[Maxima] integral of cos(1/x) with range doesn't work.

[Raymond Toy (RT/EUS)]

J.C. Pizarro wrote:
> $ maxima
> Maxima 5.14.0 http://maxima.sourceforge.net
> Using Lisp CLISP 2.41 (2006-10-13)
> Distributed under the GNU Public License. See the file COPYING.
> Dedicated to the memory of William Schelter.
> The function bug_report() provides bug reporting information.
> (%i1) integrate(cos(1/x), x);
>                                              1
>                                        / sin(-)
>                                 1      [     x
> (%o1)                       cos(-) x - I ------ dx
>                                 x      ]   x
>                                        /
> (%i2) integrate(cos(1/x), x, 0, 2/%pi);
>                                   2
>                                  ---
>                                  %pi
>                                 /
>                                 [        1
> (%o2)                           I    cos(-) dx
>                                 ]        x
>                                 /
>                                  0
> 
> 
> Why? Where is the failure of that it doesn't compute?

What's the problem?  The indefinite integral isn't in closed form either.

Also, the definite integral uses different algorithms to compute it. 
Oftentimes it doesn't even try to do the indefinite integral first.

Ray