10.1.41 Integral of a complex variable
condition: Using the Cauchy integral formula and its generalizations, calculate the integral: \[ \oint_{|z|=1} \frac{z e^{z}-z-1}{z^{3}} d z \]
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.