Calculus Examples

$\int 9 x^{- 5} d x$

Step 1

Since $9$ is constant with respect to $x$ , move $9$ out of the integral.

$9 \int x^{- 5} d x$

Step 2

By the Power Rule, the integral of $x^{- 5}$ with respect to $x$ is $- \frac{1}{4} x^{- 4}$ .

$9 (- \frac{1}{4} x^{- 4} + C)$

Step 3

Simplify the answer.

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Step 3.1

Simplify.

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Step 3.1.1

Combine $x^{- 4}$ and $\frac{1}{4}$ .

$9 (- \frac{x^{- 4}}{4} + C)$

Step 3.1.2

Move $x^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$9 (- \frac{1}{4 x^{4}} + C)$

Step 3.2

Simplify.

$9 (- \frac{1}{4 x^{4}}) + C$

Step 3.3

Simplify.

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Step 3.3.1

Multiply $- 1$ by $9$ .

$- 9 \frac{1}{4 x^{4}} + C$

Step 3.3.2

Combine $- 9$ and $\frac{1}{4 x^{4}}$ .

$\frac{- 9}{4 x^{4}} + C$

Step 3.3.3

Move the negative in front of the fraction.

$- \frac{9}{4 x^{4}} + C$