Integral of $\frac{1}{x}$

Find $\int \frac{1}{x}\, dx$.

The integral of $\frac{1}{x}$ is $\int{\frac{1}{x} d x} = \ln{\left(\left|{x}\right| \right)}$:

$${\color{red}{\int{\frac{1}{x} d x}}} = {\color{red}{\ln{\left(\left|{x}\right| \right)}}}$$

Therefore,

$$\int{\frac{1}{x} d x} = \ln{\left(\left|{x}\right| \right)}$$

Add the constant of integration:

$$\int{\frac{1}{x} d x} = \ln{\left(\left|{x}\right| \right)}+C$$

$\int \frac{1}{x}\, dx = \ln\left(\left|{x}\right|\right) + C$A