Consider the integral
$$\oint _{c}\frac{sin\left ( x \right )}{x^{2}\left ( x^{2}+4 \right )}dx$$
where $C$ is a counter-clockwise oriented circle defined as $\left | x-i \right |=2$. The value of the integral is
- $-\frac{\pi }{8}\sin\left ( 2i \right )$
- $\frac{\pi }{8}\sin\left ( 2i \right )$
- $-\frac{\pi }{4}\sin\left ( 2i \right )$
- $\frac{\pi }{4}\sin\left ( 2i \right )$