When I re-did the integral again that has been troubling, I found that I had misstated my issue to you before, though both Assumptions and Reals is an issue for me in simplifying the integration times and repetitions.When I perform Integragte[r1 r2/Sqrt[r1^2+r2^2+d+r1 r2 W],{r1,0,Sqrt[a-z1^2]},{r2,0,Sqrt[a-z2^2]}], the first integral is calulated but the second is not.