# How do you integrate int (x^(3/2)+2x+1)dx?

Jan 5, 2017

$\frac{2}{5} {x}^{\frac{5}{2}} + {x}^{2} + x + c$

#### Explanation:

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

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

$\Rightarrow \int \left({x}^{\frac{3}{2}} + 2 x + 1\right) \mathrm{dx}$

$= \frac{1}{\frac{5}{2}} {x}^{\frac{5}{2}} + \frac{2}{2} {x}^{2} + x + c$

$= \frac{2}{5} {x}^{\frac{5}{2}} + {x}^{2} + x + c$

where c is the constant of integration.