[
next
] [
prev
] [
prev-tail
] [
tail
] [
up
]
Chapter 3
Listing of integrals
3.1
\(\int x^3 \tan ^{-1}(a+b x^4) \, dx\)
3.2
\(\int x^{-1+n} \tan ^{-1}(a+b x^n) \, dx\)
3.3
\(\int x^5 \tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}) \, dx\)
3.4
\(\int x^3 \tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}) \, dx\)
3.5
\(\int x \tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}) \, dx\)
3.6
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x} \, dx\)
3.7
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x^3} \, dx\)
3.8
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x^5} \, dx\)
3.9
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x^7} \, dx\)
3.10
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x^9} \, dx\)
3.11
\(\int x^6 \tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}) \, dx\)
3.12
\(\int x^4 \tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}) \, dx\)
3.13
\(\int x^2 \tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}) \, dx\)
3.14
\(\int \tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}) \, dx\)
3.15
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x^2} \, dx\)
3.16
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x^4} \, dx\)
3.17
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x^6} \, dx\)
3.18
\(\int x^{9/2} \tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}) \, dx\)
3.19
\(\int x^{5/2} \tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}) \, dx\)
3.20
\(\int \sqrt{x} \tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}) \, dx\)
3.21
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x^{3/2}} \, dx\)
3.22
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x^{7/2}} \, dx\)
3.23
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x^{11/2}} \, dx\)
3.24
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x^{15/2}} \, dx\)
3.25
\(\int x^{7/2} \tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}) \, dx\)
3.26
\(\int x^{3/2} \tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}) \, dx\)
3.27
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{\sqrt{x}} \, dx\)
3.28
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x^{5/2}} \, dx\)
3.29
\(\int \frac{\tan ^{-1}(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}})}{x^{9/2}} \, dx\)
3.30
\(\int \frac{\tan ^{-1}(1+x+x^2)}{x^2} \, dx\)
3.31
\(\int \frac{(a+b \tan ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))^n}{1-c^2 x^2} \, dx\)
3.32
\(\int \frac{(a+b \tan ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))^3}{1-c^2 x^2} \, dx\)
3.33
\(\int \frac{(a+b \tan ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))^2}{1-c^2 x^2} \, dx\)
3.34
\(\int \frac{a+b \tan ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}})}{1-c^2 x^2} \, dx\)
3.35
\(\int \frac{1}{(1-c^2 x^2) (a+b \tan ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))} \, dx\)
3.36
\(\int \frac{1}{(1-c^2 x^2) (a+b \tan ^{-1}(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}))^2} \, dx\)
3.37
\(\int x^m \tan ^{-1}(\tan (a+b x)) \, dx\)
3.38
\(\int x^2 \tan ^{-1}(\tan (a+b x)) \, dx\)
3.39
\(\int x \tan ^{-1}(\tan (a+b x)) \, dx\)
3.40
\(\int \tan ^{-1}(\tan (a+b x)) \, dx\)
3.41
\(\int \frac{\tan ^{-1}(\tan (a+b x))}{x} \, dx\)
3.42
\(\int x^m \tan ^{-1}(\cot (a+b x)) \, dx\)
3.43
\(\int x^2 \tan ^{-1}(\cot (a+b x)) \, dx\)
3.44
\(\int x \tan ^{-1}(\cot (a+b x)) \, dx\)
3.45
\(\int \tan ^{-1}(\cot (a+b x)) \, dx\)
3.46
\(\int \frac{\tan ^{-1}(\cot (a+b x))}{x} \, dx\)
3.47
\(\int \tan ^{-1}(\tan (a+b x)) \, dx\)
3.48
\(\int x^2 \tan ^{-1}(c+d \tan (a+b x)) \, dx\)
3.49
\(\int x \tan ^{-1}(c+d \tan (a+b x)) \, dx\)
3.50
\(\int \tan ^{-1}(c+d \tan (a+b x)) \, dx\)
3.51
\(\int \frac{\tan ^{-1}(c+d \tan (a+b x))}{x} \, dx\)
3.52
\(\int x^2 \tan ^{-1}(c+(1+i c) \tan (a+b x)) \, dx\)
3.53
\(\int x \tan ^{-1}(c+(1+i c) \tan (a+b x)) \, dx\)
3.54
\(\int \tan ^{-1}(c+(1+i c) \tan (a+b x)) \, dx\)
3.55
\(\int \frac{\tan ^{-1}(c+(1+i c) \tan (a+b x))}{x} \, dx\)
3.56
\(\int x^2 \tan ^{-1}(c+(-1+i c) \tan (a+b x)) \, dx\)
3.57
\(\int x \tan ^{-1}(c+(-1+i c) \tan (a+b x)) \, dx\)
3.58
\(\int \tan ^{-1}(c+(-1+i c) \tan (a+b x)) \, dx\)
3.59
\(\int \frac{\tan ^{-1}(c+(-1+i c) \tan (a+b x))}{x} \, dx\)
3.60
\(\int \tan ^{-1}(\cot (a+b x)) \, dx\)
3.61
\(\int x^2 \tan ^{-1}(c+d \cot (a+b x)) \, dx\)
3.62
\(\int x \tan ^{-1}(c+d \cot (a+b x)) \, dx\)
3.63
\(\int \tan ^{-1}(c+d \cot (a+b x)) \, dx\)
3.64
\(\int \frac{\tan ^{-1}(c+d \cot (a+b x))}{x} \, dx\)
3.65
\(\int x^2 \tan ^{-1}(c+(1-i c) \cot (a+b x)) \, dx\)
3.66
\(\int x \tan ^{-1}(c+(1-i c) \cot (a+b x)) \, dx\)
3.67
\(\int \tan ^{-1}(c+(1-i c) \cot (a+b x)) \, dx\)
3.68
\(\int \frac{\tan ^{-1}(c+(1-i c) \cot (a+b x))}{x} \, dx\)
3.69
\(\int x^2 \tan ^{-1}(c+(-1-i c) \cot (a+b x)) \, dx\)
3.70
\(\int x \tan ^{-1}(c+(-1-i c) \cot (a+b x)) \, dx\)
3.71
\(\int \tan ^{-1}(c+(-1-i c) \cot (a+b x)) \, dx\)
3.72
\(\int \frac{\tan ^{-1}(c+(-1-i c) \cot (a+b x))}{x} \, dx\)
3.73
\(\int \tan ^{-1}(\sinh (x)) \, dx\)
3.74
\(\int x \tan ^{-1}(\sinh (x)) \, dx\)
3.75
\(\int x^2 \tan ^{-1}(\sinh (x)) \, dx\)
3.76
\(\int (e+f x)^3 \tan ^{-1}(\tanh (a+b x)) \, dx\)
3.77
\(\int (e+f x)^2 \tan ^{-1}(\tanh (a+b x)) \, dx\)
3.78
\(\int (e+f x) \tan ^{-1}(\tanh (a+b x)) \, dx\)
3.79
\(\int \tan ^{-1}(\tanh (a+b x)) \, dx\)
3.80
\(\int \frac{\tan ^{-1}(\tanh (a+b x))}{e+f x} \, dx\)
3.81
\(\int x^2 \tan ^{-1}(c+d \tanh (a+b x)) \, dx\)
3.82
\(\int x \tan ^{-1}(c+d \tanh (a+b x)) \, dx\)
3.83
\(\int \tan ^{-1}(c+d \tanh (a+b x)) \, dx\)
3.84
\(\int \frac{\tan ^{-1}(c+d \tanh (a+b x))}{x} \, dx\)
3.85
\(\int x^2 \tan ^{-1}(c+(i+c) \tanh (a+b x)) \, dx\)
3.86
\(\int x \tan ^{-1}(c+(i+c) \tanh (a+b x)) \, dx\)
3.87
\(\int \tan ^{-1}(c+(i+c) \tanh (a+b x)) \, dx\)
3.88
\(\int \frac{\tan ^{-1}(c+(i+c) \tanh (a+b x))}{x} \, dx\)
3.89
\(\int x^2 \tan ^{-1}(c-(i-c) \tanh (a+b x)) \, dx\)
3.90
\(\int x \tan ^{-1}(c-(i-c) \tanh (a+b x)) \, dx\)
3.91
\(\int \tan ^{-1}(c-(i-c) \tanh (a+b x)) \, dx\)
3.92
\(\int \frac{\tan ^{-1}(c-(i-c) \tanh (a+b x))}{x} \, dx\)
3.93
\(\int (e+f x)^3 \tan ^{-1}(\coth (a+b x)) \, dx\)
3.94
\(\int (e+f x)^2 \tan ^{-1}(\coth (a+b x)) \, dx\)
3.95
\(\int (e+f x) \tan ^{-1}(\coth (a+b x)) \, dx\)
3.96
\(\int \tan ^{-1}(\coth (a+b x)) \, dx\)
3.97
\(\int \frac{\tan ^{-1}(\coth (a+b x))}{e+f x} \, dx\)
3.98
\(\int x^2 \tan ^{-1}(c+d \coth (a+b x)) \, dx\)
3.99
\(\int x \tan ^{-1}(c+d \coth (a+b x)) \, dx\)
3.100
\(\int \tan ^{-1}(c+d \coth (a+b x)) \, dx\)
3.101
\(\int \frac{\tan ^{-1}(c+d \coth (a+b x))}{x} \, dx\)
3.102
\(\int x^2 \tan ^{-1}(c+(i+c) \coth (a+b x)) \, dx\)
3.103
\(\int x \tan ^{-1}(c+(i+c) \coth (a+b x)) \, dx\)
3.104
\(\int \tan ^{-1}(c+(i+c) \coth (a+b x)) \, dx\)
3.105
\(\int \frac{\tan ^{-1}(c+(i+c) \coth (a+b x))}{x} \, dx\)
3.106
\(\int x^2 \tan ^{-1}(c-(i-c) \coth (a+b x)) \, dx\)
3.107
\(\int x \tan ^{-1}(c-(i-c) \coth (a+b x)) \, dx\)
3.108
\(\int \tan ^{-1}(c-(i-c) \coth (a+b x)) \, dx\)
3.109
\(\int \frac{\tan ^{-1}(c-(i-c) \coth (a+b x))}{x} \, dx\)
3.110
\(\int \tan ^{-1}(e^x) \, dx\)
3.111
\(\int x \tan ^{-1}(e^x) \, dx\)
3.112
\(\int x^2 \tan ^{-1}(e^x) \, dx\)
3.113
\(\int \tan ^{-1}(e^{a+b x}) \, dx\)
3.114
\(\int x \tan ^{-1}(e^{a+b x}) \, dx\)
3.115
\(\int x^2 \tan ^{-1}(e^{a+b x}) \, dx\)
3.116
\(\int \tan ^{-1}(a+b f^{c+d x}) \, dx\)
3.117
\(\int x \tan ^{-1}(a+b f^{c+d x}) \, dx\)
3.118
\(\int x^2 \tan ^{-1}(a+b f^{c+d x}) \, dx\)
3.119
\(\int e^{-x} \tan ^{-1}(e^x) \, dx\)
3.120
\(\int \frac{\tan ^{-1}(x)}{(-1+x)^3} \, dx\)
3.121
\(\int \frac{\tan ^{-1}(1+2 x)}{(4+3 x)^3} \, dx\)
3.122
\(\int \tan ^{-1}(\sqrt{1+x}) \, dx\)
3.123
\(\int \frac{1}{(1+x^2) (2+\tan ^{-1}(x))} \, dx\)
3.124
\(\int \frac{1}{(a+a x^2) (b-2 b \tan ^{-1}(x))} \, dx\)
3.125
\(\int \frac{x+x^3+(1+x)^2 \tan ^{-1}(x)}{(1+x)^2 (1+x^2)} \, dx\)
3.126
\(\int -x^3 \tan ^{-1}(\sqrt{x}-\sqrt{1+x}) \, dx\)
3.127
\(\int -x^2 \tan ^{-1}(\sqrt{x}-\sqrt{1+x}) \, dx\)
3.128
\(\int -x \tan ^{-1}(\sqrt{x}-\sqrt{1+x}) \, dx\)
3.129
\(\int -\tan ^{-1}(\sqrt{x}-\sqrt{1+x}) \, dx\)
3.130
\(\int -\frac{\tan ^{-1}(\sqrt{x}-\sqrt{1+x})}{x} \, dx\)
3.131
\(\int -\frac{\tan ^{-1}(\sqrt{x}-\sqrt{1+x})}{x^2} \, dx\)
3.132
\(\int -\frac{\tan ^{-1}(\sqrt{x}-\sqrt{1+x})}{x^3} \, dx\)
3.133
\(\int -\frac{\tan ^{-1}(\sqrt{x}-\sqrt{1+x})}{x^4} \, dx\)
3.134
\(\int \frac{\tan ^{-1}(\frac{c x}{\sqrt{a-c^2 x^2}})^m}{\sqrt{d-\frac{c^2 d x^2}{a}}} \, dx\)
3.135
\(\int \frac{\tan ^{-1}(\frac{c x}{\sqrt{a-c^2 x^2}})^2}{\sqrt{d-\frac{c^2 d x^2}{a}}} \, dx\)
3.136
\(\int \frac{\tan ^{-1}(\frac{c x}{\sqrt{a-c^2 x^2}})}{\sqrt{d-\frac{c^2 d x^2}{a}}} \, dx\)
3.137
\(\int \frac{1}{\sqrt{d-\frac{c^2 d x^2}{a}} \tan ^{-1}(\frac{c x}{\sqrt{a-c^2 x^2}})} \, dx\)
3.138
\(\int \frac{1}{\sqrt{d-\frac{c^2 d x^2}{a}} \tan ^{-1}(\frac{c x}{\sqrt{a-c^2 x^2}})^2} \, dx\)
3.139
\(\int \frac{1}{\sqrt{d-\frac{c^2 d x^2}{a}} \tan ^{-1}(\frac{c x}{\sqrt{a-c^2 x^2}})^3} \, dx\)
3.140
\(\int \frac{\tan ^{-1}(\frac{e x}{\sqrt{-\frac{a e^2}{b}-e^2 x^2}})^m}{\sqrt{a+b x^2}} \, dx\)
3.141
\(\int \frac{\tan ^{-1}(\frac{e x}{\sqrt{-\frac{a e^2}{b}-e^2 x^2}})^2}{\sqrt{a+b x^2}} \, dx\)
3.142
\(\int \frac{\tan ^{-1}(\frac{e x}{\sqrt{-\frac{a e^2}{b}-e^2 x^2}})}{\sqrt{a+b x^2}} \, dx\)
3.143
\(\int \frac{1}{\sqrt{a+b x^2} \tan ^{-1}(\frac{e x}{\sqrt{-\frac{a e^2}{b}-e^2 x^2}})} \, dx\)
3.144
\(\int \frac{1}{\sqrt{a+b x^2} \tan ^{-1}(\frac{e x}{\sqrt{-\frac{a e^2}{b}-e^2 x^2}})^2} \, dx\)
3.145
\(\int \frac{1}{\sqrt{a+b x^2} \tan ^{-1}(\frac{e x}{\sqrt{-\frac{a e^2}{b}-e^2 x^2}})^3} \, dx\)
3.146
\(\int \frac{\tan ^{-1}(c (a+b x)) \log (d (a+b x))}{a+b x} \, dx\)
3.147
\(\int e^{c (a+b x)} \tan ^{-1}(\sinh (a c+b c x)) \, dx\)
3.148
\(\int e^{c (a+b x)} \tan ^{-1}(\cosh (a c+b c x)) \, dx\)
3.149
\(\int e^{c (a+b x)} \tan ^{-1}(\tanh (a c+b c x)) \, dx\)
3.150
\(\int e^{c (a+b x)} \tan ^{-1}(\coth (a c+b c x)) \, dx\)
3.151
\(\int e^{c (a+b x)} \tan ^{-1}(\text{sech}(a c+b c x)) \, dx\)
3.152
\(\int e^{c (a+b x)} \tan ^{-1}(\text{csch}(a c+b c x)) \, dx\)
3.153
\(\int \frac{(a+b \tan ^{-1}(c x^n)) (d+e \log (f x^m))}{x} \, dx\)
[
next
] [
prev
] [
prev-tail
] [
front
] [
up
]