57 views

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