Calculus Examples

Evaluate $\int - 24 x^{5} d x$

Step 1

Since $- 24$ is constant with respect to $x$ , move $- 24$ out of the integral.

$- 24 \int x^{5} d x$

Step 2

By the Power Rule, the integral of $x^{5}$ with respect to $x$ is $\frac{1}{6} x^{6}$ .

$- 24 (\frac{1}{6} x^{6} + C)$

Step 3

Simplify the answer.

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Step 3.1

Rewrite $- 24 (\frac{1}{6} x^{6} + C)$ as $- 24 (\frac{1}{6}) x^{6} + C$ .

$- 24 (\frac{1}{6}) x^{6} + C$

Step 3.2

Simplify.

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Step 3.2.1

Combine $- 24$ and $\frac{1}{6}$ .

$\frac{- 24}{6} x^{6} + C$

Step 3.2.2

Cancel the common factor of $- 24$ and $6$ .

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Step 3.2.2.1

Factor $6$ out of $- 24$ .

$\frac{6 \cdot - 4}{6} x^{6} + C$

Step 3.2.2.2

Cancel the common factors.

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Step 3.2.2.2.1

Factor $6$ out of $6$ .

$\frac{6 \cdot - 4}{6 (1)} x^{6} + C$

Step 3.2.2.2.2

Cancel the common factor.

$\frac{6 \cdot - 4}{6 \cdot 1} x^{6} + C$

Step 3.2.2.2.3

Rewrite the expression.

$\frac{- 4}{1} x^{6} + C$

Step 3.2.2.2.4

Divide $- 4$ by $1$ .

$- 4 x^{6} + C$