Calculus Examples

$6 x^{- 7}$

Step 1

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

$6 \int x^{- 7} d x$

Step 2

By the Power Rule, the integral of $x^{- 7}$ with respect to $x$ is $- \frac{1}{6} x^{- 6}$ .

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

Step 3

Simplify the answer.

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Step 3.1

Simplify.

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Step 3.1.1

Combine $x^{- 6}$ and $\frac{1}{6}$ .

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

Step 3.1.2

Move $x^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3.2

Simplify.

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

Step 3.3

Simplify.

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Step 3.3.1

Multiply $- 1$ by $6$ .

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

Step 3.3.2

Combine $- 6$ and $\frac{1}{6 x^{6}}$ .

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

Step 3.3.3

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

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Step 3.3.3.1

Factor $6$ out of $- 6$ .

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

Step 3.3.3.2

Cancel the common factors.

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Step 3.3.3.2.1

Factor $6$ out of $6 x^{6}$ .

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

Step 3.3.3.2.2

Cancel the common factor.

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

Step 3.3.3.2.3

Rewrite the expression.

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

Step 3.3.4

Move the negative in front of the fraction.

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