Integral Help: \int arg(x^{ix} + x^{-ix}) dx

[epkid08]

I really have no idea how to do this, please show some steps.

$$\int arg(x^{ix} + x^{-ix}) dx$$

 

[Dick]

If x is real the exp(ix)+exp(-ix) is real. Why? What is arg of a real number? Are you sure that's the whole problem?

 

[epkid08]

If x is real the exp(ix)+exp(-ix) is real. Why? What is arg of a real number? Are you sure that's the whole problem?

I'm pretty sure that when x is real, the inside does not necessarily equal a real number. I'm looking at the graph right now and y = arg(...) is not zero, and also this isn't homework.

 

[Dick]

Hmm. Ok, what is x? Do they give you a contour to integrate along? It's pretty tricky to define the general complex power of a complex number.