       Re: Solving difficult integral

• To: mathgroup at smc.vnet.net
• Subject: [mg18644] Re: Solving difficult integral
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Thu, 15 Jul 1999 01:45:39 -0400
• Organization: University of Western Australia
• References: <7mek2g\$9il@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Christian Gudrian wrote:

> I need to solve the following integral:
>
> Integrate[Sqrt[C0+C1*x+C2*x^2+C3*x^3+C4*x^4],{x,0,t}]

Do you _really_ need to do this?  If you re-write the integrand as

Integrate[Sqrt[(t - a) (t - b) (t - c) (t - d)], t]

Mathematica certainly will give you a rather complicated answer in terms
of elliptic functions -- but I question whether this answer will be all
that useful in practical situations.

It's analogous to asking if Mathematica can find a closed-form
expression for the roots of a cubic or quartic.  It can -- but such
closed form expressions are rarely useful.

For any polynomial, Mathematica can represent the roots as Root objects
(and since Mathematica can do algebra with Root objects such a
representation is often more useful) so, effectively, the re-written
form is sufficient.

The real question is why do you need the general solution and, if you
have it, what do you want to do with it?

Cheers,
Paul

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

```

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