10.1.53 Integral of a complex variable
condition: Find the integral using the general Cauchy integration formula: \[ \int_{|z|=\frac{1}{2}} \frac{1-\cos z}{z^{3}} d z \text {. } \]
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.