I want to calculate following integral $$
\int_{1- i\infty}^{1+i\infty}\frac{a^z}{z^2} dz
$$ where $0<a<\infty$. I considered the following curve 
I need to show that $$ \int_{C_R}^{}\frac{a^z}{z^2} dz $$ goes to zero as $R$ goes to zero ($C_R$ is only the half circle exluding the line segment). So by Residue theorem I can calculate the answer. However I am stuck there. Any help would be appreciated! Thank you!