$$$\frac{\ln^{2}\left(x\right)}{x}$$$ の $$$t$$$ に関する積分

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

$$$c=\frac{\ln{\left(x \right)}^{2}}{x}$$$ に対して定数則 $$$\int c\, dt = c t$$$ を適用する:

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

したがって、

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

積分定数を加える:

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

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