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Can Mathematica NIntegrate a Log-type singularity?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92642] Can Mathematica NIntegrate a Log-type singularity?
  • From: Aaron Fude <aaronfude at gmail.com>
  • Date: Thu, 9 Oct 2008 06:36:32 -0400 (EDT)

Hi,

I would like to evaluate the following:

NIntegrate[alpha^2 Log[2 Cos[alpha/2]]^2, { alpha, -Pi, Pi}]

How do I help Mathematica deal with the LogSquared type singularity at
either end of the interval. If I try it straight, Mathematica
complains and gives a wrong answer.

Please note, that Mathematica has absolutely no problem Integrating or
NIntegrating the function

Log[Cos[alpha/2]]^2

from -Pi to Pi, each time giving the correct answer, but the multiple
of alpha^2, throws it off.

Many thanks in advance,

Aaron.

PS: By the way, I'm pretty sure that that integral must be some
rational number times Pi^5.


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