The Attempt at a Solution
I was told to solve using partial fractions. When I set up the partial fraction I got:
A/e^x+1 + B/e^x-1 = 2e^x
When I broke it up, I solved for A and B and got that A and B should both equal 1/2. When I plugged it back into the integral, I pulled out the 2 in the numerator, substituted A and B in (so the 2 and the 1/2s all cancel) and integrated 1/e^2x+1 dx and 1/e^2x-1 dx
After I integrated, I got ln(e^x+1) + ln(e^x-1) + C
However, when I looked up the answer online to check my answer, they had something a little different. The answer (on Wolfram Alpha) was nearly the same, but instead was: ln(1-e^x)-ln(e^x+1) +C
I was wondering where I could have gone wrong?
Just to be clear, when I set up the partial fractions, I did the following:
A/e^x+1 + B/e^x-1 =2e^x/(e^x+1)(e^x-1).
I set this equal to the numerator in the integral:
(A+B)e^x+(B-A)=e^2x ---- I pulled the two outside of the integral in the first step
Any idea where I went wrong?