3.1 \(\int \frac{1}{\left (2^{2/3}+x\right ) \sqrt{1+x^3}} \, dx\)
 3.2 \(\int \frac{1}{\left (2^{2/3}-x\right ) \sqrt{1-x^3}} \, dx\)
 3.3 \(\int \frac{1}{\left (2^{2/3}-x\right ) \sqrt{-1+x^3}} \, dx\)
 3.4 \(\int \frac{1}{\left (2^{2/3}+x\right ) \sqrt{-1-x^3}} \, dx\)
 3.5 \(\int \frac{1}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
 3.6 \(\int \frac{1}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
 3.7 \(\int \frac{1}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
 3.8 \(\int \frac{1}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
 3.9 \(\int \frac{1}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx\)
 3.10 \(\int \frac{1}{\left (1+\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
 3.11 \(\int \frac{1}{\left (1+\sqrt{3}-x\right ) \sqrt{1-x^3}} \, dx\)
 3.12 \(\int \frac{1}{\left (1+\sqrt{3}-x\right ) \sqrt{-1+x^3}} \, dx\)
 3.13 \(\int \frac{1}{\left (1+\sqrt{3}+x\right ) \sqrt{-1-x^3}} \, dx\)
 3.14 \(\int \frac{1}{(3+x) \sqrt{1+x^3}} \, dx\)
 3.15 \(\int \frac{1}{(3+x) \sqrt{1-x^3}} \, dx\)
 3.16 \(\int \frac{1}{(3+x) \sqrt{-1+x^3}} \, dx\)
 3.17 \(\int \frac{1}{(3+x) \sqrt{-1-x^3}} \, dx\)
 3.18 \(\int \frac{1}{(c+d x) \sqrt [3]{-c^3+d^3 x^3}} \, dx\)
 3.19 \(\int \frac{1}{(c+d x) \sqrt [3]{2 c^3+d^3 x^3}} \, dx\)
 3.20 \(\int \frac{2^{2/3}-2 x}{\left (2^{2/3}+x\right ) \sqrt{1+x^3}} \, dx\)
 3.21 \(\int \frac{2^{2/3}+2 x}{\left (2^{2/3}-x\right ) \sqrt{1-x^3}} \, dx\)
 3.22 \(\int \frac{2^{2/3}+2 x}{\left (2^{2/3}-x\right ) \sqrt{-1+x^3}} \, dx\)
 3.23 \(\int \frac{2^{2/3}-2 x}{\left (2^{2/3}+x\right ) \sqrt{-1-x^3}} \, dx\)
 3.24 \(\int \frac{2^{2/3} \sqrt [3]{a}-2 \sqrt [3]{b} x}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
 3.25 \(\int \frac{2^{2/3} \sqrt [3]{a}+2 \sqrt [3]{b} x}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
 3.26 \(\int \frac{2^{2/3} \sqrt [3]{a}+2 \sqrt [3]{b} x}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
 3.27 \(\int \frac{2^{2/3} \sqrt [3]{a}-2 \sqrt [3]{b} x}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
 3.28 \(\int \frac{c-2 d x}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx\)
 3.29 \(\int \frac{2+3 x}{\left (2^{2/3}+x\right ) \sqrt{1+x^3}} \, dx\)
 3.30 \(\int \frac{2+3 x}{\left (2^{2/3}-x\right ) \sqrt{1-x^3}} \, dx\)
 3.31 \(\int \frac{2+3 x}{\left (2^{2/3}-x\right ) \sqrt{-1+x^3}} \, dx\)
 3.32 \(\int \frac{2+3 x}{\left (2^{2/3}+x\right ) \sqrt{-1-x^3}} \, dx\)
 3.33 \(\int \frac{e+f x}{\left (2^{2/3}+x\right ) \sqrt{1+x^3}} \, dx\)
 3.34 \(\int \frac{e+f x}{\left (2^{2/3}-x\right ) \sqrt{1-x^3}} \, dx\)
 3.35 \(\int \frac{e+f x}{\left (2^{2/3}-x\right ) \sqrt{-1+x^3}} \, dx\)
 3.36 \(\int \frac{e+f x}{\left (2^{2/3}+x\right ) \sqrt{-1-x^3}} \, dx\)
 3.37 \(\int \frac{e+f x}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
 3.38 \(\int \frac{e+f x}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
 3.39 \(\int \frac{e+f x}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
 3.40 \(\int \frac{e+f x}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
 3.41 \(\int \frac{e+f x}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx\)
 3.42 \(\int \frac{x}{\left (2^{2/3}+x\right ) \sqrt{1+x^3}} \, dx\)
 3.43 \(\int \frac{x}{\left (2^{2/3}-x\right ) \sqrt{1-x^3}} \, dx\)
 3.44 \(\int \frac{x}{\left (2^{2/3}-x\right ) \sqrt{-1+x^3}} \, dx\)
 3.45 \(\int \frac{x}{\left (2^{2/3}+x\right ) \sqrt{-1-x^3}} \, dx\)
 3.46 \(\int \frac{x}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
 3.47 \(\int \frac{x}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
 3.48 \(\int \frac{x}{\left (2^{2/3} \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
 3.49 \(\int \frac{x}{\left (2^{2/3} \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
 3.50 \(\int \frac{x}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx\)
 3.51 \(\int \frac{1+x}{(2-x) \sqrt{1+x^3}} \, dx\)
 3.52 \(\int \frac{1-x}{(2+x) \sqrt{1-x^3}} \, dx\)
 3.53 \(\int \frac{1-x}{(2+x) \sqrt{-1+x^3}} \, dx\)
 3.54 \(\int \frac{1+x}{(2-x) \sqrt{-1-x^3}} \, dx\)
 3.55 \(\int \frac{\sqrt [3]{a}+\sqrt [3]{b} x}{\left (2 \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
 3.56 \(\int \frac{\sqrt [3]{a}-\sqrt [3]{b} x}{\left (2 \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
 3.57 \(\int \frac{\sqrt [3]{a}-\sqrt [3]{b} x}{\left (2 \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
 3.58 \(\int \frac{\sqrt [3]{a}+\sqrt [3]{b} x}{\left (2 \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
 3.59 \(\int \frac{c-2 d x}{(c+d x) \sqrt{c^3-8 d^3 x^3}} \, dx\)
 3.60 \(\int \frac{e+f x}{(2-x) \sqrt{1+x^3}} \, dx\)
 3.61 \(\int \frac{e+f x}{(2+x) \sqrt{1-x^3}} \, dx\)
 3.62 \(\int \frac{e+f x}{(2+x) \sqrt{-1+x^3}} \, dx\)
 3.63 \(\int \frac{e+f x}{(2-x) \sqrt{-1-x^3}} \, dx\)
 3.64 \(\int \frac{e+f x}{\left (2 \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
 3.65 \(\int \frac{e+f x}{\left (2 \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
 3.66 \(\int \frac{e+f x}{\left (2 \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
 3.67 \(\int \frac{e+f x}{\left (2 \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
 3.68 \(\int \frac{e+f x}{(c+d x) \sqrt{c^3-8 d^3 x^3}} \, dx\)
 3.69 \(\int \frac{x}{(2-x) \sqrt{1+x^3}} \, dx\)
 3.70 \(\int \frac{x}{(2+x) \sqrt{1-x^3}} \, dx\)
 3.71 \(\int \frac{x}{(2+x) \sqrt{-1+x^3}} \, dx\)
 3.72 \(\int \frac{x}{(2-x) \sqrt{-1-x^3}} \, dx\)
 3.73 \(\int \frac{x}{\left (2 \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
 3.74 \(\int \frac{x}{\left (2 \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
 3.75 \(\int \frac{x}{\left (2 \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
 3.76 \(\int \frac{x}{\left (2 \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
 3.77 \(\int \frac{x}{(c+d x) \sqrt{c^3-8 d^3 x^3}} \, dx\)
 3.78 \(\int \frac{1+\sqrt{3}+x}{\left (1-\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
 3.79 \(\int \frac{1+\sqrt{3}-x}{\left (1-\sqrt{3}-x\right ) \sqrt{1-x^3}} \, dx\)
 3.80 \(\int \frac{1+\sqrt{3}-x}{\left (1-\sqrt{3}-x\right ) \sqrt{-1+x^3}} \, dx\)
 3.81 \(\int \frac{1+\sqrt{3}+x}{\left (1-\sqrt{3}+x\right ) \sqrt{-1-x^3}} \, dx\)
 3.82 \(\int \frac{\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
 3.83 \(\int \frac{\left (1+\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
 3.84 \(\int \frac{\left (1+\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
 3.85 \(\int \frac{\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
 3.86 \(\int \frac{1+\sqrt{3}+\sqrt [3]{\frac{b}{a}} x}{\left (1-\sqrt{3}+\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{a+b x^3}} \, dx\)
 3.87 \(\int \frac{1+\sqrt{3}-\sqrt [3]{\frac{b}{a}} x}{\left (1-\sqrt{3}-\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{a-b x^3}} \, dx\)
 3.88 \(\int \frac{1+\sqrt{3}-\sqrt [3]{\frac{b}{a}} x}{\left (1-\sqrt{3}-\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{-a+b x^3}} \, dx\)
 3.89 \(\int \frac{1+\sqrt{3}+\sqrt [3]{\frac{b}{a}} x}{\left (1-\sqrt{3}+\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{-a-b x^3}} \, dx\)
 3.90 \(\int \frac{1-\sqrt{3}+x}{\left (1+\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
 3.91 \(\int \frac{1-\sqrt{3}-x}{\left (1+\sqrt{3}-x\right ) \sqrt{1-x^3}} \, dx\)
 3.92 \(\int \frac{1-\sqrt{3}-x}{\left (1+\sqrt{3}-x\right ) \sqrt{-1+x^3}} \, dx\)
 3.93 \(\int \frac{1-\sqrt{3}+x}{\left (1+\sqrt{3}+x\right ) \sqrt{-1-x^3}} \, dx\)
 3.94 \(\int \frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
 3.95 \(\int \frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
 3.96 \(\int \frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
 3.97 \(\int \frac{\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x}{\left (\left (1+\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
 3.98 \(\int \frac{1-\sqrt{3}+\sqrt [3]{\frac{b}{a}} x}{\left (1+\sqrt{3}+\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{a+b x^3}} \, dx\)
 3.99 \(\int \frac{1-\sqrt{3}-\sqrt [3]{\frac{b}{a}} x}{\left (1+\sqrt{3}-\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{a-b x^3}} \, dx\)
 3.100 \(\int \frac{1-\sqrt{3}-\sqrt [3]{\frac{b}{a}} x}{\left (1+\sqrt{3}-\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{-a+b x^3}} \, dx\)
 3.101 \(\int \frac{1-\sqrt{3}+\sqrt [3]{\frac{b}{a}} x}{\left (1+\sqrt{3}+\sqrt [3]{\frac{b}{a}} x\right ) \sqrt{-a-b x^3}} \, dx\)
 3.102 \(\int \frac{1+x}{\left (1+\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
 3.103 \(\int \frac{1+x}{\left (1-\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
 3.104 \(\int \frac{e+f x}{\left (1+\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
 3.105 \(\int \frac{e+f x}{\left (1+\sqrt{3}-x\right ) \sqrt{1-x^3}} \, dx\)
 3.106 \(\int \frac{e+f x}{\left (1+\sqrt{3}-x\right ) \sqrt{-1+x^3}} \, dx\)
 3.107 \(\int \frac{e+f x}{\left (1+\sqrt{3}+x\right ) \sqrt{-1-x^3}} \, dx\)
 3.108 \(\int \frac{e+f x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
 3.109 \(\int \frac{e+f x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
 3.110 \(\int \frac{e+f x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
 3.111 \(\int \frac{e+f x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
 3.112 \(\int \frac{x}{\left (1+\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
 3.113 \(\int \frac{x}{\left (1+\sqrt{3}-x\right ) \sqrt{1-x^3}} \, dx\)
 3.114 \(\int \frac{x}{\left (1+\sqrt{3}-x\right ) \sqrt{-1+x^3}} \, dx\)
 3.115 \(\int \frac{x}{\left (1+\sqrt{3}+x\right ) \sqrt{-1-x^3}} \, dx\)
 3.116 \(\int \frac{x}{\left (1-\sqrt{3}+x\right ) \sqrt{1+x^3}} \, dx\)
 3.117 \(\int \frac{x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{a+b x^3}} \, dx\)
 3.118 \(\int \frac{x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{a-b x^3}} \, dx\)
 3.119 \(\int \frac{x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}-\sqrt [3]{b} x\right ) \sqrt{-a+b x^3}} \, dx\)
 3.120 \(\int \frac{x}{\left (\left (1-\sqrt{3}\right ) \sqrt [3]{a}+\sqrt [3]{b} x\right ) \sqrt{-a-b x^3}} \, dx\)
 3.121 \(\int \frac{1+\sqrt{3}+x}{(c+d x) \sqrt{1+x^3}} \, dx\)
 3.122 \(\int \frac{1+\sqrt{3}-x}{(c+d x) \sqrt{1-x^3}} \, dx\)
 3.123 \(\int \frac{1+\sqrt{3}-x}{(c+d x) \sqrt{-1+x^3}} \, dx\)
 3.124 \(\int \frac{1+\sqrt{3}+x}{(c+d x) \sqrt{-1-x^3}} \, dx\)
 3.125 \(\int \frac{1-\sqrt{3}+x}{(c+d x) \sqrt{1+x^3}} \, dx\)
 3.126 \(\int \frac{1-\sqrt{3}-x}{(c+d x) \sqrt{1-x^3}} \, dx\)
 3.127 \(\int \frac{1-\sqrt{3}-x}{(c+d x) \sqrt{-1+x^3}} \, dx\)
 3.128 \(\int \frac{1-\sqrt{3}+x}{(c+d x) \sqrt{-1-x^3}} \, dx\)
 3.129 \(\int \frac{1+\sqrt{3}+x}{x \sqrt{1+x^3}} \, dx\)
 3.130 \(\int \frac{1+\sqrt{3}-x}{x \sqrt{1-x^3}} \, dx\)
 3.131 \(\int \frac{1+\sqrt{3}-x}{x \sqrt{-1+x^3}} \, dx\)
 3.132 \(\int \frac{1+\sqrt{3}+x}{x \sqrt{-1-x^3}} \, dx\)
 3.133 \(\int \frac{1-\sqrt{3}+x}{x \sqrt{1+x^3}} \, dx\)
 3.134 \(\int \frac{1-\sqrt{3}-x}{x \sqrt{1-x^3}} \, dx\)
 3.135 \(\int \frac{1-\sqrt{3}-x}{x \sqrt{-1+x^3}} \, dx\)
 3.136 \(\int \frac{1-\sqrt{3}+x}{x \sqrt{-1-x^3}} \, dx\)
 3.137 \(\int \frac{x}{(3+x) \sqrt{1+x^3}} \, dx\)
 3.138 \(\int \frac{x}{(3+x) \sqrt{1-x^3}} \, dx\)
 3.139 \(\int \frac{x}{(3+x) \sqrt{-1+x^3}} \, dx\)
 3.140 \(\int \frac{x}{(3+x) \sqrt{-1-x^3}} \, dx\)
 3.141 \(\int \frac{e+f x}{(c+d x) \sqrt{1+x^3}} \, dx\)
 3.142 \(\int \frac{e+f x}{(c+d x) \sqrt{1-x^3}} \, dx\)
 3.143 \(\int \frac{e+f x}{(c+d x) \sqrt{-1+x^3}} \, dx\)
 3.144 \(\int \frac{e+f x}{(c+d x) \sqrt{-1-x^3}} \, dx\)
 3.145 \(\int \frac{e+f x}{x \sqrt{1+x^3}} \, dx\)
 3.146 \(\int \frac{e+f x}{x \sqrt{1-x^3}} \, dx\)
 3.147 \(\int \frac{e+f x}{x \sqrt{-1+x^3}} \, dx\)
 3.148 \(\int \frac{e+f x}{x \sqrt{-1-x^3}} \, dx\)
 3.149 \(\int \frac{c-d x}{(c+d x) \sqrt [3]{2 c^3+d^3 x^3}} \, dx\)
 3.150 \(\int \frac{e+f x}{(c+d x) \sqrt [3]{-c^3+d^3 x^3}} \, dx\)
 3.151 \(\int x^2 (a+b x)^n \left (c+d x^3\right ) \, dx\)
 3.152 \(\int x (a+b x)^n \left (c+d x^3\right ) \, dx\)
 3.153 \(\int (a+b x)^n \left (c+d x^3\right ) \, dx\)
 3.154 \(\int \frac{(a+b x)^n \left (c+d x^3\right )}{x} \, dx\)
 3.155 \(\int x^2 (a+b x)^n \left (c+d x^3\right )^2 \, dx\)
 3.156 \(\int x (a+b x)^n \left (c+d x^3\right )^2 \, dx\)
 3.157 \(\int (a+b x)^n \left (c+d x^3\right )^2 \, dx\)
 3.158 \(\int \frac{(a+b x)^n \left (c+d x^3\right )^2}{x} \, dx\)
 3.159 \(\int x^2 (a+b x)^n \left (c+d x^3\right )^3 \, dx\)
 3.160 \(\int x (a+b x)^n \left (c+d x^3\right )^3 \, dx\)
 3.161 \(\int (a+b x)^n \left (c+d x^3\right )^3 \, dx\)
 3.162 \(\int \frac{(a+b x)^n \left (c+d x^3\right )^3}{x} \, dx\)
 3.163 \(\int \frac{x^5 (e+f x)^n}{a+b x^3} \, dx\)
 3.164 \(\int \frac{x^4 (e+f x)^n}{a+b x^3} \, dx\)
 3.165 \(\int \frac{x^3 (e+f x)^n}{a+b x^3} \, dx\)
 3.166 \(\int \frac{x^2 (e+f x)^n}{a+b x^3} \, dx\)
 3.167 \(\int \frac{x (e+f x)^n}{a+b x^3} \, dx\)
 3.168 \(\int \frac{(e+f x)^n}{a+b x^3} \, dx\)
 3.169 \(\int \frac{(e+f x)^n}{x \left (a+b x^3\right )} \, dx\)
 3.170 \(\int \frac{(e+f x)^n}{x^2 \left (a+b x^3\right )} \, dx\)
 3.171 \(\int \frac{x^2 (c+d x)^{1+n}}{a+b x^3} \, dx\)
 3.172 \(\int \frac{x^m (e+f x)^n}{a+b x^3} \, dx\)
 3.173 \(\int \frac{\sqrt{c+d x^3}}{a+b x} \, dx\)
 3.174 \(\int \frac{\left (d^3+e^3 x^3\right )^p}{d+e x} \, dx\)
 3.175 \(\int \frac{2-2 x-x^2}{\left (2+x^2\right ) \sqrt{1+x^3}} \, dx\)
 3.176 \(\int \frac{2+2 x-x^2}{\left (2+x^2\right ) \sqrt{1-x^3}} \, dx\)
 3.177 \(\int \frac{2+2 x-x^2}{\left (2+x^2\right ) \sqrt{-1+x^3}} \, dx\)
 3.178 \(\int \frac{2-2 x-x^2}{\left (2+x^2\right ) \sqrt{-1-x^3}} \, dx\)
 3.179 \(\int \frac{2-2 x-x^2}{\left (2+d+d x+x^2\right ) \sqrt{1+x^3}} \, dx\)
 3.180 \(\int \frac{2+2 x-x^2}{\left (2-d+d x+x^2\right ) \sqrt{1-x^3}} \, dx\)
 3.181 \(\int \frac{2+2 x-x^2}{\left (2-d+d x+x^2\right ) \sqrt{-1+x^3}} \, dx\)
 3.182 \(\int \frac{2-2 x-x^2}{\left (2+d+d x+x^2\right ) \sqrt{-1-x^3}} \, dx\)
 3.183 \(\int (d+e x)^3 \sqrt{a+c x^4} \, dx\)
 3.184 \(\int (d+e x)^2 \sqrt{a+c x^4} \, dx\)
 3.185 \(\int (d+e x) \sqrt{a+c x^4} \, dx\)
 3.186 \(\int \sqrt{a+c x^4} \, dx\)
 3.187 \(\int \frac{\sqrt{a+c x^4}}{d+e x} \, dx\)
 3.188 \(\int \frac{\sqrt{a+c x^4}}{(d+e x)^2} \, dx\)
 3.189 \(\int \frac{(d+e x)^3}{\sqrt{a+c x^4}} \, dx\)
 3.190 \(\int \frac{(d+e x)^2}{\sqrt{a+c x^4}} \, dx\)
 3.191 \(\int \frac{d+e x}{\sqrt{a+c x^4}} \, dx\)
 3.192 \(\int \frac{1}{\sqrt{a+c x^4}} \, dx\)
 3.193 \(\int \frac{1}{(d+e x) \sqrt{a+c x^4}} \, dx\)
 3.194 \(\int \frac{1}{(d+e x)^2 \sqrt{a+c x^4}} \, dx\)
 3.195 \(\int \frac{1}{(d+e x)^3 \sqrt{a+c x^4}} \, dx\)
 3.196 \(\int \frac{(d+e x)^3}{\left (a+c x^4\right )^{3/2}} \, dx\)
 3.197 \(\int \frac{(d+e x)^2}{\left (a+c x^4\right )^{3/2}} \, dx\)
 3.198 \(\int \frac{d+e x}{\left (a+c x^4\right )^{3/2}} \, dx\)
 3.199 \(\int \frac{1}{\left (a+c x^4\right )^{3/2}} \, dx\)
 3.200 \(\int \frac{1}{(d+e x) \left (a+c x^4\right )^{3/2}} \, dx\)
 3.201 \(\int \frac{1}{(d+e x)^2 \left (a+c x^4\right )^{3/2}} \, dx\)
 3.202 \(\int \frac{x^3 (c+d x)^n}{a+b x^4} \, dx\)
 3.203 \(\int \frac{x^3 (c+d x)^{1+n}}{a+b x^4} \, dx\)
 3.204 \(\int \frac{1}{\left (c+d x+e x^2\right ) \sqrt{a+b x^4}} \, dx\)
 3.205 \(\int \frac{\sqrt{a x^{23}}}{\sqrt{1+x^5}} \, dx\)
 3.206 \(\int \frac{\sqrt{a x^{13}}}{\sqrt{1+x^5}} \, dx\)
 3.207 \(\int \frac{\sqrt{a x^3}}{\sqrt{1+x^5}} \, dx\)
 3.208 \(\int \frac{\sqrt{\frac{a}{x^7}}}{\sqrt{1+x^5}} \, dx\)
 3.209 \(\int \frac{\sqrt{\frac{a}{x^{17}}}}{\sqrt{1+x^5}} \, dx\)
 3.210 \(\int \frac{\sqrt{a x^6}}{x \left (1-x^4\right )} \, dx\)
 3.211 \(\int \frac{\sqrt{a x^6}}{x-x^5} \, dx\)
 3.212 \(\int \frac{\left (a x^6\right )^{3/2}}{x \left (1-x^4\right )} \, dx\)
 3.213 \(\int \left (\frac{1}{1-x^4}-\frac{\sqrt{a x^6}}{x \left (1-x^4\right )}\right ) \, dx\)
 3.214 \(\int \left (\frac{1}{1-x^4}-\frac{\sqrt{a x^6}}{x-x^5}\right ) \, dx\)
 3.215 \(\int \frac{\sqrt{a x^3}}{x-x^3} \, dx\)
 3.216 \(\int \frac{\sqrt{a x^4}}{\sqrt{1+x^2}} \, dx\)
 3.217 \(\int \frac{\sqrt{a x^3}}{\sqrt{1+x^2}} \, dx\)
 3.218 \(\int \frac{\sqrt{a x^2}}{\sqrt{1+x^2}} \, dx\)
 3.219 \(\int \frac{\sqrt{a x}}{\sqrt{1+x^2}} \, dx\)
 3.220 \(\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{1+x^2}} \, dx\)
 3.221 \(\int \frac{\sqrt{\frac{a}{x^2}}}{\sqrt{1+x^2}} \, dx\)
 3.222 \(\int \frac{\sqrt{\frac{a}{x^3}}}{\sqrt{1+x^2}} \, dx\)
 3.223 \(\int \frac{\sqrt{\frac{a}{x^4}}}{\sqrt{1+x^2}} \, dx\)
 3.224 \(\int \frac{\sqrt{a x^4}}{\sqrt{1+x^3}} \, dx\)
 3.225 \(\int \frac{\sqrt{a x^3}}{\sqrt{1+x^3}} \, dx\)
 3.226 \(\int \frac{\sqrt{a x^2}}{\sqrt{1+x^3}} \, dx\)
 3.227 \(\int \frac{\sqrt{a x}}{\sqrt{1+x^3}} \, dx\)
 3.228 \(\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{1+x^3}} \, dx\)
 3.229 \(\int \frac{\sqrt{\frac{a}{x^2}}}{\sqrt{1+x^3}} \, dx\)
 3.230 \(\int \frac{\sqrt{\frac{a}{x^3}}}{\sqrt{1+x^3}} \, dx\)
 3.231 \(\int \frac{\sqrt{\frac{a}{x^4}}}{\sqrt{1+x^3}} \, dx\)
 3.232 \(\int \frac{\sqrt{a x^{2 n}}}{\sqrt{1+x^n}} \, dx\)
 3.233 \(\int \frac{\sqrt{a x^n}}{\sqrt{1+x^n}} \, dx\)
 3.234 \(\int \frac{\sqrt{a x^{n/2}}}{\sqrt{1+x^n}} \, dx\)
 3.235 \(\int \left (\frac{\sqrt{a x^{2 n}}}{\sqrt{1+x^n}}+\frac{2 x^{-n} \sqrt{a x^{2 n}}}{(2+n) \sqrt{1+x^n}}\right ) \, dx\)
 3.236 \(\int \frac{\sqrt{a x}}{\sqrt{d+e x} \sqrt{e+f x}} \, dx\)
 3.237 \(\int \left (a x^m\right )^r \, dx\)
 3.238 \(\int \left (a x^m\right )^r \left (b x^n\right )^s \, dx\)
 3.239 \(\int \left (a x^m\right )^r \left (b x^n\right )^s \left (c x^p\right )^t \, dx\)
 3.240 \(\int \frac{x^2}{\sqrt{a+b x}+\sqrt{c+b x}} \, dx\)
 3.241 \(\int \frac{x}{\sqrt{a+b x}+\sqrt{c+b x}} \, dx\)
 3.242 \(\int \frac{1}{\sqrt{a+b x}+\sqrt{c+b x}} \, dx\)
 3.243 \(\int \frac{1}{x \left (\sqrt{a+b x}+\sqrt{c+b x}\right )} \, dx\)
 3.244 \(\int \frac{1}{x^2 \left (\sqrt{a+b x}+\sqrt{c+b x}\right )} \, dx\)
 3.245 \(\int \frac{x^2}{\left (\sqrt{a+b x}+\sqrt{c+b x}\right )^2} \, dx\)
 3.246 \(\int \frac{x}{\left (\sqrt{a+b x}+\sqrt{c+b x}\right )^2} \, dx\)
 3.247 \(\int \frac{1}{\left (\sqrt{a+b x}+\sqrt{c+b x}\right )^2} \, dx\)
 3.248 \(\int \frac{1}{x \left (\sqrt{a+b x}+\sqrt{c+b x}\right )^2} \, dx\)
 3.249 \(\int \frac{1}{x^2 \left (\sqrt{a+b x}+\sqrt{c+b x}\right )^2} \, dx\)
 3.250 \(\int \frac{x^2}{\left (\sqrt{a+b x}+\sqrt{c+b x}\right )^3} \, dx\)
 3.251 \(\int \frac{x}{\left (\sqrt{a+b x}+\sqrt{c+b x}\right )^3} \, dx\)
 3.252 \(\int \frac{1}{\left (\sqrt{a+b x}+\sqrt{c+b x}\right )^3} \, dx\)
 3.253 \(\int \frac{1}{x \left (\sqrt{a+b x}+\sqrt{c+b x}\right )^3} \, dx\)
 3.254 \(\int \frac{1}{x^2 \left (\sqrt{a+b x}+\sqrt{c+b x}\right )^3} \, dx\)
 3.255 \(\int \frac{1}{\sqrt{x}+\sqrt{1+x}} \, dx\)
 3.256 \(\int \frac{1}{\sqrt{-1+x}+\sqrt{x}} \, dx\)
 3.257 \(\int \frac{1}{\sqrt{-1+x}+\sqrt{1+x}} \, dx\)
 3.258 \(\int x^3 \left (\sqrt{1-x}+\sqrt{1+x}\right )^2 \, dx\)
 3.259 \(\int x^2 \left (\sqrt{1-x}+\sqrt{1+x}\right )^2 \, dx\)
 3.260 \(\int x \left (\sqrt{1-x}+\sqrt{1+x}\right )^2 \, dx\)
 3.261 \(\int \left (\sqrt{1-x}+\sqrt{1+x}\right )^2 \, dx\)
 3.262 \(\int \frac{\left (\sqrt{1-x}+\sqrt{1+x}\right )^2}{x} \, dx\)
 3.263 \(\int \frac{\left (\sqrt{1-x}+\sqrt{1+x}\right )^2}{x^2} \, dx\)
 3.264 \(\int \frac{\left (\sqrt{1-x}+\sqrt{1+x}\right )^2}{x^3} \, dx\)
 3.265 \(\int \frac{x^3}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx\)
 3.266 \(\int \frac{x^2}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx\)
 3.267 \(\int \frac{x}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx\)
 3.268 \(\int \frac{1}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx\)
 3.269 \(\int \frac{1}{x \left (\sqrt{a+b x}+\sqrt{a+c x}\right )} \, dx\)
 3.270 \(\int \frac{1}{x^2 \left (\sqrt{a+b x}+\sqrt{a+c x}\right )} \, dx\)
 3.271 \(\int \frac{x^3}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^2} \, dx\)
 3.272 \(\int \frac{x^2}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^2} \, dx\)
 3.273 \(\int \frac{x}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^2} \, dx\)
 3.274 \(\int \frac{1}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^2} \, dx\)
 3.275 \(\int \frac{1}{x \left (\sqrt{a+b x}+\sqrt{a+c x}\right )^2} \, dx\)
 3.276 \(\int \frac{1}{x^2 \left (\sqrt{a+b x}+\sqrt{a+c x}\right )^2} \, dx\)
 3.277 \(\int \frac{x^4}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^3} \, dx\)
 3.278 \(\int \frac{x^3}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^3} \, dx\)
 3.279 \(\int \frac{x^2}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^3} \, dx\)
 3.280 \(\int \frac{x}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^3} \, dx\)
 3.281 \(\int \frac{1}{\left (\sqrt{a+b x}+\sqrt{a+c x}\right )^3} \, dx\)
 3.282 \(\int \sqrt{1-x} \left (\sqrt{1-x}+\sqrt{1+x}\right ) \, dx\)
 3.283 \(\int x^3 \left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right ) \, dx\)
 3.284 \(\int x^2 \left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right ) \, dx\)
 3.285 \(\int x \left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right ) \, dx\)
 3.286 \(\int \left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right ) \, dx\)
 3.287 \(\int \frac{\left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right )}{x} \, dx\)
 3.288 \(\int \frac{\left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right )}{x^2} \, dx\)
 3.289 \(\int \frac{\left (-\sqrt{1-x}-\sqrt{1+x}\right ) \left (\sqrt{1-x}+\sqrt{1+x}\right )}{x^3} \, dx\)
 3.290 \(\int \frac{\sqrt{1-x}+\sqrt{1+x}}{-\sqrt{1-x}+\sqrt{1+x}} \, dx\)
 3.291 \(\int \frac{-\sqrt{-1+x}+\sqrt{1+x}}{\sqrt{-1+x}+\sqrt{1+x}} \, dx\)
 3.292 \(\int \left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
 3.293 \(\int \left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^3 \, dx\)
 3.294 \(\int \left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^2 \, dx\)
 3.295 \(\int \left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right ) \, dx\)
 3.296 \(\int \frac{1}{d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}} \, dx\)
 3.297 \(\int \frac{1}{\left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^2} \, dx\)
 3.298 \(\int \frac{1}{\left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^3} \, dx\)
 3.299 \(\int \left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^{5/2} \, dx\)
 3.300 \(\int \left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^{3/2} \, dx\)
 3.301 \(\int \sqrt{d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}} \, dx\)
 3.302 \(\int \frac{1}{\sqrt{d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}}} \, dx\)
 3.303 \(\int \frac{1}{\left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^{3/2}} \, dx\)
 3.304 \(\int \frac{1}{\left (d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right )^{5/2}} \, dx\)
 3.305 \(\int \sqrt{x-\sqrt{-4+x^2}} \, dx\)
 3.306 \(\int \sqrt{a x+b \sqrt{c+\frac{a^2 x^2}{b^2}}} \, dx\)
 3.307 \(\int \sqrt{1+\sqrt{1-x^2}} \, dx\)
 3.308 \(\int \sqrt{1+\sqrt{1+x^2}} \, dx\)
 3.309 \(\int \sqrt{5+\sqrt{25+x^2}} \, dx\)
 3.310 \(\int \sqrt{a+b \sqrt{\frac{a^2}{b^2}+c x^2}} \, dx\)
 3.311 \(\int \left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
 3.312 \(\int \left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^3 \, dx\)
 3.313 \(\int \left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^2 \, dx\)
 3.314 \(\int \left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right ) \, dx\)
 3.315 \(\int \frac{1}{d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}} \, dx\)
 3.316 \(\int \frac{1}{\left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^2} \, dx\)
 3.317 \(\int \frac{1}{\left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^3} \, dx\)
 3.318 \(\int \left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^{5/2} \, dx\)
 3.319 \(\int \left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^{3/2} \, dx\)
 3.320 \(\int \sqrt{d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}} \, dx\)
 3.321 \(\int \frac{1}{\sqrt{d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}}} \, dx\)
 3.322 \(\int \frac{1}{\left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^{3/2}} \, dx\)
 3.323 \(\int \frac{1}{\left (d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right )^{5/2}} \, dx\)
 3.324 \(\int \left (a+x^2\right )^2 \left (x+\sqrt{a+x^2}\right )^n \, dx\)
 3.325 \(\int \left (a+x^2\right ) \left (x+\sqrt{a+x^2}\right )^n \, dx\)
 3.326 \(\int \left (x+\sqrt{a+x^2}\right )^n \, dx\)
 3.327 \(\int \frac{\left (x+\sqrt{a+x^2}\right )^n}{a+x^2} \, dx\)
 3.328 \(\int \frac{\left (x+\sqrt{a+x^2}\right )^n}{\left (a+x^2\right )^2} \, dx\)
 3.329 \(\int \left (a+x^2\right )^2 \left (x-\sqrt{a+x^2}\right )^n \, dx\)
 3.330 \(\int \left (a+x^2\right ) \left (x-\sqrt{a+x^2}\right )^n \, dx\)
 3.331 \(\int \left (x-\sqrt{a+x^2}\right )^n \, dx\)
 3.332 \(\int \frac{\left (x-\sqrt{a+x^2}\right )^n}{a+x^2} \, dx\)
 3.333 \(\int \frac{\left (x-\sqrt{a+x^2}\right )^n}{\left (a+x^2\right )^2} \, dx\)
 3.334 \(\int \left (a+x^2\right )^{5/2} \left (x+\sqrt{a+x^2}\right )^n \, dx\)
 3.335 \(\int \left (a+x^2\right )^{3/2} \left (x+\sqrt{a+x^2}\right )^n \, dx\)
 3.336 \(\int \sqrt{a+x^2} \left (x+\sqrt{a+x^2}\right )^n \, dx\)
 3.337 \(\int \frac{\left (x+\sqrt{a+x^2}\right )^n}{\sqrt{a+x^2}} \, dx\)
 3.338 \(\int \frac{\left (x+\sqrt{a+x^2}\right )^n}{\left (a+x^2\right )^{3/2}} \, dx\)
 3.339 \(\int \frac{\left (x+\sqrt{a+x^2}\right )^n}{\left (a+x^2\right )^{5/2}} \, dx\)
 3.340 \(\int \left (a+x^2\right )^{5/2} \left (x-\sqrt{a+x^2}\right )^n \, dx\)
 3.341 \(\int \left (a+x^2\right )^{3/2} \left (x-\sqrt{a+x^2}\right )^n \, dx\)
 3.342 \(\int \sqrt{a+x^2} \left (x-\sqrt{a+x^2}\right )^n \, dx\)
 3.343 \(\int \frac{\left (x-\sqrt{a+x^2}\right )^n}{\sqrt{a+x^2}} \, dx\)
 3.344 \(\int \frac{\left (x-\sqrt{a+x^2}\right )^n}{\left (a+x^2\right )^{3/2}} \, dx\)
 3.345 \(\int \frac{\left (x-\sqrt{a+x^2}\right )^n}{\left (a+x^2\right )^{5/2}} \, dx\)
 3.346 \(\int \left (a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right )^2 \left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
 3.347 \(\int \left (a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right ) \left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
 3.348 \(\int \left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
 3.349 \(\int \frac{\left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n}{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \, dx\)
 3.350 \(\int \frac{\left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n}{\left (a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right )^2} \, dx\)
 3.351 \(\int \left (d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}\right )^n \, dx\)
 3.352 \(\int \frac{\left (d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}\right )^n}{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \, dx\)
 3.353 \(\int \left (a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right )^{3/2} \left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
 3.354 \(\int \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
 3.355 \(\int \frac{\left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n}{\sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}} \, dx\)
 3.356 \(\int \frac{\left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n}{\left (a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right )^{3/2}} \, dx\)
 3.357 \(\int \frac{\left (d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}\right )^n}{\sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}} \, dx\)
 3.358 \(\int \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}} \left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n \, dx\)
 3.359 \(\int \frac{\left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n}{\sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}}} \, dx\)
 3.360 \(\int \frac{\left (d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right )^n}{\left (a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}\right )^{3/2}} \, dx\)
 3.361 \(\int \frac{\left (d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}\right )^n}{\sqrt{\frac{a f^2 g+e g x (2 d+e x)}{f^2}}} \, dx\)
 3.362 \(\int \frac{1}{(a+b x) \sqrt{c+d x^2} \sqrt{e+f x^2}} \, dx\)
 3.363 \(\int \frac{e-2 f x^2}{e^2+4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\)
 3.364 \(\int \frac{e-2 f x^2}{e^2-4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx\)
 3.365 \(\int \frac{e-4 f x^3}{e^2+4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\)
 3.366 \(\int \frac{e-4 f x^3}{e^2-4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx\)
 3.367 \(\int \frac{e-2 f (-1+n) x^n}{e^2+4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
 3.368 \(\int \frac{e-2 f (-1+n) x^n}{e^2-4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
 3.369 \(\int \frac{x}{e^2+4 e f x^2+4 d f x^4+4 f^2 x^4} \, dx\)
 3.370 \(\int \frac{x}{e^2+4 e f x^2-4 d f x^4+4 f^2 x^4} \, dx\)
 3.371 \(\int \frac{x^2 \left (3 e+2 f x^2\right )}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^6} \, dx\)
 3.372 \(\int \frac{x^2 \left (3 e+2 f x^2\right )}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^6} \, dx\)
 3.373 \(\int \frac{x^m \left (e (1+m)+2 f (-1+m) x^2\right )}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^{2+2 m}} \, dx\)
 3.374 \(\int \frac{x^m \left (e (1+m)+2 f (-1+m) x^2\right )}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^{2+2 m}} \, dx\)
 3.375 \(\int \frac{x \left (2 e-2 f x^3\right )}{e^2+4 e f x^3+4 d f x^4+4 f^2 x^6} \, dx\)
 3.376 \(\int \frac{x \left (2 e-2 f x^3\right )}{e^2+4 e f x^3-4 d f x^4+4 f^2 x^6} \, dx\)
 3.377 \(\int \frac{x^2}{e^2+4 e f x^3+4 d f x^6+4 f^2 x^6} \, dx\)
 3.378 \(\int \frac{x^2}{e^2+4 e f x^3-4 d f x^6+4 f^2 x^6} \, dx\)
 3.379 \(\int \frac{x^m \left (e (1+m)+2 f (-2+m) x^3\right )}{e^2+4 e f x^3+4 f^2 x^6+4 d f x^{2+2 m}} \, dx\)
 3.380 \(\int \frac{x^m \left (e (1+m)+2 f (-2+m) x^3\right )}{e^2+4 e f x^3+4 f^2 x^6-4 d f x^{2+2 m}} \, dx\)
 3.381 \(\int \frac{x^m \left (e (1+m)+2 f (1+m-n) x^n\right )}{e^2+4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
 3.382 \(\int \frac{x^m \left (e (1+m)+2 f (1+m-n) x^n\right )}{e^2-4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx\)
 3.383 \(\int \frac{x^5}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
 3.384 \(\int \frac{x^3}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
 3.385 \(\int \frac{x}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
 3.386 \(\int \frac{1}{x \left (a c+b c x^2+d \sqrt{a+b x^2}\right )} \, dx\)
 3.387 \(\int \frac{1}{x^3 \left (a c+b c x^2+d \sqrt{a+b x^2}\right )} \, dx\)
 3.388 \(\int \frac{x^2}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
 3.389 \(\int \frac{1}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx\)
 3.390 \(\int \frac{1}{x^2 \left (a c+b c x^2+d \sqrt{a+b x^2}\right )} \, dx\)
 3.391 \(\int \frac{x^8}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
 3.392 \(\int \frac{x^5}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
 3.393 \(\int \frac{x^2}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
 3.394 \(\int \frac{1}{x \left (a c+b c x^3+d \sqrt{a+b x^3}\right )} \, dx\)
 3.395 \(\int \frac{1}{x^4 \left (a c+b c x^3+d \sqrt{a+b x^3}\right )} \, dx\)
 3.396 \(\int \frac{x^3}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
 3.397 \(\int \frac{x}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
 3.398 \(\int \frac{1}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx\)
 3.399 \(\int \frac{1}{x^2 \left (a c+b c x^3+d \sqrt{a+b x^3}\right )} \, dx\)
 3.400 \(\int \frac{1}{x^3 \left (a c+b c x^3+d \sqrt{a+b x^3}\right )} \, dx\)
 3.401 \(\int \frac{1}{a c+b c x^n+d \sqrt{a+b x^n}} \, dx\)
 3.402 \(\int \frac{x^m}{a c+b c x^n+d \sqrt{a+b x^n}} \, dx\)
 3.403 \(\int \frac{x^{-1+n}}{a c+b c x^n+d \sqrt{a+b x^n}} \, dx\)
 3.404 \(\int \frac{1}{\sqrt{x}+4 x^{3/2}} \, dx\)
 3.405 \(\int \frac{1}{\sqrt{x}-x^{5/2}} \, dx\)
 3.406 \(\int \frac{1}{-\sqrt [4]{x}+\sqrt{x}} \, dx\)
 3.407 \(\int \frac{1}{\sqrt [3]{x}+\sqrt{x}} \, dx\)
 3.408 \(\int \frac{1}{\sqrt [4]{x}+\sqrt{x}} \, dx\)
 3.409 \(\int \frac{1}{-\sqrt [3]{x}+x^{2/3}} \, dx\)
 3.410 \(\int \frac{1}{\frac{1}{\sqrt [4]{x}}+\sqrt{x}} \, dx\)
 3.411 \(\int \frac{1}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\)
 3.412 \(\int \frac{1}{\frac{1}{\sqrt [3]{x}}+\frac{1}{\sqrt [4]{x}}} \, dx\)
 3.413 \(\int \frac{1}{-\frac{1}{\sqrt [3]{x}}+\sqrt{x}} \, dx\)
 3.414 \(\int \frac{\sqrt{x}}{x+x^2} \, dx\)
 3.415 \(\int \frac{x}{4 \sqrt{x}+x} \, dx\)
 3.416 \(\int \frac{\sqrt{x}}{\sqrt [3]{x}+x} \, dx\)
 3.417 \(\int \frac{\sqrt [3]{x}}{\sqrt [4]{x}+\sqrt{x}} \, dx\)
 3.418 \(\int \frac{\sqrt{x}}{\sqrt [4]{x}+\sqrt [3]{x}} \, dx\)
 3.419 \(\int \frac{\sqrt{x}}{-\frac{1}{\sqrt [3]{x}}+\sqrt{x}} \, dx\)
 3.420 \(\int \frac{\sqrt{b-\frac{a}{x}} x^m}{\sqrt{a-b x}} \, dx\)
 3.421 \(\int \frac{\sqrt{b-\frac{a}{x}} x^2}{\sqrt{a-b x}} \, dx\)
 3.422 \(\int \frac{\sqrt{b-\frac{a}{x}} x}{\sqrt{a-b x}} \, dx\)
 3.423 \(\int \frac{\sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}} \, dx\)
 3.424 \(\int \frac{\sqrt{b-\frac{a}{x}}}{x \sqrt{a-b x}} \, dx\)
 3.425 \(\int \frac{\sqrt{b-\frac{a}{x}}}{x^2 \sqrt{a-b x}} \, dx\)
 3.426 \(\int \left (a+\frac{b}{x}\right )^m (c+d x)^n \, dx\)
 3.427 \(\int \left (a+\frac{b}{x}\right )^m (c+d x)^2 \, dx\)
 3.428 \(\int \left (a+\frac{b}{x}\right )^m (c+d x) \, dx\)
 3.429 \(\int \left (a+\frac{b}{x}\right )^m \, dx\)
 3.430 \(\int \frac{\left (a+\frac{b}{x}\right )^m}{c+d x} \, dx\)
 3.431 \(\int \frac{\left (a+\frac{b}{x}\right )^m}{(c+d x)^2} \, dx\)
 3.432 \(\int \frac{\left (a+\frac{b}{x}\right )^m}{(c+d x)^3} \, dx\)
 3.433 \(\int \frac{\left (a+\frac{b}{x}\right )^m}{(c+d x)^4} \, dx\)
 3.434 \(\int \frac{\sqrt{b-\frac{a}{x^2}} x^m}{\sqrt{a-b x^2}} \, dx\)
 3.435 \(\int \frac{\sqrt{b-\frac{a}{x^2}} x^2}{\sqrt{a-b x^2}} \, dx\)
 3.436 \(\int \frac{\sqrt{b-\frac{a}{x^2}} x}{\sqrt{a-b x^2}} \, dx\)
 3.437 \(\int \frac{\sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}} \, dx\)
 3.438 \(\int \frac{\sqrt{b-\frac{a}{x^2}}}{x \sqrt{a-b x^2}} \, dx\)
 3.439 \(\int \frac{\sqrt{b-\frac{a}{x^2}}}{x^2 \sqrt{a-b x^2}} \, dx\)
 3.440 \(\int \frac{(c+d x)^{3/2}}{\sqrt{a+\frac{b}{x^2}}} \, dx\)
 3.441 \(\int \frac{-1+x^3}{\left (-4 x+x^4\right )^{2/3}} \, dx\)
 3.442 \(\int \left (2-x^2\right ) \sqrt [4]{6 x-x^3} \, dx\)
 3.443 \(\int \left (1+x^4\right ) \sqrt{5 x+x^5} \, dx\)
 3.444 \(\int \left (2+5 x^4\right ) \sqrt{2 x+x^5} \, dx\)
 3.445 \(\int \frac{x+3 x^2}{\sqrt{x^2+2 x^3}} \, dx\)
 3.446 \(\int \frac{2+\sqrt [3]{1-5 x}}{3+\sqrt [3]{1-5 x}} \, dx\)
 3.447 \(\int \frac{1+\sqrt{x}}{-1+\sqrt{x}} \, dx\)
 3.448 \(\int \frac{1-\sqrt{2+3 x}}{1+\sqrt{2+3 x}} \, dx\)
 3.449 \(\int \frac{-1+\sqrt{a+b x}}{1+\sqrt{a+b x}} \, dx\)
 3.450 \(\int \frac{a+b n x^{-1+n}}{a x+b x^n} \, dx\)
 3.451 \(\int \frac{x^{-n} \left (a+b n x^{-1+n}\right )}{b+a x^{1-n}} \, dx\)
 3.452 \(\int x \left (a+b x+c x^2\right )^m \left (d+e x+f x^2+g x^3\right )^n \left (2 a d+(3 b d+3 a e+b d m+a e n) x+(4 c d+4 b e+4 a f+2 c d m+b e m+b e n+2 a f n) x^2+(5 c e+5 b f+5 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(6 c f+6 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (7+2 m+3 n) x^5\right ) \, dx\)
 3.453 \(\int \left (a+b x+c x^2\right )^m \left (d+e x+f x^2+g x^3\right )^n \left (a d+(2 b d+2 a e+b d m+a e n) x+(3 c d+3 b e+3 a f+2 c d m+b e m+b e n+2 a f n) x^2+(4 c e+4 b f+4 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(5 c f+5 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (6+2 m+3 n) x^5\right ) \, dx\)
 3.454 \(\int \left (a+b x+c x^2\right )^m \left (d+e x+f x^2+g x^3\right )^n \left (b d+a e+b d m+a e n+(2 c d+2 b e+2 a f+2 c d m+b e m+b e n+2 a f n) x+(3 c e+3 b f+3 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^2+(4 c f+4 b g+2 c f m+b g m+2 c f n+3 b g n) x^3+c g (5+2 m+3 n) x^4\right ) \, dx\)
 3.455 \(\int \frac{\left (a+b x+c x^2\right )^m \left (d+e x+f x^2+g x^3\right )^n \left (-a d+(b d m+a e n) x+(c d+b e+a f+2 c d m+b e m+b e n+2 a f n) x^2+(2 c e+2 b f+2 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(3 c f+3 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (4+2 m+3 n) x^5\right )}{x^2} \, dx\)
 3.456 \(\int \frac{\left (a+b x+c x^2\right )^m \left (d+e x+f x^2+g x^3\right )^n \left (-2 a d+(-b d-a e+b d m+a e n) x+(2 c d m+b e m+b e n+2 a f n) x^2+(c e+b f+a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(2 c f+2 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (3+2 m+3 n) x^5\right )}{x^3} \, dx\)
 3.457 \(\int x^3 \left (a+b \sqrt{c+d x}\right )^2 \, dx\)
 3.458 \(\int x^2 \left (a+b \sqrt{c+d x}\right )^2 \, dx\)
 3.459 \(\int x \left (a+b \sqrt{c+d x}\right )^2 \, dx\)
 3.460 \(\int \left (a+b \sqrt{c+d x}\right )^2 \, dx\)
 3.461 \(\int \frac{\left (a+b \sqrt{c+d x}\right )^2}{x} \, dx\)
 3.462 \(\int \frac{\left (a+b \sqrt{c+d x}\right )^2}{x^2} \, dx\)
 3.463 \(\int \frac{\left (a+b \sqrt{c+d x}\right )^2}{x^3} \, dx\)
 3.464 \(\int x^3 \sqrt{a+b \sqrt{c+d x}} \, dx\)
 3.465 \(\int x^2 \sqrt{a+b \sqrt{c+d x}} \, dx\)
 3.466 \(\int x \sqrt{a+b \sqrt{c+d x}} \, dx\)
 3.467 \(\int \sqrt{a+b \sqrt{c+d x}} \, dx\)
 3.468 \(\int \frac{\sqrt{a+b \sqrt{c+d x}}}{x} \, dx\)
 3.469 \(\int \frac{\sqrt{a+b \sqrt{c+d x}}}{x^2} \, dx\)
 3.470 \(\int \frac{\sqrt{a+b \sqrt{c+d x}}}{x^3} \, dx\)
 3.471 \(\int \frac{x^3}{a+b \sqrt{c+d x}} \, dx\)
 3.472 \(\int \frac{x^2}{a+b \sqrt{c+d x}} \, dx\)
 3.473 \(\int \frac{x}{a+b \sqrt{c+d x}} \, dx\)
 3.474 \(\int \frac{1}{a+b \sqrt{c+d x}} \, dx\)
 3.475 \(\int \frac{1}{x \left (a+b \sqrt{c+d x}\right )} \, dx\)
 3.476 \(\int \frac{1}{x^2 \left (a+b \sqrt{c+d x}\right )} \, dx\)
 3.477 \(\int \frac{1}{x^3 \left (a+b \sqrt{c+d x}\right )} \, dx\)
 3.478 \(\int \frac{x^3}{\left (a+b \sqrt{c+d x}\right )^2} \, dx\)
 3.479 \(\int \frac{x^2}{\left (a+b \sqrt{c+d x}\right )^2} \, dx\)
 3.480 \(\int \frac{x}{\left (a+b \sqrt{c+d x}\right )^2} \, dx\)
 3.481 \(\int \frac{1}{\left (a+b \sqrt{c+d x}\right )^2} \, dx\)
 3.482 \(\int \frac{1}{x \left (a+b \sqrt{c+d x}\right )^2} \, dx\)
 3.483 \(\int \frac{1}{x^2 \left (a+b \sqrt{c+d x}\right )^2} \, dx\)
 3.484 \(\int \frac{1}{x^3 \left (a+b \sqrt{c+d x}\right )^2} \, dx\)
 3.485 \(\int \frac{x^3}{\sqrt{a+b \sqrt{c+d x}}} \, dx\)
 3.486 \(\int \frac{x^2}{\sqrt{a+b \sqrt{c+d x}}} \, dx\)
 3.487 \(\int \frac{x}{\sqrt{a+b \sqrt{c+d x}}} \, dx\)
 3.488 \(\int \frac{1}{\sqrt{a+b \sqrt{c+d x}}} \, dx\)
 3.489 \(\int \frac{1}{x \sqrt{a+b \sqrt{c+d x}}} \, dx\)
 3.490 \(\int \frac{1}{x^2 \sqrt{a+b \sqrt{c+d x}}} \, dx\)
 3.491 \(\int \frac{1}{x^3 \sqrt{a+b \sqrt{c+d x}}} \, dx\)
 3.492 \(\int x^3 \left (a+b \sqrt{c+d x}\right )^p \, dx\)
 3.493 \(\int x^2 \left (a+b \sqrt{c+d x}\right )^p \, dx\)
 3.494 \(\int x \left (a+b \sqrt{c+d x}\right )^p \, dx\)
 3.495 \(\int \left (a+b \sqrt{c+d x}\right )^p \, dx\)
 3.496 \(\int \frac{\left (a+b \sqrt{c+d x}\right )^p}{x} \, dx\)
 3.497 \(\int \frac{\left (a+b (c x)^n\right )^{5/2}}{x} \, dx\)
 3.498 \(\int \frac{\left (a+b (c x)^n\right )^{3/2}}{x} \, dx\)
 3.499 \(\int \frac{\sqrt{a+b (c x)^n}}{x} \, dx\)
 3.500 \(\int \frac{1}{x \sqrt{a+b (c x)^n}} \, dx\)
 3.501 \(\int \frac{1}{x \left (a+b (c x)^n\right )^{3/2}} \, dx\)
 3.502 \(\int \frac{1}{x \left (a+b (c x)^n\right )^{5/2}} \, dx\)
 3.503 \(\int \frac{\left (-a+b (c x)^n\right )^{5/2}}{x} \, dx\)
 3.504 \(\int \frac{\left (-a+b (c x)^n\right )^{3/2}}{x} \, dx\)
 3.505 \(\int \frac{\sqrt{-a+b (c x)^n}}{x} \, dx\)
 3.506 \(\int \frac{1}{x \sqrt{-a+b (c x)^n}} \, dx\)
 3.507 \(\int \frac{1}{x \left (-a+b (c x)^n\right )^{3/2}} \, dx\)
 3.508 \(\int \frac{1}{x \left (-a+b (c x)^n\right )^{5/2}} \, dx\)
 3.509 \(\int \frac{1}{x \sqrt{a+b x}} \, dx\)
 3.510 \(\int \frac{1}{x \sqrt{a+b (c x)^m}} \, dx\)
 3.511 \(\int \frac{1}{x \sqrt{a+b \left (c (d x)^m\right )^n}} \, dx\)
 3.512 \(\int \frac{1}{x \sqrt{a+b \left (c \left (d (e x)^m\right )^n\right )^p}} \, dx\)
 3.513 \(\int \frac{1}{x \sqrt{a+b \left (c \left (d \left (e (f x)^m\right )^n\right )^p\right )^q}} \, dx\)
 3.514 \(\int \frac{\sqrt{-1+\frac{1}{x^2}} \left (-1+x^2\right )^3}{x} \, dx\)
 3.515 \(\int \frac{\sqrt{-1+\frac{1}{x^2}} \left (-1+x^2\right )^2}{x} \, dx\)
 3.516 \(\int \frac{\sqrt{-1+\frac{1}{x^2}} \left (-1+x^2\right )}{x} \, dx\)
 3.517 \(\int \frac{\sqrt{-1+\frac{1}{x^2}}}{x \left (-1+x^2\right )} \, dx\)
 3.518 \(\int \frac{\sqrt{-1+\frac{1}{x^2}}}{x \left (-1+x^2\right )^2} \, dx\)
 3.519 \(\int \frac{\sqrt{-1+\frac{1}{x^2}}}{x \left (-1+x^2\right )^3} \, dx\)
 3.520 \(\int \frac{\sqrt{1+\frac{1}{x^2}} x}{\left (1+x^2\right )^2} \, dx\)
 3.521 \(\int \frac{1}{\sqrt{1+\frac{1}{x^2}} x \left (1+x^2\right )} \, dx\)
 3.522 \(\int \frac{x}{a+b x^2+\sqrt{a+b x^2}} \, dx\)
 3.523 \(\int \frac{x}{x^2-\sqrt [3]{x^2}} \, dx\)
 3.524 \(\int x \left (1+x^2\right )^3 \sqrt{2+2 x^2+x^4} \, dx\)
 3.525 \(\int x \sqrt{\frac{1-x^2}{1+x^2}} \, dx\)
 3.526 \(\int x \sqrt{\frac{5-7 x^2}{7+5 x^2}} \, dx\)
 3.527 \(\int x^2 \sqrt{\frac{1-x^3}{1+x^3}} \, dx\)
 3.528 \(\int x^5 \sqrt{1-x^3} \left (1+x^9\right )^2 \, dx\)
 3.529 \(\int x^8 \sqrt{\frac{1-x^3}{1+x^3}} \, dx\)
 3.530 \(\int x^9 \sqrt{\frac{5-7 x^5}{7+5 x^5}} \, dx\)
 3.531 \(\int \left (\frac{x}{\left (a+b x^2\right )^{3/2}}+\frac{x}{\left (1+x^2\right ) \sqrt{a+b x^2}}\right ) \, dx\)
 3.532 \(\int \frac{x \left (1+a+x^2+b x^2\right )}{\left (1+x^2\right ) \left (a+b x^2\right )^{3/2}} \, dx\)
 3.533 \(\int \left (\frac{x}{\left (a+b x^2\right )^{5/2}}+\frac{x}{\left (a+b x^2\right )^{3/2}}+\frac{x}{\left (1+x^2\right ) \sqrt{a+b x^2}}\right ) \, dx\)
 3.534 \(\int \frac{x \left (1+a+a^2+x^2+a x^2+b x^2+2 a b x^2+b x^4+b^2 x^4\right )}{\left (1+x^2\right ) \left (a+b x^2\right )^{5/2}} \, dx\)
 3.535 \(\int \frac{1}{\sqrt{\sqrt{x}+x}} \, dx\)
 3.536 \(\int \sqrt{\sqrt{x}+x} \, dx\)
 3.537 \(\int \sqrt{-x} \left (\sqrt{-x}+x\right ) \, dx\)
 3.538 \(\int \frac{5+\sqrt [4]{x}}{-6+x} \, dx\)
 3.539 \(\int \frac{1}{4+\sqrt{4-x}-x} \, dx\)
 3.540 \(\int \frac{1}{1+x-\sqrt{2+x}} \, dx\)
 3.541 \(\int \frac{1}{4+x+\sqrt{1+x}} \, dx\)
 3.542 \(\int \frac{1}{x-\sqrt{1+x}} \, dx\)
 3.543 \(\int \frac{1}{x-\sqrt{2+x}} \, dx\)
 3.544 \(\int \frac{1}{-\sqrt{1-x}+x} \, dx\)
 3.545 \(\int \sqrt{1+\sqrt{x}+x} \, dx\)
 3.546 \(\int \sqrt{1+x+\sqrt{1+x}} \, dx\)
 3.547 \(\int \sqrt{\sqrt{-1+x}+x} \, dx\)
 3.548 \(\int \sqrt{2 x+\sqrt{-1+2 x}} \, dx\)
 3.549 \(\int \sqrt{3 x+\sqrt{-7+8 x}} \, dx\)
 3.550 \(\int \frac{1}{\sqrt{x+\sqrt{1+x}}} \, dx\)
 3.551 \(\int \frac{1+x}{4+x+\sqrt{-9+6 x}} \, dx\)
 3.552 \(\int \frac{12-x}{4+x+\sqrt{-9+6 x}} \, dx\)
 3.553 \(\int \frac{-1+x^3}{\sqrt{x} \left (1+x^2\right )} \, dx\)
 3.554 \(\int \frac{1}{2 \sqrt{-1+x} \sqrt{-\sqrt{-1+x}+x}} \, dx\)
 3.555 \(\int \frac{1+x^{7/2}}{1-x^2} \, dx\)
 3.556 \(\int \frac{4+2 x}{\sqrt [3]{-1+2 x}+\sqrt{-1+2 x}} \, dx\)
 3.557 \(\int \frac{1}{\sqrt{2+\sqrt{1+\sqrt{x}}}} \, dx\)
 3.558 \(\int \sqrt{2+\sqrt{4+\sqrt{x}}} \, dx\)
 3.559 \(\int \sqrt{2-\sqrt{4+\sqrt{-9+5 x}}} \, dx\)
 3.560 \(\int \frac{1}{\sqrt{2+\sqrt{1+\sqrt{x}}}} \, dx\)
 3.561 \(\int \sqrt{1+\sqrt{1+\sqrt{1+\sqrt{x}}}} \, dx\)
 3.562 \(\int \sqrt{2+\sqrt{3+\sqrt{-1+2 \sqrt{x}}}} \, dx\)
 3.563 \(\int \sqrt{1+\sqrt{1+\sqrt{-1+x}}} x \, dx\)
 3.564 \(\int \frac{1}{\sqrt{-1+x} \sqrt{-\sqrt{-1+x}+x}} \, dx\)
 3.565 \(\int \frac{1}{\sqrt{1+x+\sqrt{-1+2 x}}} \, dx\)
 3.566 \(\int \frac{q+p x}{\sqrt{b+a x} \left (f+\sqrt{b+a x}\right )} \, dx\)
 3.567 \(\int \sqrt{1-\sqrt{x}-x} \, dx\)
 3.568 \(\int \frac{9+6 \sqrt{x}+x}{4 \sqrt{x}+x} \, dx\)
 3.569 \(\int \frac{6-8 x^{7/2}}{5-9 \sqrt{x}} \, dx\)
 3.570 \(\int \frac{\sqrt{1+x} \left (1+x^3\right )}{1+x^2} \, dx\)
 3.571 \(\int \frac{\sqrt{-1-\sqrt{x}+x}}{(-1+x) \sqrt{x}} \, dx\)
 3.572 \(\int \frac{1+2 \sqrt{1+x}}{x \sqrt{1+x} \sqrt{x+\sqrt{1+x}}} \, dx\)
 3.573 \(\int \frac{1}{\sqrt{x} \sqrt{1+x}} \, dx\)
 3.574 \(\int \frac{\sqrt{\frac{x}{1+x}}}{x} \, dx\)
 3.575 \(\int \frac{\sqrt{x}}{\sqrt{1+x}} \, dx\)
 3.576 \(\int \sqrt{\frac{x}{1+x}} \, dx\)
 3.577 \(\int \frac{\sqrt{-1+x}}{x^2 \sqrt{1+x}} \, dx\)
 3.578 \(\int \frac{\sqrt{\frac{-1+x}{1+x}}}{x^2} \, dx\)
 3.579 \(\int \frac{\sqrt{-1+x} x^3}{\sqrt{1+x}} \, dx\)
 3.580 \(\int x^3 \sqrt{\frac{-1+x}{1+x}} \, dx\)
 3.581 \(\int \frac{\sqrt{-\frac{x}{1+x}}}{x} \, dx\)
 3.582 \(\int \frac{\sqrt{\frac{1-x}{1+x}}}{-1+x} \, dx\)
 3.583 \(\int \frac{\sqrt{\frac{a+b x}{c-b x}}}{a+b x} \, dx\)
 3.584 \(\int \frac{\sqrt{\frac{a+b x}{c+d x}}}{a+b x} \, dx\)
 3.585 \(\int \sqrt{-\frac{x}{1+x}} \, dx\)
 3.586 \(\int \sqrt{\frac{1-x}{1+x}} \, dx\)
 3.587 \(\int \sqrt{\frac{a+x}{a-x}} \, dx\)
 3.588 \(\int \sqrt{\frac{-a+x}{a+x}} \, dx\)
 3.589 \(\int \sqrt{\frac{a+b x}{c+d x}} \, dx\)
 3.590 \(\int \sqrt{\frac{-1+x}{5+3 x}} \, dx\)
 3.591 \(\int \frac{\sqrt{\frac{-1+5 x}{1+7 x}}}{x^2} \, dx\)
 3.592 \(\int \frac{x}{\sqrt{\frac{1-x}{1+x}} (1+x)} \, dx\)
 3.593 \(\int \frac{x}{(1+x) \sqrt{-1+\frac{2}{1+x}}} \, dx\)
 3.594 \(\int \frac{x}{(1+x) \sqrt{\frac{2+x}{3+x}}} \, dx\)
 3.595 \(\int \frac{\sqrt{1+\frac{1}{x}}}{(1+x)^2} \, dx\)
 3.596 \(\int \frac{\sqrt{1+\frac{1}{x}}}{\sqrt{1-x^2}} \, dx\)
 3.597 \(\int \frac{1}{x+\sqrt{3-2 x-x^2}} \, dx\)
 3.598 \(\int \frac{1}{\left (x+\sqrt{3-2 x-x^2}\right )^2} \, dx\)
 3.599 \(\int \frac{1}{\left (x+\sqrt{3-2 x-x^2}\right )^3} \, dx\)
 3.600 \(\int \frac{1}{x+\sqrt{-3-2 x+x^2}} \, dx\)
 3.601 \(\int \frac{1}{\left (x+\sqrt{-3-2 x+x^2}\right )^2} \, dx\)
 3.602 \(\int \frac{1}{\left (x+\sqrt{-3-2 x+x^2}\right )^3} \, dx\)
 3.603 \(\int \frac{1}{x+\sqrt{-3-4 x-x^2}} \, dx\)
 3.604 \(\int \frac{1}{\left (x+\sqrt{-3-4 x-x^2}\right )^2} \, dx\)
 3.605 \(\int \frac{1}{\left (x+\sqrt{-3-4 x-x^2}\right )^3} \, dx\)
 3.606 \(\int x^3 (1+x)^3 (1+2 x) \sqrt{1-x^2-2 x^3-x^4} \, dx\)
 3.607 \(\int (1+2 x) \left (x+x^2\right )^3 \sqrt{1-\left (x+x^2\right )^2} \, dx\)
 3.608 \(\int \left (8 x-8 x^2+4 x^3-x^4\right )^{3/2} \, dx\)
 3.609 \(\int \sqrt{8 x-8 x^2+4 x^3-x^4} \, dx\)
 3.610 \(\int \frac{1}{\sqrt{8 x-8 x^2+4 x^3-x^4}} \, dx\)
 3.611 \(\int \frac{1}{\left (8 x-8 x^2+4 x^3-x^4\right )^{3/2}} \, dx\)
 3.612 \(\int \frac{1}{\left (8 x-8 x^2+4 x^3-x^4\right )^{5/2}} \, dx\)
 3.613 \(\int \left ((2-x) x \left (4-2 x+x^2\right )\right )^{3/2} \, dx\)
 3.614 \(\int \sqrt{(2-x) x \left (4-2 x+x^2\right )} \, dx\)
 3.615 \(\int \frac{1}{\sqrt{(2-x) x \left (4-2 x+x^2\right )}} \, dx\)
 3.616 \(\int \frac{1}{\left ((2-x) x \left (4-2 x+x^2\right )\right )^{3/2}} \, dx\)
 3.617 \(\int \frac{1}{\left ((2-x) x \left (4-2 x+x^2\right )\right )^{5/2}} \, dx\)
 3.618 \(\int \left (4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right )^{3/2} \, dx\)
 3.619 \(\int \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4} \, dx\)
 3.620 \(\int \frac{1}{\sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}} \, dx\)
 3.621 \(\int \frac{1}{\left (4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right )^{3/2}} \, dx\)
 3.622 \(\int \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4} \, dx\)
 3.623 \(\int \frac{1}{\sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}} \, dx\)
 3.624 \(\int \frac{1}{\left (8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right )^{3/2}} \, dx\)
 3.625 \(\int \left (a+8 x-8 x^2+4 x^3-x^4\right )^{3/2} \, dx\)
 3.626 \(\int \sqrt{a+8 x-8 x^2+4 x^3-x^4} \, dx\)
 3.627 \(\int \frac{1}{\sqrt{a+8 x-8 x^2+4 x^3-x^4}} \, dx\)
 3.628 \(\int \frac{1}{\left (a+8 x-8 x^2+4 x^3-x^4\right )^{3/2}} \, dx\)
 3.629 \(\int \frac{1}{\left (a+8 x-8 x^2+4 x^3-x^4\right )^{5/2}} \, dx\)
 3.630 \(\int x \left (a+8 x-8 x^2+4 x^3-x^4\right )^{3/2} \, dx\)
 3.631 \(\int x \sqrt{a+8 x-8 x^2+4 x^3-x^4} \, dx\)
 3.632 \(\int \frac{x}{\sqrt{a+8 x-8 x^2+4 x^3-x^4}} \, dx\)
 3.633 \(\int \frac{x}{\left (a+8 x-8 x^2+4 x^3-x^4\right )^{3/2}} \, dx\)
 3.634 \(\int \frac{x}{\left (a+8 x-8 x^2+4 x^3-x^4\right )^{5/2}} \, dx\)
 3.635 \(\int x^2 \left (a+8 x-8 x^2+4 x^3-x^4\right )^{3/2} \, dx\)
 3.636 \(\int x^2 \sqrt{a+8 x-8 x^2+4 x^3-x^4} \, dx\)
 3.637 \(\int \frac{x^2}{\sqrt{a+8 x-8 x^2+4 x^3-x^4}} \, dx\)
 3.638 \(\int \frac{x^2}{\left (a+8 x-8 x^2+4 x^3-x^4\right )^{3/2}} \, dx\)
 3.639 \(\int \frac{x^2}{\left (a+8 x-8 x^2+4 x^3-x^4\right )^{5/2}} \, dx\)
 3.640 \(\int \frac{1}{\sqrt{8+8 x-x^3+8 x^4}} \, dx\)
 3.641 \(\int \frac{1}{\left (8+8 x-x^3+8 x^4\right )^{3/2}} \, dx\)
 3.642 \(\int \frac{1}{\sqrt{1+4 x+4 x^2+4 x^4}} \, dx\)
 3.643 \(\int \frac{1}{\left (1+4 x+4 x^2+4 x^4\right )^{3/2}} \, dx\)
 3.644 \(\int \frac{1}{\sqrt{8+24 x+8 x^2-15 x^3+8 x^4}} \, dx\)
 3.645 \(\int \frac{1}{\left (8+24 x+8 x^2-15 x^3+8 x^4\right )^{3/2}} \, dx\)
 3.646 \(\int \frac{1}{\left (8+24 x+8 x^2-15 x^3+8 x^4\right )^{5/2}} \, dx\)
 3.647 \(\int \frac{1}{\sqrt{9-6 x-44 x^2+15 x^3+3 x^4}} \, dx\)
 3.648 \(\int \frac{1}{\left (9-6 x-44 x^2+15 x^3+3 x^4\right )^{3/2}} \, dx\)
 3.649 \(\int \frac{\left (2 \sqrt{3-x}+\frac{3}{\sqrt{1+x}}\right )^2}{x} \, dx\)
 3.650 \(\int \frac{-1+x+x^2}{1+\sqrt{1+x^2}} \, dx\)
 3.651 \(\int \frac{-1+x+x^2}{1+x+\sqrt{1+x^2}} \, dx\)
 3.652 \(\int \frac{2 \sqrt{-1+x}+x}{\sqrt{-1+x} x} \, dx\)
 3.653 \(\int \left (a+c \sqrt{x}+b x^{2/3}\right )^2 \, dx\)
 3.654 \(\int \left (a+c \sqrt{x}+b x^{2/3}\right )^3 \, dx\)
 3.655 \(\int \frac{-1+x^2}{\sqrt{a-b+\frac{b}{x^2}} x^3} \, dx\)
 3.656 \(\int \frac{-1+x^2}{\sqrt{a+b \left (-1+\frac{1}{x^2}\right )} x^3} \, dx\)
 3.657 \(\int \frac{1+x}{\left (4+x^2\right ) \sqrt{9+x^2}} \, dx\)
 3.658 \(\int x \left (1+\sqrt{1-x^2}\right ) \, dx\)
 3.659 \(\int x \left (1+\sqrt{1-x} \sqrt{1+x}\right ) \, dx\)
 3.660 \(\int x \left (1+\frac{1}{\sqrt{2+x} \sqrt{3+x}}\right ) \, dx\)
 3.661 \(\int \frac{x-\sqrt{x^6}}{x \left (1-x^4\right )} \, dx\)
 3.662 \(\int \frac{1-\frac{\sqrt{x^6}}{x}}{1-x^4} \, dx\)
 3.663 \(\int \frac{x-\sqrt{x^6}}{x-x^5} \, dx\)
 3.664 \(\int \frac{x}{x+\sqrt{x^6}} \, dx\)
 3.665 \(\int \frac{\sqrt{x}-\sqrt{x^3}}{x-x^3} \, dx\)
 3.666 \(\int \frac{1}{\sqrt{x}+\sqrt{x^3}} \, dx\)
 3.667 \(\int \frac{1}{\sqrt{-1+x}+\sqrt{(-1+x)^3}} \, dx\)
 3.668 \(\int \left (-\frac{3}{(4+5 x)^2}-\frac{5+4 x}{(4+5 x)^2 \sqrt{1-x^2}}\right ) \, dx\)
 3.669 \(\int \frac{-5-4 x-3 \sqrt{1-x^2}}{(4+5 x)^2 \sqrt{1-x^2}} \, dx\)
 3.670 \(\int \frac{1}{(-5-4 x) \sqrt{1-x^2}+3 \left (1-x^2\right )} \, dx\)
 3.671 \(\int \frac{1}{3-3 x^2-5 \sqrt{1-x^2}-4 x \sqrt{1-x^2}} \, dx\)
 3.672 \(\int \frac{-1+\sqrt{1-x^2}}{\sqrt{1-x^2} \left (2+x-2 \sqrt{1-x^2}\right )^2} \, dx\)
 3.673 \(\int \frac{a+b x^{-1+n}}{c x+d x^n} \, dx\)
 3.674 \(\int \frac{\sqrt{1+2 x^2}}{1+\sqrt{1+2 x^2}} \, dx\)
 3.675 \(\int \frac{\sqrt{-1+4 x^2}}{x+\sqrt{-1+4 x^2}} \, dx\)
 3.676 \(\int \frac{a+b x+c x^2}{(d+e x)^3 \sqrt{-1+x^2}} \, dx\)
 3.677 \(\int \frac{1+2 x^8}{x \left (1+x^8\right )^{3/2}} \, dx\)
 3.678 \(\int \frac{\sqrt{1+x^8} \left (1+2 x^8\right )}{x+2 x^9+x^{17}} \, dx\)
 3.679 \(\int \left (1-9 x^2+\frac{x}{\sqrt{1-9 x^2}}\right ) \, dx\)
 3.680 \(\int \frac{x+\left (1-9 x^2\right )^{3/2}}{\sqrt{1-9 x^2}} \, dx\)
 3.681 \(\int \frac{\left (-3+2 \sqrt{x}\right ) \left (-3 \sqrt{x}+x\right )^{2/3}}{\sqrt{x}} \, dx\)
 3.682 \(\int \frac{9-9 \sqrt{x}+2 x}{\sqrt [3]{-3 \sqrt{x}+x}} \, dx\)
 3.683 \(\int \frac{1}{\sqrt{4-9 x^2}} \, dx\)
 3.684 \(\int \frac{1}{\sqrt{2-3 x} \sqrt{2+3 x}} \, dx\)
 3.685 \(\int \frac{1}{\sqrt{(2-3 x) (2+3 x)}} \, dx\)
 3.686 \(\int \frac{1}{\sqrt{15-2 x-x^2}} \, dx\)
 3.687 \(\int \frac{1}{\sqrt{3-x} \sqrt{5+x}} \, dx\)
 3.688 \(\int \frac{1}{\sqrt{(3-x) (5+x)}} \, dx\)
 3.689 \(\int \frac{1}{\sqrt{-15-8 x-x^2}} \, dx\)
 3.690 \(\int \frac{1}{\sqrt{-3-x} \sqrt{5+x}} \, dx\)
 3.691 \(\int \frac{1}{\sqrt{(-3-x) (5+x)}} \, dx\)
 3.692 \(\int \left (1-\sqrt{x}\right ) \, dx\)
 3.693 \(\int \frac{1-x}{1+\sqrt{x}} \, dx\)
 3.694 \(\int \sqrt{\frac{1}{1-x^2}} \, dx\)
 3.695 \(\int \sqrt{\frac{1+x^2}{1-x^4}} \, dx\)
 3.696 \(\int \sqrt{\frac{1}{-1+x^2}} \, dx\)
 3.697 \(\int \sqrt{\frac{1+x^2}{-1+x^4}} \, dx\)
 3.698 \(\int \frac{1}{\sqrt{1-x}} \, dx\)
 3.699 \(\int \frac{\sqrt{1+x}}{\sqrt{1-x^2}} \, dx\)
 3.700 \(\int \frac{1}{\sqrt{1+x}} \, dx\)
 3.701 \(\int \frac{\sqrt{1-x}}{\sqrt{1-x^2}} \, dx\)
 3.702 \(\int \sqrt{1-x} \, dx\)
 3.703 \(\int \frac{\sqrt{1-x^2}}{\sqrt{1+x}} \, dx\)
 3.704 \(\int \sqrt{1+x} \, dx\)
 3.705 \(\int \frac{\sqrt{1-x^2}}{\sqrt{1-x}} \, dx\)
 3.706 \(\int \frac{\sqrt{2+3 x}}{\sqrt{1+x}} \, dx\)
 3.707 \(\int \frac{\sqrt{1-x} \sqrt{2+3 x}}{\sqrt{1-x^2}} \, dx\)
 3.708 \(\int \frac{(1+x)^{3/2}}{(1-x)^{3/2} x} \, dx\)
 3.709 \(\int \frac{(1+x)^3}{x \left (1-x^2\right )^{3/2}} \, dx\)
 3.710 \(\int \frac{(1+a x)^{3/2}}{x (1-a x)^{3/2}} \, dx\)
 3.711 \(\int \frac{(1+a x)^3}{x \left (1-a^2 x^2\right )^{3/2}} \, dx\)
 3.712 \(\int \frac{1}{\sqrt{1-x^2}} \, dx\)
 3.713 \(\int \frac{\sqrt{1+x^2}}{\sqrt{1-x^4}} \, dx\)
 3.714 \(\int \frac{1}{\sqrt{1+x^2}} \, dx\)
 3.715 \(\int \frac{\sqrt{1-x^2}}{\sqrt{1-x^4}} \, dx\)
 3.716 \(\int \sqrt{1-x^2} \, dx\)
 3.717 \(\int \frac{\sqrt{1-x^4}}{\sqrt{1+x^2}} \, dx\)
 3.718 \(\int \sqrt{1+x^2} \, dx\)
 3.719 \(\int \frac{\sqrt{1-x^4}}{\sqrt{1-x^2}} \, dx\)
 3.720 \(\int \left (\frac{a+b+c x^2}{d}\right )^m \, dx\)
 3.721 \(\int \frac{1}{x-\sqrt{1+x^2}} \, dx\)
 3.722 \(\int \frac{1}{x-\sqrt{1-x^2}} \, dx\)
 3.723 \(\int \frac{1}{x-\sqrt{1+2 x^2}} \, dx\)
 3.724 \(\int \frac{2 x-x^3+x^2 \sqrt{2-x^2}}{-2+2 x^2} \, dx\)
 3.725 \(\int \frac{x \sqrt{2-x^2}}{x-\sqrt{2-x^2}} \, dx\)
 3.726 \(\int \frac{x}{-x+\sqrt{2 x-x^2}} \, dx\)
 3.727 \(\int \frac{x+\sqrt{2 x-x^2}}{2-2 x} \, dx\)
 3.728 \(\int \frac{\sqrt{2-x} \sqrt{x}+x}{2-2 x} \, dx\)
 3.729 \(\int \frac{\sqrt{x}}{\sqrt{2-x}-\sqrt{x}} \, dx\)
 3.730 \(\int \frac{\sqrt{\frac{x^2}{-1+x^2}}}{1+x^2} \, dx\)
 3.731 \(\int \frac{\sqrt{\frac{x^2}{-1+a+(1+a) x^2}}}{1+x^2} \, dx\)
 3.732 \(\int \frac{1}{\left ((1+x) \left (-1+x^2\right )\right )^{2/3}} \, dx\)
 3.733 \(\int \frac{-1+x^2}{\left (1+x^2\right ) \sqrt{x \left (1+x^2\right )}} \, dx\)
 3.734 \(\int \frac{-1+x^2}{\left (1+x^2\right ) \sqrt{x+x^3}} \, dx\)
 3.735 \(\int \frac{\sqrt{\frac{\left (-1+x^2\right )^2}{x \left (1+x^2\right )}}}{1+x^2} \, dx\)
 3.736 \(\int \frac{\sqrt{\frac{\left (-1+x^2\right )^2}{x+x^3}}}{1+x^2} \, dx\)
 3.737 \(\int \frac{1}{\sqrt{a+\frac{b}{x^2}} \sqrt{c+d x^2}} \, dx\)
 3.738 \(\int \frac{\sqrt{-2 x^2+x^4}}{\left (-1+x^2\right ) \left (2+x^2\right )} \, dx\)
 3.739 \(\int \frac{\sqrt{1-\frac{1}{\left (-1+x^2\right )^2}}}{2-x^2} \, dx\)
 3.740 \(\int \frac{\sqrt{\frac{-2 x^2+x^4}{\left (-1+x^2\right )^2}}}{2+x^2} \, dx\)
 3.741 \(\int \left (1+\frac{2 x}{1+x^2}\right )^{5/2} \, dx\)
 3.742 \(\int \left (1+\frac{2 x}{1+x^2}\right )^{3/2} \, dx\)
 3.743 \(\int \sqrt{1+\frac{2 x}{1+x^2}} \, dx\)
 3.744 \(\int \frac{1}{\sqrt{1+\frac{2 x}{1+x^2}}} \, dx\)
 3.745 \(\int \frac{1}{\left (1+\frac{2 x}{1+x^2}\right )^{3/2}} \, dx\)
 3.746 \(\int \frac{\sqrt{1+\frac{2 x}{1+x^2}}}{1+x^2} \, dx\)
 3.747 \(\int x^2 \left (\frac{c}{a+b x^2}\right )^{3/2} \, dx\)
 3.748 \(\int x \left (\frac{c}{a+b x^2}\right )^{3/2} \, dx\)
 3.749 \(\int \left (\frac{c}{a+b x^2}\right )^{3/2} \, dx\)
 3.750 \(\int \frac{\left (\frac{c}{a+b x^2}\right )^{3/2}}{x} \, dx\)
 3.751 \(\int \frac{\left (\frac{c}{a+b x^2}\right )^{3/2}}{x^2} \, dx\)
 3.752 \(\int \frac{\left (\frac{c}{a+b x^2}\right )^{3/2}}{x^3} \, dx\)
 3.753 \(\int x^2 \left (c \left (a+b x^2\right )^3\right )^{3/2} \, dx\)
 3.754 \(\int x \left (c \left (a+b x^2\right )^3\right )^{3/2} \, dx\)
 3.755 \(\int \left (c \left (a+b x^2\right )^3\right )^{3/2} \, dx\)
 3.756 \(\int \frac{\left (c \left (a+b x^2\right )^3\right )^{3/2}}{x} \, dx\)
 3.757 \(\int \frac{\left (c \left (a+b x^2\right )^3\right )^{3/2}}{x^2} \, dx\)
 3.758 \(\int \frac{\left (c \left (a+b x^2\right )^3\right )^{3/2}}{x^3} \, dx\)
 3.759 \(\int \sqrt{x-x^2} F(x) \, dx\)
 3.760 \(\int \frac{F(x)}{\sqrt{x-x^2}} \, dx\)
 3.761 \(\int \sqrt{1-x} \sqrt{x} F(x) \, dx\)
 3.762 \(\int \frac{F(x)}{\sqrt{1-x} \sqrt{x}} \, dx\)
 3.763 \(\int f\left (\frac{a+b x}{x}\right ) \, dx\)
 3.764 \(\int f\left (\frac{a+b x^2}{x^2}\right ) \, dx\)
 3.765 \(\int f\left (\frac{x}{a+b x}\right ) \, dx\)
 3.766 \(\int f\left (\frac{x^2}{a+b x^2}\right ) \, dx\)
 3.767 \(\int f\left (\frac{x^2}{(a+b x)^2}\right ) \, dx\)
 3.768 \(\int f\left (\frac{x^4}{\left (a+b x^2\right )^2}\right ) \, dx\)
 3.769 \(\int \frac{\sqrt{b x^2+\sqrt{a+b^2 x^4}}}{\sqrt{a+b^2 x^4}} \, dx\)
 3.770 \(\int \frac{\sqrt{-b x^2+\sqrt{a+b^2 x^4}}}{\sqrt{a+b^2 x^4}} \, dx\)
 3.771 \(\int \frac{\sqrt{2 x^2+\sqrt{3+4 x^4}}}{(c+d x) \sqrt{3+4 x^4}} \, dx\)
 3.772 \(\int \frac{\sqrt{2 x^2+\sqrt{3+4 x^4}}}{(c+d x)^2 \sqrt{3+4 x^4}} \, dx\)
 3.773 \(\int \frac{-4+x}{\left (1+\sqrt [3]{x}\right ) \sqrt{x}} \, dx\)
 3.774 \(\int \frac{1+\sqrt{x}}{x^{5/6}+x^{7/6}} \, dx\)
 3.775 \(\int \frac{1+\sqrt{x}}{\left (1+\sqrt [3]{x}\right ) \sqrt{x}} \, dx\)
 3.776 \(\int \frac{\sqrt{2+\frac{b}{x^2}}}{b+2 x^2} \, dx\)
 3.777 \(\int \frac{\sqrt{2-\frac{b}{x^2}}}{-b+2 x^2} \, dx\)
 3.778 \(\int \frac{\sqrt{a+\frac{c}{x^2}}}{d+e x} \, dx\)
 3.779 \(\int \frac{\sqrt{a+\frac{c}{x^2}+\frac{b}{x}}}{d+e x} \, dx\)
 3.780 \(\int \frac{\sqrt [6]{x}+\sqrt [5]{x^3}}{\sqrt{x}} \, dx\)
 3.781 \(\int \frac{2+x}{\sqrt{4 x-x^2}} \, dx\)
 3.782 \(\int \frac{3+x}{\sqrt [3]{6 x+x^2}} \, dx\)
 3.783 \(\int \frac{4+x}{\left (6 x-x^2\right )^{3/2}} \, dx\)
 3.784 \(\int \frac{1}{(1+x) \sqrt{2 x+x^2}} \, dx\)
 3.785 \(\int \frac{1}{(1+2 x) \sqrt{x+x^2}} \, dx\)
 3.786 \(\int \frac{-1+x}{\sqrt{2 x-x^2}} \, dx\)
 3.787 \(\int \frac{\sqrt{x-x^2}}{1+x} \, dx\)
 3.788 \(\int \sqrt{\sqrt [4]{x}+x} \, dx\)
 3.789 \(\int \sqrt{x+x^{3/2}} \, dx\)
 3.790 \(\int x \sqrt{x+x^{3/2}} \, dx\)
 3.791 \(\int \left (1-x^2\right ) \sqrt{\frac{1}{2-x^2}} \, dx\)
 3.792 \(\int \sqrt{x^2+x^3-x^4} \, dx\)
 3.793 \(\int \frac{1}{\sqrt{\left (a^2+x^2\right )^3}} \, dx\)
 3.794 \(\int \frac{\sqrt{x}}{1+\sqrt{x}+x} \, dx\)
 3.795 \(\int \frac{x}{1+\sqrt{x}+x} \, dx\)
 3.796 \(\int \frac{1}{\sqrt{x} \left (1+\sqrt{x}+x\right )^{7/2}} \, dx\)
 3.797 \(\int \frac{-1+x}{1+\sqrt{1+x^2}} \, dx\)
 3.798 \(\int \frac{1}{(1+x)^{2/3} \left (-1+x^2\right )^{2/3}} \, dx\)
 3.799 \(\int \left (\left (1-x^6\right )^{2/3}+\frac{\left (1-x^6\right )^{2/3}}{x^6}\right ) \, dx\)
 3.800 \(\int \frac{x^{-1+m} \left (2 a m+b (2 m-n) x^n\right )}{2 \left (a+b x^n\right )^{3/2}} \, dx\)
 3.801 \(\int \frac{x-2 x^3}{\sqrt{2+3 x}} \, dx\)
 3.802 \(\int \frac{1}{\sqrt [4]{1+x}+\sqrt{1+x}} \, dx\)
 3.803 \(\int \frac{1+2 x}{\sqrt{x+x^2}} \, dx\)
 3.804 \(\int \frac{1}{2 \sqrt{x} (1+x)} \, dx\)
 3.805 \(\int \frac{1}{x \sqrt{6 x-x^2}} \, dx\)
 3.806 \(\int \left (1+\sqrt{x}\right ) \sqrt{x} \, dx\)
 3.807 \(\int \frac{1-\sqrt{x}}{\sqrt [3]{x}} \, dx\)
 3.808 \(\int \frac{\sqrt{x}}{1+\sqrt [3]{x}} \, dx\)
 3.809 \(\int \frac{\sqrt [3]{1+\sqrt{x}}}{x} \, dx\)
 3.810 \(\int \left (1-\sqrt{x}\right ) \, dx\)
 3.811 \(\int \left (1-\sqrt [4]{x}\right ) \, dx\)
 3.812 \(\int \frac{1-\sqrt{x}}{1+\sqrt [4]{x}} \, dx\)
 3.813 \(\int \frac{1}{\sqrt{(a+b x) (c+d x)}} \, dx\)
 3.814 \(\int \frac{1}{\sqrt{(a+b x) (c-d x)}} \, dx\)
 3.815 \(\int \frac{1}{\sqrt{x} \left (1-x^2\right )} \, dx\)
 3.816 \(\int \frac{\sqrt{x}}{x-x^3} \, dx\)
 3.817 \(\int \frac{x}{2-\sqrt{3}+\left (1+\sqrt{3}\right ) x+x^2} \, dx\)
 3.818 \(\int \sqrt{x^2+x^3} \, dx\)
 3.819 \(\int \frac{1}{(1+x) \sqrt{2 x+x^2}} \, dx\)
 3.820 \(\int \sqrt{1-\sqrt{x}-x} \sqrt{x} \, dx\)
 3.821 \(\int \sqrt [3]{1+\sqrt{-3+x}} \, dx\)
 3.822 \(\int \frac{1}{\sqrt{3+\sqrt{-1+2 x}}} \, dx\)
 3.823 \(\int \frac{\sqrt{1-x}}{1+\sqrt{x}} \, dx\)
 3.824 \(\int \frac{\sqrt{1-x}}{1-\sqrt{x}} \, dx\)
 3.825 \(\int \frac{x}{x-\sqrt{1+x^2}} \, dx\)
 3.826 \(\int \frac{x}{x-\sqrt{1-x^2}} \, dx\)
 3.827 \(\int \frac{x}{x-\sqrt{1+2 x^2}} \, dx\)
 3.828 \(\int \sqrt{x} \sqrt{\sqrt{x}+x} \, dx\)
 3.829 \(\int \frac{1+\sqrt [3]{x}}{1+\sqrt{x}} \, dx\)
 3.830 \(\int \frac{1+\sqrt [3]{x}}{1+\sqrt [4]{x}} \, dx\)
 3.831 \(\int \frac{x^2}{-1+x^2+\sqrt{1-x^2}} \, dx\)
 3.832 \(\int \sqrt{\frac{1+x}{x}} \, dx\)
 3.833 \(\int \sqrt{\frac{1-x}{x}} \, dx\)
 3.834 \(\int \sqrt{\frac{-1+x}{x}} \, dx\)
 3.835 \(\int \frac{\sqrt{\frac{1+x}{x}}}{x} \, dx\)
 3.836 \(\int \sqrt{\frac{x}{1+x}} \, dx\)
 3.837 \(\int \frac{1}{\sqrt{\frac{-1-x}{x}}} \, dx\)
 3.838 \(\int \sqrt{(4-x) x} \, dx\)
 3.839 \(\int \frac{1}{\sqrt{(1-x) x}} \, dx\)
 3.840 \(\int \frac{x}{(x (2+x))^{3/2}} \, dx\)
 3.841 \(\int \frac{\sqrt{1+\frac{1}{x}}}{1-x^2} \, dx\)
 3.842 \(\int \frac{1}{1+\sqrt{5}-x^2+\sqrt{5} x^2} \, dx\)
 3.843 \(\int \sqrt{(b-x) (-a+x)} \, dx\)
 3.844 \(\int \frac{1}{\sqrt{(b-x) (-a+x)}} \, dx\)
 3.845 \(\int \sqrt{\left (1-x^2\right ) \left (3+x^2\right )} \, dx\)
 3.846 \(\int \frac{1}{\sqrt{\left (1-x^2\right ) \left (3+x^2\right )}} \, dx\)
 3.847 \(\int \frac{1}{\sqrt{a x+b x^2}} \, dx\)
 3.848 \(\int \frac{1}{\sqrt{x (a+b x)}} \, dx\)
 3.849 \(\int \frac{1}{\sqrt{\left (b+\frac{a}{x}\right ) x^2}} \, dx\)
 3.850 \(\int \frac{1}{\sqrt{\left (\frac{a}{x^2}+\frac{b}{x}\right ) x^3}} \, dx\)
 3.851 \(\int \frac{1}{\sqrt{\frac{a x^2+b x^3}{x}}} \, dx\)
 3.852 \(\int \frac{1}{\sqrt{\frac{a x^3+b x^4}{x^2}}} \, dx\)
 3.853 \(\int \frac{1}{\sqrt{a c x+b c x^2}} \, dx\)
 3.854 \(\int \frac{1}{\sqrt{c \left (a x+b x^2\right )}} \, dx\)
 3.855 \(\int \frac{1}{\sqrt{c x (a+b x)}} \, dx\)
 3.856 \(\int \frac{1}{\sqrt{c \left (b+\frac{a}{x}\right ) x^2}} \, dx\)
 3.857 \(\int \sqrt{1-x^2+x \sqrt{-1+x^2}} \, dx\)
 3.858 \(\int \frac{\sqrt{-x+\sqrt{x} \sqrt{1+x}}}{\sqrt{1+x}} \, dx\)
 3.859 \(\int -\frac{x+2 \sqrt{1+x^2}}{x+x^3+\sqrt{1+x^2}} \, dx\)
 3.860 \(\int \frac{1+2 x}{\left (1+x^2\right ) \sqrt{2+2 x+x^2}} \, dx\)
 3.861 \(\int \frac{1}{\left (1+x^4\right ) \sqrt{-x^2+\sqrt{1+x^4}}} \, dx\)
 3.862 \(\int \frac{1}{\left (a+b x^4\right ) \sqrt{c x^2+d \sqrt{a+b x^4}}} \, dx\)
 3.863 \(\int \frac{1}{\left (a+b x^4\right ) \sqrt{-c x^2+d \sqrt{a+b x^4}}} \, dx\)
 3.864 \(\int \frac{x}{\sqrt{a+b c^4+4 b c^3 d x+6 b c^2 d^2 x^2+4 b c d^3 x^3+b d^4 x^4}} \, dx\)
 3.865 \(\int \frac{1}{\sqrt{a+b c^4+4 b c^3 d x+6 b c^2 d^2 x^2+4 b c d^3 x^3+b d^4 x^4}} \, dx\)
 3.866 \(\int \frac{a-c x^4}{\sqrt{a+b x^2+c x^4} \left (a d+a e x^2+c d x^4\right )} \, dx\)
 3.867 \(\int \frac{a-c x^4}{\sqrt{a-b x^2+c x^4} \left (a d+a e x^2+c d x^4\right )} \, dx\)
 3.868 \(\int \frac{1}{\sqrt{5-2 x+x^2} \left (8+x^3\right )} \, dx\)
 3.869 \(\int \sqrt{\frac{x^2}{1+x^2}} \, dx\)
 3.870 \(\int \sqrt{\frac{x^n}{1+x^n}} \, dx\)
 3.871 \(\int \frac{e f-e f x^2}{\left (a d+b d x+a d x^2\right ) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx\)
 3.872 \(\int \frac{e f-e f x^2}{\left (-a d+b d x-a d x^2\right ) \sqrt{-a+b x+c x^2+b x^3-a x^4}} \, dx\)
 3.873 \(\int \frac{\sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}}{x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx\)
 3.874 \(\int \frac{\sqrt{-a x^2+b x \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}}{x \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx\)
 3.875 \(\int \frac{\sqrt{x \left (a x+b \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}\right )}}{x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx\)
 3.876 \(\int \frac{\sqrt{x \left (-a x+b \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}\right )}}{x \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx\)
 3.877 \(\int \frac{-\sqrt{-4+x}-4 \sqrt{-1+x}+\sqrt{-4+x} x+\sqrt{-1+x} x}{\left (1+\sqrt{-4+x}+\sqrt{-1+x}\right ) \left (4-5 x+x^2\right )} \, dx\)
 3.878 \(\int \frac{1}{x \left (3+3 x+x^2\right ) \sqrt [3]{3+3 x+3 x^2+x^3}} \, dx\)
 3.879 \(\int \frac{1-x^2}{\left (1-x+x^2\right ) \left (1-x^3\right )^{2/3}} \, dx\)
 3.880 \(\int \frac{x^2}{\sqrt{-1+x^4} \left (1+x^4\right )} \, dx\)
 3.881 \(\int \frac{a-c x^4}{\left (a e+c d x^2\right ) \left (d+e x^2\right ) \sqrt{a+b x^2+c x^4}} \, dx\)
 3.882 \(\int \left (x+\frac{1-x^2}{1+x}\right ) \, dx\)
 3.883 \(\int \frac{1}{\frac{1}{x}+\sqrt{1-x^2}} \, dx\)
 3.884 \(\int \frac{x \sqrt{1-x^2}}{x-x^3+\sqrt{1-x^2}} \, dx\)
 3.885 \(\int \left (1+x+x^2+x^3\right )^{-n} \left (1-x^4\right )^n \, dx\)