Answer
$$\frac{2}{{27}}{\left( {4 + 9x} \right)^{3/2}} + C$$
Work Step by Step
$$\eqalign{
& \int {\sqrt {4 + 9x} } dx \cr
& \int {{{\left( {4 + 9x} \right)}^{1/2}}dx} \cr
& {\text{substitute }}u = 4 + 9x,{\text{ }}du = 9dx \cr
& \int {{{\left( {4 + 9x} \right)}^{1/2}}dx} = \int {{u^{1/2}}} \left( {\frac{1}{9}du} \right) \cr
& = \frac{1}{9}\int {{u^{1/2}}} du \cr
& {\text{power rule}} \cr
& = \frac{1}{9}\left( {\frac{{{u^{3/2}}}}{{3/2}}} \right) + C \cr
& = \frac{2}{{27}}{u^{3/2}} + C \cr
& {\text{write in terms of }}x \cr
& = \frac{2}{{27}}{\left( {4 + 9x} \right)^{3/2}} + C \cr} $$
