Calculus Examples

$h (x) = x^{- 4}$

Step 1

The function $H (x)$ can be found by finding the indefinite integral of the derivative $h (x)$ .

$H (x) = \int h (x) d x$

Step 2

Set up the integral to solve.

$H (x) = \int x^{- 4} d x$

Step 3

By the Power Rule, the integral of $x^{- 4}$ with respect to $x$ is $- \frac{1}{3} x^{- 3}$ .

$- \frac{1}{3} x^{- 3} + C$

Step 4

Simplify the answer.

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Step 4.1

Rewrite $- \frac{1}{3} x^{- 3} + C$ as $- \frac{1}{3} \cdot \frac{1}{x^{3}} + C$ .

$- \frac{1}{3} \cdot \frac{1}{x^{3}} + C$

Step 4.2

Simplify.

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Step 4.2.1

Multiply $\frac{1}{x^{3}}$ by $\frac{1}{3}$ .

$- \frac{1}{x^{3} \cdot 3} + C$

Step 4.2.2

Move $3$ to the left of $x^{3}$ .

$- \frac{1}{3 x^{3}} + C$

Step 5

The answer is the antiderivative of the function $h (x) = x^{- 4}$ .

$H (x) =$ $- \frac{1}{3 x^{3}} + C$