I know how to do this problem the easy way, where I have trouble though is when I apply Euler's formula.

integral Cos^3(x)dx= Sin(x) - (1/3) Sin^3(x)+c

however when I try to do this with complex numbers I get stuck at this point.

I can do the integral I am just not sure how to go back to trig functions.

Cos^3(x) = (1/4) ((e^3ix - e^-3ix)/2 - 3(e^ix - e^-ix)/2)

I think this part -3(e^ix - e^-ix)/2) becomes -3Cos(x)

but what about the rest?

ps- I'm on spring break or else I would ask my professor (calc 2)