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MathGroup Archive 2004

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Re: Forcing functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51041] Re: [mg51006] Forcing functions
  • From: DrBob <drbob at bigfoot.com>
  • Date: Sat, 2 Oct 2004 03:18:35 -0400 (EDT)
  • References: <200302110942.EAA26084@smc.vnet.net> <b2d1cl$eaa$1@smc.vnet.net> <200410010848.EAA11554@smc.vnet.net>
  • Reply-to: drbob at bigfoot.com
  • Sender: owner-wri-mathgroup at wolfram.com

Here are three methods:

raw = Integrate[x*Sqrt[x^2 + 2x + 4], x];
FullSimplify[raw, ComplexityFunction -> (Count[{#1}, _ArcSinh, Infinity] &)]
FullSimplify[raw, ComplexityFunction -> (LeafCount[#] + 20Count[{#1}, \
_ArcSinh, Infinity] &)]
TrigToExp@raw

(1/12)*(10*Sqrt[4 + 2*x + x^2] +
    2*x*Sqrt[4 + 2*x + x^2] +
    4*x^2*Sqrt[4 + 2*x + x^2] +
    9*Log[3] -
    18*Log[1 + x + Sqrt[
        4 + 2*x + x^2]])
(1/6)*((5 + x + 2*x^2)*
     Sqrt[4 + x*(2 + x)] +
    (9/2)*(Log[3] -
      2*Log[1 + x + Sqrt[
          4 + x*(2 + x)]]))
(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]])

I think you'll prefer TrigToExp.

Bobby

On Fri, 1 Oct 2004 04:48:48 -0400 (EDT), Barry Tesman <tesman at dickinson.edu> wrote:

> 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
>
>
>
>



-- 
DrBob at bigfoot.com
www.eclecticdreams.net


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