Residue solution: If f(z) has only a finite number of isolated singularities (including infinity points) on the extended complex plane, the sum of residues of f(z) at each point is zero. As shown in the figure:

Application: Using residue theorem, we can transform the required integral into the integral of complex variable function along the closed curve, thus transforming the required integral into the calculation of residue. Residue is a very important concept in the theory of complex variable functions, which is closely related to Laurent expansion of analytic functions on isolated singularities and Cauchy compound closed-circuit theorem.

Residue is one of the important concepts in the theory of complex variable functions, which is closely related to Laurent expansion of analytic functions at isolated singularities and Cauchy's compound closed-circuit theorem. Residue theory is the product of the combination of complex integral and complex series theory. Correct application of residue theorem can transform the integral along the closed loop into the residue of isolated points.