It is neither even nor odd: the real and imaginary parts have different parity.Ashley1nOnly said:Homework Statement
(e^(ikx)/(x^2+a^2))dx (-infinity, +infinitiy)
Isn't this function odd so it should be zero?Homework Equations
The Attempt at a Solution
I know how to complete the entire problem but I'm having troubles integrating this. I'm looking for someone to reference ( a website or an equation ) where I could learn how to properly integrate this function.
Please don't solve.
Integration by parts didn't work.
The formula for integrating e^(ikx)/(x^2+a^2)dx is ∫ e^(ikx)/(x^2+a^2)dx = (1/a) arctan(x/a) + C.
The variable 'i' represents the imaginary unit, 'k' represents the wavenumber, 'x' represents the independent variable, 'a' represents a constant, and 'C' represents the constant of integration.
The purpose of integrating e^(ikx)/(x^2+a^2)dx is to find the integral of a function that involves the exponential function and a quadratic term in the denominator. This type of integral arises in various areas of physics, such as in the study of waves and oscillations.
The steps for integrating e^(ikx)/(x^2+a^2)dx are as follows:
Yes, there are a few special cases for integrating e^(ikx)/(x^2+a^2)dx. For example, if a = 0, the integral becomes ∫ e^(ikx)/x^2 dx, which does not have an elementary antiderivative. Additionally, if k = 0, the integral becomes ∫ 1/(x^2+a^2) dx, which can be solved using trigonometric substitution.