$$$\frac{\ln^{2}\left(x\right)}{x}$$$ 對 $$$t$$$ 的積分

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

配合 $$$c=\frac{\ln{\left(x \right)}^{2}}{x}$$$，應用常數法則 $$$\int c\, dt = c t$$$：

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

因此，

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

加上積分常數：

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

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