Calculus Examples

$x^{- 1}$

Step 1

Write $x^{- 1}$ as a function.

$f (x) = x^{- 1}$

Step 2

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

$F (x) = \int f (x) d x$

Step 3

Set up the integral to solve.

$F (x) = \int x^{- 1} d x$

Step 4

The integral of $x^{- 1}$ with respect to $x$ is $\ln (| x |)$ .

$\ln (| x |) + C$

Step 5

The answer is the antiderivative of the function $f (x) = x^{- 1}$ .

$F (x) =$ $\ln (| x |) + C$