How to integrate this $\frac{1}{(1-e^{2x})^{1/2}}$?

Question

Please how to integrate this $$\frac{1}{(1-e^{2x})^{1/2}}$$ I have tried $u= e^x$ But I think that is wrong So can anyone help me ?

Answer 1

HINT. Would you try to define $u$ such that $u^2 = 1 - e^{2x} $ ? It will become quite simple.

Answer 2

Hint: $u = e^x$ should work. You get

$$\int \frac{e^x}{e^x\sqrt{1-e^{2x}}}\,dx=\int\frac{1}{u\sqrt{1-u^2}} \,du.$$

Then try trig substitution with $u = \sin\theta$.