Integral de $$$\frac{z}{x}$$$ con respecto a $$$x$$$

Halla $$$\int \frac{z}{x}\, dx$$$.

Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=z$$$ y $$$f{\left(x \right)} = \frac{1}{x}$$$:

$${\color{red}{\int{\frac{z}{x} d x}}} = {\color{red}{z \int{\frac{1}{x} d x}}}$$

La integral de $$$\frac{1}{x}$$$ es $$$\int{\frac{1}{x} d x} = \ln{\left(\left|{x}\right| \right)}$$$:

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

Por lo tanto,

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

Añade la constante de integración:

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

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