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In Version 10 you can now create ImplicitRegions and Integrate over them: region = ImplicitRegion[And @@ {0 <= x, x <= 1 - y, -1 <= y, x + 2 y <= 2}, {x, y}] Now Integrate[x + y, {x, y} ∈ region] 2/3


3

My version of Mathematica has no problems calculating analytically the integral $\int_{x-b}^{b+x} 2 r (l-r) \cos ^{-1}\left(\frac{s^2+x^2-b^2}{2 s x}\right) \, dr$ The result looks nice (IMHO) rather than "ugly". $\frac{1}{9} b^3 \left(9 L \pi -2 (2+z) (8+z (2+z)) \text{EllipticE}\left[\frac{4 (1+z)}{(2+z)^2}\right]+2 z (2+z)^2 ...



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