Answer
$$\frac{2}{{\sqrt 3 }}{\tan ^{ - 1}}\sqrt {\frac{{x - 3}}{3}} +C$$
Work Step by Step
$$\eqalign{
& \int {\frac{{dx}}{{x\sqrt {x - 3} }}} \cr
& {\text{Integrate using the table of integrals from book}} \cr
& {\text{by the formula 29}}\left( b \right):\,\,\,\,\,\,\,\int {\frac{{dx}}{{x\sqrt {ax - b} }}dx = \frac{2}{{\sqrt b }}{{\tan }^{ - 1}}\sqrt {\frac{{ax - b}}{b}} } + C \cr
& {\text{setting }}a = 1{\text{ and }}b = - 3{\text{ then}} \cr
& = \int {\frac{{dx}}{{x\sqrt {x - 3} }}} = \frac{2}{{\sqrt 3 }}{\tan ^{ - 1}}\sqrt {\frac{{x - 3}}{3}} \cr} $$
