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An integral $I$ over a counterclockwise circle $\textbf{C}$ is given by $$I=\oint _c \frac{z^2-1}{z^2+1} e^z dz.$$ If $\textbf{C}$ is defined as$\mid z \mid=3$ , then the value of $I$ is

  1. $-\pi i \sin(1)$
  2. $- 2\pi i \sin(1)$
  3. $-3\pi i \sin(1)$
  4. $-4\pi i \sin(1)$
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