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 ____________________________________________________________________