Integrating complex exponentials with Infinite limits

[Ribena]

Hi all,

I'm trying to integrate the function below with respect to x

exp(ix)-exp(-ix)

With infinity and negative infinity as the limits. Would the integration be possible?

 

[mfb]

There is a shorter way to express this function.
Alternatively, you can find the anti-derivative, and check yourself.

As you are working with complex numbers, you should add that you try to integrate this along the real axis (well, I would expect this).

Would the integration be possible?

What do you think, and why?