Integraal van $$$\frac{\ln^{2}\left(x\right)}{x}$$$ met betrekking tot $$$t$$$
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Uw invoer
Bepaal $$$\int \frac{\ln^{2}\left(x\right)}{x}\, dt$$$.
Oplossing
Pas de constantenregel $$$\int c\, dt = c t$$$ toe met $$$c=\frac{\ln{\left(x \right)}^{2}}{x}$$$:
$${\color{red}{\int{\frac{\ln{\left(x \right)}^{2}}{x} d t}}} = {\color{red}{\frac{t \ln{\left(x \right)}^{2}}{x}}}$$
Dus,
$$\int{\frac{\ln{\left(x \right)}^{2}}{x} d t} = \frac{t \ln{\left(x \right)}^{2}}{x}$$
Voeg de integratieconstante toe:
$$\int{\frac{\ln{\left(x \right)}^{2}}{x} d t} = \frac{t \ln{\left(x \right)}^{2}}{x}+C$$
Antwoord
$$$\int \frac{\ln^{2}\left(x\right)}{x}\, dt = \frac{t \ln^{2}\left(x\right)}{x} + C$$$A