10.1.52 Integral of a complex variable
Condition: Calculate the closed loop integral using the basic residue theorem: \[ \oint_{L} \frac{e^{z} d z}{z(z+1)^{2}} \text {, } \] where \( L- \) is a closed loop enclosing a point \( z=-1 \), but not covering the point \( z=0 \).
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.