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 !?