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