Calculus Examples

$\frac{d y}{d x} = \sqrt[3]{x}$

Step 1

Rewrite the equation.

$d y = \sqrt[3]{x} d x$

Step 2

Integrate both sides.

Tap for more steps...

Step 2.1

Set up an integral on each side.

$\int d y = \int \sqrt[3]{x} d x$

Step 2.2

Apply the constant rule.

$y + C_{1} = \int \sqrt[3]{x} d x$

Step 2.3

Integrate the right side.

Tap for more steps...

Step 2.3.1

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

$y + C_{1} = \int x^{\frac{1}{3}} d x$

Step 2.3.2

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

$y + C_{1} = \frac{3}{4} x^{\frac{4}{3}} + C_{2}$

Step 2.4

Group the constant of integration on the right side as $K$ .

$y = \frac{3}{4} x^{\frac{4}{3}} + K$