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Chapter 3
Listing of integrals
3.1
\(\int x^n \, dx\)
3.2
\(\int e^x \, dx\)
3.3
\(\int \frac{1}{x} \, dx\)
3.4
\(\int a^x \, dx\)
3.5
\(\int \sin (x) \, dx\)
3.6
\(\int \cos (x) \, dx\)
3.7
\(\int \sec ^2(x) \, dx\)
3.8
\(\int \csc ^2(x) \, dx\)
3.9
\(\int \sec (x) \tan (x) \, dx\)
3.10
\(\int \cot (x) \csc (x) \, dx\)
3.11
\(\int \sinh (x) \, dx\)
3.12
\(\int \cosh (x) \, dx\)
3.13
\(\int \tan (x) \, dx\)
3.14
\(\int \cot (x) \, dx\)
3.15
\(\int x \sin (x) \, dx\)
3.16
\(\int \log (x) \, dx\)
3.17
\(\int e^x x^2 \, dx\)
3.18
\(\int e^x \sin (x) \, dx\)
3.19
\(\int \tan ^{-1}(x) \, dx\)
3.20
\(\int e^{2 x} x \, dx\)
3.21
\(\int x \cos (x) \, dx\)
3.22
\(\int x \sin (4 x) \, dx\)
3.23
\(\int x \log (x) \, dx\)
3.24
\(\int x^2 \cos (3 x) \, dx\)
3.25
\(\int x^2 \sin (2 x) \, dx\)
3.26
\(\int \log ^2(x) \, dx\)
3.27
\(\int \sin ^{-1}(x) \, dx\)
3.28
\(\int t \cos (t) \sin (t) \, dt\)
3.29
\(\int t \sec ^2(t) \, dt\)
3.30
\(\int t^2 \log (t) \, dt\)
3.31
\(\int e^t t^3 \, dt\)
3.32
\(\int e^{2 t} \sin (3 t) \, dt\)
3.33
\(\int e^{-t} \cos (3 t) \, dt\)
3.34
\(\int y \sinh (y) \, dy\)
3.35
\(\int y \cosh (a y) \, dy\)
3.36
\(\int e^{-t} t \, dt\)
3.37
\(\int \sqrt{t} \log (t) \, dt\)
3.38
\(\int x \cos (2 x) \, dx\)
3.39
\(\int e^{-x} x^2 \, dx\)
3.40
\(\int \cos ^{-1}(x) \, dx\)
3.41
\(\int x \csc ^2(x) \, dx\)
3.42
\(\int \cos (5 x) \sin (3 x) \, dx\)
3.43
\(\int \sin (2 x) \sin (4 x) \, dx\)
3.44
\(\int \cos (x) \log (\sin (x)) \, dx\)
3.45
\(\int e^{x^2} x^3 \, dx\)
3.46
\(\int e^x (3+2 x) \, dx\)
3.47
\(\int 5^x x \, dx\)
3.48
\(\int \cos (\log (x)) \, dx\)
3.49
\(\int e^{\sqrt{x}} \, dx\)
3.50
\(\int \log (\sqrt{x}) \, dx\)
3.51
\(\int \sin (\log (x)) \, dx\)
3.52
\(\int \sin (\sqrt{x}) \, dx\)
3.53
\(\int x^5 \cos (x^3) \, dx\)
3.54
\(\int e^{x^2} x^5 \, dx\)
3.55
\(\int x \tan ^{-1}(x) \, dx\)
3.56
\(\int x \cos (\pi x) \, dx\)
3.57
\(\int \sqrt{x} \log (x) \, dx\)
3.58
\(\int \sin ^2(3 x) \, dx\)
3.59
\(\int \cos ^2(x) \, dx\)
3.60
\(\int \cos ^4(x) \, dx\)
3.61
\(\int \sin ^3(x) \, dx\)
3.62
\(\int \cos ^4(x) \sin ^3(x) \, dx\)
3.63
\(\int \cos ^3(x) \sin ^4(x) \, dx\)
3.64
\(\int \cos ^2(x) \sin ^4(x) \, dx\)
3.65
\(\int \cos ^2(x) \sin ^2(x) \, dx\)
3.66
\(\int (1-\sin (2 x))^2 \, dx\)
3.67
\(\int \cos (x) \sin (\frac{\pi }{6}+x) \, dx\)
3.68
\(\int \cos ^5(x) \sin ^5(x) \, dx\)
3.69
\(\int \sin ^6(x) \, dx\)
3.70
\(\int \cos ^6(x) \, dx\)
3.71
\(\int \cos ^4(2 x) \sin ^2(2 x) \, dx\)
3.72
\(\int \sin ^5(x) \, dx\)
3.73
\(\int \cos ^4(x) \sin ^4(x) \, dx\)
3.74
\(\int \sqrt{\cos (x)} \sin ^3(x) \, dx\)
3.75
\(\int \cos ^3(x) \sqrt{\sin (x)} \, dx\)
3.76
\(\int \frac{\cos ^2(\sqrt{x})}{\sqrt{x}} \, dx\)
3.77
\(\int x \sin ^3(x^2) \, dx\)
3.78
\(\int \sin ^2(x) \tan (x) \, dx\)
3.79
\(\int \cos ^2(x) \cot ^3(x) \, dx\)
3.80
\(\int \sec (x) (1-\sin (x)) \, dx\)
3.81
\(\int \frac{1}{1-\sin (x)} \, dx\)
3.82
\(\int \tan ^2(x) \, dx\)
3.83
\(\int \tan ^4(x) \, dx\)
3.84
\(\int \sec ^4(x) \, dx\)
3.85
\(\int \sec ^6(x) \, dx\)
3.86
\(\int \sec ^2(x) \tan ^4(x) \, dx\)
3.87
\(\int \sec ^4(x) \tan ^2(x) \, dx\)
3.88
\(\int \sec ^3(x) \tan (x) \, dx\)
3.89
\(\int \sec ^3(x) \tan ^3(x) \, dx\)
3.90
\(\int \tan ^5(x) \, dx\)
3.91
\(\int \tan ^6(x) \, dx\)
3.92
\(\int \sec (x) \tan ^5(x) \, dx\)
3.93
\(\int \sec ^3(x) \tan ^5(x) \, dx\)
3.94
\(\int \sec ^6(x) \tan (x) \, dx\)
3.95
\(\int \sec ^6(x) \tan ^3(x) \, dx\)
3.96
\(\int \sec ^2(x) \tan (x) \, dx\)
3.97
\(\int \sec (x) \tan ^2(x) \, dx\)
3.98
\(\int \cot ^2(x) \, dx\)
3.99
\(\int \cot ^3(x) \, dx\)
3.100
\(\int \cot ^4(x) \csc ^4(x) \, dx\)
3.101
\(\int \cot ^3(x) \csc ^4(x) \, dx\)
3.102
\(\int \csc (x) \, dx\)
3.103
\(\int \csc ^3(x) \, dx\)
3.104
\(\int \cos (x) \cot (x) \, dx\)
3.105
\(\int \csc ^4(x) \, dx\)
3.106
\(\int \sin (2 x) \sin (5 x) \, dx\)
3.107
\(\int \cos (x) \sin (3 x) \, dx\)
3.108
\(\int \cos (3 x) \cos (4 x) \, dx\)
3.109
\(\int \sin (3 x) \sin (6 x) \, dx\)
3.110
\(\int \cos ^5(x) \sin (x) \, dx\)
3.111
\(\int \cos (x) \cos (2 x) \cos (3 x) \, dx\)
3.112
\(\int \cos ^2(x) (1-\tan ^2(x)) \, dx\)
3.113
\(\int \csc (2 x) (\cos (x)+\sin (x)) \, dx\)
3.114
\(\int \sin ^2(x) \tan (x) \, dx\)
3.115
\(\int \cos ^2(x) \cot ^3(x) \, dx\)
3.116
\(\int \sec ^3(x) \tan (x) \, dx\)
3.117
\(\int \sec ^3(x) \tan ^3(x) \, dx\)
3.118
\(\int \frac{\sqrt{9-x^2}}{x^2} \, dx\)
3.119
\(\int \frac{1}{x^2 \sqrt{4+x^2}} \, dx\)
3.120
\(\int \frac{x}{\sqrt{4+x^2}} \, dx\)
3.121
\(\int \frac{1}{\sqrt{-a^2+x^2}} \, dx\)
3.122
\(\int \frac{x^3}{(9+4 x^2)^{3/2}} \, dx\)
3.123
\(\int \frac{x}{\sqrt{3-2 x-x^2}} \, dx\)
3.124
\(\int \frac{1}{x^2 \sqrt{1-x^2}} \, dx\)
3.125
\(\int x^3 \sqrt{4-x^2} \, dx\)
3.126
\(\int \frac{x}{\sqrt{1-x^2}} \, dx\)
3.127
\(\int x \sqrt{4-x^2} \, dx\)
3.128
\(\int \sqrt{1-4 x^2} \, dx\)
3.129
\(\int \frac{x^3}{\sqrt{4+x^2}} \, dx\)
3.130
\(\int \frac{1}{\sqrt{9+x^2}} \, dx\)
3.131
\(\int \sqrt{1+x^2} \, dx\)
3.132
\(\int \frac{1}{x^3 \sqrt{-16+x^2}} \, dx\)
3.133
\(\int \frac{\sqrt{-a^2+x^2}}{x^4} \, dx\)
3.134
\(\int \frac{\sqrt{-4+9 x^2}}{x} \, dx\)
3.135
\(\int \frac{1}{x^2 \sqrt{-9+16 x^2}} \, dx\)
3.136
\(\int \frac{x^2}{(a^2-x^2)^{3/2}} \, dx\)
3.137
\(\int \frac{x^2}{\sqrt{5-x^2}} \, dx\)
3.138
\(\int \frac{1}{x \sqrt{3+x^2}} \, dx\)
3.139
\(\int \frac{x}{(4+x^2)^{5/2}} \, dx\)
3.140
\(\int x^3 \sqrt{4-9 x^2} \, dx\)
3.141
\(\int x^2 \sqrt{9-x^2} \, dx\)
3.142
\(\int 5 x \sqrt{1+x^2} \, dx\)
3.143
\(\int \frac{1}{(-25+4 x^2)^{3/2}} \, dx\)
3.144
\(\int \sqrt{2 x-x^2} \, dx\)
3.145
\(\int \frac{1}{\sqrt{8+4 x+x^2}} \, dx\)
3.146
\(\int \frac{1}{\sqrt{-8+6 x+9 x^2}} \, dx\)
3.147
\(\int \frac{x^2}{\sqrt{4 x-x^2}} \, dx\)
3.148
\(\int \frac{1}{(2+2 x+x^2)^2} \, dx\)
3.149
\(\int \frac{1}{(5-4 x-x^2)^{5/2}} \, dx\)
3.150
\(\int e^t \sqrt{9-e^{2 t}} \, dt\)
3.151
\(\int \sqrt{-9+e^{2 t}} \, dt\)
3.152
\(\int \frac{1}{\sqrt{a^2+x^2}} \, dx\)
3.153
\(\int \frac{5+x}{-2+x+x^2} \, dx\)
3.154
\(\int \frac{x+x^3}{-1+x} \, dx\)
3.155
\(\int \frac{-1+2 x+x^2}{-2 x+3 x^2+2 x^3} \, dx\)
3.156
\(\int \frac{1+4 x-2 x^2+x^4}{1-x-x^2+x^3} \, dx\)
3.157
\(\int \frac{4-x+2 x^2}{4 x+x^3} \, dx\)
3.158
\(\int \frac{2-3 x+4 x^2}{3-4 x+4 x^2} \, dx\)
3.159
\(\int \frac{1+x^2+x^3}{(-1+x) x (1+x^2)^3 (1+x+x^2)} \, dx\)
3.160
\(\int \frac{1-3 x+2 x^2-x^3}{x (1+x^2)^2} \, dx\)
3.161
\(\int \frac{1}{(1+x^2)^2} \, dx\)
3.162
\(\int \frac{1}{(-1+x) (2+x)} \, dx\)
3.163
\(\int \frac{7}{-12+5 x+2 x^2} \, dx\)
3.164
\(\int \frac{-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx\)
3.165
\(\int \frac{-x^2+x^3}{(-6+x) (3+5 x)^3} \, dx\)
3.166
\(\int \frac{1}{-x^3+x^4} \, dx\)
3.167
\(\int \frac{1-x-x^2+x^3+x^4}{-x+x^3} \, dx\)
3.168
\(\int \frac{-2+x^2}{x (2+x^2)} \, dx\)
3.169
\(\int \frac{2-4 x^2+x^3}{(1+x^2) (2+x^2)} \, dx\)
3.170
\(\int \frac{1+x^2+x^4}{(1+x^2) (4+x^2)^2} \, dx\)
3.171
\(\int \frac{1+16 x}{(5+x)^2 (-3+2 x) (1+x+x^2)} \, dx\)
3.172
\(\int \frac{x^4}{(9+x^2)^3} \, dx\)
3.173
\(\int \frac{19 x}{(-1+x)^3 (3+5 x+4 x^2)^2} \, dx\)
3.174
\(\int \frac{1+x^2+x^3}{2 x^2+x^3+x^4} \, dx\)
3.175
\(\int \frac{1}{-x^3+x^6} \, dx\)
3.176
\(\int \frac{x^2}{1+x} \, dx\)
3.177
\(\int \frac{x}{-5+x} \, dx\)
3.178
\(\int \frac{-1+4 x}{(-1+x) (2+x)} \, dx\)
3.179
\(\int \frac{1}{(1+x) (2+x)} \, dx\)
3.180
\(\int \frac{-5+6 x}{3+2 x} \, dx\)
3.181
\(\int \frac{1}{(a+x) (b+x)} \, dx\)
3.182
\(\int \frac{1+x^2}{-x+x^2} \, dx\)
3.183
\(\int \frac{1-12 x+x^2+x^3}{-12+x+x^2} \, dx\)
3.184
\(\int \frac{3+2 x}{(1+x)^2} \, dx\)
3.185
\(\int \frac{1}{x (1+x) (3+2 x)} \, dx\)
3.186
\(\int \frac{-3+5 x+6 x^2}{-3 x+2 x^2+x^3} \, dx\)
3.187
\(\int \frac{x}{4+4 x+x^2} \, dx\)
3.188
\(\int \frac{1}{(-1+x)^2 (4+x)} \, dx\)
3.189
\(\int \frac{x^2}{(-3+x) (2+x)^2} \, dx\)
3.190
\(\int \frac{-2+3 x+5 x^2}{2 x^2+x^3} \, dx\)
3.191
\(\int \frac{18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx\)
3.192
\(\int \frac{2 x+x^2}{4+3 x^2+x^3} \, dx\)
3.193
\(\int \frac{1}{(-1+x)^2 x^2} \, dx\)
3.194
\(\int \frac{x^2}{(1+x)^3} \, dx\)
3.195
\(\int \frac{1}{-x^2+x^4} \, dx\)
3.196
\(\int \frac{-x+2 x^3}{1-x^2+x^4} \, dx\)
3.197
\(\int \frac{x^3}{1+x^2} \, dx\)
3.198
\(\int \frac{-1+x}{2+2 x+x^2} \, dx\)
3.199
\(\int \frac{x}{1+x+x^2} \, dx\)
3.200
\(\int \frac{7+5 x+4 x^2}{5+4 x+4 x^2} \, dx\)
3.201
\(\int \frac{5-4 x+3 x^2}{(-1+x) (1+x^2)} \, dx\)
3.202
\(\int \frac{3+2 x}{3 x+x^3} \, dx\)
3.203
\(\int \frac{1}{-1+x^3} \, dx\)
3.204
\(\int \frac{x^3}{1+x^3} \, dx\)
3.205
\(\int \frac{-1-2 x+x^2}{(-1+x)^2 (1+x^2)} \, dx\)
3.206
\(\int \frac{x^4}{-1+x^4} \, dx\)
3.207
\(\int \frac{-4+6 x-x^2+3 x^3}{(1+x^2) (2+x^2)} \, dx\)
3.208
\(\int \frac{1+x-2 x^2+x^3}{4+5 x^2+x^4} \, dx\)
3.209
\(\int \frac{-3+x}{(4+2 x+x^2)^2} \, dx\)
3.210
\(\int \frac{1+x^4}{x (1+x^2)^2} \, dx\)
3.211
\(\int \frac{\cos (x) (-3+2 \sin (x))}{2-3 \sin (x)+\sin ^2(x)} \, dx\)
3.212
\(\int \frac{\cos ^2(x) \sin (x)}{5+\cos ^2(x)} \, dx\)
3.213
\(\int \frac{1}{-3+2 x+x^2} \, dx\)
3.214
\(\int \frac{1}{-2 x+x^2} \, dx\)
3.215
\(\int \frac{1+2 x}{-7+12 x+4 x^2} \, dx\)
3.216
\(\int \frac{x}{-1+x+x^2} \, dx\)
3.217
\(\int \frac{-32+5 x-27 x^2+4 x^3}{-70-299 x-286 x^2+50 x^3-13 x^4+30 x^5} \, dx\)
3.218
\(\int \frac{8-13 x^2-7 x^3+12 x^5}{4-20 x+41 x^2-80 x^3+116 x^4-80 x^5+100 x^6} \, dx\)
3.219
\(\int \frac{\sqrt{4+x}}{x} \, dx\)
3.220
\(\int \frac{1}{-\frac{1}{\sqrt [3]{x}}+\sqrt{x}} \, dx\)
3.221
\(\int \frac{1}{-4 \cos (x)+3 \sin (x)} \, dx\)
3.222
\(\int \frac{1}{1+\sqrt{x}} \, dx\)
3.223
\(\int \frac{1}{1+\frac{1}{\sqrt [3]{x}}} \, dx\)
3.224
\(\int \frac{\sqrt{x}}{1+x} \, dx\)
3.225
\(\int \frac{1}{x \sqrt{1+x}} \, dx\)
3.226
\(\int \frac{1}{-\sqrt [3]{x}+x} \, dx\)
3.227
\(\int \frac{1}{x-\sqrt{2+x}} \, dx\)
3.228
\(\int \frac{x^2}{\sqrt{-1+x}} \, dx\)
3.229
\(\int \frac{\sqrt{-1+x}}{1+x} \, dx\)
3.230
\(\int \frac{1}{\sqrt{1+\sqrt{x}}} \, dx\)
3.231
\(\int \frac{\sqrt{x}}{x+x^2} \, dx\)
3.232
\(\int \frac{1+\sqrt{x}}{-1+\sqrt{x}} \, dx\)
3.233
\(\int \frac{1+\frac{1}{\sqrt [3]{x}}}{-1+\frac{1}{\sqrt [3]{x}}} \, dx\)
3.234
\(\int \frac{x^3}{\sqrt [3]{1+x^2}} \, dx\)
3.235
\(\int \frac{\sqrt{x}}{-\frac{1}{\sqrt [3]{x}}+\sqrt{x}} \, dx\)
3.236
\(\int \frac{1}{\frac{1}{\sqrt [4]{x}}+\sqrt{x}} \, dx\)
3.237
\(\int \frac{1}{\frac{1}{\sqrt [3]{x}}+\frac{1}{\sqrt [4]{x}}} \, dx\)
3.238
\(\int \sqrt{\frac{1-x}{x}} \, dx\)
3.239
\(\int \frac{\cos (x)}{\sin (x)+\sin ^2(x)} \, dx\)
3.240
\(\int \frac{e^{2 x}}{2+3 e^x+e^{2 x}} \, dx\)
3.241
\(\int \frac{1}{\sqrt{1+e^x}} \, dx\)
3.242
\(\int \sqrt{1-e^x} \, dx\)
3.243
\(\int \frac{1}{3-5 \sin (x)} \, dx\)
3.244
\(\int \frac{1}{\cos (x)+\sin (x)} \, dx\)
3.245
\(\int \frac{1}{1-\cos (x)+\sin (x)} \, dx\)
3.246
\(\int \frac{1}{4 \cos (x)+3 \sin (x)} \, dx\)
3.247
\(\int \frac{1}{\sin (x)+\tan (x)} \, dx\)
3.248
\(\int \frac{1}{2 \sin (x)+\sin (2 x)} \, dx\)
3.249
\(\int \frac{\sec (x)}{1+\sin (x)} \, dx\)
3.250
\(\int \frac{1}{b \cos (x)+a \sin (x)} \, dx\)
3.251
\(\int \frac{1}{b^2 \cos ^2(x)+a^2 \sin ^2(x)} \, dx\)
3.252
\(\int \frac{x}{-1+x^2} \, dx\)
3.253
\(\int (1+\sqrt{x}) \sqrt{x} \, dx\)
3.254
\(\int \frac{1}{1-\cos (x)} \, dx\)
3.255
\(\int \sec (x) \tan ^2(x) \, dx\)
3.256
\(\int \sec ^3(x) \tan ^3(x) \, dx\)
3.257
\(\int e^{\sqrt{x}} \, dx\)
3.258
\(\int \frac{1+x^5}{-10 x-3 x^2+x^3} \, dx\)
3.259
\(\int \frac{1}{x \sqrt{\log (x)}} \, dx\)
3.260
\(\int \frac{5+2 x}{-3+x} \, dx\)
3.261
\(\int e^{e^x+x} \, dx\)
3.262
\(\int \cos ^2(x) \sin ^2(x) \, dx\)
3.263
\(\int \frac{-\cos (x)+\sin (x)}{\cos (x)+\sin (x)} \, dx\)
3.264
\(\int \frac{x}{\sqrt{1-x^2}} \, dx\)
3.265
\(\int x^3 \log (x) \, dx\)
3.266
\(\int \frac{\sqrt{-2+x}}{2+x} \, dx\)
3.267
\(\int \frac{x}{(2+x)^2} \, dx\)
3.268
\(\int \log (1+x^2) \, dx\)
3.269
\(\int \frac{\sqrt{1+\log (x)}}{x \log (x)} \, dx\)
3.270
\(\int (1+\sqrt{x})^8 \, dx\)
3.271
\(\int \sec ^4(x) \tan ^3(x) \, dx\)
3.272
\(\int \frac{x}{2-2 x+x^2} \, dx\)
3.273
\(\int x \sin ^{-1}(x) \, dx\)
3.274
\(\int \frac{\sqrt{9-x^2}}{x} \, dx\)
3.275
\(\int \frac{x}{2+3 x+x^2} \, dx\)
3.276
\(\int x^2 \cosh (x) \, dx\)
3.277
\(\int \frac{1+x+x^3}{4 x+2 x^2+x^4} \, dx\)
3.278
\(\int \frac{\cos (x)}{1+\sin ^2(x)} \, dx\)
3.279
\(\int \cos (\sqrt{x}) \, dx\)
3.280
\(\int \sin (\pi x) \, dx\)
3.281
\(\int \frac{e^{2 x}}{1+e^x} \, dx\)
3.282
\(\int e^{3 x} \cos (5 x) \, dx\)
3.283
\(\int \cos (3 x) \cos (5 x) \, dx\)
3.284
\(\int \frac{1}{1+x+x^2+x^3} \, dx\)
3.285
\(\int x^2 \log (1+x) \, dx\)
3.286
\(\int e^{-x^3} x^5 \, dx\)
3.287
\(\int \tan ^2(4 x) \, dx\)
3.288
\(\int \frac{1}{\sqrt{-5+12 x+9 x^2}} \, dx\)
3.289
\(\int x^2 \tan ^{-1}(x) \, dx\)
3.290
\(\int \frac{1-\sqrt{x}}{\sqrt [3]{x}} \, dx\)
3.291
\(\int \frac{1}{-e^{-x}+e^x} \, dx\)
3.292
\(\int \frac{x}{10+2 x^2+x^4} \, dx\)
3.293
\(\int \frac{1}{\frac{1}{\sqrt [3]{x}}+x} \, dx\)
3.294
\(\int \cos ^4(x) \sin ^2(x) \, dx\)
3.295
\(\int \frac{1}{\sqrt{5-4 x-x^2}} \, dx\)
3.296
\(\int \frac{x}{1-x^2+\sqrt{1-x^2}} \, dx\)
3.297
\(\int (1+\cos (x)) \csc (x) \, dx\)
3.298
\(\int \frac{e^x}{-1+e^{2 x}} \, dx\)
3.299
\(\int \frac{1}{-8+x^3} \, dx\)
3.300
\(\int x^5 \cosh (x) \, dx\)
3.301
\(\int \csc (x) \log (\tan (x)) \sec (x) \, dx\)
3.302
\(\int (-2 x+x^2+x^3) \, dx\)
3.303
\(\int \frac{1+e^x}{1-e^x} \, dx\)
3.304
\(\int \frac{x}{(1+x^2) (4+x^2)} \, dx\)
3.305
\(\int \frac{1}{4-5 \sin (x)} \, dx\)
3.306
\(\int x \sqrt [3]{c+x} \, dx\)
3.307
\(\int e^{\sqrt [3]{x}} \, dx\)
3.308
\(\int \frac{1}{4+x+\sqrt{1+x}} \, dx\)
3.309
\(\int \frac{1+x^3}{-x^2+x^3} \, dx\)
3.310
\(\int (-3+4 x+x^2) \sin (2 x) \, dx\)
3.311
\(\int \cos (\cos (x)) \sin (x) \, dx\)
3.312
\(\int \frac{1}{\sqrt{16-x^2}} \, dx\)
3.313
\(\int \frac{x^3}{(1+x)^{10}} \, dx\)
3.314
\(\int \cot ^3(2 x) \csc ^3(2 x) \, dx\)
3.315
\(\int (x+\sin (x))^2 \, dx\)
3.316
\(\int \frac{e^{\tan ^{-1}(x)}}{1+x^2} \, dx\)
3.317
\(\int \frac{1}{x (1+x^4)} \, dx\)
3.318
\(\int e^{-2 t} t^3 \, dt\)
3.319
\(\int \frac{\sqrt{t}}{1+\sqrt [3]{t}} \, dt\)
3.320
\(\int \sin (x) \sin (2 x) \sin (3 x) \, dx\)
3.321
\(\int \log (\frac{x}{2}) \, dx\)
3.322
\(\int \sqrt{\frac{1+x}{1-x}} \, dx\)
3.323
\(\int \frac{x \log (x)}{\sqrt{-1+x^2}} \, dx\)
3.324
\(\int \frac{a+x}{a^2+x^2} \, dx\)
3.325
\(\int \sqrt{1+x-x^2} \, dx\)
3.326
\(\int \frac{x^4}{16+x^{10}} \, dx\)
3.327
\(\int \frac{2+x}{2+x+x^2} \, dx\)
3.328
\(\int x \sec (x) \tan (x) \, dx\)
3.329
\(\int \frac{x}{-a^4+x^4} \, dx\)
3.330
\(\int \frac{1}{\sqrt{x}+\sqrt{1+x}} \, dx\)
3.331
\(\int \frac{1}{1-e^{-x}+2 e^x} \, dx\)
3.332
\(\int \frac{\tan ^{-1}(\sqrt{x})}{\sqrt{x}} \, dx\)
3.333
\(\int \frac{\log (1+x)}{x^2} \, dx\)
3.334
\(\int \frac{1}{-e^x+e^{3 x}} \, dx\)
3.335
\(\int \frac{1+\cos ^2(x)}{1-\cos ^2(x)} \, dx\)
3.336
\(\int \frac{1}{x \sqrt{-25+2 x}} \, dx\)
3.337
\(\int \frac{\sin (2 x)}{\sqrt{9-\cos ^4(x)}} \, dx\)
3.338
\(\int \frac{x^2}{\sqrt{5-4 x^2}} \, dx\)
3.339
\(\int x^3 \sin (x) \, dx\)
3.340
\(\int x \sqrt{4+2 x+x^2} \, dx\)
3.341
\(\int x (5+x^2)^8 \, dx\)
3.342
\(\int \cos ^2(x) \sin ^5(x) \, dx\)
3.343
\(\int e^{-3 x} \cos (4 x) \, dx\)
3.344
\(\int \csc ^3(\frac{x}{2}) \, dx\)
3.345
\(\int \frac{\sqrt{-1+9 x^2}}{x^2} \, dx\)
3.346
\(\int \frac{\sqrt{4-3 x^2}}{x} \, dx\)
3.347
\(\int e^{3 x} x^2 \, dx\)
3.348
\(\int \frac{\cos (x) \sin (x)}{\sqrt{1+\sin (x)}} \, dx\)
3.349
\(\int x \sin ^{-1}(x^2) \, dx\)
3.350
\(\int x^3 \sin ^{-1}(x^2) \, dx\)
3.351
\(\int e^x \text{sech}(e^x) \, dx\)
3.352
\(\int x^2 \cos (3 x) \, dx\)
3.353
\(\int \sqrt{5-4 x-x^2} \, dx\)
3.354
\(\int \frac{x^5}{\sqrt{2}+x^2} \, dx\)
3.355
\(\int \sec ^5(x) \, dx\)
3.356
\(\int \sin ^6(2 x) \, dx\)
3.357
\(\int \cos (x) \log (\sin (x)) \sin ^2(x) \, dx\)
3.358
\(\int \frac{e^{-x}}{1+2 e^x} \, dx\)
3.359
\(\int \sqrt{2+3 \cos (x)} \tan (x) \, dx\)
3.360
\(\int \frac{x}{\sqrt{-4 x+x^2}} \, dx\)
3.361
\(\int \cos ^5(x) \, dx\)
3.362
\(\int e^{-x} x^4 \, dx\)
3.363
\(\int \frac{x^4}{\sqrt{-2+x^{10}}} \, dx\)
3.364
\(\int e^x \cos (4+3 x) \, dx\)
3.365
\(\int e^x \log (1+e^x) \, dx\)
3.366
\(\int x^2 \tan ^{-1}(x) \, dx\)
3.367
\(\int \sqrt{-1+e^{2 x}} \, dx\)
3.368
\(\int e^{\sin (x)} \sin (2 x) \, dx\)
3.369
\(\int x^2 \sqrt{5-x^2} \, dx\)
3.370
\(\int x^2 (1+x^3)^4 \, dx\)
3.371
\(\int \cos ^3(x) \sin ^3(x) \, dx\)
3.372
\(\int \sec ^4(x) \tan ^2(x) \, dx\)
3.373
\(\int x \sqrt{1+2 x} \, dx\)
3.374
\(\int \sin ^4(x) \, dx\)
3.375
\(\int \tan ^3(x) \, dx\)
3.376
\(\int x^5 \sqrt{1+x^2} \, dx\)
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