Calculus Examples

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

Step 1

Since $\frac{1}{4}$ is constant with respect to $x$ , move $\frac{1}{4}$ out of the integral.

$\frac{1}{4} \int \sqrt[3]{x^{4}} d x$

Step 2

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

$\frac{1}{4} \int x^{\frac{4}{3}} d x$

Step 3

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

$\frac{1}{4} (\frac{3}{7} x^{\frac{7}{3}} + C)$

Step 4

Simplify the answer.

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Step 4.1

Rewrite $\frac{1}{4} (\frac{3}{7} x^{\frac{7}{3}} + C)$ as $\frac{1}{4} \cdot \frac{3}{7} x^{\frac{7}{3}} + C$ .

$\frac{1}{4} \cdot \frac{3}{7} x^{\frac{7}{3}} + C$

Step 4.2

Simplify.

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Step 4.2.1

Multiply $\frac{1}{4}$ by $\frac{3}{7}$ .

$\frac{3}{4 \cdot 7} x^{\frac{7}{3}} + C$

Step 4.2.2

Multiply $4$ by $7$ .

$\frac{3}{28} x^{\frac{7}{3}} + C$