$$$\frac{d}{t}$$$ 关于$$$t$$$的积分

求$$$\int \frac{d}{t}\, dt$$$。

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

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

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

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

因此，

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

加上积分常数：

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

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