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

1 Answer

Jun 20, 2016

#arcsin(e^x)+C.#

Explanation:

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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