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I am stuck with two complex variable questions. Among others, I can't find residues when I have the poles, and these two questions are getting me out of hope. Maybe one of the geniuses on this site knows how to drive those 2 problems to an answer:

1) Computing the following integral:

Intergral from -oo to +oo of: (x*x) / (x*x*x*x - 4x*x + 5 ) dx

2) Computing the following integral:

Integral from 0 to 2 pi of: d(theta) / [( 1 + B cos theta)*( 1 + B cos theta) ]

Formulas: residue theorem

http://en.wikipedia.org/wiki/Residue_theorem" [Broken]

Attempts:

For the 1st one,

First I searched zeros for Q(z) = (z*z*z*z - 4z*z + 5 )

I searched for z*z first. I found

z*z = 2 - i

or

z*z = 2+i

Then using polar coord., I found:

5^(1/4) * e^(i theta/2)

- 5^(1/4) * e^(i theta/2)

5^(1/4) * e^(- i theta/2)

5^(1/4) * e^(i theta/2)

Are they right?

with theta = arcsin (5^(-1/2))

and then I would like to get to the solution but I am stuck.

Same for 2nd problem.

Thanks for your help

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Compelx variable question, the Residue Thm and applications

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