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MathGroup Archive 1997

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Re: Incorrect result for improper integral with MMA?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg8820] Re: Incorrect result for improper integral with MMA?
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Fri, 26 Sep 1997 00:33:43 -0400
  • Organization: University of Western Australia
  • Sender: owner-wri-mathgroup at wolfram.com

Chris Barker wrote:

> The command:
> 
> Integrate[1/(x*Log[x]^2),{x,3,Infinity}]
> 
> yields the result:
> 
> \!\(\*
>   RowBox[{
>   \(Integrate::"idiv"\), \( : \ \),
>     "\<"Integral of \!\(1\/\(x\\ \(Log[x]\)\^2\)\) does not converge on \
> \!\({3, \*InterpretationBox[\"\\[Infinity]\", DirectedInfinity[1]]}\)."\>"}]\)
> 
> i.e.  the integral does not converge.  However, analytic techniques seem
> to indicate that the integral does indeed converge to 1/ln(3).  Mimicing
> the analytic procedures step by step with mma also yields 1/ln(3).  Am I
> being stupid, or is mma wrong?

Mathematica easily computes the indefinite integral -- from this you
will see why the integral does not converge on [3,Infinity).

Cheers,
	Paul 
____________________________________________________________________ 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia           
Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au 
AUSTRALIA                             http://www.pd.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________


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