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## Homework Statement

using cauchy integral formula calculate

[tex]\int\limits_C\frac{e^{2z}}{z^2-4}\mbox{d}z[/tex]

where [tex]C[/tex] is closed curve (point [tex]z=2[/tex] is inside)

## The Attempt at a Solution

[tex]\ldots=\int\limits_C\frac{e^{2z}}{(z-2)(z+2)}\mbox{d}z=\int\limits_C\frac{f(z)}{z-2}\mbox{d}z=2\pi if(2)=2\pi i\frac{e^{2\cdot2}}{4}=\frac12\pi e^4i[/tex]

is it correct?