I'd start by trying to see if either -1 or -4 is a root of the top. That would help you lowert the power of that monstruosity. I doubt it is a non-reductible quintic that you got to integrate...if not, long division, get a rational expression plus a bunch of constant/linear/quadratic parts and integrate it each piece at a time.
If I recall,
\int{(a+b)}=\int{a}+\int{b}
So all components after the division should be very simple to integrate except the fraction if there is one...and that shouldn't be too bad neither.