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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

1. $-\frac{\pi }{8}\sin\left ( 2i \right )$
2. $\frac{\pi }{8}\sin\left ( 2i \right )$
3. $-\frac{\pi }{4}\sin\left ( 2i \right )$
4. $\frac{\pi }{4}\sin\left ( 2i \right )$