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

Nov 8, 2015

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

#### Explanation:

$f ' \left(x\right) = \frac{1 - \ln x}{x} ^ 2$

So the arc length is given by:

${\int}_{3}^{5} \sqrt{1 + {\left(1 - \ln x\right)}^{2} / {x}^{4}} \mathrm{dx}$

The length is a bit more than $2$. (According to Wolfram Alpha)