Question

How do you integrate `intx^2/(1+x^3)^2` using substitution?

Answer 1

`=C -1/(3(1+x^3))`

Explanation:

`u = 1+x^3 implies du = 3x^2dx`

`therefore 1/3du = x^2dx`

Integral becomes

`1/3int (du)/u^2 = -1/(3u) +C`

`=C -1/(3(1+x^3))`