improper integrals - Show that $int_{-infty}^{infty}frac{x^2dx}{(x^2+1)^2(x^2+2x+2)}=frac{7pi}{50}$

Show that

$$\int_{-\infty}^{\infty}\frac{x^2dx}{(x^2+1)^2(x^2+2x+2)}=\frac{7\pi}{50} $$

So I figured since it's an improper integral I should change the limits

$$\lim_{m_1\to-\infty}\int_{m_1}^{0}\frac{x^2dx}{(x^2+1)^2(x^2+2x+2)}+ \lim_{m_2\to\infty}\int_{0}^{m_2}\frac{x^2dx}{(x^2+1)^2(x^2+2x+2)}$$

I'm however not sure how to evaluate this. Any help would be great - thanks.