
Re: integral for fun
Posted:
Mar 1, 2014 11:30 AM


On 3/1/2014 5:28 AM, Jonas Matuzas wrote: .... regarding integrals in terms of elementary functions (or wellknown constants ...)
>> 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.
It would still not be an elementary function, even if you had all that information available.(Historical convention, I suppose.)
If you want to learn about the search for a solution to the problem of (indefinite) integration in terms of elementary functions, you can try to find work by Liouville, and then a stream of work including Robert Risch, but not ending there. Maybe Manuel Bronstein's work would be most recent.
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?
There is a question about how to do definite integrals. Maxima obviously used a residue method rather than substitution into the indefinite integral. Making a wrong choice in method can waste a lot of time.
Maxima's residue methods are described in a PhD thesis by Paul S H. Wang at MIT.
>

