
10.1.37 Integral of a complex variable
Condition: Using the Cauchy integral formula and its generalizations, calculate the integral: \[ \oint_{|z-\pi|=2} \frac{\cos ^{2} z d z}{\left(z^{2}-\pi^{2}\right)} \text {. } \]
Calculation of integrals from functions of a complex variable. Sub-integral functions can be either analytic or with singular points. Application of the main residue theorem, as well as the Cauchy formulas for calculating integrals of functions with poles in a simply connected domain.