How to evaluate the following definite integral ???
Integrate[Exp[(Cos[\[Pi] x] - 1)/(2 \[Pi])] Cos[n*\[Pi]*x], {x, 0, 1}]
You can't. There is not even an antiderivative to $e^{\cos x}$ never mind the much more complicated one you have! One way these things could be approximated is using series expansion. I'd try numerical integration after plugging some value for n. btw, The integral goes to zero quickly as n gets large.
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