Find the Function f(x)=2/x

$f (x) = \frac{2}{x}$

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

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

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int \frac{1}{x} d x$

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

$2 (\ln (| x |) + C)$

Simplify.

$2 \ln (| x |) + C$

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

$F (x) = 2 \ln (| x |) + C$