Re: Integrate[[1/(1+x+x^5),{x,-Infinity,Infinity}]
- To: mathgroup at smc.vnet.net
- Subject: [mg25396] Re: Integrate[[1/(1+x+x^5),{x,-Infinity,Infinity}]
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 29 Sep 2000 01:06:30 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <8qlol1$q86@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
it is easy to find that (1+x+x^5) has a simple pole on the
real axes at
{x -> 1/3 - (2/(25 - 3*Sqrt[69]))^(1/3)/3 -
((25 - 3*Sqrt[69])/2)^(1/3)/3}
and you will probably Infinity, with any system.
The indefined integral is calculated by
Integrate[1/((x - a)*(x - b)*(x - c)*(x - d)*(x - e)), x] /.
Thread[{a, b, c, d, e} -> (x /. Solve[1 + x + x^5 == 0, x])]
Regards
Jens
Zak Levi wrote:
>
> Dear Mathematica experts,
>
> There was some discussion of this integral in sci.math
> without clear answer to the question:
>
> How to calculate
>
> Integrate[[1/(1+x+x^5),{x,-Infinity,Infinity}]
>
> in Mathematica? -preferably NOT in M4 version,
> simply because not all users have the latter one.
>
> Thanks a lot,
> ZL