# Math Help - evaluate the integral Q2

1. ## evaluate the integral Q2

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

2. Originally Posted by twilightstr
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 $\int \frac 1{e^x \sqrt{1 - e^{-2x}}}~dx$

note that this is the same as

$\int \frac 1{\sqrt{e^{2x} - 1}}~dx = \int \frac {e^{2x}}{e^{2x} \sqrt{e^{2x} - 1}}~dx$

now, a substitution of $u^2 = e^{2x} - 1$ yields the integral

$\int \frac 1{u^2 + 1}~du$

i suppose you can take it from here. i leave it to you to fill in the steps i omitted