# What is the arc length of #f(x)=ln(x)/x# on #x in [3,5]#?

You'll need some approximation techniques to get an answer.

So the arc length is given by:

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To find the arc length of the function (f(x) = \frac{\ln(x)}{x}) on the interval ([3,5]), you would integrate the square root of (1 + \left(\frac{dy}{dx}\right)^2) over the given interval. First, find the derivative of (f(x)), which is (\frac{d}{dx}\left(\frac{\ln(x)}{x}\right)). Then, square this derivative, add 1, take the square root, and integrate the resulting expression from 3 to 5.

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