Evaluate the integral of x * sqrt(x-1) from [1,2].

Question

I let u=x-1 and du=1*dx, but then I can't get rid of the x to start integrating?

The answer in the book is 16/15.

Answer 1

Let
u^2 = x-1
2u du = dx
x = u^2+1

∫x√(x-1) dx
= ∫(u^2+1)(u)(2u du)
...