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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- From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
- Re: Can Mathematica NIntegrate a Log-type singularity?