10.1.18 Integral of a complex variable

Problem: Calculate the integral and characterize all singular points of the functions under the integral sign (including point \( \infty \) ). \[ \int_{\partial \Omega} \frac{\sin z}{\left(z^{3}-z\right)(z-i)} d z \text {, where } \Omega=\{|z-1|<1\} \text {. } \]