Calculus Examples

$\int 16 x d x$

Step 1

Since $16$ is constant with respect to $x$ , move $16$ out of the integral.

$16 \int x d x$

Step 2

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

$16 (\frac{1}{2} x^{2} + C)$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $16 (\frac{1}{2} x^{2} + C)$ as $16 (\frac{1}{2}) x^{2} + C$ .

$16 (\frac{1}{2}) x^{2} + C$

Step 3.2

Simplify.

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Step 3.2.1

Combine $16$ and $\frac{1}{2}$ .

$\frac{16}{2} x^{2} + C$

Step 3.2.2

Cancel the common factor of $16$ and $2$ .

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Step 3.2.2.1

Factor $2$ out of $16$ .

$\frac{2 \cdot 8}{2} x^{2} + C$

Step 3.2.2.2

Cancel the common factors.

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Step 3.2.2.2.1

Factor $2$ out of $2$ .

$\frac{2 \cdot 8}{2 (1)} x^{2} + C$

Step 3.2.2.2.2

Cancel the common factor.

$\frac{2 \cdot 8}{2 \cdot 1} x^{2} + C$

Step 3.2.2.2.3

Rewrite the expression.

$\frac{8}{1} x^{2} + C$

Step 3.2.2.2.4

Divide $8$ by $1$ .

$8 x^{2} + C$