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MathGroup Archive 1998

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stumping Integrate *correction*

  • To: mathgroup at smc.vnet.net
  • Subject: [mg15286] stumping Integrate *correction*
  • From: Selwyn Hollis <shollis at peachnet.campus.mci.net>
  • Date: Thu, 31 Dec 1998 04:39:39 -0500
  • Organization: fair
  • Sender: owner-wri-mathgroup at wolfram.com

I suspect that it's more-or-less well-known that one can easily
construct elementary integrals that Integrate cannot deal with. For
example,

    f[x_]:= Sqrt[x + Sqrt[x]]
    Integrate[f[x], x]

succeeds, but then

    Integrate[f[x+x^2](1+2x), x]

fails. There are a multitude of similar examples, which basically rely
on a simple substitution that Mathematica doesn't ``see."

I'm not complaining---this shortcoming is actually very useful for
convincing calculaus students that they need to know something. My
question is: Does anyone know of any other examples like this; i.e.,
elementary computations for which Mathematica fails without a little
help from the user?

Thanks!


--
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
Dr. Selwyn Hollis
Associate Professor of Mathematics
Armstrong Atlantic State University
Savannah, GA 31419 USA
<http://www.math.armstrong.edu/faculty/hollis/>
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



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