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symbolic - Mathematica 10 fails to calculate integral that Mathematica 9 can handle


The following:


Mass/2  Integrate[(r^2 + Rotation^2 (2 - Cos[θ]^2))/(r^2 + Rotation^2
  Cos[θ]^2)^2 Sin[θ], {r, r1, ∞}, {θ, 0, π},

  Assumptions -> {r1 > 0 && Rotation >= 0}] // Simplify

returns



(1/(32 Rotation))Mass (-16 ArcTan[r1/Rotation] + 1/(2 r1^2)(16 π r1^2 +
32 r1 Rotation + π Rotation^2 + 8 π r1^2 Log[r1] +
4 ArcTan[Rotation/r1] (7 Rotation^2 - 8 r1^2 Log[r1]) -
2 ArcTan[r1/(2 Rotation) - Rotation/(2 r1)] (Rotation^2 + 8 r1^2 Log[r1])))

in Mathematica 9.0.1, and




During evaluation of In[35]:= Simplify::time: Time spent on a transformation exceeded 300.` seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. >>


Out[35]= 1/2 Mass Integrate[((r^2 - Rotation^2 (-2 + Cos[θ]^2)) Sin[θ])/(r^2 + Rotation^2 Cos[θ]^2)^2, {r, r1, ∞}, {θ, 0, π}, Assumptions -> r1 > 0 && Rotation >= 0]



in Mathematica 10.0.0. In the latter case, it takes much longer to return, although it fails to produce the result. Is this a bug?




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