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Re: NIntegrate with change of variables

• To: mathgroup at smc.vnet.net
• Subject: [mg77528] Re: NIntegrate with change of variables
• From: chuck009 <dmilioto at comcast.com>
• Date: Tue, 12 Jun 2007 01:19:34 -0400 (EDT)

In my opinion, there's nothing wrong with Integrate:  In order to evaluate that integral using antiderivatives over the indicated contour, need to break it up into 4 pieces each of which needs to be evaluated using a branch of the Log function which is analytic over the piece.  When I do that I get:

ln(-1)+pi i-ln(5)+ln(5)-ln(-1)+pi i+ln(-1)+pi i-ln(5)+ln(5)-ln(-1)+pi i

which is the requested 4pi i (or just two circles around the pole gives that too using residues).  I believe the fact that integrating from -pi to pi is just a coincidence that it returns the same value as 4pi i.  Anyway, don't wish to show off or nothing, just like to get my math straight :)