# How do you find the indefinite integral of int -(5root3(x^2))/3dx?

##### 1 Answer
Feb 13, 2017

Rewrite the cube root as the $\frac{1}{3}$ power and use the linear property of integration to move the constants outside the integral, then use the Power Rule

#### Explanation:

Rewrite the cube root as the $\frac{1}{3}$ power and use the linear property of integration to move the constants outside the integral:

$\int - \frac{5 \sqrt[3]{{x}^{2}}}{3} = - \frac{5}{3} \int {x}^{\frac{2}{3}} \mathrm{dx}$

use the Power Rule for integrations, $\int {x}^{r} \mathrm{dx} = {x}^{r + 1} / \left(r + 1\right) + C$:

$- \frac{5}{3} \int {x}^{\frac{2}{3}} \mathrm{dx} = - \frac{5}{3} {x}^{\frac{5}{3}} / \left(\frac{5}{3}\right) + C$

$\int - \frac{5 \sqrt[3]{{x}^{2}}}{3} = - {x}^{\frac{5}{3}} + C$