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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: [mg8818] Re: [mg8773] Incorrect result for improper integral with MMA?
  • From: David Withoff <withoff>
  • Date: Fri, 26 Sep 1997 00:33:42 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

> 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?
>
> E-mail responses gladly accepted.

This is an error in the part of the Integrate function that checks
whether or not the integral converges.  I will see that this gets
reported so that it can be investigated.  You can also report bugs
by sending them to support at wolfram.com.

You can bypass the part of Integrate that checks the conditions under
which this integral converges using GenerateConditions -> False:

In[4]:= Integrate[1/(x*Log[x]^2),{x,3,Infinity},
                           GenerateConditions -> False]

          1
Out[4]= ------
        Log[3]

Dave Withoff
Wolfram Research


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