Vector Calculus · Superchallenge problem

Find the outward flux of $\mathbf F = \left(x^3 + y^2z,\; y^3 + xe^{z},\; z^3 + \sin(xy)\right)$ through the ellipsoid $x^2 + \dfrac{y^2}{4} + \dfrac{z^2}{9} = 1$. Give your answer in terms of $\pi$.