An integral I over a counterclockwise circle C is given by

\(I = \mathop \oint \limits_C^\; \frac{{{z^2} - 1}}{{{z^2} + 1}}{e^z}dz.\)

If C is defined as |z| = 3, then the value of I is

1
-πi sin (1)
2
-2πi sin (1)
3
-3πi sin (1)
4
-4πi sin (1)

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