# What is the arclength of f(x)=(1+x^2)/(x-1) on x in [2,3]?

Jun 3, 2018

$\approx 1.07667$

#### Explanation:

We get by the Quotient rule

$f ' \left(x\right) = \frac{2 x \left(x - 1\right) - \left(1 + {x}^{2}\right)}{x - 1} ^ 2$
$f ' \left(x\right) = \frac{{x}^{2} - 2 x - 1}{x - 1} ^ 2$
so our integral is given by

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

A numerical result is given by $\approx 1.07667$