Special delimited oscillators that maxima can't solve it.

Hello people,

i've discovered a new theory for mathematicians and engineers for
special formulas that impossibilite be applied the conventional
methods of its solving.

Maxima can't solve the problems of extracting 1000 decimal digits for the
following special formulas where its functions are oscillators
(and delimited oscillators for defined integrals for one quadrant)

* undefined integral and defined integral of below in range below:

  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)]

  5. sin(e^(1/x))     [0+,ln(2/pi)]
  6. cos(e^(1/x))     [0+,ln(2/pi)]

  7. sin(e^(1/x^2))   [0+,ln(sqrt(2)/pi)]
  8. cos(e^(1/x^2))   [0+,ln(sqrt(2)/pi)]

  f(x) := ... any above ... ;
  max_x() := ... the right side of the range [..,..] ;
  lim(integrate(f(x),x,y,max_x()),y,0);

  ( remember to substitute pi by %pi, e by %e, ln by log )

  ( 7-8 has more density of waves than 5-6, 5-6 than 3-4, 3-4 than 1-2 )

Tips (for defined integrals):
* has complex accuracy.
* need long time computation to solve it for a normal accuracy of few digits.
* is delimited (in ranges x and y).
* is convergent.
* has infinite frecuencies upto the frecuency infinite in delimited ranges x,y.
* has infinite waves in delimited ranges x,y.
* when it's reaching to zero, it grows up the velocity and acceleration
  of the quantity of waves. They aren't constant in the trayectory.
* can't be applied the Fourier transformation due to the infinite frecuencies
  upto the frecuency infinite in its resulted spectrum.
* the known conventional methods to solve it are impractical and useless
  ( the known numerical methods of integration can't be applied here ).
* he needed a lot of blank papers to solve above formulas, and i got
  series of infinite operands, each containing some factors e.g sin(..),
  cos(..), ln(x) or (ln(x)+1), x^-k (k=0,-1,-2,..) and more expressions).
* its plotting 2D is very limited and buggy (lacks the plots of finer waves)
  ( it's similar to zooming fines curves in Mandelbrot instead of fractals )

   Sincerely, J.C.Pizarro