Answer
$\frac{1}{2}arcsin(x^{2})+C$
Work Step by Step
$\int\frac{x}{\sqrt (1-x^{4})}dx$
The denominator looks like it could be $arcsin$.
$\int\frac{du}{\sqrt (a^{2}-u^{2})}dx=arcsin(\frac{u}{a})+C$
$a=1$
$u=x^{2}$
$du=2dx$
$\frac{1}{2}\int\frac{2x}{\sqrt (1-x^{4})}dx$
$\frac{1}{2}[arcsin(\frac{x^{2}}{1})]+C$
$\frac{1}{2}arcsin(x^{2})+C$
