Question

Find the anti-derivative of the integral
[3sqrt(x)(2x^2-4)]dx

Answer 1

∫3√x (2x^2-4) dx
If we let
u = √x
du = 1/2√x dx
x = u^2

and we have
∫3√x (2x^2-4) dx
∫6x (2x^2-4) dx/2√x
∫6u^2(2u^4-4) du
and that's just power stuff.