Integral dari $$$\frac{n}{d}$$$ terhadap $$$d$$$

Temukan $$$\int \frac{n}{d}\, dd$$$.

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

$${\color{red}{\int{\frac{n}{d} d d}}} = {\color{red}{n \int{\frac{1}{d} d d}}}$$

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

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

Oleh karena itu,

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

Tambahkan konstanta integrasi:

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

$$$\int \frac{n}{d}\, dd = n \ln\left(\left|{d}\right|\right) + C$$$A