(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The problem is ∫e^x/(e^x)-1 to be evaluated from -1 to 1.

2. Relevant equations

3. The attempt at a solution

I got the integral as ln|(e^x)-1|

So, for the first part, evaluating from -1 to 0, with t being the limit at 0 I got this:

ln|(e^t)-1| - ln|(e^-1)-1|

which is supposed to evaluate to negative infinity, and I don't understand that

t is approaching 0, so e^t should be 1, 1-1 is 0, and ln0 doesn't exist and (e^-1)-1 is also negative which doesnt exist, so I'm a little confused as to how it works out to negative infinity.

Can anyone point me in the right direction? Thanks.

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# Improper integral with logs

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