CVCI6

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\oint _{{|z|=1}}e^{{1/z}}\sin {\frac  {1}{z}}dz\,

In taylor series,

e^{{1/z}}=1+{\frac  {1}{z}}+{\frac  {1}{2!z}}+...\,

\sin {\frac  {1}{z}}={\frac  {1}{z}}-{\frac  {1}{3!z^{3}}}+...\,

There is an essential singularity at z=0\,

The residue at z=0 is the coefficient of 1/z in the Laurent series of the integrand, which is 1.

So \oint =2\pi i.

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