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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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