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

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Axel Vogt

Posts: 1,034
Registered: 5/5/07
Re: integral for fun
Posted: Feb 28, 2014 4:39 PM
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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)




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