Integral dari $$$\frac{a}{v}$$$ terhadap $$$v$$$

Temukan $$$\int \frac{a}{v}\, dv$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(v \right)}\, dv = c \int f{\left(v \right)}\, dv$$$ dengan $$$c=a$$$ dan $$$f{\left(v \right)} = \frac{1}{v}$$$:

$${\color{red}{\int{\frac{a}{v} d v}}} = {\color{red}{a \int{\frac{1}{v} d v}}}$$

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

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

Oleh karena itu,

$$\int{\frac{a}{v} d v} = a \ln{\left(\left|{v}\right| \right)}$$

Tambahkan konstanta integrasi:

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

$$$\int \frac{a}{v}\, dv = a \ln\left(\left|{v}\right|\right) + C$$$A