Re: Solving difficult integral a follow up

*To*: mathgroup at smc.vnet.net*Subject*: [mg18665] Re: [mg18620] Solving difficult integral a follow up*From*: Richard Gass <gass at physics.uc.edu>*Date*: Thu, 15 Jul 1999 01:45:51 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Christian wrote <I've got the following problem: <I need to solve the following integral: <Integrate[Sqrt[C0+C1*x+C2*x^2+C3*x^3+C4*x^4],{x,0,t}] <For those of you who do not recognize it at once: it's the integral of the <square root of a 4th degree polynomial in x. I've tried to solve the above <integral with Mathematica, but after, say, two hours of computing I stopped <the calculation - it looked like the Kernel crashed or whatever. Is there an <analytical solution to this problem at all? I replied that I could do the indefinite integral but that I thought the definite integral was hopeless because of branch cut problems. However my machine ( a fairly old Power Mac) run 4.0 returns an answer for Integrate[Sqrt[C0 + C1*x + C2*x^2 + C3*x^3 + C4*x^4], {x, 0, t}]. THe result takes a few minutes or so. I am not at all sure the result is correct. Richard Gass Department of Physics University of Cincinnati Cincinnati, OH 45221 phone- 513-556-0519 E-Mail gass at physics.uc.edu