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Integral de $$$\frac{1}{2 y}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \frac{1}{2 y}\, dy$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(y \right)}\, dy = c \int f{\left(y \right)}\, dy$$$ con $$$c=\frac{1}{2}$$$ y $$$f{\left(y \right)} = \frac{1}{y}$$$:
$${\color{red}{\int{\frac{1}{2 y} d y}}} = {\color{red}{\left(\frac{\int{\frac{1}{y} d y}}{2}\right)}}$$
La integral de $$$\frac{1}{y}$$$ es $$$\int{\frac{1}{y} d y} = \ln{\left(\left|{y}\right| \right)}$$$:
$$\frac{{\color{red}{\int{\frac{1}{y} d y}}}}{2} = \frac{{\color{red}{\ln{\left(\left|{y}\right| \right)}}}}{2}$$
Por lo tanto,
$$\int{\frac{1}{2 y} d y} = \frac{\ln{\left(\left|{y}\right| \right)}}{2}$$
Añade la constante de integración:
$$\int{\frac{1}{2 y} d y} = \frac{\ln{\left(\left|{y}\right| \right)}}{2}+C$$
Respuesta
$$$\int \frac{1}{2 y}\, dy = \frac{\ln\left(\left|{y}\right|\right)}{2} + C$$$A