Surface Integrals, Stokes & Divergence · Superchallenge problem

Let $\mathbf F = \dfrac{(x, y, z)}{(x^2 + y^2 + z^2)^{3/2}}$. Find the upward flux of $\mathbf F$ through the disk $x^2 + y^2 \le 3$, $z = 1$. Give an exact answer in terms of $\pi$.