Evaluating $\int e^{-x}\tan(x) \ \mathrm dx$ .

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I was told years ago by a visiting professor that this integral:$$\int e^{-x}\tan(x)dx$$ has an elementary form, but I have never been able to find it. Any suggestions? I don't think it's possible anymore, but thought I would ask...

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It can be proved to be non-elementary using the Risch algorithm.