`int x^5/sqrt(1+x^3) dx`

Answer

`(2)/(9)(1+x^(3))^(3//2)-(2)/(3)(1+x^(3))^(1//2)+C`

Explanation

`Put(1+x^(3))=t^(2)." Then",I=(2)/(3)int(t(t^(2)-1))/(sqrt(t))dt=(2)/(3)int(t^(5//2)-t^(1//2))dt`.