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Chapter 3
Listing of integrals
3.1
\(\int \frac {1}{a^2-b^2 x^2} \, dx\)
3.2
\(\int \frac {1}{a^2+b^2 x^2} \, dx\)
3.3
\(\int \sec (2 a x) \, dx\)
3.4
\(\int \frac {1}{4} \csc (\frac {x}{3}) \, dx\)
3.5
\(\int -\sec (\frac {\pi }{4}+2 x) \, dx\)
3.6
\(\int \sec (x) \tan (x) \, dx\)
3.7
\(\int \cot (x) \csc (x) \, dx\)
3.8
\(\int \csc (2 x) \tan (x) \, dx\)
3.9
\(\int \frac {1}{1+\cos (x)} \, dx\)
3.10
\(\int \frac {1}{1-\cos (x)} \, dx\)
3.11
\(\int \frac {\sin (x)}{a-b \cos (x)} \, dx\)
3.12
\(\int \frac {\cos (x)}{a^2+b^2 \sin ^2(x)} \, dx\)
3.13
\(\int \frac {\cos (x)}{a^2-b^2 \sin ^2(x)} \, dx\)
3.14
\(\int \frac {\sin (2 x)}{a^2+b^2 \sin ^2(x)} \, dx\)
3.15
\(\int \frac {\sin (2 x)}{a^2-b^2 \sin ^2(x)} \, dx\)
3.16
\(\int \frac {\sin (2 x)}{a^2+b^2 \cos ^2(x)} \, dx\)
3.17
\(\int \frac {\sin (2 x)}{a^2-b^2 \cos ^2(x)} \, dx\)
3.18
\(\int \frac {1}{4-\cos ^2(x)} \, dx\)
3.19
\(\int \frac {e^x}{-1+e^{2 x}} \, dx\)
3.20
\(\int \frac {1}{x \log (x)} \, dx\)
3.21
\(\int \frac {1}{x (1+\log ^2(x))} \, dx\)
3.22
\(\int \frac {1}{x (1-\log (x))} \, dx\)
3.23
\(\int \frac {1}{x (1+\log (\frac {x}{a}))} \, dx\)
3.24
\(\int \frac {(1-\sqrt {x}+x)^2}{x^2} \, dx\)
3.25
\(\int \frac {(2-x^{2/3}) (\sqrt {x}+x)}{x^{3/2}} \, dx\)
3.26
\(\int \frac {-1+2 x}{3+2 x} \, dx\)
3.27
\(\int \frac {-5+2 x}{-2+3 x^2} \, dx\)
3.28
\(\int \frac {-5+2 x}{2+3 x^2} \, dx\)
3.29
\(\int \sin (\frac {x}{4}) \sin (x) \, dx\)
3.30
\(\int \cos (3 x) \cos (4 x) \, dx\)
3.31
\(\int -\tan (a-x) \tan (x) \, dx\)
3.32
\(\int \sin ^2(x) \, dx\)
3.33
\(\int \cos ^2(x) \, dx\)
3.34
\(\int \cos ^3(x) \sin (x) \, dx\)
3.35
\(\int \cot ^3(x) \csc (x) \, dx\)
3.36
\(\int \csc ^2(x) \sec ^2(x) \, dx\)
3.37
\(\int \cot ^2(\frac {3 x}{4}) \, dx\)
3.38
\(\int (1+\tan (2 x))^2 \, dx\)
3.39
\(\int (-\cot (x)+\tan (x))^2 \, dx\)
3.40
\(\int (-\sec (x)+\tan (x))^2 \, dx\)
3.41
\(\int \frac {\sin (x)}{1+\sin (x)} \, dx\)
3.42
\(\int \frac {\cos (x)}{1-\cos (x)} \, dx\)
3.43
\(\int e^{-x/2} (-1+e^{x/2})^3 \, dx\)
3.44
\(\int \frac {1}{5-6 x+x^2} \, dx\)
3.45
\(\int \frac {x^2}{13-6 x^3+x^6} \, dx\)
3.46
\(\int \frac {2+x}{-1-4 x+x^2} \, dx\)
3.47
\(\int \frac {1}{1+\sqrt [3]{1+x}} \, dx\)
3.48
\(\int \frac {1}{\sqrt {x} (b+a x)} \, dx\)
3.49
\(\int x^3 \sqrt {1+x^2} \, dx\)
3.50
\(\int \frac {x}{\sqrt {a^4-x^4}} \, dx\)
3.51
\(\int \frac {1}{x \sqrt {-a^2+x^2}} \, dx\)
3.52
\(\int \frac {1}{x \sqrt {a^2-x^2}} \, dx\)
3.53
\(\int \frac {1}{x \sqrt {a^2+x^2}} \, dx\)
3.54
\(\int \frac {1}{\sqrt {2+x-x^2}} \, dx\)
3.55
\(\int \frac {1}{\sqrt {5-4 x+3 x^2}} \, dx\)
3.56
\(\int \frac {1}{\sqrt {x-x^2}} \, dx\)
3.57
\(\int \frac {1+2 x}{\sqrt {2+x-x^2}} \, dx\)
3.58
\(\int \frac {1}{x \sqrt {2+x-x^2}} \, dx\)
3.59
\(\int \frac {1}{(-2+x) \sqrt {2+x-x^2}} \, dx\)
3.60
\(\int \frac {\csc (x) (2+3 \sin (x))}{1-\cos (x)} \, dx\)
3.61
\(\int \frac {1}{2+3 \cos ^2(x)} \, dx\)
3.62
\(\int \csc (2 x) (1-\tan (x)) \, dx\)
3.63
\(\int \frac {1+\tan ^2(x)}{1-\tan ^2(x)} \, dx\)
3.64
\(\int (a^2-4 \cos ^2(x))^{3/4} \sin (2 x) \, dx\)
3.65
\(\int \frac {\sin (2 x)}{\sqrt [3]{a^2-4 \sin ^2(x)}} \, dx\)
3.66
\(\int \frac {1}{\sqrt {-1+a^{2 x}}} \, dx\)
3.67
\(\int \frac {e^{x/2}}{\sqrt {-1+e^x}} \, dx\)
3.68
\(\int \frac {\tan ^{-1}(x)^n}{1+x^2} \, dx\)
3.69
\(\int \frac {\sin ^{-1}(\frac {x}{a})^{3/2}}{\sqrt {a^2-x^2}} \, dx\)
3.70
\(\int \frac {1}{\sqrt {1-x^2} \cos ^{-1}(x)^3} \, dx\)
3.71
\(\int x \log ^2(x) \, dx\)
3.72
\(\int \frac {\log (x)}{x^5} \, dx\)
3.73
\(\int x^2 \log (\frac {-1+x}{x}) \, dx\)
3.74
\(\int \cos ^5(x) \, dx\)
3.75
\(\int \cos ^4(x) \sin ^2(x) \, dx\)
3.76
\(\int \csc ^5(x) \, dx\)
3.77
\(\int e^{-x} \sin (x) \, dx\)
3.78
\(\int e^{2 x} \sin (3 x) \, dx\)
3.79
\(\int a^x \cos (x) \, dx\)
3.80
\(\int \cos (\log (x)) \, dx\)
3.81
\(\int \log (\cos (x)) \sec ^2(x) \, dx\)
3.82
\(\int x \tan ^2(x) \, dx\)
3.83
\(\int \frac {\sin ^{-1}(x)}{x^2} \, dx\)
3.84
\(\int \sin ^{-1}(x)^2 \, dx\)
3.85
\(\int \frac {x^2 \tan ^{-1}(x)}{1+x^2} \, dx\)
3.86
\(\int \cos ^{-1}(\sqrt {\frac {x}{1+x}}) \, dx\)
3.87
\(\int (2 x+3 x^2)^3 \, dx\)
3.88
\(\int (-1+x) (-1+2 x+3 x^2)^2 \, dx\)
3.89
\(\int x^{-1+k} (a+b x^k)^n \, dx\)
3.90
\(\int \frac {x^3}{1+2 x} \, dx\)
3.91
\(\int \frac {x^6}{2+3 x^2} \, dx\)
3.92
\(\int \frac {1}{2-7 x+3 x^2} \, dx\)
3.93
\(\int \frac {-1+3 x}{1-x+x^2} \, dx\)
3.94
\(\int \frac {x^2}{5+2 x+x^2} \, dx\)
3.95
\(\int \frac {4 x^2-5 x^3+6 x^4}{1-x+2 x^2} \, dx\)
3.96
\(\int \frac {-1+x+x^2}{-6 x+x^2+x^3} \, dx\)
3.97
\(\int \frac {11 a^2-7 a x+5 x^2}{-6 a^3+11 a^2 x-6 a x^2+x^3} \, dx\)
3.98
\(\int \frac {2-x+x^2}{4-5 x^2+x^4} \, dx\)
3.99
\(\int \frac {-5+2 x^2}{6-5 x^2+x^4} \, dx\)
3.100
\(\int \frac {1}{(-4+x) (-3+x) (-2+x) (-1+x)} \, dx\)
3.101
\(\int \frac {1+x^2}{(-1+x)^3} \, dx\)
3.102
\(\int \frac {x^5}{(3+x)^2} \, dx\)
3.103
\(\int \frac {-2+5 x^3}{-27+18 x^2-8 x^3+x^4} \, dx\)
3.104
\(\int \frac {-9+3 x-6 x^2+x^3}{(3+x)^2 (4+x)^2} \, dx\)
3.105
\(\int \frac {2+x^2+x^3}{x (-1+x^2)^2} \, dx\)
3.106
\(\int \frac {1}{x^3-x^4-x^5+x^6} \, dx\)
3.107
\(\int \frac {1+x^4}{-1+x-x^2+x^3} \, dx\)
3.108
\(\int \frac {1}{x (1+x) (1+x^2)} \, dx\)
3.109
\(\int \frac {x^2}{-2+x^2+x^4} \, dx\)
3.110
\(\int \frac {6 x+4 x^2+x^3}{2+4 x+3 x^2+2 x^3+x^4} \, dx\)
3.111
\(\int \frac {x}{(1+x) (1+2 x)^2 (1+x^2)} \, dx\)
3.112
\(\int \frac {-2+x+3 x^2}{(-1+x)^3 (1+x^2)} \, dx\)
3.113
\(\int \frac {1}{1+x^2+x^4} \, dx\)
3.114
\(\int \frac {3+2 x^3}{-9 x+x^5} \, dx\)
3.115
\(\int \frac {-20+8 x+5 x^3}{(-4+x)^3 (8-4 x+x^2)} \, dx\)
3.116
\(\int \frac {1}{(1+x^2) (2+x^2) (3+x^2) (4+x^2)} \, dx\)
3.117
\(\int \frac {x}{(1+x^2) (2+x^2) (3+x^2) (4+x^2)} \, dx\)
3.118
\(\int \frac {1}{a^3+x^3} \, dx\)
3.119
\(\int \frac {x}{a^3+x^3} \, dx\)
3.120
\(\int \frac {x^2}{a^3+x^3} \, dx\)
3.121
\(\int \frac {1}{x (a^3+x^3)} \, dx\)
3.122
\(\int \frac {1}{x^2 (a^3+x^3)} \, dx\)
3.123
\(\int \frac {1}{x^3 (a^3+x^3)} \, dx\)
3.124
\(\int \frac {1}{x^4 (a^3+x^3)} \, dx\)
3.125
\(\int \frac {1}{x^5 (a^3+x^3)} \, dx\)
3.126
\(\int \frac {x^{-m}}{a^3+x^3} \, dx\)
3.127
\(\int \frac {1}{a^4-x^4} \, dx\)
3.128
\(\int \frac {x}{a^4-x^4} \, dx\)
3.129
\(\int \frac {1}{x (a^4-x^4)} \, dx\)
3.130
\(\int \frac {1}{x^2 (a^4-x^4)} \, dx\)
3.131
\(\int \frac {1}{x^3 (a^4-x^4)} \, dx\)
3.132
\(\int \frac {1}{x^4 (a^4-x^4)} \, dx\)
3.133
\(\int \frac {x^{-m}}{a^4-x^4} \, dx\)
3.134
\(\int \frac {x}{a^4+x^4} \, dx\)
3.135
\(\int \frac {x^2}{a^4+x^4} \, dx\)
3.136
\(\int \frac {1}{a^5+x^5} \, dx\)
3.137
\(\int \frac {x}{a^5+x^5} \, dx\)
3.138
\(\int \frac {x^2}{a^5+x^5} \, dx\)
3.139
\(\int \frac {x^3}{a^5+x^5} \, dx\)
3.140
\(\int \frac {x^4}{a^5+x^5} \, dx\)
3.141
\(\int \frac {1}{x (a^5+x^5)} \, dx\)
3.142
\(\int \frac {1}{x^2 (a^5+x^5)} \, dx\)
3.143
\(\int \frac {1}{x^3 (a^5+x^5)} \, dx\)
3.144
\(\int \frac {1}{x^4 (a^5+x^5)} \, dx\)
3.145
\(\int \frac {x^{-m}}{a^5+x^5} \, dx\)
3.146
\(\int \frac {1+x^4}{1+x^6} \, dx\)
3.147
\(\int \frac {1}{(5+3 x+x^2)^3} \, dx\)
3.148
\(\int \frac {1+x^2+x^4}{(1+x^2)^4} \, dx\)
3.149
\(\int \frac {B+A x}{(c+2 b x+a x^2)^2} \, dx\)
3.150
\(\int \frac {-41+55 x-27 x^2+5 x^3}{(5-4 x+x^2)^2} \, dx\)
3.151
\(\int \frac {1}{(-1+x^3)^2} \, dx\)
3.152
\(\int \frac {4+3 x^4}{x^2 (1+x^2)^3} \, dx\)
3.153
\(\int \frac {x}{1+x^6} \, dx\)
3.154
\(\int \frac {-1+x^{-1+n}}{-n x+x^n} \, dx\)
3.155
\(\int \frac {x^3}{1-2 x^2+3 x^4} \, dx\)
3.156
\(\int \frac {x^5}{-4+x^2+3 x^4} \, dx\)
3.157
\(\int \frac {x^2}{9-10 x^3+x^6} \, dx\)
3.158
\(\int \frac {1-4 x^2+x^3}{(-2+x)^4} \, dx\)
3.159
\(\int \frac {x^3}{(-1+x)^{12}} \, dx\)
3.160
\(\int \frac {-3 x+x^4}{(1+2 x)^5} \, dx\)
3.161
\(\int \frac {1}{(-1+x)^2 (1+x)^3} \, dx\)
3.162
\(\int \frac {1}{(5-6 x)^2 x^2} \, dx\)
3.163
\(\int \frac {1}{(-3-2 x+x^2)^3} \, dx\)
3.164
\(\int \frac {1}{(13-4 x+x^2)^3} \, dx\)
3.165
\(\int \frac {1}{(2+x)^3 (3+x)^4} \, dx\)
3.166
\(\int \frac {x^6}{(-2+x^2)^2} \, dx\)
3.167
\(\int \frac {x^8}{(4+x^2)^4} \, dx\)
3.168
\(\int \frac {-4+7 x}{(5+2 x+3 x^2)^2} \, dx\)
3.169
\(\int \frac {5-4 x}{(-2-4 x+3 x^2)^2} \, dx\)
3.170
\(\int \frac {x^5}{(1+x^4)^3} \, dx\)
3.171
\(\int \frac {x (1+x^2)^3}{(2+2 x^2+x^4)^2} \, dx\)
3.172
\(\int \frac {x^3}{(a^4+x^4)^3} \, dx\)
3.173
\(\int \frac {1}{x (a^4+x^4)^3} \, dx\)
3.174
\(\int \frac {1}{x^2 (a^4+x^4)^3} \, dx\)
3.175
\(\int \frac {1}{x^3 (a^4+x^4)^3} \, dx\)
3.176
\(\int \frac {x^{14}}{(3+2 x^5)^3} \, dx\)
3.177
\(\int \frac {x^6}{(3+2 x^5)^3} \, dx\)
3.178
\(\int \frac {9}{5 x^2 (3-2 x^2)^3} \, dx\)
3.179
\(\int \frac {4+3 x^4}{x^2 (1+x^2)^3} \, dx\)
3.180
\(\int \frac {5-3 x+6 x^2+5 x^3-x^4}{-1+x+2 x^2-2 x^3-x^4+x^5} \, dx\)
3.181
\(\int \frac {1+x^2}{x (1+x^3)^2} \, dx\)
3.182
\(\int \frac {-2-3 x+x^2}{(1+x)^2 (1+x+x^2)^2} \, dx\)
3.183
\(\int \frac {1}{(1-4 x)^3 (2-3 x)} \, dx\)
3.184
\(\int \frac {x^3}{(2-5 x^2)^7} \, dx\)
3.185
\(\int \frac {x^7}{(2-5 x^2)^3} \, dx\)
3.186
\(\int \frac {1}{(-2+x)^3 (1+x)^2} \, dx\)
3.187
\(\int \frac {1}{(2+x)^3 (3+x)^4} \, dx\)
3.188
\(\int \frac {x^5}{(3+x)^2} \, dx\)
3.189
\(\int (\text {b1}+\text {c1} x) (a+2 b x+c x^2) \, dx\)
3.190
\(\int (\text {b1}+\text {c1} x) (a+2 b x+c x^2)^2 \, dx\)
3.191
\(\int (\text {b1}+\text {c1} x) (a+2 b x+c x^2)^3 \, dx\)
3.192
\(\int (\text {b1}+\text {c1} x) (a+2 b x+c x^2)^4 \, dx\)
3.193
\(\int (\text {b1}+\text {c1} x) (a+2 b x+c x^2)^n \, dx\)
3.194
\(\int \frac {\text {b1}+\text {c1} x}{a+2 b x+c x^2} \, dx\)
3.195
\(\int \frac {\text {b1}+\text {c1} x}{(a+2 b x+c x^2)^2} \, dx\)
3.196
\(\int \frac {\text {b1}+\text {c1} x}{(a+2 b x+c x^2)^3} \, dx\)
3.197
\(\int \frac {\text {b1}+\text {c1} x}{(a+2 b x+c x^2)^4} \, dx\)
3.198
\(\int (\text {b1}+\text {c1} x) (a+2 b x+c x^2)^{-n} \, dx\)
3.199
\(\int \frac {x}{3+6 x+2 x^2} \, dx\)
3.200
\(\int \frac {-3+2 x}{(3+6 x+2 x^2)^3} \, dx\)
3.201
\(\int \frac {-1+x}{(4+5 x+x^2)^2} \, dx\)
3.202
\(\int \frac {1}{(2+3 x+x^2)^5} \, dx\)
3.203
\(\int \frac {1}{x^3 (7-6 x+2 x^2)^2} \, dx\)
3.204
\(\int \frac {x^9}{(2+3 x+x^2)^5} \, dx\)
3.205
\(\int \frac {(1+2 x)^2}{(3+5 x+2 x^2)^5} \, dx\)
3.206
\(\int \frac {(a-b x^2)^3}{x^7} \, dx\)
3.207
\(\int \frac {x^{13}}{(a^4+x^4)^5} \, dx\)
3.208
\(\int (2 \sqrt {x}-x)^2 x^{3/2} (1+x^2) \, dx\)
3.209
\(\int (-3 x^{3/5}+x^{3/2})^2 (-\frac {x^{2/3}}{3}+4 x^{3/2}) \, dx\)
3.210
\(\int \frac {1}{1+\sqrt {1+x}} \, dx\)
3.211
\(\int \frac {x}{1+\sqrt {1+x}} \, dx\)
3.212
\(\int \frac {1+\sqrt {1+x}}{-1+\sqrt {1+x}} \, dx\)
3.213
\(\int \frac {1}{-\sqrt {1+x}+(1+x)^{2/3}} \, dx\)
3.214
\(\int \frac {\sqrt [3]{1+\sqrt [4]{x}}}{\sqrt {x}} \, dx\)
3.215
\(\int \frac {1}{x^3 (1+x)^{3/2}} \, dx\)
3.216
\(\int \frac {1}{(1-x)^{7/2} x^5} \, dx\)
3.217
\(\int \frac {1}{(-1+x)^{2/3} x^5} \, dx\)
3.218
\(\int \sqrt {\frac {1-x}{1+x}} \, dx\)
3.219
\(\int x \sqrt {\frac {-a+x}{b-x}} \, dx\)
3.220
\(\int \frac {\sqrt {-5+x} \sqrt {3+x}}{(-1+x) (-25+x^2)} \, dx\)
3.221
\(\int \frac {x^2 \sqrt {1+x} \sqrt [4]{1-x^2}}{\sqrt {1-x} (\sqrt {1-x}-\sqrt {1+x})} \, dx\)
3.222
\(\int \frac {\sqrt {1-x} x (1+x)^{2/3}}{-(1-x)^{5/6} \sqrt [3]{1+x}+(1-x)^{2/3} \sqrt {1+x}} \, dx\)
3.223
\(\int \frac {1}{\sqrt [3]{(-1+x)^4 (1+x)^2}} \, dx\)
3.224
\(\int \frac {1}{\sqrt [4]{(-1+x)^3 (2+x)^5}} \, dx\)
3.225
\(\int \frac {1}{\sqrt [3]{(-1+x)^7 (1+x)^2}} \, dx\)
3.226
\(\int \frac {1}{\sqrt [3]{(-1+x)^2 (1+x)}} \, dx\)
3.227
\(\int \frac {\frac {1}{x}+x}{\sqrt {(-2+x) (1+x)^3}} \, dx\)
3.228
\(\int \frac {\sqrt [3]{(-1+x)^2 (1+x)}}{x^2} \, dx\)
3.229
\(\int \frac {1}{(-3-2 x+x^2)^{5/2}} \, dx\)
3.230
\(\int \frac {1}{\sqrt {9+3 x-5 x^2+x^3}} \, dx\)
3.231
\(\int \frac {1}{(9+3 x-5 x^2+x^3)^{3/2}} \, dx\)
3.232
\(\int \frac {1}{\sqrt [3]{9+3 x-5 x^2+x^3}} \, dx\)
3.233
\(\int \frac {1}{(9+3 x-5 x^2+x^3)^{2/3}} \, dx\)
3.234
\(\int \frac {1}{(9+3 x-5 x^2+x^3)^{4/3}} \, dx\)
3.235
\(\int \frac {1}{\sqrt {4+3 x-2 x^2}} \, dx\)
3.236
\(\int \frac {1}{\sqrt {-3+4 x-x^2}} \, dx\)
3.237
\(\int \frac {1}{\sqrt {-2-5 x-3 x^2}} \, dx\)
3.238
\(\int \frac {1}{\sqrt {1-x^2} (4+x^2)} \, dx\)
3.239
\(\int \frac {1}{(4+x^2) \sqrt {1+4 x^2}} \, dx\)
3.240
\(\int \frac {x}{(3-x^2) \sqrt {5-x^2}} \, dx\)
3.241
\(\int \frac {x}{\sqrt {3-x^2} (5-x^2)} \, dx\)
3.242
\(\int \frac {1}{\sqrt {2+x^2} (-1+x^4)} \, dx\)
3.243
\(\int \frac {x}{(-1+x^2) \sqrt {4+2 x+x^2}} \, dx\)
3.244
\(\int \frac {1}{\sqrt {5+2 x+x^2} (-8+x^3)} \, dx\)
3.245
\(\int \frac {x}{(4+x+x^2) \sqrt {5+4 x+4 x^2}} \, dx\)
3.246
\(\int \frac {3+x}{(1+x^2) \sqrt {1+x+x^2}} \, dx\)
3.247
\(\int \frac {1+2 x}{\sqrt {-1+6 x+x^2} (4+4 x+3 x^2)} \, dx\)
3.248
\(\int \frac {B+A x}{(17-18 x+5 x^2) \sqrt {13-22 x+10 x^2}} \, dx\)
3.249
\(\int \frac {-2+x}{(17-18 x+5 x^2) \sqrt {13-22 x+10 x^2}} \, dx\)
3.250
\(\int x^4 \sqrt {5-x^2} \, dx\)
3.251
\(\int \frac {1}{x^6 \sqrt {2+x^2}} \, dx\)
3.252
\(\int \frac {1}{(3+2 x^2)^{7/2}} \, dx\)
3.253
\(\int \frac {x}{1+x^2+a \sqrt {1+x^2}} \, dx\)
3.254
\(\int \frac {1-x+x^2}{(1+x^2)^{3/2}} \, dx\)
3.255
\(\int \frac {\sqrt {1+x^2}}{2+x^2} \, dx\)
3.256
\(\int \frac {1}{\sqrt {1+x^2} (2+x^2)^2} \, dx\)
3.257
\(\int \frac {x^2}{(-6+x^2) \sqrt {-2+x^2}} \, dx\)
3.258
\(\int \frac {5+x^2}{\sqrt {1-x^2} (1+x^2)^2} \, dx\)
3.259
\(\int \frac {4 x-\sqrt {1-x^2}}{5+\sqrt {1-x^2}} \, dx\)
3.260
\(\int \frac {x^2 (2-\sqrt {1+x^2})}{\sqrt {1+x^2} (1-x^3+(1+x^2)^{3/2})} \, dx\)
3.261
\(\int x \sqrt {2 r x-x^2} \, dx\)
3.262
\(\int x^2 \sqrt {2 r x-x^2} \, dx\)
3.263
\(\int x^3 \sqrt {2 r x-x^2} \, dx\)
3.264
\(\int \frac {1}{(-1+x^2) \sqrt {2 x+x^2}} \, dx\)
3.265
\(\int \frac {-2+3 x}{(1+x)^3 \sqrt {2 x-x^2}} \, dx\)
3.266
\(\int \frac {1}{\sqrt {1+x+x^2}} \, dx\)
3.267
\(\int \frac {x^3}{\sqrt {1+x+x^2}} \, dx\)
3.268
\(\int \frac {1}{(1+x+x^2)^{3/2}} \, dx\)
3.269
\(\int \frac {x}{(1+x+x^2)^{3/2}} \, dx\)
3.270
\(\int \frac {x^3}{(1+x+x^2)^{3/2}} \, dx\)
3.271
\(\int x^2 \sqrt {1+x+x^2} \, dx\)
3.272
\(\int (1+x+x^2)^{3/2} \, dx\)
3.273
\(\int (1+x+x^2)^{5/2} \, dx\)
3.274
\(\int \frac {1}{x^2 \sqrt {1+x+x^2}} \, dx\)
3.275
\(\int \frac {1}{x^3 \sqrt {1+x+x^2}} \, dx\)
3.276
\(\int \frac {1}{x^2 (1+x+x^2)^{3/2}} \, dx\)
3.277
\(\int \frac {1}{x^3 (1+x+x^2)^{3/2}} \, dx\)
3.278
\(\int \frac {1}{(1+x) \sqrt {1+x+x^2}} \, dx\)
3.279
\(\int \frac {1}{\sqrt {4+2 x+x^2} (-x+x^3)} \, dx\)
3.280
\(\int \frac {\sqrt {4+2 x+x^2}}{(-1+x)^2} \, dx\)
3.281
\(\int \frac {3+2 x}{(3+2 x+x^2)^2 \sqrt {4+2 x+x^2}} \, dx\)
3.282
\(\int \frac {3 x^2+2 x^3}{\sqrt {-3+2 x+x^2} (-3+x+2 x^2)} \, dx\)
3.283
\(\int \frac {1+x^4}{(1+x+x^2) \sqrt {2+x+x^2}} \, dx\)
3.284
\(\int \frac {1}{(4+2 x+x^2)^{7/2}} \, dx\)
3.285
\(\int \frac {1}{(1+8 x+3 x^2)^{5/2}} \, dx\)
3.286
\(\int \frac {1}{(5+4 x-3 x^2)^{5/2}} \, dx\)
3.287
\(\int \frac {1}{1+\sqrt {2+2 x+x^2}} \, dx\)
3.288
\(\int \frac {1}{x+\sqrt {1+x+x^2}} \, dx\)
3.289
\(\int \frac {x^2}{1+2 x+2 \sqrt {1+x+x^2}} \, dx\)
3.290
\(\int \frac {-3 x+\sqrt {1+x+x^2}}{-1+\sqrt {1+x+x^2}} \, dx\)
3.291
\(\int \frac {1+x}{-\sqrt {1+x+x^2}+\sqrt {4+2 x+x^2}} \, dx\)
3.292
\(\int \frac {1}{\sqrt {-1+x} x^3} \, dx\)
3.293
\(\int \frac {1}{(1-\frac {3}{x})^{4/3} x^2} \, dx\)
3.294
\(\int \frac {(-1+3 x)^{4/3}}{x^2} \, dx\)
3.295
\(\int (4-3 x)^{4/3} x^2 \, dx\)
3.296
\(\int \frac {(1-2 \sqrt [3]{x})^{3/4}}{x} \, dx\)
3.297
\(\int \frac {x}{(3-2 \sqrt {x})^{3/4}} \, dx\)
3.298
\(\int \frac {(-1+2 \sqrt {x})^{5/4}}{x^2} \, dx\)
3.299
\(\int x^6 \sqrt [3]{1+x^7} \, dx\)
3.300
\(\int \frac {x^6}{(1+x^7)^{5/3}} \, dx\)
3.301
\(\int \frac {1}{x (-27+2 x^7)^{2/3}} \, dx\)
3.302
\(\int \frac {(1+x^7)^{2/3}}{x^8} \, dx\)
3.303
\(\int \frac {\sqrt [4]{3+4 x^4}}{x^2} \, dx\)
3.304
\(\int x^2 (3+4 x^4)^{5/4} \, dx\)
3.305
\(\int x^6 \sqrt [4]{3+4 x^4} \, dx\)
3.306
\(\int \sqrt [3]{x (1-x^2)} \, dx\)
3.307
\(\int \sqrt {(1+\sqrt [3]{x}) x} \, dx\)
3.308
\(\int \frac {x^3}{(-1+x^4) \sqrt {1+2 x^8}} \, dx\)
3.309
\(\int x^9 \sqrt {1+x^5+x^{10}} \, dx\)
3.310
\(\int \frac {1}{x^5 \sqrt {4+2 x^2+x^4}} \, dx\)
3.311
\(\int \frac {-1+x^2}{x \sqrt {1+3 x^2+x^4}} \, dx\)
3.312
\(\int (-3 x+2 x^3) (-3 x^2+x^4)^{3/5} \, dx\)
3.313
\(\int \frac {-2 x^5+3 x^8-x^2 (-1+3 x^3)^{2/3}}{(-1+3 x^3)^{3/4}} \, dx\)
3.314
\(\int \frac {1}{(-1+x^3) \sqrt [3]{2+x^3}} \, dx\)
3.315
\(\int \frac {1}{(1+x^4) \sqrt [4]{2+x^4}} \, dx\)
3.316
\(\int \frac {-1+x^3}{\sqrt [3]{2+x^3}} \, dx\)
3.317
\(\int \frac {(1+x^4)^{3/4}}{(2+x^4)^2} \, dx\)
3.318
\(\int \frac {(-2+x^5)^2}{(3+x^5)^{16/5}} \, dx\)
3.319
\(\int \frac {1}{(3 x+3 x^2+x^3) \sqrt [3]{3+3 x+3 x^2+x^3}} \, dx\)
3.320
\(\int \frac {1-x^2}{(1+x^2) \sqrt {1+x^4}} \, dx\)
3.321
\(\int \frac {1+x^2}{(1-x^2) \sqrt {1+x^4}} \, dx\)
3.322
\(\int \frac {1+x^2}{x \sqrt {1+x^4}} \, dx\)
3.323
\(\int \frac {-1+x^2}{x \sqrt {1+x^4}} \, dx\)
3.324
\(\int \frac {1+x^2}{(1-x^2) \sqrt {1+x^2+x^4}} \, dx\)
3.325
\(\int \frac {1-x^2}{(1+x^2) \sqrt {1+x^2+x^4}} \, dx\)
3.326
\(\int \frac {-1+x^4}{x^2 \sqrt {1+x^2+x^4}} \, dx\)
3.327
\(\int \frac {1-x^2}{(1+2 a x+x^2) \sqrt {1+2 a x+2 b x^2+2 a x^3+x^4}} \, dx\)
3.328
\(\int \frac {1}{(1+x^4) \sqrt {-x^2+\sqrt {1+x^4}}} \, dx\)
3.329
\(\int \frac {1}{(1+x^{2 n}) \sqrt {-x^2+(1+x^{2 n})^{\frac {1}{n}}}} \, dx\)
3.330
\(\int \cos ^2(x) \, dx\)
3.331
\(\int \cos ^3(x) \, dx\)
3.332
\(\int \sin ^4(x) \, dx\)
3.333
\(\int \cos ^6(x) \, dx\)
3.334
\(\int \sin ^8(x) \, dx\)
3.335
\(\int \cos ^4(\frac {\pi }{4}+\frac {x}{2}) \, dx\)
3.336
\(\int -\sin ^3(\frac {\pi }{12}-3 x) \, dx\)
3.337
\(\int \csc ^6(x) \, dx\)
3.338
\(\int \csc ^7(x) \, dx\)
3.339
\(\int \sec ^{12}(x) \, dx\)
3.340
\(\int \sec ^3(\frac {\pi }{4}+3 x) \, dx\)
3.341
\(\int \tan ^6(x) \, dx\)
3.342
\(\int \cot ^5(x) \, dx\)
3.343
\(\int \cot ^4(\frac {\pi }{4}+\frac {x}{3}) \, dx\)
3.344
\(\int \cos ^6(x) \sin ^4(x) \, dx\)
3.345
\(\int \cos ^6(x) \sin ^7(x) \, dx\)
3.346
\(\int \sin ^{10}(x) \tan (x) \, dx\)
3.347
\(\int \csc ^6(x) \sec ^6(x) \, dx\)
3.348
\(\int \cos ^2(x) \sin ^2(x) \, dx\)
3.349
\(\int \cos ^4(x) \sin ^4(x) \, dx\)
3.350
\(\int \cos ^6(x) \sin ^6(x) \, dx\)
3.351
\(\int \cos ^8(x) \sin ^8(x) \, dx\)
3.352
\(\int \cos ^{2 m}(x) \sin ^{2 m}(x) \, dx\)
3.353
\(\int \csc ^3(\frac {\pi }{4}+2 x) \sec (\frac {\pi }{4}+2 x) \, dx\)
3.354
\(\int \sec ^2(x) \tan ^2(x) \, dx\)
3.355
\(\int \cot ^3(x) \csc (x) \, dx\)
3.356
\(\int \sec ^3(x) \tan (x) \, dx\)
3.357
\(\int \cot ^2(x) \csc ^3(x) \, dx\)
3.358
\(\int \cot ^3(x) \csc ^4(x) \, dx\)
3.359
\(\int \sec ^{\frac {13}{2}}(x) \sin ^5(x) \, dx\)
3.360
\(\int \sec ^4(x) \tan ^{\frac {3}{2}}(x) \, dx\)
3.361
\(\int \cot ^4(x) \csc ^3(x) \, dx\)
3.362
\(\int \sec ^3(\frac {\pi }{4}+\frac {x}{2}) \tan ^2(\frac {\pi }{4}+\frac {x}{2}) \, dx\)
3.363
\(\int (1+\cot ^3(x)) (a \sec ^2(x)-\sin (2 x))^2 \, dx\)
3.364
\(\int (4-3 \cos (x)) (1-\frac {\sin (x)}{2})^4 \, dx\)
3.365
\(\int (\frac {1}{2}-3 \cot (x)) (3-2 \cot (x))^3 \, dx\)
3.366
\(\int \cos (5 x) \sec ^5(x) \, dx\)
3.367
\(\int \cos (4 x) \sec (x) \, dx\)
3.368
\(\int \cos (x) \cos (4 x) \, dx\)
3.369
\(\int \cos (4 x) \sec ^5(x) \, dx\)
3.370
\(\int \cos ^4(x) \cos (4 x) \, dx\)
3.371
\(\int \cos (5 x) \csc ^5(x) \, dx\)
3.372
\(\int \csc ^4(x) \sin (4 x) \, dx\)
3.373
\(\int \frac {\cot (x)}{2+\sin (2 x)} \, dx\)
3.374
\(\int \cos (x) \cot (x) \sec (3 x) \, dx\)
3.375
\(\int \frac {\sin (2 x)}{\cos ^4(x)+\sin ^4(x)} \, dx\)
3.376
\(\int \frac {1}{4+\sqrt {3} \cos (x)+\sin (x)} \, dx\)
3.377
\(\int \frac {1}{3+4 \cos (x)+4 \sin (x)} \, dx\)
3.378
\(\int \frac {1}{4-3 \cos ^2(x)+5 \sin ^2(x)} \, dx\)
3.379
\(\int \frac {1}{4+4 \cot (x)+\tan (x)} \, dx\)
3.380
\(\int \frac {1}{(2 \sec (x)+\sin (x))^2} \, dx\)
3.381
\(\int \frac {1}{(\cos (x)+2 \sec (x))^2} \, dx\)
3.382
\(\int \frac {5-\tan (x)-6 \tan ^2(x)}{(1+3 \tan (x))^3} \, dx\)
3.383
\(\int \cos ^2(x) \sec (3 x) \, dx\)
3.384
\(\int \sec (2 x) \sin (x) \, dx\)
3.385
\(\int \sec (2 x) \sin ^2(x) \, dx\)
3.386
\(\int \sec (3 x) \sin ^3(x) \, dx\)
3.387
\(\int \cos (x) \csc (3 x) \, dx\)
3.388
\(\int \csc (4 x) \sin (x) \, dx\)
3.389
\(\int \csc (4 x) \sin ^3(x) \, dx\)
3.390
\(\int \sqrt {1+\sin (2 x)} \, dx\)
3.391
\(\int \sqrt {1-\sin (2 x)} \, dx\)
3.392
\(\int \frac {1}{\sqrt {1+\cos (2 x)}} \, dx\)
3.393
\(\int \frac {1}{\sqrt {1-\cos (2 x)}} \, dx\)
3.394
\(\int \frac {1}{(1-\cos (3 x))^{3/2}} \, dx\)
3.395
\(\int (1-\sin (\frac {2 x}{3}))^{5/2} \, dx\)
3.396
\(\int \frac {\cos (x) (-\cos ^2(x)+2 \sqrt [4]{1+2 \sin (x)})}{(1+2 \sin (x))^{3/2}} \, dx\)
3.397
\(\int \sqrt {\tan (x)} \, dx\)
3.398
\(\int \frac {1}{\sqrt [3]{\tan (5 x)}} \, dx\)
3.399
\(\int \frac {1}{(4+3 \tan (2 x))^{3/2}} \, dx\)
3.400
\(\int \frac {\sec ^2(x) (-\sqrt {4-3 \tan (x)}+3 \tan (x))}{(4-3 \tan (x))^{3/2}} \, dx\)
3.401
\(\int \frac {\tan (x)}{(-1+\sqrt {\tan (x)})^2} \, dx\)
3.402
\(\int \frac {\sin (x)}{\sqrt {\sin (2 x)}} \, dx\)
3.403
\(\int \frac {\cos (x)}{\sqrt {\sin (2 x)}} \, dx\)
3.404
\(\int \sin (x) \sqrt {\sin (2 x)} \, dx\)
3.405
\(\int (\cos (x)-\sin (x)) \sqrt {\sin (2 x)} \, dx\)
3.406
\(\int \frac {\sin ^7(x)}{\sin ^{\frac {7}{2}}(2 x)} \, dx\)
3.407
\(\int \frac {\cos ^7(x)}{\sin ^{\frac {7}{2}}(2 x)} \, dx\)
3.408
\(\int \csc ^5(x) \sin ^{\frac {3}{2}}(2 x) \, dx\)
3.409
\(\int \frac {\sec ^3(x)}{\sqrt {\sin (2 x)}} \, dx\)
3.410
\(\int \frac {\csc (x)}{\sin ^{\frac {3}{2}}(2 x)} \, dx\)
3.411
\(\int \frac {\cos ^3(x) (\cos (2 x)-3 \tan (x))}{(\sin ^2(x)-\sin (2 x)) \sin ^{\frac {5}{2}}(2 x)} \, dx\)
3.412
\(\int \sqrt {\sec ^4(x) \tan (x)} \, dx\)
3.413
\(\int \sqrt {\sin ^4(x) \tan (x)} \, dx\)
3.414
\(\int \sqrt [3]{\sec ^{12}(x) \tan ^2(x)} \, dx\)
3.415
\(\int \frac {1}{\sqrt [4]{\cos ^{11}(x) \sin ^{13}(x)}} \, dx\)
3.416
\(\int \frac {\cos (2 x)-\sqrt {\sin (2 x)}}{\sqrt {\cos ^3(x) \sin (x)}} \, dx\)
3.417
\(\int \frac {\sqrt {\cos (x) \sin ^3(x)}-2 \sin (2 x)}{-\sqrt {\cos ^3(x) \sin (x)}+\sqrt {\tan (x)}} \, dx\)
3.418
\(\int \frac {-3 \tan (x)+\sqrt [3]{\sec ^6(x) \tan (x)}}{(\cos ^5(x) \sin (x))^{2/3}} \, dx\)
3.419
\(\int (1+2 \cos ^2(x))^{5/2} \sin (x) \, dx\)
3.420
\(\int \cos (x) (5 \cos ^2(x)+\sin ^2(x))^{5/2} \, dx\)
3.421
\(\int \cos (x) (-\cos ^2(x)-5 \sin ^2(x))^{3/2} \, dx\)
3.422
\(\int \frac {\sin (x)}{(5 \cos ^2(x)-2 \sin ^2(x))^{7/2}} \, dx\)
3.423
\(\int \frac {\cos (x) \cos (2 x)}{(2-5 \sin ^2(x))^{3/2}} \, dx\)
3.424
\(\int \frac {\sin (5 x)}{(5 \cos ^2(x)+9 \sin ^2(x))^{5/2}} \, dx\)
3.425
\(\int \frac {\cos (x) \cos (2 x) \sin (3 x)}{(-5+4 \sin ^2(x))^{5/2}} \, dx\)
3.426
\(\int \frac {\csc ^2(x) (-2 \cos ^3(x) (-1+\sin (x))+\cos (2 x) \sin (x))}{\sqrt {-5+\sin ^2(x)}} \, dx\)
3.427
\(\int \frac {\cos (3 x)}{-\sqrt {-1+8 \cos ^2(x)}+\sqrt {3 \cos ^2(x)-\sin ^2(x)}} \, dx\)
3.428
\(\int (2-3 \sin ^2(x))^{3/5} \sin (4 x) \, dx\)
3.429
\(\int \cos (x) \sqrt {\cos (2 x)} \, dx\)
3.430
\(\int \cos ^{\frac {3}{2}}(2 x) \sin (x) \, dx\)
3.431
\(\int \frac {\sin (x)}{\cos ^{\frac {5}{2}}(2 x)} \, dx\)
3.432
\(\int \cos ^{\frac {3}{2}}(2 x) \sec ^3(x) \, dx\)
3.433
\(\int \frac {\sin ^2(x) (3 \sin ^3(x)-\cos (x) \sin (4 x))}{\cos ^{\frac {7}{2}}(2 x)} \, dx\)
3.434
\(\int (4-5 \sec ^2(x))^{3/2} \, dx\)
3.435
\(\int \frac {1}{(4-5 \sec ^2(x))^{3/2}} \, dx\)
3.436
\(\int \frac {-2 \cot ^2(x)+\sin (x)}{(1+5 \tan ^2(x))^{3/2}} \, dx\)
3.437
\(\int \frac {(-3+\cos (2 x)) \sec ^4(x)}{\sqrt {4-\cot ^2(x)}} \, dx\)
3.438
\(\int \frac {(3+\sin ^2(x)) \tan ^3(x)}{(-2+\cos ^2(x)) (5-4 \sec ^2(x))^{3/2}} \, dx\)
3.439
\(\int \frac {\csc ^2(x) (\sec ^2(x)-3 \tan (x) \sqrt {4 \sec ^2(x)+5 \tan ^2(x)})}{(4 \sec ^2(x)+5 \tan ^2(x))^{3/2}} \, dx\)
3.440
\(\int \tan (x) (1+5 \tan ^2(x))^{5/2} \, dx\)
3.441
\(\int \frac {\tan (x)}{(1+5 \tan ^2(x))^{5/2}} \, dx\)
3.442
\(\int \frac {\tan (x)}{\sqrt [3]{a^3+b^3 \tan ^2(x)}} \, dx\)
3.443
\(\int \tan (x) (1-7 \tan ^2(x))^{2/3} \, dx\)
3.444
\(\int \frac {\cot (x)}{\sqrt [4]{a^4+b^4 \csc ^2(x)}} \, dx\)
3.445
\(\int \frac {\cot (x)}{\sqrt [4]{a^4-b^4 \csc ^2(x)}} \, dx\)
3.446
\(\int \frac {\sec ^2(x) \tan (x) (\sqrt [3]{1-3 \sec ^2(x)} \sin ^2(x)+3 \tan ^2(x))}{(1-3 \sec ^2(x))^{5/6} (1-\sqrt {1-3 \sec ^2(x)})} \, dx\)
3.447
\(\int \frac {\sec ^2(x) (-\cos (2 x)+2 \tan ^2(x))}{(\tan (x) \tan (2 x))^{3/2}} \, dx\)
3.448
\(\int \frac {\tan (x)}{(a^3-b^3 \cos ^n(x))^{4/3}} \, dx\)
3.449
\(\int (1+2 \cos ^9(x))^{5/6} \tan (x) \, dx\)
3.450
\(\int \frac {\cos (x) \sin ^8(x)}{(2-5 \sin ^3(x))^{4/3}} \, dx\)
3.451
\(\int \frac {\sec ^2(x) \tan (x) (1+\sqrt [3]{1-8 \tan ^2(x)})}{(1-8 \tan ^2(x))^{2/3}} \, dx\)
3.452
\(\int \frac {\csc (x) \sec (x) (1+\sqrt [3]{1-8 \tan ^2(x)})}{(1-8 \tan ^2(x))^{2/3}} \, dx\)
3.453
\(\int \frac {(5 \cos ^2(x)-\sqrt {-1+5 \sin ^2(x)}) \tan (x)}{\sqrt [4]{-1+5 \sin ^2(x)} (2+\sqrt {-1+5 \sin ^2(x)})} \, dx\)
3.454
\(\int \cos ^3(x) \cos ^{\frac {2}{3}}(2 x) \sin (x) \, dx\)
3.455
\(\int \frac {\sin ^6(x) \tan (x)}{\cos ^{\frac {3}{4}}(2 x)} \, dx\)
3.456
\(\int \sqrt {\tan (x) \tan (2 x)} \, dx\)
3.457
\(\int \sqrt {\cot (2 x) \tan (x)} \, dx\)
3.458
\(\int \frac {1}{x^5 (5+x^2)} \, dx\)
3.459
\(\int \frac {1}{x^6 (5+x^2)} \, dx\)
3.460
\(\int \frac {1}{x (-4+x^2)^4} \, dx\)
3.461
\(\int \frac {1}{x (-2+x^2)^{5/2}} \, dx\)
3.462
\(\int \frac {(-10+x^2)^{5/2}}{x} \, dx\)
3.463
\(\int x^{1+2 n} \, dx\)
3.464
\(\int \frac {x^7}{(-5+x^2)^3} \, dx\)
3.465
\(\int \frac {-4 x^3+3 x^5}{(-1+x^2)^5} \, dx\)
3.466
\(\int x^3 (1+x^2)^{9/14} \, dx\)
3.467
\(\int \frac {x^5}{(-4+x^2)^{13/6}} \, dx\)
3.468
\(\int \frac {1}{(1+2 x^2)^{5/2}} \, dx\)
3.469
\(\int \frac {1}{(-1-2 x+x^2)^{5/2}} \, dx\)
3.470
\(\int \frac {1}{x^4 (-8+x^2)^{3/2}} \, dx\)
3.471
\(\int \frac {(5+x^2)^2}{x^{13/3}} \, dx\)
3.472
\(\int \frac {1}{x^7 (1+x^2)^3} \, dx\)
3.473
\(\int \frac {(\frac {2+x^2}{x^2})^{7/9}}{(2+x^2)^{3/2}} \, dx\)
3.474
\(\int \frac {x^4}{(\sqrt {10}-x^2)^{9/2}} \, dx\)
3.475
\(\int \frac {x^2}{(3-x^2)^{3/2}} \, dx\)
3.476
\(\int \frac {(25-x^2)^{3/2}}{x^4} \, dx\)
3.477
\(\int \frac {1}{(1-2 x^2)^{7/2}} \, dx\)
3.478
\(\int \frac {1}{(-7+6 x-x^2)^{5/2}} \, dx\)
3.479
\(\int (1-2 x-2 x^2)^3 \, dx\)
3.480
\(\int (-1+5 x) (-1-x+x^2)^2 \, dx\)
3.481
\(\int \frac {1+3 x}{(1-8 x+2 x^2)^{5/2}} \, dx\)
3.482
\(\int \frac {-1-8 x+8 x^3}{(1+2 x-4 x^2)^{5/2}} \, dx\)
3.483
\(\int x^2 \cos ^5(x) \, dx\)
3.484
\(\int x^3 \sin ^3(x) \, dx\)
3.485
\(\int x^2 \sin ^6(x) \, dx\)
3.486
\(\int x^2 \cos (x) \sin ^2(x) \, dx\)
3.487
\(\int x \cos ^2(x) \cot ^2(x) \, dx\)
3.488
\(\int x \sec (x) \tan ^3(x) \, dx\)
3.489
\(\int x \sec ^2(x) \tan (x) \, dx\)
3.490
\(\int x \sin ^2(x) \tan (x) \, dx\)
3.491
\(\int x \tan ^3(x) \, dx\)
3.492
\(\int \frac {2 x+\sin (2 x)}{(\cos (x)+x \sin (x))^2} \, dx\)
3.493
\(\int \frac {x^2}{(x \cos (x)-\sin (x))^2} \, dx\)
3.494
\(\int a^{m x} b^{n x} \, dx\)
3.495
\(\int a^{-x} b^{-x} (a^x-b^x)^2 \, dx\)
3.496
\(\int (-e^{-x}+e^x) \, dx\)
3.497
\(\int (-e^{-x}+e^x)^2 \, dx\)
3.498
\(\int (-e^{-x}+e^x)^3 \, dx\)
3.499
\(\int (-e^{-x}+e^x)^4 \, dx\)
3.500
\(\int (-e^{-x}+e^x)^n \, dx\)
3.501
\(\int (a^{-4 x}-a^{2 x})^3 \, dx\)
3.502
\(\int (a^{k x}+a^{l x}) \, dx\)
3.503
\(\int (a^{k x}+a^{l x})^2 \, dx\)
3.504
\(\int (a^{k x}+a^{l x})^3 \, dx\)
3.505
\(\int (a^{k x}+a^{l x})^4 \, dx\)
3.506
\(\int (a^{k x}+a^{l x})^n \, dx\)
3.507
\(\int (a^{k x}-a^{l x}) \, dx\)
3.508
\(\int (a^{k x}-a^{l x})^2 \, dx\)
3.509
\(\int (a^{k x}-a^{l x})^3 \, dx\)
3.510
\(\int (a^{k x}-a^{l x})^4 \, dx\)
3.511
\(\int (a^{k x}-a^{l x})^n \, dx\)
3.512
\(\int (1+a^{m x}) \, dx\)
3.513
\(\int (1+a^{m x})^2 \, dx\)
3.514
\(\int (1+a^{m x})^3 \, dx\)
3.515
\(\int (1+a^{m x})^4 \, dx\)
3.516
\(\int (1+a^{m x})^n \, dx\)
3.517
\(\int (1-a^{m x}) \, dx\)
3.518
\(\int (1-a^{m x})^2 \, dx\)
3.519
\(\int (1-a^{m x})^3 \, dx\)
3.520
\(\int (1-a^{m x})^4 \, dx\)
3.521
\(\int (1-a^{m x})^n \, dx\)
3.522
\(\int \frac {1}{b+a e^{n x}} \, dx\)
3.523
\(\int \frac {e^x}{b+a e^{3 x}} \, dx\)
3.524
\(\int \frac {-1+e^x}{1+e^x} \, dx\)
3.525
\(\int \frac {e^{4 x}}{1-2 e^{2 x}+3 e^{4 x}} \, dx\)
3.526
\(\int \frac {e^x+e^{5 x}}{-1+e^x-e^{2 x}+e^{3 x}} \, dx\)
3.527
\(\int e^{n x} (a+b e^{n x})^{r/s} \, dx\)
3.528
\(\int \sqrt [4]{1-2 e^{x/3}} \, dx\)
3.529
\(\int (a+b e^{n x})^{r/s} \, dx\)
3.530
\(\int \frac {e^x}{\sqrt {a^2+e^{2 x}}} \, dx\)
3.531
\(\int \frac {e^x}{\sqrt {-a^2+e^{2 x}}} \, dx\)
3.532
\(\int \frac {e^{3 x/4}}{(-2+e^{3 x/4}) \sqrt {-2+e^{3 x/4}+e^{3 x/2}}} \, dx\)
3.533
\(\int e^{-2 x} (-3+e^{7 x})^{2/3} \, dx\)
3.534
\(\int \frac {e^{2 x}}{(3-e^{x/2})^{3/4}} \, dx\)
3.535
\(\int e^{-x/2} x^3 \, dx\)
3.536
\(\int \frac {e^{-x/2}}{x^3} \, dx\)
3.537
\(\int a^{3 x} x^2 \, dx\)
3.538
\(\int e^{x^2} x (1+x^2) \, dx\)
3.539
\(\int \frac {x}{(e^{-x}+e^x)^2} \, dx\)
3.540
\(\int \frac {e^x (1-x-x^2)}{\sqrt {1-x^2}} \, dx\)
3.541
\(\int e^{-3 x} \cos (2 x) \, dx\)
3.542
\(\int \frac {\cos (\frac {x}{2})+\sin (\frac {x}{2})}{\sqrt [3]{e^x}} \, dx\)
3.543
\(\int \frac {\cos (\frac {3 x}{2})}{\sqrt [4]{3^{3 x}}} \, dx\)
3.544
\(\int e^{m x} \cos ^2(x) \, dx\)
3.545
\(\int e^{m x} \sin ^3(x) \, dx\)
3.546
\(\int \frac {\cos ^3(\frac {x}{3})}{\sqrt {e^x}} \, dx\)
3.547
\(\int e^{2 x} \cos ^2(x) \sin ^2(x) \, dx\)
3.548
\(\int e^{3 x} \cos ^2(\frac {3 x}{2}) \sin ^2(\frac {3 x}{2}) \, dx\)
3.549
\(\int e^{m x} \tan ^2(x) \, dx\)
3.550
\(\int e^{m x} \csc ^2(x) \, dx\)
3.551
\(\int e^{m x} \sec ^3(x) \, dx\)
3.552
\(\int \frac {e^x}{1+\cos (x)} \, dx\)
3.553
\(\int \frac {e^x}{1-\cos (x)} \, dx\)
3.554
\(\int \frac {e^x}{1+\sin (x)} \, dx\)
3.555
\(\int \frac {e^x}{1-\sin (x)} \, dx\)
3.556
\(\int \frac {e^x (1-\sin (x))}{1-\cos (x)} \, dx\)
3.557
\(\int \frac {e^x (1+\sin (x))}{1-\cos (x)} \, dx\)
3.558
\(\int \frac {e^x (1+\sin (x))}{1+\cos (x)} \, dx\)
3.559
\(\int \frac {e^x (1-\sin (x))}{1+\cos (x)} \, dx\)
3.560
\(\int \frac {e^x (1-\cos (x))}{1-\sin (x)} \, dx\)
3.561
\(\int \frac {e^x (1+\cos (x))}{1-\sin (x)} \, dx\)
3.562
\(\int \frac {e^x (1+\cos (x))}{1+\sin (x)} \, dx\)
3.563
\(\int \frac {e^x (1-\cos (x))}{1+\sin (x)} \, dx\)
3.564
\(\int e^x x \cos (x) \, dx\)
3.565
\(\int e^x x^2 \sin (x) \, dx\)
3.566
\(\int e^{-3 x} x^2 \sin (x) \, dx\)
3.567
\(\int e^{x/2} x^2 \cos ^3(x) \, dx\)
3.568
\(\int e^{2 x} x^2 \sin (4 x) \, dx\)
3.569
\(\int e^{x/2} x^2 \cos (x) \sin ^2(x) \, dx\)
3.570
\(\int \cosh (x) \, dx\)
3.571
\(\int \sinh (x) \, dx\)
3.572
\(\int \tanh (x) \, dx\)
3.573
\(\int \coth (x) \, dx\)
3.574
\(\int \text {sech}(x) \, dx\)
3.575
\(\int \text {csch}(x) \, dx\)
3.576
\(\int \cosh ^2(x) \, dx\)
3.577
\(\int \sinh ^5(x) \, dx\)
3.578
\(\int \tanh ^4(x) \, dx\)
3.579
\(\int \text {csch}^3(x) \, dx\)
3.580
\(\int \text {sech}^5(x) \, dx\)
3.581
\(\int \sinh ^4(x) \tanh (x) \, dx\)
3.582
\(\int \text {sech}^{\frac {23}{4}}(x) \sinh ^5(x) \, dx\)
3.583
\(\int \frac {1}{a+b \cosh (x)} \, dx\)
3.584
\(\int \frac {1}{(1+\cosh (x))^2} \, dx\)
3.585
\(\int \frac {1}{a+b \tanh (x)} \, dx\)
3.586
\(\int \frac {1}{a^2+b^2 \cosh ^2(x)} \, dx\)
3.587
\(\int \frac {1}{a^2-b^2 \cosh ^2(x)} \, dx\)
3.588
\(\int \frac {1}{1-\sinh ^4(x)} \, dx\)
3.589
\(\int \frac {\cosh ^3(x)-\sinh ^3(x)}{\cosh ^3(x)+\sinh ^3(x)} \, dx\)
3.590
\(\int \cosh (x) \cosh (2 x) \cosh (3 x) \, dx\)
3.591
\(\int \cosh (\frac {3 x}{2}) \sinh (x) \sinh (\frac {5 x}{2}) \, dx\)
3.592
\(\int \frac {\cosh (x) (-\cosh (2 x)+\tanh (x))}{\sqrt {\sinh (2 x)} (\sinh ^2(x)+\sinh (2 x))} \, dx\)
3.593
\(\int \frac {\sinh (x)}{(-9+4 \cosh ^2(x))^{5/2}} \, dx\)
3.594
\(\int \frac {\sinh ^2(x) \sinh (2 x)}{(1-\sinh ^2(x))^{3/2}} \, dx\)
3.595
\(\int \frac {\cosh (x)}{\sqrt {\cosh (2 x)}} \, dx\)
3.596
\(\int x \tanh ^2(x) \, dx\)
3.597
\(\int x \coth ^2(x) \, dx\)
3.598
\(\int \frac {x+\cosh (x)+\sinh (x)}{\cosh (x)-\sinh (x)} \, dx\)
3.599
\(\int \frac {x+\cosh (x)+\sinh (x)}{1+\cosh (x)} \, dx\)
3.600
\(\int e^{2 x} \text {csch}^4(x) \, dx\)
3.601
\(\int e^{-2 x} \text {sech}^4(x) \, dx\)
3.602
\(\int \frac {e^x}{\cosh (x)-\sinh (x)} \, dx\)
3.603
\(\int \frac {e^{m x}}{\cosh (x)+\sinh (x)} \, dx\)
3.604
\(\int \frac {e^x}{\cosh (x)+\sinh (x)} \, dx\)
3.605
\(\int \frac {e^x}{1-\cosh (x)} \, dx\)
3.606
\(\int \frac {e^x (1+\sinh (x))}{1+\cosh (x)} \, dx\)
3.607
\(\int \frac {e^x (1-\sinh (x))}{1-\cosh (x)} \, dx\)
3.608
\(\int x^m \log (x) \, dx\)
3.609
\(\int x^m \log ^2(x) \, dx\)
3.610
\(\int \frac {\log ^2(x)}{x^{5/2}} \, dx\)
3.611
\(\int (a+b x) \log (x) \, dx\)
3.612
\(\int (a+b x)^3 \log (x) \, dx\)
3.613
\(\int (-1-8 \log ^2(x)+3 \log ^3(x)) \, dx\)
3.614
\(\int (1+x^4) (1-2 \log (x)+\log ^3(x)) \, dx\)
3.615
\(\int \frac {1}{x^3 \log ^4(x)} \, dx\)
3.616
\(\int \frac {\log (x)}{a+b x} \, dx\)
3.617
\(\int \frac {\log (x)}{(a+b x)^2} \, dx\)
3.618
\(\int \frac {\log ^n(x)}{x} \, dx\)
3.619
\(\int \frac {(a+b \log (x))^n}{x} \, dx\)
3.620
\(\int \frac {1}{x (a+b \log (x))} \, dx\)
3.621
\(\int \frac {(a+b \log (x))^{-n}}{x} \, dx\)
3.622
\(\int \frac {1}{x \sqrt {a^2+\log ^2(x)}} \, dx\)
3.623
\(\int \frac {1}{x \sqrt {-a^2+\log ^2(x)}} \, dx\)
3.624
\(\int \frac {1}{x \sqrt {a^2-\log ^2(x)}} \, dx\)
3.625
\(\int \frac {1}{x \log (x) \sqrt {a^2+\log ^2(x)}} \, dx\)
3.626
\(\int \frac {1}{x \log (x) \sqrt {a^2-\log ^2(x)}} \, dx\)
3.627
\(\int \frac {1}{x \log (x) \sqrt {-a^2+\log ^2(x)}} \, dx\)
3.628
\(\int \frac {\log (\log (x))}{x} \, dx\)
3.629
\(\int \frac {\log ^2(\log (x))}{x} \, dx\)
3.630
\(\int \frac {\log ^3(\log (x))}{x} \, dx\)
3.631
\(\int \frac {\log ^4(\log (x))}{x} \, dx\)
3.632
\(\int \frac {\log ^n(\log (x))}{x} \, dx\)
3.633
\(\int \frac {\cot (x)}{\log (\sin (x))} \, dx\)
3.634
\(\int (\cos (x)+\sec (x)) \tan (x) \, dx\)
3.635
\(\int \log (\cosh (x)) \sinh (x) \, dx\)
3.636
\(\int \log (\cosh (x)) \tanh (x) \, dx\)
3.637
\(\int \log (x-\sqrt {1+x^2}) \, dx\)
3.638
\(\int \frac {\log (-1+x)}{x^3} \, dx\)
3.639
\(\int (-e^{-x}+e^x) \log (1+e^{2 x}) \, dx\)
3.640
\(\int e^{3 x/2} \log (-1+e^x) \, dx\)
3.641
\(\int \cos ^3(x) \log (\sin (x)) \, dx\)
3.642
\(\int \log (\tan (x)) \sec ^4(x) \, dx\)
3.643
\(\int \frac {\log (\cos (\frac {x}{2}))}{1+\cos (x)} \, dx\)
3.644
\(\int \frac {\cos (x) \log (\sin (x))}{(1+\cos (x))^2} \, dx\)
3.645
\(\int \frac {\cos ^{-1}(x)^2}{x^5} \, dx\)
3.646
\(\int x^2 \sin ^{-1}(x)^2 \, dx\)
3.647
\(\int x^3 \tan ^{-1}(x)^2 \, dx\)
3.648
\(\int \frac {\tan ^{-1}(x)^2}{x^5} \, dx\)
3.649
\(\int x^3 \csc ^{-1}(x)^2 \, dx\)
3.650
\(\int \frac {\sec ^{-1}(x)^4}{x^5} \, dx\)
3.651
\(\int \sqrt {1-x^2} \sin ^{-1}(x) \, dx\)
3.652
\(\int \sqrt {1-x^2} \cos ^{-1}(x) \, dx\)
3.653
\(\int x \sqrt {1-x^2} \cos ^{-1}(x) \, dx\)
3.654
\(\int (1-x^2)^{3/2} \sin ^{-1}(x) \, dx\)
3.655
\(\int x (1-x^2)^{3/2} \sin ^{-1}(x) \, dx\)
3.656
\(\int x^3 (1-x^2)^{3/2} \cos ^{-1}(x) \, dx\)
3.657
\(\int \frac {(1-x^2)^{3/2} \cos ^{-1}(x)}{x} \, dx\)
3.658
\(\int \frac {(1-x^2)^{3/2} \sin ^{-1}(x)}{x^6} \, dx\)
3.659
\(\int \frac {x^2 \sin ^{-1}(x)}{\sqrt {1-x^2}} \, dx\)
3.660
\(\int \frac {x^4 \sin ^{-1}(x)}{\sqrt {1-x^2}} \, dx\)
3.661
\(\int \frac {x \sin ^{-1}(x)}{(1-x^2)^{3/2}} \, dx\)
3.662
\(\int \frac {x \cos ^{-1}(x)}{(1-x^2)^{3/2}} \, dx\)
3.663
\(\int \frac {\sin ^{-1}(x)}{(1-x^2)^{5/2}} \, dx\)
3.664
\(\int \frac {x^3 \sin ^{-1}(x)}{(1-x^2)^{3/2}} \, dx\)
3.665
\(\int \frac {\sin ^{-1}(x)}{x (1-x^2)^{3/2}} \, dx\)
3.666
\(\int \frac {\cos ^{-1}(x)}{x^4 \sqrt {1-x^2}} \, dx\)
3.667
\(\int x \sqrt {1-x^2} \cos ^{-1}(x)^2 \, dx\)
3.668
\(\int \frac {x^2 \sin ^{-1}(x)^3}{\sqrt {1-x^2}} \, dx\)
3.669
\(\int \frac {x \tan ^{-1}(x)}{(1+x^2)^2} \, dx\)
3.670
\(\int \frac {x \tan ^{-1}(x)}{(1+x^2)^3} \, dx\)
3.671
\(\int \frac {x^2 \tan ^{-1}(x)}{1+x^2} \, dx\)
3.672
\(\int \frac {x^3 \tan ^{-1}(x)}{1+x^2} \, dx\)
3.673
\(\int \frac {x^2 \tan ^{-1}(x)}{(1+x^2)^2} \, dx\)
3.674
\(\int \frac {x^3 \tan ^{-1}(x)}{(1+x^2)^2} \, dx\)
3.675
\(\int \frac {x^5 \tan ^{-1}(x)}{(1+x^2)^2} \, dx\)
3.676
\(\int \frac {(1+x^2) \tan ^{-1}(x)}{x^2} \, dx\)
3.677
\(\int \frac {(1+x^2) \tan ^{-1}(x)}{x^5} \, dx\)
3.678
\(\int \frac {(1+x^2)^2 \tan ^{-1}(x)}{x^5} \, dx\)
3.679
\(\int \frac {\tan ^{-1}(x)}{x^2 (1+x^2)} \, dx\)
3.680
\(\int \frac {\tan ^{-1}(x)^2}{x^3} \, dx\)
3.681
\(\int \frac {(1+x^2) \tan ^{-1}(x)^2}{x^5} \, dx\)
3.682
\(\int \frac {x^3 \tan ^{-1}(x)^2}{(1+x^2)^3} \, dx\)
3.683
\(\int \frac {\sqrt {-1+x^2} \sec ^{-1}(x)}{x^2} \, dx\)
3.684
\(\int \frac {(-1+x^2)^{5/2} \csc ^{-1}(x)}{x^3} \, dx\)
3.685
\(\int \frac {\sqrt {-1+x^2} \sec ^{-1}(x)}{x^4} \, dx\)
3.686
\(\int \frac {\sec ^{-1}(x)}{(-1+x^2)^{5/2}} \, dx\)
3.687
\(\int \frac {x^2 \sec ^{-1}(x)}{(-1+x^2)^{5/2}} \, dx\)
3.688
\(\int \frac {x^3 \sec ^{-1}(x)}{(-1+x^2)^{5/2}} \, dx\)
3.689
\(\int \frac {x^6 \sec ^{-1}(x)}{(-1+x^2)^{5/2}} \, dx\)
3.690
\(\int \frac {\sec ^{-1}(x)}{x^2 \sqrt {-1+x^2}} \, dx\)
3.691
\(\int \frac {\csc ^{-1}(x)}{x^2 (-1+x^2)^{5/2}} \, dx\)
3.692
\(\int \frac {\csc ^{-1}(x)^4}{x^2 \sqrt {-1+x^2}} \, dx\)
3.693
\(\int \frac {(-1+x^2)^{3/2} \sec ^{-1}(x)^2}{x^5} \, dx\)
3.694
\(\int \frac {\sqrt {-1+x^2} \sec ^{-1}(x)^3}{x^4} \, dx\)
3.695
\(\int \sin ^{-1}(\sqrt {\frac {-a+x}{a+x}}) \, dx\)
3.696
\(\int \tan ^{-1}(\sqrt {\frac {-a+x}{a+x}}) \, dx\)
3.697
\(\int \frac {\tan ^{-1}(x)}{(1+x)^3} \, dx\)
3.698
\(\int -\frac {\tan ^{-1}(a-x)}{a+x} \, dx\)
3.699
\(\int \frac {\sin ^{-1}(\sqrt {1-x^2})}{\sqrt {1-x^2}} \, dx\)
3.700
\(\int \frac {x \tan ^{-1}(\sqrt {1+x^2})}{\sqrt {1+x^2}} \, dx\)
3.701
\(\int \frac {\sin ^{-1}(x)}{(1-x)^{5/2}} \, dx\)
3.702
\(\int (-1+x)^{5/2} \csc ^{-1}(x) \, dx\)
3.703
\(\int \sin ^{-1}(\sinh (x)) \text {sech}^4(x) \, dx\)
3.704
\(\int \cot ^{-1}(\cosh (x)) \coth (x) \text {csch}^3(x) \, dx\)
3.705
\(\int e^x \sin ^{-1}(\tanh (x)) \, dx\)
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