Integral de $$$\frac{4}{y}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \frac{4}{y}\, dy$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(y \right)}\, dy = c \int f{\left(y \right)}\, dy$$$ con $$$c=4$$$ y $$$f{\left(y \right)} = \frac{1}{y}$$$:
$${\color{red}{\int{\frac{4}{y} d y}}} = {\color{red}{\left(4 \int{\frac{1}{y} d y}\right)}}$$
La integral de $$$\frac{1}{y}$$$ es $$$\int{\frac{1}{y} d y} = \ln{\left(\left|{y}\right| \right)}$$$:
$$4 {\color{red}{\int{\frac{1}{y} d y}}} = 4 {\color{red}{\ln{\left(\left|{y}\right| \right)}}}$$
Por lo tanto,
$$\int{\frac{4}{y} d y} = 4 \ln{\left(\left|{y}\right| \right)}$$
Añade la constante de integración:
$$\int{\frac{4}{y} d y} = 4 \ln{\left(\left|{y}\right| \right)}+C$$
Respuesta
$$$\int \frac{4}{y}\, dy = 4 \ln\left(\left|{y}\right|\right) + C$$$A