residue calculus - Improper integral computation using complex analysis

$$pv\int_{-\infty}^{\infty} \frac{x}{(x^2+4)(x^2+2x+2)}dx$$

I get an answer of $-\frac{\pi}{5}$ but wolframalpha disagrees by a factor of $2$ ($-\frac{\pi}{10}$):

http://www.wolframalpha.com/input/?i=integration+%28z%2F%28%28z^2%2B4%29%28z^2%2B2z%2B2%29%29%29++from+-+infinity+to+infinity

I cannot spot the error.

I get these residues:

$$Res(-1+i)=\frac{1+3i}{20}$$

$$Res(2i)=\frac{-2-i}{40}$$

which I add up and multiply by $2\pi i$.

What am I doing wrong?

Answer

$$\text{Res}(2i)={x\over (x+2i)(x^2+2x+2)}\Big{|}_{x=2i}={2i\over4i(4i-2)}={1\over4(-1+2i)}={-1-2i\over20}$$