= Solution
The <residue theorem> states that if a function is <holomorphic> on and inside a positively oriented simple closed <contour> except at finitely many isolated <singularities> $a_1,\ldots,a_N$ in its interior, then
$$
\boxed{\int_\gamma f(z)\,dz=2\pi i\sum_{j=1}^N\operatorname{res}(f;a_j).}
$$
No <singularity> may lie on the <contour>. More generally, a closed <contour> has a winding-number-weighted sum of <residues>, provided it and its enclosed winding regions lie in the domain on which the isolated <singularities> are specified.
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