Calculus Examples

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

Step 1

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 2

The integral of

$\frac{1}{x}$ with respect to

$x$ is

$\ln (| x |)$ .

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

Step 3

Simplify.

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$