Question

Find the exact length of the curve
y=ln((1+e^(-x))/(1-e^(-x))) between x=1 and x=2

Answer 1

\[Length = \int\limits_{a}^{b}\sqrt{1+f'(x)^{2}} dx\]

Answer 2

the derivative on wolfram is 2e^x/e^(2x)-1

Answer 3

i get f'(x)
\[f'(x) = \frac{-2e^{-x}}{(1+e^{-x})(1-e^{-x})}\]

Answer 4

oh ok, well i didn't simplify it enough

Answer 5

\[\int\limits_{1}^{2}\sqrt{1+4e^(2x)/(e^(2x)-1)^2}\]

Answer 6

i dont know how to integrate that

Answer 7

I haven't worked it out...but you should probably combine to make one term under the radical

Answer 8

what I wrote above is what you want to do