Calculus Examples

$\int \frac{- 100 y^{4}}{5} d y$

Step 1

Cancel the common factor of $- 100$ and $5$ .

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Step 1.1

Factor $5$ out of $- 100 y^{4}$ .

$\int \frac{5 (- 20 y^{4})}{5} d y$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $5$ .

$\int \frac{5 (- 20 y^{4})}{5 (1)} d y$

Step 1.2.2

Cancel the common factor.

$\int \frac{5 (- 20 y^{4})}{5 \cdot 1} d y$

Step 1.2.3

Rewrite the expression.

$\int \frac{- 20 y^{4}}{1} d y$

Step 1.2.4

Divide $- 20 y^{4}$ by $1$ .

$\int - 20 y^{4} d y$

Step 2

Since $- 20$ is constant with respect to $y$ , move $- 20$ out of the integral.

$- 20 \int y^{4} d y$

Step 3

By the Power Rule, the integral of $y^{4}$ with respect to $y$ is $\frac{1}{5} y^{5}$ .

$- 20 (\frac{1}{5} y^{5} + C)$

Step 4

Simplify the answer.

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Step 4.1

Rewrite $- 20 (\frac{1}{5} y^{5} + C)$ as $- 20 (\frac{1}{5}) y^{5} + C$ .

$- 20 (\frac{1}{5}) y^{5} + C$

Step 4.2

Simplify.

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Step 4.2.1

Combine $- 20$ and $\frac{1}{5}$ .

$\frac{- 20}{5} y^{5} + C$

Step 4.2.2

Cancel the common factor of $- 20$ and $5$ .

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Step 4.2.2.1

Factor $5$ out of $- 20$ .

$\frac{5 \cdot - 4}{5} y^{5} + C$

Step 4.2.2.2

Cancel the common factors.

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Step 4.2.2.2.1

Factor $5$ out of $5$ .

$\frac{5 \cdot - 4}{5 (1)} y^{5} + C$

Step 4.2.2.2.2

Cancel the common factor.

$\frac{5 \cdot - 4}{5 \cdot 1} y^{5} + C$

Step 4.2.2.2.3

Rewrite the expression.

$\frac{- 4}{1} y^{5} + C$

Step 4.2.2.2.4

Divide $- 4$ by $1$ .

$- 4 y^{5} + C$