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!!

2nd guy:
(X+1)/(X^2+2X+2) + 2/(X^2+2X+2)
(X+1)/(X^2+2X+2) + 2/((X+1)^2+1)

u sub:
u = X^2+2X+2 in first case,
u = X+1 in 2nd case

3rd guy is a bit harder to integrate; I'll think about it in the future... maybe

A MATH PROBLEM IS NOT A GUY

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

Hermite reduction.

http://www.wolframalpha.com/input/?i=integral(((-1)%2F(X%2B1)+%2B+(X%2B3)%2F(X^2%2B2X%2B2)+%2B+(2X%2B3)%2F((X^2%2B2X%2B2)^2)%2CX

>>3
He is probably exasperated from the constant reference to inanimate objects by foreign-born teaching assistants as "dees guy."