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) ]
Note. 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) 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) ]
Note. 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