Calculus Examples

$4 \int x d x$

Step 1

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

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

Step 2

Simplify the answer.

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Step 2.1

Rewrite $4 (\frac{1}{2} x^{2} + C)$ as $4 (\frac{1}{2}) x^{2} + C$ .

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

Step 2.2

Simplify.

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Step 2.2.1

Combine $4$ and $\frac{1}{2}$ .

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

Step 2.2.2

Cancel the common factor of $4$ and $2$ .

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Step 2.2.2.1

Factor $2$ out of $4$ .

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

Step 2.2.2.2

Cancel the common factors.

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Step 2.2.2.2.1

Factor $2$ out of $2$ .

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

Step 2.2.2.2.2

Cancel the common factor.

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

Step 2.2.2.2.3

Rewrite the expression.

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

Step 2.2.2.2.4

Divide $2$ by $1$ .

$2 x^{2} + C$