Calculus Examples

$\int 5 x^{3} d x$

Step 1

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

$5 \int x^{3} d x$

Step 2

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

$5 (\frac{1}{4} x^{4} + C)$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $5 (\frac{1}{4} x^{4} + C)$ as $5 (\frac{1}{4}) x^{4} + C$ .

$5 (\frac{1}{4}) x^{4} + C$

Step 3.2

Combine $5$ and $\frac{1}{4}$ .

$\frac{5}{4} x^{4} + C$