Integration of a square root

While working on finding the arc length of the parametrized curve where is in . i got to an integral that i couldn't manage to integrate. Here is the work so far leading up to the problematic integral so that it may be checked for errors.

arc length by definition

by taking the partials of g

by taking the length

by simplification

...? by integration

I'm thinking it has something to do with simplifying the inside of the sqrt some more, or maybe a trig substitution (ugh!)

By the way, the answer is

(Appologies if this is posted in the wrong thread as it is coming from an analysis course, but it really is only the integral that i am needing help with, so i see it fit that i place this thread here. Thank you)