10.1.54 Integral of a complex variable
condition: Calculate the integral of a function of a complex variable along a given curve. \[ \begin{array}{l} \int_{A B C}\left(z^{2}+\cos z\right) d z, A B C \text {-broken line, } z_{A}=0 \\ z_{B}=1, z_{C}=i \end{array} \]
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.