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