integral of x*sqrt(2*x-1)

let u = 2x-1

x = (u+1)/2

du = 2 dx
dx = du/2

x*sqrt(2x-1) = (u+1)/2 * sqrt(u) * du/2
= 1/4 * (u^3/2 + u^1/2) du

can you take it from here?