Question

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

Answer 1

`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.`