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Problem with NIntegrate


Hello, I'm trying to numerically integrate a complicated expression and Mathematica keeps showing plenty of error messages, such as 
"NIntegrate::slwcon:Numerical integration converging too slowly; /.../", 
"NIntegrate::eincr: The global error of the strategy GlobalAdaptive has increased more than 2000 times./../" and so on. If I only want to see the spatial distribution of the solution (contour plots in different planes etc.) , it somehow manages to come to an end, but the problem is that I need to use this solution in NDSolve, so it would take too long for the program to find the root.

One of the problematic integrals is for instance

NIntegrate[
 R (x - R Cos[\[Phi]] )/((x - R Cos[\[Phi]] )^2 + (y - 
         R Sin[\[Phi]] )^2 + (0 - Z)^2)^(3/2), {\[Phi], 0, 2 Pi}, {R, 
  b, b + c}, {Z, R - (b + c), -R + (b + c)}

Any idea what is "wrong" with the integrand so that I get all these error messages?



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