Simple integral problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg32650] Simple integral problem*From*: kkumer at phy.hr (Kresimir Kumericki)*Date*: Fri, 1 Feb 2002 16:10:51 -0500 (EST)*Organization*: Theor.Phys.Dept, Univ. of Zagreb, Croatia*Sender*: owner-wri-mathgroup at wolfram.com

I tried this simple-looking integral in Mathematica 4.0 for Unix: Integrate[x(1 - x)Log[1 + 1/x], {x, 0, 1}] and I got -37/36 -2 Log[2]/3 ( = -1.48988 ) which seems to be wrong because: NIntegrate[x*(1 - x)*Log[1 + 1/x], {x, 0, 1}] = 0.204569 If perform undefinite Integral[ ... , x] and than do Limit[..]s, I get the right result. If I put together the argument of Log: 1+1/x -> (x+1)/x, I again get the right result: 2/3 -2 Log[2]/3. Is this some bug or am I missing something? I have to do a lot of similar integrals these days so I would be glad if someone could shed some light on this. Thanks, -- Kresimir Kumericki kkumer at phy.hr http://www.phy.hr/~kkumer/ "Fizika svemira" - http://eskola.hfd.hr/fizika_svemira/svemir.html