O15-C906
> restart:
> i:=int(exp(-t)*ln(t),t=0..infinity);evalf(%);

                             i := -gamma


                             -.5772156649

> j:=n->int((1-t/n)^n*ln(t),t=0..n);

> seq(evalf(j(20*n)),n=3..12);# Thm de CV dominée

  -.592051764, -.588442789, -.586245863, -.584767941, -.583705714,

        -.582905431, -.582280840, -.581779808, -.581368972,

        -.581025987

> a:=n->sum(1/'k','k'=1..n)-ln(n);

> seq(evalf(j(n)+a(n)*n/(n+1)+n/(n+1)^2),n=2..18);# Par IPP j(n)=-(a(n)*n/(n+1)+n/(n+1)^2), donc lim a(n)=-gamma

                       -8               -8       -8            -8
  0., 0., 0., 0., .1 10  , 0., 0., .1 10  , .1 10  , 0., -.1 10  , 0.,

              -8
        -.1 10  , 0., 0., 0., 0.

>