Mathematica can't solve simple force-generated-by-cuboidal-planet integral?

Question

f[x_,y_,z_] = Simplify[({x,y,z} - {x0,y0,z0})/Norm[{x,y,z} - {x0,y0,z0}]^3,  
Element[{x,y,z,x0,y0,z0}, Reals]] 

Integrate[f[x,y,z],{x,-1/2,1/2},{y,-1/2,1/2},{z,-1/2,1/2}] 

While attempting to help https://astronomy.stackexchange.com/questions/8237 I ran into the integral above.

It seems like a simple enough integral, but Mathematica hangs on it.

It even hangs on the much simpler:

Integrate[f[x,y,z][[1]],{x,-1/2,1/2}]  

Is this really a difficult integral or am I doing something wrong?

Answer 1

This is a start

$Version

"10.0 for Mac OS X x86 (64-bit) (December 4, 2014)"

assume = Element[{x, y, z, x0, y0, z0}, Reals];

f[x_, y_, z_] = Simplify[
   ({x, y, z} - {x0, y0, z0})/Norm[{x, y, z} - {x0, y0, z0}]^3,
   assume];

f1[x_, y_, z_] = f[x, y, z][[1]];

Simplify[
 Integrate[f1[x, y, z], {x, -1/2, 1/2}, Assumptions -> assume],
 assume]