Chapter 3
Listing of integrals

 3.1 \(\int (a+b x^3) (c+d x^3)^4 \, dx\)
 3.2 \(\int (a+b x^3) (c+d x^3)^3 \, dx\)
 3.3 \(\int (a+b x^3) (c+d x^3)^2 \, dx\)
 3.4 \(\int (a+b x^3) (c+d x^3) \, dx\)
 3.5 \(\int \frac{a+b x^3}{c+d x^3} \, dx\)
 3.6 \(\int \frac{a+b x^3}{(c+d x^3)^2} \, dx\)
 3.7 \(\int \frac{a+b x^3}{(c+d x^3)^3} \, dx\)
 3.8 \(\int (a+b x^3)^2 (c+d x^3)^3 \, dx\)
 3.9 \(\int (a+b x^3)^2 (c+d x^3)^2 \, dx\)
 3.10 \(\int (a+b x^3)^2 (c+d x^3) \, dx\)
 3.11 \(\int \frac{(a+b x^3)^2}{c+d x^3} \, dx\)
 3.12 \(\int \frac{(a+b x^3)^2}{(c+d x^3)^2} \, dx\)
 3.13 \(\int \frac{(a+b x^3)^2}{(c+d x^3)^3} \, dx\)
 3.14 \(\int \frac{(c+d x^3)^4}{a+b x^3} \, dx\)
 3.15 \(\int \frac{(c+d x^3)^3}{a+b x^3} \, dx\)
 3.16 \(\int \frac{(c+d x^3)^2}{a+b x^3} \, dx\)
 3.17 \(\int \frac{c+d x^3}{a+b x^3} \, dx\)
 3.18 \(\int \frac{1}{(a+b x^3) (c+d x^3)} \, dx\)
 3.19 \(\int \frac{1}{(a+b x^3) (c+d x^3)^2} \, dx\)
 3.20 \(\int \frac{(c+d x^3)^5}{(a+b x^3)^2} \, dx\)
 3.21 \(\int \frac{(c+d x^3)^4}{(a+b x^3)^2} \, dx\)
 3.22 \(\int \frac{(c+d x^3)^3}{(a+b x^3)^2} \, dx\)
 3.23 \(\int \frac{(c+d x^3)^2}{(a+b x^3)^2} \, dx\)
 3.24 \(\int \frac{c+d x^3}{(a+b x^3)^2} \, dx\)
 3.25 \(\int \frac{1}{(a+b x^3)^2 (c+d x^3)} \, dx\)
 3.26 \(\int \frac{1}{(a+b x^3)^2 (c+d x^3)^2} \, dx\)
 3.27 \(\int (a-b x^3) (a+b x^3)^{2/3} \, dx\)
 3.28 \(\int \frac{a-b x^3}{\sqrt [3]{a+b x^3}} \, dx\)
 3.29 \(\int \frac{a-b x^3}{(a+b x^3)^{4/3}} \, dx\)
 3.30 \(\int \frac{a-b x^3}{(a+b x^3)^{7/3}} \, dx\)
 3.31 \(\int \frac{a-b x^3}{(a+b x^3)^{10/3}} \, dx\)
 3.32 \(\int \frac{a-b x^3}{(a+b x^3)^{13/3}} \, dx\)
 3.33 \(\int \frac{a-b x^3}{(a+b x^3)^{16/3}} \, dx\)
 3.34 \(\int \frac{(a+b x^3)^{7/3}}{a-b x^3} \, dx\)
 3.35 \(\int \frac{(a+b x^3)^{4/3}}{a-b x^3} \, dx\)
 3.36 \(\int \frac{\sqrt [3]{a+b x^3}}{a-b x^3} \, dx\)
 3.37 \(\int \frac{1}{(a-b x^3) (a+b x^3)^{2/3}} \, dx\)
 3.38 \(\int \frac{1}{(a-b x^3) (a+b x^3)^{5/3}} \, dx\)
 3.39 \(\int \frac{1}{(a-b x^3) (a+b x^3)^{8/3}} \, dx\)
 3.40 \(\int (a-b x^3)^2 (a+b x^3)^{2/3} \, dx\)
 3.41 \(\int \frac{(a-b x^3)^2}{\sqrt [3]{a+b x^3}} \, dx\)
 3.42 \(\int \frac{(a-b x^3)^2}{(a+b x^3)^{4/3}} \, dx\)
 3.43 \(\int \frac{(a-b x^3)^2}{(a+b x^3)^{7/3}} \, dx\)
 3.44 \(\int \frac{(a-b x^3)^2}{(a+b x^3)^{10/3}} \, dx\)
 3.45 \(\int \frac{(a-b x^3)^2}{(a+b x^3)^{13/3}} \, dx\)
 3.46 \(\int \frac{(a-b x^3)^2}{(a+b x^3)^{16/3}} \, dx\)
 3.47 \(\int \frac{(a-b x^3)^2}{(a+b x^3)^{19/3}} \, dx\)
 3.48 \(\int (a-b x^3)^2 (a+b x^3)^{4/3} \, dx\)
 3.49 \(\int (a-b x^3)^2 \sqrt [3]{a+b x^3} \, dx\)
 3.50 \(\int \frac{(a-b x^3)^2}{(a+b x^3)^{2/3}} \, dx\)
 3.51 \(\int \frac{(a-b x^3)^2}{(a+b x^3)^{5/3}} \, dx\)
 3.52 \(\int \frac{(a-b x^3)^2}{(a+b x^3)^{8/3}} \, dx\)
 3.53 \(\int \frac{(a-b x^3)^2}{(a+b x^3)^{11/3}} \, dx\)
 3.54 \(\int \frac{(a-b x^3)^2}{(a+b x^3)^{14/3}} \, dx\)
 3.55 \(\int \frac{(a-b x^3)^2}{(a+b x^3)^{17/3}} \, dx\)
 3.56 \(\int (a+b x^3)^{5/3} (c+d x^3) \, dx\)
 3.57 \(\int (a+b x^3)^{2/3} (c+d x^3) \, dx\)
 3.58 \(\int \frac{c+d x^3}{\sqrt [3]{a+b x^3}} \, dx\)
 3.59 \(\int \frac{c+d x^3}{(a+b x^3)^{4/3}} \, dx\)
 3.60 \(\int \frac{c+d x^3}{(a+b x^3)^{7/3}} \, dx\)
 3.61 \(\int \frac{c+d x^3}{(a+b x^3)^{10/3}} \, dx\)
 3.62 \(\int \frac{c+d x^3}{(a+b x^3)^{13/3}} \, dx\)
 3.63 \(\int \frac{c+d x^3}{(a+b x^3)^{16/3}} \, dx\)
 3.64 \(\int (a+b x^3)^{7/3} (c+d x^3) \, dx\)
 3.65 \(\int (a+b x^3)^{4/3} (c+d x^3) \, dx\)
 3.66 \(\int \sqrt [3]{a+b x^3} (c+d x^3) \, dx\)
 3.67 \(\int \frac{c+d x^3}{(a+b x^3)^{2/3}} \, dx\)
 3.68 \(\int \frac{c+d x^3}{(a+b x^3)^{5/3}} \, dx\)
 3.69 \(\int \frac{c+d x^3}{(a+b x^3)^{8/3}} \, dx\)
 3.70 \(\int (a+b x^3)^{5/3} (c+d x^3)^2 \, dx\)
 3.71 \(\int (a+b x^3)^{2/3} (c+d x^3)^2 \, dx\)
 3.72 \(\int \frac{(c+d x^3)^2}{\sqrt [3]{a+b x^3}} \, dx\)
 3.73 \(\int \frac{(c+d x^3)^2}{(a+b x^3)^{4/3}} \, dx\)
 3.74 \(\int \frac{(c+d x^3)^2}{(a+b x^3)^{7/3}} \, dx\)
 3.75 \(\int \frac{(c+d x^3)^2}{(a+b x^3)^{10/3}} \, dx\)
 3.76 \(\int \frac{(c+d x^3)^2}{(a+b x^3)^{13/3}} \, dx\)
 3.77 \(\int \frac{(c+d x^3)^2}{(a+b x^3)^{16/3}} \, dx\)
 3.78 \(\int \frac{(c+d x^3)^2}{(a+b x^3)^{19/3}} \, dx\)
 3.79 \(\int (a+b x^3)^{7/3} (c+d x^3)^2 \, dx\)
 3.80 \(\int (a+b x^3)^{4/3} (c+d x^3)^2 \, dx\)
 3.81 \(\int \sqrt [3]{a+b x^3} (c+d x^3)^2 \, dx\)
 3.82 \(\int \frac{(c+d x^3)^2}{(a+b x^3)^{2/3}} \, dx\)
 3.83 \(\int \frac{(c+d x^3)^2}{(a+b x^3)^{5/3}} \, dx\)
 3.84 \(\int \frac{(c+d x^3)^2}{(a+b x^3)^{8/3}} \, dx\)
 3.85 \(\int \frac{(a+b x^3)^3}{(c+d x^3)^{13/3}} \, dx\)
 3.86 \(\int \frac{(a+b x^3)^{8/3}}{c+d x^3} \, dx\)
 3.87 \(\int \frac{(a+b x^3)^{5/3}}{c+d x^3} \, dx\)
 3.88 \(\int \frac{(a+b x^3)^{2/3}}{c+d x^3} \, dx\)
 3.89 \(\int \frac{1}{\sqrt [3]{a+b x^3} (c+d x^3)} \, dx\)
 3.90 \(\int \frac{1}{(a+b x^3)^{4/3} (c+d x^3)} \, dx\)
 3.91 \(\int \frac{1}{(a+b x^3)^{7/3} (c+d x^3)} \, dx\)
 3.92 \(\int \frac{1}{(a+b x^3)^{10/3} (c+d x^3)} \, dx\)
 3.93 \(\int \frac{(a+b x^3)^{4/3}}{c+d x^3} \, dx\)
 3.94 \(\int \frac{\sqrt [3]{a+b x^3}}{c+d x^3} \, dx\)
 3.95 \(\int \frac{1}{(a+b x^3)^{2/3} (c+d x^3)} \, dx\)
 3.96 \(\int \frac{1}{(a+b x^3)^{5/3} (c+d x^3)} \, dx\)
 3.97 \(\int \frac{1}{(a+b x^3)^{8/3} (c+d x^3)} \, dx\)
 3.98 \(\int \frac{(a+b x^3)^{8/3}}{(c+d x^3)^2} \, dx\)
 3.99 \(\int \frac{(a+b x^3)^{5/3}}{(c+d x^3)^2} \, dx\)
 3.100 \(\int \frac{(a+b x^3)^{2/3}}{(c+d x^3)^2} \, dx\)
 3.101 \(\int \frac{1}{\sqrt [3]{a+b x^3} (c+d x^3)^2} \, dx\)
 3.102 \(\int \frac{1}{(a+b x^3)^{4/3} (c+d x^3)^2} \, dx\)
 3.103 \(\int \frac{1}{(a+b x^3)^{7/3} (c+d x^3)^2} \, dx\)
 3.104 \(\int \frac{(a+b x^3)^{4/3}}{(c+d x^3)^2} \, dx\)
 3.105 \(\int \frac{\sqrt [3]{a+b x^3}}{(c+d x^3)^2} \, dx\)
 3.106 \(\int \frac{1}{(a+b x^3)^{2/3} (c+d x^3)^2} \, dx\)
 3.107 \(\int \frac{1}{(a+b x^3)^{5/3} (c+d x^3)^2} \, dx\)
 3.108 \(\int \frac{1}{(a+b x^3)^{8/3} (c+d x^3)^2} \, dx\)
 3.109 \(\int \frac{(a+b x^3)^{14/3}}{(c+d x^3)^3} \, dx\)
 3.110 \(\int \frac{(a+b x^3)^{11/3}}{(c+d x^3)^3} \, dx\)
 3.111 \(\int \frac{(a+b x^3)^{8/3}}{(c+d x^3)^3} \, dx\)
 3.112 \(\int \frac{(a+b x^3)^{5/3}}{(c+d x^3)^3} \, dx\)
 3.113 \(\int \frac{(a+b x^3)^{2/3}}{(c+d x^3)^3} \, dx\)
 3.114 \(\int \frac{1}{\sqrt [3]{a+b x^3} (c+d x^3)^3} \, dx\)
 3.115 \(\int \frac{1}{(a+b x^3)^{4/3} (c+d x^3)^3} \, dx\)
 3.116 \(\int \frac{1}{(a+b x^3)^{7/3} (c+d x^3)^3} \, dx\)
 3.117 \(\int \frac{(a+b x^3)^{4/3}}{(c+d x^3)^3} \, dx\)
 3.118 \(\int \frac{\sqrt [3]{a+b x^3}}{(c+d x^3)^3} \, dx\)
 3.119 \(\int \frac{1}{(a+b x^3)^{2/3} (c+d x^3)^3} \, dx\)
 3.120 \(\int \frac{1}{(a+b x^3)^{5/3} (c+d x^3)^3} \, dx\)
 3.121 \(\int \frac{1}{(a+b x^3)^{8/3} (c+d x^3)^3} \, dx\)
 3.122 \(\int \frac{(a+b x^3)^{7/4}}{(c+d x^3)^{37/12}} \, dx\)
 3.123 \(\int \frac{(a+b x^3)^{5/4}}{(c+d x^3)^{31/12}} \, dx\)
 3.124 \(\int \frac{(a+b x^3)^{3/4}}{(c+d x^3)^{25/12}} \, dx\)
 3.125 \(\int \frac{\sqrt [4]{a+b x^3}}{(c+d x^3)^{19/12}} \, dx\)
 3.126 \(\int \frac{1}{\sqrt [4]{a+b x^3} (c+d x^3)^{13/12}} \, dx\)
 3.127 \(\int \frac{1}{(a+b x^3)^{3/4} (c+d x^3)^{7/12}} \, dx\)
 3.128 \(\int \frac{1}{(a+b x^3)^{5/4} \sqrt [12]{c+d x^3}} \, dx\)
 3.129 \(\int \frac{(c+d x^3)^{5/12}}{(a+b x^3)^{7/4}} \, dx\)
 3.130 \(\int \frac{(c+d x^3)^{11/12}}{(a+b x^3)^{9/4}} \, dx\)
 3.131 \(\int \frac{(c+d x^3)^{17/12}}{(a+b x^3)^{11/4}} \, dx\)
 3.132 \(\int \frac{(c+d x^3)^{23/12}}{(a+b x^3)^{13/4}} \, dx\)
 3.133 \(\int (a+b x^3)^m (c+d x^3)^p \, dx\)
 3.134 \(\int (a+b x^3)^2 (c+d x^3)^q \, dx\)
 3.135 \(\int (a+b x^3) (c+d x^3)^q \, dx\)
 3.136 \(\int \frac{(c+d x^3)^q}{a+b x^3} \, dx\)
 3.137 \(\int \frac{(c+d x^3)^q}{(a+b x^3)^2} \, dx\)
 3.138 \(\int (a+b x^3)^m (c+d x^3)^3 \, dx\)
 3.139 \(\int (a+b x^3)^m (c+d x^3)^2 \, dx\)
 3.140 \(\int (a+b x^3)^m (c+d x^3) \, dx\)
 3.141 \(\int (a+b x^3)^m \, dx\)
 3.142 \(\int \frac{(a+b x^3)^m}{c+d x^3} \, dx\)
 3.143 \(\int \frac{(a+b x^3)^m}{(c+d x^3)^2} \, dx\)
 3.144 \(\int \frac{(a+b x^3)^m}{(c+d x^3)^3} \, dx\)
 3.145 \(\int (a+b x^3)^{-1-\frac{b c}{3 b c-3 a d}} (c+d x^3)^{-1+\frac{a d}{3 b c-3 a d}} \, dx\)
 3.146 \(\int (a+b x^4) (c+d x^4)^4 \, dx\)
 3.147 \(\int (a+b x^4) (c+d x^4)^3 \, dx\)
 3.148 \(\int (a+b x^4) (c+d x^4)^2 \, dx\)
 3.149 \(\int (a+b x^4) (c+d x^4) \, dx\)
 3.150 \(\int \frac{a+b x^4}{c+d x^4} \, dx\)
 3.151 \(\int \frac{a+b x^4}{(c+d x^4)^2} \, dx\)
 3.152 \(\int \frac{a+b x^4}{(c+d x^4)^3} \, dx\)
 3.153 \(\int (a+b x^4)^2 (c+d x^4)^4 \, dx\)
 3.154 \(\int (a+b x^4)^2 (c+d x^4)^3 \, dx\)
 3.155 \(\int (a+b x^4)^2 (c+d x^4)^2 \, dx\)
 3.156 \(\int (a+b x^4)^2 (c+d x^4) \, dx\)
 3.157 \(\int \frac{(a+b x^4)^2}{c+d x^4} \, dx\)
 3.158 \(\int \frac{(a+b x^4)^2}{(c+d x^4)^2} \, dx\)
 3.159 \(\int \frac{(a+b x^4)^2}{(c+d x^4)^3} \, dx\)
 3.160 \(\int \frac{(c+d x^4)^4}{a+b x^4} \, dx\)
 3.161 \(\int \frac{(c+d x^4)^3}{a+b x^4} \, dx\)
 3.162 \(\int \frac{(c+d x^4)^2}{a+b x^4} \, dx\)
 3.163 \(\int \frac{c+d x^4}{a+b x^4} \, dx\)
 3.164 \(\int \frac{1}{(a+b x^4) (c+d x^4)} \, dx\)
 3.165 \(\int \frac{1}{(a+b x^4) (c+d x^4)^2} \, dx\)
 3.166 \(\int \frac{(c+d x^4)^5}{(a+b x^4)^2} \, dx\)
 3.167 \(\int \frac{(c+d x^4)^4}{(a+b x^4)^2} \, dx\)
 3.168 \(\int \frac{(c+d x^4)^3}{(a+b x^4)^2} \, dx\)
 3.169 \(\int \frac{(c+d x^4)^2}{(a+b x^4)^2} \, dx\)
 3.170 \(\int \frac{c+d x^4}{(a+b x^4)^2} \, dx\)
 3.171 \(\int \frac{1}{(a+b x^4)^2 (c+d x^4)} \, dx\)
 3.172 \(\int \frac{1}{(a+b x^4)^2 (c+d x^4)^2} \, dx\)
 3.173 \(\int \frac{(a-b x^4)^{5/2}}{c-d x^4} \, dx\)
 3.174 \(\int \frac{(a-b x^4)^{3/2}}{c-d x^4} \, dx\)
 3.175 \(\int \frac{\sqrt{a-b x^4}}{c-d x^4} \, dx\)
 3.176 \(\int \frac{1}{\sqrt{a-b x^4} (c-d x^4)} \, dx\)
 3.177 \(\int \frac{1}{(a-b x^4)^{3/2} (c-d x^4)} \, dx\)
 3.178 \(\int \frac{1}{(a-b x^4)^{5/2} (c-d x^4)} \, dx\)
 3.179 \(\int \frac{(a+b x^4)^{3/2}}{c+d x^4} \, dx\)
 3.180 \(\int \frac{\sqrt{a+b x^4}}{c+d x^4} \, dx\)
 3.181 \(\int \frac{1}{\sqrt{a+b x^4} (c+d x^4)} \, dx\)
 3.182 \(\int \frac{1}{(a+b x^4)^{3/2} (c+d x^4)} \, dx\)
 3.183 \(\int \frac{1}{(a+b x^4)^{5/2} (c+d x^4)} \, dx\)
 3.184 \(\int \frac{(a-b x^4)^{7/2}}{(c-d x^4)^2} \, dx\)
 3.185 \(\int \frac{(a-b x^4)^{5/2}}{(c-d x^4)^2} \, dx\)
 3.186 \(\int \frac{(a-b x^4)^{3/2}}{(c-d x^4)^2} \, dx\)
 3.187 \(\int \frac{\sqrt{a-b x^4}}{(c-d x^4)^2} \, dx\)
 3.188 \(\int \frac{1}{\sqrt{a-b x^4} (c-d x^4)^2} \, dx\)
 3.189 \(\int \frac{1}{(a-b x^4)^{3/2} (c-d x^4)^2} \, dx\)
 3.190 \(\int \frac{1}{(a-b x^4)^{5/2} (c-d x^4)^2} \, dx\)
 3.191 \(\int \frac{\sqrt{a+b x^4}}{a c-b c x^4} \, dx\)
 3.192 \(\int \frac{\sqrt{a-b x^4}}{a c+b c x^4} \, dx\)
 3.193 \(\int \frac{(a+b x^4)^{7/4}}{c+d x^4} \, dx\)
 3.194 \(\int \frac{(a+b x^4)^{3/4}}{c+d x^4} \, dx\)
 3.195 \(\int \frac{1}{\sqrt [4]{a+b x^4} (c+d x^4)} \, dx\)
 3.196 \(\int \frac{1}{(a+b x^4)^{5/4} (c+d x^4)} \, dx\)
 3.197 \(\int \frac{1}{(a+b x^4)^{9/4} (c+d x^4)} \, dx\)
 3.198 \(\int \frac{1}{(a+b x^4)^{13/4} (c+d x^4)} \, dx\)
 3.199 \(\int \frac{(a+b x^4)^{9/4}}{c+d x^4} \, dx\)
 3.200 \(\int \frac{(a+b x^4)^{5/4}}{c+d x^4} \, dx\)
 3.201 \(\int \frac{\sqrt [4]{a+b x^4}}{c+d x^4} \, dx\)
 3.202 \(\int \frac{1}{(a+b x^4)^{3/4} (c+d x^4)} \, dx\)
 3.203 \(\int \frac{1}{(a+b x^4)^{7/4} (c+d x^4)} \, dx\)
 3.204 \(\int \frac{1}{(a+b x^4)^{11/4} (c+d x^4)} \, dx\)
 3.205 \(\int \frac{(a+b x^4)^{11/4}}{(c+d x^4)^2} \, dx\)
 3.206 \(\int \frac{(a+b x^4)^{7/4}}{(c+d x^4)^2} \, dx\)
 3.207 \(\int \frac{(a+b x^4)^{3/4}}{(c+d x^4)^2} \, dx\)
 3.208 \(\int \frac{1}{\sqrt [4]{a+b x^4} (c+d x^4)^2} \, dx\)
 3.209 \(\int \frac{1}{(a+b x^4)^{5/4} (c+d x^4)^2} \, dx\)
 3.210 \(\int \frac{1}{(a+b x^4)^{9/4} (c+d x^4)^2} \, dx\)
 3.211 \(\int \frac{(a+b x^4)^{9/4}}{(c+d x^4)^2} \, dx\)
 3.212 \(\int \frac{(a+b x^4)^{5/4}}{(c+d x^4)^2} \, dx\)
 3.213 \(\int \frac{\sqrt [4]{a+b x^4}}{(c+d x^4)^2} \, dx\)
 3.214 \(\int \frac{1}{(a+b x^4)^{3/4} (c+d x^4)^2} \, dx\)
 3.215 \(\int \frac{1}{(a+b x^4)^{7/4} (c+d x^4)^2} \, dx\)
 3.216 \(\int \frac{1}{\sqrt [4]{1+x^4} (2+x^4)} \, dx\)
 3.217 \(\int \frac{1}{(a-(a-b) x^4) \sqrt [4]{a+b x^4}} \, dx\)
 3.218 \(\int (a+b x^4)^p (c+d x^4)^q \, dx\)
 3.219 \(\int (a+b x^4)^2 (c+d x^4)^q \, dx\)
 3.220 \(\int (a+b x^4) (c+d x^4)^q \, dx\)
 3.221 \(\int \frac{(c+d x^4)^q}{a+b x^4} \, dx\)
 3.222 \(\int \frac{(c+d x^4)^q}{(a+b x^4)^2} \, dx\)
 3.223 \(\int \frac{1}{\sqrt [5]{a+b x^5} (c+d x^5)} \, dx\)
 3.224 \(\int \sqrt{a+\frac{b}{x}} (c+\frac{d}{x})^3 \, dx\)
 3.225 \(\int \sqrt{a+\frac{b}{x}} (c+\frac{d}{x})^2 \, dx\)
 3.226 \(\int \sqrt{a+\frac{b}{x}} (c+\frac{d}{x}) \, dx\)
 3.227 \(\int \sqrt{a+\frac{b}{x}} \, dx\)
 3.228 \(\int \frac{\sqrt{a+\frac{b}{x}}}{c+\frac{d}{x}} \, dx\)
 3.229 \(\int \frac{\sqrt{a+\frac{b}{x}}}{(c+\frac{d}{x})^2} \, dx\)
 3.230 \(\int \frac{\sqrt{a+\frac{b}{x}}}{(c+\frac{d}{x})^3} \, dx\)
 3.231 \(\int (a+\frac{b}{x})^{3/2} (c+\frac{d}{x})^3 \, dx\)
 3.232 \(\int (a+\frac{b}{x})^{3/2} (c+\frac{d}{x})^2 \, dx\)
 3.233 \(\int (a+\frac{b}{x})^{3/2} (c+\frac{d}{x}) \, dx\)
 3.234 \(\int (a+\frac{b}{x})^{3/2} \, dx\)
 3.235 \(\int \frac{(a+\frac{b}{x})^{3/2}}{c+\frac{d}{x}} \, dx\)
 3.236 \(\int \frac{(a+\frac{b}{x})^{3/2}}{(c+\frac{d}{x})^2} \, dx\)
 3.237 \(\int \frac{(a+\frac{b}{x})^{3/2}}{(c+\frac{d}{x})^3} \, dx\)
 3.238 \(\int (a+\frac{b}{x})^{5/2} (c+\frac{d}{x})^3 \, dx\)
 3.239 \(\int (a+\frac{b}{x})^{5/2} (c+\frac{d}{x})^2 \, dx\)
 3.240 \(\int (a+\frac{b}{x})^{5/2} (c+\frac{d}{x}) \, dx\)
 3.241 \(\int (a+\frac{b}{x})^{5/2} \, dx\)
 3.242 \(\int \frac{(a+\frac{b}{x})^{5/2}}{c+\frac{d}{x}} \, dx\)
 3.243 \(\int \frac{(a+\frac{b}{x})^{5/2}}{(c+\frac{d}{x})^2} \, dx\)
 3.244 \(\int \frac{(a+\frac{b}{x})^{5/2}}{(c+\frac{d}{x})^3} \, dx\)
 3.245 \(\int \frac{(c+\frac{d}{x})^3}{\sqrt{a+\frac{b}{x}}} \, dx\)
 3.246 \(\int \frac{(c+\frac{d}{x})^2}{\sqrt{a+\frac{b}{x}}} \, dx\)
 3.247 \(\int \frac{c+\frac{d}{x}}{\sqrt{a+\frac{b}{x}}} \, dx\)
 3.248 \(\int \frac{1}{\sqrt{a+\frac{b}{x}}} \, dx\)
 3.249 \(\int \frac{1}{\sqrt{a+\frac{b}{x}} (c+\frac{d}{x})} \, dx\)
 3.250 \(\int \frac{1}{\sqrt{a+\frac{b}{x}} (c+\frac{d}{x})^2} \, dx\)
 3.251 \(\int \frac{1}{\sqrt{a+\frac{b}{x}} (c+\frac{d}{x})^3} \, dx\)
 3.252 \(\int \frac{(c+\frac{d}{x})^3}{(a+\frac{b}{x})^{3/2}} \, dx\)
 3.253 \(\int \frac{(c+\frac{d}{x})^2}{(a+\frac{b}{x})^{3/2}} \, dx\)
 3.254 \(\int \frac{c+\frac{d}{x}}{(a+\frac{b}{x})^{3/2}} \, dx\)
 3.255 \(\int \frac{1}{(a+\frac{b}{x})^{3/2}} \, dx\)
 3.256 \(\int \frac{1}{(a+\frac{b}{x})^{3/2} (c+\frac{d}{x})} \, dx\)
 3.257 \(\int \frac{1}{(a+\frac{b}{x})^{3/2} (c+\frac{d}{x})^2} \, dx\)
 3.258 \(\int \frac{1}{(a+\frac{b}{x})^{3/2} (c+\frac{d}{x})^3} \, dx\)
 3.259 \(\int \frac{(c+\frac{d}{x})^3}{(a+\frac{b}{x})^{5/2}} \, dx\)
 3.260 \(\int \frac{(c+\frac{d}{x})^2}{(a+\frac{b}{x})^{5/2}} \, dx\)
 3.261 \(\int \frac{c+\frac{d}{x}}{(a+\frac{b}{x})^{5/2}} \, dx\)
 3.262 \(\int \frac{1}{(a+\frac{b}{x})^{5/2}} \, dx\)
 3.263 \(\int \frac{1}{(a+\frac{b}{x})^{5/2} (c+\frac{d}{x})} \, dx\)
 3.264 \(\int \frac{1}{(a+\frac{b}{x})^{5/2} (c+\frac{d}{x})^2} \, dx\)
 3.265 \(\int \frac{1}{(a+\frac{b}{x})^{5/2} (c+\frac{d}{x})^3} \, dx\)
 3.266 \(\int \sqrt{a+\frac{b}{x}} \sqrt{c+\frac{d}{x}} \, dx\)
 3.267 \(\int \frac{\sqrt{a+\frac{b}{x}}}{\sqrt{c+\frac{d}{x}}} \, dx\)
 3.268 \(\int \frac{\sqrt{a+\frac{b}{x}}}{(c+\frac{d}{x})^{3/2}} \, dx\)
 3.269 \(\int (a+\frac{b}{x})^p (c+\frac{d}{x})^q \, dx\)
 3.270 \(\int \frac{a+\frac{b}{x^2}}{c+\frac{d}{x^2}} \, dx\)
 3.271 \(\int \sqrt{a+\frac{b}{x^2}} \sqrt{c+\frac{d}{x^2}} \, dx\)
 3.272 \(\int \frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{c+\frac{d}{x^2}}} \, dx\)
 3.273 \(\int \frac{\sqrt{a+\frac{b}{x^2}}}{(c+\frac{d}{x^2})^{3/2}} \, dx\)
 3.274 \(\int (a+\frac{b}{x^2})^p (c+\frac{d}{x^2})^q \, dx\)
 3.275 \(\int \frac{a+\frac{b}{x^3}}{c+\frac{d}{x^3}} \, dx\)
 3.276 \(\int \frac{a+b \sqrt{x}}{c+d \sqrt{x}} \, dx\)
 3.277 \(\int \frac{-1+\sqrt [3]{x}}{1+\sqrt [3]{x}} \, dx\)
 3.278 \(\int \frac{1+x^{2/3}}{-1+x^{2/3}} \, dx\)
 3.279 \(\int \frac{-16+x^{3/4}}{16+x^{3/4}} \, dx\)
 3.280 \(\int \frac{1+\frac{1}{\sqrt [3]{x}}}{-1+\frac{1}{\sqrt [3]{x}}} \, dx\)
 3.281 \(\int (a-b x^n)^{3/2} (a+b x^n)^{3/2} \, dx\)
 3.282 \(\int \sqrt{a-b x^n} \sqrt{a+b x^n} \, dx\)
 3.283 \(\int (a-b x^n)^p (a+b x^n)^p \, dx\)
 3.284 \(\int (a+b x^n) (c+d x^n)^4 \, dx\)
 3.285 \(\int (a+b x^n) (c+d x^n)^3 \, dx\)
 3.286 \(\int (a+b x^n) (c+d x^n)^2 \, dx\)
 3.287 \(\int (a+b x^n) (c+d x^n) \, dx\)
 3.288 \(\int \frac{a+b x^n}{c+d x^n} \, dx\)
 3.289 \(\int \frac{a+b x^n}{(c+d x^n)^2} \, dx\)
 3.290 \(\int \frac{a+b x^n}{(c+d x^n)^3} \, dx\)
 3.291 \(\int \frac{a+b x^n}{(c+d x^n)^4} \, dx\)
 3.292 \(\int (a+b x^n)^2 (d+e x^n)^3 \, dx\)
 3.293 \(\int (a+b x^n)^2 (d+e x^n)^2 \, dx\)
 3.294 \(\int (a+b x^n)^2 (c+d x^n) \, dx\)
 3.295 \(\int \frac{(a+b x^n)^2}{c+d x^n} \, dx\)
 3.296 \(\int \frac{(a+b x^n)^2}{(c+d x^n)^2} \, dx\)
 3.297 \(\int \frac{(a+b x^n)^2}{(c+d x^n)^3} \, dx\)
 3.298 \(\int \frac{(c+d x^n)^4}{a+b x^n} \, dx\)
 3.299 \(\int \frac{(c+d x^n)^3}{a+b x^n} \, dx\)
 3.300 \(\int \frac{(c+d x^n)^2}{a+b x^n} \, dx\)
 3.301 \(\int \frac{c+d x^n}{a+b x^n} \, dx\)
 3.302 \(\int \frac{1}{(a+b x^n) (c+d x^n)} \, dx\)
 3.303 \(\int \frac{1}{(a+b x^n) (c+d x^n)^2} \, dx\)
 3.304 \(\int \frac{1}{(a+b x^n) (c+d x^n)^3} \, dx\)
 3.305 \(\int \frac{(c+d x^n)^4}{(a+b x^n)^2} \, dx\)
 3.306 \(\int \frac{(c+d x^n)^3}{(a+b x^n)^2} \, dx\)
 3.307 \(\int \frac{(c+d x^n)^2}{(a+b x^n)^2} \, dx\)
 3.308 \(\int \frac{c+d x^n}{(a+b x^n)^2} \, dx\)
 3.309 \(\int \frac{1}{(a+b x^n)^2 (c+d x^n)} \, dx\)
 3.310 \(\int \frac{1}{(a+b x^n)^2 (c+d x^n)^2} \, dx\)
 3.311 \(\int \frac{1}{(a+b x^n)^2 (c+d x^n)^3} \, dx\)
 3.312 \(\int (a+b x^n)^p (c+d x^n)^q \, dx\)
 3.313 \(\int (a+b x^n)^p (c+d x^n)^3 \, dx\)
 3.314 \(\int (a+b x^n)^p (c+d x^n)^2 \, dx\)
 3.315 \(\int (a+b x^n)^p (c+d x^n) \, dx\)
 3.316 \(\int (a+b x^n)^p \, dx\)
 3.317 \(\int \frac{(a+b x^n)^p}{c+d x^n} \, dx\)
 3.318 \(\int \frac{(a+b x^n)^p}{(c+d x^n)^2} \, dx\)
 3.319 \(\int \frac{(a+b x^n)^p}{(c+d x^n)^3} \, dx\)
 3.320 \(\int (a+b x^n)^p (c+d x^n)^{-1-\frac{1}{n}-p} \, dx\)
 3.321 \(\int (a+b x^n)^3 (c+d x^n)^{-4-\frac{1}{n}} \, dx\)
 3.322 \(\int (a+b x^n)^2 (c+d x^n)^{-3-\frac{1}{n}} \, dx\)
 3.323 \(\int (a+b x^n) (c+d x^n)^{-2-\frac{1}{n}} \, dx\)
 3.324 \(\int (c+d x^n)^{-1-\frac{1}{n}} \, dx\)
 3.325 \(\int \frac{(c+d x^n)^{-1/n}}{a+b x^n} \, dx\)
 3.326 \(\int \frac{(c+d x^n)^{1-\frac{1}{n}}}{(a+b x^n)^2} \, dx\)
 3.327 \(\int \frac{(c+d x^n)^{2-\frac{1}{n}}}{(a+b x^n)^3} \, dx\)
 3.328 \(\int (a+b x^n)^p (c+d x^n)^{-2-\frac{1}{n}-p} \, dx\)
 3.329 \(\int (a+b x^n)^{\frac{a d n-b c (1+n)}{(b c-a d) n}} (c+d x^n)^{\frac{a d-b c n+a d n}{b c n-a d n}} \, dx\)
 3.330 \(\int (a+b x^n)^2 (c+d x^n)^{-4-\frac{1}{n}} \, dx\)
 3.331 \(\int (a+b x^n) (c+d x^n)^{-3-\frac{1}{n}} \, dx\)
 3.332 \(\int (c+d x^n)^{-2-\frac{1}{n}} \, dx\)
 3.333 \(\int \frac{(c+d x^n)^{-1-\frac{1}{n}}}{a+b x^n} \, dx\)
 3.334 \(\int \frac{(c+d x^n)^{-1/n}}{(a+b x^n)^2} \, dx\)
 3.335 \(\int \frac{(c+d x^n)^{1-\frac{1}{n}}}{(a+b x^n)^3} \, dx\)
 3.336 \(\int \frac{(c+d x^n)^{2-\frac{1}{n}}}{(a+b x^n)^4} \, dx\)
 3.337 \(\int x^5 \sqrt{-c+d x} \sqrt{c+d x} (a+b x^2) \, dx\)
 3.338 \(\int x^3 \sqrt{-c+d x} \sqrt{c+d x} (a+b x^2) \, dx\)
 3.339 \(\int x \sqrt{-c+d x} \sqrt{c+d x} (a+b x^2) \, dx\)
 3.340 \(\int \frac{\sqrt{-c+d x} \sqrt{c+d x} (a+b x^2)}{x} \, dx\)
 3.341 \(\int \frac{\sqrt{-c+d x} \sqrt{c+d x} (a+b x^2)}{x^3} \, dx\)
 3.342 \(\int \frac{\sqrt{-c+d x} \sqrt{c+d x} (a+b x^2)}{x^5} \, dx\)
 3.343 \(\int x^4 \sqrt{-c+d x} \sqrt{c+d x} (a+b x^2) \, dx\)
 3.344 \(\int x^2 \sqrt{-c+d x} \sqrt{c+d x} (a+b x^2) \, dx\)
 3.345 \(\int \sqrt{-c+d x} \sqrt{c+d x} (a+b x^2) \, dx\)
 3.346 \(\int \frac{\sqrt{-c+d x} \sqrt{c+d x} (a+b x^2)}{x^2} \, dx\)
 3.347 \(\int \frac{\sqrt{-c+d x} \sqrt{c+d x} (a+b x^2)}{x^4} \, dx\)
 3.348 \(\int \frac{x^4 (a+b x^2)}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
 3.349 \(\int \frac{x^3 (a+b x^2)}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
 3.350 \(\int \frac{x^2 (a+b x^2)}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
 3.351 \(\int \frac{x (a+b x^2)}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
 3.352 \(\int \frac{a+b x^2}{\sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
 3.353 \(\int \frac{a+b x^2}{x \sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
 3.354 \(\int \frac{a+b x^2}{x^2 \sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
 3.355 \(\int \frac{a+b x^2}{x^3 \sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
 3.356 \(\int \frac{a+b x^2}{x^4 \sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
 3.357 \(\int \frac{a+b x^2}{x^5 \sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
 3.358 \(\int \frac{x^4 (a+b x^2)}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
 3.359 \(\int \frac{x^3 (a+b x^2)}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
 3.360 \(\int \frac{x^2 (a+b x^2)}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
 3.361 \(\int \frac{x (a+b x^2)}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
 3.362 \(\int \frac{a+b x^2}{\sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
 3.363 \(\int \frac{a+b x^2}{x \sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
 3.364 \(\int \frac{a+b x^2}{x^2 \sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
 3.365 \(\int \frac{a+b x^2}{x^3 \sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
 3.366 \(\int \frac{a+b x^2}{x^4 \sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
 3.367 \(\int \frac{a+b x^2}{x^5 \sqrt{-c+d x} \sqrt{c+d x}} \, dx\)
 3.368 \(\int \frac{x^4 (a+b x^2)}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
 3.369 \(\int \frac{x^3 (a+b x^2)}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
 3.370 \(\int \frac{x^2 (a+b x^2)}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
 3.371 \(\int \frac{x (a+b x^2)}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
 3.372 \(\int \frac{a+b x^2}{(-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
 3.373 \(\int \frac{a+b x^2}{x (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
 3.374 \(\int \frac{a+b x^2}{x^2 (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
 3.375 \(\int \frac{a+b x^2}{x^3 (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
 3.376 \(\int \frac{a+b x^2}{x^4 (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
 3.377 \(\int \frac{a+b x^2}{x^5 (-c+d x)^{3/2} (c+d x)^{3/2}} \, dx\)
 3.378 \(\int \frac{1+c^2 x^2}{x \sqrt{-1+c x} \sqrt{1+c x}} \, dx\)
 3.379 \(\int \frac{x^{-\frac{2 b^2 c+a^2 d}{b^2 c+a^2 d}} (c+d x^2)}{\sqrt{-a+b x} \sqrt{a+b x}} \, dx\)
 3.380 \(\int \frac{1}{\sqrt{-1-\sqrt{x}} \sqrt{-1+\sqrt{x}} \sqrt{1+x}} \, dx\)
 3.381 \(\int \frac{1}{\sqrt{a-b \sqrt{x}} \sqrt{a+b \sqrt{x}} \sqrt{a^2+b^2 x}} \, dx\)
 3.382 \(\int (a-b x^n)^p (a+b x^n)^p (c+d x^{2 n})^q \, dx\)
 3.383 \(\int (a-b x^n)^p (a+b x^n)^p (a^2+b^2 x^{2 n})^p \, dx\)
 3.384 \(\int \frac{(c+d x^{2 n})^p}{(a-b x^n) (a+b x^n)} \, dx\)
 3.385 \(\int (a-b x^{n/2})^p (a+b x^{n/2})^p (\frac{a^2 d (1+p)}{b^2 (1+\frac{-1-2 n-n p}{n})}+d x^n)^{\frac{-1-2 n-n p}{n}} \, dx\)