Kinda tricky integral:
\[\int_{-\infty}^\infty \frac{\cos x}{(x^2+1)(1+e^x)}\,dx\]

Kinda tricky integral:
\[\int_{-\infty}^\infty \frac{\cos x}{(x^2+1)(1+e^x)}\,dx\]

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I've got some hints in mind, but I'm debating whether or not they give too much away :)

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I don't know but I kind of feel like it has something to do with Gaussian integral.

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