Closed form : [math] \int\limits_{0}^{2\pi}d\phi \int\limits_{0}^{\pi}d\theta \frac{b^2 \sin^3 \theta \cos^2 \phi}{b^2 \sin^2\theta \cos^2 \phi +a^2 \sin^2\theta \cos^2 \phi + a^2 b^2 \cos^2 \theta}e^{-\frac{u^2}{2}\sin^2\theta \cos^2 \phi} [/math] ?
valid question