
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. > > > 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 := (2t17)^(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*t18t15)*exp(2*t15)+ > > 1/32*(2*t13*t19t16)*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

