I have been stuck with this problem for a while:
Evaluate $$ \iiint\_D\frac{1}{x^2 + y^2 + (z-1)^2}\,dx\,dy\,dz \,,$$

where $D$ is a sphere centered at $(0,0,0)$ with a radius of $1/2$.

I couldn't make any progress without the use of spherical coordinates. Furthermore substituting $D(x, y, z)$ with spherical coordinates centered at $(0,0,0)$ leads to a very complex integral. It is obvious that we need to substitute $x, y, z$ to spherical coordinates centered at $(0, 0, 1)$ so that our denominator simplifies to $r^2$. The problem arises when you try to represent D(the $(0,0,0)$ radius $= 1/2$ sphere) with spherical coordinates, because they need to be centered at $(0,0,1)$. Any help?