10.1.15 Integral of a complex variable

Problem: Calculate the integral and characterize all singular points of the functions under the integral sign (including the point \( \infty \) ): \[ \int_{\partial \Omega} \frac{z^{2} \sin ^{2} \frac{1}{z}}{(z-1)(z-2)} d z \text {, where } \Omega=\{|z|<2\} . \]