$$$\frac{n}{d}$$$ 关于$$$d$$$的积分

求$$$\int \frac{n}{d}\, dd$$$。

对 $$$c=n$$$ 和 $$$f{\left(d \right)} = \frac{1}{d}$$$ 应用常数倍法则 $$$\int c f{\left(d \right)}\, dd = c \int f{\left(d \right)}\, dd$$$：

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

$$$\frac{1}{d}$$$ 的积分为 $$$\int{\frac{1}{d} d d} = \ln{\left(\left|{d}\right| \right)}$$$:

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

因此，

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

加上积分常数：

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

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