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

[Ashley1nOnly]

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.

 

[kuruman]

I think integration by parts works. How about showing what you did and what didn't work?

 

[Ray Vickson]

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.