3.5 Integrals 401 to 500

\(\int \genfrac {}{}{}{}{(e x)^m (a (1+m)+b (1+m-n) x^n)}{(a+b x^n)^2} \, dx\) [401]
\(\int \genfrac {}{}{}{}{(e x)^m (a (1+m)+b (1+m-2 n) x^n)}{(a+b x^n)^3} \, dx\) [402]
\(\int (c x)^m (a+b x^n)^3 (A+B x^n) \, dx\) [403]
\(\int (c x)^m (a+b x^n)^2 (A+B x^n) \, dx\) [404]
\(\int (c x)^m (a+b x^n) (A+B x^n) \, dx\) [405]
\(\int (c x)^m (A+B x^n) \, dx\) [406]
\(\int \genfrac {}{}{}{}{(c x)^m (A+B x^n)}{a+b x^n} \, dx\) [407]
\(\int \genfrac {}{}{}{}{(c x)^m (A+B x^n)}{(a+b x^n)^2} \, dx\) [408]
\(\int \genfrac {}{}{}{}{(c x)^m (A+B x^n)}{(a+b x^n)^3} \, dx\) [409]
\(\int (c x)^m (a+b x^n)^{3/2} (A+B x^n) \, dx\) [410]
\(\int (c x)^m \sqrt {a+b x^n} (A+B x^n) \, dx\) [411]
\(\int \genfrac {}{}{}{}{(c x)^m (A+B x^n)}{\sqrt {a+b x^n}} \, dx\) [412]
\(\int \genfrac {}{}{}{}{(c x)^m (A+B x^n)}{(a+b x^n)^{3/2}} \, dx\) [413]
\(\int \genfrac {}{}{}{}{(c x)^m (A+B x^n)}{(a+b x^n)^{5/2}} \, dx\) [414]
\(\int x^2 (a+b x^n)^p (c+d x^n) \, dx\) [415]
\(\int x (a+b x^n)^p (c+d x^n) \, dx\) [416]
\(\int (a+b x^n)^p (c+d x^n) \, dx\) [417]
\(\int \genfrac {}{}{}{}{(a+b x^n)^p (c+d x^n)}{x} \, dx\) [418]
\(\int \genfrac {}{}{}{}{(a+b x^n)^p (c+d x^n)}{x^2} \, dx\) [419]
\(\int \genfrac {}{}{}{}{(a+b x^n)^p (c+d x^n)}{x^3} \, dx\) [420]
\(\int (e x)^{3/2} (a+b x^n)^p (c+d x^n) \, dx\) [421]
\(\int \sqrt {e x} (a+b x^n)^p (c+d x^n) \, dx\) [422]
\(\int \genfrac {}{}{}{}{(a+b x^n)^p (c+d x^n)}{\sqrt {e x}} \, dx\) [423]
\(\int \genfrac {}{}{}{}{(a+b x^n)^p (c+d x^n)}{(e x)^{3/2}} \, dx\) [424]
\(\int \genfrac {}{}{}{}{(a+b x^n)^p (c+d x^n)}{(e x)^{5/2}} \, dx\) [425]
\(\int x^2 (a+b x^n)^p (3 a+b (5+2 p) x^n) \, dx\) [426]
\(\int x (a+b x^n)^p (2 a+b (4+2 p) x^n) \, dx\) [427]
\(\int (a+b x^n)^p (a+b (3+2 p) x^n) \, dx\) [428]
\(\int b (2+2 p) x^{-1+n} (a+b x^n)^p \, dx\) [429]
\(\int x^{-n} (a+b x^n)^p (-a+b (1+2 p) x^n) \, dx\) [430]
\(\int \genfrac {}{}{}{}{(a+b x^n)^p (-2 a+2 b p x^n)}{x^3} \, dx\) [431]
\(\int \genfrac {}{}{}{}{(a+b x^n)^p (-3 a+b (-1+2 p) x^n)}{x^4} \, dx\) [432]
\(\int (e x)^m (a+b x^n)^p (c+d x^n) \, dx\) [433]
\(\int x^{-1-n (1+p)} (a+b x^n)^p (c+d x^n) \, dx\) [434]
\(\int (e x)^m (a+b x^n)^p (a (1+m)+b (1+m+n (1+p)) x^n) \, dx\) [435]
\(\int \genfrac {}{}{}{}{x^2}{(a+b x^n) (c+d x^n)} \, dx\) [436]
\(\int \genfrac {}{}{}{}{x}{(a+b x^n) (c+d x^n)} \, dx\) [437]
\(\int \genfrac {}{}{}{}{1}{(a+b x^n) (c+d x^n)} \, dx\) [438]
\(\int \genfrac {}{}{}{}{1}{x (a+b x^n) (c+d x^n)} \, dx\) [439]
\(\int \genfrac {}{}{}{}{1}{x^2 (a+b x^n) (c+d x^n)} \, dx\) [440]
\(\int \genfrac {}{}{}{}{1}{x^3 (a+b x^n) (c+d x^n)} \, dx\) [441]
\(\int \genfrac {}{}{}{}{x^2}{(a+b x^n)^2 (c+d x^n)} \, dx\) [442]
\(\int \genfrac {}{}{}{}{x}{(a+b x^n)^2 (c+d x^n)} \, dx\) [443]
\(\int \genfrac {}{}{}{}{1}{(a+b x^n)^2 (c+d x^n)} \, dx\) [444]
\(\int \genfrac {}{}{}{}{1}{x (a+b x^n)^2 (c+d x^n)} \, dx\) [445]
\(\int \genfrac {}{}{}{}{1}{x^2 (a+b x^n)^2 (c+d x^n)} \, dx\) [446]
\(\int \genfrac {}{}{}{}{1}{x^3 (a+b x^n)^2 (c+d x^n)} \, dx\) [447]
\(\int \genfrac {}{}{}{}{x}{(1-x) (1+x)^2} \, dx\) [448]
\(\int \genfrac {}{}{}{}{x^2}{(1-x^2) (1+x^2)^2} \, dx\) [449]
\(\int \genfrac {}{}{}{}{x^3}{(1-x^3) (1+x^3)^2} \, dx\) [450]
\(\int \genfrac {}{}{}{}{x^4}{(1-x^4) (1+x^4)^2} \, dx\) [451]
\(\int \genfrac {}{}{}{}{x^{-1+2 n} (a+b x^n)^3}{c+d x^n} \, dx\) [452]
\(\int \genfrac {}{}{}{}{x^{-1+2 n} (a+b x^n)^2}{c+d x^n} \, dx\) [453]
\(\int \genfrac {}{}{}{}{x^{-1+2 n} (a+b x^n)}{c+d x^n} \, dx\) [454]
\(\int \genfrac {}{}{}{}{x^{-1+2 n}}{(a+b x^n) (c+d x^n)} \, dx\) [455]
\(\int \genfrac {}{}{}{}{x^{-1+2 n}}{(a+b x^n)^2 (c+d x^n)} \, dx\) [456]
\(\int \genfrac {}{}{}{}{x^{-1+2 n}}{(a+b x^n)^3 (c+d x^n)} \, dx\) [457]
\(\int \genfrac {}{}{}{}{x^{-1+3 n} (a+b x^n)^3}{c+d x^n} \, dx\) [458]
\(\int \genfrac {}{}{}{}{x^{-1+3 n} (a+b x^n)^2}{c+d x^n} \, dx\) [459]
\(\int \genfrac {}{}{}{}{x^{-1+3 n} (a+b x^n)}{c+d x^n} \, dx\) [460]
\(\int \genfrac {}{}{}{}{x^{-1+3 n}}{(a+b x^n) (c+d x^n)} \, dx\) [461]
\(\int \genfrac {}{}{}{}{x^{-1+3 n}}{(a+b x^n)^2 (c+d x^n)} \, dx\) [462]
\(\int \genfrac {}{}{}{}{x^{-1+3 n}}{(a+b x^n)^3 (c+d x^n)} \, dx\) [463]
\(\int x^{13} (b+c x)^{13} (b+2 c x) \, dx\) [464]
\(\int x^{27} (b+c x^2)^{13} (b+2 c x^2) \, dx\) [465]
\(\int x^{41} (b+c x^3)^{13} (b+2 c x^3) \, dx\) [466]
\(\int x^{-1+14 n} (b+c x^n)^{13} (b+2 c x^n) \, dx\) [467]
\(\int x^{-1+m} (a+b x^n)^{-1+p} (a m+b (m+n p) x^n) \, dx\) [468]
\(\int \genfrac {}{}{}{}{b+2 c x}{x (b+c x)} \, dx\) [469]
\(\int \genfrac {}{}{}{}{b+2 c x^2}{x (b+c x^2)} \, dx\) [470]
\(\int \genfrac {}{}{}{}{b+2 c x^3}{x (b+c x^3)} \, dx\) [471]
\(\int \genfrac {}{}{}{}{b+2 c x^n}{x (b+c x^n)} \, dx\) [472]
\(\int \genfrac {}{}{}{}{b+2 c x}{x^8 (b+c x)^8} \, dx\) [473]
\(\int \genfrac {}{}{}{}{b+2 c x^2}{x^{15} (b+c x^2)^8} \, dx\) [474]
\(\int \genfrac {}{}{}{}{b+2 c x^3}{x^{22} (b+c x^3)^8} \, dx\) [475]
\(\int \genfrac {}{}{}{}{x^{-1-7 n} (b+2 c x^n)}{(b+c x^n)^8} \, dx\) [476]
\(\int \genfrac {}{}{}{}{x^{31} \sqrt {1+x^{16}}}{1-x^{16}} \, dx\) [477]
\(\int \genfrac {}{}{}{}{\sqrt {c+\genfrac {}{}{}{}{d}{x}}}{\sqrt {a+\genfrac {}{}{}{}{b}{x}} x} \, dx\) [478]
\(\int \genfrac {}{}{}{}{x^{-1+2 n} (a+b x^n)^{5/2}}{\sqrt {c+d x^n}} \, dx\) [479]
\(\int \genfrac {}{}{}{}{x^{-1+2 n} (a+b x^n)^{3/2}}{\sqrt {c+d x^n}} \, dx\) [480]
\(\int \genfrac {}{}{}{}{x^{-1+2 n} \sqrt {a+b x^n}}{\sqrt {c+d x^n}} \, dx\) [481]
\(\int \genfrac {}{}{}{}{x^{-1+2 n}}{\sqrt {a+b x^n} \sqrt {c+d x^n}} \, dx\) [482]
\(\int \genfrac {}{}{}{}{x^{-1+2 n}}{(a+b x^n)^{3/2} \sqrt {c+d x^n}} \, dx\) [483]
\(\int \genfrac {}{}{}{}{x^{-1+2 n}}{(a+b x^n)^{5/2} \sqrt {c+d x^n}} \, dx\) [484]
\(\int \genfrac {}{}{}{}{x^{-1+3 n} (a+b x^n)^{5/2}}{\sqrt {c+d x^n}} \, dx\) [485]
\(\int \genfrac {}{}{}{}{x^{-1+3 n} (a+b x^n)^{3/2}}{\sqrt {c+d x^n}} \, dx\) [486]
\(\int \genfrac {}{}{}{}{x^{-1+3 n} \sqrt {a+b x^n}}{\sqrt {c+d x^n}} \, dx\) [487]
\(\int \genfrac {}{}{}{}{x^{-1+3 n}}{\sqrt {a+b x^n} \sqrt {c+d x^n}} \, dx\) [488]
\(\int \genfrac {}{}{}{}{x^{-1+3 n}}{(a+b x^n)^{3/2} \sqrt {c+d x^n}} \, dx\) [489]
\(\int \genfrac {}{}{}{}{x^{-1+3 n}}{(a+b x^n)^{5/2} \sqrt {c+d x^n}} \, dx\) [490]
\(\int \genfrac {}{}{}{}{(e x)^m}{(a+b x^n) (c+d x^n)} \, dx\) [491]
\(\int \genfrac {}{}{}{}{(e x)^m}{(a+b x^n)^2 (c+d x^n)} \, dx\) [492]
\(\int \genfrac {}{}{}{}{x^m}{\sqrt {a+b x^n} (c+d x^n)} \, dx\) [493]
\(\int \genfrac {}{}{}{}{x^n}{\sqrt {a+b x^n} (c+d x^n)} \, dx\) [494]
\(\int \genfrac {}{}{}{}{x^{-1-n (-1+p)} (a+b x^n)^p}{c+d x^n} \, dx\) [495]
\(\int (e x)^m (a+b x^n)^p (c+d x^n)^3 \, dx\) [496]
\(\int (e x)^m (a+b x^n)^p (c+d x^n)^2 \, dx\) [497]
\(\int (e x)^m (a+b x^n)^p (c+d x^n) \, dx\) [498]
\(\int (e x)^m (a+b x^n)^p \, dx\) [499]
\(\int \genfrac {}{}{}{}{(e x)^m (a+b x^n)^p}{c+d x^n} \, dx\) [500]