Integration

Hi there.
I'm stuck in this qustion

$\frac{ax+b}{x^2+2x+2}+\frac{cx+d}{x^2-2x+2}=\frac{1}{x^4+4}$

I'm having trouble working out the values of a,b,c,d.

I did:
(ax+b)(x^2-2x+2)+(cx+d)(x^2+2x+2)≡1
and got when x=0
(i) 2b+2d≡1
(ii)a=-c;
(iii)-2a+b+2c+d≡0;
(iv)2a-2b+2c+2d≡0

so c=-1/8; a=1/8
d=b=1/4

This doesn't seem right because i need to integrate the two fractions and it doesn't work.

Thanks.

Thanks!
Sorry I'm not seeing it.

How did you split the fraction? Obviously there arent any factors so...