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

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Jonas Matuzas

Posts: 8
Registered: 2/28/14
Re: integral for fun
Posted: Mar 1, 2014 8:17 AM
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On Friday, February 28, 2014 11:39:02 PM UTC+2, Axel Vogt wrote:
> On 28.02.2014 22:29, Richard Fateman wrote:
>

> > On 2/28/2014 1:00 PM, Axel Vogt wrote:
>
> >> On 28.02.2014 18:55, 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]}]
>
> >> ...
>
> >>>
>
> > The free program Maxima computes this integral (a mess) in 2.68 seconds
>
> > on my 7 year old computer. Evaluating it to a 40-digit precison number gives appx
>
> > 1.138911319801756364346365520822589787737 plus an imaginary part that
>
> > seems to be about one unit in the last place of the computation...
>
> > which can be recomputed to a higher precision to check.
>
> >
>
> > This agrees with the NIntegrate from Mathematica version 9
>
> > to about 13 digits.
>
> >
>
> > RJF
>
>
>
> Maple 17 actually gives it 'immediately' in terms of hypergeometric 0F7
>
> (and your numerical value)


it is interesting ... Mathematics likes to give answer in Hypergeometrics too, but why she is not doing in this case?



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