9b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 15a d + 11a b c d + 33a b c d - 15a b c d + 18b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (- 20a c d + 39a b c d - 9a b c d - 3a b c d + 9b c )x - 3a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R 9a b c d - 9a b c d + 3a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 2 +--R (3a c d - 9a b c d + 9a b c d - 3a b c d)x +--R + +--R 5 4 3 4 5 2 3 2 6 2 3 7 +--R (3a c d - 9a b c d + 9a b c d - 3a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression Integer +--E 72 + +--S 73 of 512 +--a0114:= integrate(t0114,x) +--E 73 + +--S 74 of 512 +--m0114:= a0114-r0114 +--E 74 + +--S 75 of 512 +--d0114:= D(m0114,x) +--E 75 + +--S 76 of 512 +t0115:= 1/x/(a+b*x)^(5/2)/(c+d*x)^(5/2) +--R +--R +--R (31) +--R 1 +--R / +--R 2 2 5 2 2 4 2 2 2 2 3 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression Integer +--E 76 + +--S 77 of 512 +r0115:= 1/3/a/c/(a+b*x)^(3/2)/(c+d*x)^(3/2)-1/3*(b*c+a*d)/a/c/(b*c-a*d)/_ + (a+b*x)^(3/2)/(c+d*x)^(3/2)-2*b*(b*c+a*d)/a/c/(b*c-a*d)^2/_ + (a+b*x)^(3/2)/(c+d*x)^(1/2)+1/a^2/c^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + (b*c+a*d)/a^2/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+8/3*b^2*_ + (b*c+a*d)*(c+d*x)^(1/2)/a/c/(b*c-a*d)^3/(a+b*x)^(3/2)-16/3*b^2*d*_ + (b*c+a*d)*(c+d*x)^(1/2)/a/c/(b*c-a*d)^4/(a+b*x)^(1/2)+2*b*_ + (b*c+a*d)*(c+d*x)^(1/2)/a^2/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)-_ + 2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(5/2)/c^(5/2) +--R +--R +--R (32) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (- 6a b d + 24a b c d - 36a b c d + 24a b c d - 6b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (- 6a d + 18a b c d - 12a b c d - 12a b c d + 18a b c d - 6b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R - 6a c d + 24a b c d - 36a b c d + 24a b c d - 6a b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 3 +--R (6a b d - 22a b c d - 22a b c d + 6b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (12a b d - 36a b c d - 48a b c d - 36a b c d + 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (6a d - 6a b c d - 48a b c d - 48a b c d - 6a b c d + 6b c )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 +--R 8a c d - 24a b c d - 24a b c d + 8a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 2 5 6 2 +--R (3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d)x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R (3a c d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3a b c )x +--R + +--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression Integer +--E 77 + +--S 78 of 512 +--a0115:= integrate(t0115,x) +--E 78 + +--S 79 of 512 +--m0115:= a0115-r0115 +--E 79 + +--S 80 of 512 +--d0115:= D(m0115,x) +--E 80 + +--S 81 of 512 +t0116:= 1/x^2/(a+b*x)^(5/2)/(c+d*x)^(5/2) +--R +--R +--R (33) +--R 1 +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 3 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression Integer +--E 81 + +--S 82 of 512 +r0116:= -8/3*b*d/a/c/(b*c-a*d)/(a+b*x)^(3/2)/(c+d*x)^(3/2)-_ + 5/6*(b*c+a*d)/a^2/c^2/(a+b*x)^(3/2)/(c+d*x)^(3/2)+_ + 5/6*(b*c+a*d)^2/a^2/c^2/(b*c-a*d)/(a+b*x)^(3/2)/(c+d*x)^(3/2)-_ + 1/a/c/x/(a+b*x)^(3/2)/(c+d*x)^(3/2)-16*b^2*d/a/c/(b*c-a*d)^2/_ + (a+b*x)^(3/2)/(c+d*x)^(1/2)+5*b*(b*c+a*d)^2/a^2/c^2/(b*c-a*d)^2/_ + (a+b*x)^(3/2)/(c+d*x)^(1/2)-5/2*(b*c+a*d)/a^3/c^3/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)+5/2*(b*c+a*d)^2/a^3/c^3/(b*c-a*d)/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)+64/3*b^3*d*(c+d*x)^(1/2)/a/c/(b*c-a*d)^3/_ + (a+b*x)^(3/2)-20/3*b^2*(b*c+a*d)^2*(c+d*x)^(1/2)/a^2/c^2/_ + (b*c-a*d)^3/(a+b*x)^(3/2)-128/3*b^3*d^2*(c+d*x)^(1/2)/a/c/_ + (b*c-a*d)^4/(a+b*x)^(1/2)+40/3*b^2*d*(b*c+a*d)^2*(c+d*x)^(1/2)/_ + a^2/c^2/(b*c-a*d)^4/(a+b*x)^(1/2)-5*b*(b*c+a*d)^2*(c+d*x)^(1/2)/_ + a^3/c^3/(b*c-a*d)^2/(a+b*x)^(1/2)+5*(b*c+a*d)*_ + atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(7/2)/c^(7/2) +--R +--R +--R (34) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 15a b d - 45a b c d + 30a b c d + 30a b c d - 45a b c d +--R + +--R 6 5 +--R 15b c d +--R * +--R 3 +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 15a d - 30a b c d - 15a b c d + 60a b c d - 15a b c d +--R + +--R 5 5 6 6 +--R - 30a b c d + 15b c +--R * +--R 2 +--R x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R 15a c d - 45a b c d + 30a b c d + 30a b c d - 45a b c d +--R + +--R 5 6 +--R 15a b c +--R * +--R x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4 +--R (- 15a b d + 40a b c d - 18a b c d + 40a b c d - 15b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 30a b d + 60a b c d + 18a b c d + 18a b c d + 60a b c d +--R + +--R 6 5 +--R - 30b c d +--R * +--R 3 +--R x +--R + +--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2 +--R (- 15a d + 87a b c d - 48a b c d + 87a b c d - 15b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R - 20a c d + 48a b c d - 12a b c d - 12a b c d + 48a b c d +--R + +--R 5 6 +--R - 20a b c +--R * +--R x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R - 3a c d + 12a b c d - 18a b c d + 12a b c d - 3a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 7 3 5 6 2 4 4 5 3 5 3 4 4 6 2 3 5 7 3 +--R (3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d)x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 2 +--R (3a c d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3a b c )x +--R + +--R 8 4 4 7 5 3 6 2 6 2 5 3 7 4 4 8 +--R (3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression Integer +--E 82 + +--S 83 of 512 +--a0116:= integrate(t0116,x) +--E 83 + +--S 84 of 512 +--m0116:= a0116-r0116 +--E 84 + +--S 85 of 512 +--d0116:= D(m0116,x) +--E 858 + +--S 86 of 512 +t0117:= x^3*(a+b*x)^(1/2)*(c+d*x)^(5/2) +--R +--R +--R 2 5 4 2 3 +-------+ +-------+ +--R (35) (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression Integer +--E 86 + +--S 87 of 512 +r0117:= -33/1024*(b*c-a*d)^6*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^6/d^4-_ + 11/512*(b*c-a*d)^5*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^5/d^4-_ + 11/640*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^4/d^4-_ + 33/2240*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(7/2)/b^3/d^4-_ + 11/840*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(9/2)/b^2/d^4-_ + 1/84*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(11/2)/b/d^4+5/64*c^3*_ + (b*c-a*d)^4*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(7/2)/d^(9/2)-21/128*c^2*(b*c-a*d)^5*atanh(d^(1/2)*_ + (a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(9/2)/d^(9/2)+_ + 63/512*c*(b*c-a*d)^6*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(11/2)/d^(9/2)+1/7*(a+b*x)^(1/2)*_ + (c+d*x)^(13/2)/d^4-1/4*c^3*(a+b*x)^(1/2)*(c+d*x)^(7/2)/d^4+_ + 3/5*c^2*(a+b*x)^(1/2)*(c+d*x)^(9/2)/d^4-1/2*c*(a+b*x)^(1/2)*_ + (c+d*x)^(11/2)/d^4-33/1024*(b*c-a*d)^7*atanh(d^(1/2)*_ + (a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(13/2)/d^(9/2)+_ + 5/64*c^3*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^4-_ + 21/128*c^2*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^4/d^4+_ + 63/512*c*(b*c-a*d)^5*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^5/d^4+_ + 5/96*c^3*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^2/d^4-_ + 7/64*c^2*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^3/d^4+_ + 21/256*c*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^4/d^4+_ + 1/24*c^3*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b/d^4-_ + 7/80*c^2*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^2/d^4+_ + 21/320*c*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^3/d^4-_ + 3/40*c^2*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(7/2)/b/d^4+_ + 9/160*c*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(7/2)/b^2/d^4+_ + 1/20*c*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(9/2)/b/d^4 +--R +--R +--R (36) +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 3465a d - 11025a b c d + 11025a b c d - 2625a b c d - 525a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 315a b c d - 525a b c d + 525b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 6 6 6 5 6 6 5 5 +--R 15360b d x + (1280a b d + 37120b c d )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 1408a b d + 3840a b c d + 23680b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1584a b d - 4336a b c d + 3280a b c d + 240b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 1848a b d + 5088a b c d - 3888a b c d + 160a b c d +--R + +--R 6 4 2 +--R - 280b c d +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 2310a b d - 6426a b c d + 5004a b c d - 260a b c d +--R + +--R 5 4 2 6 5 +--R - 210a b c d + 350b c d +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 3465a d + 9870a b c d - 8043a b c d + 660a b c d + 385a b c d +--R + +--R 5 5 6 6 +--R 350a b c d - 525b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 6 4 +-+ +-+ +--R 107520b d \|b \|d +--R Type: Expression Integer +--E 87 + +--S 88 of 512 +--a0117:= integrate(t0117,x) +--E 88 + +--S 89 of 512 +--m0117:= a0117-r0117 +--E 89 + +--S 90 of 512 +--d0117:= D(m0117,x) +--E 90 + +--S 91 of 512 +t0118:= x^2*(a+b*x)^(1/2)*(c+d*x)^(5/2) +--R +--R +--R 2 4 3 2 2 +-------+ +-------+ +--R (37) (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression Integer +--E 91 + +--S 92 of 512 +r0118:= -5/64*c^2*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^3+_ + 7/64*c*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^4/d^3-_ + 21/512*(b*c-a*d)^5*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^5/d^3-_ + 5/96*c^2*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^2/d^3+_ + 7/96*c*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^3/d^3-_ + 7/256*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^4/d^3-_ + 1/24*c^2*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b/d^3+_ + 7/120*c*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^2/d^3-_ + 7/320*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^3/d^3+_ + 1/4*c^2*(a+b*x)^(1/2)*(c+d*x)^(7/2)/d^3+1/20*c*_ + (b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(7/2)/b/d^3-3/160*(b*c-a*d)^2*_ + (a+b*x)^(1/2)*(c+d*x)^(7/2)/b^2/d^3-2/5*c*(a+b*x)^(1/2)*_ + (c+d*x)^(9/2)/d^3-1/60*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(9/2)/_ + b/d^3+1/6*(a+b*x)^(1/2)*(c+d*x)^(11/2)/d^3-5/64*c^2*(b*c-a*d)^4*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(7/2)/d^(7/2)+_ + 7/64*c*(b*c-a*d)^5*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(9/2)/d^(7/2)-21/512*(b*c-a*d)^6*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(11/2)/d^(7/2) +--R +--R +--R (38) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 315a d + 1050a b c d - 1125a b c d + 300a b c d + 75a b c d +--R + +--R 5 5 6 6 +--R 90a b c d - 75b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 5 5 5 4 5 5 4 4 +--R 1280b d x + (128a b d + 3200b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 144a b d + 416a b c d + 2160b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (168a b d - 488a b c d + 408a b c d + 40b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 210a b d + 616a b c d - 524a b c d + 40a b c d - 50b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 315a d - 945a b c d + 838a b c d - 90a b c d - 65a b c d + 75b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 5 3 +-+ +-+ +--R 7680b d \|b \|d +--R Type: Expression Integer +--E 92 + +--S 93 of 512 +--a0118:= integrate(t0118,x) +--E 93 + +--S 94 of 512 +--m0118:= a0118-r0118 +--E 94 + +--S 95 of 512 +--d0118:= D(m0118,x) +--E 95 + +--S 96 of 512 +t0119:= x*(a+b*x)^(1/2)*(c+d*x)^(5/2) +--R +--R +--R 2 3 2 2 +-------+ +-------+ +--R (39) (d x + 2c d x + c x)\|b x + a \|d x + c +--R Type: Expression Integer +--E 96 + +--S 97 of 512 +r0119:= 5/64*c*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^2-_ + 7/128*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^4/d^2+_ + 5/96*c*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^2/d^2-_ + 7/192*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^3/d^2+_ + 1/24*c*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b/d^2-_ + 7/240*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^2/d^2-_ + 11/40*c*(a+b*x)^(1/2)*(c+d*x)^(7/2)/d^2+1/40*a*(a+b*x)^(1/2)*_ + (c+d*x)^(7/2)/b/d+1/5*(a+b*x)^(1/2)*(c+d*x)^(9/2)/d^2+_ + 5/64*c*(b*c-a*d)^4*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(5/2)-7/128*(b*c-a*d)^5*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(9/2)/d^(5/2) +--R +--R +--R (40) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 105a d - 375a b c d + 450a b c d - 150a b c d - 75a b c d +--R + +--R 5 5 +--R 45b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 4 4 3 4 4 3 3 +--R 384b d x + (48a b d + 1008b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 56a b d + 176a b c d + 744b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (70a b d - 222a b c d + 218a b c d + 30b c d)x - 105a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 340a b c d - 346a b c d + 60a b c d - 45b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 4 2 +-+ +-+ +--R 1920b d \|b \|d +--R Type: Expression Integer +--E 97 + +--S 98 of 512 +--a0119:= integrate(t0119,x) +--E 98 + +--S 99 of 512 +--m0119:= a0119-r0119 +--E 99 + +--S 100 of 512 +--d0119:= D(m0119,x) +--E 100 + +--S 101 of 512 +t0120:= (a+b*x)^(1/2)*(c+d*x)^(5/2) +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (41) (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression Integer +--E 101 + +--S 102 of 512 +r0120:= -5/64*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d-_ + 5/96*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^2/d-_ + 1/24*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b/d+_ + 1/4*(a+b*x)^(1/2)*(c+d*x)^(7/2)/d-5/64*(b*c-a*d)^4*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(7/2)/d^(3/2) +--R +--R +--R (42) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 15a d + 60a b c d - 90a b c d + 60a b c d - 15b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b d x + (8a b d + 136b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 10a b d + 36a b c d + 118b c d)x + 15a d - 55a b c d +--R + +--R 2 2 3 3 +--R 73a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 +-+ +-+ +--R 192b d\|b \|d +--R Type: Expression Integer +--E 102 + +--S 103 of 512 +--a0120:= integrate(t0120,x) +--E 103 + +--S 104 of 512 +--m0120:= a0120-r0120 +--E 104 + +--S 105 of 512 +--d0120:= D(m0120,x) +--E 105 + +--S 106 of 512 +t0121:= (a+b*x)^(1/2)*(c+d*x)^(5/2)/x +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R (43) ---------------------------------------- +--R x +--R Type: Expression Integer +--E 106 + +--S 107 of 512 +r0121:= 1/24/b^(5/2)*(-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*a^2*d^(5/2)*b^(1/2)+_ + 45*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))*a*b^2*d*c^2-_ + 15*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))*a^2*b*d^2*c+_ + 15*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))*b^3*c^3+_ + 3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))*a^3*d^3+_ + 14*(a+b*x)^(1/2)*(c+d*x)^(1/2)*a*d^(3/2)*b^(3/2)*c+33*c^2*_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)*b^(5/2)*d^(1/2)-48*a^(1/2)*c^(5/2)*_ + atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))*b^(5/2)*d^(1/2)+_ + 2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*d^(5/2)*b^(3/2)*a*x+_ + 26*(a+b*x)^(1/2)*(c+d*x)^(1/2)*b^(5/2)*d^(3/2)*c*x+_ + 8*(a+b*x)^(1/2)*(c+d*x)^(1/2)*d^(5/2)*b^(5/2)*x^2)/d^(1/2) +--R +--R +--R (44) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (3a d - 15a b c d + 45a b c d + 15b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ +-+ +-+ \|c \|b x + a +--R - 48b c \|a \|b \|c \|d atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (2a b d + 26b c d)x - 3a d + 14a b c d + 33b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 24b \|b \|d +--R Type: Expression Integer +--E 107 + +--S 108 of 512 +--a0121:= integrate(t0121,x) +--E 108 + +--S 109 of 512 +--m0121:= a0121-r0121 +--E 109 + +--S 110 of 512 +--d0121:= D(m0121,x) +--E 110 + +--S 111 of 512 +t0122:= x^3*(1+x)^(1/2)/(1-x)^(5/2) +--R +--R +--R 3 +-----+ +--R x \|x + 1 +--R (45) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression Integer +--E 111 + +--S 112 of 512 +r0122:= -6*(1+x)^(1/2)/(1-x)^(1/2)-3*(1-x)^(1/2)*(1+x)^(1/2)+_ + 1/3*(1+x)^(3/2)/(1-x)^(3/2)-1/2*x*(1-x^2)^(1/2)+11/2*asin(x) +--R +--R +--R (46) +--R 2 +-----+ +--R (18x - 74x + 52)\|x + 1 +--R + +--R +--------+ +--R 2 | 2 +-------+ +--R ((- 3x + 3x)\|- x + 1 + (33x - 33)asin(x))\|- x + 1 +--R / +--R +-------+ +--R (6x - 6)\|- x + 1 +--R Type: Expression Integer +--E 112 + +--S 113 of 512 +--a0122:= integrate(t0122,x) +--E 113 + +--S 114 of 512 +--m0122:= a0122-r0122 +--E 114 + +--S 115 of 512 +--d0122:= D(m0122,x) +--E 115 + +--S 116 of 512 +t0123:= x^2*(1+x)^(1/2)/(1-x)^(5/2) +--R +--R +--R 2 +-----+ +--R x \|x + 1 +--R (47) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression Integer +--E 116 + +--S 117 of 512 +r0123:= -4*(1+x)^(1/2)/(1-x)^(1/2)-(1-x)^(1/2)*(1+x)^(1/2)+_ + 1/3*(1+x)^(3/2)/(1-x)^(3/2)+3*asin(x) +--R +--R +--R 2 +-----+ +-------+ +--R (3x - 19x + 14)\|x + 1 + (9x - 9)asin(x)\|- x + 1 +--R (48) ---------------------------------------------------- +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression Integer +--E 117 + +--S 118 of 512 +--a0123:= integrate(t0123,x) +--E 118 + +--S 119 of 512 +--m0123:= a0123-r0123 +--E 119 + +--S 120 of 512 +--d0123:= D(m0123,x) +--E 120 + +--S 121 of 512 +t0124:= x*(1+x)^(1/2)/(1-x)^(5/2) +--R +--R +--R +-----+ +--R x\|x + 1 +--R (49) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression Integer +--E 121 + +--S 122 of 512 +r0124:= -2*(1+x)^(1/2)/(1-x)^(1/2)+1/3*(1+x)^(3/2)/(1-x)^(3/2)+asin(x) +--R +--R +--R +-----+ +-------+ +--R (- 7x + 5)\|x + 1 + (3x - 3)asin(x)\|- x + 1 +--R (50) ---------------------------------------------- +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression Integer +--E 122 + +--S 123 of 512 +--a0124:= integrate(t0124,x) +--E 123 + +--S 124 of 512 +--m0124:= a0124-r0124 +--E 124 + +--S 125 of 512 +--d0124:= D(m0124,x) +--E 125 + +--S 126 of 512 +t0125:= x^2*(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 2 +-------+ +--R x \|b x + a +--R (51) ------------ +--R +-------+ +--R \|d x + c +--R Type: Expression Integer +--E 126 + +--S 127 of 512 +r0125:= 3/2*a*c*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d^2-1/2*a^2*(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/b^2/d+5/8*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/_ + b^2/d^3-5/12*c*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b/d^2-7/12*a*_ + (a+b*x)^(3/2)*(c+d*x)^(1/2)/b^2/d+1/3*(a+b*x)^(5/2)*(c+d*x)^(1/2)/_ + b^2/d-a^2*(b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(3/2)-3/2*a*(b*c-a*d)^2*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/_ + d^(5/2)-5/8*(b*c-a*d)^3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(7/2) +--R +--R +--R (52) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (3a d + 3a b c d + 9a b c d - 15b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (2a b d - 10b c d)x - 3a d - 4a b c d + 15b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 3 +-+ +-+ +--R 24b d \|b \|d +--R Type: Expression Integer +--E 127 + +--S 128 of 512 +--a0125:= integrate(t0125,x) +--E 128 + +--S 129 of 512 +--m0125:= a0125-r0125 +--E 129 + +--S 130 of 512 +--d0125:= D(m0125,x) +--E 130 + +--S 131 of 512 +t0126:= x*(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R x\|b x + a +--R (53) ----------- +--R +-------+ +--R \|d x + c +--R Type: Expression Integer +--E 131 + +--S 132 of 512 +r0126:= -3/4*c*(a+b*x)^(1/2)*(c+d*x)^(1/2)/d^2-1/4*a*(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/b/d+1/2*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b/d+a*_ + (b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(3/2)/d^(3/2)+3/4*(b*c-a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(3/2)/d^(5/2) +--R +--R +--R (54) +--R +-+ +-------+ +--R 2 2 2 2 \|d \|b x + a +--R (- a d - 2a b c d + 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2b d x + a d - 3b c)\|b \|d \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 4b d \|b \|d +--R Type: Expression Integer +--E 132 + +--S 133 of 512 +--a0126:= integrate(t0126,x) +--E 133 + +--S 134 of 512 +--m0126:= a0126-r0126 +--E 134 + +--S 135 of 512 +--d0126:= D(m0126,x) +--E 135 + +--S 136 of 512 +t0127:= (a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (55) ---------- +--R +-------+ +--R \|d x + c +--R Type: Expression Integer +--E 136 + +--S 137 of 512 +r0127:= (a+b*x)^(1/2)*(c+d*x)^(1/2)/d-(b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +-+ +-+ +-------+ +-------+ +--R (a d - b c)atanh(--------------) + \|b \|d \|b x + a \|d x + c +--R +-+ +-------+ +--R \|b \|d x + c +--R (56) --------------------------------------------------------------- +--R +-+ +-+ +--R d\|b \|d +--R Type: Expression Integer +--E 137 + +--S 138 of 512 +--a0127:= integrate(t0127,x) +--E 138 + +--S 139 of 512 +--m0127:= a0127-r0127 +--E 139 + +--S 140 of 512 +--d0127:= D(m0127,x) +--E 140 + +--S 141 of 512 +t0128:= (a+b*x)^(1/2)/x/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (57) ----------- +--R +-------+ +--R x\|d x + c +--R Type: Expression Integer +--E 141 + +--S 142 of 512 +r0128:= -2*a^(1/2)*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/_ + c^(1/2)+2*b^(1/2)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/d^(1/2) +--R +--R +--R +-+ +-------+ +-+ +-------+ +--R +-+ +-+ \|d \|b x + a +-+ +-+ \|c \|b x + a +--R 2\|b \|c atanh(--------------) - 2\|a \|d atanh(--------------) +--R +-+ +-------+ +-+ +-------+ +--R \|b \|d x + c \|a \|d x + c +--R (58) --------------------------------------------------------------- +--R +-+ +-+ +--R \|c \|d +--R Type: Expression Integer +--E 142 + +--S 143 of 512 +--a0128:= integrate(t0128,x) +--E 143 + +--S 144 of 512 +--m0128:= a0128-r0128 +--E 144 + +--S 145 of 512 +--d0128:= D(m0128,x) +-- >> Error detected within library code: +-- integrate: implementation incomplete (non-algebraic residues) +--E 145 + +--S 146 of 512 +t0129:= (a+b*x)^(1/2)/x^2/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (59) ------------ +--R 2 +-------+ +--R x \|d x + c +--R Type: Expression Integer +--E 146 + +--S 147 of 512 +r0129:= -(a+b*x)^(1/2)*(c+d*x)^(1/2)/c/x-(b*c-a*d)*_ + atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(3/2) +--R +--R +--R +-+ +-------+ +--R \|c \|b x + a +-+ +-+ +-------+ +-------+ +--R (a d - b c)x atanh(--------------) - \|a \|c \|b x + a \|d x + c +--R +-+ +-------+ +--R \|a \|d x + c +--R (60) ----------------------------------------------------------------- +--R +-+ +-+ +--R c x\|a \|c +--R Type: Expression Integer +--E 147 + +--S 148 of 512 +--a0129:= integrate(t0129,x) +--E 148 + +--S 149 of 512 +--m0129:= a0129-r0129 +--E 149 + +--S 150 of 512 +--d0129:= D(m0129,x) +--E 150 + +--S 151 of 512 +t0130:= x^2/(-1+x)^(1/2)/(1+x)^(1/2) +--R +--R +--R 2 +--R x +--R (61) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression Integer +--E 151 + +--S 152 of 512 +r0130:= 1/2*(-1+x)^(1/2)*x*(1+x)^(1/2)+1/2*acosh(x) +--R +--R +--R +-----+ +-----+ +--R x\|x - 1 \|x + 1 + acosh(x) +--R (62) ---------------------------- +--R 2 +--R Type: Expression Integer +--E 152 + +--S 153 of 512 +--a0130:= integrate(t0130,x) +--E 153 + +--S 154 of 512 +--m0130:= a0130-r0130 +--E 154 + +--S 155 of 512 +--d0130:= D(m0130,x) +--E 155 + +--S 156 of 512 +t0131:= 1/(-1+x)^(1/2)/(1+x)^(1/2) +--R +--R +--R 1 +--R (63) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression Integer +--E 156 + +--S 157 of 512 +r0131:= acosh(x) +--R +--R +--R (64) acosh(x) +--R Type: Expression Integer +--E 157 + +--S 158 of 512 +a0131:= integrate(t0131,x) +--R +--R +--R +-----+ +-----+ +--R (65) - 2log(\|x + 1 - \|x - 1 ) +--R Type: Union(Expression Integer,...) +--E 158 + +--S 159 of 512 +m0131:= a0131-r0131 +--R +--R +--R +-----+ +-----+ +--R (66) - 2log(\|x + 1 - \|x - 1 ) - acosh(x) +--R Type: Expression Integer +--E 159 + +--S 160 of 512 +d0131:= D(m0131,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (67) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|x - 1 +--R Type: Expression Integer +--E 160 + +--S 161 of 512 +t0132:= 1/(-1+x)^(1/2)/x/(1+x)^(1/2) +--R +--R +--R 1 +--R (68) ----------------- +--R +-----+ +-----+ +--R x\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 161 + +--S 162 of 512 +r0132:= 2*atan((-1+x)^(1/2)/(1+x)^(1/2)) +--R +--R +--R +-----+ +--R \|x - 1 +--R (69) 2atan(--------) +--R +-----+ +--R \|x + 1 +--R Type: Expression Integer +--E 162 + +--S 163 of 512 +a0132:= integrate(t0132,x) +--R +--R +--R +-----+ +-----+ +--R 416\|x - 1 \|x + 1 + 87 +--R (70) - atan(------------------------) +--R +-----+ +-----+ +--R 87\|x - 1 \|x + 1 - 416 +--R Type: Union(Expression Integer,...) +--E 163 + +--S 164 of 512 +m0132:= a0132-r0132 +--R +--R +--R +-----+ +-----+ +-----+ +--R 416\|x - 1 \|x + 1 + 87 \|x - 1 +--R (71) - atan(------------------------) - 2atan(--------) +--R +-----+ +-----+ +-----+ +--R 87\|x - 1 \|x + 1 - 416 \|x + 1 +--R Type: Expression Integer +--E 164 + +--S 165 of 512 +d0132:= D(m0132,x) +--R +--R +--R (72) 0 +--R Type: Expression Integer +--E 165 + +--S 166 of 512 +t0133:= x^2*(-1+x)^(1/2)*(1+x)^(1/2) +--R +--R +--R 2 +-----+ +-----+ +--R (73) x \|x - 1 \|x + 1 +--R Type: Expression Integer +--E 166 + +--S 167 of 512 +r0133:= -1/8*(-1+x)^(1/2)*x*(1+x)^(1/2)+1/4*(-1+x)^(1/2)*x^3*(1+x)^(1/2)-_ + 1/8*acosh(x) +--R +--R +--R 3 +-----+ +-----+ +--R (2x - x)\|x - 1 \|x + 1 - acosh(x) +--R (74) ------------------------------------ +--R 8 +--R Type: Expression Integer +--E 167 + +--S 168 of 512 +a0133:= integrate(t0133,x) +--R +--R +--R +-----+ +-----+ 3 +-----+ +-----+ +--R - log(\|x - 1 \|x + 1 + x) + (2x - x)\|x - 1 \|x + 1 +--R (75) ------------------------------------------------------- +--R 8 +--R Type: Union(Expression Integer,...) +--E 168 + +--S 169 of 512 +m0133:= a0133-r0133 +--R +--R +--R +-----+ +-----+ +--R - log(\|x - 1 \|x + 1 + x) + acosh(x) +--R (76) -------------------------------------- +--R 8 +--R Type: Expression Integer +--E 169 + +--S 170 of 512 +d0133:= D(m0133,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R - \|x - 1 + \|x - 1 \|x + 1 +--R (77) ------------------------------ +--R +------+ +--R +-----+ +-----+ | 2 +--R 8\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression Integer +--E 170 + +--S 171 of 512 +t0134:= (-1+x)^(1/2)*(1+x)^(1/2) +--R +--R +--R +-----+ +-----+ +--R (78) \|x - 1 \|x + 1 +--R Type: Expression Integer +--E 171 + +--S 172 of 512 +r0134:= 1/2*(-1+x)^(1/2)*x*(1+x)^(1/2)-1/2*acosh(x) +--R +--R +--R +-----+ +-----+ +--R x\|x - 1 \|x + 1 - acosh(x) +--R (79) ---------------------------- +--R 2 +--R Type: Expression Integer +--E 172 + +--S 173 of 512 +a0134:= integrate(t0134,x) +--R +--R +--R (80) +--R +-----+ +-----+ 2 +-----+ +-----+ +--R (4x\|x - 1 \|x + 1 - 4x + 2)log(\|x + 1 - \|x - 1 ) +--R + +--R 3 +-----+ +-----+ 4 2 +--R (- 2x + x)\|x - 1 \|x + 1 + 2x - 2x +--R / +--R +-----+ +-----+ 2 +--R 4x\|x - 1 \|x + 1 - 4x + 2 +--R Type: Union(Expression Integer,...) +--E 173 + +--S 174 of 512 +m0134:= a0134-r0134 +--R +--R +--R +-----+ +-----+ +--R 2log(\|x + 1 - \|x - 1 ) + acosh(x) +--R (81) ------------------------------------ +--R 2 +--R Type: Expression Integer +--E 174 + +--S 175 of 512 +d0134:= D(m0134,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R - \|x - 1 + \|x - 1 \|x + 1 +--R (82) ------------------------------ +--R +------+ +--R +-----+ +-----+ | 2 +--R 2\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression Integer +--E 175 + +--S 176 of 512 +t0135:= (-1+x)^(1/2)*(1+x)^(1/2)/x^2 +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R (83) ---------------- +--R 2 +--R x +--R Type: Expression Integer +--E 176 + +--S 177 of 512 +r0135:= -(-1+x)^(1/2)*(1+x)^(1/2)/x+acosh(x) +--R +--R +--R +-----+ +-----+ +--R - \|x - 1 \|x + 1 + x acosh(x) +--R (84) ------------------------------- +--R x +--R Type: Expression Integer +--E 177 + +--S 178 of 512 +a0135:= integrate(t0135,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ +--R - x log(\|x - 1 \|x + 1 - x) - \|x - 1 \|x + 1 + x +--R (85) ---------------------------------------------------- +--R x +--R Type: Union(Expression Integer,...) +--E 178 + +--S 179 of 512 +m0135:= a0135-r0135 +--R +--R +--R +-----+ +-----+ +--R (86) - log(\|x - 1 \|x + 1 - x) - acosh(x) + 1 +--R Type: Expression Integer +--E 179 + +--S 180 of 512 +d0135:= D(m0135,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (87) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|x - 1 +--R Type: Expression Integer +--E 180 + +--S 181 of 512 +t0136:= 1/(1+2*x)^(1/2)/(3+2*x)^(1/2) +--R +--R +--R 1 +--R (88) ------------------ +--R +------+ +------+ +--R \|2x + 1 \|2x + 3 +--R Type: Expression Integer +--E 181 + +--S 182 of 512 +r0136:= asinh(1/2*(1+2*x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +------+ +--R \|2 \|2x + 1 +--R (89) asinh(-------------) +--R 2 +--R Type: Expression Integer +--E 182 + +--S 183 of 512 +a0136:= integrate(t0136,x) +--R +--R +--R +------+ +------+ +--R (90) - log(\|2x + 3 - \|2x + 1 ) +--R Type: Union(Expression Integer,...) +--E 183 + +--S 184 of 512 +m0136:= a0136-r0136 +--R +--R +--R +-+ +------+ +--R +------+ +------+ \|2 \|2x + 1 +--R (91) - log(\|2x + 3 - \|2x + 1 ) - asinh(-------------) +--R 2 +--R Type: Expression Integer +--E 184 + +--S 185 of 512 +d0136:= D(m0136,x) +--R +--R +--R (92) 0 +--R Type: Expression Integer +--E 185 + +--S 186 of 512 +t0137:= 1/x/(-2+3*x)^(1/2)/(3+5*x)^(1/2) +--R +--R +--R 1 +--R (93) ------------------- +--R +------+ +------+ +--R x\|3x - 2 \|5x + 3 +--R Type: Expression Integer +--E 186 + +--S 187 of 512 +r0137:= 1/3*6^(1/2)*atan(1/2*6^(1/2)*(-2+3*x)^(1/2)/(3+5*x)^(1/2)) +--R +--R +--R +-+ +------+ +--R +-+ \|6 \|3x - 2 +--R \|6 atan(-------------) +--R +------+ +--R 2\|5x + 3 +--R (94) ----------------------- +--R 3 +--R Type: Expression Integer +--E 187 + +--S 188 of 512 +a0137:= integrate(t0137,x) +--R +--R +--R +-+ +-+ +------+ +------+ +-+ +-+ +--R +-+ +-+ 912\|2 \|3 \|3x - 2 \|5x + 3 + (337x + 4044)\|2 \|3 +--R \|2 \|3 atan(-----------------------------------------------------) +--R +------+ +------+ +--R 4044\|3x - 2 \|5x + 3 - 456x - 5472 +--R (95) - ------------------------------------------------------------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 188 + +--S 189 of 512 +m0137:= a0137-r0137 +--R +--R +--R (96) +--R +-+ +-+ +------+ +------+ +-+ +-+ +--R +-+ +-+ 912\|2 \|3 \|3x - 2 \|5x + 3 + (337x + 4044)\|2 \|3 +--R - \|2 \|3 atan(-----------------------------------------------------) +--R +------+ +------+ +--R 4044\|3x - 2 \|5x + 3 - 456x - 5472 +--R + +--R +-+ +------+ +--R +-+ \|6 \|3x - 2 +--R - 2\|6 atan(-------------) +--R +------+ +--R 2\|5x + 3 +--R / +--R 6 +--R Type: Expression Integer +--E 189 + +--S 190 of 512 +d0137:= D(m0137,x) +--R +--R +--R (97) 0 +--R Type: Expression Integer +--E 190 + +--S 191 of 512 +t0138:= 1/(-1+x)^(3/2)/x/(1+x)^(3/2) +--R +--R +--R 1 +--R (98) ------------------------ +--R 3 +-----+ +-----+ +--R (x - x)\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 191 + +--S 192 of 512 +r0138:= -1/(-1+x)^(1/2)/(1+x)^(1/2)-2*atan((-1+x)^(1/2)/(1+x)^(1/2)) +--R +--R +--R +-----+ +--R +-----+ +-----+ \|x - 1 +--R - 2\|x - 1 \|x + 1 atan(--------) - 1 +--R +-----+ +--R \|x + 1 +--R (99) ------------------------------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression Integer +--E 192 + +--S 193 of 512 +a0138:= integrate(t0138,x) +--R +--R +--R (100) +--R +-----+ +-----+ 2 +-----+ +-----+ +--R (- 2x\|x - 1 \|x + 1 + 2x - 2)atan(\|x - 1 \|x + 1 - x) +--R + +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 - x +--R / +--R +-----+ +-----+ 2 +--R x\|x - 1 \|x + 1 - x + 1 +--R Type: Union(Expression Integer,...) +--E 193 + +--S 194 of 512 +m0138:= a0138-r0138 +--R +--R +--R +-----+ +--R +-----+ +-----+ \|x - 1 +--R (101) - 2atan(\|x - 1 \|x + 1 - x) + 2atan(--------) +--R +-----+ +--R \|x + 1 +--R Type: Expression Integer +--E 194 + +--S 195 of 512 +d0138:= D(m0138,x) +--R +--R +--R (102) 0 +--R Type: Expression Integer +--E 195 + +--S 196 of 512 +t0139:= x*(1-x)^(1/2)*(1+x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (103) x\|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 196 + +--S 197 of 512 +r0139:= -1/3*(1-x^2)^(3/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (x - 1)\|- x + 1 +--R (104) ------------------- +--R 3 +--R Type: Expression Integer +--E 197 + +--S 198 of 512 +a0139:= integrate(t0139,x) +--R +--R +--R 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|x + 1 +--R (105) -------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 198 + +--S 199 of 512 +m0139:= a0139-r0139 +--R +--R +--R +--------+ +--R 2 +-------+ +-----+ 2 | 2 +--R (x - 1)\|- x + 1 \|x + 1 + (- x + 1)\|- x + 1 +--R (106) -------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 199 + +--S 200 of 512 +d0139:= D(m0139,x) +--R +--R +--R +--------+ +--R 3 +-------+ +-----+ 3 | 2 +--R (x - x)\|- x + 1 \|x + 1 + (- x + x)\|- x + 1 +--R (107) -------------------------------------------------- +--R +--------+ +--R | 2 +-------+ +-----+ +--R \|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 200 + +--S 201 of 512 +t0140:= x*(1+(1-x)^(1/2)*(1+x)^(1/2)) +--R +--R +--R +-------+ +-----+ +--R (108) x\|- x + 1 \|x + 1 + x +--R Type: Expression Integer +--E 201 + +--S 202 of 512 +r0140:= 1/2*x^2-1/3*(1-x^2)^(3/2) +--R +--R +--R +--------+ +--R 2 | 2 2 +--R (2x - 2)\|- x + 1 + 3x +--R (109) -------------------------- +--R 6 +--R Type: Expression Integer +--E 202 + +--S 203 of 512 +a0140:= integrate(t0140,x) +--R +--R +--R 2 +-------+ +-----+ 2 +--R (2x - 2)\|- x + 1 \|x + 1 + 3x +--R (110) --------------------------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 203 + +--S 204 of 512 +m0140:= a0140-r0140 +--R +--R +--R +--------+ +--R 2 +-------+ +-----+ 2 | 2 +--R (x - 1)\|- x + 1 \|x + 1 + (- x + 1)\|- x + 1 +--R (111) -------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 204 + +--S 205 of 512 +d0140:= D(m0140,x) +--R +--R +--R +--------+ +--R 3 +-------+ +-----+ 3 | 2 +--R (x - x)\|- x + 1 \|x + 1 + (- x + x)\|- x + 1 +--R (112) -------------------------------------------------- +--R +--------+ +--R | 2 +-------+ +-----+ +--R \|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 205 + +--S 206 of 512 +t0141:= x*(1+1/(2+x)^(1/2)/(3+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R x\|x + 2 \|x + 3 + x +--R (113) --------------------- +--R +-----+ +-----+ +--R \|x + 2 \|x + 3 +--R Type: Expression Integer +--E 206 + +--S 207 of 512 +r0141:= 1/2*x^2+(2+x)^(1/2)*(3+x)^(1/2)-5*asinh((2+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +-----+ 2 +--R - 10asinh(\|x + 2 ) + 2\|x + 2 \|x + 3 + x +--R (114) -------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 207 + +--S 208 of 512 +a0141:= integrate(t0141,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ 2 +--R - 5log(- 2\|x + 2 \|x + 3 - 2x - 5) + 2\|x + 2 \|x + 3 + x +--R (115) ------------------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 208 + +--S 209 of 512 +m0141:= a0141-r0141 +--R +--R +--R +-----+ +-----+ +-----+ +--R - 5log(- 2\|x + 2 \|x + 3 - 2x - 5) + 10asinh(\|x + 2 ) +--R (116) -------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 209 + +--S 210 of 512 +d0141:= D(m0141,x) +--R +--R +--R (117) 0 +--R Type: Expression Integer +--E 210 + +--S 211 of 512 +t0142:= x^(-3+n)/((a+b*x)^n) +--R +--R +--R n - 3 +--R x +--R (118) ---------- +--R n +--R (b x + a) +--R Type: Expression Integer +--E 211 + +--S 212 of 512 +r0142:= 1/a^2/(-1+n)/(-2+n)*(a+b*x)^(-n)*(-x^(-2+n)*a^2+x^(-2+n)*a^2*n+x^(-1+n)*a*n*b+x^n*b^2) +--R +--R +--R 2 n n - 1 2 2 n - 2 - n +--R (b x + a b n x + (a n - a )x )(b x + a) +--R (119) ---------------------------------------------------- +--R 2 2 2 2 +--R a n - 3a n + 2a +--R Type: Expression Integer +--E 212 + +--S 213 of 512 +a0142:= integrate(t0142,x) +--R +--R +--R 2 3 2 2 2 (n - 3)log(x) +--R (b x + a b n x + (a n - a )x)%e +--R (120) ---------------------------------------------- +--R 2 2 2 2 n log(b x + a) +--R (a n - 3a n + 2a )%e +--R Type: Union(Expression Integer,...) +--E 213 + +--S 214 of 512 +m0142:= a0142-r0142 +--R +--R +--R (121) +--R 2 n n - 1 2 2 n - 2 - n n log(b x + a) +--R (- b x - a b n x + (- a n + a )x )(b x + a) %e +--R + +--R 2 3 2 2 2 (n - 3)log(x) +--R (b x + a b n x + (a n - a )x)%e +--R / +--R 2 2 2 2 n log(b x + a) +--R (a n - 3a n + 2a )%e +--R Type: Expression Integer +--E 214 + +--S 215 of 512 +d0142:= D(m0142,x) +--R +--R +--R (122) +--R 2 n - 1 2 n - 2 +--R - b n x + (- a b n + a b n)x +--R + +--R 2 2 2 2 n - 3 +--R (- a n + 3a n - 2a )x +--R * +--R - n +--R (b x + a) +--R + +--R 3 n 2 2 n - 1 2 2 2 n - 2 - n - 1 +--R (b n x + a b n x + (a b n - a b n)x )(b x + a) +--R * +--R n log(b x + a) +--R %e +--R + +--R 2 2 2 2 (n - 3)log(x) +--R (a n - 3a n + 2a )%e +--R / +--R 2 2 2 2 n log(b x + a) +--R (a n - 3a n + 2a )%e +--R Type: Expression Integer +--E 215 + +--S 216 of 512 +t0143:= (a+b*x^(1/2))^3 +--R +--R +--R 3 2 +-+ 2 3 +--R (123) (b x + 3a b)\|x + 3a b x + a +--R Type: Expression Integer +--E 216 + +--S 217 of 512 +r0143:= 1/10*(a+b*x^(1/2))^4*(-a+4*b*x^(1/2))/b^2 +--R +--R +--R 5 2 2 3 +-+ 4 2 3 2 5 +--R (4b x + 20a b x)\|x + 15a b x + 10a b x - a +--R (124) ----------------------------------------------- +--R 2 +--R 10b +--R Type: Expression Integer +--E 217 + +--S 218 of 512 +a0143:= integrate(t0143,x) +--R +--R +--R 3 2 2 +-+ 2 2 3 +--R (4b x + 20a b x)\|x + 15a b x + 10a x +--R (125) ---------------------------------------- +--R 10 +--R Type: Union(Expression Integer,...) +--E 218 + +--S 219 of 512 +m0143:= a0143-r0143 +--R +--R +--R 5 +--R a +--R (126) ---- +--R 2 +--R 10b +--R Type: Expression Integer +--E 219 + +--S 220 of 512 +d0143:= D(m0143,x) +--R +--R +--R (127) 0 +--R Type: Expression Integer +--E 220 + +--S 221 of 512 +t0144:= (a+b*x^(1/2))^4 +--R +--R +--R 3 3 +-+ 4 2 2 2 4 +--R (128) (4a b x + 4a b)\|x + b x + 6a b x + a +--R Type: Expression Integer +--E 221 + +--S 222 of 512 +r0144:= 1/15*(a+b*x^(1/2))^5*(-a+5*b*x^(1/2))/b^2 +--R +--R +--R 5 2 3 3 +-+ 6 3 2 4 2 4 2 6 +--R (24a b x + 40a b x)\|x + 5b x + 45a b x + 15a b x - a +--R (129) ---------------------------------------------------------- +--R 2 +--R 15b +--R Type: Expression Integer +--E 222 + +--S 223 of 512 +a0144:= integrate(t0144,x) +--R +--R +--R 3 2 3 +-+ 4 3 2 2 2 4 +--R (24a b x + 40a b x)\|x + 5b x + 45a b x + 15a x +--R (130) --------------------------------------------------- +--R 15 +--R Type: Union(Expression Integer,...) +--E 223 + +--S 224 of 512 +m0144:= a0144-r0144 +--R +--R +--R 6 +--R a +--R (131) ---- +--R 2 +--R 15b +--R Type: Expression Integer +--E 224 + +--S 225 of 512 +d0144:= D(m0144,x) +--R +--R +--R (132) 0 +--R Type: Expression Integer +--E 225 + +--S 226 of 512 +t0145:= (a+b*x^(1/2))^5 +--R +--R +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (133) (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a +--R Type: Expression Integer +--E 226 + +--S 227 of 512 +r0145:= 1/21*(a+b*x^(1/2))^6*(-a+6*b*x^(1/2))/b^2 +--R +--R +--R (134) +--R 7 3 2 5 2 4 3 +-+ 6 3 3 4 2 5 2 7 +--R (6b x + 84a b x + 70a b x)\|x + 35a b x + 105a b x + 21a b x - a +--R ---------------------------------------------------------------------- +--R 2 +--R 21b +--R Type: Expression Integer +--E 227 + +--S 228 of 512 +a0145:= integrate(t0145,x) +--R +--R +--R 5 3 2 3 2 4 +-+ 4 3 3 2 2 5 +--R (6b x + 84a b x + 70a b x)\|x + 35a b x + 105a b x + 21a x +--R (135) --------------------------------------------------------------- +--R 21 +--R Type: Union(Expression Integer,...) +--E 228 + +--S 229 of 512 +m0145:= a0145-r0145 +--R +--R +--R 7 +--R a +--R (136) ---- +--R 2 +--R 21b +--R Type: Expression Integer +--E 229 + +--S 230 of 512 +d0145:= D(m0145,x) +--R +--R +--R (137) 0 +--R Type: Expression Integer +--E 230 + +--S 231 of 512 +t0146:= (a+b*x^(1/2))^6 +--R +--R +--R 5 2 3 3 5 +-+ 6 3 2 4 2 4 2 6 +--R (138) (6a b x + 20a b x + 6a b)\|x + b x + 15a b x + 15a b x + a +--R Type: Expression Integer +--E 231 + +--S 232 of 512 +r0146:= 1/28*(a+b*x^(1/2))^7*(-a+7*b*x^(1/2))/b^2 +--R +--R +--R (139) +--R 7 3 3 5 2 5 3 +-+ 8 4 2 6 3 4 4 2 +--R (48a b x + 224a b x + 112a b x)\|x + 7b x + 140a b x + 210a b x +--R + +--R 6 2 8 +--R 28a b x - a +--R / +--R 2 +--R 28b +--R Type: Expression Integer +--E 232 + +--S 233 of 512 +a0146:= integrate(t0146,x) +--R +--R +--R (140) +--R 5 3 3 3 2 5 +-+ 6 4 2 4 3 4 2 2 6 +--R (48a b x + 224a b x + 112a b x)\|x + 7b x + 140a b x + 210a b x + 28a x +--R ----------------------------------------------------------------------------- +--R 28 +--R Type: Union(Expression Integer,...) +--E 233 + +--S 234 of 512 +m0146:= a0146-r0146 +--R +--R +--R 8 +--R a +--R (141) ---- +--R 2 +--R 28b +--R Type: Expression Integer +--E 234 + +--S 235 of 512 +d0146:= D(m0146,x) +--R +--R +--R (142) 0 +--R Type: Expression Integer +--E 235 + +--S 236 of 512 +t0147:= (a+b*x^(1/2))^7 +--R +--R +--R (143) +--R 7 3 2 5 2 4 3 6 +-+ 6 3 3 4 2 5 2 7 +--R (b x + 21a b x + 35a b x + 7a b)\|x + 7a b x + 35a b x + 21a b x + a +--R Type: Expression Integer +--E 236 + +--S 237 of 512 +r0147:= 1/36*(a+b*x^(1/2))^8*(-a+8*b*x^(1/2))/b^2 +--R +--R +--R (144) +--R 9 4 2 7 3 4 5 2 6 3 +-+ 8 4 3 6 3 +--R (8b x + 216a b x + 504a b x + 168a b x)\|x + 63a b x + 420a b x +--R + +--R 5 4 2 7 2 9 +--R 378a b x + 36a b x - a +--R / +--R 2 +--R 36b +--R Type: Expression Integer +--E 237 + +--S 238 of 512 +a0147:= integrate(t0147,x) +--R +--R +--R (145) +--R 7 4 2 5 3 4 3 2 6 +-+ 6 4 3 4 3 +--R (8b x + 216a b x + 504a b x + 168a b x)\|x + 63a b x + 420a b x +--R + +--R 5 2 2 7 +--R 378a b x + 36a x +--R / +--R 36 +--R Type: Union(Expression Integer,...) +--E 238 + +--S 239 of 512 +m0147:= a0147-r0147 +--R +--R +--R 9 +--R a +--R (146) ---- +--R 2 +--R 36b +--R Type: Expression Integer +--E 239 + +--S 240 of 512 +d0147:= D(m0147,x) +--R +--R +--R (147) 0 +--R Type: Expression Integer +--E 240 + +--S 241 of 512 +t0148:= (a+b*x^(1/2))^8 +--R +--R +--R (148) +--R 7 3 3 5 2 5 3 7 +-+ 8 4 2 6 3 4 4 2 +--R (8a b x + 56a b x + 56a b x + 8a b)\|x + b x + 28a b x + 70a b x +--R + +--R 6 2 8 +--R 28a b x + a +--R Type: Expression Integer +--E 241 + +--S 242 of 512 +r0148:= 1/45*(a+b*x^(1/2))^9*(-a+9*b*x^(1/2))/b^2 +--R +--R +--R (149) +--R 9 4 3 7 3 5 5 2 7 3 +-+ 10 5 2 8 4 +--R (80a b x + 720a b x + 1008a b x + 240a b x)\|x + 9b x + 315a b x +--R + +--R 4 6 3 6 4 2 8 2 10 +--R 1050a b x + 630a b x + 45a b x - a +--R / +--R 2 +--R 45b +--R Type: Expression Integer +--E 242 + +--S 243 of 512 +a0148:= integrate(t0148,x) +--R +--R +--R (150) +--R 7 4 3 5 3 5 3 2 7 +-+ 8 5 2 6 4 +--R (80a b x + 720a b x + 1008a b x + 240a b x)\|x + 9b x + 315a b x +--R + +--R 4 4 3 6 2 2 8 +--R 1050a b x + 630a b x + 45a x +--R / +--R 45 +--R Type: Union(Expression Integer,...) +--E 243 + +--S 244 of 512 +m0148:= a0148-r0148 +--R +--R +--R 10 +--R a +--R (151) ---- +--R 2 +--R 45b +--R Type: Expression Integer +--E 244 + +--S 245 of 512 +d0148:= D(m0148,x) +--R +--R +--R (152) 0 +--R Type: Expression Integer +--E 245 + +--S 246 of 512 +t0149:= 1/(4+b*x)^(1/2)/(-4+b*x)^(1/2) +--R +--R +--R 1 +--R (153) -------------------- +--R +-------+ +-------+ +--R \|b x - 4 \|b x + 4 +--R Type: Expression Integer +--E 246 + +--S 247 of 512 +r0149:= acosh(1/4*b*x)/b +--R +--R +--R b x +--R acosh(---) +--R 4 +--R (154) ---------- +--R b +--R Type: Expression Integer +--E 247 + +--S 248 of 512 +--a0149:= integrate(t0149,x) +--E 248 + +--S 249 of 512 +--m0149:= a0149-r0149 +--E 249 + +--S 250 of 512 +--d0149:= D(m0149,x) +-- >> Error detected within library code: +-- integrate: implementation incomplete (non-algebraic residues) +--E 250 + +--S 251 of 512 +t0150:= 1/((-b+b*c)/d+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (155) ---------------------------- +--R +---------------+ +--R |b d x + b c - b +-------+ +--R |--------------- \|d x + c +--R \| d +--R Type: Expression Integer +--E 251 + +--S 252 of 512 +r0150:= 2*asinh(d^(1/2)*(b*(-1+c+d*x)/d)^(1/2)/b^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +---------------+ +--R +-+ |b d x + b c - b +--R \|d |--------------- +--R \| d +--R 2asinh(----------------------) +--R +-+ +--R \|b +--R (156) ------------------------------ +--R +-+ +-+ +--R \|b \|d +--R Type: Expression Integer +--E 252 + +--S 253 of 512 +--a0150:= integrate(t0150,x) +--E 253 + +--S 254 of 512 +--m0150:= a0150-r0150 +--E 254 + +--S 255 of 512 +--d0150:= D(m0150,x) +--E 255 + +--S 256 of 512 +t0151:= 1/x^(1/2)/(-3+2*x)^(1/2) +--R +--R +--R 1 +--R (157) ------------- +--R +-+ +------+ +--R \|x \|2x - 3 +--R Type: Expression Integer +--E 256 + +--S 257 of 512 +r0151:= 2^(1/2)*asinh(1/3*(-3+2*x)^(1/2)*3^(1/2)) +--R +--R +--R +-+ +------+ +--R +-+ \|3 \|2x - 3 +--R (158) \|2 asinh(-------------) +--R 3 +--R Type: Expression Integer +--E 257 + +--S 258 of 512 +--a0151:= integrate(t0151,x) +--E 258 + +--S 259 of 512 +--m0151:= a0151-r0151 +--E 259 + +--S 260 of 512 +--d0151:= D(m0151,x) +--E 260 + +--S 261 of 512 +t0152:= 1/(2+3*x)^(1/2)/(-3+2*x)^(1/2) +--R +--R +--R 1 +--R (159) ------------------ +--R +------+ +------+ +--R \|2x - 3 \|3x + 2 +--R Type: Expression Integer +--E 261 + +--S 262 of 512 +r0152:= 1/3*6^(1/2)*asinh(1/13*39^(1/2)*(-3+2*x)^(1/2)) +--R +--R +--R +--+ +------+ +--R +-+ \|39 \|2x - 3 +--R \|6 asinh(--------------) +--R 13 +--R (160) ------------------------- +--R 3 +--R Type: Expression Integer +--E 262 + +--S 263 of 512 +--a0152:= integrate(t0152,x) +--E 263 + +--S 264 of 512 +--m0152:= a0152-r0152 +--E 264 + +--S 265 of 512 +--d0152:= D(m0152,x) +--E 265 + +--S 266 of 512 +t0153:= 1/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (161) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression Integer +--E 266 + +--S 267 of 512 +r0153:= 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +--R 2atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R (162) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression Integer +--E 267 + +--S 268 of 512 +--a0153:= integrate(t0153,x) +--E 268 + +--S 269 of 512 +--m0153:= a0153-r0153 +--E 269 + +--S 270 of 512 +--d0153:= D(m0153,x) +--E 270 + +--S 271 of 512 +t0154:= 1/((b-b*c)/d+b*x)^(1/2)/(c-d*x)^(1/2) +--R +--R +--R 1 +--R (163) ------------------------------ +--R +---------------+ +--R +---------+ |b d x - b c + b +--R \|- d x + c |--------------- +--R \| d +--R Type: Expression Integer +--E 271 + +--S 272 of 512 +r0154:= 2*asin(d^(1/2)*(-b*(-1+c-d*x)/d)^(1/2)/b^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +---------------+ +--R +-+ |b d x - b c + b +--R \|d |--------------- +--R \| d +--R 2asin(----------------------) +--R +-+ +--R \|b +--R (164) ----------------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression Integer +--E 272 + +--S 273 of 512 +--a0154:= integrate(t0154,x) +--E 273 + +--S 274 of 512 +--m0154:= a0154-r0154 +--E 274 + +--S 275 of 512 +--d0154:= D(m0154,x) +--E 275 + +--S 276 of 512 +t0155:= 1/(4-x)^(1/2)/x^(1/2) +--R +--R +--R 1 +--R (165) -------------- +--R +-------+ +-+ +--R \|- x + 4 \|x +--R Type: Expression Integer +--E 276 + +--S 277 of 512 +r0155:= 2*asin(1/2*x^(1/2)) +--R +--R +--R +-+ +--R \|x +--R (166) 2asin(----) +--R 2 +--R Type: Expression Integer +--E 277 + +--S 278 of 512 +--a0155:= integrate(t0155,x) +--E 278 + +--S 279 of 512 +--m0155:= a0155-r0155 +--E 279 + +--S 280 of 512 +--d0155:= D(m0155,x) +--E 280 + +--S 281 of 512 +t0156:= 1/x^(1/2)/(3-2*x)^(1/2) +--R +--R +--R 1 +--R (167) --------------- +--R +--------+ +-+ +--R \|- 2x + 3 \|x +--R Type: Expression Integer +--E 281 + +--S 282 of 512 +r0156:= 2^(1/2)*asin(1/3*6^(1/2)*x^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ \|6 \|x +--R (168) \|2 asin(--------) +--R 3 +--R Type: Expression Integer +--E 282 + +--S 283 of 512 +--a0156:= integrate(t0156,x) +--E 283 + +--S 284 of 512 +--m0156:= a0156-r0156 +--E 284 + +--S 285 of 512 +--d0156:= D(m0156,x) +--E 285 + +--S 286 of 512 +t0157:= 1/(3+5*x)^(1/2)/(3-2*x)^(1/2) +--R +--R +--R 1 +--R (169) -------------------- +--R +--------+ +------+ +--R \|- 2x + 3 \|5x + 3 +--R Type: Expression Integer +--E 286 + +--S 287 of 512 +r0157:= 1/5*10^(1/2)*asin(1/21*42^(1/2)*(3+5*x)^(1/2)) +--R +--R +--R +--+ +------+ +--R +--+ \|42 \|5x + 3 +--R \|10 asin(--------------) +--R 21 +--R (170) ------------------------- +--R 5 +--R Type: Expression Integer +--E 287 + +--S 288 of 512 +--a0157:= integrate(t0157,x) +--E 288 + +--S 289 of 512 +--m0157:= a0157-r0157 +--E 289 + +--S 290 of 512 +--d0157:= D(m0157,x) +--E 290 + +--S 291 of 512 +t0158:= 1/(a-b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (171) ---------------------- +--R +---------+ +-------+ +--R \|- b x + a \|d x + c +--R Type: Expression Integer +--E 291 + +--S 292 of 512 +r0158:= -2*atan(d^(1/2)*(a-b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +---------+ +-+ +--R \|- b x + a \|d +--R 2atan(----------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R (172) - ----------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression Integer +--E 292 + +--S 293 of 512 +--a0158:= integrate(t0158,x) +--E 293 + +--S 294 of 512 +--m0158:= a0158-r0158 +--E 294 + +--S 295 of 512 +--d0158:= D(m0158,x) +--E 295 + +--S 296 of 512 +t0159:= 1/(a+b*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (173) --------------- +--R +-------+ +--R b\|d x + c + a +--R Type: Expression Integer +--E 296 + +--S 297 of 512 +r0159:= -2*(-b*(c+d*x)^(1/2)+a*log(a+b*(c+d*x)^(1/2)))/b^2/d +--R +--R +--R +-------+ +-------+ +--R - 2a log(b\|d x + c + a) + 2b\|d x + c +--R (174) ---------------------------------------- +--R 2 +--R b d +--R Type: Expression Integer +--E 297 + +--S 298 of 512 +a0159:= integrate(t0159,x) +--R +--R +--R +-------+ +-------+ +--R - 2a log(b\|d x + c + a) + 2b\|d x + c +--R (175) ---------------------------------------- +--R 2 +--R b d +--R Type: Union(Expression Integer,...) +--E 298 + +--S 299 of 512 +m0159:= a0159-r0159 +--R +--R +--R (176) 0 +--R Type: Expression Integer +--E 299 + +--S 300 of 512 +d0159:= D(m0159,x) +--R +--R +--R (177) 0 +--R Type: Expression Integer +--E 300 + +--S 301 of 512 +t0160:= x^(1/2)/(1-x^2) +--R +--R +--R +-+ +--R \|x +--R (178) - ------ +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 301 + +--S 302 of 512 +r0160:= -atan(x^(1/2))+atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (179) atanh(\|x ) - atan(\|x ) +--R Type: Expression Integer +--E 302 + +--S 303 of 512 +a0160:= integrate(t0160,x) +--R +--R +--R +-+ +-+ +-+ +--R log(\|x + 1) - log(\|x - 1) - 2atan(\|x ) +--R (180) ------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 303 + +--S 304 of 512 +m0160:= a0160-r0160 +--R +--R +--R +-+ +-+ +-+ +--R log(\|x + 1) - log(\|x - 1) - 2atanh(\|x ) +--R (181) -------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 304 + +--S 305 of 512 +d0160:= D(m0160,x) +--R +--R +--R (182) 0 +--R Type: Expression Integer +--E 305 + +--S 306 of 512 +t0161:= x^(1/2)/(a-b*x^2) +--R +--R +--R +-+ +--R \|x +--R (183) - -------- +--R 2 +--R b x - a +--R Type: Expression Integer +--E 306 + +--S 307 of 512 +r0161:= -(atan(b^(1/4)*x^(1/2)/a^(1/4))-_ + atanh(b^(1/4)*x^(1/2)/a^(1/4)))/a^(1/4)/b^(3/4) +--R +--R +--R 4+-+ +-+ 4+-+ +-+ +--R \|b \|x \|b \|x +--R atanh(--------) - atan(--------) +--R 4+-+ 4+-+ +--R \|a \|a +--R (184) -------------------------------- +--R 4+-+4+-+3 +--R \|a \|b +--R Type: Expression Integer +--E 307 + +--S 308 of 512 +a0161:= integrate(t0161,x) +--R +--R +--R (185) +--R +------+ +------+3 +------+ +------+3 +--R | 1 +-+ 2 | 1 | 1 +-+ 2 | 1 +--R |------ log(\|x + 8a b |------ ) - |------ log(\|x - 8a b |------ ) +--R 4| 3 4| 3 4| 3 4| 3 +--R \|16a b \|16a b \|16a b \|16a b +--R + +--R +------+3 +--R 2 | 1 +--R 8a b |------ +--R +------+ 4| 3 +--R | 1 \|16a b +--R 2 |------ atan(---------------) +--R 4| 3 +-+ +--R \|16a b \|x +--R Type: Union(Expression Integer,...) +--E 308 + +--S 309 of 512 +m0161:= a0161-r0161 +--R +--R +--R (186) +--R +------+ +------+3 +--R | 1 4+-+4+-+3 +-+ 2 | 1 +--R |------ \|a \|b log(\|x + 8a b |------ ) +--R 4| 3 4| 3 +--R \|16a b \|16a b +--R + +--R +------+ +------+3 4+-+ +-+ +--R | 1 4+-+4+-+3 +-+ 2 | 1 \|b \|x +--R - |------ \|a \|b log(\|x - 8a b |------ ) - atanh(--------) +--R 4| 3 4| 3 4+-+ +--R \|16a b \|16a b \|a +--R + +--R +------+3 +--R 2 | 1 +--R 8a b |------ +--R 4+-+ +-+ +------+ 4| 3 +--R \|b \|x | 1 4+-+4+-+3 \|16a b +--R atan(--------) + 2 |------ \|a \|b atan(---------------) +--R 4+-+ 4| 3 +-+ +--R \|a \|16a b \|x +--R / +--R 4+-+4+-+3 +--R \|a \|b +--R Type: Expression Integer +--E 309 + +--S 310 of 512 +d0161:= D(m0161,x) +--R +--R +--R (187) 0 +--R Type: Expression Integer +--E 310 + +--S 311 of 512 +t0162:= (2+3*x)^(1/2)/(a+b*x^2) +--R +--R +--R +------+ +--R \|3x + 2 +--R (188) --------- +--R 2 +--R b x + a +--R Type: Expression Integer +--E 311 + +--S 312 of 512 +r0162:= -(-(-3*a^(1/2)*(-b)^(1/2)-2*b)^(1/2)*_ + atanh((-b)^(1/2)*(2+3*x)^(1/2)/(-3*a^(1/2)*(-b)^(1/2)-2*b)^(1/2))+_ + (3*a^(1/2)*(-b)^(1/2)-2*b)^(1/2)*_ + atanh((-b)^(1/2)*(2+3*x)^(1/2)/_ + (3*a^(1/2)*(-b)^(1/2)-2*b)^(1/2)))/a^(1/2)/b +--R +--R +--R (189) +--R +------------------+ +---+ +------+ +--R | +---+ +-+ \|- b \|3x + 2 +--R \|- 3\|- b \|a - 2b atanh(---------------------) +--R +------------------+ +--R | +---+ +-+ +--R \|- 3\|- b \|a - 2b +--R + +--R +----------------+ +---+ +------+ +--R | +---+ +-+ \|- b \|3x + 2 +--R - \|3\|- b \|a - 2b atanh(-------------------) +--R +----------------+ +--R | +---+ +-+ +--R \|3\|- b \|a - 2b +--R / +--R +-+ +--R b\|a +--R Type: Expression Integer +--E 312 + +--S 313 of 512 +a0162:= integrate(t0162,x) +--R +--R +--R (190) +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R | | 3 +--R | \| 4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(2a b |- ----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R | | 3 +--R | \| 4a b +--R |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(2a b |- ----- |-------------------- + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R | | 3 +--R | \| 4a b +--R |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(- 2a b |- ----- |-------------------- + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R | | 3 +--R | \| 4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(- 2a b |- ----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 313 + +--S 314 of 512 +m0162:= a0162-r0162 +--R +--R +--R (191) +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R | | 3 +--R +-+ | \| 4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(2a b |- ----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R | | 3 +--R +-+ | \| 4a b +--R b\|a |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(2a b |- ----- |-------------------- + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R | | 3 +--R +-+ | \| 4a b +--R b\|a |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(- 2a b |- ----- |-------------------- + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R | | 3 +--R +-+ | \| 4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(- 2a b |- ----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +------------------+ +---+ +------+ +--R | +---+ +-+ \|- b \|3x + 2 +--R - 2\|- 3\|- b \|a - 2b atanh(---------------------) +--R +------------------+ +--R | +---+ +-+ +--R \|- 3\|- b \|a - 2b +--R + +--R +----------------+ +---+ +------+ +--R | +---+ +-+ \|- b \|3x + 2 +--R 2\|3\|- b \|a - 2b atanh(-------------------) +--R +----------------+ +--R | +---+ +-+ +--R \|3\|- b \|a - 2b +--R / +--R +-+ +--R 2b\|a +--R Type: Expression Integer +--E 314 + +--S 315 of 512 +d0162:= D(m0162,x) +--R +--R +--R (192) 0 +--R Type: Expression Integer +--E 315 + +--S 316 of 512 +t0163:= (2+3*x)^(1/2)/(a-b*x^2) +--R +--R +--R +------+ +--R \|3x + 2 +--R (193) - --------- +--R 2 +--R b x - a +--R Type: Expression Integer +--E 316 + +--S 317 of 512 +r0163:= -(-3*a^(1/2)*b^(1/2)+2*b)^(1/2)*atanh(b^(1/2)*(2+3*x)^(1/2)/_ + (-3*a^(1/2)*b^(1/2)+2*b)^(1/2))/a^(1/2)/b+_ + (3*a^(1/2)*b^(1/2)+2*b)^(1/2)*_ + atanh(b^(1/2)*(2+3*x)^(1/2)/(3*a^(1/2)*b^(1/2)+2*b)^(1/2))/a^(1/2)/b +--R +--R +--R (194) +--R +----------------+ +-+ +------+ +--R | +-+ +-+ \|b \|3x + 2 +--R - \|- 3\|a \|b + 2b atanh(-------------------) +--R +----------------+ +--R | +-+ +-+ +--R \|- 3\|a \|b + 2b +--R + +--R +--------------+ +-+ +------+ +--R | +-+ +-+ \|b \|3x + 2 +--R \|3\|a \|b + 2b atanh(-----------------) +--R +--------------+ +--R | +-+ +-+ +--R \|3\|a \|b + 2b +--R / +--R +-+ +--R b\|a +--R Type: Expression Integer +--E 317 + +--S 318 of 512 +a0163:= integrate(t0163,x) +--R +--R +--R (195) +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 1 | | 1 +--R |6a b |----- + 2 |6a b |----- + 2 +--R | | 3 +-----+ | | 3 +--R | \|4a b 2 | 1 | \|4a b +------+ +--R |---------------- log(2a b |----- |---------------- + \|3x + 2 ) +--R \| a b | 3 \| a b +--R \|4a b +--R + +--R - +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R | | 3 +--R | \|4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(2a b |----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R | | 3 +--R | \|4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(- 2a b |----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 1 | | 1 +--R |6a b |----- + 2 |6a b |----- + 2 +--R | | 3 +-----+ | | 3 +--R | \|4a b 2 | 1 | \|4a b +------+ +--R - |---------------- log(- 2a b |----- |---------------- + \|3x + 2 ) +--R \| a b | 3 \| a b +--R \|4a b +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 318 + +--S 319 of 512 +m0163:= a0163-r0163 +--R +--R +--R (196) +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 1 | | 1 +--R |6a b |----- + 2 |6a b |----- + 2 +--R | | 3 +-----+ | | 3 +--R +-+ | \|4a b 2 | 1 | \|4a b +------+ +--R b\|a |---------------- log(2a b |----- |---------------- + \|3x + 2 ) +--R \| a b | 3 \| a b +--R \|4a b +--R + +--R - +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R | | 3 +--R +-+ | \|4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(2a b |----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R | | 3 +--R +-+ | \|4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(- 2a b |----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R - +--R +----------------+ +--R | +-----+ +--R | | 1 +--R |6a b |----- + 2 +--R | | 3 +--R +-+ | \|4a b +--R b\|a |---------------- +--R \| a b +--R * +--R +----------------+ +--R | +-----+ +--R | | 1 +--R |6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(- 2a b |----- |---------------- + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R +----------------+ +-+ +------+ +--R | +-+ +-+ \|b \|3x + 2 +--R 2\|- 3\|a \|b + 2b atanh(-------------------) +--R +----------------+ +--R | +-+ +-+ +--R \|- 3\|a \|b + 2b +--R + +--R +--------------+ +-+ +------+ +--R | +-+ +-+ \|b \|3x + 2 +--R - 2\|3\|a \|b + 2b atanh(-----------------) +--R +--------------+ +--R | +-+ +-+ +--R \|3\|a \|b + 2b +--R / +--R +-+ +--R 2b\|a +--R Type: Expression Integer +--E 319 + +--S 320 of 512 +d0163:= D(m0163,x) +--R +--R +--R (197) 0 +--R Type: Expression Integer +--E 320 + +--S 321 of 512 +t0164:= (c+d*x)^(1/2)/(1+x^2) +--R +--R +--R +-------+ +--R \|d x + c +--R (198) ---------- +--R 2 +--R x + 1 +--R Type: Expression Integer +--E 321 + +--S 322 of 512 +r0164:= d*((c-(-d^2)^(1/2))^(1/2)*atanh((c+d*x)^(1/2)/_ + (c-(-d^2)^(1/2))^(1/2))-(c+(-d^2)^(1/2))^(1/2)*_ + atanh((c+d*x)^(1/2)/(c+(-d^2)^(1/2))^(1/2)))/(-d^2)^(1/2) +--R +--R +--R (199) +--R +-------------+ +--R | +----+ +-------+ +--R | | 2 \|d x + c +--R d\|- \|- d + c atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- d + c +--R + +--R +-----------+ +--R | +----+ +-------+ +--R | | 2 \|d x + c +--R - d\|\|- d + c atanh(--------------) +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- d + c +--R / +--R +----+ +--R | 2 +--R \|- d +--R Type: Expression Integer +--E 322 + +--S 323 of 512 +a0164:= integrate(t0164,x) +--R +--R +--R (200) +--R +--+ +--R | 2 +--R \|d +--R +-------+ atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R * +--R log +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R d \|d + c sin(-----------) +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 +-------+ c +--R 2\|d \|d + c \|d x + c sin(-----------) +--R 2 +--R + +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c 2 +--R d \|d + c cos(-----------) + d x + c d +--R 2 +--R + +--R - +--R +--+ +--R | 2 +--R \|d +--R +-------+ atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R * +--R log +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R d \|d + c sin(-----------) +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 +-------+ c +--R - 2\|d \|d + c \|d x + c sin(-----------) +--R 2 +--R + +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c 2 +--R d \|d + c cos(-----------) + d x + c d +--R 2 +--R + +--R - +--R +--+ +--R | 2 +--R \|d +--R +-------+ atan(-----) +--R 4| 2 2 c +--R 2\|d + c sin(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R atan(---------------------------------------------) +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +-------+ +--R \|d \|d + c sin(-----------) - d\|d x + c +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +-------+ atan(-----) +--R 4| 2 2 c +--R 2\|d + c sin(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R atan(---------------------------------------------) +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +-------+ +--R \|d \|d + c sin(-----------) + d\|d x + c +--R 2 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 323 + +--S 324 of 512 +m0164:= a0164-r0164 +--R +--R +--R (201) +--R +--+ +--R | 2 +--R \|d +--R +----+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|- d \|d + c cos(-----------) +--R 2 +--R * +--R log +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R d \|d + c sin(-----------) +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 +-------+ c +--R 2\|d \|d + c \|d x + c sin(-----------) +--R 2 +--R + +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c 2 +--R d \|d + c cos(-----------) + d x + c d +--R 2 +--R + +--R - +--R +--+ +--R | 2 +--R \|d +--R +----+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|- d \|d + c cos(-----------) +--R 2 +--R * +--R log +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R d \|d + c sin(-----------) +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 +-------+ c +--R - 2\|d \|d + c \|d x + c sin(-----------) +--R 2 +--R + +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c 2 +--R d \|d + c cos(-----------) + d x + c d +--R 2 +--R + +--R - +--R +--+ +--R | 2 +--R \|d +--R +----+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R 2\|- d \|d + c sin(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R atan(---------------------------------------------) +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +-------+ +--R \|d \|d + c sin(-----------) - d\|d x + c +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +----+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R 2\|- d \|d + c sin(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R atan(---------------------------------------------) +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +-------+ +--R \|d \|d + c sin(-----------) + d\|d x + c +--R 2 +--R + +--R +-------------+ +--R | +----+ +-------+ +--R | | 2 \|d x + c +--R - 2d\|- \|- d + c atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- d + c +--R + +--R +-----------+ +--R | +----+ +-------+ +--R | | 2 \|d x + c +--R 2d\|\|- d + c atanh(--------------) +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- d + c +--R / +--R +----+ +--R | 2 +--R 2\|- d +--R Type: Expression Integer +--E 324 + +--S 325 of 512 +d0164:= D(m0164,x) +--R +--R +--R (202) +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- d - 3c d - 3c d - c d)x - c d - 3c d - 3c d - c ) +--R * +--R +--+ 12 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- 4d - 12c d - 12c d - 4c d)x - 4c d - 12c d - 12c d - 4c ) +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 +--R (6d + 12c d + 6c d )x + (12c d + 24c d + 12c d)x + 6c d +--R + +--R 4 2 6 +--R 12c d + 6c +--R * +--R +-------+2 +--R 4| 2 2 +--R \|d + c +--R * +--R +--+ 10 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 2d - 4c d - 2c d)x + (- 2c d - 4c d - 2c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 2d - 4c d - 2c d)x - 2c d - 4c d - 2c +--R * +--R +--+ +--+ 9 +--R | 2 | 2 +--R \|d \|d +--R +--+ +-------+2 atan(-----) atan(-----) +--R | 2 4| 2 2 c c +--R \|d \|d + c cos(-----------)sin(-----------) +--R 2 2 +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- 6d - 18c d - 18c d - 6c d)x - 6c d - 18c d - 18c d - 6c ) +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 +--R (12d + 24c d + 12c d )x + (24c d + 48c d + 24c d)x + 12c d +--R + +--R 4 2 6 +--R 24c d + 12c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (- 15d - 30c d - 15c d )x + (- 45c d - 90c d - 45c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (- 45c d - 90c d - 45c d)x - 15c d - 30c d - 15c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 4d - 8c d - 4c d)x + (- 4c d - 8c d - 4c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 4d - 8c d - 4c d)x - 4c d - 8c d - 4c +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (8d + 16c d + 8c d )x + (16c d + 32c d + 16c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (8d + 24c d + 24c d + 8c )x + (16c d + 32c d + 16c d)x +--R + +--R 2 4 4 2 6 +--R 8c d + 16c d + 8c +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R * +--R +--+ 7 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- 4d - 12c d - 12c d - 4c d)x - 4c d - 12c d - 12c d - 4c ) +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 +--R (8d + 16c d + 8c d )x + (16c d + 32c d + 16c d)x + 8c d +--R + +--R 4 2 6 +--R 16c d + 8c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (- 8d - 16c d - 8c d )x + (- 24c d - 48c d - 24c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (- 24c d - 48c d - 24c d)x - 8c d - 16c d - 8c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 5 3 3 3 2 4 4 2 2 +--R (20d + 20c d )x + (80c d + 80c d )x + (120c d + 120c d )x +--R + +--R 3 3 5 4 2 6 +--R (80c d + 80c d)x + 20c d + 20c +--R * +--R +-------+2 +--R 4| 2 2 +--R \|d + c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 2d - 4c d - 2c d)x + (- 2c d - 4c d - 2c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 2d - 4c d - 2c d)x - 2c d - 4c d - 2c +--R * +--R +--+ 5 +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (4d + 8c d + 4c d )x + (8c d + 16c d + 8c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (4d + 12c d + 12c d + 4c )x + (8c d + 16c d + 8c d)x +--R + +--R 2 4 4 2 6 +--R 4c d + 8c d + 4c +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 12d - 12c d )x + (- 36c d - 36c d )x +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 12d - 48c d - 36c d)x + (- 36c d - 48c d - 12c )x +--R + +--R 2 3 4 3 2 5 +--R (- 36c d - 36c d)x - 12c d - 12c +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R * +--R +--+ 5 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- d - 3c d - 3c d - c d)x - c d - 3c d - 3c d - c ) +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 +--R (4d + 8c d + 4c d )x + (8c d + 16c d + 8c d)x + 4c d +--R + +--R 4 2 6 +--R 8c d + 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (- 4d - 8c d - 4c d )x + (- 12c d - 24c d - 12c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (- 12c d - 24c d - 12c d)x - 4c d - 8c d - 4c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 5 3 3 3 2 4 4 2 2 +--R (- 8d - 8c d )x + (- 32c d - 32c d )x + (- 48c d - 48c d )x +--R + +--R 3 3 5 4 2 6 +--R (- 32c d - 32c d)x - 8c d - 8c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 5 6 3 4 4 2 5 4 3 3 +--R (- 15d - 15c d )x + (- 75c d - 75c d )x + (- 150c d - 150c d )x +--R + +--R 3 4 5 2 2 4 3 6 5 2 7 +--R (- 150c d - 150c d )x + (- 75c d - 75c d)x - 15c d - 15c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (4d + 8c d + 4c d )x + (8c d + 16c d + 8c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (4d + 12c d + 12c d + 4c )x + (8c d + 16c d + 8c d)x +--R + +--R 2 4 4 2 6 +--R 4c d + 8c d + 4c +--R * +--R +--+ 5 +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 5 2 3 4 3 +--R (4d + 4c d )x + (12c d + 12c d )x + (4d + 16c d + 12c d)x +--R + +--R 4 3 2 5 2 2 3 4 3 2 5 +--R (12c d + 16c d + 4c )x + (12c d + 12c d)x + 4c d + 4c +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 6 2 4 4 2 4 +--R (8d + 8c d )x + (32c d + 32c d )x + (8d + 56c d + 48c d )x +--R + +--R 5 3 3 5 3 2 4 4 2 6 2 +--R (32c d + 64c d + 32c d)x + (48c d + 56c d + 8c )x +--R + +--R 3 3 5 4 2 6 +--R (32c d + 32c d)x + 8c d + 8c +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 4 2 +--R (2d + 4c d + 2c d )x + (4c d + 8c d + 4c d)x + 2c d + 4c d +--R + +--R 6 +--R 2c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (4d + 8c d + 4c d )x + (12c d + 24c d + 12c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (12c d + 24c d + 12c d)x + 4c d + 8c d + 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 5 3 3 3 2 4 4 2 2 +--R (8d + 8c d )x + (32c d + 32c d )x + (48c d + 48c d )x +--R + +--R 3 3 5 4 2 6 +--R (32c d + 32c d)x + 8c d + 8c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 5 6 3 4 4 2 5 4 3 3 +--R (12d + 12c d )x + (60c d + 60c d )x + (120c d + 120c d )x +--R + +--R 3 4 5 2 2 4 3 6 5 2 7 +--R (120c d + 120c d )x + (60c d + 60c d)x + 12c d + 12c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R 6d x + 36c d x + 90c d x + 120c d x + 90c d x + 36c d x +--R + +--R 6 +--R 6c +--R * +--R +-------+2 +--R 4| 2 2 +--R \|d + c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 2d - 2c d )x + (- 6c d - 6c d )x +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 2d - 8c d - 6c d)x + (- 6c d - 8c d - 2c )x +--R + +--R 2 3 4 3 2 5 +--R (- 6c d - 6c d)x - 2c d - 2c +--R * +--R +--+ 5 +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 +--R (- 4d - 4c d )x + (- 16c d - 16c d )x +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (- 4d - 28c d - 24c d )x + (- 16c d - 32c d - 16c d)x +--R + +--R 2 4 4 2 6 2 3 3 5 4 2 6 +--R (- 24c d - 28c d - 4c )x + (- 16c d - 16c d)x - 4c d - 4c +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R + +--R 5 7 4 6 5 2 3 5 4 3 2 4 +--R - 2d x - 10c d x + (- 2d - 20c d )x + (- 10c d - 20c d )x +--R + +--R 2 3 4 3 3 2 5 2 4 5 +--R (- 20c d - 10c d)x + (- 20c d - 2c )x - 10c d x - 2c +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (- d - 2c d - c d )x + (- 3c d - 6c d - 3c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (- 3c d - 6c d - 3c d)x - c d - 2c d - c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 5 3 3 3 2 4 4 2 2 +--R (- 4d - 4c d )x + (- 16c d - 16c d )x + (- 24c d - 24c d )x +--R + +--R 3 3 5 4 2 6 +--R (- 16c d - 16c d)x - 4c d - 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 5 6 3 4 4 2 5 4 3 3 +--R (- 6d - 6c d )x + (- 30c d - 30c d )x + (- 60c d - 60c d )x +--R + +--R 3 4 5 2 2 4 3 6 5 2 7 +--R (- 60c d - 60c d )x + (- 30c d - 30c d)x - 6c d - 6c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (- 4d x - 24c d x - 60c d x - 80c d x - 60c d x - 24c d x - 4c ) +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - d x - 7c d x - 21c d x - 35c d x - 35c d x - 21c d x - 7c d x - c +--R / +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +-------+ +--R ((d + 3c d + 3c d + c )x + d + 3c d + 3c d + c )\|d x + c +--R * +--R +--+ 12 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R ((4d + 12c d + 12c d + 4c )x + 4d + 12c d + 12c d + 4c ) +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 6d - 12c d - 6c d)x + (- 6c d - 12c d - 6c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 6d - 12c d - 6c d)x - 6c d - 12c d - 6c +--R * +--R +-------+2 +--R 4| 2 2 +-------+ +--R \|d + c \|d x + c +--R * +--R +--+ 10 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R ((6d + 18c d + 18c d + 6c )x + 6d + 18c d + 18c d + 6c ) +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 12d - 24c d - 12c d)x + (- 12c d - 24c d - 12c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 12d - 24c d - 12c d)x - 12c d - 24c d - 12c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (15d + 30c d + 15c d )x + (30c d + 60c d + 30c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (15d + 45c d + 45c d + 15c )x + (30c d + 60c d + 30c d)x +--R + +--R 2 4 4 2 6 +--R 15c d + 30c d + 15c +--R * +--R +-------+ +--R \|d x + c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R ((4d + 12c d + 12c d + 4c )x + 4d + 12c d + 12c d + 4c ) +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 8d - 16c d - 8c d)x + (- 8c d - 16c d - 8c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 8d - 16c d - 8c d)x - 8c d - 16c d - 8c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (8d + 16c d + 8c d )x + (16c d + 32c d + 16c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (8d + 24c d + 24c d + 8c )x + (16c d + 32c d + 16c d)x +--R + +--R 2 4 4 2 6 +--R 8c d + 16c d + 8c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 20d - 20c d )x + (- 60c d - 60c d )x +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 20d - 80c d - 60c d)x + (- 60c d - 80c d - 20c )x +--R + +--R 2 3 4 3 2 5 +--R (- 60c d - 60c d)x - 20c d - 20c +--R * +--R +-------+2 +--R 4| 2 2 +-------+ +--R \|d + c \|d x + c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +-------+ +--R ((d + 3c d + 3c d + c )x + d + 3c d + 3c d + c )\|d x + c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 4d - 8c d - 4c d)x + (- 4c d - 8c d - 4c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 4d - 8c d - 4c d)x - 4c d - 8c d - 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (4d + 8c d + 4c d )x + (8c d + 16c d + 8c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (4d + 12c d + 12c d + 4c )x + (8c d + 16c d + 8c d)x +--R + +--R 2 4 4 2 6 +--R 4c d + 8c d + 4c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 5 2 3 4 3 +--R (8d + 8c d )x + (24c d + 24c d )x + (8d + 32c d + 24c d)x +--R + +--R 4 3 2 5 2 2 3 4 3 2 5 +--R (24c d + 32c d + 8c )x + (24c d + 24c d)x + 8c d + 8c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 +--R (15d + 15c d )x + (60c d + 60c d )x +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (15d + 105c d + 90c d )x + (60c d + 120c d + 60c d)x +--R + +--R 2 4 4 2 6 2 3 3 5 4 2 6 +--R (90c d + 105c d + 15c )x + (60c d + 60c d)x + 15c d + 15c +--R * +--R +-------+ +--R \|d x + c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 2d - 4c d - 2c d)x + (- 2c d - 4c d - 2c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 2d - 4c d - 2c d)x - 2c d - 4c d - 2c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (- 4d - 8c d - 4c d )x + (- 8c d - 16c d - 8c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (- 4d - 12c d - 12c d - 4c )x + (- 8c d - 16c d - 8c d)x +--R + +--R 2 4 4 2 6 +--R - 4c d - 8c d - 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 8d - 8c d )x + (- 24c d - 24c d )x +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 8d - 32c d - 24c d)x + (- 24c d - 32c d - 8c )x +--R + +--R 2 3 4 3 2 5 +--R (- 24c d - 24c d)x - 8c d - 8c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 +--R (- 12d - 12c d )x + (- 48c d - 48c d )x +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (- 12d - 84c d - 72c d )x + (- 48c d - 96c d - 48c d)x +--R + +--R 2 4 4 2 6 2 3 3 5 4 2 6 +--R (- 72c d - 84c d - 12c )x + (- 48c d - 48c d)x - 12c d - 12c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 7 4 6 5 2 3 5 4 3 2 4 +--R - 6d x - 30c d x + (- 6d - 60c d )x + (- 30c d - 60c d )x +--R + +--R 2 3 4 3 3 2 5 2 4 5 +--R (- 60c d - 30c d)x + (- 60c d - 6c )x - 30c d x - 6c +--R * +--R +-------+2 +--R 4| 2 2 +-------+ +--R \|d + c \|d x + c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (d + 2c d + c d )x + (2c d + 4c d + 2c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 2 4 4 2 +--R (d + 3c d + 3c d + c )x + (2c d + 4c d + 2c d)x + c d + 2c d +--R + +--R 6 +--R c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 5 2 3 4 3 +--R (4d + 4c d )x + (12c d + 12c d )x + (4d + 16c d + 12c d)x +--R + +--R 4 3 2 5 2 2 3 4 3 2 5 +--R (12c d + 16c d + 4c )x + (12c d + 12c d)x + 4c d + 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 6 2 4 4 2 4 +--R (6d + 6c d )x + (24c d + 24c d )x + (6d + 42c d + 36c d )x +--R + +--R 5 3 3 5 3 2 4 4 2 6 2 +--R (24c d + 48c d + 24c d)x + (36c d + 42c d + 6c )x +--R + +--R 3 3 5 4 2 6 +--R (24c d + 24c d)x + 6c d + 6c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 7 4 6 5 2 3 5 4 3 2 4 +--R 4d x + 20c d x + (4d + 40c d )x + (20c d + 40c d )x +--R + +--R 2 3 4 3 3 2 5 2 4 5 +--R (40c d + 20c d)x + (40c d + 4c )x + 20c d x + 4c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 8 5 7 6 2 4 6 5 3 3 5 +--R d x + 6c d x + (d + 15c d )x + (6c d + 20c d )x +--R + +--R 2 4 4 2 4 3 3 5 3 4 2 6 2 5 6 +--R (15c d + 15c d )x + (20c d + 6c d)x + (15c d + c )x + 6c d x + c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression Integer +--E 325 + +--S 326 of 512 +t0165:= (c+d*x)^(1/2)/(a+b*x^2) +--R +--R +--R +-------+ +--R \|d x + c +--R (203) ---------- +--R 2 +--R b x + a +--R Type: Expression Integer +--E 326 + +--S 327 of 512 +r0165:= -(-(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2)*atanh(b^(1/2)*(c+d*x)^(1/2)/_ + (b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2))+_ + (b*c+a^(1/2)*(-b)^(1/2)*d)^(1/2)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c+a^(1/2)*(-b)^(1/2)*d)^(1/2)))/_ + a^(1/2)/(-b)^(1/2)/b^(1/2) +--R +--R +--R (204) +--R +-------------------+ +-+ +-------+ +--R | +---+ +-+ \|b \|d x + c +--R \|- d\|- b \|a + b c atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-----------------+ +-+ +-------+ +--R | +---+ +-+ \|b \|d x + c +--R - \|d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +---+ +-+ +-+ +--R \|- b \|a \|b +--R Type: Expression Integer +--E 327 + +--S 328 of 512 +a0165:= integrate(t0165,x) +--R +--R +--R (205) +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |2a b |- ----- - c +--R | | 3 +--R | \| 4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(2a b |- ----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |- 2a b |- ----- - c +--R | | 3 +--R | \| 4a b +--R |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |- 2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(2a b |- ----- |-------------------- + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |- 2a b |- ----- - c +--R | | 3 +--R | \| 4a b +--R |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |- 2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(- 2a b |- ----- |-------------------- + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |2a b |- ----- - c +--R | | 3 +--R | \| 4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(- 2a b |- ----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 328 + +--S 329 of 512 +m0165:= a0165-r0165 +--R +--R +--R (206) +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |2a b |- ----- - c +--R | | 3 +--R +---+ +-+ +-+ | \| 4a b +--R \|- b \|a \|b |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(2a b |- ----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |- 2a b |- ----- - c +--R | | 3 +--R +---+ +-+ +-+ | \| 4a b +--R \|- b \|a \|b |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |- 2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(2a b |- ----- |-------------------- + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |- 2a b |- ----- - c +--R | | 3 +--R +---+ +-+ +-+ | \| 4a b +--R \|- b \|a \|b |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |- 2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(- 2a b |- ----- |-------------------- + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |2a b |- ----- - c +--R | | 3 +--R +---+ +-+ +-+ | \| 4a b +--R \|- b \|a \|b |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(- 2a b |- ----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +-------------------+ +-+ +-------+ +--R | +---+ +-+ \|b \|d x + c +--R - 2\|- d\|- b \|a + b c atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-----------------+ +-+ +-------+ +--R | +---+ +-+ \|b \|d x + c +--R 2\|d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +---+ +-+ +-+ +--R 2\|- b \|a \|b +--R Type: Expression Integer +--E 329 + +--S 330 of 512 +d0165:= D(m0165,x) +--R +--R +--R (207) 0 +--R Type: Expression Integer +--E 330 + +--S 331 of 512 +t0166:= (c+d*x)^(1/2)/(a-b*x^2) +--R +--R +--R +-------+ +--R \|d x + c +--R (208) - ---------- +--R 2 +--R b x - a +--R Type: Expression Integer +--E 331 + +--S 332 of 512 +r0166:= -(b*c-a^(1/2)*b^(1/2)*d)^(1/2)*atanh(b^(1/2)*(c+d*x)^(1/2)/_ + (b*c-a^(1/2)*b^(1/2)*d)^(1/2))/a^(1/2)/b+_ + (b*c+a^(1/2)*b^(1/2)*d)^(1/2)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c+a^(1/2)*b^(1/2)*d)^(1/2))/a^(1/2)/b +--R +--R +--R (209) +--R +-----------------+ +-+ +-------+ +--R | +-+ +-+ \|b \|d x + c +--R - \|- d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +---------------+ +-+ +-------+ +--R | +-+ +-+ \|b \|d x + c +--R \|d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R / +--R +-+ +--R b\|a +--R Type: Expression Integer +--E 332 + +--S 333 of 512 +a0166:= integrate(t0166,x) +--R +--R +--R (210) +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 2 | | 2 +--R | | d | | d +--R |2a b |----- + c +-----+ |2a b |----- + c +--R | | 3 | 2 | | 3 +--R | \|4a b 2 | d | \|4a b +-------+ +--R |---------------- log(2a b |----- |---------------- + d\|d x + c ) +--R \| a b | 3 \| a b +--R \|4a b +--R + +--R - +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |- 2a b |----- + c +--R | | 3 +--R | \|4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |- 2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(2a b |----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |- 2a b |----- + c +--R | | 3 +--R | \|4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |- 2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(- 2a b |----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 2 | | 2 +--R | | d | | d +--R |2a b |----- + c +-----+ |2a b |----- + c +--R | | 3 | 2 | | 3 +--R | \|4a b 2 | d | \|4a b +-------+ +--R - |---------------- log(- 2a b |----- |---------------- + d\|d x + c ) +--R \| a b | 3 \| a b +--R \|4a b +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 333 + +--S 334 of 512 +m0166:= a0166-r0166 +--R +--R +--R (211) +--R +----------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |2a b |----- + c +--R | | 3 +--R +-+ | \|4a b +--R b\|a |---------------- +--R \| a b +--R * +--R +----------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(2a b |----- |---------------- + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R - +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |- 2a b |----- + c +--R | | 3 +--R +-+ | \|4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |- 2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(2a b |----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |- 2a b |----- + c +--R | | 3 +--R +-+ | \|4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |- 2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(- 2a b |----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R - +--R +----------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |2a b |----- + c +--R | | 3 +--R +-+ | \|4a b +--R b\|a |---------------- +--R \| a b +--R * +--R +----------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(- 2a b |----- |---------------- + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R +-----------------+ +-+ +-------+ +--R | +-+ +-+ \|b \|d x + c +--R 2\|- d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +---------------+ +-+ +-------+ +--R | +-+ +-+ \|b \|d x + c +--R - 2\|d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R / +--R +-+ +--R 2b\|a +--R Type: Expression Integer +--E 334 + +--S 335 of 512 +d0166:= D(m0166,x) +--R +--R +--R (212) 0 +--R Type: Expression Integer +--E 335 + +--S 336 of 512 +t0167:= 1/(c+d*x)^(1/2)/(a+b*x^2) +--R +--R +--R 1 +--R (213) -------------------- +--R 2 +-------+ +--R (b x + a)\|d x + c +--R Type: Expression Integer +--E 336 + +--S 337 of 512 +r0167:= b^(1/2)*atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2))/_ + a^(1/2)/(-b)^(1/2)/(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2)-b^(1/2)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c+a^(1/2)*(-b)^(1/2)*d)^(1/2))/_ + a^(1/2)/(-b)^(1/2)/(b*c+a^(1/2)*(-b)^(1/2)*d)^(1/2) +--R +--R +--R (214) +--R +-----------------+ +-+ +-------+ +--R +-+ | +---+ +-+ \|b \|d x + c +--R \|b \|d\|- b \|a + b c atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-------------------+ +-+ +-------+ +--R +-+ | +---+ +-+ \|b \|d x + c +--R - \|b \|- d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +-------------------+ +-----------------+ +--R +---+ +-+ | +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R Type: Expression Integer +--E 337 + +--S 338 of 512 +a0167:= integrate(t0167,x) +--R +--R +--R (215) +--R - +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (2a b c d + 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R - a d +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d 2 +--R ((2a b c d + 2a b c ) |- ----------------------------- + a d ) +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R - +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (- 2a b c d - 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R - a d +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (- 2a b c d - 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R a d +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 338 + +--S 339 of 512 +m0167:= a0167-r0167 +--R +--R +--R (216) +--R - +--R +-------------------+ +--R +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (2a b c d + 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R - a d +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +-------------------+ +--R +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d 2 +--R ((2a b c d + 2a b c ) |- ----------------------------- + a d ) +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R - +--R +-------------------+ +--R +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (- 2a b c d - 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R - a d +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +-------------------+ +--R +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (- 2a b c d - 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R a d +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +-----------------+ +-+ +-------+ +--R +-+ | +---+ +-+ \|b \|d x + c +--R - 2\|b \|d\|- b \|a + b c atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-------------------+ +-+ +-------+ +--R +-+ | +---+ +-+ \|b \|d x + c +--R 2\|b \|- d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +-------------------+ +-----------------+ +--R +---+ +-+ | +---+ +-+ | +---+ +-+ +--R 2\|- b \|a \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R Type: Expression Integer +--E 339 + +--S 340 of 512 +d0167:= D(m0167,x) +--R +--R +--R (217) 0 +--R Type: Expression Integer +--E 340 + +--S 341 of 512 +t0168:= (c+d*x)^(3/2)/(a-b*x^2) +--R +--R +--R +-------+ +--R (- d x - c)\|d x + c +--R (218) --------------------- +--R 2 +--R b x - a +--R Type: Expression Integer +--E 341 + +--S 342 of 512 +r0168:= -2*d*(c+d*x)^(1/2)/b+(2*b^(1/2)*c*d-(b*c^2+a*d^2)/a^(1/2))*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c-a^(1/2)*b^(1/2)*d)^(1/2))/_ + b/(b*c-a^(1/2)*b^(1/2)*d)^(1/2)+(2*b^(1/2)*c*d+(b*c^2+a*d^2)/_ + a^(1/2))*atanh(b^(1/2)*(c+d*x)^(1/2)/_ + (b*c+a^(1/2)*b^(1/2)*d)^(1/2))/b/(b*c+a^(1/2)*b^(1/2)*d)^(1/2) +--R +--R +--R (219) +--R +---------------+ +-+ +-------+ +--R +-+ +-+ 2 2 | +-+ +-+ \|b \|d x + c +--R (2c d\|a \|b - a d - b c )\|d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +-----------------+ +-+ +-------+ +--R +-+ +-+ 2 2 | +-+ +-+ \|b \|d x + c +--R (2c d\|a \|b + a d + b c )\|- d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R + +--R +-----------------+ +---------------+ +--R +-+ +-------+ | +-+ +-+ | +-+ +-+ +--R - 2d\|a \|d x + c \|- d\|a \|b + b c \|d\|a \|b + b c +--R / +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R b\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R Type: Expression Integer +--E 342 + +--S 343 of 512 +a0168:= integrate(t0168,x) +--R +--R +--R (220) +--R - +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R b |--------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (2a b c |-------------------------- - a b d - 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R b |----------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (2a b c |-------------------------- + a b d + 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |----------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R - +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R b |----------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (- 2a b c |-------------------------- - a b d - 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |----------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R b |--------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (- 2a b c |-------------------------- + a b d + 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +-------+ +--R - 4d\|d x + c +--R / +--R 2b +--R Type: Union(Expression Integer,...) +--E 343 + +--S 344 of 512 +m0168:= a0168-r0168 +--R +--R +--R (221) +--R - +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R b\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (2a b c |-------------------------- - a b d - 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R +-+ | \| 4a b +--R b\|a |----------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R +-----------------+ +---------------+ +--R | +-+ +-+ | +-+ +-+ +--R \|- d\|a \|b + b c \|d\|a \|b + b c +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (2a b c |-------------------------- + a b d + 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |----------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R - +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R +-+ | \| 4a b +--R b\|a |----------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R +-----------------+ +---------------+ +--R | +-+ +-+ | +-+ +-+ +--R \|- d\|a \|b + b c \|d\|a \|b + b c +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (- 2a b c |-------------------------- - a b d - 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |----------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R b\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (- 2a b c |-------------------------- + a b d + 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +---------------+ +--R +-+ +-+ 2 2 | +-+ +-+ +--R (- 4c d\|a \|b + 2a d + 2b c )\|d\|a \|b + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +-----------------+ +--R +-+ +-+ 2 2 | +-+ +-+ +--R (- 4c d\|a \|b - 2a d - 2b c )\|- d\|a \|b + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R / +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R 2b\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R Type: Expression Integer +--E 344 + +--S 345 of 512 +d0168:= D(m0168,x) +--R +--R +--R (222) 0 +--R Type: Expression Integer +--E 345 + +--S 346 of 512 +t0169:= 1/(c+d*x)^(3/2)/(a+b*x^2) +--R +--R +--R 1 +--R (223) ----------------------------------------- +--R 3 2 +-------+ +--R (b d x + b c x + a d x + a c)\|d x + c +--R Type: Expression Integer +--E 346 + +--S 347 of 512 +r0169:= -2*d/(b*c^2+a*d^2)/(c+d*x)^(1/2)+((-b)^(3/2)*c/a^(1/2)+b*d)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2))/_ + b^(1/2)/(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2)/(b*c^2+a*d^2)-_ + ((-b)^(3/2)*c/a^(1/2)-b*d)*atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c+_ + a^(1/2)*(-b)^(1/2)*d)^(1/2))/b^(1/2)/(b*c+a^(1/2)*_ + (-b)^(1/2)*d)^(1/2)/(b*c^2+a*d^2) +--R +--R +--R (224) +--R +-----------------+ +--R +-+ +---+ +-------+ | +---+ +-+ +--R (b d\|a - b c\|- b )\|d x + c \|d\|- b \|a + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-------------------+ +--R +-+ +---+ +-------+ | +---+ +-+ +--R (b d\|a + b c\|- b )\|d x + c \|- d\|- b \|a + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R + +--R +-------------------+ +-----------------+ +--R +-+ +-+ | +---+ +-+ | +---+ +-+ +--R - 2d\|a \|b \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R / +--R +-------------------+ +-----------------+ +--R 2 2 +-+ +-+ +-------+ | +---+ +-+ | +---+ +-+ +--R (a d + b c )\|a \|b \|d x + c \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R Type: Expression Integer +--E 347 + +--S 348 of 512 +a0169:= integrate(t0169,x) +--R +--R +--R (225) +--R 2 2 +-------+ +--R (- a d - b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d + 4a b c d - 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (a d + b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d + 4a b c d - 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (- a d - b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d - 4a b c d + 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (a d + b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d - 4a b c d + 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R - 4d +--R / +--R 2 2 +-------+ +--R (2a d + 2b c )\|d x + c +--R Type: Union(Expression Integer,...) +--E 348 + +--S 349 of 512 +m0169:= a0169-r0169 +--R +--R +--R (226) +--R +-------------------+ +--R 2 2 +-+ +-+ | +---+ +-+ +--R (- a d - b c )\|a \|b \|- d\|- b \|a + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d + 4a b c d - 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R +-------------------+ +--R 2 2 +-+ +-+ | +---+ +-+ +--R (a d + b c )\|a \|b \|- d\|- b \|a + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d + 4a b c d - 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R +-------------------+ +--R 2 2 +-+ +-+ | +---+ +-+ +--R (- a d - b c )\|a \|b \|- d\|- b \|a + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d - 4a b c d + 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R +-------------------+ +--R 2 2 +-+ +-+ | +---+ +-+ +--R (a d + b c )\|a \|b \|- d\|- b \|a + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d - 4a b c d + 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R +-----------------+ +--R +-+ +---+ | +---+ +-+ +--R (- 2b d\|a + 2b c\|- b )\|d\|- b \|a + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-------------------+ +-+ +-------+ +--R +-+ +---+ | +---+ +-+ \|b \|d x + c +--R (- 2b d\|a - 2b c\|- b )\|- d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +-------------------+ +-----------------+ +--R 2 2 +-+ +-+ | +---+ +-+ | +---+ +-+ +--R (2a d + 2b c )\|a \|b \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R Type: Expression Integer +--E 349 + +--S 350 of 512 +d0169:= D(m0169,x) +--R +--R +--R (227) 0 +--R Type: Expression Integer +--E 350 + +--S 351 of 512 +t0170:= 1/(c+d*x)^(3/2)/(a-b*x^2) +--R +--R +--R 1 +--R (228) - ----------------------------------------- +--R 3 2 +-------+ +--R (b d x + b c x - a d x - a c)\|d x + c +--R Type: Expression Integer +--E 351 + +--S 352 of 512 +r0170:= 2*d/(b*c^2-a*d^2)/(c+d*x)^(1/2)-b^(1/2)*(b^(1/2)*c/a^(1/2)+d)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c-a^(1/2)*b^(1/2)*d)^(1/2))/_ + (b*c-a^(1/2)*b^(1/2)*d)^(1/2)/(b*c^2-a*d^2)+b^(1/2)*(b^(1/2)*c/_ + a^(1/2)-d)*atanh(b^(1/2)*(c+d*x)^(1/2)/_ + (b*c+a^(1/2)*b^(1/2)*d)^(1/2))/(b*c+a^(1/2)*b^(1/2)*d)^(1/2)/_ + (b*c^2-a*d^2) +--R +--R +--R (229) +--R +---------------+ +-+ +-------+ +--R +-+ +-+ +-------+ | +-+ +-+ \|b \|d x + c +--R (d\|a \|b + b c)\|d x + c \|d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +-----------------+ +-+ +-------+ +--R +-+ +-+ +-------+ | +-+ +-+ \|b \|d x + c +--R (d\|a \|b - b c)\|d x + c \|- d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R + +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R - 2d\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R / +--R +-----------------+ +---------------+ +--R 2 2 +-+ +-------+ | +-+ +-+ | +-+ +-+ +--R (a d - b c )\|a \|d x + c \|- d\|a \|b + b c \|d\|a \|b + b c +--R Type: Expression Integer +--E 352 + +--S 353 of 512 +a0170:= integrate(t0170,x) +--R +--R +--R (230) +--R 2 2 +-------+ +--R (a d - b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d - 4a b c d + 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (- a d + b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d - 4a b c d + 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (a d - b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d + 4a b c d - 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (- a d + b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d + 4a b c d - 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R - 4d +--R / +--R 2 2 +-------+ +--R (2a d - 2b c )\|d x + c +--R Type: Union(Expression Integer,...) +--E 353 + +--S 354 of 512 +m0170:= a0170-r0170 +--R +--R +--R (231) +--R +-----------------+ +--R 2 2 +-+ | +-+ +-+ +--R (a d - b c )\|a \|- d\|a \|b + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d - 4a b c d + 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R +-----------------+ +--R 2 2 +-+ | +-+ +-+ +--R (- a d + b c )\|a \|- d\|a \|b + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d - 4a b c d + 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R +-----------------+ +--R 2 2 +-+ | +-+ +-+ +--R (a d - b c )\|a \|- d\|a \|b + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d + 4a b c d - 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R +-----------------+ +--R 2 2 +-+ | +-+ +-+ +--R (- a d + b c )\|a \|- d\|a \|b + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d + 4a b c d - 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R +---------------+ +-+ +-------+ +--R +-+ +-+ | +-+ +-+ \|b \|d x + c +--R (- 2d\|a \|b - 2b c)\|d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +-----------------+ +-+ +-------+ +--R +-+ +-+ | +-+ +-+ \|b \|d x + c +--R (- 2d\|a \|b + 2b c)\|- d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R / +--R +-----------------+ +---------------+ +--R 2 2 +-+ | +-+ +-+ | +-+ +-+ +--R (2a d - 2b c )\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R Type: Expression Integer +--E 354 + +--S 355 of 512 +d0170:= D(m0170,x) +--R +--R +--R (232) 0 +--R Type: Expression Integer +--E 355 + +--S 356 of 512 +t0171:= (d+e*x)^(1/2)/(a+b*x+c*x^2) +--R +--R +--R +-------+ +--R \|e x + d +--R (233) -------------- +--R 2 +--R c x + b x + a +--R Type: Expression Integer +--E 356 + +--S 357 of 512 +r0171:= 2^(1/2)*(e-(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ + atan(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)/(-2*c*d+_ + (b+(b^2-4*a*c)^(1/2))*e)^(1/2))/c^(1/2)/_ + (-2*c*d+(b+(b^2-4*a*c)^(1/2))*e)^(1/2)-2^(1/2)*_ + (e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*atanh(2^(1/2)*c^(1/2)*_ + (d+e*x)^(1/2)/(2*c*d-(b-(b^2-4*a*c)^(1/2))*e)^(1/2))/_ + c^(1/2)/(2*c*d-(b-(b^2-4*a*c)^(1/2))*e)^(1/2) +--R +--R +--R (234) +--R +-----------+ +--R +-+ | 2 +-+ +--R (- e\|2 \|- 4a c + b + (b e - 2c d)\|2 ) +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b + b e - 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R (e\|2 \|- 4a c + b + (b e - 2c d)\|2 )\|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atan(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R / +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-+ | | 2 +--R \|- 4a c + b \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R Type: Expression Integer +--E 357 + +--S 358 of 512 +a0171:= integrate(t0171,x) +--R +--R +--R (235) +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (4a c - b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R - +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (4a c - b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (- 4a c + b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R - +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (- 4a c + b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 358 + +--S 359 of 512 +m0171:= a0171-r0171 +--R +--R +--R (236) +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 4a c - b c +--R \|- 4a c + b \|c |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (4a c - b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R - +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 4a c - b c +--R \|- 4a c + b \|c |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (4a c - b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 4a c - b c +--R \|- 4a c + b \|c |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (- 4a c + b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R - +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 4a c - b c +--R \|- 4a c + b \|c |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (- 4a c + b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (2e\|2 \|- 4a c + b + (- 2b e + 4c d)\|2 ) +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b + b e - 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (- 2e\|2 \|- 4a c + b + (- 2b e + 4c d)\|2 ) +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atan(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R / +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-+ | | 2 +--R 2\|- 4a c + b \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R Type: Expression Integer +--E 359 + +--S 360 of 512 +d0171:= D(m0171,x) +--R +--R +--R (237) 0 +--R Type: Expression Integer +--E 360 + +--S 361 of 512 +t0172:= 1/(d+e*x)^(3/2)/(a+b*x+c*x^2) +--R +--R +--R 1 +--R (238) ------------------------------------------------------- +--R 3 2 +-------+ +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|e x + d +--R Type: Expression Integer +--E 361 + +--S 362 of 512 +r0172:= -2*e/(c*d^2-b*d*e+a*e^2)/(d+e*x)^(1/2)-2^(1/2)*c^(1/2)*_ + (e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*atan(2^(1/2)*c^(1/2)*_ + (d+e*x)^(1/2)/(-2*c*d+(b+(b^2-4*a*c)^(1/2))*e)^(1/2))/_ + (-2*c*d+(b+(b^2-4*a*c)^(1/2))*e)^(1/2)/(c*d^2-b*d*e+a*e^2)+_ + 2^(1/2)*c^(1/2)*(e-(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ + atanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)/_ + (2*c*d-(b-(b^2-4*a*c)^(1/2))*e)^(1/2))/_ + (2*c*d-(b-(b^2-4*a*c)^(1/2))*e)^(1/2)/(c*d^2-b*d*e+a*e^2) +--R +--R +--R (239) +--R +-----------+ +--R +-+ | 2 +-+ +-+ +-------+ +--R (e\|2 \|- 4a c + b + (b e - 2c d)\|2 )\|c \|e x + d +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b + b e - 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +-+ +-------+ +--R (- e\|2 \|- 4a c + b + (b e - 2c d)\|2 )\|c \|e x + d +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atan(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R + +--R - +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R 2e\|- 4a c + b \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R / +--R +-----------+ +--R 2 2 | 2 +-------+ +--R (a e - b d e + c d )\|- 4a c + b \|e x + d +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R Type: Expression Integer +--E 362 + +--S 363 of 512 +a0172:= integrate(t0172,x) +--R +--R +--R (240) +--R 2 2 +-------+ +--R (- a e + b d e - c d )\|e x + d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (24a c + 18a b c - 6b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 6 +--R (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (12a c + 9a b c - 3a b )d e + (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R * +--R log +--R 5 2 4 2 3 4 8 +--R (8a c - 6a b c + a b )e +--R + +--R 4 2 3 3 2 5 7 +--R (- 16a b c + 16a b c - 3a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 6 +--R (16a c - 16a b c - 9a b c + 3a b )d e +--R + +--R 2 3 2 5 7 3 5 +--R (40a b c - 6a b c - b )d e +--R + +--R 2 2 3 4 2 6 4 4 +--R (- 60a b c - 5a b c + 5b c)d e +--R + +--R 2 4 3 3 5 2 5 3 +--R (48a b c + 32a b c - 11b c )d e +--R + +--R 2 5 2 4 4 3 6 2 5 3 4 7 +--R (- 16a c - 48a b c + 13b c )d e + (32a b c - 8b c )d e +--R + +--R 6 2 5 8 +--R (- 8a c + 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (4a b c - 5a b c + b )e + (- 8a c + 22a b c - 5b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 +--R (- 36a b c + 9b c )d e + (24a c - 6b c )d e +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (24a c + 18a b c - 6b c)d e +--R + +--R 3 3 2 5 4 2 3 6 +--R (- 24a b c + 6b c )d e + (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 +--R (- a c + 2a b c - b )e +--R + +--R 2 3 5 3 2 2 2 4 +--R (- 6a b c + 6b c)d e + (6a c - 15b c )d e +--R + +--R 3 3 3 4 4 2 +--R 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 +--R (80a c + 340a b c + 30a b c - 26a b c - b ) +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (12a c + 9a b c - 3a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R + +--R 3 2 2 3 3 2 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d e)\|e x + d +--R + +--R 2 2 +-------+ +--R (a e - b d e + c d )\|e x + d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (- 8a c + 2a b )e + (24a b c - 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (- 24a c - 18a b c + 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (48a b c - 4a b c - 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (- 24a c - 18a b c + 6b c)d e + (24a b c - 6b c )d e +--R + +--R 4 2 3 6 +--R (- 8a c + 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (12a c + 9a b c - 3a b )d e + (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R * +--R log +--R 5 2 4 2 3 4 8 +--R (8a c - 6a b c + a b )e +--R + +--R 4 2 3 3 2 5 7 +--R (- 16a b c + 16a b c - 3a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 6 +--R (16a c - 16a b c - 9a b c + 3a b )d e +--R + +--R 2 3 2 5 7 3 5 +--R (40a b c - 6a b c - b )d e +--R + +--R 2 2 3 4 2 6 4 4 +--R (- 60a b c - 5a b c + 5b c)d e +--R + +--R 2 4 3 3 5 2 5 3 +--R (48a b c + 32a b c - 11b c )d e +--R + +--R 2 5 2 4 4 3 6 2 5 3 4 7 +--R (- 16a c - 48a b c + 13b c )d e + (32a b c - 8b c )d e +--R + +--R 6 2 5 8 +--R (- 8a c + 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (- 4a b c + 5a b c - b )e + (8a c - 22a b c + 5b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 +--R (36a b c - 9b c )d e + (- 24a c + 6b c )d e +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (- 8a c + 2a b )e + (24a b c - 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (- 24a c - 18a b c + 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (48a b c - 4a b c - 2b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (- 24a c - 18a b c + 6b c)d e +--R + +--R 3 3 2 5 4 2 3 6 +--R (24a b c - 6b c )d e + (- 8a c + 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 +--R (- a c + 2a b c - b )e +--R + +--R 2 3 5 3 2 2 2 4 +--R (- 6a b c + 6b c)d e + (6a c - 15b c )d e +--R + +--R 3 3 3 4 4 2 +--R 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 +--R (80a c + 340a b c + 30a b c - 26a b c - b ) +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (12a c + 9a b c - 3a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R + +--R 3 2 2 3 3 2 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d e)\|e x + d +--R + +--R 2 2 +-------+ +--R (- a e + b d e - c d )\|e x + d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (- 8a c + 2a b )e + (24a b c - 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (- 24a c - 18a b c + 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (48a b c - 4a b c - 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (- 24a c - 18a b c + 6b c)d e + (24a b c - 6b c )d e +--R + +--R 4 2 3 6 +--R (- 8a c + 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - 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15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (12a c + 9a b c - 3a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R + +--R 3 2 2 3 3 2 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d e)\|e x + d +--R + +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 +--R (a e - b d e + c d )\|- 4a c + b \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (24a c + 18a b c - 6b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 6 +--R (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (12a c + 9a b c - 3a b )d e + (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R * +--R log +--R 5 2 4 2 3 4 8 +--R (- 8a c + 6a b c - a b )e +--R + +--R 4 2 3 3 2 5 7 +--R (16a b c - 16a b c + 3a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 6 +--R (- 16a c + 16a b c + 9a b c - 3a b )d e +--R + +--R 2 3 2 5 7 3 5 +--R (- 40a b c + 6a b c + b )d e +--R + +--R 2 2 3 4 2 6 4 4 +--R (60a b c + 5a b c - 5b c)d e +--R + +--R 2 4 3 3 5 2 5 3 +--R (- 48a b c - 32a b c + 11b c )d e +--R + +--R 2 5 2 4 4 3 6 2 5 3 4 7 +--R (16a c + 48a b c - 13b c )d e + (- 32a b c + 8b c )d e +--R + +--R 6 2 5 8 +--R (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (- 4a b c + 5a b c - b )e + (8a c - 22a b c + 5b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 +--R (36a b c - 9b c )d e + (- 24a c + 6b c )d e +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (24a c + 18a b c - 6b c)d e +--R + +--R 3 3 2 5 4 2 3 6 +--R (- 24a b c + 6b c )d e + (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 +--R (- a c + 2a b c - b )e +--R + +--R 2 3 5 3 2 2 2 4 +--R (- 6a b c + 6b c)d e + (6a c - 15b c )d e +--R + +--R 3 3 3 4 4 2 +--R 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 +--R (80a c + 340a b c + 30a b c - 26a b c - b ) +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (12a c + 9a b c - 3a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R + +--R 3 2 2 3 3 2 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d e)\|e x + d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +-+ +--R (- 2e\|2 \|- 4a c + b + (- 2b e + 4c d)\|2 )\|c +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b + b e - 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +-+ +--R (2e\|2 \|- 4a c + b + (- 2b e + 4c d)\|2 )\|c +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atan(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R / +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 +--R (2a e - 2b d e + 2c d )\|- 4a c + b \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R Type: Expression Integer +--E 364 + +--S 365 of 512 +d0172:= D(m0172,x) +--R +--R +--R (242) 0 +--R Type: Expression Integer +--E 365 + +--S 366 of 512 +t0173:= 1/(-2+x)/(2+x)^(1/2) +--R +--R +--R 1 +--R (243) --------------- +--R +-----+ +--R (x - 2)\|x + 2 +--R Type: Expression Integer +--E 366 + +--S 367 of 512 +r0173:= -atanh(1/2*(2+x)^(1/2)) +--R +--R +--R +-----+ +--R \|x + 2 +--R (244) - atanh(--------) +--R 2 +--R Type: Expression Integer +--E 367 + +--S 368 of 512 +a0173:= integrate(t0173,x) +--R +--R +--R +-----+ +-----+ +--R - log(\|x + 2 + 2) + log(\|x + 2 - 2) +--R (245) --------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 368 + +--S 369 of 512 +m0173:= a0173-r0173 +--R +--R +--R +-----+ +--R +-----+ +-----+ \|x + 2 +--R - log(\|x + 2 + 2) + log(\|x + 2 - 2) + 2atanh(--------) +--R 2 +--R (246) ---------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 369 + +--S 370 of 512 +d0173:= D(m0173,x) +--R +--R +--R (247) 0 +--R Type: Expression Integer +--E 370 + +--S 371 of 512 +t0174:= 1/(1+x-(2+x)^(1/2)) +--R +--R +--R 1 +--R (248) - ---------------- +--R +-----+ +--R \|x + 2 - x - 1 +--R Type: Expression Integer +--E 371 + +--S 372 of 512 +r0174:= 2/5*atanh(1/5*(1-2*(2+x)^(1/2))*5^(1/2))*5^(1/2)+log(-1-x+(2+x)^(1/2)) +--R +--R +--R +-+ +-----+ +-+ +--R +-----+ +-+ 2\|5 \|x + 2 - \|5 +--R 5log(\|x + 2 - x - 1) - 2\|5 atanh(--------------------) +--R 5 +--R (249) --------------------------------------------------------- +--R 5 +--R Type: Expression Integer +--E 372 + +--S 373 of 512 +a0174:= integrate(t0174,x) +--R +--R +--R (250) +--R +-+ +-----+ +-+ +--R (2\|5 + 10)\|x + 2 + (- 2x - 7)\|5 - 5 +-+ +-----+ +--R log(-----------------------------------------) + \|5 log(- \|x + 2 + x + 1) +--R +-----+ +--R \|x + 2 - x - 1 +--R ---------------------------------------------------------------------------- +--R +-+ +--R \|5 +--R Type: Union(Expression Integer,...) +--E 373 + +--S 374 of 512 +m0174:= a0174-r0174 +--R +--R +--R (251) +--R +-+ +-----+ +--R - \|5 log(\|x + 2 - x - 1) +--R + +--R +-+ +-----+ +-+ +--R (2\|5 + 10)\|x + 2 + (- 2x - 7)\|5 - 5 +--R log(-----------------------------------------) +--R +-----+ +--R \|x + 2 - x - 1 +--R + +--R +-+ +-----+ +-+ +--R +-+ +-----+ 2\|5 \|x + 2 - \|5 +--R \|5 log(- \|x + 2 + x + 1) + 2atanh(--------------------) +--R 5 +--R / +--R +-+ +--R \|5 +--R Type: Expression Integer +--E 374 + +--S 375 of 512 +d0174:= D(m0174,x) +--R +--R +--R (252) 0 +--R Type: Expression Integer +--E 375 + +--S 376 of 512 +t0175:= 1/(x-(1+x)^(1/2)) +--R +--R +--R 1 +--R (253) - ------------ +--R +-----+ +--R \|x + 1 - x +--R Type: Expression Integer +--E 376 + +--S 377 of 512 +r0175:= 2/5*atanh(1/5*(1-2*(1+x)^(1/2))*5^(1/2))*5^(1/2)+log(-x+(1+x)^(1/2)) +--R +--R +--R +-+ +-----+ +-+ +--R +-----+ +-+ 2\|5 \|x + 1 - \|5 +--R 5log(\|x + 1 - x) - 2\|5 atanh(--------------------) +--R 5 +--R (254) ----------------------------------------------------- +--R 5 +--R Type: Expression Integer +--E 377 + +--S 378 of 512 +a0175:= integrate(t0175,x) +--R +--R +--R (255) +--R +-+ +-----+ +-+ +--R (2\|5 + 10)\|x + 1 + (- 2x - 5)\|5 - 5 +-+ +-----+ +--R log(-----------------------------------------) + \|5 log(- \|x + 1 + x) +--R +-----+ +--R \|x + 1 - x +--R ------------------------------------------------------------------------ +--R +-+ +--R \|5 +--R Type: Union(Expression Integer,...) +--E 378 + +--S 379 of 512 +m0175:= a0175-r0175 +--R +--R +--R (256) +--R +-+ +-----+ +-+ +--R +-+ +-----+ (2\|5 + 10)\|x + 1 + (- 2x - 5)\|5 - 5 +--R - \|5 log(\|x + 1 - x) + log(-----------------------------------------) +--R +-----+ +--R \|x + 1 - x +--R + +--R +-+ +-----+ +-+ +--R +-+ +-----+ 2\|5 \|x + 1 - \|5 +--R \|5 log(- \|x + 1 + x) + 2atanh(--------------------) +--R 5 +--R / +--R +-+ +--R \|5 +--R Type: Expression Integer +--E 379 + +--S 380 of 512 +d0175:= D(m0175,x) +--R +--R +--R (257) 0 +--R Type: Expression Integer +--E 380 + +--S 381 of 512 +t0176:= 1/(x-(2+x)^(1/2)) +--R +--R +--R 1 +--R (258) - ------------ +--R +-----+ +--R \|x + 2 - x +--R Type: Expression Integer +--E 381 + +--S 382 of 512 +r0176:= 4/3*log(2-(2+x)^(1/2))+2/3*log(1+(2+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R 2log(\|x + 2 + 1) + 4log(- \|x + 2 + 2) +--R (259) ----------------------------------------- +--R 3 +--R Type: Expression Integer +--E 382 + +--S 383 of 512 +a0176:= integrate(t0176,x) +--R +--R +--R +-----+ +-----+ +--R 2log(\|x + 2 + 1) + 4log(\|x + 2 - 2) +--R (260) --------------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 383 + +--S 384 of 512 +m0176:= a0176-r0176 +--R +--R +--R +-----+ +-----+ +--R 4log(\|x + 2 - 2) - 4log(- \|x + 2 + 2) +--R (261) ----------------------------------------- +--R 3 +--R Type: Expression Integer +--E 384 + +--S 385 of 512 +d0176:= D(m0176,x) +--R +--R +--R (262) 0 +--R Type: Expression Integer +--E 385 + +--S 386 of 512 +t0177:= 1/(x-(1-x)^(1/2)) +--R +--R +--R 1 +--R (263) - -------------- +--R +-------+ +--R \|- x + 1 - x +--R Type: Expression Integer +--E 386 + +--S 387 of 512 +r0177:= 2/5*atanh(1/5*(1+2*(1-x)^(1/2))*5^(1/2))*5^(1/2)+log(x-(1-x)^(1/2)) +--R +--R +--R +-+ +-------+ +-+ +--R +-------+ +-+ 2\|5 \|- x + 1 + \|5 +--R 5log(- \|- x + 1 + x) + 2\|5 atanh(----------------------) +--R 5 +--R (264) ----------------------------------------------------------- +--R 5 +--R Type: Expression Integer +--E 387 + +--S 388 of 512 +a0177:= integrate(t0177,x) +--R +--R +--R (265) +--R +-+ +-------+ +-+ +--R +-+ +-------+ (2\|5 + 10)\|- x + 1 + (- 2x + 5)\|5 + 5 +--R \|5 log(\|- x + 1 - x) + log(-------------------------------------------) +--R +-------+ +--R \|- x + 1 - x +--R -------------------------------------------------------------------------- +--R +-+ +--R \|5 +--R Type: Union(Expression Integer,...) +--E 388 + +--S 389 of 512 +m0177:= a0177-r0177 +--R +--R +--R (266) +--R +-+ +-------+ +--R \|5 log(\|- x + 1 - x) +--R + +--R +-+ +-------+ +-+ +--R (2\|5 + 10)\|- x + 1 + (- 2x + 5)\|5 + 5 +--R log(-------------------------------------------) +--R +-------+ +--R \|- x + 1 - x +--R + +--R +-+ +-------+ +-+ +--R +-+ +-------+ 2\|5 \|- x + 1 + \|5 +--R - \|5 log(- \|- x + 1 + x) - 2atanh(----------------------) +--R 5 +--R / +--R +-+ +--R \|5 +--R Type: Expression Integer +--E 389 + +--S 390 of 512 +d0177:= D(m0177,x) +--R +--R +--R (267) 0 +--R Type: Expression Integer +--E 390 + +--S 391 of 512 +t0178:= 1/(4+(4-x)^(1/2)-x) +--R +--R +--R 1 +--R (268) ------------------ +--R +-------+ +--R \|- x + 4 - x + 4 +--R Type: Expression Integer +--E 391 + +--S 392 of 512 +r0178:= -2*log(1+(4-x)^(1/2)) +--R +--R +--R +-------+ +--R (269) - 2log(\|- x + 4 + 1) +--R Type: Expression Integer +--E 392 + +--S 393 of 512 +a0178:= integrate(t0178,x) +--R +--R +--R +-------+ +--R (270) - 2log(\|- x + 4 + 1) +--R Type: Union(Expression Integer,...) +--E 393 + +--S 394 of 512 +m0178:= a0178-r0178 +--R +--R +--R (271) 0 +--R Type: Expression Integer +--E 394 + +--S 395 of 512 +d0178:= D(m0178,x) +--R +--R +--R (272) 0 +--R Type: Expression Integer +--E 395 + +--S 396 of 512 +t0179:= ((1-x)^(1/2)+(1+x)^(1/2))*(1-x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (273) \|- x + 1 \|x + 1 - x + 1 +--R Type: Expression Integer +--E 396 + +--S 397 of 512 +r0179:= x-1/2*x^2+1/2*x*(1-x^2)^(1/2)+1/2*asin(x) +--R +--R +--R +--------+ +--R | 2 2 +--R x\|- x + 1 + asin(x) - x + 2x +--R (274) -------------------------------- +--R 2 +--R Type: Expression Integer +--E 397 + +--S 398 of 512 +--a0179:= integrate(t0179,x) +--E 398 + +--S 399 of 512 +--m0179:= a0179-r0179 +--E 399 + +--S 400 of 512 +--d0179:= D(m0179,x) +--E 400 + +--S 401 of 512 +t0180:= ((1-x)^(1/2)+(1+x)^(1/2))^2 +--R +--R +--R +-------+ +-----+ +--R (275) 2\|- x + 1 \|x + 1 + 2 +--R Type: Expression Integer +--E 401 + +--S 402 of 512 +r0180:= 2*x+x*(1-x^2)^(1/2)+asin(x) +--R +--R +--R +--------+ +--R | 2 +--R (276) x\|- x + 1 + asin(x) + 2x +--R Type: Expression Integer +--E 402 + +--S 403 of 512 +--a0180:= integrate(t0180,x) +--E 403 + +--S 404 of 512 +--m0180:= a0180-r0180 +--E 404 + +--S 405 of 512 +--d0180:= D(m0180,x) +--E 405 + +--S 406 of 512 +t0181:= (-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2)) +--R +--R +--R +-------+ +-----+ +--R (277) - 2\|- x + 1 \|x + 1 - 2 +--R Type: Expression Integer +--E 406 + +--S 407 of 512 +r0181:= -2*x-x*(1-x^2)^(1/2)-asin(x) +--R +--R +--R +--------+ +--R | 2 +--R (278) - x\|- x + 1 - asin(x) - 2x +--R Type: Expression Integer +--E 407 + +--S 408 of 512 +--a0181:= integrate(t0181,x) +--E 408 + +--S 409 of 512 +--m0181:= a0181-r0181 +--E 409 + +--S 410 of 512 +--d0181:= D(m0181,x) +--E 410 + +--S 411 of 512 +t0182:= ((1-x)^(1/2)+(1+x)^(1/2))^2/x +--R +--R +--R +-------+ +-----+ +--R 2\|- x + 1 \|x + 1 + 2 +--R (279) ----------------------- +--R x +--R Type: Expression Integer +--E 411 + +--S 412 of 512 +r0182:= 2*(1-x^2)^(1/2)-2*atanh((1-x^2)^(1/2))+2*log(x) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R (280) - 2atanh(\|- x + 1 ) + 2\|- x + 1 + 2log(x) +--R Type: Expression Integer +--E 412 + +--S 413 of 512 +a0182:= integrate(t0182,x) +--R +--R +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 + 1 +-------+ +-----+ +--R (281) - 2log(----------------------) + 2\|- x + 1 \|x + 1 +--R 2 +--R x +--R Type: Union(Expression Integer,...) +--E 413 + +--S 414 of 512 +m0182:= a0182-r0182 +--R +--R +--R (282) +--R +-------+ +-----+ +--------+ +--R \|- x + 1 \|x + 1 + 1 | 2 +-------+ +-----+ +--R - 2log(----------------------) + 2atanh(\|- x + 1 ) + 2\|- x + 1 \|x + 1 +--R 2 +--R x +--R + +--R +--------+ +--R | 2 +--R - 2\|- x + 1 - 2log(x) +--R Type: Expression Integer +--E 414 + +--S 415 of 512 +d0182:= D(m0182,x) +--R +--R +--R (283) +--R +--------+ +--------+ +--R | 2 2 +-------+ +-----+ 2 | 2 2 +--R (2\|- x + 1 + 2x - 2)\|- x + 1 \|x + 1 + (- 2x + 2)\|- x + 1 + 2x - 2 +--R ----------------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ | 2 +--R x\|- x + 1 \|- x + 1 \|x + 1 + x\|- x + 1 +--R Type: Expression Integer +--E 415 + +--S 416 of 512 +t0183:= (-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2))/x +--R +--R +--R +-------+ +-----+ +--R - 2\|- x + 1 \|x + 1 - 2 +--R (284) ------------------------- +--R x +--R Type: Expression Integer +--E 416 + +--S 417 of 512 +r0183:= -2*(1-x^2)^(1/2)+2*atanh((1-x^2)^(1/2))-2*log(x) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R (285) 2atanh(\|- x + 1 ) - 2\|- x + 1 - 2log(x) +--R Type: Expression Integer +--E 417 + +--S 418 of 512 +a0183:= integrate(t0183,x) +--R +--R +--R +-------+ +-----+ +-------+ +-----+ +--R (286) - 2log(\|- x + 1 \|x + 1 - 1) - 2\|- x + 1 \|x + 1 +--R Type: Union(Expression Integer,...) +--E 418 + +--S 419 of 512 +m0183:= a0183-r0183 +--R +--R +--R (287) +--R +--------+ +--R +-------+ +-----+ | 2 +-------+ +-----+ +--R - 2log(\|- x + 1 \|x + 1 - 1) - 2atanh(\|- x + 1 ) - 2\|- x + 1 \|x + 1 +--R + +--R +--------+ +--R | 2 +--R 2\|- x + 1 + 2log(x) +--R Type: Expression Integer +--E 419 + +--S 420 of 512 +d0183:= D(m0183,x) +--R +--R +--R (288) +--R +--------+ +--------+ +--R | 2 2 +-------+ +-----+ 2 | 2 2 +--R (2\|- x + 1 - 2x + 2)\|- x + 1 \|x + 1 + (2x - 2)\|- x + 1 + 2x - 2 +--R --------------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ | 2 +--R x\|- x + 1 \|- x + 1 \|x + 1 - x\|- x + 1 +--R Type: Expression Integer +--E 420 + +--S 421 of 512 +t0184:= ((1-x)^(1/2)+(1+x)^(1/2))/(-(1-x)^(1/2)+(1+x)^(1/2)) +--R +--R +--R +-----+ +-------+ +--R \|x + 1 + \|- x + 1 +--R (289) --------------------- +--R +-----+ +-------+ +--R \|x + 1 - \|- x + 1 +--R Type: Expression Integer +--E 421 + +--S 422 of 512 +r0184:= (1-x^2)^(1/2)-atanh((1-x^2)^(1/2))+log(x) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R (290) - atanh(\|- x + 1 ) + \|- x + 1 + log(x) +--R Type: Expression Integer +--E 422 + +--S 423 of 512 +a0184:= integrate(t0184,x) +--R +--R +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 + 1 +-------+ +-----+ +--R (291) - log(----------------------) + \|- x + 1 \|x + 1 +--R 2 +--R x +--R Type: Union(Expression Integer,...) +--E 423 + +--S 424 of 512 +m0184:= a0184-r0184 +--R +--R +--R (292) +--R +-------+ +-----+ +--------+ +--R \|- x + 1 \|x + 1 + 1 | 2 +-------+ +-----+ +--R - log(----------------------) + atanh(\|- x + 1 ) + \|- x + 1 \|x + 1 +--R 2 +--R x +--R + +--R +--------+ +--R | 2 +--R - \|- x + 1 - log(x) +--R Type: Expression Integer +--E 424 + +--S 425 of 512 +d0184:= D(m0184,x) +--R +--R +--R (293) +--R +--------+ +--------+ +--R | 2 2 +-------+ +-----+ 2 | 2 2 +--R (\|- x + 1 + x - 1)\|- x + 1 \|x + 1 + (- x + 1)\|- x + 1 + x - 1 +--R ------------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ | 2 +--R x\|- x + 1 \|- x + 1 \|x + 1 + x\|- x + 1 +--R Type: Expression Integer +--E 425 + +--S 426 of 512 +t0185:= (-(-1+x)^(1/2)+(1+x)^(1/2))/((-1+x)^(1/2)+(1+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R \|x + 1 - \|x - 1 +--R (294) ------------------- +--R +-----+ +-----+ +--R \|x + 1 + \|x - 1 +--R Type: Expression Integer +--E 426 + +--S 427 of 512 +r0185:= 1/2*x^2-1/2*(-1+x)^(1/2)*x*(1+x)^(1/2)+1/2*acosh(x) +--R +--R +--R +-----+ +-----+ 2 +--R - x\|x - 1 \|x + 1 + acosh(x) + x +--R (295) ----------------------------------- +--R 2 +--R Type: Expression Integer +--E 427 + +--S 428 of 512 +a0185:= integrate(t0185,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ 2 +--R - log(\|x - 1 \|x + 1 - x) - x\|x - 1 \|x + 1 + x +--R (296) ---------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 428 + +--S 429 of 512 +m0185:= a0185-r0185 +--R +--R +--R +-----+ +-----+ +--R - log(\|x - 1 \|x + 1 - x) - acosh(x) +--R (297) -------------------------------------- +--R 2 +--R Type: Expression Integer +--E 429 + +--S 430 of 512 +d0185:= D(m0185,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (298) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R 2\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression Integer +--E 430 + +--S 431 of 512 +t0186:= (2*(3-x)^(1/2)+3/(1+x)^(1/2))^2/x +--R +--R +--R +-------+ +-----+ 2 +--R 12\|- x + 3 \|x + 1 - 4x + 8x + 21 +--R (299) ------------------------------------ +--R 2 +--R x + x +--R Type: Expression Integer +--E 431 + +--S 432 of 512 +r0186:= -4*x-12*asin(-1/2+1/2*x)-24*3^(1/2)*_ + atanh(1/3*(3-x)^(1/2)*3^(1/2)/(1+x)^(1/2))+21*log(x)-9*log(1+x) +--R +--R +--R (300) +--R +-+ +-------+ +--R +-+ \|3 \|- x + 3 x - 1 +--R - 24\|3 atanh(--------------) - 9log(x + 1) + 21log(x) - 12asin(-----) - 4x +--R +-----+ 2 +--R 3\|x + 1 +--R Type: Expression Integer +--E 432 + +--S 433 of 512 +--a0186:= integrate(t0186,x) +--E 433 + +--S 434 of 512 +--m0186:= a0186-r0186 +--E 434 + +--S 435 of 512 +--d0186:= D(m0186,x) +-- >> Error detected within library code: +-- integrate: +-- implementation incomplete (residue poly has multiple non-linear factors) +--E 435 + +--S 436 of 512 +t0187:= (1-x)^(1/2)/(1+x^(1/2)) +--R +--R +--R +-------+ +--R \|- x + 1 +--R (301) ---------- +--R +-+ +--R \|x + 1 +--R Type: Expression Integer +--E 436 + +--S 437 of 512 +r0187:= -2*(1-x)^(1/2)+(1-x)^(1/2)*x^(1/2)-asin(x^(1/2)) +--R +--R +--R +-+ +-------+ +-+ +-------+ +--R (302) - asin(\|x ) + \|- x + 1 \|x - 2\|- x + 1 +--R Type: Expression Integer +--E 437 + +--S 438 of 512 +--a0187:= integrate(t0187,x) +--E 438 + +--S 439 of 512 +--m0187:= a0187-r0187 +--E 439 + +--S 440 of 512 +--d0187:= D(m0187,x) +--E 440 + +--S 441 of 512 +t0188:= (1-x)^(1/2)/(1-x^(1/2)) +--R +--R +--R +-------+ +--R \|- x + 1 +--R (303) - ---------- +--R +-+ +--R \|x - 1 +--R Type: Expression Integer +--E 441 + +--S 442 of 512 +r0188:= -2*(1-x)^(1/2)-(1-x)^(1/2)*x^(1/2)+asin(x^(1/2)) +--R +--R +--R +-+ +-------+ +-+ +-------+ +--R (304) asin(\|x ) - \|- x + 1 \|x - 2\|- x + 1 +--R Type: Expression Integer +--E 442 + +--S 443 of 512 +--a0188:= integrate(t0188,x) +--E 443 + +--S 444 of 512 +--m0188:= a0188-r0188 +--E 444 + +--S 445 of 512 +--d0188:= D(m0188,x) +--E 445 + +--S 446 of 512 +t0189:= x/(1+x)/(2+x)^(1/2) +--R +--R +--R x +--R (305) --------------- +--R +-----+ +--R (x + 1)\|x + 2 +--R Type: Expression Integer +--E 446 + +--S 447 of 512 +r0189:= 2*(2+x)^(1/2)+2*atanh((2+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R (306) 2atanh(\|x + 2 ) + 2\|x + 2 +--R Type: Expression Integer +--E 447 + +--S 448 of 512 +a0189:= integrate(t0189,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R (307) log(\|x + 2 + 1) - log(\|x + 2 - 1) + 2\|x + 2 +--R Type: Union(Expression Integer,...) +--E 448 + +--S 449 of 512 +m0189:= a0189-r0189 +--R +--R +--R +-----+ +-----+ +-----+ +--R (308) log(\|x + 2 + 1) - log(\|x + 2 - 1) - 2atanh(\|x + 2 ) +--R Type: Expression Integer +--E 449 + +--S 450 of 512 +d0189:= D(m0189,x) +--R +--R +--R (309) 0 +--R Type: Expression Integer +--E 450 + +--S 451 of 512 +t0190:= (1+x^2)^(1/2)/(-1+x^2) +--R +--R +--R +------+ +--R | 2 +--R \|x + 1 +--R (310) --------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 451 + +--S 452 of 512 +r0190:= asinh(x)-2^(1/2)*atanh(2^(1/2)*x/(1+x^2)^(1/2)) +--R +--R +--R +-+ +--R +-+ x\|2 +--R (311) - \|2 atanh(---------) + asinh(x) +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression Integer +--E 452 + +--S 453 of 512 +a0190:= integrate(t0190,x) +--R +--R +--R (312) +--R +------+ +--R | 2 +--R - 2log(\|x + 1 - x) +--R + +--R +------+ +--R +-+ 3 | 2 2 +-+ 4 2 +--R +-+ (2x\|2 + 2x - 2x)\|x + 1 + (- 2x + 2)\|2 - 2x + x - 3 +--R \|2 log(-------------------------------------------------------------) +--R +------+ +--R 3 | 2 4 2 +--R (2x - 2x)\|x + 1 - 2x + x + 1 +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 453 + +--S 454 of 512 +m0190:= a0190-r0190 +--R +--R +--R (313) +--R +------+ +--R | 2 +--R - 2log(\|x + 1 - x) +--R + +--R +------+ +--R +-+ 3 | 2 2 +-+ 4 2 +--R +-+ (2x\|2 + 2x - 2x)\|x + 1 + (- 2x + 2)\|2 - 2x + x - 3 +--R \|2 log(-------------------------------------------------------------) +--R +------+ +--R 3 | 2 4 2 +--R (2x - 2x)\|x + 1 - 2x + x + 1 +--R + +--R +-+ +--R +-+ x\|2 +--R 2\|2 atanh(---------) - 2asinh(x) +--R +------+ +--R | 2 +--R \|x + 1 +--R / +--R 2 +--R Type: Expression Integer +--E 454 + +--S 455 of 512 +d0190:= D(m0190,x) +--R +--R +--R (314) 0 +--R Type: Expression Integer +--E 455 + +--S 456 of 512 +t0191:= (1+x)^(1/2)*(1+x^3)/(1+x^2) +--R +--R +--R 3 +-----+ +--R (x + 1)\|x + 1 +--R (315) ---------------- +--R 2 +--R x + 1 +--R Type: Expression Integer +--E 456 + +--S 457 of 512 +r0191:= -2*(1+x)^(1/2)-2/3*(1+x)^(3/2)+2/5*(1+x)^(5/2)-_ + atan(((2+2*2^(1/2))^(1/2)-2*(1+x)^(1/2))/_ + (-2+2*2^(1/2))^(1/2))/(2^(1/2)-1)^(1/2)+_ + atan(((2+2*2^(1/2))^(1/2)+2*(1+x)^(1/2))/_ + (-2+2*2^(1/2))^(1/2))/(2^(1/2)-1)^(1/2)-_ + 1/2*log(1+2^(1/2)+x-(2+2*2^(1/2))^(1/2)*(1+x)^(1/2))/_ + (1+2^(1/2))^(1/2)+1/2*log(1+2^(1/2)+x+_ + (2+2*2^(1/2))^(1/2)*(1+x)^(1/2))/(1+2^(1/2))^(1/2) +--R +--R +--R (316) +--R +--------+ +---------+ +--R | +-+ +-----+ | +-+ +-+ +--R 15\|\|2 - 1 log(\|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +--------+ +---------+ +--R | +-+ +-----+ | +-+ +-+ +--R - 15\|\|2 - 1 log(- \|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 + 2\|x + 1 +--R 30\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 - 2\|x + 1 +--R - 30\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +--------+ +--------+ +--R 2 +-----+ | +-+ | +-+ +--R (12x + 4x - 68)\|x + 1 \|\|2 - 1 \|\|2 + 1 +--R / +--R +--------+ +--------+ +--R | +-+ | +-+ +--R 30\|\|2 - 1 \|\|2 + 1 +--R Type: Expression Integer +--E 457 + +--S 458 of 512 +a0191:= integrate(t0191,x) +--R +--R +--R (317) +--R - +--R 4+-+ %pi +--R 15\|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (2\|8 sin(---) - 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R 4+-+ %pi +--R 15\|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (- 2\|8 sin(---) + 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +--R - 30\|8 sin(---)atan(---------------------------------------) +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 - \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +--R - 30\|8 sin(---)atan(---------------------------------------) +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 + \|8 sin(---) - \|8 cos(---) +--R 8 8 +--R + +--R 2 +-----+ +--R (12x + 4x - 68)\|x + 1 +--R / +--R 30 +--R Type: Union(Expression Integer,...) +--E 458 + +--S 459 of 512 +m0191:= a0191-r0191 +--R +--R +--R (318) +--R +--------+ +---------+ +--R | +-+ +-----+ | +-+ +-+ +--R - \|\|2 - 1 log(\|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R - +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R \|8 cos(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (2\|8 sin(---) - 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R \|8 cos(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (- 2\|8 sin(---) + 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R +--------+ +---------+ +--R | +-+ +-----+ | +-+ +-+ +--R \|\|2 - 1 log(- \|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 + 2\|x + 1 +--R - 2\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 - 2\|x + 1 +--R 2\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R - +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R 2\|8 sin(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R atan(---------------------------------------) +--R +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 - \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R + +--R - +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R 2\|8 sin(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R atan(---------------------------------------) +--R +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 + \|8 sin(---) - \|8 cos(---) +--R 8 8 +--R / +--R +--------+ +--------+ +--R | +-+ | +-+ +--R 2\|\|2 - 1 \|\|2 + 1 +--R Type: Expression Integer +--E 459 + +--S 460 of 512 +d0191:= D(m0191,x) +--R +--R +--R (319) +--R +-+ %pi 12 +--R ((4x + 8)\|2 - 4x - 12)sin(---) +--R 8 +--R + +--R +-+ %pi %pi 11 +--R ((- 16x - 32)\|2 + 16x + 48)cos(---)sin(---) +--R 8 8 +--R + +--R +-+ %pi 2 +--R ((40x + 80)\|2 - 40x - 120)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 +--R ((- 4x - 12x - 8)\|2 + 4x + 16x + 12)\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 3 +--R ((- 80x - 160)\|2 + 80x + 240)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi +--R ((16x + 48x + 32)\|2 - 16x - 64x - 48)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 4 +--R ((124x + 248)\|2 - 124x - 372)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 2 +--R ((- 52x - 156x - 104)\|2 + 52x + 208x + 156)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (12x + 48x + 60x + 24)\|2 - 12x - 60x - 84x - 36 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 5 +--R ((- 160x - 320)\|2 + 160x + 480)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 3 +--R ((96x + 288x + 192)\|2 - 96x - 384x - 288)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((- 80x - 320x - 400x - 160)\|2 + 80x + 400x + 560x + 240) +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 6 +--R ((176x + 352)\|2 - 176x - 528)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 4 +--R ((- 136x - 408x - 272)\|2 + 136x + 544x + 408)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (224x + 896x + 1120x + 448)\|2 - 224x - 1120x - 1568x +--R + +--R - 672 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 4x - 20x - 36x - 28x - 8)\|2 + 4x + 24x + 48x + 40x +--R + +--R 12 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 7 +--R ((- 160x - 320)\|2 + 160x + 480)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 5 +--R ((160x + 480x + 320)\|2 - 160x - 640x - 480)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 368x - 1472x - 1840x - 736)\|2 + 368x + 1840x + 2576x +--R + +--R 1104 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (28x + 140x + 252x + 196x + 56)\|2 - 28x - 168x - 336x +--R + +--R - 280x - 84 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 8 +--R ((124x + 248)\|2 - 124x - 372)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 6 +--R ((- 136x - 408x - 272)\|2 + 136x + 544x + 408)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (552x + 2208x + 2760x + 1104)\|2 - 552x - 2760x - 3864x +--R + +--R - 1656 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 60x - 300x - 540x - 420x - 120)\|2 + 60x + 360x +--R + +--R 2 +--R 720x + 600x + 180 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 3 +--R (9x + 54x + 126x + 144x + 81x + 18)\|2 - 9x - 63x - 162x +--R + +--R 2 +--R - 198x - 117x - 27 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 9 +--R ((- 80x - 160)\|2 + 80x + 240)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 7 +--R ((96x + 288x + 192)\|2 - 96x - 384x - 288)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 368x - 1472x - 1840x - 736)\|2 + 368x + 1840x + 2576x +--R + +--R 1104 +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (136x + 680x + 1224x + 952x + 272)\|2 - 136x - 816x +--R + +--R 2 +--R - 1632x - 1360x - 408 +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 36x - 216x - 504x - 576x - 324x - 72)\|2 + 36x +--R + +--R 4 3 2 +--R 252x + 648x + 792x + 468x + 108 +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 10 +--R ((40x + 80)\|2 - 40x - 120)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 8 +--R ((- 52x - 156x - 104)\|2 + 52x + 208x + 156)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (224x + 896x + 1120x + 448)\|2 - 224x - 1120x - 1568x +--R + +--R - 672 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 60x - 300x - 540x - 420x - 120)\|2 + 60x + 360x +--R + +--R 2 +--R 720x + 600x + 180 +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (150x + 900x + 2100x + 2400x + 1350x + 300)\|2 - 150x +--R + +--R 4 3 2 +--R - 1050x - 2700x - 3300x - 1950x - 450 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 5 +--R (- x - 7x - 20x - 30x - 25x - 11x - 2)\|2 + x + 8x +--R + +--R 4 3 2 +--R 25x + 40x + 35x + 16x + 3 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 11 +--R ((- 16x - 32)\|2 + 16x + 48)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 9 +--R ((16x + 48x + 32)\|2 - 16x - 64x - 48)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((- 80x - 320x - 400x - 160)\|2 + 80x + 400x + 560x + 240) +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (28x + 140x + 252x + 196x + 56)\|2 - 28x - 168x - 336x +--R + +--R - 280x - 84 +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 36x - 216x - 504x - 576x - 324x - 72)\|2 + 36x +--R + +--R 4 3 2 +--R 252x + 648x + 792x + 468x + 108 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (10x + 70x + 200x + 300x + 250x + 110x + 20)\|2 - 10x +--R + +--R 5 4 3 2 +--R - 80x - 250x - 400x - 350x - 160x - 30 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R +-+ %pi 12 +--R ((4x + 8)\|2 - 4x - 12)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 10 +--R ((- 4x - 12x - 8)\|2 + 4x + 16x + 12)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 8 +--R ((12x + 48x + 60x + 24)\|2 - 12x - 60x - 84x - 36)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 4x - 20x - 36x - 28x - 8)\|2 + 4x + 24x + 48x + 40x +--R + +--R 12 +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 3 +--R (9x + 54x + 126x + 144x + 81x + 18)\|2 - 9x - 63x - 162x +--R + +--R 2 +--R - 198x - 117x - 27 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 5 4 +--R (- x - 7x - 20x - 30x - 25x - 11x - 2)\|2 + x + 8x + 25x +--R + +--R 3 2 +--R 40x + 35x + 16x + 3 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ 7 6 +--R (2x + 16x + 54x + 100x + 110x + 72x + 26x + 4)\|2 - 2x - 18x +--R + +--R 5 4 3 2 +--R - 66x - 130x - 150x - 102x - 38x - 6 +--R * +--R +--------+ +---------+ +--R +-----+ | +-+ | +-+ +--R \|x + 1 \|\|2 + 1 \|2\|2 + 2 +--R + +--R +-+ %pi 12 +--R ((- 4x - 8)\|2 - 4x - 12)sin(---) +--R 8 +--R + +--R +-+ %pi %pi 11 +--R ((16x + 32)\|2 + 16x + 48)cos(---)sin(---) +--R 8 8 +--R + +--R +-+ %pi 2 +--R ((- 40x - 80)\|2 - 40x - 120)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 +--R ((4x + 12x + 8)\|2 + 4x + 16x + 12)\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 3 +--R ((80x + 160)\|2 + 80x + 240)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi +--R ((- 16x - 48x - 32)\|2 - 16x - 64x - 48)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 4 +--R ((- 124x - 248)\|2 - 124x - 372)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 2 +--R ((52x + 156x + 104)\|2 + 52x + 208x + 156)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 12x - 48x - 60x - 24)\|2 - 12x - 60x - 84x - 36 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 5 +--R ((160x + 320)\|2 + 160x + 480)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 3 +--R ((- 96x - 288x - 192)\|2 - 96x - 384x - 288)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((80x + 320x + 400x + 160)\|2 + 80x + 400x + 560x + 240) +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 6 +--R ((- 176x - 352)\|2 - 176x - 528)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 4 +--R ((136x + 408x + 272)\|2 + 136x + 544x + 408)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 224x - 896x - 1120x - 448)\|2 - 224x - 1120x - 1568x +--R + +--R - 672 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (4x + 20x + 36x + 28x + 8)\|2 + 4x + 24x + 48x + 40x +--R + +--R 12 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 7 +--R ((160x + 320)\|2 + 160x + 480)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 5 +--R ((- 160x - 480x - 320)\|2 - 160x - 640x - 480)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (368x + 1472x + 1840x + 736)\|2 + 368x + 1840x + 2576x +--R + +--R 1104 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 28x - 140x - 252x - 196x - 56)\|2 - 28x - 168x +--R + +--R 2 +--R - 336x - 280x - 84 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 8 +--R ((- 124x - 248)\|2 - 124x - 372)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 6 +--R ((136x + 408x + 272)\|2 + 136x + 544x + 408)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 552x - 2208x - 2760x - 1104)\|2 - 552x - 2760x +--R + +--R - 3864x - 1656 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (60x + 300x + 540x + 420x + 120)\|2 + 60x + 360x +--R + +--R 2 +--R 720x + 600x + 180 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (- 9x - 54x - 126x - 144x - 81x - 18)\|2 - 9x - 63x +--R + +--R 3 2 +--R - 162x - 198x - 117x - 27 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 9 +--R ((80x + 160)\|2 + 80x + 240)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 7 +--R ((- 96x - 288x - 192)\|2 - 96x - 384x - 288)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (368x + 1472x + 1840x + 736)\|2 + 368x + 1840x + 2576x +--R + +--R 1104 +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 136x - 680x - 1224x - 952x - 272)\|2 - 136x - 816x +--R + +--R 2 +--R - 1632x - 1360x - 408 +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (36x + 216x + 504x + 576x + 324x + 72)\|2 + 36x + 252x +--R + +--R 3 2 +--R 648x + 792x + 468x + 108 +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 10 +--R ((- 40x - 80)\|2 - 40x - 120)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 8 +--R ((52x + 156x + 104)\|2 + 52x + 208x + 156)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 224x - 896x - 1120x - 448)\|2 - 224x - 1120x - 1568x +--R + +--R - 672 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (60x + 300x + 540x + 420x + 120)\|2 + 60x + 360x +--R + +--R 2 +--R 720x + 600x + 180 +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 150x - 900x - 2100x - 2400x - 1350x - 300)\|2 - 150x +--R + +--R 4 3 2 +--R - 1050x - 2700x - 3300x - 1950x - 450 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 5 +--R (x + 7x + 20x + 30x + 25x + 11x + 2)\|2 + x + 8x +--R + +--R 4 3 2 +--R 25x + 40x + 35x + 16x + 3 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 11 +--R ((16x + 32)\|2 + 16x + 48)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 9 +--R ((- 16x - 48x - 32)\|2 - 16x - 64x - 48)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((80x + 320x + 400x + 160)\|2 + 80x + 400x + 560x + 240) +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 28x - 140x - 252x - 196x - 56)\|2 - 28x - 168x +--R + +--R 2 +--R - 336x - 280x - 84 +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (36x + 216x + 504x + 576x + 324x + 72)\|2 + 36x + 252x +--R + +--R 3 2 +--R 648x + 792x + 468x + 108 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ +--R (- 10x - 70x - 200x - 300x - 250x - 110x - 20)\|2 +--R + +--R 6 5 4 3 2 +--R - 10x - 80x - 250x - 400x - 350x - 160x - 30 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R +-+ %pi 12 +--R ((- 4x - 8)\|2 - 4x - 12)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 10 +--R ((4x + 12x + 8)\|2 + 4x + 16x + 12)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 8 +--R ((- 12x - 48x - 60x - 24)\|2 - 12x - 60x - 84x - 36)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R ((4x + 20x + 36x + 28x + 8)\|2 + 4x + 24x + 48x + 40x + 12) +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (- 9x - 54x - 126x - 144x - 81x - 18)\|2 - 9x - 63x +--R + +--R 3 2 +--R - 162x - 198x - 117x - 27 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 5 4 +--R (x + 7x + 20x + 30x + 25x + 11x + 2)\|2 + x + 8x + 25x +--R + +--R 3 2 +--R 40x + 35x + 16x + 3 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ 7 +--R (- 2x - 16x - 54x - 100x - 110x - 72x - 26x - 4)\|2 - 2x +--R + +--R 6 5 4 3 2 +--R - 18x - 66x - 130x - 150x - 102x - 38x - 6 +--R * +--R +--------+ +---------+ +--R +-----+ | +-+ | +-+ +--R \|x + 1 \|\|2 - 1 \|2\|2 - 2 +--R + +--R 2 %pi 12 2 %pi %pi 11 +--R (8x + 8)sin(---) + (- 32x - 32)cos(---)sin(---) +--R 8 8 8 +--R + +--R 2 %pi 2 3 2 4+-+2 %pi 10 +--R ((80x + 80)cos(---) + (- 6x - 6x - 6x - 6)\|8 )sin(---) +--R 8 8 +--R + +--R 2 %pi 3 3 2 4+-+2 %pi +--R ((- 160x - 160)cos(---) + (20x + 20x + 20x + 20)\|8 cos(---)) +--R 8 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 2 %pi 4 3 2 4+-+2 %pi 2 +--R (248x + 248)cos(---) + (- 74x - 74x - 74x - 74)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 +--R 4x + 8x + 8x + 8x + 4 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 2 %pi 5 +--R (- 320x - 320)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 3 +--R (144x + 144x + 144x + 144)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi +--R (- 64x - 128x - 128x - 128x - 64)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 2 %pi 6 +--R (352x + 352)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 4 +--R (- 212x - 212x - 212x - 212)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 2 +--R (224x + 448x + 448x + 448x + 224)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 +--R (x + 3x + 4x + 4x + 3x + 1)\|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 2 %pi 7 +--R (- 320x - 320)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 5 +--R (264x + 264x + 264x + 264)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 3 +--R (- 352x - 704x - 704x - 704x - 352)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi +--R (14x + 42x + 56x + 56x + 42x + 14)\|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 2 %pi 8 +--R (248x + 248)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 6 +--R (- 236x - 236x - 236x - 236)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 4 +--R (728x + 1456x + 1456x + 1456x + 728)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 +--R (- 11x - 33x - 44x - 44x - 33x - 11)\|8 cos(---) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 2 %pi 9 +--R (- 160x - 160)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 7 +--R (176x + 176x + 176x + 176)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 5 +--R (- 576x - 1152x - 1152x - 1152x - 576)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 3 +--R (140x + 420x + 560x + 560x + 420x + 140)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi +--R (32x + 128x + 224x + 256x + 224x + 128x + 32)cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 2 %pi 10 +--R (80x + 80)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 8 +--R (- 102x - 102x - 102x - 102)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 6 +--R (416x + 832x + 832x + 832x + 416)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (- 93x - 279x - 372x - 372x - 279x - 93)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 2 +--R (112x + 448x + 784x + 896x + 784x + 448x + 112)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 +--R (2x + 10x + 22x + 30x + 30x + 22x + 10x + 2)\|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 2 %pi 11 3 2 4+-+2 %pi 9 +--R (- 32x - 32)cos(---) + (36x + 36x + 36x + 36)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 7 +--R (- 160x - 320x - 320x - 320x - 160)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 5 +--R (54x + 162x + 216x + 216x + 162x + 54)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 3 +--R (- 64x - 256x - 448x - 512x - 448x - 256x - 64)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi +--R (4x + 20x + 44x + 60x + 60x + 44x + 20x + 4)\|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 2 %pi 12 3 2 4+-+2 %pi 10 +--R (8x + 8)cos(---) + (- 10x - 10x - 10x - 10)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 8 +--R (36x + 72x + 72x + 72x + 36)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (- 9x - 27x - 36x - 36x - 27x - 9)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 4 +--R (16x + 64x + 112x + 128x + 112x + 64x + 16)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi 2 +--R (- 2x - 10x - 22x - 30x - 30x - 22x - 10x - 2)\|8 cos(---) +--R 8 +--R * +--R +-----+ +--R \|x + 1 +--R / +--R 3 2 %pi 12 +--R (8x + 8x + 8x + 8)sin(---) +--R 8 +--R + +--R 3 2 %pi %pi 11 +--R (- 32x - 32x - 32x - 32)cos(---)sin(---) +--R 8 8 +--R + +--R 3 2 %pi 2 +--R (80x + 80x + 80x + 80)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 +--R (- 8x - 16x - 16x - 16x - 8)\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 3 +--R (- 160x - 160x - 160x - 160)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi +--R (32x + 64x + 64x + 64x + 32)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 4 +--R (248x + 248x + 248x + 248)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 2 5 4 +--R (- 104x - 208x - 208x - 208x - 104)\|8 cos(---) + 24x + 72x +--R 8 +--R + +--R 3 2 +--R 96x + 96x + 72x + 24 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 5 +--R (- 320x - 320x - 320x - 320)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 3 +--R (192x + 384x + 384x + 384x + 192)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi +--R (- 160x - 480x - 640x - 640x - 480x - 160)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 6 +--R (352x + 352x + 352x + 352)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 4 +--R (- 272x - 544x - 544x - 544x - 272)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 2 +--R (448x + 1344x + 1792x + 1792x + 1344x + 448)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 +--R (- 8x - 32x - 56x - 64x - 56x - 32x - 8)\|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 7 +--R (- 320x - 320x - 320x - 320)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 5 +--R (320x + 640x + 640x + 640x + 320)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 3 +--R (- 736x - 2208x - 2944x - 2944x - 2208x - 736)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi +--R (56x + 224x + 392x + 448x + 392x + 224x + 56)\|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 8 +--R (248x + 248x + 248x + 248)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 6 +--R (- 272x - 544x - 544x - 544x - 272)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 4 +--R (1104x + 3312x + 4416x + 4416x + 3312x + 1104)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 2 +--R (- 120x - 480x - 840x - 960x - 840x - 480x - 120)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R 18x + 90x + 198x + 270x + 270x + 198x + 90x + 18 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 9 +--R (- 160x - 160x - 160x - 160)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 7 +--R (192x + 384x + 384x + 384x + 192)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 5 +--R (- 736x - 2208x - 2944x - 2944x - 2208x - 736)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 +--R (272x + 1088x + 1904x + 2176x + 1904x + 1088x + 272)\|8 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi +--R (- 72x - 360x - 792x - 1080x - 1080x - 792x - 360x - 72)cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 10 +--R (80x + 80x + 80x + 80)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 8 +--R (- 104x - 208x - 208x - 208x - 104)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 6 +--R (448x + 1344x + 1792x + 1792x + 1344x + 448)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 4 +--R (- 120x - 480x - 840x - 960x - 840x - 480x - 120)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (300x + 1500x + 3300x + 4500x + 4500x + 3300x + 1500x + 300) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 4+-+2 +--R (- 2x - 12x - 32x - 52x - 60x - 52x - 32x - 12x - 2)\|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 11 +--R (- 32x - 32x - 32x - 32)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 9 +--R (32x + 64x + 64x + 64x + 32)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 7 +--R (- 160x - 480x - 640x - 640x - 480x - 160)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 5 +--R (56x + 224x + 392x + 448x + 392x + 224x + 56)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 72x - 360x - 792x - 1080x - 1080x - 792x - 360x - 72) +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (20x + 120x + 320x + 520x + 600x + 520x + 320x + 120x + 20) +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 12 +--R (8x + 8x + 8x + 8)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 10 +--R (- 8x - 16x - 16x - 16x - 8)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 8 +--R (24x + 72x + 96x + 96x + 72x + 24)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 6 +--R (- 8x - 32x - 56x - 64x - 56x - 32x - 8)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi 4 +--R (18x + 90x + 198x + 270x + 270x + 198x + 90x + 18)cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 4+-+2 %pi 2 +--R (- 2x - 12x - 32x - 52x - 60x - 52x - 32x - 12x - 2)\|8 cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 2 +--R 4x + 28x + 88x + 168x + 224x + 224x + 168x + 88x + 28x + 4 +--R Type: Expression Integer +--E 460 + +--S 461 of 512 +t0192:= (-1+x)^(1/3)/(1+x)^(1/3) +--R +--R +--R 3+-----+ +--R \|x - 1 +--R (320) -------- +--R 3+-----+ +--R \|x + 1 +--R Type: Expression Integer +--E 461 + +--S 462 of 512 +r0192:= (-1+x)^(1/3)*(1+x)^(2/3)-2/3*_ + atan(1/3*(1+2*(-1+x)^(1/3)/(1+x)^(1/3))*3^(1/2))*3^(1/2)+_ + 2/3*log(1-(-1+x)^(1/3)/(1+x)^(1/3))-_ + 1/3*log(1+(-1+x)^(2/3)/(1+x)^(2/3)+(-1+x)^(1/3)/(1+x)^(1/3)) +--R +--R +--R (321) +--R 3+-----+2 3+-----+3+-----+ 3+-----+2 +--R \|x + 1 + \|x - 1 \|x + 1 + \|x - 1 +--R - log(----------------------------------------) +--R 3+-----+2 +--R \|x + 1 +--R + +--R 3+-----+ 3+-----+ +-+3+-----+ +-+3+-----+ +--R \|x + 1 - \|x - 1 +-+ \|3 \|x + 1 + 2\|3 \|x - 1 +--R 2log(-------------------) - 2\|3 atan(----------------------------) +--R 3+-----+ 3+-----+ +--R \|x + 1 3\|x + 1 +--R + +--R 3+-----+3+-----+2 +--R 3\|x - 1 \|x + 1 +--R / +--R 3 +--R Type: Expression Integer +--E 462 + +--S 463 of 512 +--a0192:= integrate(t0192,x) +--E 463 + +--S 464 of 512 +--m0192:= a0192-r0192 +--E 464 + +--S 465 of 512 +--d0192:= D(m0192,x) +--E 465 + +--S 466 of 512 +t0193:= x^(1/2)/((2-x)^(1/2)-x^(1/2)) +--R +--R +--R +-+ +--R \|x +--R (322) - ----------------- +--R +-+ +-------+ +--R \|x - \|- x + 2 +--R Type: Expression Integer +--E 466 + +--S 467 of 512 +r0193:= -1/2*x-1/2*(-(-2+x)*x)^(1/2)+atanh((2-x)^(1/2)/x^(1/2))-1/2*log(1-x) +--R +--R +--R +-------+ +---------+ +--R \|- x + 2 | 2 +--R 2atanh(----------) - \|- x + 2x - log(- x + 1) - x +--R +-+ +--R \|x +--R (323) ---------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 467 + +--S 468 of 512 +a0193:= integrate(t0193,x) +--R +--R +--R +-------+ +-+ +--R \|- x + 2 \|x + 1 +-------+ +-+ +--R log(------------------) - \|- x + 2 \|x - x +--R 2 +--R x - 2x + 1 +--R (324) -------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 468 + +--S 469 of 512 +m0193:= a0193-r0193 +--R +--R +--R (325) +--R +-------+ +-+ +-------+ +--R \|- x + 2 \|x + 1 \|- x + 2 +-------+ +-+ +--R log(------------------) - 2atanh(----------) - \|- x + 2 \|x +--R 2 +-+ +--R x - 2x + 1 \|x +--R + +--R +---------+ +--R | 2 +--R \|- x + 2x + log(- x + 1) +--R / +--R 2 +--R Type: Expression Integer +--E 469 + +--S 470 of 512 +d0193:= D(m0193,x) +--R +--R +--R +---------+ +--R +-------+ +-+ | 2 +--R (- x + 1)\|- x + 2 \|x + (x - 1)\|- x + 2x +--R (326) --------------------------------------------- +--R +---------+ +--R | 2 +-------+ +-+ +--R 2\|- x + 2x \|- x + 2 \|x +--R Type: Expression Integer +--E 470 + +--S 471 of 512 +t0194:= 1/(9+b*x^2)^(1/2) +--R +--R +--R 1 +--R (327) ----------- +--R +--------+ +--R | 2 +--R \|b x + 9 +--R Type: Expression Integer +--E 471 + +--S 472 of 512 +r0194:= asinh(1/3*b^(1/2)*x)/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R asinh(-----) +--R 3 +--R (328) ------------ +--R +-+ +--R \|b +--R Type: Expression Integer +--E 472 + +--S 473 of 512 +a0194:= integrate(t0194,x) +--R +--R +--R (329) +--R +--------+ +--R +-+ | 2 2 +-+ +--R (3\|b - b x)\|b x + 9 + (- b x - 9)\|b + 3b x +--R log(--------------------------------------------------) +--R +--------+ +--R | 2 +--R \|b x + 9 - 3 +--R [-------------------------------------------------------, +--R +-+ +--R \|b +--R +--------+ +--R +---+ | 2 +---+ +--R \|- b \|b x + 9 - 3\|- b +--R 2atan(---------------------------) +--R b x +--R ----------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List Expression Integer,...) +--E 473 + +--S 474 of 512 +m0194a:= a0194.1-r0194 +--R +--R +--R (330) +--R +--------+ +--R +-+ | 2 2 +-+ +-+ +--R (3\|b - b x)\|b x + 9 + (- b x - 9)\|b + 3b x x\|b +--R log(--------------------------------------------------) - asinh(-----) +--R +--------+ 3 +--R | 2 +--R \|b x + 9 - 3 +--R ---------------------------------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 474 + +--S 475 of 512 +d0194a:= D(m0194a,x) +--R +--R +--R (331) 0 +--R Type: Expression Integer +--E 475 + +--S 476 of 512 +m0194b:= a0194.2-r0194 +--R +--R +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R +-+ \|- b \|b x + 9 - 3\|- b +---+ x\|b +--R 2\|b atan(---------------------------) - \|- b asinh(-----) +--R b x 3 +--R (332) ----------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression Integer +--E 476 + +--S 477 of 512 +d0194b:= D(m0194a,x) +--R +--R +--R (333) 0 +--R Type: Expression Integer +--E 477 + +--S 478 of 512 +t0195:= 1/(9-b*x^2)^(1/2) +--R +--R +--R 1 +--R (334) ------------- +--R +----------+ +--R | 2 +--R \|- b x + 9 +--R Type: Expression Integer +--E 478 + +--S 479 of 512 +r0195:= asin(1/3*b^(1/2)*x)/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R asin(-----) +--R 3 +--R (335) ----------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 479 + +--S 480 of 512 +a0195:= integrate(t0195,x) +--R +--R +--R (336) +--R +----------+ +----------+ +--R | 2 2 +---+ | 2 +--R (3\|- b x + 9 + b x - 9)\|- b + b x\|- b x + 9 - 3b x +--R log(-----------------------------------------------------------) +--R +----------+ +--R | 2 +--R \|- b x + 9 - 3 +--R [----------------------------------------------------------------, +--R +---+ +--R \|- b +--R +----------+ +--R | 2 +-+ +--R (\|- b x + 9 - 3)\|b +--R 2atan(-----------------------) +--R b x +--R - ------------------------------] +--R +-+ +--R \|b +--R Type: Union(List Expression Integer,...) +--E 480 + +--S 481 of 512 +m0195a:= a0195.1-r0195 +--R +--R +--R (337) +--R +----------+ +----------+ +--R | 2 2 +---+ | 2 +--R +-+ (3\|- b x + 9 + b x - 9)\|- b + b x\|- b x + 9 - 3b x +--R \|b log(-----------------------------------------------------------) +--R +----------+ +--R | 2 +--R \|- b x + 9 - 3 +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b asin(-----) +--R 3 +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression Integer +--E 481 + +--S 482 of 512 +d0195a:= D(m0195a,x) +--R +--R +--R (338) 0 +--R Type: Expression Integer +--E 482 + +--S 483 of 512 +m0195b:= a0195.2-r0195 +--R +--R +--R +----------+ +--R | 2 +-+ +-+ +--R (\|- b x + 9 - 3)\|b x\|b +--R - 2atan(-----------------------) - asin(-----) +--R b x 3 +--R (339) ---------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 483 + +--S 484 of 512 +d0195b:= D(m0195b,x) +--R +--R +--R (340) 0 +--R Type: Expression Integer +--E 484 + +--S 485 of 512 +t0196:= 1/(%pi+b*x^2)^(1/2) +--R +--R +--R 1 +--R (341) ------------- +--R +----------+ +--R | 2 +--R \|b x + %pi +--R Type: Expression Integer +--E 485 + +--S 486 of 512 +r0196:= asinh(b^(1/2)*x/%pi^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R asinh(------) +--R +---+ +--R \|%pi +--R (342) ------------- +--R +-+ +--R \|b +--R Type: Expression Integer +--E 486 + +--S 487 of 512 +a0196:= integrate(t0196,x) +--R +--R +--R (343) +--R +----------+ +--R +-+ +---+ | 2 +---+ 2 +-+ +--R (\|b \|%pi - b x)\|b x + %pi + b x\|%pi + (- b x - %pi)\|b +--R log(----------------------------------------------------------------) +--R +----------+ +--R +---+ | 2 +--R \|%pi \|b x + %pi - %pi +--R [---------------------------------------------------------------------, +--R +-+ +--R \|b +--R +----------+ +--R +---+ | 2 +---+ +---+ +--R \|- b \|b x + %pi - \|- b \|%pi +--R 2atan(----------------------------------) +--R b x +--R -----------------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List Expression Integer,...) +--E 487 + +--S 488 of 512 +m0196a:= a0196.1-r0196 +--R +--R +--R (344) +--R +----------+ +--R +-+ +---+ | 2 +---+ 2 +-+ +--R (\|b \|%pi - b x)\|b x + %pi + b x\|%pi + (- b x - %pi)\|b +--R log(----------------------------------------------------------------) +--R +----------+ +--R +---+ | 2 +--R \|%pi \|b x + %pi - %pi +--R + +--R +-+ +--R x\|b +--R - asinh(------) +--R +---+ +--R \|%pi +--R / +--R +-+ +--R \|b +--R Type: Expression Integer +--E 488 + +--S 489 of 512 +d0196a:= D(m0196a,x) +--R +--R +--R (345) +--R +----------+ +--R | 2 +--R 2 2 +-+ +---+ 2 3 2 |b x + %pi +--R ((3b %pi x + 4%pi )\|b \|%pi - b %pi x - 4b %pi x) |---------- +--R \| %pi +--R + +--R 2 4 2 2 +-+ +---+ 2 3 2 +--R (b x + 5b %pi x + 4%pi )\|b \|%pi - 3b %pi x - 4b %pi x +--R * +--R +----------+ +--R | 2 +--R \|b x + %pi +--R + +--R 2 3 2 +---+ 2 4 2 2 3 +-+ +--R ((3b %pi x + 4b %pi x)\|%pi + (- b %pi x - 5b %pi x - 4%pi )\|b ) +--R * +--R +----------+ +--R | 2 +--R |b x + %pi +--R |---------- +--R \| %pi +--R + +--R 3 5 2 3 2 +---+ 2 4 2 2 3 +-+ +--R (b x + 5b %pi x + 4b %pi x)\|%pi + (- 3b %pi x - 7b %pi x - 4%pi )\|b +--R / +--R 2 3 2 +---+ 2 4 2 2 3 +-+ +--R ((3b %pi x + 4b %pi x)\|%pi + (- b %pi x - 5b %pi x - 4%pi )\|b ) +--R * +--R +----------+ +--R | 2 +----------+ +--R |b x + %pi | 2 +--R |---------- \|b x + %pi +--R \| %pi +--R + +--R 2 4 2 2 3 +-+ +---+ 3 5 2 2 3 +--R (3b %pi x + 7b %pi x + 4%pi )\|b \|%pi - b %pi x - 5b %pi x +--R + +--R 3 +--R - 4b %pi x +--R * +--R +----------+ +--R | 2 +--R |b x + %pi +--R |---------- +--R \| %pi +--R Type: Expression Integer +--E 489 + +--S 490 of 512 +m0196b:= a0196.2-r0196 +--R +--R +--R +----------+ +--R +---+ | 2 +---+ +---+ +-+ +--R +-+ \|- b \|b x + %pi - \|- b \|%pi +---+ x\|b +--R 2\|b atan(----------------------------------) - \|- b asinh(------) +--R b x +---+ +--R \|%pi +--R (346) ------------------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression Integer +--E 490 + +--S 491 of 512 +d0196b:= D(m0196b,x) +--R +--R +--R +----------+ +--R +----------+ | 2 +--R +---+ | 2 |b x + %pi +--R - \|%pi \|b x + %pi + %pi |---------- +--R \| %pi +--R (347) ---------------------------------------- +--R +----------+ +--R | 2 +----------+ +--R |b x + %pi | 2 +--R %pi |---------- \|b x + %pi +--R \| %pi +--R Type: Expression Integer +--E 491 + +--S 492 of 512 +t0197:= 1/(%pi-b*x^2)^(1/2) +--R +--R +--R 1 +--R (348) --------------- +--R +------------+ +--R | 2 +--R \|- b x + %pi +--R Type: Expression Integer +--E 492 + +--S 493 of 512 +r0197:= asin(b^(1/2)*x/%pi^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R asin(------) +--R +---+ +--R \|%pi +--R (349) ------------ +--R +-+ +--R \|b +--R Type: Expression Integer +--E 493 + +--S 494 of 512 +a0197:= integrate(t0197,x) +--R +--R +--R (350) +--R [ +--R log +--R +------------+ +--R | 2 +---+ +---+ 2 +---+ +--R (\|- b x + %pi \|- b - b x)\|%pi + (b x - %pi)\|- b +--R + +--R +------------+ +--R | 2 +--R b x\|- b x + %pi +--R / +--R +------------+ +--R | 2 +---+ +--R \|- b x + %pi \|%pi - %pi +--R / +--R +---+ +--R \|- b +--R , +--R +------------+ +--R +-+ +---+ | 2 +-+ +--R \|b \|%pi - \|- b x + %pi \|b +--R 2atan(--------------------------------) +--R b x +--R ---------------------------------------] +--R +-+ +--R \|b +--R Type: Union(List Expression Integer,...) +--E 494 + +--S 495 of 512 +m0197a:= a0197.1-r0197 +--R +--R +--R (351) +--R +-+ +--R \|b +--R * +--R log +--R +------------+ +--R | 2 +---+ +---+ 2 +---+ +--R (\|- b x + %pi \|- b - b x)\|%pi + (b x - %pi)\|- b +--R + +--R +------------+ +--R | 2 +--R b x\|- b x + %pi +--R / +--R +------------+ +--R | 2 +---+ +--R \|- b x + %pi \|%pi - %pi +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b asin(------) +--R +---+ +--R \|%pi +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression Integer +--E 495 + +--S 496 of 512 +d0197a:= D(m0197a,x) +--R +--R +--R (352) +--R +------------+ +--R +------------+ | 2 +--R 2 2 | 2 |- b x + %pi +--R (- 3b %pi x + 4%pi )\|- b x + %pi |------------ +--R \| %pi +--R + +--R +------------+ +--R 2 4 2 2 | 2 +--R (b x - 5b %pi x + 4%pi )\|- b x + %pi +--R * +--R +---+ +--R \|- b +--R + +--R +------------+ +--R | 2 +--R 2 3 2 |- b x + %pi 3 5 2 3 2 +--R (3b %pi x - 4b %pi x) |------------ - b x + 5b %pi x - 4b %pi x +--R \| %pi +--R * +--R +---+ +--R \|%pi +--R + +--R +------------+ +--R | 2 +--R 2 4 2 2 3 |- b x + %pi 2 4 +--R (- b %pi x + 5b %pi x - 4%pi ) |------------ - 3b %pi x +--R \| %pi +--R + +--R 2 2 3 +--R 7b %pi x - 4%pi +--R * +--R +---+ +--R \|- b +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 3 2 | 2 |- b x + %pi +--R (- b %pi x + 4b %pi x)\|- b x + %pi |------------ +--R \| %pi +--R + +--R +------------+ +--R 2 3 2 | 2 +--R (- 3b %pi x + 4b %pi x)\|- b x + %pi +--R / +--R +------------+ +--R | 2 +--R 2 4 2 2 3 |- b x + %pi +---+ +--R (3b %pi x - 7b %pi x + 4%pi ) |------------ \|- b +--R \| %pi +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 3 2 | 2 |- b x + %pi +--R (3b %pi x - 4b %pi x)\|- b x + %pi |------------ +--R \| %pi +--R * +--R +---+ +--R \|%pi +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 4 2 2 3 | 2 |- b x + %pi +---+ +--R (- b %pi x + 5b %pi x - 4%pi )\|- b x + %pi |------------ \|- b +--R \| %pi +--R + +--R +------------+ +--R | 2 +--R 3 5 2 2 3 3 |- b x + %pi +--R (b %pi x - 5b %pi x + 4b %pi x) |------------ +--R \| %pi +--R Type: Expression Integer +--E 496 + +--S 497 of 512 +m0197b:= a0197.2-r0197 +--R +--R +--R +------------+ +--R +-+ +---+ | 2 +-+ +-+ +--R \|b \|%pi - \|- b x + %pi \|b x\|b +--R 2atan(--------------------------------) - asin(------) +--R b x +---+ +--R \|%pi +--R (353) ------------------------------------------------------ +--R +-+ +--R \|b +--R Type: Expression Integer +--E 497 + +--S 498 of 512 +d0197b:= D(m0197b,x) +--R +--R +--R +------------+ +--R +------------+ | 2 +--R | 2 +---+ |- b x + %pi +--R - \|- b x + %pi \|%pi + %pi |------------ +--R \| %pi +--R (354) -------------------------------------------- +--R +------------+ +--R +------------+ | 2 +--R | 2 |- b x + %pi +--R %pi\|- b x + %pi |------------ +--R \| %pi +--R Type: Expression Integer +--E 498 + +--S 499 of 512 +t0198:= 1/(a+b*x)/(c+d*x^2)^(1/2) +--R +--R +--R 1 +--R (355) -------------------- +--R +--------+ +--R | 2 +--R (b x + a)\|d x + c +--R Type: Expression Integer +--E 499 + +--S 500 of 512 +r0198:= atanh((b^2*c+a^2*d)^(1/2)*(c+d*x^2)^(1/2)/_ + (-b*c+a*d*x))/(b^2*c+a^2*d)^(1/2) +--R +--R +--R +---------+ +--------+ +--R | 2 2 | 2 +--R \|a d + b c \|d x + c +--R atanh(-----------------------) +--R a d x - b c +--R (356) ------------------------------ +--R +---------+ +--R | 2 2 +--R \|a d + b c +--R Type: Expression Integer +--E 500 + +--S 501 of 512 +a0198:= integrate(t0198,x) +--R +--R +--R (357) +--R [ +--R log +--R +---------+ +--------+ +--R 2 +-+ | 2 2 3 2 | 2 +--R ((a b x + a )\|c \|a d + b c + (- a d - a b c)x)\|d x + c +--R + +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((- a d - b c)x - a b c x - a c)\|a d + b c +--R + +--R 2 3 2 3 2 +-+ +--R ((a b d + b c)x + (a d + a b c)x)\|c +--R / +--R +--------+ +--R +-+ | 2 +--R (b x + a)\|c \|d x + c - b c x - a c +--R / +--R +---------+ +--R | 2 2 +--R \|a d + b c +--R , +--R +-----------+ +--------+ +-----------+ +--R | 2 2 | 2 | 2 2 +-+ +--R a\|- a d - b c \|d x + c + (- b x - a)\|- a d - b c \|c +--R 2atan(----------------------------------------------------------) +--R 2 2 +--R (a d + b c)x +--R -----------------------------------------------------------------] +--R +-----------+ +--R | 2 2 +--R \|- a d - b c +--R Type: Union(List Expression Integer,...) +--E 501 + +--S 502 of 512 +m0198a:= a0198.1-r0198 +--R +--R +--R (358) +--R log +--R +---------+ +--------+ +--R 2 +-+ | 2 2 3 2 | 2 +--R ((a b x + a )\|c \|a d + b c + (- a d - a b c)x)\|d x + c +--R + +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((- a d - b c)x - a b c x - a c)\|a d + b c +--R + +--R 2 3 2 3 2 +-+ +--R ((a b d + b c)x + (a d + a b c)x)\|c +--R / +--R +--------+ +--R +-+ | 2 +--R (b x + a)\|c \|d x + c - b c x - a c +--R + +--R +---------+ +--------+ +--R | 2 2 | 2 +--R \|a d + b c \|d x + c +--R - atanh(-----------------------) +--R a d x - b c +--R / +--R +---------+ +--R | 2 2 +--R \|a d + b c +--R Type: Expression Integer +--E 502 + +--S 503 of 512 +d0198a:= D(m0198a,x) +--R +--R +--R (359) 0 +--R Type: Expression Integer +--E 503 + +--S 504 of 512 +m0198b:= a0198.2-r0198 +--R +--R +--R (360) +--R +---------+ +--------+ +--R +-----------+ | 2 2 | 2 +--R | 2 2 \|a d + b c \|d x + c +--R - \|- a d - b c atanh(-----------------------) +--R a d x - b c +--R + +--R +---------+ +--R | 2 2 +--R 2\|a d + b c +--R * +--R +-----------+ +--------+ +-----------+ +--R | 2 2 | 2 | 2 2 +-+ +--R a\|- a d - b c \|d x + c + (- b x - a)\|- a d - b c \|c +--R atan(----------------------------------------------------------) +--R 2 2 +--R (a d + b c)x +--R / +--R +-----------+ +---------+ +--R | 2 2 | 2 2 +--R \|- a d - b c \|a d + b c +--R Type: Expression Integer +--E 504 + +--S 505 of 512 +d0198b:= D(m0198b,x) +--R +--R +--R (361) 0 +--R Type: Expression Integer +--E 505 + +--S 506 of 512 +t0199:= 1/(a+b*x)/(-c+d*x^2)^(1/2) +--R +--R +--R 1 +--R (362) -------------------- +--R +--------+ +--R | 2 +--R (b x + a)\|d x - c +--R Type: Expression Integer +--E 506 + +--S 507 of 512 +r0199:= atan((b^2*c-a^2*d)^(1/2)*(-c+d*x^2)^(1/2)/(b*c+a*d*x))/(b^2*c-a^2*d)^(1/2) +--R +--R +--R +-----------+ +--------+ +--R | 2 2 | 2 +--R \|- a d + b c \|d x - c +--R atan(-------------------------) +--R a d x + b c +--R (363) ------------------------------- +--R +-----------+ +--R | 2 2 +--R \|- a d + b c +--R Type: Expression Integer +--E 507 + +--S 508 of 512 +a0199:= integrate(t0199,x) +--R +--R +--R (364) +--R [ +--R log +--R +---------+ +--------+ +--R 2 +---+ | 2 2 3 2 | 2 +--R ((a b x + a )\|- c \|a d - b c + (- a d + a b c)x)\|d x - c +--R + +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((- a d + b c)x + a b c x + a c)\|a d - b c +--R + +--R 2 3 2 3 2 +---+ +--R ((a b d - b c)x + (a d - a b c)x)\|- c +--R / +--R +--------+ +--R +---+ | 2 +--R (b x + a)\|- c \|d x - c + b c x + a c +--R / +--R +---------+ +--R | 2 2 +--R \|a d - b c +--R , +--R +-----------+ +--------+ +-----------+ +--R | 2 2 | 2 | 2 2 +---+ +--R a\|- a d + b c \|d x - c + (- b x - a)\|- a d + b c \|- c +--R 2atan(------------------------------------------------------------) +--R 2 2 +--R (a d - b c)x +--R -------------------------------------------------------------------] +--R +-----------+ +--R | 2 2 +--R \|- a d + b c +--R Type: Union(List Expression Integer,...) +--E 508 + +--S 509 of 512 +m0199a:= a0199.1-r0199 +--R +--R +--R (365) +--R +-----------+ +--R | 2 2 +--R \|- a d + b c +--R * +--R log +--R +---------+ +--------+ +--R 2 +---+ | 2 2 3 2 | 2 +--R ((a b x + a )\|- c \|a d - b c + (- a d + a b c)x)\|d x - c +--R + +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((- a d + b c)x + a b c x + a c)\|a d - b c +--R + +--R 2 3 2 3 2 +---+ +--R ((a b d - b c)x + (a d - a b c)x)\|- c +--R / +--R +--------+ +--R +---+ | 2 +--R (b x + a)\|- c \|d x - c + b c x + a c +--R + +--R +-----------+ +--------+ +--R +---------+ | 2 2 | 2 +--R | 2 2 \|- a d + b c \|d x - c +--R - \|a d - b c atan(-------------------------) +--R a d x + b c +--R / +--R +-----------+ +---------+ +--R | 2 2 | 2 2 +--R \|- a d + b c \|a d - b c +--R Type: Expression Integer +--E 509 + +--S 510 of 512 +d0199a:= D(m0199a,x) +--R +--R +--R (366) 0 +--R Type: Expression Integer +--E 510 + +--S 511 of 512 +m0199b:= a0199.2-r0199 +--R +--R +--R (367) +--R +-----------+ +--------+ +-----------+ +--R | 2 2 | 2 | 2 2 +---+ +--R a\|- a d + b c \|d x - c + (- b x - a)\|- a d + b c \|- c +--R 2atan(------------------------------------------------------------) +--R 2 2 +--R (a d - b c)x +--R + +--R +-----------+ +--------+ +--R | 2 2 | 2 +--R \|- a d + b c \|d x - c +--R - atan(-------------------------) +--R a d x + b c +--R / +--R +-----------+ +--R | 2 2 +--R \|- a d + b c +--R Type: Expression Integer +--E 511 + +--S 512 of 512 +d0199b:= D(m0199b,x) +--R +--R +--R (368) 0 +--R Type: Expression Integer +--E 512 + +)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}