Find the Function f(x)=3/x

$f (x) = \frac{3}{x}$

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 $3$ is constant with respect to $x$ , move $3$ out of the integral.

$3 \int \frac{1}{x} d x$

Step 3

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

$3 (\ln (| x |) + C)$

Step 4

Simplify.

$3 \ln (| x |) + C$

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.

$F (x) = 3 \ln (| x |) + C$