Answer
$\ln(|cos(e^{-x})|)+C$
Work Step by Step
$\int e^{-x}\tan(e^{-x})dx$
let $e^{-x}=u$
$-e^{-x}dx=du$
$\int e^{-x}\tan(e^{-x})dx$
$=-\int \tan(u) du$
$=-(-\ln|cos(u)|)+C$
$=\ln(|cos(e^{-x}|)+C$
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