Re: Can Mathematica NIntegrate a Log-type singularity?

*To*: mathgroup at smc.vnet.net*Subject*: [mg92675] Re: Can Mathematica NIntegrate a Log-type singularity?*From*: Peter Pein <petsie at dordos.net>*Date*: Fri, 10 Oct 2008 04:34:29 -0400 (EDT)*References*: <gckmrr$ng7$1@smc.vnet.net>

This must be another version of Mathematica than "6.0 for Linux x86 (64-bit) (March 13, 2008)" I get: In[1]:= NIntegrate[alpha^2*Log[2*Cos[alpha/2]]^2, {alpha, -Pi, Pi}] Out[1]= 37.40240591819764 In[2]:= NIntegrate[alpha^2*Log[2*Cos[alpha/2]]^2, {alpha, -Pi, Pi}, WorkingPrecision -> 30] == Pi^5*(11/90) Out[2]= True Aaron Fude schrieb: > 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. >