Hello, Johngalt13!
If you inserted absolute values, your second answer is correct.
I've done it a few ways and gotten...
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I solved it like this . . .
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integrate (-4-4e^x)/(1-e^x) using u substitution where u=e^x4ln(e^x)+4ln(1-e^x)+4ln(e^x-1)+c
I've done it a few ways and gotten...
4ln(1-e^-x)+4ln(1-e^x)+c
8ln(1-e^x)-4x+c
neither of which are correct, any insight on what I'm doing wrong?