Question

\[\int\limits_{}^{}\frac{ \sqrt{x ^{2}-9} }{ x }\]

Answer 1

\[\frac{ \sqrt{9\tan ^{2}\theta } }{ 3\sec \theta }*3\sec \theta \tan \theta \]

Answer 2

then \[\int\limits_{}^{}3\tan ^{2}\theta \]

Answer 3

then use the identity :
tan^2 (θ) = sec^2 (θ) - 1

see the integral becomes: