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Re: Re: Re: Integration

  • To: mathgroup at
  • Subject: [mg44371] Re: [mg44308] Re: [mg44277] Re: Integration
  • From: Murray Eisenberg <murray at>
  • Date: Fri, 7 Nov 2003 05:16:14 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <bmg0li$e9k$> <bmj2os$prs$> <> <>
  • Reply-to: murray at
  • Sender: owner-wri-mathgroup at

Is the difficulty here merely one of time and space, or an incomplete 
implementation in Mathematica?  After all, Risch's by-now old algorithm 
determines whether a given elementary function has an elementary 
antiderivative and, if there is one, finds it in finitely many steps.

Andrzej Kozlowski wrote:

> On 4 Nov 2003, at 17:23, Alex wrote:
>>Wolfram proudly declares that his Mathematika can handle any integral
>>computable in terms of elementary functions.  Well, here is one, which
>>it can not handle, and I am pretty sure, this is not the only one.
>   There is no computer program or a human being who can do that and no 
> sane person would make this sort of claim. Unless, that is,"can handle" 
> means "can handle in principle" - in other words, there are no specific 
> types of such integrals it "can't handle", in which case the claim is 
> valid.
> Andrzej Kozlowski
> Yokohama, Japan

Murray Eisenberg                     murray at
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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