$(1$ point$)$ Compute the flux integral ${}_S$vec$(F)*dvec(S),$ where

vec$(F)=($:$\frac{x}{(4x^2+2y^2+z^2{)}^{\frac{3}{2}}},\frac{y}{(4x^2+2y^2+z^2{)}^{\frac{3}{2}}},\frac{z}{(4x^2+2y^2+z^2{)}^{\frac{3}{2}}}$:$)$

and $S$ is the sphere $x^2+y^2+z^2=1,$ pointing outward. Hint: $(1)$ Compute the divergence of vec$(F)$; $(2)$ vec$(F)$ is not continuous at the origin.