# Thread: Integrating complex exponential function

1. ## Integrating complex exponential function

Hello,

How do I integrate the following:

$\int_{0}^{1} e^{-2\pi x \gamma i}dx$

Thanks.

2. Originally Posted by surjective
Hello,

How do I integrate the following:

$\int_{0}^{1} e^{-2\pi x \gamma i}dx$

Thanks.
You can integrate complex valued functions just like real valued functions.

So $\int e^{-2\pi x \gamma i}dx = \frac{i}{2\pi\gamma}e^{-2\pi x \gamma i} + C$

Can you take it from here?

3. ## integrating complex exponential function

Hey,

How did you arrive at that? Could you please break it down. I have never integrated complex functions before.

Thanks a million

4. Originally Posted by surjective
Hey,

With that said, what's $\int e^{ax}dx$?