Thread: calc2. find the arc length of a function

y=ln[(e^x +1)/(e^x -1)]
interval [ln2,ln3]

please help

thanks

I assume you know the arc-lenght formula for this case.

Show your work please, or may be an attempt.

y'= (-2e^x)/(e^2x - 1)
(y'^2)= [4e^(2x)]/[(e^2x - 1)^2]
sqroot of [1+ (y'^2)]= (e^2x +1) / (e^2x -1)

then i got stuck. i have no idea how to take the integral of (e^2x +1) / (e^2x -1)

thanks

Originally Posted by tichua

i have no idea how to take the integral of (e^2x +1) / (e^2x -1)

I'll assume your work is fine.

Now, to integrate that, just observe that and by differentiating you'll get which is the numerator, so I think you know what's the proper substitution.