Answer
$\dfrac{53}{6}$
Work Step by Step
The formula to calculate the arc length is as follows: $L=\int_{c}^{d} \sqrt {1+[f'(x)]^2} dx$
Re-write the equation as follows: $L=\int_{1}^{3} [x^2+\dfrac{1}{4x^2}] dx $
Separate the terms and integrate as follows: $L=\int_{1}^{3} [x^2+\dfrac{1}{4x^2}] dx \\=[ \dfrac{x^3}{3}-\dfrac{1}{4x} ]_1^{3}=\dfrac{53}{6}$
