So I'm given the problem "An object fills the ellipsoid $x^2 + y^2 + 2z^2 = 1$ and that its density is given by $r^2 \sin(\theta)$" and asked to solve for the mass.
Converting to Spherical I said it's $$\int_0^{2\pi}\int_0^\pi \int_0^{(1+\cos^2\theta)^{-1/2}} r^4 \sin^2\theta\, dr\,d\theta\,d\phi$$ The integral seems impossible to evaluate so I know I messed up somewhere but don't know where.