- #1
MadCow999
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Homework Statement
Integral from 0 to 2*pi of [(Cos(3*theta)) / (5 - 4Cos(theta))] (d*theta)
Homework 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)
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 don't know what voodoo magic they pulled there, but i would like to find out!
thanks for your time!