Yesterday I asked a question about the **non converging integral**. Woods told me that it is due to the function which has a singularity along a line which passes through the integration region. 
(<http://mathematica.stackexchange.com/questions/18854/why-does-this-numeric-integral-fail-to-converge>)
Now the question is that how can I find a correct answer for this integral? Should I eliminate these singularities from the integral bound?
I read **singularity handling** in documentation center, but I couldn't solve the problem using **Exclusions**.(<http://reference.wolfram.com/mathematica/tutorial/NIntegrateIntegrationStrategies.html#122144792>)

function:

 Msq2[w1_, 
 w2_] := (12.8228 + 10.518/(0.948338 - 2.0134 w1 - 2.0134 w2) - 
 6.69841/(1.72935 - 2.0134 w1 - 2.0134 w2) - 
 57.4434/(2.01348 - 2.0134 w1 - 2.0134 w2) - 
 13.4997/(3.45415 - 2.0134 w1 - 2.0134 w2) + 
 9.50782 (1/(-0.110612 + 2.0134 w1) + 
 1/(-0.110612 + 2.0134 w2)) - 
 82.5202 (1/(1.14046 + 2.0134 w1) + 1/(1.14046 + 2.0134 w2)))^2;
The region of the integral:

 rpp = RegionPlot[
 Re[r2] < mphy - w1 - w2 < Re[r1], {w1, .11, .4}, {w2, .11, .4}, 
 BoundaryStyle -> Blue, FrameLabel -> {"w1", "w2"}, 
 PlotRangePadding -> 0];
Where:

 r1 = Sqrt[0.283 + (Sqrt[-0.018769 + w1^2] + Sqrt[-0.018769 + w2^2])^2];
 r2 = Sqrt[0.283 + (Sqrt[-0.018769 + w1^2] - Sqrt[-0.018769 + w2^2])^2];
 mphy = 1.007;

Integration:

 NIntegrate[
 Boole[Re[r2] < mphy - w1 - w2 < Re[r1]] 1/(64*Pi^3*mphy)*
 Msq2[w1, w2], {w1, w1min, w1max}, {w2, w2min, w2max}, 
 AccuracyGoal -> 14] // Chop
Where:

 w1min = w2min = Min@rpp[[1, 1, All, 1]];
 w1max = w2max = Max@rpp[[1, 1, All, 1]];
The green line is the singular curve which a part of it is in the integration region:

 With[{sing = Solve[1/Msq2[w1, w2] == 0, {w1, w2}] /. Rule -> Equal}, 
 Show[rpp, ContourPlot[sing, {w1, 0, 1}, {w2, 0, 1}]]]

![enter image description here][1]


 [1]: https://i.sstatic.net/nLSNY.png