MathProblemsBank

10.1.40 Integral of a complex variable

Condition: Using the Cauchy integral formula and its generalizations, calculate the integral: \[ \oint_{|z-1|=2} \frac{(z+\pi) d z}{z^{2}\left(z^{2}+4\right)} \text {. } \]

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.

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