# What is the antiderivative of  2x^(-2/3)?

Jan 5, 2017

$6 {x}^{\frac{1}{3}} + c$

#### Explanation:

Using the $\textcolor{b l u e}{\text{power rule for integration}}$

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

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

$= \frac{2}{\frac{1}{3}} {x}^{\frac{1}{3}} + c = 6 {x}^{\frac{1}{3}} + c$

where c is the constant of integration.