Special delimited oscillators that maxima can't solve it.

>On Tuesday 15 April 2008 03:16, J.C. Pizarro wrote:
>
>>>> 1. sin(1/x)         [0+,2/pi]
>>>> 2. cos(1/x)         [0+,2/pi]
>>>>
>>>> 3. sin(1/x^2)       [0+,sqrt(2/pi)]
>>>> 4. cos(1/x^2)       [0+,sqrt(2/pi)]
>>>>
>>>> ...
>>>
>>> Well, at least sine, cosine, and Fresnel integrals are not hard to
>>> compute, and implement in Maxima too.
>>
>> I don't believe that these integrals are not hard to compute and implement
>> because they are new and were unknown for people until now.
>>
>> Soon, you will get stuck in somewhere of the implementation in  Maxima
>> because this new theory is a rare case that difficult you.
>>
>> The Fresnel integrals are not related to here, in this harder solving.
>
>Actually, they are related to indefinite integrals:
>
>\int sin(1/x) dx = x sin(1/x) - Ci(1/x),
>\int cos(1/x) dx = x cos(1/x) + Si(1/x),
>\int sin(1/x^2) dx = x sin(1/x^2) - sqrt(2 pi) C (sqrt(2/pi)/x),
>\int cos(1/x^2) dx = x cos(1/x^2) + sqrt(2 pi) S (sqrt(2/pi)/x).
>
>--
>Alexey Beshenov <al at beshenov.ru>
>http://beshenov.ru/

They are still unsolved indefinite integrals.
They are not primitives!.

I don't know the meaning of the speciality of Ci and Si that
they are unsolved indefinite integrals too.

I've some handwritten elaboration in paper,

\int cos(1/x) dx = x cos(1/x) - ln(x) sin(1/x) + (( ln(x)+1 ) / x ) cos(1/x)
      - ( ln(x) / ( x^2 ) ) sin(1/x) + ... still more undefined integrals ...

   Sincerely, J.C.Pizarro