diff --git a/changelog b/changelog index 58514b9..e73a059 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100617 tpd src/axiom-website/patches.html 20100617.01.tpd.patch +20100617 tpd src/input/Makefile rule-based log integration +20100617 tpd src/input/richlog000-099.input rule-based log integration 20100616 tpd src/axiom-website/patches.html 20100616.02.tpd.patch 20100616 tpd src/input/Makefile rule-based hyper integration 20100616 tpd src/input/richhyper900-999.input rule-based hyper integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index a53a7e4..d3c497b 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2908,6 +2908,8 @@ src/input/richhyper700-799.input rule-based hyper integration
src/input/richhyper800-899.input rule-based hyper integration
20100616.02.tpd.patch src/input/richhyper900-999.input rule-based hyper integration
+20100617.01.tpd.patch +src/input/richlog000-099.input rule-based log integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 1a9d5fa..00909ed 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -385,6 +385,8 @@ REGRES= ackermann.regress \ richhyper700-799.regress \ richhyper800-899.regress \ richhyper900-999.regress \ + richhyper1000-1098.regress \ + richlog000-099.regress \ richrational.regress \ richtrig000-099.regress \ richtrig100-199.regress \ @@ -724,6 +726,8 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richhyper700-799.input \ ${OUT}/richhyper800-899.input \ ${OUT}/richhyper900-999.input \ + ${OUT}/richhyper1000-1098.input \ + ${OUT}/richlog000-099.input \ ${OUT}/richrational.input \ ${OUT}/richtrig000-099.input \ ${OUT}/richtrig100-199.input \ @@ -1092,6 +1096,8 @@ DOCFILES= \ ${DOC}/richhyper700-799.input.dvi \ ${DOC}/richhyper800-899.input.dvi \ ${DOC}/richhyper900-999.input.dvi \ + ${DOC}/richhyper1000-1098.input.dvi \ + ${DOC}/richlog000-099.input.dvi \ ${DOC}/richrational.input.dvi \ ${DOC}/richtrig000-099.input.dvi \ ${DOC}/richtrig100-199.input.dvi \ diff --git a/src/input/richlog000-099.input.pamphlet b/src/input/richlog000-099.input.pamphlet new file mode 100644 index 0000000..6c5ef78 --- /dev/null +++ b/src/input/richlog000-099.input.pamphlet @@ -0,0 +1,5358 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richlog000-099.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richlog000-099.output +)spool richlog000-099.output +)set message auto off +)clear all + +--S 1 of 500 +t0000:= x^2*log(a*x^n) +--R +--R +--R 2 n +--R (1) x log(a x ) +--R Type: Expression Integer +--E 1 + +--S 2 of 500 +r0000:= 1/9*x^3*(-n+3*log(a*x^n)) +--R +--R +--R 3 n 3 +--R 3x log(a x ) - n x +--R (2) ------------------- +--R 9 +--R Type: Expression Integer +--E 2 + +--S 3 of 500 +a0000:= integrate(t0000,x) +--R +--R +--R 3 3 3 +--R 3n x log(x) + 3x log(a) - n x +--R (3) ------------------------------ +--R 9 +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 500 +m0000:= a0000-r0000 +--R +--R +--R 3 n 3 3 +--R - x log(a x ) + n x log(x) + x log(a) +--R (4) ------------------------------------- +--R 3 +--R Type: Expression Integer +--E 4 + +--S 5 of 500 +d0000:= D(m0000,x) +--R +--R +--R 2 n n 2 2 2 n 3 n - 1 +--R - 3x x log(a x ) + (3n x log(x) + 3x log(a) + n x )x - n x x +--R (5) ------------------------------------------------------------------ +--R n +--R 3x +--R Type: Expression Integer +--E 5 + +--S 6 of 500 +t0001:= x^3*log(a*x^n) +--R +--R +--R 3 n +--R (6) x log(a x ) +--R Type: Expression Integer +--E 6 + +--S 7 of 500 +r0001:= 1/16*x^4*(-n+4*log(a*x^n)) +--R +--R +--R 4 n 4 +--R 4x log(a x ) - n x +--R (7) ------------------- +--R 16 +--R Type: Expression Integer +--E 7 + +--S 8 of 500 +a0001:= integrate(t0001,x) +--R +--R +--R 4 4 4 +--R 4n x log(x) + 4x log(a) - n x +--R (8) ------------------------------ +--R 16 +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 500 +m0001:= a0001-r0001 +--R +--R +--R 4 n 4 4 +--R - x log(a x ) + n x log(x) + x log(a) +--R (9) ------------------------------------- +--R 4 +--R Type: Expression Integer +--E 9 + +--S 10 of 500 +d0001:= D(m0001,x) +--R +--R +--R 3 n n 3 3 3 n 4 n - 1 +--R - 4x x log(a x ) + (4n x log(x) + 4x log(a) + n x )x - n x x +--R (10) ------------------------------------------------------------------ +--R n +--R 4x +--R Type: Expression Integer +--E 10 + +--S 11 of 500 +t0002:= log(a*x^n)/x^2 +--R +--R +--R n +--R log(a x ) +--R (11) --------- +--R 2 +--R x +--R Type: Expression Integer +--E 11 + +--S 12 of 500 +r0002:= -1/x*(log(a*x^n)+n) +--R +--R +--R n +--R - log(a x ) - n +--R (12) --------------- +--R x +--R Type: Expression Integer +--E 12 + +--S 13 of 500 +a0002:= integrate(t0002,x) +--R +--R +--R - n log(x) - log(a) - n +--R (13) ----------------------- +--R x +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 500 +m0002:= a0002-r0002 +--R +--R +--R n +--R log(a x ) - n log(x) - log(a) +--R (14) ----------------------------- +--R x +--R Type: Expression Integer +--E 14 + +--S 15 of 500 +d0002:= D(m0002,x) +--R +--R +--R n n n n - 1 +--R - x log(a x ) + (n log(x) + log(a) - n)x + n x x +--R (15) ------------------------------------------------------ +--R 2 n +--R x x +--R Type: Expression Integer +--E 15 + +--S 16 of 500 +t0003:= log(a*x^n)/x^3 +--R +--R +--R n +--R log(a x ) +--R (16) --------- +--R 3 +--R x +--R Type: Expression Integer +--E 16 + +--S 17 of 500 +r0003:= -1/4/x^2*(2*log(a*x^n)+n) +--R +--R +--R n +--R - 2log(a x ) - n +--R (17) ---------------- +--R 2 +--R 4x +--R Type: Expression Integer +--E 17 + +--S 18 of 500 +a0003:= integrate(t0003,x) +--R +--R +--R - 2n log(x) - 2log(a) - n +--R (18) ------------------------- +--R 2 +--R 4x +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 500 +m0003:= a0003-r0003 +--R +--R +--R n +--R log(a x ) - n log(x) - log(a) +--R (19) ----------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E 19 + +--S 20 of 500 +d0003:= D(m0003,x) +--R +--R +--R n n n n - 1 +--R - 2x log(a x ) + (2n log(x) + 2log(a) - n)x + n x x +--R (20) --------------------------------------------------------- +--R 3 n +--R 2x x +--R Type: Expression Integer +--E 20 + +--S 21 of 500 +t0004:= x^m*log(a*x^n) +--R +--R +--R m n +--R (21) x log(a x ) +--R Type: Expression Integer +--E 21 + +--S 22 of 500 +r0004:= 1/(1+m)^2*x^(1+m)*(-n+log(a*x^n)+log(a*x^n)*m) +--R +--R +--R m + 1 n m + 1 +--R (m + 1)x log(a x ) - n x +--R (22) --------------------------------- +--R 2 +--R m + 2m + 1 +--R Type: Expression Integer +--E 22 + +--S 23 of 500 +a0004:= integrate(t0004,x) +--R +--R +--R m log(x) +--R ((m + 1)n x log(x) + (m + 1)x log(a) - n x)%e +--R (23) ----------------------------------------------------- +--R 2 +--R m + 2m + 1 +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 500 +m0004:= a0004-r0004 +--R +--R +--R (24) +--R m + 1 n +--R (- m - 1)x log(a x ) +--R + +--R m log(x) m + 1 +--R ((m + 1)n x log(x) + (m + 1)x log(a) - n x)%e + n x +--R / +--R 2 +--R m + 2m + 1 +--R Type: Expression Integer +--E 24 + +--S 25 of 500 +d0004:= D(m0004,x) +--R +--R +--R (25) +--R m n n n m log(x) +--R (- m - 1)x x log(a x ) + ((m + 1)n log(x) + (m + 1)log(a))x %e +--R + +--R m n m + 1 n - 1 +--R n x x - n x x +--R / +--R n +--R (m + 1)x +--R Type: Expression Integer +--E 25 + +--S 26 of 500 +t0005:= x^3*log(c*(a*x^n)^p) +--R +--R +--R 3 n p +--R (26) x log(c (a x ) ) +--R Type: Expression Integer +--E 26 + +--S 27 of 500 +r0005:= 1/16*x^4*(-n*p+4*log(c*(a*x^n)^p)) +--R +--R +--R 4 n p 4 +--R 4x log(c (a x ) ) - n p x +--R (27) -------------------------- +--R 16 +--R Type: Expression Integer +--E 27 + +--S 28 of 500 +a0005:= integrate(t0005,x) +--R +--R +--R 4 4 4 4 +--R 4n p x log(x) + 4x log(c) + 4p x log(a) - n p x +--R (28) ------------------------------------------------ +--R 16 +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 500 +m0005:= a0005-r0005 +--R +--R +--R 4 n p 4 4 4 +--R - x log(c (a x ) ) + n p x log(x) + x log(c) + p x log(a) +--R (29) --------------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 29 + +--S 30 of 500 +d0005:= D(m0005,x) +--R +--R +--R (30) +--R 3 n p n p +--R - 4x (a x ) log(c (a x ) ) +--R + +--R 3 3 3 3 n p +--R (4n p x log(x) + 4x log(c) + 4p x log(a) + n p x )(a x ) +--R + +--R 4 n - 1 n p - 1 +--R - a n p x x (a x ) +--R / +--R n p +--R 4(a x ) +--R Type: Expression Integer +--E 30 + +--S 31 of 500 +t0006:= x^m*log(c*(a*x^n)^p) +--R +--R +--R m n p +--R (31) x log(c (a x ) ) +--R Type: Expression Integer +--E 31 + +--S 32 of 500 +r0006:= -n*p*x^(1+m)/(1+m)^2+x^(1+m)*log(c*(a*x^n)^p)/(1+m) +--R +--R +--R m + 1 n p m + 1 +--R (m + 1)x log(c (a x ) ) - n p x +--R (32) ---------------------------------------- +--R 2 +--R m + 2m + 1 +--R Type: Expression Integer +--E 32 + +--S 33 of 500 +a0006:= integrate(t0006,x) +--R +--R +--R (33) +--R m log(x) +--R ((m + 1)n p x log(x) + (m + 1)x log(c) + (m + 1)p x log(a) - n p x)%e +--R ----------------------------------------------------------------------------- +--R 2 +--R m + 2m + 1 +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 500 +m0006:= a0006-r0006 +--R +--R +--R (34) +--R m + 1 n p +--R (- m - 1)x log(c (a x ) ) +--R + +--R ((m + 1)n p x log(x) + (m + 1)x log(c) + (m + 1)p x log(a) - n p x) +--R * +--R m log(x) +--R %e +--R + +--R m + 1 +--R n p x +--R / +--R 2 +--R m + 2m + 1 +--R Type: Expression Integer +--E 34 + +--S 35 of 500 +d0006:= D(m0006,x) +--R +--R +--R (35) +--R m n p n p +--R (- m - 1)x (a x ) log(c (a x ) ) +--R + +--R m log(x) +--R ((m + 1)n p log(x) + (m + 1)log(c) + (m + 1)p log(a))%e +--R + +--R m +--R n p x +--R * +--R n p +--R (a x ) +--R + +--R m + 1 n - 1 n p - 1 +--R - a n p x x (a x ) +--R / +--R n p +--R (m + 1)(a x ) +--R Type: Expression Integer +--E 35 + +--S 36 of 500 +t0007:= x*log(a*x^n)^2 +--R +--R +--R n 2 +--R (36) x log(a x ) +--R Type: Expression Integer +--E 36 + +--S 37 of 500 +r0007:= 1/4*x^2*(n^2-2*n*log(a*x^n)+2*log(a*x^n)^2) +--R +--R +--R 2 n 2 2 n 2 2 +--R 2x log(a x ) - 2n x log(a x ) + n x +--R (37) ------------------------------------- +--R 4 +--R Type: Expression Integer +--E 37 + +--S 38 of 500 +a0007:= integrate(t0007,x) +--R +--R +--R (38) +--R 2 2 2 2 2 2 2 2 2 2 2 +--R 2n x log(x) + (4n x log(a) - 2n x )log(x) + 2x log(a) - 2n x log(a) + n x +--R ---------------------------------------------------------------------------- +--R 4 +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 500 +m0007:= a0007-r0007 +--R +--R +--R (39) +--R 2 n 2 2 n 2 2 2 2 2 2 +--R - x log(a x ) + n x log(a x ) + n x log(x) + (2n x log(a) - n x )log(x) +--R + +--R 2 2 2 +--R x log(a) - n x log(a) +--R / +--R 2 +--R Type: Expression Integer +--E 39 + +--S 40 of 500 +d0007:= D(m0007,x) +--R +--R +--R (40) +--R n n 2 n 2 n - 1 n +--R - 2x x log(a x ) + (2n x x - 2n x x )log(a x ) +--R + +--R 2 2 2 2 n 2 2 n - 1 +--R (2n x log(x) + 4n x log(a)log(x) + 2x log(a) - n x)x + n x x +--R / +--R n +--R 2x +--R Type: Expression Integer +--E 40 + +--S 41 of 500 +t0008:= x^2*log(a*x^n)^2 +--R +--R +--R 2 n 2 +--R (41) x log(a x ) +--R Type: Expression Integer +--E 41 + +--S 42 of 500 +r0008:= 1/27*x^3*(2*n^2-6*n*log(a*x^n)+9*log(a*x^n)^2) +--R +--R +--R 3 n 2 3 n 2 3 +--R 9x log(a x ) - 6n x log(a x ) + 2n x +--R (42) -------------------------------------- +--R 27 +--R Type: Expression Integer +--E 42 + +--S 43 of 500 +a0008:= integrate(t0008,x) +--R +--R +--R (43) +--R 2 3 2 3 2 3 3 2 3 +--R 9n x log(x) + (18n x log(a) - 6n x )log(x) + 9x log(a) - 6n x log(a) +--R + +--R 2 3 +--R 2n x +--R / +--R 27 +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 500 +m0008:= a0008-r0008 +--R +--R +--R (44) +--R 3 n 2 3 n 2 3 2 +--R - 3x log(a x ) + 2n x log(a x ) + 3n x log(x) +--R + +--R 3 2 3 3 2 3 +--R (6n x log(a) - 2n x )log(x) + 3x log(a) - 2n x log(a) +--R / +--R 9 +--R Type: Expression Integer +--E 44 + +--S 45 of 500 +d0008:= D(m0008,x) +--R +--R +--R (45) +--R 2 n n 2 2 n 3 n - 1 n +--R - 9x x log(a x ) + (6n x x - 6n x x )log(a x ) +--R + +--R 2 2 2 2 2 2 2 2 n 2 3 n - 1 +--R (9n x log(x) + 18n x log(a)log(x) + 9x log(a) - 2n x )x + 2n x x +--R / +--R n +--R 9x +--R Type: Expression Integer +--E 45 + +--S 46 of 500 +t0009:= x^3*log(a*x^n)^2 +--R +--R +--R 3 n 2 +--R (46) x log(a x ) +--R Type: Expression Integer +--E 46 + +--S 47 of 500 +r0009:= 1/32*x^4*(n^2-4*n*log(a*x^n)+8*log(a*x^n)^2) +--R +--R +--R 4 n 2 4 n 2 4 +--R 8x log(a x ) - 4n x log(a x ) + n x +--R (47) ------------------------------------- +--R 32 +--R Type: Expression Integer +--E 47 + +--S 48 of 500 +a0009:= integrate(t0009,x) +--R +--R +--R (48) +--R 2 4 2 4 2 4 4 2 4 2 4 +--R 8n x log(x) + (16n x log(a) - 4n x )log(x) + 8x log(a) - 4n x log(a) + n x +--R ----------------------------------------------------------------------------- +--R 32 +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 500 +m0009:= a0009-r0009 +--R +--R +--R (49) +--R 4 n 2 4 n 2 4 2 +--R - 2x log(a x ) + n x log(a x ) + 2n x log(x) +--R + +--R 4 2 4 4 2 4 +--R (4n x log(a) - n x )log(x) + 2x log(a) - n x log(a) +--R / +--R 8 +--R Type: Expression Integer +--E 49 + +--S 50 of 500 +d0009:= D(m0009,x) +--R +--R +--R (50) +--R 3 n n 2 3 n 4 n - 1 n +--R - 8x x log(a x ) + (4n x x - 4n x x )log(a x ) +--R + +--R 2 3 2 3 3 2 2 3 n 2 4 n - 1 +--R (8n x log(x) + 16n x log(a)log(x) + 8x log(a) - n x )x + n x x +--R / +--R n +--R 8x +--R Type: Expression Integer +--E 50 + +--S 51 of 500 +t0000:= log(a*x^n)^2/x^2 +--R +--R +--R n 2 +--R log(a x ) +--R (51) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 51 + +--S 52 of 500 +r0000:= -1/x*(2*n^2+2*n*log(a*x^n)+log(a*x^n)^2) +--R +--R +--R n 2 n 2 +--R - log(a x ) - 2n log(a x ) - 2n +--R (52) --------------------------------- +--R x +--R Type: Expression Integer +--E 52 + +--S 53 of 500 +a0000:= integrate(t0000,x) +--R +--R +--R 2 2 2 2 2 +--R - n log(x) + (- 2n log(a) - 2n )log(x) - log(a) - 2n log(a) - 2n +--R (53) ------------------------------------------------------------------- +--R x +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 500 +m0000:= a0000-r0000 +--R +--R +--R (54) +--R n 2 n 2 2 2 +--R log(a x ) + 2n log(a x ) - n log(x) + (- 2n log(a) - 2n )log(x) +--R + +--R 2 +--R - log(a) - 2n log(a) +--R / +--R x +--R Type: Expression Integer +--E 54 + +--S 55 of 500 +d0000:= D(m0000,x) +--R +--R +--R (55) +--R n n 2 n n - 1 n +--R - x log(a x ) + (- 2n x + 2n x x )log(a x ) +--R + +--R 2 2 2 2 n 2 n - 1 +--R (n log(x) + 2n log(a)log(x) + log(a) - 2n )x + 2n x x +--R / +--R 2 n +--R x x +--R Type: Expression Integer +--E 55 + +--S 56 of 500 +t0011:= log(a*x^n)^2/x^3 +--R +--R +--R n 2 +--R log(a x ) +--R (56) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 56 + +--S 57 of 500 +r0011:= -1/4/x^2*(n^2+2*n*log(a*x^n)+2*log(a*x^n)^2) +--R +--R +--R n 2 n 2 +--R - 2log(a x ) - 2n log(a x ) - n +--R (57) --------------------------------- +--R 2 +--R 4x +--R Type: Expression Integer +--E 57 + +--S 58 of 500 +a0011:= integrate(t0011,x) +--R +--R +--R 2 2 2 2 2 +--R - 2n log(x) + (- 4n log(a) - 2n )log(x) - 2log(a) - 2n log(a) - n +--R (58) -------------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 500 +m0011:= a0011-r0011 +--R +--R +--R (59) +--R n 2 n 2 2 2 2 +--R log(a x ) + n log(a x ) - n log(x) + (- 2n log(a) - n )log(x) - log(a) +--R + +--R - n log(a) +--R / +--R 2 +--R 2x +--R Type: Expression Integer +--E 59 + +--S 60 of 500 +d0011:= D(m0011,x) +--R +--R +--R (60) +--R n n 2 n n - 1 n +--R - 2x log(a x ) + (- 2n x + 2n x x )log(a x ) +--R + +--R 2 2 2 2 n 2 n - 1 +--R (2n log(x) + 4n log(a)log(x) + 2log(a) - n )x + n x x +--R / +--R 3 n +--R 2x x +--R Type: Expression Integer +--E 60 + +--S 61 of 500 +t0012:= x^m*log(a*x^n)^2 +--R +--R +--R m n 2 +--R (61) x log(a x ) +--R Type: Expression Integer +--E 61 + +--S 62 of 500 +r0012:= 2*n^2*x^(1+m)/(1+m)^3-2*n*x^(1+m)*log(a*x^n)/(1+m)^2+x^(1+m)*log(a*x^n)^2/(1+m) +--R +--R +--R (62) +--R 2 m + 1 n 2 m + 1 n 2 m + 1 +--R (m + 2m + 1)x log(a x ) + (- 2m - 2)n x log(a x ) + 2n x +--R ----------------------------------------------------------------------- +--R 3 2 +--R m + 3m + 3m + 1 +--R Type: Expression Integer +--E 62 + +--S 63 of 500 +a0012:= integrate(t0012,x) +--R +--R +--R (63) +--R 2 2 2 +--R (m + 2m + 1)n x log(x) +--R + +--R 2 2 +--R ((2m + 4m + 2)n x log(a) + (- 2m - 2)n x)log(x) +--R + +--R 2 2 2 +--R (m + 2m + 1)x log(a) + (- 2m - 2)n x log(a) + 2n x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 3m + 3m + 1 +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 500 +m0012:= a0012-r0012 +--R +--R +--R (64) +--R 2 m + 1 n 2 m + 1 n +--R (- m - 2m - 1)x log(a x ) + (2m + 2)n x log(a x ) +--R + +--R 2 2 2 +--R (m + 2m + 1)n x log(x) +--R + +--R 2 2 +--R ((2m + 4m + 2)n x log(a) + (- 2m - 2)n x)log(x) +--R + +--R 2 2 2 +--R (m + 2m + 1)x log(a) + (- 2m - 2)n x log(a) + 2n x +--R * +--R m log(x) +--R %e +--R + +--R 2 m + 1 +--R - 2n x +--R / +--R 3 2 +--R m + 3m + 3m + 1 +--R Type: Expression Integer +--E 64 + +--S 65 of 500 +d0012:= D(m0012,x) +--R +--R +--R (65) +--R 2 m n n 2 +--R (- m - 2m - 1)x x log(a x ) +--R + +--R m n m + 1 n - 1 n +--R ((2m + 2)n x x + (- 2m - 2)n x x )log(a x ) +--R + +--R 2 2 2 2 +--R (m + 2m + 1)n log(x) + (2m + 4m + 2)n log(a)log(x) +--R + +--R 2 2 +--R (m + 2m + 1)log(a) +--R * +--R n m log(x) +--R x %e +--R + +--R 2 m n 2 m + 1 n - 1 +--R - 2n x x + 2n x x +--R / +--R 2 n +--R (m + 2m + 1)x +--R Type: Expression Integer +--E 65 + +--S 66 of 500 +t0013:= x^m*log(a*x)^3 +--R +--R +--R 3 m +--R (66) log(a x) x +--R Type: Expression Integer +--E 66 + +--S 67 of 500 +r0013:= -6*x^(1+m)/(1+m)^4+6*x^(1+m)*log(a*x)/(1+m)^3-3*x^(1+m)*log(a*x)^2/(1+m)^2+x^(1+m)*log(a*x)^3/(1+m) +--R +--R +--R (67) +--R 3 2 3 2 2 +--R (m + 3m + 3m + 1)log(a x) + (- 3m - 6m - 3)log(a x) +--R + +--R (6m + 6)log(a x) - 6 +--R * +--R m + 1 +--R x +--R / +--R 4 3 2 +--R m + 4m + 6m + 4m + 1 +--R Type: Expression Integer +--E 67 + +--S 68 of 500 +a0013:= integrate(t0013,x) +--R +--R +--R (68) +--R 3 2 3 +--R (m + 3m + 3m + 1)x log(x) +--R + +--R 3 2 2 2 +--R ((3m + 9m + 9m + 3)x log(a) + (- 3m - 6m - 3)x)log(x) +--R + +--R 3 2 2 2 +--R (3m + 9m + 9m + 3)x log(a) + (- 6m - 12m - 6)x log(a) +--R + +--R (6m + 6)x +--R * +--R log(x) +--R + +--R 3 2 3 2 2 +--R (m + 3m + 3m + 1)x log(a) + (- 3m - 6m - 3)x log(a) +--R + +--R (6m + 6)x log(a) - 6x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 4m + 6m + 4m + 1 +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 of 500 +m0013:= a0013-r0013 +--R +--R +--R (69) +--R 3 2 3 +--R (m + 3m + 3m + 1)x log(x) +--R + +--R 3 2 2 2 +--R ((3m + 9m + 9m + 3)x log(a) + (- 3m - 6m - 3)x)log(x) +--R + +--R 3 2 2 2 +--R (3m + 9m + 9m + 3)x log(a) + (- 6m - 12m - 6)x log(a) +--R + +--R (6m + 6)x +--R * +--R log(x) +--R + +--R 3 2 3 2 2 +--R (m + 3m + 3m + 1)x log(a) + (- 3m - 6m - 3)x log(a) +--R + +--R (6m + 6)x log(a) - 6x +--R * +--R m log(x) +--R %e +--R + +--R 3 2 3 2 2 +--R (- m - 3m - 3m - 1)log(a x) + (3m + 6m + 3)log(a x) +--R + +--R (- 6m - 6)log(a x) + 6 +--R * +--R m + 1 +--R x +--R / +--R 4 3 2 +--R m + 4m + 6m + 4m + 1 +--R Type: Expression Integer +--E 69 + +--S 70 of 500 +d0013:= D(m0013,x) +--R +--R +--R (70) +--R 3 2 3 3 2 2 +--R (m + 3m + 3m + 1)x log(x) + (3m + 9m + 9m + 3)x log(a)log(x) +--R + +--R 3 2 2 3 2 3 +--R (3m + 9m + 9m + 3)x log(a) log(x) + (m + 3m + 3m + 1)x log(a) +--R * +--R m log(x) +--R %e +--R + +--R 2 2 m + 1 +--R ((- 3m - 6m - 3)log(a x) + (6m + 6)log(a x) - 6)x +--R + +--R 3 2 3 2 2 +--R (- m - 3m - 3m - 1)x log(a x) + (3m + 6m + 3)x log(a x) +--R + +--R (- 6m - 6)x log(a x) + 6x +--R * +--R m +--R x +--R / +--R 3 2 +--R (m + 3m + 3m + 1)x +--R Type: Expression Integer +--E 70 + +--S 71 of 500 +t0014:= log(a*x^n)^3 +--R +--R +--R n 3 +--R (71) log(a x ) +--R Type: Expression Integer +--E 71 + +--S 72 of 500 +r0014:= x*(-6*n^3+6*n^2*log(a*x^n)-3*n*log(a*x^n)^2+log(a*x^n)^3) +--R +--R +--R n 3 n 2 2 n 3 +--R (72) x log(a x ) - 3n x log(a x ) + 6n x log(a x ) - 6n x +--R Type: Expression Integer +--E 72 + +--S 73 of 500 +a0014:= integrate(t0014,x) +--R +--R +--R (73) +--R 3 3 2 3 2 +--R n x log(x) + (3n x log(a) - 3n x)log(x) +--R + +--R 2 2 3 3 2 +--R (3n x log(a) - 6n x log(a) + 6n x)log(x) + x log(a) - 3n x log(a) +--R + +--R 2 3 +--R 6n x log(a) - 6n x +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 500 +m0014:= a0014-r0014 +--R +--R +--R (74) +--R n 3 n 2 2 n 3 3 +--R - x log(a x ) + 3n x log(a x ) - 6n x log(a x ) + n x log(x) +--R + +--R 2 3 2 2 2 3 +--R (3n x log(a) - 3n x)log(x) + (3n x log(a) - 6n x log(a) + 6n x)log(x) +--R + +--R 3 2 2 +--R x log(a) - 3n x log(a) + 6n x log(a) +--R Type: Expression Integer +--E 74 + +--S 75 of 500 +d0014:= D(m0014,x) +--R +--R +--R (75) +--R n n 3 n n - 1 n 2 +--R - x log(a x ) + (3n x - 3n x x )log(a x ) +--R + +--R 2 n 2 n - 1 n +--R (- 6n x + 6n x x )log(a x ) +--R + +--R 3 3 2 2 2 3 3 n +--R (n log(x) + 3n log(a)log(x) + 3n log(a) log(x) + log(a) + 6n )x +--R + +--R 3 n - 1 +--R - 6n x x +--R / +--R n +--R x +--R Type: Expression Integer +--E 75 + +--S 76 of 500 +t0015:= x*log(a*x^n)^3 +--R +--R +--R n 3 +--R (76) x log(a x ) +--R Type: Expression Integer +--E 76 + +--S 77 of 500 +r0015:= 1/8*x^2*(-3*n^3+6*n^2*log(a*x^n)-6*n*log(a*x^n)^2+4*log(a*x^n)^3) +--R +--R +--R 2 n 3 2 n 2 2 2 n 3 2 +--R 4x log(a x ) - 6n x log(a x ) + 6n x log(a x ) - 3n x +--R (77) -------------------------------------------------------- +--R 8 +--R Type: Expression Integer +--E 77 + +--S 78 of 500 +a0015:= integrate(t0015,x) +--R +--R +--R (78) +--R 3 2 3 2 2 3 2 2 +--R 4n x log(x) + (12n x log(a) - 6n x )log(x) +--R + +--R 2 2 2 2 3 2 2 3 2 2 +--R (12n x log(a) - 12n x log(a) + 6n x )log(x) + 4x log(a) - 6n x log(a) +--R + +--R 2 2 3 2 +--R 6n x log(a) - 3n x +--R / +--R 8 +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 500 +m0015:= a0015-r0015 +--R +--R +--R (79) +--R 2 n 3 2 n 2 2 2 n 3 2 3 +--R - 2x log(a x ) + 3n x log(a x ) - 3n x log(a x ) + 2n x log(x) +--R + +--R 2 2 3 2 2 2 2 2 2 3 2 +--R (6n x log(a) - 3n x )log(x) + (6n x log(a) - 6n x log(a) + 3n x )log(x) +--R + +--R 2 3 2 2 2 2 +--R 2x log(a) - 3n x log(a) + 3n x log(a) +--R / +--R 4 +--R Type: Expression Integer +--E 79 + +--S 80 of 500 +d0015:= D(m0015,x) +--R +--R +--R (80) +--R n n 3 n 2 n - 1 n 2 +--R - 4x x log(a x ) + (6n x x - 6n x x )log(a x ) +--R + +--R 2 n 2 2 n - 1 n +--R (- 6n x x + 6n x x )log(a x ) +--R + +--R 3 3 2 2 2 3 +--R 4n x log(x) + 12n x log(a)log(x) + 12n x log(a) log(x) + 4x log(a) +--R + +--R 3 +--R 3n x +--R * +--R n +--R x +--R + +--R 3 2 n - 1 +--R - 3n x x +--R / +--R n +--R 4x +--R Type: Expression Integer +--E 80 + +--S 81 of 500 +t0016:= x^2*log(a*x^n)^3 +--R +--R +--R 2 n 3 +--R (81) x log(a x ) +--R Type: Expression Integer +--E 81 + +--S 82 of 500 +r0016:= 1/27*x^3*(-2*n^3+6*n^2*log(a*x^n)-9*n*log(a*x^n)^2+9*log(a*x^n)^3) +--R +--R +--R 3 n 3 3 n 2 2 3 n 3 3 +--R 9x log(a x ) - 9n x log(a x ) + 6n x log(a x ) - 2n x +--R (82) -------------------------------------------------------- +--R 27 +--R Type: Expression Integer +--E 82 + +--S 83 of 500 +a0016:= integrate(t0016,x) +--R +--R +--R (83) +--R 3 3 3 2 3 3 3 2 +--R 9n x log(x) + (27n x log(a) - 9n x )log(x) +--R + +--R 3 2 2 3 3 3 3 3 3 2 +--R (27n x log(a) - 18n x log(a) + 6n x )log(x) + 9x log(a) - 9n x log(a) +--R + +--R 2 3 3 3 +--R 6n x log(a) - 2n x +--R / +--R 27 +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 500 +m0016:= a0016-r0016 +--R +--R +--R (84) +--R 3 n 3 3 n 2 2 3 n 3 3 3 +--R - 3x log(a x ) + 3n x log(a x ) - 2n x log(a x ) + 3n x log(x) +--R + +--R 2 3 3 3 2 3 2 2 3 3 3 +--R (9n x log(a) - 3n x )log(x) + (9n x log(a) - 6n x log(a) + 2n x )log(x) +--R + +--R 3 3 3 2 2 3 +--R 3x log(a) - 3n x log(a) + 2n x log(a) +--R / +--R 9 +--R Type: Expression Integer +--E 84 + +--S 85 of 500 +d0016:= D(m0016,x) +--R +--R +--R (85) +--R 2 n n 3 2 n 3 n - 1 n 2 +--R - 9x x log(a x ) + (9n x x - 9n x x )log(a x ) +--R + +--R 2 2 n 2 3 n - 1 n +--R (- 6n x x + 6n x x )log(a x ) +--R + +--R 3 2 3 2 2 2 2 2 2 3 +--R 9n x log(x) + 27n x log(a)log(x) + 27n x log(a) log(x) + 9x log(a) +--R + +--R 3 2 +--R 2n x +--R * +--R n +--R x +--R + +--R 3 3 n - 1 +--R - 2n x x +--R / +--R n +--R 9x +--R Type: Expression Integer +--E 85 + +--S 86 of 500 +t0017:= x^3*log(a*x^n)^3 +--R +--R +--R 3 n 3 +--R (86) x log(a x ) +--R Type: Expression Integer +--E 86 + +--S 87 of 500 +r0017:= 1/128*x^4*(-3*n^3+12*n^2*log(a*x^n)-24*n*log(a*x^n)^2+32*log(a*x^n)^3) +--R +--R +--R 4 n 3 4 n 2 2 4 n 3 4 +--R 32x log(a x ) - 24n x log(a x ) + 12n x log(a x ) - 3n x +--R (87) ----------------------------------------------------------- +--R 128 +--R Type: Expression Integer +--E 87 + +--S 88 of 500 +a0017:= integrate(t0017,x) +--R +--R +--R (88) +--R 3 4 3 2 4 3 4 2 +--R 32n x log(x) + (96n x log(a) - 24n x )log(x) +--R + +--R 4 2 2 4 3 4 4 3 +--R (96n x log(a) - 48n x log(a) + 12n x )log(x) + 32x log(a) +--R + +--R 4 2 2 4 3 4 +--R - 24n x log(a) + 12n x log(a) - 3n x +--R / +--R 128 +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 of 500 +m0017:= a0017-r0017 +--R +--R +--R (89) +--R 4 n 3 4 n 2 2 4 n 3 4 3 +--R - 8x log(a x ) + 6n x log(a x ) - 3n x log(a x ) + 8n x log(x) +--R + +--R 2 4 3 4 2 +--R (24n x log(a) - 6n x )log(x) +--R + +--R 4 2 2 4 3 4 4 3 4 2 +--R (24n x log(a) - 12n x log(a) + 3n x )log(x) + 8x log(a) - 6n x log(a) +--R + +--R 2 4 +--R 3n x log(a) +--R / +--R 32 +--R Type: Expression Integer +--E 89 + +--S 90 of 500 +d0017:= D(m0017,x) +--R +--R +--R (90) +--R 3 n n 3 3 n 4 n - 1 n 2 +--R - 32x x log(a x ) + (24n x x - 24n x x )log(a x ) +--R + +--R 2 3 n 2 4 n - 1 n +--R (- 12n x x + 12n x x )log(a x ) +--R + +--R 3 3 3 2 3 2 3 2 +--R 32n x log(x) + 96n x log(a)log(x) + 96n x log(a) log(x) +--R + +--R 3 3 3 3 +--R 32x log(a) + 3n x +--R * +--R n +--R x +--R + +--R 3 4 n - 1 +--R - 3n x x +--R / +--R n +--R 32x +--R Type: Expression Integer +--E 90 + +--S 91 of 500 +t0018:= log(a*x^n)^3/x^2 +--R +--R +--R n 3 +--R log(a x ) +--R (91) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 91 + +--S 92 of 500 +r0018:= -1/x*(6*n^3+6*n^2*log(a*x^n)+3*n*log(a*x^n)^2+log(a*x^n)^3) +--R +--R +--R n 3 n 2 2 n 3 +--R - log(a x ) - 3n log(a x ) - 6n log(a x ) - 6n +--R (92) ------------------------------------------------- +--R x +--R Type: Expression Integer +--E 92 + +--S 93 of 500 +a0018:= integrate(t0018,x) +--R +--R +--R (93) +--R 3 3 2 3 2 +--R - n log(x) + (- 3n log(a) - 3n )log(x) +--R + +--R 2 2 3 3 2 2 +--R (- 3n log(a) - 6n log(a) - 6n )log(x) - log(a) - 3n log(a) - 6n log(a) +--R + +--R 3 +--R - 6n +--R / +--R x +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 500 +m0018:= a0018-r0018 +--R +--R +--R (94) +--R n 3 n 2 2 n 3 3 +--R log(a x ) + 3n log(a x ) + 6n log(a x ) - n log(x) +--R + +--R 2 3 2 2 2 3 +--R (- 3n log(a) - 3n )log(x) + (- 3n log(a) - 6n log(a) - 6n )log(x) +--R + +--R 3 2 2 +--R - log(a) - 3n log(a) - 6n log(a) +--R / +--R x +--R Type: Expression Integer +--E 94 + +--S 95 of 500 +d0018:= D(m0018,x) +--R +--R +--R (95) +--R n n 3 n n - 1 n 2 +--R - x log(a x ) + (- 3n x + 3n x x )log(a x ) +--R + +--R 2 n 2 n - 1 n +--R (- 6n x + 6n x x )log(a x ) +--R + +--R 3 3 2 2 2 3 3 n +--R (n log(x) + 3n log(a)log(x) + 3n log(a) log(x) + log(a) - 6n )x +--R + +--R 3 n - 1 +--R 6n x x +--R / +--R 2 n +--R x x +--R Type: Expression Integer +--E 95 + +--S 96 of 500 +t0019:= log(a*x^n)^3/x^3 +--R +--R +--R n 3 +--R log(a x ) +--R (96) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 96 + +--S 97 of 500 +r0019:= -1/8/x^2*(3*n^3+6*n^2*log(a*x^n)+6*n*log(a*x^n)^2+4*log(a*x^n)^3) +--R +--R +--R n 3 n 2 2 n 3 +--R - 4log(a x ) - 6n log(a x ) - 6n log(a x ) - 3n +--R (97) -------------------------------------------------- +--R 2 +--R 8x +--R Type: Expression Integer +--E 97 + +--S 98 of 500 +a0019:= integrate(t0019,x) +--R +--R +--R (98) +--R 3 3 2 3 2 +--R - 4n log(x) + (- 12n log(a) - 6n )log(x) +--R + +--R 2 2 3 3 2 +--R (- 12n log(a) - 12n log(a) - 6n )log(x) - 4log(a) - 6n log(a) +--R + +--R 2 3 +--R - 6n log(a) - 3n +--R / +--R 2 +--R 8x +--R Type: Union(Expression Integer,...) +--E 98 + +--S 99 of 500 +m0019:= a0019-r0019 +--R +--R +--R (99) +--R n 3 n 2 2 n 3 3 +--R 2log(a x ) + 3n log(a x ) + 3n log(a x ) - 2n log(x) +--R + +--R 2 3 2 2 2 3 +--R (- 6n log(a) - 3n )log(x) + (- 6n log(a) - 6n log(a) - 3n )log(x) +--R + +--R 3 2 2 +--R - 2log(a) - 3n log(a) - 3n log(a) +--R / +--R 2 +--R 4x +--R Type: Expression Integer +--E 99 + +--S 100 of 500 +d0019:= D(m0019,x) +--R +--R +--R (100) +--R n n 3 n n - 1 n 2 +--R - 4x log(a x ) + (- 6n x + 6n x x )log(a x ) +--R + +--R 2 n 2 n - 1 n +--R (- 6n x + 6n x x )log(a x ) +--R + +--R 3 3 2 2 2 3 3 n +--R (4n log(x) + 12n log(a)log(x) + 12n log(a) log(x) + 4log(a) - 3n )x +--R + +--R 3 n - 1 +--R 3n x x +--R / +--R 3 n +--R 4x x +--R Type: Expression Integer +--E 100 + +--S 101 of 500 +t0020:= x^m*log(a*x^n)^3 +--R +--R +--R m n 3 +--R (101) x log(a x ) +--R Type: Expression Integer +--E 101 + +--S 102 of 500 +r0020:= -6*n^3*x^(1+m)/(1+m)^4+6*n^2*x^(1+m)*log(a*x^n)/(1+m)^3-3*n*x^(1+m)*log(a*x^n)^2/(1+m)^2+x^(1+m)*log(a*x^n)^3/(1+m) +--R +--R +--R (102) +--R 3 2 m + 1 n 3 2 m + 1 n 2 +--R (m + 3m + 3m + 1)x log(a x ) + (- 3m - 6m - 3)n x log(a x ) +--R + +--R 2 m + 1 n 3 m + 1 +--R (6m + 6)n x log(a x ) - 6n x +--R / +--R 4 3 2 +--R m + 4m + 6m + 4m + 1 +--R Type: Expression Integer +--E 102 + +--S 103 of 500 +a0020:= integrate(t0020,x) +--R +--R +--R (103) +--R 3 2 3 3 +--R (m + 3m + 3m + 1)n x log(x) +--R + +--R 3 2 2 2 3 2 +--R ((3m + 9m + 9m + 3)n x log(a) + (- 3m - 6m - 3)n x)log(x) +--R + +--R 3 2 2 2 2 +--R (3m + 9m + 9m + 3)n x log(a) + (- 6m - 12m - 6)n x log(a) +--R + +--R 3 +--R (6m + 6)n x +--R * +--R log(x) +--R + +--R 3 2 3 2 2 +--R (m + 3m + 3m + 1)x log(a) + (- 3m - 6m - 3)n x log(a) +--R + +--R 2 3 +--R (6m + 6)n x log(a) - 6n x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 4m + 6m + 4m + 1 +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 of 500 +m0020:= a0020-r0020 +--R +--R +--R (104) +--R 3 2 m + 1 n 3 2 m + 1 n 2 +--R (- m - 3m - 3m - 1)x log(a x ) + (3m + 6m + 3)n x log(a x ) +--R + +--R 2 m + 1 n +--R (- 6m - 6)n x log(a x ) +--R + +--R 3 2 3 3 +--R (m + 3m + 3m + 1)n x log(x) +--R + +--R 3 2 2 2 3 2 +--R ((3m + 9m + 9m + 3)n x log(a) + (- 3m - 6m - 3)n x)log(x) +--R + +--R 3 2 2 2 2 +--R (3m + 9m + 9m + 3)n x log(a) + (- 6m - 12m - 6)n x log(a) +--R + +--R 3 +--R (6m + 6)n x +--R * +--R log(x) +--R + +--R 3 2 3 2 2 +--R (m + 3m + 3m + 1)x log(a) + (- 3m - 6m - 3)n x log(a) +--R + +--R 2 3 +--R (6m + 6)n x log(a) - 6n x +--R * +--R m log(x) +--R %e +--R + +--R 3 m + 1 +--R 6n x +--R / +--R 4 3 2 +--R m + 4m + 6m + 4m + 1 +--R Type: Expression Integer +--E 104 + +--S 105 of 500 +d0020:= D(m0020,x) +--R +--R +--R (105) +--R 3 2 m n n 3 +--R (- m - 3m - 3m - 1)x x log(a x ) +--R + +--R 2 m n 2 m + 1 n - 1 n 2 +--R ((3m + 6m + 3)n x x + (- 3m - 6m - 3)n x x )log(a x ) +--R + +--R 2 m n 2 m + 1 n - 1 n +--R ((- 6m - 6)n x x + (6m + 6)n x x )log(a x ) +--R + +--R 3 2 3 3 3 2 2 2 +--R (m + 3m + 3m + 1)n log(x) + (3m + 9m + 9m + 3)n log(a)log(x) +--R + +--R 3 2 2 3 2 3 +--R (3m + 9m + 9m + 3)n log(a) log(x) + (m + 3m + 3m + 1)log(a) +--R * +--R n m log(x) +--R x %e +--R + +--R 3 m n 3 m + 1 n - 1 +--R 6n x x - 6n x x +--R / +--R 3 2 n +--R (m + 3m + 3m + 1)x +--R Type: Expression Integer +--E 105 + +--S 106 of 500 +t0021:= 1/log(a*x) +--R +--R +--R 1 +--R (106) -------- +--R log(a x) +--R Type: Expression Integer +--E 106 + +--S 107 of 500 +r0021:= li(a*x)/a +--R +--R +--R li(a x) +--R (107) ------- +--R a +--R Type: Expression Integer +--E 107 + +--S 108 of 500 +a0021:= integrate(t0021,x) +--R +--R +--R li(a x) +--R (108) ------- +--R a +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 of 500 +m0021:= a0021-r0021 +--R +--R +--R (109) 0 +--R Type: Expression Integer +--E 109 + +--S 110 of 500 +d0021:= D(m0021,x) +--R +--R +--R (110) 0 +--R Type: Expression Integer +--E 110 + +--S 111 of 500 +t0022:= x^m/log(a*x) +--R +--R +--R m +--R x +--R (111) -------- +--R log(a x) +--R Type: Expression Integer +--E 111 + +--S 112 of 500 +r0022:= x^m/a*(a*x)^(-m)*Ei((1+m)*log(a*x)) +--R +--R +--R m - m +--R x (a x) Ei((m + 1)log(a x)) +--R (112) ----------------------------- +--R a +--R Type: Expression Integer +--E 112 + +--S 113 of 500 +a0022:= integrate(t0022,x) +--R +--R +--R x m +--R ++ %D +--R (113) | --------- d%D +--R ++ log(%D a) +--R Type: Union(Expression Integer,...) +--E 113 + +--S 114 of 500 +--m0022:= a0022-r0022 +--E 114 + +--S 115 of 500 +--d0022:= D(m0022,x) +--E 115 + +--S 116 of 500 +t0023:= 1/log(a*x^n) +--R +--R +--R 1 +--R (114) --------- +--R n +--R log(a x ) +--R Type: Expression Integer +--E 116 + +--S 117 of 500 +r0023:= x*Ei(log(a*x^n)/n)/n/((a*x^n)^(1/n)) +--R +--R +--R n +--R log(a x ) +--R x Ei(---------) +--R n +--R (115) --------------- +--R 1 +--R - +--R n n +--R n (a x ) +--R Type: Expression Integer +--E 117 + +--S 118 of 500 +a0023:= integrate(t0023,x) +--R +--R +--R x +--R ++ 1 +--R (116) | ---------- d%D +--R ++ n +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 118 + +--S 119 of 500 +--m0023:= a0023-r0023 +--E 119 + +--S 120 of 500 +--d0023:= D(m0023,x) +--E 120 + +--S 121 of 500 +t0024:= x/log(a*x^n) +--R +--R +--R x +--R (117) --------- +--R n +--R log(a x ) +--R Type: Expression Integer +--E 121 + +--S 122 of 500 +r0024:= x^2*Ei(2*log(a*x^n)/n)/n*(a*x^n)^(-2/n) +--R +--R +--R 2 +--R - - n +--R 2 n n 2log(a x ) +--R x (a x ) Ei(----------) +--R n +--R (118) ------------------------- +--R n +--R Type: Expression Integer +--E 122 + +--S 123 of 500 +--a0024:= integrate(t0024,x) +--E 123 + +--S 124 of 500 +--m0024:= a0024-r0024 +--E 124 + +--S 125 of 500 +d0024:= D(m0024,x) +--R +--R +--R (119) 0 +--R Type: Polynomial Integer +--E 125 + +--S 126 of 500 +t0025:= x^2/log(a*x^n) +--R +--R +--R 2 +--R x +--R (120) --------- +--R n +--R log(a x ) +--R Type: Expression Integer +--E 126 + +--S 127 of 500 +r0025:= x^3*Ei(3*log(a*x^n)/n)/n*(a*x^n)^(-3/n) +--R +--R +--R 3 +--R - - n +--R 3 n n 3log(a x ) +--R x (a x ) Ei(----------) +--R n +--R (121) ------------------------- +--R n +--R Type: Expression Integer +--E 127 + +--S 128 of 500 +a0025:= integrate(t0025,x) +--R +--R +--R x 2 +--R ++ %D +--R (122) | ---------- d%D +--R ++ n +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 128 + +--S 129 of 500 +--m0025:= a0025-r0025 +--E 129 + +--S 130 of 500 +--d0025:= D(m0025,x) +--E 130 + +--S 131 of 500 +t0026:= x^3/log(a*x^n) +--R +--R +--R 3 +--R x +--R (123) --------- +--R n +--R log(a x ) +--R Type: Expression Integer +--E 131 + +--S 132 of 500 +r0026:= x^4*Ei(4*log(a*x^n)/n)/n*(a*x^n)^(-4/n) +--R +--R +--R 4 +--R - - n +--R 4 n n 4log(a x ) +--R x (a x ) Ei(----------) +--R n +--R (124) ------------------------- +--R n +--R Type: Expression Integer +--E 132 + +--S 133 of 500 +a0026:= integrate(t0026,x) +--R +--R +--R x 3 +--R ++ %D +--R (125) | ---------- d%D +--R ++ n +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 133 + +--S 134 of 500 +--m0026:= a0026-r0026 +--E 134 + +--S 135 of 500 +--d0026:= D(m0026,x) +--E 135 + +--S 136 of 500 +t0027:= 1/x^2/log(a*x^n) +--R +--R +--R 1 +--R (126) ----------- +--R 2 n +--R x log(a x ) +--R Type: Expression Integer +--E 136 + +--S 137 of 500 +r0027:= (a*x^n)^(1/n)*Ei(-log(a*x^n)/n)/n/x +--R +--R +--R 1 +--R - n +--R n n log(a x ) +--R (a x ) Ei(- ---------) +--R n +--R (127) ---------------------- +--R n x +--R Type: Expression Integer +--E 137 + +--S 138 of 500 +a0027:= integrate(t0027,x) +--R +--R +--R x +--R ++ 1 +--R (128) | ------------- d%D +--R ++ 2 n +--R %D log(a %D ) +--R Type: Union(Expression Integer,...) +--E 138 + +--S 139 of 500 +--m0027:= a0027-r0027 +--E 139 + +--S 140 of 500 +--d0027:= D(m0027,x) +--E 140 + +--S 141 of 500 +t0028:= 1/x^3/log(a*x^n) +--R +--R +--R 1 +--R (129) ----------- +--R 3 n +--R x log(a x ) +--R Type: Expression Integer +--E 141 + +--S 142 of 500 +r0028:= (a*x^n)^(2/n)*Ei(-2*log(a*x^n)/n)/n/x^2 +--R +--R +--R 2 +--R - n +--R n n 2log(a x ) +--R (a x ) Ei(- ----------) +--R n +--R (130) ----------------------- +--R 2 +--R n x +--R Type: Expression Integer +--E 142 + +--S 143 of 500 +a0028:= integrate(t0028,x) +--R +--R +--R x +--R ++ 1 +--R (131) | ------------- d%D +--R ++ 3 n +--R %D log(a %D ) +--R Type: Union(Expression Integer,...) +--E 143 + +--S 144 of 500 +--m0028:= a0028-r0028 +--E 144 + +--S 145 of 500 +--d0028:= D(m0028,x) +--E 145 + +--S 146 of 500 +t0029:= x^m/log(a*x^n) +--R +--R +--R m +--R x +--R (132) --------- +--R n +--R log(a x ) +--R Type: Expression Integer +--E 146 + +--S 147 of 500 +r0029:= x^(1+m)*Ei((1+m)*log(a*x^n)/n)/n*(a*x^n)^(-(1+m)/n) +--R +--R +--R - m - 1 +--R ------- n +--R m + 1 n n (m + 1)log(a x ) +--R x (a x ) Ei(----------------) +--R n +--R (133) --------------------------------------- +--R n +--R Type: Expression Integer +--E 147 + +--S 148 of 500 +a0029:= integrate(t0029,x) +--R +--R +--R x m +--R ++ %D +--R (134) | ---------- d%D +--R ++ n +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 148 + +--S 149 of 500 +--m0029:= a0029-r0029 +--E 149 + +--S 150 of 500 +--d0029:= D(m0029,x) +--E 150 + +--S 151 of 500 +t0030:= x^m/log(c*(a*x^n)^p) +--R +--R +--R m +--R x +--R (135) -------------- +--R n p +--R log(c (a x ) ) +--R Type: Expression Integer +--E 151 + +--S 152 of 500 +r0030:= x^(1+m)*Ei((1+m)*log(c*(a*x^n)^p)/n/p)*(c*(a*x^n)^p)^(-(1+m)/n/p)/n/p +--R +--R +--R - m - 1 +--R ------- n p +--R m + 1 n p n p (m + 1)log(c (a x ) ) +--R x (c (a x ) ) Ei(---------------------) +--R n p +--R (136) ------------------------------------------------- +--R n p +--R Type: Expression Integer +--E 152 + +--S 153 of 500 +a0030:= integrate(t0030,x) +--R +--R +--R x m +--R ++ %D +--R (137) | --------------- d%D +--R ++ n p +--R log(c (a %D ) ) +--R Type: Union(Expression Integer,...) +--E 153 + +--S 154 of 500 +--m0030:= a0030-r0030 +--E 154 + +--S 155 of 500 +--d0030:= D(m0030,x) +--E 155 + +--S 156 of 500 +t0031:= x^m/log(a*x)^2 +--R +--R +--R m +--R x +--R (138) --------- +--R 2 +--R log(a x) +--R Type: Expression Integer +--E 156 + +--S 157 of 500 +r0031:= (1+m)*x^(1+m)*(a*x)^(-1-m)*Ei((1+m)*log(a*x))-x^(1+m)/log(a*x) +--R +--R +--R m + 1 - m - 1 m + 1 +--R (m + 1)log(a x)x (a x) Ei((m + 1)log(a x)) - x +--R (139) ------------------------------------------------------------- +--R log(a x) +--R Type: Expression Integer +--E 157 + +--S 158 of 500 +a0031:= integrate(t0031,x) +--R +--R +--R x m +--R ++ %D +--R (140) | ---------- d%D +--R ++ 2 +--R log(%D a) +--R Type: Union(Expression Integer,...) +--E 158 + +--S 159 of 500 +--m0031:= a0031-r0031 +--E 159 + +--S 160 of 500 +--d0031:= D(m0031,x) +--E 160 + +--S 161 of 500 +t0032:= 1/log(a*x^n)^2 +--R +--R +--R 1 +--R (141) ---------- +--R n 2 +--R log(a x ) +--R Type: Expression Integer +--E 161 + +--S 162 of 500 +r0032:= x*Ei(log(a*x^n)/n)/((a*x^n)^(1/n))/n^2-x/n/log(a*x^n) +--R +--R +--R 1 +--R n - +--R n log(a x ) n n +--R x log(a x )Ei(---------) - n x (a x ) +--R n +--R (142) -------------------------------------- +--R 1 +--R - +--R 2 n n n +--R n log(a x )(a x ) +--R Type: Expression Integer +--E 162 + +--S 163 of 500 +a0032:= integrate(t0032,x) +--R +--R +--R x +--R ++ 1 +--R (143) | ----------- d%D +--R ++ n 2 +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 163 + +--S 164 of 500 +--m0032:= a0032-r0032 +--E 164 + +--S 165 of 500 +--d0032:= D(m0032,x) +--E 165 + +--S 166 of 500 +t0033:= x/log(a*x^n)^2 +--R +--R +--R x +--R (144) ---------- +--R n 2 +--R log(a x ) +--R Type: Expression Integer +--E 166 + +--S 167 of 500 +r0033:= 2*x^2*Ei(2*log(a*x^n)/n)/((a*x^n)^(2/n))/n^2-x^2/n/log(a*x^n) +--R +--R +--R 2 +--R n - +--R 2 n 2log(a x ) 2 n n +--R 2x log(a x )Ei(----------) - n x (a x ) +--R n +--R (145) ---------------------------------------- +--R 2 +--R - +--R 2 n n n +--R n log(a x )(a x ) +--R Type: Expression Integer +--E 167 + +--S 168 of 500 +a0033:= integrate(t0033,x) +--R +--R +--R x +--R ++ %D +--R (146) | ----------- d%D +--R ++ n 2 +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 168 + +--S 169 of 500 +--m0033:= a0033-r0033 +--E 169 + +--S 170 of 500 +--d0033:= D(m0033,x) +--E 170 + +--S 171 of 500 +t0034:= x^2/log(a*x^n)^2 +--R +--R +--R 2 +--R x +--R (147) ---------- +--R n 2 +--R log(a x ) +--R Type: Expression Integer +--E 171 + +--S 172 of 500 +r0034:= 3*x^3*Ei(3*log(a*x^n)/n)/((a*x^n)^(3/n))/n^2-x^3/n/log(a*x^n) +--R +--R +--R 3 +--R n - +--R 3 n 3log(a x ) 3 n n +--R 3x log(a x )Ei(----------) - n x (a x ) +--R n +--R (148) ---------------------------------------- +--R 3 +--R - +--R 2 n n n +--R n log(a x )(a x ) +--R Type: Expression Integer +--E 172 + +--S 173 of 500 +a0034:= integrate(t0034,x) +--R +--R +--R x 2 +--R ++ %D +--R (149) | ----------- d%D +--R ++ n 2 +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 173 + +--S 174 of 500 +--m0034:= a0034-r0034 +--E 174 + +--S 175 of 500 +--d0034:= D(m0034,x) +--E 175 + +--S 176 of 500 +t0035:= x^3/log(a*x^n)^2 +--R +--R +--R 3 +--R x +--R (150) ---------- +--R n 2 +--R log(a x ) +--R Type: Expression Integer +--E 176 + +--S 177 of 500 +r0035:= 4*x^4*Ei(4*log(a*x^n)/n)/((a*x^n)^(4/n))/n^2-x^4/n/log(a*x^n) +--R +--R +--R 4 +--R n - +--R 4 n 4log(a x ) 4 n n +--R 4x log(a x )Ei(----------) - n x (a x ) +--R n +--R (151) ---------------------------------------- +--R 4 +--R - +--R 2 n n n +--R n log(a x )(a x ) +--R Type: Expression Integer +--E 177 + +--S 178 of 500 +a0035:= integrate(t0035,x) +--R +--R +--R x 3 +--R ++ %D +--R (152) | ----------- d%D +--R ++ n 2 +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 178 + +--S 179 of 500 +--m0035:= a0035-r0035 +--E 179 + +--S 180 of 500 +--d0035:= D(m0035,x) +--E 180 + +--S 181 of 500 +t0036:= 1/x^2/log(a*x^n)^2 +--R +--R +--R 1 +--R (153) ------------ +--R 2 n 2 +--R x log(a x ) +--R Type: Expression Integer +--E 181 + +--S 182 of 500 +r0036:= -(a*x^n)^(1/n)*Ei(-log(a*x^n)/n)/n^2/x-1/n/x/log(a*x^n) +--R +--R +--R 1 +--R - n +--R n n n log(a x ) +--R - log(a x )(a x ) Ei(- ---------) - n +--R n +--R (154) ------------------------------------- +--R 2 n +--R n x log(a x ) +--R Type: Expression Integer +--E 182 + +--S 183 of 500 +a0036:= integrate(t0036,x) +--R +--R +--R x +--R ++ 1 +--R (155) | -------------- d%D +--R ++ 2 n 2 +--R %D log(a %D ) +--R Type: Union(Expression Integer,...) +--E 183 + +--S 184 of 500 +--m0036:= a0036-r0036 +--E 184 + +--S 185 of 500 +--d0036:= D(m0036,x) +--E 185 + +--S 186 of 500 +t0037:= 1/x^3/log(a*x^n)^2 +--R +--R +--R 1 +--R (156) ------------ +--R 3 n 2 +--R x log(a x ) +--R Type: Expression Integer +--E 186 + +--S 187 of 500 +r0037:= -2*(a*x^n)^(2/n)*Ei(-2*log(a*x^n)/n)/n^2/x^2-1/n/x^2/log(a*x^n) +--R +--R +--R 2 +--R - n +--R n n n 2log(a x ) +--R - 2log(a x )(a x ) Ei(- ----------) - n +--R n +--R (157) --------------------------------------- +--R 2 2 n +--R n x log(a x ) +--R Type: Expression Integer +--E 187 + +--S 188 of 500 +a0037:= integrate(t0037,x) +--R +--R +--R x +--R ++ 1 +--R (158) | -------------- d%D +--R ++ 3 n 2 +--R %D log(a %D ) +--R Type: Union(Expression Integer,...) +--E 188 + +--S 189 of 500 +--m0037:= a0037-r0037 +--E 189 + +--S 190 of 500 +--d0037:= D(m0037,x) +--E 190 + +--S 191 of 500 +t0038:= x^m/log(a*x^n)^2 +--R +--R +--R m +--R x +--R (159) ---------- +--R n 2 +--R log(a x ) +--R Type: Expression Integer +--E 191 + +--S 192 of 500 +r0038:= (1+m)*x^(1+m)*Ei((1+m)*log(a*x^n)/n)/((a*x^n)^((1+m)/n))/n^2-x^(1+m)/n/log(a*x^n) +--R +--R +--R m + 1 +--R n ----- +--R m + 1 n (m + 1)log(a x ) m + 1 n n +--R (m + 1)x log(a x )Ei(----------------) - n x (a x ) +--R n +--R (160) ---------------------------------------------------------------- +--R m + 1 +--R ----- +--R 2 n n n +--R n log(a x )(a x ) +--R Type: Expression Integer +--E 192 + +--S 193 of 500 +a0038:= integrate(t0038,x) +--R +--R +--R x m +--R ++ %D +--R (161) | ----------- d%D +--R ++ n 2 +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 193 + +--S 194 of 500 +--m0038:= a0038-r0038 +--E 194 + +--S 195 of 500 +--d0038:= D(m0038,x) +--E 195 + +--S 196 of 500 +t0039:= x^m/log(a*x)^3 +--R +--R +--R m +--R x +--R (162) --------- +--R 3 +--R log(a x) +--R Type: Expression Integer +--E 196 + +--S 197 of 500 +r0039:= 1/2*(1+m)^2*x^(1+m)*(a*x)^(-1-m)*Ei((1+m)*log(a*x))-1/2*x^(1+m)/log(a*x)^2-1/2*(1+m)*x^(1+m)/log(a*x) +--R +--R +--R (163) +--R 2 2 m + 1 - m - 1 +--R (m + 2m + 1)log(a x) x (a x) Ei((m + 1)log(a x)) +--R + +--R m + 1 +--R ((- m - 1)log(a x) - 1)x +--R / +--R 2 +--R 2log(a x) +--R Type: Expression Integer +--E 197 + +--S 198 of 500 +a0039:= integrate(t0039,x) +--R +--R +--R x m +--R ++ %D +--R (164) | ---------- d%D +--R ++ 3 +--R log(%D a) +--R Type: Union(Expression Integer,...) +--E 198 + +--S 199 of 500 +--m0039:= a0039-r0039 +--E 199 + +--S 200 of 500 +--d0039:= D(m0039,x) +--E 200 + +--S 201 of 500 +t0040:= 1/log(a*x^n)^3 +--R +--R +--R 1 +--R (165) ---------- +--R n 3 +--R log(a x ) +--R Type: Expression Integer +--E 201 + +--S 202 of 500 +r0040:= 1/2/n^3/log(a*x^n)^2*x*(Ei(log(a*x^n)/n)*(a*x^n)^(-1/n)*log(a*x^n)^2-n^2-n*log(a*x^n)) +--R +--R +--R 1 +--R - - n +--R n 2 n n log(a x ) n 2 +--R x log(a x ) (a x ) Ei(---------) - n x log(a x ) - n x +--R n +--R (166) -------------------------------------------------------- +--R 3 n 2 +--R 2n log(a x ) +--R Type: Expression Integer +--E 202 + +--S 203 of 500 +a0040:= integrate(t0040,x) +--R +--R +--R x +--R ++ 1 +--R (167) | ----------- d%D +--R ++ n 3 +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 203 + +--S 204 of 500 +--m0040:= a0040-r0040 +--E 204 + +--S 205 of 500 +--d0040:= D(m0040,x) +--E 205 + +--S 206 of 500 +t0041:= x/log(a*x^n)^3 +--R +--R +--R x +--R (168) ---------- +--R n 3 +--R log(a x ) +--R Type: Expression Integer +--E 206 + +--S 207 of 500 +r0041:= 1/2/n^3/log(a*x^n)^2*x^2*(4*Ei(2*log(a*x^n)/n)*(a*x^n)^(-2/n)*log(a*x^n)^2-n^2-2*n*log(a*x^n)) +--R +--R +--R 2 +--R - - n +--R 2 n 2 n n 2log(a x ) 2 n 2 2 +--R 4x log(a x ) (a x ) Ei(----------) - 2n x log(a x ) - n x +--R n +--R (169) ------------------------------------------------------------ +--R 3 n 2 +--R 2n log(a x ) +--R Type: Expression Integer +--E 207 + +--S 208 of 500 +a0041:= integrate(t0041,x) +--R +--R +--R x +--R ++ %D +--R (170) | ----------- d%D +--R ++ n 3 +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 208 + +--S 209 of 500 +--m0041:= a0041-r0041 +--E 209 + +--S 210 of 500 +--d0041:= D(m0041,x) +--E 210 + +--S 211 of 500 +t0042:= x^2/log(a*x^n)^3 +--R +--R +--R 2 +--R x +--R (171) ---------- +--R n 3 +--R log(a x ) +--R Type: Expression Integer +--E 211 + +--S 212 of 500 +r0042:= 1/2/n^3/log(a*x^n)^2*x^3*(9*Ei(3*log(a*x^n)/n)*(a*x^n)^(-3/n)*log(a*x^n)^2-n^2-3*n*log(a*x^n)) +--R +--R +--R 3 +--R - - n +--R 3 n 2 n n 3log(a x ) 3 n 2 3 +--R 9x log(a x ) (a x ) Ei(----------) - 3n x log(a x ) - n x +--R n +--R (172) ------------------------------------------------------------ +--R 3 n 2 +--R 2n log(a x ) +--R Type: Expression Integer +--E 212 + +--S 213 of 500 +a0042:= integrate(t0042,x) +--R +--R +--R x 2 +--R ++ %D +--R (173) | ----------- d%D +--R ++ n 3 +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 213 + +--S 214 of 500 +--m0042:= a0042-r0042 +--E 214 + +--S 215 of 500 +--d0042:= D(m0042,x) +--E 215 + +--S 216 of 500 +t0043:= x^3/log(a*x^n)^3 +--R +--R +--R 3 +--R x +--R (174) ---------- +--R n 3 +--R log(a x ) +--R Type: Expression Integer +--E 216 + +--S 217 of 500 +r0043:= 1/2/n^3/log(a*x^n)^2*x^4*(16*Ei(4*log(a*x^n)/n)*(a*x^n)^(-4/n)*log(a*x^n)^2-n^2-4*n*log(a*x^n)) +--R +--R +--R 4 +--R - - n +--R 4 n 2 n n 4log(a x ) 4 n 2 4 +--R 16x log(a x ) (a x ) Ei(----------) - 4n x log(a x ) - n x +--R n +--R (175) ------------------------------------------------------------- +--R 3 n 2 +--R 2n log(a x ) +--R Type: Expression Integer +--E 217 + +--S 218 of 500 +a0043:= integrate(t0043,x) +--R +--R +--R x 3 +--R ++ %D +--R (176) | ----------- d%D +--R ++ n 3 +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 218 + +--S 219 of 500 +--m0043:= a0043-r0043 +--E 219 + +--S 220 of 500 +--d0043:= D(m0043,x) +--E 220 + +--S 221 of 500 +t0044:= 1/x^2/log(a*x^n)^3 +--R +--R +--R 1 +--R (177) ------------ +--R 2 n 3 +--R x log(a x ) +--R Type: Expression Integer +--E 221 + +--S 222 of 500 +r0044:= 1/2/n^3/x/log(a*x^n)^2*((a*x^n)^(1/n)*Ei(-log(a*x^n)/n)*log(a*x^n)^2-n^2+n*log(a*x^n)) +--R +--R +--R 1 +--R - n +--R n 2 n n log(a x ) n 2 +--R log(a x ) (a x ) Ei(- ---------) + n log(a x ) - n +--R n +--R (178) --------------------------------------------------- +--R 3 n 2 +--R 2n x log(a x ) +--R Type: Expression Integer +--E 222 + +--S 223 of 500 +a0044:= integrate(t0044,x) +--R +--R +--R x +--R ++ 1 +--R (179) | -------------- d%D +--R ++ 2 n 3 +--R %D log(a %D ) +--R Type: Union(Expression Integer,...) +--E 223 + +--S 224 of 500 +--m0044:= a0044-r0044 +--E 224 + +--S 225 of 500 +--d0044:= D(m0044,x) +--E 225 + +--S 226 of 500 +t0045:= 1/x^3/log(a*x^n)^3 +--R +--R +--R 1 +--R (180) ------------ +--R 3 n 3 +--R x log(a x ) +--R Type: Expression Integer +--E 226 + +--S 227 of 500 +r0045:= 2*(a*x^n)^(2/n)*Ei(-2*log(a*x^n)/n)/n^3/x^2-1/2/n/x^2/log(a*x^n)^2+1/n^2/x^2/log(a*x^n) +--R +--R +--R 2 +--R - n +--R n 2 n n 2log(a x ) n 2 +--R 4log(a x ) (a x ) Ei(- ----------) + 2n log(a x ) - n +--R n +--R (181) ------------------------------------------------------ +--R 3 2 n 2 +--R 2n x log(a x ) +--R Type: Expression Integer +--E 227 + +--S 228 of 500 +a0045:= integrate(t0045,x) +--R +--R +--R x +--R ++ 1 +--R (182) | -------------- d%D +--R ++ 3 n 3 +--R %D log(a %D ) +--R Type: Union(Expression Integer,...) +--E 228 + +--S 229 of 500 +--m0045:= a0045-r0045 +--E 229 + +--S 230 of 500 +--d0045:= D(m0045,x) +--E 230 + +--S 231 of 500 +t0046:= x^m/log(a*x^n)^3 +--R +--R +--R m +--R x +--R (183) ---------- +--R n 3 +--R log(a x ) +--R Type: Expression Integer +--E 231 + +--S 232 of 500 +r0046:= 1/2*(1+m)^2*x^(1+m)*Ei((1+m)*log(a*x^n)/n)/((a*x^n)^((1+m)/n))/n^3-1/2*x^(1+m)/n/log(a*x^n)^2-1/2*(1+m)*x^(1+m)/n^2/log(a*x^n) +--R +--R +--R (184) +--R n +--R 2 m + 1 n 2 (m + 1)log(a x ) +--R (m + 2m + 1)x log(a x ) Ei(----------------) +--R n +--R + +--R m + 1 +--R ----- +--R m + 1 n 2 m + 1 n n +--R ((- m - 1)n x log(a x ) - n x )(a x ) +--R / +--R m + 1 +--R ----- +--R 3 n 2 n n +--R 2n log(a x ) (a x ) +--R Type: Expression Integer +--E 232 + +--S 233 of 500 +a0046:= integrate(t0046,x) +--R +--R +--R x m +--R ++ %D +--R (185) | ----------- d%D +--R ++ n 3 +--R log(a %D ) +--R Type: Union(Expression Integer,...) +--E 233 + +--S 234 of 500 +--m0046:= a0046-r0046 +--E 234 + +--S 235 of 500 +--d0046:= D(m0046,x) +--E 235 + +--S 236 of 500 +t0047:= log(a*x^n)^(3/2) +--R +--R +--R +---------+ +--R n | n +--R (186) log(a x )\|log(a x ) +--R Type: Expression Integer +--E 236 + +--S 237 of 500 +r0047:= 1/4*x*(3*(a*x^n)^(-1/n)*n^(3/2)*%pi^(1/2)*erfi(log(a*x^n)^(1/2)/n^(1/2))-6*n*log(a*x^n)^(1/2)+4*log(a*x^n)^(3/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 237 + +--S 238 of 500 +a0047:= integrate(t0047,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 238 + +--S 239 of 500 +--m0047:= a0047-r0047 +--E 239 + +--S 240 of 500 +--d0047:= D(m0047,x) +--E 240 + +--S 241 of 500 +t0048:= x*log(a*x^n)^(3/2) +--R +--R +--R +---------+ +--R n | n +--R (187) x log(a x )\|log(a x ) +--R Type: Expression Integer +--E 241 + +--S 242 of 500 +r0048:= 1/32*x^2*(3*(a*x^n)^(-2/n)*n^(3/2)*2^(1/2)*%pi^(1/2)*erfi(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))-12*n*log(a*x^n)^(1/2)+16*log(a*x^n)^(3/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 242 + +--S 243 of 500 +a0048:= integrate(t0048,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 243 + +--S 244 of 500 +--m0048:= a0048-r0048 +--E 244 + +--S 245 of 500 +--d0048:= D(m0048,x) +--E 245 + +--S 246 of 500 +t0049:= x^2*log(a*x^n)^(3/2) +--R +--R +--R +---------+ +--R 2 n | n +--R (188) x log(a x )\|log(a x ) +--R Type: Expression Integer +--E 246 + +--S 247 of 500 +r0049:= 1/36*x^3*((a*x^n)^(-3/n)*n^(3/2)*3^(1/2)*%pi^(1/2)*erfi(3^(1/2)*log(a*x^n)^(1/2)/n^(1/2))-6*n*log(a*x^n)^(1/2)+12*log(a*x^n)^(3/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 247 + +--S 248 of 500 +a0049:= integrate(t0049,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 248 + +--S 249 of 500 +--m0049:= a0049-r0049 +--E 249 + +--S 250 of 500 +--d0049:= D(m0049,x) +--E 250 + +--S 251 of 500 +t0050:= x^3*log(a*x^n)^(3/2) +--R +--R +--R +---------+ +--R 3 n | n +--R (189) x log(a x )\|log(a x ) +--R Type: Expression Integer +--E 251 + +--S 252 of 500 +r0050:= 1/128*x^4*(3*(a*x^n)^(-4/n)*n^(3/2)*%pi^(1/2)*erfi(2*log(a*x^n)^(1/2)/n^(1/2))-12*n*log(a*x^n)^(1/2)+32*log(a*x^n)^(3/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 252 + +--S 253 of 500 +a0050:= integrate(t0050,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 253 + +--S 254 of 500 +--m0050:= a0050-r0050 +--E 254 + +--S 255 of 500 +--d0050:= D(m0050,x) +--E 255 + +--S 256 of 500 +t0051:= log(a*x^n)^(3/2)/x^2 +--R +--R +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R (190) --------------------- +--R 2 +--R x +--R Type: Expression Integer +--E 256 + +--S 257 of 500 +r0051:= -1/4*(-3*n^(3/2)*%pi^(1/2)*(a*x^n)^(1/n)*erf(log(a*x^n)^(1/2)/n^(1/2))+6*n*log(a*x^n)^(1/2)+4*log(a*x^n)^(3/2))/x +--R +--R +--R (191) +--R 1 +---------+ +--R - | n +---------+ +--R +-+ +---+ n n \|log(a x ) n | n +--R 3n\|n \|%pi (a x ) erf(------------) + (- 4log(a x ) - 6n)\|log(a x ) +--R +-+ +--R \|n +--R ---------------------------------------------------------------------- +--R 4x +--R Type: Expression Integer +--E 257 + +--S 258 of 500 +a0051:= integrate(t0051,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 258 + +--S 259 of 500 +--m0051:= a0051-r0051 +--E 259 + +--S 260 of 500 +--d0051:= D(m0051,x) +--E 260 + +--S 261 of 500 +t0052:= log(a*x^n)^(3/2)/x^3 +--R +--R +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R (192) --------------------- +--R 3 +--R x +--R Type: Expression Integer +--E 261 + +--S 262 of 500 +r0052:= -1/32*(-3*n^(3/2)*2^(1/2)*%pi^(1/2)*(a*x^n)^(2/n)*erf(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))+12*n*log(a*x^n)^(1/2)+16*log(a*x^n)^(3/2))/x^2 +--R +--R +--R (193) +--R 2 +---------+ +--R - +-+ | n +--R +-+ +-+ +---+ n n \|2 \|log(a x ) +--R 3n\|2 \|n \|%pi (a x ) erf(----------------) +--R +-+ +--R \|n +--R + +--R +---------+ +--R n | n +--R (- 16log(a x ) - 12n)\|log(a x ) +--R / +--R 2 +--R 32x +--R Type: Expression Integer +--E 262 + +--S 263 of 500 +a0052:= integrate(t0052,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 263 + +--S 264 of 500 +--m0052:= a0052-r0052 +--E 264 + +--S 265 of 500 +--d0052:= D(m0052,x) +--E 265 + +--S 266 of 500 +t0053:= x^m*log(a*x^n)^(3/2) +--R +--R +--R +---------+ +--R m n | n +--R (194) x log(a x )\|log(a x ) +--R Type: Expression Integer +--E 266 + +--S 267 of 500 +r0053:= 3/4*n^(3/2)*%pi^(1/2)*x^(1+m)*erfi((1+m)^(1/2)*log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^((1+m)/n))/(1+m)^(5/2)-3/2*n*x^(1+m)*log(a*x^n)^(1/2)/(1+m)^2+x^(1+m)*log(a*x^n)^(3/2)/(1+m) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 267 + +--S 268 of 500 +a0053:= integrate(t0053,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 268 + +--S 269 of 500 +--m0053:= a0053-r0053 +--E 269 + +--S 270 of 500 +--d0053:= D(m0053,x) +--E 270 + +--S 271 of 500 +t0054:= log(a*x^n)^(1/2) +--R +--R +--R +---------+ +--R | n +--R (195) \|log(a x ) +--R Type: Expression Integer +--E 271 + +--S 272 of 500 +r0054:= -1/2*n^(1/2)*%pi^(1/2)*x*erfi(log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^(1/n))+x*log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 272 + +--S 273 of 500 +a0054:= integrate(t0054,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 273 + +--S 274 of 500 +--m0054:= a0054-r0054 +--E 274 + +--S 275 of 500 +--d0054:= D(m0054,x) +--E 275 + +--S 276 of 500 +t0055:= x*log(a*x^n)^(1/2) +--R +--R +--R +---------+ +--R | n +--R (196) x\|log(a x ) +--R Type: Expression Integer +--E 276 + +--S 277 of 500 +r0055:= 1/8*x^2*(-(a*x^n)^(-2/n)*n^(1/2)*2^(1/2)*%pi^(1/2)*erfi(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))+4*log(a*x^n)^(1/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 277 + +--S 278 of 500 +a0055:= integrate(t0055,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 278 + +--S 279 of 500 +--m0055:= a0055-r0055 +--E 279 + +--S 280 of 500 +--d0055:= D(m0055,x) +--E 280 + +--S 281 of 500 +t0056:= x^2*log(a*x^n)^(1/2) +--R +--R +--R +---------+ +--R 2 | n +--R (197) x \|log(a x ) +--R Type: Expression Integer +--E 281 + +--S 282 of 500 +r0056:= 1/18*x^3*(-(a*x^n)^(-3/n)*n^(1/2)*3^(1/2)*%pi^(1/2)*erfi(3^(1/2)*log(a*x^n)^(1/2)/n^(1/2))+6*log(a*x^n)^(1/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 282 + +--S 283 of 500 +a0056:= integrate(t0056,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 283 + +--S 284 of 500 +--m0056:= a0056-r0056 +--E 284 + +--S 285 of 500 +--d0056:= D(m0056,x) +--E 285 + +--S 286 of 500 +t0057:= x^3*log(a*x^n)^(1/2) +--R +--R +--R +---------+ +--R 3 | n +--R (198) x \|log(a x ) +--R Type: Expression Integer +--E 286 + +--S 287 of 500 +r0057:= 1/16*x^4*(-(a*x^n)^(-4/n)*n^(1/2)*%pi^(1/2)*erfi(2*log(a*x^n)^(1/2)/n^(1/2))+4*log(a*x^n)^(1/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 287 + +--S 288 of 500 +a0057:= integrate(t0057,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 288 + +--S 289 of 500 +--m0057:= a0057-r0057 +--E 289 + +--S 290 of 500 +--d0057:= D(m0057,x) +--E 290 + +--S 291 of 500 +t0058:= log(a*x^n)^(1/2)/x^2 +--R +--R +--R +---------+ +--R | n +--R \|log(a x ) +--R (199) ------------ +--R 2 +--R x +--R Type: Expression Integer +--E 291 + +--S 292 of 500 +r0058:= -1/2*(-n^(1/2)*%pi^(1/2)*(a*x^n)^(1/n)*erf(log(a*x^n)^(1/2)/n^(1/2))+2*log(a*x^n)^(1/2))/x +--R +--R +--R 1 +---------+ +--R - | n +---------+ +--R +-+ +---+ n n \|log(a x ) | n +--R \|n \|%pi (a x ) erf(------------) - 2\|log(a x ) +--R +-+ +--R \|n +--R (200) -------------------------------------------------- +--R 2x +--R Type: Expression Integer +--E 292 + +--S 293 of 500 +a0058:= integrate(t0058,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 293 + +--S 294 of 500 +--m0058:= a0058-r0058 +--E 294 + +--S 295 of 500 +--d0058:= D(m0058,x) +--E 295 + +--S 296 of 500 +t0059:= log(a*x^n)^(1/2)/x^3 +--R +--R +--R +---------+ +--R | n +--R \|log(a x ) +--R (201) ------------ +--R 3 +--R x +--R Type: Expression Integer +--E 296 + +--S 297 of 500 +r0059:= -1/8*(-n^(1/2)*2^(1/2)*%pi^(1/2)*(a*x^n)^(2/n)*erf(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))+4*log(a*x^n)^(1/2))/x^2 +--R +--R +--R 2 +---------+ +--R - +-+ | n +---------+ +--R +-+ +-+ +---+ n n \|2 \|log(a x ) | n +--R \|2 \|n \|%pi (a x ) erf(----------------) - 4\|log(a x ) +--R +-+ +--R \|n +--R (202) ---------------------------------------------------------- +--R 2 +--R 8x +--R Type: Expression Integer +--E 297 + +--S 298 of 500 +a0059:= integrate(t0059,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 298 + +--S 299 of 500 +--m0059:= a0059-r0059 +--E 299 + +--S 300 of 500 +--d0059:= D(m0059,x) +--E 300 + +--S 301 of 500 +t0060:= x^m*log(a*x^n)^(1/2) +--R +--R +--R +---------+ +--R m | n +--R (203) x \|log(a x ) +--R Type: Expression Integer +--E 301 + +--S 302 of 500 +r0060:= 1/2*x*x^m*(-(a*x^n)^(-(1+m)/n)*n^(1/2)*%pi^(1/2)*erfi((1+m)^(1/2)*log(a*x^n)^(1/2)/n^(1/2))+2*(1+m)^(1/2)*log(a*x^n)^(1/2))/(1+m)^(3/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 302 + +--S 303 of 500 +a0060:= integrate(t0060,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 303 + +--S 304 of 500 +--m0060:= a0060-r0060 +--E 304 + +--S 305 of 500 +--d0060:= D(m0060,x) +--E 305 + +--S 306 of 500 +t0061:= 1/log(a*x^n)^(1/2) +--R +--R +--R 1 +--R (204) ------------ +--R +---------+ +--R | n +--R \|log(a x ) +--R Type: Expression Integer +--E 306 + +--S 307 of 500 +r0061:= %pi^(1/2)*x*erfi(log(a*x^n)^(1/2)/n^(1/2))/n^(1/2)/((a*x^n)^(1/n)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 307 + +--S 308 of 500 +a0061:= integrate(t0061,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 308 + +--S 309 of 500 +--m0061:= a0061-r0061 +--E 309 + +--S 310 of 500 +--d0061:= D(m0061,x) +--E 310 + +--S 311 of 500 +t0062:= x/log(a*x^n)^(1/2) +--R +--R +--R x +--R (205) ------------ +--R +---------+ +--R | n +--R \|log(a x ) +--R Type: Expression Integer +--E 311 + +--S 312 of 500 +r0062:= 1/2*2^(1/2)*%pi^(1/2)*x^2*erfi(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))/n^(1/2)*(a*x^n)^(-2/n) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 312 + +--S 313 of 500 +a0062:= integrate(t0062,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 313 + +--S 314 of 500 +--m0062:= a0062-r0062 +--E 314 + +--S 315 of 500 +--d0062:= D(m0062,x) +--E 315 + +--S 316 of 500 +t0063:= x^2/log(a*x^n)^(1/2) +--R +--R +--R 2 +--R x +--R (206) ------------ +--R +---------+ +--R | n +--R \|log(a x ) +--R Type: Expression Integer +--E 316 + +--S 317 of 500 +r0063:= 1/3*3^(1/2)*%pi^(1/2)*x^3*erfi(3^(1/2)*log(a*x^n)^(1/2)/n^(1/2))/n^(1/2)*(a*x^n)^(-3/n) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 317 + +--S 318 of 500 +a0063:= integrate(t0063,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 318 + +--S 319 of 500 +--m0063:= a0063-r0063 +--E 319 + +--S 320 of 500 +--d0063:= D(m0063,x) +--E 320 + +--S 321 of 500 +t0064:= x^3/log(a*x^n)^(1/2) +--R +--R +--R 3 +--R x +--R (207) ------------ +--R +---------+ +--R | n +--R \|log(a x ) +--R Type: Expression Integer +--E 321 + +--S 322 of 500 +r0064:= 1/2*%pi^(1/2)*x^4*erfi(2*log(a*x^n)^(1/2)/n^(1/2))/n^(1/2)*(a*x^n)^(-4/n) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 322 + +--S 323 of 500 +a0064:= integrate(t0064,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 323 + +--S 324 of 500 +--m0064:= a0064-r0064 +--E 324 + +--S 325 of 500 +--d0064:= D(m0064,x) +--E 325 + +--S 326 of 500 +t0065:= 1/x^2/log(a*x^n)^(1/2) +--R +--R +--R 1 +--R (208) -------------- +--R +---------+ +--R 2 | n +--R x \|log(a x ) +--R Type: Expression Integer +--E 326 + +--S 327 of 500 +r0065:= %pi^(1/2)*(a*x^n)^(1/n)*erf(log(a*x^n)^(1/2)/n^(1/2))/n^(1/2)/x +--R +--R +--R 1 +---------+ +--R - | n +--R +---+ n n \|log(a x ) +--R \|%pi (a x ) erf(------------) +--R +-+ +--R \|n +--R (209) ------------------------------ +--R +-+ +--R x\|n +--R Type: Expression Integer +--E 327 + +--S 328 of 500 +a0065:= integrate(t0065,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 328 + +--S 329 of 500 +--m0065:= a0065-r0065 +--E 329 + +--S 330 of 500 +--d0065:= D(m0065,x) +--E 330 + +--S 331 of 500 +t0066:= 1/x^3/log(a*x^n)^(1/2) +--R +--R +--R 1 +--R (210) -------------- +--R +---------+ +--R 3 | n +--R x \|log(a x ) +--R Type: Expression Integer +--E 331 + +--S 332 of 500 +r0066:= 1/2*2^(1/2)*%pi^(1/2)*(a*x^n)^(2/n)*erf(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))/n^(1/2)/x^2 +--R +--R +--R 2 +---------+ +--R - +-+ | n +--R +-+ +---+ n n \|2 \|log(a x ) +--R \|2 \|%pi (a x ) erf(----------------) +--R +-+ +--R \|n +--R (211) -------------------------------------- +--R 2 +-+ +--R 2x \|n +--R Type: Expression Integer +--E 332 + +--S 333 of 500 +a0066:= integrate(t0066,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 333 + +--S 334 of 500 +--m0066:= a0066-r0066 +--E 334 + +--S 335 of 500 +--d0066:= D(m0066,x) +--E 335 + +--S 336 of 500 +t0067:= x^m/log(a*x^n)^(1/2) +--R +--R +--R m +--R x +--R (212) ------------ +--R +---------+ +--R | n +--R \|log(a x ) +--R Type: Expression Integer +--E 336 + +--S 337 of 500 +r0067:= %pi^(1/2)*x^(1+m)*erfi((1+m)^(1/2)*log(a*x^n)^(1/2)/n^(1/2))*(a*x^n)^(-(1+m)/n)/(1+m)^(1/2)/n^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 337 + +--S 338 of 500 +a0067:= integrate(t0067,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 338 + +--S 339 of 500 +--m0067:= a0067-r0067 +--E 339 + +--S 340 of 500 +--d0067:= D(m0067,x) +--E 340 + +--S 341 of 500 +t0068:= 1/log(a*x^n)^(3/2) +--R +--R +--R 1 +--R (213) --------------------- +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R Type: Expression Integer +--E 341 + +--S 342 of 500 +r0068:= 2*%pi^(1/2)*x*erfi(log(a*x^n)^(1/2)/n^(1/2))/n^(3/2)/((a*x^n)^(1/n))-2*x/n/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 342 + +--S 343 of 500 +a0068:= integrate(t0068,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 343 + +--S 344 of 500 +--m0068:= a0068-r0068 +--E 344 + +--S 345 of 500 +--d0068:= D(m0068,x) +--E 345 + +--S 346 of 500 +t0069:= x/log(a*x^n)^(3/2) +--R +--R +--R x +--R (214) --------------------- +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R Type: Expression Integer +--E 346 + +--S 347 of 500 +r0069:= 2*2^(1/2)*%pi^(1/2)*x^2*erfi(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^(2/n))/n^(3/2)-2*x^2/n/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 347 + +--S 348 of 500 +a0069:= integrate(t0069,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 348 + +--S 349 of 500 +--m0069:= a0069-r0069 +--E 349 + +--S 350 of 500 +--d0069:= D(m0069,x) +--E 350 + +--S 351 of 500 +t0070:= x^2/log(a*x^n)^(3/2) +--R +--R +--R 2 +--R x +--R (215) --------------------- +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R Type: Expression Integer +--E 351 + +--S 352 of 500 +r0070:= 2*3^(1/2)*%pi^(1/2)*x^3*erfi(3^(1/2)*log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^(3/n))/n^(3/2)-2*x^3/n/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 352 + +--S 353 of 500 +a0070:= integrate(t0070,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 353 + +--S 354 of 500 +--m0070:= a0070-r0070 +--E 354 + +--S 355 of 500 +--d0070:= D(m0070,x) +--E 355 + +--S 356 of 500 +t0071:= x^3/log(a*x^n)^(3/2) +--R +--R +--R 3 +--R x +--R (216) --------------------- +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R Type: Expression Integer +--E 356 + +--S 357 of 500 +r0071:= 4*%pi^(1/2)*x^4*erfi(2*log(a*x^n)^(1/2)/n^(1/2))/n^(3/2)/((a*x^n)^(4/n))-2*x^4/n/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 357 + +--S 358 of 500 +a0071:= integrate(t0071,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 358 + +--S 359 of 500 +--m0071:= a0071-r0071 +--E 359 + +--S 360 of 500 +--d0071:= D(m0071,x) +--E 360 + +--S 361 of 500 +t0072:= 1/x^2/log(a*x^n)^(3/2) +--R +--R +--R 1 +--R (217) ----------------------- +--R +---------+ +--R 2 n | n +--R x log(a x )\|log(a x ) +--R Type: Expression Integer +--E 361 + +--S 362 of 500 +r0072:= -2*%pi^(1/2)*(a*x^n)^(1/n)*erf(log(a*x^n)^(1/2)/n^(1/2))/n^(3/2)/x-2/n/x/log(a*x^n)^(1/2) +--R +--R +--R 1 +---------+ +--R - +---------+ | n +--R +---+ n n | n \|log(a x ) +-+ +--R - 2\|%pi (a x ) \|log(a x ) erf(------------) - 2\|n +--R +-+ +--R \|n +--R (218) ----------------------------------------------------- +--R +---------+ +--R +-+ | n +--R n x\|n \|log(a x ) +--R Type: Expression Integer +--E 362 + +--S 363 of 500 +a0072:= integrate(t0072,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 363 + +--S 364 of 500 +--m0072:= a0072-r0072 +--E 364 + +--S 365 of 500 +--d0072:= D(m0072,x) +--E 365 + +--S 366 of 500 +t0073:= 1/x^3/log(a*x^n)^(3/2) +--R +--R +--R 1 +--R (219) ----------------------- +--R +---------+ +--R 3 n | n +--R x log(a x )\|log(a x ) +--R Type: Expression Integer +--E 366 + +--S 367 of 500 +r0073:= -2*2^(1/2)*%pi^(1/2)*(a*x^n)^(2/n)*erf(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))/n^(3/2)/x^2-2/n/x^2/log(a*x^n)^(1/2) +--R +--R +--R 2 +---------+ +--R - +---------+ +-+ | n +--R +-+ +---+ n n | n \|2 \|log(a x ) +-+ +--R - 2\|2 \|%pi (a x ) \|log(a x ) erf(----------------) - 2\|n +--R +-+ +--R \|n +--R (220) ------------------------------------------------------------- +--R +---------+ +--R 2 +-+ | n +--R n x \|n \|log(a x ) +--R Type: Expression Integer +--E 367 + +--S 368 of 500 +a0073:= integrate(t0073,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 368 + +--S 369 of 500 +--m0073:= a0073-r0073 +--E 369 + +--S 370 of 500 +--d0073:= D(m0073,x) +--E 370 + +--S 371 of 500 +t0074:= x^m/log(a*x^n)^(3/2) +--R +--R +--R m +--R x +--R (221) --------------------- +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R Type: Expression Integer +--E 371 + +--S 372 of 500 +r0074:= 2*(1+m)^(1/2)*%pi^(1/2)*x^(1+m)*erfi((1+m)^(1/2)*log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^((1+m)/n))/n^(3/2)-2*x^(1+m)/n/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 372 + +--S 373 of 500 +a0074:= integrate(t0074,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 373 + +--S 374 of 500 +--m0074:= a0074-r0074 +--E 374 + +--S 375 of 500 +--d0074:= D(m0074,x) +--E 375 + +--S 376 of 500 +t0075:= 1/log(a*x^n)^(5/2) +--R +--R +--R 1 +--R (222) ---------------------- +--R +---------+ +--R n 2 | n +--R log(a x ) \|log(a x ) +--R Type: Expression Integer +--E 376 + +--S 377 of 500 +r0075:= 4/3*%pi^(1/2)*x*erfi(log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^(1/n))/n^(5/2)-2/3*x/n/log(a*x^n)^(3/2)-4/3*x/n^2/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 377 + +--S 378 of 500 +a0075:= integrate(t0075,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 378 + +--S 379 of 500 +--m0075:= a0075-r0075 +--E 379 + +--S 380 of 500 +--d0075:= D(m0075,x) +--E 380 + +--S 381 of 500 +t0076:= x/log(a*x^n)^(5/2) +--R +--R +--R x +--R (223) ---------------------- +--R +---------+ +--R n 2 | n +--R log(a x ) \|log(a x ) +--R Type: Expression Integer +--E 381 + +--S 382 of 500 +r0076:= 8/3*2^(1/2)*%pi^(1/2)*x^2*erfi(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^(2/n))/n^(5/2)-2/3*x^2/n/log(a*x^n)^(3/2)-8/3*x^2/n^2/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 382 + +--S 383 of 500 +a0076:= integrate(t0076,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 383 + +--S 384 of 500 +--m0076:= a0076-r0076 +--E 384 + +--S 385 of 500 +--d0076:= D(m0076,x) +--E 385 + +--S 386 of 500 +t0077:= x^2/log(a*x^n)^(5/2) +--R +--R +--R 2 +--R x +--R (224) ---------------------- +--R +---------+ +--R n 2 | n +--R log(a x ) \|log(a x ) +--R Type: Expression Integer +--E 386 + +--S 387 of 500 +r0077:= 4*3^(1/2)*%pi^(1/2)*x^3*erfi(3^(1/2)*log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^(3/n))/n^(5/2)-2/3*x^3/n/log(a*x^n)^(3/2)-4*x^3/n^2/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 387 + +--S 388 of 500 +a0077:= integrate(t0077,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 388 + +--S 389 of 500 +--m0077:= a0077-r0077 +--E 389 + +--S 390 of 500 +--d0077:= D(m0077,x) +--E 390 + +--S 391 of 500 +t0078:= x^3/log(a*x^n)^(5/2) +--R +--R +--R 3 +--R x +--R (225) ---------------------- +--R +---------+ +--R n 2 | n +--R log(a x ) \|log(a x ) +--R Type: Expression Integer +--E 391 + +--S 392 of 500 +r0078:= 32/3*%pi^(1/2)*x^4*erfi(2*log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^(4/n))/n^(5/2)-2/3*x^4/n/log(a*x^n)^(3/2)-16/3*x^4/n^2/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 392 + +--S 393 of 500 +a0078:= integrate(t0078,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 393 + +--S 394 of 500 +--m0078:= a0078-r0078 +--E 394 + +--S 395 of 500 +--d0078:= D(m0078,x) +--E 395 + +--S 396 of 500 +t0079:= 1/x^2/log(a*x^n)^(5/2) +--R +--R +--R 1 +--R (226) ------------------------ +--R +---------+ +--R 2 n 2 | n +--R x log(a x ) \|log(a x ) +--R Type: Expression Integer +--E 396 + +--S 397 of 500 +r0079:= 4/3*%pi^(1/2)*(a*x^n)^(1/n)*erf(log(a*x^n)^(1/2)/n^(1/2))/n^(5/2)/x-2/3/n/x/log(a*x^n)^(3/2)+4/3/n^2/x/log(a*x^n)^(1/2) +--R +--R +--R (227) +--R 1 +---------+ +--R - +---------+ | n +--R +---+ n n n | n \|log(a x ) +-+ n +--R 4\|%pi log(a x )(a x ) \|log(a x ) erf(------------) + 4\|n log(a x ) +--R +-+ +--R \|n +--R + +--R +-+ +--R - 2n\|n +--R / +--R +---------+ +--R 2 +-+ n | n +--R 3n x\|n log(a x )\|log(a x ) +--R Type: Expression Integer +--E 397 + +--S 398 of 500 +a0079:= integrate(t0079,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 398 + +--S 399 of 500 +--m0079:= a0079-r0079 +--E 399 + +--S 400 of 500 +--d0079:= D(m0079,x) +--E 400 + +--S 401 of 500 +t0080:= 1/x^3/log(a*x^n)^(5/2) +--R +--R +--R 1 +--R (228) ------------------------ +--R +---------+ +--R 3 n 2 | n +--R x log(a x ) \|log(a x ) +--R Type: Expression Integer +--E 401 + +--S 402 of 500 +r0080:= 8/3*2^(1/2)*%pi^(1/2)*(a*x^n)^(2/n)*erf(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))/n^(5/2)/x^2-2/3/n/x^2/log(a*x^n)^(3/2)+8/3/n^2/x^2/log(a*x^n)^(1/2) +--R +--R +--R (229) +--R 2 +---------+ +--R - +---------+ +-+ | n +--R +-+ +---+ n n n | n \|2 \|log(a x ) +--R 8\|2 \|%pi log(a x )(a x ) \|log(a x ) erf(----------------) +--R +-+ +--R \|n +--R + +--R +-+ n +-+ +--R 8\|n log(a x ) - 2n\|n +--R / +--R +---------+ +--R 2 2 +-+ n | n +--R 3n x \|n log(a x )\|log(a x ) +--R Type: Expression Integer +--E 402 + +--S 403 of 500 +a0080:= integrate(t0080,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 403 + +--S 404 of 500 +--m0080:= a0080-r0080 +--E 404 + +--S 405 of 500 +--d0080:= D(m0080,x) +--E 405 + +--S 406 of 500 +t0081:= x^m/log(a*x^n)^(5/2) +--R +--R +--R m +--R x +--R (230) ---------------------- +--R +---------+ +--R n 2 | n +--R log(a x ) \|log(a x ) +--R Type: Expression Integer +--E 406 + +--S 407 of 500 +r0081:= 4/3*(1+m)^(3/2)*%pi^(1/2)*x^(1+m)*erfi((1+m)^(1/2)*log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^((1+m)/n))/n^(5/2)-2/3*x^(1+m)/n/log(a*x^n)^(3/2)-4/3*(1+m)*x^(1+m)/n^2/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 407 + +--S 408 of 500 +a0081:= integrate(t0081,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 408 + +--S 409 of 500 +--m0081:= a0081-r0081 +--E 409 + +--S 410 of 500 +--d0081:= D(m0081,x) +--E 410 + +--S 411 of 500 +t0082:= log(a*x)^p +--R +--R +--R p +--R (231) log(a x) +--R Type: Expression Integer +--E 411 + +--S 412 of 500 +r0082:= Gamma(p+1,-log(a*x))*log(a*x)^p/((-log(a*x))^p)/a +--R +--R +--R p _ +--R log(a x) | (p + 1,- log(a x)) +--R (232) ----------------------------- +--R p +--R a (- log(a x)) +--R Type: Expression Integer +--E 412 + +--S 413 of 500 +a0082:= integrate(t0082,x) +--R +--R +--R x +--R ++ p +--R (233) | log(%D a) d%D +--R ++ +--R Type: Union(Expression Integer,...) +--E 413 + +--S 414 of 500 +--m0082:= a0082-r0082 +--E 414 + +--S 415 of 500 +--d0082:= D(m0082,x) +--E 415 + +--S 416 of 500 +t0083:= x*log(a*x)^p +--R +--R +--R p +--R (234) x log(a x) +--R Type: Expression Integer +--E 416 + +--S 417 of 500 +r0083:= 2^(-1-p)*Gamma(p+1,-2*log(a*x))*log(a*x)^p/((-log(a*x))^p)/a^2 +--R +--R +--R - p - 1 p _ +--R 2 log(a x) | (p + 1,- 2log(a x)) +--R (235) -------------------------------------- +--R 2 p +--R a (- log(a x)) +--R Type: Expression Integer +--E 417 + +--S 418 of 500 +a0083:= integrate(t0083,x) +--R +--R +--R x +--R ++ p +--R (236) | %D log(%D a) d%D +--R ++ +--R Type: Union(Expression Integer,...) +--E 418 + +--S 419 of 500 +--m0083:= a0083-r0083 +--E 419 + +--S 420 of 500 +--d0083:= D(m0083,x) +--E 420 + +--S 421 of 500 +t0084:= x^2*log(a*x)^p +--R +--R +--R 2 p +--R (237) x log(a x) +--R Type: Expression Integer +--E 421 + +--S 422 of 500 +r0084:= 3^(-1-p)*Gamma(p+1,-3*log(a*x))*log(a*x)^p/((-log(a*x))^p)/a^3 +--R +--R +--R - p - 1 p _ +--R 3 log(a x) | (p + 1,- 3log(a x)) +--R (238) -------------------------------------- +--R 3 p +--R a (- log(a x)) +--R Type: Expression Integer +--E 422 + +--S 423 of 500 +a0084:= integrate(t0084,x) +--R +--R +--R x +--R ++ 2 p +--R (239) | %D log(%D a) d%D +--R ++ +--R Type: Union(Expression Integer,...) +--E 423 + +--S 424 of 500 +--m0084:= a0084-r0084 +--E 424 + +--S 425 of 500 +--d0084:= D(m0084,x) +--E 425 + +--S 426 of 500 +t0085:= x^3*log(a*x)^p +--R +--R +--R 3 p +--R (240) x log(a x) +--R Type: Expression Integer +--E 426 + +--S 427 of 500 +r0085:= 4^(-1-p)*Gamma(p+1,-4*log(a*x))*log(a*x)^p/((-log(a*x))^p)/a^4 +--R +--R +--R - p - 1 p _ +--R 4 log(a x) | (p + 1,- 4log(a x)) +--R (241) -------------------------------------- +--R 4 p +--R a (- log(a x)) +--R Type: Expression Integer +--E 427 + +--S 428 of 500 +a0085:= integrate(t0085,x) +--R +--R +--R x +--R ++ 3 p +--R (242) | %D log(%D a) d%D +--R ++ +--R Type: Union(Expression Integer,...) +--E 428 + +--S 429 of 500 +--m0085:= a0085-r0085 +--E 429 + +--S 430 of 500 +--d0085:= D(m0085,x) +--E 430 + +--S 431 of 500 +t0086:= log(a*x)^p/x^2 +--R +--R +--R p +--R log(a x) +--R (243) --------- +--R 2 +--R x +--R Type: Expression Integer +--E 431 + +--S 432 of 500 +r0086:= -a*Gamma(p+1,log(a*x)) +--R +--R +--R _ +--R (244) - a| (p + 1,log(a x)) +--R Type: Expression Integer +--E 432 + +--S 433 of 500 +a0086:= integrate(t0086,x) +--R +--R +--R x p +--R ++ log(%D a) +--R (245) | ---------- d%D +--R ++ 2 +--R %D +--R Type: Union(Expression Integer,...) +--E 433 + +--S 434 of 500 +--m0086:= a0086-r0086 +--E 434 + +--S 435 of 500 +--d0086:= D(m0086,x) +--E 435 + +--S 436 of 500 +t0087:= log(a*x)^p/x^3 +--R +--R +--R p +--R log(a x) +--R (246) --------- +--R 3 +--R x +--R Type: Expression Integer +--E 436 + +--S 437 of 500 +r0087:= -2^(-1-p)*a^2*Gamma(p+1,2*log(a*x)) +--R +--R +--R 2 - p - 1 _ +--R (247) - a 2 | (p + 1,2log(a x)) +--R Type: Expression Integer +--E 437 + +--S 438 of 500 +a0087:= integrate(t0087,x) +--R +--R +--R x p +--R ++ log(%D a) +--R (248) | ---------- d%D +--R ++ 3 +--R %D +--R Type: Union(Expression Integer,...) +--E 438 + +--S 439 of 500 +--m0087:= a0087-r0087 +--E 439 + +--S 440 of 500 +--d0087:= D(m0087,x) +--E 440 + +--S 441 of 500 +t0088:= x^m*log(a*x)^p +--R +--R +--R m p +--R (249) x log(a x) +--R Type: Expression Integer +--E 441 + +--S 442 of 500 +r0088:= x^m/a*(a*x)^(-m)*Gamma(p+1,-(1+m)*log(a*x))*log(a*x)^p*(-(1+m)*log(a*x))^(-p)/(1+m) +--R +--R +--R m - m - p p _ +--R x (a x) ((- m - 1)log(a x)) log(a x) | (p + 1,(- m - 1)log(a x)) +--R (250) -------------------------------------------------------------------- +--R a m + a +--R Type: Expression Integer +--E 442 + +--S 443 of 500 +a0088:= integrate(t0088,x) +--R +--R +--R x +--R ++ m p +--R (251) | %D log(%D a) d%D +--R ++ +--R Type: Union(Expression Integer,...) +--E 443 + +--S 444 of 500 +--m0088:= a0088-r0088 +--E 444 + +--S 445 of 500 +--d0088:= D(m0088,x) +--E 445 + +--S 446 of 500 +t0089:= log(a*x^n)^p +--R +--R +--R n p +--R (252) log(a x ) +--R Type: Expression Integer +--E 446 + +--S 447 of 500 +r0089:= x*Gamma(p+1,-log(a*x^n)/n)*log(a*x^n)^p/((a*x^n)^(1/n))/((-log(a*x^n)/n)^p) +--R +--R +--R n +--R n p _ log(a x ) +--R x log(a x ) | (p + 1,- ---------) +--R n +--R (253) --------------------------------- +--R 1 +--R - n p +--R n n log(a x ) +--R (a x ) (- ---------) +--R n +--R Type: Expression Integer +--E 447 + +--S 448 of 500 +a0089:= integrate(t0089,x) +--R +--R +--R x +--R ++ n p +--R (254) | log(a %D ) d%D +--R ++ +--R Type: Union(Expression Integer,...) +--E 448 + +--S 449 of 500 +--m0089:= a0089-r0089 +--E 449 + +--S 450 of 500 +--d0089:= D(m0089,x) +--E 450 + +--S 451 of 500 +t0090:= x*log(a*x^n)^p +--R +--R +--R n p +--R (255) x log(a x ) +--R Type: Expression Integer +--E 451 + +--S 452 of 500 +r0090:= 2^(-1-p)*x^2*Gamma(p+1,-2*log(a*x^n)/n)*log(a*x^n)^p*(a*x^n)^(-2/n)*(-log(a*x^n)/n)^(-p) +--R +--R +--R 2 +--R - - n - p n +--R 2 - p - 1 n n log(a x ) n p _ 2log(a x ) +--R (256) x 2 (a x ) (- ---------) log(a x ) | (p + 1,- ----------) +--R n n +--R Type: Expression Integer +--E 452 + +--S 453 of 500 +a0090:= integrate(t0090,x) +--R +--R +--R x +--R ++ n p +--R (257) | %D log(a %D ) d%D +--R ++ +--R Type: Union(Expression Integer,...) +--E 453 + +--S 454 of 500 +--m0090:= a0090-r0090 +--E 454 + +--S 455 of 500 +--d0090:= D(m0090,x) +--E 455 + +--S 456 of 500 +t0091:= x^2*log(a*x^n)^p +--R +--R +--R 2 n p +--R (258) x log(a x ) +--R Type: Expression Integer +--E 456 + +--S 457 of 500 +r0091:= 3^(-1-p)*x^3*Gamma(p+1,-3*log(a*x^n)/n)*log(a*x^n)^p*(a*x^n)^(-3/n)*(-log(a*x^n)/n)^(-p) +--R +--R +--R 3 +--R - - n - p n +--R 3 - p - 1 n n log(a x ) n p _ 3log(a x ) +--R (259) x 3 (a x ) (- ---------) log(a x ) | (p + 1,- ----------) +--R n n +--R Type: Expression Integer +--E 457 + +--S 458 of 500 +a0091:= integrate(t0091,x) +--R +--R +--R x +--R ++ 2 n p +--R (260) | %D log(a %D ) d%D +--R ++ +--R Type: Union(Expression Integer,...) +--E 458 + +--S 459 of 500 +--m0091:= a0091-r0091 +--E 459 + +--S 460 of 500 +--d0091:= D(m0091,x) +--E 460 + +--S 461 of 500 +t0092:= x^3*log(a*x^n)^p +--R +--R +--R 3 n p +--R (261) x log(a x ) +--R Type: Expression Integer +--E 461 + +--S 462 of 500 +r0092:= 2^(-2*p-2)*x^4*Gamma(p+1,-4*log(a*x^n)/n)*log(a*x^n)^p*(a*x^n)^(-4/n)*(-log(a*x^n)/n)^(-p) +--R +--R +--R 4 +--R - - n - p n +--R 4 - 2p - 2 n n log(a x ) n p _ 4log(a x ) +--R (262) x 2 (a x ) (- ---------) log(a x ) | (p + 1,- ----------) +--R n n +--R Type: Expression Integer +--E 462 + +--S 463 of 500 +a0092:= integrate(t0092,x) +--R +--R +--R x +--R ++ 3 n p +--R (263) | %D log(a %D ) d%D +--R ++ +--R Type: Union(Expression Integer,...) +--E 463 + +--S 464 of 500 +--m0092:= a0092-r0092 +--E 464 + +--S 465 of 500 +--d0092:= D(m0092,x) +--E 465 + +--S 466 of 500 +t0093:= log(a*x^n)^p/x^2 +--R +--R +--R n p +--R log(a x ) +--R (264) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 466 + +--S 467 of 500 +r0093:= -(a*x^n)^(1/n)*Gamma(p+1,log(a*x^n)/n)*log(a*x^n)^p/((log(a*x^n)/n)^p)/x +--R +--R +--R 1 +--R - n +--R n n n p _ log(a x ) +--R (a x ) log(a x ) | (p + 1,---------) +--R n +--R (265) - ------------------------------------ +--R n p +--R log(a x ) +--R x (---------) +--R n +--R Type: Expression Integer +--E 467 + +--S 468 of 500 +a0093:= integrate(t0093,x) +--R +--R +--R x n p +--R ++ log(a %D ) +--R (266) | ----------- d%D +--R ++ 2 +--R %D +--R Type: Union(Expression Integer,...) +--E 468 + +--S 469 of 500 +--m0093:= a0093-r0093 +--E 469 + +--S 470 of 500 +--d0093:= D(m0093,x) +--E 470 + +--S 471 of 500 +t0094:= log(a*x^n)^p/x^3 +--R +--R +--R n p +--R log(a x ) +--R (267) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 471 + +--S 472 of 500 +r0094:= -2^(-1-p)*(a*x^n)^(2/n)*Gamma(p+1,2*log(a*x^n)/n)*log(a*x^n)^p/((log(a*x^n)/n)^p)/x^2 +--R +--R +--R 2 +--R - n +--R - p - 1 n n n p _ 2log(a x ) +--R 2 (a x ) log(a x ) | (p + 1,----------) +--R n +--R (268) - --------------------------------------------- +--R n p +--R 2 log(a x ) +--R x (---------) +--R n +--R Type: Expression Integer +--E 472 + +--S 473 of 500 +a0094:= integrate(t0094,x) +--R +--R +--R x n p +--R ++ log(a %D ) +--R (269) | ----------- d%D +--R ++ 3 +--R %D +--R Type: Union(Expression Integer,...) +--E 473 + +--S 474 of 500 +--m0094:= a0094-r0094 +--E 474 + +--S 475 of 500 +--d0094:= D(m0094,x) +--E 475 + +--S 476 of 500 +t0095:= x^m*log(a*x^n)^p +--R +--R +--R m n p +--R (270) x log(a x ) +--R Type: Expression Integer +--E 476 + +--S 477 of 500 +r0095:= x^(1+m)*Gamma(p+1,-(1+m)*log(a*x^n)/n)*log(a*x^n)^p*(a*x^n)^(-(1+m)/n)*(-(1+m)*log(a*x^n)/n)^(-p)/(1+m) +--R +--R +--R (271) +--R - m - 1 +--R ------- n - p +--R m + 1 n n (- m - 1)log(a x ) n p +--R x (a x ) (------------------) log(a x ) +--R n +--R * +--R n +--R _ (- m - 1)log(a x ) +--R | (p + 1,------------------) +--R n +--R / +--R m + 1 +--R Type: Expression Integer +--E 477 + +--S 478 of 500 +a0095:= integrate(t0095,x) +--R +--R +--R x +--R ++ m n p +--R (272) | %D log(a %D ) d%D +--R ++ +--R Type: Union(Expression Integer,...) +--E 478 + +--S 479 of 500 +--m0095:= a0095-r0095 +--E 479 + +--S 480 of 500 +--d0095:= D(m0095,x) +--E 480 + +--S 481 of 500 +t0096:= (a+b*log(c*x^n))^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R (273) b log(c x ) + 3a b log(c x ) + 3a b log(c x ) + a +--R Type: Expression Integer +--E 481 + +--S 482 of 500 +r0096:= 6*a*b^2*n^2*x-6*b^3*n^3*x+6*b^3*n^2*x*log(c*x^n)-3*b*n*x*(a+b*log(c*x^n))^2+x*(a+b*log(c*x^n))^3 +--R +--R +--R (274) +--R 3 n 3 3 2 n 2 +--R b x log(c x ) + (- 3b n + 3a b )x log(c x ) +--R + +--R 3 2 2 2 n 3 3 2 2 2 3 +--R (6b n - 6a b n + 3a b)x log(c x ) + (- 6b n + 6a b n - 3a b n + a )x +--R Type: Expression Integer +--E 482 + +--S 483 of 500 +a0096:= integrate(t0096,x) +--R +--R +--R (275) +--R 3 3 3 3 2 3 3 2 2 2 +--R b n x log(x) + (3b n x log(c) + (- 3b n + 3a b n )x)log(x) +--R + +--R 3 2 3 2 2 +--R 3b n x log(c) + (- 6b n + 6a b n)x log(c) +--R + +--R 3 3 2 2 2 +--R (6b n - 6a b n + 3a b n)x +--R * +--R log(x) +--R + +--R 3 3 3 2 2 3 2 2 2 +--R b x log(c) + (- 3b n + 3a b )x log(c) + (6b n - 6a b n + 3a b)x log(c) +--R + +--R 3 3 2 2 2 3 +--R (- 6b n + 6a b n - 3a b n + a )x +--R Type: Union(Expression Integer,...) +--E 483 + +--S 484 of 500 +m0096:= a0096-r0096 +--R +--R +--R (276) +--R 3 n 3 3 2 n 2 +--R - b x log(c x ) + (3b n - 3a b )x log(c x ) +--R + +--R 3 2 2 2 n 3 3 3 +--R (- 6b n + 6a b n - 3a b)x log(c x ) + b n x log(x) +--R + +--R 3 2 3 3 2 2 2 +--R (3b n x log(c) + (- 3b n + 3a b n )x)log(x) +--R + +--R 3 2 3 2 2 +--R 3b n x log(c) + (- 6b n + 6a b n)x log(c) +--R + +--R 3 3 2 2 2 +--R (6b n - 6a b n + 3a b n)x +--R * +--R log(x) +--R + +--R 3 3 3 2 2 3 2 2 2 +--R b x log(c) + (- 3b n + 3a b )x log(c) + (6b n - 6a b n + 3a b)x log(c) +--R Type: Expression Integer +--E 484 + +--S 485 of 500 +d0096:= D(m0096,x) +--R +--R +--R (277) +--R 3 n n 3 3 2 n 3 n - 1 n 2 +--R - b x log(c x ) + ((3b n - 3a b )x - 3b n x x )log(c x ) +--R + +--R 3 2 2 2 n 3 2 2 n - 1 n +--R ((- 6b n + 6a b n - 3a b)x + (6b n - 6a b n)x x )log(c x ) +--R + +--R 3 3 3 3 2 2 2 2 +--R b n log(x) + (3b n log(c) + 3a b n )log(x) +--R + +--R 3 2 2 2 3 3 +--R (3b n log(c) + 6a b n log(c) + 3a b n)log(x) + b log(c) +--R + +--R 2 2 2 3 3 2 2 2 +--R 3a b log(c) + 3a b log(c) + 6b n - 6a b n + 3a b n +--R * +--R n +--R x +--R + +--R 3 3 2 2 2 n - 1 +--R (- 6b n + 6a b n - 3a b n)x x +--R / +--R n +--R x +--R Type: Expression Integer +--E 485 + +--S 486 of 500 +t0097:= 1/(a+b*log(c*x^n)) +--R +--R +--R 1 +--R (278) --------------- +--R n +--R b log(c x ) + a +--R Type: Expression Integer +--E 486 + +--S 487 of 500 +r0097:= x*Ei((a+b*log(c*x^n))/b/n)/b*exp(-a/b/n)/n*(c*x^n)^(-1/n) +--R +--R +--R a 1 +--R - --- - - n +--R b n n n b log(c x ) + a +--R x %e (c x ) Ei(---------------) +--R b n +--R (279) ------------------------------------- +--R b n +--R Type: Expression Integer +--E 487 + +--S 488 of 500 +a0097:= integrate(t0097,x) +--R +--R +--R x +--R ++ 1 +--R (280) | ---------------- d%D +--R ++ n +--R b log(c %D ) + a +--R Type: Union(Expression Integer,...) +--E 488 + +--S 489 of 500 +--m0097:= a0097-r0097 +--E 489 + +--S 490 of 500 +--d0097:= D(m0097,x) +--E 490 + +--S 491 of 500 +t0098:= 1/(a+b*log(c*x^n))^2 +--R +--R +--R 1 +--R (281) ---------------------------------- +--R 2 n 2 n 2 +--R b log(c x ) + 2a b log(c x ) + a +--R Type: Expression Integer +--E 491 + +--S 492 of 500 +r0098:= x*Ei((a+b*log(c*x^n))/b/n)/(exp(1)^(a/b/n))/((c*x^n)^(1/n))/b^2/n^2-x/b/n/(a+b*log(c*x^n)) +--R +--R +--R a 1 +--R n --- - +--R n b log(c x ) + a b n n n +--R (b x log(c x ) + a x)Ei(---------------) - b n x %e (c x ) +--R b n +--R (282) ------------------------------------------------------------- +--R a a 1 +--R --- --- - +--R 3 2 b n n 2 2 b n n n +--R (b n %e log(c x ) + a b n %e )(c x ) +--R Type: Expression Integer +--E 492 + +--S 493 of 500 +a0098:= integrate(t0098,x) +--R +--R +--R x +--R ++ 1 +--R (283) | ------------------------------------ d%D +--R ++ 2 n 2 n 2 +--R b log(c %D ) + 2a b log(c %D ) + a +--R Type: Union(Expression Integer,...) +--E 493 + +--S 494 of 500 +--m0098:= a0098-r0098 +--E 494 + +--S 495 of 500 +--d0098:= D(m0098,x) +--E 495 + +--S 496 of 500 +t0099:= 1/(a+b*log(c*x^n))^3 +--R +--R +--R 1 +--R (284) ---------------------------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b log(c x ) + 3a b log(c x ) + 3a b log(c x ) + a +--R Type: Expression Integer +--E 496 + +--S 497 of 500 +r0099:= 1/2*x*Ei((a+b*log(c*x^n))/b/n)/(exp(1)^(a/b/n))/((c*x^n)^(1/n))/b^3/n^3-1/2*x/b/n/(a+b*log(c*x^n))^2-1/2*x/b^2/n^2/(a+b*log(c*x^n)) +--R +--R +--R (285) +--R n +--R 2 n 2 n 2 b log(c x ) + a +--R (b x log(c x ) + 2a b x log(c x ) + a x)Ei(---------------) +--R b n +--R + +--R a a 1 +--R --- --- - +--R 2 b n n 2 2 b n n n +--R (- b n x %e log(c x ) + (- b n - a b n)x %e )(c x ) +--R / +--R a a a 1 +--R --- --- --- - +--R 5 3 b n n 2 4 3 b n n 2 3 3 b n n n +--R (2b n %e log(c x ) + 4a b n %e log(c x ) + 2a b n %e )(c x ) +--R Type: Expression Integer +--E 497 + +--S 498 of 500 +a0099:= integrate(t0099,x) +--R +--R +--R x +--R ++ 1 +--R (286) | ------------------------------------------------------- d%D +--R ++ 3 n 3 2 n 2 2 n 3 +--R b log(c %D ) + 3a b log(c %D ) + 3a b log(c %D ) + a +--R Type: Union(Expression Integer,...) +--E 498 + +--S 499 of 500 +--m0099:= a0099-r0099 +--E 499 + +--S 500 of 500 +--d0099:= D(m0099,x) +--E 500 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}