Complex integral without cauchy

[Daniiel]

Hey,

I've been trying to do this integral without cauchy's theorem (with the theorem i get 6ipi in like 2 steps). I am stuck at this point, I have found afew ways to do the integral I am stuck on but they all involve multiple variable changes and I was wondering if there is a simple way to do this that I'm not seeing.

[PLAIN]http://img832.imageshack.us/img832/7958/intup.jpg sorry typo, its not supposed to be 1/2 ln(1+2e^(it)) just ln(1+2e^(it))

Thanks in advanced

 

[vela]

It helps to note that the numerators are all of the form i(2e^it)ⁿ. Try using the substitution u=2e^it+1 on all of them.