Answer
$\frac{1}{7}arcsec\frac{|3x|}{7}+C$
Work Step by Step
$\int\frac{1}{x\sqrt (9x^{2}-49)}dx$
The denominator looks like $arcsec$.
$\int\frac{du}{u\sqrt (u^{2}-a^{2})}dx=\frac{1}{a}arcsec(\frac{|u|}{a})+C$
$a=7$
$u=3x$
$du=3dx$
$\int\frac{3}{3x\sqrt (9x^{2}-49)}dx$
$\frac{1}{3}arcsec(\frac{|3x|}{7})+C$
