Question:
$\frac{x^{3}}{\sqrt{1-x^{8}}}$
Solution:
$\frac{x^{3}}{\sqrt{1-x^{8}}}$
Let $x^{4}=t \Rightarrow 4 x^{3} d x=d t$
$\Rightarrow \int \frac{x^{3}}{\sqrt{1-x^{8}}} d x=\frac{1}{4} \int \frac{d t}{\sqrt{1-t^{2}}}$
$=\frac{1}{4} \sin ^{-1} t+C$
$=\frac{1}{4} \sin ^{-1}\left(x^{4}\right)+C$