Vector Calculus · Superchallenge problem

Let $\mathbf F = \dfrac{(x, y, z)}{(x^2 + y^2 + z^2)^{3/2}} + (x, 0, 0)$ and let $S$ be the sphere $(x - 1)^2 + y^2 + z^2 = 4$ with outward normal. Find $\displaystyle\iint_S\mathbf F\cdot d\mathbf S$. Give your answer in terms of $\pi$.