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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: 1,036
Registered: 5/5/07
Re: integral for fun
Posted: Feb 28, 2014 12:55 PM
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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.
> Do you have some thoughts about this case?
> 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





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