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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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