Integral of $$$\frac{\ln^{2}\left(x\right)}{x}$$$ with respect to $$$t$$$

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

Apply the constant rule $$$\int c\, dt = c t$$$ with $$$c=\frac{\ln{\left(x \right)}^{2}}{x}$$$:

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

Therefore,

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

Add the constant of integration:

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

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