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

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SUMMARY

The integral of the function e^(ikx)/(x^2+a^2) over the entire real line is not zero, as the function is neither even nor odd due to the differing parity of its real and imaginary components. The user is seeking resources to effectively integrate this function, having encountered difficulties with integration by parts. The discussion emphasizes the need for a deeper understanding of complex integration techniques rather than relying solely on basic integration methods.

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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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