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Simple integral problem

  • To: mathgroup at
  • Subject: [mg32650] Simple integral problem
  • From: kkumer at (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

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
"Fizika svemira" -

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