Calculus Examples

$\int \frac{8}{\sqrt[7]{x^{6}}} d x$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[7]{x^{6}}$ as $x^{\frac{6}{7}}$ .

$\frac{d}{d x} [\int \frac{8}{x^{\frac{6}{7}}} d x]$

Step 2

$\int \frac{8}{x^{\frac{6}{7}}} d x$ is an antiderivative of $\frac{8}{x^{\frac{6}{7}}}$ , so by definition $\frac{d}{d x} [\int \frac{8}{x^{\frac{6}{7}}} d x]$ is $\frac{8}{x^{\frac{6}{7}}}$ .

$\frac{8}{x^{\frac{6}{7}}}$