I am asked to evaluate
$$\int_{\vert z \vert = 2}\frac{e^z}{z^2-1}dz.$$
By partial fractions I found
$$\frac{e^z}{z^2-1}=-\frac{1}{2e}\frac{1}{z+1}+\frac{e}{2}\frac{1}{z-1}.$$
So is the answer just
$$\pi i (\frac{e^2-1}{e}).$$
Is this correct?
2026-04-02 06:06:52.1775110012
complex integral involving $e^z$ over unit $2$ circle.
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