Question

$\int 5x^2\sqrt{1-x^3}dx$

Answer 1

$-\frac{10}{9}(1-x^3)^{\frac{3}{2}}+C$

Answer 2

Substitute $u=1-x^3$ so that $du=-3x^2dx$; rewrite and integrate $u^{1/2}$ to get the answer.