Integral de $$$\frac{d}{t}$$$ con respecto a $$$t$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \frac{d}{t}\, dt$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ con $$$c=d$$$ y $$$f{\left(t \right)} = \frac{1}{t}$$$:
$${\color{red}{\int{\frac{d}{t} d t}}} = {\color{red}{d \int{\frac{1}{t} d t}}}$$
La integral de $$$\frac{1}{t}$$$ es $$$\int{\frac{1}{t} d t} = \ln{\left(\left|{t}\right| \right)}$$$:
$$d {\color{red}{\int{\frac{1}{t} d t}}} = d {\color{red}{\ln{\left(\left|{t}\right| \right)}}}$$
Por lo tanto,
$$\int{\frac{d}{t} d t} = d \ln{\left(\left|{t}\right| \right)}$$
Añade la constante de integración:
$$\int{\frac{d}{t} d t} = d \ln{\left(\left|{t}\right| \right)}+C$$
Respuesta
$$$\int \frac{d}{t}\, dt = d \ln\left(\left|{t}\right|\right) + C$$$A