Calculus Examples

$\int 57 \sqrt[3]{x} d x$

Step 1

Since $57$ is constant with respect to $x$ , move $57$ out of the integral.

$57 \int \sqrt[3]{x} d x$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x}$ as $x^{\frac{1}{3}}$ .

$57 \int x^{\frac{1}{3}} d x$

Step 3

By the Power Rule, the integral of $x^{\frac{1}{3}}$ with respect to $x$ is $\frac{3}{4} x^{\frac{4}{3}}$ .

$57 (\frac{3}{4} x^{\frac{4}{3}} + C)$

Step 4

Simplify the answer.

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Step 4.1

Rewrite $57 (\frac{3}{4} x^{\frac{4}{3}} + C)$ as $57 (\frac{3}{4}) x^{\frac{4}{3}} + C$ .

$57 (\frac{3}{4}) x^{\frac{4}{3}} + C$

Step 4.2

Simplify.

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Step 4.2.1

Combine $57$ and $\frac{3}{4}$ .

$\frac{57 \cdot 3}{4} x^{\frac{4}{3}} + C$

Step 4.2.2

Multiply $57$ by $3$ .

$\frac{171}{4} x^{\frac{4}{3}} + C$