Evaluate the triple integral of $f(x,y,z)=z(x^2+y^2+z^2)^{-3/2}$ over the part of the ball $x^2+y^2+z^2\le 4$ defined by $z\ge 1$.

$\int\!\!\int\!\!\int _{\mathcal{W}} f( x,y,z ) \,dV =$