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Integrate yields complex results

• To: mathgroup at smc.vnet.net
• Subject: [mg127969] Integrate yields complex results
• From: matteo.poggi.fi at gmail.com
• Date: Thu, 6 Sep 2012 04:13:54 -0400 (EDT)
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• Delivered-to: l-mathgroup@wolfram.com
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Hi, using Mathematica 8.0 I computed this expression:

Integrate[((1 + y^2) (1 + x^2 + y^2)^(1/2))^(-1), y]

obtaining ugly complex Logarithms which cannot be simplified even with ExpToTrig. The correct real result is given by Mathematica 5.2 and is

ArcTan[xy/((x+^2+y^2+1)^(1/2))]

How is possible to obtain this result with 8.0 version.
I even tried to calculate Real and Imaginary part, but 8.0 refuses to do that. Please help me. I need to use Mathematica for research.