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MathGroup Archive 2002

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Re: Simple integral problem

  • To: mathgroup at
  • Subject: [mg32660] Re: [mg32650] Simple integral problem
  • From: BobHanlon at
  • Date: Sat, 2 Feb 2002 01:19:36 -0500 (EST)
  • Sender: owner-wri-mathgroup at

In a message dated 2/1/02 5:40:01 PM, kkumer at writes:

>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

I find that Integrate is more reliable if the integrand is 
simplified as much as practical prior to integration.


(-(2/3))*(-1 + Log[2])



and, as you noted,



Bob Hanlon
Chantilly, VA  USA

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