Find the value of $\int_{-\infty}^\infty \int_{-\infty}^\infty e^{-(x^2+xy+y^2)} \, dx\,dy$ 
Given that $\int_{-\infty}^\infty e^{-x^2} \, dx=\sqrt{\pi}$. Find the value of $$\int_{-\infty}^\infty\int_{-\infty}^\infty e^{-(x^2+xy+y^2)} \, dx\,dy$$

I don't understand how I find this double integral by using the given data. Please help.

Integrate in polar coordinates
$$
\begin{align}
&\int_{-\infty}^\infty\int_{-\infty}^\infty e^{-(x^2+xy+y^2)}\,\mathrm{d}x\,\mathrm{d}y\\
=&\int_{0}^{2\pi} \int_{0}^\infty e^{-r^2(1+\frac12\sin2\theta)}rdr d\theta
= \int_{0}^{2\pi} \frac{d\theta}{2+\sin2\theta}
=\frac{2\pi}{\sqrt3}
\end{align}
$$
