Calculus Examples

$g (x) = \frac{1}{2 x}$

Step 1

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

$G (x) = \int g (x) d x$

Step 2

Set up the integral to solve.

$G (x) = \int \frac{1}{2 x} d x$

Step 3

Since $\frac{1}{2}$ is constant with respect to $x$ , move $\frac{1}{2}$ out of the integral.

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

Step 4

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

$\frac{1}{2} (\ln (| x |) + C)$

Step 5

Simplify.

$\frac{1}{2} \ln (| x |) + C$

Step 6

The answer is the antiderivative of the function $g (x) = \frac{1}{2 x}$ .

$G (x) =$ $\frac{1}{2} \ln (| x |) + C$