I am trying to calculate the coefficients of a fourier series of the function $e^{-|x|}cosx$. Since the function is even when I calculate $B_n$ I go from 0 to pi
$$B_n=\frac{2}{\pi} \int_0 ^{\pi}e^{-x}cosx\cdot cos(nx) dx $$
Now I get to my issue, how can this be evaluated? Intergration by parts will not do anything and I cant see how to simplify it.