## anonymous one year ago how should I approach (integral (e^x + e^-x) / (e^x - e^-x) dx? I tried splitting it into integral of (e^x +e^-x)dx * integral of (1/ (e^x - e^-x) dx and I got (e^x - e^-x)* ln |e^x - e^-x| +C but i don't think that's the correct answer...

1. anonymous

|dw:1434557340743:dw|

2. anonymous

Setting $$u=e^x-e^{-x}$$ should work fine. This gives $$du=(e^x+e^{-x})\,dx$$, so you have $\int\frac{e^x+e^{-x}}{e^x-e^{-x}}\,dx=\int\frac{du}{u}$ You can't pull out $$e^x+e^{-x}$$ like you did because you're integrating with respect to $$x$$. Anything containing an $$x$$ belongs inside the integral.

3. anonymous

oh, thank you so much

4. anonymous

yw