Calculus Examples

$\int \frac{14 y^{3}}{3} d y$

Step 1

Since $\frac{14}{3}$ is constant with respect to $y$ , move $\frac{14}{3}$ out of the integral.

$\frac{14}{3} \int y^{3} d y$

Step 2

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

$\frac{14}{3} (\frac{1}{4} y^{4} + C)$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $\frac{14}{3} (\frac{1}{4} y^{4} + C)$ as $\frac{14}{3} \cdot \frac{1}{4} y^{4} + C$ .

$\frac{14}{3} \cdot \frac{1}{4} y^{4} + C$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $\frac{14}{3}$ by $\frac{1}{4}$ .

$\frac{14}{3 \cdot 4} y^{4} + C$

Step 3.2.2

Multiply $3$ by $4$ .

$\frac{14}{12} y^{4} + C$

Step 3.2.3

Cancel the common factor of $14$ and $12$ .

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Step 3.2.3.1

Factor $2$ out of $14$ .

$\frac{2 (7)}{12} y^{4} + C$

Step 3.2.3.2

Cancel the common factors.

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Step 3.2.3.2.1

Factor $2$ out of $12$ .

$\frac{2 \cdot 7}{2 \cdot 6} y^{4} + C$

Step 3.2.3.2.2

Cancel the common factor.

$\frac{2 \cdot 7}{2 \cdot 6} y^{4} + C$

Step 3.2.3.2.3

Rewrite the expression.

$\frac{7}{6} y^{4} + C$