Calculus Examples

$f' (x) = \frac{4}{x}$

Step 1

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

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

Step 2

Since $4$ is constant with respect to $x$ , move $4$ out of the integral.

$4 \int \frac{1}{x} d x$

Step 3

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

$4 (\ln (| x |) + C)$

Step 4

Simplify.

$4 \ln (| x |) + C$

Step 5

The function $f$ if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.

$f (x) = 4 \ln (| x |) + C$