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Let a be a real number with |a|>1. Compute $$\int_0^{2\pi}\frac{ 1-a\cos\theta}{1-2a\cos\theta + a²} dθ$$

I know i should think of a circle since the bounds are from 0 to 2π. I have the soltuions to this question. But what i don't understand is how do we assume that we should start the problem with

$$∫_{|z|=1} \frac{dz}{z-a}dz\,\;\; ?????\;\;\;\text{How do i assume this at the start???} $$

and then use $\,\,z=e^{iθ}\,\,$ and $\,\,dz= ie^{iθ}\,\,$ to get a similar integral as the one above after doing some algebra.

I have not learnt the Residual formula yet. I have only learnt until the Cauchy Integral Formula

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    Is acos = a*cos or arccos? Please consider giving $\LaTeX$ format to your question.2012-10-24
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    Check whether my editing is accurate...and please learn how to use LaTeX for mathematics in this site!2012-10-24
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    Related: http://math.stackexchange.com/questions/211058/evaluating-frac12-pi-int-02-pi-frac11-2t-cos-theta-t2d-theta2012-10-24

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