Calculus Examples

$x^{- 5} d x$

Step 1

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

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

Step 2

Simplify the answer.

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Step 2.1

Rewrite $- \frac{1}{4} x^{- 4} + C$ as $- \frac{1}{4} \cdot \frac{1}{x^{4}} + C$ .

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

Step 2.2

Simplify.

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Step 2.2.1

Multiply $\frac{1}{x^{4}}$ by $\frac{1}{4}$ .

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

Step 2.2.2

Move $4$ to the left of $x^{4}$ .

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