diff --git a/changelog b/changelog index 964e533..8221e2a 100644 --- a/changelog +++ b/changelog @@ -1,4 +1,6 @@ -20100629 rhx src/axiom-website/patches.html 20100629.01.tpd.patch +20100629 tpd src/axiom-website/patches.html 20100629.02.tpd.patch +20100629 tpd src/input/richrational.input add documentation +20100629 tpd src/axiom-website/patches.html 20100629.01.tpd.patch 20100629 tpd src/input/richhyper100-199,input rule-based hyper integration 20100623 rhx src/axiom-website/patches.html 20100623.01.rhx.patch 20100623 rhx books/axbook.tgz rewrite section 8.3.2 for current output diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index c6e78ae..4decf03 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2940,6 +2940,8 @@ src/input/richtrig000-099, richtrig100-199 remove useless derivatives
books/bookvol0 rewrite section 8.3.2 for current output
20100629.01.tpd.patch src/input/richhyper100-199,input rule-based hyper integration
+20100629.02.tpd.patch +src/input/richrational.input add documentation
diff --git a/src/input/richrational.input.pamphlet b/src/input/richrational.input.pamphlet index 6442910..c52bf0b 100644 --- a/src/input/richrational.input.pamphlet +++ b/src/input/richrational.input.pamphlet @@ -9,6 +9,298 @@ \eject \tableofcontents \eject +\section{Summary} +\begin{verbatim} +========================================================================== +RATIONAL +========================================================================== +10 exact matches +98 differ by a constant +136 differ by a variable +all integrations succeeded. +axiom is visibly shorter in 57 cases, possibly others + +integrand rich axiom difference derivative difference derivative +0000 ok ok constant 0 +0001 ok ok constant 0 +0002 ok ok constant 0 +0003 ok ok constant 0 +0004 ok ok constant 0 +0005 ok ok constant 0 +0006 ok exact 0 0 +0007 ok exact 0 0 +0008 ok ok constant 0 +0009 ok ok constant 0 +0010 ok ok constant 0 +0011 ok ok constant 0 +0012 ok ok constant 0 +0013 ok ok constant 0 +0014 ok ok constant 0 +0015 ok ok constant 0 +0016 ok ok constant 0 +0017 ok ok constant 0 +0018 ok ok constant 0 +0019 ok exact 0 0 +0020 ok ok constant 0 +0021 ok ok constant 0 +0022 ok ok constant 0 +0023 ok ok constant 0 (axiom is shorter) +0024 ok ok constant 0 (axiom is shorter) +0025 ok ok constant 0 (axiom is shorter) +0026 ok ok var 0 +0027 ok ok constant 0 +0028 ok ok constant 0 +0029 ok ok constant 0 (axiom is shorter) +0030 ok ok constant 0 (axiom is shorter) +0031 ok ok constant 0 (axiom is shorter) +0032 ok ok constant 0 (axiom is shorter) +0033 ok ok constant 0 (axiom is shorter) +0034 ok ok constant 0 +0035 ok ok constant 0 +0036 ok ok constant 0 +0037 ok ok constant 0 (axiom is shorter) +0038 ok ok constant 0 (axiom is shorter) +0039 ok ok constant 0 (axiom is shorter) +0040 ok ok constant 0 (axiom is shorter) +0041 ok ok constant 0 (axiom is shorter) +0042 ok ok constant 0 (axiom is shorter) +0043 ok ok constant 0 (axiom is shorter) +0044 ok ok constant 0 (axiom is shorter) +0045 ok ok constant 0 (axiom is shorter) +0046 ok ok constant 0 (axiom is shorter) +0047 ok ok constant 0 (axiom is shorter) +0048 ok ok constant 0 (axiom is shorter) +0049 ok ok constant 0 (axiom is shorter) +0050 ok ok constant 0 (axiom is shorter) +0051 ok ok constant 0 (axiom is shorter) +0052 ok ok constant 0 (axiom is shorter) +0053 ok ok constant 0 (axiom is shorter) +0054 ok ok constant 0 (axiom is shorter) +0055 ok ok constant 0 (axiom is shorter) +0056 ok ok constant 0 (axiom is shorter) +0057 ok ok constant 0 (axiom is shorter) +0058 ok ok constant 0 (axiom is shorter) +0059 ok ok constant 0 (axiom is shorter) +0060 ok ok constant 0 (axiom is shorter) +0061 ok ok constant 0 +0062 ok exact 0 0 +0063 ok exact 0 0 +0064 ok ok constant 0 +0065 ok ok constant 0 +0066 ok ok constant 0 +0067 ok ok constant 0 +0068 ok ok constant 0 +0069 ok ok constant 0 +0070 ok ok constant 0 +0071 ok exact 0 0 +0072 ok exact 0 0 +0073 ok ok constant 0 +0074 ok ok constant 0 +0075 ok ok constant 0 +0076 ok ok constant 0 +0077 ok ok constant 0 (axiom is shorter) +0078 ok ok var 0 +0079 ok ok constant 0 (axiom is shorter) +0080 ok ok constant 0 (axiom is shorter) +0081 ok ok constant 0 (axiom is shorter) +0082 ok ok constant 0 (axiom is shorter) +0083 ok ok constant 0 (axiom is shorter) +0084 ok ok constant 0 (axiom is shorter) +0085 ok ok constant 0 (axiom is shorter) +0086 ok ok constant 0 (axiom is shorter) +0087 ok ok constant 0 (axiom is shorter) +0088 ok ok constant 0 (axiom is shorter) +0089 ok ok constant 0 (axiom is shorter) +0090 ok ok constant 0 (axiom is shorter) +0091 ok ok var 0 (axiom 2nd sol. is shorter) +0092 ok ok var 0 (two solutions) +0093 ok ok var 0 (two solutions) +0094 ok ok var 0 (two solutions) +0095 ok ok var 0 (two solutions) +0096 ok ok var 0 (two solutions) +0097 ok ok var 0 (two solutions) +0098 ok ok var 0 (two solutions) +0099 ok ok var 0 (two solutions) + +0100 ok ok var 0 (oddly differ by sign in log) +0101 ok ok var 0 (log vs atan expansion) +0102 ok ok var 0 (log vs atan expansion) +0103 ok ok var 0 (log vs atan expansion) +0104 ok ok var 0 (log vs atan expansion) +0105 ok ok var 0 +0106 ok ok var 0 (two solutions) +0107 ok ok var 0 (two solutions) +0108 ok ok var 0 (two solutions) +0109 ok ok var 0 (two solutions) +0110 ok ok var 0 (axiom 2nd sol. is shorter) +0111 ok ok constant 0 (axiom is shorter) +0112 ok ok constant 0 (axiom is shorter) +0113 ok ok constant 0 (axiom is shorter) +0114 ok ok constant 0 (axiom is shorter) +0115 ok ok var 0 +0116 ok ok var 0 +0117 ok ok var 0 +0118 ok ok var 0 +0119 ok ok var 0 +0120 ok ok var 0 +0121 ok ok var 0 +0122 ok ok var 0 +0123 ok ok constant 0 (axiom is shorter) +0124 ok ok constant 0 (axiom is shorter) +0125 ok ok constant 0 (axiom is shorter) +0126 ok ok var 0 +0127 ok ok var 0 +0128 ok ok var 0 +0129 ok ok var 0 +0130 ok ok var 0 +0131 ok ok var 0 +0132 ok ok var 0 +0133 ok ok var 0 +0134 ok ok var 0 +0135 ok ok var 0 +0136 ok ok var 0 +0137 ok ok var 0 +0138 ok ok var 0 +0139 ok ok var 0 +0140 ok ok var 0 +0141 ok ok var 0 +0142 ok ok var 0 +0143 ok ok var 0 +0144 ok ok var 0 +0145 ok ok var 0 +0146 ok ok var 0 +0147 ok ok var 0 +0148 ok ok constant 0 (axiom is shorter) +0149 ok ok constant 0 (axiom is shorter) +0150 ok ok var 0 (axiom is shorter) +0151 ok ok var 0 +0152 ok ok var 0 +0153 ok ok var 0 +0154 ok ok var 0 +0155 ok ok var 0 +0156 ok ok var 0 +0157 ok ok var 0 +0158 ok ok var 0 +0159 ok ok var 0 +0160 ok ok var 0 +0161 ok ok var 0 +0162 ok ok constant 0 +0163 ok ok constant 0 +0164 ok ok constant 0 (axiom is shorter) +0165 ok ok var var (axiom differentiates ok) +0166 ok ok var 0 +0167 ok ok var 0 +0168 ok ok var 0 +0169 ok ok var 0 +0170 ok ok var 0 +0171 ok ok var 0 +0172 ok ok var 0 +0173 ok ok var 0 +0174 ok ok var 0 +0175 ok ok var 0 +0176 ok ok var 0 +0177 ok ok var 0 +0178 ok ok var 0 +0179 ok ok var 0 +0180 ok ok var 0 +0181 ok ok var 0 +0182 ok ok var 0 +0183 ok ok var 0 +0184 ok ok constant 0 +0185 ok ok constant 0 +0186 ok ok var var (axiom differentiates ok) +0187 ok ok var 0 +0188 ok ok var 0 (two answers) +0189 ok ok var 0 +0190 ok ok var 0 (two answers) +0191 ok ok var 0 (two answers) +0192 ok ok var 0 +0193 ok ok var 0 +0194 ok ok var 0 (two answers) +0195 ok ok var 0 (two answers) +0196 ok ok var 0 (two answers) +0197 ok ok var 0 (two answers) +0198 ok ok var 0 (two answers) +0199 ok ok var 0 (two answers) + +0200 ok ok var 0 (two answers) +0201 ok ok var 0 (two answers) +0202 ok ok var 0 (two answers) +0203 ok ok var 0 (two answers) +0204 ok ok var 0 (two answers) +0205 ok ok var 0 (two answers) +0206 ok ok var 0 (two answers) +0207 ok ok var 0 (two answers) +0208 ok ok var 0 (two answers) +0209 ok ok var 0 (two answers) +0210 ok ok var 0 (two answers) +0211 ok ok var 0 (two answers) +0212 ok ok var 0 (two answers) +0213 ok ok var 0 (two answers ) +0214 ok ok var 0 +0215 ok ok var 0 (two answers) +0216 ok ok var 0 (two answers) +0217 ok ok var 0 (two answers) +0218 ok ok var 0 (two answers) +0219 ok ok var 0 (two answers) +0220 ok ok var 0 (two answers) +0221 ok ok var 0 (two answers) +0222 ok ok var 0 (two answers) +0223 ok ok var 0 (two answers) +0224 ok ok var 0 (two answers) +0225 ok ok constant 0 +0226 ok ok var 0 +0227 ok ok var 0 +0228 ok ok constant 0 +0229 ok ok var 0 +0230 ok ok var 0 +0231 ok ok var 0 +0232 ok ok var 0 +0233 ok ok var 0 +0234 ok ok var 0 +0235 ok ok var 0 +0236 ok ok var 0 (two answers) +0237 ok ok var 0 +0238 ok ok var 0 +0239 ok ok var 0 +0240 ok ok var bug? (rich differentiates ok) +0241 ok ok var bug? (NEITHER IS OK) +0242 ok ok var 0 +0243 ok ok var 0 +0244 ok ok var E(C(F(I))) +0245 ok ok var E(C(F(I))) +0246 ok ok var bug? (NEITHER IS OK) +0247 ok ok var bug? (rich differentiates ok) +0248 ok ok var 0 +0249 ok ok 0 0 +0250 ok ok 0 0 +0251 ok ok var 0 +0252 ok ok var 0 +0253 ok ok var 0 +0254 ok ok var 0 +0255 ok ok var 0 +0256 ok ok var 0 +0257 ok ok var 0 +0258 ok ok var 0 +0259 ok ok var 0 +0260 ok ok var 0 +0261 ok ok var bug? (NEITHER IS OK) +0262 ok ok var 0 +0263 ok ok var 0 +0264 ok ok var 0 +0265 ok ok var 0 +0266 ok ok var 0 +0267 ok ok var 0 +0268 ok ok var 0 +0269 ok ok var 0 +0270 ok ok var 0 +0271 ok ok var 0 +0272 ok ok var 0 +0273 ok exact 0 0 +0274 ok exact 0 0 +0275 ok exact 0 0 +0276 ok ok var 0 +\end{verbatim} \begin{chunk}{*} )set break resume )sys rm -f richrational.output @@ -17570,14 +17862,10 @@ m0152:=a0152-r0152 --E 792 --S 793 of 1483 -d0152:=D(m0152,x) +d0152:=normalize(D(m0152,x)) --R --R ---R 2 4+-+2 2 +-+ 4+-+2 4+-+2 +-+ ---R ((- d x - c)\|a + d x \|a )\|b + c \|a \|b ---R (793) ------------------------------------------------- ---R 4 4+-+2 4+-+2 ---R (b x - a)\|a \|b +--R (793) 0 --R Type: Expression Integer --E 793 @@ -18556,33 +18844,10 @@ m0154:=a0154-r0154 --E 802 --S 803 of 1483 -d0154:=D(m0154,x) +d0154:=normalize(D(m0154,x)) --R --R ---R (803) ---R 4 2 4+-+2 +-+ ---R (- b c x + 2a e x + a c)\|a \|b ---R + ---R 4 2 +-+4+-+2 4 2 ---R (- b e x + 2b c x + a e)\|a \|a + 4a b e x + 4a b c x ---R * ---R 4+-+2 ---R \|b ---R + ---R 4 2 +-+4+-+2 4 2 2 +-+ ---R ((- 4b e x - 4b c x )\|a \|a + a b e x - 2a b c x - a e)\|b ---R + ---R 2 6 2 4 2 4+-+2 ---R (- 2b e x - 2b c x - 2a b e x - 2a b c)\|a ---R + ---R 2 6 2 4 +-+ ---R (2b e x + 3b c x + a b c)\|a ---R / ---R 2 6 2 2 4+-+2 2 6 2 +-+4+-+2 +-+ ---R (4a b x + 4a b x )\|b + (- 4b x - 4a b x )\|a \|a \|b ---R + ---R 3 8 2 4 2 4+-+2 ---R (- 2b x - 4a b x - 2a b)\|a +--R (803) 0 --R Type: Expression Integer --E 803 @@ -18886,14 +19151,10 @@ m0155:=a0155-r0155 --E 807 --S 808 of 1483 -d0155:=D(m0155,x) +d0155:=normalize(D(m0155,x)) --R --R ---R 2 4+-+2 2 +-+ 4+-+2 4+-+2 +-+ ---R ((- x - 1)\|a + x \|a )\|b + \|a \|b ---R (808) ------------------------------------------- ---R 4 4+-+2 4+-+2 ---R (b x - a)\|a \|b +--R (808) 0 --R Type: Expression Integer --E 808 @@ -19729,14 +19990,10 @@ m0156:=a0156-r0156 --E 812 --S 813 of 1483 -d0156:=D(m0156,x) +d0156:=normalize(D(m0156,x)) --R --R ---R 2 4+-+2 2 +-+ 4+-+2 4+-+2 +-+ ---R ((- e x - c)\|a + e x \|a )\|b + c \|a \|b ---R (813) ------------------------------------------------- ---R 4 4+-+2 4+-+2 ---R (b x - a)\|a \|b +--R (813) 0 --R Type: Expression Integer --E 813 @@ -20287,93 +20544,10 @@ m0157:=a0157-r0157 --E 817 --S 818 of 1483 -d0157:=D(m0157,x) +d0157:=normalize(D(m0157,x)) --R --R ---R (818) ---R 3 4 4 4 3 3 5 2 2 6 2 ---R b c d x + 4b c d x + (6b c - 6a c)d x + (4b c - 12a c )d x ---R + ---R 7 3 ---R b c - 7a c ---R * ---R 4+-+2 +-+ ---R \|a \|b ---R + ---R 4 4 2 3 3 3 2 2 4 5 +-+ ---R (3b c d x + 12b c d x + 16b c d x + 8b c d x + b c - 3a c)\|a ---R * ---R 4+-+2 ---R \|a ---R + ---R 4 4 2 3 3 3 2 2 4 5 ---R - 12a b c d x - 48a b c d x - 76a b c d x - 56a b c d x - 16a b c ---R * ---R 4+-+2 ---R \|b ---R + ---R 4 4 2 3 3 3 2 2 4 5 +-+4+-+2 ---R (12b c d x + 48b c d x + 76b c d x + 56b c d x + 16b c )\|a \|a ---R + ---R 4 4 2 3 3 3 2 2 4 5 ---R - 3a b c d x - 12a b c d x - 16a b c d x - 8a b c d x - a b c ---R + ---R 2 ---R 3a c ---R * ---R +-+ ---R \|b ---R + ---R 2 6 6 2 2 5 5 2 3 4 4 2 4 3 3 ---R 6b c d x + 36b c d x + 92b c d x + 128b c d x ---R + ---R 2 5 2 2 2 6 2 2 7 3 ---R (102b c + 6a b c)d x + (44b c + 12a b c )d x + 8b c + 8a b c ---R * ---R 4+-+2 ---R \|a ---R + ---R 2 6 6 2 2 5 5 2 3 4 4 2 4 3 3 2 5 2 2 ---R - 6b c d x - 36b c d x - 93b c d x - 132b c d x - 108b c d x ---R + ---R 2 6 2 7 3 ---R - 48b c d x - 9b c - a b c ---R * ---R +-+ ---R \|a ---R / ---R 2 9 6 2 8 5 2 2 7 4 2 3 6 3 ---R 4a b d x + 24a b c d x + 60a b c d x + 80a b c d x ---R + ---R 2 4 2 5 2 2 5 2 4 2 6 2 2 3 ---R (60a b c + 4a b)d x + (24a b c + 8a b c)d x + (4a b c + 4a b c )d ---R * ---R 4+-+2 ---R \|b ---R + ---R 2 9 6 2 8 5 2 2 7 4 2 3 6 3 ---R - 4b d x - 24b c d x - 60b c d x - 80b c d x ---R + ---R 2 4 5 2 2 5 4 2 6 2 3 ---R (- 60b c - 4a b)d x + (- 24b c - 8a b c)d x + (- 4b c - 4a b c )d ---R * ---R +-+4+-+2 +-+ ---R \|a \|a \|b ---R + ---R 3 11 8 3 10 7 3 2 9 6 3 3 8 5 ---R - 2b d x - 16b c d x - 56b c d x - 112b c d x ---R + ---R 3 4 2 7 4 3 5 2 6 3 ---R (- 140b c - 4a b )d x + (- 112b c - 16a b c)d x ---R + ---R 3 6 2 2 5 2 3 7 2 3 4 ---R (- 56b c - 24a b c )d x + (- 16b c - 16a b c )d x ---R + ---R 3 8 2 4 2 3 ---R (- 2b c - 4a b c - 2a b)d ---R * ---R 4+-+2 ---R \|a +--R (818) 0 --R Type: Expression Integer --E 818 @@ -20781,87 +20955,10 @@ m0158:=a0158-r0158 --E 822 --S 823 of 1483 -d0158:=D(m0158,x) +d0158:=normalize(D(m0158,x)) --R --R ---R (823) ---R 2 4 4 3 3 3 4 2 2 5 ---R - b c d x - 4b c d x + (- 6b c + 2a)d x + (- 4b c + 4a c)d x ---R + ---R 6 2 ---R - b c + 3a c ---R * ---R 4+-+2 +-+ ---R \|a \|b ---R + ---R 4 4 3 3 2 2 2 4 +-+4+-+2 4 4 ---R (- b d x - 4b c d x - 4b c d x + b c + a)\|a \|a + 4a b d x ---R + ---R 3 3 2 2 2 3 4 ---R 16a b c d x + 28a b c d x + 24a b c d x + 8a b c ---R * ---R 4+-+2 ---R \|b ---R + ---R 4 4 3 3 2 2 2 3 4 +-+4+-+2 ---R (- 4b d x - 16b c d x - 28b c d x - 24b c d x - 8b c )\|a \|a ---R + ---R 4 4 3 3 2 2 2 4 2 ---R a b d x + 4a b c d x + 4a b c d x - a b c - a ---R * ---R +-+ ---R \|b ---R + ---R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 ---R - 2b d x - 12b c d x - 32b c d x - 48b c d x ---R + ---R 2 4 2 2 2 5 2 6 2 ---R (- 42b c - 2a b)d x + (- 20b c - 4a b c)d x - 4b c - 4a b c ---R * ---R 4+-+2 ---R \|a ---R + ---R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 ---R 2b d x + 12b c d x + 33b c d x + 52b c d x + 48b c d x ---R + ---R 2 5 2 6 2 ---R 24b c d x + 5b c + a b c ---R * ---R +-+ ---R \|a ---R / ---R 2 8 6 2 7 5 2 2 6 4 2 3 5 3 ---R 4a b d x + 24a b c d x + 60a b c d x + 80a b c d x ---R + ---R 2 4 2 4 2 2 5 2 3 2 6 2 2 2 ---R (60a b c + 4a b)d x + (24a b c + 8a b c)d x + (4a b c + 4a b c )d ---R * ---R 4+-+2 ---R \|b ---R + ---R 2 8 6 2 7 5 2 2 6 4 2 3 5 3 ---R - 4b d x - 24b c d x - 60b c d x - 80b c d x ---R + ---R 2 4 4 2 2 5 3 2 6 2 2 ---R (- 60b c - 4a b)d x + (- 24b c - 8a b c)d x + (- 4b c - 4a b c )d ---R * ---R +-+4+-+2 +-+ ---R \|a \|a \|b ---R + ---R 3 10 8 3 9 7 3 2 8 6 3 3 7 5 ---R - 2b d x - 16b c d x - 56b c d x - 112b c d x ---R + ---R 3 4 2 6 4 3 5 2 5 3 ---R (- 140b c - 4a b )d x + (- 112b c - 16a b c)d x ---R + ---R 3 6 2 2 4 2 3 7 2 3 3 ---R (- 56b c - 24a b c )d x + (- 16b c - 16a b c )d x ---R + ---R 3 8 2 4 2 2 ---R (- 2b c - 4a b c - 2a b)d ---R * ---R 4+-+2 ---R \|a +--R (823) 0 --R Type: Expression Integer --E 823 @@ -21167,60 +21264,10 @@ m0159:=a0159-r0159 --E 827 --S 828 of 1483 -d0159:=D(m0159,x) +d0159:=normalize(D(m0159,x)) --R --R ---R (828) ---R 4 4 2 3 3 3 2 2 4 5 ---R (- 3b c d x - 12b c d x - 18b c d x - 12b c d x - 3b c - a c) ---R * ---R +-+ +-+ ---R \|a \|b ---R + ---R 2 2 2 3 ---R - 2a b c d x - 4a b c d x - 2a b c ---R * ---R 4+-+2 ---R \|b ---R + ---R 2 2 2 3 +-+4+-+2 +-+ ---R (2b c d x + 4b c d x + 2b c )\|a \|a \|b ---R + ---R 2 4 4 2 2 3 3 2 3 2 2 2 4 2 5 4+-+2 ---R (3b c d x + 12b c d x + 18b c d x + 12b c d x + 3b c + a b c)\|a ---R / ---R 2 7 6 2 6 5 2 2 5 4 2 3 4 3 ---R 4a b d x + 24a b c d x + 60a b c d x + 80a b c d x ---R + ---R 2 4 2 3 2 2 5 2 2 2 6 2 2 ---R (60a b c + 4a b)d x + (24a b c + 8a b c)d x + (4a b c + 4a b c )d ---R * ---R 4+-+2 ---R \|b ---R + ---R 2 7 6 2 6 5 2 2 5 4 2 3 4 3 ---R - 4b d x - 24b c d x - 60b c d x - 80b c d x ---R + ---R 2 4 3 2 2 5 2 2 6 2 ---R (- 60b c - 4a b)d x + (- 24b c - 8a b c)d x + (- 4b c - 4a b c )d ---R * ---R +-+4+-+2 +-+ ---R \|a \|a \|b ---R + ---R 3 9 8 3 8 7 3 2 7 6 3 3 6 5 ---R - 2b d x - 16b c d x - 56b c d x - 112b c d x ---R + ---R 3 4 2 5 4 3 5 2 4 3 ---R (- 140b c - 4a b )d x + (- 112b c - 16a b c)d x ---R + ---R 3 6 2 2 3 2 3 7 2 3 2 ---R (- 56b c - 24a b c )d x + (- 16b c - 16a b c )d x ---R + ---R 3 8 2 4 2 ---R (- 2b c - 4a b c - 2a b)d ---R * ---R 4+-+2 ---R \|a +--R (828) 0 --R Type: Expression Integer --E 828 @@ -21357,57 +21404,10 @@ m0160:=a0160-r0160 --E 832 --S 833 of 1483 -d0160:=D(m0160,x) +d0160:=normalize(D(m0160,x)) --R --R ---R (833) ---R 4 4 3 3 2 2 2 3 4 +-+ +-+ ---R (3b d x + 12b c d x + 18b c d x + 12b c d x + 3b c + a)\|a \|b ---R + ---R 2 2 2 ---R 2a b d x + 4a b c d x + 2a b c ---R * ---R 4+-+2 ---R \|b ---R + ---R 2 2 2 +-+4+-+2 +-+ ---R (- 2b d x - 4b c d x - 2b c )\|a \|a \|b ---R + ---R 2 4 4 2 3 3 2 2 2 2 2 3 2 4 4+-+2 ---R (- 3b d x - 12b c d x - 18b c d x - 12b c d x - 3b c - a b)\|a ---R / ---R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 ---R 4a b d x + 24a b c d x + 60a b c d x + 80a b c d x ---R + ---R 2 4 2 2 2 2 5 2 2 6 2 2 ---R (60a b c + 4a b)d x + (24a b c + 8a b c)d x + 4a b c + 4a b c ---R * ---R 4+-+2 ---R \|b ---R + ---R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 ---R - 4b d x - 24b c d x - 60b c d x - 80b c d x ---R + ---R 2 4 2 2 2 5 2 6 2 ---R (- 60b c - 4a b)d x + (- 24b c - 8a b c)d x - 4b c - 4a b c ---R * ---R +-+4+-+2 +-+ ---R \|a \|a \|b ---R + ---R 3 8 8 3 7 7 3 2 6 6 3 3 5 5 ---R - 2b d x - 16b c d x - 56b c d x - 112b c d x ---R + ---R 3 4 2 4 4 3 5 2 3 3 ---R (- 140b c - 4a b )d x + (- 112b c - 16a b c)d x ---R + ---R 3 6 2 2 2 2 3 7 2 3 3 8 ---R (- 56b c - 24a b c )d x + (- 16b c - 16a b c )d x - 2b c ---R + ---R 2 4 2 ---R - 4a b c - 2a b ---R * ---R 4+-+2 ---R \|a +--R (833) 0 --R Type: Expression Integer --E 833 @@ -21829,99 +21829,10 @@ m0161:=a0161-r0161 --E 837 --S 838 of 1483 -d0161:=D(m0161,x) +d0161:=normalize(D(m0161,x)) --R --R ---R (838) ---R 5 4 2 4 3 3 3 2 4 2 ---R - 3b c d x - 12b c d x - 20b c d x - 16b c d x ---R + ---R 5 ---R (- 5b c - a c)d ---R * ---R +-+4+-+2 +-+ ---R \|a \|a \|b ---R + ---R 2 3 5 4 2 4 4 3 2 5 3 2 ---R - 3b c d x - 12b c d x + (- 18b c - 2a b c)d x ---R + ---R 2 6 2 2 2 7 3 ---R (- 12b c - 4a b c )d x + (- 3b c - 3a b c )d ---R * ---R 4+-+2 ---R \|a ---R * ---R 4+-+2 ---R \|b ---R + ---R 2 3 5 4 2 4 4 3 2 5 3 2 ---R 3b c d x + 12b c d x + (18b c + 2a b c)d x ---R + ---R 2 6 2 2 2 7 3 ---R (12b c + 4a b c )d x + (3b c + 3a b c )d ---R * ---R +-+ +-+ ---R \|a \|b ---R + ---R 2 5 4 2 2 4 3 2 3 3 2 2 4 2 ---R 3a b c d x + 12a b c d x + 20a b c d x + 16a b c d x ---R + ---R 2 5 2 ---R (5a b c + a b c)d ---R / ---R 2 4 6 6 2 5 5 5 ---R (4b c + 4a b)d x + (24b c + 24a b c)d x ---R + ---R 2 6 2 4 4 2 7 3 3 3 ---R (60b c + 60a b c )d x + (80b c + 80a b c )d x ---R + ---R 2 8 4 2 2 2 2 9 5 2 ---R (60b c + 64a b c + 4a )d x + (24b c + 32a b c + 8a c)d x ---R + ---R 2 10 6 2 2 ---R 4b c + 8a b c + 4a c ---R * ---R +-+4+-+2 +-+ ---R \|a \|a \|b ---R + ---R 3 4 2 8 8 3 5 2 7 7 ---R (2b c + 2a b )d x + (16b c + 16a b c)d x ---R + ---R 3 6 2 2 6 6 3 7 2 3 5 5 ---R (56b c + 56a b c )d x + (112b c + 112a b c )d x ---R + ---R 3 8 2 4 2 4 4 ---R (140b c + 144a b c + 4a b)d x ---R + ---R 3 9 2 5 2 3 3 ---R (112b c + 128a b c + 16a b c)d x ---R + ---R 3 10 2 6 2 2 2 2 ---R (56b c + 80a b c + 24a b c )d x ---R + ---R 3 11 2 7 2 3 3 12 2 8 2 4 ---R (16b c + 32a b c + 16a b c )d x + 2b c + 6a b c + 6a b c ---R + ---R 3 ---R 2a ---R * ---R 4+-+2 ---R \|a ---R * ---R 4+-+2 ---R \|b ---R + ---R 3 4 2 2 6 6 3 5 2 2 5 5 ---R (- 4a b c - 4a b )d x + (- 24a b c - 24a b c)d x ---R + ---R 3 6 2 2 2 4 4 3 7 2 2 3 3 3 ---R (- 60a b c - 60a b c )d x + (- 80a b c - 80a b c )d x ---R + ---R 3 8 2 2 4 3 2 2 3 9 2 2 5 3 ---R (- 60a b c - 64a b c - 4a b)d x + (- 24a b c - 32a b c - 8a b c)d x ---R + ---R 3 10 2 2 6 3 2 ---R - 4a b c - 8a b c - 4a b c +--R (838) 0 --R Type: Expression Integer --E 838 @@ -22591,7 +22502,7 @@ m0165:=a0165-r0165 --E 857 --S 858 of 1483 -d0165:=D(m0165,x) +d0165:=normalize(D(m0165,x)) --R --R --R (858) @@ -23072,31 +22983,24 @@ t0169:= x^7/(1-x^6) --E 874 --S 875 of 1483 -r0169:= -1/2*x^2+1/6*atan(1/3*(1+2*x^2)*3^(1/2))*3^(1/2)-_ +r0169:= -1/2*x^2+1/6*atan(1/3*(1+2*x^2)*3^(1/2)::EXPR(INT))*3^(1/2)-_ 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) --R ---R There are 2 exposed and 5 unexposed library operations named atan ---R having 1 argument(s) but none was determined to be applicable. ---R Use HyperDoc Browse, or issue ---R )display op atan ---R to learn more about the available operations. Perhaps ---R package-calling the operation or using coercions on the arguments ---R will allow you to apply the operation. ---R ---RDaly Bug ---R Cannot find a definition or applicable library operation named atan ---R with argument type(s) ---R UnivariatePolynomial(x,AlgebraicNumber) ---R ---R Perhaps you should use "@" to indicate the required return type, ---R or "$" to specify which version of the function you need. +--R +--R 2 +-+ +--R 4 2 2 +-+ (2x + 1)\|3 2 +--R log(x + x + 1) - 2log(- x + 1) + 2\|3 atan(-------------) - 6x +--R 3 +--R (875) ------------------------------------------------------------------ +--R 12 +--R Type: Expression Integer --E 875 --S 876 of 1483 a0169:=integrate(t0169,x) --R --R ---R (875) +--R (876) --R 2 +-+ --R +-+ 4 2 +-+ 2 (2x + 1)\|3 2 +-+ --R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) - 6x \|3 @@ -23111,17 +23015,10 @@ a0169:=integrate(t0169,x) m0169:=a0169-r0169 --R --R ---R (876) ---R 2 +-+ ---R +-+ 4 2 +-+ 2 (2x + 1)\|3 ---R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) ---R 3 ---R + ---R 2 +-+ ---R (- 6x - 12r0169)\|3 ---R / ---R +-+ ---R 12\|3 +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (877) ----------------------------- +--R 6 --R Type: Expression Integer --E 877 @@ -23129,11 +23026,7 @@ m0169:=a0169-r0169 d0169:=D(m0169,x) --R --R ---R 7 ---R x ---R (877) - ------ ---R 6 ---R x - 1 +--R (878) 0 --R Type: Expression Integer --E 878 @@ -23143,7 +23036,7 @@ t0170:= x^5/(1-x^6) --R --R 5 --R x ---R (878) - ------ +--R (879) - ------ --R 6 --R x - 1 --R Type: Fraction Polynomial Integer @@ -23155,7 +23048,7 @@ r0170:= -1/6*log(1-x^6) --R --R 6 --R log(- x + 1) ---R (879) - ------------- +--R (880) - ------------- --R 6 --R Type: Expression Integer --E 880 @@ -23166,7 +23059,7 @@ a0170:=integrate(t0170,x) --R --R 6 --R log(x - 1) ---R (880) - ----------- +--R (881) - ----------- --R 6 --R Type: Union(Expression Integer,...) --E 881 @@ -23177,7 +23070,7 @@ m0170:=a0170-r0170 --R --R 6 6 --R - log(x - 1) + log(- x + 1) ---R (881) ----------------------------- +--R (882) ----------------------------- --R 6 --R Type: Expression Integer --E 882 @@ -23186,7 +23079,7 @@ m0170:=a0170-r0170 d0170:=D(m0170,x) --R --R ---R (882) 0 +--R (883) 0 --R Type: Expression Integer --E 883 @@ -23196,31 +23089,24 @@ t0171:= x^3/(1-x^6) --R --R 3 --R x ---R (883) - ------ +--R (884) - ------ --R 6 --R x - 1 --R Type: Fraction Polynomial Integer --E 884 --S 885 of 1483 -r0171:= -1/6*atan(1/3*(1+2*x^2)*3^(1/2))*3^(1/2)-_ +r0171:= -1/6*atan(1/3*(1+2*x^2)*3^(1/2)::EXPR(INT))*3^(1/2)-_ 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) --R ---R There are 2 exposed and 5 unexposed library operations named atan ---R having 1 argument(s) but none was determined to be applicable. ---R Use HyperDoc Browse, or issue ---R )display op atan ---R to learn more about the available operations. Perhaps ---R package-calling the operation or using coercions on the arguments ---R will allow you to apply the operation. ---R ---RDaly Bug ---R Cannot find a definition or applicable library operation named atan ---R with argument type(s) ---R UnivariatePolynomial(x,AlgebraicNumber) ---R ---R Perhaps you should use "@" to indicate the required return type, ---R or "$" to specify which version of the function you need. +--R +--R 2 +-+ +--R 4 2 2 +-+ (2x + 1)\|3 +--R log(x + x + 1) - 2log(- x + 1) - 2\|3 atan(-------------) +--R 3 +--R (885) ------------------------------------------------------------ +--R 12 +--R Type: Expression Integer --E 885 --S 886 of 1483 @@ -23231,7 +23117,7 @@ a0171:=integrate(t0171,x) --R +-+ 4 2 +-+ 2 (2x + 1)\|3 --R \|3 log(x + x + 1) - 2\|3 log(x - 1) - 6atan(-------------) --R 3 ---R (884) -------------------------------------------------------------- +--R (886) -------------------------------------------------------------- --R +-+ --R 12\|3 --R Type: Union(Expression Integer,...) @@ -23241,14 +23127,10 @@ a0171:=integrate(t0171,x) m0171:=a0171-r0171 --R --R ---R (885) ---R 2 +-+ ---R +-+ 4 2 +-+ 2 (2x + 1)\|3 +-+ ---R \|3 log(x + x + 1) - 2\|3 log(x - 1) - 6atan(-------------) - 12r0171\|3 ---R 3 ---R ---------------------------------------------------------------------------- ---R +-+ ---R 12\|3 +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (887) ----------------------------- +--R 6 --R Type: Expression Integer --E 887 @@ -23256,11 +23138,7 @@ m0171:=a0171-r0171 d0171:=D(m0171,x) --R --R ---R 3 ---R x ---R (886) - ------ ---R 6 ---R x - 1 +--R (888) 0 --R Type: Expression Integer --E 888 @@ -23270,7 +23148,7 @@ t0172:= x^2/(1-x^6) --R --R 2 --R x ---R (887) - ------ +--R (889) - ------ --R 6 --R x - 1 --R Type: Fraction Polynomial Integer @@ -23282,7 +23160,7 @@ r0172:= 1/3*atanh(x^3) --R --R 3 --R atanh(x ) ---R (888) --------- +--R (890) --------- --R 3 --R Type: Expression Integer --E 890 @@ -23293,7 +23171,7 @@ a0172:=integrate(t0172,x) --R --R 3 3 --R log(x + 1) - log(x - 1) ---R (889) ------------------------- +--R (891) ------------------------- --R 6 --R Type: Union(Expression Integer,...) --E 891 @@ -23304,7 +23182,7 @@ m0172:=a0172-r0172 --R --R 3 3 3 --R log(x + 1) - log(x - 1) - 2atanh(x ) ---R (890) -------------------------------------- +--R (892) -------------------------------------- --R 6 --R Type: Expression Integer --E 892 @@ -23313,7 +23191,7 @@ m0172:=a0172-r0172 d0172:=D(m0172,x) --R --R ---R (891) 0 +--R (893) 0 --R Type: Expression Integer --E 893 @@ -23322,31 +23200,24 @@ t0173:= x/(1-x^6) --R --R --R x ---R (892) - ------ +--R (894) - ------ --R 6 --R x - 1 --R Type: Fraction Polynomial Integer --E 894 --S 895 of 1483 -r0173:= 1/6*atan(1/3*(1+2*x^2)*3^(1/2))*3^(1/2)-_ +r0173:= 1/6*atan(1/3*(1+2*x^2)*3^(1/2)::EXPR(INT))*3^(1/2)-_ 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) --R ---R There are 2 exposed and 5 unexposed library operations named atan ---R having 1 argument(s) but none was determined to be applicable. ---R Use HyperDoc Browse, or issue ---R )display op atan ---R to learn more about the available operations. Perhaps ---R package-calling the operation or using coercions on the arguments ---R will allow you to apply the operation. ---R ---RDaly Bug ---R Cannot find a definition or applicable library operation named atan ---R with argument type(s) ---R UnivariatePolynomial(x,AlgebraicNumber) ---R ---R Perhaps you should use "@" to indicate the required return type, ---R or "$" to specify which version of the function you need. +--R +--R 2 +-+ +--R 4 2 2 +-+ (2x + 1)\|3 +--R log(x + x + 1) - 2log(- x + 1) + 2\|3 atan(-------------) +--R 3 +--R (895) ------------------------------------------------------------ +--R 12 +--R Type: Expression Integer --E 895 --S 896 of 1483 @@ -23357,7 +23228,7 @@ a0173:=integrate(t0173,x) --R +-+ 4 2 +-+ 2 (2x + 1)\|3 --R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) --R 3 ---R (893) -------------------------------------------------------------- +--R (896) -------------------------------------------------------------- --R +-+ --R 12\|3 --R Type: Union(Expression Integer,...) @@ -23367,14 +23238,10 @@ a0173:=integrate(t0173,x) m0173:=a0173-r0173 --R --R ---R (894) ---R 2 +-+ ---R +-+ 4 2 +-+ 2 (2x + 1)\|3 +-+ ---R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) - 12r0173\|3 ---R 3 ---R ---------------------------------------------------------------------------- ---R +-+ ---R 12\|3 +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (897) ----------------------------- +--R 6 --R Type: Expression Integer --E 897 @@ -23382,10 +23249,7 @@ m0173:=a0173-r0173 d0173:=D(m0173,x) --R --R ---R x ---R (895) - ------ ---R 6 ---R x - 1 +--R (898) 0 --R Type: Expression Integer --E 898 @@ -23394,7 +23258,7 @@ t0174:= 1/x/(1-x^6) --R --R --R 1 ---R (896) - ------ +--R (899) - ------ --R 7 --R x - x --R Type: Fraction Polynomial Integer @@ -23406,7 +23270,7 @@ r0174:= log(x)-1/6*log(1-x^6) --R --R 6 --R 6log(x) - log(- x + 1) ---R (897) ----------------------- +--R (900) ----------------------- --R 6 --R Type: Expression Integer --E 900 @@ -23417,7 +23281,7 @@ a0174:=integrate(t0174,x) --R --R 6 --R - log(x - 1) + 6log(x) ---R (898) ----------------------- +--R (901) ----------------------- --R 6 --R Type: Union(Expression Integer,...) --E 901 @@ -23428,7 +23292,7 @@ m0174:=a0174-r0174 --R --R 6 6 --R - log(x - 1) + log(- x + 1) ---R (899) ----------------------------- +--R (902) ----------------------------- --R 6 --R Type: Expression Integer --E 902 @@ -23437,7 +23301,7 @@ m0174:=a0174-r0174 d0174:=D(m0174,x) --R --R ---R (900) 0 +--R (903) 0 --R Type: Expression Integer --E 903 @@ -23446,38 +23310,33 @@ t0175:= 1/x^3/(1-x^6) --R --R --R 1 ---R (901) - ------- +--R (904) - ------- --R 9 3 --R x - x --R Type: Fraction Polynomial Integer --E 904 --S 905 of 1483 -r0175:= -1/2/x^2-1/6*atan(1/3*(1+2*x^2)*3^(1/2))*3^(1/2)-_ +r0175:= -1/2/x^2-1/6*atan(1/3*(1+2*x^2)*3^(1/2)::EXPR(INT))*3^(1/2)-_ 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) --R ---R There are 2 exposed and 5 unexposed library operations named atan ---R having 1 argument(s) but none was determined to be applicable. ---R Use HyperDoc Browse, or issue ---R )display op atan ---R to learn more about the available operations. Perhaps ---R package-calling the operation or using coercions on the arguments ---R will allow you to apply the operation. ---R ---RDaly Bug ---R Cannot find a definition or applicable library operation named atan ---R with argument type(s) ---R UnivariatePolynomial(x,AlgebraicNumber) ---R ---R Perhaps you should use "@" to indicate the required return type, ---R or "$" to specify which version of the function you need. +--R +--R (905) +--R 2 +-+ +--R 2 4 2 2 2 2 +-+ (2x + 1)\|3 +--R x log(x + x + 1) - 2x log(- x + 1) - 2x \|3 atan(-------------) - 6 +--R 3 +--R ---------------------------------------------------------------------- +--R 2 +--R 12x +--R Type: Expression Integer --E 905 --S 906 of 1483 a0175:=integrate(t0175,x) --R --R ---R (902) +--R (906) --R 2 +-+ --R 2 +-+ 4 2 2 +-+ 2 2 (2x + 1)\|3 +-+ --R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) - 6x atan(-------------) - 6\|3 @@ -23492,28 +23351,18 @@ a0175:=integrate(t0175,x) m0175:=a0175-r0175 --R --R ---R (903) ---R 2 +-+ ---R 2 +-+ 4 2 2 +-+ 2 2 (2x + 1)\|3 ---R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) - 6x atan(-------------) ---R 3 ---R + ---R 2 +-+ ---R (- 12r0175 x - 6)\|3 ---R / ---R 2 +-+ ---R 12x \|3 +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (907) ----------------------------- +--R 6 --R Type: Expression Integer --E 907 --S 908 of 1483 -d0175:=D(m0175,x) +d0175:=normalize(D(m0175,x)) --R --R ---R 1 ---R (904) - ------- ---R 9 3 ---R x - x +--R (908) 0 --R Type: Expression Integer --E 908 @@ -23522,7 +23371,7 @@ t0176:= 1/x^4/(1-x^6) --R --R --R 1 ---R (905) - -------- +--R (909) - -------- --R 10 4 --R x - x --R Type: Fraction Polynomial Integer @@ -23534,7 +23383,7 @@ r0176:= -1/3/x^3+1/3*atanh(x^3) --R --R 3 3 --R x atanh(x ) - 1 ---R (906) --------------- +--R (910) --------------- --R 3 --R 3x --R Type: Expression Integer @@ -23546,7 +23395,7 @@ a0176:=integrate(t0176,x) --R --R 3 3 3 3 --R x log(x + 1) - x log(x - 1) - 2 ---R (907) --------------------------------- +--R (911) --------------------------------- --R 3 --R 6x --R Type: Union(Expression Integer,...) @@ -23558,7 +23407,7 @@ m0176:=a0176-r0176 --R --R 3 3 3 --R log(x + 1) - log(x - 1) - 2atanh(x ) ---R (908) -------------------------------------- +--R (912) -------------------------------------- --R 6 --R Type: Expression Integer --E 912 @@ -23567,7 +23416,7 @@ m0176:=a0176-r0176 d0176:=D(m0176,x) --R --R ---R (909) 0 +--R (913) 0 --R Type: Expression Integer --E 913 @@ -23576,38 +23425,33 @@ t0177:= 1/x^5/(1-x^6) --R --R --R 1 ---R (910) - -------- +--R (914) - -------- --R 11 5 --R x - x --R Type: Fraction Polynomial Integer --E 914 --S 915 of 1483 -r0177:= -1/4/x^4+1/6*atan(1/3*(1+2*x^2)*3^(1/2))*3^(1/2)-_ +r0177:= -1/4/x^4+1/6*atan(1/3*(1+2*x^2)*3^(1/2)::EXPR(INT))*3^(1/2)-_ 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) --R ---R There are 2 exposed and 5 unexposed library operations named atan ---R having 1 argument(s) but none was determined to be applicable. ---R Use HyperDoc Browse, or issue ---R )display op atan ---R to learn more about the available operations. Perhaps ---R package-calling the operation or using coercions on the arguments ---R will allow you to apply the operation. ---R ---RDaly Bug ---R Cannot find a definition or applicable library operation named atan ---R with argument type(s) ---R UnivariatePolynomial(x,AlgebraicNumber) ---R ---R Perhaps you should use "@" to indicate the required return type, ---R or "$" to specify which version of the function you need. +--R +--R (915) +--R 2 +-+ +--R 4 4 2 4 2 4 +-+ (2x + 1)\|3 +--R x log(x + x + 1) - 2x log(- x + 1) + 2x \|3 atan(-------------) - 3 +--R 3 +--R ---------------------------------------------------------------------- +--R 4 +--R 12x +--R Type: Expression Integer --E 915 --S 916 of 1483 a0177:=integrate(t0177,x) --R --R ---R (911) +--R (916) --R 2 +-+ --R 4 +-+ 4 2 4 +-+ 2 4 (2x + 1)\|3 +-+ --R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) + 6x atan(-------------) - 3\|3 @@ -23622,28 +23466,18 @@ a0177:=integrate(t0177,x) m0177:=a0177-r0177 --R --R ---R (912) ---R 2 +-+ ---R 4 +-+ 4 2 4 +-+ 2 4 (2x + 1)\|3 ---R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) + 6x atan(-------------) ---R 3 ---R + ---R 4 +-+ ---R (- 12r0177 x - 3)\|3 ---R / ---R 4 +-+ ---R 12x \|3 +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (917) ----------------------------- +--R 6 --R Type: Expression Integer --E 917 --S 918 of 1483 -d0177:=D(m0177,x) +d0177:=normalize(D(m0177,x)) --R --R ---R 1 ---R (913) - -------- ---R 11 5 ---R x - x +--R (918) 0 --R Type: Expression Integer --E 918 @@ -23652,7 +23486,7 @@ t0178:= 1/(a+b*x^6) --R --R --R 1 ---R (914) -------- +--R (919) -------- --R 6 --R b x + a --R Type: Fraction Polynomial Integer @@ -23667,7 +23501,7 @@ r0178:= -1/12*(-4*atan(b^(1/6)*x/a^(1/6))-_ b^(1/3)*x^2))*3^(1/2))/a^(5/6)/b^(1/6) --R --R ---R (915) +--R (920) --R +-+6+-+6+-+ 2 3+-+ 3+-+ --R +-+ x\|3 \|a \|b + x \|b + \|a --R \|3 log(-----------------------------) @@ -23695,7 +23529,7 @@ r0178:= -1/12*(-4*atan(b^(1/6)*x/a^(1/6))-_ a0178:=integrate(t0178,x) --R --R ---R (916) +--R (921) --R +----------+ +----------+2 +----------+ --R | 1 2 | 1 | 1 2 --R |- -------- log(36a |- -------- + 6a x |- -------- + x ) @@ -23752,7 +23586,7 @@ a0178:=integrate(t0178,x) m0178:=a0178-r0178 --R --R ---R (917) +--R (922) --R +-+6+-+6+-+ 2 3+-+ 3+-+ --R +-+ x\|3 \|a \|b + x \|b + \|a --R - \|3 log(-----------------------------) @@ -23825,36 +23659,10 @@ m0178:=a0178-r0178 --E 922 --S 923 of 1483 -d0178:=D(m0178,x) +d0178:=normalize(D(m0178,x)) --R --R ---R (918) ---R 2 6+-+4 ---R 3a x \|b ---R + ---R 4 6+-+4 3+-+2 2 3+-+6+-+4 8 2 3+-+ 3+-+2 6+-+4 ---R - x \|a \|b + (- 2x \|a \|a - b x - a x )\|b - \|a \|a ---R + ---R 6 6+-+2 6 3+-+ ---R - 3b x \|a + (b x + a)\|a ---R * ---R 6+-+2 ---R \|b ---R + ---R 8 3+-+2 6 3+-+3+-+ 4 3+-+2 ---R b x \|b + 2b x \|a \|b + b x \|a ---R / ---R 8 2 2 6+-+4 ---R (6a b x + 6a x )\|b ---R + ---R 10 4 6+-+4 3+-+2 8 2 3+-+6+-+4 3+-+ ---R (- 2b x - 2a x )\|a \|b + (- 4b x - 4a x )\|a \|a \|b ---R + ---R 6 3+-+2 6+-+4 ---R (- 2b x - 2a)\|a \|a ---R * ---R 6+-+2 ---R \|b +--R (923) 0 --R Type: Expression Integer --E 923 @@ -23863,7 +23671,7 @@ t0179:= 1/x^2/(a+b*x^6) --R --R --R 1 ---R (919) ----------- +--R (924) ----------- --R 8 2 --R b x + a x --R Type: Fraction Polynomial Integer @@ -23878,7 +23686,7 @@ r0179:= -1/a/x-1/3*b^(1/6)*atan(b^(1/6)*x/a^(1/6))/a^(7/6)-_ 3^(1/2)*a^(1/6)*x/b^(1/6)+x^2)*3^(1/2)/a^(7/6) --R --R ---R (920) +--R (925) --R 2 3+-+ 3+-+ 6+-+ +-+6+-+3+-+ --R +-+6+-+ (x \|b + \|a )\|b + x\|3 \|a \|b --R x\|3 \|b log(-----------------------------------) @@ -23912,7 +23720,7 @@ r0179:= -1/a/x-1/3*b^(1/6)*atan(b^(1/6)*x/a^(1/6))/a^(7/6)-_ a0179:=integrate(t0179,x) --R --R ---R (921) +--R (926) --R +---------+ +---------+5 +---------+4 --R | b 6 | b 5 | b 2 --R - a x |- ------- log(7776a x |- ------- - 1296a |- ------- + b x ) @@ -23969,7 +23777,7 @@ a0179:=integrate(t0179,x) m0179:=a0179-r0179 --R --R ---R (922) +--R (927) --R - --R +---------+ --R | b 6+-+ @@ -24055,30 +23863,10 @@ m0179:=a0179-r0179 --E 927 --S 928 of 1483 -d0179:=D(m0179,x) +d0179:=normalize(D(m0179,x)) --R --R ---R (923) ---R 4 3+-+2 2 3+-+3+-+ 3+-+2 6+-+4 ---R (a x \|b + 2a x \|a \|b + a \|a )\|b ---R + ---R 2 6+-+2 3+-+2 6 3+-+6+-+2 3+-+ 4 3+-+2 6+-+6+-+2 ---R (- 2a x \|a \|b + (- 3b x - a)\|a \|a \|b - b x \|a \|a)\|b ---R + ---R 6 6+-+4 3+-+2 ---R 3b x \|a \|b ---R / ---R 10 2 4 6+-+2 3+-+2 8 2 2 3+-+6+-+2 3+-+ ---R (2a b x + 2a x )\|a \|b + (4a b x + 4a x )\|a \|a \|b ---R + ---R 6 2 3+-+2 6+-+2 ---R (2a b x + 2a )\|a \|a ---R * ---R 6+-+2 ---R \|b ---R + ---R 8 2 2 6+-+4 3+-+2 ---R (- 6a b x - 6a x )\|a \|b +--R (928) 0 --R Type: Expression Integer --E 928 @@ -24087,7 +23875,7 @@ t0180:= 1/(a-b*x^6) --R --R --R 1 ---R (924) - -------- +--R (929) - -------- --R 6 --R b x - a --R Type: Fraction Polynomial Integer @@ -24101,7 +23889,7 @@ r0180:= 1/12*(2*atan(1/3*3^(1/2)*(-a^(1/6)+2*b^(1/6)*x)/a^(1/6))*3^(1/2)+_ a^(1/6)*x*b^(1/6)+b^(1/3)*x^2)))/a^(5/6)/b^(1/6) --R --R ---R (925) +--R (930) --R 6+-+6+-+ 2 3+-+ 3+-+ 6+-+6+-+ 2 3+-+ 3+-+ --R x\|a \|b + x \|b + \|a - x\|a \|b + x \|b + \|a --R log(-------------------------) - log(---------------------------) @@ -24129,7 +23917,7 @@ r0180:= 1/12*(2*atan(1/3*3^(1/2)*(-a^(1/6)+2*b^(1/6)*x)/a^(1/6))*3^(1/2)+_ a0180:=integrate(t0180,x) --R --R ---R (926) +--R (931) --R +--------+ +--------+2 +--------+ --R | 1 2 | 1 | 1 2 --R |-------- log(36a |-------- + 6a x |-------- + x ) @@ -24180,7 +23968,7 @@ a0180:=integrate(t0180,x) m0180:=a0180-r0180 --R --R ---R (927) +--R (932) --R 6+-+6+-+ 2 3+-+ 3+-+ --R x\|a \|b + x \|b + \|a --R - log(-------------------------) @@ -24253,36 +24041,10 @@ m0180:=a0180-r0180 --E 932 --S 933 of 1483 -d0180:=D(m0180,x) +d0180:=normalize(D(m0180,x)) --R --R ---R (928) ---R 6 6+-+2 3+-+2 4 3+-+6+-+2 3+-+ 2 3+-+2 6+-+2 2 6+-+4 ---R (- 2x \|a \|b - 4x \|a \|a \| - 2x \|a \|a - a x )\|b ---R + ---R 4 6+-+4 3+-+2 2 3+-+6+-+4 8 2 3+-+ 3+-+2 6+-+4 ---R x \|a \|b + (2x \|a \|a - b x + a x )\|b + \|a \|a ---R + ---R 6 6+-+2 6 3+-+ ---R - b x \|a + (b x - a)\|a ---R * ---R 6+-+2 ---R \|b ---R + ---R 8 3+-+2 6 3+-+3+-+ 4 6+-+4 4 3+-+2 ---R b x \|b + 2b x \|a \|b + 2b x \|a + b x \|a ---R / ---R 8 2 2 6+-+4 ---R (6a b x - 6a x )\|b ---R + ---R 10 4 6+-+4 3+-+2 8 2 3+-+6+-+4 3+-+ ---R (- 6b x + 6a x )\|a \|b + (- 12b x + 12a x )\|a \|a \|b ---R + ---R 6 3+-+2 6+-+4 ---R (- 6b x + 6a)\|a \|a ---R * ---R 6+-+2 ---R \|b +--R (933) 0 --R Type: Expression Integer --E 933 @@ -24291,7 +24053,7 @@ t0181:= 1/x^2/(a-b*x^6) --R --R --R 1 ---R (929) - ----------- +--R (934) - ----------- --R 8 2 --R b x - a x --R Type: Fraction Polynomial Integer @@ -24306,7 +24068,7 @@ r0181:= -1/12/a^(7/6)*(12*a^(1/6)+2*b^(1/6)*atan(1/3*3^(1/2)*(-a^(1/6)+_ (a^(1/3)+a^(1/6)*x*b^(1/6)+b^(1/3)*x^2))*x)/x --R --R ---R (930) +--R (935) --R 6+-+6+-+ 2 3+-+ 3+-+ --R 6+-+ x\|a \|b + x \|b + \|a --R x\|b log(-------------------------) @@ -24340,7 +24102,7 @@ r0181:= -1/12/a^(7/6)*(12*a^(1/6)+2*b^(1/6)*atan(1/3*3^(1/2)*(-a^(1/6)+_ a0181:=integrate(t0181,x) --R --R ---R (931) +--R (936) --R +-------+ +-------+5 +-------+4 --R | b 6 | b 5 | b 2 --R a x |------- log(7776a x |------- + 1296a |------- + b x ) @@ -24397,7 +24159,7 @@ a0181:=integrate(t0181,x) m0181:=a0181-r0181 --R --R ---R (932) +--R (937) --R 6+-+6+-+ 2 3+-+ 3+-+ --R 6+-+ x\|a \|b + x \|b + \|a --R - \|b log(-------------------------) @@ -24476,30 +24238,10 @@ m0181:=a0181-r0181 --E 937 --S 938 of 1483 -d0181:=D(m0181,x) +d0181:=normalize(D(m0181,x)) --R --R ---R (933) ---R 6 6+-+4 3+-+2 4 3+-+6+-+4 3+-+ 2 3+-+2 6+-+4 2 6+-+26+-+4 ---R (- 2x \|a \|b - 4x \|a \|a \| - 2x \|a \|a - a x \|a )\|b ---R + ---R 4 3+-+2 8 2 6+-+2 2 3+-+3+-+ 6 6+-+4 ---R a x \|b + ((- b x + a x )\|a + 2a x \|a)\|b - b x \|a ---R + ---R 6 3+-+6+-+2 3+-+2 ---R (b x - a)\|a \|a + a \|a ---R * ---R 6+-+2 ---R \|b ---R + ---R 8 6+-+2 3+-+2 6 3+-+6+-+2 3+-+ 4 3+-+2 6+-+2 4 ---R b x \|a \|b + 2b x \|a \|a \| + b x \|a \|a + 2a b x ---R / ---R 8 2 2 6+-+4 6+-+2 10 2 4 6+-+2 3+-+2 ---R (6a b x - 6a x )\|a \|b + (- 6a b x + 6a x )\|a \|b ---R + ---R 8 2 2 3+-+6+-+2 3+-+ 6 2 3+-+2 6+-+2 ---R (- 12a b x + 12a x )\|a \|a \|b + (- 6a b x + 6a )\|a \|a +--R (938) 0 --R Type: Expression Integer --E 938 @@ -24508,7 +24250,7 @@ t0182:= 1/(a-b*x^8) --R --R --R 1 ---R (934) - -------- +--R (939) - -------- --R 8 --R b x - a --R Type: Fraction Polynomial Integer @@ -24523,7 +24265,7 @@ r0182:= 1/16*(4*atan(b^(1/8)*x/a^(1/8))+2*atan((-a^(1/8)+2^(1/2)*_ a^(7/8)/b^(1/8) --R --R ---R (935) +--R (940) --R +-+8+-+8+-+ 2 4+-+ 4+-+ --R +-+ x\|2 \|a \|b + x \|b + \|a --R \|2 log(-----------------------------) @@ -24551,7 +24293,7 @@ r0182:= 1/16*(4*atan(b^(1/8)*x/a^(1/8))+2*atan((-a^(1/8)+2^(1/2)*_ a0182:=integrate(t0182,x) --R --R ---R (936) +--R (941) --R +-----------+ +-----------+2 +-----------+ --R | 1 2 | 1 +-+ | 1 2 --R |----------- log(64a |----------- + 8a x\|2 |----------- + x ) @@ -24618,7 +24360,7 @@ a0182:=integrate(t0182,x) m0182:=a0182-r0182 --R --R ---R (937) +--R (942) --R +-+8+-+8+-+ 2 4+-+ 4+-+ --R x\|2 \|a \|b + x \|b + \|a --R - log(-----------------------------) @@ -24713,39 +24455,10 @@ m0182:=a0182-r0182 --E 942 --S 943 of 1483 -d0182:=D(m0182,x) +d0182:=normalize(D(m0182,x)) --R --R ---R (938) ---R 8 8+-+2 4+-+2 6 4+-+8+-+2 4+-+ 4 8+-+6 4 4+-+2 8+-+8+-+6 ---R (- x \|a \|b - 2x \|a \|a \| + 2x \|a - x \|a \|a)\|b ---R + ---R 6 8+-+4 4+-+2 4 4+-+8+-+4 4+-+ 2 4+-+2 8+-+4 2 8+-+4 ---R (- x \|a \|b - 2x \|a \|a \| - x \|a \|a - 2a x )\|b ---R + ---R 4 8+-+6 4+-+2 2 4+-+8+-+6 10 2 4+-+ 4+-+2 8+-+6 ---R x \|a \|b + (2x \|a \|a - b x + a x )\|b + \|a \|a ---R + ---R 8 8+-+2 8 4+-+ ---R - 2b x \|a + (b x - a)\|a ---R * ---R 8+-+2 ---R \|b ---R + ---R 10 4+-+2 8 4+-+4+-+ 6 8+-+4 6 4+-+2 ---R b x \|b + 2b x \|a \|b + 2b x \|a + b x \|a ---R / ---R 10 2 2 8+-+4 ---R (8a b x - 8a x )\|b ---R + ---R 12 4 8+-+6 4+-+2 10 2 4+-+8+-+6 4+-+ ---R (- 4b x + 4a x )\|a \|b + (- 8b x + 8a x )\|a \|a \|b ---R + ---R 8 4+-+2 8+-+6 ---R (- 4b x + 4a)\|a \|a ---R * ---R 8+-+2 ---R \|b +--R (943) 0 --R Type: Expression Integer --E 943 @@ -24755,7 +24468,7 @@ t0183:= x^5/(9-x^12) --R --R 5 --R x ---R (939) - ------- +--R (944) - ------- --R 12 --R x - 9 --R Type: Fraction Polynomial Integer @@ -24769,7 +24482,7 @@ r0183:= 1/18*atanh(1/3*x^6) --R x --R atanh(--) --R 3 ---R (940) --------- +--R (945) --------- --R 18 --R Type: Expression Integer --E 945 @@ -24780,7 +24493,7 @@ a0183:=integrate(t0183,x) --R --R 6 6 --R log(x + 3) - log(x - 3) ---R (941) ------------------------- +--R (946) ------------------------- --R 36 --R Type: Union(Expression Integer,...) --E 946 @@ -24793,7 +24506,7 @@ m0183:=a0183-r0183 --R 6 6 x --R log(x + 3) - log(x - 3) - 2atanh(--) --R 3 ---R (942) -------------------------------------- +--R (947) -------------------------------------- --R 36 --R Type: Expression Integer --E 947 @@ -24802,7 +24515,7 @@ m0183:=a0183-r0183 d0183:=D(m0183,x) --R --R ---R (943) 0 +--R (948) 0 --R Type: Expression Integer --E 948 @@ -24812,7 +24525,7 @@ t0184:= (a+b/x^2)^3/x^3 --R --R 3 6 2 4 2 2 3 --R a x + 3a b x + 3a b x + b ---R (944) ----------------------------- +--R (949) ----------------------------- --R 9 --R x --R Type: Fraction Polynomial Integer @@ -24824,7 +24537,7 @@ r0184:= -1/8*(a+b/x^2)^4/b --R --R 4 8 3 6 2 2 4 3 2 4 --R - a x - 4a b x - 6a b x - 4a b x - b ---R (945) ----------------------------------------- +--R (950) ----------------------------------------- --R 8 --R 8b x --R Type: Fraction Polynomial Integer @@ -24836,7 +24549,7 @@ a0184:=integrate(t0184,x) --R --R 3 6 2 4 2 2 3 --R - 4a x - 6a b x - 4a b x - b ---R (946) -------------------------------- +--R (951) -------------------------------- --R 8 --R 8x --R Type: Union(Expression Integer,...) @@ -24848,7 +24561,7 @@ m0184:=a0184-r0184 --R --R 4 --R a ---R (947) -- +--R (952) -- --R 8b --R Type: Expression Integer --E 952 @@ -24857,7 +24570,7 @@ m0184:=a0184-r0184 d0184:=D(m0184,x) --R --R ---R (948) 0 +--R (953) 0 --R Type: Expression Integer --E 953 @@ -24867,7 +24580,7 @@ t0185:= 1/x^3/(a+b/x^2)^3 --R --R 3 --R x ---R (949) ----------------------------- +--R (954) ----------------------------- --R 3 6 2 4 2 2 3 --R a x + 3a b x + 3a b x + b --R Type: Fraction Polynomial Integer @@ -24880,7 +24593,7 @@ r0185:= 1/4/b/(a+b/x^2)^2 --R 1 4 --R - x --R 4 ---R (950) --------------------- +--R (955) --------------------- --R 2 4 2 2 3 --R a b x + 2a b x + b --R Type: Fraction Polynomial Fraction Integer @@ -24892,7 +24605,7 @@ a0185:=integrate(t0185,x) --R --R 2 --R - 2a x - b ---R (951) ----------------------- +--R (956) ----------------------- --R 4 4 3 2 2 2 --R 4a x + 8a b x + 4a b --R Type: Union(Expression Integer,...) @@ -24903,7 +24616,7 @@ m0185:=a0185-r0185 --R --R --R 1 ---R (952) - ---- +--R (957) - ---- --R 2 --R 4a b --R Type: Expression Integer @@ -24913,7 +24626,7 @@ m0185:=a0185-r0185 d0185:=D(m0185,x) --R --R ---R (953) 0 +--R (958) 0 --R Type: Expression Integer --E 958 @@ -24923,7 +24636,7 @@ t0186:= 1/(a+b/x^5) --R --R 5 --R x ---R (954) -------- +--R (959) -------- --R 5 --R a x + b --R Type: Fraction Polynomial Integer @@ -24940,7 +24653,7 @@ r0186:= x/a-1/10*(10-2*5^(1/2))^(1/2)*b^(1/5)*atan(-(5^(1/2)+1)/_ log(2*b^(2/5)/a^(2/5)-(5^(1/2)+1)*b^(1/5)*x/a^(1/5)+2*x^2)/a^(6/5) --R --R ---R (955) +--R (960) --R 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 --R +-+ 5+-+ 2\|b + (x\|5 - x)\|a \|b + 2x \|a --R (- \|5 + 1)\|b log(---------------------------------------) @@ -25004,7 +24717,7 @@ r0186:= x/a-1/10*(10-2*5^(1/2))^(1/2)*b^(1/5)*atan(-(5^(1/2)+1)/_ a0186:=integrate(t0186,x) --R --R ---R (956) +--R (961) --R - --R 5a --R * @@ -25108,7 +24821,7 @@ a0186:=integrate(t0186,x) m0186:=a0186-r0186 --R --R ---R (957) +--R (962) --R - --R 5+-+ --R 10a\|a @@ -25259,10 +24972,10 @@ m0186:=a0186-r0186 --E 962 --S 963 of 1483 -d0186:=D(m0186,x) +d0186:=normalize(D(m0186,x)) --R --R ---R (958) +--R (963) --R +------------+ +----------+ --R 5 | +-+ | +-+ 5 +-+ 5+-+2 5+-+4 --R (a x \|- 2\|5 + 10 \|- \|5 + 5 + (2a x + 2b)\|2 )\|a \|b @@ -25376,7 +25089,7 @@ t0187:= 1/(a+b/x^6) --R --R 6 --R x ---R (959) -------- +--R (964) -------- --R 6 --R a x + b --R Type: Fraction Polynomial Integer @@ -25391,7 +25104,7 @@ r0187:= x/a-1/3*b^(1/6)*atan(a^(1/6)*x/b^(1/6))/a^(7/6)-1/6*b^(1/6)*_ x^2)*3^(1/2)/a^(7/6) --R --R ---R (960) +--R (965) --R +-+3+-+6+-+ 6+-+3+-+ 2 3+-+6+-+ --R +-+6+-+ x\|3 \|a \|b + \|a \|b + x \|a \|a --R - \|3 \|b log(-------------------------------------) @@ -25425,7 +25138,7 @@ r0187:= x/a-1/3*b^(1/6)*atan(a^(1/6)*x/b^(1/6))/a^(7/6)-1/6*b^(1/6)*_ a0187:=integrate(t0187,x) --R --R ---R (961) +--R (966) --R +---------+ +---------+2 +---------+ --R | b 2 | b | b 2 --R - a |- ------- log(36a |- ------- + 6a x |- ------- + x ) @@ -25482,7 +25195,7 @@ a0187:=integrate(t0187,x) m0187:=a0187-r0187 --R --R ---R (962) +--R (967) --R +-+3+-+6+-+ 6+-+3+-+ 2 3+-+6+-+ --R +-+6+-+ x\|3 \|a \|b + \|a \|b + x \|a \|a --R \|3 \|b log(-------------------------------------) @@ -25555,24 +25268,10 @@ m0187:=a0187-r0187 --E 967 --S 968 of 1483 -d0187:=D(m0187,x) +d0187:=normalize(D(m0187,x)) --R --R ---R (963) ---R 6 3+-+2 6+-+4 ---R 3a x \|a \|b ---R + ---R 4 6+-+2 3+-+2 6 3+-+6+-+2 3+-+ 2 3+-+2 6+-+6+-+2 ---R (- a x \|a \|b + (- 3a x - b)\|a \|a \|b - 2b x \|a \|a)\|b ---R + ---R 6+-+4 3+-+2 2 3+-+6+-+4 3+-+ 4 3+-+2 6+-+4 ---R b \|a \|b + 2b x \|a \|a \| + b x \|a \|a ---R / ---R 2 8 2 3+-+2 6+-+2 6+-+2 2 6 6+-+4 3+-+2 ---R (6a x + 6a b x )\|a \|a \|b + (- 2a x - 2a b)\|a \|b ---R + ---R 2 8 2 3+-+6+-+4 3+-+ 2 10 4 3+-+2 6+-+4 ---R (- 4a x - 4a b x )\|a \|a \|b + (- 2a x - 2a b x )\|a \|a +--R (968) 0 --R Type: Expression Integer --E 968 @@ -25582,7 +25281,7 @@ t0188:= (a+b/x^2)/(c+d/x^2) --R --R 2 --R a x + b ---R (964) -------- +--R (969) -------- --R 2 --R c x + d --R Type: Fraction Polynomial Integer @@ -25597,7 +25296,7 @@ r0188:= a*x/c+(b*c-a*d)*atan(c^(1/2)*x/d^(1/2))/c^(3/2)/d^(1/2) --R (- a d + b c)atan(-----) + a x\|c \|d --R +-+ --R \|d ---R (965) -------------------------------------- +--R (970) -------------------------------------- --R +-+ +-+ --R c\|c \|d --R Type: Expression Integer @@ -25607,7 +25306,7 @@ r0188:= a*x/c+(b*c-a*d)*atan(c^(1/2)*x/d^(1/2))/c^(3/2)/d^(1/2) a0188:=integrate(t0188,x) --R --R ---R (966) +--R (971) --R 2 +-----+ --R (c x - d)\|- c d - 2c d x +-----+ --R (a d - b c)log(---------------------------) + 2a x\|- c d @@ -25630,7 +25329,7 @@ a0188:=integrate(t0188,x) m0188a:=a0188.1-r0188 --R --R ---R (967) +--R (972) --R 2 +-----+ --R +-+ +-+ (c x - d)\|- c d - 2c d x --R (a d - b c)\|c \|d log(---------------------------) @@ -25652,7 +25351,7 @@ m0188a:=a0188.1-r0188 d0188a:=D(m0188a,x) --R --R ---R (968) 0 +--R (973) 0 --R Type: Expression Integer --E 973 @@ -25665,7 +25364,7 @@ m0188b:=a0188.2-r0188 --R (- a d + b c)\|c \|d atan(-------) + (a d - b c)\|c d atan(-----) --R d +-+ --R \|d ---R (969) ----------------------------------------------------------------- +--R (974) ----------------------------------------------------------------- --R +-+ +-+ +---+ --R c\|c \|d \|c d --R Type: Expression Integer @@ -25675,7 +25374,7 @@ m0188b:=a0188.2-r0188 d0188b:=D(m0188b,x) --R --R ---R (970) 0 +--R (975) 0 --R Type: Expression Integer --E 975 @@ -25685,7 +25384,7 @@ t0189:= (a+b/x^3)/(c+d/x^3) --R --R 3 --R a x + b ---R (971) -------- +--R (976) -------- --R 3 --R c x + d --R Type: Fraction Polynomial Integer @@ -25698,7 +25397,7 @@ r0189:= a*x/c+1/3*(b*c-a*d)*atan(-1/3*3^(1/2)+2/3*c^(1/3)*_ log(d^(2/3)/c^(2/3)-d^(1/3)*x/c^(1/3)+x^2)/c^(4/3)/d^(2/3) --R --R ---R (972) +--R (977) --R 3+-+2 3+-+3+-+ 2 3+-+2 --R \|d - x\|c \|d + x \|c --R (a d - b c)log(---------------------------) @@ -25726,7 +25425,7 @@ r0189:= a*x/c+1/3*(b*c-a*d)*atan(-1/3*3^(1/2)+2/3*c^(1/3)*_ a0189:=integrate(t0189,x) --R --R ---R (973) +--R (978) --R +------+2 +------+ --R +-+ 2 3| 2 3| 2 2 --R (- a d + b c)\|3 log(x \|- c d + d x\|- c d + d ) @@ -25751,7 +25450,7 @@ a0189:=integrate(t0189,x) m0189:=a0189-r0189 --R --R ---R (974) +--R (979) --R +------+ 3+-+2 3+-+3+-+ 2 3+-+2 --R +-+3| 2 \|d - x\|c \|d + x \|c --R (- a d + b c)\|3 \|- c d log(---------------------------) @@ -25794,7 +25493,7 @@ m0189:=a0189-r0189 d0189:=D(m0189,x) --R --R ---R (975) 0 +--R (980) 0 --R Type: Expression Integer --E 980 @@ -25802,7 +25501,7 @@ d0189:=D(m0189,x) t0190:= 1/(a+b*(c+d*x)^2)^2 --R --R ---R (976) +--R (981) --R 1 --R / --R 2 4 4 2 3 3 2 2 2 2 2 3 2 4 @@ -25818,7 +25517,7 @@ r0190:= 1/2*(c+d*x)/a/d/(a+b*c^2+2*b*c*d*x+b*d^2*x^2)+1/2*_ atan(b^(1/2)*(c+d*x)/a^(1/2))/a^(3/2)/b^(1/2)/d --R --R ---R (977) +--R (982) --R +-+ --R 2 2 2 (d x + c)\|b +-+ +-+ --R (b d x + 2b c d x + b c + a)atan(-------------) + (d x + c)\|a \|b @@ -25834,7 +25533,7 @@ r0190:= 1/2*(c+d*x)/a/d/(a+b*c^2+2*b*c*d*x+b*d^2*x^2)+1/2*_ a0190:=integrate(t0190,x) --R --R ---R (978) +--R (983) --R [ --R 2 2 2 --R (b d x + 2b c d x + b c + a) @@ -25865,7 +25564,7 @@ a0190:=integrate(t0190,x) m0190a:=a0190.1-r0190 --R --R ---R (979) +--R (984) --R 2 2 2 +-----+ --R +-+ +-+ (b d x + 2b c d x + b c - a)\|- a b + 2a b d x + 2a b c --R \|a \|b log(----------------------------------------------------------) @@ -25887,7 +25586,7 @@ m0190a:=a0190.1-r0190 d0190a:=D(m0190a,x) --R --R ---R (980) 0 +--R (985) 0 --R Type: Expression Integer --E 985 @@ -25900,7 +25599,7 @@ m0190b:=a0190.2-r0190 --R \|a \|b atan(---------------) - \|a b atan(-------------) --R a +-+ --R \|a ---R (981) --------------------------------------------------------- +--R (986) --------------------------------------------------------- --R +-+ +-+ +---+ --R 2a d\|a \|b \|a b --R Type: Expression Integer @@ -25910,7 +25609,7 @@ m0190b:=a0190.2-r0190 d0190b:=D(m0190b,x) --R --R ---R (982) 0 +--R (987) 0 --R Type: Expression Integer --E 987 @@ -25918,7 +25617,7 @@ d0190b:=D(m0190b,x) t0191:= 1/(a+b*(c+d*x)^2)^3 --R --R ---R (983) +--R (988) --R 1 --R / --R 3 6 6 3 5 5 3 2 2 4 4 3 3 2 3 3 @@ -25938,7 +25637,7 @@ r0191:= 1/4*(c+d*x)/a/d/(a+b*c^2+2*b*c*d*x+b*d^2*x^2)^2+_ 3/8*atan(b^(1/2)*(c+d*x)/a^(1/2))/a^(5/2)/b^(1/2)/d --R --R ---R (984) +--R (989) --R 2 4 4 2 3 3 2 2 2 2 2 3 --R 3b d x + 12b c d x + (18b c + 6a b)d x + (12b c + 12a b c)d x --R + @@ -25969,7 +25668,7 @@ r0191:= 1/4*(c+d*x)/a/d/(a+b*c^2+2*b*c*d*x+b*d^2*x^2)^2+_ a0191:=integrate(t0191,x) --R --R ---R (985) +--R (990) --R [ --R 2 4 4 2 3 3 2 2 2 2 2 3 --R 3b d x + 12b c d x + (18b c + 6a b)d x + (12b c + 12a b c)d x @@ -26026,7 +25725,7 @@ a0191:=integrate(t0191,x) m0191a:=a0191.1-r0191 --R --R ---R (986) +--R (991) --R 2 2 2 +-----+ --R +-+ +-+ (b d x + 2b c d x + b c - a)\|- a b + 2a b d x + 2a b c --R 3\|a \|b log(----------------------------------------------------------) @@ -26048,7 +25747,7 @@ m0191a:=a0191.1-r0191 d0191a:=D(m0191a,x) --R --R ---R (987) 0 +--R (992) 0 --R Type: Expression Integer --E 992 @@ -26061,7 +25760,7 @@ m0191b:=a0191.2-r0191 --R 3\|a \|b atan(---------------) - 3\|a b atan(-------------) --R a +-+ --R \|a ---R (988) ----------------------------------------------------------- +--R (993) ----------------------------------------------------------- --R 2 +-+ +-+ +---+ --R 8a d\|a \|b \|a b --R Type: Expression Integer @@ -26071,7 +25770,7 @@ m0191b:=a0191.2-r0191 d0191b:=D(m0191b,x) --R --R ---R (989) 0 +--R (994) 0 --R Type: Expression Integer --E 994 @@ -26080,7 +25779,7 @@ t0192:= 1/(1-(c+d*x)^2) --R --R --R 1 ---R (990) - ---------------------- +--R (995) - ---------------------- --R 2 2 2 --R d x + 2c d x + c - 1 --R Type: Fraction Polynomial Integer @@ -26091,7 +25790,7 @@ r0192:= atanh(c+d*x)/d --R --R --R atanh(d x + c) ---R (991) -------------- +--R (996) -------------- --R d --R Type: Expression Integer --E 996 @@ -26101,7 +25800,7 @@ a0192:=integrate(t0192,x) --R --R --R log(d x + c + 1) - log(d x + c - 1) ---R (992) ----------------------------------- +--R (997) ----------------------------------- --R 2d --R Type: Union(Expression Integer,...) --E 997 @@ -26111,7 +25810,7 @@ m0192:=a0192-r0192 --R --R --R log(d x + c + 1) - log(d x + c - 1) - 2atanh(d x + c) ---R (993) ----------------------------------------------------- +--R (998) ----------------------------------------------------- --R 2d --R Type: Expression Integer --E 998 @@ -26120,7 +25819,7 @@ m0192:=a0192-r0192 d0192:=D(m0192,x) --R --R ---R (994) 0 +--R (999) 0 --R Type: Expression Integer --E 999 @@ -26128,10 +25827,10 @@ d0192:=D(m0192,x) t0193:= 1/(1-(1+x)^2) --R --R ---R 1 ---R (995) - ------- ---R 2 ---R x + 2x +--R 1 +--R (1000) - ------- +--R 2 +--R x + 2x --R Type: Fraction Polynomial Integer --E 1000 @@ -26139,7 +25838,7 @@ t0193:= 1/(1-(1+x)^2) r0193:= atanh(1+x) --R --R ---R (996) atanh(x + 1) +--R (1001) atanh(x + 1) --R Type: Expression Integer --E 1001 @@ -26147,9 +25846,9 @@ r0193:= atanh(1+x) a0193:=integrate(t0193,x) --R --R ---R log(x + 2) - log(x) ---R (997) ------------------- ---R 2 +--R log(x + 2) - log(x) +--R (1002) ------------------- +--R 2 --R Type: Union(Expression Integer,...) --E 1002 @@ -26157,9 +25856,9 @@ a0193:=integrate(t0193,x) m0193:=a0193-r0193 --R --R ---R log(x + 2) - log(x) - 2atanh(x + 1) ---R (998) ----------------------------------- ---R 2 +--R log(x + 2) - log(x) - 2atanh(x + 1) +--R (1003) ----------------------------------- +--R 2 --R Type: Expression Integer --E 1003 @@ -26167,7 +25866,7 @@ m0193:=a0193-r0193 d0193:=D(m0193,x) --R --R ---R (999) 0 +--R (1004) 0 --R Type: Expression Integer --E 1004 @@ -26177,7 +25876,7 @@ t0194:= x^3/(a+b*x+c*x^2) --R --R 3 --R x ---R (1000) -------------- +--R (1005) -------------- --R 2 --R c x + b x + a --R Type: Fraction Polynomial Integer @@ -26189,7 +25888,7 @@ r0194:= -b*x/c^2+1/2*x^2/c+b*(b^2-3*a*c)*atanh((b+2*c*x)/_ 1/2*(b^2-a*c)*log(a+b*x+c*x^2)/c^3 --R --R ---R (1001) +--R (1006) --R 3 2c x + b --R (- 6a b c + 2b )atanh(--------------) --R +-----------+ @@ -26210,7 +25909,7 @@ r0194:= -b*x/c^2+1/2*x^2/c+b*(b^2-3*a*c)*atanh((b+2*c*x)/_ a0194:=integrate(t0194,x) --R --R ---R (1002) +--R (1007) --R [ --R 3 --R (3a b c - b ) @@ -26257,7 +25956,7 @@ a0194:=integrate(t0194,x) m0194a:=a0194.1-r0194 --R --R ---R (1003) +--R (1008) --R 3 --R (3a b c - b ) --R * @@ -26288,7 +25987,7 @@ m0194a:=a0194.1-r0194 d0194a:=D(m0194a,x) --R --R ---R (1004) 0 +--R (1009) 0 --R Type: Expression Integer --E 1009 @@ -26296,7 +25995,7 @@ d0194a:=D(m0194a,x) m0194b:=a0194.2-r0194 --R --R ---R (1005) +--R (1010) --R +---------+ --R 3 | 2 2c x + b --R (3a b c - b )\|4a c - b atanh(--------------) @@ -26321,7 +26020,7 @@ m0194b:=a0194.2-r0194 d0194b:=D(m0194b,x) --R --R ---R (1006) 0 +--R (1011) 0 --R Type: Expression Integer --E 1011 @@ -26331,7 +26030,7 @@ t0195:= x^2/(a+b*x+c*x^2) --R --R 2 --R x ---R (1007) -------------- +--R (1012) -------------- --R 2 --R c x + b x + a --R Type: Fraction Polynomial Integer @@ -26342,7 +26041,7 @@ r0195:= x/c-(b^2-2*a*c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ c^2/(b^2-4*a*c)^(1/2)-1/2*b*log(a+b*x+c*x^2)/c^2 --R --R ---R (1008) +--R (1013) --R 2 2c x + b --R (4a c - 2b )atanh(--------------) --R +-----------+ @@ -26363,7 +26062,7 @@ r0195:= x/c-(b^2-2*a*c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ a0195:=integrate(t0195,x) --R --R ---R (1009) +--R (1014) --R [ --R 2 --R (2a c - b ) @@ -26410,7 +26109,7 @@ a0195:=integrate(t0195,x) m0195a:=a0195.1-r0195 --R --R ---R (1010) +--R (1015) --R 2 --R (2a c - b ) --R * @@ -26441,7 +26140,7 @@ m0195a:=a0195.1-r0195 d0195a:=D(m0195a,x) --R --R ---R (1011) 0 +--R (1016) 0 --R Type: Expression Integer --E 1016 @@ -26449,7 +26148,7 @@ d0195a:=D(m0195a,x) m0195b:=a0195.2-r0195 --R --R ---R (1012) +--R (1017) --R +---------+ --R 2 | 2 2c x + b --R (- 2a c + b )\|4a c - b atanh(--------------) @@ -26474,7 +26173,7 @@ m0195b:=a0195.2-r0195 d0195b:=D(m0195b,x) --R --R ---R (1013) 0 +--R (1018) 0 --R Type: Expression Integer --E 1018 @@ -26483,7 +26182,7 @@ t0196:= 1/((a/b)^(2/n)+x^2-2*(a/b)^(1/n)*x*cos((%pi-2*k*%pi)/n)) --R --R --R 1 ---R (1014) ----------------------------------- +--R (1019) ----------------------------------- --R 2 1 --R - - --R a n (2k - 1)%pi a n 2 @@ -26508,7 +26207,7 @@ r0196:= -atan((-x+(a/b)^(1/n)*cos((%pi-2*k*%pi)/n))/((a/b)^(1/n))/_ --R (2k - 1)%pi a n --R sin(-----------)(-) --R n b ---R (1015) - ------------------------------ +--R (1020) - ------------------------------ --R 1 --R - --R (2k - 1)%pi a n @@ -26521,7 +26220,7 @@ r0196:= -atan((-x+(a/b)^(1/n)*cos((%pi-2*k*%pi)/n))/((a/b)^(1/n))/_ a0196:=integrate(t0196,x) --R --R ---R (1016) +--R (1021) --R [ --R log --R 2 2 @@ -26688,7 +26387,7 @@ a0196:=integrate(t0196,x) m0196a:=a0196.1-r0196 --R --R ---R (1017) +--R (1022) --R 1 --R - --R (2k - 1)%pi a n @@ -26827,133 +26526,10 @@ m0196a:=a0196.1-r0196 --E 1022 --S 1023 of 1483 -d0196a:=D(m0196a,x) +d0196a:=normalize(D(m0196a,x)) --R --R ---R (1018) ---R 2 2 ---R - ---R a n ---R - ((-) ) ---R b ---R + ---R 1 2 ---R - ---R (2k - 1)%pi 2 (2k - 1)%pi 4 (2k - 1)%pi 2 a n ---R (sin(-----------) + cos(-----------) + 2cos(-----------) )((-) ) ---R n n n b ---R + ---R 1 ---R - ---R (2k - 1)%pi 3 a n 2 (2k - 1)%pi 2 ---R - 2x cos(-----------) (-) + x cos(-----------) ---R n b n ---R * ---R 2 ---R - ---R a n ---R (-) ---R b ---R + ---R 1 4 ---R - ---R (2k - 1)%pi 2 (2k - 1)%pi 2 (2k - 1)%pi 4 a n ---R (- cos(-----------) sin(-----------) - 2cos(-----------) )((-) ) ---R n n n b ---R + ---R 1 3 1 2 ---R - - ---R (2k - 1)%pi 3 a n 2 (2k - 1)%pi 2 a n ---R 2x cos(-----------) ((-) ) - x cos(-----------) ((-) ) ---R n b n b ---R / ---R 1 2 ---R - ---R (2k - 1)%pi 2 (2k - 1)%pi 2 a n ---R (sin(-----------) + cos(-----------) )((-) ) ---R n n b ---R + ---R 1 ---R - ---R (2k - 1)%pi a n 2 ---R - 2x cos(-----------)(-) + x ---R n b ---R * ---R 2 2 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R (2k - 1)%pi 4 (2k - 1)%pi 2 (2k - 1)%pi 2 ---R (- cos(-----------) - cos(-----------) )sin(-----------) ---R n n n ---R + ---R (2k - 1)%pi 6 (2k - 1)%pi 4 ---R - cos(-----------) - cos(-----------) ---R n n ---R * ---R 1 4 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R (2k - 1)%pi 3 (2k - 1)%pi (2k - 1)%pi 2 ---R (2x cos(-----------) - 2x cos(-----------))sin(-----------) ---R n n n ---R + ---R (2k - 1)%pi 5 ---R 4x cos(-----------) ---R n ---R * ---R 1 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 2 (2k - 1)%pi 2 2 (2k - 1)%pi 2 ---R (- x cos(-----------) + x )sin(-----------) ---R n n ---R + ---R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 ---R - 6x cos(-----------) + 4x cos(-----------) ---R n n ---R * ---R 1 2 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 1 ---R - ---R 3 (2k - 1)%pi 3 3 (2k - 1)%pi a n ---R (4x cos(-----------) - 4x cos(-----------))(-) ---R n n b ---R + ---R 4 (2k - 1)%pi 2 4 ---R - x cos(-----------) + x ---R n ---R * ---R 2 ---R - ---R a n ---R (-) ---R b ---R + ---R 1 6 ---R - ---R (2k - 1)%pi 4 (2k - 1)%pi 2 (2k - 1)%pi 6 a n ---R (cos(-----------) sin(-----------) + cos(-----------) )((-) ) ---R n n n b ---R + ---R 1 5 1 4 ---R - - ---R (2k - 1)%pi 5 a n 2 (2k - 1)%pi 4 a n ---R - 2x cos(-----------) ((-) ) + x cos(-----------) ((-) ) ---R n b n b +--R (1023) 0 --R Type: Expression Integer --E 1023 @@ -26961,7 +26537,7 @@ d0196a:=D(m0196a,x) m0196b:=a0196.2-r0196 --R --R ---R (1019) +--R (1024) --R 1 --R - --R (2k - 1)%pi a n @@ -27023,133 +26599,10 @@ m0196b:=a0196.2-r0196 --E 1024 --S 1025 of 1483 -d0196b:=D(m0196b,x) +d0196b:=normalize(D(m0196b,x)) --R --R ---R (1020) ---R 2 2 ---R - ---R a n ---R - ((-) ) ---R b ---R + ---R 1 2 ---R - ---R (2k - 1)%pi 2 (2k - 1)%pi 4 (2k - 1)%pi 2 a n ---R (sin(-----------) + cos(-----------) + 2cos(-----------) )((-) ) ---R n n n b ---R + ---R 1 ---R - ---R (2k - 1)%pi 3 a n 2 (2k - 1)%pi 2 ---R - 2x cos(-----------) (-) + x cos(-----------) ---R n b n ---R * ---R 2 ---R - ---R a n ---R (-) ---R b ---R + ---R 1 4 ---R - ---R (2k - 1)%pi 2 (2k - 1)%pi 2 (2k - 1)%pi 4 a n ---R (- cos(-----------) sin(-----------) - 2cos(-----------) )((-) ) ---R n n n b ---R + ---R 1 3 1 2 ---R - - ---R (2k - 1)%pi 3 a n 2 (2k - 1)%pi 2 a n ---R 2x cos(-----------) ((-) ) - x cos(-----------) ((-) ) ---R n b n b ---R / ---R 1 2 ---R - ---R (2k - 1)%pi 2 (2k - 1)%pi 2 a n ---R (sin(-----------) + cos(-----------) )((-) ) ---R n n b ---R + ---R 1 ---R - ---R (2k - 1)%pi a n 2 ---R - 2x cos(-----------)(-) + x ---R n b ---R * ---R 2 2 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R (2k - 1)%pi 4 (2k - 1)%pi 2 (2k - 1)%pi 2 ---R (- cos(-----------) - cos(-----------) )sin(-----------) ---R n n n ---R + ---R (2k - 1)%pi 6 (2k - 1)%pi 4 ---R - cos(-----------) - cos(-----------) ---R n n ---R * ---R 1 4 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R (2k - 1)%pi 3 (2k - 1)%pi (2k - 1)%pi 2 ---R (2x cos(-----------) - 2x cos(-----------))sin(-----------) ---R n n n ---R + ---R (2k - 1)%pi 5 ---R 4x cos(-----------) ---R n ---R * ---R 1 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 2 (2k - 1)%pi 2 2 (2k - 1)%pi 2 ---R (- x cos(-----------) + x )sin(-----------) ---R n n ---R + ---R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 ---R - 6x cos(-----------) + 4x cos(-----------) ---R n n ---R * ---R 1 2 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 1 ---R - ---R 3 (2k - 1)%pi 3 3 (2k - 1)%pi a n ---R (4x cos(-----------) - 4x cos(-----------))(-) ---R n n b ---R + ---R 4 (2k - 1)%pi 2 4 ---R - x cos(-----------) + x ---R n ---R * ---R 2 ---R - ---R a n ---R (-) ---R b ---R + ---R 1 6 ---R - ---R (2k - 1)%pi 4 (2k - 1)%pi 2 (2k - 1)%pi 6 a n ---R (cos(-----------) sin(-----------) + cos(-----------) )((-) ) ---R n n n b ---R + ---R 1 5 1 4 ---R - - ---R (2k - 1)%pi 5 a n 2 (2k - 1)%pi 4 a n ---R - 2x cos(-----------) ((-) ) + x cos(-----------) ((-) ) ---R n b n b +--R (1025) 0 --R Type: Expression Integer --E 1025 @@ -27158,7 +26611,7 @@ t0197:= 1/x^2/(a+b*x+c*x^2) --R --R --R 1 ---R (1021) ------------------ +--R (1026) ------------------ --R 4 3 2 --R c x + b x + a x --R Type: Fraction Polynomial Integer @@ -27169,7 +26622,7 @@ r0197:= -1/a/x-(b^2-2*a*c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a^2/_ (b^2-4*a*c)^(1/2)-b*log(x)/a^2+1/2*b*log(a+b*x+c*x^2)/a^2 --R --R ---R (1022) +--R (1027) --R 2 2c x + b --R (4a c - 2b )x atanh(--------------) --R +-----------+ @@ -27190,7 +26643,7 @@ r0197:= -1/a/x-(b^2-2*a*c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a^2/_ a0197:=integrate(t0197,x) --R --R ---R (1023) +--R (1028) --R [ --R 2 --R (2a c - b )x @@ -27237,7 +26690,7 @@ a0197:=integrate(t0197,x) m0197a:=a0197.1-r0197 --R --R ---R (1024) +--R (1029) --R 2 --R (2a c - b ) --R * @@ -27268,7 +26721,7 @@ m0197a:=a0197.1-r0197 d0197a:=D(m0197a,x) --R --R ---R (1025) 0 +--R (1030) 0 --R Type: Expression Integer --E 1030 @@ -27276,7 +26729,7 @@ d0197a:=D(m0197a,x) m0197b:=a0197.2-r0197 --R --R ---R (1026) +--R (1031) --R +---------+ --R 2 | 2 2c x + b --R (- 2a c + b )\|4a c - b atanh(--------------) @@ -27301,7 +26754,7 @@ m0197b:=a0197.2-r0197 d0197b:=D(m0197b,x) --R --R ---R (1027) 0 +--R (1032) 0 --R Type: Expression Integer --E 1032 @@ -27310,7 +26763,7 @@ t0198:= 1/x^3/(a+b*x+c*x^2) --R --R --R 1 ---R (1028) ------------------ +--R (1033) ------------------ --R 5 4 3 --R c x + b x + a x --R Type: Fraction Polynomial Integer @@ -27322,7 +26775,7 @@ r0198:= -1/2/a/x^2+b/a^2/x+b*(b^2-3*a*c)*atanh((b+2*c*x)/_ log(x)/a^3-1/2*(b^2-a*c)*log(a+b*x+c*x^2)/a^3 --R --R ---R (1029) +--R (1034) --R 3 2 2c x + b --R (- 6a b c + 2b )x atanh(--------------) --R +-----------+ @@ -27349,7 +26802,7 @@ r0198:= -1/2/a/x^2+b/a^2/x+b*(b^2-3*a*c)*atanh((b+2*c*x)/_ a0198:=integrate(t0198,x) --R --R ---R (1030) +--R (1035) --R [ --R 3 2 --R (3a b c - b )x @@ -27408,7 +26861,7 @@ a0198:=integrate(t0198,x) m0198a:=a0198.1-r0198 --R --R ---R (1031) +--R (1036) --R 3 --R (3a b c - b ) --R * @@ -27439,7 +26892,7 @@ m0198a:=a0198.1-r0198 d0198a:=D(m0198a,x) --R --R ---R (1032) 0 +--R (1037) 0 --R Type: Expression Integer --E 1037 @@ -27447,7 +26900,7 @@ d0198a:=D(m0198a,x) m0198b:=a0198.2-r0198 --R --R ---R (1033) +--R (1038) --R +---------+ --R 3 | 2 2c x + b --R (3a b c - b )\|4a c - b atanh(--------------) @@ -27472,7 +26925,7 @@ m0198b:=a0198.2-r0198 d0198b:=D(m0198b,x) --R --R ---R (1034) 0 +--R (1039) 0 --R Type: Expression Integer --E 1039 @@ -27482,7 +26935,7 @@ t0199:= x^3/(a+b*x+c*x^2)^2 --R --R 3 --R x ---R (1035) -------------------------------------------- +--R (1040) -------------------------------------------- --R 2 4 3 2 2 2 --R c x + 2b c x + (2a c + b )x + 2a b x + a --R Type: Fraction Polynomial Integer @@ -27496,7 +26949,7 @@ r0199:= -1/2*(b^2-a*c)/c^3/(a+b*x+c*x^2)+1/2*b*(b^2-3*a*c)*(b+2*c*x)/_ 1/2*log(a+b*x+c*x^2)/c^2 --R --R ---R (1036) +--R (1041) --R 2 3 2 2 4 2 3 --R ((12a b c - 2b c)x + (12a b c - 2b )x + 12a b c - 2a b ) --R * @@ -27526,7 +26979,7 @@ r0199:= -1/2*(b^2-a*c)/c^3/(a+b*x+c*x^2)+1/2*b*(b^2-3*a*c)*(b+2*c*x)/_ a0199:=integrate(t0199,x) --R --R ---R (1037) +--R (1042) --R [ --R 2 3 2 2 4 2 3 --R ((6a b c - b c)x + (6a b c - b )x + 6a b c - a b ) @@ -27588,7 +27041,7 @@ a0199:=integrate(t0199,x) m0199a:=a0199.1-r0199 --R --R ---R (1038) +--R (1043) --R 3 --R (6a b c - b ) --R * @@ -27619,7 +27072,7 @@ m0199a:=a0199.1-r0199 d0199a:=D(m0199a,x) --R --R ---R (1039) 0 +--R (1044) 0 --R Type: Expression Integer --E 1044 @@ -27627,7 +27080,7 @@ d0199a:=D(m0199a,x) m0199b:=a0199.2-r0199 --R --R ---R (1040) +--R (1045) --R +---------+ --R 3 | 2 2c x + b --R (- 6a b c + b )\|4a c - b atanh(--------------) @@ -27652,7 +27105,7 @@ m0199b:=a0199.2-r0199 d0199b:=D(m0199b,x) --R --R ---R (1041) 0 +--R (1046) 0 --R Type: Expression Integer --E 1046 @@ -27662,7 +27115,7 @@ t0200:= x^2/(a+b*x+c*x^2)^2 --R --R 2 --R x ---R (1042) -------------------------------------------- +--R (1047) -------------------------------------------- --R 2 4 3 2 2 2 --R c x + 2b c x + (2a c + b )x + 2a b x + a --R Type: Fraction Polynomial Integer @@ -27673,7 +27126,7 @@ r0200:= -x/c/(a+b*x+c*x^2)-a*(b+2*c*x)/c/(b^2-4*a*c)/(a+b*x+c*x^2)+_ 4*a*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(3/2) --R --R ---R (1043) +--R (1048) --R 2 2 2 2c x + b --R (- 4a c x - 4a b c x - 4a c)atanh(--------------) --R +-----------+ @@ -27694,7 +27147,7 @@ r0200:= -x/c/(a+b*x+c*x^2)-a*(b+2*c*x)/c/(b^2-4*a*c)/(a+b*x+c*x^2)+_ a0200:=integrate(t0200,x) --R --R ---R (1044) +--R (1049) --R [ --R 2 2 2 --R (2a c x + 2a b c x + 2a c) @@ -27741,7 +27194,7 @@ a0200:=integrate(t0200,x) m0200a:=a0200.1-r0200 --R --R ---R (1045) +--R (1050) --R 2a --R * --R log @@ -27771,7 +27224,7 @@ m0200a:=a0200.1-r0200 d0200a:=D(m0200a,x) --R --R ---R (1046) 0 +--R (1051) 0 --R Type: Expression Integer --E 1051 @@ -27779,7 +27232,7 @@ d0200a:=D(m0200a,x) m0200b:=a0200.2-r0200 --R --R ---R (1047) +--R (1052) --R +---------+ --R | 2 2c x + b --R 4a\|4a c - b atanh(--------------) @@ -27804,7 +27257,7 @@ m0200b:=a0200.2-r0200 d0200b:=D(m0200b,x) --R --R ---R (1048) 0 +--R (1053) 0 --R Type: Expression Integer --E 1053 @@ -27813,7 +27266,7 @@ t0201:= 1/x^2/(a+b*x+c*x^2)^2 --R --R --R 1 ---R (1049) ----------------------------------------------- +--R (1054) ----------------------------------------------- --R 2 6 5 2 4 3 2 2 --R c x + 2b c x + (2a c + b )x + 2a b x + a x --R Type: Fraction Polynomial Integer @@ -27827,7 +27280,7 @@ r0201:= -1/a^2/x-1/2*b/a^2/(a+b*x+c*x^2)-1/2*(b^2-2*a*c)*(b+2*c*x)/_ (b^2-4*a*c)^(1/2)-2*b*log(x)/a^3+b*log(a+b*x+c*x^2)/a^3 --R --R ---R (1050) +--R (1055) --R 2 3 2 2 4 3 2 2 3 5 2 --R (12a c - 12a b c + 2b c)x + (12a b c - 12a b c + 2b )x --R + @@ -27868,7 +27321,7 @@ r0201:= -1/a^2/x-1/2*b/a^2/(a+b*x+c*x^2)-1/2*(b^2-2*a*c)*(b+2*c*x)/_ a0201:=integrate(t0201,x) --R --R ---R (1051) +--R (1056) --R [ --R 2 3 2 2 4 3 2 2 3 5 2 --R (6a c - 6a b c + b c)x + (6a b c - 6a b c + b )x @@ -27952,7 +27405,7 @@ a0201:=integrate(t0201,x) m0201a:=a0201.1-r0201 --R --R ---R (1052) +--R (1057) --R 2 2 2 4 --R (6a c - 6a b c + b ) --R * @@ -27983,7 +27436,7 @@ m0201a:=a0201.1-r0201 d0201a:=D(m0201a,x) --R --R ---R (1053) 0 +--R (1058) 0 --R Type: Expression Integer --E 1058 @@ -27991,7 +27444,7 @@ d0201a:=D(m0201a,x) m0201b:=a0201.2-r0201 --R --R ---R (1054) +--R (1059) --R +---------+ --R 2 2 2 4 | 2 2c x + b --R (- 12a c + 12a b c - 2b )\|4a c - b atanh(--------------) @@ -28016,7 +27469,7 @@ m0201b:=a0201.2-r0201 d0201b:=D(m0201b,x) --R --R ---R (1055) 0 +--R (1060) 0 --R Type: Expression Integer --E 1060 @@ -28025,7 +27478,7 @@ t0202:= 1/x^3/(a+b*x+c*x^2)^2 --R --R --R 1 ---R (1056) ----------------------------------------------- +--R (1061) ----------------------------------------------- --R 2 7 6 2 5 4 2 3 --R c x + 2b c x + (2a c + b )x + 2a b x + a x --R Type: Fraction Polynomial Integer @@ -28040,7 +27493,7 @@ r0202:= -1/2/a^2/x^2+2*b/a^3/x+1/2*(b^2-a*c)/a^3/(a+b*x+c*x^2)+_ 1/2*(3*b^2-2*a*c)*log(a+b*x+c*x^2)/a^4 --R --R ---R (1057) +--R (1062) --R 2 3 3 2 5 4 2 2 2 4 6 3 --R (- 60a b c + 40a b c - 6b c)x + (- 60a b c + 40a b c - 6b )x --R + @@ -28090,7 +27543,7 @@ r0202:= -1/2/a^2/x^2+2*b/a^3/x+1/2*(b^2-a*c)/a^3/(a+b*x+c*x^2)+_ a0202:=integrate(t0202,x) --R --R ---R (1058) +--R (1063) --R [ --R 2 3 3 2 5 4 2 2 2 4 6 3 --R (30a b c - 20a b c + 3b c)x + (30a b c - 20a b c + 3b )x @@ -28195,7 +27648,7 @@ a0202:=integrate(t0202,x) m0202a:=a0202.1-r0202 --R --R ---R (1059) +--R (1064) --R 2 2 3 5 --R (30a b c - 20a b c + 3b ) --R * @@ -28226,7 +27679,7 @@ m0202a:=a0202.1-r0202 d0202a:=D(m0202a,x) --R --R ---R (1060) 0 +--R (1065) 0 --R Type: Expression Integer --E 1065 @@ -28234,7 +27687,7 @@ d0202a:=D(m0202a,x) m0202b:=a0202.2-r0202 --R --R ---R (1061) +--R (1066) --R +---------+ --R 2 2 3 5 | 2 2c x + b --R (30a b c - 20a b c + 3b )\|4a c - b atanh(--------------) @@ -28259,7 +27712,7 @@ m0202b:=a0202.2-r0202 d0202b:=D(m0202b,x) --R --R ---R (1062) 0 +--R (1067) 0 --R Type: Expression Integer --E 1067 @@ -28267,7 +27720,7 @@ d0202b:=D(m0202b,x) t0203:= x^3/(a+b*x+c*x^2)^3 --R --R ---R (1063) +--R (1068) --R 3 --R x --R / @@ -28286,7 +27739,7 @@ r0203:= -1/4*a/c^2/(a+b*x+c*x^2)^2-1/2*x^2/c/(a+b*x+c*x^2)^2+_ 6*a*b*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(5/2) --R --R ---R (1064) +--R (1069) --R 3 4 2 2 3 2 2 3 2 2 2 --R 12a b c x + 24a b c x + (24a b c + 12a b c)x + 24a b c x --R + @@ -28328,7 +27781,7 @@ r0203:= -1/4*a/c^2/(a+b*x+c*x^2)^2-1/2*x^2/c/(a+b*x+c*x^2)^2+_ a0203:=integrate(t0203,x) --R --R ---R (1065) +--R (1070) --R [ --R 3 4 2 2 3 2 2 3 2 2 2 3 --R (6a b c x + 12a b c x + (12a b c + 6a b c)x + 12a b c x + 6a b c) @@ -28411,7 +27864,7 @@ a0203:=integrate(t0203,x) m0203a:=a0203.1-r0203 --R --R ---R (1066) +--R (1071) --R 3a b --R * --R log @@ -28441,7 +27894,7 @@ m0203a:=a0203.1-r0203 d0203a:=D(m0203a,x) --R --R ---R (1067) 0 +--R (1072) 0 --R Type: Expression Integer --E 1072 @@ -28449,7 +27902,7 @@ d0203a:=D(m0203a,x) m0203b:=a0203.2-r0203 --R --R ---R (1068) +--R (1073) --R +---------+ --R | 2 2c x + b --R - 6a b\|4a c - b atanh(--------------) @@ -28474,7 +27927,7 @@ m0203b:=a0203.2-r0203 d0203b:=D(m0203b,x) --R --R ---R (1069) 0 +--R (1074) 0 --R Type: Expression Integer --E 1074 @@ -28482,7 +27935,7 @@ d0203b:=D(m0203b,x) t0204:= x^2/(a+b*x+c*x^2)^3 --R --R ---R (1070) +--R (1075) --R 2 --R x --R / @@ -28501,7 +27954,7 @@ r0204:= 1/12*b/c^2/(a+b*x+c*x^2)^2-1/3*x/c/(a+b*x+c*x^2)^2-_ 2*(b^2+2*a*c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(5/2) --R --R ---R (1071) +--R (1076) --R 3 2 2 4 2 3 3 --R (- 8a c - 4b c )x + (- 16a b c - 8b c)x --R + @@ -28540,7 +27993,7 @@ r0204:= 1/12*b/c^2/(a+b*x+c*x^2)^2-1/3*x/c/(a+b*x+c*x^2)^2-_ a0204:=integrate(t0204,x) --R --R ---R (1072) +--R (1077) --R [ --R 3 2 2 4 2 3 3 2 2 2 4 2 --R (4a c + 2b c )x + (8a b c + 4b c)x + (8a c + 8a b c + 2b )x @@ -28620,7 +28073,7 @@ a0204:=integrate(t0204,x) m0204a:=a0204.1-r0204 --R --R ---R (1073) +--R (1078) --R 2 --R (2a c + b ) --R * @@ -28651,7 +28104,7 @@ m0204a:=a0204.1-r0204 d0204a:=D(m0204a,x) --R --R ---R (1074) 0 +--R (1079) 0 --R Type: Expression Integer --E 1079 @@ -28659,7 +28112,7 @@ d0204a:=D(m0204a,x) m0204b:=a0204.2-r0204 --R --R ---R (1075) +--R (1080) --R +---------+ --R 2 | 2 2c x + b --R (4a c + 2b )\|4a c - b atanh(--------------) @@ -28684,7 +28137,7 @@ m0204b:=a0204.2-r0204 d0204b:=D(m0204b,x) --R --R ---R (1076) 0 +--R (1081) 0 --R Type: Expression Integer --E 1081 @@ -28692,7 +28145,7 @@ d0204b:=D(m0204b,x) t0205:= 1/(a+b*x+c*x^2)^3 --R --R ---R (1077) +--R (1082) --R 1 --R / --R 3 6 2 5 2 2 4 3 3 2 2 2 @@ -28709,7 +28162,7 @@ r0205:= -1/2*(b+2*c*x)/(b^2-4*a*c)/(a+b*x+c*x^2)^2+_ 12*c^2*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(5/2) --R --R ---R (1078) +--R (1083) --R 4 4 3 3 3 2 2 2 2 2 2 --R (- 24c x - 48b c x + (- 48a c - 24b c )x - 48a b c x - 24a c ) --R * @@ -28742,7 +28195,7 @@ r0205:= -1/2*(b+2*c*x)/(b^2-4*a*c)/(a+b*x+c*x^2)^2+_ a0205:=integrate(t0205,x) --R --R ---R (1079) +--R (1084) --R [ --R 4 4 3 3 3 2 2 2 2 2 2 --R (12c x + 24b c x + (24a c + 12b c )x + 24a b c x + 12a c ) @@ -28810,7 +28263,7 @@ a0205:=integrate(t0205,x) m0205a:=a0205.1-r0205 --R --R ---R (1080) +--R (1085) --R 2 --R 6c --R * @@ -28841,7 +28294,7 @@ m0205a:=a0205.1-r0205 d0205a:=D(m0205a,x) --R --R ---R (1081) 0 +--R (1086) 0 --R Type: Expression Integer --E 1086 @@ -28849,7 +28302,7 @@ d0205a:=D(m0205a,x) m0205b:=a0205.2-r0205 --R --R ---R (1082) +--R (1087) --R +---------+ --R 2 | 2 2c x + b --R 12c \|4a c - b atanh(--------------) @@ -28874,7 +28327,7 @@ m0205b:=a0205.2-r0205 d0205b:=D(m0205b,x) --R --R ---R (1083) 0 +--R (1088) 0 --R Type: Expression Integer --E 1088 @@ -28882,7 +28335,7 @@ d0205b:=D(m0205b,x) t0206:= 1/x/(a+b*x+c*x^2)^3 --R --R ---R (1084) +--R (1089) --R 1 --R / --R 3 7 2 6 2 2 5 3 4 2 2 3 @@ -28903,7 +28356,7 @@ r0206:= 1/4/a/(a+b*x+c*x^2)^2+1/4*b*(b+2*c*x)/a/(b^2-4*a*c)/(a+b*x+c*x^2)^2+_ log(x)/a^3-1/2*log(a+b*x+c*x^2)/a^3 --R --R ---R (1085) +--R (1090) --R 2 4 3 3 5 2 4 2 2 3 4 2 6 3 --R (60a b c - 20a b c + 2b c )x + (120a b c - 40a b c + 4b c)x --R + @@ -28971,7 +28424,7 @@ r0206:= 1/4/a/(a+b*x+c*x^2)^2+1/4*b*(b+2*c*x)/a/(b^2-4*a*c)/(a+b*x+c*x^2)^2+_ a0206:=integrate(t0206,x) --R --R ---R (1086) +--R (1091) --R [ --R 2 4 3 3 5 2 4 2 2 3 4 2 6 3 --R (30a b c - 10a b c + b c )x + (60a b c - 20a b c + 2b c)x @@ -29112,7 +28565,7 @@ a0206:=integrate(t0206,x) m0206a:=a0206.1-r0206 --R --R ---R (1087) +--R (1092) --R 2 2 3 5 --R (30a b c - 10a b c + b ) --R * @@ -29143,7 +28596,7 @@ m0206a:=a0206.1-r0206 d0206a:=D(m0206a,x) --R --R ---R (1088) 0 +--R (1093) 0 --R Type: Expression Integer --E 1093 @@ -29151,7 +28604,7 @@ d0206a:=D(m0206a,x) m0206b:=a0206.2-r0206 --R --R ---R (1089) +--R (1094) --R +---------+ --R 2 2 3 5 | 2 2c x + b --R (- 30a b c + 10a b c - b )\|4a c - b atanh(--------------) @@ -29176,7 +28629,7 @@ m0206b:=a0206.2-r0206 d0206b:=D(m0206b,x) --R --R ---R (1090) 0 +--R (1095) 0 --R Type: Expression Integer --E 1095 @@ -29184,7 +28637,7 @@ d0206b:=D(m0206b,x) t0207:= 1/x^2/(a+b*x+c*x^2)^3 --R --R ---R (1091) +--R (1096) --R 1 --R / --R 3 8 2 7 2 2 6 3 5 2 2 4 @@ -29207,7 +28660,7 @@ r0207:= -1/a^3/x-1/4*b/a^2/(a+b*x+c*x^2)^2-1/4*(b^2-2*a*c)*(b+2*c*x)/a^2/(b^2-_ 3/2*b*log(a+b*x+c*x^2)/a^4 --R --R ---R (1092) +--R (1097) --R 3 5 2 2 4 4 3 6 2 5 --R (120a c - 180a b c + 60a b c - 6b c )x --R + @@ -29293,7 +28746,7 @@ r0207:= -1/a^3/x-1/4*b/a^2/(a+b*x+c*x^2)^2-1/4*(b^2-2*a*c)*(b+2*c*x)/a^2/(b^2-_ a0207:=integrate(t0207,x) --R --R ---R (1093) +--R (1098) --R [ --R 3 5 2 2 4 4 3 6 2 5 --R (60a c - 90a b c + 30a b c - 3b c )x @@ -29467,7 +28920,7 @@ a0207:=integrate(t0207,x) m0207a:=a0207.1-r0207 --R --R ---R (1094) +--R (1099) --R 3 3 2 2 2 4 6 --R (60a c - 90a b c + 30a b c - 3b ) --R * @@ -29498,7 +28951,7 @@ m0207a:=a0207.1-r0207 d0207a:=D(m0207a,x) --R --R ---R (1095) 0 +--R (1100) 0 --R Type: Expression Integer --E 1100 @@ -29506,7 +28959,7 @@ d0207a:=D(m0207a,x) m0207b:=a0207.2-r0207 --R --R ---R (1096) +--R (1101) --R +---------+ --R 3 3 2 2 2 4 6 | 2 2c x + b --R (- 60a c + 90a b c - 30a b c + 3b )\|4a c - b atanh(--------------) @@ -29535,7 +28988,7 @@ m0207b:=a0207.2-r0207 d0207b:=D(m0207b,x) --R --R ---R (1097) 0 +--R (1102) 0 --R Type: Expression Integer --E 1102 @@ -29543,7 +28996,7 @@ d0207b:=D(m0207b,x) t0208:= x^3/(c+d*x+e*x^2)^4 --R --R ---R (1098) +--R (1103) --R 3 --R x --R / @@ -29567,7 +29020,7 @@ r0208:= -1/60*(d^2+5*c*e)/e^3/(c+d*x+e*x^2)^3+1/20*d*x/e^2/(c+d*x+e*x^2)^3-_ atanh((d+2*e*x)/(d^2-4*c*e)^(1/2))/(d^2-4*c*e)^(7/2) --R --R ---R (1099) +--R (1104) --R 4 3 3 6 2 3 4 2 5 --R (72c d e + 12d e )x + (216c d e + 36d e )x --R + @@ -29630,7 +29083,7 @@ r0208:= -1/60*(d^2+5*c*e)/e^3/(c+d*x+e*x^2)^3+1/20*d*x/e^2/(c+d*x+e*x^2)^3-_ a0208:=integrate(t0208,x) --R --R ---R (1100) +--R (1105) --R [ --R 4 3 3 6 2 3 4 2 5 --R (36c d e + 6d e )x + (108c d e + 18d e )x @@ -29761,7 +29214,7 @@ a0208:=integrate(t0208,x) m0208a:=a0208.1-r0208 --R --R ---R (1101) +--R (1106) --R 3 --R (6c d e + d ) --R * @@ -29792,7 +29245,7 @@ m0208a:=a0208.1-r0208 d0208a:=D(m0208a,x) --R --R ---R (1102) 0 +--R (1107) 0 --R Type: Expression Integer --E 1107 @@ -29800,7 +29253,7 @@ d0208a:=D(m0208a,x) m0208b:=a0208.2-r0208 --R --R ---R (1103) +--R (1108) --R +---------+ --R 3 | 2 2e x + d --R (- 12c d e - 2d )\|4c e - d atanh(--------------) @@ -29825,7 +29278,7 @@ m0208b:=a0208.2-r0208 d0208b:=D(m0208b,x) --R --R ---R (1104) 0 +--R (1109) 0 --R Type: Expression Integer --E 1109 @@ -29835,7 +29288,7 @@ t0209:= (d+e*x)^3/(a+b*x+c*x^2) --R --R 3 3 2 2 2 3 --R e x + 3d e x + 3d e x + d ---R (1105) ---------------------------- +--R (1110) ---------------------------- --R 2 --R c x + b x + a --R Type: Fraction Polynomial Integer @@ -29848,7 +29301,7 @@ r0209:= e^2*(3*c*d-b*e)*x/c^2+1/2*e^3*x^2/c-(2*c*d-b*e)*(c^2*d^2+b^2*e^2-_ log(a+b*x+c*x^2)/c^3 --R --R ---R (1106) +--R (1111) --R 3 3 2 2 2 2 2 3 3 --R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d ) --R * @@ -29878,7 +29331,7 @@ r0209:= e^2*(3*c*d-b*e)*x/c^2+1/2*e^3*x^2/c-(2*c*d-b*e)*(c^2*d^2+b^2*e^2-_ a0209:=integrate(t0209,x) --R --R ---R (1107) +--R (1112) --R [ --R 3 3 2 2 2 2 2 3 3 --R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d ) @@ -29940,7 +29393,7 @@ a0209:=integrate(t0209,x) m0209a:=a0209.1-r0209 --R --R ---R (1108) +--R (1113) --R 3 3 2 2 2 2 2 3 3 --R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d ) --R * @@ -29974,7 +29427,7 @@ m0209a:=a0209.1-r0209 d0209a:=D(m0209a,x) --R --R ---R (1109) 0 +--R (1114) 0 --R Type: Expression Integer --E 1114 @@ -29982,7 +29435,7 @@ d0209a:=D(m0209a,x) m0209b:=a0209.2-r0209 --R --R ---R (1110) +--R (1115) --R +---------+ --R 3 3 2 2 2 2 2 3 3 | 2 --R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d )\|4a c - b @@ -30013,7 +29466,7 @@ m0209b:=a0209.2-r0209 d0209b:=D(m0209b,x) --R --R ---R (1111) 0 +--R (1116) 0 --R Type: Expression Integer --E 1116 @@ -30023,7 +29476,7 @@ t0210:= (d+e*x)^2/(a+b*x+c*x^2) --R --R 2 2 2 --R e x + 2d e x + d ---R (1112) ------------------ +--R (1117) ------------------ --R 2 --R c x + b x + a --R Type: Fraction Polynomial Integer @@ -30035,7 +29488,7 @@ r0210:= e^2*x/c-(b^2*e^2+2*c*(c*d^2-e*(b*d+a*e)))*atanh((b+2*c*x)/_ 1/2*e*(2*c*d-b*e)*log(a+b*x+c*x^2)/c^2 --R --R ---R (1113) +--R (1118) --R 2 2 2 2 2c x + b --R ((4a c - 2b )e + 4b c d e - 4c d )atanh(--------------) --R +-----------+ @@ -30056,7 +29509,7 @@ r0210:= e^2*x/c-(b^2*e^2+2*c*(c*d^2-e*(b*d+a*e)))*atanh((b+2*c*x)/_ a0210:=integrate(t0210,x) --R --R ---R (1114) +--R (1119) --R [ --R 2 2 2 2 --R ((2a c - b )e + 2b c d e - 2c d ) @@ -30103,7 +29556,7 @@ a0210:=integrate(t0210,x) m0210a:=a0210.1-r0210 --R --R ---R (1115) +--R (1120) --R 2 2 2 2 --R ((2a c - b )e + 2b c d e - 2c d ) --R * @@ -30134,7 +29587,7 @@ m0210a:=a0210.1-r0210 d0210a:=D(m0210a,x) --R --R ---R (1116) 0 +--R (1121) 0 --R Type: Expression Integer --E 1121 @@ -30142,7 +29595,7 @@ d0210a:=D(m0210a,x) m0210b:=a0210.2-r0210 --R --R ---R (1117) +--R (1122) --R +---------+ --R 2 2 2 2 | 2 2c x + b --R ((- 2a c + b )e - 2b c d e + 2c d )\|4a c - b atanh(--------------) @@ -30171,7 +29624,7 @@ m0210b:=a0210.2-r0210 d0210b:=D(m0210b,x) --R --R ---R (1118) 0 +--R (1123) 0 --R Type: Expression Integer --E 1123 @@ -30180,7 +29633,7 @@ t0211:= (d+e*x)/(a+b*x+c*x^2) --R --R --R e x + d ---R (1119) -------------- +--R (1124) -------------- --R 2 --R c x + b x + a --R Type: Fraction Polynomial Integer @@ -30191,7 +29644,7 @@ r0211:= -(2*d-b*e/c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(1/2)+_ 1/2*e*log(a+b*x+c*x^2)/c --R --R ---R (1120) +--R (1125) --R +-----------+ --R 2c x + b 2 | 2 --R (2b e - 4c d)atanh(--------------) + e log(c x + b x + a)\|- 4a c + b @@ -30209,7 +29662,7 @@ r0211:= -(2*d-b*e/c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(1/2)+_ a0211:=integrate(t0211,x) --R --R ---R (1121) +--R (1126) --R [ --R (b e - 2c d) --R * @@ -30255,7 +29708,7 @@ a0211:=integrate(t0211,x) m0211a:=a0211.1-r0211 --R --R ---R (1122) +--R (1127) --R (b e - 2c d) --R * --R log @@ -30285,7 +29738,7 @@ m0211a:=a0211.1-r0211 d0211a:=D(m0211a,x) --R --R ---R (1123) 0 +--R (1128) 0 --R Type: Expression Integer --E 1128 @@ -30293,7 +29746,7 @@ d0211a:=D(m0211a,x) m0211b:=a0211.2-r0211 --R --R ---R (1124) +--R (1129) --R +---------+ --R | 2 2c x + b --R (- b e + 2c d)\|4a c - b atanh(--------------) @@ -30318,7 +29771,7 @@ m0211b:=a0211.2-r0211 d0211b:=D(m0211b,x) --R --R ---R (1125) 0 +--R (1130) 0 --R Type: Expression Integer --E 1130 @@ -30326,7 +29779,7 @@ d0211b:=D(m0211b,x) t0212:= 1/(d+e*x)^2/(a+b*x+c*x^2) --R --R ---R (1126) +--R (1131) --R 1 --R / --R 2 4 2 3 2 2 2 2 @@ -30345,7 +29798,7 @@ r0212:= -e/(c*d^2-e*(b*d-a*e))/(d+e*x)-(2*c^2*d^2+b^2*e^2-_ log(a+b*x+c*x^2)/(c*d^2-e*(b*d-a*e))^2 --R --R ---R (1127) +--R (1132) --R 2 3 2 2 2 2 2 2 --R ((4a c - 2b )e + 4b c d e - 4c d e)x + (4a c - 2b )d e + 4b c d e --R + @@ -30387,7 +29840,7 @@ r0212:= -e/(c*d^2-e*(b*d-a*e))/(d+e*x)-(2*c^2*d^2+b^2*e^2-_ a0212:=integrate(t0212,x) --R --R ---R (1128) +--R (1133) --R [ --R 2 3 2 2 2 2 2 2 --R ((2a c - b )e + 2b c d e - 2c d e)x + (2a c - b )d e + 2b c d e @@ -30473,7 +29926,7 @@ a0212:=integrate(t0212,x) m0212a:=a0212.1-r0212 --R --R ---R (1129) +--R (1134) --R 2 2 2 2 --R ((2a c - b )e + 2b c d e - 2c d ) --R * @@ -30504,7 +29957,7 @@ m0212a:=a0212.1-r0212 d0212a:=D(m0212a,x) --R --R ---R (1130) 0 +--R (1135) 0 --R Type: Expression Integer --E 1135 @@ -30512,7 +29965,7 @@ d0212a:=D(m0212a,x) m0212b:=a0212.2-r0212 --R --R ---R (1131) +--R (1136) --R +---------+ --R 2 2 2 2 | 2 2c x + b --R ((- 2a c + b )e - 2b c d e + 2c d )\|4a c - b atanh(--------------) @@ -30545,7 +29998,7 @@ m0212b:=a0212.2-r0212 d0212b:=D(m0212b,x) --R --R ---R (1132) 0 +--R (1137) 0 --R Type: Expression Integer --E 1137 @@ -30559,7 +30012,7 @@ t0213:= 2*((a/b)^(1/n)-x*cos((-1+2*k)*%pi/n))/((a/b)^(2/n)+x^2-_ --R a n (2k - 1)%pi --R 2(-) - 2x cos(-----------) --R b n ---R (1133) ----------------------------------- +--R (1138) ----------------------------------- --R 2 1 --R - - --R a n (2k - 1)%pi a n 2 @@ -30574,7 +30027,7 @@ r0213:= -cos((1-2*k)*%pi/n)*log((a/b)^(2/n)+x^2-2*(a/b)^(1/n)*x*_ csc((1-2*k)*%pi/n)/((a/b)^(1/n)))*sin((1-2*k)*%pi/n) --R --R ---R (1134) +--R (1139) --R 2 1 --R - - --R (2k - 1)%pi a n (2k - 1)%pi a n 2 @@ -30604,7 +30057,7 @@ r0213:= -cos((1-2*k)*%pi/n)*log((a/b)^(2/n)+x^2-2*(a/b)^(1/n)*x*_ a0213:=integrate(t0213,x) --R --R ---R (1135) +--R (1140) --R [ --R +---------------------+ --R | (2k - 1)%pi 2 @@ -30770,7 +30223,7 @@ a0213:=integrate(t0213,x) m0213a:=a0213.1-r0213 --R --R ---R (1136) +--R (1141) --R +---------------------+ --R | (2k - 1)%pi 2 --R |cos(-----------) - 1 @@ -30891,405 +30344,10 @@ m0213a:=a0213.1-r0213 --E 1141 --S 1142 of 1483 -d0213a:=D(m0213a,x) +d0213a:=normalize(D(m0213a,x)) --R --R ---R (1137) ---R 1 ---R - ---R (2k - 1)%pi (2k - 1)%pi (2k - 1)%pi 2 a n ---R (- 2csc(-----------)sin(-----------) - 4cos(-----------) + 2)(-) ---R n n n b ---R + ---R (2k - 1)%pi ---R 2x cos(-----------) ---R n ---R * ---R 2 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R (2k - 1)%pi 2 (2k - 1)%pi (2k - 1)%pi ---R 4cos(-----------) csc(-----------)sin(-----------) ---R n n n ---R + ---R (2k - 1)%pi 4 (2k - 1)%pi 2 (2k - 1)%pi 2 ---R (- 4cos(-----------) + 2cos(-----------) )csc(-----------) ---R n n n ---R + ---R (2k - 1)%pi 4 ---R 4cos(-----------) ---R n ---R * ---R 1 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R (2k - 1)%pi (2k - 1)%pi (2k - 1)%pi ---R 4x cos(-----------)csc(-----------)sin(-----------) ---R n n n ---R + ---R (2k - 1)%pi 3 (2k - 1)%pi (2k - 1)%pi 2 ---R (10x cos(-----------) - 4x cos(-----------))csc(-----------) ---R n n n ---R + ---R (2k - 1)%pi 3 (2k - 1)%pi ---R 2x cos(-----------) - 6x cos(-----------) ---R n n ---R * ---R 1 2 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 2 (2k - 1)%pi (2k - 1)%pi ---R - 2x csc(-----------)sin(-----------) ---R n n ---R + ---R 2 (2k - 1)%pi 2 2 (2k - 1)%pi 2 ---R (- 8x cos(-----------) + 2x )csc(-----------) ---R n n ---R + ---R 2 (2k - 1)%pi 2 2 ---R - 2x cos(-----------) + 2x ---R n ---R * ---R 1 ---R - ---R a n ---R (-) ---R b ---R + ---R 3 (2k - 1)%pi (2k - 1)%pi 2 ---R 2x cos(-----------)csc(-----------) ---R n n ---R * ---R 2 2 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R (2k - 1)%pi 2 (2k - 1)%pi (2k - 1)%pi ---R - 2cos(-----------) csc(-----------)sin(-----------) ---R n n n ---R + ---R (2k - 1)%pi 6 (2k - 1)%pi 2 (2k - 1)%pi 4 ---R 4cos(-----------) csc(-----------) - 2cos(-----------) ---R n n n ---R * ---R 1 5 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R (2k - 1)%pi 3 (2k - 1)%pi (2k - 1)%pi ---R (- 12x cos(-----------) + 4x cos(-----------))csc(-----------) ---R n n n ---R * ---R (2k - 1)%pi ---R sin(-----------) ---R n ---R + ---R (2k - 1)%pi 5 (2k - 1)%pi 3 (2k - 1)%pi 2 ---R (- 6x cos(-----------) - 6x cos(-----------) )csc(-----------) ---R n n n ---R + ---R (2k - 1)%pi 5 (2k - 1)%pi 3 ---R - 4x cos(-----------) + 6x cos(-----------) ---R n n ---R * ---R 1 4 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 2 (2k - 1)%pi 2 2 (2k - 1)%pi (2k - 1)%pi ---R (6x cos(-----------) - 2x )csc(-----------)sin(-----------) ---R n n n ---R + ---R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 (2k - 1)%pi 2 ---R (- 2x cos(-----------) + 14x cos(-----------) )csc(-----------) ---R n n n ---R + ---R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 ---R 2x cos(-----------) - 2x cos(-----------) ---R n n ---R * ---R 1 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 1 2 ---R - ---R 3 (2k - 1)%pi 3 3 (2k - 1)%pi (2k - 1)%pi 2 a n ---R (6x cos(-----------) - 10x cos(-----------))csc(-----------) ((-) ) ---R n n n b ---R + ---R 1 ---R - ---R 4 (2k - 1)%pi 2 4 (2k - 1)%pi 2 a n ---R (- 2x cos(-----------) + 2x )csc(-----------) (-) ---R n n b ---R * ---R 2 ---R - ---R a n ---R (-) ---R b ---R + ---R 1 7 ---R - ---R (2k - 1)%pi 6 (2k - 1)%pi 2 a n ---R - 2cos(-----------) csc(-----------) ((-) ) ---R n n b ---R + ---R (2k - 1)%pi 3 (2k - 1)%pi (2k - 1)%pi ---R 4x cos(-----------) csc(-----------)sin(-----------) ---R n n n ---R + ---R (2k - 1)%pi 7 (2k - 1)%pi 5 (2k - 1)%pi 2 ---R (- 4x cos(-----------) + 10x cos(-----------) )csc(-----------) ---R n n n ---R * ---R 1 6 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 (2k - 1)%pi ---R (8x cos(-----------) - 10x cos(-----------) )csc(-----------) ---R n n n ---R * ---R (2k - 1)%pi ---R sin(-----------) ---R n ---R + ---R 2 (2k - 1)%pi 6 2 (2k - 1)%pi 4 (2k - 1)%pi 2 ---R (10x cos(-----------) - 16x cos(-----------) )csc(-----------) ---R n n n ---R * ---R 1 5 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 3 (2k - 1)%pi 3 3 (2k - 1)%pi (2k - 1)%pi ---R (- 8x cos(-----------) + 8x cos(-----------))csc(-----------) ---R n n n ---R * ---R (2k - 1)%pi ---R sin(-----------) ---R n ---R + ---R 3 (2k - 1)%pi 5 3 (2k - 1)%pi 3 (2k - 1)%pi 2 ---R (- 8x cos(-----------) + 10x cos(-----------) )csc(-----------) ---R n n n ---R * ---R 1 4 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 4 (2k - 1)%pi 2 4 (2k - 1)%pi (2k - 1)%pi ---R (2x cos(-----------) - 2x )csc(-----------)sin(-----------) ---R n n n ---R + ---R 4 (2k - 1)%pi 4 4 (2k - 1)%pi 2 (2k - 1)%pi 2 ---R (2x cos(-----------) - 2x cos(-----------) )csc(-----------) ---R n n n ---R * ---R 1 3 ---R - ---R a n ---R ((-) ) ---R b ---R / ---R 2 4 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 1 2 ---R - ---R (2k - 1)%pi 2 (2k - 1)%pi 2 (2k - 1)%pi 2 a n ---R (cos(-----------) csc(-----------) - 2cos(-----------) )((-) ) ---R n n n b ---R + ---R 1 ---R - ---R (2k - 1)%pi (2k - 1)%pi 2 (2k - 1)%pi a n ---R (- 2x cos(-----------)csc(-----------) - 2x cos(-----------))(-) ---R n n n b ---R + ---R 2 (2k - 1)%pi 2 2 ---R x csc(-----------) + x ---R n ---R * ---R 2 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 1 4 ---R - ---R (2k - 1)%pi 4 (2k - 1)%pi 2 (2k - 1)%pi 2 a n ---R (- 2cos(-----------) csc(-----------) + cos(-----------) )((-) ) ---R n n n b ---R + ---R (2k - 1)%pi 3 (2k - 1)%pi 2 (2k - 1)%pi 3 ---R 2x cos(-----------) csc(-----------) + 6x cos(-----------) ---R n n n ---R + ---R (2k - 1)%pi ---R - 2x cos(-----------) ---R n ---R * ---R 1 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 2 (2k - 1)%pi 2 (2k - 1)%pi 2 2 (2k - 1)%pi 2 2 ---R (3x cos(-----------) csc(-----------) - 3x cos(-----------) + x ) ---R n n n ---R * ---R 1 2 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 1 ---R - ---R 3 (2k - 1)%pi (2k - 1)%pi 2 a n 4 (2k - 1)%pi 2 ---R - 4x cos(-----------)csc(-----------) (-) + x csc(-----------) ---R n n b n ---R * ---R 2 2 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 1 6 ---R - ---R (2k - 1)%pi 4 (2k - 1)%pi 2 a n ---R cos(-----------) csc(-----------) ((-) ) ---R n n b ---R + ---R (2k - 1)%pi 5 (2k - 1)%pi 3 (2k - 1)%pi 2 ---R (6x cos(-----------) - 4x cos(-----------) )csc(-----------) ---R n n n ---R + ---R (2k - 1)%pi 3 ---R - 2x cos(-----------) ---R n ---R * ---R 1 5 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 (2k - 1)%pi 2 ---R (- 15x cos(-----------) + 6x cos(-----------) )csc(-----------) ---R n n n ---R + ---R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 ---R - 4x cos(-----------) + 5x cos(-----------) ---R n n ---R * ---R 1 4 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 3 (2k - 1)%pi 3 3 (2k - 1)%pi (2k - 1)%pi 2 ---R (12x cos(-----------) - 4x cos(-----------))csc(-----------) ---R n n n ---R + ---R 3 (2k - 1)%pi 3 3 (2k - 1)%pi ---R 4x cos(-----------) - 4x cos(-----------) ---R n n ---R * ---R 1 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 4 (2k - 1)%pi 2 4 (2k - 1)%pi 2 ---R (- 3x cos(-----------) + x )csc(-----------) ---R n n ---R + ---R 4 (2k - 1)%pi 2 4 ---R - x cos(-----------) + x ---R n ---R * ---R 1 2 ---R - ---R a n ---R ((-) ) ---R b ---R * ---R 2 ---R - ---R a n ---R (-) ---R b ---R + ---R 1 7 ---R - ---R (2k - 1)%pi 5 (2k - 1)%pi 2 a n ---R - 2x cos(-----------) csc(-----------) ((-) ) ---R n n b ---R + ---R 1 6 ---R - ---R 2 (2k - 1)%pi 6 2 (2k - 1)%pi 4 (2k - 1)%pi 2 a n ---R (- 4x cos(-----------) + 9x cos(-----------) )csc(-----------) ((-) ) ---R n n n b ---R + ---R 1 5 ---R - ---R 3 (2k - 1)%pi 5 3 (2k - 1)%pi 3 (2k - 1)%pi 2 a n ---R (12x cos(-----------) - 16x cos(-----------) )csc(-----------) ((-) ) ---R n n n b ---R + ---R 1 4 ---R - ---R 4 (2k - 1)%pi 4 4 (2k - 1)%pi 2 (2k - 1)%pi 2 a n ---R (- 13x cos(-----------) + 14x cos(-----------) )csc(-----------) ((-) ) ---R n n n b ---R + ---R 1 3 ---R - ---R 5 (2k - 1)%pi 3 5 (2k - 1)%pi (2k - 1)%pi 2 a n ---R (6x cos(-----------) - 6x cos(-----------))csc(-----------) ((-) ) ---R n n n b ---R + ---R 1 2 ---R - ---R 6 (2k - 1)%pi 2 6 (2k - 1)%pi 2 a n ---R (- x cos(-----------) + x )csc(-----------) ((-) ) ---R n n b +--R (1142) 0 --R Type: Expression Integer --E 1142 @@ -31297,7 +30355,7 @@ d0213a:=D(m0213a,x) m0213b:=a0213.2-r0213 --R --R ---R (1138) +--R (1143) --R - --R +-----------------------+ --R | (2k - 1)%pi 2 @@ -31378,405 +30436,10 @@ m0213b:=a0213.2-r0213 --E 1143 --S 1144 of 1483 -d0213b:=D(m0213b,x) +d0213b:=normalize(D(m0213b,x)) --R --R ---R (1139) ---R 1 ---R - ---R (2k - 1)%pi (2k - 1)%pi (2k - 1)%pi 2 a n ---R (- 2csc(-----------)sin(-----------) - 4cos(-----------) + 2)(-) ---R n n n b ---R + ---R (2k - 1)%pi ---R 2x cos(-----------) ---R n ---R * ---R 2 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R (2k - 1)%pi 2 (2k - 1)%pi (2k - 1)%pi ---R 4cos(-----------) csc(-----------)sin(-----------) ---R n n n ---R + ---R (2k - 1)%pi 4 (2k - 1)%pi 2 (2k - 1)%pi 2 ---R (- 4cos(-----------) + 2cos(-----------) )csc(-----------) ---R n n n ---R + ---R (2k - 1)%pi 4 ---R 4cos(-----------) ---R n ---R * ---R 1 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R (2k - 1)%pi (2k - 1)%pi (2k - 1)%pi ---R 4x cos(-----------)csc(-----------)sin(-----------) ---R n n n ---R + ---R (2k - 1)%pi 3 (2k - 1)%pi (2k - 1)%pi 2 ---R (10x cos(-----------) - 4x cos(-----------))csc(-----------) ---R n n n ---R + ---R (2k - 1)%pi 3 (2k - 1)%pi ---R 2x cos(-----------) - 6x cos(-----------) ---R n n ---R * ---R 1 2 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 2 (2k - 1)%pi (2k - 1)%pi ---R - 2x csc(-----------)sin(-----------) ---R n n ---R + ---R 2 (2k - 1)%pi 2 2 (2k - 1)%pi 2 ---R (- 8x cos(-----------) + 2x )csc(-----------) ---R n n ---R + ---R 2 (2k - 1)%pi 2 2 ---R - 2x cos(-----------) + 2x ---R n ---R * ---R 1 ---R - ---R a n ---R (-) ---R b ---R + ---R 3 (2k - 1)%pi (2k - 1)%pi 2 ---R 2x cos(-----------)csc(-----------) ---R n n ---R * ---R 2 2 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R (2k - 1)%pi 2 (2k - 1)%pi (2k - 1)%pi ---R - 2cos(-----------) csc(-----------)sin(-----------) ---R n n n ---R + ---R (2k - 1)%pi 6 (2k - 1)%pi 2 (2k - 1)%pi 4 ---R 4cos(-----------) csc(-----------) - 2cos(-----------) ---R n n n ---R * ---R 1 5 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R (2k - 1)%pi 3 (2k - 1)%pi (2k - 1)%pi ---R (- 12x cos(-----------) + 4x cos(-----------))csc(-----------) ---R n n n ---R * ---R (2k - 1)%pi ---R sin(-----------) ---R n ---R + ---R (2k - 1)%pi 5 (2k - 1)%pi 3 (2k - 1)%pi 2 ---R (- 6x cos(-----------) - 6x cos(-----------) )csc(-----------) ---R n n n ---R + ---R (2k - 1)%pi 5 (2k - 1)%pi 3 ---R - 4x cos(-----------) + 6x cos(-----------) ---R n n ---R * ---R 1 4 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 2 (2k - 1)%pi 2 2 (2k - 1)%pi (2k - 1)%pi ---R (6x cos(-----------) - 2x )csc(-----------)sin(-----------) ---R n n n ---R + ---R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 (2k - 1)%pi 2 ---R (- 2x cos(-----------) + 14x cos(-----------) )csc(-----------) ---R n n n ---R + ---R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 ---R 2x cos(-----------) - 2x cos(-----------) ---R n n ---R * ---R 1 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 1 2 ---R - ---R 3 (2k - 1)%pi 3 3 (2k - 1)%pi (2k - 1)%pi 2 a n ---R (6x cos(-----------) - 10x cos(-----------))csc(-----------) ((-) ) ---R n n n b ---R + ---R 1 ---R - ---R 4 (2k - 1)%pi 2 4 (2k - 1)%pi 2 a n ---R (- 2x cos(-----------) + 2x )csc(-----------) (-) ---R n n b ---R * ---R 2 ---R - ---R a n ---R (-) ---R b ---R + ---R 1 7 ---R - ---R (2k - 1)%pi 6 (2k - 1)%pi 2 a n ---R - 2cos(-----------) csc(-----------) ((-) ) ---R n n b ---R + ---R (2k - 1)%pi 3 (2k - 1)%pi (2k - 1)%pi ---R 4x cos(-----------) csc(-----------)sin(-----------) ---R n n n ---R + ---R (2k - 1)%pi 7 (2k - 1)%pi 5 (2k - 1)%pi 2 ---R (- 4x cos(-----------) + 10x cos(-----------) )csc(-----------) ---R n n n ---R * ---R 1 6 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 (2k - 1)%pi ---R (8x cos(-----------) - 10x cos(-----------) )csc(-----------) ---R n n n ---R * ---R (2k - 1)%pi ---R sin(-----------) ---R n ---R + ---R 2 (2k - 1)%pi 6 2 (2k - 1)%pi 4 (2k - 1)%pi 2 ---R (10x cos(-----------) - 16x cos(-----------) )csc(-----------) ---R n n n ---R * ---R 1 5 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 3 (2k - 1)%pi 3 3 (2k - 1)%pi (2k - 1)%pi ---R (- 8x cos(-----------) + 8x cos(-----------))csc(-----------) ---R n n n ---R * ---R (2k - 1)%pi ---R sin(-----------) ---R n ---R + ---R 3 (2k - 1)%pi 5 3 (2k - 1)%pi 3 (2k - 1)%pi 2 ---R (- 8x cos(-----------) + 10x cos(-----------) )csc(-----------) ---R n n n ---R * ---R 1 4 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 4 (2k - 1)%pi 2 4 (2k - 1)%pi (2k - 1)%pi ---R (2x cos(-----------) - 2x )csc(-----------)sin(-----------) ---R n n n ---R + ---R 4 (2k - 1)%pi 4 4 (2k - 1)%pi 2 (2k - 1)%pi 2 ---R (2x cos(-----------) - 2x cos(-----------) )csc(-----------) ---R n n n ---R * ---R 1 3 ---R - ---R a n ---R ((-) ) ---R b ---R / ---R 2 4 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 1 2 ---R - ---R (2k - 1)%pi 2 (2k - 1)%pi 2 (2k - 1)%pi 2 a n ---R (cos(-----------) csc(-----------) - 2cos(-----------) )((-) ) ---R n n n b ---R + ---R 1 ---R - ---R (2k - 1)%pi (2k - 1)%pi 2 (2k - 1)%pi a n ---R (- 2x cos(-----------)csc(-----------) - 2x cos(-----------))(-) ---R n n n b ---R + ---R 2 (2k - 1)%pi 2 2 ---R x csc(-----------) + x ---R n ---R * ---R 2 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 1 4 ---R - ---R (2k - 1)%pi 4 (2k - 1)%pi 2 (2k - 1)%pi 2 a n ---R (- 2cos(-----------) csc(-----------) + cos(-----------) )((-) ) ---R n n n b ---R + ---R (2k - 1)%pi 3 (2k - 1)%pi 2 (2k - 1)%pi 3 ---R 2x cos(-----------) csc(-----------) + 6x cos(-----------) ---R n n n ---R + ---R (2k - 1)%pi ---R - 2x cos(-----------) ---R n ---R * ---R 1 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 2 (2k - 1)%pi 2 (2k - 1)%pi 2 2 (2k - 1)%pi 2 2 ---R (3x cos(-----------) csc(-----------) - 3x cos(-----------) + x ) ---R n n n ---R * ---R 1 2 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 1 ---R - ---R 3 (2k - 1)%pi (2k - 1)%pi 2 a n 4 (2k - 1)%pi 2 ---R - 4x cos(-----------)csc(-----------) (-) + x csc(-----------) ---R n n b n ---R * ---R 2 2 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 1 6 ---R - ---R (2k - 1)%pi 4 (2k - 1)%pi 2 a n ---R cos(-----------) csc(-----------) ((-) ) ---R n n b ---R + ---R (2k - 1)%pi 5 (2k - 1)%pi 3 (2k - 1)%pi 2 ---R (6x cos(-----------) - 4x cos(-----------) )csc(-----------) ---R n n n ---R + ---R (2k - 1)%pi 3 ---R - 2x cos(-----------) ---R n ---R * ---R 1 5 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 (2k - 1)%pi 2 ---R (- 15x cos(-----------) + 6x cos(-----------) )csc(-----------) ---R n n n ---R + ---R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 ---R - 4x cos(-----------) + 5x cos(-----------) ---R n n ---R * ---R 1 4 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 3 (2k - 1)%pi 3 3 (2k - 1)%pi (2k - 1)%pi 2 ---R (12x cos(-----------) - 4x cos(-----------))csc(-----------) ---R n n n ---R + ---R 3 (2k - 1)%pi 3 3 (2k - 1)%pi ---R 4x cos(-----------) - 4x cos(-----------) ---R n n ---R * ---R 1 3 ---R - ---R a n ---R ((-) ) ---R b ---R + ---R 4 (2k - 1)%pi 2 4 (2k - 1)%pi 2 ---R (- 3x cos(-----------) + x )csc(-----------) ---R n n ---R + ---R 4 (2k - 1)%pi 2 4 ---R - x cos(-----------) + x ---R n ---R * ---R 1 2 ---R - ---R a n ---R ((-) ) ---R b ---R * ---R 2 ---R - ---R a n ---R (-) ---R b ---R + ---R 1 7 ---R - ---R (2k - 1)%pi 5 (2k - 1)%pi 2 a n ---R - 2x cos(-----------) csc(-----------) ((-) ) ---R n n b ---R + ---R 1 6 ---R - ---R 2 (2k - 1)%pi 6 2 (2k - 1)%pi 4 (2k - 1)%pi 2 a n ---R (- 4x cos(-----------) + 9x cos(-----------) )csc(-----------) ((-) ) ---R n n n b ---R + ---R 1 5 ---R - ---R 3 (2k - 1)%pi 5 3 (2k - 1)%pi 3 (2k - 1)%pi 2 a n ---R (12x cos(-----------) - 16x cos(-----------) )csc(-----------) ((-) ) ---R n n n b ---R + ---R 1 4 ---R - ---R 4 (2k - 1)%pi 4 4 (2k - 1)%pi 2 (2k - 1)%pi 2 a n ---R (- 13x cos(-----------) + 14x cos(-----------) )csc(-----------) ((-) ) ---R n n n b ---R + ---R 1 3 ---R - ---R 5 (2k - 1)%pi 3 5 (2k - 1)%pi (2k - 1)%pi 2 a n ---R (6x cos(-----------) - 6x cos(-----------))csc(-----------) ((-) ) ---R n n n b ---R + ---R 1 2 ---R - ---R 6 (2k - 1)%pi 2 6 (2k - 1)%pi 2 a n ---R (- x cos(-----------) + x )csc(-----------) ((-) ) ---R n n b +--R (1144) 0 --R Type: Expression Integer --E 1144 @@ -31786,7 +30449,7 @@ t0214:= (d+e*x)^2/(a+b*x+c*x^2)^2 --R --R 2 2 2 --R e x + 2d e x + d ---R (1140) -------------------------------------------- +--R (1145) -------------------------------------------- --R 2 4 3 2 2 2 --R c x + 2b c x + (2a c + b )x + 2a b x + a --R Type: Fraction Polynomial Integer @@ -31798,7 +30461,7 @@ r0214:= -(c*d^2-e*(b*d-a*e))*(b+2*c*x)/c/(b^2-4*a*c)/(a+b*x+c*x^2)-_ atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(3/2) --R --R ---R (1141) +--R (1146) --R 2 2 2 3 2 2 --R (- 4a c e + 4b c d e - 4c d )x --R + @@ -31828,7 +30491,7 @@ r0214:= -(c*d^2-e*(b*d-a*e))*(b+2*c*x)/c/(b^2-4*a*c)/(a+b*x+c*x^2)-_ a0214:=integrate(t0214,x) --R --R ---R (1142) +--R (1147) --R [ --R 2 2 2 3 2 2 2 2 2 2 --R (2a c e - 2b c d e + 2c d )x + (2a b c e - 2b c d e + 2b c d )x @@ -31890,7 +30553,7 @@ a0214:=integrate(t0214,x) m0214a:=a0214.1-r0214 --R --R ---R (1143) +--R (1148) --R 2 2 --R (2a e - 2b d e + 2c d ) --R * @@ -31921,7 +30584,7 @@ m0214a:=a0214.1-r0214 d0214a:=D(m0214a,x) --R --R ---R (1144) 0 +--R (1149) 0 --R Type: Expression Integer --E 1149 @@ -31929,7 +30592,7 @@ d0214a:=D(m0214a,x) m0214b:=a0214.2-r0214 --R --R ---R (1145) +--R (1150) --R +---------+ --R 2 2 | 2 2c x + b --R (4a e - 4b d e + 4c d )\|4a c - b atanh(--------------) @@ -31954,7 +30617,7 @@ m0214b:=a0214.2-r0214 d0214b:=D(m0214b,x) --R --R ---R (1146) 0 +--R (1151) 0 --R Type: Expression Integer --E 1151 @@ -31962,7 +30625,7 @@ d0214b:=D(m0214b,x) t0215:= 1/(d+e*x)/(a+b*x+c*x^2)^2 --R --R ---R (1147) +--R (1152) --R 1 --R / --R 2 5 2 4 2 3 @@ -31983,7 +30646,7 @@ r0215:= 1/2*e/(c*d^2-e*(b*d-a*e))/(a+b*x+c*x^2)-1/2*(2*c*d-b*e)*_ 1/2*e^3*log(a+b*x+c*x^2)/(c*d^2-e*(b*d-a*e))^2 --R --R ---R (1148) +--R (1153) --R 2 3 3 3 2 3 2 4 3 2 --R ((12a b c - 2b c)e - 24a c d e + 12b c d e - 8c d )x --R + @@ -32062,7 +30725,7 @@ r0215:= 1/2*e/(c*d^2-e*(b*d-a*e))/(a+b*x+c*x^2)-1/2*(2*c*d-b*e)*_ a0215:=integrate(t0215,x) --R --R ---R (1149) +--R (1154) --R [ --R 2 3 3 3 2 3 2 4 3 2 --R ((6a b c - b c)e - 12a c d e + 6b c d e - 4c d )x @@ -32222,7 +30885,7 @@ a0215:=integrate(t0215,x) m0215a:=a0215.1-r0215 --R --R ---R (1150) +--R (1155) --R 3 3 2 2 2 2 3 3 --R ((6a b c - b )e - 12a c d e + 6b c d e - 4c d ) --R * @@ -32259,7 +30922,7 @@ m0215a:=a0215.1-r0215 d0215a:=D(m0215a,x) --R --R ---R (1151) 0 +--R (1156) 0 --R Type: Expression Integer --E 1156 @@ -32267,7 +30930,7 @@ d0215a:=D(m0215a,x) m0215b:=a0215.2-r0215 --R --R ---R (1152) +--R (1157) --R +---------+ --R 3 3 2 2 2 2 3 3 | 2 --R ((- 6a b c + b )e + 12a c d e - 6b c d e + 4c d )\|4a c - b @@ -32305,7 +30968,7 @@ m0215b:=a0215.2-r0215 d0215b:=D(m0215b,x) --R --R ---R (1153) 0 +--R (1158) 0 --R Type: Expression Integer --E 1158 @@ -32315,7 +30978,7 @@ t0216:= x^4*(d+e*x)/(a+b*x+c*x^2) --R --R 5 4 --R e x + d x ---R (1154) -------------- +--R (1159) -------------- --R 2 --R c x + b x + a --R Type: Fraction Polynomial Integer @@ -32330,7 +30993,7 @@ r0216:= (b^2*c*d-a*c^2*d-b^3*e+2*a*b*c*e)*x/c^4-_ a^2*c^2*e)*log(a+b*x+c*x^2)/c^5 --R --R ---R (1155) +--R (1160) --R 2 2 3 5 2 3 2 2 4 --R ((60a b c - 60a b c + 12b )e + (- 24a c + 48a b c - 12b c)d) --R * @@ -32363,7 +31026,7 @@ r0216:= (b^2*c*d-a*c^2*d-b^3*e+2*a*b*c*e)*x/c^4-_ a0216:=integrate(t0216,x) --R --R ---R (1156) +--R (1161) --R [ --R 2 2 3 5 2 3 2 2 4 --R ((30a b c - 30a b c + 6b )e + (- 12a c + 24a b c - 6b c)d) @@ -32431,7 +31094,7 @@ a0216:=integrate(t0216,x) m0216a:=a0216.1-r0216 --R --R ---R (1157) +--R (1162) --R 2 2 3 5 2 3 2 2 4 --R ((5a b c - 5a b c + b )e + (- 2a c + 4a b c - b c)d) --R * @@ -32465,7 +31128,7 @@ m0216a:=a0216.1-r0216 d0216a:=D(m0216a,x) --R --R ---R (1158) 0 +--R (1163) 0 --R Type: Expression Integer --E 1163 @@ -32473,7 +31136,7 @@ d0216a:=D(m0216a,x) m0216b:=a0216.2-r0216 --R --R ---R (1159) +--R (1164) --R +---------+ --R 2 2 3 5 2 3 2 2 4 | 2 --R ((- 5a b c + 5a b c - b )e + (2a c - 4a b c + b c)d)\|4a c - b @@ -32505,7 +31168,7 @@ m0216b:=a0216.2-r0216 d0216b:=D(m0216b,x) --R --R ---R (1160) 0 +--R (1165) 0 --R Type: Expression Integer --E 1165 @@ -32515,7 +31178,7 @@ t0217:= x^3*(d+e*x)/(a+b*x+c*x^2) --R --R 4 3 --R e x + d x ---R (1161) -------------- +--R (1166) -------------- --R 2 --R c x + b x + a --R Type: Fraction Polynomial Integer @@ -32528,7 +31191,7 @@ r0217:= -(b*c*d-b^2*e+a*c*e)*x/c^3+1/2*(c*d-b*e)*x^2/c^2+1/3*e*x^3/c-_ 1/2*(b^2*c*d-a*c^2*d-b^3*e+2*a*b*c*e)*log(a+b*x+c*x^2)/c^4 --R --R ---R (1162) +--R (1167) --R 2 2 2 4 2 3 2c x + b --R ((- 12a c + 24a b c - 6b )e + (- 18a b c + 6b c)d)atanh(--------------) --R +-----------+ @@ -32555,7 +31218,7 @@ r0217:= -(b*c*d-b^2*e+a*c*e)*x/c^3+1/2*(c*d-b*e)*x^2/c^2+1/3*e*x^3/c-_ a0217:=integrate(t0217,x) --R --R ---R (1163) +--R (1168) --R [ --R 2 2 2 4 2 3 --R ((6a c - 12a b c + 3b )e + (9a b c - 3b c)d) @@ -32617,7 +31280,7 @@ a0217:=integrate(t0217,x) m0217a:=a0217.1-r0217 --R --R ---R (1164) +--R (1169) --R 2 2 2 4 2 3 --R ((2a c - 4a b c + b )e + (3a b c - b c)d) --R * @@ -32648,7 +31311,7 @@ m0217a:=a0217.1-r0217 d0217a:=D(m0217a,x) --R --R ---R (1165) 0 +--R (1170) 0 --R Type: Expression Integer --E 1170 @@ -32656,7 +31319,7 @@ d0217a:=D(m0217a,x) m0217b:=a0217.2-r0217 --R --R ---R (1166) +--R (1171) --R +---------+ --R 2 2 2 4 2 3 | 2 --R ((2a c - 4a b c + b )e + (3a b c - b c)d)\|4a c - b @@ -32688,7 +31351,7 @@ m0217b:=a0217.2-r0217 d0217b:=D(m0217b,x) --R --R ---R (1167) 0 +--R (1172) 0 --R Type: Expression Integer --E 1172 @@ -32698,7 +31361,7 @@ t0218:= x^2*(d+e*x)/(a+b*x+c*x^2) --R --R 3 2 --R e x + d x ---R (1168) -------------- +--R (1173) -------------- --R 2 --R c x + b x + a --R Type: Fraction Polynomial Integer @@ -32710,7 +31373,7 @@ r0218:= (c*d-b*e)*x/c^2+1/2*e*x^2/c+(b^3*e-c*(b^2*d-2*a*c*d+3*a*b*e))*_ 1/2*(b*c*d-b^2*e+a*c*e)*log(a+b*x+c*x^2)/c^3 --R --R ---R (1169) +--R (1174) --R 3 2 2 2c x + b --R ((- 6a b c + 2b )e + (4a c - 2b c)d)atanh(--------------) --R +-----------+ @@ -32737,7 +31400,7 @@ r0218:= (c*d-b*e)*x/c^2+1/2*e*x^2/c+(b^3*e-c*(b^2*d-2*a*c*d+3*a*b*e))*_ a0218:=integrate(t0218,x) --R --R ---R (1170) +--R (1175) --R [ --R 3 2 2 --R ((3a b c - b )e + (- 2a c + b c)d) @@ -32796,7 +31459,7 @@ a0218:=integrate(t0218,x) m0218a:=a0218.1-r0218 --R --R ---R (1171) +--R (1176) --R 3 2 2 --R ((3a b c - b )e + (- 2a c + b c)d) --R * @@ -32827,7 +31490,7 @@ m0218a:=a0218.1-r0218 d0218a:=D(m0218a,x) --R --R ---R (1172) 0 +--R (1177) 0 --R Type: Expression Integer --E 1177 @@ -32835,7 +31498,7 @@ d0218a:=D(m0218a,x) m0218b:=a0218.2-r0218 --R --R ---R (1173) +--R (1178) --R +---------+ --R 3 2 2 | 2 2c x + b --R ((3a b c - b )e + (- 2a c + b c)d)\|4a c - b atanh(--------------) @@ -32864,7 +31527,7 @@ m0218b:=a0218.2-r0218 d0218b:=D(m0218b,x) --R --R ---R (1174) 0 +--R (1179) 0 --R Type: Expression Integer --E 1179 @@ -32874,7 +31537,7 @@ t0219:= x*(d+e*x)/(a+b*x+c*x^2) --R --R 2 --R e x + d x ---R (1175) -------------- +--R (1180) -------------- --R 2 --R c x + b x + a --R Type: Fraction Polynomial Integer @@ -32885,7 +31548,7 @@ r0219:= e*x/c-(b^2*e-c*(b*d+2*a*e))*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ c^2/(b^2-4*a*c)^(1/2)+1/2*(c*d-b*e)*log(a+b*x+c*x^2)/c^2 --R --R ---R (1176) +--R (1181) --R 2 2c x + b --R ((4a c - 2b )e + 2b c d)atanh(--------------) --R +-----------+ @@ -32906,7 +31569,7 @@ r0219:= e*x/c-(b^2*e-c*(b*d+2*a*e))*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ a0219:=integrate(t0219,x) --R --R ---R (1177) +--R (1182) --R [ --R 2 --R ((2a c - b )e + b c d) @@ -32953,7 +31616,7 @@ a0219:=integrate(t0219,x) m0219a:=a0219.1-r0219 --R --R ---R (1178) +--R (1183) --R 2 --R ((2a c - b )e + b c d) --R * @@ -32984,7 +31647,7 @@ m0219a:=a0219.1-r0219 d0219a:=D(m0219a,x) --R --R ---R (1179) 0 +--R (1184) 0 --R Type: Expression Integer --E 1184 @@ -32992,7 +31655,7 @@ d0219a:=D(m0219a,x) m0219b:=a0219.2-r0219 --R --R ---R (1180) +--R (1185) --R +---------+ --R 2 | 2 2c x + b --R ((- 2a c + b )e - b c d)\|4a c - b atanh(--------------) @@ -33017,7 +31680,7 @@ m0219b:=a0219.2-r0219 d0219b:=D(m0219b,x) --R --R ---R (1181) 0 +--R (1186) 0 --R Type: Expression Integer --E 1186 @@ -33026,7 +31689,7 @@ t0220:= (d+e*x)/(a+b*x+c*x^2) --R --R --R e x + d ---R (1182) -------------- +--R (1187) -------------- --R 2 --R c x + b x + a --R Type: Fraction Polynomial Integer @@ -33037,7 +31700,7 @@ r0220:= -(2*d-b*e/c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(1/2)+_ 1/2*e*log(a+b*x+c*x^2)/c --R --R ---R (1183) +--R (1188) --R +-----------+ --R 2c x + b 2 | 2 --R (2b e - 4c d)atanh(--------------) + e log(c x + b x + a)\|- 4a c + b @@ -33055,7 +31718,7 @@ r0220:= -(2*d-b*e/c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(1/2)+_ a0220:=integrate(t0220,x) --R --R ---R (1184) +--R (1189) --R [ --R (b e - 2c d) --R * @@ -33101,7 +31764,7 @@ a0220:=integrate(t0220,x) m0220a:=a0220.1-r0220 --R --R ---R (1185) +--R (1190) --R (b e - 2c d) --R * --R log @@ -33131,7 +31794,7 @@ m0220a:=a0220.1-r0220 d0220a:=D(m0220a,x) --R --R ---R (1186) 0 +--R (1191) 0 --R Type: Expression Integer --E 1191 @@ -33139,7 +31802,7 @@ d0220a:=D(m0220a,x) m0220b:=a0220.2-r0220 --R --R ---R (1187) +--R (1192) --R +---------+ --R | 2 2c x + b --R (- b e + 2c d)\|4a c - b atanh(--------------) @@ -33164,7 +31827,7 @@ m0220b:=a0220.2-r0220 d0220b:=D(m0220b,x) --R --R ---R (1188) 0 +--R (1193) 0 --R Type: Expression Integer --E 1193 @@ -33173,7 +31836,7 @@ t0221:= (d+e*x)/x/(a+b*x+c*x^2) --R --R --R e x + d ---R (1189) ----------------- +--R (1194) ----------------- --R 3 2 --R c x + b x + a x --R Type: Fraction Polynomial Integer @@ -33184,7 +31847,7 @@ r0221:= (b*d-2*a*e)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a/(b^2-4*a*c)^(1/2)+_ d*log(x)/a-1/2*d*log(a+b*x+c*x^2)/a --R --R ---R (1190) +--R (1195) --R 2c x + b --R (- 4a e + 2b d)atanh(--------------) --R +-----------+ @@ -33205,7 +31868,7 @@ r0221:= (b*d-2*a*e)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a/(b^2-4*a*c)^(1/2)+_ a0221:=integrate(t0221,x) --R --R ---R (1191) +--R (1196) --R [ --R (2a e - b d) --R * @@ -33251,7 +31914,7 @@ a0221:=integrate(t0221,x) m0221a:=a0221.1-r0221 --R --R ---R (1192) +--R (1197) --R (2a e - b d) --R * --R log @@ -33281,7 +31944,7 @@ m0221a:=a0221.1-r0221 d0221a:=D(m0221a,x) --R --R ---R (1193) 0 +--R (1198) 0 --R Type: Expression Integer --E 1198 @@ -33289,7 +31952,7 @@ d0221a:=D(m0221a,x) m0221b:=a0221.2-r0221 --R --R ---R (1194) +--R (1199) --R +---------+ --R | 2 2c x + b --R (2a e - b d)\|4a c - b atanh(--------------) @@ -33314,7 +31977,7 @@ m0221b:=a0221.2-r0221 d0221b:=D(m0221b,x) --R --R ---R (1195) 0 +--R (1200) 0 --R Type: Expression Integer --E 1200 @@ -33323,7 +31986,7 @@ t0222:= (d+e*x)/x^2/(a+b*x+c*x^2) --R --R --R e x + d ---R (1196) ------------------ +--R (1201) ------------------ --R 4 3 2 --R c x + b x + a x --R Type: Fraction Polynomial Integer @@ -33335,7 +31998,7 @@ r0222:= -d/a/x-(b^2*d-2*a*c*d-a*b*e)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ log(a+b*x+c*x^2)/a^2 --R --R ---R (1197) +--R (1202) --R 2 2c x + b --R (2a b e + (4a c - 2b )d)x atanh(--------------) --R +-----------+ @@ -33359,7 +32022,7 @@ r0222:= -d/a/x-(b^2*d-2*a*c*d-a*b*e)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ a0222:=integrate(t0222,x) --R --R ---R (1198) +--R (1203) --R [ --R 2 --R (a b e + (2a c - b )d)x @@ -33412,7 +32075,7 @@ a0222:=integrate(t0222,x) m0222a:=a0222.1-r0222 --R --R ---R (1199) +--R (1204) --R 2 --R (a b e + (2a c - b )d) --R * @@ -33443,7 +32106,7 @@ m0222a:=a0222.1-r0222 d0222a:=D(m0222a,x) --R --R ---R (1200) 0 +--R (1205) 0 --R Type: Expression Integer --E 1205 @@ -33451,7 +32114,7 @@ d0222a:=D(m0222a,x) m0222b:=a0222.2-r0222 --R --R ---R (1201) +--R (1206) --R +---------+ --R 2 | 2 2c x + b --R (- a b e + (- 2a c + b )d)\|4a c - b atanh(--------------) @@ -33476,7 +32139,7 @@ m0222b:=a0222.2-r0222 d0222b:=D(m0222b,x) --R --R ---R (1202) 0 +--R (1207) 0 --R Type: Expression Integer --E 1207 @@ -33485,7 +32148,7 @@ t0223:= (d+e*x)/x^3/(a+b*x+c*x^2) --R --R --R e x + d ---R (1203) ------------------ +--R (1208) ------------------ --R 5 4 3 --R c x + b x + a x --R Type: Fraction Polynomial Integer @@ -33498,7 +32161,7 @@ r0223:= -1/2*d/a/x^2+(b*d-a*e)/a^2/x+(b^3*d-3*a*b*c*d-a*b^2*e+2*a^2*c*e)*_ log(a+b*x+c*x^2)/a^3 --R --R ---R (1204) +--R (1209) --R 2 2 3 2 2c x + b --R ((4a c - 2a b )e + (- 6a b c + 2b )d)x atanh(--------------) --R +-----------+ @@ -33525,7 +32188,7 @@ r0223:= -1/2*d/a/x^2+(b*d-a*e)/a^2/x+(b^3*d-3*a*b*c*d-a*b^2*e+2*a^2*c*e)*_ a0223:=integrate(t0223,x) --R --R ---R (1205) +--R (1210) --R [ --R 2 2 3 2 --R ((2a c - a b )e + (- 3a b c + b )d)x @@ -33584,7 +32247,7 @@ a0223:=integrate(t0223,x) m0223a:=a0223.1-r0223 --R --R ---R (1206) +--R (1211) --R 2 2 3 --R ((2a c - a b )e + (- 3a b c + b )d) --R * @@ -33615,7 +32278,7 @@ m0223a:=a0223.1-r0223 d0223a:=D(m0223a,x) --R --R ---R (1207) 0 +--R (1212) 0 --R Type: Expression Integer --E 1212 @@ -33623,7 +32286,7 @@ d0223a:=D(m0223a,x) m0223b:=a0223.2-r0223 --R --R ---R (1208) +--R (1213) --R +---------+ --R 2 2 3 | 2 2c x + b --R ((- 2a c + a b )e + (3a b c - b )d)\|4a c - b atanh(--------------) @@ -33652,7 +32315,7 @@ m0223b:=a0223.2-r0223 d0223b:=D(m0223b,x) --R --R ---R (1209) 0 +--R (1214) 0 --R Type: Expression Integer --E 1214 @@ -33661,7 +32324,7 @@ t0224:= (d+e*x)/x^4/(a+b*x+c*x^2) --R --R --R e x + d ---R (1210) ------------------ +--R (1215) ------------------ --R 6 5 4 --R c x + b x + a x --R Type: Fraction Polynomial Integer @@ -33675,7 +32338,7 @@ r0224:= -1/3*d/a/x^3+1/2*(b*d-a*e)/a^2/x^2-(b^2*d-a*c*d-a*b*e)/a^3/x-_ 1/2*(b^3*d-2*a*b*c*d-a*b^2*e+a^2*c*e)*log(a+b*x+c*x^2)/a^4 --R --R ---R (1211) +--R (1216) --R 2 3 2 2 2 4 3 --R ((- 18a b c + 6a b )e + (- 12a c + 24a b c - 6b )d)x --R * @@ -33708,7 +32371,7 @@ r0224:= -1/3*d/a/x^3+1/2*(b*d-a*e)/a^2/x^2-(b^2*d-a*c*d-a*b*e)/a^3/x-_ a0224:=integrate(t0224,x) --R --R ---R (1212) +--R (1217) --R [ --R 2 3 2 2 2 4 3 --R ((9a b c - 3a b )e + (6a c - 12a b c + 3b )d)x @@ -33776,7 +32439,7 @@ a0224:=integrate(t0224,x) m0224a:=a0224.1-r0224 --R --R ---R (1213) +--R (1218) --R 2 3 2 2 2 4 --R ((3a b c - a b )e + (2a c - 4a b c + b )d) --R * @@ -33807,7 +32470,7 @@ m0224a:=a0224.1-r0224 d0224a:=D(m0224a,x) --R --R ---R (1214) 0 +--R (1219) 0 --R Type: Expression Integer --E 1219 @@ -33815,7 +32478,7 @@ d0224a:=D(m0224a,x) m0224b:=a0224.2-r0224 --R --R ---R (1215) +--R (1220) --R +---------+ --R 2 3 2 2 2 4 | 2 --R ((3a b c - a b )e + (2a c - 4a b c + b )d)\|4a c - b @@ -33847,7 +32510,7 @@ m0224b:=a0224.2-r0224 d0224b:=D(m0224b,x) --R --R ---R (1216) 0 +--R (1221) 0 --R Type: Expression Integer --E 1221 @@ -33857,7 +32520,7 @@ t0225:= (a+b*x)^3/(a*c+(b*c+a*d)*x+b*d*x^2) --R --R 2 2 2 --R b x + 2a b x + a ---R (1217) ------------------ +--R (1222) ------------------ --R d x + c --R Type: Fraction Polynomial Integer --E 1222 @@ -33866,7 +32529,7 @@ t0225:= (a+b*x)^3/(a*c+(b*c+a*d)*x+b*d*x^2) r0225:= -b*(b*c-a*d)*x/d^2+1/2*(a+b*x)^2/d+(b*c-a*d)^2*log(c+d*x)/d^3 --R --R ---R (1218) +--R (1223) --R 2 2 2 2 2 2 2 2 2 2 2 --R (2a d - 4a b c d + 2b c )log(d x + c) + b d x + (4a b d - 2b c d)x + a d --R ---------------------------------------------------------------------------- @@ -33879,7 +32542,7 @@ r0225:= -b*(b*c-a*d)*x/d^2+1/2*(a+b*x)^2/d+(b*c-a*d)^2*log(c+d*x)/d^3 a0225:=integrate(t0225,x) --R --R ---R (1219) +--R (1224) --R 2 2 2 2 2 2 2 2 2 --R (2a d - 4a b c d + 2b c )log(d x + c) + b d x + (4a b d - 2b c d)x --R --------------------------------------------------------------------- @@ -33894,7 +32557,7 @@ m0225:=a0225-r0225 --R --R 2 --R a ---R (1220) - -- +--R (1225) - -- --R 2d --R Type: Expression Integer --E 1225 @@ -33903,7 +32566,7 @@ m0225:=a0225-r0225 d0225:=D(m0225,x) --R --R ---R (1221) 0 +--R (1226) 0 --R Type: Expression Integer --E 1226 @@ -33912,7 +32575,7 @@ t0226:= 1/(2+5*x+3*x^2) --R --R --R 1 ---R (1222) ------------ +--R (1227) ------------ --R 2 --R 3x + 5x + 2 --R Type: Fraction Polynomial Integer @@ -33922,7 +32585,7 @@ t0226:= 1/(2+5*x+3*x^2) r0226:= -2*atanh(5+6*x) --R --R ---R (1223) - 2atanh(6x + 5) +--R (1228) - 2atanh(6x + 5) --R Type: Expression Integer --E 1228 @@ -33930,7 +32593,7 @@ r0226:= -2*atanh(5+6*x) a0226:=integrate(t0226,x) --R --R ---R (1224) log(3x + 2) - log(x + 1) +--R (1229) log(3x + 2) - log(x + 1) --R Type: Union(Expression Integer,...) --E 1229 @@ -33938,7 +32601,7 @@ a0226:=integrate(t0226,x) m0226:=a0226-r0226 --R --R ---R (1225) log(3x + 2) - log(x + 1) + 2atanh(6x + 5) +--R (1230) log(3x + 2) - log(x + 1) + 2atanh(6x + 5) --R Type: Expression Integer --E 1230 @@ -33946,7 +32609,7 @@ m0226:=a0226-r0226 d0226:=D(m0226,x) --R --R ---R (1226) 0 +--R (1231) 0 --R Type: Expression Integer --E 1231 @@ -33955,7 +32618,7 @@ t0227:= 1/(2+5*x-3*x^2) --R --R --R 1 ---R (1227) - ------------ +--R (1232) - ------------ --R 2 --R 3x - 5x - 2 --R Type: Fraction Polynomial Integer @@ -33968,7 +32631,7 @@ r0227:= 2/7*atanh(-5/7+6/7*x) --R 6x - 5 --R 2atanh(------) --R 7 ---R (1228) -------------- +--R (1233) -------------- --R 7 --R Type: Expression Integer --E 1233 @@ -33978,7 +32641,7 @@ a0227:=integrate(t0227,x) --R --R --R log(3x + 1) - log(x - 2) ---R (1229) ------------------------ +--R (1234) ------------------------ --R 7 --R Type: Union(Expression Integer,...) --E 1234 @@ -33990,7 +32653,7 @@ m0227:=a0227-r0227 --R 6x - 5 --R log(3x + 1) - log(x - 2) - 2atanh(------) --R 7 ---R (1230) ----------------------------------------- +--R (1235) ----------------------------------------- --R 7 --R Type: Expression Integer --E 1235 @@ -33999,7 +32662,7 @@ m0227:=a0227-r0227 d0227:=D(m0227,x) --R --R ---R (1231) 0 +--R (1236) 0 --R Type: Expression Integer --E 1236 @@ -34007,7 +32670,7 @@ d0227:=D(m0227,x) t0228:= (b+2*c*x)^5/(a+b*x+c*x^2)^3 --R --R ---R (1232) +--R (1237) --R 5 5 4 4 2 3 3 3 2 2 4 5 --R 32c x + 80b c x + 80b c x + 40b c x + 10b c x + b --R / @@ -34024,7 +32687,7 @@ r0228:= -1/2*(b+2*c*x)^4/(a+b*x+c*x^2)^2-4*c*(b+2*c*x)^2/(a+b*x+c*x^2)+_ 16*c^2*log(a+b*x+c*x^2) --R --R ---R (1233) +--R (1238) --R 4 4 3 3 3 2 2 2 2 2 2 --R (32c x + 64b c x + (64a c + 32b c )x + 64a b c x + 32a c ) --R * @@ -34046,7 +32709,7 @@ r0228:= -1/2*(b+2*c*x)^4/(a+b*x+c*x^2)^2-4*c*(b+2*c*x)^2/(a+b*x+c*x^2)+_ a0228:=integrate(t0228,x) --R --R ---R (1234) +--R (1239) --R 4 4 3 3 3 2 2 2 2 2 2 --R (32c x + 64b c x + (64a c + 32b c )x + 64a b c x + 32a c ) --R * @@ -34066,7 +32729,7 @@ m0228:=a0228-r0228 --R --R --R 2 ---R (1235) 24c +--R (1240) 24c --R Type: Expression Integer --E 1240 @@ -34074,7 +32737,7 @@ m0228:=a0228-r0228 d0228:=D(m0228,x) --R --R ---R (1236) 0 +--R (1241) 0 --R Type: Expression Integer --E 1241 @@ -34083,7 +32746,7 @@ t0229:= 1/(2+13*x+15*x^2) --R --R --R 1 ---R (1237) -------------- +--R (1242) -------------- --R 2 --R 15x + 13x + 2 --R Type: Fraction Polynomial Integer @@ -34096,7 +32759,7 @@ r0229:= -2/7*atanh(13/7+30/7*x) --R 30x + 13 --R 2atanh(--------) --R 7 ---R (1238) - ---------------- +--R (1243) - ---------------- --R 7 --R Type: Expression Integer --E 1243 @@ -34106,7 +32769,7 @@ a0229:=integrate(t0229,x) --R --R --R log(5x + 1) - log(3x + 2) ---R (1239) ------------------------- +--R (1244) ------------------------- --R 7 --R Type: Union(Expression Integer,...) --E 1244 @@ -34118,7 +32781,7 @@ m0229:=a0229-r0229 --R 30x + 13 --R log(5x + 1) - log(3x + 2) + 2atanh(--------) --R 7 ---R (1240) -------------------------------------------- +--R (1245) -------------------------------------------- --R 7 --R Type: Expression Integer --E 1245 @@ -34127,7 +32790,7 @@ m0229:=a0229-r0229 d0229:=D(m0229,x) --R --R ---R (1241) 0 +--R (1246) 0 --R Type: Expression Integer --E 1246 @@ -34136,7 +32799,7 @@ t0230:= 1/x/(2/x+13+15*x) --R --R --R 1 ---R (1242) -------------- +--R (1247) -------------- --R 2 --R 15x + 13x + 2 --R Type: Fraction Polynomial Integer @@ -34149,7 +32812,7 @@ r0230:= -2/7*atanh(13/7+30/7*x) --R 30x + 13 --R 2atanh(--------) --R 7 ---R (1243) - ---------------- +--R (1248) - ---------------- --R 7 --R Type: Expression Integer --E 1248 @@ -34159,7 +32822,7 @@ a0230:=integrate(t0230,x) --R --R --R log(5x + 1) - log(3x + 2) ---R (1244) ------------------------- +--R (1249) ------------------------- --R 7 --R Type: Union(Expression Integer,...) --E 1249 @@ -34171,7 +32834,7 @@ m0230:=a0230-r0230 --R 30x + 13 --R log(5x + 1) - log(3x + 2) + 2atanh(--------) --R 7 ---R (1245) -------------------------------------------- +--R (1250) -------------------------------------------- --R 7 --R Type: Expression Integer --E 1250 @@ -34180,7 +32843,7 @@ m0230:=a0230-r0230 d0230:=D(m0230,x) --R --R ---R (1246) 0 +--R (1251) 0 --R Type: Expression Integer --E 1251 @@ -34189,7 +32852,7 @@ t0231:= 1/x^2/(2/x^2+13/x+15) --R --R --R 1 ---R (1247) -------------- +--R (1252) -------------- --R 2 --R 15x + 13x + 2 --R Type: Fraction Polynomial Integer @@ -34202,7 +32865,7 @@ r0231:= 2/7*atanh(13/7+4/7/x) --R 13x + 4 --R 2atanh(-------) --R 7x ---R (1248) --------------- +--R (1253) --------------- --R 7 --R Type: Expression Integer --E 1253 @@ -34212,7 +32875,7 @@ a0231:=integrate(t0231,x) --R --R --R log(5x + 1) - log(3x + 2) ---R (1249) ------------------------- +--R (1254) ------------------------- --R 7 --R Type: Union(Expression Integer,...) --E 1254 @@ -34224,7 +32887,7 @@ m0231:=a0231-r0231 --R 13x + 4 --R log(5x + 1) - log(3x + 2) - 2atanh(-------) --R 7x ---R (1250) ------------------------------------------- +--R (1255) ------------------------------------------- --R 7 --R Type: Expression Integer --E 1255 @@ -34233,7 +32896,7 @@ m0231:=a0231-r0231 d0231:=D(m0231,x) --R --R ---R (1251) 0 +--R (1256) 0 --R Type: Expression Integer --E 1256 @@ -34242,7 +32905,7 @@ t0232:= x/(2*x+13*x^2+15*x^3) --R --R --R 1 ---R (1252) -------------- +--R (1257) -------------- --R 2 --R 15x + 13x + 2 --R Type: Fraction Polynomial Integer @@ -34255,7 +32918,7 @@ r0232:= -2/7*atanh(13/7+30/7*x) --R 30x + 13 --R 2atanh(--------) --R 7 ---R (1253) - ---------------- +--R (1258) - ---------------- --R 7 --R Type: Expression Integer --E 1258 @@ -34265,7 +32928,7 @@ a0232:=integrate(t0232,x) --R --R --R log(5x + 1) - log(3x + 2) ---R (1254) ------------------------- +--R (1259) ------------------------- --R 7 --R Type: Union(Expression Integer,...) --E 1259 @@ -34277,7 +32940,7 @@ m0232:=a0232-r0232 --R 30x + 13 --R log(5x + 1) - log(3x + 2) + 2atanh(--------) --R 7 ---R (1255) -------------------------------------------- +--R (1260) -------------------------------------------- --R 7 --R Type: Expression Integer --E 1260 @@ -34286,7 +32949,7 @@ m0232:=a0232-r0232 d0232:=D(m0232,x) --R --R ---R (1256) 0 +--R (1261) 0 --R Type: Expression Integer --E 1261 @@ -34296,7 +32959,7 @@ t0233:= x^4/(a+b*x^2+c*x^4) --R --R 4 --R x ---R (1257) --------------- +--R (1262) --------------- --R 4 2 --R c x + b x + a --R Type: Fraction Polynomial Integer @@ -34311,7 +32974,7 @@ r0233:= x/c-1/2*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*atan(2^(1/2)*c^(1/2)*x/_ (b+(b^2-4*a*c)^(1/2))^(1/2) --R --R ---R (1258) +--R (1263) --R +------------------+ --R +-----------+ | +-----------+ --R +-+ | 2 2 +-+ | | 2 @@ -34354,7 +33017,7 @@ r0233:= x/c-1/2*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*atan(2^(1/2)*c^(1/2)*x/_ a0233:=integrate(t0233,x) --R --R ---R (1259) +--R (1264) --R +-----------------------------------------------------+ --R | +--------------------+ --R | | 2 2 2 4 @@ -34511,7 +33174,7 @@ a0233:=integrate(t0233,x) m0233:=a0233-r0233 --R --R ---R (1260) +--R (1265) --R +--------------------+ +------------------+ --R +-----------+ | +-----------+ | +-----------+ --R | 2 +-+ | | 2 | | 2 @@ -34723,7 +33386,7 @@ m0233:=a0233-r0233 d0233:=D(m0233,x) --R --R ---R (1261) 0 +--R (1266) 0 --R Type: Expression Integer --E 1266 @@ -34733,7 +33396,7 @@ t0234:= x^2/(a+b*x^2+c*x^4) --R --R 2 --R x ---R (1262) --------------- +--R (1267) --------------- --R 4 2 --R c x + b x + a --R Type: Fraction Polynomial Integer @@ -34747,7 +33410,7 @@ r0234:= 1/2*2^(1/2)*(-(b-(b^2-4*a*c)^(1/2))^(1/2)*_ c^(1/2)/(b^2-4*a*c)^(1/2) --R --R ---R (1263) +--R (1268) --R +--------------------+ --R | +-----------+ +-+ +-+ --R +-+ | | 2 x\|2 \|c @@ -34776,7 +33439,7 @@ r0234:= 1/2*2^(1/2)*(-(b-(b^2-4*a*c)^(1/2))^(1/2)*_ a0234:=integrate(t0234,x) --R --R ---R (1264) +--R (1269) --R +---------------------------------------+ --R | +-----------------+ --R | 2 2 | 1 @@ -34903,7 +33566,7 @@ a0234:=integrate(t0234,x) m0234:=a0234-r0234 --R --R ---R (1265) +--R (1270) --R +---------------------------------------+ --R | +-----------------+ --R | 2 2 | 1 @@ -35050,7 +33713,7 @@ m0234:=a0234-r0234 d0234:=D(m0234,x) --R --R ---R (1266) 0 +--R (1271) 0 --R Type: Expression Integer --E 1271 @@ -35059,7 +33722,7 @@ t0235:= 1/x^2/(a+b*x^2+c*x^4) --R --R --R 1 ---R (1267) ------------------ +--R (1272) ------------------ --R 6 4 2 --R c x + b x + a x --R Type: Fraction Polynomial Integer @@ -35073,7 +33736,7 @@ r0235:= -1/a/x-1/2*c^(1/2)*(1+b/(b^2-4*a*c)^(1/2))*_ a/(b+(b^2-4*a*c)^(1/2))^(1/2) --R --R ---R (1268) +--R (1273) --R +------------------+ --R +-----------+ | +-----------+ --R +-+ | 2 +-+ +-+ | | 2 @@ -35116,7 +33779,7 @@ r0235:= -1/a/x-1/2*c^(1/2)*(1+b/(b^2-4*a*c)^(1/2))*_ a0235:=integrate(t0235,x) --R --R ---R (1269) +--R (1274) --R - --R +----------------------------------------------------+ --R | +--------------------+ @@ -35273,7 +33936,7 @@ a0235:=integrate(t0235,x) m0235:=a0235-r0235 --R --R ---R (1270) +--R (1275) --R - --R +--------------------+ +------------------+ --R +-----------+ | +-----------+ | +-----------+ @@ -35485,7 +34148,7 @@ m0235:=a0235-r0235 d0235:=D(m0235,x) --R --R ---R (1271) 0 +--R (1276) 0 --R Type: Expression Integer --E 1276 @@ -35494,7 +34157,7 @@ t0236:= 1/x^3/(a+b*x^2+c*x^4) --R --R --R 1 ---R (1272) ------------------ +--R (1277) ------------------ --R 7 5 3 --R c x + b x + a x --R Type: Fraction Polynomial Integer @@ -35506,7 +34169,7 @@ r0236:= -1/2/a/x^2-1/2*(b^2-2*a*c)*_ b*log(x)/a^2+1/4*b*log(a+b*x^2+c*x^4)/a^2 --R --R ---R (1273) +--R (1278) --R 2 --R 2 2 2c x + b --R (4a c - 2b )x atanh(--------------) @@ -35528,7 +34191,7 @@ r0236:= -1/2/a/x^2-1/2*(b^2-2*a*c)*_ a0236:=integrate(t0236,x) --R --R ---R (1274) +--R (1279) --R [ --R 2 2 --R (2a c - b )x @@ -35575,7 +34238,7 @@ a0236:=integrate(t0236,x) m0236a:=a0236.1-r0236 --R --R ---R (1275) +--R (1280) --R 2 --R (2a c - b ) --R * @@ -35607,7 +34270,7 @@ m0236a:=a0236.1-r0236 d0236a:=D(m0236a,x) --R --R ---R (1276) 0 +--R (1281) 0 --R Type: Expression Integer --E 1281 @@ -35615,7 +34278,7 @@ d0236a:=D(m0236a,x) m0236b:=a0236.2-r0236 --R --R ---R (1277) +--R (1282) --R +---------+ 2 --R 2 | 2 2c x + b --R (- 2a c + b )\|4a c - b atanh(--------------) @@ -35640,7 +34303,7 @@ m0236b:=a0236.2-r0236 d0236b:=D(m0236b,x) --R --R ---R (1278) 0 +--R (1283) 0 --R Type: Expression Integer --E 1283 @@ -35650,7 +34313,7 @@ t0237:= x^4/(a-b*x^2+c*x^4) --R --R 4 --R x ---R (1279) --------------- +--R (1284) --------------- --R 4 2 --R c x - b x + a --R Type: Fraction Polynomial Integer @@ -35665,7 +34328,7 @@ r0237:= x/c+1/2*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ (b+(b^2-4*a*c)^(1/2))^(1/2) --R --R ---R (1280) +--R (1285) --R +------------------+ --R +-----------+ | +-----------+ --R +-+ | 2 2 +-+ | | 2 @@ -35708,7 +34371,7 @@ r0237:= x/c+1/2*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ a0237:=integrate(t0237,x) --R --R ---R (1281) +--R (1286) --R - --R +-----------------------------------------------------+ --R | +--------------------+ @@ -35865,7 +34528,7 @@ a0237:=integrate(t0237,x) m0237:=a0237-r0237 --R --R ---R (1282) +--R (1287) --R - --R +------------------+ +------------------+ --R +-----------+ | +-----------+ | +-----------+ @@ -36077,7 +34740,7 @@ m0237:=a0237-r0237 d0237:=D(m0237,x) --R --R ---R (1283) 0 +--R (1288) 0 --R Type: Expression Integer --E 1288 @@ -36087,7 +34750,7 @@ t0238:= x^2/(a-b*x^2+c*x^4) --R --R 2 --R x ---R (1284) --------------- +--R (1289) --------------- --R 4 2 --R c x - b x + a --R Type: Fraction Polynomial Integer @@ -36100,7 +34763,7 @@ r0238:= -1/2*2^(1/2)*(-(-b+(b^2-4*a*c)^(1/2))^(1/2)*_ x/(b+(b^2-4*a*c)^(1/2))^(1/2)))/c^(1/2)/(b^2-4*a*c)^(1/2) --R --R ---R (1285) +--R (1290) --R +------------------+ --R | +-----------+ +-+ +-+ --R +-+ | | 2 x\|2 \|c @@ -36129,7 +34792,7 @@ r0238:= -1/2*2^(1/2)*(-(-b+(b^2-4*a*c)^(1/2))^(1/2)*_ a0238:=integrate(t0238,x) --R --R ---R (1286) +--R (1291) --R +---------------------------------------+ --R | +-----------------+ --R | 2 2 | 1 @@ -36256,7 +34919,7 @@ a0238:=integrate(t0238,x) m0238:=a0238-r0238 --R --R ---R (1287) +--R (1292) --R +---------------------------------------+ --R | +-----------------+ --R | 2 2 | 1 @@ -36403,7 +35066,7 @@ m0238:=a0238-r0238 d0238:=D(m0238,x) --R --R ---R (1288) 0 +--R (1293) 0 --R Type: Expression Integer --E 1293 @@ -36412,7 +35075,7 @@ t0239:= 1/(a^2+b+2*a*x^2+x^4) --R --R --R 1 ---R (1289) ------------------- +--R (1294) ------------------- --R 4 2 2 --R x + 2a x + b + a --R Type: Fraction Polynomial Integer @@ -36424,7 +35087,7 @@ r0239:= 1/2*atan(x/(a-(-b)^(1/2))^(1/2))/(a-(-b)^(1/2))^(1/2)/_ (a+(-b)^(1/2))^(1/2)/(-b)^(1/2) --R --R ---R (1290) +--R (1295) --R +----------+ +------------+ --R | +---+ x | +---+ x --R \|\|- b + a atan(---------------) - \|- \|- b + a atan(-------------) @@ -36442,7 +35105,7 @@ r0239:= 1/2*atan(x/(a-(-b)^(1/2))^(1/2))/(a-(-b)^(1/2))^(1/2)/_ a0239:=integrate(t0239,x) --R --R ---R (1291) +--R (1296) --R +-------------------------------------------+ --R | +------------------------+ --R | 2 2 | 1 @@ -36569,7 +35232,7 @@ a0239:=integrate(t0239,x) m0239:=a0239-r0239 --R --R ---R (1292) +--R (1297) --R +------------+ +----------+ --R +---+ | +---+ | +---+ --R \|- b \|- \|- b + a \|\|- b + a @@ -36721,7 +35384,7 @@ m0239:=a0239-r0239 d0239:=D(m0239,x) --R --R ---R (1293) 0 +--R (1298) 0 --R Type: Expression Integer --E 1298 @@ -36730,7 +35393,7 @@ t0240:= 1/(1+a^2+2*a*x^2+x^4) --R --R --R 1 ---R (1294) ------------------- +--R (1299) ------------------- --R 4 2 2 --R x + 2a x + a + 1 --R Type: Fraction Polynomial Integer @@ -36747,7 +35410,7 @@ r0240:= -1/8*2^(1/2)*(2*atan(1/2*(2^(1/2)*(-a+(1+a^2)^(1/2))^(1/2)-2*x)*_ (-a+(1+a^2)^(1/2))^(1/2) --R --R ---R (1295) +--R (1300) --R +-------------+ +-------------+ --R | +------+ | +------+ +------+ --R +-+ | | 2 +-+ | | 2 | 2 2 @@ -36789,7 +35452,7 @@ r0240:= -1/8*2^(1/2)*(2*atan(1/2*(2^(1/2)*(-a+(1+a^2)^(1/2))^(1/2)-2*x)*_ a0240:=integrate(t0240,x) --R --R ---R (1296) +--R (1301) --R - --R +-----------------+ --R 2 | 1 @@ -37054,7 +35717,7 @@ a0240:=integrate(t0240,x) m0240:=a0240-r0240 --R --R ---R (1297) +--R (1302) --R - --R +-------------+ +-------------+ --R +---------+ +------+ | +------+ | +------+ @@ -37373,774 +36036,573 @@ m0240:=a0240-r0240 --E 1302 --S 1303 of 1483 -d0240:=D(m0240,x) +d0240:=normalize(D(m0240,x)) --R --R ---R (1298) ---R 4 2 4 5 3 2 ---R ((a + 2a + 1)x + (2a + 4a + 2a)x ) ---R * ---R +-----------------+ 8 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 ---R + ---R 4 2 4 5 3 2 ---R ((4a + 8a + 4)x + (8a + 16a + 8a)x ) ---R * ---R +-----------------+ 2 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 ---R + ---R 4 2 6 5 3 4 ---R (- 4a + 8a + 12)x + (- 8a + 16a + 24a)x +--R (1303) +--R 9 7 5 3 10 +--R (512a + 1568a + 1680a + 704a + 80a)x +--R + +--R 10 8 6 4 2 8 +--R (1024a + 3136a + 3360a + 1408a + 160a )x +--R + +--R 11 9 7 5 3 6 +--R (1024a + 2112a + 224a - 1952a - 1248a - 160a)x +--R + +--R 12 10 8 6 4 2 4 +--R (1024a + 8256a + 19040a + 18208a + 7200a + 800a )x +--R + +--R 13 11 9 7 5 3 2 +--R (512a + 544a - 2992a - 7360a - 6368a - 2272a - 240a)x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 7 5 3 10 +--R (- 64a - 132a - 78a - 10a)x +--R + +--R 8 6 4 2 8 +--R (- 128a - 264a - 156a - 20a )x +--R + +--R 9 7 5 3 6 +--R (- 256a - 528a - 312a - 40a )x --R + ---R 6 4 2 2 ---R (12a + 20a + 4a - 4)x +--R 10 8 6 4 2 4 +--R (128a - 120a - 636a - 448a - 60a )x +--R + +--R 11 9 7 5 3 2 +--R (- 192a - 524a - 434a - 54a + 58a + 10a)x --R * --R +---------+2 --R | 1 --R |--------- --R 4| 2 --R \|16a + 16 ---R * ---R +-----------------+ 6 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 ---R + ---R 7 5 3 6 8 6 4 2 4 ---R (64a + 448a + 704a + 320a)x + (128a + 896a + 1408a + 640a )x ---R + ---R 9 5 3 2 ---R (64a - 384a - 512a - 192a)x ---R * ---R +-----------------+ +---------+2 ---R | 1 | 1 ---R |----------------- |--------- ---R | 4 2 4| 2 ---R \|64a + 128a + 64 \|16a + 16 ---R * ---R +-----------------+ ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 ---R * ---R +-----------------+ 5 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 ---R + ---R 4 2 4 5 3 2 ---R ((6a + 12a + 6)x + (12a + 24a + 12a)x ) ---R * ---R +-----------------+ 4 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 --R + ---R 4 2 6 5 3 4 ---R (- 4a + 8a + 12)x + (- 8a + 16a + 24a)x +--R 9 7 5 3 8 +--R (256a - 368a - 1056a - 432a )x +--R + +--R 10 8 6 4 6 +--R (512a - 736a - 2112a - 864a )x --R + ---R 6 4 2 2 ---R (12a + 20a + 4a - 4)x +--R 11 9 7 5 3 4 +--R (256a - 2160a - 2576a + 560a + 720a )x --R * ---R +-----------------+ 2 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R +---------+2 atan(-----------------------------) ---R | 1 a ---R |--------- cos(-----------------------------------) ---R 4| 2 2 ---R \|16a + 16 +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 7 5 3 8 8 6 4 2 6 +--R (- 32a + 78a + 54a )x + (- 32a + 238a + 176a + 18a )x --R + ---R 2 8 3 6 4 2 4 ---R (- a + 3)x + (- 2a + 6a)x + (- 7a + 6a - 3)x +--R 9 7 5 3 4 +--R (- 96a + 138a - 116a - 126a )x +--R + +--R 10 8 6 4 2 2 +--R (32a + 114a + 150a + 86a + 18a )x --R * ---R +-----------------+ 4 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 +--R 3 +--R %CW --R + ---R 7 5 3 6 ---R (128a + 896a + 1408a + 640a)x +--R 8 6 4 2 10 +--R (- 640a - 1792a - 1664a - 512a )x +--R + +--R 9 7 5 3 8 +--R (- 1280a - 3584a - 3328a - 1024a )x +--R + +--R 10 8 6 4 2 6 +--R (- 1280a - 2304a + 256a + 2304a + 1024a )x +--R + +--R 11 9 7 5 3 4 +--R (- 1280a - 9984a - 21248a - 17664a - 5120a )x +--R + +--R 12 10 8 6 4 2 2 +--R (- 640a - 512a + 3840a + 8192a + 6016a + 1536a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 --R + ---R 8 6 4 2 4 ---R (256a + 1792a + 2816a + 1280a )x +--R 6 4 2 10 7 5 3 8 +--R (80a + 144a + 64a )x + (160a + 288a + 128a )x --R + ---R 9 5 3 2 ---R (128a - 768a - 1024a - 384a)x ---R * ---R +-----------------+ +---------+2 ---R | 1 | 1 ---R |----------------- |--------- ---R | 4 2 4| 2 ---R \|64a + 128a + 64 \|16a + 16 +--R 8 6 4 6 9 7 5 3 4 +--R (320a + 576a + 256a )x + (- 160a + 192a + 736a + 384a )x +--R + +--R 10 8 6 4 2 2 +--R (240a + 592a + 400a - 16a - 64a )x --R * ---R +-----------------+ 3 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 +--R +---------+2 +--R | 1 +--R |--------- +--R 4| 2 +--R \|16a + 16 --R + ---R 5 3 8 6 4 2 6 ---R (- 32a + 64a + 96a)x + (- 64a + 128a + 192a )x +--R 8 6 4 2 8 +--R (- 320a + 544a + 1152a + 288a )x --R + ---R 7 5 3 4 ---R (- 32a + 288a + 160a - 160a)x +--R 9 7 5 3 6 +--R (- 640a + 1088a + 2304a + 576a )x +--R + +--R 10 8 6 4 2 4 +--R (- 320a + 2784a + 2464a - 1120a - 480a )x --R * ---R +-----------------+ ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R +-----------------+ atan(-----------------------------) ---R | 1 a ---R |----------------- cos(-----------------------------------) ---R | 4 2 2 +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 --R \|64a + 128a + 64 +--R + +--R 6 4 2 8 7 5 3 6 +--R (40a - 108a - 36a )x + (40a - 308a - 136a - 12a)x +--R + +--R 8 6 4 2 4 +--R (120a - 204a + 208a + 84a )x +--R + +--R 9 7 5 3 2 +--R (- 40a - 132a - 156a - 76a - 12a)x --R * ---R +-----------------+ 3 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 +--R 2 +--R %CW --R + ---R 4 2 4 5 3 2 ---R ((4a + 8a + 4)x + (8a + 16a + 8a)x ) ---R * ---R +-----------------+ 6 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 ---R + ---R 4 2 6 5 3 4 ---R (4a - 8a - 12)x + (8a - 16a - 24a)x +--R 9 7 5 3 10 +--R (- 512a - 1440a - 1360a - 448a - 16a)x +--R + +--R 10 8 6 4 2 8 +--R (- 1024a - 2880a - 2720a - 896a - 32a )x +--R + +--R 11 9 7 5 3 6 +--R (- 1024a - 1856a + 160a + 1824a + 864a + 32a)x +--R + +--R 12 10 8 6 4 2 4 +--R (- 1024a - 8000a - 17120a - 14496a - 4512a - 160a )x +--R + +--R 13 11 9 7 5 3 2 +--R (- 512a - 416a + 3056a + 6592a + 4960a + 1376a + 48a)x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 7 5 3 10 8 6 4 2 8 +--R (64a + 116a + 54a + 2a)x + (128a + 232a + 108a + 4a )x +--R + +--R 9 7 5 3 6 +--R (256a + 464a + 216a + 8a )x --R + ---R 6 4 2 2 ---R (- 12a - 20a - 4a + 4)x +--R 10 8 6 4 2 4 +--R (- 128a + 152a + 588a + 320a + 12a )x +--R + +--R 11 9 7 5 3 2 +--R (192a + 476a + 330a - 2a - 50a - 2a)x --R * ---R +-----------------+ 4 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R +---------+2 atan(-----------------------------) ---R | 1 a ---R |--------- cos(-----------------------------------) ---R 4| 2 2 +--R +---------+2 +--R | 1 +--R |--------- +--R 4| 2 --R \|16a + 16 --R + ---R 2 8 3 6 4 2 4 ---R ((22a - 2)x + (44a - 4a)x + (26a - 68a + 2)x ) +--R 9 7 5 3 8 +--R (- 256a + 432a + 928a + 240a )x +--R + +--R 10 8 6 4 6 +--R (- 512a + 864a + 1856a + 480a )x +--R + +--R 11 9 7 5 3 4 +--R (- 256a + 2224a + 2000a - 880a - 400a )x --R * ---R +-----------------+ 2 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 7 5 3 8 8 6 4 2 6 +--R (32a - 86a - 30a )x + (32a - 246a - 112a - 10a )x --R + ---R +---------+2 ---R 2 10 3 8 4 2 6 | 1 ---R ((4a + 4)x + (8a + 8a)x + (20a + 8a - 12)x ) |--------- ---R 4| 2 ---R \|16a + 16 +--R 9 7 5 3 4 +--R (96a - 162a + 164a + 70a )x +--R + +--R 10 8 6 4 2 2 +--R (- 32a - 106a - 126a - 62a - 10a )x --R * ---R +-----------------+ 2 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 +--R %CW --R + ---R 7 5 3 6 ---R (64a + 448a + 704a + 320a)x +--R 8 6 4 2 10 +--R (128a + 352a + 320a + 96a )x --R + ---R 8 6 4 2 4 ---R (128a + 896a + 1408a + 640a )x +--R 9 7 5 3 8 +--R (256a + 704a + 640a + 192a )x --R + ---R 9 5 3 2 ---R (64a - 384a - 512a - 192a)x ---R * ---R +-----------------+ +---------+2 ---R | 1 | 1 ---R |----------------- |--------- ---R | 4 2 4| 2 ---R \|64a + 128a + 64 \|16a + 16 ---R * ---R +-----------------+ 5 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 ---R + ---R 5 3 8 6 4 2 6 ---R (32a - 64a - 96a)x + (64a - 128a - 192a )x +--R 10 8 6 4 2 6 +--R (256a + 448a - 64a - 448a - 192a )x +--R + +--R 11 9 7 5 3 4 +--R (256a + 1984a + 4160a + 3392a + 960a )x --R + ---R 7 5 3 4 ---R (32a - 288a - 160a + 160a)x +--R 12 10 8 6 4 2 2 +--R (128a + 96a - 768a - 1600a - 1152a - 288a )x --R * ---R +-----------------+ 3 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R +-----------------+ atan(-----------------------------) ---R | 1 a ---R |----------------- cos(-----------------------------------) ---R | 4 2 2 +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 --R \|64a + 128a + 64 --R + ---R 5 3 10 6 4 2 8 ---R (64a + 128a + 64a)x + (128a + 256a + 128a )x ---R + ---R 7 5 3 6 ---R (64a - 320a - 832a - 448a)x ---R * ---R +-----------------+ +---------+2 ---R | 1 | 1 ---R |----------------- |--------- ---R | 4 2 4| 2 ---R \|64a + 128a + 64 \|16a + 16 ---R * ---R +-----------------+ ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 ---R * ---R +-----------------+ ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 ---R + ---R 4 2 4 5 3 2 ---R ((a + 2a + 1)x + (2a + 4a + 2a)x ) +--R 6 4 2 10 7 5 3 8 +--R (- 16a - 28a - 12a )x + (- 32a - 56a - 24a )x +--R + +--R 8 6 4 6 9 7 5 3 4 +--R (- 64a - 112a - 48a )x + (32a - 40a - 144a - 72a )x +--R + +--R 10 8 6 4 2 2 +--R (- 48a - 116a - 76a + 4a + 12a )x --R * ---R +-----------------+ 8 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 ---R + ---R 4 2 6 5 3 4 ---R (4a - 8a - 12)x + (8a - 16a - 24a)x ---R + ---R 6 4 2 2 ---R (- 12a - 20a - 4a + 4)x ---R * ---R +-----------------+ 6 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R +---------+2 atan(-----------------------------) ---R | 1 a ---R |--------- cos(-----------------------------------) ---R 4| 2 2 +--R +---------+2 +--R | 1 +--R |--------- +--R 4| 2 --R \|16a + 16 --R + ---R 2 8 3 6 4 2 4 ---R ((- a + 3)x + (- 2a + 6a)x + (- 7a + 6a - 3)x ) +--R 8 6 4 2 8 9 7 5 3 6 +--R (64a - 112a - 224a - 48a )x + (128a - 224a - 448a - 96a )x +--R + +--R 10 8 6 4 2 4 +--R (64a - 560a - 464a + 240a + 80a )x --R * ---R +-----------------+ 4 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 --R + ---R +---------+2 ---R 2 10 3 8 4 2 6 | 1 ---R ((- 4a - 4)x + (- 8a - 8a)x + (- 20a - 8a + 12)x ) |--------- ---R 4| 2 ---R \|16a + 16 ---R * ---R +-----------------+ 2 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 +--R 6 4 2 8 7 5 3 6 +--R (- 8a + 22a + 6a )x + (- 8a + 62a + 24a + 2a)x --R + ---R 2 8 ---R (- a - 1)x +--R 8 6 4 2 4 9 7 5 3 2 +--R (- 24a + 42a - 44a - 14a )x + (8a + 26a + 30a + 14a + 2a)x --R / ---R 6 4 2 4 7 5 3 2 8 6 4 ---R (a + 3a + 3a + 1)x + (2a + 6a + 6a + 2a)x + a + 4a + 6a ---R + ---R 2 ---R 4a + 1 ---R * ---R +-----------------+ 8 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 ---R + ---R 6 4 2 4 7 5 3 2 8 ---R (4a + 12a + 12a + 4)x + (8a + 24a + 24a + 8a)x + 4a +--R 9 7 5 3 10 +--R (4096a + 12544a + 13440a + 5632a + 640a)x +--R + +--R 10 8 6 4 2 8 +--R (8192a + 25088a + 26880a + 11264a + 1280a )x +--R + +--R 11 9 7 5 3 6 +--R (8192a + 33280a + 51968a + 38144a + 12544a + 1280a)x +--R + +--R 12 10 8 6 4 2 4 +--R (8192a + 33280a + 51968a + 38144a + 12544a + 1280a )x +--R + +--R 13 11 9 7 5 3 +--R 4096a + 20736a + 42624a + 45056a + 25344a + 6912a +--R + +--R 640a +--R * +--R 2 +--R x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 --R + ---R 6 4 2 ---R 16a + 24a + 16a + 4 ---R * ---R +-----------------+ 2 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 ---R + ---R 6 4 2 6 7 5 3 4 ---R (- 16a - 16a + 16a + 16)x + (- 32a - 32a + 32a + 32a)x +--R 9 7 5 3 10 +--R (256a + 272a - 216a - 272a - 40a)x +--R + +--R 10 8 6 4 2 8 +--R (512a + 544a - 432a - 544a - 80a )x +--R + +--R 11 9 7 5 3 6 +--R (512a + 1056a + 112a - 976a - 624a - 80a)x --R + ---R 8 6 2 2 ---R (- 16a - 32a + 32a + 16)x +--R 12 10 8 6 4 2 4 +--R (512a + 1056a + 112a - 976a - 624a - 80a )x +--R + +--R 13 11 9 7 5 3 2 +--R (256a + 784a + 584a - 432a - 800a - 352a - 40a)x --R * --R +---------+2 --R | 1 --R |--------- --R 4| 2 --R \|16a + 16 ---R * ---R +-----------------+ 6 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 ---R + ---R 7 5 3 6 ---R (512a + 1536a + 1536a + 512a)x ---R + ---R 8 6 4 2 4 ---R (1024a + 3072a + 3072a + 1024a )x --R + ---R 9 7 5 3 2 ---R (512a + 2048a + 3072a + 2048a + 512a)x ---R * ---R +-----------------+ +---------+2 ---R | 1 | 1 ---R |----------------- |--------- ---R | 4 2 4| 2 ---R \|64a + 128a + 64 \|16a + 16 ---R * ---R +-----------------+ ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 ---R * ---R +-----------------+ 5 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 ---R + ---R 6 4 2 4 7 5 3 2 8 ---R (6a + 18a + 18a + 6)x + (12a + 36a + 36a + 12a)x + 6a +--R 9 7 5 3 8 +--R (2048a + 1152a - 2048a - 1152a )x --R + ---R 6 4 2 ---R 24a + 36a + 24a + 6 ---R * ---R +-----------------+ 4 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 ---R + ---R 6 4 2 6 7 5 3 4 ---R (- 16a - 16a + 16a + 16)x + (- 32a - 32a + 32a + 32a)x +--R 10 8 6 4 6 +--R (4096a + 2304a - 4096a - 2304a )x --R + ---R 8 6 2 2 ---R (- 16a - 32a + 32a + 16)x +--R 11 9 7 5 3 4 +--R (2048a + 3200a - 896a - 3200a - 1152a )x --R * ---R +-----------------+ 2 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R +---------+2 atan(-----------------------------) ---R | 1 a ---R |--------- cos(-----------------------------------) ---R 4| 2 2 ---R \|16a + 16 +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 7 5 3 12 8 6 4 2 10 +--R (16a + 41a + 34a + 9a)x + (32a + 82a + 68a + 18a )x +--R + +--R 9 7 5 3 8 +--R (112a + 79a + 473a + 309a + 27a)x +--R + +--R 10 8 6 4 2 6 +--R (192a + 44a + 796a + 532a + 36a )x +--R + +--R 11 9 7 5 3 4 +--R (112a + 191a + 552a + 782a + 336a + 27a)x --R + ---R 4 2 8 5 3 6 6 4 2 4 ---R (6a - 4a + 6)x + (12a - 8a + 12a)x + (6a + 2a + 2a + 6)x +--R 12 10 8 6 4 2 2 13 11 +--R (32a + 146a + 264a + 236a + 104a + 18a )x + 16a + 89a +--R + +--R 9 7 5 3 +--R 205a + 250a + 170a + 61a + 9a --R * ---R +-----------------+ 4 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 +--R 3 +--R %CW --R + ---R 7 5 3 6 ---R (1024a + 3072a + 3072a + 1024a)x +--R 8 6 4 2 10 +--R (- 5120a - 14336a - 13312a - 4096a )x +--R + +--R 9 7 5 3 8 +--R (- 10240a - 28672a - 26624a - 8192a )x +--R + +--R 10 8 6 4 2 6 +--R (- 10240a - 38912a - 55296a - 34816a - 8192a )x +--R + +--R 11 9 7 5 3 4 +--R (- 10240a - 38912a - 55296a - 34816a - 8192a )x +--R + +--R 12 10 8 6 4 2 2 +--R (- 5120a - 24576a - 47104a - 45056a - 21504a - 4096a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 --R + ---R 8 6 4 2 4 ---R (2048a + 6144a + 6144a + 2048a )x +--R 8 6 4 2 10 +--R (- 320a - 256a + 320a + 256a )x --R + ---R 9 7 5 3 2 ---R (1024a + 4096a + 6144a + 4096a + 1024a)x ---R * ---R +-----------------+ +---------+2 ---R | 1 | 1 ---R |----------------- |--------- ---R | 4 2 4| 2 ---R \|64a + 128a + 64 \|16a + 16 +--R 9 7 5 3 8 +--R (- 640a - 512a + 640a + 512a )x +--R + +--R 10 8 6 4 2 6 +--R (- 640a - 1152a + 128a + 1152a + 512a )x +--R + +--R 11 9 7 5 3 4 +--R (- 640a - 1152a + 128a + 1152a + 512a )x +--R + +--R 12 10 8 6 4 2 2 +--R (- 320a - 896a - 512a + 640a + 832a + 256a )x --R * ---R +-----------------+ 3 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 +--R +---------+2 +--R | 1 +--R |--------- +--R 4| 2 +--R \|16a + 16 --R + ---R 5 8 6 2 6 ---R (- 256a + 256a)x + (- 512a + 512a )x +--R 8 6 4 2 8 +--R (- 2560a - 768a + 2560a + 768a )x --R + ---R 7 5 3 4 ---R (- 256a - 256a + 256a + 256a)x +--R 9 7 5 3 6 +--R (- 5120a - 1536a + 5120a + 1536a )x +--R + +--R 10 8 6 4 2 4 +--R (- 2560a - 3328a + 1792a + 3328a + 768a )x --R * ---R +-----------------+ ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R +-----------------+ atan(-----------------------------) ---R | 1 a ---R |----------------- cos(-----------------------------------) ---R | 4 2 2 +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 --R \|64a + 128a + 64 +--R + +--R 6 4 2 12 7 5 3 10 +--R (- 20a - 46a - 32a - 6)x + (- 40a - 92a - 64a - 12a)x +--R + +--R 8 6 4 2 8 +--R (- 140a - 62a - 586a - 234a - 18)x +--R + +--R 9 7 5 3 6 +--R (- 240a + 8a - 1016a - 392a - 24a)x +--R + +--R 10 8 6 4 2 4 +--R (- 140a - 202a - 648a - 820a - 252a - 18)x +--R + +--R 11 9 7 5 3 2 12 10 +--R (- 40a - 172a - 288a - 232a - 88a - 12a)x - 20a - 106a +--R + +--R 8 6 4 2 +--R - 230a - 260a - 160a - 50a - 6 --R * ---R +-----------------+ 3 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 +--R 2 +--R %CW --R + ---R 6 4 2 4 7 5 3 2 8 ---R (4a + 12a + 12a + 4)x + (8a + 24a + 24a + 8a)x + 4a +--R 9 7 5 3 10 +--R (- 4096a - 11520a - 10880a - 3584a - 128a)x +--R + +--R 10 8 6 4 2 8 +--R (- 8192a - 23040a - 21760a - 7168a - 256a )x +--R + +--R 11 9 7 5 3 6 +--R (- 8192a - 31232a - 44800a - 28928a - 7424a - 256a)x +--R + +--R 12 10 8 6 4 2 4 +--R (- 8192a - 31232a - 44800a - 28928a - 7424a - 256a )x +--R + +--R 13 11 9 7 5 +--R - 4096a - 19712a - 38016a - 36864a - 18176a +--R + +--R 3 +--R - 3840a - 128a +--R * +--R 2 +--R x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 --R + ---R 6 4 2 ---R 16a + 24a + 16a + 4 ---R * ---R +-----------------+ 6 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 ---R + ---R 6 4 2 6 7 5 3 4 ---R (16a + 16a - 16a - 16)x + (32a + 32a - 32a - 32a)x +--R 9 7 5 3 10 +--R (- 256a - 208a + 248a + 208a + 8a)x --R + ---R 8 6 2 2 ---R (16a + 32a - 32a - 16)x ---R * ---R +-----------------+ 4 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R +---------+2 atan(-----------------------------) ---R | 1 a ---R |--------- cos(-----------------------------------) ---R 4| 2 2 ---R \|16a + 16 ---R + ---R 4 2 8 5 3 6 ---R (- 4a + 88a - 4)x + (- 8a + 176a - 8a)x +--R 10 8 6 4 2 8 +--R (- 512a - 416a + 496a + 416a + 16a )x --R + ---R 6 4 2 4 ---R (- 4a + 84a + 84a - 4)x ---R * ---R +-----------------+ 2 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 ---R + ---R 4 10 5 8 ---R (- 16a + 16)x + (- 32a + 32a)x ---R + ---R 6 4 2 6 ---R (- 16a - 16a + 16a + 16)x +--R 11 9 7 5 3 6 +--R (- 512a - 928a + 80a + 912a + 432a + 16a)x +--R + +--R 12 10 8 6 4 2 4 +--R (- 512a - 928a + 80a + 912a + 432a + 16a )x +--R + +--R 13 11 9 7 5 3 2 +--R (- 256a - 720a - 424a + 496a + 672a + 224a + 8a)x --R * --R +---------+2 --R | 1 --R |--------- --R 4| 2 --R \|16a + 16 ---R * ---R +-----------------+ 2 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 ---R + ---R 7 5 3 6 ---R (512a + 1536a + 1536a + 512a)x +--R + +--R 9 7 5 3 8 +--R (- 2048a - 640a + 2048a + 640a )x --R + ---R 8 6 4 2 4 ---R (1024a + 3072a + 3072a + 1024a )x +--R 10 8 6 4 6 +--R (- 4096a - 1280a + 4096a + 1280a )x --R + ---R 9 7 5 3 2 ---R (512a + 2048a + 3072a + 2048a + 512a)x ---R * ---R +-----------------+ +---------+2 ---R | 1 | 1 ---R |----------------- |--------- ---R | 4 2 4| 2 ---R \|64a + 128a + 64 \|16a + 16 +--R 11 9 7 5 3 4 +--R (- 2048a - 2688a + 1408a + 2688a + 640a )x --R * ---R +-----------------+ 5 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 7 5 3 12 8 6 4 2 10 +--R (- 16a - 37a - 26a - 5a)x + (- 32a - 74a - 52a - 10a )x +--R + +--R 9 7 5 3 8 +--R (- 112a - 51a - 469a - 193a - 15a)x +--R + +--R 10 8 6 4 2 6 +--R (- 192a + 4a - 812a - 324a - 20a )x +--R + +--R 11 9 7 5 3 4 +--R (- 112a - 163a - 520a - 662a - 208a - 15a)x --R + ---R 5 8 6 2 6 ---R (256a - 256a)x + (512a - 512a )x +--R 12 10 8 6 4 2 2 13 11 +--R (- 32a - 138a - 232a - 188a - 72a - 10a )x - 16a - 85a +--R + +--R 9 7 5 3 +--R - 185a - 210a - 130a - 41a - 5a +--R * +--R %CW +--R + +--R 8 6 4 2 10 +--R (1024a + 2816a + 2560a + 768a )x +--R + +--R 9 7 5 3 8 +--R (2048a + 5632a + 5120a + 1536a )x +--R + +--R 10 8 6 4 2 6 +--R (2048a + 7680a + 10752a + 6656a + 1536a )x +--R + +--R 11 9 7 5 3 4 +--R (2048a + 7680a + 10752a + 6656a + 1536a )x --R + ---R 7 5 3 4 ---R (256a + 256a - 256a - 256a)x +--R 12 10 8 6 4 2 2 +--R (1024a + 4864a + 9216a + 8704a + 4096a + 768a )x --R * ---R +-----------------+ 3 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R +-----------------+ atan(-----------------------------) ---R | 1 a ---R |----------------- cos(-----------------------------------) ---R | 4 2 2 +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 --R \|64a + 128a + 64 --R + ---R 5 3 10 6 4 2 8 ---R (512a + 1024a + 512a)x + (1024a + 2048a + 1024a )x ---R + ---R 7 5 3 6 ---R (512a + 1536a + 1536a + 512a)x ---R * ---R +-----------------+ +---------+2 ---R | 1 | 1 ---R |----------------- |--------- ---R | 4 2 4| 2 ---R \|64a + 128a + 64 \|16a + 16 ---R * ---R +-----------------+ ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 +--R 8 6 4 2 10 9 7 5 3 8 +--R (64a + 48a - 64a - 48a )x + (128a + 96a - 128a - 96a )x +--R + +--R 10 8 6 4 2 6 +--R (128a + 224a - 32a - 224a - 96a )x +--R + +--R 11 9 7 5 3 4 +--R (128a + 224a - 32a - 224a - 96a )x +--R + +--R 12 10 8 6 4 2 2 +--R (64a + 176a + 96a - 128a - 160a - 48a )x --R * ---R +-----------------+ ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R sin(-----------------------------------) ---R 2 +--R +---------+2 +--R | 1 +--R |--------- +--R 4| 2 +--R \|16a + 16 --R + ---R 6 4 2 4 7 5 3 2 8 6 4 ---R (a + 3a + 3a + 1)x + (2a + 6a + 6a + 2a)x + a + 4a + 6a +--R 8 6 4 2 8 +--R (512a + 128a - 512a - 128a )x --R + ---R 2 ---R 4a + 1 +--R 9 7 5 3 6 +--R (1024a + 256a - 1024a - 256a )x +--R + +--R 10 8 6 4 2 4 +--R (512a + 640a - 384a - 640a - 128a )x --R * ---R +-----------------+ 8 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 --R + ---R 6 4 2 6 7 5 3 4 ---R (16a + 16a - 16a - 16)x + (32a + 32a - 32a - 32a)x ---R + ---R 8 6 2 2 ---R (16a + 32a - 32a - 16)x ---R * ---R +-----------------+ 6 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R +---------+2 atan(-----------------------------) ---R | 1 a ---R |--------- cos(-----------------------------------) ---R 4| 2 2 ---R \|16a + 16 +--R 6 4 2 12 7 5 3 10 +--R (4a + 9a + 6a + 1)x + (8a + 18a + 12a + 2a)x --R + ---R 4 2 8 5 3 6 6 4 2 4 ---R ((6a - 4a + 6)x + (12a - 8a + 12a)x + (6a + 2a + 2a + 6)x ) ---R * ---R +-----------------+ 4 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R atan(-----------------------------) ---R a ---R cos(-----------------------------------) ---R 2 +--R 8 6 4 2 8 9 7 5 3 6 +--R (28a + 11a + 117a + 41a + 3)x + (48a - 4a + 204a + 68a + 4a)x --R + ---R 4 10 5 8 6 4 2 6 ---R ((16a - 16)x + (32a - 32a)x + (16a + 16a - 16a - 16)x ) ---R * ---R +-----------------+ 2 ---R 2 | 1 ---R (8a + 8) |----------------- ---R | 4 2 ---R \|64a + 128a + 64 ---R +---------+2 atan(-----------------------------) ---R | 1 a ---R |--------- cos(-----------------------------------) ---R 4| 2 2 ---R \|16a + 16 +--R 10 8 6 4 2 4 +--R (28a + 39a + 128a + 158a + 44a + 3)x --R + ---R 2 12 3 10 4 2 8 ---R (a + 1)x + (2a + 2a)x + (a + 2a + 1)x +--R 11 9 7 5 3 2 12 10 8 6 +--R (8a + 34a + 56a + 44a + 16a + 2a)x + 4a + 21a + 45a + 50a +--R + +--R 4 2 +--R 30a + 9a + 1 --R Type: Expression Integer --E 1303 @@ -38150,7 +36612,7 @@ t0241:= (a+b*x^2)/(2+x^2+x^4) --R --R 2 --R b x + a ---R (1299) ----------- +--R (1304) ----------- --R 4 2 --R x + x + 2 --R Type: Fraction Polynomial Integer @@ -38169,7 +36631,7 @@ r0241:= -1/2*a*atan(((-1+2*2^(1/2))^(1/2)-2*x)/(1+2*2^(1/2))^(1/2))/_ (-1+2*2^(1/2))^(1/2)*x+x^2)/(-1+2*2^(1/2))^(1/2) --R --R ---R (1300) +--R (1305) --R +---------+ +---------+ +---------+ +---------+ +---------+ --R | +-+ | +-+ | +-+ | +-+ | +-+ --R (- b\|2\|2 + 1 \|4\|2 - 2 + a\|2\|2 - 1 \|2\|2 + 1 )\|4\|2 + 2 @@ -38224,7 +36686,7 @@ r0241:= -1/2*a*atan(((-1+2*2^(1/2))^(1/2)-2*x)/(1+2*2^(1/2))^(1/2))/_ a0241:=integrate(t0241,x) --R --R ---R (1301) +--R (1306) --R - --R +----------------+ --R | 4 2 2 4 @@ -38496,7 +36958,7 @@ a0241:=integrate(t0241,x) m0241:=a0241-r0241 --R --R ---R (1302) +--R (1307) --R - --R +-------------------------------+ +---------+ +---------+ --R 4| 4 3 2 2 3 4 | +-+ | +-+ @@ -38826,1225 +37288,4783 @@ m0241:=a0241-r0241 --E 1307 --S 1308 of 1483 -d0241:=D(m0241,x) ---R ---R ---R (1303) ---R 6 2 5 3 4 5 2 6 7 2 ---R (1408a b - 1408a b + 1056a b - 528a b + 352a b - 176a )x ---R + ---R 6 2 5 3 4 5 2 6 7 ---R - 1600a b + 1600a b - 1200a b + 600a b - 400a b + 200a +d0241:=normalize(D(m0241,x)) +--R +--R +--R (1308) +--R 2 9 3 8 4 7 +--R 35530880a b - 175567392a b + 486945536a b +--R + +--R 5 6 6 5 7 4 +--R - 663806528a b + 672982464a b - 409959088a b +--R + +--R 8 3 9 2 10 +--R 180379584a b - 48665232a b + 7429576a b +--R + +--R 11 +--R - 555170a +--R * +--R 8 +--R x +--R + +--R 2 9 3 8 4 7 +--R - 40376000a b + 199508400a b - 553347200a b +--R + +--R 5 6 6 5 7 4 +--R 754325600a b - 764752800a b + 465862600a b +--R + +--R 8 3 9 2 10 +--R - 204976800a b + 55301400a b - 8442700a b +--R + +--R 11 +--R 630875a +--R * +--R 6 +--R x +--R + +--R 2 9 3 8 4 7 +--R 71061760a b - 351134784a b + 973891072a b +--R + +--R 5 6 6 5 7 4 +--R - 1327613056a b + 1345964928a b - 819918176a b +--R + +--R 8 3 9 2 10 +--R 360759168a b - 97330464a b + 14859152a b +--R + +--R 11 +--R - 1110340a +--R * +--R 4 +--R x +--R + +--R 2 9 3 8 4 7 +--R - 80752000a b + 399016800a b - 1106694400a b +--R + +--R 5 6 6 5 7 4 +--R 1508651200a b - 1529505600a b + 931725200a b +--R + +--R 8 3 9 2 10 +--R - 409953600a b + 110602800a b - 16885400a b +--R + +--R 11 +--R 1261750a +--R * +--R 2 +--R x +--R * +--R +-+ +--R \|2 +--R + +--R 2 9 3 8 4 7 +--R - 40376000a b + 199508400a b - 553347200a b +--R + +--R 5 6 6 5 7 4 +--R 754325600a b - 764752800a b + 465862600a b +--R + +--R 8 3 9 2 10 +--R - 204976800a b + 55301400a b - 8442700a b +--R + +--R 11 +--R 630875a +--R * +--R 8 +--R x +--R + +--R 2 9 3 8 4 7 +--R 71061760a b - 351134784a b + 973891072a b +--R + +--R 5 6 6 5 7 4 +--R - 1327613056a b + 1345964928a b - 819918176a b +--R + +--R 8 3 9 2 10 +--R 360759168a b - 97330464a b + 14859152a b +--R + +--R 11 +--R - 1110340a +--R * +--R 6 +--R x +--R + +--R 2 9 3 8 4 7 +--R - 80752000a b + 399016800a b - 1106694400a b +--R + +--R 5 6 6 5 7 4 +--R 1508651200a b - 1529505600a b + 931725200a b +--R + +--R 8 3 9 2 10 +--R - 409953600a b + 110602800a b - 16885400a b +--R + +--R 11 +--R 1261750a +--R * +--R 4 +--R x +--R + +--R 2 9 3 8 4 7 +--R 142123520a b - 702269568a b + 1947782144a b +--R + +--R 5 6 6 5 7 4 +--R - 2655226112a b + 2691929856a b - 1639836352a b +--R + +--R 8 3 9 2 10 +--R 721518336a b - 194660928a b + 29718304a b +--R + +--R 11 +--R - 2220680a +--R * +--R 2 +--R x +--R * +--R +-------------------------------+2 +--R 4| 4 3 2 2 3 4 +--R \|4b - 4a b + 5a b - 2a b + a +--R + +--R 2 11 3 10 4 9 +--R 6228992a b - 64596224a b + 246498560a b +--R + +--R 5 8 6 7 7 6 +--R - 470138592a b + 557632768a b - 337301888a b +--R + +--R 8 5 9 4 10 3 +--R 53537792a b + 30222192a b - 22313984a b +--R + +--R 11 2 12 13 +--R 6341104a b - 799568a b + 36498a +--R * +--R 6 +--R x +--R + +--R 2 11 3 10 4 9 +--R - 7078400a b + 73404800a b - 280112000a b +--R + +--R 5 8 6 7 7 6 +--R 534248400a b - 633673600a b + 383297600a b +--R + +--R 8 5 9 4 10 3 +--R - 60838400a b - 34343400a b + 25356800a b +--R + +--R 11 2 12 13 +--R - 7205800a b + 908600a b - 41475a +--R * +--R 4 +--R x +--R * +--R +-+ +--R \|2 +--R + +--R 2 11 3 10 4 9 +--R - 7078400a b + 73404800a b - 280112000a b +--R + +--R 5 8 6 7 7 6 +--R 534248400a b - 633673600a b + 383297600a b +--R + +--R 8 5 9 4 10 3 +--R - 60838400a b - 34343400a b + 25356800a b +--R + +--R 11 2 12 13 +--R - 7205800a b + 908600a b - 41475a +--R * +--R 6 +--R x +--R + +--R 2 11 3 10 4 9 +--R 12457984a b - 129192448a b + 492997120a b +--R + +--R 5 8 6 7 7 6 +--R - 940277184a b + 1115265536a b - 674603776a b +--R + +--R 8 5 9 4 10 3 +--R 107075584a b + 60444384a b - 44627968a b +--R + +--R 11 2 12 13 +--R 12682208a b - 1599136a b + 72996a +--R * +--R 4 +--R x +--R * +--R 4+--+2 +--R \|98 --R * ---R +-+ ---R \|2 +--R +----------------+ +--R | 4 2 2 4 +--R \|4b - 4a b + a --R + ---R 6 2 5 3 4 5 2 6 7 2 ---R (- 1600a b + 1600a b - 1200a b + 600a b - 400a b + 200a )x ---R + ---R 6 2 5 3 4 5 2 6 7 ---R 2816a b - 2816a b + 2112a b - 1056a b + 704a b - 352a ---R * ---R +---------+ +---------+ ---R 4+--+2 | +-+ | +-+ ---R \|98 \|2\|2 + 1 \|4\|2 + 2 ---R + ---R 6 2 5 3 4 5 2 6 7 2 ---R (- 896a b + 896a b - 672a b + 336a b - 224a b + 112a )x +--R 12 2 11 3 10 +--R 20303360a b - 186613504a b + 726204864a b +--R + +--R 4 9 5 8 6 7 +--R - 1637722240a b + 2144140768a b - 1868175232a b +--R + +--R 7 6 8 5 9 4 +--R 981083488a b - 192354624a b - 64604848a b +--R + +--R 10 3 11 2 12 13 +--R 78100176a b - 24113012a b + 3818584a b - 237930a +--R * +--R 8 +--R x +--R + +--R 12 2 11 3 10 +--R - 23072000a b + 212060800a b - 825232800a b +--R + +--R 4 9 5 8 6 7 +--R 1861048000a b - 2436523600a b + 2122926400a b +--R + +--R 7 6 8 5 9 4 +--R - 1114867600a b + 218584800a b + 73414600a b +--R + +--R 10 3 11 2 12 +--R - 88750200a b + 27401150a b - 4339300a b +--R + +--R 13 +--R 270375a +--R * +--R 6 +--R x +--R + +--R 12 2 11 3 10 +--R 40606720a b - 373227008a b + 1452409728a b +--R + +--R 4 9 5 8 6 7 +--R - 3275444480a b + 4288281536a b - 3736350464a b +--R + +--R 7 6 8 5 9 4 +--R 1962166976a b - 384709248a b - 129209696a b +--R + +--R 10 3 11 2 12 +--R 156200352a b - 48226024a b + 7637168a b +--R + +--R 13 +--R - 475860a +--R * +--R 4 +--R x +--R + +--R 12 2 11 3 10 +--R - 46144000a b + 424121600a b - 1650465600a b +--R + +--R 4 9 5 8 6 7 +--R 3722096000a b - 4873047200a b + 4245852800a b +--R + +--R 7 6 8 5 9 4 +--R - 2229735200a b + 437169600a b + 146829200a b +--R + +--R 10 3 11 2 12 +--R - 177500400a b + 54802300a b - 8678600a b +--R + +--R 13 +--R 540750a +--R * +--R 2 +--R x +--R * +--R +-+ +--R \|2 --R + ---R 6 2 5 3 4 5 2 6 7 ---R - 448a b + 448a b - 336a b + 168a b - 112a b + 56a ---R * ---R +-+ ---R \|2 ---R + ---R 6 2 5 3 4 5 2 6 7 2 ---R (448a b - 448a b + 336a b - 168a b + 112a b - 56a )x ---R + ---R 6 2 5 3 4 5 2 6 7 ---R 1792a b - 1792a b + 1344a b - 672a b + 448a b - 224a ---R * ---R +---------+ +---------+ ---R 4+--+2 | +-+ | +-+ ---R \|98 \|2\|2 - 1 \|4\|2 - 2 ---R + ---R 6 2 5 3 4 5 2 6 ---R 3584a b - 3584a b + 2688a b - 1344a b + 896a b ---R + ---R 7 ---R - 448a +--R 12 2 11 3 10 +--R - 23072000a b + 212060800a b - 825232800a b +--R + +--R 4 9 5 8 6 7 +--R 1861048000a b - 2436523600a b + 2122926400a b +--R + +--R 7 6 8 5 9 4 +--R - 1114867600a b + 218584800a b + 73414600a b +--R + +--R 10 3 11 2 12 13 +--R - 88750200a b + 27401150a b - 4339300a b + 270375a --R * ---R 4 +--R 8 --R x --R + ---R 7 6 2 5 3 4 4 3 ---R - 7168b + 10752a b - 8960a b + 2688a b + 2688a b +--R 12 2 11 3 10 +--R 40606720a b - 373227008a b + 1452409728a b +--R + +--R 4 9 5 8 6 7 +--R - 3275444480a b + 4288281536a b - 3736350464a b --R + ---R 5 2 6 7 ---R - 3136a b + 1792a b - 448a +--R 7 6 8 5 9 4 +--R 1962166976a b - 384709248a b - 129209696a b +--R + +--R 10 3 11 2 12 13 +--R 156200352a b - 48226024a b + 7637168a b - 475860a --R * ---R 2 +--R 6 --R x --R + ---R 6 2 5 3 4 5 2 6 7 ---R 7168a b - 7168a b + 5376a b - 2688a b + 1792a b - 896a ---R * ---R +-+ ---R \|2 ---R + ---R 6 2 5 3 4 5 2 6 ---R - 8064a b + 8064a b - 6048a b + 3024a b - 2016a b ---R + ---R 7 ---R 1008a ---R * ---R 4 ---R x ---R + ---R 7 6 2 5 3 4 4 3 ---R 16128b - 24192a b + 20160a b - 6048a b - 6048a b +--R 12 2 11 3 10 +--R - 46144000a b + 424121600a b - 1650465600a b +--R + +--R 4 9 5 8 6 7 +--R 3722096000a b - 4873047200a b + 4245852800a b +--R + +--R 7 6 8 5 9 4 +--R - 2229735200a b + 437169600a b + 146829200a b +--R + +--R 10 3 11 2 12 13 +--R - 177500400a b + 54802300a b - 8678600a b + 540750a +--R * +--R 4 +--R x --R + ---R 5 2 6 7 ---R 7056a b - 4032a b + 1008a +--R 12 2 11 3 10 +--R 81213440a b - 746454016a b + 2904819456a b +--R + +--R 4 9 5 8 6 7 +--R - 6550888960a b + 8576563072a b - 7472700928a b +--R + +--R 7 6 8 5 9 4 +--R 3924333952a b - 769418496a b - 258419392a b +--R + +--R 10 3 11 2 12 13 +--R 312400704a b - 96452048a b + 15274336a b - 951720a +--R * +--R 2 +--R x --R * ---R 2 ---R x +--R +-------------------------------+2 +--R 4| 4 3 2 2 3 4 +--R \|4b - 4a b + 5a b - 2a b + a --R + ---R 6 2 5 3 4 5 2 6 7 ---R - 16128a b + 16128a b - 12096a b + 6048a b - 4032a b + 2016a ---R * ---R 4+--+2 ---R \|98 ---R * ---R +----------------+ 8 ---R | 4 2 2 4 ---R 7\|4b - 4a b + a ---R atan(---------------------) ---R 2 2 +-+ ---R (2b - 8a b + a )\|7 ---R sin(---------------------------) ---R 2 ---R + ---R 6 2 5 3 4 5 2 6 ---R 5632a b - 5632a b + 4224a b - 2112a b + 1408a b +--R 14 2 13 3 12 +--R 1779712a b - 13561856a b + 43366400a b --R + ---R 7 ---R - 704a +--R 4 11 5 10 6 9 +--R - 97219584a b + 152423040a b - 189353472a b +--R + +--R 7 8 8 7 9 6 +--R 182745024a b - 144866304a b + 91372512a b +--R + +--R 10 5 11 4 12 3 +--R - 47338368a b + 19052880a b - 6076224a b +--R + +--R 13 2 14 15 +--R 1355200a b - 211904a b + 13904a +--R * +--R 10 +--R x +--R + +--R 14 2 13 3 12 +--R - 2022400a b + 15411200a b - 49280000a b +--R + +--R 4 11 5 10 6 9 +--R 110476800a b - 173208000a b + 215174400a b +--R + +--R 7 8 8 7 9 6 +--R - 207664800a b + 164620800a b - 103832400a b +--R + +--R 10 5 11 4 12 3 +--R 53793600a b - 21651000a b + 6904800a b +--R + +--R 13 2 14 15 +--R - 1540000a b + 240800a b - 15800a +--R * +--R 8 +--R x +--R + +--R 14 2 13 3 12 +--R 8898560a b - 80267264a b + 346024448a b +--R + +--R 4 11 5 10 6 9 +--R - 972866048a b + 1637796160a b - 1815534336a b +--R + +--R 7 8 8 7 9 6 +--R 1118190304a b - 273774336a b + 59116288a b +--R + +--R 10 5 11 4 12 3 +--R - 138526080a b + 112804384a b - 51095968a b +--R + +--R 13 2 14 15 +--R 13044108a b - 1859088a b + 106018a +--R * +--R 6 +--R x +--R + +--R 14 2 13 3 12 +--R - 10112000a b + 91212800a b - 393209600a b +--R + +--R 4 11 5 10 6 9 +--R 1105529600a b - 1861132000a b + 2063107200a b +--R + +--R 7 8 8 7 9 6 +--R - 1270670800a b + 311107200a b - 67177600a b +--R + +--R 10 5 11 4 12 3 +--R 157416000a b - 128186800a b + 58063600a b +--R + +--R 13 2 14 15 +--R - 14822850a b + 2112600a b - 120475a +--R * +--R 4 +--R x +--R + +--R 14 2 13 3 12 +--R 7118848a b - 54247424a b + 173465600a b +--R + +--R 4 11 5 10 6 9 +--R - 388878336a b + 609692160a b - 757413888a b +--R + +--R 7 8 8 7 9 6 +--R 730980096a b - 579465216a b + 365490048a b +--R + +--R 10 5 11 4 12 3 +--R - 189353472a b + 76211520a b - 24304896a b +--R + +--R 13 2 14 15 +--R 5420800a b - 847616a b + 55616a --R * --R 2 --R x --R + ---R 6 2 5 3 4 5 2 6 ---R - 6400a b + 6400a b - 4800a b + 2400a b - 1600a b +--R 14 2 13 3 12 +--R - 8089600a b + 61644800a b - 197120000a b --R + ---R 7 ---R 800a +--R 4 11 5 10 6 9 +--R 441907200a b - 692832000a b + 860697600a b +--R + +--R 7 8 8 7 9 6 +--R - 830659200a b + 658483200a b - 415329600a b +--R + +--R 10 5 11 4 12 3 +--R 215174400a b - 86604000a b + 27619200a b +--R + +--R 13 2 14 15 +--R - 6160000a b + 963200a b - 63200a --R * --R +-+ --R \|2 --R + ---R 6 2 5 3 4 5 2 6 ---R - 6400a b + 6400a b - 4800a b + 2400a b - 1600a b +--R 14 2 13 3 12 +--R - 2022400a b + 15411200a b - 49280000a b --R + ---R 7 ---R 800a +--R 4 11 5 10 6 9 +--R 110476800a b - 173208000a b + 215174400a b +--R + +--R 7 8 8 7 9 6 +--R - 207664800a b + 164620800a b - 103832400a b +--R + +--R 10 5 11 4 12 3 +--R 53793600a b - 21651000a b + 6904800a b +--R + +--R 13 2 14 15 +--R - 1540000a b + 240800a b - 15800a +--R * +--R 10 +--R x +--R + +--R 14 2 13 3 12 +--R 3559424a b - 27123712a b + 86732800a b +--R + +--R 4 11 5 10 6 9 +--R - 194439168a b + 304846080a b - 378706944a b +--R + +--R 7 8 8 7 9 6 +--R 365490048a b - 289732608a b + 182745024a b +--R + +--R 10 5 11 4 12 3 +--R - 94676736a b + 38105760a b - 12152448a b +--R + +--R 13 2 14 15 +--R 2710400a b - 423808a b + 27808a +--R * +--R 8 +--R x +--R + +--R 14 2 13 3 12 +--R - 10112000a b + 91212800a b - 393209600a b +--R + +--R 4 11 5 10 6 9 +--R 1105529600a b - 1861132000a b + 2063107200a b +--R + +--R 7 8 8 7 9 6 +--R - 1270670800a b + 311107200a b - 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784a )x + (12544a b - 3136a )x ---R * ---R +-------------------------------+2 +----------------+ ---R +-+4| 4 3 2 2 3 4 | 4 2 2 4 ---R \|7 \|4b - 4a b + 5a b - 2a b + a \|4b - 4a b + a +--R 7 8 8 7 9 6 +--R - 1834926912a b + 538884864a b + 594651456a b +--R + +--R 10 5 11 4 12 3 +--R - 842006592a b + 453206880a b - 145131336a b +--R + +--R 13 2 14 15 +--R 28305144a b - 3293388a b + 167076a --R * ---R +---------+ +---------+ ---R | +-+ | +-+ ---R \|2\|2 - 1 \|4\|2 - 2 +--R 8 +--R x --R + ---R 3 2 2 3 6 ---R (7168b - 5376a b + 17024a b - 4032a )x ---R + ---R 3 2 2 3 4 ---R (7168b - 55552a b + 29568a b - 4032a )x ---R + ---R 3 2 2 3 2 ---R (14336b - 10752a b + 34048a b - 8064a )x ---R * ---R +-+ ---R \|2 +--R 15 14 2 13 +--R - 65802240b + 708019200a b - 3530483712a b +--R + +--R 3 12 4 11 5 10 +--R 10699153920a b - 19891146240a b + 22794210432a b --R + ---R 3 2 2 3 6 ---R (- 16128b + 12096a b - 38304a b + 9072a )x +--R 6 9 7 8 8 7 +--R - 12266037504a b + 568564416a b + 428020992a b --R + ---R 3 2 2 3 4 ---R (- 16128b + 124992a b - 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7607283712a b + 6066995200a b - 3803641856a b +--R + +--R 9 5 10 4 11 3 +--R 1935990784a b - 753292288a b + 227397632a b +--R + +--R 12 2 13 14 +--R - 46362624a b + 6221824a b - 365568a --R * --R +-+ --R \|2 --R + ---R 6 5 2 4 3 3 4 2 ---R 32256b - 32256a b - 314496a b + 169344a b + 136080a b +--R 14 13 2 12 +--R 13160448b - 111992832a b + 417263616a b +--R + +--R 3 11 4 10 5 9 +--R - 1023289344a b + 1694907648a b - 2177989632a b +--R + +--R 6 8 7 7 8 6 +--R 2139548544a b - 1706342400a b + 1069774272a b +--R + +--R 9 5 10 4 11 3 +--R - 544497408a b + 211863456a b - 63955584a b +--R + +--R 12 2 13 14 +--R 13039488a b - 1749888a b + 102816a +--R * +--R 12 +--R x +--R + +--R 14 13 2 12 +--R 13160448b - 111992832a b + 417263616a b +--R + +--R 3 11 4 10 5 9 +--R - 1023289344a b + 1694907648a b - 2177989632a b --R + ---R 5 6 ---R - 76608a b + 6552a +--R 6 8 7 7 8 6 +--R 2139548544a b - 1706342400a b + 1069774272a b +--R + +--R 9 5 10 4 11 3 +--R - 544497408a b + 211863456a b - 63955584a b +--R + +--R 12 2 13 14 +--R 13039488a b - 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1752145920a b + 7916267520a b --R + ---R 5 6 ---R - 153216a b + 13104a +--R 3 11 4 10 5 9 +--R - 23327926272a b + 43634868480a b - 53947579392a b +--R + +--R 6 8 7 7 8 6 +--R 36441191808a b - 11632352256a b + 4500824832a b +--R + +--R 9 5 10 4 11 3 +--R - 5728117248a b + 3732228864a b - 1381000320a b +--R + +--R 12 2 13 14 +--R 297502128a b - 37283904a b + 1979208a --R * --R 4 --R x ---R * ---R +----------------+ 2 ---R | 4 2 2 4 ---R 7\|4b - 4a b + a ---R atan(---------------------) ---R 2 2 +-+ ---R 4+--+2 (2b - 8a b + a )\|7 ---R \|98 cos(---------------------------) ---R 2 ---R + ---R 4 3 2 2 3 4 10 ---R (- 50176b + 25088a b + 43904a b - 12544a b - 9408a )x +--R + +--R 14 13 2 12 +--R 52641792b - 447971328a b + 1669054464a b --R + ---R 4 3 2 2 3 4 8 ---R (- 50176b + 25088a b + 43904a b - 12544a b - 9408a )x +--R 3 11 4 10 5 9 +--R - 4093157376a b + 6779630592a b - 8711958528a b --R + ---R 4 3 2 2 3 4 6 ---R (- 100352b + 50176a b + 87808a b - 25088a b - 18816a )x +--R 6 8 7 7 8 6 +--R 8558194176a b - 6825369600a b + 4279097088a b +--R + +--R 9 5 10 4 11 3 +--R - 2177989632a b + 847453824a b - 255822336a b +--R + +--R 12 2 13 14 +--R 52157952a b - 6999552a b + 411264a --R * ---R +-+ ---R \|2 +--R 2 +--R x +--R + +--R 14 13 2 12 3 11 +--R 105283584b - 895942656a b + 3338108928a b - 8186314752a b +--R + +--R 4 10 5 9 6 8 +--R 13559261184a b - 17423917056a b + 17116388352a b --R + ---R 4 3 2 2 3 4 10 ---R (112896b - 56448a b - 98784a b + 28224a b + 21168a )x +--R 7 7 8 6 9 5 +--R - 13650739200a b + 8558194176a b - 4355979264a b --R + ---R 4 3 2 2 3 4 8 ---R (112896b - 56448a b - 98784a b + 28224a b + 21168a )x +--R 10 4 11 3 12 2 13 +--R 1694907648a b - 511644672a b + 104315904a b - 13999104a b --R + ---R 4 3 2 2 3 4 6 ---R (225792b - 112896a b - 197568a b + 56448a b + 42336a )x +--R 14 +--R 822528a --R * ---R +-------------------------------+2 ---R 4| 4 3 2 2 3 4 ---R \|4b - 4a b + 5a b - 2a b + a +--R 4+--+2 +--R \|98 --R * ---R +----------------+ 2 ---R | 4 2 2 4 ---R 7\|4b - 4a b + a ---R atan(---------------------) ---R 2 2 +-+ ---R (2b - 8a b + a )\|7 ---R sin(---------------------------) ---R 2 +--R %CY --R + ---R 2 6 2 4 ---R (50176a b - 12544a )x + (50176a b - 12544a )x +--R 9 2 8 3 7 +--R 17561600a b - 97115648a b + 146112512a b +--R + +--R 4 6 5 5 6 4 +--R - 138912256a b + 27044864a b + 54089728a b +--R + +--R 7 3 8 2 9 10 +--R - 44255232a b + 19273856a b - 3995264a b + 274400a +--R * +--R 10 +--R x +--R + +--R 9 2 8 3 7 +--R 17561600a b - 97115648a b + 146112512a b +--R + +--R 4 6 5 5 6 4 +--R - 138912256a b + 27044864a b + 54089728a b +--R + +--R 7 3 8 2 9 10 +--R - 44255232a b + 19273856a b - 3995264a b + 274400a +--R * +--R 8 +--R x --R + ---R 2 2 ---R (100352a b - 25088a )x +--R 9 2 8 3 7 +--R 70246400a b - 388462592a b + 584450048a b +--R + +--R 4 6 5 5 6 4 +--R - 555649024a b + 108179456a b + 216358912a b +--R + +--R 7 3 8 2 9 10 +--R - 177020928a b + 77095424a b - 15981056a b + 1097600a +--R * +--R 6 +--R x +--R + +--R 9 2 8 3 7 +--R 35123200a b - 194231296a b + 292225024a b +--R + +--R 4 6 5 5 6 4 +--R - 277824512a b + 54089728a b + 108179456a b +--R + +--R 7 3 8 2 9 10 +--R - 88510464a b + 38547712a b - 7990528a b + 548800a +--R * +--R 4 +--R x +--R + +--R 9 2 8 3 7 +--R 70246400a b - 388462592a b + 584450048a b +--R + +--R 4 6 5 5 6 4 +--R - 555649024a b + 108179456a b + 216358912a b +--R + +--R 7 3 8 2 9 10 +--R - 177020928a b + 77095424a b - 15981056a b + 1097600a +--R * +--R 2 +--R x --R * --R +-+ --R \|2 --R + ---R 2 6 2 4 ---R (- 112896a b + 28224a )x + (- 112896a b + 28224a )x +--R 9 2 8 3 7 +--R - 39513600a b + 218510208a b - 328753152a b +--R + +--R 4 6 5 5 6 4 7 3 +--R 312552576a b - 60850944a b - 121701888a b + 99574272a b +--R + +--R 8 2 9 10 +--R - 43366176a b + 8989344a b - 617400a +--R * +--R 10 +--R x --R + ---R 2 2 ---R (- 225792a b + 56448a )x ---R * ---R +-------------------------------+2 +----------------+ ---R +-+4| 4 3 2 2 3 4 | 4 2 2 4 ---R \|7 \|4b - 4a b + 5a b - 2a b + a \|4b - 4a b + a ---R * ---R +----------------+ 5 ---R | 4 2 2 4 ---R 7\|4b - 4a b + a ---R atan(---------------------) ---R 2 2 +-+ ---R (2b - 8a b + a )\|7 ---R cos(---------------------------) ---R 2 ---R + ---R 3 2 2 3 4 8 ---R (14336a b - 10752a b - 3584a b + 1344a )x +--R 9 2 8 3 7 +--R - 39513600a b + 218510208a b - 328753152a b --R + ---R 3 2 2 3 4 6 ---R (14336a b - 10752a b - 3584a b + 1344a )x +--R 4 6 5 5 6 4 7 3 +--R 312552576a b - 60850944a b - 121701888a b + 99574272a b --R + ---R 3 2 2 3 4 4 ---R (28672a b - 21504a b - 7168a b + 2688a )x +--R 8 2 9 10 +--R - 43366176a b + 8989344a b - 617400a --R * ---R +-+ ---R \|2 +--R 8 +--R x --R + ---R 3 2 2 3 4 8 ---R (- 32256a b + 24192a b + 8064a b - 3024a )x +--R 9 2 8 3 7 +--R - 158054400a b + 874040832a b - 1315012608a b +--R + +--R 4 6 5 5 6 4 +--R 1250210304a b - 243403776a b - 486807552a b +--R + +--R 7 3 8 2 9 10 +--R 398297088a b - 173464704a b + 35957376a b - 2469600a +--R * +--R 6 +--R x --R + ---R 3 2 2 3 4 6 ---R (- 32256a b + 24192a b + 8064a b - 3024a )x +--R 9 2 8 3 7 +--R - 79027200a b + 437020416a b - 657506304a b +--R + +--R 4 6 5 5 6 4 7 3 +--R 625105152a b - 121701888a b - 243403776a b + 199148544a b +--R + +--R 8 2 9 10 +--R - 86732352a b + 17978688a b - 1234800a +--R * +--R 4 +--R x --R + ---R 3 2 2 3 4 4 ---R (- 64512a b + 48384a b + 16128a b - 6048a )x +--R 9 2 8 3 7 +--R - 158054400a b + 874040832a b - 1315012608a b +--R + +--R 4 6 5 5 6 4 +--R 1250210304a b - 243403776a b - 486807552a b +--R + +--R 7 3 8 2 9 10 +--R 398297088a b - 173464704a b + 35957376a b - 2469600a +--R * +--R 2 +--R x --R * ---R +----------------+ 3 ---R | 4 2 2 4 ---R 7\|4b - 4a b + a ---R atan(---------------------) ---R +----------------+ 2 2 +-+ ---R +-+4+--+2 | 4 2 2 4 (2b - 8a b + a )\|7 ---R \|7 \|98 \|4b - 4a b + a cos(---------------------------) ---R 2 +--R +-------------------------------+2 +--R +-+4| 4 3 2 2 3 4 +--R \|7 \|4b - 4a b + 5a b - 2a b + a --R + ---R 2 10 2 8 ---R (25088a b - 6272a )x + (25088a b - 6272a )x +--R 11 2 10 3 9 +--R 4415488a b - 33818624a b + 97642496a b +--R + +--R 4 8 5 7 6 6 +--R - 144393984a b + 49824768a b + 78763776a b +--R + +--R 7 5 8 4 9 3 10 2 +--R - 63748608a b + 6096384a b + 6083840a b - 2524480a b +--R + +--R 11 12 +--R 426496a b - 25872a +--R * +--R 8 +--R x +--R + +--R 11 2 10 3 9 +--R 4415488a b - 33818624a b + 97642496a b +--R + +--R 4 8 5 7 6 6 +--R - 144393984a b + 49824768a b + 78763776a b +--R + +--R 7 5 8 4 9 3 10 2 +--R - 63748608a b + 6096384a b + 6083840a b - 2524480a b +--R + +--R 11 12 +--R 426496a b - 25872a +--R * +--R 6 +--R x --R + ---R 2 6 ---R (50176a b - 12544a )x +--R 11 2 10 3 9 +--R 8830976a b - 67637248a b + 195284992a b +--R + +--R 4 8 5 7 6 6 +--R - 288787968a b + 99649536a b + 157527552a b +--R + +--R 7 5 8 4 9 3 +--R - 127497216a b + 12192768a b + 12167680a b +--R + +--R 10 2 11 12 +--R - 5048960a b + 852992a b - 51744a +--R * +--R 4 +--R x --R * --R +-+ --R \|2 --R + ---R 2 10 2 8 ---R (- 56448a b + 14112a )x + (- 56448a b + 14112a )x +--R 11 2 10 3 9 +--R - 9934848a b + 76091904a b - 219695616a b +--R + +--R 4 8 5 7 6 6 7 5 +--R 324886464a b - 112105728a b - 177218496a b + 143434368a b +--R + +--R 8 4 9 3 10 2 11 +--R - 13716864a b - 13688640a b + 5680080a b - 959616a b +--R + +--R 12 +--R 58212a +--R * +--R 8 +--R x --R + ---R 2 6 ---R (- 112896a b + 28224a )x ---R * ---R +-------------------------------+2 +----------------+ ---R +-+4| 4 3 2 2 3 4 | 4 2 2 4 ---R \|7 \|4b - 4a b + 5a b - 2a b + a \|4b - 4a b + a +--R 11 2 10 3 9 +--R - 9934848a b + 76091904a b - 219695616a b +--R + +--R 4 8 5 7 6 6 7 5 +--R 324886464a b - 112105728a b - 177218496a b + 143434368a b +--R + +--R 8 4 9 3 10 2 11 +--R - 13716864a b - 13688640a b + 5680080a b - 959616a b +--R + +--R 12 +--R 58212a +--R * +--R 6 +--R x +--R + +--R 11 2 10 3 9 +--R - 19869696a b + 152183808a b - 439391232a b +--R + +--R 4 8 5 7 6 6 7 5 +--R 649772928a b - 224211456a b - 354436992a b + 286868736a b +--R + +--R 8 4 9 3 10 2 11 +--R - 27433728a b - 27377280a b + 11360160a b - 1919232a b +--R + +--R 12 +--R 116424a +--R * +--R 4 +--R x --R * ---R +----------------+ ---R | 4 2 2 4 ---R 7\|4b - 4a b + a ---R atan(---------------------) ---R 2 2 +-+ ---R (2b - 8a b + a )\|7 ---R cos(---------------------------) ---R 2 +--R +-+4+--+2 +--R \|7 \|98 --R * ---R +----------------+ ---R | 4 2 2 4 ---R 7\|4b - 4a b + a ---R atan(---------------------) ---R 2 2 +-+ ---R (2b - 8a b + a )\|7 ---R sin(---------------------------) ---R 2 +--R +----------------+ +--R | 4 2 2 4 +--R \|4b - 4a b + a --R + ---R 6 5 2 4 4 2 5 6 4 ---R (7168b - 7168a b + 5376a b - 2688a b + 1792a b - 896a )x +--R 12 11 2 10 3 9 +--R 10035200b - 98144256a b + 330007552a b - 477976576a b +--R + +--R 4 8 5 7 6 6 7 5 +--R 359335424a b - 2709504a b - 247091712a b + 162921472a b +--R + +--R 8 4 9 3 10 2 11 +--R - 29114624a b - 10850560a b + 10239040a b - 2025856a b +--R + +--R 12 +--R 117600a +--R * +--R 10 +--R x --R + ---R 6 5 2 4 4 2 5 6 2 ---R (7168b - 7168a b + 5376a b - 2688a b + 1792a b - 896a )x +--R 12 11 2 10 3 9 +--R 10035200b - 98144256a b + 330007552a b - 477976576a b +--R + +--R 4 8 5 7 6 6 7 5 +--R 359335424a b - 2709504a b - 247091712a b + 162921472a b +--R + +--R 8 4 9 3 10 2 11 +--R - 29114624a b - 10850560a b + 10239040a b - 2025856a b +--R + +--R 12 +--R 117600a +--R * +--R 8 +--R x +--R + +--R 12 11 2 10 +--R 40140800b - 392577024a b + 1320030208a b +--R + +--R 3 9 4 8 5 7 +--R - 1911906304a b + 1437341696a b - 10838016a b +--R + +--R 6 6 7 5 8 4 +--R - 988366848a b + 651685888a b - 116458496a b +--R + +--R 9 3 10 2 11 12 +--R - 43402240a b + 40956160a b - 8103424a b + 470400a +--R * +--R 6 +--R x --R + ---R 6 5 2 4 4 2 5 6 ---R 14336b - 14336a b + 10752a b - 5376a b + 3584a b - 1792a +--R 12 11 2 10 3 9 +--R 20070400b - 196288512a b + 660015104a b - 955953152a b +--R + +--R 4 8 5 7 6 6 7 5 +--R 718670848a b - 5419008a b - 494183424a b + 325842944a b +--R + +--R 8 4 9 3 10 2 11 +--R - 58229248a b - 21701120a b + 20478080a b - 4051712a b +--R + +--R 12 +--R 235200a +--R * +--R 4 +--R x +--R + +--R 12 11 2 10 +--R 40140800b - 392577024a b + 1320030208a b +--R + +--R 3 9 4 8 5 7 +--R - 1911906304a b + 1437341696a b - 10838016a b +--R + +--R 6 6 7 5 8 4 +--R - 988366848a b + 651685888a b - 116458496a b +--R + +--R 9 3 10 2 11 12 +--R - 43402240a b + 40956160a b - 8103424a b + 470400a +--R * +--R 2 +--R x --R * --R +-+ --R \|2 --R + ---R 6 5 2 4 4 2 5 6 4 ---R (- 16128b + 16128a b - 12096a b + 6048a b - 4032a b + 2016a )x ---R + ---R 6 5 2 4 4 2 5 6 2 ---R (- 16128b + 16128a b - 12096a b + 6048a b - 4032a b + 2016a )x +--R 12 11 2 10 3 9 +--R - 22579200b + 220824576a b - 742516992a b + 1075447296a b +--R + +--R 4 8 5 7 6 6 7 5 +--R - 808504704a b + 6096384a b + 555956352a b - 366573312a b +--R + +--R 8 4 9 3 10 2 11 +--R 65507904a b + 24413760a b - 23037840a b + 4558176a b +--R + +--R 12 +--R - 264600a +--R * +--R 10 +--R x --R + ---R 6 5 2 4 4 2 5 6 ---R - 32256b + 32256a b - 24192a b + 12096a b - 8064a b + 4032a ---R * ---R +----------------+ 8 ---R | 4 2 2 4 ---R 7\|4b - 4a b + a ---R atan(---------------------) ---R 2 2 +-+ ---R 4+--+2 (2b - 8a b + a )\|7 ---R \|98 cos(---------------------------) ---R 2 ---R + ---R 4 3 2 2 3 4 6 ---R (100352b - 50176a b - 87808a b + 25088a b + 18816a )x +--R 12 11 2 10 3 9 +--R - 22579200b + 220824576a b - 742516992a b + 1075447296a b +--R + +--R 4 8 5 7 6 6 7 5 +--R - 808504704a b + 6096384a b + 555956352a b - 366573312a b --R + ---R 4 3 2 2 3 4 4 ---R (100352b - 50176a b - 87808a b + 25088a b + 18816a )x +--R 8 4 9 3 10 2 11 +--R 65507904a b + 24413760a b - 23037840a b + 4558176a b --R + ---R 4 3 2 2 3 4 2 ---R (200704b - 100352a b - 175616a b + 50176a b + 37632a )x +--R 12 +--R - 264600a --R * ---R +-+ ---R \|2 +--R 8 +--R x --R + ---R 4 3 2 2 3 4 6 ---R (- 225792b + 112896a b + 197568a b - 56448a b - 42336a )x +--R 12 11 2 10 3 9 +--R - 90316800b + 883298304a b - 2970067968a b + 4301789184a b +--R + +--R 4 8 5 7 6 6 7 5 +--R - 3234018816a b + 24385536a b + 2223825408a b - 1466293248a b +--R + +--R 8 4 9 3 10 2 11 +--R 262031616a b + 97655040a b - 92151360a b + 18232704a b +--R + +--R 12 +--R - 1058400a +--R * +--R 6 +--R x --R + ---R 4 3 2 2 3 4 4 ---R (- 225792b + 112896a b + 197568a b - 56448a b - 42336a )x +--R 12 11 2 10 3 9 +--R - 45158400b + 441649152a b - 1485033984a b + 2150894592a b +--R + +--R 4 8 5 7 6 6 7 5 +--R - 1617009408a b + 12192768a b + 1111912704a b - 733146624a b +--R + +--R 8 4 9 3 10 2 11 +--R 131015808a b + 48827520a b - 46075680a b + 9116352a b +--R + +--R 12 +--R - 529200a +--R * +--R 4 +--R x --R + ---R 4 3 2 2 3 4 2 ---R (- 451584b + 225792a b + 395136a b - 112896a b - 84672a )x +--R 12 11 2 10 3 9 +--R - 90316800b + 883298304a b - 2970067968a b + 4301789184a b +--R + +--R 4 8 5 7 6 6 7 5 +--R - 3234018816a b + 24385536a b + 2223825408a b - 1466293248a b +--R + +--R 8 4 9 3 10 2 11 +--R 262031616a b + 97655040a b - 92151360a b + 18232704a b +--R + +--R 12 +--R - 1058400a +--R * +--R 2 +--R x --R * ---R +----------------+ 6 ---R | 4 2 2 4 ---R 7\|4b - 4a b + a ---R atan(---------------------) ---R +-------------------------------+2 2 2 +-+ ---R 4| 4 3 2 2 3 4 (2b - 8a b + a )\|7 ---R \|4b - 4a b + 5a b - 2a b + a cos(---------------------------) ---R 2 +--R +-------------------------------+2 +--R +-+4| 4 3 2 2 3 4 +--R \|7 \|4b - 4a b + 5a b - 2a b + a --R + ---R 6 5 2 4 3 3 4 2 ---R 21504b - 21504a b - 8960a b + 12544a b + 2912a b +--R 14 13 2 12 3 11 +--R 1261568b - 6193152a b + 18120704a b - 29990912a b +--R + +--R 4 10 5 9 6 8 8 6 +--R 35804160a b - 28442624a b + 13888000a b - 6944000a b +--R + +--R 9 5 10 4 11 3 12 2 +--R 7110656a b - 4475520a b + 1874432a b - 566272a b +--R + +--R 13 14 +--R 96768a b - 9856a +--R * +--R 12 +--R x +--R + +--R 14 13 2 12 3 11 +--R 1261568b - 6193152a b + 18120704a b - 29990912a b +--R + +--R 4 10 5 9 6 8 8 6 +--R 35804160a b - 28442624a b + 13888000a b - 6944000a b +--R + +--R 9 5 10 4 11 3 12 2 +--R 7110656a b - 4475520a b + 1874432a b - 566272a b +--R + +--R 13 14 +--R 96768a b - 9856a +--R * +--R 10 +--R x +--R + +--R 14 13 2 12 3 11 +--R 8830976b - 52183040a b + 194482176a b - 400805888a b --R + ---R 5 6 ---R - 896a b - 1904a +--R 4 10 5 9 6 8 +--R 505598464a b - 201105408a b - 204705536a b +--R + +--R 7 7 8 6 9 5 10 4 +--R 177321984a b + 17963008a b - 26141696a b - 20183296a b +--R + +--R 11 3 12 2 13 14 +--R 18351872a b - 6436640a b + 1103872a b - 94864a --R * --R 8 --R x --R + ---R 6 5 2 4 3 3 4 2 ---R 21504b - 21504a b - 8960a b + 12544a b + 2912a b +--R 14 13 2 12 3 11 +--R 6307840b - 39796736a b + 158240768a b - 340824064a b +--R + +--R 4 10 5 9 6 8 +--R 433990144a b - 144220160a b - 232481536a b --R + ---R 5 6 ---R - 896a b - 1904a +--R 7 7 8 6 9 5 10 4 +--R 177321984a b + 31851008a b - 40363008a b - 11232256a b +--R + +--R 11 3 12 2 13 14 +--R 14603008a b - 5304096a b + 910336a b - 75152a --R * --R 6 --R x --R + ---R 6 5 2 4 3 3 4 2 ---R 43008b - 43008a b - 17920a b + 25088a b + 5824a b +--R 14 13 2 12 +--R 17661952b - 104366080a b + 388964352a b +--R + +--R 3 11 4 10 5 9 +--R - 801611776a b + 1011196928a b - 402210816a b +--R + +--R 6 8 7 7 8 6 9 5 +--R - 409411072a b + 354643968a b + 35926016a b - 52283392a b --R + ---R 5 6 ---R - 1792a b - 3808a +--R 10 4 11 3 12 2 13 +--R - 40366592a b + 36703744a b - 12873280a b + 2207744a b +--R + +--R 14 +--R - 189728a --R * --R 4 --R x +--R + +--R 14 13 2 12 3 11 +--R 5046272b - 24772608a b + 72482816a b - 119963648a b +--R + +--R 4 10 5 9 6 8 8 6 +--R 143216640a b - 113770496a b + 55552000a b - 27776000a b +--R + +--R 9 5 10 4 11 3 12 2 +--R 28442624a b - 17902080a b + 7497728a b - 2265088a b +--R + +--R 13 14 +--R 387072a b - 39424a +--R * +--R 2 +--R x +--R + +--R 14 13 2 12 3 11 +--R 10092544b - 49545216a b + 144965632a b - 239927296a b +--R + +--R 4 10 5 9 6 8 8 6 +--R 286433280a b - 227540992a b + 111104000a b - 55552000a b +--R + +--R 9 5 10 4 11 3 12 2 +--R 56885248a b - 35804160a b + 14995456a b - 4530176a b +--R + +--R 13 14 +--R 774144a b - 78848a --R * --R +-+ --R \|2 --R + ---R 6 5 2 4 3 3 4 2 ---R - 48384b + 48384a b + 20160a b - 28224a b - 6552a b +--R 14 13 2 12 3 11 +--R - 2838528b + 13934592a b - 40771584a b + 67479552a b --R + ---R 5 6 ---R 2016a b + 4284a +--R 4 10 5 9 6 8 8 6 +--R - 80559360a b + 63995904a b - 31248000a b + 15624000a b +--R + +--R 9 5 10 4 11 3 12 2 +--R - 15998976a b + 10069920a b - 4217472a b + 1274112a b +--R + +--R 13 14 +--R - 217728a b + 22176a --R * ---R 8 +--R 12 --R x --R + ---R 6 5 2 4 3 3 4 2 ---R - 48384b + 48384a b + 20160a b - 28224a b - 6552a b +--R 14 13 2 12 3 11 +--R - 2838528b + 13934592a b - 40771584a b + 67479552a b --R + ---R 5 6 ---R 2016a b + 4284a +--R 4 10 5 9 6 8 8 6 +--R - 80559360a b + 63995904a b - 31248000a b + 15624000a b +--R + +--R 9 5 10 4 11 3 12 2 +--R - 15998976a b + 10069920a b - 4217472a b + 1274112a b +--R + +--R 13 14 +--R - 217728a b + 22176a --R * ---R 6 +--R 10 --R x --R + ---R 6 5 2 4 3 3 4 2 ---R - 96768b + 96768a b + 40320a b - 56448a b - 13104a b +--R 14 13 2 12 3 11 +--R - 19869696b + 117411840a b - 437584896a b + 901813248a b --R + ---R 5 6 ---R 4032a b + 8568a +--R 4 10 5 9 6 8 7 7 +--R - 1137596544a b + 452487168a b + 460587456a b - 398974464a b +--R + +--R 8 6 9 5 10 4 11 3 +--R - 40416768a b + 58818816a b + 45412416a b - 41291712a b +--R + +--R 12 2 13 14 +--R 14482440a b - 2483712a b + 213444a --R * ---R 4 +--R 8 --R x ---R * ---R +----------------+ 4 ---R | 4 2 2 4 ---R 7\|4b - 4a b + a ---R atan(---------------------) ---R 2 2 +-+ ---R 4+--+2 (2b - 8a b + a )\|7 ---R \|98 cos(---------------------------) ---R 2 ---R + ---R 4 3 2 2 3 4 10 ---R (50176b - 25088a b - 43904a b + 12544a b + 9408a )x +--R + +--R 14 13 2 12 3 11 +--R - 14192640b + 89542656a b - 356041728a b + 766854144a b +--R + +--R 4 10 5 9 6 8 7 7 +--R - 976477824a b + 324495360a b + 523083456a b - 398974464a b --R + ---R 4 3 2 2 3 4 8 ---R (50176b - 25088a b - 43904a b + 12544a b + 9408a )x +--R 8 6 9 5 10 4 11 3 +--R - 71664768a b + 90816768a b + 25272576a b - 32856768a b --R + ---R 4 3 2 2 3 4 6 ---R (100352b - 50176a b - 87808a b + 25088a b + 18816a )x +--R 12 2 13 14 +--R 11934216a b - 2048256a b + 169092a --R * ---R +-+ ---R \|2 ---R + ---R 4 3 2 2 3 4 10 ---R (- 112896b + 56448a b + 98784a b - 28224a b - 21168a )x +--R 6 +--R x --R + ---R 4 3 2 2 3 4 8 ---R (- 112896b + 56448a b + 98784a b - 28224a b - 21168a )x +--R 14 13 2 12 3 11 +--R - 39739392b + 234823680a b - 875169792a b + 1803626496a b +--R + +--R 4 10 5 9 6 8 7 7 +--R - 2275193088a b + 904974336a b + 921174912a b - 797948928a b +--R + +--R 8 6 9 5 10 4 11 3 +--R - 80833536a b + 117637632a b + 90824832a b - 82583424a b +--R + +--R 12 2 13 14 +--R 28964880a b - 4967424a b + 426888a +--R * +--R 4 +--R x --R + ---R 4 3 2 2 3 4 6 ---R (- 225792b + 112896a b + 197568a b - 56448a b - 42336a )x ---R * ---R +----------------+ 2 ---R | 4 2 2 4 ---R 7\|4b - 4a b + a ---R atan(---------------------) ---R +-------------------------------+2 2 2 +-+ ---R 4| 4 3 2 2 3 4 (2b - 8a b + a )\|7 ---R \|4b - 4a b + 5a b - 2a b + a cos(---------------------------) ---R 2 ---R + ---R 6 5 2 4 4 2 5 6 12 ---R (1792b - 1792a b + 1344a b - 672a b + 448a b - 224a )x +--R 14 13 2 12 3 11 +--R - 11354112b + 55738368a b - 163086336a b + 269918208a b --R + ---R 6 5 2 4 4 2 5 6 10 ---R (1792b - 1792a b + 1344a b - 672a b + 448a b - 224a )x +--R 4 10 5 9 6 8 8 6 +--R - 322237440a b + 255983616a b - 124992000a b + 62496000a b --R + ---R 6 5 2 4 4 2 5 6 8 ---R (3584b - 3584a b + 2688a b - 1344a b + 896a b - 448a )x +--R 9 5 10 4 11 3 12 2 +--R - 63995904a b + 40279680a b - 16869888a b + 5096448a b +--R + +--R 13 14 +--R - 870912a b + 88704a --R * ---R +-+ ---R \|2 +--R 2 +--R x +--R + +--R 14 13 2 12 3 11 +--R - 22708224b + 111476736a b - 326172672a b + 539836416a b --R + ---R 6 5 2 4 4 2 5 6 12 ---R (- 4032b + 4032a b - 3024a b + 1512a b - 1008a b + 504a )x +--R 4 10 5 9 6 8 8 6 +--R - 644474880a b + 511967232a b - 249984000a b + 124992000a b --R + ---R 6 5 2 4 4 2 5 6 10 ---R (- 4032b + 4032a b - 3024a b + 1512a b - 1008a b + 504a )x +--R 9 5 10 4 11 3 12 2 +--R - 127991808a b + 80559360a b - 33739776a b + 10192896a b --R + ---R 6 5 2 4 4 2 5 6 8 ---R (- 8064b + 8064a b - 6048a b + 3024a b - 2016a b + 1008a )x +--R 13 14 +--R - 1741824a b + 177408a --R * ---R 4+--+2 ---R \|98 +--R +-+4+--+2 +--R \|7 \|98 --R Type: Expression Integer --E 1308 @@ -41726,7 +46669,7 @@ t0242:= (a+b*x^2)/(c+d*x^2+e*x^4) --R --R 2 --R b x + a ---R (1304) --------------- +--R (1309) --------------- --R 4 2 --R e x + d x + c --R Type: Fraction Polynomial Integer @@ -41740,7 +46683,7 @@ r0242:= 1/2*(b-(b*d-2*a*e)/(d^2-4*c*e)^(1/2))*atan(2^(1/2)*e^(1/2)*x/_ e^(1/2)/(d+(d^2-4*c*e)^(1/2))^(1/2) --R --R ---R (1305) +--R (1310) --R +------------------+ --R +-----------+ | +-----------+ --R +-+ | 2 +-+ | | 2 @@ -41778,7 +46721,7 @@ r0242:= 1/2*(b-(b*d-2*a*e)/(d^2-4*c*e)^(1/2))*atan(2^(1/2)*e^(1/2)*x/_ a0242:=integrate(t0242,x) --R --R ---R (1306) +--R (1311) --R ROOT --R +------------------------+ --R | 4 2 2 2 4 2 @@ -41969,7 +46912,7 @@ a0242:=integrate(t0242,x) m0242:=a0242-r0242 --R --R ---R (1307) +--R (1312) --R +--------------------+ +------------------+ --R +-----------+ | +-----------+ | +-----------+ --R | 2 +-+ | | 2 | | 2 @@ -42217,7 +47160,7 @@ m0242:=a0242-r0242 d0242:=D(m0242,x) --R --R ---R (1308) 0 +--R (1313) 0 --R Type: Expression Integer --E 1313 @@ -42227,7 +47170,7 @@ t0243:= (a+b*x^2)/(c+d*x^2+e*x^4)^2 --R --R 2 --R b x + a ---R (1309) --------------------------------------------- +--R (1314) --------------------------------------------- --R 2 8 6 2 4 2 2 --R e x + 2d e x + (2c e + d )x + 2c d x + c --R Type: Fraction Polynomial Integer @@ -42255,7 +47198,7 @@ r0243:= -1/2*b*x*(d+2*e*x^2)/(d^2-4*c*e)/(c+d*x^2+e*x^4)+1/2*a*x*_ (d+(d^2-4*c*e)^(1/2))^(1/2))*2^(1/2)/c/(d^2-4*c*e)^(3/2) --R --R ---R (1310) +--R (1315) --R 4 2 2 2 +-+ --R ((- a d + 2b c)e x + (- a d + 2b c d)x - a c d + 2b c )\|2 --R * @@ -42330,7 +47273,7 @@ r0243:= -1/2*b*x*(d+2*e*x^2)/(d^2-4*c*e)/(c+d*x^2+e*x^4)+1/2*a*x*_ a0243:=integrate(t0243,x) --R --R ---R (1311) +--R (1316) --R 2 2 2 4 2 3 2 3 2 2 --R ((4c e - c d e)x + (4c d e - c d )x + 4c e - c d ) --R * @@ -42723,7 +47666,7 @@ a0243:=integrate(t0243,x) m0243:=a0243-r0243 --R --R ---R (1312) +--R (1317) --R +--------------------+ --R +-----------+ | +-----------+ --R 2 2 | 2 | | 2 @@ -43167,7 +48110,7 @@ m0243:=a0243-r0243 d0243:=D(m0243,x) --R --R ---R (1313) 0 +--R (1318) 0 --R Type: Expression Integer --E 1318 @@ -43176,7 +48119,7 @@ t0244:= 1/(2+x^3+x^6) --R --R --R 1 ---R (1314) ----------- +--R (1319) ----------- --R 6 3 --R x + x + 2 --R Type: Fraction Polynomial Integer @@ -43196,7 +48139,7 @@ r0244:= 1/21*%i*atan(1/3*((1/2-1/2*%i*7^(1/2))^(1/3)-2*x)*3^(1/2)/_ 2^(2/3)*7^(1/2)/(1+%i*7^(1/2))^(2/3) --R --R ---R (1315) +--R (1320) --R - --R +------------+2 +--------------+2 +------------+2 --R 1 3+-+2 +-+3| +-+ | 1 +-+ 1 |1 +-+ 1 @@ -43281,7 +48224,7 @@ r0244:= 1/21*%i*atan(1/3*((1/2-1/2*%i*7^(1/2))^(1/3)-2*x)*3^(1/2)/_ a0244:=integrate(t0244,x) --R --R ---R (1316) +--R (1321) --R 3 3 --R atan(----) atan(----) --R +-+ +-+ @@ -43438,7 +48381,7 @@ a0244:=integrate(t0244,x) m0244:=a0244-r0244 --R --R ---R (1317) +--R (1322) --R +------------+2 +--------------+2 +------------+2 --R 1 +-+3| +-+ | 1 +-+ 1 |1 +-+ 1 --R - \|3 \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - @@ -43713,10 +48656,10 @@ m0244:=a0244-r0244 --E 1322 --S 1323 of 1483 -d0244:=D(m0244,x) +d0244:=normalize(D(m0244,x)) --R --R ---R (1318) +--R (1323) --R 1 7 1 4 1 3+-+2 +-+ --R (--- %i x + --- %i x + --- %i x)\|2 \|7 --R 336 336 168 @@ -53425,7 +58368,7 @@ t0245:= x^3/(2+x^3+x^6) --R --R 3 --R x ---R (1319) ----------- +--R (1324) ----------- --R 6 3 --R x + x + 2 --R Type: Fraction Polynomial Integer @@ -53444,7 +58387,7 @@ r0245:= -1/84*%i*7^(1/2)*(2*(4-4*%i*7^(1/2))^(1/3)*_ 2*(4+4*%i*7^(1/2))^(1/3)*x+4*x^2)) --R --R ---R (1320) +--R (1325) --R +-----------+ +-----------+2 +-----------+ --R 1 +-+3| +-+ 3| +-+ 3| +-+ 2 --R -- %i\|7 \|4%i\|7 + 4 log(\|4%i\|7 + 4 - 2x\|4%i\|7 + 4 + 4x ) @@ -53494,7 +58437,7 @@ r0245:= -1/84*%i*7^(1/2)*(2*(4-4*%i*7^(1/2))^(1/3)*_ a0245:=integrate(t0245,x) --R --R ---R (1321) +--R (1326) --R 1 --R atan(----) --R +-+ @@ -53632,7 +58575,7 @@ a0245:=integrate(t0245,x) m0245:=a0245-r0245 --R --R ---R (1322) +--R (1327) --R 1 6+-+ 1 1 --R - \|2 cos(- atan(----)) --R 3 3 +-+ @@ -53765,10 +58708,10 @@ m0245:=a0245-r0245 --E 1327 --S 1328 of 1483 -d0245:=D(m0245,x) +d0245:=normalize(D(m0245,x)) --R --R ---R (1323) +--R (1328) --R 3 1 1 12 3 1 1 2 1 1 10 --R - x sin(- atan(----)) - 6x cos(- atan(----)) sin(- atan(----)) --R 3 +-+ 3 +-+ 3 +-+ @@ -54018,7 +58961,7 @@ t0246:= x/(2+x^4+x^8) --R --R --R x ---R (1324) ----------- +--R (1329) ----------- --R 8 4 --R x + x + 2 --R Type: Fraction Polynomial Integer @@ -54032,7 +58975,7 @@ r0246:= -1/4*atan(((-1+2*2^(1/2))^(1/2)-2*x^2)/(1+2*2^(1/2))^(1/2))/_ 1/8*log(2^(1/2)+(-1+2*2^(1/2))^(1/2)*x^2+x^4)/(-2+4*2^(1/2))^(1/2) --R --R ---R (1325) +--R (1330) --R +---------+ +---------+ --R | +-+ 2 | +-+ +-+ 4 --R \|4\|2 + 2 log(x \|2\|2 - 1 + \|2 + x ) @@ -54063,7 +59006,7 @@ r0246:= -1/4*atan(((-1+2*2^(1/2))^(1/2)-2*x^2)/(1+2*2^(1/2))^(1/2))/_ a0246:=integrate(t0246,x) --R --R ---R (1326) +--R (1331) --R - --R 7 --R atan(----) @@ -54161,7 +59104,7 @@ a0246:=integrate(t0246,x) m0246:=a0246-r0246 --R --R ---R (1327) +--R (1332) --R - --R 7 --R atan(----) @@ -54286,10 +59229,10 @@ m0246:=a0246-r0246 --E 1332 --S 1333 of 1483 -d0246:=D(m0246,x) +d0246:=normalize(D(m0246,x)) --R --R ---R (1328) +--R (1333) --R +---------+ +---------+ --R 5 +-+ 5 4+--+2 | +-+ | +-+ --R ((176x - 200x)\|2 - 200x + 352x)\|98 \|2\|2 + 1 \|4\|2 + 2 @@ -55010,7 +59953,7 @@ t0247:= x^4/(2+x^4+x^8) --R --R 4 --R x ---R (1329) ----------- +--R (1334) ----------- --R 8 4 --R x + x + 2 --R Type: Fraction Polynomial Integer @@ -55042,7 +59985,7 @@ r0247:= 1/8/(-1+2*2^(1/2))^(1/2)*(2*atan(((2*2^(1/4)-_ (-1+2*2^(1/2))^(1/2))^(1/2) --R --R ---R (1330) +--R (1335) --R +----------------------+ --R +---------+ | +---------+ --R +-+ | +-+ | | +-+ 4+-+ @@ -55222,7 +60165,7 @@ r0247:= 1/8/(-1+2*2^(1/2))^(1/2)*(2*atan(((2*2^(1/4)-_ a0247:=integrate(t0247,x) --R --R ---R (1331) +--R (1336) --R - --R 7 --R atan(----) @@ -55546,7 +60489,7 @@ a0247:=integrate(t0247,x) m0247:=a0247-r0247 --R --R ---R (1332) +--R (1337) --R - --R +----------------------+ +--------------------+ --R | +---------+ | +---------+ @@ -56090,57 +61033,23 @@ m0247:=a0247-r0247 --E 1337 --S 1338 of 1483 -d0247:=D(m0247,x) +d0247:=normalize(D(m0247,x)) --R --R ---R (1333) ---R 12 8 4 +-+ 12 8 4 ---R ((- 224x - 1400x - 448x )\|2 + 1288x + 1092x + 2576x ) ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (700x + 896x + 1400x )\|2 - 546x + 1806x - 1092x ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R sin(----------) ---R 2 +--R (1338) +--R 7 4 7 2 7 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R 4 \|7 4 \|7 \|7 +--R - 14x sin(----------) - 28x cos(----------) sin(----------) +--R 2 2 2 --R + ---R 12 8 4 +-+ 12 8 4 ---R ((- 448x - 2800x - 896x )\|2 + 2576x + 2184x + 5152x ) ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (1400x + 1792x + 2800x )\|2 - 1092x + 3612x - 2184x ---R * ---R 7 2 7 2 ---R atan(----) atan(----) ---R +-+ +-+ ---R \|7 \|7 ---R cos(----------) sin(----------) ---R 2 2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R ((- 224x - 1400x - 448x )\|2 + 1288x + 1092x + 2576x ) ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (700x + 896x + 1400x )\|2 - 546x + 1806x - 1092x ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R cos(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 4 \|7 +--R - 14x cos(----------) +--R 2 --R * --R 7 8 --R atan(----) @@ -56158,62 +61067,19 @@ d0247:=D(m0247,x) --R sin(---------------------) --R 2 --R + ---R 12 8 4 +-+ 12 8 ---R (- 896x - 5600x - 1792x )\|2 + 5152x + 4368x ---R + ---R 4 ---R 10304x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (2800x + 3584x + 5600x )\|2 - 2184x + 7224x - 4368x ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R sin(----------) ---R 2 ---R + ---R 12 8 4 +-+ 12 8 ---R (- 1792x - 11200x - 3584x )\|2 + 10304x + 8736x ---R + ---R 4 ---R 20608x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (5600x + 7168x + 11200x )\|2 - 4368x + 14448x - 8736x ---R * ---R 7 2 7 2 ---R atan(----) atan(----) ---R +-+ +-+ ---R \|7 \|7 ---R cos(----------) sin(----------) ---R 2 2 +--R 7 4 7 2 7 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R 4 \|7 4 \|7 \|7 +--R - 56x sin(----------) - 112x cos(----------) sin(----------) +--R 2 2 2 --R + ---R 12 8 4 +-+ 12 8 ---R (- 896x - 5600x - 1792x )\|2 + 5152x + 4368x ---R + ---R 4 ---R 10304x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (2800x + 3584x + 5600x )\|2 - 2184x + 7224x - 4368x ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R cos(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 4 \|7 +--R - 56x cos(----------) +--R 2 --R * --R 7 2 --R atan(----) @@ -56231,49 +61097,12 @@ d0247:=D(m0247,x) --R cos(---------------------) --R 2 --R + ---R 14 10 6 +-+ 14 10 ---R (6272x + 39200x + 12544x )\|2 - 36064x - 30576x ---R + ---R 6 ---R - 72128x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 14 10 6 +-+ 14 10 ---R (- 19600x - 25088x - 39200x )\|2 + 15288x - 50568x ---R + ---R 6 ---R 30576x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) ---R 2 ---R + ---R 14 10 6 +-+ 14 10 ---R (6272x + 39200x + 12544x )\|2 - 36064x - 30576x ---R + ---R 6 ---R - 72128x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 14 10 6 +-+ 14 10 ---R (- 19600x - 25088x - 39200x )\|2 + 15288x - 50568x ---R + ---R 6 ---R 30576x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) ---R 2 +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4+-+2 \|7 6 4+-+2 \|7 +--R (392x \|8 sin(----------) + 392x \|8 cos(----------)) +--R 2 2 --R * --R +-----------------------------------+2 --R | 7 2 7 2 @@ -56302,49 +61131,19 @@ d0247:=D(m0247,x) --R sin(---------------------) --R 2 --R + ---R 18 14 10 6 2 +-+ ---R (896x + 11200x + 10752x + 22400x + 3584x )\|2 ---R + ---R 18 14 10 6 2 ---R - 5152x - 8736x - 61824x - 17472x - 20608x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (- 2800x - 7168x + 22064x - 14336x - 11200x )\|2 ---R + ---R 18 14 10 6 2 ---R 2184x - 14448x - 1624x - 28896x + 8736x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R +-+4+-+2 \|7 ---R \|7 \|8 sin(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 +-+4+-+2 \|7 +--R (56x + 56x + 112x )\|7 \|8 sin(----------) +--R 2 --R + ---R 18 14 10 6 2 +-+ ---R (896x + 11200x + 10752x + 22400x + 3584x )\|2 ---R + ---R 18 14 10 6 2 ---R - 5152x - 8736x - 61824x - 17472x - 20608x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (- 2800x - 7168x + 22064x - 14336x - 11200x )\|2 ---R + ---R 18 14 10 6 2 ---R 2184x - 14448x - 1624x - 28896x + 8736x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R +-+4+-+2 \|7 ---R \|7 \|8 cos(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 +-+4+-+2 \|7 +--R (56x + 56x + 112x )\|7 \|8 cos(----------) +--R 2 --R * --R 7 --R atan(----) @@ -56379,62 +61178,19 @@ d0247:=D(m0247,x) --R sin(---------------------) --R 2 --R + ---R 12 8 4 +-+ 12 8 ---R (- 1344x - 8400x - 2688x )\|2 + 7728x + 6552x ---R + ---R 4 ---R 15456x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (4200x + 5376x + 8400x )\|2 - 3276x + 10836x - 6552x ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R sin(----------) ---R 2 ---R + ---R 12 8 4 +-+ 12 8 ---R (- 2688x - 16800x - 5376x )\|2 + 15456x + 13104x ---R + ---R 4 ---R 30912x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (8400x + 10752x + 16800x )\|2 - 6552x + 21672x - 13104x ---R * ---R 7 2 7 2 ---R atan(----) atan(----) ---R +-+ +-+ ---R \|7 \|7 ---R cos(----------) sin(----------) ---R 2 2 +--R 7 4 7 2 7 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R 4 \|7 4 \|7 \|7 +--R - 84x sin(----------) - 168x cos(----------) sin(----------) +--R 2 2 2 --R + ---R 12 8 4 +-+ 12 8 ---R (- 1344x - 8400x - 2688x )\|2 + 7728x + 6552x ---R + ---R 4 ---R 15456x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (4200x + 5376x + 8400x )\|2 - 3276x + 10836x - 6552x ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R cos(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 4 \|7 +--R - 84x cos(----------) +--R 2 --R * --R 7 4 --R atan(----) @@ -56452,49 +61208,12 @@ d0247:=D(m0247,x) --R cos(---------------------) --R 2 --R + ---R 14 10 6 +-+ 14 10 ---R (6272x + 39200x + 12544x )\|2 - 36064x - 30576x ---R + ---R 6 ---R - 72128x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 14 10 6 +-+ 14 10 ---R (- 19600x - 25088x - 39200x )\|2 + 15288x - 50568x ---R + ---R 6 ---R 30576x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) ---R 2 ---R + ---R 14 10 6 +-+ 14 10 ---R (6272x + 39200x + 12544x )\|2 - 36064x - 30576x ---R + ---R 6 ---R - 72128x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 14 10 6 +-+ 14 10 ---R (- 19600x - 25088x - 39200x )\|2 + 15288x - 50568x ---R + ---R 6 ---R 30576x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) ---R 2 +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4+-+2 \|7 6 4+-+2 \|7 +--R (392x \|8 sin(----------) + 392x \|8 cos(----------)) +--R 2 2 --R * --R 7 2 --R atan(----) @@ -56513,37 +61232,12 @@ d0247:=D(m0247,x) --R 4| 4+-+2 2 --R \| 196\|8 --R + ---R 16 12 8 +-+ 16 12 8 ---R ((- 336x - 2100x - 672x )\|2 + 1932x + 1638x + 3864x ) ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 +-+ 16 12 8 ---R (1050x + 1344x + 2100x )\|2 - 819x + 2709x - 1638x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) ---R 2 ---R + ---R 16 12 8 +-+ 16 12 8 ---R ((- 336x - 2100x - 672x )\|2 + 1932x + 1638x + 3864x ) ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 +-+ 16 12 8 ---R (1050x + 1344x + 2100x )\|2 - 819x + 2709x - 1638x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) ---R 2 +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4+-+2 \|7 8 4+-+2 \|7 +--R - 21x \|8 sin(----------) - 21x \|8 cos(----------) +--R 2 2 --R * --R 7 4 --R atan(----) @@ -56561,49 +61255,19 @@ d0247:=D(m0247,x) --R sin(---------------------) --R 2 --R + ---R 18 14 10 6 2 +-+ ---R (1792x + 22400x + 21504x + 44800x + 7168x )\|2 ---R + ---R 18 14 10 6 2 ---R - 10304x - 17472x - 123648x - 34944x - 41216x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (- 5600x - 14336x + 44128x - 28672x - 22400x )\|2 ---R + ---R 18 14 10 6 2 ---R 4368x - 28896x - 3248x - 57792x + 17472x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R +-+4+-+2 \|7 ---R \|7 \|8 sin(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 +-+4+-+2 \|7 +--R (112x + 112x + 224x )\|7 \|8 sin(----------) +--R 2 --R + ---R 18 14 10 6 2 +-+ ---R (1792x + 22400x + 21504x + 44800x + 7168x )\|2 ---R + ---R 18 14 10 6 2 ---R - 10304x - 17472x - 123648x - 34944x - 41216x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (- 5600x - 14336x + 44128x - 28672x - 22400x )\|2 ---R + ---R 18 14 10 6 2 ---R 4368x - 28896x - 3248x - 57792x + 17472x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R +-+4+-+2 \|7 ---R \|7 \|8 cos(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 +-+4+-+2 \|7 +--R (112x + 112x + 224x )\|7 \|8 cos(----------) +--R 2 --R * --R 7 3 --R atan(----) @@ -56622,49 +61286,19 @@ d0247:=D(m0247,x) --R 4| 4+-+2 2 --R \| 196\|8 --R + ---R 20 16 12 8 4 +-+ 20 ---R (- 64x - 800x - 768x - 1600x - 256x )\|2 + 368x ---R + ---R 16 12 8 4 ---R 624x + 4416x + 1248x + 1472x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 20 16 12 8 4 +-+ 20 ---R (200x + 512x - 1576x + 1024x + 800x )\|2 - 156x ---R + ---R 16 12 8 4 ---R 1032x + 116x + 2064x - 624x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R +-+4+-+2 \|7 ---R \|7 \|8 sin(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 +-+4+-+2 \|7 +--R (- 4x - 4x - 8x )\|7 \|8 sin(----------) +--R 2 --R + ---R 20 16 12 8 4 +-+ 20 ---R (- 64x - 800x - 768x - 1600x - 256x )\|2 + 368x ---R + ---R 16 12 8 4 ---R 624x + 4416x + 1248x + 1472x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 20 16 12 8 4 +-+ 20 ---R (200x + 512x - 1576x + 1024x + 800x )\|2 - 156x ---R + ---R 16 12 8 4 ---R 1032x + 116x + 2064x - 624x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R +-+4+-+2 \|7 ---R \|7 \|8 cos(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 +-+4+-+2 \|7 +--R (- 4x - 4x - 8x )\|7 \|8 cos(----------) +--R 2 --R * --R 7 --R atan(----) @@ -56698,62 +61332,19 @@ d0247:=D(m0247,x) --R sin(---------------------) --R 2 --R + ---R 12 8 4 +-+ 12 8 ---R (- 896x - 5600x - 1792x )\|2 + 5152x + 4368x ---R + ---R 4 ---R 10304x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (2800x + 3584x + 5600x )\|2 - 2184x + 7224x - 4368x ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R sin(----------) ---R 2 ---R + ---R 12 8 4 +-+ 12 8 ---R (- 1792x - 11200x - 3584x )\|2 + 10304x + 8736x ---R + ---R 4 ---R 20608x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (5600x + 7168x + 11200x )\|2 - 4368x + 14448x - 8736x ---R * ---R 7 2 7 2 ---R atan(----) atan(----) ---R +-+ +-+ ---R \|7 \|7 ---R cos(----------) sin(----------) ---R 2 2 +--R 7 4 7 2 7 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R 4 \|7 4 \|7 \|7 +--R - 56x sin(----------) - 112x cos(----------) sin(----------) +--R 2 2 2 --R + ---R 12 8 4 +-+ 12 8 ---R (- 896x - 5600x - 1792x )\|2 + 5152x + 4368x ---R + ---R 4 ---R 10304x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (2800x + 3584x + 5600x )\|2 - 2184x + 7224x - 4368x ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R cos(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 4 \|7 +--R - 56x cos(----------) +--R 2 --R * --R 7 6 --R atan(----) @@ -56771,49 +61362,12 @@ d0247:=D(m0247,x) --R cos(---------------------) --R 2 --R + ---R 14 10 6 +-+ 14 ---R (- 6272x - 39200x - 12544x )\|2 + 36064x ---R + ---R 10 6 ---R 30576x + 72128x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 14 10 6 +-+ 14 10 ---R (19600x + 25088x + 39200x )\|2 - 15288x + 50568x ---R + ---R 6 ---R - 30576x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) ---R 2 ---R + ---R 14 10 6 +-+ 14 ---R (- 6272x - 39200x - 12544x )\|2 + 36064x ---R + ---R 10 6 ---R 30576x + 72128x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 14 10 6 +-+ 14 10 ---R (19600x + 25088x + 39200x )\|2 - 15288x + 50568x ---R + ---R 6 ---R - 30576x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) ---R 2 +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4+-+2 \|7 6 4+-+2 \|7 +--R (- 392x \|8 sin(----------) - 392x \|8 cos(----------)) +--R 2 2 --R * --R 7 4 --R atan(----) @@ -56832,43 +61386,12 @@ d0247:=D(m0247,x) --R 4| 4+-+2 2 --R \| 196\|8 --R + ---R 16 12 8 +-+ 16 12 ---R (224x + 1400x + 448x )\|2 - 1288x - 1092x ---R + ---R 8 ---R - 2576x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 +-+ 16 12 8 ---R (- 700x - 896x - 1400x )\|2 + 546x - 1806x + 1092x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) ---R 2 ---R + ---R 16 12 8 +-+ 16 12 ---R (224x + 1400x + 448x )\|2 - 1288x - 1092x ---R + ---R 8 ---R - 2576x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 +-+ 16 12 8 ---R (- 700x - 896x - 1400x )\|2 + 546x - 1806x + 1092x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) ---R 2 +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4+-+2 \|7 8 4+-+2 \|7 +--R (14x \|8 sin(----------) + 14x \|8 cos(----------)) +--R 2 2 --R * --R 7 2 --R atan(----) @@ -56886,31 +61409,16 @@ d0247:=D(m0247,x) --R cos(---------------------) --R 2 --R + ---R 18 14 10 +-+ 18 14 ---R (12544x + 78400x + 25088x )\|2 - 72128x - 61152x ---R + ---R 10 ---R - 144256x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 +-+ 18 14 ---R (- 39200x - 50176x - 78400x )\|2 + 30576x - 101136x ---R + ---R 10 ---R 61152x ---R * ---R +-----------------------------------+2 ---R | 7 2 7 2 ---R | atan(----) atan(----) ---R | +-+ +-+ ---R | \|7 \|7 ---R |sin(----------) + cos(----------) ---R | 2 2 ---R |----------------------------------- ---R 4| 4+-+2 ---R \| 196\|8 +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R 10 | 2 2 +--R 784x |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 --R * --R 7 2 --R atan(----) @@ -56928,49 +61436,19 @@ d0247:=D(m0247,x) --R sin(---------------------) --R 2 --R + ---R 18 14 10 6 2 +-+ ---R (896x + 11200x + 10752x + 22400x + 3584x )\|2 ---R + ---R 18 14 10 6 2 ---R - 5152x - 8736x - 61824x - 17472x - 20608x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (- 2800x - 7168x + 22064x - 14336x - 11200x )\|2 ---R + ---R 18 14 10 6 2 ---R 2184x - 14448x - 1624x - 28896x + 8736x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R +-+4+-+2 \|7 ---R \|7 \|8 sin(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 +-+4+-+2 \|7 +--R (56x + 56x + 112x )\|7 \|8 sin(----------) +--R 2 --R + ---R 18 14 10 6 2 +-+ ---R (896x + 11200x + 10752x + 22400x + 3584x )\|2 ---R + ---R 18 14 10 6 2 ---R - 5152x - 8736x - 61824x - 17472x - 20608x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (- 2800x - 7168x + 22064x - 14336x - 11200x )\|2 ---R + ---R 18 14 10 6 2 ---R 2184x - 14448x - 1624x - 28896x + 8736x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R +-+4+-+2 \|7 ---R \|7 \|8 cos(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 +-+4+-+2 \|7 +--R (56x + 56x + 112x )\|7 \|8 cos(----------) +--R 2 --R * --R 7 5 --R atan(----) @@ -56989,49 +61467,19 @@ d0247:=D(m0247,x) --R 4| 4+-+2 2 --R \| 196\|8 --R + ---R 20 16 12 8 4 +-+ 20 ---R (64x + 800x + 768x + 1600x + 256x )\|2 - 368x ---R + ---R 16 12 8 4 ---R - 624x - 4416x - 1248x - 1472x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 20 16 12 8 4 +-+ 20 ---R (- 200x - 512x + 1576x - 1024x - 800x )\|2 + 156x ---R + ---R 16 12 8 4 ---R - 1032x - 116x - 2064x + 624x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R +-+4+-+2 \|7 ---R \|7 \|8 sin(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 +-+4+-+2 \|7 +--R (4x + 4x + 8x )\|7 \|8 sin(----------) +--R 2 --R + ---R 20 16 12 8 4 +-+ 20 ---R (64x + 800x + 768x + 1600x + 256x )\|2 - 368x ---R + ---R 16 12 8 4 ---R - 624x - 4416x - 1248x - 1472x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 20 16 12 8 4 +-+ 20 ---R (- 200x - 512x + 1576x - 1024x - 800x )\|2 + 156x ---R + ---R 16 12 8 4 ---R - 1032x - 116x - 2064x + 624x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R +-+4+-+2 \|7 ---R \|7 \|8 cos(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 +-+4+-+2 \|7 +--R (4x + 4x + 8x )\|7 \|8 cos(----------) +--R 2 --R * --R 7 3 --R atan(----) @@ -57049,37 +61497,25 @@ d0247:=D(m0247,x) --R cos(---------------------) --R 2 --R + ---R 22 18 14 10 6 +-+ ---R (1792x + 22400x + 21504x + 44800x + 7168x )\|2 ---R + ---R 22 18 14 10 6 ---R - 10304x - 17472x - 123648x - 34944x - 41216x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 22 18 14 10 6 +-+ ---R (- 5600x - 14336x + 44128x - 28672x - 22400x )\|2 ---R + ---R 22 18 14 10 6 ---R 4368x - 28896x - 3248x - 57792x + 17472x +--R 14 10 6 +-+ +--R (112x + 112x + 224x )\|7 --R * ---R 7 ---R atan(----) ---R +-+ ---R \|7 ---R sin(----------) ---R 2 ---R +-----------------------------------+2 atan(---------------) ---R | 7 2 7 2 7 ---R | atan(----) atan(----) atan(----) ---R | +-+ +-+ +-+ ---R | \|7 \|7 \|7 ---R |sin(----------) + cos(----------) cos(----------) ---R +-+ | 2 2 2 ---R \|7 |----------------------------------- cos(---------------------) ---R 4| 4+-+2 2 ---R \| 196\|8 +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+2 atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 --R * --R 7 --R atan(----) @@ -57097,53 +61533,19 @@ d0247:=D(m0247,x) --R sin(---------------------) --R 2 --R + ---R 12 8 4 +-+ 12 8 4 ---R ((- 224x - 1400x - 448x )\|2 + 1288x + 1092x + 2576x ) ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (700x + 896x + 1400x )\|2 - 546x + 1806x - 1092x ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R sin(----------) ---R 2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R ((- 448x - 2800x - 896x )\|2 + 2576x + 2184x + 5152x ) ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (1400x + 1792x + 2800x )\|2 - 1092x + 3612x - 2184x ---R * ---R 7 2 7 2 ---R atan(----) atan(----) ---R +-+ +-+ ---R \|7 \|7 ---R cos(----------) sin(----------) ---R 2 2 +--R 7 4 7 2 7 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R 4 \|7 4 \|7 \|7 +--R - 14x sin(----------) - 28x cos(----------) sin(----------) +--R 2 2 2 --R + ---R 12 8 4 +-+ 12 8 4 ---R ((- 224x - 1400x - 448x )\|2 + 1288x + 1092x + 2576x ) ---R * ---R 4+-+2 ---R \|2 ---R + ---R 12 8 4 +-+ 12 8 4 ---R (700x + 896x + 1400x )\|2 - 546x + 1806x - 1092x ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R cos(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 4 \|7 +--R - 14x cos(----------) +--R 2 --R * --R 7 8 --R atan(----) @@ -57161,43 +61563,12 @@ d0247:=D(m0247,x) --R cos(---------------------) --R 2 --R + ---R 14 10 6 +-+ 14 10 ---R (- 6272x - 39200x - 12544x )\|2 + 36064x + 30576x ---R + ---R 6 ---R 72128x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 14 10 6 +-+ 14 10 6 ---R (19600x + 25088x + 39200x )\|2 - 15288x + 50568x - 30576x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) ---R 2 ---R + ---R 14 10 6 +-+ 14 10 ---R (- 6272x - 39200x - 12544x )\|2 + 36064x + 30576x ---R + ---R 6 ---R 72128x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 14 10 6 +-+ 14 10 6 ---R (19600x + 25088x + 39200x )\|2 - 15288x + 50568x - 30576x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) ---R 2 +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4+-+2 \|7 6 4+-+2 \|7 +--R (- 392x \|8 sin(----------) - 392x \|8 cos(----------)) +--R 2 2 --R * --R 7 6 --R atan(----) @@ -57216,37 +61587,12 @@ d0247:=D(m0247,x) --R 4| 4+-+2 2 --R \| 196\|8 --R + ---R 16 12 8 +-+ 16 12 8 ---R ((- 336x - 2100x - 672x )\|2 + 1932x + 1638x + 3864x ) ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 +-+ 16 12 8 ---R (1050x + 1344x + 2100x )\|2 - 819x + 2709x - 1638x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) ---R 2 ---R + ---R 16 12 8 +-+ 16 12 8 ---R ((- 336x - 2100x - 672x )\|2 + 1932x + 1638x + 3864x ) ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 +-+ 16 12 8 ---R (1050x + 1344x + 2100x )\|2 - 819x + 2709x - 1638x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) ---R 2 +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4+-+2 \|7 8 4+-+2 \|7 +--R (- 21x \|8 sin(----------) - 21x \|8 cos(----------)) +--R 2 2 --R * --R 7 4 --R atan(----) @@ -57264,106 +61610,57 @@ d0247:=D(m0247,x) --R cos(---------------------) --R 2 --R + ---R 18 14 10 +-+ 18 14 ---R (- 12544x - 78400x - 25088x )\|2 + 72128x + 61152x ---R + ---R 10 ---R 144256x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 +-+ 18 14 10 ---R (39200x + 50176x + 78400x )\|2 - 30576x + 101136x - 61152x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R \|7 ---R sin(----------) ---R 2 ---R +-----------------------------------+2 atan(---------------) ---R | 7 2 7 2 7 ---R | atan(----) atan(----) atan(----) ---R | +-+ +-+ +-+ ---R | \|7 \|7 \|7 ---R |sin(----------) + cos(----------) cos(----------) ---R | 2 2 2 ---R |----------------------------------- cos(---------------------) ---R 4| 4+-+2 2 ---R \| 196\|8 ---R + ---R 20 16 12 +-+ 20 16 12 4+-+2 ---R ((- 112x - 700x - 224x )\|2 + 644x + 546x + 1288x )\|2 +--R - +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R 10 | 2 2 +--R 784x |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 --R + ---R 20 16 12 +-+ 20 16 12 ---R (350x + 448x + 700x )\|2 - 273x + 903x - 546x +--R 12 +--R - 7x --R / ---R 16 12 8 4 +-+ 16 ---R (224x + 2800x + 2688x + 5600x + 896)\|2 - 1288x ---R + ---R 12 8 4 ---R - 2184x - 15456x - 4368x - 5152 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ 16 ---R (- 700x - 1792x + 5516x - 3584x - 2800)\|2 + 546x ---R + ---R 12 8 4 ---R - 3612x - 406x - 7224x + 2184 ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R sin(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (14x + 14x + 28)sin(----------) +--R 2 --R + ---R 16 12 8 4 +-+ 16 ---R (448x + 5600x + 5376x + 11200x + 1792)\|2 - 2576x ---R + ---R 12 8 4 ---R - 4368x - 30912x - 8736x - 10304 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ 16 ---R (- 1400x - 3584x + 11032x - 7168x - 5600)\|2 + 1092x ---R + ---R 12 8 4 ---R - 7224x - 812x - 14448x + 4368 ---R * ---R 7 2 7 2 ---R atan(----) atan(----) ---R +-+ +-+ ---R \|7 \|7 ---R cos(----------) sin(----------) ---R 2 2 +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4 \|7 \|7 +--R (28x + 28x + 56)cos(----------) sin(----------) +--R 2 2 --R + ---R 16 12 8 4 +-+ 16 ---R (224x + 2800x + 2688x + 5600x + 896)\|2 - 1288x ---R + ---R 12 8 4 ---R - 2184x - 15456x - 4368x - 5152 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ 16 ---R (- 700x - 1792x + 5516x - 3584x - 2800)\|2 + 546x ---R + ---R 12 8 4 ---R - 3612x - 406x - 7224x + 2184 ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R cos(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (14x + 14x + 28)cos(----------) +--R 2 --R * --R 7 8 --R atan(----) @@ -57381,71 +61678,26 @@ d0247:=D(m0247,x) --R sin(---------------------) --R 2 --R + ---R 16 12 8 4 +-+ ---R (896x + 11200x + 10752x + 22400x + 3584)\|2 ---R + ---R 16 12 8 4 ---R - 5152x - 8736x - 61824x - 17472x - 20608 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ ---R (- 2800x - 7168x + 22064x - 14336x - 11200)\|2 ---R + ---R 16 12 8 4 ---R 2184x - 14448x - 1624x - 28896x + 8736 ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R sin(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (56x + 56x + 112)sin(----------) +--R 2 --R + ---R 16 12 8 4 +-+ ---R (1792x + 22400x + 21504x + 44800x + 7168)\|2 ---R + ---R 16 12 8 4 ---R - 10304x - 17472x - 123648x - 34944x - 41216 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ ---R (- 5600x - 14336x + 44128x - 28672x - 22400)\|2 ---R + ---R 16 12 8 4 ---R 4368x - 28896x - 3248x - 57792x + 17472 ---R * ---R 7 2 7 2 ---R atan(----) atan(----) ---R +-+ +-+ ---R \|7 \|7 ---R cos(----------) sin(----------) ---R 2 2 +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4 \|7 \|7 +--R (112x + 112x + 224)cos(----------) sin(----------) +--R 2 2 --R + ---R 16 12 8 4 +-+ ---R (896x + 11200x + 10752x + 22400x + 3584)\|2 ---R + ---R 16 12 8 4 ---R - 5152x - 8736x - 61824x - 17472x - 20608 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ ---R (- 2800x - 7168x + 22064x - 14336x - 11200)\|2 ---R + ---R 16 12 8 4 ---R 2184x - 14448x - 1624x - 28896x + 8736 ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R cos(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (56x + 56x + 112)cos(----------) +--R 2 --R * --R 7 2 --R atan(----) @@ -57463,55 +61715,19 @@ d0247:=D(m0247,x) --R cos(---------------------) --R 2 --R + ---R 18 14 10 6 2 ---R (- 6272x - 78400x - 75264x - 156800x - 25088x ) ---R * ---R +-+ ---R \|2 ---R + ---R 18 14 10 6 2 ---R 36064x + 61152x + 432768x + 122304x + 144256x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (19600x + 50176x - 154448x + 100352x + 78400x )\|2 ---R + ---R 18 14 10 6 2 ---R - 15288x + 101136x + 11368x + 202272x - 61152x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (- 392x - 392x - 784x )\|8 sin(----------) +--R 2 --R + ---R 18 14 10 6 2 ---R (- 6272x - 78400x - 75264x - 156800x - 25088x ) ---R * ---R +-+ ---R \|2 ---R + ---R 18 14 10 6 2 ---R 36064x + 61152x + 432768x + 122304x + 144256x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (19600x + 50176x - 154448x + 100352x + 78400x )\|2 ---R + ---R 18 14 10 6 2 ---R - 15288x + 101136x + 11368x + 202272x - 61152x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (- 392x - 392x - 784x )\|8 cos(----------) +--R 2 --R * --R +-----------------------------------+2 --R | 7 2 7 2 @@ -57540,71 +61756,26 @@ d0247:=D(m0247,x) --R sin(---------------------) --R 2 --R + ---R 16 12 8 4 +-+ ---R (1344x + 16800x + 16128x + 33600x + 5376)\|2 ---R + ---R 16 12 8 4 ---R - 7728x - 13104x - 92736x - 26208x - 30912 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ ---R (- 4200x - 10752x + 33096x - 21504x - 16800)\|2 ---R + ---R 16 12 8 4 ---R 3276x - 21672x - 2436x - 43344x + 13104 ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R sin(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (84x + 84x + 168)sin(----------) +--R 2 --R + ---R 16 12 8 4 +-+ ---R (2688x + 33600x + 32256x + 67200x + 10752)\|2 ---R + ---R 16 12 8 4 ---R - 15456x - 26208x - 185472x - 52416x - 61824 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ ---R (- 8400x - 21504x + 66192x - 43008x - 33600)\|2 ---R + ---R 16 12 8 4 ---R 6552x - 43344x - 4872x - 86688x + 26208 ---R * ---R 7 2 7 2 ---R atan(----) atan(----) ---R +-+ +-+ ---R \|7 \|7 ---R cos(----------) sin(----------) ---R 2 2 +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4 \|7 \|7 +--R (168x + 168x + 336)cos(----------) sin(----------) +--R 2 2 --R + ---R 16 12 8 4 +-+ ---R (1344x + 16800x + 16128x + 33600x + 5376)\|2 ---R + ---R 16 12 8 4 ---R - 7728x - 13104x - 92736x - 26208x - 30912 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ ---R (- 4200x - 10752x + 33096x - 21504x - 16800)\|2 ---R + ---R 16 12 8 4 ---R 3276x - 21672x - 2436x - 43344x + 13104 ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R cos(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (84x + 84x + 168)cos(----------) +--R 2 --R * --R 7 4 --R atan(----) @@ -57622,55 +61793,19 @@ d0247:=D(m0247,x) --R cos(---------------------) --R 2 --R + ---R 18 14 10 6 2 ---R (- 6272x - 78400x - 75264x - 156800x - 25088x ) ---R * ---R +-+ ---R \|2 ---R + ---R 18 14 10 6 2 ---R 36064x + 61152x + 432768x + 122304x + 144256x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (19600x + 50176x - 154448x + 100352x + 78400x )\|2 ---R + ---R 18 14 10 6 2 ---R - 15288x + 101136x + 11368x + 202272x - 61152x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (- 392x - 392x - 784x )\|8 sin(----------) +--R 2 --R + ---R 18 14 10 6 2 ---R (- 6272x - 78400x - 75264x - 156800x - 25088x ) ---R * ---R +-+ ---R \|2 ---R + ---R 18 14 10 6 2 ---R 36064x + 61152x + 432768x + 122304x + 144256x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (19600x + 50176x - 154448x + 100352x + 78400x )\|2 ---R + ---R 18 14 10 6 2 ---R - 15288x + 101136x + 11368x + 202272x - 61152x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (- 392x - 392x - 784x )\|8 cos(----------) +--R 2 --R * --R 7 2 --R atan(----) @@ -57689,49 +61824,19 @@ d0247:=D(m0247,x) --R 4| 4+-+2 2 --R \| 196\|8 --R + ---R 20 16 12 8 4 +-+ 20 ---R (336x + 4200x + 4032x + 8400x + 1344x )\|2 - 1932x ---R + ---R 16 12 8 4 ---R - 3276x - 23184x - 6552x - 7728x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 20 16 12 8 4 +-+ 20 ---R (- 1050x - 2688x + 8274x - 5376x - 4200x )\|2 + 819x ---R + ---R 16 12 8 4 ---R - 5418x - 609x - 10836x + 3276x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 4+-+2 \|7 +--R (21x + 21x + 42x )\|8 sin(----------) +--R 2 --R + ---R 20 16 12 8 4 +-+ 20 ---R (336x + 4200x + 4032x + 8400x + 1344x )\|2 - 1932x ---R + ---R 16 12 8 4 ---R - 3276x - 23184x - 6552x - 7728x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 20 16 12 8 4 +-+ 20 ---R (- 1050x - 2688x + 8274x - 5376x - 4200x )\|2 + 819x ---R + ---R 16 12 8 4 ---R - 5418x - 609x - 10836x + 3276x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 4+-+2 \|7 +--R (21x + 21x + 42x )\|8 cos(----------) +--R 2 --R * --R 7 4 --R atan(----) @@ -57749,71 +61854,26 @@ d0247:=D(m0247,x) --R sin(---------------------) --R 2 --R + ---R 16 12 8 4 +-+ ---R (896x + 11200x + 10752x + 22400x + 3584)\|2 ---R + ---R 16 12 8 4 ---R - 5152x - 8736x - 61824x - 17472x - 20608 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ ---R (- 2800x - 7168x + 22064x - 14336x - 11200)\|2 ---R + ---R 16 12 8 4 ---R 2184x - 14448x - 1624x - 28896x + 8736 ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R sin(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (56x + 56x + 112)sin(----------) +--R 2 --R + ---R 16 12 8 4 +-+ ---R (1792x + 22400x + 21504x + 44800x + 7168)\|2 ---R + ---R 16 12 8 4 ---R - 10304x - 17472x - 123648x - 34944x - 41216 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ ---R (- 5600x - 14336x + 44128x - 28672x - 22400)\|2 ---R + ---R 16 12 8 4 ---R 4368x - 28896x - 3248x - 57792x + 17472 ---R * ---R 7 2 7 2 ---R atan(----) atan(----) ---R +-+ +-+ ---R \|7 \|7 ---R cos(----------) sin(----------) ---R 2 2 +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4 \|7 \|7 +--R (112x + 112x + 224)cos(----------) sin(----------) +--R 2 2 --R + ---R 16 12 8 4 +-+ ---R (896x + 11200x + 10752x + 22400x + 3584)\|2 ---R + ---R 16 12 8 4 ---R - 5152x - 8736x - 61824x - 17472x - 20608 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ ---R (- 2800x - 7168x + 22064x - 14336x - 11200)\|2 ---R + ---R 16 12 8 4 ---R 2184x - 14448x - 1624x - 28896x + 8736 ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R cos(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (56x + 56x + 112)cos(----------) +--R 2 --R * --R 7 6 --R atan(----) @@ -57831,49 +61891,19 @@ d0247:=D(m0247,x) --R cos(---------------------) --R 2 --R + ---R 18 14 10 6 2 +-+ ---R (6272x + 78400x + 75264x + 156800x + 25088x )\|2 ---R + ---R 18 14 10 6 2 ---R - 36064x - 61152x - 432768x - 122304x - 144256x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (- 19600x - 50176x + 154448x - 100352x - 78400x )\|2 ---R + ---R 18 14 10 6 2 ---R 15288x - 101136x - 11368x - 202272x + 61152x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (392x + 392x + 784x )\|8 sin(----------) +--R 2 --R + ---R 18 14 10 6 2 +-+ ---R (6272x + 78400x + 75264x + 156800x + 25088x )\|2 ---R + ---R 18 14 10 6 2 ---R - 36064x - 61152x - 432768x - 122304x - 144256x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (- 19600x - 50176x + 154448x - 100352x - 78400x )\|2 ---R + ---R 18 14 10 6 2 ---R 15288x - 101136x - 11368x - 202272x + 61152x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (392x + 392x + 784x )\|8 cos(----------) +--R 2 --R * --R 7 4 --R atan(----) @@ -57892,49 +61922,19 @@ d0247:=D(m0247,x) --R 4| 4+-+2 2 --R \| 196\|8 --R + ---R 20 16 12 8 4 +-+ ---R (- 224x - 2800x - 2688x - 5600x - 896x )\|2 ---R + ---R 20 16 12 8 4 ---R 1288x + 2184x + 15456x + 4368x + 5152x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 20 16 12 8 4 +-+ 20 ---R (700x + 1792x - 5516x + 3584x + 2800x )\|2 - 546x ---R + ---R 16 12 8 4 ---R 3612x + 406x + 7224x - 2184x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 4+-+2 \|7 +--R (- 14x - 14x - 28x )\|8 sin(----------) +--R 2 --R + ---R 20 16 12 8 4 +-+ ---R (- 224x - 2800x - 2688x - 5600x - 896x )\|2 ---R + ---R 20 16 12 8 4 ---R 1288x + 2184x + 15456x + 4368x + 5152x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 20 16 12 8 4 +-+ 20 ---R (700x + 1792x - 5516x + 3584x + 2800x )\|2 - 546x ---R + ---R 16 12 8 4 ---R 3612x + 406x + 7224x - 2184x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 4+-+2 \|7 +--R (- 14x - 14x - 28x )\|8 cos(----------) +--R 2 --R * --R 7 2 --R atan(----) @@ -57952,34 +61952,16 @@ d0247:=D(m0247,x) --R cos(---------------------) --R 2 --R + ---R 22 18 14 10 6 ---R (- 12544x - 156800x - 150528x - 313600x - 50176x ) ---R * ---R +-+ ---R \|2 ---R + ---R 22 18 14 10 6 ---R 72128x + 122304x + 865536x + 244608x + 288512x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 22 18 14 10 6 +-+ ---R (39200x + 100352x - 308896x + 200704x + 156800x )\|2 ---R + ---R 22 18 14 10 6 ---R - 30576x + 202272x + 22736x + 404544x - 122304x ---R * ---R +-----------------------------------+2 ---R | 7 2 7 2 ---R | atan(----) atan(----) ---R | +-+ +-+ ---R | \|7 \|7 ---R |sin(----------) + cos(----------) ---R | 2 2 ---R |----------------------------------- ---R 4| 4+-+2 ---R \| 196\|8 +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R 14 10 6 | 2 2 +--R (- 784x - 784x - 1568x ) |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 --R * --R 7 2 --R atan(----) @@ -57997,71 +61979,26 @@ d0247:=D(m0247,x) --R sin(---------------------) --R 2 --R + ---R 16 12 8 4 +-+ 16 ---R (224x + 2800x + 2688x + 5600x + 896)\|2 - 1288x ---R + ---R 12 8 4 ---R - 2184x - 15456x - 4368x - 5152 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ 16 ---R (- 700x - 1792x + 5516x - 3584x - 2800)\|2 + 546x ---R + ---R 12 8 4 ---R - 3612x - 406x - 7224x + 2184 ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R sin(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (14x + 14x + 28)sin(----------) +--R 2 --R + ---R 16 12 8 4 +-+ 16 ---R (448x + 5600x + 5376x + 11200x + 1792)\|2 - 2576x ---R + ---R 12 8 4 ---R - 4368x - 30912x - 8736x - 10304 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ 16 ---R (- 1400x - 3584x + 11032x - 7168x - 5600)\|2 + 1092x ---R + ---R 12 8 4 ---R - 7224x - 812x - 14448x + 4368 ---R * ---R 7 2 7 2 ---R atan(----) atan(----) ---R +-+ +-+ ---R \|7 \|7 ---R cos(----------) sin(----------) ---R 2 2 +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4 \|7 \|7 +--R (28x + 28x + 56)cos(----------) sin(----------) +--R 2 2 --R + ---R 16 12 8 4 +-+ 16 ---R (224x + 2800x + 2688x + 5600x + 896)\|2 - 1288x ---R + ---R 12 8 4 ---R - 2184x - 15456x - 4368x - 5152 ---R * ---R 4+-+2 ---R \|2 ---R + ---R 16 12 8 4 +-+ 16 ---R (- 700x - 1792x + 5516x - 3584x - 2800)\|2 + 546x ---R + ---R 12 8 4 ---R - 3612x - 406x - 7224x + 2184 ---R * ---R 7 4 ---R atan(----) ---R +-+ ---R \|7 ---R cos(----------) ---R 2 +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (14x + 14x + 28)cos(----------) +--R 2 --R * --R 7 8 --R atan(----) @@ -58079,49 +62016,19 @@ d0247:=D(m0247,x) --R cos(---------------------) --R 2 --R + ---R 18 14 10 6 2 +-+ ---R (6272x + 78400x + 75264x + 156800x + 25088x )\|2 ---R + ---R 18 14 10 6 2 ---R - 36064x - 61152x - 432768x - 122304x - 144256x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (- 19600x - 50176x + 154448x - 100352x - 78400x )\|2 ---R + ---R 18 14 10 6 2 ---R 15288x - 101136x - 11368x - 202272x + 61152x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (392x + 392x + 784x )\|8 sin(----------) +--R 2 --R + ---R 18 14 10 6 2 +-+ ---R (6272x + 78400x + 75264x + 156800x + 25088x )\|2 ---R + ---R 18 14 10 6 2 ---R - 36064x - 61152x - 432768x - 122304x - 144256x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 18 14 10 6 2 +-+ ---R (- 19600x - 50176x + 154448x - 100352x - 78400x )\|2 ---R + ---R 18 14 10 6 2 ---R 15288x - 101136x - 11368x - 202272x + 61152x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) ---R 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (392x + 392x + 784x )\|8 cos(----------) +--R 2 --R * --R 7 6 --R atan(----) @@ -58140,51 +62047,48 @@ d0247:=D(m0247,x) --R 4| 4+-+2 2 --R \| 196\|8 --R + ---R 20 16 12 8 4 +-+ 20 ---R (336x + 4200x + 4032x + 8400x + 1344x )\|2 - 1932x ---R + ---R 16 12 8 4 ---R - 3276x - 23184x - 6552x - 7728x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 20 16 12 8 4 +-+ 20 ---R (- 1050x - 2688x + 8274x - 5376x - 4200x )\|2 + 819x ---R + ---R 16 12 8 4 ---R - 5418x - 609x - 10836x + 3276x ---R * ---R 7 2 +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 4+-+2 \|7 +--R (21x + 21x + 42x )\|8 sin(----------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 4+-+2 \|7 +--R (21x + 21x + 42x )\|8 cos(----------) +--R 2 +--R * +--R 7 4 --R atan(----) --R +-+ ---R 4+-+2 \|7 ---R \|8 sin(----------) +--R \|7 +--R sin(----------) --R 2 ---R + ---R 20 16 12 8 4 +-+ 20 ---R (336x + 4200x + 4032x + 8400x + 1344x )\|2 - 1932x ---R + ---R 16 12 8 4 ---R - 3276x - 23184x - 6552x - 7728x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 20 16 12 8 4 +-+ 20 ---R (- 1050x - 2688x + 8274x - 5376x - 4200x )\|2 + 819x ---R + ---R 16 12 8 4 ---R - 5418x - 609x - 10836x + 3276x ---R * ---R 7 2 +--R atan(---------------) +--R 7 --R atan(----) --R +-+ ---R 4+-+2 \|7 ---R \|8 cos(----------) +--R \|7 +--R cos(----------) --R 2 +--R cos(---------------------) +--R 2 +--R + +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R 14 10 6 | 2 2 +--R (784x + 784x + 1568x ) |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 --R * ---R 7 4 +--R 7 2 --R atan(----) --R +-+ --R \|7 @@ -58200,52 +62104,8 @@ d0247:=D(m0247,x) --R cos(---------------------) --R 2 --R + ---R 22 18 14 10 6 +-+ ---R (12544x + 156800x + 150528x + 313600x + 50176x )\|2 ---R + ---R 22 18 14 10 6 ---R - 72128x - 122304x - 865536x - 244608x - 288512x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 22 18 14 10 6 +-+ ---R (- 39200x - 100352x + 308896x - 200704x - 156800x )\|2 ---R + ---R 22 18 14 10 6 ---R 30576x - 202272x - 22736x - 404544x + 122304x ---R * ---R 7 2 ---R atan(----) ---R +-+ ---R \|7 ---R sin(----------) ---R 2 ---R +-----------------------------------+2 atan(---------------) ---R | 7 2 7 2 7 ---R | atan(----) atan(----) atan(----) ---R | +-+ +-+ +-+ ---R | \|7 \|7 \|7 ---R |sin(----------) + cos(----------) cos(----------) ---R | 2 2 2 ---R |----------------------------------- cos(---------------------) ---R 4| 4+-+2 2 ---R \| 196\|8 ---R + ---R 24 20 16 12 8 +-+ 24 20 ---R (112x + 1400x + 1344x + 2800x + 448x )\|2 - 644x - 1092x ---R + ---R 16 12 8 ---R - 7728x - 2184x - 2576x ---R * ---R 4+-+2 ---R \|2 ---R + ---R 24 20 16 12 8 +-+ 24 20 ---R (- 350x - 896x + 2758x - 1792x - 1400x )\|2 + 273x - 1806x ---R + ---R 16 12 8 ---R - 203x - 3612x + 1092x +--R 16 12 8 +--R 7x + 7x + 14x --R Type: Expression Integer --E 1338 @@ -58255,7 +62115,7 @@ t0248:= x^3/(2+3*x^4+x^8) --R --R 3 --R x ---R (1334) ------------ +--R (1339) ------------ --R 8 4 --R x + 3x + 2 --R Type: Fraction Polynomial Integer @@ -58267,7 +62127,7 @@ r0248:= -1/2*atanh(3+2*x^4) --R --R 4 --R atanh(2x + 3) ---R (1335) - -------------- +--R (1340) - -------------- --R 2 --R Type: Expression Integer --E 1340 @@ -58278,7 +62138,7 @@ a0248:=integrate(t0248,x) --R --R 4 4 --R - log(x + 2) + log(x + 1) ---R (1336) --------------------------- +--R (1341) --------------------------- --R 4 --R Type: Union(Expression Integer,...) --E 1341 @@ -58289,7 +62149,7 @@ m0248:=a0248-r0248 --R --R 4 4 4 --R - log(x + 2) + log(x + 1) + 2atanh(2x + 3) ---R (1337) --------------------------------------------- +--R (1342) --------------------------------------------- --R 4 --R Type: Expression Integer --E 1342 @@ -58298,7 +62158,7 @@ m0248:=a0248-r0248 d0248:=D(m0248,x) --R --R ---R (1338) 0 +--R (1343) 0 --R Type: Expression Integer --E 1343 @@ -58307,30 +62167,23 @@ t0249:= 1/x/(1+x^5+x^10) --R --R --R 1 ---R (1339) ------------ +--R (1344) ------------ --R 11 6 --R x + x + x --R Type: Fraction Polynomial Integer --E 1344 --S 1345 of 1483 -r0249:= -1/15*atan(1/3*(1+2*x^5)*3^(1/2))*3^(1/2)+log(x)-1/10*log(1+x^5+x^10) ---R ---R There are 2 exposed and 5 unexposed library operations named atan ---R having 1 argument(s) but none was determined to be applicable. ---R Use HyperDoc Browse, or issue ---R )display op atan ---R to learn more about the available operations. Perhaps ---R package-calling the operation or using coercions on the arguments ---R will allow you to apply the operation. ---R ---RDaly Bug ---R Cannot find a definition or applicable library operation named atan ---R with argument type(s) ---R UnivariatePolynomial(x,AlgebraicNumber) ---R ---R Perhaps you should use "@" to indicate the required return type, ---R or "$" to specify which version of the function you need. +r0249:= -1/15*atan(1/3*(1+2*x^5)*3^(1/2)::EXPR(INT))*3^(1/2)+log(x)-1/10*log(1+x^5+x^10) +--R +--R +--R 5 +-+ +--R 10 5 +-+ (2x + 1)\|3 +--R - 3log(x + x + 1) + 30log(x) - 2\|3 atan(-------------) +--R 3 +--R (1345) ---------------------------------------------------------- +--R 30 +--R Type: Expression Integer --E 1345 --S 1346 of 1483 @@ -58341,7 +62194,7 @@ a0249:=integrate(t0249,x) --R +-+ 10 5 +-+ (2x + 1)\|3 --R - \|3 log(x + x + 1) + 10\|3 log(x) - 2atan(-------------) --R 3 ---R (1340) ------------------------------------------------------------- +--R (1346) ------------------------------------------------------------- --R +-+ --R 10\|3 --R Type: Union(Expression Integer,...) @@ -58351,14 +62204,7 @@ a0249:=integrate(t0249,x) m0249:=a0249-r0249 --R --R ---R (1341) ---R 5 +-+ ---R +-+ 10 5 +-+ (2x + 1)\|3 +-+ ---R - \|3 log(x + x + 1) + 10\|3 log(x) - 2atan(-------------) - 10r0249\|3 ---R 3 ---R --------------------------------------------------------------------------- ---R +-+ ---R 10\|3 +--R (1347) 0 --R Type: Expression Integer --E 1347 @@ -58366,10 +62212,7 @@ m0249:=a0249-r0249 d0249:=D(m0249,x) --R --R ---R 1 ---R (1342) ------------ ---R 11 6 ---R x + x + x +--R (1348) 0 --R Type: Expression Integer --E 1348 @@ -58378,30 +62221,23 @@ t0250:= 1/(x+x^6+x^11) --R --R --R 1 ---R (1343) ------------ +--R (1349) ------------ --R 11 6 --R x + x + x --R Type: Fraction Polynomial Integer --E 1349 --S 1350 of 1483 -r0250:= -1/15*atan(1/3*(1+2*x^5)*3^(1/2))*3^(1/2)+log(x)-1/10*log(1+x^5+x^10) ---R ---R There are 2 exposed and 5 unexposed library operations named atan ---R having 1 argument(s) but none was determined to be applicable. ---R Use HyperDoc Browse, or issue ---R )display op atan ---R to learn more about the available operations. Perhaps ---R package-calling the operation or using coercions on the arguments ---R will allow you to apply the operation. ---R ---RDaly Bug ---R Cannot find a definition or applicable library operation named atan ---R with argument type(s) ---R UnivariatePolynomial(x,AlgebraicNumber) ---R ---R Perhaps you should use "@" to indicate the required return type, ---R or "$" to specify which version of the function you need. +r0250:= -1/15*atan(1/3*(1+2*x^5)*3^(1/2)::EXPR(INT))*3^(1/2)+log(x)-1/10*log(1+x^5+x^10) +--R +--R +--R 5 +-+ +--R 10 5 +-+ (2x + 1)\|3 +--R - 3log(x + x + 1) + 30log(x) - 2\|3 atan(-------------) +--R 3 +--R (1350) ---------------------------------------------------------- +--R 30 +--R Type: Expression Integer --E 1350 --S 1351 of 1483 @@ -58412,7 +62248,7 @@ a0250:=integrate(t0250,x) --R +-+ 10 5 +-+ (2x + 1)\|3 --R - \|3 log(x + x + 1) + 10\|3 log(x) - 2atan(-------------) --R 3 ---R (1344) ------------------------------------------------------------- +--R (1351) ------------------------------------------------------------- --R +-+ --R 10\|3 --R Type: Union(Expression Integer,...) @@ -58422,14 +62258,7 @@ a0250:=integrate(t0250,x) m0250:=a0250-r0250 --R --R ---R (1345) ---R 5 +-+ ---R +-+ 10 5 +-+ (2x + 1)\|3 +-+ ---R - \|3 log(x + x + 1) + 10\|3 log(x) - 2atan(-------------) - 10r0250\|3 ---R 3 ---R --------------------------------------------------------------------------- ---R +-+ ---R 10\|3 +--R (1352) 0 --R Type: Expression Integer --E 1352 @@ -58437,10 +62266,7 @@ m0250:=a0250-r0250 d0250:=D(m0250,x) --R --R ---R 1 ---R (1346) ------------ ---R 11 6 ---R x + x + x +--R (1353) 0 --R Type: Expression Integer --E 1353 @@ -58449,7 +62275,7 @@ t0251:= (3+2*x)/(-2+x)/(5+x) --R --R --R 2x + 3 ---R (1347) ------------ +--R (1354) ------------ --R 2 --R x + 3x - 10 --R Type: Fraction Polynomial Integer @@ -58459,7 +62285,7 @@ t0251:= (3+2*x)/(-2+x)/(5+x) r0251:= log(2-x)+log(5+x) --R --R ---R (1348) log(x + 5) + log(- x + 2) +--R (1355) log(x + 5) + log(- x + 2) --R Type: Expression Integer --E 1355 @@ -58468,7 +62294,7 @@ a0251:=integrate(t0251,x) --R --R --R 2 ---R (1349) log(x + 3x - 10) +--R (1356) log(x + 3x - 10) --R Type: Union(Expression Integer,...) --E 1356 @@ -58477,7 +62303,7 @@ m0251:=a0251-r0251 --R --R --R 2 ---R (1350) log(x + 3x - 10) - log(x + 5) - log(- x + 2) +--R (1357) log(x + 3x - 10) - log(x + 5) - log(- x + 2) --R Type: Expression Integer --E 1357 @@ -58485,7 +62311,7 @@ m0251:=a0251-r0251 d0251:=D(m0251,x) --R --R ---R (1351) 0 +--R (1358) 0 --R Type: Expression Integer --E 1358 @@ -58494,7 +62320,7 @@ t0252:= x/(-1+x^2) --R --R --R x ---R (1352) ------ +--R (1359) ------ --R 2 --R x - 1 --R Type: Fraction Polynomial Integer @@ -58506,7 +62332,7 @@ r0252:= 1/2*log(1-x^2) --R --R 2 --R log(- x + 1) ---R (1353) ------------- +--R (1360) ------------- --R 2 --R Type: Expression Integer --E 1360 @@ -58517,7 +62343,7 @@ a0252:=integrate(t0252,x) --R --R 2 --R log(x - 1) ---R (1354) ----------- +--R (1361) ----------- --R 2 --R Type: Union(Expression Integer,...) --E 1361 @@ -58528,7 +62354,7 @@ m0252:=a0252-r0252 --R --R 2 2 --R log(x - 1) - log(- x + 1) ---R (1355) --------------------------- +--R (1362) --------------------------- --R 2 --R Type: Expression Integer --E 1362 @@ -58537,7 +62363,7 @@ m0252:=a0252-r0252 d0252:=D(m0252,x) --R --R ---R (1356) 0 +--R (1363) 0 --R Type: Expression Integer --E 1363 @@ -58546,7 +62372,7 @@ t0253:= 1/(-1+x^2)^2 --R --R --R 1 ---R (1357) ------------ +--R (1364) ------------ --R 4 2 --R x - 2x + 1 --R Type: Fraction Polynomial Integer @@ -58558,7 +62384,7 @@ r0253:= x/(2-2*x^2)+1/2*atanh(x) --R --R 2 --R (x - 1)atanh(x) - x ---R (1358) -------------------- +--R (1365) -------------------- --R 2 --R 2x - 2 --R Type: Expression Integer @@ -58570,7 +62396,7 @@ a0253:=integrate(t0253,x) --R --R 2 2 --R (x - 1)log(x + 1) + (- x + 1)log(x - 1) - 2x ---R (1359) ---------------------------------------------- +--R (1366) ---------------------------------------------- --R 2 --R 4x - 4 --R Type: Union(Expression Integer,...) @@ -58581,7 +62407,7 @@ m0253:=a0253-r0253 --R --R --R log(x + 1) - log(x - 1) - 2atanh(x) ---R (1360) ----------------------------------- +--R (1367) ----------------------------------- --R 4 --R Type: Expression Integer --E 1367 @@ -58590,7 +62416,7 @@ m0253:=a0253-r0253 d0253:=D(m0253,x) --R --R ---R (1361) 0 +--R (1368) 0 --R Type: Expression Integer --E 1368 @@ -58600,7 +62426,7 @@ t0254:= (-1+4*x^5)/(1+x+x^5)^2 --R --R 5 --R 4x - 1 ---R (1362) ----------------------------- +--R (1369) ----------------------------- --R 10 6 5 2 --R x + 2x + 2x + x + 2x + 1 --R Type: Fraction Polynomial Integer @@ -58611,7 +62437,7 @@ r0254:= -x/(1+x+x^5) --R --R --R x ---R (1363) - ---------- +--R (1370) - ---------- --R 5 --R x + x + 1 --R Type: Fraction Polynomial Integer @@ -58622,7 +62448,7 @@ a0254:=integrate(t0254,x) --R --R --R x ---R (1364) - ---------- +--R (1371) - ---------- --R 5 --R x + x + 1 --R Type: Union(Expression Integer,...) @@ -58632,7 +62458,7 @@ a0254:=integrate(t0254,x) m0254:=a0254-r0254 --R --R ---R (1365) 0 +--R (1372) 0 --R Type: Expression Integer --E 1372 @@ -58640,7 +62466,7 @@ m0254:=a0254-r0254 d0254:=D(m0254,x) --R --R ---R (1366) 0 +--R (1373) 0 --R Type: Expression Integer --E 1373 @@ -58649,7 +62475,7 @@ t0255:= (5+3*x)/(1-x-x^2+x^3) --R --R --R 3x + 5 ---R (1367) --------------- +--R (1374) --------------- --R 3 2 --R x - x - x + 1 --R Type: Fraction Polynomial Integer @@ -58660,7 +62486,7 @@ r0255:= 4/(1-x)+atanh(x) --R --R --R (x - 1)atanh(x) - 4 ---R (1368) ------------------- +--R (1375) ------------------- --R x - 1 --R Type: Expression Integer --E 1375 @@ -58670,7 +62496,7 @@ a0255:=integrate(t0255,x) --R --R --R (x - 1)log(x + 1) + (- x + 1)log(x - 1) - 8 ---R (1369) ------------------------------------------- +--R (1376) ------------------------------------------- --R 2x - 2 --R Type: Union(Expression Integer,...) --E 1376 @@ -58680,7 +62506,7 @@ m0255:=a0255-r0255 --R --R --R log(x + 1) - log(x - 1) - 2atanh(x) ---R (1370) ----------------------------------- +--R (1377) ----------------------------------- --R 2 --R Type: Expression Integer --E 1377 @@ -58689,7 +62515,7 @@ m0255:=a0255-r0255 d0255:=D(m0255,x) --R --R ---R (1371) 0 +--R (1378) 0 --R Type: Expression Integer --E 1378 @@ -58699,7 +62525,7 @@ t0256:= (3+2*x^2)/(1-2*x^2+x^4) --R --R 2 --R 2x + 3 ---R (1372) ------------ +--R (1379) ------------ --R 4 2 --R x - 2x + 1 --R Type: Fraction Polynomial Integer @@ -58711,7 +62537,7 @@ r0256:= 5*x/(2-2*x^2)+1/2*atanh(x) --R --R 2 --R (x - 1)atanh(x) - 5x ---R (1373) --------------------- +--R (1380) --------------------- --R 2 --R 2x - 2 --R Type: Expression Integer @@ -58723,7 +62549,7 @@ a0256:=integrate(t0256,x) --R --R 2 2 --R (x - 1)log(x + 1) + (- x + 1)log(x - 1) - 10x ---R (1374) ----------------------------------------------- +--R (1381) ----------------------------------------------- --R 2 --R 4x - 4 --R Type: Union(Expression Integer,...) @@ -58734,7 +62560,7 @@ m0256:=a0256-r0256 --R --R --R log(x + 1) - log(x - 1) - 2atanh(x) ---R (1375) ----------------------------------- +--R (1382) ----------------------------------- --R 4 --R Type: Expression Integer --E 1382 @@ -58743,7 +62569,7 @@ m0256:=a0256-r0256 d0256:=D(m0256,x) --R --R ---R (1376) 0 +--R (1383) 0 --R Type: Expression Integer --E 1383 @@ -58753,7 +62579,7 @@ t0257:= (x+x^2)/(4+x)/(-4+x^2) --R --R 2 --R x + x ---R (1377) ------------------ +--R (1384) ------------------ --R 3 2 --R x + 4x - 4x - 16 --R Type: Fraction Polynomial Integer @@ -58766,7 +62592,7 @@ r0257:= -1/2*atanh(1/2*x)+log(4+x) --R x --R 2log(x + 4) - atanh(-) --R 2 ---R (1378) ---------------------- +--R (1385) ---------------------- --R 2 --R Type: Expression Integer --E 1385 @@ -58776,7 +62602,7 @@ a0257:=integrate(t0257,x) --R --R --R 4log(x + 4) - log(x + 2) + log(x - 2) ---R (1379) ------------------------------------- +--R (1386) ------------------------------------- --R 4 --R Type: Union(Expression Integer,...) --E 1386 @@ -58788,7 +62614,7 @@ m0257:=a0257-r0257 --R x --R - log(x + 2) + log(x - 2) + 2atanh(-) --R 2 ---R (1380) ------------------------------------- +--R (1387) ------------------------------------- --R 4 --R Type: Expression Integer --E 1387 @@ -58797,7 +62623,7 @@ m0257:=a0257-r0257 d0257:=D(m0257,x) --R --R ---R (1381) 0 +--R (1388) 0 --R Type: Expression Integer --E 1388 @@ -58806,7 +62632,7 @@ t0258:= 1/(4-5*x^2+x^4) --R --R --R 1 ---R (1382) ------------ +--R (1389) ------------ --R 4 2 --R x - 5x + 4 --R Type: Fraction Polynomial Integer @@ -58819,7 +62645,7 @@ r0258:= -1/6*atanh(1/2*x)+1/3*atanh(x) --R x --R 2atanh(x) - atanh(-) --R 2 ---R (1383) -------------------- +--R (1390) -------------------- --R 6 --R Type: Expression Integer --E 1390 @@ -58829,7 +62655,7 @@ a0258:=integrate(t0258,x) --R --R --R - log(x + 2) + 2log(x + 1) - 2log(x - 1) + log(x - 2) ---R (1384) ----------------------------------------------------- +--R (1391) ----------------------------------------------------- --R 12 --R Type: Union(Expression Integer,...) --E 1391 @@ -58838,7 +62664,7 @@ a0258:=integrate(t0258,x) m0258:=a0258-r0258 --R --R ---R (1385) +--R (1392) --R x --R - log(x + 2) + 2log(x + 1) - 2log(x - 1) + log(x - 2) - 4atanh(x) + 2atanh(-) --R 2 @@ -58851,7 +62677,7 @@ m0258:=a0258-r0258 d0258:=D(m0258,x) --R --R ---R (1386) 0 +--R (1393) 0 --R Type: Expression Integer --E 1393 @@ -58861,7 +62687,7 @@ t0259:= x^2/(-1+x)^2/(1+x)^2 --R --R 2 --R x ---R (1387) ------------ +--R (1394) ------------ --R 4 2 --R x - 2x + 1 --R Type: Fraction Polynomial Integer @@ -58873,7 +62699,7 @@ r0259:= x/(2-2*x^2)-1/2*atanh(x) --R --R 2 --R (- x + 1)atanh(x) - x ---R (1388) ---------------------- +--R (1395) ---------------------- --R 2 --R 2x - 2 --R Type: Expression Integer @@ -58885,7 +62711,7 @@ a0259:=integrate(t0259,x) --R --R 2 2 --R (- x + 1)log(x + 1) + (x - 1)log(x - 1) - 2x ---R (1389) ---------------------------------------------- +--R (1396) ---------------------------------------------- --R 2 --R 4x - 4 --R Type: Union(Expression Integer,...) @@ -58896,7 +62722,7 @@ m0259:=a0259-r0259 --R --R --R - log(x + 1) + log(x - 1) + 2atanh(x) ---R (1390) ------------------------------------- +--R (1397) ------------------------------------- --R 4 --R Type: Expression Integer --E 1397 @@ -58905,7 +62731,7 @@ m0259:=a0259-r0259 d0259:=D(m0259,x) --R --R ---R (1391) 0 +--R (1398) 0 --R Type: Expression Integer --E 1398 @@ -58914,7 +62740,7 @@ t0260:= x/(1+x^2)/(4+x^2) --R --R --R x ---R (1392) ------------ +--R (1399) ------------ --R 4 2 --R x + 5x + 4 --R Type: Fraction Polynomial Integer @@ -58928,7 +62754,7 @@ r0260:= -1/3*atanh(5/3+2/3*x^2) --R 2x + 5 --R atanh(-------) --R 3 ---R (1393) - -------------- +--R (1400) - -------------- --R 3 --R Type: Expression Integer --E 1400 @@ -58939,7 +62765,7 @@ a0260:=integrate(t0260,x) --R --R 2 2 --R - log(x + 4) + log(x + 1) ---R (1394) --------------------------- +--R (1401) --------------------------- --R 6 --R Type: Union(Expression Integer,...) --E 1401 @@ -58952,7 +62778,7 @@ m0260:=a0260-r0260 --R 2 2 2x + 5 --R - log(x + 4) + log(x + 1) + 2atanh(-------) --R 3 ---R (1395) --------------------------------------------- +--R (1402) --------------------------------------------- --R 6 --R Type: Expression Integer --E 1402 @@ -58961,7 +62787,7 @@ m0260:=a0260-r0260 d0260:=D(m0260,x) --R --R ---R (1396) 0 +--R (1403) 0 --R Type: Expression Integer --E 1403 @@ -58970,7 +62796,7 @@ t0261:= 1/(2+2*x^2+x^4) --R --R --R 1 ---R (1397) ------------ +--R (1404) ------------ --R 4 2 --R x + 2x + 2 --R Type: Fraction Polynomial Integer @@ -58984,7 +62810,7 @@ r0261:= -1/4*atan(((-2+2*2^(1/2))^(1/2)-2*x)/(2+2*2^(1/2))^(1/2))/_ 1/8*log(2^(1/2)+(-2+2*2^(1/2))^(1/2)*x+x^2)/(2^(1/2)-1)^(1/2) --R --R ---R (1398) +--R (1405) --R +--------+ +---------+ --R | +-+ | +-+ +-+ 2 --R \|\|2 + 1 log(x\|2\|2 - 2 + \|2 + x ) @@ -59015,7 +62841,7 @@ r0261:= -1/4*atan(((-2+2*2^(1/2))^(1/2)-2*x)/(2+2*2^(1/2))^(1/2))/_ a0261:=integrate(t0261,x) --R --R ---R (1399) +--R (1406) --R - --R 4+-+ %pi --R \|2 cos(---) @@ -59068,7 +62894,7 @@ a0261:=integrate(t0261,x) m0261:=a0261-r0261 --R --R ---R (1400) +--R (1407) --R +--------+ +---------+ --R +-+ | +-+ | +-+ +-+ 2 --R - \|2 \|\|2 + 1 log(x\|2\|2 - 2 + \|2 + x ) @@ -59157,25 +62983,25 @@ m0261:=a0261-r0261 --E 1407 --S 1408 of 1483 -d0261:=D(m0261,x) +d0261:=normalize(D(m0261,x)) --R --R ---R (1401) ---R 2 +-+ 2 %pi 8 ---R ((20x - 28)\|2 - 28x + 40)sin(---) ---R 8 +--R (1408) +--R 2 4+-+2 2 %pi 8 +--R ((20x - 28)\|2 - 28x + 40)sin(---) +--R 8 --R + ---R 2 +-+ 2 %pi 2 %pi 6 ---R ((80x - 112)\|2 - 112x + 160)cos(---) sin(---) ---R 8 8 +--R 2 4+-+2 2 %pi 2 %pi 6 +--R ((80x - 112)\|2 - 112x + 160)cos(---) sin(---) +--R 8 8 --R + ---R 4 2 +-+ 4 2 4+-+2 %pi %pi 5 ---R ((80x - 112x )\|2 - 112x + 160x )\|2 cos(---)sin(---) ---R 8 8 +--R 4 2 4+-+2 4 2 %pi %pi 5 +--R ((- 112x + 160x )\|2 + 160x - 224x )cos(---)sin(---) +--R 8 8 --R + ---R 2 +-+ 2 %pi 4 6 4 +-+ ---R ((120x - 168)\|2 - 168x + 240)cos(---) + (20x - 28x )\|2 ---R 8 +--R 2 4+-+2 2 %pi 4 6 4 4+-+2 +--R ((120x - 168)\|2 - 168x + 240)cos(---) + (20x - 28x )\|2 +--R 8 --R + --R 6 4 --R - 28x + 40x @@ -59184,64 +63010,64 @@ d0261:=D(m0261,x) --R sin(---) --R 8 --R + ---R 4 2 +-+ 4 2 4+-+2 %pi 3 %pi 3 ---R ((160x - 224x )\|2 - 224x + 320x )\|2 cos(---) sin(---) ---R 8 8 +--R 4 2 4+-+2 4 2 %pi 3 %pi 3 +--R ((- 224x + 320x )\|2 + 320x - 448x )cos(---) sin(---) +--R 8 8 --R + ---R 2 +-+ 2 %pi 6 ---R ((80x - 112)\|2 - 112x + 160)cos(---) ---R 8 +--R 2 4+-+2 2 %pi 6 +--R ((80x - 112)\|2 - 112x + 160)cos(---) +--R 8 --R + ---R 6 4 +-+ 6 4 %pi 2 ---R ((200x - 280x )\|2 - 280x + 400x )cos(---) ---R 8 +--R 6 4 4+-+2 6 4 %pi 2 +--R ((200x - 280x )\|2 - 280x + 400x )cos(---) +--R 8 --R * --R %pi 2 --R sin(---) --R 8 --R + ---R 4 2 +-+ 4 2 4+-+2 %pi 5 ---R ((80x - 112x )\|2 - 112x + 160x )\|2 cos(---) ---R 8 +--R 4 2 4+-+2 4 2 %pi 5 +--R ((- 112x + 160x )\|2 + 160x - 224x )cos(---) +--R 8 --R + ---R 8 6 +-+ 8 6 4+-+2 %pi ---R ((40x - 56x )\|2 - 56x + 80x )\|2 cos(---) ---R 8 +--R 8 6 4+-+2 8 6 %pi +--R ((- 56x + 80x )\|2 + 80x - 112x )cos(---) +--R 8 --R * --R %pi --R sin(---) --R 8 --R + ---R 2 +-+ 2 %pi 8 ---R ((20x - 28)\|2 - 28x + 40)cos(---) ---R 8 +--R 2 4+-+2 2 %pi 8 +--R ((20x - 28)\|2 - 28x + 40)cos(---) +--R 8 --R + ---R 6 4 +-+ 6 4 %pi 4 10 8 +-+ 10 ---R ((20x - 28x )\|2 - 28x + 40x )cos(---) + (5x - 7x )\|2 - 7x ---R 8 +--R 6 4 4+-+2 6 4 %pi 4 10 8 4+-+2 +--R ((20x - 28x )\|2 - 28x + 40x )cos(---) + (5x - 7x )\|2 +--R 8 --R + ---R 8 ---R 10x +--R 10 8 +--R - 7x + 10x --R * ---R +--------+ +---------+ ---R | +-+ | +-+ ---R \|\|2 + 1 \|2\|2 + 2 +--R +---------+ +----------+ +--R |4+-+2 | 4+-+2 +--R \|\|2 + 1 \|2\|2 + 2 --R + ---R 2 +-+ 2 %pi 8 ---R ((- 4x - 4)\|2 + 4x + 8)sin(---) ---R 8 +--R 2 4+-+2 2 %pi 8 +--R ((- 4x - 4)\|2 + 4x + 8)sin(---) +--R 8 --R + ---R 2 +-+ 2 %pi 2 %pi 6 ---R ((- 16x - 16)\|2 + 16x + 32)cos(---) sin(---) ---R 8 8 +--R 2 4+-+2 2 %pi 2 %pi 6 +--R ((- 16x - 16)\|2 + 16x + 32)cos(---) sin(---) +--R 8 8 --R + ---R 4 2 +-+ 4 2 4+-+2 %pi %pi 5 ---R ((- 16x - 16x )\|2 + 16x + 32x )\|2 cos(---)sin(---) ---R 8 8 +--R 4 2 4+-+2 4 2 %pi %pi 5 +--R ((16x + 32x )\|2 - 32x - 32x )cos(---)sin(---) +--R 8 8 --R + ---R 2 +-+ 2 %pi 4 6 4 +-+ ---R ((- 24x - 24)\|2 + 24x + 48)cos(---) + (- 4x - 4x )\|2 ---R 8 +--R 2 4+-+2 2 %pi 4 6 4 4+-+2 +--R ((- 24x - 24)\|2 + 24x + 48)cos(---) + (- 4x - 4x )\|2 +--R 8 --R + --R 6 4 --R 4x + 8x @@ -59250,212 +63076,211 @@ d0261:=D(m0261,x) --R sin(---) --R 8 --R + ---R 4 2 +-+ 4 2 4+-+2 %pi 3 %pi 3 ---R ((- 32x - 32x )\|2 + 32x + 64x )\|2 cos(---) sin(---) ---R 8 8 +--R 4 2 4+-+2 4 2 %pi 3 %pi 3 +--R ((32x + 64x )\|2 - 64x - 64x )cos(---) sin(---) +--R 8 8 --R + ---R 2 +-+ 2 %pi 6 ---R ((- 16x - 16)\|2 + 16x + 32)cos(---) ---R 8 +--R 2 4+-+2 2 %pi 6 +--R ((- 16x - 16)\|2 + 16x + 32)cos(---) +--R 8 --R + ---R 6 4 +-+ 6 4 %pi 2 ---R ((- 40x - 40x )\|2 + 40x + 80x )cos(---) ---R 8 +--R 6 4 4+-+2 6 4 %pi 2 +--R ((- 40x - 40x )\|2 + 40x + 80x )cos(---) +--R 8 --R * --R %pi 2 --R sin(---) --R 8 --R + ---R 4 2 +-+ 4 2 4+-+2 %pi 5 ---R ((- 16x - 16x )\|2 + 16x + 32x )\|2 cos(---) ---R 8 +--R 4 2 4+-+2 4 2 %pi 5 +--R ((16x + 32x )\|2 - 32x - 32x )cos(---) +--R 8 --R + ---R 8 6 +-+ 8 6 4+-+2 %pi ---R ((- 8x - 8x )\|2 + 8x + 16x )\|2 cos(---) ---R 8 +--R 8 6 4+-+2 8 6 %pi +--R ((8x + 16x )\|2 - 16x - 16x )cos(---) +--R 8 --R * --R %pi --R sin(---) --R 8 --R + ---R 2 +-+ 2 %pi 8 ---R ((- 4x - 4)\|2 + 4x + 8)cos(---) ---R 8 +--R 2 4+-+2 2 %pi 8 +--R ((- 4x - 4)\|2 + 4x + 8)cos(---) +--R 8 +--R + +--R 6 4 4+-+2 6 4 %pi 4 10 8 4+-+2 10 +--R ((- 4x - 4x )\|2 + 4x + 8x )cos(---) + (- x - x )\|2 + x +--R 8 --R + ---R 6 4 +-+ 6 4 %pi 4 10 8 +-+ 10 8 ---R ((- 4x - 4x )\|2 + 4x + 8x )cos(---) + (- x - x )\|2 + x + 2x ---R 8 +--R 8 +--R 2x --R * ---R +--------+ +---------+ ---R | +-+ | +-+ ---R \|\|2 - 1 \|2\|2 - 2 +--R +---------+ +----------+ +--R |4+-+2 | 4+-+2 +--R \|\|2 - 1 \|2\|2 - 2 --R + ---R 4 2 +-+ 4 2 %pi 8 ---R ((16x + 32x + 32)\|2 - 24x - 48x - 48)sin(---) ---R 8 +--R 4 2 4+-+2 4 2 %pi 8 +--R ((16x + 32x + 32)\|2 - 24x - 48x - 48)sin(---) +--R 8 --R + ---R 4 2 +-+ 4 2 %pi 2 ---R ((64x + 128x + 128)\|2 - 96x - 192x - 192)cos(---) ---R 8 +--R 4 2 4+-+2 4 2 %pi 2 +--R ((64x + 128x + 128)\|2 - 96x - 192x - 192)cos(---) +--R 8 --R + ---R 6 4 2 +-+ 6 4 2 4+-+2 ---R ((8x + 16x + 16x )\|2 - 12x - 24x - 24x )\|2 +--R 6 4 2 4+-+2 6 4 2 +--R (- 12x - 24x - 24x )\|2 + 16x + 32x + 32x --R * --R %pi 6 --R sin(---) --R 8 --R + ---R 6 4 2 +-+ 6 4 2 4+-+2 %pi %pi 5 ---R ((48x + 96x + 96x )\|2 - 72x - 144x - 144x )\|2 cos(---)sin(---) +--R 6 4 2 4+-+2 6 4 2 %pi %pi 5 +--R ((- 72x - 144x - 144x )\|2 + 96x + 192x + 192x )cos(---)sin(---) --R 8 8 --R + ---R 4 2 +-+ 4 2 %pi 4 ---R ((96x + 192x + 192)\|2 - 144x - 288x - 288)cos(---) ---R 8 +--R 4 2 4+-+2 4 2 %pi 4 +--R ((96x + 192x + 192)\|2 - 144x - 288x - 288)cos(---) +--R 8 --R + ---R 6 4 2 +-+ 6 4 2 4+-+2 %pi 2 ---R ((8x + 16x + 16x )\|2 - 12x - 24x - 24x )\|2 cos(---) ---R 8 +--R 6 4 2 4+-+2 6 4 2 %pi 2 +--R ((- 12x - 24x - 24x )\|2 + 16x + 32x + 32x )cos(---) +--R 8 --R + ---R 8 6 4 +-+ 8 6 4 ---R (8x + 16x + 16x )\|2 - 12x - 24x - 24x +--R 8 6 4 4+-+2 8 6 4 +--R (8x + 16x + 16x )\|2 - 12x - 24x - 24x --R * --R %pi 4 --R sin(---) --R 8 --R + ---R 6 4 2 +-+ 6 4 2 4+-+2 %pi 3 ---R ((96x + 192x + 192x )\|2 - 144x - 288x - 288x )\|2 cos(---) ---R 8 +--R 6 4 2 4+-+2 6 4 2 %pi 3 +--R ((- 144x - 288x - 288x )\|2 + 192x + 384x + 384x )cos(---) +--R 8 --R + ---R 8 6 4 +-+ 8 6 4 %pi ---R ((32x + 64x + 64x )\|2 - 48x - 96x - 96x )cos(---) ---R 8 +--R 8 6 4 4+-+2 8 6 4 %pi +--R ((32x + 64x + 64x )\|2 - 48x - 96x - 96x )cos(---) +--R 8 --R * --R %pi 3 --R sin(---) --R 8 --R + ---R 4 2 +-+ 4 2 %pi 6 ---R ((64x + 128x + 128)\|2 - 96x - 192x - 192)cos(---) ---R 8 +--R 4 2 4+-+2 4 2 %pi 6 +--R ((64x + 128x + 128)\|2 - 96x - 192x - 192)cos(---) +--R 8 --R + ---R 6 4 2 +-+ 6 4 2 4+-+2 %pi 4 ---R ((- 8x - 16x - 16x )\|2 + 12x + 24x + 24x )\|2 cos(---) ---R 8 +--R 6 4 2 4+-+2 6 4 2 %pi 4 +--R ((12x + 24x + 24x )\|2 - 16x - 32x - 32x )cos(---) +--R 8 --R + ---R 8 6 4 +-+ 8 6 4 %pi 2 ---R ((80x + 160x + 160x )\|2 - 120x - 240x - 240x )cos(---) ---R 8 +--R 8 6 4 4+-+2 8 6 4 %pi 2 +--R ((80x + 160x + 160x )\|2 - 120x - 240x - 240x )cos(---) +--R 8 --R + ---R 10 8 6 +-+ 10 8 6 4+-+2 ---R ((4x + 8x + 8x )\|2 - 6x - 12x - 12x )\|2 +--R 10 8 6 4+-+2 10 8 6 +--R (- 6x - 12x - 12x )\|2 + 8x + 16x + 16x --R * --R %pi 2 --R sin(---) --R 8 --R + ---R 6 4 2 +-+ 6 4 2 4+-+2 %pi 5 ---R ((48x + 96x + 96x )\|2 - 72x - 144x - 144x )\|2 cos(---) +--R 6 4 2 4+-+2 6 4 2 %pi 5 +--R ((- 72x - 144x - 144x )\|2 + 96x + 192x + 192x )cos(---) --R 8 --R + ---R 8 6 4 +-+ 8 6 4 %pi 3 ---R ((- 32x - 64x - 64x )\|2 + 48x + 96x + 96x )cos(---) ---R 8 +--R 8 6 4 4+-+2 8 6 4 %pi 3 +--R ((- 32x - 64x - 64x )\|2 + 48x + 96x + 96x )cos(---) +--R 8 --R + ---R 10 8 6 +-+ 10 8 6 4+-+2 %pi ---R ((8x + 16x + 16x )\|2 - 12x - 24x - 24x )\|2 cos(---) ---R 8 +--R 10 8 6 4+-+2 10 8 6 %pi +--R ((- 12x - 24x - 24x )\|2 + 16x + 32x + 32x )cos(---) +--R 8 --R * --R %pi --R sin(---) --R 8 --R + ---R 4 2 +-+ 4 2 %pi 8 ---R ((16x + 32x + 32)\|2 - 24x - 48x - 48)cos(---) ---R 8 +--R 4 2 4+-+2 4 2 %pi 8 +--R ((16x + 32x + 32)\|2 - 24x - 48x - 48)cos(---) +--R 8 --R + ---R 6 4 2 +-+ 6 4 2 4+-+2 %pi 6 ---R ((- 8x - 16x - 16x )\|2 + 12x + 24x + 24x )\|2 cos(---) ---R 8 +--R 6 4 2 4+-+2 6 4 2 %pi 6 +--R ((12x + 24x + 24x )\|2 - 16x - 32x - 32x )cos(---) +--R 8 --R + ---R 8 6 4 +-+ 8 6 4 %pi 4 ---R ((8x + 16x + 16x )\|2 - 12x - 24x - 24x )cos(---) ---R 8 +--R 8 6 4 4+-+2 8 6 4 %pi 4 +--R ((8x + 16x + 16x )\|2 - 12x - 24x - 24x )cos(---) +--R 8 --R + ---R 10 8 6 +-+ 10 8 6 4+-+2 %pi 2 ---R ((- 4x - 8x - 8x )\|2 + 6x + 12x + 12x )\|2 cos(---) ---R 8 +--R 10 8 6 4+-+2 10 8 6 %pi 2 +--R ((6x + 12x + 12x )\|2 - 8x - 16x - 16x )cos(---) +--R 8 --R / ---R 4 2 +-+ 4 2 %pi 8 ---R ((32x + 64x + 64)\|2 - 48x - 96x - 96)sin(---) ---R 8 +--R 4 2 4+-+2 4 2 %pi 8 +--R ((32x + 64x + 64)\|2 - 48x - 96x - 96)sin(---) +--R 8 --R + ---R 4 2 +-+ 4 2 %pi 2 %pi 6 ---R ((128x + 256x + 256)\|2 - 192x - 384x - 384)cos(---) sin(---) ---R 8 8 +--R 4 2 4+-+2 4 2 %pi 2 %pi 6 +--R ((128x + 256x + 256)\|2 - 192x - 384x - 384)cos(---) sin(---) +--R 8 8 --R + ---R 6 4 2 +-+ 6 4 2 4+-+2 %pi ---R ((128x + 256x + 256x )\|2 - 192x - 384x - 384x )\|2 cos(---) ---R 8 ---R * ---R %pi 5 ---R sin(---) ---R 8 +--R 6 4 2 4+-+2 6 4 2 %pi %pi 5 +--R ((- 192x - 384x - 384x )\|2 + 256x + 512x + 512x )cos(---)sin(---) +--R 8 8 --R + ---R 4 2 +-+ 4 2 %pi 4 ---R ((192x + 384x + 384)\|2 - 288x - 576x - 576)cos(---) ---R 8 +--R 4 2 4+-+2 4 2 %pi 4 +--R ((192x + 384x + 384)\|2 - 288x - 576x - 576)cos(---) +--R 8 --R + ---R 8 6 4 +-+ 8 6 4 ---R (32x + 64x + 64x )\|2 - 48x - 96x - 96x +--R 8 6 4 4+-+2 8 6 4 +--R (32x + 64x + 64x )\|2 - 48x - 96x - 96x --R * --R %pi 4 --R sin(---) --R 8 --R + ---R 6 4 2 +-+ 6 4 2 4+-+2 %pi 3 ---R ((256x + 512x + 512x )\|2 - 384x - 768x - 768x )\|2 cos(---) +--R 6 4 2 4+-+2 6 4 2 %pi 3 +--R ((- 384x - 768x - 768x )\|2 + 512x + 1024x + 1024x )cos(---) --R 8 --R * --R %pi 3 --R sin(---) --R 8 --R + ---R 4 2 +-+ 4 2 %pi 6 ---R ((128x + 256x + 256)\|2 - 192x - 384x - 384)cos(---) ---R 8 +--R 4 2 4+-+2 4 2 %pi 6 +--R ((128x + 256x + 256)\|2 - 192x - 384x - 384)cos(---) +--R 8 --R + ---R 8 6 4 +-+ 8 6 4 %pi 2 ---R ((320x + 640x + 640x )\|2 - 480x - 960x - 960x )cos(---) ---R 8 +--R 8 6 4 4+-+2 8 6 4 %pi 2 +--R ((320x + 640x + 640x )\|2 - 480x - 960x - 960x )cos(---) +--R 8 --R * --R %pi 2 --R sin(---) --R 8 --R + ---R 6 4 2 +-+ 6 4 2 4+-+2 %pi 5 ---R ((128x + 256x + 256x )\|2 - 192x - 384x - 384x )\|2 cos(---) ---R 8 +--R 6 4 2 4+-+2 6 4 2 %pi 5 +--R ((- 192x - 384x - 384x )\|2 + 256x + 512x + 512x )cos(---) +--R 8 --R + ---R 10 8 6 +-+ 10 8 6 4+-+2 %pi ---R ((64x + 128x + 128x )\|2 - 96x - 192x - 192x )\|2 cos(---) ---R 8 +--R 10 8 6 4+-+2 10 8 6 %pi +--R ((- 96x - 192x - 192x )\|2 + 128x + 256x + 256x )cos(---) +--R 8 --R * --R %pi --R sin(---) --R 8 --R + ---R 4 2 +-+ 4 2 %pi 8 ---R ((32x + 64x + 64)\|2 - 48x - 96x - 96)cos(---) ---R 8 +--R 4 2 4+-+2 4 2 %pi 8 +--R ((32x + 64x + 64)\|2 - 48x - 96x - 96)cos(---) +--R 8 --R + ---R 8 6 4 +-+ 8 6 4 %pi 4 ---R ((32x + 64x + 64x )\|2 - 48x - 96x - 96x )cos(---) ---R 8 +--R 8 6 4 4+-+2 8 6 4 %pi 4 +--R ((32x + 64x + 64x )\|2 - 48x - 96x - 96x )cos(---) +--R 8 --R + ---R 12 10 8 +-+ 12 10 8 ---R (8x + 16x + 16x )\|2 - 12x - 24x - 24x +--R 12 10 8 4+-+2 12 10 8 +--R (8x + 16x + 16x )\|2 - 12x - 24x - 24x --R Type: Expression Integer --E 1408 @@ -59465,7 +63290,7 @@ t0262:= x^5/(x-x^3) --R --R 4 --R x ---R (1402) - ------ +--R (1409) - ------ --R 2 --R x - 1 --R Type: Fraction Polynomial Integer @@ -59477,7 +63302,7 @@ r0262:= -x-1/3*x^3+atanh(x) --R --R 3 --R 3atanh(x) - x - 3x ---R (1403) ------------------- +--R (1410) ------------------- --R 3 --R Type: Expression Integer --E 1410 @@ -59488,7 +63313,7 @@ a0262:=integrate(t0262,x) --R --R 3 --R 3log(x + 1) - 3log(x - 1) - 2x - 6x ---R (1404) ------------------------------------ +--R (1411) ------------------------------------ --R 6 --R Type: Union(Expression Integer,...) --E 1411 @@ -59498,7 +63323,7 @@ m0262:=a0262-r0262 --R --R --R log(x + 1) - log(x - 1) - 2atanh(x) ---R (1405) ----------------------------------- +--R (1412) ----------------------------------- --R 2 --R Type: Expression Integer --E 1412 @@ -59507,7 +63332,7 @@ m0262:=a0262-r0262 d0262:=D(m0262,x) --R --R ---R (1406) 0 +--R (1413) 0 --R Type: Expression Integer --E 1413 @@ -59517,7 +63342,7 @@ t0263:= x^3/(x-x^3) --R --R 2 --R x ---R (1407) - ------ +--R (1414) - ------ --R 2 --R x - 1 --R Type: Fraction Polynomial Integer @@ -59527,7 +63352,7 @@ t0263:= x^3/(x-x^3) r0263:= -x+atanh(x) --R --R ---R (1408) atanh(x) - x +--R (1415) atanh(x) - x --R Type: Expression Integer --E 1415 @@ -59536,7 +63361,7 @@ a0263:=integrate(t0263,x) --R --R --R log(x + 1) - log(x - 1) - 2x ---R (1409) ---------------------------- +--R (1416) ---------------------------- --R 2 --R Type: Union(Expression Integer,...) --E 1416 @@ -59546,7 +63371,7 @@ m0263:=a0263-r0263 --R --R --R log(x + 1) - log(x - 1) - 2atanh(x) ---R (1410) ----------------------------------- +--R (1417) ----------------------------------- --R 2 --R Type: Expression Integer --E 1417 @@ -59555,7 +63380,7 @@ m0263:=a0263-r0263 d0263:=D(m0263,x) --R --R ---R (1411) 0 +--R (1418) 0 --R Type: Expression Integer --E 1418 @@ -59564,7 +63389,7 @@ t0264:= x^2/(x-x^3) --R --R --R x ---R (1412) - ------ +--R (1419) - ------ --R 2 --R x - 1 --R Type: Fraction Polynomial Integer @@ -59576,7 +63401,7 @@ r0264:= -1/2*log(1-x^2) --R --R 2 --R log(- x + 1) ---R (1413) - ------------- +--R (1420) - ------------- --R 2 --R Type: Expression Integer --E 1420 @@ -59587,7 +63412,7 @@ a0264:=integrate(t0264,x) --R --R 2 --R log(x - 1) ---R (1414) - ----------- +--R (1421) - ----------- --R 2 --R Type: Union(Expression Integer,...) --E 1421 @@ -59598,7 +63423,7 @@ m0264:=a0264-r0264 --R --R 2 2 --R - log(x - 1) + log(- x + 1) ---R (1415) ----------------------------- +--R (1422) ----------------------------- --R 2 --R Type: Expression Integer --E 1422 @@ -59607,7 +63432,7 @@ m0264:=a0264-r0264 d0264:=D(m0264,x) --R --R ---R (1416) 0 +--R (1423) 0 --R Type: Expression Integer --E 1423 @@ -59616,7 +63441,7 @@ t0265:= 1/x/(x-x^3) --R --R --R 1 ---R (1417) - ------- +--R (1424) - ------- --R 4 2 --R x - x --R Type: Fraction Polynomial Integer @@ -59627,7 +63452,7 @@ r0265:= -1/x+atanh(x) --R --R --R x atanh(x) - 1 ---R (1418) -------------- +--R (1425) -------------- --R x --R Type: Expression Integer --E 1425 @@ -59637,7 +63462,7 @@ a0265:=integrate(t0265,x) --R --R --R x log(x + 1) - x log(x - 1) - 2 ---R (1419) ------------------------------- +--R (1426) ------------------------------- --R 2x --R Type: Union(Expression Integer,...) --E 1426 @@ -59647,7 +63472,7 @@ m0265:=a0265-r0265 --R --R --R log(x + 1) - log(x - 1) - 2atanh(x) ---R (1420) ----------------------------------- +--R (1427) ----------------------------------- --R 2 --R Type: Expression Integer --E 1427 @@ -59656,7 +63481,7 @@ m0265:=a0265-r0265 d0265:=D(m0265,x) --R --R ---R (1421) 0 +--R (1428) 0 --R Type: Expression Integer --E 1428 @@ -59665,7 +63490,7 @@ t0266:= 1/x^3/(x-x^3) --R --R --R 1 ---R (1422) - ------- +--R (1429) - ------- --R 6 4 --R x - x --R Type: Fraction Polynomial Integer @@ -59677,7 +63502,7 @@ r0266:= -1/3/x^3-1/x+atanh(x) --R --R 3 2 --R 3x atanh(x) - 3x - 1 ---R (1423) --------------------- +--R (1430) --------------------- --R 3 --R 3x --R Type: Expression Integer @@ -59689,7 +63514,7 @@ a0266:=integrate(t0266,x) --R --R 3 3 2 --R 3x log(x + 1) - 3x log(x - 1) - 6x - 2 ---R (1424) --------------------------------------- +--R (1431) --------------------------------------- --R 3 --R 6x --R Type: Union(Expression Integer,...) @@ -59700,7 +63525,7 @@ m0266:=a0266-r0266 --R --R --R log(x + 1) - log(x - 1) - 2atanh(x) ---R (1425) ----------------------------------- +--R (1432) ----------------------------------- --R 2 --R Type: Expression Integer --E 1432 @@ -59709,7 +63534,7 @@ m0266:=a0266-r0266 d0266:=D(m0266,x) --R --R ---R (1426) 0 +--R (1433) 0 --R Type: Expression Integer --E 1433 @@ -59719,7 +63544,7 @@ t0267:= (1-2*x^2)/(x^2-x^4) --R --R 2 --R 2x - 1 ---R (1427) ------- +--R (1434) ------- --R 4 2 --R x - x --R Type: Fraction Polynomial Integer @@ -59730,7 +63555,7 @@ r0267:= -1/x-atanh(x) --R --R --R - x atanh(x) - 1 ---R (1428) ---------------- +--R (1435) ---------------- --R x --R Type: Expression Integer --E 1435 @@ -59740,7 +63565,7 @@ a0267:=integrate(t0267,x) --R --R --R - x log(x + 1) + x log(x - 1) - 2 ---R (1429) --------------------------------- +--R (1436) --------------------------------- --R 2x --R Type: Union(Expression Integer,...) --E 1436 @@ -59750,7 +63575,7 @@ m0267:=a0267-r0267 --R --R --R - log(x + 1) + log(x - 1) + 2atanh(x) ---R (1430) ------------------------------------- +--R (1437) ------------------------------------- --R 2 --R Type: Expression Integer --E 1437 @@ -59759,7 +63584,7 @@ m0267:=a0267-r0267 d0267:=D(m0267,x) --R --R ---R (1431) 0 +--R (1438) 0 --R Type: Expression Integer --E 1438 @@ -59769,7 +63594,7 @@ t0268:= (1+x^6)/(x-x^7) --R --R 6 --R - x - 1 ---R (1432) -------- +--R (1439) -------- --R 7 --R x - x --R Type: Fraction Polynomial Integer @@ -59781,7 +63606,7 @@ r0268:= log(x)-1/3*log(1-x^6) --R --R 6 --R 3log(x) - log(- x + 1) ---R (1433) ----------------------- +--R (1440) ----------------------- --R 3 --R Type: Expression Integer --E 1440 @@ -59792,7 +63617,7 @@ a0268:=integrate(t0268,x) --R --R 6 --R - log(x - 1) + 3log(x) ---R (1434) ----------------------- +--R (1441) ----------------------- --R 3 --R Type: Union(Expression Integer,...) --E 1441 @@ -59803,7 +63628,7 @@ m0268:=a0268-r0268 --R --R 6 6 --R - log(x - 1) + log(- x + 1) ---R (1435) ----------------------------- +--R (1442) ----------------------------- --R 3 --R Type: Expression Integer --E 1442 @@ -59812,7 +63637,7 @@ m0268:=a0268-r0268 d0268:=D(m0268,x) --R --R ---R (1436) 0 +--R (1443) 0 --R Type: Expression Integer --E 1443 @@ -59822,7 +63647,7 @@ t0269:= (8+5*x^10)/(x-x^11) --R --R 10 --R - 5x - 8 ---R (1437) ---------- +--R (1444) ---------- --R 11 --R x - x --R Type: Fraction Polynomial Integer @@ -59834,7 +63659,7 @@ r0269:= 8*log(x)-13/10*log(1-x^10) --R --R 10 --R 80log(x) - 13log(- x + 1) ---R (1438) --------------------------- +--R (1445) --------------------------- --R 10 --R Type: Expression Integer --E 1445 @@ -59845,7 +63670,7 @@ a0269:=integrate(t0269,x) --R --R 10 --R - 13log(x - 1) + 80log(x) ---R (1439) --------------------------- +--R (1446) --------------------------- --R 10 --R Type: Union(Expression Integer,...) --E 1446 @@ -59856,7 +63681,7 @@ m0269:=a0269-r0269 --R --R 10 10 --R - 13log(x - 1) + 13log(- x + 1) ---R (1440) ----------------------------------- +--R (1447) ----------------------------------- --R 10 --R Type: Expression Integer --E 1447 @@ -59865,7 +63690,7 @@ m0269:=a0269-r0269 d0269:=D(m0269,x) --R --R ---R (1441) 0 +--R (1448) 0 --R Type: Expression Integer --E 1448 @@ -59875,7 +63700,7 @@ t0270:= (1+x^2)/x/(3+x^2) --R --R 2 --R x + 1 ---R (1442) ------- +--R (1449) ------- --R 3 --R x + 3x --R Type: Fraction Polynomial Integer @@ -59887,7 +63712,7 @@ r0270:= 1/3*log(x)+1/3*log(3+x^2) --R --R 2 --R log(x + 3) + log(x) ---R (1443) -------------------- +--R (1450) -------------------- --R 3 --R Type: Expression Integer --E 1450 @@ -59898,7 +63723,7 @@ a0270:=integrate(t0270,x) --R --R 3 --R log(x + 3x) ---R (1444) ------------ +--R (1451) ------------ --R 3 --R Type: Union(Expression Integer,...) --E 1451 @@ -59909,7 +63734,7 @@ m0270:=a0270-r0270 --R --R 3 2 --R log(x + 3x) - log(x + 3) - log(x) ---R (1445) ----------------------------------- +--R (1452) ----------------------------------- --R 3 --R Type: Expression Integer --E 1452 @@ -59918,7 +63743,7 @@ m0270:=a0270-r0270 d0270:=D(m0270,x) --R --R ---R (1446) 0 +--R (1453) 0 --R Type: Expression Integer --E 1453 @@ -59928,7 +63753,7 @@ t0271:= (1+x^6)/x/(1-x^6) --R --R 6 --R - x - 1 ---R (1447) -------- +--R (1454) -------- --R 7 --R x - x --R Type: Fraction Polynomial Integer @@ -59940,7 +63765,7 @@ r0271:= log(x)-1/3*log(1-x^6) --R --R 6 --R 3log(x) - log(- x + 1) ---R (1448) ----------------------- +--R (1455) ----------------------- --R 3 --R Type: Expression Integer --E 1455 @@ -59951,7 +63776,7 @@ a0271:=integrate(t0271,x) --R --R 6 --R - log(x - 1) + 3log(x) ---R (1449) ----------------------- +--R (1456) ----------------------- --R 3 --R Type: Union(Expression Integer,...) --E 1456 @@ -59962,7 +63787,7 @@ m0271:=a0271-r0271 --R --R 6 6 --R - log(x - 1) + log(- x + 1) ---R (1450) ----------------------------- +--R (1457) ----------------------------- --R 3 --R Type: Expression Integer --E 1457 @@ -59971,7 +63796,7 @@ m0271:=a0271-r0271 d0271:=D(m0271,x) --R --R ---R (1451) 0 +--R (1458) 0 --R Type: Expression Integer --E 1458 @@ -59980,7 +63805,7 @@ t0272:= (x+x^2)/(-2*x-x^2+x^3) --R --R --R 1 ---R (1452) ----- +--R (1459) ----- --R x - 2 --R Type: Fraction Polynomial Integer --E 1459 @@ -59989,7 +63814,7 @@ t0272:= (x+x^2)/(-2*x-x^2+x^3) r0272:= log(2-x) --R --R ---R (1453) log(- x + 2) +--R (1460) log(- x + 2) --R Type: Expression Integer --E 1460 @@ -59997,7 +63822,7 @@ r0272:= log(2-x) a0272:=integrate(t0272,x) --R --R ---R (1454) log(x - 2) +--R (1461) log(x - 2) --R Type: Union(Expression Integer,...) --E 1461 @@ -60005,7 +63830,7 @@ a0272:=integrate(t0272,x) m0272:=a0272-r0272 --R --R ---R (1455) log(x - 2) - log(- x + 2) +--R (1462) log(x - 2) - log(- x + 2) --R Type: Expression Integer --E 1462 @@ -60013,7 +63838,7 @@ m0272:=a0272-r0272 d0272:=D(m0272,x) --R --R ---R (1456) 0 +--R (1463) 0 --R Type: Expression Integer --E 1463 @@ -60021,7 +63846,7 @@ d0272:=D(m0272,x) t0273:= (b*c-a*d-2*a*e*x-b*e*x^2-3*a*f*x^2-2*b*f*x^3)/(c+d*x+e*x^2+f*x^3)^2 --R --R ---R (1457) +--R (1464) --R 3 2 --R - 2b f x + (- 3a f - b e)x - 2a e x - a d + b c --R / @@ -60038,7 +63863,7 @@ r0273:= (a+b*x)/(c+d*x+e*x^2+f*x^3) --R --R --R b x + a ---R (1458) --------------------- +--R (1465) --------------------- --R 3 2 --R f x + e x + d x + c --R Type: Fraction Polynomial Integer @@ -60049,7 +63874,7 @@ a0273:=integrate(t0273,x) --R --R --R b x + a ---R (1459) --------------------- +--R (1466) --------------------- --R 3 2 --R f x + e x + d x + c --R Type: Union(Expression Integer,...) @@ -60059,7 +63884,7 @@ a0273:=integrate(t0273,x) m0273:=a0273-r0273 --R --R ---R (1460) 0 +--R (1467) 0 --R Type: Expression Integer --E 1467 @@ -60067,7 +63892,7 @@ m0273:=a0273-r0273 d0273:=D(m0273,x) --R --R ---R (1461) 0 +--R (1468) 0 --R Type: Expression Integer --E 1468 @@ -60077,7 +63902,7 @@ t0274:= (9-40*x-18*x^2+174*x^4+24*x^5+26*x^6-39*x^8)/(3+2*x^2+x^4)^3 --R --R 8 6 5 4 2 --R - 39x + 26x + 24x + 174x - 18x - 40x + 9 ---R (1462) --------------------------------------------- +--R (1469) --------------------------------------------- --R 12 10 8 6 4 2 --R x + 6x + 21x + 44x + 63x + 54x + 27 --R Type: Fraction Polynomial Integer @@ -60089,7 +63914,7 @@ r0274:= (2+3*x-4*x^2+13*x^5)/(3+2*x^2+x^4)^2 --R --R 5 2 --R 13x - 4x + 3x + 2 ---R (1463) -------------------------- +--R (1470) -------------------------- --R 8 6 4 2 --R x + 4x + 10x + 12x + 9 --R Type: Fraction Polynomial Integer @@ -60101,7 +63926,7 @@ a0274:=integrate(t0274,x) --R --R 5 2 --R 13x - 4x + 3x + 2 ---R (1464) -------------------------- +--R (1471) -------------------------- --R 8 6 4 2 --R x + 4x + 10x + 12x + 9 --R Type: Union(Expression Integer,...) @@ -60111,7 +63936,7 @@ a0274:=integrate(t0274,x) m0274:=a0274-r0274 --R --R ---R (1465) 0 +--R (1472) 0 --R Type: Expression Integer --E 1472 @@ -60119,7 +63944,7 @@ m0274:=a0274-r0274 d0274:=D(m0274,x) --R --R ---R (1466) 0 +--R (1473) 0 --R Type: Expression Integer --E 1473 @@ -60128,7 +63953,7 @@ t0275:= (-3+10*x+4*x^3-30*x^5)/(3+x+x^4)^3-_ 3*(1+4*x^3)*(2-3*x+5*x^2+x^4-5*x^6)/(3+x+x^4)^4 --R --R ---R (1467) +--R (1474) --R 9 7 6 5 4 3 2 --R 30x - 8x - 15x - 140x + 34x - 12x - 5x + 36x - 15 --R / @@ -60146,7 +63971,7 @@ r0275:= (2-3*x+5*x^2+x^4-5*x^6)/(3+x+x^4)^3 --R --R 6 4 2 --R - 5x + x + 5x - 3x + 2 ---R (1468) --------------------------------------------------------- +--R (1475) --------------------------------------------------------- --R 12 9 8 6 5 4 3 2 --R x + 3x + 9x + 3x + 18x + 27x + x + 9x + 27x + 27 --R Type: Fraction Polynomial Integer @@ -60158,7 +63983,7 @@ a0275:=integrate(t0275,x) --R --R 6 4 2 --R - 5x + x + 5x - 3x + 2 ---R (1469) --------------------------------------------------------- +--R (1476) --------------------------------------------------------- --R 12 9 8 6 5 4 3 2 --R x + 3x + 9x + 3x + 18x + 27x + x + 9x + 27x + 27 --R Type: Union(Expression Integer,...) @@ -60168,7 +63993,7 @@ a0275:=integrate(t0275,x) m0275:=a0275-r0275 --R --R ---R (1470) 0 +--R (1477) 0 --R Type: Expression Integer --E 1477 @@ -60176,7 +64001,7 @@ m0275:=a0275-r0275 d0275:=D(m0275,x) --R --R ---R (1471) 0 +--R (1478) 0 --R Type: Expression Integer --E 1478 @@ -60185,7 +64010,7 @@ t0276:= 1/(1+x^2)/(3+10*x/(1+x^2)) --R --R --R 1 ---R (1472) ------------- +--R (1479) ------------- --R 2 --R 3x + 10x + 3 --R Type: Fraction Polynomial Integer @@ -60198,7 +64023,7 @@ r0276:= -1/4*atanh(5/4+3/4*x) --R 3x + 5 --R atanh(------) --R 4 ---R (1473) - ------------- +--R (1480) - ------------- --R 4 --R Type: Expression Integer --E 1480 @@ -60208,7 +64033,7 @@ a0276:=integrate(t0276,x) --R --R --R log(3x + 1) - log(x + 3) ---R (1474) ------------------------ +--R (1481) ------------------------ --R 8 --R Type: Union(Expression Integer,...) --E 1481 @@ -60220,7 +64045,7 @@ m0276:=a0276-r0276 --R 3x + 5 --R log(3x + 1) - log(x + 3) + 2atanh(------) --R 4 ---R (1475) ----------------------------------------- +--R (1482) ----------------------------------------- --R 8 --R Type: Expression Integer --E 1482 @@ -60229,7 +64054,7 @@ m0276:=a0276-r0276 d0276:=D(m0276,x) --R --R ---R (1476) 0 +--R (1483) 0 --R Type: Expression Integer --E 1483