I want to show that the integral $\displaystyle \int_{\gamma_R}\frac{dz}{z^{2n}+1} \to 0

$ as $\displaystyle R\to \infty$

,where $\displaystyle \gamma_R$ is the upper semi-circle from R to -R

For $\displaystyle n\geq 2$ this is easy to show. But how to show this for n=1?