I'm stuck on the following vector integral
For a sphere of uniform p (so it is not a function of y in this case). Where x is the position vector of a point lying outside the sphere and y is the position vector of a point lying inside the sphere.
The Attempt at a Solution
I attempted this by taking advantage of the symmetry and picking x to lie along the z axis. I then attempted to integrate it in spherical polar coordinates and wrote the components of y in terms of theta and phi (the latter being the azimuthal angle). I wrote the volume element in spherical polars ignoring the vector notation for now. But after doing all this I get to an expression:
Which seem's like a very difficult integral to me.
Thanks in advance for your help.