I am beginner at this topic, i need help to solve the following question for my exam preparation.
Evaluate $$\int_\gamma \frac{1+z}{1-\cos z} dz$$ where $\gamma$ is origin centered circle with radius 7.
Any help would be really appreciated.
2026-03-27 04:38:14.1774586294
Evaluate $\int_\gamma \frac{1+z}{1-\cos z} dz$ where $\gamma$ is origin centered circle with radius 7
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If you have learned the Residue Theorem, you should be able to apply it; calculate the residues at each pole inside the contour.
If not, you can 1) plug in a suitable parameterization of the path, and use brute force to compute the resulting integral (with a real variable), or 2) obtain the indefinite integral away from the pole, it should contain branch cut(s), and your integral can be obtained by monodromy.