Integration By substitution

Question

ive been given this equation

int x^2(x^3-6)^3 dx using u = x^3 -6

but i don't understand how to do it
please help

Answer 1

If you let u = x^3 -6, then
du = 2 x^2 dx
and the integral can be rewritten as
int (1/2) u^3 du
which is (1/6)u^4/4 = (1/6)(x^3-6)^4