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MathGroup Archive 2004

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Re: Forcing functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51030] Re: [mg51006] Forcing functions
  • From: "David Park" <djmp at earthlink.net>
  • Date: Sat, 2 Oct 2004 03:17:59 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Barry,

Your students could manipulate the output after using Integrate to obtain a
Log form. In this case TrigToExp will generate the Log form.

Integrate[ x * Sqrt[x^2 + 2x + 4], x]
% // TrigToExp
% // Simplify

(1/6)*(Sqrt[4 + 2*x + x^2]*(5 + x + 2*x^2) -
   9*ArcSinh[(1 + x)/Sqrt[3]])

(1/6)*(Sqrt[4 + 2*x + x^2]*(5 + x + 2*x^2) -
   9*Log[(1 + x)/Sqrt[3] +
      Sqrt[1 + (1/3)*(1 + x)^2]])

(1/6)*(Sqrt[4 + 2*x + x^2]*(5 + x + 2*x^2) -
   9*Log[(1 + x + Sqrt[4 + 2*x + x^2])/Sqrt[3]])

Since there are often many different forms for an indefinite integral, and a
CAS will produce one of them depending on its internal methods, it is
probably just as well that students learn that they will often have to
manipulate the output to a desired form.

And on a related discussion with Jens-Peer Kuska, on the use of % in the
FrontEnd, I don't see anything wrong with using % here because it always
refers to output within the same cell and therefore is always safe. I do
think it is sloppy to use % when it refers to output from 'previous' cells.

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/


From: Barry Tesman [mailto:tesman at dickinson.edu]
To: mathgroup at smc.vnet.net

Can you "force" Mathematica to not use certain functions?  E.g., I
want to give my students some problems to antidifferentiate.  One
such problem is:

Integrate[ x * Sqrt[x^2 + 2x +4], x]

The answer uses arcsinh.  Can one force Mathematica to use natural
log instead?

Thanks,
Barry





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