Answer
$$\frac{1}{3}{x^{3/2}} + C$$
Work Step by Step
$$\eqalign{
& \int {\frac{{\sqrt x }}{2}} dx \cr
& {\text{write the radical }}\sqrt x {\text{ as }}{x^{1/2}} \cr
& = \int {\frac{{{x^{1/2}}}}{2}} dx \cr
& {\text{use multiple constant rule }}\int {k \cdot f\left( x \right)} dx = k\int {f\left( x \right)} dx \cr
& = \frac{1}{2}\int {{x^{1/2}}} dx \cr
& {\text{use power rule }}\int {{x^x}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \cr
& = \frac{1}{2}\left( {\frac{{{x^{1/2 + 1}}}}{{1/2 + 1}}} \right) + C \cr
& {\text{simplifying}} \cr
& = \frac{1}{2}\left( {\frac{{{x^{3/2}}}}{{3/2}}} \right) + C \cr
& = \frac{1}{3}{x^{3/2}} + C \cr} $$
