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Calculus Examples

\int 3 - 3 x d x

$\int 3 - 3 x d x$

Step 1

Split the single integral into multiple integrals.

\int 3 d x + \int - 3 x d x

$\int 3 d x + \int - 3 x d x$

Step 2

Apply the constant rule.

3 x + C + \int - 3 x d x

$3 x + C + \int - 3 x d x$

Step 3

Since

- 3

$- 3$ is constant with respect to

x

$x$ , move

- 3

$- 3$ out of the integral.

3 x + C - 3 \int x d x

$3 x + C - 3 \int x d x$

Step 4

By the Power Rule, the integral of

x

$x$ with respect to

x

$x$ is

\frac{1}{2} x^{2}

$\frac{1}{2} x^{2}$ .

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

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

Step 5

Simplify.

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Step 5.1

Simplify.

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

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

Step 5.2

Simplify.

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Step 5.2.1

Combine

- 3

$- 3$ and

\frac{1}{2}

$\frac{1}{2}$ .

3 x + \frac{- 3}{2} x^{2} + C

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

Step 5.2.2

Move the negative in front of the fraction.

3 x - \frac{3}{2} x^{2} + C

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

3 x - \frac{3}{2} x^{2} + C

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

3 x - \frac{3}{2} x^{2} + C

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

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

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