Integraali $$$\frac{\ln^{2}\left(x\right)}{x}$$$:stä muuttujan $$$t$$$ suhteen

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

Sovella vakiosääntöä $$$\int c\, dt = c t$$$ käyttäen $$$c=\frac{\ln{\left(x \right)}^{2}}{x}$$$:

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

Näin ollen,

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

Lisää integrointivakio:

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

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