Integrate the following functions `x^3/sqrt(1-x^8)`

Explanation

`int x^3/sqrt(1-x^8) dx = int x^3/sqrt(1-(x^4)^2) dx`.
put `t = x^4`. Then `dt = 4x^3 dx`
therefore Required integral
=`int 1/sqrt(1-t^2) 1/4 dt = 1/4 sin^-1 t+c`
=`1/4 sin^-1 x^4 +c`