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 :)