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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: [mg8841] Re: [mg8773] Incorrect result for improper integral with MMA?
  • From: seanross at worldnet.att.net
  • Date: Mon, 29 Sep 1997 02:40:07 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Chris Barker wrote:
> 
> The command:
> 
> Integrate[1/(x*Log[x]^2),{x,3,Infinity}]
> 
> yields the result:

I am not sure I understand the internal workings of Integrate and the
internal difference between Integrate[f,x] and Integrate[f,{x,a,b}], but


fi[a_]=Integrate[1/(x*Log[x]^2),x]/.x->a;
fi[3]-fi[Infinity]

returns a correct result.  Also,
Integrate[1/(x*Log[x]^2),{x,3,a}]
returns a correct result for any finite a greater than three, including
huge values where the integrand is extremely small.

If I had to guess at a reason, it would be that there is no way that
mathematica can know if a function is reasonably behaved on an interval
that goes to infinity, so it defaults to a different behavior when
Infinity is one of the limits.


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