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

Integral from 0 to 2*pi of [(Cos(3*theta)) / (5 - 4Cos(theta))] (d*theta)

2. Relevant equations

z=exp(i*theta),

Cos(theta) = (z + z^(-1)) / 2,

Cos(3*theta) = ((exp(3*i*theta)+exp(-3*i*theta)) / 2 = (z^(3) + z^(-3)) / 2,

dz = (i*z) (d*theta)

3. The attempt at a solution

This was an example in my book that didnt show all the steps T_T

Heres what they did:

=>(integral of...){[(z^(3) + z^(-3))/2] / [5 - 4(z + z^(-1))} (dz/iz)

==>-(1/2i)(integral sign)[(z^(6) + 1) / [(z^(3))(2z - 1)(z - 2)]] (dz)

i dont know what voodoo magic they pulled there, but i would like to find out!

thanks for your time!

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# Homework Help: Complex Variables: Missing Step in Example

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