calculus , double integral at ellipse region Let S be the region satisfying $ 3x^2 + 2xy + y^2 \leq\ 1$ in the real plane $R^{2}$.
Then compute the value of the double integral 
$$\int\int_S\ e^{(3x^2+2xy+y^2)}dxdy$$
i learned double integral at polar coordinates.
but i didn't solve this problem.
Please give me hint or answer.

$$3x^2 +2xy +y^2 = 3(x + y/3)^2 + \frac{2 y^2}{3}$$
So try the substitution
$u = \sqrt{3} x + y/\sqrt{3}, 
v = \sqrt{2/3} y$
This should transform it into an integral over the unit circle. Then you can use polar coordinates.
