we have the integral : $\lim_{T\to \infty }\int_{2-iT}^{2+iT}\frac{(s-1)^{n}}{s}ds$
which diverges for every value of n except $n=0$ if we perform the change of variables :
$s\rightarrow \frac{1}{s}$
then : $\lim_{T\to \infty }\int_{2-iT}^{2+iT}\frac{(s-1)^{n}}{s}ds=\int_{-i}^{i}\frac{(1-s)^{n}}{s^{n+1}}ds$
which converges . am i missing something here , or is this correct !?