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Chapter 3
Listing of integrals
3.1
\(\int \text{sech}(a+b x) \, dx\)
3.2
\(\int \text{sech}^2(a+b x) \, dx\)
3.3
\(\int \text{sech}^3(a+b x) \, dx\)
3.4
\(\int \text{sech}^4(a+b x) \, dx\)
3.5
\(\int \text{sech}^5(a+b x) \, dx\)
3.6
\(\int \text{sech}^6(a+b x) \, dx\)
3.7
\(\int \text{sech}^4(7 x) \, dx\)
3.8
\(\int \text{sech}^6(\pi x) \, dx\)
3.9
\(\int \text{sech}^{\frac{5}{2}}(a+b x) \, dx\)
3.10
\(\int \text{sech}^{\frac{3}{2}}(a+b x) \, dx\)
3.11
\(\int \sqrt{\text{sech}(a+b x)} \, dx\)
3.12
\(\int \frac{1}{\sqrt{\text{sech}(a+b x)}} \, dx\)
3.13
\(\int \frac{1}{\text{sech}^{\frac{3}{2}}(a+b x)} \, dx\)
3.14
\(\int \frac{1}{\text{sech}^{\frac{5}{2}}(a+b x)} \, dx\)
3.15
\(\int (b \text{sech}(c+d x))^{7/2} \, dx\)
3.16
\(\int (b \text{sech}(c+d x))^{5/2} \, dx\)
3.17
\(\int (b \text{sech}(c+d x))^{3/2} \, dx\)
3.18
\(\int \sqrt{b \text{sech}(c+d x)} \, dx\)
3.19
\(\int \frac{1}{\sqrt{b \text{sech}(c+d x)}} \, dx\)
3.20
\(\int \frac{1}{(b \text{sech}(c+d x))^{3/2}} \, dx\)
3.21
\(\int \frac{1}{(b \text{sech}(c+d x))^{5/2}} \, dx\)
3.22
\(\int \frac{1}{(b \text{sech}(c+d x))^{7/2}} \, dx\)
3.23
\(\int (b \text{sech}(c+d x))^n \, dx\)
3.24
\(\int \text{sech}^2(a+b x)^{7/2} \, dx\)
3.25
\(\int \text{sech}^2(a+b x)^{5/2} \, dx\)
3.26
\(\int \text{sech}^2(a+b x)^{3/2} \, dx\)
3.27
\(\int \sqrt{\text{sech}^2(a+b x)} \, dx\)
3.28
\(\int \frac{1}{\sqrt{\text{sech}^2(a+b x)}} \, dx\)
3.29
\(\int \frac{1}{\text{sech}^2(a+b x)^{3/2}} \, dx\)
3.30
\(\int \frac{1}{\text{sech}^2(a+b x)^{5/2}} \, dx\)
3.31
\(\int \frac{1}{\text{sech}^2(a+b x)^{7/2}} \, dx\)
3.32
\(\int (a \text{sech}^2(x))^{5/2} \, dx\)
3.33
\(\int (a \text{sech}^2(x))^{3/2} \, dx\)
3.34
\(\int \sqrt{a \text{sech}^2(x)} \, dx\)
3.35
\(\int \frac{1}{\sqrt{a \text{sech}^2(x)}} \, dx\)
3.36
\(\int \frac{1}{(a \text{sech}^2(x))^{3/2}} \, dx\)
3.37
\(\int \frac{1}{(a \text{sech}^2(x))^{5/2}} \, dx\)
3.38
\(\int \frac{1}{(a \text{sech}^2(x))^{7/2}} \, dx\)
3.39
\(\int (a \text{sech}^3(x))^{5/2} \, dx\)
3.40
\(\int (a \text{sech}^3(x))^{3/2} \, dx\)
3.41
\(\int \sqrt{a \text{sech}^3(x)} \, dx\)
3.42
\(\int \frac{1}{\sqrt{a \text{sech}^3(x)}} \, dx\)
3.43
\(\int \frac{1}{(a \text{sech}^3(x))^{3/2}} \, dx\)
3.44
\(\int \frac{1}{(a \text{sech}^3(x))^{5/2}} \, dx\)
3.45
\(\int (a \text{sech}^4(x))^{7/2} \, dx\)
3.46
\(\int (a \text{sech}^4(x))^{5/2} \, dx\)
3.47
\(\int (a \text{sech}^4(x))^{3/2} \, dx\)
3.48
\(\int \sqrt{a \text{sech}^4(x)} \, dx\)
3.49
\(\int \frac{1}{\sqrt{a \text{sech}^4(x)}} \, dx\)
3.50
\(\int \frac{1}{(a \text{sech}^4(x))^{3/2}} \, dx\)
3.51
\(\int \frac{1}{(a \text{sech}^4(x))^{5/2}} \, dx\)
3.52
\(\int \frac{\sinh ^4(x)}{a+a \text{sech}(x)} \, dx\)
3.53
\(\int \frac{\sinh ^3(x)}{a+a \text{sech}(x)} \, dx\)
3.54
\(\int \frac{\sinh ^2(x)}{a+a \text{sech}(x)} \, dx\)
3.55
\(\int \frac{\sinh (x)}{a+a \text{sech}(x)} \, dx\)
3.56
\(\int \frac{\text{csch}(x)}{a+a \text{sech}(x)} \, dx\)
3.57
\(\int \frac{\text{csch}^2(x)}{a+a \text{sech}(x)} \, dx\)
3.58
\(\int \frac{\text{csch}^3(x)}{a+a \text{sech}(x)} \, dx\)
3.59
\(\int \frac{\text{csch}^4(x)}{a+a \text{sech}(x)} \, dx\)
3.60
\(\int \frac{\sinh ^4(x)}{a+b \text{sech}(x)} \, dx\)
3.61
\(\int \frac{\sinh ^3(x)}{a+b \text{sech}(x)} \, dx\)
3.62
\(\int \frac{\sinh ^2(x)}{a+b \text{sech}(x)} \, dx\)
3.63
\(\int \frac{\sinh (x)}{a+b \text{sech}(x)} \, dx\)
3.64
\(\int \frac{\text{csch}(x)}{a+b \text{sech}(x)} \, dx\)
3.65
\(\int \frac{\text{csch}^2(x)}{a+b \text{sech}(x)} \, dx\)
3.66
\(\int \frac{\text{csch}^3(x)}{a+b \text{sech}(x)} \, dx\)
3.67
\(\int \frac{\text{csch}^4(x)}{a+b \text{sech}(x)} \, dx\)
3.68
\(\int \frac{\cosh ^4(x)}{a+a \text{sech}(x)} \, dx\)
3.69
\(\int \frac{\cosh ^3(x)}{a+a \text{sech}(x)} \, dx\)
3.70
\(\int \frac{\cosh ^2(x)}{a+a \text{sech}(x)} \, dx\)
3.71
\(\int \frac{\cosh (x)}{a+a \text{sech}(x)} \, dx\)
3.72
\(\int \frac{\text{sech}(x)}{a+a \text{sech}(x)} \, dx\)
3.73
\(\int \frac{\text{sech}^2(x)}{a+a \text{sech}(x)} \, dx\)
3.74
\(\int \frac{\text{sech}^3(x)}{a+a \text{sech}(x)} \, dx\)
3.75
\(\int \frac{\text{sech}^4(x)}{a+a \text{sech}(x)} \, dx\)
3.76
\(\int \frac{1}{a+a \text{sech}(c+d x)} \, dx\)
3.77
\(\int \frac{1}{a-a \text{sech}(c+d x)} \, dx\)
3.78
\(\int (a+a \text{sech}(c+d x))^{5/2} \, dx\)
3.79
\(\int (a+a \text{sech}(c+d x))^{3/2} \, dx\)
3.80
\(\int \sqrt{a+a \text{sech}(c+d x)} \, dx\)
3.81
\(\int \frac{1}{\sqrt{a+a \text{sech}(c+d x)}} \, dx\)
3.82
\(\int \frac{1}{(a+a \text{sech}(c+d x))^{3/2}} \, dx\)
3.83
\(\int \sqrt{a-a \text{sech}(c+d x)} \, dx\)
3.84
\(\int \frac{1}{\sqrt{a-a \text{sech}(c+d x)}} \, dx\)
3.85
\(\int \sqrt{3+3 \text{sech}(x)} \, dx\)
3.86
\(\int \sqrt{3-3 \text{sech}(x)} \, dx\)
3.87
\(\int (a+b \text{sech}(c+d x))^4 \, dx\)
3.88
\(\int (a+b \text{sech}(c+d x))^3 \, dx\)
3.89
\(\int (a+b \text{sech}(c+d x))^2 \, dx\)
3.90
\(\int (a+b \text{sech}(c+d x)) \, dx\)
3.91
\(\int \frac{1}{a+b \text{sech}(c+d x)} \, dx\)
3.92
\(\int \frac{1}{(a+b \text{sech}(c+d x))^2} \, dx\)
3.93
\(\int \frac{1}{(a+b \text{sech}(c+d x))^3} \, dx\)
3.94
\(\int \frac{1}{\sqrt{a+b \text{sech}(c+d x)}} \, dx\)
3.95
\(\int \frac{\cosh ^4(x)}{a+b \text{sech}(x)} \, dx\)
3.96
\(\int \frac{\cosh ^3(x)}{a+b \text{sech}(x)} \, dx\)
3.97
\(\int \frac{\cosh ^2(x)}{a+b \text{sech}(x)} \, dx\)
3.98
\(\int \frac{\cosh (x)}{a+b \text{sech}(x)} \, dx\)
3.99
\(\int \frac{\text{sech}(x)}{a+b \text{sech}(x)} \, dx\)
3.100
\(\int \frac{\text{sech}^2(x)}{a+b \text{sech}(x)} \, dx\)
3.101
\(\int \frac{\text{sech}^3(x)}{a+b \text{sech}(x)} \, dx\)
3.102
\(\int \frac{\text{sech}^4(x)}{a+b \text{sech}(x)} \, dx\)
3.103
\(\int \frac{\tanh ^6(x)}{a+a \text{sech}(x)} \, dx\)
3.104
\(\int \frac{\tanh ^5(x)}{a+a \text{sech}(x)} \, dx\)
3.105
\(\int \frac{\tanh ^4(x)}{a+a \text{sech}(x)} \, dx\)
3.106
\(\int \frac{\tanh ^3(x)}{a+a \text{sech}(x)} \, dx\)
3.107
\(\int \frac{\tanh ^2(x)}{a+a \text{sech}(x)} \, dx\)
3.108
\(\int \frac{\tanh (x)}{a+a \text{sech}(x)} \, dx\)
3.109
\(\int \frac{\coth (x)}{a+a \text{sech}(x)} \, dx\)
3.110
\(\int \frac{\coth ^2(x)}{a+a \text{sech}(x)} \, dx\)
3.111
\(\int \frac{\coth ^3(x)}{a+a \text{sech}(x)} \, dx\)
3.112
\(\int \frac{\coth ^4(x)}{a+a \text{sech}(x)} \, dx\)
3.113
\(\int \frac{\tanh ^7(x)}{a+b \text{sech}(x)} \, dx\)
3.114
\(\int \frac{\tanh ^6(x)}{a+b \text{sech}(x)} \, dx\)
3.115
\(\int \frac{\tanh ^5(x)}{a+b \text{sech}(x)} \, dx\)
3.116
\(\int \frac{\tanh ^4(x)}{a+b \text{sech}(x)} \, dx\)
3.117
\(\int \frac{\tanh ^3(x)}{a+b \text{sech}(x)} \, dx\)
3.118
\(\int \frac{\tanh ^2(x)}{a+b \text{sech}(x)} \, dx\)
3.119
\(\int \frac{\tanh (x)}{a+b \text{sech}(x)} \, dx\)
3.120
\(\int \frac{\coth (x)}{a+b \text{sech}(x)} \, dx\)
3.121
\(\int \frac{\coth ^2(x)}{a+b \text{sech}(x)} \, dx\)
3.122
\(\int \frac{\coth ^3(x)}{a+b \text{sech}(x)} \, dx\)
3.123
\(\int \frac{\coth ^4(x)}{a+b \text{sech}(x)} \, dx\)
3.124
\(\int \frac{\coth ^5(x)}{a+b \text{sech}(x)} \, dx\)
3.125
\(\int \sqrt{a+b \text{sech}(c+d x)} \tanh ^5(c+d x) \, dx\)
3.126
\(\int \sqrt{a+b \text{sech}(c+d x)} \tanh ^3(c+d x) \, dx\)
3.127
\(\int \sqrt{a+b \text{sech}(c+d x)} \tanh (c+d x) \, dx\)
3.128
\(\int \coth (c+d x) \sqrt{a+b \text{sech}(c+d x)} \, dx\)
3.129
\(\int \coth ^3(c+d x) \sqrt{a+b \text{sech}(c+d x)} \, dx\)
3.130
\(\int \sqrt{a+b \text{sech}(c+d x)} \tanh ^2(c+d x) \, dx\)
3.131
\(\int \sqrt{a+b \text{sech}(c+d x)} \, dx\)
3.132
\(\int \coth ^2(c+d x) \sqrt{a+b \text{sech}(c+d x)} \, dx\)
3.133
\(\int \frac{\tanh ^5(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx\)
3.134
\(\int \frac{\tanh ^3(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx\)
3.135
\(\int \frac{\tanh (c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx\)
3.136
\(\int \frac{\coth (c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx\)
3.137
\(\int \frac{\coth ^3(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx\)
3.138
\(\int \frac{\tanh ^4(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx\)
3.139
\(\int \frac{\tanh ^2(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx\)
3.140
\(\int \frac{1}{\sqrt{a+b \text{sech}(c+d x)}} \, dx\)
3.141
\(\int \frac{\coth ^2(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx\)
3.142
\(\int \frac{\tanh ^5(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx\)
3.143
\(\int \frac{\tanh ^3(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx\)
3.144
\(\int \frac{\tanh (c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx\)
3.145
\(\int \frac{\coth (c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx\)
3.146
\(\int \frac{\coth ^3(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx\)
3.147
\(\int \frac{\tanh ^4(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx\)
3.148
\(\int \frac{\tanh ^2(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx\)
3.149
\(\int \frac{1}{(a+b \text{sech}(c+d x))^{3/2}} \, dx\)
3.150
\(\int \frac{\coth ^2(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx\)
3.151
\(\int e^{c (a+b x)} \text{sech}^2(a c+b c x)^{7/2} \, dx\)
3.152
\(\int e^{c (a+b x)} \text{sech}^2(a c+b c x)^{5/2} \, dx\)
3.153
\(\int e^{c (a+b x)} \text{sech}^2(a c+b c x)^{3/2} \, dx\)
3.154
\(\int e^{c (a+b x)} \sqrt{\text{sech}^2(a c+b c x)} \, dx\)
3.155
\(\int \frac{e^{c (a+b x)}}{\sqrt{\text{sech}^2(a c+b c x)}} \, dx\)
3.156
\(\int \frac{e^{c (a+b x)}}{\text{sech}^2(a c+b c x)^{3/2}} \, dx\)
3.157
\(\int \frac{e^{c (a+b x)}}{\text{sech}^2(a c+b c x)^{5/2}} \, dx\)
3.158
\(\int \frac{x^5}{\sqrt{\text{sech}(2 \log (c x))}} \, dx\)
3.159
\(\int \frac{x^4}{\sqrt{\text{sech}(2 \log (c x))}} \, dx\)
3.160
\(\int \frac{x^3}{\sqrt{\text{sech}(2 \log (c x))}} \, dx\)
3.161
\(\int \frac{x^2}{\sqrt{\text{sech}(2 \log (c x))}} \, dx\)
3.162
\(\int \frac{x}{\sqrt{\text{sech}(2 \log (c x))}} \, dx\)
3.163
\(\int \frac{1}{\sqrt{\text{sech}(2 \log (c x))}} \, dx\)
3.164
\(\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x} \, dx\)
3.165
\(\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x^2} \, dx\)
3.166
\(\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x^3} \, dx\)
3.167
\(\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x^4} \, dx\)
3.168
\(\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x^5} \, dx\)
3.169
\(\int \frac{x^8}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx\)
3.170
\(\int \frac{x^7}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx\)
3.171
\(\int \frac{x^6}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx\)
3.172
\(\int \frac{x^5}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx\)
3.173
\(\int \frac{x^4}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx\)
3.174
\(\int \frac{x^3}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx\)
3.175
\(\int \frac{x^2}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx\)
3.176
\(\int \frac{x}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx\)
3.177
\(\int \frac{1}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx\)
3.178
\(\int \frac{\text{sech}^{\frac{3}{2}}(2 \log (c x))}{x} \, dx\)
3.179
\(\int \frac{\text{sech}^{\frac{3}{2}}(2 \log (c x))}{x^2} \, dx\)
3.180
\(\int \frac{\text{sech}^{\frac{3}{2}}(2 \log (c x))}{x^3} \, dx\)
3.181
\(\int \frac{\text{sech}^{\frac{3}{2}}(2 \log (c x))}{x^4} \, dx\)
3.182
\(\int \text{sech}(a+b \log (c x^n)) \, dx\)
3.183
\(\int \text{sech}^2(a+b \log (c x^n)) \, dx\)
3.184
\(\int \text{sech}^3(a+b \log (c x^n)) \, dx\)
3.185
\(\int \text{sech}^4(a+b \log (c x^n)) \, dx\)
3.186
\(\int ((1-b^2 n^2) \text{sech}(a+b \log (c x^n))+2 b^2 n^2 \text{sech}^3(a+b \log (c x^n))) \, dx\)
3.187
\(\int \text{sech}^3(a+2 \log (c \sqrt{x})) \, dx\)
3.188
\(\int \text{sech}^3(a+2 \log (\frac{c}{\sqrt{x}})) \, dx\)
3.189
\(\int \text{sech}^p(a+\frac{\log (c x^n)}{n (-2+p)}) \, dx\)
3.190
\(\int \text{sech}^p(a-\frac{\log (c x^n)}{n (-2+p)}) \, dx\)
3.191
\(\int \frac{\text{sech}(a+b \log (c x^n))}{x} \, dx\)
3.192
\(\int \frac{\text{sech}^2(a+b \log (c x^n))}{x} \, dx\)
3.193
\(\int \frac{\text{sech}^3(a+b \log (c x^n))}{x} \, dx\)
3.194
\(\int \frac{\text{sech}^4(a+b \log (c x^n))}{x} \, dx\)
3.195
\(\int \frac{\text{sech}^5(a+b \log (c x^n))}{x} \, dx\)
3.196
\(\int \frac{\text{sech}^{\frac{5}{2}}(a+b \log (c x^n))}{x} \, dx\)
3.197
\(\int \frac{\text{sech}^{\frac{3}{2}}(a+b \log (c x^n))}{x} \, dx\)
3.198
\(\int \frac{\sqrt{\text{sech}(a+b \log (c x^n))}}{x} \, dx\)
3.199
\(\int \frac{1}{x \sqrt{\text{sech}(a+b \log (c x^n))}} \, dx\)
3.200
\(\int \frac{1}{x \text{sech}^{\frac{3}{2}}(a+b \log (c x^n))} \, dx\)
3.201
\(\int \frac{1}{x \text{sech}^{\frac{5}{2}}(a+b \log (c x^n))} \, dx\)
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