Triple Integrals & Coordinate Systems · Superchallenge problem

Let $B$ be the solid unit ball $x^2 + y^2 + z^2 \le 1$ and $N = (0, 0, 1)$, its north pole. Evaluate the improper integral $\displaystyle\iiint_B\dfrac{dV}{x^2 + y^2 + (z - 1)^2}$ (the integrand is the reciprocal of the squared distance to $N$). Give your answer in terms of $\pi$.