Chapter 3
Listing of integrals

 3.1 \(\int x^2 (a x^2+b x^3+c x^4) \, dx\)
 3.2 \(\int x (a x^2+b x^3+c x^4) \, dx\)
 3.3 \(\int (a x^2+b x^3+c x^4) \, dx\)
 3.4 \(\int \frac{a x^2+b x^3+c x^4}{x} \, dx\)
 3.5 \(\int \frac{a x^2+b x^3+c x^4}{x^2} \, dx\)
 3.6 \(\int x^2 (a x^2+b x^3+c x^4)^2 \, dx\)
 3.7 \(\int x (a x^2+b x^3+c x^4)^2 \, dx\)
 3.8 \(\int (a x^2+b x^3+c x^4)^2 \, dx\)
 3.9 \(\int \frac{(a x^2+b x^3+c x^4)^2}{x} \, dx\)
 3.10 \(\int \frac{(a x^2+b x^3+c x^4)^2}{x^2} \, dx\)
 3.11 \(\int \frac{x^5}{a x^2+b x^3+c x^4} \, dx\)
 3.12 \(\int \frac{x^4}{a x^2+b x^3+c x^4} \, dx\)
 3.13 \(\int \frac{x^3}{a x^2+b x^3+c x^4} \, dx\)
 3.14 \(\int \frac{x^2}{a x^2+b x^3+c x^4} \, dx\)
 3.15 \(\int \frac{x}{a x^2+b x^3+c x^4} \, dx\)
 3.16 \(\int \frac{1}{a x^2+b x^3+c x^4} \, dx\)
 3.17 \(\int \frac{1}{x (a x^2+b x^3+c x^4)} \, dx\)
 3.18 \(\int \frac{1}{x^2 (a x^2+b x^3+c x^4)} \, dx\)
 3.19 \(\int \frac{x^8}{(a x^2+b x^3+c x^4)^2} \, dx\)
 3.20 \(\int \frac{x^7}{(a x^2+b x^3+c x^4)^2} \, dx\)
 3.21 \(\int \frac{x^6}{(a x^2+b x^3+c x^4)^2} \, dx\)
 3.22 \(\int \frac{x^5}{(a x^2+b x^3+c x^4)^2} \, dx\)
 3.23 \(\int \frac{x^4}{(a x^2+b x^3+c x^4)^2} \, dx\)
 3.24 \(\int \frac{x^3}{(a x^2+b x^3+c x^4)^2} \, dx\)
 3.25 \(\int \frac{x^2}{(a x^2+b x^3+c x^4)^2} \, dx\)
 3.26 \(\int \frac{x}{(a x^2+b x^3+c x^4)^2} \, dx\)
 3.27 \(\int \frac{1}{(a x^2+b x^3+c x^4)^2} \, dx\)
 3.28 \(\int \frac{1}{x (a x^2+b x^3+c x^4)^2} \, dx\)
 3.29 \(\int x^2 \sqrt{a x^2+b x^3+c x^4} \, dx\)
 3.30 \(\int x \sqrt{a x^2+b x^3+c x^4} \, dx\)
 3.31 \(\int \sqrt{a x^2+b x^3+c x^4} \, dx\)
 3.32 \(\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x} \, dx\)
 3.33 \(\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^2} \, dx\)
 3.34 \(\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^3} \, dx\)
 3.35 \(\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^4} \, dx\)
 3.36 \(\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^5} \, dx\)
 3.37 \(\int \frac{\sqrt{a x^2+b x^3+c x^4}}{x^6} \, dx\)
 3.38 \(\int x (a x^2+b x^3+c x^4)^{3/2} \, dx\)
 3.39 \(\int (a x^2+b x^3+c x^4)^{3/2} \, dx\)
 3.40 \(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x} \, dx\)
 3.41 \(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^2} \, dx\)
 3.42 \(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^3} \, dx\)
 3.43 \(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^4} \, dx\)
 3.44 \(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^5} \, dx\)
 3.45 \(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^6} \, dx\)
 3.46 \(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^7} \, dx\)
 3.47 \(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^8} \, dx\)
 3.48 \(\int \frac{(a x^2+b x^3+c x^4)^{3/2}}{x^9} \, dx\)
 3.49 \(\int \frac{x^3}{\sqrt{a x^2+b x^3+c x^4}} \, dx\)
 3.50 \(\int \frac{x^2}{\sqrt{a x^2+b x^3+c x^4}} \, dx\)
 3.51 \(\int \frac{x}{\sqrt{a x^2+b x^3+c x^4}} \, dx\)
 3.52 \(\int \frac{1}{\sqrt{a x^2+b x^3+c x^4}} \, dx\)
 3.53 \(\int \frac{1}{x \sqrt{a x^2+b x^3+c x^4}} \, dx\)
 3.54 \(\int \frac{1}{x^2 \sqrt{a x^2+b x^3+c x^4}} \, dx\)
 3.55 \(\int \frac{x^7}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
 3.56 \(\int \frac{x^6}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
 3.57 \(\int \frac{x^5}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
 3.58 \(\int \frac{x^4}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
 3.59 \(\int \frac{x^3}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
 3.60 \(\int \frac{x^2}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
 3.61 \(\int \frac{x}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
 3.62 \(\int \frac{1}{(a x^2+b x^3+c x^4)^{3/2}} \, dx\)
 3.63 \(\int \frac{1}{x (a x^2+b x^3+c x^4)^{3/2}} \, dx\)
 3.64 \(\int \frac{1}{x^2 (a x^2+b x^3+c x^4)^{3/2}} \, dx\)
 3.65 \(\int x^m (a x+b x^3+c x^5) \, dx\)
 3.66 \(\int x^2 (a x+b x^3+c x^5) \, dx\)
 3.67 \(\int x (a x+b x^3+c x^5) \, dx\)
 3.68 \(\int (a x+b x^3+c x^5) \, dx\)
 3.69 \(\int \frac{a x+b x^3+c x^5}{x} \, dx\)
 3.70 \(\int \frac{a x+b x^3+c x^5}{x^2} \, dx\)
 3.71 \(\int \frac{a x+b x^3+c x^5}{x^3} \, dx\)
 3.72 \(\int x^m (a x+b x^3+c x^5)^2 \, dx\)
 3.73 \(\int x^2 (a x+b x^3+c x^5)^2 \, dx\)
 3.74 \(\int x (a x+b x^3+c x^5)^2 \, dx\)
 3.75 \(\int (a x+b x^3+c x^5)^2 \, dx\)
 3.76 \(\int \frac{(a x+b x^3+c x^5)^2}{x} \, dx\)
 3.77 \(\int \frac{(a x+b x^3+c x^5)^2}{x^2} \, dx\)
 3.78 \(\int \frac{x^8}{a x+b x^3+c x^5} \, dx\)
 3.79 \(\int \frac{x^7}{a x+b x^3+c x^5} \, dx\)
 3.80 \(\int \frac{x^6}{a x+b x^3+c x^5} \, dx\)
 3.81 \(\int \frac{x^5}{a x+b x^3+c x^5} \, dx\)
 3.82 \(\int \frac{x^4}{a x+b x^3+c x^5} \, dx\)
 3.83 \(\int \frac{x^3}{a x+b x^3+c x^5} \, dx\)
 3.84 \(\int \frac{x^2}{a x+b x^3+c x^5} \, dx\)
 3.85 \(\int \frac{x}{a x+b x^3+c x^5} \, dx\)
 3.86 \(\int \frac{1}{a x+b x^3+c x^5} \, dx\)
 3.87 \(\int \frac{1}{x (a x+b x^3+c x^5)} \, dx\)
 3.88 \(\int \frac{1}{x^2 (a x+b x^3+c x^5)} \, dx\)
 3.89 \(\int \frac{x^{11}}{(a x+b x^3+c x^5)^2} \, dx\)
 3.90 \(\int \frac{x^{10}}{(a x+b x^3+c x^5)^2} \, dx\)
 3.91 \(\int \frac{x^9}{(a x+b x^3+c x^5)^2} \, dx\)
 3.92 \(\int \frac{x^8}{(a x+b x^3+c x^5)^2} \, dx\)
 3.93 \(\int \frac{x^7}{(a x+b x^3+c x^5)^2} \, dx\)
 3.94 \(\int \frac{x^6}{(a x+b x^3+c x^5)^2} \, dx\)
 3.95 \(\int \frac{x^5}{(a x+b x^3+c x^5)^2} \, dx\)
 3.96 \(\int \frac{x^4}{(a x+b x^3+c x^5)^2} \, dx\)
 3.97 \(\int \frac{x^3}{(a x+b x^3+c x^5)^2} \, dx\)
 3.98 \(\int \frac{x^2}{(a x+b x^3+c x^5)^2} \, dx\)
 3.99 \(\int \frac{x}{(a x+b x^3+c x^5)^2} \, dx\)
 3.100 \(\int \frac{1}{(a x+b x^3+c x^5)^2} \, dx\)
 3.101 \(\int \frac{1}{x (a x+b x^3+c x^5)^2} \, dx\)
 3.102 \(\int \frac{1}{x^2 (a x+b x^3+c x^5)^2} \, dx\)
 3.103 \(\int \frac{1}{x^3 (a x+b x^3+c x^5)^2} \, dx\)
 3.104 \(\int \frac{x}{\sqrt{a x+b x^3+c x^5}} \, dx\)
 3.105 \(\int x^{3/2} \sqrt{a x+b x^3+c x^5} \, dx\)
 3.106 \(\int \sqrt{x} \sqrt{a x+b x^3+c x^5} \, dx\)
 3.107 \(\int \frac{\sqrt{a x+b x^3+c x^5}}{\sqrt{x}} \, dx\)
 3.108 \(\int \frac{\sqrt{a x+b x^3+c x^5}}{x^{3/2}} \, dx\)
 3.109 \(\int x^{3/2} (a x+b x^3+c x^5)^{3/2} \, dx\)
 3.110 \(\int \sqrt{x} (a x+b x^3+c x^5)^{3/2} \, dx\)
 3.111 \(\int \frac{(a x+b x^3+c x^5)^{3/2}}{\sqrt{x}} \, dx\)
 3.112 \(\int \frac{(a x+b x^3+c x^5)^{3/2}}{x^{3/2}} \, dx\)
 3.113 \(\int \frac{x^{3/2}}{\sqrt{a x+b x^3+c x^5}} \, dx\)
 3.114 \(\int \frac{\sqrt{x}}{\sqrt{a x+b x^3+c x^5}} \, dx\)
 3.115 \(\int \frac{1}{\sqrt{x} \sqrt{a x+b x^3+c x^5}} \, dx\)
 3.116 \(\int \frac{1}{x^{3/2} \sqrt{a x+b x^3+c x^5}} \, dx\)
 3.117 \(\int \frac{x^{3/2}}{(a x+b x^3+c x^5)^{3/2}} \, dx\)
 3.118 \(\int \frac{\sqrt{x}}{(a x+b x^3+c x^5)^{3/2}} \, dx\)
 3.119 \(\int \frac{1}{\sqrt{x} (a x+b x^3+c x^5)^{3/2}} \, dx\)
 3.120 \(\int \frac{1}{x^{3/2} (a x+b x^3+c x^5)^{3/2}} \, dx\)
 3.121 \(\int \frac{x^{\frac{3}{2} (-1+n)}}{(a x^{-1+n}+b x^n+c x^{1+n})^{3/2}} \, dx\)
 3.122 \(\int \frac{x (d+e x^2)}{\sqrt{a x+b x^3+c x^5}} \, dx\)
 3.123 \(\int \frac{1}{\sqrt{3 x^2-3 x^4+x^6}} \, dx\)
 3.124 \(\int \frac{1}{\sqrt{x^2 (3-3 x^2+x^4)}} \, dx\)
 3.125 \(\int \frac{1}{\sqrt{1-(1-x^2)^3}} \, dx\)
 3.126 \(\int \sqrt{3 x^2-3 x^4+x^6} \, dx\)
 3.127 \(\int \sqrt{x^2 (3-3 x^2+x^4)} \, dx\)
 3.128 \(\int \sqrt{1-(1-x^2)^3} \, dx\)
 3.129 \(\int \frac{1}{x \sqrt{a+b x+c x^2}} \, dx\)
 3.130 \(\int \frac{1}{\sqrt{x^2 (a+b x+c x^2)}} \, dx\)
 3.131 \(\int \frac{1}{\sqrt{x} \sqrt{x (a+b x+c x^2)}} \, dx\)
 3.132 \(\int \frac{\sqrt{x}}{\sqrt{x^3 (a+b x+c x^2)}} \, dx\)
 3.133 \(\int \frac{1}{x \sqrt{a+b x^2+c x^4}} \, dx\)
 3.134 \(\int \frac{1}{\sqrt{x^2 (a+b x^2+c x^4)}} \, dx\)
 3.135 \(\int \frac{1}{\sqrt{x} \sqrt{x (a+b x^2+c x^4)}} \, dx\)
 3.136 \(\int \frac{\sqrt{x}}{\sqrt{x^3 (a+b x^2+c x^4)}} \, dx\)
 3.137 \(\int \frac{1}{x \sqrt{3-3 x^2+x^4}} \, dx\)
 3.138 \(\int \frac{1}{\sqrt{x^2 (3-3 x^2+x^4)}} \, dx\)
 3.139 \(\int \frac{1}{\sqrt{x} \sqrt{x (3-3 x+x^2)}} \, dx\)
 3.140 \(\int \frac{x^{-1+\frac{q}{2}}}{\sqrt{b x^n+c x^{2 n-q}+a x^q}} \, dx\)