Integration problem with e^(ix)

[Mr Cheese]

So I basically want to integrate this expression

\int\sqrt{1 - e^{(aix)}}

where a is some general term and i = \sqrt{-1}

I thought maybe of converting it to a single complex number in polar form and then just halfing the angle to get rid of the root, but i really have no idea how to go about this problem.

 

[jackmell]

Just treat the complex constant as just a regular constant, say call it k=ia and when you finally get the answer, back-subsitute what k is. Then write:

\int \sqrt{1-e^{kx}}

You can do that huh? Takes several substitutions unless someone has a better way. So what happens if you start the first one by letting:

u=1-e^{kx}