Calculus Examples

$\int \sqrt[3]{x^{11}} d x$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{11}}$ as $x^{\frac{11}{3}}$ .

$\int x^{\frac{11}{3}} d x$

Step 2

By the Power Rule, the integral of $x^{\frac{11}{3}}$ with respect to $x$ is $\frac{3}{14} x^{\frac{14}{3}}$ .

$\frac{3}{14} x^{\frac{14}{3}} + C$