$$$\frac{\ln^{2}\left(x\right)}{x}$$$ 关于$$$t$$$的积分

求$$$\int \frac{\ln^{2}\left(x\right)}{x}\, dt$$$。

应用常数法则 $$$\int c\, dt = c t$$$，使用 $$$c=\frac{\ln{\left(x \right)}^{2}}{x}$$$：

$${\color{red}{\int{\frac{\ln{\left(x \right)}^{2}}{x} d t}}} = {\color{red}{\frac{t \ln{\left(x \right)}^{2}}{x}}}$$

因此，

$$\int{\frac{\ln{\left(x \right)}^{2}}{x} d t} = \frac{t \ln{\left(x \right)}^{2}}{x}$$

加上积分常数：

$$\int{\frac{\ln{\left(x \right)}^{2}}{x} d t} = \frac{t \ln{\left(x \right)}^{2}}{x}+C$$

$$$\int \frac{\ln^{2}\left(x\right)}{x}\, dt = \frac{t \ln^{2}\left(x\right)}{x} + C$$$A