$$$- \frac{1}{u}$$$ 的积分

求$$$\int \left(- \frac{1}{u}\right)\, du$$$。

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

$${\color{red}{\int{\left(- \frac{1}{u}\right)d u}}} = {\color{red}{\left(- \int{\frac{1}{u} d u}\right)}}$$

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

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

因此，

$$\int{\left(- \frac{1}{u}\right)d u} = - \ln{\left(\left|{u}\right| \right)}$$

加上积分常数：

$$\int{\left(- \frac{1}{u}\right)d u} = - \ln{\left(\left|{u}\right| \right)}+C$$

$$$\int \left(- \frac{1}{u}\right)\, du = - \ln\left(\left|{u}\right|\right) + C$$$A