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Chapter 3
Listing of integrals
3.1
\(\int e^{i \tan ^{-1}(a x)} x^4 \, dx\)
3.2
\(\int e^{i \tan ^{-1}(a x)} x^3 \, dx\)
3.3
\(\int e^{i \tan ^{-1}(a x)} x^2 \, dx\)
3.4
\(\int e^{i \tan ^{-1}(a x)} x \, dx\)
3.5
\(\int e^{i \tan ^{-1}(a x)} \, dx\)
3.6
\(\int \frac{e^{i \tan ^{-1}(a x)}}{x} \, dx\)
3.7
\(\int \frac{e^{i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.8
\(\int \frac{e^{i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.9
\(\int \frac{e^{i \tan ^{-1}(a x)}}{x^4} \, dx\)
3.10
\(\int \frac{e^{i \tan ^{-1}(a x)}}{x^5} \, dx\)
3.11
\(\int e^{2 i \tan ^{-1}(a x)} x^3 \, dx\)
3.12
\(\int e^{2 i \tan ^{-1}(a x)} x^2 \, dx\)
3.13
\(\int e^{2 i \tan ^{-1}(a x)} x \, dx\)
3.14
\(\int e^{2 i \tan ^{-1}(a x)} \, dx\)
3.15
\(\int \frac{e^{2 i \tan ^{-1}(a x)}}{x} \, dx\)
3.16
\(\int \frac{e^{2 i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.17
\(\int \frac{e^{2 i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.18
\(\int \frac{e^{2 i \tan ^{-1}(a x)}}{x^4} \, dx\)
3.19
\(\int e^{3 i \tan ^{-1}(a x)} x^3 \, dx\)
3.20
\(\int e^{3 i \tan ^{-1}(a x)} x^2 \, dx\)
3.21
\(\int e^{3 i \tan ^{-1}(a x)} x \, dx\)
3.22
\(\int e^{3 i \tan ^{-1}(a x)} \, dx\)
3.23
\(\int \frac{e^{3 i \tan ^{-1}(a x)}}{x} \, dx\)
3.24
\(\int \frac{e^{3 i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.25
\(\int \frac{e^{3 i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.26
\(\int \frac{e^{3 i \tan ^{-1}(a x)}}{x^4} \, dx\)
3.27
\(\int e^{4 i \tan ^{-1}(a x)} x^3 \, dx\)
3.28
\(\int e^{4 i \tan ^{-1}(a x)} x^2 \, dx\)
3.29
\(\int e^{4 i \tan ^{-1}(a x)} x \, dx\)
3.30
\(\int e^{4 i \tan ^{-1}(a x)} \, dx\)
3.31
\(\int \frac{e^{4 i \tan ^{-1}(a x)}}{x} \, dx\)
3.32
\(\int \frac{e^{4 i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.33
\(\int \frac{e^{4 i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.34
\(\int \frac{e^{4 i \tan ^{-1}(a x)}}{x^4} \, dx\)
3.35
\(\int e^{-i \tan ^{-1}(a x)} x^3 \, dx\)
3.36
\(\int e^{-i \tan ^{-1}(a x)} x^2 \, dx\)
3.37
\(\int e^{-i \tan ^{-1}(a x)} x \, dx\)
3.38
\(\int e^{-i \tan ^{-1}(a x)} \, dx\)
3.39
\(\int \frac{e^{-i \tan ^{-1}(a x)}}{x} \, dx\)
3.40
\(\int \frac{e^{-i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.41
\(\int \frac{e^{-i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.42
\(\int \frac{e^{-i \tan ^{-1}(a x)}}{x^4} \, dx\)
3.43
\(\int \frac{e^{-i \tan ^{-1}(a x)}}{x^5} \, dx\)
3.44
\(\int e^{-2 i \tan ^{-1}(a x)} x^3 \, dx\)
3.45
\(\int e^{-2 i \tan ^{-1}(a x)} x^2 \, dx\)
3.46
\(\int e^{-2 i \tan ^{-1}(a x)} x \, dx\)
3.47
\(\int e^{-2 i \tan ^{-1}(a x)} \, dx\)
3.48
\(\int \frac{e^{-2 i \tan ^{-1}(a x)}}{x} \, dx\)
3.49
\(\int \frac{e^{-2 i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.50
\(\int \frac{e^{-2 i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.51
\(\int \frac{e^{-2 i \tan ^{-1}(a x)}}{x^4} \, dx\)
3.52
\(\int e^{-3 i \tan ^{-1}(a x)} x^3 \, dx\)
3.53
\(\int e^{-3 i \tan ^{-1}(a x)} x^2 \, dx\)
3.54
\(\int e^{-3 i \tan ^{-1}(a x)} x \, dx\)
3.55
\(\int e^{-3 i \tan ^{-1}(a x)} \, dx\)
3.56
\(\int \frac{e^{-3 i \tan ^{-1}(a x)}}{x} \, dx\)
3.57
\(\int \frac{e^{-3 i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.58
\(\int \frac{e^{-3 i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.59
\(\int \frac{e^{-3 i \tan ^{-1}(a x)}}{x^4} \, dx\)
3.60
\(\int \frac{e^{-3 i \tan ^{-1}(a x)}}{x^5} \, dx\)
3.61
\(\int e^{\frac{1}{2} i \tan ^{-1}(a x)} x^2 \, dx\)
3.62
\(\int e^{\frac{1}{2} i \tan ^{-1}(a x)} x \, dx\)
3.63
\(\int e^{\frac{1}{2} i \tan ^{-1}(a x)} \, dx\)
3.64
\(\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a x)}}{x} \, dx\)
3.65
\(\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.66
\(\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.67
\(\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a x)}}{x^4} \, dx\)
3.68
\(\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a x)}}{x^5} \, dx\)
3.69
\(\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a x)}}{x^6} \, dx\)
3.70
\(\int e^{\frac{3}{2} i \tan ^{-1}(a x)} x^3 \, dx\)
3.71
\(\int e^{\frac{3}{2} i \tan ^{-1}(a x)} x^2 \, dx\)
3.72
\(\int e^{\frac{3}{2} i \tan ^{-1}(a x)} x \, dx\)
3.73
\(\int e^{\frac{3}{2} i \tan ^{-1}(a x)} \, dx\)
3.74
\(\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a x)}}{x} \, dx\)
3.75
\(\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.76
\(\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.77
\(\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a x)}}{x^4} \, dx\)
3.78
\(\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a x)}}{x^5} \, dx\)
3.79
\(\int e^{\frac{5}{2} i \tan ^{-1}(a x)} x^3 \, dx\)
3.80
\(\int e^{\frac{5}{2} i \tan ^{-1}(a x)} x^2 \, dx\)
3.81
\(\int e^{\frac{5}{2} i \tan ^{-1}(a x)} x \, dx\)
3.82
\(\int e^{\frac{5}{2} i \tan ^{-1}(a x)} \, dx\)
3.83
\(\int \frac{e^{\frac{5}{2} i \tan ^{-1}(a x)}}{x} \, dx\)
3.84
\(\int \frac{e^{\frac{5}{2} i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.85
\(\int \frac{e^{\frac{5}{2} i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.86
\(\int \frac{e^{\frac{5}{2} i \tan ^{-1}(a x)}}{x^4} \, dx\)
3.87
\(\int \frac{e^{\frac{5}{2} i \tan ^{-1}(a x)}}{x^5} \, dx\)
3.88
\(\int e^{-\frac{1}{2} i \tan ^{-1}(a x)} x^3 \, dx\)
3.89
\(\int e^{-\frac{1}{2} i \tan ^{-1}(a x)} x^2 \, dx\)
3.90
\(\int e^{-\frac{1}{2} i \tan ^{-1}(a x)} x \, dx\)
3.91
\(\int e^{-\frac{1}{2} i \tan ^{-1}(a x)} \, dx\)
3.92
\(\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a x)}}{x} \, dx\)
3.93
\(\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.94
\(\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.95
\(\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a x)}}{x^4} \, dx\)
3.96
\(\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a x)}}{x^5} \, dx\)
3.97
\(\int e^{-\frac{3}{2} i \tan ^{-1}(a x)} x^3 \, dx\)
3.98
\(\int e^{-\frac{3}{2} i \tan ^{-1}(a x)} x^2 \, dx\)
3.99
\(\int e^{-\frac{3}{2} i \tan ^{-1}(a x)} x \, dx\)
3.100
\(\int e^{-\frac{3}{2} i \tan ^{-1}(a x)} \, dx\)
3.101
\(\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a x)}}{x} \, dx\)
3.102
\(\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.103
\(\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.104
\(\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a x)}}{x^4} \, dx\)
3.105
\(\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a x)}}{x^5} \, dx\)
3.106
\(\int e^{-\frac{5}{2} i \tan ^{-1}(a x)} x^3 \, dx\)
3.107
\(\int e^{-\frac{5}{2} i \tan ^{-1}(a x)} x^2 \, dx\)
3.108
\(\int e^{-\frac{5}{2} i \tan ^{-1}(a x)} x \, dx\)
3.109
\(\int e^{-\frac{5}{2} i \tan ^{-1}(a x)} \, dx\)
3.110
\(\int \frac{e^{-\frac{5}{2} i \tan ^{-1}(a x)}}{x} \, dx\)
3.111
\(\int \frac{e^{-\frac{5}{2} i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.112
\(\int \frac{e^{-\frac{5}{2} i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.113
\(\int \frac{e^{-\frac{5}{2} i \tan ^{-1}(a x)}}{x^4} \, dx\)
3.114
\(\int \frac{e^{-\frac{5}{2} i \tan ^{-1}(a x)}}{x^5} \, dx\)
3.115
\(\int e^{\frac{1}{3} i \tan ^{-1}(x)} x^2 \, dx\)
3.116
\(\int e^{\frac{1}{3} i \tan ^{-1}(x)} x \, dx\)
3.117
\(\int e^{\frac{1}{3} i \tan ^{-1}(x)} \, dx\)
3.118
\(\int \frac{e^{\frac{1}{3} i \tan ^{-1}(x)}}{x} \, dx\)
3.119
\(\int \frac{e^{\frac{1}{3} i \tan ^{-1}(x)}}{x^2} \, dx\)
3.120
\(\int \frac{e^{\frac{1}{3} i \tan ^{-1}(x)}}{x^3} \, dx\)
3.121
\(\int \frac{e^{\frac{1}{3} i \tan ^{-1}(x)}}{x^4} \, dx\)
3.122
\(\int e^{\frac{2}{3} i \tan ^{-1}(x)} x^2 \, dx\)
3.123
\(\int e^{\frac{2}{3} i \tan ^{-1}(x)} x \, dx\)
3.124
\(\int e^{\frac{2}{3} i \tan ^{-1}(x)} \, dx\)
3.125
\(\int \frac{e^{\frac{2}{3} i \tan ^{-1}(x)}}{x} \, dx\)
3.126
\(\int \frac{e^{\frac{2}{3} i \tan ^{-1}(x)}}{x^2} \, dx\)
3.127
\(\int \frac{e^{\frac{2}{3} i \tan ^{-1}(x)}}{x^3} \, dx\)
3.128
\(\int e^{\frac{1}{4} i \tan ^{-1}(a x)} x^2 \, dx\)
3.129
\(\int e^{\frac{1}{4} i \tan ^{-1}(a x)} x \, dx\)
3.130
\(\int e^{\frac{1}{4} i \tan ^{-1}(a x)} \, dx\)
3.131
\(\int \frac{e^{\frac{1}{4} i \tan ^{-1}(a x)}}{x} \, dx\)
3.132
\(\int \frac{e^{\frac{1}{4} i \tan ^{-1}(a x)}}{x^2} \, dx\)
3.133
\(\int \frac{e^{\frac{1}{4} i \tan ^{-1}(a x)}}{x^3} \, dx\)
3.134
\(\int e^{6 i \tan ^{-1}(a x)} x^m \, dx\)
3.135
\(\int e^{4 i \tan ^{-1}(a x)} x^m \, dx\)
3.136
\(\int e^{2 i \tan ^{-1}(a x)} x^m \, dx\)
3.137
\(\int e^{-2 i \tan ^{-1}(a x)} x^m \, dx\)
3.138
\(\int e^{-4 i \tan ^{-1}(a x)} x^m \, dx\)
3.139
\(\int e^{-6 i \tan ^{-1}(a x)} x^m \, dx\)
3.140
\(\int e^{3 i \tan ^{-1}(a x)} x^m \, dx\)
3.141
\(\int e^{i \tan ^{-1}(a x)} x^m \, dx\)
3.142
\(\int e^{-i \tan ^{-1}(a x)} x^m \, dx\)
3.143
\(\int e^{-3 i \tan ^{-1}(a x)} x^m \, dx\)
3.144
\(\int e^{\frac{5}{2} i \tan ^{-1}(a x)} x^m \, dx\)
3.145
\(\int e^{\frac{3}{2} i \tan ^{-1}(a x)} x^m \, dx\)
3.146
\(\int e^{\frac{1}{2} i \tan ^{-1}(a x)} x^m \, dx\)
3.147
\(\int e^{-\frac{1}{2} i \tan ^{-1}(a x)} x^m \, dx\)
3.148
\(\int e^{-\frac{3}{2} i \tan ^{-1}(a x)} x^m \, dx\)
3.149
\(\int e^{-\frac{5}{2} i \tan ^{-1}(a x)} x^m \, dx\)
3.150
\(\int e^{\frac{2}{3} \tan ^{-1}(x)} x^m \, dx\)
3.151
\(\int e^{\frac{1}{3} \tan ^{-1}(x)} x^m \, dx\)
3.152
\(\int e^{\frac{1}{4} i \tan ^{-1}(a x)} x^m \, dx\)
3.153
\(\int e^{i n \tan ^{-1}(a x)} x^m \, dx\)
3.154
\(\int e^{i n \tan ^{-1}(a x)} x^3 \, dx\)
3.155
\(\int e^{i n \tan ^{-1}(a x)} x^2 \, dx\)
3.156
\(\int e^{i n \tan ^{-1}(a x)} x \, dx\)
3.157
\(\int e^{i n \tan ^{-1}(a x)} \, dx\)
3.158
\(\int \frac{e^{i n \tan ^{-1}(a x)}}{x} \, dx\)
3.159
\(\int \frac{e^{i n \tan ^{-1}(a x)}}{x^2} \, dx\)
3.160
\(\int \frac{e^{i n \tan ^{-1}(a x)}}{x^3} \, dx\)
3.161
\(\int \frac{e^{i n \tan ^{-1}(a x)}}{x^4} \, dx\)
3.162
\(\int e^{i \tan ^{-1}(a+b x)} x^4 \, dx\)
3.163
\(\int e^{i \tan ^{-1}(a+b x)} x^3 \, dx\)
3.164
\(\int e^{i \tan ^{-1}(a+b x)} x^2 \, dx\)
3.165
\(\int e^{i \tan ^{-1}(a+b x)} x \, dx\)
3.166
\(\int e^{i \tan ^{-1}(a+b x)} \, dx\)
3.167
\(\int \frac{e^{i \tan ^{-1}(a+b x)}}{x} \, dx\)
3.168
\(\int \frac{e^{i \tan ^{-1}(a+b x)}}{x^2} \, dx\)
3.169
\(\int \frac{e^{i \tan ^{-1}(a+b x)}}{x^3} \, dx\)
3.170
\(\int \frac{e^{i \tan ^{-1}(a+b x)}}{x^4} \, dx\)
3.171
\(\int e^{2 i \tan ^{-1}(a+b x)} x^4 \, dx\)
3.172
\(\int e^{2 i \tan ^{-1}(a+b x)} x^3 \, dx\)
3.173
\(\int e^{2 i \tan ^{-1}(a+b x)} x^2 \, dx\)
3.174
\(\int e^{2 i \tan ^{-1}(a+b x)} x \, dx\)
3.175
\(\int e^{2 i \tan ^{-1}(a+b x)} \, dx\)
3.176
\(\int \frac{e^{2 i \tan ^{-1}(a+b x)}}{x} \, dx\)
3.177
\(\int \frac{e^{2 i \tan ^{-1}(a+b x)}}{x^2} \, dx\)
3.178
\(\int \frac{e^{2 i \tan ^{-1}(a+b x)}}{x^3} \, dx\)
3.179
\(\int \frac{e^{2 i \tan ^{-1}(a+b x)}}{x^4} \, dx\)
3.180
\(\int e^{3 i \tan ^{-1}(a+b x)} x^4 \, dx\)
3.181
\(\int e^{3 i \tan ^{-1}(a+b x)} x^3 \, dx\)
3.182
\(\int e^{3 i \tan ^{-1}(a+b x)} x^2 \, dx\)
3.183
\(\int e^{3 i \tan ^{-1}(a+b x)} x \, dx\)
3.184
\(\int e^{3 i \tan ^{-1}(a+b x)} \, dx\)
3.185
\(\int \frac{e^{3 i \tan ^{-1}(a+b x)}}{x} \, dx\)
3.186
\(\int \frac{e^{3 i \tan ^{-1}(a+b x)}}{x^2} \, dx\)
3.187
\(\int \frac{e^{3 i \tan ^{-1}(a+b x)}}{x^3} \, dx\)
3.188
\(\int \frac{e^{3 i \tan ^{-1}(a+b x)}}{x^4} \, dx\)
3.189
\(\int e^{-i \tan ^{-1}(a+b x)} x^4 \, dx\)
3.190
\(\int e^{-i \tan ^{-1}(a+b x)} x^3 \, dx\)
3.191
\(\int e^{-i \tan ^{-1}(a+b x)} x^2 \, dx\)
3.192
\(\int e^{-i \tan ^{-1}(a+b x)} x \, dx\)
3.193
\(\int e^{-i \tan ^{-1}(a+b x)} \, dx\)
3.194
\(\int \frac{e^{-i \tan ^{-1}(a+b x)}}{x} \, dx\)
3.195
\(\int \frac{e^{-i \tan ^{-1}(a+b x)}}{x^2} \, dx\)
3.196
\(\int \frac{e^{-i \tan ^{-1}(a+b x)}}{x^3} \, dx\)
3.197
\(\int \frac{e^{-i \tan ^{-1}(a+b x)}}{x^4} \, dx\)
3.198
\(\int e^{-2 i \tan ^{-1}(a+b x)} x^4 \, dx\)
3.199
\(\int e^{-2 i \tan ^{-1}(a+b x)} x^3 \, dx\)
3.200
\(\int e^{-2 i \tan ^{-1}(a+b x)} x^2 \, dx\)
3.201
\(\int e^{-2 i \tan ^{-1}(a+b x)} x \, dx\)
3.202
\(\int e^{-2 i \tan ^{-1}(a+b x)} \, dx\)
3.203
\(\int \frac{e^{-2 i \tan ^{-1}(a+b x)}}{x} \, dx\)
3.204
\(\int \frac{e^{-2 i \tan ^{-1}(a+b x)}}{x^2} \, dx\)
3.205
\(\int \frac{e^{-2 i \tan ^{-1}(a+b x)}}{x^3} \, dx\)
3.206
\(\int \frac{e^{-2 i \tan ^{-1}(a+b x)}}{x^4} \, dx\)
3.207
\(\int e^{-3 i \tan ^{-1}(a+b x)} x^4 \, dx\)
3.208
\(\int e^{-3 i \tan ^{-1}(a+b x)} x^3 \, dx\)
3.209
\(\int e^{-3 i \tan ^{-1}(a+b x)} x^2 \, dx\)
3.210
\(\int e^{-3 i \tan ^{-1}(a+b x)} x \, dx\)
3.211
\(\int e^{-3 i \tan ^{-1}(a+b x)} \, dx\)
3.212
\(\int \frac{e^{-3 i \tan ^{-1}(a+b x)}}{x} \, dx\)
3.213
\(\int \frac{e^{-3 i \tan ^{-1}(a+b x)}}{x^2} \, dx\)
3.214
\(\int \frac{e^{-3 i \tan ^{-1}(a+b x)}}{x^3} \, dx\)
3.215
\(\int \frac{e^{-3 i \tan ^{-1}(a+b x)}}{x^4} \, dx\)
3.216
\(\int e^{\frac{1}{2} i \tan ^{-1}(a+b x)} x^2 \, dx\)
3.217
\(\int e^{\frac{1}{2} i \tan ^{-1}(a+b x)} x \, dx\)
3.218
\(\int e^{\frac{1}{2} i \tan ^{-1}(a+b x)} \, dx\)
3.219
\(\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a+b x)}}{x} \, dx\)
3.220
\(\int \frac{e^{\frac{1}{2} i \tan ^{-1}(a+b x)}}{x^2} \, dx\)
3.221
\(\int e^{\frac{3}{2} i \tan ^{-1}(a+b x)} x^2 \, dx\)
3.222
\(\int e^{\frac{3}{2} i \tan ^{-1}(a+b x)} x \, dx\)
3.223
\(\int e^{\frac{3}{2} i \tan ^{-1}(a+b x)} \, dx\)
3.224
\(\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a+b x)}}{x} \, dx\)
3.225
\(\int \frac{e^{\frac{3}{2} i \tan ^{-1}(a+b x)}}{x^2} \, dx\)
3.226
\(\int e^{-\frac{1}{2} i \tan ^{-1}(a+b x)} x^2 \, dx\)
3.227
\(\int e^{-\frac{1}{2} i \tan ^{-1}(a+b x)} x \, dx\)
3.228
\(\int e^{-\frac{1}{2} i \tan ^{-1}(a+b x)} \, dx\)
3.229
\(\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a+b x)}}{x} \, dx\)
3.230
\(\int \frac{e^{-\frac{1}{2} i \tan ^{-1}(a+b x)}}{x^2} \, dx\)
3.231
\(\int e^{-\frac{3}{2} i \tan ^{-1}(a+b x)} x^2 \, dx\)
3.232
\(\int e^{-\frac{3}{2} i \tan ^{-1}(a+b x)} x \, dx\)
3.233
\(\int e^{-\frac{3}{2} i \tan ^{-1}(a+b x)} \, dx\)
3.234
\(\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a+b x)}}{x} \, dx\)
3.235
\(\int \frac{e^{-\frac{3}{2} i \tan ^{-1}(a+b x)}}{x^2} \, dx\)
3.236
\(\int e^{n \tan ^{-1}(a+b x)} x^m \, dx\)
3.237
\(\int e^{n \tan ^{-1}(a+b x)} x^3 \, dx\)
3.238
\(\int e^{n \tan ^{-1}(a+b x)} x^2 \, dx\)
3.239
\(\int e^{n \tan ^{-1}(a+b x)} x \, dx\)
3.240
\(\int e^{n \tan ^{-1}(a+b x)} \, dx\)
3.241
\(\int \frac{e^{n \tan ^{-1}(a+b x)}}{x} \, dx\)
3.242
\(\int \frac{e^{n \tan ^{-1}(a+b x)}}{x^2} \, dx\)
3.243
\(\int \frac{e^{n \tan ^{-1}(a+b x)}}{x^3} \, dx\)
3.244
\(\int e^{\tan ^{-1}(a x)} (c+a^2 c x^2)^p \, dx\)
3.245
\(\int e^{\tan ^{-1}(a x)} (c+a^2 c x^2)^2 \, dx\)
3.246
\(\int e^{\tan ^{-1}(a x)} (c+a^2 c x^2) \, dx\)
3.247
\(\int e^{\tan ^{-1}(a x)} \, dx\)
3.248
\(\int \frac{e^{\tan ^{-1}(a x)}}{c+a^2 c x^2} \, dx\)
3.249
\(\int \frac{e^{\tan ^{-1}(a x)}}{(c+a^2 c x^2)^2} \, dx\)
3.250
\(\int \frac{e^{\tan ^{-1}(a x)}}{(c+a^2 c x^2)^3} \, dx\)
3.251
\(\int \frac{e^{\tan ^{-1}(a x)}}{(c+a^2 c x^2)^4} \, dx\)
3.252
\(\int \frac{e^{\tan ^{-1}(a x)}}{(c+a^2 c x^2)^5} \, dx\)
3.253
\(\int e^{\tan ^{-1}(a x)} (c+a^2 c x^2)^{3/2} \, dx\)
3.254
\(\int e^{\tan ^{-1}(a x)} \sqrt{c+a^2 c x^2} \, dx\)
3.255
\(\int \frac{e^{\tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.256
\(\int \frac{e^{\tan ^{-1}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.257
\(\int \frac{e^{\tan ^{-1}(a x)}}{(c+a^2 c x^2)^{5/2}} \, dx\)
3.258
\(\int \frac{e^{\tan ^{-1}(a x)}}{(c+a^2 c x^2)^{7/2}} \, dx\)
3.259
\(\int e^{2 \tan ^{-1}(a x)} (c+a^2 c x^2)^p \, dx\)
3.260
\(\int e^{2 \tan ^{-1}(a x)} (c+a^2 c x^2)^2 \, dx\)
3.261
\(\int e^{2 \tan ^{-1}(a x)} (c+a^2 c x^2) \, dx\)
3.262
\(\int e^{2 \tan ^{-1}(a x)} \, dx\)
3.263
\(\int \frac{e^{2 \tan ^{-1}(a x)}}{c+a^2 c x^2} \, dx\)
3.264
\(\int \frac{e^{2 \tan ^{-1}(a x)}}{(c+a^2 c x^2)^2} \, dx\)
3.265
\(\int \frac{e^{2 \tan ^{-1}(a x)}}{(c+a^2 c x^2)^3} \, dx\)
3.266
\(\int \frac{e^{2 \tan ^{-1}(a x)}}{(c+a^2 c x^2)^4} \, dx\)
3.267
\(\int e^{2 \tan ^{-1}(a x)} (c+a^2 c x^2)^{3/2} \, dx\)
3.268
\(\int e^{2 \tan ^{-1}(a x)} \sqrt{c+a^2 c x^2} \, dx\)
3.269
\(\int \frac{e^{2 \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.270
\(\int \frac{e^{2 \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.271
\(\int \frac{e^{2 \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{5/2}} \, dx\)
3.272
\(\int \frac{e^{2 \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{7/2}} \, dx\)
3.273
\(\int e^{-\tan ^{-1}(a x)} (c+a^2 c x^2)^p \, dx\)
3.274
\(\int e^{-\tan ^{-1}(a x)} (c+a^2 c x^2)^2 \, dx\)
3.275
\(\int e^{-\tan ^{-1}(a x)} (c+a^2 c x^2) \, dx\)
3.276
\(\int e^{-\tan ^{-1}(a x)} \, dx\)
3.277
\(\int \frac{e^{-\tan ^{-1}(a x)}}{c+a^2 c x^2} \, dx\)
3.278
\(\int \frac{e^{-\tan ^{-1}(a x)}}{(c+a^2 c x^2)^2} \, dx\)
3.279
\(\int \frac{e^{-\tan ^{-1}(a x)}}{(c+a^2 c x^2)^3} \, dx\)
3.280
\(\int \frac{e^{-\tan ^{-1}(a x)}}{(c+a^2 c x^2)^4} \, dx\)
3.281
\(\int e^{-\tan ^{-1}(a x)} (c+a^2 c x^2)^{3/2} \, dx\)
3.282
\(\int e^{-\tan ^{-1}(a x)} \sqrt{c+a^2 c x^2} \, dx\)
3.283
\(\int \frac{e^{-\tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.284
\(\int \frac{e^{-\tan ^{-1}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.285
\(\int \frac{e^{-\tan ^{-1}(a x)}}{(c+a^2 c x^2)^{5/2}} \, dx\)
3.286
\(\int \frac{e^{-\tan ^{-1}(a x)}}{(c+a^2 c x^2)^{7/2}} \, dx\)
3.287
\(\int e^{-2 \tan ^{-1}(a x)} (c+a^2 c x^2)^p \, dx\)
3.288
\(\int e^{-2 \tan ^{-1}(a x)} (c+a^2 c x^2)^2 \, dx\)
3.289
\(\int e^{-2 \tan ^{-1}(a x)} (c+a^2 c x^2) \, dx\)
3.290
\(\int e^{-2 \tan ^{-1}(a x)} \, dx\)
3.291
\(\int \frac{e^{-2 \tan ^{-1}(a x)}}{c+a^2 c x^2} \, dx\)
3.292
\(\int \frac{e^{-2 \tan ^{-1}(a x)}}{(c+a^2 c x^2)^2} \, dx\)
3.293
\(\int \frac{e^{-2 \tan ^{-1}(a x)}}{(c+a^2 c x^2)^3} \, dx\)
3.294
\(\int \frac{e^{-2 \tan ^{-1}(a x)}}{(c+a^2 c x^2)^4} \, dx\)
3.295
\(\int e^{-2 \tan ^{-1}(a x)} (c+a^2 c x^2)^{3/2} \, dx\)
3.296
\(\int e^{-2 \tan ^{-1}(a x)} \sqrt{c+a^2 c x^2} \, dx\)
3.297
\(\int \frac{e^{-2 \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.298
\(\int \frac{e^{-2 \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.299
\(\int \frac{e^{-2 \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{5/2}} \, dx\)
3.300
\(\int \frac{e^{-2 \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{7/2}} \, dx\)
3.301
\(\int \frac{e^{5 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx\)
3.302
\(\int \frac{e^{4 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx\)
3.303
\(\int \frac{e^{3 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx\)
3.304
\(\int \frac{e^{2 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx\)
3.305
\(\int \frac{e^{i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx\)
3.306
\(\int \frac{e^{-i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx\)
3.307
\(\int \frac{e^{-2 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx\)
3.308
\(\int \frac{e^{-3 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx\)
3.309
\(\int \frac{e^{-4 i \tan ^{-1}(a x)}}{\sqrt{1+a^2 x^2}} \, dx\)
3.310
\(\int \frac{e^{5 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.311
\(\int \frac{e^{4 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.312
\(\int \frac{e^{3 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.313
\(\int \frac{e^{2 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.314
\(\int \frac{e^{i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.315
\(\int \frac{e^{-i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.316
\(\int \frac{e^{-2 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.317
\(\int \frac{e^{-3 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.318
\(\int \frac{e^{-4 i \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.319
\(\int \frac{e^{5 i \tan ^{-1}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\)
3.320
\(\int \frac{e^{4 i \tan ^{-1}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\)
3.321
\(\int \frac{e^{3 i \tan ^{-1}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\)
3.322
\(\int \frac{e^{2 i \tan ^{-1}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\)
3.323
\(\int \frac{e^{i \tan ^{-1}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\)
3.324
\(\int \frac{e^{-i \tan ^{-1}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\)
3.325
\(\int \frac{e^{-2 i \tan ^{-1}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\)
3.326
\(\int \frac{e^{-3 i \tan ^{-1}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\)
3.327
\(\int \frac{e^{-4 i \tan ^{-1}(a x)}}{(1+a^2 x^2)^{3/2}} \, dx\)
3.328
\(\int \frac{e^{5 i \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.329
\(\int \frac{e^{4 i \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.330
\(\int \frac{e^{3 i \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.331
\(\int \frac{e^{2 i \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.332
\(\int \frac{e^{i \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.333
\(\int \frac{e^{-i \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.334
\(\int \frac{e^{-2 i \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.335
\(\int \frac{e^{-3 i \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.336
\(\int \frac{e^{-4 i \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.337
\(\int e^{n \tan ^{-1}(a x)} (c+a^2 c x^2)^2 \, dx\)
3.338
\(\int e^{n \tan ^{-1}(a x)} (c+a^2 c x^2) \, dx\)
3.339
\(\int e^{n \tan ^{-1}(a x)} \, dx\)
3.340
\(\int \frac{e^{n \tan ^{-1}(a x)} x^3}{c+a^2 c x^2} \, dx\)
3.341
\(\int \frac{e^{n \tan ^{-1}(a x)} x^2}{c+a^2 c x^2} \, dx\)
3.342
\(\int \frac{e^{n \tan ^{-1}(a x)} x}{c+a^2 c x^2} \, dx\)
3.343
\(\int \frac{e^{n \tan ^{-1}(a x)}}{c+a^2 c x^2} \, dx\)
3.344
\(\int \frac{e^{n \tan ^{-1}(a x)}}{x (c+a^2 c x^2)} \, dx\)
3.345
\(\int \frac{e^{n \tan ^{-1}(a x)}}{x^2 (c+a^2 c x^2)} \, dx\)
3.346
\(\int \frac{e^{n \tan ^{-1}(a x)}}{x^3 (c+a^2 c x^2)} \, dx\)
3.347
\(\int \frac{e^{n \tan ^{-1}(a x)}}{(c+a^2 c x^2)^4} \, dx\)
3.348
\(\int e^{n \tan ^{-1}(a x)} (c+a^2 c x^2)^{3/2} \, dx\)
3.349
\(\int e^{n \tan ^{-1}(a x)} \sqrt{c+a^2 c x^2} \, dx\)
3.350
\(\int \frac{e^{n \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.351
\(\int e^{n \tan ^{-1}(a x)} x^2 (c+a^2 c x^2)^{3/2} \, dx\)
3.352
\(\int e^{n \tan ^{-1}(a x)} x^2 \sqrt{c+a^2 c x^2} \, dx\)
3.353
\(\int \frac{e^{n \tan ^{-1}(a x)} x^3}{\sqrt{c+a^2 c x^2}} \, dx\)
3.354
\(\int \frac{e^{n \tan ^{-1}(a x)} x^2}{\sqrt{c+a^2 c x^2}} \, dx\)
3.355
\(\int \frac{e^{n \tan ^{-1}(a x)} x}{\sqrt{c+a^2 c x^2}} \, dx\)
3.356
\(\int \frac{e^{n \tan ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx\)
3.357
\(\int \frac{e^{n \tan ^{-1}(a x)}}{x \sqrt{c+a^2 c x^2}} \, dx\)
3.358
\(\int \frac{e^{n \tan ^{-1}(a x)}}{x^2 \sqrt{c+a^2 c x^2}} \, dx\)
3.359
\(\int \frac{e^{n \tan ^{-1}(a x)}}{x^3 \sqrt{c+a^2 c x^2}} \, dx\)
3.360
\(\int e^{n \tan ^{-1}(a x)} \sqrt [3]{c+a^2 c x^2} \, dx\)
3.361
\(\int \frac{e^{n \tan ^{-1}(a x)}}{\sqrt [3]{c+a^2 c x^2}} \, dx\)
3.362
\(\int \frac{e^{n \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{2/3}} \, dx\)
3.363
\(\int \frac{e^{n \tan ^{-1}(a x)}}{(c+a^2 c x^2)^{4/3}} \, dx\)
3.364
\(\int e^{n \tan ^{-1}(a x)} x^m (c+a^2 c x^2) \, dx\)
3.365
\(\int \frac{e^{n \tan ^{-1}(a x)} x^m}{c+a^2 c x^2} \, dx\)
3.366
\(\int \frac{e^{n \tan ^{-1}(a x)} x^m}{(c+a^2 c x^2)^2} \, dx\)
3.367
\(\int \frac{e^{n \tan ^{-1}(a x)} x^m}{(c+a^2 c x^2)^3} \, dx\)
3.368
\(\int \frac{e^{n \tan ^{-1}(a x)} x^m}{\sqrt{c+a^2 c x^2}} \, dx\)
3.369
\(\int \frac{e^{n \tan ^{-1}(a x)} x^m}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.370
\(\int \frac{e^{n \tan ^{-1}(a x)} x^m}{(c+a^2 c x^2)^{5/2}} \, dx\)
3.371
\(\int e^{n \tan ^{-1}(a x)} (c+a^2 c x^2)^p \, dx\)
3.372
\(\int e^{-2 i p \tan ^{-1}(a x)} (c+a^2 c x^2)^p \, dx\)
3.373
\(\int e^{2 i p \tan ^{-1}(a x)} (c+a^2 c x^2)^p \, dx\)
3.374
\(\int e^{i n \tan ^{-1}(a x)} x^2 (c+a^2 c x^2)^{-1-\frac{n^2}{2}} \, dx\)
3.375
\(\int \frac{e^{6 i \tan ^{-1}(a x)} x^2}{(c+a^2 c x^2)^{19}} \, dx\)
3.376
\(\int \frac{e^{4 i \tan ^{-1}(a x)} x^2}{(c+a^2 c x^2)^9} \, dx\)
3.377
\(\int \frac{e^{2 i \tan ^{-1}(a x)} x^2}{(c+a^2 c x^2)^3} \, dx\)
3.378
\(\int \frac{e^{-2 i \tan ^{-1}(a x)} x^2}{(c+a^2 c x^2)^3} \, dx\)
3.379
\(\int \frac{e^{-4 i \tan ^{-1}(a x)} x^2}{(c+a^2 c x^2)^9} \, dx\)
3.380
\(\int \frac{e^{5 i \tan ^{-1}(a x)} x^2}{(c+a^2 c x^2)^{27/2}} \, dx\)
3.381
\(\int \frac{e^{3 i \tan ^{-1}(a x)} x^2}{(c+a^2 c x^2)^{11/2}} \, dx\)
3.382
\(\int \frac{e^{i \tan ^{-1}(a x)} x^2}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.383
\(\int \frac{e^{-i \tan ^{-1}(a x)} x^2}{(c+a^2 c x^2)^{3/2}} \, dx\)
3.384
\(\int \frac{e^{-3 i \tan ^{-1}(a x)} x^2}{(c+a^2 c x^2)^{11/2}} \, dx\)
3.385
\(\int \frac{e^{-5 i \tan ^{-1}(a x)} x^2}{(c+a^2 c x^2)^{27/2}} \, dx\)
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