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Chapter 3
Listing of integrals
3.1
\(\int (a+b x^3) (c+d x^3)^4 \, dx\)
3.2
\(\int (a+b x^3) (c+d x^3)^3 \, dx\)
3.3
\(\int (a+b x^3) (c+d x^3)^2 \, dx\)
3.4
\(\int (a+b x^3) (c+d x^3) \, dx\)
3.5
\(\int \frac{a+b x^3}{c+d x^3} \, dx\)
3.6
\(\int \frac{a+b x^3}{(c+d x^3)^2} \, dx\)
3.7
\(\int \frac{a+b x^3}{(c+d x^3)^3} \, dx\)
3.8
\(\int (a+b x^3)^2 (c+d x^3)^3 \, dx\)
3.9
\(\int (a+b x^3)^2 (c+d x^3)^2 \, dx\)
3.10
\(\int (a+b x^3)^2 (c+d x^3) \, dx\)
3.11
\(\int \frac{(a+b x^3)^2}{c+d x^3} \, dx\)
3.12
\(\int \frac{(a+b x^3)^2}{(c+d x^3)^2} \, dx\)
3.13
\(\int \frac{(a+b x^3)^2}{(c+d x^3)^3} \, dx\)
3.14
\(\int \frac{(c+d x^3)^4}{a+b x^3} \, dx\)
3.15
\(\int \frac{(c+d x^3)^3}{a+b x^3} \, dx\)
3.16
\(\int \frac{(c+d x^3)^2}{a+b x^3} \, dx\)
3.17
\(\int \frac{c+d x^3}{a+b x^3} \, dx\)
3.18
\(\int \frac{1}{(a+b x^3) (c+d x^3)} \, dx\)
3.19
\(\int \frac{1}{(a+b x^3) (c+d x^3)^2} \, dx\)
3.20
\(\int \frac{(c+d x^3)^5}{(a+b x^3)^2} \, dx\)
3.21
\(\int \frac{(c+d x^3)^4}{(a+b x^3)^2} \, dx\)
3.22
\(\int \frac{(c+d x^3)^3}{(a+b x^3)^2} \, dx\)
3.23
\(\int \frac{(c+d x^3)^2}{(a+b x^3)^2} \, dx\)
3.24
\(\int \frac{c+d x^3}{(a+b x^3)^2} \, dx\)
3.25
\(\int \frac{1}{(a+b x^3)^2 (c+d x^3)} \, dx\)
3.26
\(\int \frac{1}{(a+b x^3)^2 (c+d x^3)^2} \, dx\)
3.27
\(\int (a-b x^3) (a+b x^3)^{2/3} \, dx\)
3.28
\(\int \frac{a-b x^3}{\sqrt [3]{a+b x^3}} \, dx\)
3.29
\(\int \frac{a-b x^3}{(a+b x^3)^{4/3}} \, dx\)
3.30
\(\int \frac{a-b x^3}{(a+b x^3)^{7/3}} \, dx\)
3.31
\(\int \frac{a-b x^3}{(a+b x^3)^{10/3}} \, dx\)
3.32
\(\int \frac{a-b x^3}{(a+b x^3)^{13/3}} \, dx\)
3.33
\(\int \frac{a-b x^3}{(a+b x^3)^{16/3}} \, dx\)
3.34
\(\int \frac{(a+b x^3)^{7/3}}{a-b x^3} \, dx\)
3.35
\(\int \frac{(a+b x^3)^{4/3}}{a-b x^3} \, dx\)
3.36
\(\int \frac{\sqrt [3]{a+b x^3}}{a-b x^3} \, dx\)
3.37
\(\int \frac{1}{(a-b x^3) (a+b x^3)^{2/3}} \, dx\)
3.38
\(\int \frac{1}{(a-b x^3) (a+b x^3)^{5/3}} \, dx\)
3.39
\(\int \frac{1}{(a-b x^3) (a+b x^3)^{8/3}} \, dx\)
3.40
\(\int (a-b x^3)^2 (a+b x^3)^{2/3} \, dx\)
3.41
\(\int \frac{(a-b x^3)^2}{\sqrt [3]{a+b x^3}} \, dx\)
3.42
\(\int \frac{(a-b x^3)^2}{(a+b x^3)^{4/3}} \, dx\)
3.43
\(\int \frac{(a-b x^3)^2}{(a+b x^3)^{7/3}} \, dx\)
3.44
\(\int \frac{(a-b x^3)^2}{(a+b x^3)^{10/3}} \, dx\)
3.45
\(\int \frac{(a-b x^3)^2}{(a+b x^3)^{13/3}} \, dx\)
3.46
\(\int \frac{(a-b x^3)^2}{(a+b x^3)^{16/3}} \, dx\)
3.47
\(\int \frac{(a-b x^3)^2}{(a+b x^3)^{19/3}} \, dx\)
3.48
\(\int (a-b x^3)^2 (a+b x^3)^{4/3} \, dx\)
3.49
\(\int (a-b x^3)^2 \sqrt [3]{a+b x^3} \, dx\)
3.50
\(\int \frac{(a-b x^3)^2}{(a+b x^3)^{2/3}} \, dx\)
3.51
\(\int \frac{(a-b x^3)^2}{(a+b x^3)^{5/3}} \, dx\)
3.52
\(\int \frac{(a-b x^3)^2}{(a+b x^3)^{8/3}} \, dx\)
3.53
\(\int \frac{(a-b x^3)^2}{(a+b x^3)^{11/3}} \, dx\)
3.54
\(\int \frac{(a-b x^3)^2}{(a+b x^3)^{14/3}} \, dx\)
3.55
\(\int \frac{(a-b x^3)^2}{(a+b x^3)^{17/3}} \, dx\)
3.56
\(\int (a+b x^3)^{5/3} (c+d x^3) \, dx\)
3.57
\(\int (a+b x^3)^{2/3} (c+d x^3) \, dx\)
3.58
\(\int \frac{c+d x^3}{\sqrt [3]{a+b x^3}} \, dx\)
3.59
\(\int \frac{c+d x^3}{(a+b x^3)^{4/3}} \, dx\)
3.60
\(\int \frac{c+d x^3}{(a+b x^3)^{7/3}} \, dx\)
3.61
\(\int \frac{c+d x^3}{(a+b x^3)^{10/3}} \, dx\)
3.62
\(\int \frac{c+d x^3}{(a+b x^3)^{13/3}} \, dx\)
3.63
\(\int \frac{c+d x^3}{(a+b x^3)^{16/3}} \, dx\)
3.64
\(\int (a+b x^3)^{7/3} (c+d x^3) \, dx\)
3.65
\(\int (a+b x^3)^{4/3} (c+d x^3) \, dx\)
3.66
\(\int \sqrt [3]{a+b x^3} (c+d x^3) \, dx\)
3.67
\(\int \frac{c+d x^3}{(a+b x^3)^{2/3}} \, dx\)
3.68
\(\int \frac{c+d x^3}{(a+b x^3)^{5/3}} \, dx\)
3.69
\(\int \frac{c+d x^3}{(a+b x^3)^{8/3}} \, dx\)
3.70
\(\int (a+b x^3)^{5/3} (c+d x^3)^2 \, dx\)
3.71
\(\int (a+b x^3)^{2/3} (c+d x^3)^2 \, dx\)
3.72
\(\int \frac{(c+d x^3)^2}{\sqrt [3]{a+b x^3}} \, dx\)
3.73
\(\int \frac{(c+d x^3)^2}{(a+b x^3)^{4/3}} \, dx\)
3.74
\(\int \frac{(c+d x^3)^2}{(a+b x^3)^{7/3}} \, dx\)
3.75
\(\int \frac{(c+d x^3)^2}{(a+b x^3)^{10/3}} \, dx\)
3.76
\(\int \frac{(c+d x^3)^2}{(a+b x^3)^{13/3}} \, dx\)
3.77
\(\int \frac{(c+d x^3)^2}{(a+b x^3)^{16/3}} \, dx\)
3.78
\(\int \frac{(c+d x^3)^2}{(a+b x^3)^{19/3}} \, dx\)
3.79
\(\int (a+b x^3)^{7/3} (c+d x^3)^2 \, dx\)
3.80
\(\int (a+b x^3)^{4/3} (c+d x^3)^2 \, dx\)
3.81
\(\int \sqrt [3]{a+b x^3} (c+d x^3)^2 \, dx\)
3.82
\(\int \frac{(c+d x^3)^2}{(a+b x^3)^{2/3}} \, dx\)
3.83
\(\int \frac{(c+d x^3)^2}{(a+b x^3)^{5/3}} \, dx\)
3.84
\(\int \frac{(c+d x^3)^2}{(a+b x^3)^{8/3}} \, dx\)
3.85
\(\int \frac{(a+b x^3)^3}{(c+d x^3)^{13/3}} \, dx\)
3.86
\(\int \frac{(a+b x^3)^{8/3}}{c+d x^3} \, dx\)
3.87
\(\int \frac{(a+b x^3)^{5/3}}{c+d x^3} \, dx\)
3.88
\(\int \frac{(a+b x^3)^{2/3}}{c+d x^3} \, dx\)
3.89
\(\int \frac{1}{\sqrt [3]{a+b x^3} (c+d x^3)} \, dx\)
3.90
\(\int \frac{1}{(a+b x^3)^{4/3} (c+d x^3)} \, dx\)
3.91
\(\int \frac{1}{(a+b x^3)^{7/3} (c+d x^3)} \, dx\)
3.92
\(\int \frac{1}{(a+b x^3)^{10/3} (c+d x^3)} \, dx\)
3.93
\(\int \frac{(a+b x^3)^{4/3}}{c+d x^3} \, dx\)
3.94
\(\int \frac{\sqrt [3]{a+b x^3}}{c+d x^3} \, dx\)
3.95
\(\int \frac{1}{(a+b x^3)^{2/3} (c+d x^3)} \, dx\)
3.96
\(\int \frac{1}{(a+b x^3)^{5/3} (c+d x^3)} \, dx\)
3.97
\(\int \frac{1}{(a+b x^3)^{8/3} (c+d x^3)} \, dx\)
3.98
\(\int \frac{(a+b x^3)^{8/3}}{(c+d x^3)^2} \, dx\)
3.99
\(\int \frac{(a+b x^3)^{5/3}}{(c+d x^3)^2} \, dx\)
3.100
\(\int \frac{(a+b x^3)^{2/3}}{(c+d x^3)^2} \, dx\)
3.101
\(\int \frac{1}{\sqrt [3]{a+b x^3} (c+d x^3)^2} \, dx\)
3.102
\(\int \frac{1}{(a+b x^3)^{4/3} (c+d x^3)^2} \, dx\)
3.103
\(\int \frac{1}{(a+b x^3)^{7/3} (c+d x^3)^2} \, dx\)
3.104
\(\int \frac{(a+b x^3)^{4/3}}{(c+d x^3)^2} \, dx\)
3.105
\(\int \frac{\sqrt [3]{a+b x^3}}{(c+d x^3)^2} \, dx\)
3.106
\(\int \frac{1}{(a+b x^3)^{2/3} (c+d x^3)^2} \, dx\)
3.107
\(\int \frac{1}{(a+b x^3)^{5/3} (c+d x^3)^2} \, dx\)
3.108
\(\int \frac{1}{(a+b x^3)^{8/3} (c+d x^3)^2} \, dx\)
3.109
\(\int \frac{(a+b x^3)^{14/3}}{(c+d x^3)^3} \, dx\)
3.110
\(\int \frac{(a+b x^3)^{11/3}}{(c+d x^3)^3} \, dx\)
3.111
\(\int \frac{(a+b x^3)^{8/3}}{(c+d x^3)^3} \, dx\)
3.112
\(\int \frac{(a+b x^3)^{5/3}}{(c+d x^3)^3} \, dx\)
3.113
\(\int \frac{(a+b x^3)^{2/3}}{(c+d x^3)^3} \, dx\)
3.114
\(\int \frac{1}{\sqrt [3]{a+b x^3} (c+d x^3)^3} \, dx\)
3.115
\(\int \frac{1}{(a+b x^3)^{4/3} (c+d x^3)^3} \, dx\)
3.116
\(\int \frac{1}{(a+b x^3)^{7/3} (c+d x^3)^3} \, dx\)
3.117
\(\int \frac{(a+b x^3)^{4/3}}{(c+d x^3)^3} \, dx\)
3.118
\(\int \frac{\sqrt [3]{a+b x^3}}{(c+d x^3)^3} \, dx\)
3.119
\(\int \frac{1}{(a+b x^3)^{2/3} (c+d x^3)^3} \, dx\)
3.120
\(\int \frac{1}{(a+b x^3)^{5/3} (c+d x^3)^3} \, dx\)
3.121
\(\int \frac{1}{(a+b x^3)^{8/3} (c+d x^3)^3} \, dx\)
3.122
\(\int \frac{(a+b x^3)^{7/4}}{(c+d x^3)^{37/12}} \, dx\)
3.123
\(\int \frac{(a+b x^3)^{5/4}}{(c+d x^3)^{31/12}} \, dx\)
3.124
\(\int \frac{(a+b x^3)^{3/4}}{(c+d x^3)^{25/12}} \, dx\)
3.125
\(\int \frac{\sqrt [4]{a+b x^3}}{(c+d x^3)^{19/12}} \, dx\)
3.126
\(\int \frac{1}{\sqrt [4]{a+b x^3} (c+d x^3)^{13/12}} \, dx\)
3.127
\(\int \frac{1}{(a+b x^3)^{3/4} (c+d x^3)^{7/12}} \, dx\)
3.128
\(\int \frac{1}{(a+b x^3)^{5/4} \sqrt [12]{c+d x^3}} \, dx\)
3.129
\(\int \frac{(c+d x^3)^{5/12}}{(a+b x^3)^{7/4}} \, dx\)
3.130
\(\int \frac{(c+d x^3)^{11/12}}{(a+b x^3)^{9/4}} \, dx\)
3.131
\(\int \frac{(c+d x^3)^{17/12}}{(a+b x^3)^{11/4}} \, dx\)
3.132
\(\int \frac{(c+d x^3)^{23/12}}{(a+b x^3)^{13/4}} \, dx\)
3.133
\(\int (a+b x^3)^m (c+d x^3)^p \, dx\)
3.134
\(\int (a+b x^3)^2 (c+d x^3)^q \, dx\)
3.135
\(\int (a+b x^3) (c+d x^3)^q \, dx\)
3.136
\(\int \frac{(c+d x^3)^q}{a+b x^3} \, dx\)
3.137
\(\int \frac{(c+d x^3)^q}{(a+b x^3)^2} \, dx\)
3.138
\(\int (a+b x^3)^m (c+d x^3)^3 \, dx\)
3.139
\(\int (a+b x^3)^m (c+d x^3)^2 \, dx\)
3.140
\(\int (a+b x^3)^m (c+d x^3) \, dx\)
3.141
\(\int (a+b x^3)^m \, dx\)
3.142
\(\int \frac{(a+b x^3)^m}{c+d x^3} \, dx\)
3.143
\(\int \frac{(a+b x^3)^m}{(c+d x^3)^2} \, dx\)
3.144
\(\int \frac{(a+b x^3)^m}{(c+d x^3)^3} \, dx\)
3.145
\(\int (a+b x^3)^{-1-\frac{b c}{3 b c-3 a d}} (c+d x^3)^{-1+\frac{a d}{3 b c-3 a d}} \, dx\)
3.146
\(\int (a+b x^4) (c+d x^4)^4 \, dx\)
3.147
\(\int (a+b x^4) (c+d x^4)^3 \, dx\)
3.148
\(\int (a+b x^4) (c+d x^4)^2 \, dx\)
3.149
\(\int (a+b x^4) (c+d x^4) \, dx\)
3.150
\(\int \frac{a+b x^4}{c+d x^4} \, dx\)
3.151
\(\int \frac{a+b x^4}{(c+d x^4)^2} \, dx\)
3.152
\(\int \frac{a+b x^4}{(c+d x^4)^3} \, dx\)
3.153
\(\int (a+b x^4)^2 (c+d x^4)^4 \, dx\)
3.154
\(\int (a+b x^4)^2 (c+d x^4)^3 \, dx\)
3.155
\(\int (a+b x^4)^2 (c+d x^4)^2 \, dx\)
3.156
\(\int (a+b x^4)^2 (c+d x^4) \, dx\)
3.157
\(\int \frac{(a+b x^4)^2}{c+d x^4} \, dx\)
3.158
\(\int \frac{(a+b x^4)^2}{(c+d x^4)^2} \, dx\)
3.159
\(\int \frac{(a+b x^4)^2}{(c+d x^4)^3} \, dx\)
3.160
\(\int \frac{(c+d x^4)^4}{a+b x^4} \, dx\)
3.161
\(\int \frac{(c+d x^4)^3}{a+b x^4} \, dx\)
3.162
\(\int \frac{(c+d x^4)^2}{a+b x^4} \, dx\)
3.163
\(\int \frac{c+d x^4}{a+b x^4} \, dx\)
3.164
\(\int \frac{1}{(a+b x^4) (c+d x^4)} \, dx\)
3.165
\(\int \frac{1}{(a+b x^4) (c+d x^4)^2} \, dx\)
3.166
\(\int \frac{(c+d x^4)^5}{(a+b x^4)^2} \, dx\)
3.167
\(\int \frac{(c+d x^4)^4}{(a+b x^4)^2} \, dx\)
3.168
\(\int \frac{(c+d x^4)^3}{(a+b x^4)^2} \, dx\)
3.169
\(\int \frac{(c+d x^4)^2}{(a+b x^4)^2} \, dx\)
3.170
\(\int \frac{c+d x^4}{(a+b x^4)^2} \, dx\)
3.171
\(\int \frac{1}{(a+b x^4)^2 (c+d x^4)} \, dx\)
3.172
\(\int \frac{1}{(a+b x^4)^2 (c+d x^4)^2} \, dx\)
3.173
\(\int \frac{(a-b x^4)^{5/2}}{c-d x^4} \, dx\)
3.174
\(\int \frac{(a-b x^4)^{3/2}}{c-d x^4} \, dx\)
3.175
\(\int \frac{\sqrt{a-b x^4}}{c-d x^4} \, dx\)
3.176
\(\int \frac{1}{\sqrt{a-b x^4} (c-d x^4)} \, dx\)
3.177
\(\int \frac{1}{(a-b x^4)^{3/2} (c-d x^4)} \, dx\)
3.178
\(\int \frac{1}{(a-b x^4)^{5/2} (c-d x^4)} \, dx\)
3.179
\(\int \frac{(a+b x^4)^{3/2}}{c+d x^4} \, dx\)
3.180
\(\int \frac{\sqrt{a+b x^4}}{c+d x^4} \, dx\)
3.181
\(\int \frac{1}{\sqrt{a+b x^4} (c+d x^4)} \, dx\)
3.182
\(\int \frac{1}{(a+b x^4)^{3/2} (c+d x^4)} \, dx\)
3.183
\(\int \frac{1}{(a+b x^4)^{5/2} (c+d x^4)} \, dx\)
3.184
\(\int \frac{(a-b x^4)^{7/2}}{(c-d x^4)^2} \, dx\)
3.185
\(\int \frac{(a-b x^4)^{5/2}}{(c-d x^4)^2} \, dx\)
3.186
\(\int \frac{(a-b x^4)^{3/2}}{(c-d x^4)^2} \, dx\)
3.187
\(\int \frac{\sqrt{a-b x^4}}{(c-d x^4)^2} \, dx\)
3.188
\(\int \frac{1}{\sqrt{a-b x^4} (c-d x^4)^2} \, dx\)
3.189
\(\int \frac{1}{(a-b x^4)^{3/2} (c-d x^4)^2} \, dx\)
3.190
\(\int \frac{1}{(a-b x^4)^{5/2} (c-d x^4)^2} \, dx\)
3.191
\(\int \frac{\sqrt{a+b x^4}}{a c-b c x^4} \, dx\)
3.192
\(\int \frac{\sqrt{a-b x^4}}{a c+b c x^4} \, dx\)
3.193
\(\int \frac{(a+b x^4)^{7/4}}{c+d x^4} \, dx\)
3.194
\(\int \frac{(a+b x^4)^{3/4}}{c+d x^4} \, dx\)
3.195
\(\int \frac{1}{\sqrt [4]{a+b x^4} (c+d x^4)} \, dx\)
3.196
\(\int \frac{1}{(a+b x^4)^{5/4} (c+d x^4)} \, dx\)
3.197
\(\int \frac{1}{(a+b x^4)^{9/4} (c+d x^4)} \, dx\)
3.198
\(\int \frac{1}{(a+b x^4)^{13/4} (c+d x^4)} \, dx\)
3.199
\(\int \frac{(a+b x^4)^{9/4}}{c+d x^4} \, dx\)
3.200
\(\int \frac{(a+b x^4)^{5/4}}{c+d x^4} \, dx\)
3.201
\(\int \frac{\sqrt [4]{a+b x^4}}{c+d x^4} \, dx\)
3.202
\(\int \frac{1}{(a+b x^4)^{3/4} (c+d x^4)} \, dx\)
3.203
\(\int \frac{1}{(a+b x^4)^{7/4} (c+d x^4)} \, dx\)
3.204
\(\int \frac{1}{(a+b x^4)^{11/4} (c+d x^4)} \, dx\)
3.205
\(\int \frac{(a+b x^4)^{11/4}}{(c+d x^4)^2} \, dx\)
3.206
\(\int \frac{(a+b x^4)^{7/4}}{(c+d x^4)^2} \, dx\)
3.207
\(\int \frac{(a+b x^4)^{3/4}}{(c+d x^4)^2} \, dx\)
3.208
\(\int \frac{1}{\sqrt [4]{a+b x^4} (c+d x^4)^2} \, dx\)
3.209
\(\int \frac{1}{(a+b x^4)^{5/4} (c+d x^4)^2} \, dx\)
3.210
\(\int \frac{1}{(a+b x^4)^{9/4} (c+d x^4)^2} \, dx\)
3.211
\(\int \frac{(a+b x^4)^{9/4}}{(c+d x^4)^2} \, dx\)
3.212
\(\int \frac{(a+b x^4)^{5/4}}{(c+d x^4)^2} \, dx\)
3.213
\(\int \frac{\sqrt [4]{a+b x^4}}{(c+d x^4)^2} \, dx\)
3.214
\(\int \frac{1}{(a+b x^4)^{3/4} (c+d x^4)^2} \, dx\)
3.215
\(\int \frac{1}{(a+b x^4)^{7/4} (c+d x^4)^2} \, dx\)
3.216
\(\int \frac{1}{\sqrt [4]{1+x^4} (2+x^4)} \, dx\)
3.217
\(\int \frac{1}{(a-(a-b) x^4) \sqrt [4]{a+b x^4}} \, dx\)
3.218
\(\int (a+b x^4)^p (c+d x^4)^q \, dx\)
3.219
\(\int (a+b x^4)^2 (c+d x^4)^q \, dx\)
3.220
\(\int (a+b x^4) (c+d x^4)^q \, dx\)
3.221
\(\int \frac{(c+d x^4)^q}{a+b x^4} \, dx\)
3.222
\(\int \frac{(c+d x^4)^q}{(a+b x^4)^2} \, dx\)
3.223
\(\int \frac{1}{\sqrt [5]{a+b x^5} (c+d x^5)} \, dx\)
3.224
\(\int \sqrt{a+\frac{b}{x}} (c+\frac{d}{x})^3 \, dx\)
3.225
\(\int \sqrt{a+\frac{b}{x}} (c+\frac{d}{x})^2 \, dx\)
3.226
\(\int \sqrt{a+\frac{b}{x}} (c+\frac{d}{x}) \, dx\)
3.227
\(\int \sqrt{a+\frac{b}{x}} \, dx\)
3.228
\(\int \frac{\sqrt{a+\frac{b}{x}}}{c+\frac{d}{x}} \, dx\)
3.229
\(\int \frac{\sqrt{a+\frac{b}{x}}}{(c+\frac{d}{x})^2} \, dx\)
3.230
\(\int \frac{\sqrt{a+\frac{b}{x}}}{(c+\frac{d}{x})^3} \, dx\)
3.231
\(\int (a+\frac{b}{x})^{3/2} (c+\frac{d}{x})^3 \, dx\)
3.232
\(\int (a+\frac{b}{x})^{3/2} (c+\frac{d}{x})^2 \, dx\)
3.233
\(\int (a+\frac{b}{x})^{3/2} (c+\frac{d}{x}) \, dx\)
3.234
\(\int (a+\frac{b}{x})^{3/2} \, dx\)
3.235
\(\int \frac{(a+\frac{b}{x})^{3/2}}{c+\frac{d}{x}} \, dx\)
3.236
\(\int \frac{(a+\frac{b}{x})^{3/2}}{(c+\frac{d}{x})^2} \, dx\)
3.237
\(\int \frac{(a+\frac{b}{x})^{3/2}}{(c+\frac{d}{x})^3} \, dx\)
3.238
\(\int (a+\frac{b}{x})^{5/2} (c+\frac{d}{x})^3 \, dx\)
3.239
\(\int (a+\frac{b}{x})^{5/2} (c+\frac{d}{x})^2 \, dx\)
3.240
\(\int (a+\frac{b}{x})^{5/2} (c+\frac{d}{x}) \, dx\)
3.241
\(\int (a+\frac{b}{x})^{5/2} \, dx\)
3.242
\(\int \frac{(a+\frac{b}{x})^{5/2}}{c+\frac{d}{x}} \, dx\)
3.243
\(\int \frac{(a+\frac{b}{x})^{5/2}}{(c+\frac{d}{x})^2} \, dx\)
3.244
\(\int \frac{(a+\frac{b}{x})^{5/2}}{(c+\frac{d}{x})^3} \, dx\)
3.245
\(\int \frac{(c+\frac{d}{x})^3}{\sqrt{a+\frac{b}{x}}} \, dx\)
3.246
\(\int \frac{(c+\frac{d}{x})^2}{\sqrt{a+\frac{b}{x}}} \, dx\)
3.247
\(\int \frac{c+\frac{d}{x}}{\sqrt{a+\frac{b}{x}}} \, dx\)
3.248
\(\int \frac{1}{\sqrt{a+\frac{b}{x}}} \, dx\)
3.249
\(\int \frac{1}{\sqrt{a+\frac{b}{x}} (c+\frac{d}{x})} \, dx\)
3.250
\(\int \frac{1}{\sqrt{a+\frac{b}{x}} (c+\frac{d}{x})^2} \, dx\)
3.251
\(\int \frac{1}{\sqrt{a+\frac{b}{x}} (c+\frac{d}{x})^3} \, dx\)
3.252
\(\int \frac{(c+\frac{d}{x})^3}{(a+\frac{b}{x})^{3/2}} \, dx\)
3.253
\(\int \frac{(c+\frac{d}{x})^2}{(a+\frac{b}{x})^{3/2}} \, dx\)
3.254
\(\int \frac{c+\frac{d}{x}}{(a+\frac{b}{x})^{3/2}} \, dx\)
3.255
\(\int \frac{1}{(a+\frac{b}{x})^{3/2}} \, dx\)
3.256
\(\int \frac{1}{(a+\frac{b}{x})^{3/2} (c+\frac{d}{x})} \, dx\)
3.257
\(\int \frac{1}{(a+\frac{b}{x})^{3/2} (c+\frac{d}{x})^2} \, dx\)
3.258
\(\int \frac{1}{(a+\frac{b}{x})^{3/2} (c+\frac{d}{x})^3} \, dx\)
3.259
\(\int \frac{(c+\frac{d}{x})^3}{(a+\frac{b}{x})^{5/2}} \, dx\)
3.260
\(\int \frac{(c+\frac{d}{x})^2}{(a+\frac{b}{x})^{5/2}} \, dx\)
3.261
\(\int \frac{c+\frac{d}{x}}{(a+\frac{b}{x})^{5/2}} \, dx\)
3.262
\(\int \frac{1}{(a+\frac{b}{x})^{5/2}} \, dx\)
3.263
\(\int \frac{1}{(a+\frac{b}{x})^{5/2} (c+\frac{d}{x})} \, dx\)
3.264
\(\int \frac{1}{(a+\frac{b}{x})^{5/2} (c+\frac{d}{x})^2} \, dx\)
3.265
\(\int \frac{1}{(a+\frac{b}{x})^{5/2} (c+\frac{d}{x})^3} \, dx\)
3.266
\(\int \sqrt{a+\frac{b}{x}} \sqrt{c+\frac{d}{x}} \, dx\)
3.267
\(\int \frac{\sqrt{a+\frac{b}{x}}}{\sqrt{c+\frac{d}{x}}} \, dx\)
3.268
\(\int \frac{\sqrt{a+\frac{b}{x}}}{(c+\frac{d}{x})^{3/2}} \, dx\)
3.269
\(\int (a+\frac{b}{x})^p (c+\frac{d}{x})^q \, dx\)
3.270
\(\int \frac{a+\frac{b}{x^2}}{c+\frac{d}{x^2}} \, dx\)
3.271
\(\int \sqrt{a+\frac{b}{x^2}} \sqrt{c+\frac{d}{x^2}} \, dx\)
3.272
\(\int \frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{c+\frac{d}{x^2}}} \, dx\)
3.273
\(\int \frac{\sqrt{a+\frac{b}{x^2}}}{(c+\frac{d}{x^2})^{3/2}} \, dx\)
3.274
\(\int (a+\frac{b}{x^2})^p (c+\frac{d}{x^2})^q \, dx\)
3.275
\(\int \frac{a+\frac{b}{x^3}}{c+\frac{d}{x^3}} \, dx\)
3.276
\(\int \frac{a+b \sqrt{x}}{c+d \sqrt{x}} \, dx\)
3.277
\(\int \frac{-1+\sqrt [3]{x}}{1+\sqrt [3]{x}} \, dx\)
3.278
\(\int \frac{1+x^{2/3}}{-1+x^{2/3}} \, dx\)
3.279
\(\int \frac{-16+x^{3/4}}{16+x^{3/4}} \, dx\)
3.280
\(\int \frac{1+\frac{1}{\sqrt [3]{x}}}{-1+\frac{1}{\sqrt [3]{x}}} \, dx\)
3.281
\(\int (a-b x^n)^{3/2} (a+b x^n)^{3/2} \, dx\)
3.282
\(\int \sqrt{a-b x^n} \sqrt{a+b x^n} \, dx\)
3.283
\(\int (a-b x^n)^p (a+b x^n)^p \, dx\)
3.284
\(\int (a+b x^n) (c+d x^n)^4 \, dx\)
3.285
\(\int (a+b x^n) (c+d x^n)^3 \, dx\)
3.286
\(\int (a+b x^n) (c+d x^n)^2 \, dx\)
3.287
\(\int (a+b x^n) (c+d x^n) \, dx\)
3.288
\(\int \frac{a+b x^n}{c+d x^n} \, dx\)
3.289
\(\int \frac{a+b x^n}{(c+d x^n)^2} \, dx\)
3.290
\(\int \frac{a+b x^n}{(c+d x^n)^3} \, dx\)
3.291
\(\int \frac{a+b x^n}{(c+d x^n)^4} \, dx\)
3.292
\(\int (a+b x^n)^2 (d+e x^n)^3 \, dx\)
3.293
\(\int (a+b x^n)^2 (d+e x^n)^2 \, dx\)
3.294
\(\int (a+b x^n)^2 (c+d x^n) \, dx\)
3.295
\(\int \frac{(a+b x^n)^2}{c+d x^n} \, dx\)
3.296
\(\int \frac{(a+b x^n)^2}{(c+d x^n)^2} \, dx\)
3.297
\(\int \frac{(a+b x^n)^2}{(c+d x^n)^3} \, dx\)
3.298
\(\int \frac{(c+d x^n)^4}{a+b x^n} \, dx\)
3.299
\(\int \frac{(c+d x^n)^3}{a+b x^n} \, dx\)
3.300
\(\int \frac{(c+d x^n)^2}{a+b x^n} \, dx\)
3.301
\(\int \frac{c+d x^n}{a+b x^n} \, dx\)
3.302
\(\int \frac{1}{(a+b x^n) (c+d x^n)} \, dx\)
3.303
\(\int \frac{1}{(a+b x^n) (c+d x^n)^2} \, dx\)
3.304
\(\int \frac{1}{(a+b x^n) (c+d x^n)^3} \, dx\)
3.305
\(\int \frac{(c+d x^n)^4}{(a+b x^n)^2} \, dx\)
3.306
\(\int \frac{(c+d x^n)^3}{(a+b x^n)^2} \, dx\)
3.307
\(\int \frac{(c+d x^n)^2}{(a+b x^n)^2} \, dx\)
3.308
\(\int \frac{c+d x^n}{(a+b x^n)^2} \, dx\)
3.309
\(\int \frac{1}{(a+b x^n)^2 (c+d x^n)} \, dx\)
3.310
\(\int \frac{1}{(a+b x^n)^2 (c+d x^n)^2} \, dx\)
3.311
\(\int \frac{1}{(a+b x^n)^2 (c+d x^n)^3} \, dx\)
3.312
\(\int (a+b x^n)^p (c+d x^n)^q \, dx\)
3.313
\(\int (a+b x^n)^p (c+d x^n)^3 \, dx\)
3.314
\(\int (a+b x^n)^p (c+d x^n)^2 \, dx\)
3.315
\(\int (a+b x^n)^p (c+d x^n) \, dx\)
3.316
\(\int (a+b x^n)^p \, dx\)
3.317
\(\int \frac{(a+b x^n)^p}{c+d x^n} \, dx\)
3.318
\(\int \frac{(a+b x^n)^p}{(c+d x^n)^2} \, dx\)
3.319
\(\int \frac{(a+b x^n)^p}{(c+d x^n)^3} \, dx\)
3.320
\(\int (a+b x^n)^p (c+d x^n)^{-1-\frac{1}{n}-p} \, dx\)
3.321
\(\int (a+b x^n)^3 (c+d x^n)^{-4-\frac{1}{n}} \, dx\)
3.322
\(\int (a+b x^n)^2 (c+d x^n)^{-3-\frac{1}{n}} \, dx\)
3.323
\(\int (a+b x^n) (c+d x^n)^{-2-\frac{1}{n}} \, dx\)
3.324
\(\int (c+d x^n)^{-1-\frac{1}{n}} \, dx\)
3.325
\(\int \frac{(c+d x^n)^{-1/n}}{a+b x^n} \, dx\)
3.326
\(\int \frac{(c+d x^n)^{1-\frac{1}{n}}}{(a+b x^n)^2} \, dx\)
3.327
\(\int \frac{(c+d x^n)^{2-\frac{1}{n}}}{(a+b x^n)^3} \, dx\)
3.328
\(\int (a+b x^n)^p (c+d x^n)^{-2-\frac{1}{n}-p} \, dx\)
3.329
\(\int (a+b x^n)^{\frac{a d n-b c (1+n)}{(b c-a d) n}} (c+d x^n)^{\frac{a d-b c n+a d n}{b c n-a d n}} \, dx\)
3.330
\(\int (a+b x^n)^2 (c+d x^n)^{-4-\frac{1}{n}} \, dx\)
3.331
\(\int (a+b x^n) (c+d x^n)^{-3-\frac{1}{n}} \, dx\)
3.332
\(\int (c+d x^n)^{-2-\frac{1}{n}} \, dx\)
3.333
\(\int \frac{(c+d x^n)^{-1-\frac{1}{n}}}{a+b x^n} \, dx\)
3.334
\(\int \frac{(c+d x^n)^{-1/n}}{(a+b x^n)^2} \, dx\)
3.335
\(\int \frac{(c+d x^n)^{1-\frac{1}{n}}}{(a+b x^n)^3} \, dx\)
3.336
\(\int \frac{(c+d x^n)^{2-\frac{1}{n}}}{(a+b x^n)^4} \, dx\)
3.337
\(\int x^5 \sqrt{-c+d x} \sqrt{c+d x} (a+b x^2) \, dx\)
3.338
\(\int x^3 \sqrt{-c+d x} \sqrt{c+d x} (a+b x^2) \, dx\)
3.339
\(\int x \sqrt{-c+d x} \sqrt{c+d x} (a+b x^2) \, dx\)
3.340
\(\int \frac{\sqrt{-c+d x} \sqrt{c+d x} (a+b x^2)}{x} \, dx\)
3.341
\(\int \frac{\sqrt{-c+d x} \sqrt{c+d x} (a+b x^2)}{x^3} \, dx\)
3.342
\(\int \frac{\sqrt{-c+d x} \sqrt{c+d x} (a+b x^2)}{x^5} \, dx\)
3.343
\(\int x^4 \sqrt{-c+d x} \sqrt{c+d x} (a+b x^2) \, dx\)
3.344
\(\int x^2 \sqrt{-c+d x} \sqrt{c+d x} (a+b x^2) \, dx\)
3.345
\(\int \sqrt{-c+d x} \sqrt{c+d x} (a+b x^2) \, dx\)
3.346
\(\int \frac{\sqrt{-c+d x} \sqrt{c+d x} (a+b x^2)}{x^2} \, dx\)
3.347
\(\int \frac{\sqrt{-c+d x} \sqrt{c+d x} (a+b x^2)}{x^4} \, dx\)
3.348
\(\int \frac{x^4 (a+b x^2)}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
3.349
\(\int \frac{x^3 (a+b x^2)}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
3.350
\(\int \frac{x^2 (a+b x^2)}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
3.351
\(\int \frac{x (a+b x^2)}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
3.352
\(\int \frac{a+b x^2}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
3.353
\(\int \frac{a+b x^2}{x \sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
3.354
\(\int \frac{a+b x^2}{x^2 \sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
3.355
\(\int \frac{a+b x^2}{x^3 \sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
3.356
\(\int \frac{a+b x^2}{x^4 \sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
3.357
\(\int \frac{a+b x^2}{x^5 \sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
3.358
\(\int \frac{x^4 (a+b x^2)}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
3.359
\(\int \frac{x^3 (a+b x^2)}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
3.360
\(\int \frac{x^2 (a+b x^2)}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
3.361
\(\int \frac{x (a+b x^2)}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
3.362
\(\int \frac{a+b x^2}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
3.363
\(\int \frac{a+b x^2}{x \sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
3.364
\(\int \frac{a+b x^2}{x^2 \sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
3.365
\(\int \frac{a+b x^2}{x^3 \sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
3.366
\(\int \frac{a+b x^2}{x^4 \sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
3.367
\(\int \frac{a+b x^2}{x^5 \sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
3.368
\(\int \frac{x^4 (a+b x^2)}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
3.369
\(\int \frac{x^3 (a+b x^2)}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
3.370
\(\int \frac{x^2 (a+b x^2)}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
3.371
\(\int \frac{x (a+b x^2)}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
3.372
\(\int \frac{a+b x^2}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
3.373
\(\int \frac{a+b x^2}{x (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
3.374
\(\int \frac{a+b x^2}{x^2 (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
3.375
\(\int \frac{a+b x^2}{x^3 (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
3.376
\(\int \frac{a+b x^2}{x^4 (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
3.377
\(\int \frac{a+b x^2}{x^5 (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
3.378
\(\int \frac{1+c^2 x^2}{x \sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
3.379
\(\int \frac{x^{-\frac{2 b^2 c+a^2 d}{b^2 c+a^2 d}} (c+d x^2)}{\sqrt{-a+b x} \sqrt{a+b x}} \, dx\)
3.380
\(\int \frac{1}{\sqrt{-1-\sqrt{x}} \sqrt{-1+\sqrt{x}} \sqrt{1+x}} \, dx\)
3.381
\(\int \frac{1}{\sqrt{a-b \sqrt{x}} \sqrt{a+b \sqrt{x}} \sqrt{a^2+b^2 x}} \, dx\)
3.382
\(\int (a-b x^n)^p (a+b x^n)^p (c+d x^{2 n})^q \, dx\)
3.383
\(\int (a-b x^n)^p (a+b x^n)^p (a^2+b^2 x^{2 n})^p \, dx\)
3.384
\(\int \frac{(c+d x^{2 n})^p}{(a-b x^n) (a+b x^n)} \, dx\)
3.385
\(\int (a-b x^{n/2})^p (a+b x^{n/2})^p (\frac{a^2 d (1+p)}{b^2 (1+\frac{-1-2 n-n p}{n})}+d x^n)^{\frac{-1-2 n-n p}{n}} \, dx\)
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