Integral de $$$\frac{\ln^{2}\left(x\right)}{x}$$$ con respecto a $$$t$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \frac{\ln^{2}\left(x\right)}{x}\, dt$$$.
Solución
Aplica la regla de la constante $$$\int c\, dt = c t$$$ con $$$c=\frac{\ln{\left(x \right)}^{2}}{x}$$$:
$${\color{red}{\int{\frac{\ln{\left(x \right)}^{2}}{x} d t}}} = {\color{red}{\frac{t \ln{\left(x \right)}^{2}}{x}}}$$
Por lo tanto,
$$\int{\frac{\ln{\left(x \right)}^{2}}{x} d t} = \frac{t \ln{\left(x \right)}^{2}}{x}$$
Añade la constante de integración:
$$\int{\frac{\ln{\left(x \right)}^{2}}{x} d t} = \frac{t \ln{\left(x \right)}^{2}}{x}+C$$
Respuesta
$$$\int \frac{\ln^{2}\left(x\right)}{x}\, dt = \frac{t \ln^{2}\left(x\right)}{x} + C$$$A