Calculus Examples

$\int \sqrt[5]{x^{2}} d x$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{x^{2}}$ as $x^{\frac{2}{5}}$ .

$\int x^{\frac{2}{5}} d x$

Step 2

By the Power Rule, the integral of $x^{\frac{2}{5}}$ with respect to $x$ is $\frac{5}{7} x^{\frac{7}{5}}$ .

$\frac{5}{7} x^{\frac{7}{5}} + C$