Evaluate the integral from 0 to INF of:
(x^a)/(x^2 +4)^2 dx, -1 < a < 3
We are to use f(z)= (z^a)/(z^2 +4)^2,
with z^a = e^(a Log z), Log z= ln|z| + i Arg z, and
-pi/2 < Arg z < 3pi/2.
I have found the residue at 2i to be:
[2^a(1-a)/16]*[cos ((pi*a)/2) + i sin ((pi*a)/2).
Please let me know if this is correct and how to solve this problem.
Many thanks for your help.© BrainMass Inc. brainmass.com February 24, 2021, 2:23 pm ad1c9bdddf
The residue theorem is used to evaluate an integral. The solution is well presented and includes a diagram.