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Re: Why no simplification ?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg2582] Re: Why no simplification ?
*From*: groskyd at gv.ssi1.com (David Rosky)
*Date*: Mon, 27 Nov 1995 21:31:10 -0500
*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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