# Evaluating an Integral with 2nd Order Pole : Moivre-Laplace Fomulation

Not what you're looking for?

Problem: 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.

Use the branch cut of the negative Im axis, and use the following curve:

C= -R to R, -p to p, p to R, and Cr from 0 to pi.

Can anyone do this problem using these parameters?

##### Purchase this Solution

##### Solution Summary

An integral is found using a Moivre-Laplace formulation. The solution is detailed and well presented.

##### Solution Preview

The integral in question is

; where -1 < a < 3.

Corresponding function of complex variable is f(z) = . It should be integrated over the closed contour: [- R; -r] Cr [ r; R] CR ; where Cr - semi-circle of small radius r, and CR - semi-circle of large radius R in the upper part of the complex plane, with the ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Probability Quiz

Some questions on probability

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.