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Topic: integral for fun
Replies: 25   Last Post: Mar 6, 2014 4:10 PM

 Messages: [ Previous | Next ]
 Jonas Matuzas Posts: 8 Registered: 2/28/14
Re: integral for fun
Posted: Mar 1, 2014 8:13 AM

On Friday, February 28, 2014 7:55:08 PM UTC+2, Axel Vogt wrote:
> On 28.02.2014 15:32, Jonas Matuzas wrote:
>

> > I wrote integral in Mathematica:
>
> > Integrate[Cos[x]^4/(1 + x^8), {x, -\[Infinity], \[Infinity]}]
>
> >
>
> > for fun,( for speed compassion between win7 and Linux (actual I found that in Linux 4x faster with more simple integrals ))
>
> > and... This integral is still calculating, it is already passed 1.5 day , I am getting curios ... I am gonna to leave it for weekend in work place . My computer is almost front end- (i7 4770, 16 GB RAM), integral is running on Linux.
>
> > I am a bit lazy but I think this integral can by taken with pencil and paper using residual theory.
>
> > I find publication is talking about similar problem , and writing that in this case residual theory is not complete..:
>
> > http://www.csm.ornl.gov/~bowman/fjts312.pdf
>
> >
>
> > What do you think - is it connected with so long calculation time.
>
>
> > I am just curios :)
>
>
>
> Maple + using FTOC + simplification, here as procedure
>
>
>
> val := proc()
>
> local result, t13, t14, t15, t16, t17, t18, t19;
>
>
>
> t17 := 2^(1/2);
>
> t15 := (2+t17)^(1/2);
>
> t13 := cos(t15);
>
> t16 := (2-t17)^(1/2);
>
> t19 := t15*sin(t15)+t16*t13;
>
> t14 := cos(t16);
>
> t18 := t16*sin(t16)+t15*t14;
>
> result := (1/8*t18*exp(-t15)+1/8*t19*exp(-t16)+3/32*t16+
>
> 3/32*t15+1/32*(2*t14*t18-t15)*exp(-2*t15)+
>
> 1/32*(2*t13*t19-t16)*exp(-2*t16))*Pi
>
> end proc

is it solution of this my integral? for me it is not obvious... - I will check later ... thank you

Date Subject Author
2/28/14 Jonas Matuzas
2/28/14 Jean-Michel Collard
3/1/14 Jonas Matuzas
2/28/14 Axel Vogt
2/28/14 Axel Vogt
2/28/14 Richard Fateman
2/28/14 Axel Vogt
2/28/14 Nasser Abbasi
2/28/14 Richard Fateman
3/1/14 Axel Vogt
3/1/14 Axel Vogt
3/1/14 Jonas Matuzas
3/1/14 Richard Fateman
3/1/14 Axel Vogt
3/1/14 Nasser Abbasi
3/3/14 Waldek Hebisch
3/4/14 Richard Fateman
3/4/14 Waldek Hebisch
3/4/14 Richard Fateman
3/6/14 Waldek Hebisch
3/1/14 Jonas Matuzas
3/2/14 clicliclic@freenet.de
3/3/14 Jonas Matuzas
3/1/14 Jonas Matuzas
3/1/14 Jonas Matuzas
3/1/14 Jonas Matuzas