Chapter 3
Listing of integrals

 3.1 \(\int \frac{c+d x^2}{a+b x^4} \, dx\)
 3.2 \(\int \frac{c-d x^2}{a+b x^4} \, dx\)
 3.3 \(\int \frac{c+d x^2}{a-b x^4} \, dx\)
 3.4 \(\int \frac{c-d x^2}{a-b x^4} \, dx\)
 3.5 \(\int \frac{2+3 x^2}{4+9 x^4} \, dx\)
 3.6 \(\int \frac{2-3 x^2}{4+9 x^4} \, dx\)
 3.7 \(\int \frac{2+3 x^2}{4-9 x^4} \, dx\)
 3.8 \(\int \frac{2-3 x^2}{4-9 x^4} \, dx\)
 3.9 \(\int \frac{\sqrt{a} \sqrt{b}+b x^2}{a+b x^4} \, dx\)
 3.10 \(\int \frac{\sqrt{a} \sqrt{b}-b x^2}{a+b x^4} \, dx\)
 3.11 \(\int \frac{d+e x^2}{d^2+e^2 x^4} \, dx\)
 3.12 \(\int \frac{d-e x^2}{d^2+e^2 x^4} \, dx\)
 3.13 \(\int \frac{5+2 x^2}{-1+x^4} \, dx\)
 3.14 \(\int \frac{1+b x^2}{\sqrt{1-b^2 x^4}} \, dx\)
 3.15 \(\int \frac{1-b x^2}{\sqrt{1-b^2 x^4}} \, dx\)
 3.16 \(\int \frac{1+b x^2}{\sqrt{-1+b^2 x^4}} \, dx\)
 3.17 \(\int \frac{1-b x^2}{\sqrt{-1+b^2 x^4}} \, dx\)
 3.18 \(\int \frac{1-b x^2}{\sqrt{1+b^2 x^4}} \, dx\)
 3.19 \(\int \frac{1+b x^2}{\sqrt{1+b^2 x^4}} \, dx\)
 3.20 \(\int \frac{1-b x^2}{\sqrt{-1-b^2 x^4}} \, dx\)
 3.21 \(\int \frac{1+b x^2}{\sqrt{-1-b^2 x^4}} \, dx\)
 3.22 \(\int \frac{\sqrt{1+c^2 x^2}}{\sqrt{1-c^2 x^2}} \, dx\)
 3.23 \(\int \frac{1+c^2 x^2}{\sqrt{1-c^4 x^4}} \, dx\)
 3.24 \(\int \frac{\sqrt{1-c^2 x^2}}{\sqrt{1+c^2 x^2}} \, dx\)
 3.25 \(\int \frac{1-c^2 x^2}{\sqrt{1-c^4 x^4}} \, dx\)
 3.26 \(\int \frac{d+e x^2}{d^2+b x^2+e^2 x^4} \, dx\)
 3.27 \(\int \frac{d+e x^2}{d^2+f x^2+e^2 x^4} \, dx\)
 3.28 \(\int \frac{d+e x^2}{d^2-b x^2+e^2 x^4} \, dx\)
 3.29 \(\int \frac{d+e x^2}{d^2-f x^2+e^2 x^4} \, dx\)
 3.30 \(\int \frac{d-e x^2}{d^2+b x^2+e^2 x^4} \, dx\)
 3.31 \(\int \frac{d-e x^2}{d^2+f x^2+e^2 x^4} \, dx\)
 3.32 \(\int \frac{d-e x^2}{d^2-b x^2+e^2 x^4} \, dx\)
 3.33 \(\int \frac{d-e x^2}{d^2-f x^2+e^2 x^4} \, dx\)
 3.34 \(\int \frac{d-e x^2}{\frac{c d^2}{e^2}+b x^2+c x^4} \, dx\)
 3.35 \(\int \frac{d+e x^2}{\frac{c d^2}{e^2}+b x^2+c x^4} \, dx\)
 3.36 \(\int \frac{d+e x^2}{b x^2+c (\frac{d^2}{e^2}+x^4)} \, dx\)
 3.37 \(\int \frac{a-b x^2}{a^2+(-1+2 a b) x^2+b^2 x^4} \, dx\)
 3.38 \(\int \frac{a+b x^2}{a^2+(-1+2 a b) x^2+b^2 x^4} \, dx\)
 3.39 \(\int \frac{1+2 x^2}{1+b x^2+4 x^4} \, dx\)
 3.40 \(\int \frac{1+2 x^2}{1-b x^2+4 x^4} \, dx\)
 3.41 \(\int \frac{1+2 x^2}{1+6 x^2+4 x^4} \, dx\)
 3.42 \(\int \frac{1+2 x^2}{1+5 x^2+4 x^4} \, dx\)
 3.43 \(\int \frac{1+2 x^2}{1+4 x^2+4 x^4} \, dx\)
 3.44 \(\int \frac{1+2 x^2}{1+3 x^2+4 x^4} \, dx\)
 3.45 \(\int \frac{1+2 x^2}{1+2 x^2+4 x^4} \, dx\)
 3.46 \(\int \frac{1+2 x^2}{1+x^2+4 x^4} \, dx\)
 3.47 \(\int \frac{1+2 x^2}{1+4 x^4} \, dx\)
 3.48 \(\int \frac{1+2 x^2}{1-x^2+4 x^4} \, dx\)
 3.49 \(\int \frac{1+2 x^2}{1-2 x^2+4 x^4} \, dx\)
 3.50 \(\int \frac{1+2 x^2}{1-3 x^2+4 x^4} \, dx\)
 3.51 \(\int \frac{1+2 x^2}{1-4 x^2+4 x^4} \, dx\)
 3.52 \(\int \frac{1+2 x^2}{1-5 x^2+4 x^4} \, dx\)
 3.53 \(\int \frac{1+2 x^2}{1-6 x^2+4 x^4} \, dx\)
 3.54 \(\int \frac{1-2 x^2}{1+b x^2+4 x^4} \, dx\)
 3.55 \(\int \frac{1-2 x^2}{1+6 x^2+4 x^4} \, dx\)
 3.56 \(\int \frac{1-2 x^2}{1+5 x^2+4 x^4} \, dx\)
 3.57 \(\int \frac{1-2 x^2}{1+4 x^2+4 x^4} \, dx\)
 3.58 \(\int \frac{1-2 x^2}{1+3 x^2+4 x^4} \, dx\)
 3.59 \(\int \frac{1-2 x^2}{1+2 x^2+4 x^4} \, dx\)
 3.60 \(\int \frac{1-2 x^2}{1+x^2+4 x^4} \, dx\)
 3.61 \(\int \frac{1-2 x^2}{1+4 x^4} \, dx\)
 3.62 \(\int \frac{1-2 x^2}{1-x^2+4 x^4} \, dx\)
 3.63 \(\int \frac{1-2 x^2}{1-2 x^2+4 x^4} \, dx\)
 3.64 \(\int \frac{1-2 x^2}{1-3 x^2+4 x^4} \, dx\)
 3.65 \(\int \frac{1-2 x^2}{1-4 x^2+4 x^4} \, dx\)
 3.66 \(\int \frac{1-2 x^2}{1-5 x^2+4 x^4} \, dx\)
 3.67 \(\int \frac{1-2 x^2}{1-6 x^2+4 x^4} \, dx\)
 3.68 \(\int \frac{1+x^2}{1+b x^2+x^4} \, dx\)
 3.69 \(\int \frac{1+x^2}{1+5 x^2+x^4} \, dx\)
 3.70 \(\int \frac{1+x^2}{1+4 x^2+x^4} \, dx\)
 3.71 \(\int \frac{1+x^2}{1+3 x^2+x^4} \, dx\)
 3.72 \(\int \frac{1+x^2}{1+2 x^2+x^4} \, dx\)
 3.73 \(\int \frac{1+x^2}{1+x^2+x^4} \, dx\)
 3.74 \(\int \frac{1+x^2}{1+x^4} \, dx\)
 3.75 \(\int \frac{1+x^2}{1-x^2+x^4} \, dx\)
 3.76 \(\int \frac{1+x^2}{1-2 x^2+x^4} \, dx\)
 3.77 \(\int \frac{1+x^2}{1-3 x^2+x^4} \, dx\)
 3.78 \(\int \frac{1+x^2}{1-4 x^2+x^4} \, dx\)
 3.79 \(\int \frac{1+x^2}{1-5 x^2+x^4} \, dx\)
 3.80 \(\int \frac{1-x^2}{1+b x^2+x^4} \, dx\)
 3.81 \(\int \frac{1-x^2}{1+5 x^2+x^4} \, dx\)
 3.82 \(\int \frac{1-x^2}{1+4 x^2+x^4} \, dx\)
 3.83 \(\int \frac{1-x^2}{1+3 x^2+x^4} \, dx\)
 3.84 \(\int \frac{1-x^2}{1+2 x^2+x^4} \, dx\)
 3.85 \(\int \frac{1-x^2}{1+x^2+x^4} \, dx\)
 3.86 \(\int \frac{1-x^2}{1+x^4} \, dx\)
 3.87 \(\int \frac{1-x^2}{1-x^2+x^4} \, dx\)
 3.88 \(\int \frac{1-x^2}{1-2 x^2+x^4} \, dx\)
 3.89 \(\int \frac{1-x^2}{1-3 x^2+x^4} \, dx\)
 3.90 \(\int \frac{1-x^2}{1-4 x^2+x^4} \, dx\)
 3.91 \(\int \frac{1-x^2}{1-5 x^2+x^4} \, dx\)
 3.92 \(\int -\frac{1+3 x^2}{1+2 x^2+9 x^4} \, dx\)
 3.93 \(\int \frac{1+3 x^2}{-1-2 x^2-9 x^4} \, dx\)
 3.94 \(\int \frac{3+2 x^2}{1-2 x^2+x^4} \, dx\)
 3.95 \(\int \frac{2+3 x^2}{5-8 x^2+3 x^4} \, dx\)
 3.96 \(\int \frac{d+e x^2}{5-8 x^2+3 x^4} \, dx\)
 3.97 \(\int \frac{3+x^2}{1+3 x^2+x^4} \, dx\)
 3.98 \(\int \frac{a+b x^2}{1+x^2+x^4} \, dx\)
 3.99 \(\int \frac{a+b x^2}{(1+x^2+x^4)^2} \, dx\)
 3.100 \(\int \frac{a+b x^2}{2+x^2+x^4} \, dx\)
 3.101 \(\int \frac{a+b x^2}{(2+x^2+x^4)^2} \, dx\)
 3.102 \(\int \frac{\sqrt{2}-x^2}{1-\sqrt{2} x^2+x^4} \, dx\)
 3.103 \(\int \frac{\sqrt{2}+x^2}{1+\sqrt{2} x^2+x^4} \, dx\)
 3.104 \(\int \frac{\sqrt{2}-x^2}{1+b x^2+x^4} \, dx\)
 3.105 \(\int \frac{\sqrt{2}+x^2}{1+b x^2+x^4} \, dx\)
 3.106 \(\int \frac{2 a-x^2}{a^2-a x^2+x^4} \, dx\)
 3.107 \(\int \frac{2 \sqrt{a}-x^2}{a-\sqrt{a} x^2+x^4} \, dx\)
 3.108 \(\int \frac{2 b^{2/3}+x^2}{b^{4/3}+b^{2/3} x^2+x^4} \, dx\)
 3.109 \(\int \frac{A+B x^2}{a^2-a x^2+x^4} \, dx\)
 3.110 \(\int \frac{A+B x^2}{a-\sqrt{a} x^2+x^4} \, dx\)
 3.111 \(\int \frac{A+B x^2}{a-\sqrt{a c} x^2+c x^4} \, dx\)
 3.112 \(\int \frac{A+B x^2}{a-\sqrt{a} \sqrt{c} x^2+c x^4} \, dx\)
 3.113 \(\int \frac{3-x^2}{\sqrt{3+x^2-x^4}} \, dx\)
 3.114 \(\int \frac{3-x^2}{\sqrt{3+2 x^2-x^4}} \, dx\)
 3.115 \(\int \frac{3-x^2}{\sqrt{3+3 x^2-x^4}} \, dx\)
 3.116 \(\int \frac{3-x^2}{\sqrt{3-x^2-x^4}} \, dx\)
 3.117 \(\int \frac{3-x^2}{\sqrt{3-2 x^2-x^4}} \, dx\)
 3.118 \(\int \frac{3-x^2}{\sqrt{3-3 x^2-x^4}} \, dx\)
 3.119 \(\int \frac{b-\sqrt{b^2-4 a c}+2 c x^2}{\sqrt{a+b x^2+c x^4}} \, dx\)
 3.120 \(\int (d+e x^2)^4 (a+c x^4) \, dx\)
 3.121 \(\int (d+e x^2)^3 (a+c x^4) \, dx\)
 3.122 \(\int (d+e x^2)^2 (a+c x^4) \, dx\)
 3.123 \(\int (d+e x^2) (a+c x^4) \, dx\)
 3.124 \(\int \frac{a+c x^4}{d+e x^2} \, dx\)
 3.125 \(\int \frac{a+c x^4}{(d+e x^2)^2} \, dx\)
 3.126 \(\int \frac{a+c x^4}{(d+e x^2)^3} \, dx\)
 3.127 \(\int \frac{a+c x^4}{(d+e x^2)^4} \, dx\)
 3.128 \(\int (d+e x^2)^3 (a+c x^4)^2 \, dx\)
 3.129 \(\int (d+e x^2)^2 (a+c x^4)^2 \, dx\)
 3.130 \(\int (d+e x^2) (a+c x^4)^2 \, dx\)
 3.131 \(\int (a+c x^4)^2 \, dx\)
 3.132 \(\int \frac{(a+c x^4)^2}{d+e x^2} \, dx\)
 3.133 \(\int \frac{(a+c x^4)^2}{(d+e x^2)^2} \, dx\)
 3.134 \(\int \frac{(a+c x^4)^2}{(d+e x^2)^3} \, dx\)
 3.135 \(\int \frac{(a+c x^4)^2}{(d+e x^2)^4} \, dx\)
 3.136 \(\int \frac{(a+c x^4)^2}{(d+e x^2)^5} \, dx\)
 3.137 \(\int \frac{(d+e x^2)^4}{a+c x^4} \, dx\)
 3.138 \(\int \frac{(d+e x^2)^3}{a+c x^4} \, dx\)
 3.139 \(\int \frac{(d+e x^2)^2}{a+c x^4} \, dx\)
 3.140 \(\int \frac{d+e x^2}{a+c x^4} \, dx\)
 3.141 \(\int \frac{1}{a+c x^4} \, dx\)
 3.142 \(\int \frac{1}{(d+e x^2) (a+c x^4)} \, dx\)
 3.143 \(\int \frac{1}{(d+e x^2)^2 (a+c x^4)} \, dx\)
 3.144 \(\int \frac{(d+e x^2)^3}{(a+c x^4)^2} \, dx\)
 3.145 \(\int \frac{(d+e x^2)^2}{(a+c x^4)^2} \, dx\)
 3.146 \(\int \frac{d+e x^2}{(a+c x^4)^2} \, dx\)
 3.147 \(\int \frac{1}{(a+c x^4)^2} \, dx\)
 3.148 \(\int \frac{1}{(d+e x^2) (a+c x^4)^2} \, dx\)
 3.149 \(\int \frac{1}{(d+e x^2)^2 (a+c x^4)^2} \, dx\)
 3.150 \(\int \frac{(d+e x^2)^4}{\sqrt{a+c x^4}} \, dx\)
 3.151 \(\int \frac{(d+e x^2)^3}{\sqrt{a+c x^4}} \, dx\)
 3.152 \(\int \frac{(d+e x^2)^2}{\sqrt{a+c x^4}} \, dx\)
 3.153 \(\int \frac{d+e x^2}{\sqrt{a+c x^4}} \, dx\)
 3.154 \(\int \frac{1}{(d+e x^2) \sqrt{a+c x^4}} \, dx\)
 3.155 \(\int \frac{1}{(d+e x^2)^2 \sqrt{a+c x^4}} \, dx\)
 3.156 \(\int \frac{1}{(d+e x^2)^3 \sqrt{a+c x^4}} \, dx\)
 3.157 \(\int \frac{(d+e x^2)^3}{\sqrt{a-c x^4}} \, dx\)
 3.158 \(\int \frac{(d+e x^2)^2}{\sqrt{a-c x^4}} \, dx\)
 3.159 \(\int \frac{d+e x^2}{\sqrt{a-c x^4}} \, dx\)
 3.160 \(\int \frac{1}{(d+e x^2) \sqrt{a-c x^4}} \, dx\)
 3.161 \(\int \frac{1}{(d+e x^2)^2 \sqrt{a-c x^4}} \, dx\)
 3.162 \(\int \frac{1}{(d+e x^2)^3 \sqrt{a-c x^4}} \, dx\)
 3.163 \(\int \frac{1}{(d+e x^2)^4 \sqrt{a-c x^4}} \, dx\)
 3.164 \(\int \frac{d+e x^2}{\sqrt{-a+c x^4}} \, dx\)
 3.165 \(\int \frac{1}{(d+e x^2) \sqrt{-a+c x^4}} \, dx\)
 3.166 \(\int \frac{\sqrt{a}+\sqrt{c} x^2}{\sqrt{-a+c x^4}} \, dx\)
 3.167 \(\int \frac{1+\sqrt{\frac{c}{a}} x^2}{\sqrt{-a+c x^4}} \, dx\)
 3.168 \(\int \frac{d+e x^2}{\sqrt{-a-c x^4}} \, dx\)
 3.169 \(\int \frac{1}{(d+e x^2) \sqrt{-a-c x^4}} \, dx\)
 3.170 \(\int \frac{1}{(a+b x^2) \sqrt{4-5 x^4}} \, dx\)
 3.171 \(\int \frac{1}{(a+b x^2) \sqrt{4+5 x^4}} \, dx\)
 3.172 \(\int \frac{1}{(a+b x^2) \sqrt{4-d x^4}} \, dx\)
 3.173 \(\int \frac{1}{(a+b x^2) \sqrt{4+d x^4}} \, dx\)
 3.174 \(\int \frac{\sqrt{a+b x^2}}{\sqrt{1-x^4}} \, dx\)
 3.175 \(\int (c+e x^2)^q (a+b x^4)^p \, dx\)
 3.176 \(\int (c+e x^2)^3 (a+b x^4)^p \, dx\)
 3.177 \(\int (c+e x^2)^2 (a+b x^4)^p \, dx\)
 3.178 \(\int (c+e x^2) (a+b x^4)^p \, dx\)
 3.179 \(\int (a+b x^4)^p \, dx\)
 3.180 \(\int \frac{(a+b x^4)^p}{c+e x^2} \, dx\)
 3.181 \(\int \frac{(a+b x^4)^p}{(c+e x^2)^2} \, dx\)
 3.182 \(\int (1-x^2)^3 (1+b x^4)^p \, dx\)
 3.183 \(\int (1-x^2)^2 (1+b x^4)^p \, dx\)
 3.184 \(\int (1-x^2) (1+b x^4)^p \, dx\)
 3.185 \(\int (1+b x^4)^p \, dx\)
 3.186 \(\int \frac{(1+b x^4)^p}{1-x^2} \, dx\)
 3.187 \(\int \frac{(1+b x^4)^p}{(1-x^2)^2} \, dx\)
 3.188 \(\int \frac{(1+b x^4)^p}{(1-x^2)^3} \, dx\)
 3.189 \(\int \frac{(d+e x^2)^4}{d^2-e^2 x^4} \, dx\)
 3.190 \(\int \frac{(d+e x^2)^3}{d^2-e^2 x^4} \, dx\)
 3.191 \(\int \frac{(d+e x^2)^2}{d^2-e^2 x^4} \, dx\)
 3.192 \(\int \frac{d+e x^2}{d^2-e^2 x^4} \, dx\)
 3.193 \(\int \frac{1}{(d+e x^2) (d^2-e^2 x^4)} \, dx\)
 3.194 \(\int \frac{1}{(d+e x^2)^2 (d^2-e^2 x^4)} \, dx\)
 3.195 \(\int \frac{(d+e x^2)^{3/2}}{d^2-e^2 x^4} \, dx\)
 3.196 \(\int \frac{\sqrt{d+e x^2}}{d^2-e^2 x^4} \, dx\)
 3.197 \(\int \frac{1}{\sqrt{d+e x^2} (d^2-e^2 x^4)} \, dx\)
 3.198 \(\int \frac{1}{(d+e x^2)^{3/2} (d^2-e^2 x^4)} \, dx\)
 3.199 \(\int \frac{(a+b x^2)^{5/2}}{\sqrt{a^2-b^2 x^4}} \, dx\)
 3.200 \(\int \frac{(a+b x^2)^{3/2}}{\sqrt{a^2-b^2 x^4}} \, dx\)
 3.201 \(\int \frac{\sqrt{a+b x^2}}{\sqrt{a^2-b^2 x^4}} \, dx\)
 3.202 \(\int \frac{1}{\sqrt{a+b x^2} \sqrt{a^2-b^2 x^4}} \, dx\)
 3.203 \(\int \frac{1}{(a+b x^2)^{3/2} \sqrt{a^2-b^2 x^4}} \, dx\)
 3.204 \(\int \frac{1}{(a+b x^2)^{5/2} \sqrt{a^2-b^2 x^4}} \, dx\)
 3.205 \(\int \frac{(a-b x^2)^{5/2}}{\sqrt{a^2-b^2 x^4}} \, dx\)
 3.206 \(\int \frac{(a-b x^2)^{3/2}}{\sqrt{a^2-b^2 x^4}} \, dx\)
 3.207 \(\int \frac{\sqrt{a-b x^2}}{\sqrt{a^2-b^2 x^4}} \, dx\)
 3.208 \(\int \frac{1}{\sqrt{a-b x^2} \sqrt{a^2-b^2 x^4}} \, dx\)
 3.209 \(\int \frac{1}{(a-b x^2)^{3/2} \sqrt{a^2-b^2 x^4}} \, dx\)
 3.210 \(\int \frac{1}{(a-b x^2)^{5/2} \sqrt{a^2-b^2 x^4}} \, dx\)
 3.211 \(\int \frac{\sqrt{-1+x^2}}{\sqrt{-1+x^4}} \, dx\)
 3.212 \(\int \frac{\sqrt{1+x^2}}{\sqrt{-1+x^4}} \, dx\)
 3.213 \(\int \frac{-\sqrt{-1+x^2}+\sqrt{1+x^2}}{\sqrt{-1+x^4}} \, dx\)
 3.214 \(\int \frac{(d+e x^2)^4}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx\)
 3.215 \(\int \frac{(d+e x^2)^3}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx\)
 3.216 \(\int \frac{(d+e x^2)^2}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx\)
 3.217 \(\int \frac{d+e x^2}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx\)
 3.218 \(\int \frac{1}{(d+e x^2) (-c d^2+b d e+b e^2 x^2+c e^2 x^4)} \, dx\)
 3.219 \(\int \frac{1}{(d+e x^2)^2 (-c d^2+b d e+b e^2 x^2+c e^2 x^4)} \, dx\)
 3.220 \(\int \frac{(d+e x^2)^{5/2}}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx\)
 3.221 \(\int \frac{(d+e x^2)^{3/2}}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx\)
 3.222 \(\int \frac{\sqrt{d+e x^2}}{-c d^2+b d e+b e^2 x^2+c e^2 x^4} \, dx\)
 3.223 \(\int \frac{1}{\sqrt{d+e x^2} (-c d^2+b d e+b e^2 x^2+c e^2 x^4)} \, dx\)
 3.224 \(\int \frac{1}{(d+e x^2)^{3/2} (-c d^2+b d e+b e^2 x^2+c e^2 x^4)} \, dx\)
 3.225 \(\int (1+x^2)^3 \sqrt{1+x^2+x^4} \, dx\)
 3.226 \(\int (1+x^2)^2 \sqrt{1+x^2+x^4} \, dx\)
 3.227 \(\int (1+x^2) \sqrt{1+x^2+x^4} \, dx\)
 3.228 \(\int \frac{\sqrt{1+x^2+x^4}}{1+x^2} \, dx\)
 3.229 \(\int \frac{\sqrt{1+x^2+x^4}}{(1+x^2)^2} \, dx\)
 3.230 \(\int \frac{\sqrt{1+x^2+x^4}}{(1+x^2)^3} \, dx\)
 3.231 \(\int \frac{\sqrt{1+x^2+x^4}}{(1+x^2)^4} \, dx\)
 3.232 \(\int \frac{(1+x^2)^3}{\sqrt{1+x^2+x^4}} \, dx\)
 3.233 \(\int \frac{(1+x^2)^2}{\sqrt{1+x^2+x^4}} \, dx\)
 3.234 \(\int \frac{1+x^2}{\sqrt{1+x^2+x^4}} \, dx\)
 3.235 \(\int \frac{1}{(1+x^2) \sqrt{1+x^2+x^4}} \, dx\)
 3.236 \(\int \frac{1}{(1+x^2)^2 \sqrt{1+x^2+x^4}} \, dx\)
 3.237 \(\int \frac{1}{(1+x^2)^3 \sqrt{1+x^2+x^4}} \, dx\)
 3.238 \(\int \frac{(1+x^2)^3}{(1+x^2+x^4)^{3/2}} \, dx\)
 3.239 \(\int \frac{(1+x^2)^2}{(1+x^2+x^4)^{3/2}} \, dx\)
 3.240 \(\int \frac{1+x^2}{(1+x^2+x^4)^{3/2}} \, dx\)
 3.241 \(\int \frac{1}{(1+x^2) (1+x^2+x^4)^{3/2}} \, dx\)
 3.242 \(\int \frac{1}{(1+x^2)^2 (1+x^2+x^4)^{3/2}} \, dx\)
 3.243 \(\int \frac{1}{(1+x^2)^3 (1+x^2+x^4)^{3/2}} \, dx\)
 3.244 \(\int (d+e x^2)^4 (a+b x^2+c x^4) \, dx\)
 3.245 \(\int (d+e x^2)^3 (a+b x^2+c x^4) \, dx\)
 3.246 \(\int (d+e x^2)^2 (a+b x^2+c x^4) \, dx\)
 3.247 \(\int (d+e x^2) (a+b x^2+c x^4) \, dx\)
 3.248 \(\int \frac{a+b x^2+c x^4}{d+e x^2} \, dx\)
 3.249 \(\int \frac{a+b x^2+c x^4}{(d+e x^2)^2} \, dx\)
 3.250 \(\int \frac{a+b x^2+c x^4}{(d+e x^2)^3} \, dx\)
 3.251 \(\int \frac{a+b x^2+c x^4}{(d+e x^2)^4} \, dx\)
 3.252 \(\int (d+e x^2)^3 (a+b x^2+c x^4)^2 \, dx\)
 3.253 \(\int (d+e x^2)^2 (a+b x^2+c x^4)^2 \, dx\)
 3.254 \(\int (d+e x^2) (a+b x^2+c x^4)^2 \, dx\)
 3.255 \(\int (a+b x^2+c x^4)^2 \, dx\)
 3.256 \(\int \frac{(a+b x^2+c x^4)^2}{d+e x^2} \, dx\)
 3.257 \(\int \frac{(a+b x^2+c x^4)^2}{(d+e x^2)^2} \, dx\)
 3.258 \(\int \frac{(a+b x^2+c x^4)^2}{(d+e x^2)^3} \, dx\)
 3.259 \(\int \frac{(a+b x^2+c x^4)^2}{(d+e x^2)^4} \, dx\)
 3.260 \(\int \frac{(a+b x^2+c x^4)^2}{(d+e x^2)^5} \, dx\)
 3.261 \(\int \frac{a+b x^2+c x^4}{(d+e x^2)^2} \, dx\)
 3.262 \(\int \frac{a+x^2 (b+c x^2)}{(d+e x^2)^2} \, dx\)
 3.263 \(\int \frac{(d+e x^2)^4}{a+b x^2+c x^4} \, dx\)
 3.264 \(\int \frac{(d+e x^2)^3}{a+b x^2+c x^4} \, dx\)
 3.265 \(\int \frac{(d+e x^2)^2}{a+b x^2+c x^4} \, dx\)
 3.266 \(\int \frac{d+e x^2}{a+b x^2+c x^4} \, dx\)
 3.267 \(\int \frac{1}{a+b x^2+c x^4} \, dx\)
 3.268 \(\int \frac{1}{(d+e x^2) (a+b x^2+c x^4)} \, dx\)
 3.269 \(\int \frac{1}{(d+e x^2)^2 (a+b x^2+c x^4)} \, dx\)
 3.270 \(\int \frac{(d+e x^2)^3}{(a+b x^2+c x^4)^2} \, dx\)
 3.271 \(\int \frac{(d+e x^2)^2}{(a+b x^2+c x^4)^2} \, dx\)
 3.272 \(\int \frac{d+e x^2}{(a+b x^2+c x^4)^2} \, dx\)
 3.273 \(\int \frac{1}{(a+b x^2+c x^4)^2} \, dx\)
 3.274 \(\int \frac{1}{(d+e x^2) (a+b x^2+c x^4)^2} \, dx\)
 3.275 \(\int \frac{1}{(d+e x^2)^2 (a+b x^2+c x^4)^2} \, dx\)
 3.276 \(\int (d+e x^2)^{5/2} (a+b x^2+c x^4) \, dx\)
 3.277 \(\int (d+e x^2)^{3/2} (a+b x^2+c x^4) \, dx\)
 3.278 \(\int \sqrt{d+e x^2} (a+b x^2+c x^4) \, dx\)
 3.279 \(\int \frac{a+b x^2+c x^4}{\sqrt{d+e x^2}} \, dx\)
 3.280 \(\int \frac{a+b x^2+c x^4}{(d+e x^2)^{3/2}} \, dx\)
 3.281 \(\int \frac{a+b x^2+c x^4}{(d+e x^2)^{5/2}} \, dx\)
 3.282 \(\int \frac{a+b x^2+c x^4}{(d+e x^2)^{7/2}} \, dx\)
 3.283 \(\int \frac{a+b x^2+c x^4}{(d+e x^2)^{9/2}} \, dx\)
 3.284 \(\int \frac{a+b x^2+c x^4}{(d+e x^2)^{11/2}} \, dx\)
 3.285 \(\int \frac{a+b x^2+c x^4}{(d+e x^2)^{13/2}} \, dx\)
 3.286 \(\int (7+5 x^2)^3 \sqrt{2+3 x^2+x^4} \, dx\)
 3.287 \(\int (7+5 x^2)^2 \sqrt{2+3 x^2+x^4} \, dx\)
 3.288 \(\int (7+5 x^2) \sqrt{2+3 x^2+x^4} \, dx\)
 3.289 \(\int \sqrt{2+3 x^2+x^4} \, dx\)
 3.290 \(\int \frac{\sqrt{2+3 x^2+x^4}}{7+5 x^2} \, dx\)
 3.291 \(\int \frac{\sqrt{2+3 x^2+x^4}}{(7+5 x^2)^2} \, dx\)
 3.292 \(\int \frac{\sqrt{2+3 x^2+x^4}}{(7+5 x^2)^3} \, dx\)
 3.293 \(\int (7+5 x^2)^3 (2+3 x^2+x^4)^{3/2} \, dx\)
 3.294 \(\int (7+5 x^2)^2 (2+3 x^2+x^4)^{3/2} \, dx\)
 3.295 \(\int (7+5 x^2) (2+3 x^2+x^4)^{3/2} \, dx\)
 3.296 \(\int (2+3 x^2+x^4)^{3/2} \, dx\)
 3.297 \(\int \frac{(2+3 x^2+x^4)^{3/2}}{7+5 x^2} \, dx\)
 3.298 \(\int \frac{(2+3 x^2+x^4)^{3/2}}{(7+5 x^2)^2} \, dx\)
 3.299 \(\int \frac{(2+3 x^2+x^4)^{3/2}}{(7+5 x^2)^3} \, dx\)
 3.300 \(\int \frac{(7+5 x^2)^3}{\sqrt{2+3 x^2+x^4}} \, dx\)
 3.301 \(\int \frac{(7+5 x^2)^2}{\sqrt{2+3 x^2+x^4}} \, dx\)
 3.302 \(\int \frac{7+5 x^2}{\sqrt{2+3 x^2+x^4}} \, dx\)
 3.303 \(\int \frac{1}{\sqrt{2+3 x^2+x^4}} \, dx\)
 3.304 \(\int \frac{1}{(7+5 x^2) \sqrt{2+3 x^2+x^4}} \, dx\)
 3.305 \(\int \frac{1}{(7+5 x^2)^2 \sqrt{2+3 x^2+x^4}} \, dx\)
 3.306 \(\int \frac{1}{(7+5 x^2)^3 \sqrt{2+3 x^2+x^4}} \, dx\)
 3.307 \(\int \frac{(7+5 x^2)^5}{(2+3 x^2+x^4)^{3/2}} \, dx\)
 3.308 \(\int \frac{(7+5 x^2)^4}{(2+3 x^2+x^4)^{3/2}} \, dx\)
 3.309 \(\int \frac{(7+5 x^2)^3}{(2+3 x^2+x^4)^{3/2}} \, dx\)
 3.310 \(\int \frac{(7+5 x^2)^2}{(2+3 x^2+x^4)^{3/2}} \, dx\)
 3.311 \(\int \frac{7+5 x^2}{(2+3 x^2+x^4)^{3/2}} \, dx\)
 3.312 \(\int \frac{1}{(2+3 x^2+x^4)^{3/2}} \, dx\)
 3.313 \(\int \frac{1}{(7+5 x^2) (2+3 x^2+x^4)^{3/2}} \, dx\)
 3.314 \(\int \frac{1}{(7+5 x^2)^2 (2+3 x^2+x^4)^{3/2}} \, dx\)
 3.315 \(\int \frac{1}{(7+5 x^2)^3 (2+3 x^2+x^4)^{3/2}} \, dx\)
 3.316 \(\int (7+5 x^2)^4 \sqrt{2+x^2-x^4} \, dx\)
 3.317 \(\int (7+5 x^2)^3 \sqrt{2+x^2-x^4} \, dx\)
 3.318 \(\int (7+5 x^2)^2 \sqrt{2+x^2-x^4} \, dx\)
 3.319 \(\int (7+5 x^2) \sqrt{2+x^2-x^4} \, dx\)
 3.320 \(\int \sqrt{2+x^2-x^4} \, dx\)
 3.321 \(\int \frac{\sqrt{2+x^2-x^4}}{7+5 x^2} \, dx\)
 3.322 \(\int \frac{\sqrt{2+x^2-x^4}}{(7+5 x^2)^2} \, dx\)
 3.323 \(\int \frac{\sqrt{2+x^2-x^4}}{(7+5 x^2)^3} \, dx\)
 3.324 \(\int (7+5 x^2)^4 (2+x^2-x^4)^{3/2} \, dx\)
 3.325 \(\int (7+5 x^2)^3 (2+x^2-x^4)^{3/2} \, dx\)
 3.326 \(\int (7+5 x^2)^2 (2+x^2-x^4)^{3/2} \, dx\)
 3.327 \(\int (7+5 x^2) (2+x^2-x^4)^{3/2} \, dx\)
 3.328 \(\int (2+x^2-x^4)^{3/2} \, dx\)
 3.329 \(\int \frac{(2+x^2-x^4)^{3/2}}{7+5 x^2} \, dx\)
 3.330 \(\int \frac{(2+x^2-x^4)^{3/2}}{(7+5 x^2)^2} \, dx\)
 3.331 \(\int \frac{(2+x^2-x^4)^{3/2}}{(7+5 x^2)^3} \, dx\)
 3.332 \(\int \frac{(7+5 x^2)^3}{\sqrt{2+x^2-x^4}} \, dx\)
 3.333 \(\int \frac{(7+5 x^2)^2}{\sqrt{2+x^2-x^4}} \, dx\)
 3.334 \(\int \frac{7+5 x^2}{\sqrt{2+x^2-x^4}} \, dx\)
 3.335 \(\int \frac{1}{\sqrt{2+x^2-x^4}} \, dx\)
 3.336 \(\int \frac{1}{(7+5 x^2) \sqrt{2+x^2-x^4}} \, dx\)
 3.337 \(\int \frac{1}{(7+5 x^2)^2 \sqrt{2+x^2-x^4}} \, dx\)
 3.338 \(\int \frac{1}{(7+5 x^2)^3 \sqrt{2+x^2-x^4}} \, dx\)
 3.339 \(\int \frac{(7+5 x^2)^5}{(2+x^2-x^4)^{3/2}} \, dx\)
 3.340 \(\int \frac{(7+5 x^2)^4}{(2+x^2-x^4)^{3/2}} \, dx\)
 3.341 \(\int \frac{(7+5 x^2)^3}{(2+x^2-x^4)^{3/2}} \, dx\)
 3.342 \(\int \frac{(7+5 x^2)^2}{(2+x^2-x^4)^{3/2}} \, dx\)
 3.343 \(\int \frac{7+5 x^2}{(2+x^2-x^4)^{3/2}} \, dx\)
 3.344 \(\int \frac{1}{(2+x^2-x^4)^{3/2}} \, dx\)
 3.345 \(\int \frac{1}{(7+5 x^2) (2+x^2-x^4)^{3/2}} \, dx\)
 3.346 \(\int \frac{1}{(7+5 x^2)^2 (2+x^2-x^4)^{3/2}} \, dx\)
 3.347 \(\int \frac{1}{(7+5 x^2)^3 (2+x^2-x^4)^{3/2}} \, dx\)
 3.348 \(\int (7+5 x^2)^4 \sqrt{4+3 x^2+x^4} \, dx\)
 3.349 \(\int (7+5 x^2)^3 \sqrt{4+3 x^2+x^4} \, dx\)
 3.350 \(\int (7+5 x^2)^2 \sqrt{4+3 x^2+x^4} \, dx\)
 3.351 \(\int (7+5 x^2) \sqrt{4+3 x^2+x^4} \, dx\)
 3.352 \(\int \sqrt{4+3 x^2+x^4} \, dx\)
 3.353 \(\int \frac{\sqrt{4+3 x^2+x^4}}{7+5 x^2} \, dx\)
 3.354 \(\int \frac{\sqrt{4+3 x^2+x^4}}{(7+5 x^2)^2} \, dx\)
 3.355 \(\int \frac{\sqrt{4+3 x^2+x^4}}{(7+5 x^2)^3} \, dx\)
 3.356 \(\int (7+5 x^2)^4 (4+3 x^2+x^4)^{3/2} \, dx\)
 3.357 \(\int (7+5 x^2)^3 (4+3 x^2+x^4)^{3/2} \, dx\)
 3.358 \(\int (7+5 x^2)^2 (4+3 x^2+x^4)^{3/2} \, dx\)
 3.359 \(\int (7+5 x^2) (4+3 x^2+x^4)^{3/2} \, dx\)
 3.360 \(\int (4+3 x^2+x^4)^{3/2} \, dx\)
 3.361 \(\int \frac{(4+3 x^2+x^4)^{3/2}}{7+5 x^2} \, dx\)
 3.362 \(\int \frac{(4+3 x^2+x^4)^{3/2}}{(7+5 x^2)^2} \, dx\)
 3.363 \(\int \frac{(4+3 x^2+x^4)^{3/2}}{(7+5 x^2)^3} \, dx\)
 3.364 \(\int \frac{(7+5 x^2)^3}{\sqrt{4+3 x^2+x^4}} \, dx\)
 3.365 \(\int \frac{(7+5 x^2)^2}{\sqrt{4+3 x^2+x^4}} \, dx\)
 3.366 \(\int \frac{7+5 x^2}{\sqrt{4+3 x^2+x^4}} \, dx\)
 3.367 \(\int \frac{1}{\sqrt{4+3 x^2+x^4}} \, dx\)
 3.368 \(\int \frac{1}{(7+5 x^2) \sqrt{4+3 x^2+x^4}} \, dx\)
 3.369 \(\int \frac{1}{(7+5 x^2)^2 \sqrt{4+3 x^2+x^4}} \, dx\)
 3.370 \(\int \frac{1}{(7+5 x^2)^3 \sqrt{4+3 x^2+x^4}} \, dx\)
 3.371 \(\int \frac{(7+5 x^2)^5}{(4+3 x^2+x^4)^{3/2}} \, dx\)
 3.372 \(\int \frac{(7+5 x^2)^4}{(4+3 x^2+x^4)^{3/2}} \, dx\)
 3.373 \(\int \frac{(7+5 x^2)^3}{(4+3 x^2+x^4)^{3/2}} \, dx\)
 3.374 \(\int \frac{(7+5 x^2)^2}{(4+3 x^2+x^4)^{3/2}} \, dx\)
 3.375 \(\int \frac{7+5 x^2}{(4+3 x^2+x^4)^{3/2}} \, dx\)
 3.376 \(\int \frac{1}{(4+3 x^2+x^4)^{3/2}} \, dx\)
 3.377 \(\int \frac{1}{(7+5 x^2) (4+3 x^2+x^4)^{3/2}} \, dx\)
 3.378 \(\int \frac{1}{(7+5 x^2)^2 (4+3 x^2+x^4)^{3/2}} \, dx\)
 3.379 \(\int \frac{1}{(7+5 x^2)^3 (4+3 x^2+x^4)^{3/2}} \, dx\)
 3.380 \(\int \frac{(d+e x^2)^3}{\sqrt{a+b x^2+c x^4}} \, dx\)
 3.381 \(\int \frac{(d+e x^2)^2}{\sqrt{a+b x^2+c x^4}} \, dx\)
 3.382 \(\int \frac{d+e x^2}{\sqrt{a+b x^2+c x^4}} \, dx\)
 3.383 \(\int \frac{1}{(d+e x^2) \sqrt{a+b x^2+c x^4}} \, dx\)
 3.384 \(\int \frac{1}{(d+e x^2)^2 \sqrt{a+b x^2+c x^4}} \, dx\)
 3.385 \(\int \frac{(d+e x^2)^3}{\sqrt{a+b x^2-c x^4}} \, dx\)
 3.386 \(\int \frac{(d+e x^2)^2}{\sqrt{a+b x^2-c x^4}} \, dx\)
 3.387 \(\int \frac{d+e x^2}{\sqrt{a+b x^2-c x^4}} \, dx\)
 3.388 \(\int \frac{1}{(d+e x^2) \sqrt{a+b x^2-c x^4}} \, dx\)
 3.389 \(\int \frac{1}{(d+e x^2)^2 \sqrt{a+b x^2-c x^4}} \, dx\)
 3.390 \(\int \frac{d+e x^2}{\sqrt{-a+b x^2+c x^4}} \, dx\)
 3.391 \(\int \frac{1}{(d+e x^2) \sqrt{-a+b x^2+c x^4}} \, dx\)
 3.392 \(\int \frac{d+e x^2}{\sqrt{-a+b x^2-c x^4}} \, dx\)
 3.393 \(\int \frac{1}{(d+e x^2) \sqrt{-a+b x^2-c x^4}} \, dx\)
 3.394 \(\int \frac{(d+e x^2)^3}{\sqrt{2+3 x^2+x^4}} \, dx\)
 3.395 \(\int \frac{(d+e x^2)^2}{\sqrt{2+3 x^2+x^4}} \, dx\)
 3.396 \(\int \frac{d+e x^2}{\sqrt{2+3 x^2+x^4}} \, dx\)
 3.397 \(\int \frac{1}{(d+e x^2) \sqrt{2+3 x^2+x^4}} \, dx\)
 3.398 \(\int \frac{1}{(d+e x^2)^2 \sqrt{2+3 x^2+x^4}} \, dx\)
 3.399 \(\int (c+e x^2)^q (a+c x^2+b x^4)^p \, dx\)
 3.400 \(\int (c+e x^2)^3 (a+c x^2+b x^4)^p \, dx\)
 3.401 \(\int (c+e x^2)^2 (a+c x^2+b x^4)^p \, dx\)
 3.402 \(\int (c+e x^2) (a+c x^2+b x^4)^p \, dx\)
 3.403 \(\int (a+c x^2+b x^4)^p \, dx\)
 3.404 \(\int \frac{(a+c x^2+b x^4)^p}{c+e x^2} \, dx\)
 3.405 \(\int \frac{(a+c x^2+b x^4)^p}{(c+e x^2)^2} \, dx\)
 3.406 \(\int \frac{f+g x}{(d+e x) \sqrt{a+c x^4}} \, dx\)
 3.407 \(\int \frac{f+g x}{(d+e x) \sqrt{-a+c x^4}} \, dx\)
 3.408 \(\int \frac{1-\sqrt{3}+x}{(1+\sqrt{3}+x) \sqrt{-4+4 \sqrt{3} x^2+x^4}} \, dx\)
 3.409 \(\int \frac{1+\sqrt{3}+x}{(1-\sqrt{3}+x) \sqrt{-4-4 \sqrt{3} x^2+x^4}} \, dx\)
 3.410 \(\int \frac{1-\sqrt{3}+2 x}{(1+\sqrt{3}+2 x) \sqrt{-1+4 \sqrt{3} x^2+4 x^4}} \, dx\)
 3.411 \(\int \frac{1+\sqrt{3}+2 x}{(1-\sqrt{3}+2 x) \sqrt{-1-4 \sqrt{3} x^2+4 x^4}} \, dx\)
 3.412 \(\int \frac{f+g x}{(d+e x) \sqrt{a+b x^2+c x^4}} \, dx\)
 3.413 \(\int \frac{f+g x}{(d+e x) \sqrt{-a+b x^2+c x^4}} \, dx\)