Calculus Examples

$\int \frac{1}{\sqrt[3]{x^{2}}} d x$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{2}}$ as $x^{\frac{2}{3}}$ .

$\frac{d}{d x} [\int \frac{1}{x^{\frac{2}{3}}} d x]$

Step 2

$\int \frac{1}{x^{\frac{2}{3}}} d x$ is an antiderivative of $\frac{1}{x^{\frac{2}{3}}}$ , so by definition $\frac{d}{d x} [\int \frac{1}{x^{\frac{2}{3}}} d x]$ is $\frac{1}{x^{\frac{2}{3}}}$ .

$\frac{1}{x^{\frac{2}{3}}}$