Calculus Examples

$8 x^{3}$

Step 1

Since $8$ is constant with respect to $x$ , move $8$ out of the integral.

$8 \int x^{3} d x$

Step 2

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

$8 (\frac{1}{4} x^{4} + C)$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $8 (\frac{1}{4} x^{4} + C)$ as $8 (\frac{1}{4}) x^{4} + C$ .

$8 (\frac{1}{4}) x^{4} + C$

Step 3.2

Simplify.

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Step 3.2.1

Combine $8$ and $\frac{1}{4}$ .

$\frac{8}{4} x^{4} + C$

Step 3.2.2

Cancel the common factor of $8$ and $4$ .

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Step 3.2.2.1

Factor $4$ out of $8$ .

$\frac{4 \cdot 2}{4} x^{4} + C$

Step 3.2.2.2

Cancel the common factors.

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Step 3.2.2.2.1

Factor $4$ out of $4$ .

$\frac{4 \cdot 2}{4 (1)} x^{4} + C$

Step 3.2.2.2.2

Cancel the common factor.

$\frac{4 \cdot 2}{4 \cdot 1} x^{4} + C$

Step 3.2.2.2.3

Rewrite the expression.

$\frac{2}{1} x^{4} + C$

Step 3.2.2.2.4

Divide $2$ by $1$ .

$2 x^{4} + C$