Integral of $\displaystyle
(e^x-e^-x)/(e^x+e^-x)
$
I have tried adding the conjugate to the top and bottom but don't know where to go from there. Should I continue that or try a different technique?
Hello, stevo970!
If you look at it the right way, it's easy . . .
$\displaystyle \int\frac{e^x-e^{-x}}{e^x+e^{-x}}\,dx$
Let $\displaystyle u$ = the denominator.
We have: .$\displaystyle \begin{array}{ccc}u &=& e^x + e^{-x} \\ du &=& (e^x - e^{-x})\,dx \end{array}$
Hence, we have: .$\displaystyle \int\frac{du}{u}$
Got it?