Calculus Examples

$\int \sqrt[3]{x} d x$

Step 1

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt[3]{x}$ as

$x^{\frac{1}{3}}$ .

$\int x^{\frac{1}{3}} d x$

Step 2

By the Power Rule, the integral of

$x^{\frac{1}{3}}$ with respect to

$x$ is

$\frac{3}{4} x^{\frac{4}{3}}$ .

$\frac{3}{4} x^{\frac{4}{3}} + C$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$