Calculus Examples

$\int 5 yd y d y$

Step 1

Since $5 yd$ is constant with respect to $y$ , move $5 yd$ out of the integral.

$5 yd \int y d y$

Step 2

By the Power Rule, the integral of $y$ with respect to $y$ is $\frac{1}{2} y^{2}$ .

$5 yd (\frac{1}{2} y^{2} + C)$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $5 yd (\frac{1}{2} y^{2} + C)$ as $5 yd \frac{1}{2} y^{2} + C$ .

$5 yd \frac{1}{2} y^{2} + C$

Step 3.2

Simplify.

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Step 3.2.1

Combine $\frac{1}{2}$ and $5$ .

$\frac{5}{2} yd y^{2} + C$

Step 3.2.2

Combine $y^{2}$ and $\frac{5}{2}$ .

$\frac{y^{2} \cdot 5}{2} yd + C$

Step 3.2.3

Move $5$ to the left of $y^{2}$ .

$\frac{5 y^{2}}{2} yd + C$

Step 3.3

Reorder terms.

$\frac{5}{2} y^{2} yd + C$