10.1.43 Integral of a complex variable
condition: Calculate the integral of the function of a complex variable: \[ \oint \frac{\cos ^{2} z+3}{2 z^{2}+\pi^{2}} d z, \quad\left|z+\frac{3}{2} i\right|=1\]
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.