Calculus Examples

$\int 12 x d x$

Step 1

Since $12$ is constant with respect to $x$ , move $12$ out of the integral.

$12 \int x d x$

Step 2

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

$12 (\frac{1}{2} x^{2} + C)$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $12 (\frac{1}{2} x^{2} + C)$ as $12 (\frac{1}{2}) x^{2} + C$ .

$12 (\frac{1}{2}) x^{2} + C$

Step 3.2

Simplify.

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Step 3.2.1

Combine $12$ and $\frac{1}{2}$ .

$\frac{12}{2} x^{2} + C$

Step 3.2.2

Cancel the common factor of $12$ and $2$ .

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Step 3.2.2.1

Factor $2$ out of $12$ .

$\frac{2 \cdot 6}{2} x^{2} + C$

Step 3.2.2.2

Cancel the common factors.

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Step 3.2.2.2.1

Factor $2$ out of $2$ .

$\frac{2 \cdot 6}{2 (1)} x^{2} + C$

Step 3.2.2.2.2

Cancel the common factor.

$\frac{2 \cdot 6}{2 \cdot 1} x^{2} + C$

Step 3.2.2.2.3

Rewrite the expression.

$\frac{6}{1} x^{2} + C$

Step 3.2.2.2.4

Divide $6$ by $1$ .

$6 x^{2} + C$