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MathGroup Archive 2007

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Re: Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74222] Re: Integrate
  • From: "Michael Weyrauch" <michael.weyrauch at gmx.de>
  • Date: Wed, 14 Mar 2007 04:00:37 -0500 (EST)
  • References: <esls78$q0v$1@smc.vnet.net> <et5o76$jor$1@smc.vnet.net>

Hello,

  Dimitris, this is a marvelous solution to my problem. I really appreciate
your help. I will now see if I can solve all my other (similar) integrals using the same trick.
Timing is not really the big issue if I get results in a reasonable amount of time.

Also the references you cited are quite interesting, because they give some insight
what might go on inside Mathematica concerning integration.

I also agree with you that it is my task as a programmer to "help" Mathematica
and guide it into the direction I want it to go. Sometimes this is an "art"...

Nevertheless, in the present situation I do not really understand why Mathematica wants
me to do that rather trivial variable transformation, which is at the heart of your solution.
The integrand is still a rather complicated rational function of the same order. The form 
of the integrand did not really change
substantially as it is the case with some other ingenious substitutions one uses in order to
do some complicated looking integrals "by hand".

I think the fact that we are forced to such tricks shows that the Mathematica integrator
is still a bit "immature" in special cases, as also the very interesting article by D. Lichtblau,
which you cite, seems to indicate. So all this is probably perfectly known to the 
Mathematica devellopers. And I hope the next Mathematica version has all this "ironed out"??

Many thanks again,  Michael


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