Calculus Examples

$\int 11 x^{- 6} d x$

Step 1

Since $11$ is constant with respect to $x$ , move $11$ out of the integral.

$11 \int x^{- 6} d x$

Step 2

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

$11 (- \frac{1}{5} x^{- 5} + C)$

Step 3

Simplify the answer.

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Step 3.1

Simplify.

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Step 3.1.1

Combine $x^{- 5}$ and $\frac{1}{5}$ .

$11 (- \frac{x^{- 5}}{5} + C)$

Step 3.1.2

Move $x^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$11 (- \frac{1}{5 x^{5}} + C)$

Step 3.2

Simplify.

$11 (- \frac{1}{5 x^{5}}) + C$

Step 3.3

Simplify.

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Step 3.3.1

Multiply $- 1$ by $11$ .

$- 11 \frac{1}{5 x^{5}} + C$

Step 3.3.2

Combine $- 11$ and $\frac{1}{5 x^{5}}$ .

$\frac{- 11}{5 x^{5}} + C$

Step 3.3.3

Move the negative in front of the fraction.

$- \frac{11}{5 x^{5}} + C$