Chapter 8: Techniques of Integration - Section 8.6 - Integral Tables and Computer Algebra Systems - Exercises 8.6 - Page 481: 14

$\sqrt{x^2-4}-2\sec^{-1}|\dfrac{x}{2}\Big|+C$

Apply formula : $\int \dfrac{\sqrt{x^2-a^2}}{x}dx=\sqrt{x^2-a^2}-a\sec^{-1} |\dfrac{x}{a}|+C$ Consider $I=\int\dfrac{\sqrt{x^2-4}}{x}dx \\=\sqrt{x^2-4}-2\sec^{-1}|\dfrac{x}{2}|+C$