Calculus Examples

$5 x^{4}$

Step 1

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

$5 \int x^{4} d x$

Step 2

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

$5 (\frac{1}{5} x^{5} + C)$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $5 (\frac{1}{5} x^{5} + C)$ as $5 (\frac{1}{5}) x^{5} + C$ .

$5 (\frac{1}{5}) x^{5} + C$

Step 3.2

Simplify.

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Step 3.2.1

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

$\frac{5}{5} x^{5} + C$

Step 3.2.2

Cancel the common factor of $5$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{5}{5} x^{5} + C$

Step 3.2.2.2

Rewrite the expression.

$1 x^{5} + C$

Step 3.2.3

Multiply $x^{5}$ by $1$ .

$x^{5} + C$