Calculus Examples

$\int 6 x^{2} d x$

Step 1

Since $6$ is constant with respect to $x$ , move $6$ out of the integral.

$6 \int x^{2} d x$

Step 2

By the Power Rule, the integral of $x^{2}$ with respect to $x$ is $\frac{1}{3} x^{3}$ .

$6 (\frac{1}{3} x^{3} + C)$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $6 (\frac{1}{3} x^{3} + C)$ as $6 (\frac{1}{3}) x^{3} + C$ .

$6 (\frac{1}{3}) x^{3} + C$

Step 3.2

Simplify.

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Step 3.2.1

Combine $6$ and $\frac{1}{3}$ .

$\frac{6}{3} x^{3} + C$

Step 3.2.2

Cancel the common factor of $6$ and $3$ .

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Step 3.2.2.1

Factor $3$ out of $6$ .

$\frac{3 \cdot 2}{3} x^{3} + C$

Step 3.2.2.2

Cancel the common factors.

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Step 3.2.2.2.1

Factor $3$ out of $3$ .

$\frac{3 \cdot 2}{3 (1)} x^{3} + C$

Step 3.2.2.2.2

Cancel the common factor.

$\frac{3 \cdot 2}{3 \cdot 1} x^{3} + C$

Step 3.2.2.2.3

Rewrite the expression.

$\frac{2}{1} x^{3} + C$

Step 3.2.2.2.4

Divide $2$ by $1$ .

$2 x^{3} + C$

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