Calculus Examples

$\int \frac{2 x}{4} d x$

Step 1

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

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Step 1.1

Factor $2$ out of $2 x$ .

$\int \frac{2 (x)}{4} d x$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $4$ .

$\int \frac{2 x}{2 \cdot 2} d x$

Step 1.2.2

Cancel the common factor.

$\int \frac{2 x}{2 \cdot 2} d x$

Step 1.2.3

Rewrite the expression.

$\int \frac{x}{2} d x$

Step 2

Since $\frac{1}{2}$ is constant with respect to $x$ , move $\frac{1}{2}$ out of the integral.

$\frac{1}{2} \int x d x$

Step 3

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

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

Step 4

Simplify the answer.

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Step 4.1

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

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

Step 4.2

Simplify.

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Step 4.2.1

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

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

Step 4.2.2

Multiply $2$ by $2$ .

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