How does one find the Fourier Series for a non-periodic function on an arbitrary interval $[-\frac{L}{2},\frac{L}{2}]$ using the complex exponential?

Question

I was given three functions, and told to find the coefficients of their Fourier Series using
$\tilde{f_k} = \frac{1}{\sqrt{L}}\int_{-\frac{L}{2}}^{\frac{L}{2}} f(x) e^{i2\pi kx/L}dx$ where $\tilde{f_k}$ is the $k$th coefficient of the Fourier Series of $f(x)$. I was given 1) $f(x) = x^n$, 2) $f(x) = e^{-a|x|}$ , and 3) $f(x) = e^{-ax^2}$. I have expressions for each of these, but they turned out to be very ugly, and I'm not sure how to verify them. Any tips would be appreciated.