Bug in Integrate in Version 5.1?

*To*: mathgroup at smc.vnet.net*Subject*: [mg56737] Bug in Integrate in Version 5.1?*From*: A.Reischl at gmail.com*Date*: Thu, 5 May 2005 06:01:20 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello, Integrate gives the following answer for this integral: a = Integrate[x^3 /(Exp[x] - 1), {x, 0, Infinity}] N[a] Out[1]= Pi^4/15 Out[2]= 6.49394 which I think is correct. This integral, which should be the same ( by partial integration), gives: b = Integrate[-3 x^2 Log[1 - Exp[-x]], {x, 0, Infinity}] N[b] Out[3]= (11*Pi^4)/60 Out[4]= 17.8583 while numerical integration gives: NIntegrate[-3x^2 Log[1 - Exp[-x]], {x, 0, Infinity}] Out[5]= 6.49394 This is done with version 5.1. Version 4.2 gives c=Integrate[-3*x^2*Log[1 - Exp[-x]], {x, 0, Infinity}] N[c] Out[1]= Pi^4/15 Out[2]= 6.49394 (Remarkably version 4.2. complaints: "Series::esss: Essential singularity encountered in ..." while calculating the correct result. ) So the result in version 5.1. looks wrong. Or did I make a mistake? Cheers Alexander

**Follow-Ups**:**Re: Bug in Integrate in Version 5.1?***From:*yehuda ben-shimol <bsyehuda@gmail.com>

**Re: Bug in Integrate in Version 5.1?***From:*Chris Chiasson <chris.chiasson@gmail.com>