This simple looking integral turned out to be a monster. See what people came up with here
The major step is as follows:
You need to factorize the polynomial into irreducible polynomials in .
The best way to do this is to factorize this in in linear factors.
We need to find all solutions to,
De Moiver's theorem,
But why you want to do that I have no idea. I guess that is why you are a CrazyAsian.