# What is the arc length of #f(x)=-xln(1/x)-xlnx# on #x in [3,5]#?

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To find the arc length of ( f(x) = -x \ln\left(\frac{1}{x}\right) - x \ln(x) ) on the interval ([3, 5]), you can use the formula for arc length:

[ L = \int_{a}^{b} \sqrt{1 + \left(f'(x)\right)^2} , dx ]

First, find the derivative ( f'(x) ). Then plug it into the formula along with the given interval [3, 5] to evaluate the integral. This will give you the arc length ( L ) of the function over the specified interval.

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