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Chapter 3
Listing of integrals
3.1
\(\int x^5 \tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}) \, dx\)
3.2
\(\int x^3 \tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}) \, dx\)
3.3
\(\int x \tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}) \, dx\)
3.4
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x} \, dx\)
3.5
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x^3} \, dx\)
3.6
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x^5} \, dx\)
3.7
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x^7} \, dx\)
3.8
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x^9} \, dx\)
3.9
\(\int x^6 \tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}) \, dx\)
3.10
\(\int x^4 \tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}) \, dx\)
3.11
\(\int x^2 \tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}) \, dx\)
3.12
\(\int \tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}) \, dx\)
3.13
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x^2} \, dx\)
3.14
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x^4} \, dx\)
3.15
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x^6} \, dx\)
3.16
\(\int x^{9/2} \tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}) \, dx\)
3.17
\(\int x^{5/2} \tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}) \, dx\)
3.18
\(\int \sqrt{x} \tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}) \, dx\)
3.19
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x^{3/2}} \, dx\)
3.20
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x^{7/2}} \, dx\)
3.21
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x^{11/2}} \, dx\)
3.22
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x^{15/2}} \, dx\)
3.23
\(\int x^{7/2} \tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}) \, dx\)
3.24
\(\int x^{3/2} \tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}) \, dx\)
3.25
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{\sqrt{x}} \, dx\)
3.26
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x^{5/2}} \, dx\)
3.27
\(\int \frac{\tanh ^{-1}(\frac{\sqrt{e} x}{\sqrt{d+e x^2}})}{x^{9/2}} \, dx\)
3.28
\(\int x^3 \tanh ^{-1}(a+b x^4) \, dx\)
3.29
\(\int x^{-1+n} \tanh ^{-1}(a+b x^n) \, dx\)
3.30
\(\int \frac{(a+b \tanh ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))^n}{1-c^2 x^2} \, dx\)
3.31
\(\int \frac{(a+b \tanh ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))^3}{1-c^2 x^2} \, dx\)
3.32
\(\int \frac{(a+b \tanh ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))^2}{1-c^2 x^2} \, dx\)
3.33
\(\int \frac{a+b \tanh ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}})}{1-c^2 x^2} \, dx\)
3.34
\(\int \frac{1}{(1-c^2 x^2) (a+b \tanh ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))} \, dx\)
3.35
\(\int \frac{1}{(1-c^2 x^2) (a+b \tanh ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))^2} \, dx\)
3.36
\(\int x^m \tanh ^{-1}(\tanh (a+b x)) \, dx\)
3.37
\(\int x^2 \tanh ^{-1}(\tanh (a+b x)) \, dx\)
3.38
\(\int x \tanh ^{-1}(\tanh (a+b x)) \, dx\)
3.39
\(\int \tanh ^{-1}(\tanh (a+b x)) \, dx\)
3.40
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x} \, dx\)
3.41
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^2} \, dx\)
3.42
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^3} \, dx\)
3.43
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^4} \, dx\)
3.44
\(\int x^m \tanh ^{-1}(\tanh (a+b x))^2 \, dx\)
3.45
\(\int x^3 \tanh ^{-1}(\tanh (a+b x))^2 \, dx\)
3.46
\(\int x^2 \tanh ^{-1}(\tanh (a+b x))^2 \, dx\)
3.47
\(\int x \tanh ^{-1}(\tanh (a+b x))^2 \, dx\)
3.48
\(\int \tanh ^{-1}(\tanh (a+b x))^2 \, dx\)
3.49
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x} \, dx\)
3.50
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^2} \, dx\)
3.51
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^3} \, dx\)
3.52
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^4} \, dx\)
3.53
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^5} \, dx\)
3.54
\(\int x^m \tanh ^{-1}(\tanh (a+b x))^3 \, dx\)
3.55
\(\int x^3 \tanh ^{-1}(\tanh (a+b x))^3 \, dx\)
3.56
\(\int x^2 \tanh ^{-1}(\tanh (a+b x))^3 \, dx\)
3.57
\(\int x \tanh ^{-1}(\tanh (a+b x))^3 \, dx\)
3.58
\(\int \tanh ^{-1}(\tanh (a+b x))^3 \, dx\)
3.59
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x} \, dx\)
3.60
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^2} \, dx\)
3.61
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^3} \, dx\)
3.62
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^4} \, dx\)
3.63
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^5} \, dx\)
3.64
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^6} \, dx\)
3.65
\(\int x^m \tanh ^{-1}(\tanh (a+b x))^4 \, dx\)
3.66
\(\int x^6 \tanh ^{-1}(\tanh (a+b x))^4 \, dx\)
3.67
\(\int x^5 \tanh ^{-1}(\tanh (a+b x))^4 \, dx\)
3.68
\(\int x^4 \tanh ^{-1}(\tanh (a+b x))^4 \, dx\)
3.69
\(\int x^3 \tanh ^{-1}(\tanh (a+b x))^4 \, dx\)
3.70
\(\int x^2 \tanh ^{-1}(\tanh (a+b x))^4 \, dx\)
3.71
\(\int x \tanh ^{-1}(\tanh (a+b x))^4 \, dx\)
3.72
\(\int \tanh ^{-1}(\tanh (a+b x))^4 \, dx\)
3.73
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x} \, dx\)
3.74
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^2} \, dx\)
3.75
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^3} \, dx\)
3.76
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^4} \, dx\)
3.77
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^5} \, dx\)
3.78
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^6} \, dx\)
3.79
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^7} \, dx\)
3.80
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^8} \, dx\)
3.81
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^9} \, dx\)
3.82
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^{10}} \, dx\)
3.83
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^{11}} \, dx\)
3.84
\(\int x \tanh ^{-1}(\tanh (a+b x))^6 \, dx\)
3.85
\(\int \frac{x^m}{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.86
\(\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.87
\(\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.88
\(\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.89
\(\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.90
\(\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.91
\(\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.92
\(\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.93
\(\int \frac{x^m}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.94
\(\int \frac{x^4}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.95
\(\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.96
\(\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.97
\(\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.98
\(\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.99
\(\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.100
\(\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.101
\(\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.102
\(\int \frac{x^m}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.103
\(\int \frac{x^4}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.104
\(\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.105
\(\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.106
\(\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.107
\(\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.108
\(\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.109
\(\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.110
\(\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.111
\(\int x^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.112
\(\int x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.113
\(\int x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.114
\(\int x \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.115
\(\int \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.116
\(\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x} \, dx\)
3.117
\(\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^2} \, dx\)
3.118
\(\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^3} \, dx\)
3.119
\(\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^4} \, dx\)
3.120
\(\int x^4 \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx\)
3.121
\(\int x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx\)
3.122
\(\int x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx\)
3.123
\(\int x \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx\)
3.124
\(\int \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx\)
3.125
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x} \, dx\)
3.126
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^2} \, dx\)
3.127
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^3} \, dx\)
3.128
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^4} \, dx\)
3.129
\(\int x^4 \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx\)
3.130
\(\int x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx\)
3.131
\(\int x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx\)
3.132
\(\int x \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx\)
3.133
\(\int \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx\)
3.134
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x} \, dx\)
3.135
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^2} \, dx\)
3.136
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^3} \, dx\)
3.137
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^4} \, dx\)
3.138
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^5} \, dx\)
3.139
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^6} \, dx\)
3.140
\(\int \frac{x^4}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.141
\(\int \frac{x^3}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.142
\(\int \frac{x^2}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.143
\(\int \frac{x}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.144
\(\int \frac{1}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.145
\(\int \frac{1}{x \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.146
\(\int \frac{1}{x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.147
\(\int \frac{1}{x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.148
\(\int \frac{1}{x^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.149
\(\int \frac{x^4}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.150
\(\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.151
\(\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.152
\(\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.153
\(\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.154
\(\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.155
\(\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.156
\(\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.157
\(\int \frac{1}{x^4 \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.158
\(\int \frac{x^4}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.159
\(\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.160
\(\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.161
\(\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.162
\(\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.163
\(\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.164
\(\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.165
\(\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.166
\(\int \frac{1}{x^4 \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.167
\(\int x^{7/2} \tanh ^{-1}(\tanh (a+b x)) \, dx\)
3.168
\(\int x^{5/2} \tanh ^{-1}(\tanh (a+b x)) \, dx\)
3.169
\(\int x^{3/2} \tanh ^{-1}(\tanh (a+b x)) \, dx\)
3.170
\(\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x)) \, dx\)
3.171
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))}{\sqrt{x}} \, dx\)
3.172
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^{3/2}} \, dx\)
3.173
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^{5/2}} \, dx\)
3.174
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^{7/2}} \, dx\)
3.175
\(\int x^{7/2} \tanh ^{-1}(\tanh (a+b x))^2 \, dx\)
3.176
\(\int x^{5/2} \tanh ^{-1}(\tanh (a+b x))^2 \, dx\)
3.177
\(\int x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2 \, dx\)
3.178
\(\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^2 \, dx\)
3.179
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{\sqrt{x}} \, dx\)
3.180
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^{3/2}} \, dx\)
3.181
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^{5/2}} \, dx\)
3.182
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^{7/2}} \, dx\)
3.183
\(\int x^{7/2} \tanh ^{-1}(\tanh (a+b x))^3 \, dx\)
3.184
\(\int x^{5/2} \tanh ^{-1}(\tanh (a+b x))^3 \, dx\)
3.185
\(\int x^{3/2} \tanh ^{-1}(\tanh (a+b x))^3 \, dx\)
3.186
\(\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^3 \, dx\)
3.187
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{\sqrt{x}} \, dx\)
3.188
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^{3/2}} \, dx\)
3.189
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^{5/2}} \, dx\)
3.190
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^{7/2}} \, dx\)
3.191
\(\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.192
\(\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.193
\(\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.194
\(\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.195
\(\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.196
\(\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.197
\(\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.198
\(\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.199
\(\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.200
\(\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.201
\(\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.202
\(\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.203
\(\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.204
\(\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.205
\(\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.206
\(\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))^2} \, dx\)
3.207
\(\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.208
\(\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.209
\(\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.210
\(\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.211
\(\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.212
\(\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.213
\(\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.214
\(\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))^3} \, dx\)
3.215
\(\int x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.216
\(\int \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx\)
3.217
\(\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{x}} \, dx\)
3.218
\(\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{3/2}} \, dx\)
3.219
\(\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{5/2}} \, dx\)
3.220
\(\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{7/2}} \, dx\)
3.221
\(\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{9/2}} \, dx\)
3.222
\(\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{11/2}} \, dx\)
3.223
\(\int x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx\)
3.224
\(\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx\)
3.225
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{\sqrt{x}} \, dx\)
3.226
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{3/2}} \, dx\)
3.227
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{5/2}} \, dx\)
3.228
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{7/2}} \, dx\)
3.229
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{9/2}} \, dx\)
3.230
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{11/2}} \, dx\)
3.231
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{13/2}} \, dx\)
3.232
\(\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx\)
3.233
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{\sqrt{x}} \, dx\)
3.234
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{3/2}} \, dx\)
3.235
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{5/2}} \, dx\)
3.236
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{7/2}} \, dx\)
3.237
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{9/2}} \, dx\)
3.238
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{11/2}} \, dx\)
3.239
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{13/2}} \, dx\)
3.240
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{15/2}} \, dx\)
3.241
\(\int \frac{x^{5/2}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.242
\(\int \frac{x^{3/2}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.243
\(\int \frac{\sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.244
\(\int \frac{1}{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.245
\(\int \frac{1}{x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.246
\(\int \frac{1}{x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.247
\(\int \frac{1}{x^{7/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.248
\(\int \frac{1}{x^{9/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx\)
3.249
\(\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.250
\(\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.251
\(\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.252
\(\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.253
\(\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.254
\(\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.255
\(\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.256
\(\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx\)
3.257
\(\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.258
\(\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.259
\(\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.260
\(\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.261
\(\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.262
\(\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.263
\(\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.264
\(\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx\)
3.265
\(\int x^m \tanh ^{-1}(\tanh (a+b x))^n \, dx\)
3.266
\(\int x^4 \tanh ^{-1}(\tanh (a+b x))^n \, dx\)
3.267
\(\int x^3 \tanh ^{-1}(\tanh (a+b x))^n \, dx\)
3.268
\(\int x^2 \tanh ^{-1}(\tanh (a+b x))^n \, dx\)
3.269
\(\int x \tanh ^{-1}(\tanh (a+b x))^n \, dx\)
3.270
\(\int \tanh ^{-1}(\tanh (a+b x))^n \, dx\)
3.271
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^n}{x} \, dx\)
3.272
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^n}{x^2} \, dx\)
3.273
\(\int \frac{\tanh ^{-1}(\tanh (a+b x))^n}{x^3} \, dx\)
3.274
\(\int x^m \coth ^{-1}(\tanh (a+b x)) \, dx\)
3.275
\(\int x^2 \tanh ^{-1}(\coth (a+b x)) \, dx\)
3.276
\(\int x \tanh ^{-1}(\coth (a+b x)) \, dx\)
3.277
\(\int \tanh ^{-1}(\coth (a+b x)) \, dx\)
3.278
\(\int \frac{\tanh ^{-1}(\coth (a+b x))}{x} \, dx\)
3.279
\(\int \frac{\tanh ^{-1}(\coth (a+b x))}{x^2} \, dx\)
3.280
\(\int \frac{\tanh ^{-1}(\coth (a+b x))}{x^3} \, dx\)
3.281
\(\int \tanh ^{-1}(\cosh (x)) \, dx\)
3.282
\(\int x \tanh ^{-1}(\cosh (x)) \, dx\)
3.283
\(\int x^2 \tanh ^{-1}(\cosh (x)) \, dx\)
3.284
\(\int x^2 \tanh ^{-1}(c+d \tanh (a+b x)) \, dx\)
3.285
\(\int x \tanh ^{-1}(c+d \tanh (a+b x)) \, dx\)
3.286
\(\int \tanh ^{-1}(c+d \tanh (a+b x)) \, dx\)
3.287
\(\int \frac{\tanh ^{-1}(c+d \tanh (a+b x))}{x} \, dx\)
3.288
\(\int x^3 \tanh ^{-1}(1+d+d \tanh (a+b x)) \, dx\)
3.289
\(\int x^2 \tanh ^{-1}(1+d+d \tanh (a+b x)) \, dx\)
3.290
\(\int x \tanh ^{-1}(1+d+d \tanh (a+b x)) \, dx\)
3.291
\(\int \tanh ^{-1}(1+d+d \tanh (a+b x)) \, dx\)
3.292
\(\int \frac{\tanh ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx\)
3.293
\(\int x^3 \tanh ^{-1}(1-d-d \tanh (a+b x)) \, dx\)
3.294
\(\int x^2 \tanh ^{-1}(1-d-d \tanh (a+b x)) \, dx\)
3.295
\(\int x \tanh ^{-1}(1-d-d \tanh (a+b x)) \, dx\)
3.296
\(\int \tanh ^{-1}(1-d-d \tanh (a+b x)) \, dx\)
3.297
\(\int \frac{\tanh ^{-1}(1-d-d \tanh (a+b x))}{x} \, dx\)
3.298
\(\int x^2 \tanh ^{-1}(c+d \coth (a+b x)) \, dx\)
3.299
\(\int x \tanh ^{-1}(c+d \coth (a+b x)) \, dx\)
3.300
\(\int \tanh ^{-1}(c+d \coth (a+b x)) \, dx\)
3.301
\(\int \frac{\tanh ^{-1}(c+d \coth (a+b x))}{x} \, dx\)
3.302
\(\int x^3 \tanh ^{-1}(1+d+d \coth (a+b x)) \, dx\)
3.303
\(\int x^2 \tanh ^{-1}(1+d+d \coth (a+b x)) \, dx\)
3.304
\(\int x \tanh ^{-1}(1+d+d \coth (a+b x)) \, dx\)
3.305
\(\int \tanh ^{-1}(1+d+d \coth (a+b x)) \, dx\)
3.306
\(\int \frac{\tanh ^{-1}(1+d+d \coth (a+b x))}{x} \, dx\)
3.307
\(\int x^3 \tanh ^{-1}(1-d-d \coth (a+b x)) \, dx\)
3.308
\(\int x^2 \tanh ^{-1}(1-d-d \coth (a+b x)) \, dx\)
3.309
\(\int x \tanh ^{-1}(1-d-d \coth (a+b x)) \, dx\)
3.310
\(\int \tanh ^{-1}(1-d-d \coth (a+b x)) \, dx\)
3.311
\(\int \frac{\tanh ^{-1}(1-d-d \coth (a+b x))}{x} \, dx\)
3.312
\(\int (e+f x)^3 \tanh ^{-1}(\tan (a+b x)) \, dx\)
3.313
\(\int (e+f x)^2 \tanh ^{-1}(\tan (a+b x)) \, dx\)
3.314
\(\int (e+f x) \tanh ^{-1}(\tan (a+b x)) \, dx\)
3.315
\(\int \tanh ^{-1}(\tan (a+b x)) \, dx\)
3.316
\(\int \frac{\tanh ^{-1}(\tan (a+b x))}{e+f x} \, dx\)
3.317
\(\int x^2 \tanh ^{-1}(c+d \tan (a+b x)) \, dx\)
3.318
\(\int x \tanh ^{-1}(c+d \tan (a+b x)) \, dx\)
3.319
\(\int \tanh ^{-1}(c+d \tan (a+b x)) \, dx\)
3.320
\(\int \frac{\tanh ^{-1}(c+d \tan (a+b x))}{x} \, dx\)
3.321
\(\int x^2 \tanh ^{-1}(1-i d+d \tan (a+b x)) \, dx\)
3.322
\(\int x \tanh ^{-1}(1-i d+d \tan (a+b x)) \, dx\)
3.323
\(\int \tanh ^{-1}(1-i d+d \tan (a+b x)) \, dx\)
3.324
\(\int \frac{\tanh ^{-1}(1-i d+d \tan (a+b x))}{x} \, dx\)
3.325
\(\int x^2 \tanh ^{-1}(1+i d-d \tan (a+b x)) \, dx\)
3.326
\(\int x \tanh ^{-1}(1+i d-d \tan (a+b x)) \, dx\)
3.327
\(\int \tanh ^{-1}(1+i d-d \tan (a+b x)) \, dx\)
3.328
\(\int \frac{\tanh ^{-1}(1+i d-d \tan (a+b x))}{x} \, dx\)
3.329
\(\int (e+f x)^3 \tanh ^{-1}(\cot (a+b x)) \, dx\)
3.330
\(\int (e+f x)^2 \tanh ^{-1}(\cot (a+b x)) \, dx\)
3.331
\(\int (e+f x) \tanh ^{-1}(\cot (a+b x)) \, dx\)
3.332
\(\int \tanh ^{-1}(\cot (a+b x)) \, dx\)
3.333
\(\int \frac{\tanh ^{-1}(\cot (a+b x))}{e+f x} \, dx\)
3.334
\(\int x^2 \tanh ^{-1}(c+d \cot (a+b x)) \, dx\)
3.335
\(\int x \tanh ^{-1}(c+d \cot (a+b x)) \, dx\)
3.336
\(\int \tanh ^{-1}(c+d \cot (a+b x)) \, dx\)
3.337
\(\int \frac{\tanh ^{-1}(c+d \cot (a+b x))}{x} \, dx\)
3.338
\(\int x^2 \tanh ^{-1}(1+i d+d \cot (a+b x)) \, dx\)
3.339
\(\int x \tanh ^{-1}(1+i d+d \cot (a+b x)) \, dx\)
3.340
\(\int \tanh ^{-1}(1+i d+d \cot (a+b x)) \, dx\)
3.341
\(\int \frac{\tanh ^{-1}(1+i d+d \cot (a+b x))}{x} \, dx\)
3.342
\(\int x^2 \tanh ^{-1}(1-i d-d \cot (a+b x)) \, dx\)
3.343
\(\int x \tanh ^{-1}(1-i d-d \cot (a+b x)) \, dx\)
3.344
\(\int \tanh ^{-1}(1-i d-d \cot (a+b x)) \, dx\)
3.345
\(\int \frac{\tanh ^{-1}(1-i d-d \cot (a+b x))}{x} \, dx\)
3.346
\(\int \tanh ^{-1}(e^x) \, dx\)
3.347
\(\int x \tanh ^{-1}(e^x) \, dx\)
3.348
\(\int x^2 \tanh ^{-1}(e^x) \, dx\)
3.349
\(\int \tanh ^{-1}(e^{a+b x}) \, dx\)
3.350
\(\int x \tanh ^{-1}(e^{a+b x}) \, dx\)
3.351
\(\int x^2 \tanh ^{-1}(e^{a+b x}) \, dx\)
3.352
\(\int \tanh ^{-1}(a+b f^{c+d x}) \, dx\)
3.353
\(\int x \tanh ^{-1}(a+b f^{c+d x}) \, dx\)
3.354
\(\int x^2 \tanh ^{-1}(a+b f^{c+d x}) \, dx\)
3.355
\(\int e^{c (a+b x)} \tanh ^{-1}(\sinh (a c+b c x)) \, dx\)
3.356
\(\int e^{c (a+b x)} \tanh ^{-1}(\cosh (a c+b c x)) \, dx\)
3.357
\(\int e^{c (a+b x)} \tanh ^{-1}(\tanh (a c+b c x)) \, dx\)
3.358
\(\int e^{c (a+b x)} \tanh ^{-1}(\coth (a c+b c x)) \, dx\)
3.359
\(\int e^{c (a+b x)} \tanh ^{-1}(\text{sech}(a c+b c x)) \, dx\)
3.360
\(\int e^{c (a+b x)} \tanh ^{-1}(\text{csch}(a c+b c x)) \, dx\)
3.361
\(\int \frac{(a+b \tanh ^{-1}(c x^n)) (d+e \log (f x^m))}{x} \, dx\)
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