Calculus Examples

$\int 8 x - 4 x^{- 1} d x$

Step 1

$\int 8 x - 4 x^{- 1} d x$ is an antiderivative of $8 x - 4 x^{- 1}$ , so by definition $\frac{d}{d x} [\int 8 x - 4 x^{- 1} d x]$ is $8 x - 4 x^{- 1}$ .

$8 x - 4 x^{- 1}$

Step 2

Simplify each term.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$8 x - 4 \frac{1}{x}$

Step 2.2

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

$8 x + \frac{- 4}{x}$

Step 2.3

Move the negative in front of the fraction.

$8 x - \frac{4}{x}$