Integral de $$$\frac{1}{126 t}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \frac{1}{126 t}\, dt$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ con $$$c=\frac{1}{126}$$$ y $$$f{\left(t \right)} = \frac{1}{t}$$$:
$${\color{red}{\int{\frac{1}{126 t} d t}}} = {\color{red}{\left(\frac{\int{\frac{1}{t} d t}}{126}\right)}}$$
La integral de $$$\frac{1}{t}$$$ es $$$\int{\frac{1}{t} d t} = \ln{\left(\left|{t}\right| \right)}$$$:
$$\frac{{\color{red}{\int{\frac{1}{t} d t}}}}{126} = \frac{{\color{red}{\ln{\left(\left|{t}\right| \right)}}}}{126}$$
Por lo tanto,
$$\int{\frac{1}{126 t} d t} = \frac{\ln{\left(\left|{t}\right| \right)}}{126}$$
Añade la constante de integración:
$$\int{\frac{1}{126 t} d t} = \frac{\ln{\left(\left|{t}\right| \right)}}{126}+C$$
Respuesta
$$$\int \frac{1}{126 t}\, dt = \frac{\ln\left(\left|{t}\right|\right)}{126} + C$$$A