Calculus Examples

Evaluate $\int 12 x^{2} d x$

Step 1

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

$12 \int x^{2} d x$

Step 2

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

$12 (\frac{1}{3} x^{3} + C)$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Rewrite $12 (\frac{1}{3} x^{3} + C)$ as $12 (\frac{1}{3}) x^{3} + C$ .

$12 (\frac{1}{3}) x^{3} + C$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

Combine $12$ and $\frac{1}{3}$ .

$\frac{12}{3} x^{3} + C$

Step 3.2.2

Cancel the common factor of $12$ and $3$ .

Tap for more steps...

Step 3.2.2.1

Factor $3$ out of $12$ .

$\frac{3 \cdot 4}{3} x^{3} + C$

Step 3.2.2.2

Cancel the common factors.

Tap for more steps...

Step 3.2.2.2.1

Factor $3$ out of $3$ .

$\frac{3 \cdot 4}{3 (1)} x^{3} + C$

Step 3.2.2.2.2

Cancel the common factor.

$\frac{3 \cdot 4}{3 \cdot 1} x^{3} + C$

Step 3.2.2.2.3

Rewrite the expression.

$\frac{4}{1} x^{3} + C$

Step 3.2.2.2.4

Divide $4$ by $1$ .

$4 x^{3} + C$