Calculus Examples

$\int 3 \sqrt[3]{x^{2}} d x$

Step 1

Since $3$ is constant with respect to $x$ , move $3$ out of the integral.

$3 \int \sqrt[3]{x^{2}} d x$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{2}}$ as $x^{\frac{2}{3}}$ .

$3 \int x^{\frac{2}{3}} d x$

Step 3

By the Power Rule, the integral of $x^{\frac{2}{3}}$ with respect to $x$ is $\frac{3}{5} x^{\frac{5}{3}}$ .

$3 (\frac{3}{5} x^{\frac{5}{3}} + C)$

Step 4

Simplify the answer.

Tap for more steps...

Step 4.1

Rewrite $3 (\frac{3}{5} x^{\frac{5}{3}} + C)$ as $3 (\frac{3}{5}) x^{\frac{5}{3}} + C$ .

$3 (\frac{3}{5}) x^{\frac{5}{3}} + C$

Step 4.2

Simplify.

Tap for more steps...

Step 4.2.1

Combine $3$ and $\frac{3}{5}$ .

$\frac{3 \cdot 3}{5} x^{\frac{5}{3}} + C$

Step 4.2.2

Multiply $3$ by $3$ .

$\frac{9}{5} x^{\frac{5}{3}} + C$