Re: Can Mathematica NIntegrate a Log-type singularity?

*To*: mathgroup at smc.vnet.net*Subject*: [mg92682] Re: Can Mathematica NIntegrate a Log-type singularity?*From*: "David W.Cantrell" <DWCantrell at sigmaxi.net>*Date*: Fri, 10 Oct 2008 04:35:45 -0400 (EDT)*References*: <gckmrr$ng7$1@smc.vnet.net>

Aaron Fude <aaronfude at gmail.com> wrote: > 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. When I try it straight, Mathematica 6 does not complain and gives an answer which I suspect is correct. > 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. It seems to be 11/90 * Pi^5. David