Answer
$${\sin ^{ - 1}}\left( {\frac{x}{3}} \right) + C $$
Work Step by Step
$$\eqalign{
& \int {\frac{{dx}}{{\sqrt {9 - {x^2}} }}} \cr
& {\text{write }}9 - {x^2}{\text{ as }}{\left( 3 \right)^2} - {x^2} \cr
& = \int {\frac{{dx}}{{\sqrt {{{\left( 3 \right)}^2} - {x^2}} }}} \cr
& {\text{intgrate by using the formula }}\int {\frac{{du}}{{\sqrt {{a^2} - {u^2}} }} = {{\sin }^{ - 1}}\left( {\frac{u}{a}} \right) + C\,\,\,\left( {{\text{see page 419}}} \right)} \cr
& {\text{with }}a = 3{\text{ and }}u = x,\,\,\,\,du = dx \cr
& = \int {\frac{{dx}}{{\sqrt {{{\left( 3 \right)}^2} - {x^2}} }}} = {\sin ^{ - 1}}\left( {\frac{x}{3}} \right) + C \cr} $$
