12.7.3 Can you answer these questions?

12.7.3.1 Is there any way to get an exact solution for this integral of a piecewise function that has singularities?
12.7.3.1 Is there any way to get an exact solution for this integral of a piecewise function that has singularities?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=318752

I want to find the exact (not approximate) value of a definite double-integral involving a complicated piecewise-defined two-variable function  p[Theta, Phi]  (whose ... 
[calculus-and-analysis] [piecewise] [singularity]
 
asked by Lawton https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=92961 Score of 1