Integral von $$$\frac{\ln^{2}\left(x\right)}{x}$$$ nach $$$t$$$

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

Wenden Sie die Konstantenregel $$$\int c\, dt = c t$$$ mit $$$c=\frac{\ln{\left(x \right)}^{2}}{x}$$$ an:

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

Daher,

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

Fügen Sie die Integrationskonstante hinzu:

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

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