3.5.1 \(\int \genfrac {}{}{}{}{\sqrt {c x}}{(a x+b x^n)^{3/2}} \, dx\) [401]
3.5.2 \(\int \genfrac {}{}{}{}{1}{c x (a+b x^n)^{3/2}} \, dx\) [402]
3.5.3 \(\int \genfrac {}{}{}{}{1}{(c x)^{5/2} (\genfrac {}{}{}{}{a}{x}+b x^n)^{3/2}} \, dx\) [403]
3.5.4 \(\int \genfrac {}{}{}{}{1}{c^4 x^4 (\genfrac {}{}{}{}{a}{x^2}+b x^n)^{3/2}} \, dx\) [404]
3.5.5 \(\int \genfrac {}{}{}{}{1}{(c x)^{11/2} (\genfrac {}{}{}{}{a}{x^3}+b x^n)^{3/2}} \, dx\) [405]
3.5.6 \(\int \genfrac {}{}{}{}{1}{c^7 x^7 (\genfrac {}{}{}{}{a}{x^4}+b x^n)^{3/2}} \, dx\) [406]
3.5.7 \(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a+b x^3}{x}}} \, dx\) [407]
3.5.8 \(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a+b x^4}{x^2}}} \, dx\) [408]
3.5.9 \(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a+b x^5}{x^3}}} \, dx\) [409]
3.5.10 \(\int \genfrac {}{}{}{}{1}{\sqrt {x^{2-n} (a+b x^n)}} \, dx\) [410]
3.5.11 \(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a-b x^3}{x}}} \, dx\) [411]
3.5.12 \(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a-b x^4}{x^2}}} \, dx\) [412]
3.5.13 \(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a-b x^5}{x^3}}} \, dx\) [413]
3.5.14 \(\int \genfrac {}{}{}{}{1}{\sqrt {x^{2-n} (a-b x^n)}} \, dx\) [414]
3.5.15 \(\int \genfrac {}{}{}{}{1}{\sqrt {x^n (a+b x^{2-n})}} \, dx\) [415]
3.5.16 \(\int \genfrac {}{}{}{}{1}{\sqrt {x^2 (b+a x^{-2+n})}} \, dx\) [416]
3.5.17 \(\int \genfrac {}{}{}{}{1}{\sqrt {x (b x+a x^{-1+n})}} \, dx\) [417]
3.5.18 \(\int \genfrac {}{}{}{}{1}{\sqrt {x^n (a-b x^{2-n})}} \, dx\) [418]
3.5.19 \(\int \genfrac {}{}{}{}{1}{\sqrt {x^2 (-b+a x^{-2+n})}} \, dx\) [419]
3.5.20 \(\int \genfrac {}{}{}{}{1}{\sqrt {x (-b x+a x^{-1+n})}} \, dx\) [420]
3.5.21 \(\int (c x)^m (a x^j+b x^n)^{3/2} \, dx\) [421]
3.5.22 \(\int (c x)^m \sqrt {a x^j+b x^n} \, dx\) [422]
3.5.23 \(\int \genfrac {}{}{}{}{(c x)^m}{\sqrt {a x^j+b x^n}} \, dx\) [423]
3.5.24 \(\int \genfrac {}{}{}{}{(c x)^m}{(a x^j+b x^n)^{3/2}} \, dx\) [424]
3.5.25 \(\int \genfrac {}{}{}{}{(c x)^m}{(a x^j+b x^n)^{5/2}} \, dx\) [425]
3.5.26 \(\int (a x^j+b x^n)^{3/2} \, dx\) [426]
3.5.27 \(\int \sqrt {a x^j+b x^n} \, dx\) [427]
3.5.28 \(\int \genfrac {}{}{}{}{1}{\sqrt {a x^j+b x^n}} \, dx\) [428]
3.5.29 \(\int \genfrac {}{}{}{}{1}{(a x^j+b x^n)^{3/2}} \, dx\) [429]
3.5.30 \(\int \genfrac {}{}{}{}{1}{(a x^j+b x^n)^{5/2}} \, dx\) [430]
3.5.31 \(\int \sqrt {\genfrac {}{}{}{}{1+x}{x^5}} \, dx\) [431]
3.5.32 \(\int \sqrt {x+x^{5/2}} \, dx\) [432]
3.5.33 \(\int \genfrac {}{}{}{}{1}{\sqrt {x}+x^{3/2}} \, dx\) [433]
3.5.34 \(\int x \sqrt {x^2 (a+b x^3)} \, dx\) [434]
3.5.35 \(\int x \sqrt {a x^2+b x^5} \, dx\) [435]
3.5.36 \(\int \sqrt {x^4 (a+b x^3)} \, dx\) [436]
3.5.37 \(\int \genfrac {}{}{}{}{1}{\sqrt [3]{a \sqrt [3]{x}+b x^{2/3}}} \, dx\) [437]
3.5.38 \(\int \genfrac {}{}{}{}{1}{(a \sqrt [3]{x}+b x^{2/3})^{2/3}} \, dx\) [438]
3.5.39 \(\int x^m (a x^j+b x^n)^p \, dx\) [439]
3.5.40 \(\int x^{-1-p q} (b x^n+a x^q)^p \, dx\) [440]
3.5.41 \(\int x^{-1-n p} (b x^n+a x^q)^p \, dx\) [441]
3.5.42 \(\int x^{-1-n-(-1+p) q} (b x^n+a x^q)^p \, dx\) [442]
3.5.43 \(\int x^{-1-n (-1+p)-q} (b x^n+a x^q)^p \, dx\) [443]
3.5.44 \(\int (a x^m+b x^{1+m+m p})^p \, dx\) [444]
3.5.45 \(\int (x^m (a+b x^{1+m p}))^p \, dx\) [445]
3.5.46 \(\int x^n (x^m (a+b x^{1+n+m p}))^p \, dx\) [446]
3.5.47 \(\int x^n (a x^m+b x^{1+m+n+m p})^p \, dx\) [447]
3.5.48 \(\int \sqrt {x^{2 (-1+n)} (a+b x^n)} \, dx\) [448]
3.5.49 \(\int \sqrt [3]{x^{3 (-1+n)} (a+b x^n)} \, dx\) [449]
3.5.50 \(\int \sqrt [4]{x^{4 (-1+n)} (a+b x^n)} \, dx\) [450]
3.5.51 \(\int (x^{(-1+n) p} (a+b x^n))^{\genfrac {}{}{}{}{1}{p}} \, dx\) [451]
3.5.52 \(\int (x^{\genfrac {}{}{}{}{-1+n}{p}} (a+b x^n))^p \, dx\) [452]
3.5.53 \(\int x^{-1+n-p (1+q)} (a x^n+b x^p)^q \, dx\) [453]
3.5.54 \(\int x^{-1-n q-p (1+q)} (x^n (a+b x^p))^q \, dx\) [454]