Integral of expression with radical

[ghastlymeanlo]

Homework Statement

There's a problem that involves triple integrals, but basically, I've boiled all of it down to the following single integral but cannot proceed any further.

∫u² sqrt(a²-u²) du
from 0 to a

where a is a constant

Homework Equations

The Attempt at a Solution

I attempted to use a change of variables, where
v = a² - u² and
dv = -2udu

but i still can't integrate it after substituting in for all u's.

 

[vela]

How about a trig substitution?