# How do you integrate int (root3x)?

Feb 21, 2017

$\int \sqrt[3]{x} \mathrm{dx} = \frac{3}{4} x \sqrt[3]{x} + C$

#### Explanation:

You can integrate using the power rule:

$\int {x}^{\alpha} \mathrm{dx} = {x}^{\alpha + 1} / \left(\alpha + 1\right) + C$

In our case:

$\int \sqrt[3]{x} \mathrm{dx} = \int {x}^{\frac{1}{3}} \mathrm{dx} = {x}^{\frac{4}{3}} / \left(\frac{4}{3}\right) + C = \frac{3}{4} x \sqrt[3]{x} + C$