10.1.45 Integral of a complex variable
Condition: Calculate the integral. \[ \int_{|z+1|=2} \frac{1}{\left(z^{2}+1\right)^{2}\left(z^{2}-4\right)} d z . \]
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.