Integral with singularities

*To*: mathgroup at smc.vnet.net*Subject*: [mg116666] Integral with singularities*From*: "gmarkowsky at gmail.com" <gmarkowsky at gmail.com>*Date*: Wed, 23 Feb 2011 05:24:46 -0500 (EST)

Hello all, I am doing NIntegrate[ 1/Sqrt[(x^2 + y^2) ((x - 1)^2 + y^2) ((x - a)^2 + (y - b)^2)], {x, -3, 3}, {y, -3, 3}] Somehow it is not working very well. This doesn't seem to be a particularly difficult request but Mathematica is having trouble. It keeps saying stuff like NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >> NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after 18 recursive bisections in x near {x,y} = {1.,2.06474}. NIntegrate obtained 76.80413981137505` and 101.86483781265876` for the integral and error estimates. >> I guess that near 0, 1, and a+bi the integrand blows up. I have tried to exclude small areas around those points, but I don't seem to be doing it right. Can anyone help? Greg