(Couldn't figure out how to make the pi symbol, but that is a pi in the denominator at the beginning. Also the limit is from 0 to inf.). I'm supposed to show this integral equals 1/(4*pi*r*r') times the delta function of (r-r').

I solved the integral and ended up with

With k ranging from 0 to infinity. Now my problem is, I'm not sure exactly how to get a delta function out of this result. I can sort of see how it might emerge on the right sided term, but I'm confused as to how to express that mathematically. Also there is apparently a pi term that comes out as well when I compare it to the expected answer. Can anyone help me?