# How do you find the indefinite integral of int (7u^(3/2)+2u^(1/2))du?

Oct 7, 2016

$\frac{14}{5} {u}^{\frac{5}{2}} + \frac{4}{3} {u}^{\frac{3}{2}} + c$

#### Explanation:

We can integrate each term using the $\textcolor{b l u e}{\text{power rule}}$

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

$\Rightarrow \int \left(7 {u}^{\frac{3}{2}} + 2 {u}^{\frac{1}{2}}\right) \mathrm{du}$

$= \frac{7}{\frac{5}{2}} {u}^{\frac{3}{2} + 1} + \frac{2}{\frac{3}{2}} {u}^{\frac{1}{2} + 1} + c$

$= \frac{14}{5} {u}^{\frac{5}{2}} + \frac{4}{3} {u}^{\frac{3}{2}} + c$

where c is the constant of integration.