Is e^(ikx)/(x^2+a^2) Integrateable over All Reals?

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The function e^(ikx)/(x^2+a^2) is being analyzed for its integrability over all reals. A participant questions whether the function is odd, suggesting it should integrate to zero, but it is clarified that the function is neither even nor odd due to differing parities in its real and imaginary components. The user is seeking resources or references to assist with the integration process, as their attempts, including integration by parts, have not been successful. The discussion emphasizes the need for proper understanding of the function's properties before proceeding with integration. Overall, the focus is on finding effective methods for integrating this complex function.
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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.
 
Last edited:
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I think integration by parts works. How about showing what you did and what didn't work?
 
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.
It is neither even nor odd: the real and imaginary parts have different parity.
 

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