What's the antiderivative of x(2x-6)^(1/2)?
Let 2x-6 = v
x = (v/2) + 3
dx = dv/2
You want the integral of
(v/2)^v^1/2 dv/2 + 3 v^1/2 dv/2
= (1/4) v^3/2 dv + (3/2) v^1/2 dv
When you are through doing that integratrion, substitute (2x-6) for v