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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 8:28 AM
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On Saturday, March 1, 2014 6:33:56 AM UTC+2, Richard Fateman wrote:
> I don't consider a solution that includes
>
> Si, Ci, or hypergeometric functions as a solution
>
> in closed form in terms of elementary functions.
>
>
>
> Unless there is no way of expressing the answer in
>
> terms of elementary functions.
>
>
>
> After all, you could always decide that the
>
> difficult integral in question deserves its own
>
> name, say FooI, and then return the answer in terms
>
> of FooI.
>
>
>
> RJF


I agree with you. You can name my integral Matuzas[a]=Integrate[Cos[x]^4/(a^8 + x^8), {x, -\[Infinity], \[Infinity]}] as new function. But you have to do table of this integral properties: differentiation, integration, differential equation it supports, Fourier series, expressions with another functions.
And everybody should use it :) How to evaluate numerical -it is no problem . Actually the same is with Ci, Si and ect... Numerically we know how to evaluate. But the same is with elementary functions, is'n it?



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