Chapter 3
Listing of integrals

 3.1 \(\int \frac{a+b x+\frac{b f x^2}{e}}{\sqrt{d+e x+f x^2}} \, dx\)
 3.2 \(\int \frac{1}{\sqrt{d+e x+f x^2} (a+b x+\frac{b f x^2}{e})} \, dx\)
 3.3 \(\int \frac{1}{\sqrt{a+b x+c x^2} (d+b x+c x^2)} \, dx\)
 3.4 \(\int \frac{1}{\sqrt{a+b x+c x^2} (d+b x+c x^2)^2} \, dx\)
 3.5 \(\int \frac{1}{\sqrt{a+b x+c x^2} (d+b x+c x^2)^3} \, dx\)
 3.6 \(\int \frac{1}{\sqrt{a+b x+c x^2} (d+b x+c x^2)^4} \, dx\)
 3.7 \(\int \frac{1}{\sqrt{d+e x+f x^2} (a e+b e x+b f x^2)^2} \, dx\)
 3.8 \(\int \frac{1}{(4+2 x+x^2) \sqrt{5+2 x+x^2}} \, dx\)
 3.9 \(\int (a+\frac{e x}{2}+c x^2)^p (2 a+e x+2 c x^2)^q \, dx\)
 3.10 \(\int (a+\frac{c e x}{f}+c x^2)^p (\frac{a f}{c}+e x+f x^2)^q \, dx\)
 3.11 \(\int \frac{\sqrt{1+2 x+x^2}}{\sqrt{1+x^2}} \, dx\)
 3.12 \(\int \frac{1}{(-1+x^2)^2 \sqrt{-1+x+x^2}} \, dx\)
 3.13 \(\int \frac{1}{\sqrt{a+b x+c x^2} \sqrt{d+f x^2}} \, dx\)
 3.14 \(\int \frac{\sqrt{-3-4 x-x^2}}{3+4 x+2 x^2} \, dx\)
 3.15 \(\int (3-x+2 x^2) (2+3 x+5 x^2)^4 \, dx\)
 3.16 \(\int (3-x+2 x^2) (2+3 x+5 x^2)^3 \, dx\)
 3.17 \(\int (3-x+2 x^2) (2+3 x+5 x^2)^2 \, dx\)
 3.18 \(\int (3-x+2 x^2) (2+3 x+5 x^2) \, dx\)
 3.19 \(\int \frac{3-x+2 x^2}{2+3 x+5 x^2} \, dx\)
 3.20 \(\int \frac{3-x+2 x^2}{(2+3 x+5 x^2)^2} \, dx\)
 3.21 \(\int \frac{3-x+2 x^2}{(2+3 x+5 x^2)^3} \, dx\)
 3.22 \(\int (3-x+2 x^2)^2 (2+3 x+5 x^2)^4 \, dx\)
 3.23 \(\int (3-x+2 x^2)^2 (2+3 x+5 x^2)^3 \, dx\)
 3.24 \(\int (3-x+2 x^2)^2 (2+3 x+5 x^2)^2 \, dx\)
 3.25 \(\int (3-x+2 x^2)^2 (2+3 x+5 x^2) \, dx\)
 3.26 \(\int \frac{(3-x+2 x^2)^2}{2+3 x+5 x^2} \, dx\)
 3.27 \(\int \frac{(3-x+2 x^2)^2}{(2+3 x+5 x^2)^2} \, dx\)
 3.28 \(\int \frac{(3-x+2 x^2)^2}{(2+3 x+5 x^2)^3} \, dx\)
 3.29 \(\int \frac{(3-x+2 x^2)^2}{(2+3 x+5 x^2)^4} \, dx\)
 3.30 \(\int (3-x+2 x^2)^3 (2+3 x+5 x^2)^4 \, dx\)
 3.31 \(\int (3-x+2 x^2)^3 (2+3 x+5 x^2)^3 \, dx\)
 3.32 \(\int (3-x+2 x^2)^3 (2+3 x+5 x^2)^2 \, dx\)
 3.33 \(\int (3-x+2 x^2)^3 (2+3 x+5 x^2) \, dx\)
 3.34 \(\int \frac{(3-x+2 x^2)^3}{2+3 x+5 x^2} \, dx\)
 3.35 \(\int \frac{(3-x+2 x^2)^3}{(2+3 x+5 x^2)^2} \, dx\)
 3.36 \(\int \frac{(3-x+2 x^2)^3}{(2+3 x+5 x^2)^3} \, dx\)
 3.37 \(\int \frac{(2+3 x+5 x^2)^4}{3-x+2 x^2} \, dx\)
 3.38 \(\int \frac{(2+3 x+5 x^2)^3}{3-x+2 x^2} \, dx\)
 3.39 \(\int \frac{(2+3 x+5 x^2)^2}{3-x+2 x^2} \, dx\)
 3.40 \(\int \frac{2+3 x+5 x^2}{3-x+2 x^2} \, dx\)
 3.41 \(\int \frac{1}{(3-x+2 x^2) (2+3 x+5 x^2)} \, dx\)
 3.42 \(\int \frac{1}{(3-x+2 x^2) (2+3 x+5 x^2)^2} \, dx\)
 3.43 \(\int \frac{1}{(3-x+2 x^2) (2+3 x+5 x^2)^3} \, dx\)
 3.44 \(\int \frac{(2+3 x+5 x^2)^4}{(3-x+2 x^2)^2} \, dx\)
 3.45 \(\int \frac{(2+3 x+5 x^2)^3}{(3-x+2 x^2)^2} \, dx\)
 3.46 \(\int \frac{(2+3 x+5 x^2)^2}{(3-x+2 x^2)^2} \, dx\)
 3.47 \(\int \frac{2+3 x+5 x^2}{(3-x+2 x^2)^2} \, dx\)
 3.48 \(\int \frac{1}{(3-x+2 x^2)^2 (2+3 x+5 x^2)} \, dx\)
 3.49 \(\int \frac{1}{(3-x+2 x^2)^2 (2+3 x+5 x^2)^2} \, dx\)
 3.50 \(\int \frac{1}{(3-x+2 x^2)^2 (2+3 x+5 x^2)^3} \, dx\)
 3.51 \(\int \frac{(2+3 x+5 x^2)^4}{(3-x+2 x^2)^3} \, dx\)
 3.52 \(\int \frac{(2+3 x+5 x^2)^3}{(3-x+2 x^2)^3} \, dx\)
 3.53 \(\int \frac{(2+3 x+5 x^2)^2}{(3-x+2 x^2)^3} \, dx\)
 3.54 \(\int \frac{2+3 x+5 x^2}{(3-x+2 x^2)^3} \, dx\)
 3.55 \(\int \frac{1}{(3-x+2 x^2)^3 (2+3 x+5 x^2)} \, dx\)
 3.56 \(\int \frac{1}{(3-x+2 x^2)^3 (2+3 x+5 x^2)^2} \, dx\)
 3.57 \(\int \frac{1}{(3-x+2 x^2)^3 (2+3 x+5 x^2)^3} \, dx\)
 3.58 \(\int \sqrt{3-x+2 x^2} (2+3 x+5 x^2)^4 \, dx\)
 3.59 \(\int \sqrt{3-x+2 x^2} (2+3 x+5 x^2)^3 \, dx\)
 3.60 \(\int \sqrt{3-x+2 x^2} (2+3 x+5 x^2)^2 \, dx\)
 3.61 \(\int \sqrt{3-x+2 x^2} (2+3 x+5 x^2) \, dx\)
 3.62 \(\int \frac{\sqrt{3-x+2 x^2}}{2+3 x+5 x^2} \, dx\)
 3.63 \(\int \frac{\sqrt{3-x+2 x^2}}{(2+3 x+5 x^2)^2} \, dx\)
 3.64 \(\int \frac{\sqrt{3-x+2 x^2}}{(2+3 x+5 x^2)^3} \, dx\)
 3.65 \(\int (3-x+2 x^2)^{3/2} (2+3 x+5 x^2)^4 \, dx\)
 3.66 \(\int (3-x+2 x^2)^{3/2} (2+3 x+5 x^2)^3 \, dx\)
 3.67 \(\int (3-x+2 x^2)^{3/2} (2+3 x+5 x^2)^2 \, dx\)
 3.68 \(\int (3-x+2 x^2)^{3/2} (2+3 x+5 x^2) \, dx\)
 3.69 \(\int \frac{(3-x+2 x^2)^{3/2}}{2+3 x+5 x^2} \, dx\)
 3.70 \(\int \frac{(3-x+2 x^2)^{3/2}}{(2+3 x+5 x^2)^2} \, dx\)
 3.71 \(\int \frac{(3-x+2 x^2)^{3/2}}{(2+3 x+5 x^2)^3} \, dx\)
 3.72 \(\int (3-x+2 x^2)^{5/2} (2+3 x+5 x^2)^4 \, dx\)
 3.73 \(\int (3-x+2 x^2)^{5/2} (2+3 x+5 x^2)^3 \, dx\)
 3.74 \(\int (3-x+2 x^2)^{5/2} (2+3 x+5 x^2)^2 \, dx\)
 3.75 \(\int (3-x+2 x^2)^{5/2} (2+3 x+5 x^2) \, dx\)
 3.76 \(\int \frac{(3-x+2 x^2)^{5/2}}{2+3 x+5 x^2} \, dx\)
 3.77 \(\int \frac{(3-x+2 x^2)^{5/2}}{(2+3 x+5 x^2)^2} \, dx\)
 3.78 \(\int \frac{(3-x+2 x^2)^{5/2}}{(2+3 x+5 x^2)^3} \, dx\)
 3.79 \(\int \frac{(2+3 x+5 x^2)^4}{\sqrt{3-x+2 x^2}} \, dx\)
 3.80 \(\int \frac{(2+3 x+5 x^2)^3}{\sqrt{3-x+2 x^2}} \, dx\)
 3.81 \(\int \frac{(2+3 x+5 x^2)^2}{\sqrt{3-x+2 x^2}} \, dx\)
 3.82 \(\int \frac{2+3 x+5 x^2}{\sqrt{3-x+2 x^2}} \, dx\)
 3.83 \(\int \frac{1}{\sqrt{3-x+2 x^2} (2+3 x+5 x^2)} \, dx\)
 3.84 \(\int \frac{1}{\sqrt{3-x+2 x^2} (2+3 x+5 x^2)^2} \, dx\)
 3.85 \(\int \frac{1}{\sqrt{3-x+2 x^2} (2+3 x+5 x^2)^3} \, dx\)
 3.86 \(\int \frac{(2+3 x+5 x^2)^4}{(3-x+2 x^2)^{3/2}} \, dx\)
 3.87 \(\int \frac{(2+3 x+5 x^2)^3}{(3-x+2 x^2)^{3/2}} \, dx\)
 3.88 \(\int \frac{(2+3 x+5 x^2)^2}{(3-x+2 x^2)^{3/2}} \, dx\)
 3.89 \(\int \frac{2+3 x+5 x^2}{(3-x+2 x^2)^{3/2}} \, dx\)
 3.90 \(\int \frac{1}{(3-x+2 x^2)^{3/2} (2+3 x+5 x^2)} \, dx\)
 3.91 \(\int \frac{1}{(3-x+2 x^2)^{3/2} (2+3 x+5 x^2)^2} \, dx\)
 3.92 \(\int \frac{1}{(3-x+2 x^2)^{3/2} (2+3 x+5 x^2)^3} \, dx\)
 3.93 \(\int \frac{(2+3 x+5 x^2)^4}{(3-x+2 x^2)^{5/2}} \, dx\)
 3.94 \(\int \frac{(2+3 x+5 x^2)^3}{(3-x+2 x^2)^{5/2}} \, dx\)
 3.95 \(\int \frac{(2+3 x+5 x^2)^2}{(3-x+2 x^2)^{5/2}} \, dx\)
 3.96 \(\int \frac{2+3 x+5 x^2}{(3-x+2 x^2)^{5/2}} \, dx\)
 3.97 \(\int \frac{1}{(3-x+2 x^2)^{5/2} (2+3 x+5 x^2)} \, dx\)
 3.98 \(\int \frac{1}{(3-x+2 x^2)^{5/2} (2+3 x+5 x^2)^2} \, dx\)
 3.99 \(\int \frac{1}{(3-x+2 x^2)^{5/2} (2+3 x+5 x^2)^3} \, dx\)
 3.100 \(\int \sqrt{a+b x+c x^2} (d+e x+f x^2)^2 \, dx\)
 3.101 \(\int \sqrt{a+b x+c x^2} (d+e x+f x^2) \, dx\)
 3.102 \(\int \frac{\sqrt{a+b x+c x^2}}{d+e x+f x^2} \, dx\)
 3.103 \(\int \frac{\sqrt{a+b x+c x^2}}{(d+e x+f x^2)^2} \, dx\)
 3.104 \(\int (a+b x+c x^2)^{3/2} (d+e x+f x^2)^2 \, dx\)
 3.105 \(\int (a+b x+c x^2)^{3/2} (d+e x+f x^2) \, dx\)
 3.106 \(\int \frac{(a+b x+c x^2)^{3/2}}{d+e x+f x^2} \, dx\)
 3.107 \(\int \frac{(a+b x+c x^2)^{3/2}}{(d+e x+f x^2)^2} \, dx\)
 3.108 \(\int \frac{(a+b x+c x^2)^{3/2}}{(d+e x+f x^2)^3} \, dx\)
 3.109 \(\int \frac{(d+e x+f x^2)^3}{\sqrt{a+b x+c x^2}} \, dx\)
 3.110 \(\int \frac{(d+e x+f x^2)^2}{\sqrt{a+b x+c x^2}} \, dx\)
 3.111 \(\int \frac{d+e x+f x^2}{\sqrt{a+b x+c x^2}} \, dx\)
 3.112 \(\int \frac{1}{\sqrt{a+b x+c x^2} (d+e x+f x^2)} \, dx\)
 3.113 \(\int \frac{1}{\sqrt{a+b x+c x^2} (d+e x+f x^2)^2} \, dx\)
 3.114 \(\int \frac{(d+e x+f x^2)^3}{(a+b x+c x^2)^{3/2}} \, dx\)
 3.115 \(\int \frac{(d+e x+f x^2)^2}{(a+b x+c x^2)^{3/2}} \, dx\)
 3.116 \(\int \frac{d+e x+f x^2}{(a+b x+c x^2)^{3/2}} \, dx\)
 3.117 \(\int \frac{1}{(a+b x+c x^2)^{3/2} (d+e x+f x^2)} \, dx\)
 3.118 \(\int \frac{(d+e x+f x^2)^3}{(a+b x+c x^2)^{5/2}} \, dx\)
 3.119 \(\int \frac{(d+e x+f x^2)^2}{(a+b x+c x^2)^{5/2}} \, dx\)
 3.120 \(\int \frac{d+e x+f x^2}{(a+b x+c x^2)^{5/2}} \, dx\)
 3.121 \(\int \frac{1}{\sqrt{-7+2 x+5 x^2} (8+12 x+5 x^2)} \, dx\)
 3.122 \(\int \frac{1}{\sqrt{a+b x+c x^2} \sqrt{d+e x+f x^2}} \, dx\)
 3.123 \(\int \frac{1}{\sqrt{3-x+2 x^2} \sqrt{2+3 x+5 x^2}} \, dx\)