Been beating my head against the wall on an integral for awhile now.... (Headbang)

The question is this:

Compute the surface area generated by revolving the curve

about the x-axis.

I took the 1st derivative of the equation:

Easy enough. Then I went into my integral:

That didn't look very pretty, and I didn't seem to be getting anywhere trying to solve it (no u-sub, and integration by parts didn't seem to be working), so I tried to manipulate the equation several times to see if a different variation would work...

and

and

and

But I can't find one to work out. My professor stated on the assignment that the integral can be done exactly, otherwise I would have approximated it a long time ago.

Would one of you be able to possibly hint where I'm going wrong, or which form you'd take?