what did i do wrong? Integral problem:
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?