3.5 Integrals 401 to 500

\(\int \genfrac {}{}{}{}{x^3}{(c x^2)^{3/2} (a+b x)^2} \, dx\) [401]
\(\int \genfrac {}{}{}{}{x^2}{(c x^2)^{3/2} (a+b x)^2} \, dx\) [402]
\(\int \genfrac {}{}{}{}{x}{(c x^2)^{3/2} (a+b x)^2} \, dx\) [403]
\(\int \genfrac {}{}{}{}{1}{(c x^2)^{3/2} (a+b x)^2} \, dx\) [404]
\(\int (d x)^m (c x^2)^{5/2} (a+b x) \, dx\) [405]
\(\int (d x)^m (c x^2)^{3/2} (a+b x) \, dx\) [406]
\(\int (d x)^m \sqrt {c x^2} (a+b x) \, dx\) [407]
\(\int \genfrac {}{}{}{}{(d x)^m (a+b x)}{\sqrt {c x^2}} \, dx\) [408]
\(\int \genfrac {}{}{}{}{(d x)^m (a+b x)}{(c x^2)^{3/2}} \, dx\) [409]
\(\int \genfrac {}{}{}{}{(d x)^m (a+b x)}{(c x^2)^{5/2}} \, dx\) [410]
\(\int (d x)^m (c x^2)^{5/2} (a+b x)^2 \, dx\) [411]
\(\int (d x)^m (c x^2)^{3/2} (a+b x)^2 \, dx\) [412]
\(\int (d x)^m \sqrt {c x^2} (a+b x)^2 \, dx\) [413]
\(\int \genfrac {}{}{}{}{(d x)^m (a+b x)^2}{\sqrt {c x^2}} \, dx\) [414]
\(\int \genfrac {}{}{}{}{(d x)^m (a+b x)^2}{(c x^2)^{3/2}} \, dx\) [415]
\(\int \genfrac {}{}{}{}{(d x)^m (a+b x)^2}{(c x^2)^{5/2}} \, dx\) [416]
\(\int x^2 \sqrt {c x^2} (a+b x)^p \, dx\) [417]
\(\int x \sqrt {c x^2} (a+b x)^p \, dx\) [418]
\(\int \sqrt {c x^2} (a+b x)^p \, dx\) [419]
\(\int \genfrac {}{}{}{}{\sqrt {c x^2} (a+b x)^p}{x} \, dx\) [420]
\(\int \genfrac {}{}{}{}{\sqrt {c x^2} (a+b x)^p}{x^2} \, dx\) [421]
\(\int \genfrac {}{}{}{}{\sqrt {c x^2} (a+b x)^p}{x^3} \, dx\) [422]
\(\int \genfrac {}{}{}{}{\sqrt {c x^2} (a+b x)^p}{x^4} \, dx\) [423]
\(\int x (c x^2)^{3/2} (a+b x)^p \, dx\) [424]
\(\int (c x^2)^{3/2} (a+b x)^p \, dx\) [425]
\(\int \genfrac {}{}{}{}{(c x^2)^{3/2} (a+b x)^p}{x} \, dx\) [426]
\(\int \genfrac {}{}{}{}{(c x^2)^{3/2} (a+b x)^p}{x^2} \, dx\) [427]
\(\int \genfrac {}{}{}{}{(c x^2)^{3/2} (a+b x)^p}{x^3} \, dx\) [428]
\(\int \genfrac {}{}{}{}{(c x^2)^{3/2} (a+b x)^p}{x^4} \, dx\) [429]
\(\int \genfrac {}{}{}{}{(c x^2)^{3/2} (a+b x)^p}{x^5} \, dx\) [430]
\(\int \genfrac {}{}{}{}{(c x^2)^{3/2} (a+b x)^p}{x^6} \, dx\) [431]
\(\int (c x^2)^{5/2} (a+b x)^p \, dx\) [432]
\(\int \genfrac {}{}{}{}{(c x^2)^{5/2} (a+b x)^p}{x} \, dx\) [433]
\(\int \genfrac {}{}{}{}{(c x^2)^{5/2} (a+b x)^p}{x^2} \, dx\) [434]
\(\int \genfrac {}{}{}{}{(c x^2)^{5/2} (a+b x)^p}{x^3} \, dx\) [435]
\(\int \genfrac {}{}{}{}{(c x^2)^{5/2} (a+b x)^p}{x^4} \, dx\) [436]
\(\int \genfrac {}{}{}{}{(c x^2)^{5/2} (a+b x)^p}{x^5} \, dx\) [437]
\(\int \genfrac {}{}{}{}{(c x^2)^{5/2} (a+b x)^p}{x^6} \, dx\) [438]
\(\int \genfrac {}{}{}{}{(c x^2)^{5/2} (a+b x)^p}{x^7} \, dx\) [439]
\(\int \genfrac {}{}{}{}{x^4 (a+b x)^p}{\sqrt {c x^2}} \, dx\) [440]
\(\int \genfrac {}{}{}{}{x^3 (a+b x)^p}{\sqrt {c x^2}} \, dx\) [441]
\(\int \genfrac {}{}{}{}{x^2 (a+b x)^p}{\sqrt {c x^2}} \, dx\) [442]
\(\int \genfrac {}{}{}{}{x (a+b x)^p}{\sqrt {c x^2}} \, dx\) [443]
\(\int \genfrac {}{}{}{}{(a+b x)^p}{\sqrt {c x^2}} \, dx\) [444]
\(\int \genfrac {}{}{}{}{(a+b x)^p}{x \sqrt {c x^2}} \, dx\) [445]
\(\int \genfrac {}{}{}{}{(a+b x)^p}{x^2 \sqrt {c x^2}} \, dx\) [446]
\(\int \genfrac {}{}{}{}{x^6 (a+b x)^p}{(c x^2)^{3/2}} \, dx\) [447]
\(\int \genfrac {}{}{}{}{x^5 (a+b x)^p}{(c x^2)^{3/2}} \, dx\) [448]
\(\int \genfrac {}{}{}{}{x^4 (a+b x)^p}{(c x^2)^{3/2}} \, dx\) [449]
\(\int \genfrac {}{}{}{}{x^3 (a+b x)^p}{(c x^2)^{3/2}} \, dx\) [450]
\(\int \genfrac {}{}{}{}{x^2 (a+b x)^p}{(c x^2)^{3/2}} \, dx\) [451]
\(\int \genfrac {}{}{}{}{x (a+b x)^p}{(c x^2)^{3/2}} \, dx\) [452]
\(\int \genfrac {}{}{}{}{(a+b x)^p}{(c x^2)^{3/2}} \, dx\) [453]
\(\int \genfrac {}{}{}{}{(a+b x)^p}{x (c x^2)^{3/2}} \, dx\) [454]
\(\int \genfrac {}{}{}{}{x^8 (a+b x)^p}{(c x^2)^{5/2}} \, dx\) [455]
\(\int \genfrac {}{}{}{}{x^7 (a+b x)^p}{(c x^2)^{5/2}} \, dx\) [456]
\(\int \genfrac {}{}{}{}{x^6 (a+b x)^p}{(c x^2)^{5/2}} \, dx\) [457]
\(\int \genfrac {}{}{}{}{x^5 (a+b x)^p}{(c x^2)^{5/2}} \, dx\) [458]
\(\int \genfrac {}{}{}{}{x^4 (a+b x)^p}{(c x^2)^{5/2}} \, dx\) [459]
\(\int \genfrac {}{}{}{}{x^3 (a+b x)^p}{(c x^2)^{5/2}} \, dx\) [460]
\(\int \genfrac {}{}{}{}{x^2 (a+b x)^p}{(c x^2)^{5/2}} \, dx\) [461]
\(\int \genfrac {}{}{}{}{x (a+b x)^p}{(c x^2)^{5/2}} \, dx\) [462]
\(\int (d x)^m (c x^2)^{5/2} (a+b x)^p \, dx\) [463]
\(\int (d x)^m (c x^2)^{3/2} (a+b x)^p \, dx\) [464]
\(\int (d x)^m \sqrt {c x^2} (a+b x)^p \, dx\) [465]
\(\int \genfrac {}{}{}{}{(d x)^m (a+b x)^p}{\sqrt {c x^2}} \, dx\) [466]
\(\int \genfrac {}{}{}{}{(d x)^m (a+b x)^p}{(c x^2)^{3/2}} \, dx\) [467]
\(\int \genfrac {}{}{}{}{(d x)^m (a+b x)^p}{(c x^2)^{5/2}} \, dx\) [468]
\(\int \sqrt {\genfrac {}{}{}{}{1}{x}} \sqrt {x} \sqrt {a+b x} \, dx\) [469]
\(\int x^3 (d x^2)^n (a+b x)^{-5-2 n} \, dx\) [470]
\(\int x^2 (d x^2)^n (a+b x)^{-4-2 n} \, dx\) [471]
\(\int x (d x^2)^n (a+b x)^{-3-2 n} \, dx\) [472]
\(\int (d x^2)^n (a+b x)^{-2-2 n} \, dx\) [473]
\(\int \genfrac {}{}{}{}{(d x^2)^n (a+b x)^{-1-2 n}}{x} \, dx\) [474]
\(\int \genfrac {}{}{}{}{(d x^2)^n (a+b x)^{-2 n}}{x^2} \, dx\) [475]
\(\int \genfrac {}{}{}{}{(d x^2)^n (a+b x)^{1-2 n}}{x^3} \, dx\) [476]
\(\int \genfrac {}{}{}{}{(d x^2)^n (a+b x)^{2-2 n}}{x^4} \, dx\) [477]
\(\int x^m (d x^2)^n (a+b x)^{-2-m-2 n} \, dx\) [478]
\(\int (c x)^m (d x^2)^n (a+b x)^{-2-m-2 n} \, dx\) [479]
\(\int x^m (d x^2)^n (a+b x)^p \, dx\) [480]
\(\int (c x)^m (d x^2)^n (a+b x)^p \, dx\) [481]
\(\int \genfrac {}{}{}{}{x^5}{\sqrt {d x^2} (a+b x^2)} \, dx\) [482]
\(\int \genfrac {}{}{}{}{x^3}{\sqrt {d x^2} (a+b x^2)} \, dx\) [483]
\(\int \genfrac {}{}{}{}{x}{\sqrt {d x^2} (a+b x^2)} \, dx\) [484]
\(\int \genfrac {}{}{}{}{1}{x \sqrt {d x^2} (a+b x^2)} \, dx\) [485]
\(\int \genfrac {}{}{}{}{1}{x^3 \sqrt {d x^2} (a+b x^2)} \, dx\) [486]
\(\int x^{-1+n} (d x^n)^p (a+b x^n)^q \, dx\) [487]
\(\int x^{-1+n} (d x^n)^p (a+b x^n+c x^{2 n})^q \, dx\) [488]
\(\int \genfrac {}{}{}{}{\sqrt {a x^4}}{\sqrt {1+x^2}} \, dx\) [489]
\(\int \genfrac {}{}{}{}{\sqrt {a x^3}}{\sqrt {1+x^2}} \, dx\) [490]
\(\int \genfrac {}{}{}{}{\sqrt {a x^2}}{\sqrt {1+x^2}} \, dx\) [491]
\(\int \genfrac {}{}{}{}{\sqrt {a x}}{\sqrt {1+x^2}} \, dx\) [492]
\(\int \genfrac {}{}{}{}{\sqrt {\genfrac {}{}{}{}{a}{x}}}{\sqrt {1+x^2}} \, dx\) [493]
\(\int \genfrac {}{}{}{}{\sqrt {\genfrac {}{}{}{}{a}{x^2}}}{\sqrt {1+x^2}} \, dx\) [494]
\(\int \genfrac {}{}{}{}{\sqrt {\genfrac {}{}{}{}{a}{x^3}}}{\sqrt {1+x^2}} \, dx\) [495]
\(\int \genfrac {}{}{}{}{\sqrt {\genfrac {}{}{}{}{a}{x^4}}}{\sqrt {1+x^2}} \, dx\) [496]
\(\int \genfrac {}{}{}{}{\sqrt {a x^4}}{\sqrt {1+x^3}} \, dx\) [497]
\(\int \genfrac {}{}{}{}{\sqrt {a x^3}}{\sqrt {1+x^3}} \, dx\) [498]
\(\int \genfrac {}{}{}{}{\sqrt {a x^2}}{\sqrt {1+x^3}} \, dx\) [499]
\(\int \genfrac {}{}{}{}{\sqrt {a x}}{\sqrt {1+x^3}} \, dx\) [500]