Calculus Examples

$\int \sqrt[5]{x} d x$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{x}$ as $x^{\frac{1}{5}}$ .

$\int x^{\frac{1}{5}} d x$

Step 2

By the Power Rule, the integral of $x^{\frac{1}{5}}$ with respect to $x$ is $\frac{5}{6} x^{\frac{6}{5}}$ .

$\frac{5}{6} x^{\frac{6}{5}} + C$