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## Homework Statement

count integral: [tex]\int\limits_C\frac{e^{2z}}{z^2-4}\mbox{d}z[/tex] where [tex]C[/tex] is closed curve containing [tex]z=\pm2[/tex]

## The Attempt at a Solution

[tex]\ldots=\int\limits_C\frac{e^{2z}}{(z-2)(z+2)}\mbox{d}z[/tex]

so function has two poles [tex]z=\pm2[/tex] and integral will be

[tex]\ldots=\int\limits_{C_1}\frac{e^{2z}}{(z-2)(z+2)}\mbox{d}z+\int\limits_{C_2}\frac{e^{2z}}{(z-2)(z+2)}\mbox{d}z=4\pi i[/tex]

corrrect?