3.4 Integrals 301 to 396

\(\int \genfrac {}{}{}{}{1}{x^4 (a-b x^2)^{3/2} \sqrt {c+d x^2} (e+f x^2)^2} \, dx\) [301]
\(\int x^4 \sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2} \, dx\) [302]
\(\int x^2 \sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2} \, dx\) [303]
\(\int \sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2} \, dx\) [304]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}}{x^2} \, dx\) [305]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}}{x^4} \, dx\) [306]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}}{x^6} \, dx\) [307]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}}{x^8} \, dx\) [308]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}}{x^{10}} \, dx\) [309]
\(\int x^4 \sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2} \, dx\) [310]
\(\int x^2 \sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2} \, dx\) [311]
\(\int \sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2} \, dx\) [312]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2}}{x^2} \, dx\) [313]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2}}{x^4} \, dx\) [314]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2}}{x^6} \, dx\) [315]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2}}{x^8} \, dx\) [316]
\(\int \genfrac {}{}{}{}{x^4 \sqrt {a+b x^2} \sqrt {c+d x^2}}{\sqrt {e+f x^2}} \, dx\) [317]
\(\int \genfrac {}{}{}{}{x^2 \sqrt {a+b x^2} \sqrt {c+d x^2}}{\sqrt {e+f x^2}} \, dx\) [318]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{\sqrt {e+f x^2}} \, dx\) [319]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{x^2 \sqrt {e+f x^2}} \, dx\) [320]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{x^4 \sqrt {e+f x^2}} \, dx\) [321]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{x^6 \sqrt {e+f x^2}} \, dx\) [322]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{x^8 \sqrt {e+f x^2}} \, dx\) [323]
\(\int \genfrac {}{}{}{}{x^4 \sqrt {a+b x^2} \sqrt {c+d x^2}}{(e+f x^2)^{3/2}} \, dx\) [324]
\(\int \genfrac {}{}{}{}{x^2 \sqrt {a+b x^2} \sqrt {c+d x^2}}{(e+f x^2)^{3/2}} \, dx\) [325]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{(e+f x^2)^{3/2}} \, dx\) [326]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{x^2 (e+f x^2)^{3/2}} \, dx\) [327]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{x^4 (e+f x^2)^{3/2}} \, dx\) [328]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{x^6 (e+f x^2)^{3/2}} \, dx\) [329]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{x^8 (e+f x^2)^{3/2}} \, dx\) [330]
\(\int \genfrac {}{}{}{}{x^6 \sqrt {a+b x^2} \sqrt {c+d x^2}}{(e+f x^2)^{5/2}} \, dx\) [331]
\(\int \genfrac {}{}{}{}{x^4 \sqrt {a+b x^2} \sqrt {c+d x^2}}{(e+f x^2)^{5/2}} \, dx\) [332]
\(\int \genfrac {}{}{}{}{x^2 \sqrt {a+b x^2} \sqrt {c+d x^2}}{(e+f x^2)^{5/2}} \, dx\) [333]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{(e+f x^2)^{5/2}} \, dx\) [334]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{x^2 (e+f x^2)^{5/2}} \, dx\) [335]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{x^4 (e+f x^2)^{5/2}} \, dx\) [336]
\(\int \genfrac {}{}{}{}{\sqrt {a+b x^2} \sqrt {c+d x^2}}{x^6 (e+f x^2)^{5/2}} \, dx\) [337]
\(\int \genfrac {}{}{}{}{x^4 \sqrt {e+f x^2}}{\sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [338]
\(\int \genfrac {}{}{}{}{x^2 \sqrt {e+f x^2}}{\sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [339]
\(\int \genfrac {}{}{}{}{\sqrt {e+f x^2}}{\sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [340]
\(\int \genfrac {}{}{}{}{\sqrt {e+f x^2}}{x^2 \sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [341]
\(\int \genfrac {}{}{}{}{\sqrt {e+f x^2}}{x^4 \sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [342]
\(\int \genfrac {}{}{}{}{\sqrt {e+f x^2}}{x^6 \sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [343]
\(\int \genfrac {}{}{}{}{x^4 (e+f x^2)^{3/2}}{\sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [344]
\(\int \genfrac {}{}{}{}{x^2 (e+f x^2)^{3/2}}{\sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [345]
\(\int \genfrac {}{}{}{}{(e+f x^2)^{3/2}}{\sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [346]
\(\int \genfrac {}{}{}{}{(e+f x^2)^{3/2}}{x^2 \sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [347]
\(\int \genfrac {}{}{}{}{(e+f x^2)^{3/2}}{x^4 \sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [348]
\(\int \genfrac {}{}{}{}{(e+f x^2)^{3/2}}{x^6 \sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [349]
\(\int \genfrac {}{}{}{}{(e+f x^2)^{3/2}}{x^8 \sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [350]
\(\int \genfrac {}{}{}{}{\sqrt {e+f x^2}}{x^2 \sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [351]
\(\int \genfrac {}{}{}{}{\sqrt {e+f x^2}}{x^2 \sqrt {a-b x^2} \sqrt {c+d x^2}} \, dx\) [352]
\(\int \genfrac {}{}{}{}{\sqrt {e+f x^2}}{x^2 \sqrt {a+b x^2} \sqrt {c-d x^2}} \, dx\) [353]
\(\int \genfrac {}{}{}{}{\sqrt {e+f x^2}}{x^2 \sqrt {a-b x^2} \sqrt {c-d x^2}} \, dx\) [354]
\(\int \genfrac {}{}{}{}{\sqrt {e-f x^2}}{x^2 \sqrt {a+b x^2} \sqrt {c+d x^2}} \, dx\) [355]
\(\int \genfrac {}{}{}{}{\sqrt {e-f x^2}}{x^2 \sqrt {a-b x^2} \sqrt {c+d x^2}} \, dx\) [356]
\(\int \genfrac {}{}{}{}{\sqrt {e-f x^2}}{x^2 \sqrt {a+b x^2} \sqrt {c-d x^2}} \, dx\) [357]
\(\int \genfrac {}{}{}{}{\sqrt {e-f x^2}}{x^2 \sqrt {a-b x^2} \sqrt {c-d x^2}} \, dx\) [358]
\(\int \genfrac {}{}{}{}{x^6}{\sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}} \, dx\) [359]
\(\int \genfrac {}{}{}{}{x^4}{\sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}} \, dx\) [360]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}} \, dx\) [361]
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}} \, dx\) [362]
\(\int \genfrac {}{}{}{}{1}{x^2 \sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}} \, dx\) [363]
\(\int \genfrac {}{}{}{}{1}{x^4 \sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}} \, dx\) [364]
\(\int \genfrac {}{}{}{}{1}{x^6 \sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}} \, dx\) [365]
\(\int \genfrac {}{}{}{}{x^8}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2}} \, dx\) [366]
\(\int \genfrac {}{}{}{}{x^6}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2}} \, dx\) [367]
\(\int \genfrac {}{}{}{}{x^4}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2}} \, dx\) [368]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2}} \, dx\) [369]
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2}} \, dx\) [370]
\(\int \genfrac {}{}{}{}{1}{x^2 \sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2}} \, dx\) [371]
\(\int \genfrac {}{}{}{}{1}{x^4 \sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2}} \, dx\) [372]
\(\int \genfrac {}{}{}{}{x^{10}}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{5/2}} \, dx\) [373]
\(\int \genfrac {}{}{}{}{x^8}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{5/2}} \, dx\) [374]
\(\int \genfrac {}{}{}{}{x^6}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{5/2}} \, dx\) [375]
\(\int \genfrac {}{}{}{}{x^4}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{5/2}} \, dx\) [376]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{5/2}} \, dx\) [377]
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{5/2}} \, dx\) [378]
\(\int \genfrac {}{}{}{}{1}{x^2 \sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{5/2}} \, dx\) [379]
\(\int \genfrac {}{}{}{}{1}{x^4 \sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{5/2}} \, dx\) [380]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}} \, dx\) [381]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a-b x^2} \sqrt {c+d x^2} \sqrt {e+f x^2}} \, dx\) [382]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b x^2} \sqrt {c-d x^2} \sqrt {e+f x^2}} \, dx\) [383]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a-b x^2} \sqrt {c-d x^2} \sqrt {e+f x^2}} \, dx\) [384]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b x^2} \sqrt {c+d x^2} \sqrt {e-f x^2}} \, dx\) [385]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a-b x^2} \sqrt {c+d x^2} \sqrt {e-f x^2}} \, dx\) [386]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b x^2} \sqrt {c-d x^2} \sqrt {e-f x^2}} \, dx\) [387]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a-b x^2} \sqrt {c-d x^2} \sqrt {e-f x^2}} \, dx\) [388]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2}} \, dx\) [389]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a-b x^2} \sqrt {c+d x^2} (e+f x^2)^{3/2}} \, dx\) [390]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b x^2} \sqrt {c-d x^2} (e+f x^2)^{3/2}} \, dx\) [391]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a-b x^2} \sqrt {c-d x^2} (e+f x^2)^{3/2}} \, dx\) [392]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b x^2} \sqrt {c+d x^2} (e-f x^2)^{3/2}} \, dx\) [393]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a-b x^2} \sqrt {c+d x^2} (e-f x^2)^{3/2}} \, dx\) [394]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b x^2} \sqrt {c-d x^2} (e-f x^2)^{3/2}} \, dx\) [395]
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a-b x^2} \sqrt {c-d x^2} (e-f x^2)^{3/2}} \, dx\) [396]