An HP48/49 CAS question Message #1 Posted by Valentin Albillo on 17 Oct 2003, 5:01 a.m.
Hi everybody. Not owning any HP48/49 model, there's no immediate way for me to test this, so I'd appreciate if any of you HP48/49 owners would try this for me and post here the results.
The question is: what result does the HP48/49 symbolic algebra system produce for the following indefinite integral:
Integral[ sin(x^n) . dx ]
where n is a constant ? Specifically, I'm interested to know if it does produce some kind of exact closed result, in terms of known functions (elementary or not). I'm not interested in Taylorseriesexpansion based results or any other nonclosed approximations (not to mention purely numerical results).
In case it can't produce a closed result for general, arbitrary n, I would then be interested to know if it can produce a closed result for some particular values of n, and if so, the specific values of n it can solve. I would expect it to be able to produce a closed result for n = 0 and n = 1 at the very least, but what about other values of n, both integer and noninteger (n = 2, 3, ..., 1/2, 1/3, ...) ? What about negative values of n (n = 1, 2, ..., 1/2, ...) ?
Thanks in advance for any results or comments and best regards from V.
