Answer
$5x + \frac{4}{3}{x^{3/2}} + C$
Work Step by Step
$$\eqalign{
& \int {\left( {5 + 2\sqrt x } \right)} dx \cr
& {\text{Rewrite}}{\text{, use the radical properties}} \cr
& = \int {\left( {5 + 2{x^{1/2}}} \right)} dx \cr
& {\text{Use the sum rule for integration}} \cr
& = \int 5 dx + \int {2{x^{1/2}}} dx \cr
& {\text{Pull out the constants}} \cr
& = 5\int {dx} + 2\int {{x^{1/2}}} dx \cr
& {\text{use the power rule for integration }}\int {{x^n}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \cr
& = 5\left( {\frac{{{x^{0 + 1}}}}{{0 + 1}}} \right) + 2\left( {\frac{{{x^{1/2 + 1}}}}{{1/2 + 1}}} \right) + C \cr
& {\text{Simplify}} \cr
& = 5\left( x \right) + 2\left( {\frac{{{x^{3/2}}}}{{3/2}}} \right) + C \cr
& = 5x + \frac{4}{3}{x^{3/2}} + C \cr} $$
