# How do you integrate int (x+3)dx?

Jan 6, 2017

$\frac{1}{2} {x}^{2} + 3 x + c$

#### Explanation:

Integrate each term using the $\textcolor{b l u e}{\text{power rule for integration}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\int \left(a {x}^{n}\right) \mathrm{dx} = \frac{a}{n + 1} {x}^{n + 1}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow \int \left(x + 3\right) \mathrm{dx}$

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

where c is the constant of integration.

$\textcolor{b l u e}{\text{Note }} 3 = 3 {x}^{0} \Rightarrow \int 3 {x}^{0} \mathrm{dx} = 3 x$