Sorry Guys - One last Improper Integration question (e^x)/ ((e^x) -1) Why Divergent??

Sorry. I'm coming to the end of my four hour review. I try not to disturb you guys too much but I guess I'm just brain dead now.

So the problem is the integral of (e^x) / ((e^x) -1) from -1 to 1

I wasn't sure what to do at first so I made it

(e^x) -1) +1 / ((e^x) -1)

so that I could split the integral into

(e^x -1)/(e^x-1) and get x

and then

1 / ((e^x) - 1)

And then I just solved it straightup. I won't show that because it's obviously completely wrong if it's divergent.

How exactly is this done. Sorry to disturb you guys again and thank you * 1000000 + Lim x-> inifinity of x^2 (Nod)

Re: Sorry Guys - One last Improper Integration question (e^x)/ ((e^x) -1) Why Diverge

if part of the definite integral diverges, it all diverges ...

$\displaystyle \lim_{a \to 0^+} \int_a^1 \frac{e^{x}}{e^x - 1} \, dx$

$\displaystyle \lim_{a \to 0^+} \left[\ln(e^x - 1) \right]_a^1$

$\displaystyle \lim_{a \to 0^+} \left[\ln(e - 1) - \ln(e^a - 1) \right]$

$\displaystyle \lim_{a \to 0^+} \ln \left(\frac{e - 1}{e^a - 1}\right) = \infty$