### Answer & Explanation

Use the Power Rule:

$\int \left(a{x}^{n}\right)dx=\frac{a}{n+1}{x}^{n+1}$

$\int (x+3)dx$

$=\frac{1}{2}{x}^{2}+3x+C$

$\int (x+3)dx$

Apply the Sum Rule

$\int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx$

$=\int xdx+\int 3dx$

$\int xdx=\frac{{x}^{2}}{2}$

And

$\int 3dx=3x$

Thus,

$=\frac{{x}^{2}}{2}+3x+C$

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