Average electric field in spherical volume

[jam357]

Homework Statement

Show that the average electric field within a spherical region, due to a single point charge, q at a distance r from the center, within the sphere is the same as the field at r due to a uniformly charged sphere with charge density p = -3q/4pi(R^3)

Homework Equations

The Attempt at a Solution

I can set up the integral for the average electric field, but run into problems when trying to evaluate it. I don't know whether there is a better way to tackle this problem, but i would appreciate any advice on how to tackle this problem.
This is a problem out of Griffiths Intro to Electrodynamics, problem 3.41

 

[gabbagabbahey]

Direct integration is the only way, so show us the integral you've come up with.

 

[jam357]

The integral is not particularly nice, but i found a more cunning way to solve the problem, but thanks anyway. I also don't know how to write mathematical expressions on this thing