3.1 \(\int \frac{(a+b x)^3 \left (A+B x+C x^2+D x^3\right )}{\sqrt{c+d x}} \, dx\)
 3.2 \(\int \frac{(a+b x)^2 \left (A+B x+C x^2+D x^3\right )}{\sqrt{c+d x}} \, dx\)
 3.3 \(\int \frac{(a+b x) \left (A+B x+C x^2+D x^3\right )}{\sqrt{c+d x}} \, dx\)
 3.4 \(\int \frac{A+B x+C x^2+D x^3}{\sqrt{c+d x}} \, dx\)
 3.5 \(\int \frac{A+B x+C x^2+D x^3}{(a+b x) \sqrt{c+d x}} \, dx\)
 3.6 \(\int \frac{A+B x+C x^2+D x^3}{(a+b x)^2 \sqrt{c+d x}} \, dx\)
 3.7 \(\int \frac{A+B x+C x^2+D x^3}{(a+b x)^3 \sqrt{c+d x}} \, dx\)
 3.8 \(\int \frac{A+B x+C x^2+D x^3}{(a+b x)^4 \sqrt{c+d x}} \, dx\)
 3.9 \(\int \frac{A+B x+C x^2+D x^3}{(a+b x)^5 \sqrt{c+d x}} \, dx\)
 3.10 \(\int \frac{(a+b x)^3 \left (A+B x+C x^2+D x^3\right )}{(c+d x)^{3/2}} \, dx\)
 3.11 \(\int \frac{(a+b x)^2 \left (A+B x+C x^2+D x^3\right )}{(c+d x)^{3/2}} \, dx\)
 3.12 \(\int \frac{(a+b x) \left (A+B x+C x^2+D x^3\right )}{(c+d x)^{3/2}} \, dx\)
 3.13 \(\int \frac{A+B x+C x^2+D x^3}{(c+d x)^{3/2}} \, dx\)
 3.14 \(\int \frac{A+B x+C x^2+D x^3}{(a+b x) (c+d x)^{3/2}} \, dx\)
 3.15 \(\int \frac{A+B x+C x^2+D x^3}{(a+b x)^2 (c+d x)^{3/2}} \, dx\)
 3.16 \(\int \frac{A+B x+C x^2+D x^3}{(a+b x)^3 (c+d x)^{3/2}} \, dx\)
 3.17 \(\int \frac{A+B x+C x^2+D x^3}{(a+b x)^4 (c+d x)^{3/2}} \, dx\)
 3.18 \(\int \frac{(a+b x)^3 \left (A+B x+C x^2+D x^3\right )}{(c+d x)^{5/2}} \, dx\)
 3.19 \(\int \frac{(a+b x)^2 \left (A+B x+C x^2+D x^3\right )}{(c+d x)^{5/2}} \, dx\)
 3.20 \(\int \frac{(a+b x) \left (A+B x+C x^2+D x^3\right )}{(c+d x)^{5/2}} \, dx\)
 3.21 \(\int \frac{A+B x+C x^2+D x^3}{(c+d x)^{5/2}} \, dx\)
 3.22 \(\int \frac{A+B x+C x^2+D x^3}{(a+b x) (c+d x)^{5/2}} \, dx\)
 3.23 \(\int \frac{A+B x+C x^2+D x^3}{(a+b x)^2 (c+d x)^{5/2}} \, dx\)
 3.24 \(\int \frac{A+B x+C x^2+D x^3}{(a+b x)^3 (c+d x)^{5/2}} \, dx\)
 3.25 \(\int (a+b x)^3 (c+d x)^n \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.26 \(\int (a+b x)^2 (c+d x)^n \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.27 \(\int (a+b x) (c+d x)^n \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.28 \(\int (c+d x)^n \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.29 \(\int \frac{(c+d x)^n \left (A+B x+C x^2+D x^3\right )}{a+b x} \, dx\)
 3.30 \(\int \frac{(c+d x)^n \left (A+B x+C x^2+D x^3\right )}{(a+b x)^2} \, dx\)
 3.31 \(\int \frac{(c+d x)^n \left (A+B x+C x^2+D x^3\right )}{(a+b x)^3} \, dx\)
 3.32 \(\int (a+b x)^m (A+B x) (c+d x)^n \, dx\)
 3.33 \(\int (a+b x)^m (c+d x)^n \left (A+B x+C x^2\right ) \, dx\)
 3.34 \(\int (a+b x)^m (c+d x)^n \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.35 \(\int \sqrt{1-d x} \sqrt{1+d x} (e+f x)^3 \left (A+B x+C x^2\right ) \, dx\)
 3.36 \(\int \sqrt{1-d x} \sqrt{1+d x} (e+f x)^2 \left (A+B x+C x^2\right ) \, dx\)
 3.37 \(\int \sqrt{1-d x} \sqrt{1+d x} (e+f x) \left (A+B x+C x^2\right ) \, dx\)
 3.38 \(\int \sqrt{1-d x} \sqrt{1+d x} \left (A+B x+C x^2\right ) \, dx\)
 3.39 \(\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)} \, dx\)
 3.40 \(\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)^2} \, dx\)
 3.41 \(\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)^3} \, dx\)
 3.42 \(\int \frac{(e+f x)^3 \left (A+B x+C x^2\right )}{\sqrt{1-d x} \sqrt{1+d x}} \, dx\)
 3.43 \(\int \frac{(e+f x)^2 \left (A+B x+C x^2\right )}{\sqrt{1-d x} \sqrt{1+d x}} \, dx\)
 3.44 \(\int \frac{(e+f x) \left (A+B x+C x^2\right )}{\sqrt{1-d x} \sqrt{1+d x}} \, dx\)
 3.45 \(\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x}} \, dx\)
 3.46 \(\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)} \, dx\)
 3.47 \(\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)^2} \, dx\)
 3.48 \(\int \frac{A+B x+C x^2}{\sqrt{1-d x} \sqrt{1+d x} (e+f x)^3} \, dx\)
 3.49 \(\int \frac{x \left (a+b x+c x^2\right )}{\sqrt{1-d x} \sqrt{1+d x}} \, dx\)
 3.50 \(\int \frac{a+b x+c x^2}{\sqrt{1-d x} \sqrt{1+d x}} \, dx\)
 3.51 \(\int \frac{a+b x+c x^2}{x \sqrt{1-d x} \sqrt{1+d x}} \, dx\)
 3.52 \(\int \frac{a+b x+c x^2}{x^2 \sqrt{1-d x} \sqrt{1+d x}} \, dx\)
 3.53 \(\int \frac{a+b x+c x^2}{x^3 \sqrt{1-d x} \sqrt{1+d x}} \, dx\)
 3.54 \(\int \sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^3 \left (A+B x+C x^2\right ) \, dx\)
 3.55 \(\int \sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^2 \left (A+B x+C x^2\right ) \, dx\)
 3.56 \(\int \sqrt{a+b x} \sqrt{a c-b c x} (e+f x) \left (A+B x+C x^2\right ) \, dx\)
 3.57 \(\int \sqrt{a+b x} \sqrt{a c-b c x} \left (A+B x+C x^2\right ) \, dx\)
 3.58 \(\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)} \, dx\)
 3.59 \(\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^2} \, dx\)
 3.60 \(\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^3} \, dx\)
 3.61 \(\int \frac{(e+f x)^3 \left (A+B x+C x^2\right )}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx\)
 3.62 \(\int \frac{(e+f x)^2 \left (A+B x+C x^2\right )}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx\)
 3.63 \(\int \frac{(e+f x) \left (A+B x+C x^2\right )}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx\)
 3.64 \(\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x}} \, dx\)
 3.65 \(\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)} \, dx\)
 3.66 \(\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^2} \, dx\)
 3.67 \(\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{a c-b c x} (e+f x)^3} \, dx\)
 3.68 \(\int \frac{x \left (a+b x+c x^2\right )}{\sqrt{-1+d x} \sqrt{1+d x}} \, dx\)
 3.69 \(\int \frac{a+b x+c x^2}{\sqrt{-1+d x} \sqrt{1+d x}} \, dx\)
 3.70 \(\int \frac{a+b x+c x^2}{x \sqrt{-1+d x} \sqrt{1+d x}} \, dx\)
 3.71 \(\int \frac{a+b x+c x^2}{x^2 \sqrt{-1+d x} \sqrt{1+d x}} \, dx\)
 3.72 \(\int \frac{a+b x+c x^2}{x^3 \sqrt{-1+d x} \sqrt{1+d x}} \, dx\)
 3.73 \(\int \frac{a+b x+c x^2}{x^4 \sqrt{-1+d x} \sqrt{1+d x}} \, dx\)
 3.74 \(\int \frac{a+b x+c x^2}{\sqrt{-1+x} \sqrt{1+x} (d+e x)^3} \, dx\)
 3.75 \(\int (a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} \left (A+B x+C x^2\right ) \, dx\)
 3.76 \(\int (a+b x) \sqrt{c+d x} \sqrt{e+f x} \left (A+B x+C x^2\right ) \, dx\)
 3.77 \(\int \sqrt{c+d x} \sqrt{e+f x} \left (A+B x+C x^2\right ) \, dx\)
 3.78 \(\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left (A+B x+C x^2\right )}{a+b x} \, dx\)
 3.79 \(\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left (A+B x+C x^2\right )}{(a+b x)^2} \, dx\)
 3.80 \(\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left (A+B x+C x^2\right )}{(a+b x)^3} \, dx\)
 3.81 \(\int \frac{(a+b x)^2 \sqrt{c+d x} \left (A+B x+C x^2\right )}{\sqrt{e+f x}} \, dx\)
 3.82 \(\int \frac{(a+b x) \sqrt{c+d x} \left (A+B x+C x^2\right )}{\sqrt{e+f x}} \, dx\)
 3.83 \(\int \frac{\sqrt{c+d x} \left (A+B x+C x^2\right )}{\sqrt{e+f x}} \, dx\)
 3.84 \(\int \frac{\sqrt{c+d x} \left (A+B x+C x^2\right )}{(a+b x) \sqrt{e+f x}} \, dx\)
 3.85 \(\int \frac{\sqrt{c+d x} \left (A+B x+C x^2\right )}{(a+b x)^2 \sqrt{e+f x}} \, dx\)
 3.86 \(\int \frac{\sqrt{c+d x} \left (A+B x+C x^2\right )}{(a+b x)^3 \sqrt{e+f x}} \, dx\)
 3.87 \(\int \frac{\sqrt{c+d x} \left (A+B x+C x^2\right )}{(a+b x)^4 \sqrt{e+f x}} \, dx\)
 3.88 \(\int \frac{(a+b x)^2 \left (A+B x+C x^2\right )}{\sqrt{c+d x} \sqrt{e+f x}} \, dx\)
 3.89 \(\int \frac{(a+b x) \left (A+B x+C x^2\right )}{\sqrt{c+d x} \sqrt{e+f x}} \, dx\)
 3.90 \(\int \frac{A+B x+C x^2}{\sqrt{c+d x} \sqrt{e+f x}} \, dx\)
 3.91 \(\int \frac{A+B x+C x^2}{(a+b x) \sqrt{c+d x} \sqrt{e+f x}} \, dx\)
 3.92 \(\int \frac{A+B x+C x^2}{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x}} \, dx\)
 3.93 \(\int \frac{A+B x+C x^2}{(a+b x)^3 \sqrt{c+d x} \sqrt{e+f x}} \, dx\)
 3.94 \(\int \frac{A+B x+C x^2}{(a+b x)^4 \sqrt{c+d x} \sqrt{e+f x}} \, dx\)
 3.95 \(\int \sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \left (A+B x+C x^2\right ) \, dx\)
 3.96 \(\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left (A+B x+C x^2\right )}{\sqrt{a+b x}} \, dx\)
 3.97 \(\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left (A+B x+C x^2\right )}{(a+b x)^{3/2}} \, dx\)
 3.98 \(\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left (A+B x+C x^2\right )}{(a+b x)^{5/2}} \, dx\)
 3.99 \(\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left (A+B x+C x^2\right )}{(a+b x)^{7/2}} \, dx\)
 3.100 \(\int \frac{\sqrt{c+d x} \sqrt{e+f x} \left (A+B x+C x^2\right )}{(a+b x)^{9/2}} \, dx\)
 3.101 \(\int \frac{(a+b x)^{3/2} \sqrt{c+d x} \left (A+B x+C x^2\right )}{\sqrt{e+f x}} \, dx\)
 3.102 \(\int \frac{\sqrt{a+b x} \sqrt{c+d x} \left (A+B x+C x^2\right )}{\sqrt{e+f x}} \, dx\)
 3.103 \(\int \frac{\sqrt{c+d x} \left (A+B x+C x^2\right )}{\sqrt{a+b x} \sqrt{e+f x}} \, dx\)
 3.104 \(\int \frac{\sqrt{c+d x} \left (A+B x+C x^2\right )}{(a+b x)^{3/2} \sqrt{e+f x}} \, dx\)
 3.105 \(\int \frac{\sqrt{c+d x} \left (A+B x+C x^2\right )}{(a+b x)^{5/2} \sqrt{e+f x}} \, dx\)
 3.106 \(\int \frac{\sqrt{c+d x} \left (A+B x+C x^2\right )}{(a+b x)^{7/2} \sqrt{e+f x}} \, dx\)
 3.107 \(\int \frac{(a+b x)^{3/2} \left (A+B x+C x^2\right )}{\sqrt{c+d x} \sqrt{e+f x}} \, dx\)
 3.108 \(\int \frac{\sqrt{a+b x} \left (A+B x+C x^2\right )}{\sqrt{c+d x} \sqrt{e+f x}} \, dx\)
 3.109 \(\int \frac{A+B x+C x^2}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x}} \, dx\)
 3.110 \(\int \frac{A+B x+C x^2}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx\)
 3.111 \(\int \frac{A+B x+C x^2}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx\)
 3.112 \(\int \frac{A+B x+C x^2}{(a+b x)^{7/2} \sqrt{c+d x} \sqrt{e+f x}} \, dx\)
 3.113 \(\int \frac{(a+b x) \left (a b B-a^2 C+b^2 B x+b^2 C x^2\right )}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.114 \(\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.115 \(\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.116 \(\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.117 \(\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{(a+b x)^3 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.118 \(\int \frac{\sqrt{a+b x} \left (a b B-a^2 C+b^2 B x+b^2 C x^2\right )}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.119 \(\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.120 \(\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.121 \(\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.122 \(\int \frac{a b B-a^2 C+b^2 B x+b^2 C x^2}{(a+b x)^{7/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.123 \(\int \frac{(a+b x)^2 (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.124 \(\int \frac{(a+b x) (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.125 \(\int \frac{A+B x}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.126 \(\int \frac{A+B x}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.127 \(\int \frac{A+B x}{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.128 \(\int \frac{(a+b x)^{3/2} (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.129 \(\int \frac{\sqrt{a+b x} (A+B x)}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.130 \(\int \frac{A+B x}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.131 \(\int \frac{A+B x}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.132 \(\int \frac{A+B x}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.133 \(\int \frac{(a+b x)^2 \left (A+C x^2\right )}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.134 \(\int \frac{(a+b x) \left (A+C x^2\right )}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.135 \(\int \frac{A+C x^2}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.136 \(\int \frac{A+C x^2}{(a+b x) \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.137 \(\int \frac{A+C x^2}{(a+b x)^2 \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.138 \(\int \frac{(a+b x)^{3/2} \left (A+C x^2\right )}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.139 \(\int \frac{\sqrt{a+b x} \left (A+C x^2\right )}{\sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.140 \(\int \frac{A+C x^2}{\sqrt{a+b x} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.141 \(\int \frac{A+C x^2}{(a+b x)^{3/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)
 3.142 \(\int \frac{A+C x^2}{(a+b x)^{5/2} \sqrt{c+d x} \sqrt{e+f x} \sqrt{g+h x}} \, dx\)