hi, this is really frustrating because I've been working on this one integral for the last 2 1/2 horus and i cant figure out what I did wrong...(adsbygoogle = window.adsbygoogle || []).push({});

it's the Integral sin^2(x)/(3-2cos(x)) dx from x=0 to x=2pi

I tried the substitution z=e^(itheta) plugging in sin and cos as functions of z and I

ultimately get:

i * integral (z^4+2z^2+1)/(z^2-3z+1)dz over |z|=1

Then the poles inside the unit circle are @ z=0 and (3-sqrt(5))/2

so I find the residue @ z=0 to be 3 and @ (3-sqrt5)/2 something like

(looking in my mess of notes) 4(15-6sqrt(5))^2/((3-sqrt(5)^2(-sqrt(5))

then I plug in 2pi X Sum residues X i

but it doesn't agree with the answer I get on my calculator which is around 1.19

any help is really appreciated thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Complex Integral I just can't figure out

**Physics Forums | Science Articles, Homework Help, Discussion**