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MathGroup Archive 1999

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Re: Solving difficult integral

  • To: mathgroup at
  • Subject: [mg18644] Re: Solving difficult integral
  • From: Paul Abbott <paul at>
  • Date: Thu, 15 Jul 1999 01:45:39 -0400
  • Organization: University of Western Australia
  • References: <7mek2g$>
  • Sender: owner-wri-mathgroup at

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?


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 

            God IS a weakly left-handed dice player

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