Changing order of integration problem

[Chandasouk]

http://img576.imageshack.us/f/64147491.jpg/

I understand how to obtain the new bounds when you change integration, I'm just having problems actually integrating. How did they rewrite the equation to that of step 2?

 

[LCKurtz]

The inner integral is a dy integral of this form (because x is constant in the dy integral)

\int \frac a {(b+y)^\frac 1 2}\ dy

Let u = b + y, du = dy so it looks like

\int a(u)^{-\frac 1 2}\ du

and integrate it.