10.1.16 Integral of a complex variable

Problem: Calculate the integral and characterize all singular points of the functions under the integral sign (including point \( \infty \) ). \[ \int_{\partial \Omega} \frac{z^{3}}{z+1} e^{\frac{1}{z}} d z \text {, where } \Omega=\{|z|<2\} \text {. } \]