Calculus Examples

$\int {(\sqrt[3]{x})}^{4} d x$

Step 1

Rewrite ${(\sqrt[3]{x})}^{4}$ as $\sqrt[3]{x^{4}}$ .

$\int \sqrt[3]{x^{4}} d x$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{4}}$ as $x^{\frac{4}{3}}$ .

$\int x^{\frac{4}{3}} d x$

Step 3

By the Power Rule, the integral of $x^{\frac{4}{3}}$ with respect to $x$ is $\frac{3}{7} x^{\frac{7}{3}}$ .

$\frac{3}{7} x^{\frac{7}{3}} + C$