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Re: definite double integral issue


Correction to my previous reply: in 8.0.1 (Mac), your second integral indeed crashes the kernel reproducibly. In v9, it works fine:

Integrate[x/Sqrt[x^2 + y^2], {y, -1/2, 3/2}, {x, -1, 1/2 - y}]

1/32 (2 Sqrt[5] - 2 Sqrt[13] - 16 ArcSinh[1/2] - 16 ArcSinh[3/2] + 
   Sqrt[2] ArcSinh[3] + Sqrt[2] ArcSinh[5])

Integrate[x/Sqrt[x^2 + y^2], {y, -0.5, 1.5}, {x, -1.0, 0.5 - y}]

-0.741019



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