Calculus Examples

\int 3 x^{2} d x

$\int 3 x^{2} d x$

Step 1

Since

3

$3$ is constant with respect to

x

$x$ , move

3

$3$ out of the integral.

3 \int x^{2} d x

$3 \int x^{2} d x$

Step 2

By the Power Rule, the integral of

x^{2}

$x^{2}$ with respect to

x

$x$ is

\frac{1}{3} x^{3}

$\frac{1}{3} x^{3}$ .

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

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

Step 3

Simplify the answer.

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Step 3.1

Rewrite

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

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

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

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

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

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

Step 3.2

Simplify.

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Step 3.2.1

Combine

3

$3$ and

\frac{1}{3}

$\frac{1}{3}$ .

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

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

Step 3.2.2

Cancel the common factor of

3

$3$ .

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Step 3.2.2.1

Cancel the common factor.

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

Step 3.2.2.2

Rewrite the expression.

$1 x^{3} + C$

$1 x^{3} + C$

Step 3.2.3

Multiply

$x^{3}$ by

$1$ .

$x^{3} + C$

$x^{3} + C$

$x^{3} + C$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$