Question

Integrate $\frac{dx}{[1-e^{2x}{]}^{(}1/2)}$

Answer 1

Let $e^{2x}=t$

$2e^{2x}dx=dt$

$dx=\frac{dt}{2e^{2x}}$

Now putting the value of $dx$ in gven question we get

$\int \frac{dt}{(1-t)t}=\int \frac{dt}{t}+\int \frac{dt}{1-t}$

$\int \frac{dt}{(1-t)t}=$ $\ln t+ln(1-t)$

Now putting the value of t we get

$\int \frac{2dx}{(1-e^{2x})}=$ $2x+ln(1-e^{2x})$