       Re: Solving difficult integral

• To: mathgroup at smc.vnet.net
• Subject: [mg18664] Re: [mg18620] Solving difficult integral
• From: Richard Gass <gass at physics.uc.edu>
• Date: Thu, 15 Jul 1999 01:45:50 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Christian,
You 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 was able to do the indefinte integral
Integrate[Sqrt[C0 + C1*x + C2*x^2 + C3*x^3 + C4*x^4], x] in a couple of
seconds on my Power Mac ( a 200 MHz 604e) with 4.0 The result is very
complicated as you might expect. I think the definte integral is basically
hopeless. It is a question of branch cuts and for general coefficients I do
not think Mathematica can get them right.

Richard Gass
Department of Physics
University of Cincinnati
Cincinnati, OH 45221
phone- 513-556-0519
E-Mail gass at physics.uc.edu

```

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