Answer
$${x^2} + 3x + C$$
Work Step by Step
$$\eqalign{
& \int {\left( {2x + 3} \right)} dx \cr
& {\text{distribute the integrand by using the sum rule }} \cr
& \int {\left[ {f\left( x \right) \pm g\left( x \right)} \right]} dx = \int {f\left( x \right)} dx \pm \int {g\left( x \right)} dx \cr
& \cr
& = \int {2x} dx + \int 3 dx \cr
& {\text{use multiple constant rule }}\int {k \cdot f\left( x \right)} dx = k\int {f\left( x \right)} dx \cr
& = 2\int x dx + 3\int {dx} \cr
& {\text{use power rule }}\int {{x^x}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \cr
& = 2\left( {\frac{{{x^{1 + 1}}}}{{1 + 1}}} \right) + 3\left( {\frac{{{x^{0 + 1}}}}{{0 + 1}}} \right) + C \cr
& {\text{simplifying}} \cr
& = 2\left( {\frac{{{x^2}}}{2}} \right) + 3\left( x \right) + C \cr
& = {x^2} + 3x + C \cr} $$
