10.1.51 Integral of a complex variable
condition: Calculate the closed loop integral using the basic theorem on residues: \[ \oint_{L}\left(z^{2}+1\right) e^{\frac{3}{z}} d z, \text { where } L-\text { circle }|z|=1 . \]
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.