Letting
u = x3 + 1
, we compute the relevant integral:
dx
=
=
du
=
(log(u)|2m3+1)
=
log
This quantity clearly has no limit as
m→∞
, so the series
diverges. Notice that there are far more efficient ways to show the divergence
of this series; for instance one could use the comparison test with the
harmonic series
1/n
.