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  • $\begingroup$ I don't think MonteCarlo or any method that doesn't use the principal value will work, in the same way that it doesn't work for the integral of 1/x. In spherical coordinates one ends up having the integral of dq/(q^2+w/b), which is of the dx/x type (the edit was mine :P but I thought I was logged in). However, I will use your suggestion when I have some singularity whose integral doesn't diverge on each side. $\endgroup$ Commented Sep 23, 2015 at 3:11
  • $\begingroup$ I guess this is what comes of having basically written NIntegrate. Wow. $\endgroup$ Commented Sep 24, 2015 at 5:34
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    $\begingroup$ Hey, thanks for the detailed reply! I'll have to read it later. I was actually thinking about writing the solution I decided to implement in a few days when I get more time; now I should finish rounding up what I have. But what I ended up doing is evaluating the interpolating functions in the singularity surface (narrow strip), since they vary smoothly there. And I just have dq/(q^2+w/b) which I can solve analytically. So in this way I treat the hard (singularity) part analytically, and the rest I do with NIntegrate without needing to change coordinates :), using Exclusions->{0,0,0}. $\endgroup$ Commented Sep 24, 2015 at 18:23
  • $\begingroup$ Thanks for your feedback, guys! @wikiwert it seems that the solution you outlined is very similar to the one I am proposing. I am also trying to avoid the coordinate change. $\endgroup$ Commented Sep 25, 2015 at 1:21
  • $\begingroup$ Silly thing...but I couldn't even find PiecewiseNIntegrate in the documentation. I'll have to read for some time before I can understand the syntax. But mainly, I don't know how to go about using PrincipalValue for two lists. $\endgroup$ Commented Sep 28, 2015 at 7:33