Calculus Examples

$\int 7 x \frac{3}{4} d x$

Step 1

Simplify.

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Step 1.1

Combine $7$ and $\frac{3}{4}$ .

$\int x \frac{7 \cdot 3}{4} d x$

Step 1.2

Multiply $7$ by $3$ .

$\int x \frac{21}{4} d x$

Step 1.3

Combine $x$ and $\frac{21}{4}$ .

$\int \frac{x \cdot 21}{4} d x$

Step 1.4

Move $21$ to the left of $x$ .

$\int \frac{21 x}{4} d x$

Step 2

Since $\frac{21}{4}$ is constant with respect to $x$ , move $\frac{21}{4}$ out of the integral.

$\frac{21}{4} \int x d x$

Step 3

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

$\frac{21}{4} (\frac{1}{2} x^{2} + C)$

Step 4

Simplify the answer.

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Step 4.1

Rewrite $\frac{21}{4} (\frac{1}{2} x^{2} + C)$ as $\frac{21}{4} \cdot \frac{1}{2} x^{2} + C$ .

$\frac{21}{4} \cdot \frac{1}{2} x^{2} + C$

Step 4.2

Simplify.

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Step 4.2.1

Multiply $\frac{21}{4}$ by $\frac{1}{2}$ .

$\frac{21}{4 \cdot 2} x^{2} + C$

Step 4.2.2

Multiply $4$ by $2$ .

$\frac{21}{8} x^{2} + C$