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Real integration help

• To: mathgroup at smc.vnet.net
• Subject: [mg127204] Real integration help
• From: Mark Williams <mwilliams at mint.ua.edu>
• Date: Sat, 7 Jul 2012 05:31:08 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

The Group,



I am doing symbolic integration using all real values. The particular integration returns a function which when evaluated is complex. In particular:

Integrate[ArcTan[x*y/(z*Sqrt[x^2+z^2+y^2])],y] returns



y ArcTan[(x y)/(z [https://mail.mint.ua.edu/owa/Image1.gif] )]+z ArcTanh[[https://mail.mint.ua.edu/owa/Image1.gif]/x]  in the blanks are

Sqrt[x^2+z^2+y^2]



The ArcTanh is only real on (-1, 1). Is there a way to constrain Mathematica to real results? I dislike the idea of doing the integral by hand.



Thanks in advance.



Mark Williams