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 Taylor-series-expansion based results or any other non-closed 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 non-integer (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.
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