Is this what you mean?:
\(\displaystyle \L\\\int[sin(\frac{2{\pi}x}{e^{2{\pi}x}})]dx\)
I see in your heading you said 'complex', but I see no 'i' in your post. This looks like a complex analysis problem.
If so, I don't think it's doable by elementary means. I couldn't even get Maple to give me a general form.
That 'e' in there poses a problem.
If you had liits of integration, you could use an approximation method to evaluate it. But, an indefinite is a booger.
This thing gives a really wacky graph. I can see why it isn't easily done. When I graphed it the calculator read,"trig function argument too big for accurate reduction".
