3.1 \(\int x^3 (A+B x) \sqrt{a+b x^2} \, dx\)
 3.2 \(\int x^2 (A+B x) \sqrt{a+b x^2} \, dx\)
 3.3 \(\int x (A+B x) \sqrt{a+b x^2} \, dx\)
 3.4 \(\int (A+B x) \sqrt{a+b x^2} \, dx\)
 3.5 \(\int \frac{(A+B x) \sqrt{a+b x^2}}{x} \, dx\)
 3.6 \(\int \frac{(A+B x) \sqrt{a+b x^2}}{x^2} \, dx\)
 3.7 \(\int \frac{(A+B x) \sqrt{a+b x^2}}{x^3} \, dx\)
 3.8 \(\int x^3 (A+B x) \left (a+b x^2\right )^{3/2} \, dx\)
 3.9 \(\int x^2 (A+B x) \left (a+b x^2\right )^{3/2} \, dx\)
 3.10 \(\int x (A+B x) \left (a+b x^2\right )^{3/2} \, dx\)
 3.11 \(\int (A+B x) \left (a+b x^2\right )^{3/2} \, dx\)
 3.12 \(\int \frac{(A+B x) \left (a+b x^2\right )^{3/2}}{x} \, dx\)
 3.13 \(\int \frac{(A+B x) \left (a+b x^2\right )^{3/2}}{x^2} \, dx\)
 3.14 \(\int \frac{(A+B x) \left (a+b x^2\right )^{3/2}}{x^3} \, dx\)
 3.15 \(\int x^3 (A+B x) \left (a+b x^2\right )^{5/2} \, dx\)
 3.16 \(\int x^2 (A+B x) \left (a+b x^2\right )^{5/2} \, dx\)
 3.17 \(\int x (A+B x) \left (a+b x^2\right )^{5/2} \, dx\)
 3.18 \(\int (A+B x) \left (a+b x^2\right )^{5/2} \, dx\)
 3.19 \(\int \frac{(A+B x) \left (a+b x^2\right )^{5/2}}{x} \, dx\)
 3.20 \(\int \frac{(A+B x) \left (a+b x^2\right )^{5/2}}{x^2} \, dx\)
 3.21 \(\int \frac{(A+B x) \left (a+b x^2\right )^{5/2}}{x^3} \, dx\)
 3.22 \(\int \frac{x^3 (A+B x)}{\sqrt{a+b x^2}} \, dx\)
 3.23 \(\int \frac{x^2 (A+B x)}{\sqrt{a+b x^2}} \, dx\)
 3.24 \(\int \frac{x (A+B x)}{\sqrt{a+b x^2}} \, dx\)
 3.25 \(\int \frac{A+B x}{\sqrt{a+b x^2}} \, dx\)
 3.26 \(\int \frac{A+B x}{x \sqrt{a+b x^2}} \, dx\)
 3.27 \(\int \frac{A+B x}{x^2 \sqrt{a+b x^2}} \, dx\)
 3.28 \(\int \frac{A+B x}{x^3 \sqrt{a+b x^2}} \, dx\)
 3.29 \(\int \frac{x^3 (A+B x)}{\left (a+b x^2\right )^{3/2}} \, dx\)
 3.30 \(\int \frac{x^2 (A+B x)}{\left (a+b x^2\right )^{3/2}} \, dx\)
 3.31 \(\int \frac{x (A+B x)}{\left (a+b x^2\right )^{3/2}} \, dx\)
 3.32 \(\int \frac{A+B x}{\left (a+b x^2\right )^{3/2}} \, dx\)
 3.33 \(\int \frac{A+B x}{x \left (a+b x^2\right )^{3/2}} \, dx\)
 3.34 \(\int \frac{A+B x}{x^2 \left (a+b x^2\right )^{3/2}} \, dx\)
 3.35 \(\int \frac{A+B x}{x^3 \left (a+b x^2\right )^{3/2}} \, dx\)
 3.36 \(\int \frac{x^3 (A+B x)}{\left (a+b x^2\right )^{5/2}} \, dx\)
 3.37 \(\int \frac{x^2 (A+B x)}{\left (a+b x^2\right )^{5/2}} \, dx\)
 3.38 \(\int \frac{x (A+B x)}{\left (a+b x^2\right )^{5/2}} \, dx\)
 3.39 \(\int \frac{A+B x}{\left (a+b x^2\right )^{5/2}} \, dx\)
 3.40 \(\int \frac{A+B x}{x \left (a+b x^2\right )^{5/2}} \, dx\)
 3.41 \(\int \frac{A+B x}{x^2 \left (a+b x^2\right )^{5/2}} \, dx\)
 3.42 \(\int \frac{A+B x}{x^3 \left (a+b x^2\right )^{5/2}} \, dx\)
 3.43 \(\int \frac{(1-x) x}{\sqrt{1-x^2}} \, dx\)
 3.44 \(\int \frac{x-x^2}{\sqrt{1-x^2}} \, dx\)
 3.45 \(\int \frac{3+x^2}{-3+x^2} \, dx\)
 3.46 \(\int \frac{-1+x^2}{1+x^2} \, dx\)
 3.47 \(\int \frac{x^7 \left (A+B x+C x^2\right )}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.48 \(\int \frac{x^6 \left (A+B x+C x^2\right )}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.49 \(\int \frac{x^5 \left (A+B x+C x^2\right )}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.50 \(\int \frac{x^4 \left (A+B x+C x^2\right )}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.51 \(\int \frac{x^3 \left (A+B x+C x^2\right )}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.52 \(\int \frac{x^2 \left (A+B x+C x^2\right )}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.53 \(\int \frac{x \left (A+B x+C x^2\right )}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.54 \(\int \frac{A+B x+C x^2}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.55 \(\int \frac{A+B x+C x^2}{x \left (a+b x^2\right )^{9/2}} \, dx\)
 3.56 \(\int \frac{A+B x+C x^2}{x^2 \left (a+b x^2\right )^{9/2}} \, dx\)
 3.57 \(\int \frac{A+B x+C x^2}{x^3 \left (a+b x^2\right )^{9/2}} \, dx\)
 3.58 \(\int \frac{A (c x)^m}{a+b x^2} \, dx\)
 3.59 \(\int \frac{(c x)^m (A+B x)}{a+b x^2} \, dx\)
 3.60 \(\int \frac{(c x)^m \left (A+C x^2\right )}{a+b x^2} \, dx\)
 3.61 \(\int \frac{(c x)^m \left (A+B x+C x^2\right )}{a+b x^2} \, dx\)
 3.62 \(\int x^3 \left (a+b x^2\right ) \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.63 \(\int x^2 \left (a+b x^2\right ) \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.64 \(\int x \left (a+b x^2\right ) \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.65 \(\int \left (a+b x^2\right ) \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.66 \(\int \frac{\left (a+b x^2\right ) \left (A+B x+C x^2+D x^3\right )}{x} \, dx\)
 3.67 \(\int \frac{\left (a+b x^2\right ) \left (A+B x+C x^2+D x^3\right )}{x^2} \, dx\)
 3.68 \(\int \frac{\left (a+b x^2\right ) \left (A+B x+C x^2+D x^3\right )}{x^3} \, dx\)
 3.69 \(\int \frac{\left (a+b x^2\right ) \left (A+B x+C x^2+D x^3\right )}{x^4} \, dx\)
 3.70 \(\int x^3 \left (a+b x^2\right )^2 \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.71 \(\int x^2 \left (a+b x^2\right )^2 \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.72 \(\int x \left (a+b x^2\right )^2 \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.73 \(\int \left (a+b x^2\right )^2 \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.74 \(\int \frac{\left (a+b x^2\right )^2 \left (A+B x+C x^2+D x^3\right )}{x} \, dx\)
 3.75 \(\int \frac{\left (a+b x^2\right )^2 \left (A+B x+C x^2+D x^3\right )}{x^2} \, dx\)
 3.76 \(\int \frac{\left (a+b x^2\right )^2 \left (A+B x+C x^2+D x^3\right )}{x^3} \, dx\)
 3.77 \(\int \frac{\left (a+b x^2\right )^2 \left (A+B x+C x^2+D x^3\right )}{x^4} \, dx\)
 3.78 \(\int x^3 \left (a+b x^2\right )^3 \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.79 \(\int x^2 \left (a+b x^2\right )^3 \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.80 \(\int x \left (a+b x^2\right )^3 \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.81 \(\int \left (a+b x^2\right )^3 \left (A+B x+C x^2+D x^3\right ) \, dx\)
 3.82 \(\int \frac{\left (a+b x^2\right )^3 \left (A+B x+C x^2+D x^3\right )}{x} \, dx\)
 3.83 \(\int \frac{\left (a+b x^2\right )^3 \left (A+B x+C x^2+D x^3\right )}{x^2} \, dx\)
 3.84 \(\int \frac{\left (a+b x^2\right )^3 \left (A+B x+C x^2+D x^3\right )}{x^3} \, dx\)
 3.85 \(\int \frac{\left (a+b x^2\right )^3 \left (A+B x+C x^2+D x^3\right )}{x^4} \, dx\)
 3.86 \(\int \frac{x^4 \left (A+B x+C x^2+D x^3\right )}{a+b x^2} \, dx\)
 3.87 \(\int \frac{x^3 \left (A+B x+C x^2+D x^3\right )}{a+b x^2} \, dx\)
 3.88 \(\int \frac{x^2 \left (A+B x+C x^2+D x^3\right )}{a+b x^2} \, dx\)
 3.89 \(\int \frac{x \left (A+B x+C x^2+D x^3\right )}{a+b x^2} \, dx\)
 3.90 \(\int \frac{A+B x+C x^2+D x^3}{a+b x^2} \, dx\)
 3.91 \(\int \frac{A+B x+C x^2+D x^3}{x \left (a+b x^2\right )} \, dx\)
 3.92 \(\int \frac{A+B x+C x^2+D x^3}{x^2 \left (a+b x^2\right )} \, dx\)
 3.93 \(\int \frac{A+B x+C x^2+D x^3}{x^3 \left (a+b x^2\right )} \, dx\)
 3.94 \(\int \frac{x^4 \left (A+B x+C x^2+D x^3\right )}{\left (a+b x^2\right )^2} \, dx\)
 3.95 \(\int \frac{x^3 \left (A+B x+C x^2+D x^3\right )}{\left (a+b x^2\right )^2} \, dx\)
 3.96 \(\int \frac{x^2 \left (A+B x+C x^2+D x^3\right )}{\left (a+b x^2\right )^2} \, dx\)
 3.97 \(\int \frac{x \left (A+B x+C x^2+D x^3\right )}{\left (a+b x^2\right )^2} \, dx\)
 3.98 \(\int \frac{A+B x+C x^2+D x^3}{\left (a+b x^2\right )^2} \, dx\)
 3.99 \(\int \frac{A+B x+C x^2+D x^3}{x \left (a+b x^2\right )^2} \, dx\)
 3.100 \(\int \frac{A+B x+C x^2+D x^3}{x^2 \left (a+b x^2\right )^2} \, dx\)
 3.101 \(\int \frac{A+B x+C x^2+D x^3}{x^3 \left (a+b x^2\right )^2} \, dx\)
 3.102 \(\int \frac{x^4 \left (A+B x+C x^2+D x^3\right )}{\left (a+b x^2\right )^3} \, dx\)
 3.103 \(\int \frac{x^3 \left (A+B x+C x^2+D x^3\right )}{\left (a+b x^2\right )^3} \, dx\)
 3.104 \(\int \frac{x^2 \left (A+B x+C x^2+D x^3\right )}{\left (a+b x^2\right )^3} \, dx\)
 3.105 \(\int \frac{x \left (A+B x+C x^2+D x^3\right )}{\left (a+b x^2\right )^3} \, dx\)
 3.106 \(\int \frac{A+B x+C x^2+D x^3}{\left (a+b x^2\right )^3} \, dx\)
 3.107 \(\int \frac{A+B x+C x^2+D x^3}{x \left (a+b x^2\right )^3} \, dx\)
 3.108 \(\int \frac{A+B x+C x^2+D x^3}{x^2 \left (a+b x^2\right )^3} \, dx\)
 3.109 \(\int \frac{A+B x+C x^2+D x^3}{x^3 \left (a+b x^2\right )^3} \, dx\)
 3.110 \(\int \frac{-x+4 x^3}{\left (5+x^2\right )^2} \, dx\)
 3.111 \(\int \frac{-x+x^3}{\sqrt{-2+x^2}} \, dx\)
 3.112 \(\int \frac{-x^2+2 x^4}{1+2 x^2} \, dx\)
 3.113 \(\int \frac{x^3+x^4}{1+x^2} \, dx\)
 3.114 \(\int \frac{x^6 \left (c+d x^2+e x^4+f x^6\right )}{a+b x^2} \, dx\)
 3.115 \(\int \frac{x^4 \left (c+d x^2+e x^4+f x^6\right )}{a+b x^2} \, dx\)
 3.116 \(\int \frac{x^2 \left (c+d x^2+e x^4+f x^6\right )}{a+b x^2} \, dx\)
 3.117 \(\int \frac{c+d x^2+e x^4+f x^6}{a+b x^2} \, dx\)
 3.118 \(\int \frac{c+d x^2+e x^4+f x^6}{x^2 \left (a+b x^2\right )} \, dx\)
 3.119 \(\int \frac{c+d x^2+e x^4+f x^6}{x^4 \left (a+b x^2\right )} \, dx\)
 3.120 \(\int \frac{c+d x^2+e x^4+f x^6}{x^6 \left (a+b x^2\right )} \, dx\)
 3.121 \(\int \frac{c+d x^2+e x^4+f x^6}{x^8 \left (a+b x^2\right )} \, dx\)
 3.122 \(\int \frac{c+d x^2+e x^4+f x^6}{x^{10} \left (a+b x^2\right )} \, dx\)
 3.123 \(\int \frac{c+d x^2+e x^4+f x^6}{x^{12} \left (a+b x^2\right )} \, dx\)
 3.124 \(\int \frac{x^6 \left (c+d x^2+e x^4+f x^6\right )}{\left (a+b x^2\right )^2} \, dx\)
 3.125 \(\int \frac{x^4 \left (c+d x^2+e x^4+f x^6\right )}{\left (a+b x^2\right )^2} \, dx\)
 3.126 \(\int \frac{x^2 \left (c+d x^2+e x^4+f x^6\right )}{\left (a+b x^2\right )^2} \, dx\)
 3.127 \(\int \frac{c+d x^2+e x^4+f x^6}{\left (a+b x^2\right )^2} \, dx\)
 3.128 \(\int \frac{c+d x^2+e x^4+f x^6}{x^2 \left (a+b x^2\right )^2} \, dx\)
 3.129 \(\int \frac{c+d x^2+e x^4+f x^6}{x^4 \left (a+b x^2\right )^2} \, dx\)
 3.130 \(\int \frac{c+d x^2+e x^4+f x^6}{x^6 \left (a+b x^2\right )^2} \, dx\)
 3.131 \(\int \frac{c+d x^2+e x^4+f x^6}{x^8 \left (a+b x^2\right )^2} \, dx\)
 3.132 \(\int \frac{c+d x^2+e x^4+f x^6}{x^{10} \left (a+b x^2\right )^2} \, dx\)
 3.133 \(\int \frac{x^8 \left (c+d x^2+e x^4+f x^6\right )}{\left (a+b x^2\right )^3} \, dx\)
 3.134 \(\int \frac{x^6 \left (c+d x^2+e x^4+f x^6\right )}{\left (a+b x^2\right )^3} \, dx\)
 3.135 \(\int \frac{x^4 \left (c+d x^2+e x^4+f x^6\right )}{\left (a+b x^2\right )^3} \, dx\)
 3.136 \(\int \frac{x^2 \left (c+d x^2+e x^4+f x^6\right )}{\left (a+b x^2\right )^3} \, dx\)
 3.137 \(\int \frac{c+d x^2+e x^4+f x^6}{\left (a+b x^2\right )^3} \, dx\)
 3.138 \(\int \frac{c+d x^2+e x^4+f x^6}{x^2 \left (a+b x^2\right )^3} \, dx\)
 3.139 \(\int \frac{c+d x^2+e x^4+f x^6}{x^4 \left (a+b x^2\right )^3} \, dx\)
 3.140 \(\int \frac{c+d x^2+e x^4+f x^6}{x^6 \left (a+b x^2\right )^3} \, dx\)
 3.141 \(\int \frac{c+d x^2+e x^4+f x^6}{x^8 \left (a+b x^2\right )^3} \, dx\)
 3.142 \(\int \frac{c+d x^2+e x^4+f x^6}{x^{10} \left (a+b x^2\right )^3} \, dx\)
 3.143 \(\int \frac{x^5 \left (c+d x^2+e x^4+f x^6\right )}{\sqrt{a+b x^2}} \, dx\)
 3.144 \(\int \frac{x^3 \left (c+d x^2+e x^4+f x^6\right )}{\sqrt{a+b x^2}} \, dx\)
 3.145 \(\int \frac{x \left (c+d x^2+e x^4+f x^6\right )}{\sqrt{a+b x^2}} \, dx\)
 3.146 \(\int \frac{c+d x^2+e x^4+f x^6}{x \sqrt{a+b x^2}} \, dx\)
 3.147 \(\int \frac{c+d x^2+e x^4+f x^6}{x^3 \sqrt{a+b x^2}} \, dx\)
 3.148 \(\int \frac{c+d x^2+e x^4+f x^6}{x^5 \sqrt{a+b x^2}} \, dx\)
 3.149 \(\int \frac{c+d x^2+e x^4+f x^6}{x^7 \sqrt{a+b x^2}} \, dx\)
 3.150 \(\int \frac{c+d x^2+e x^4+f x^6}{x^9 \sqrt{a+b x^2}} \, dx\)
 3.151 \(\int \frac{x^4 \left (c+d x^2+e x^4+f x^6\right )}{\sqrt{a+b x^2}} \, dx\)
 3.152 \(\int \frac{x^2 \left (c+d x^2+e x^4+f x^6\right )}{\sqrt{a+b x^2}} \, dx\)
 3.153 \(\int \frac{c+d x^2+e x^4+f x^6}{\sqrt{a+b x^2}} \, dx\)
 3.154 \(\int \frac{c+d x^2+e x^4+f x^6}{x^2 \sqrt{a+b x^2}} \, dx\)
 3.155 \(\int \frac{c+d x^2+e x^4+f x^6}{x^4 \sqrt{a+b x^2}} \, dx\)
 3.156 \(\int \frac{c+d x^2+e x^4+f x^6}{x^6 \sqrt{a+b x^2}} \, dx\)
 3.157 \(\int \frac{c+d x^2+e x^4+f x^6}{x^8 \sqrt{a+b x^2}} \, dx\)
 3.158 \(\int \frac{c+d x^2+e x^4+f x^6}{x^{10} \sqrt{a+b x^2}} \, dx\)
 3.159 \(\int \frac{x^8 \left (A+B x^2+C x^4+D x^6\right )}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.160 \(\int \frac{x^6 \left (A+B x^2+C x^4+D x^6\right )}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.161 \(\int \frac{x^4 \left (A+B x^2+C x^4+D x^6\right )}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.162 \(\int \frac{x^2 \left (A+B x^2+C x^4+D x^6\right )}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.163 \(\int \frac{A+B x^2+C x^4+D x^6}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.164 \(\int \frac{A+B x^2+C x^4+D x^6}{x^2 \left (a+b x^2\right )^{9/2}} \, dx\)
 3.165 \(\int \frac{A+B x^2+C x^4+D x^6}{x^4 \left (a+b x^2\right )^{9/2}} \, dx\)
 3.166 \(\int \frac{A+B x^2+C x^4+D x^6}{x^6 \left (a+b x^2\right )^{9/2}} \, dx\)
 3.167 \(\int \frac{A+B x^2+C x^4+D x^6}{x^8 \left (a+b x^2\right )^{9/2}} \, dx\)
 3.168 \(\int \frac{A+B x^2+C x^4+D x^6}{x^{10} \left (a+b x^2\right )^{9/2}} \, dx\)
 3.169 \(\int \frac{c x^5+d x^7+e x^9+f x^{11}}{\sqrt{a+b x^2}} \, dx\)
 3.170 \(\int \frac{c x^3+d x^5+e x^7+f x^9}{\sqrt{a+b x^2}} \, dx\)
 3.171 \(\int \frac{c x+d x^3+e x^5+f x^7}{\sqrt{a+b x^2}} \, dx\)
 3.172 \(\int \frac{x^2 \left (A+B x^2+C x^4+D x^6+F x^8\right )}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.173 \(\int \frac{A+B x^2+C x^4+D x^6+F x^8}{\left (a+b x^2\right )^{9/2}} \, dx\)
 3.174 \(\int \frac{A+B x^2+C x^4+D x^6+F x^8}{x^2 \left (a+b x^2\right )^{9/2}} \, dx\)