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 \(\int \frac{e^{-5 i \tan ^{-1}(a x)} x^2}{(c+a^2 c x^2)^{27/2}} \, dx\)