How do I integrate this

The problem is:
Integrate( (2X^3 + 3X^2 + X - 1)/((X + 1)(X^2 + 2X + 2)^2) dX)

I get to Integrate( ((-1)/(X+1) + (X+3)/(X^2+2X+2) + (2X+3)/((X^2+2X+2)^2) dX)

I know how to integrate the first one, but not the second two terms. Please help!!

A MATH PROBLEM IS NOT A GUY

I've noticed a few of my profs saying this. Is it an American thing?