3.4 Integrals 301 to 400

\(\int \genfrac {}{}{}{}{1}{(a x+b x)^3} \, dx\) [301]
\(\int \genfrac {}{}{}{}{1}{a x^2+b x^2} \, dx\) [302]
\(\int \genfrac {}{}{}{}{1}{a x^n+b x^n} \, dx\) [303]
\(\int \genfrac {}{}{}{}{1}{(a x^n+b x^n)^2} \, dx\) [304]
\(\int \genfrac {}{}{}{}{1}{(a x^n+b x^n)^3} \, dx\) [305]
\(\int (a x+b x^{14})^{12} \, dx\) [306]
\(\int x^{12} (a x+b x^{26})^{12} \, dx\) [307]
\(\int x^{24} (a x+b x^{38})^{12} \, dx\) [308]
\(\int x^{12 (-1+m)} (a x+b x^{2+12 m})^{12} \, dx\) [309]
\(\int (a x+b x^{14})^{12} \, dx\) [310]
\(\int (a x^2+b x^{27})^{12} \, dx\) [311]
\(\int (a x^3+b x^{40})^{12} \, dx\) [312]
\(\int (a x^m+b x^{1+13 m})^{12} \, dx\) [313]
\(\int (a x^m+b x^{1+6 m})^5 \, dx\) [314]
\(\int \genfrac {}{}{}{}{1}{(b x^{1-2 m}+a x^m)^3} \, dx\) [315]
\(\int \genfrac {}{}{}{}{1}{\genfrac {}{}{}{}{b}{x}+a x} \, dx\) [316]
\(\int \genfrac {}{}{}{}{1}{\genfrac {}{}{}{}{b}{x^2}+a x} \, dx\) [317]
\(\int \genfrac {}{}{}{}{1}{\genfrac {}{}{}{}{b}{x^3}+a x} \, dx\) [318]
\(\int \genfrac {}{}{}{}{1}{(\genfrac {}{}{}{}{b}{x}+a x)^3} \, dx\) [319]
\(\int \genfrac {}{}{}{}{1}{(\genfrac {}{}{}{}{b}{x^3}+a x^2)^3} \, dx\) [320]
\(\int \genfrac {}{}{}{}{1}{(\genfrac {}{}{}{}{b}{x^5}+a x^3)^3} \, dx\) [321]
\(\int (\genfrac {}{}{}{}{a}{x}+b x)^2 \, dx\) [322]
\(\int (\genfrac {}{}{}{}{a}{x}+b x)^3 \, dx\) [323]
\(\int (\genfrac {}{}{}{}{a}{x}+b x)^4 \, dx\) [324]
\(\int \genfrac {}{}{}{}{x}{\genfrac {}{}{}{}{1}{x}+x} \, dx\) [325]
\(\int \genfrac {}{}{}{}{1}{\genfrac {}{}{}{}{1}{x^2}+x^3} \, dx\) [326]
\(\int x^p (a x^n+b x^{1+13 n+p})^{12} \, dx\) [327]
\(\int x^{12} (a+b x^{13})^{12} \, dx\) [328]
\(\int x^{12} (a x+b x^{26})^{12} \, dx\) [329]
\(\int x^{12} (a x^2+b x^{39})^{12} \, dx\) [330]
\(\int x^{24} (a+b x^{25})^{12} \, dx\) [331]
\(\int x^{24} (a x+b x^{38})^{12} \, dx\) [332]
\(\int x^{36} (a+b x^{37})^{12} \, dx\) [333]
\(\int \genfrac {}{}{}{}{1}{a x+b x^n} \, dx\) [334]
\(\int \genfrac {}{}{}{}{1}{a x+b x^{1+n}} \, dx\) [335]
\(\int \genfrac {}{}{}{}{1}{a x+b x^{1-n}} \, dx\) [336]
\(\int \genfrac {}{}{}{}{1}{2 x+3 x^{1+n}} \, dx\) [337]
\(\int \genfrac {}{}{}{}{1}{2 x+3 x^{1-n}} \, dx\) [338]
\(\int \genfrac {}{}{}{}{1}{-\sqrt {x}+x} \, dx\) [339]
\(\int \genfrac {}{}{}{}{1}{-x^{3/5}+x} \, dx\) [340]
\(\int \genfrac {}{}{}{}{1}{\genfrac {}{}{}{}{1}{\sqrt [3]{x}}+x} \, dx\) [341]
\(\int \genfrac {}{}{}{}{1}{x+x^{\sqrt {2}}} \, dx\) [342]
\(\int x^{-1-\genfrac {}{}{}{}{j}{2}} \sqrt {a x^j+b x^n} \, dx\) [343]
\(\int (c x)^{-1-\genfrac {}{}{}{}{j}{2}} \sqrt {a x^j+b x^n} \, dx\) [344]
\(\int \genfrac {}{}{}{}{\sqrt {a x^3+b x^n}}{(c x)^{5/2}} \, dx\) [345]
\(\int \genfrac {}{}{}{}{\sqrt {a x^2+b x^n}}{c^2 x^2} \, dx\) [346]
\(\int \genfrac {}{}{}{}{\sqrt {a x+b x^n}}{(c x)^{3/2}} \, dx\) [347]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^n}}{c x} \, dx\) [348]
\(\int \genfrac {}{}{}{}{\sqrt {\genfrac {}{}{}{}{a}{x}+b x^n}}{\sqrt {c x}} \, dx\) [349]
\(\int \sqrt {\genfrac {}{}{}{}{a}{x^2}+b x^n} \, dx\) [350]
\(\int \sqrt {c x} \sqrt {\genfrac {}{}{}{}{a}{x^3}+b x^n} \, dx\) [351]
\(\int (c x)^{-1-\genfrac {}{}{}{}{3 j}{2}} (a x^j+b x^n)^{3/2} \, dx\) [352]
\(\int \genfrac {}{}{}{}{(a x^3+b x^n)^{3/2}}{(c x)^{11/2}} \, dx\) [353]
\(\int \genfrac {}{}{}{}{(a x^2+b x^n)^{3/2}}{c^4 x^4} \, dx\) [354]
\(\int \genfrac {}{}{}{}{(a x+b x^n)^{3/2}}{(c x)^{5/2}} \, dx\) [355]
\(\int \genfrac {}{}{}{}{(a+b x^n)^{3/2}}{c x} \, dx\) [356]
\(\int \sqrt {c x} (\genfrac {}{}{}{}{a}{x}+b x^n)^{3/2} \, dx\) [357]
\(\int c^2 x^2 (\genfrac {}{}{}{}{a}{x^2}+b x^n)^{3/2} \, dx\) [358]
\(\int (c x)^{7/2} (\genfrac {}{}{}{}{a}{x^3}+b x^n)^{3/2} \, dx\) [359]
\(\int c^5 x^5 (\genfrac {}{}{}{}{a}{x^4}+b x^n)^{3/2} \, dx\) [360]
\(\int \sqrt {\genfrac {}{}{}{}{a+b x}{x^2}} \, dx\) [361]
\(\int \sqrt {\genfrac {}{}{}{}{a+b x^2}{x^2}} \, dx\) [362]
\(\int \sqrt {\genfrac {}{}{}{}{a+b x^3}{x^2}} \, dx\) [363]
\(\int \sqrt {\genfrac {}{}{}{}{a+b x^n}{x^2}} \, dx\) [364]
\(\int \sqrt {\genfrac {}{}{}{}{-a+b x}{x^2}} \, dx\) [365]
\(\int \sqrt {\genfrac {}{}{}{}{-a+b x^2}{x^2}} \, dx\) [366]
\(\int \sqrt {\genfrac {}{}{}{}{-a+b x^3}{x^2}} \, dx\) [367]
\(\int \sqrt {\genfrac {}{}{}{}{-a+b x^n}{x^2}} \, dx\) [368]
\(\int \genfrac {}{}{}{}{(c x)^{-1+\genfrac {}{}{}{}{j}{2}}}{\sqrt {a x^j+b x^n}} \, dx\) [369]
\(\int \genfrac {}{}{}{}{\sqrt {c x}}{\sqrt {a x^3+b x^n}} \, dx\) [370]
\(\int \genfrac {}{}{}{}{1}{\sqrt {a x^2+b x^n}} \, dx\) [371]
\(\int \genfrac {}{}{}{}{1}{\sqrt {c x} \sqrt {a x+b x^n}} \, dx\) [372]
\(\int \genfrac {}{}{}{}{1}{c x \sqrt {a+b x^n}} \, dx\) [373]
\(\int \genfrac {}{}{}{}{1}{(c x)^{3/2} \sqrt {\genfrac {}{}{}{}{a}{x}+b x^n}} \, dx\) [374]
\(\int \genfrac {}{}{}{}{1}{c^2 x^2 \sqrt {\genfrac {}{}{}{}{a}{x^2}+b x^n}} \, dx\) [375]
\(\int \genfrac {}{}{}{}{1}{(c x)^{5/2} \sqrt {\genfrac {}{}{}{}{a}{x^3}+b x^n}} \, dx\) [376]
\(\int \genfrac {}{}{}{}{(c x)^{-1+\genfrac {}{}{}{}{3 j}{2}}}{(a x^j+b x^n)^{3/2}} \, dx\) [377]
\(\int \genfrac {}{}{}{}{(c x)^{7/2}}{(a x^3+b x^n)^{3/2}} \, dx\) [378]
\(\int \genfrac {}{}{}{}{c^2 x^2}{(a x^2+b x^n)^{3/2}} \, dx\) [379]
\(\int \genfrac {}{}{}{}{\sqrt {c x}}{(a x+b x^n)^{3/2}} \, dx\) [380]
\(\int \genfrac {}{}{}{}{1}{c x (a+b x^n)^{3/2}} \, dx\) [381]
\(\int \genfrac {}{}{}{}{1}{(c x)^{5/2} (\genfrac {}{}{}{}{a}{x}+b x^n)^{3/2}} \, dx\) [382]
\(\int \genfrac {}{}{}{}{1}{c^4 x^4 (\genfrac {}{}{}{}{a}{x^2}+b x^n)^{3/2}} \, dx\) [383]
\(\int \genfrac {}{}{}{}{1}{(c x)^{11/2} (\genfrac {}{}{}{}{a}{x^3}+b x^n)^{3/2}} \, dx\) [384]
\(\int \genfrac {}{}{}{}{1}{c^7 x^7 (\genfrac {}{}{}{}{a}{x^4}+b x^n)^{3/2}} \, dx\) [385]
\(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a+b x^3}{x}}} \, dx\) [386]
\(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a+b x^4}{x^2}}} \, dx\) [387]
\(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a+b x^5}{x^3}}} \, dx\) [388]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x^{2-n} (a+b x^n)}} \, dx\) [389]
\(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a-b x^3}{x}}} \, dx\) [390]
\(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a-b x^4}{x^2}}} \, dx\) [391]
\(\int \genfrac {}{}{}{}{1}{\sqrt {\genfrac {}{}{}{}{a-b x^5}{x^3}}} \, dx\) [392]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x^{2-n} (a-b x^n)}} \, dx\) [393]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x^n (a+b x^{2-n})}} \, dx\) [394]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x^2 (b+a x^{-2+n})}} \, dx\) [395]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x (b x+a x^{-1+n})}} \, dx\) [396]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x^n (a-b x^{2-n})}} \, dx\) [397]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x^2 (-b+a x^{-2+n})}} \, dx\) [398]
\(\int \genfrac {}{}{}{}{1}{\sqrt {x (-b x+a x^{-1+n})}} \, dx\) [399]
\(\int (c x)^m (a x^j+b x^n)^{3/2} \, dx\) [400]