Integral dari $$$\frac{4}{y}$$$

Temukan $$$\int \frac{4}{y}\, dy$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(y \right)}\, dy = c \int f{\left(y \right)}\, dy$$$ dengan $$$c=4$$$ dan $$$f{\left(y \right)} = \frac{1}{y}$$$:

$${\color{red}{\int{\frac{4}{y} d y}}} = {\color{red}{\left(4 \int{\frac{1}{y} d y}\right)}}$$

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

$$4 {\color{red}{\int{\frac{1}{y} d y}}} = 4 {\color{red}{\ln{\left(\left|{y}\right| \right)}}}$$

Oleh karena itu,

$$\int{\frac{4}{y} d y} = 4 \ln{\left(\left|{y}\right| \right)}$$

Tambahkan konstanta integrasi:

$$\int{\frac{4}{y} d y} = 4 \ln{\left(\left|{y}\right| \right)}+C$$

$$$\int \frac{4}{y}\, dy = 4 \ln\left(\left|{y}\right|\right) + C$$$A