Calculus Examples

$\int \sqrt[6]{x} d x$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{x}$ as $x^{\frac{1}{6}}$ .

$\int x^{\frac{1}{6}} d x$

Step 2

By the Power Rule, the integral of $x^{\frac{1}{6}}$ with respect to $x$ is $\frac{6}{7} x^{\frac{7}{6}}$ .

$\frac{6}{7} x^{\frac{7}{6}} + C$