Question

How do you integrate `int x^3/(1+x^4)^(1/3)` using substitution?

Answer 1

`3/8(1+x^4)^(2/3) + C`

Explanation:

Let `1+x^4=t`. Then `4x^3 dx = dt` and the integral becomes

`1/4 int t^(-1/3) dt`

`=(1/4)t^(-1/3+1)/((-1/3+1)) + C`

`=3/8(1+x^4)^(2/3) + C`