Purchase Solution

Computing integrals via analytic continuation

Not what you're looking for?

Ask Custom Question

Using the identity:

Integral from 0 to infinity of x^(-q)/(1+x) dx = pi/[sin(pi q)]

valid for 0 < q < 1

Compute the integral:

Integral from 0 to infinity of x^p/(x^2+4 x + 3) dx

for -1 < p < 1

Purchase this Solution

Solution Summary

We explain in detail how one can use analytic continuation of the given integral to compute the desired integral.

Solution Preview

The denominator of the integrand factors as follows:

x^2+4 x + 3 = (x+1)(x+3)

We can perform the partial fraction expansion:

1/(x^2+4 x + 3 ) = 1/[(x+1)(x+3)] = 1/2 [1/(x+1) - 1/(x+3)]

The integral can thus be written as

I(p) = 1/2 Integral from 0 to infinity of x^p [1/(x+1) - 1/(x+3)] dx

It now looks straightforward to split up the integrals into two ...

Purchase this Solution


Free BrainMass Quizzes
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.

Exponential Expressions

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

Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.