$$$\frac{3}{2 y}$$$'nin integrali

Bulun: $$$\int \frac{3}{2 y}\, dy$$$.

Sabit katsayı kuralı $$$\int c f{\left(y \right)}\, dy = c \int f{\left(y \right)}\, dy$$$'i $$$c=\frac{3}{2}$$$ ve $$$f{\left(y \right)} = \frac{1}{y}$$$ ile uygula:

$${\color{red}{\int{\frac{3}{2 y} d y}}} = {\color{red}{\left(\frac{3 \int{\frac{1}{y} d y}}{2}\right)}}$$

$$$\frac{1}{y}$$$'nin integrali $$$\int{\frac{1}{y} d y} = \ln{\left(\left|{y}\right| \right)}$$$:

$$\frac{3 {\color{red}{\int{\frac{1}{y} d y}}}}{2} = \frac{3 {\color{red}{\ln{\left(\left|{y}\right| \right)}}}}{2}$$

Dolayısıyla,

$$\int{\frac{3}{2 y} d y} = \frac{3 \ln{\left(\left|{y}\right| \right)}}{2}$$

İntegrasyon sabitini ekleyin:

$$\int{\frac{3}{2 y} d y} = \frac{3 \ln{\left(\left|{y}\right| \right)}}{2}+C$$

$$$\int \frac{3}{2 y}\, dy = \frac{3 \ln\left(\left|{y}\right|\right)}{2} + C$$$A