How do you integrate $e^x / sqrt(1-e^(2x)) dx$ ?

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Answer 1 · 2016-06-20T16:51:19

$arcsin(e^x)+C.$

We use Method of Substitution :

Let $e^x=t$ , so that, $e^xdx=dt.$ Also, note that, $e^(2x)=t^2.$

Hence, $I=inte^x/sqrt(1-e^(2x))dx=int1/sqrt(1-t^2)dt=arcsint=arcsin(e^x)+C.$

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