> jjf@Z61m:~$ maxima
> 
> Maxima 5.22.1 http://maxima.sourceforge.net
> using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (a.k.a. GCL)
> 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) (amax / 2) * sin((%pi * t / dtmax) -(%pi / 2) ) + amax /2 ;
>                                             %pi t
>                                    amax cos(-----)
>                             amax            dtmax
> (%o1)                       ---- - ---------------
>                              2            2
> (%i2) integrate(%o1,t)
> ;
>                                                 %pi t
>                                  amax dtmax sin(-----)
>                         amax t                  dtmax
> (%o2)                   ------ - ---------------------
>                           2              2 %pi
> (%i3) integrate(%o2,t);
>                                  2     %pi t
>                        amax dtmax  cos(-----)         2
>                                        dtmax    amax t
> (%o3)                  ---------------------- + -------
>                                     2              4
>                                2 %pi
> (%i4) 
> 
> (%i4) fortran(%o2);
>       amax*t/2.0E+0-amax*dtmax*sin(%pi*t/dtmax)/%pi/2.0E+0
> (%o4)                                done
> (%i5) fortran(%o3);
>       amax*dtmax**2*cos(%pi*t/dtmax)/%pi**2/2.0E+0+amax*t**2/4.0E+0
> (%o5)                                done
> 
> 

small correction:

jjf@Z61m:~$ maxima

Maxima 5.22.1 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (a.k.a. GCL)
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) (amax / 2) * sin((%pi * t / dtmax) -(%pi / 2) ) + amax /2 ;
                                            %pi t
                                   amax cos(-----)
                            amax            dtmax
(%o1)                       ---- - ---------------
                             2            2
(%i2) integrate(%o1,t);
                                                %pi t
                                 amax dtmax sin(-----)
                        amax t                  dtmax
(%o2)                   ------ - ---------------------
                          2              2 %pi
(%i3) %o2 + c0;
                                      %pi t
                       amax dtmax sin(-----)
                                      dtmax    amax t
(%o3)                - --------------------- + ------ + c0
                               2 %pi             2
(%i4) integrate(%o3,t);
                              2     %pi t
                    amax dtmax  cos(-----)         2
                                    dtmax    amax t
(%o4)               ---------------------- + ------- + c0 t
                                 2              4
                            2 %pi
(%i5) diff(%o4,t);
                                      %pi t
                       amax dtmax sin(-----)
                                      dtmax    amax t
(%o5)                - --------------------- + ------ + c0
                               2 %pi             2
(%i6) diff(%o5,t);
                                            %pi t
                                   amax cos(-----)
                            amax            dtmax
(%o6)                       ---- - ---------------
                             2            2
Joachim

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