(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the integral [itex]I_1 = \int_0^{2\pi} \frac{d\theta}{(5-3sin\theta)^2}[/itex]

2. Relevant equations

3. The attempt at a solution

I start off by switching the sine term for a complex exponential [itex]e^{i\theta}=cos\theta +isin\theta[/itex]

I will consider only the Imaginary component of the solution.

now make the substitution: [itex]z=e^{i\theta}[/itex]

so we have:

[itex]I_1 = Im\left(I_2\right)[/itex]

[itex]I_2 = \int_0^{2\pi} \frac{1}{(5-3z)^2}\frac{dz}{iz}=\frac{1}{i}\int_0^{2\pi}\frac{dz}{z(5-3z)^2}[/itex]

so we have 2 poles: a simple pole at z=0 and a second order pole at z=5/3

I'm not sure wether i need to include both residues. the question does not indicate the contour to integrate. Should it be a unit circle? I'm not sure why it would be. any ideas?

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# Homework Help: Slightly Harder Cauchy Integral

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