Surface Integrals, Stokes & Divergence · Challenge problem

Let $\mathbf F = \dfrac{(x, y, z)}{(x^2 + y^2 + z^2)^{3/2}}$. Find the flux of $\mathbf F$ outward (away from the $z$-axis) through the lateral surface of the cylinder $x^2 + y^2 = 1$, $-1 \le z \le 1$ (the side only, no top or bottom). Give an exact answer.