Solve integral:`int (dx)/sqrt(1-e^(2x))`

`f(x)=
-tanh^-1(sqrt(1-e^(2x)) + C` is not an incorrect solution.

The derivative of
tanh^-1(x) is `1/(1-x^2)` .

The solution that you have proposed is just
tanh^-1 expressed on the complex plane.

 

 

href="https://en.wikipedia.org/wiki/Inverse_hyperbolic_function">https://en.wikipedia.org/wiki/Inverse_hyperbolic_function