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MathGroup Archive 1995

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Re: Why no simplification ?

  • Subject: [mg2582] Re: Why no simplification ?
  • From: groskyd at gv.ssi1.com (David Rosky)
  • Date: Mon, 27 Nov 1995 21:31:10 -0500
  • Approved: usenet@wri.com
  • Distribution: local
  • Newsgroups: wri.mathgroup
  • Organization: Silicon Systems, Inc.

In <48h4bc$rcr at ralph.vnet.net>, crobc at epix.net (Christopher R. Carlen) writes:
>
>I evaluated the integral
>
>Integrate[ Sqrt[4t^2 + 4 + t^-2], {t, 1, E} ]
>
>by hand, which of course works out to E^2.  By adding the terms over the 
>common denominator t^2, a perfect square trinomial results in the 
>numerator.  Taking the square root yields just Integrate[ (2t^2 + 1)/t, 
>{t, 1, E} ] which is valid for t > 0 .
>
>Now I can understand that Sqrt[ x^2 ] really can't be simplified to x, 
>but is really |x| .  But in the case of a perfect square trinomial like 
>the above, which is always positive, why doesn't Mathematica recognize 
>this ?  
>
>Because it fails to recognize this simplification, the output is a big 
>mess, containing another integral.  But anyone can see that this is 
>really quite a simple integral.
>
>Anyone have any ideas how to get this integral to come out in a more 
>simple manner ?
>


I entered the above integral into Mathcad (which I also use) and it
was able to recognize the simplification and produced the result e^2.
It also generated the indefinite integral as t^2 + ln(t).  Mathcad uses 
the Maple symbolic processor.

In Mathematica, the Simplify function also failed to see it.  I assume that
Integrate probably calls Simplify on the integrand, but I thought I would
check nevertheless.

You may want to send this example directly to WRI at their suggestions or
support address.  It appears to be a valid oversight.

Regards,
David Rosky
(groskyd at gv.ssi1.com)





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