Notice how the top is the derivative of the bottom. This gives you your first time: is one of the result you should have at your fingertips.

No it's not, I'm talking rubbish. Sorry, forget I spoke ...

Okay, so make the top (x + 1 - 5) and get 2 integrals, one of x+1 / x^2 + 2x + 5, and one of -5 / x^2 + 2x + 5

and the first part drops out.