
10.1.42 Integral of a complex variable
condition: Calculate the integral over \( (2,3) \) \( \int_{(0,1)}(z+\operatorname{Re} z) d z \) along a straight line connecting the points.
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.