$$$\frac{68}{r}$$$ 的积分

求$$$\int \frac{68}{r}\, dr$$$。

对 $$$c=68$$$ 和 $$$f{\left(r \right)} = \frac{1}{r}$$$ 应用常数倍法则 $$$\int c f{\left(r \right)}\, dr = c \int f{\left(r \right)}\, dr$$$：

$${\color{red}{\int{\frac{68}{r} d r}}} = {\color{red}{\left(68 \int{\frac{1}{r} d r}\right)}}$$

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

$$68 {\color{red}{\int{\frac{1}{r} d r}}} = 68 {\color{red}{\ln{\left(\left|{r}\right| \right)}}}$$

因此，

$$\int{\frac{68}{r} d r} = 68 \ln{\left(\left|{r}\right| \right)}$$

加上积分常数：

$$\int{\frac{68}{r} d r} = 68 \ln{\left(\left|{r}\right| \right)}+C$$

$$$\int \frac{68}{r}\, dr = 68 \ln\left(\left|{r}\right|\right) + C$$$A