Calculus Examples

$x^{- 3}$

Step 1

By the Power Rule, the integral of $x^{- 3}$ with respect to $x$ is $- \frac{1}{2} x^{- 2}$ .

$- \frac{1}{2} x^{- 2} + C$

Step 2

Simplify the answer.

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Step 2.1

Rewrite $- \frac{1}{2} x^{- 2} + C$ as $- \frac{1}{2} \cdot \frac{1}{x^{2}} + C$ .

$- \frac{1}{2} \cdot \frac{1}{x^{2}} + C$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $\frac{1}{x^{2}}$ by $\frac{1}{2}$ .

$- \frac{1}{x^{2} \cdot 2} + C$

Step 2.2.2

Move $2$ to the left of $x^{2}$ .

$- \frac{1}{2 x^{2}} + C$