I need to integrate this:

1/(x^4+4)

I have that it factors to (x^2+2x+2)(x^2-2x+2). I did the partial fraction decomposition correctly (I think), and I got this:

A=1/8

B=1/4

C=-1/8

D=1/8

I pulled 1/8 from the top of the integrations so I have to integrate:

(1/8)* the integral (x+2)/(x^2+2x+2) - (1/8)*the integral (x+2)/(x^2-2x+2).

That's where I'm stuck. Any help?