Integral dari $$$\frac{d f}{x}$$$ terhadap $$$x$$$

Temukan $$$\int \frac{d f}{x}\, dx$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=d f$$$ dan $$$f{\left(x \right)} = \frac{1}{x}$$$:

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

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

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

Oleh karena itu,

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

Tambahkan konstanta integrasi:

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

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