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