                           3/2      s + 1
                               s    sqrt(-----)
                                           s
(%i8) assume(exp(%pi*s)&gt;1)$
(%i9) laplace(sum((-1)^n*unit_step(t-n*%pi)*sin(t),n,0,inf),t,s),simpsum;
                         %i                         %i
              ------------------------ - ------------------------
                              - %pi s                    - %pi s
              (s + %i) (1 - %e       )   (s - %i) (1 - %e       )
(%o9)         ------