Also two other questions...
1) Do all constants hold over? No matter if they are from the original problem or from the differentiation of U?
2) If there is a plus or minus a number in the original problem, do I put that out in front of the integral and let it hold over, or do I integrate at the same time I integrate Ul?
My rule to choose substitution is whatever you don't like replace with a new letter. You tried that, but it didn't give you a simpler integral. I know that I have to change x^4, since a linear expresion did not work, a quadratic on the bottom I can deal with.
If you have square roots, or radical, almost all the times works by using a new variable for the whole radical.