Am i doing this problem wrong?

Evaluate the integral

$\displaystyle

\int (e^(2x)) / (e^x - 2)) dx$ <-- that is e^(2x)

i expanded the problem to:

$\displaystyle \int(e^x * e^x * (1/ (e^x - 2)) dx $

i picked u to be e^x - 2

$\displaystyle u = e^x - 2, e^x = u + 2$

$\displaystyle du = e^x $

rewrite to:

$\displaystyle \int((u + 2) * 1/ (u) dx$

multiply all out to

$\displaystyle \int 1 + 2*(1/u) dx$

integrate and get:

$\displaystyle u + 2ln|u| + C$

$\displaystyle (e^x - 2) + 2ln|e^x - 2|+C$

but the answer says its:

$\displaystyle e^x + 2ln|e^x - 2|+C$

what did i do wrong?