Hi guys. I am trying to integrate

by trig substiution, but I'm not really sure if you can even do trig sub here since we are dealing with square roots. If I'm right, is there another method besides trig sub to evaluate this, even if it's not necessarily easier? This is what I got:

Let

So

Substitution yields

Simplification yields

or simply:

So now we have

Using a right triangle to make substitutions, my final answer is

So again, even if this right, is there another way to evaluate this?

Thanks for any help,

James