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

Infinite or arguably undefined, since $f \left(5\right)$ is undefined.
$f \left(x\right)$ has a vertical asymptote at $x = 5$ so the arc length in the interval $\left[1 , 5\right)$ is infinite.
You could say that the arc length in $\left[1 , 5\right]$ is undefined since $f \left(5\right)$ is undefined.