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