integrate 1/(e^xsquareroot1-e^-2x)dx
how i started it:
u= 1-1/e^2x du= -2e^-2xdx
integrate dx/[(-u +1)u^1/2]
dont know how to integrate the above
i assume you mean $\displaystyle \int \frac 1{e^x \sqrt{1 - e^{-2x}}}~dx$
note that this is the same as
$\displaystyle \int \frac 1{\sqrt{e^{2x} - 1}}~dx = \int \frac {e^{2x}}{e^{2x} \sqrt{e^{2x} - 1}}~dx$
now, a substitution of $\displaystyle u^2 = e^{2x} - 1$ yields the integral
$\displaystyle \int \frac 1{u^2 + 1}~du$
i suppose you can take it from here. i leave it to you to fill in the steps i omitted