How to integrate without using trigonometric substitution: $\int{\frac{x}{\sqrt{1-x^4}}}dx$?

Question

How can I integrate the following without using Trigonometric substitution? $$\int{\frac{x}{\sqrt{1-x^4}}}dx$$ I tried substituting, $t = 1 - x^4$ but that didn't work. The solution according to my book is $$\frac{1}{2}\arcsin{\left(x^2\right)}+C$$

Answer 1

Factorize $1-x^4$ to $(1-x^2)(1+x^2)$. Substitute $t=x^2$.

Answer 2

HINT: Put $x$ square equal to $t$.