The problem is:
Evaluate the integral from 0 to INF of:
[(x^(1/3))*(ln x)]/(x^2 +9) dx
by using f(z)= [(z^(1/3))*(Log z)]/(z^2 +9), with
-pi/2 < Log z < 3pi/2.
Also, with z^(1/3)= e^[(1/3)Log z].
We are to use the curve C:
from -R to -p, -p to p around origin, p to R, and Cr from 0 to pi.
Many thanks in advance for your help. This is TOUGH one!© BrainMass Inc. brainmass.com March 4, 2021, 5:55 pm ad1c9bdddf
Please see the attached file for the full solution.
Thanks for using BrainMass.
Let , we use the following figure:
Since , ...
An integral is evaluated using Jordan's lemma. A diagrm is included in this well presented solution.