Re: Integral

From: mike3 (mike4ty4_at_yahoo.com)
Date: 12/27/04 

Date: Mon, 27 Dec 2004 02:59:02 GMT

I want *exact* answers. Can the quintic be solved
in a finite number of elementary functions -- ie.
both algebraic and (elementary!) trascendental functions
(ie. sin, cos, tan, etc.)? I know you can't solve it using just
+, -, *, /, and radicals, but what about elementary
functions in general? Or has that too been proven
impossible and hence the integral cannot be expressed in
closed form in terms of elementary functions?

"Dave Seaman" <dseaman@no.such.host> wrote in message
news:cq019b$qnk$1@mailhub227.itcs.purdue.edu...
> On 17 Dec 2004 16:15:32 -0800, mike4ty4@yahoo.com wrote:
> > Hi.
>
> > What is the integral of 1/(x^5 + x^2 + x - 1) dx in closed form?
>
> The hard part is solving the quintic. There is a real root near 0.568544,
a
> complex conjugate pair near 0.91612 +/- 0.57771 i, and another pair near
> 0.622848 +/- 1.03222 i.
>
> Once you have the factors, it's an easy partial fractions decomposition,
> provided you don't mind approximate answers.
>
> Mathematica 5.0 for Mac OS X
> Copyright 1988-2003 Wolfram Research, Inc.
> -- Terminal graphics initialized --
>
> In[1]:= Integrate[1./(x^5+x^2+x-1),x]
>
> Out[1]= 1. (-0.22894 ArcTan[0.484391 (-1.2457 + 2. x)] -
>
> > 0.189874 ArcTan[0.865487 (1.83224 + 2. x)] +
>
> > 0.361679 Log[0.586544 - 1. x] -
>
> 2
> > 0.0641575 Log[1.45342 - 1.2457 x + x ] -
>
> 2
> > 0.116682 Log[1.17302 + 1.83224 x + x ])
>
>
>
>
> --
> Dave Seaman
> Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
> <http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>

Relevant Pages

  • Re: Integral
    ... > both algebraic and trascendental functions ... > (ie. sin, cos, tan, etc.)? ...
    (sci.math)
  • Re: analytic vs. algebraic
    ... > like exp, log, sin, arcsin, and so on. ... it will include the elementary functions. ...
    (sci.math)