Chapter 3
Listing of integrals

 3.1 \(\int (b x+c x^2)^{7/2} \, dx\)
 3.2 \(\int (3 i x+4 x^2)^{7/2} \, dx\)
 3.3 \(\int (3 i x+4 x^2)^{5/2} \, dx\)
 3.4 \(\int (3 i x+4 x^2)^{3/2} \, dx\)
 3.5 \(\int \sqrt{3 i x+4 x^2} \, dx\)
 3.6 \(\int (3 x-4 x^2)^{7/2} \, dx\)
 3.7 \(\int (3 x-4 x^2)^{5/2} \, dx\)
 3.8 \(\int (3 x-4 x^2)^{3/2} \, dx\)
 3.9 \(\int \sqrt{3 x-4 x^2} \, dx\)
 3.10 \(\int \sqrt{6 x-x^2} \, dx\)
 3.11 \(\int \sqrt{5 x-9 x^2} \, dx\)
 3.12 \(\int (x-x^2)^{3/2} \, dx\)
 3.13 \(\int \sqrt{4 x+x^2} \, dx\)
 3.14 \(\int \sqrt{-8 x+x^2} \, dx\)
 3.15 \(\int \sqrt{-x+x^2} \, dx\)
 3.16 \(\int \frac{1}{(b x+c x^2)^{7/2}} \, dx\)
 3.17 \(\int \frac{1}{\sqrt{3 i x+4 x^2}} \, dx\)
 3.18 \(\int \frac{1}{(3 i x+4 x^2)^{3/2}} \, dx\)
 3.19 \(\int \frac{1}{(3 i x+4 x^2)^{5/2}} \, dx\)
 3.20 \(\int \frac{1}{(3 i x+4 x^2)^{7/2}} \, dx\)
 3.21 \(\int \frac{1}{\sqrt{3 x-4 x^2}} \, dx\)
 3.22 \(\int \frac{1}{(3 x-4 x^2)^{3/2}} \, dx\)
 3.23 \(\int \frac{1}{(3 x-4 x^2)^{5/2}} \, dx\)
 3.24 \(\int \frac{1}{(3 x-4 x^2)^{7/2}} \, dx\)
 3.25 \(\int \frac{1}{\sqrt{b x-b^2 x^2}} \, dx\)
 3.26 \(\int \frac{1}{\sqrt{b x+b^2 x^2}} \, dx\)
 3.27 \(\int \frac{1}{\sqrt{6 x-x^2}} \, dx\)
 3.28 \(\int \frac{1}{\sqrt{4 x+x^2}} \, dx\)
 3.29 \(\int \frac{1}{\sqrt{-2 x+x^2}} \, dx\)
 3.30 \(\int (b x+c x^2)^{4/3} \, dx\)
 3.31 \(\int \sqrt [3]{b x+c x^2} \, dx\)
 3.32 \(\int \frac{1}{(b x+c x^2)^{2/3}} \, dx\)
 3.33 \(\int \frac{1}{(b x+c x^2)^{5/3}} \, dx\)
 3.34 \(\int \frac{1}{(b x+c x^2)^{8/3}} \, dx\)
 3.35 \(\int (b x+c x^2)^{5/3} \, dx\)
 3.36 \(\int (b x+c x^2)^{2/3} \, dx\)
 3.37 \(\int \frac{1}{\sqrt [3]{b x+c x^2}} \, dx\)
 3.38 \(\int \frac{1}{(b x+c x^2)^{4/3}} \, dx\)
 3.39 \(\int \frac{1}{(b x+c x^2)^{7/3}} \, dx\)
 3.40 \(\int (b x+c x^2)^{5/4} \, dx\)
 3.41 \(\int (b x+c x^2)^{3/4} \, dx\)
 3.42 \(\int \sqrt [4]{b x+c x^2} \, dx\)
 3.43 \(\int \frac{1}{\sqrt [4]{b x+c x^2}} \, dx\)
 3.44 \(\int \frac{1}{(b x+c x^2)^{3/4}} \, dx\)
 3.45 \(\int \frac{1}{(b x+c x^2)^{5/4}} \, dx\)
 3.46 \(\int \frac{1}{(b x+c x^2)^{9/4}} \, dx\)
 3.47 \(\int \frac{1}{(b x+c x^2)^{13/4}} \, dx\)
 3.48 \(\int (b x+c x^2)^p \, dx\)
 3.49 \(\int (a+c x^2)^4 \, dx\)
 3.50 \(\int (a+c x^2)^3 \, dx\)
 3.51 \(\int (a+c x^2)^2 \, dx\)
 3.52 \(\int (a+c x^2) \, dx\)
 3.53 \(\int \frac{1}{a+c x^2} \, dx\)
 3.54 \(\int \frac{1}{(a+c x^2)^2} \, dx\)
 3.55 \(\int \frac{1}{(a+c x^2)^3} \, dx\)
 3.56 \(\int (a+c x^2)^{5/2} \, dx\)
 3.57 \(\int (a+c x^2)^{3/2} \, dx\)
 3.58 \(\int \sqrt{a+c x^2} \, dx\)
 3.59 \(\int \frac{1}{\sqrt{a+c x^2}} \, dx\)
 3.60 \(\int \frac{1}{(a+c x^2)^{3/2}} \, dx\)
 3.61 \(\int \frac{1}{(a+c x^2)^{5/2}} \, dx\)
 3.62 \(\int \frac{1}{(a+c x^2)^{7/2}} \, dx\)
 3.63 \(\int \frac{1}{(a+c x^2)^{9/2}} \, dx\)
 3.64 \(\int (4+12 x+9 x^2)^{3/2} \, dx\)
 3.65 \(\int \sqrt{4+12 x+9 x^2} \, dx\)
 3.66 \(\int \frac{1}{\sqrt{4+12 x+9 x^2}} \, dx\)
 3.67 \(\int \frac{1}{(4+12 x+9 x^2)^{3/2}} \, dx\)
 3.68 \(\int \sqrt{4-12 x+9 x^2} \, dx\)
 3.69 \(\int \frac{1}{\sqrt{4-12 x+9 x^2}} \, dx\)
 3.70 \(\int \sqrt{-4+12 x-9 x^2} \, dx\)
 3.71 \(\int \frac{1}{\sqrt{-4+12 x-9 x^2}} \, dx\)
 3.72 \(\int \sqrt{-4-12 x-9 x^2} \, dx\)
 3.73 \(\int \frac{1}{\sqrt{-4-12 x-9 x^2}} \, dx\)
 3.74 \(\int (\frac{-1+b^2}{4 c}+b x+c x^2)^5 \, dx\)
 3.75 \(\int (\frac{-4+b^2}{4 c}+b x+c x^2)^5 \, dx\)
 3.76 \(\int (\frac{-9+b^2}{4 c}+b x+c x^2)^5 \, dx\)
 3.77 \(\int (\frac{-16+b^2}{4 c}+b x+c x^2)^5 \, dx\)
 3.78 \(\int \frac{1}{2+4 x+3 x^2} \, dx\)
 3.79 \(\int \frac{1}{4-2 \sqrt{3} x+x^2} \, dx\)
 3.80 \(\int \frac{1}{2+4 x-3 x^2} \, dx\)
 3.81 \(\int \frac{1}{2+5 x+3 x^2} \, dx\)
 3.82 \(\int \frac{1}{2+5 x-3 x^2} \, dx\)
 3.83 \(\int \frac{1}{3+4 x+x^2} \, dx\)
 3.84 \(\int \frac{1}{1+\pi x+2 x^2} \, dx\)
 3.85 \(\int \frac{1}{1+\pi x-2 x^2} \, dx\)
 3.86 \(\int \frac{1}{1+\pi x+3 x^2} \, dx\)
 3.87 \(\int \frac{1}{1+\pi x-3 x^2} \, dx\)
 3.88 \(\int \frac{1}{a+c x+b x^2} \, dx\)
 3.89 \(\int \frac{1}{b+2 a x+b x^2} \, dx\)
 3.90 \(\int \frac{1}{b+2 a x-b x^2} \, dx\)
 3.91 \(\int \frac{1}{(2+4 x+3 x^2)^2} \, dx\)
 3.92 \(\int \frac{1}{(2+4 x-3 x^2)^2} \, dx\)
 3.93 \(\int \frac{1}{(2+5 x+3 x^2)^2} \, dx\)
 3.94 \(\int \frac{1}{(2+5 x-3 x^2)^2} \, dx\)
 3.95 \(\int \frac{1}{(a+c x+b x^2)^2} \, dx\)
 3.96 \(\int \frac{1}{(b+2 a x+b x^2)^2} \, dx\)
 3.97 \(\int \frac{1}{(b+2 a x-b x^2)^2} \, dx\)
 3.98 \(\int \frac{1}{(\frac{a}{b})^{2/n}+x^2-2 (\frac{a}{b})^{\frac{1}{n}} x \cos (\frac{\pi -2 k \pi }{n})} \, dx\)
 3.99 \(\int \frac{1}{a b+\sqrt{b^2-4 a b^3} x-b^2 x^2} \, dx\)
 3.100 \(\int \frac{1}{a b-\sqrt{b^2-4 a b^3} x-b^2 x^2} \, dx\)
 3.101 \(\int \frac{1}{1+x^2+2 x \cos (\frac{1}{7})} \, dx\)
 3.102 \(\int \frac{1}{1+x^2+2 x \cos (\frac{\pi }{7})} \, dx\)
 3.103 \(\int \sqrt{5-6 x+9 x^2} \, dx\)
 3.104 \(\int \sqrt{3-4 x-4 x^2} \, dx\)
 3.105 \(\int \sqrt{-8+6 x+9 x^2} \, dx\)
 3.106 \(\int \sqrt{2+4 x+3 x^2} \, dx\)
 3.107 \(\int \sqrt{2+4 x-3 x^2} \, dx\)
 3.108 \(\int \sqrt{2+5 x+3 x^2} \, dx\)
 3.109 \(\int \sqrt{2+5 x-3 x^2} \, dx\)
 3.110 \(\int \sqrt{-2+4 x+3 x^2} \, dx\)
 3.111 \(\int \sqrt{-2+4 x-3 x^2} \, dx\)
 3.112 \(\int \sqrt{-2+5 x+3 x^2} \, dx\)
 3.113 \(\int \sqrt{-2+5 x-3 x^2} \, dx\)
 3.114 \(\int \frac{1}{\sqrt{5-6 x+9 x^2}} \, dx\)
 3.115 \(\int \frac{1}{\sqrt{3-4 x-4 x^2}} \, dx\)
 3.116 \(\int \frac{1}{\sqrt{-8+6 x+9 x^2}} \, dx\)
 3.117 \(\int \frac{1}{\sqrt{2+4 x+3 x^2}} \, dx\)
 3.118 \(\int \frac{1}{\sqrt{2+4 x-3 x^2}} \, dx\)
 3.119 \(\int \frac{1}{\sqrt{2+5 x+3 x^2}} \, dx\)
 3.120 \(\int \frac{1}{\sqrt{2+5 x-3 x^2}} \, dx\)
 3.121 \(\int \frac{1}{\sqrt{-2+4 x+3 x^2}} \, dx\)
 3.122 \(\int \frac{1}{\sqrt{-2+4 x-3 x^2}} \, dx\)
 3.123 \(\int \frac{1}{\sqrt{-2+5 x+3 x^2}} \, dx\)
 3.124 \(\int \frac{1}{\sqrt{-2+5 x-3 x^2}} \, dx\)
 3.125 \(\int \frac{1}{\sqrt{\frac{b^2+4 c}{4 c}+b x+c x^2}} \, dx\)
 3.126 \(\int \frac{1}{\sqrt{\frac{-b^2+4 c}{4 c}+b x-c x^2}} \, dx\)
 3.127 \(\int \frac{1}{\sqrt{\frac{-b^2+c}{4 c}+b x-c x^2}} \, dx\)
 3.128 \(\int \frac{1}{(2+3 x+x^2)^{3/2}} \, dx\)
 3.129 \(\int \frac{1}{(27-24 x+4 x^2)^{3/2}} \, dx\)
 3.130 \(\int \frac{x}{(5-4 x-x^2)^{3/2}} \, dx\)
 3.131 \(\int \frac{1}{(5-4 x-x^2)^{5/2}} \, dx\)
 3.132 \(\int (a+b x+c x^2)^p \, dx\)
 3.133 \(\int (3+4 x+5 x^2)^p \, dx\)
 3.134 \(\int (3+4 x+4 x^2)^p \, dx\)
 3.135 \(\int (3+4 x+3 x^2)^p \, dx\)
 3.136 \(\int (3+4 x+2 x^2)^p \, dx\)
 3.137 \(\int (3+4 x+x^2)^p \, dx\)
 3.138 \(\int (3+4 x)^p \, dx\)
 3.139 \(\int (3+4 x-x^2)^p \, dx\)
 3.140 \(\int (3+4 x-2 x^2)^p \, dx\)
 3.141 \(\int (3+4 x-3 x^2)^p \, dx\)
 3.142 \(\int (3+4 x-4 x^2)^p \, dx\)
 3.143 \(\int (3+4 x-5 x^2)^p \, dx\)