Integral de $$$\frac{6}{u}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \frac{6}{u}\, du$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(u \right)}\, du = c \int f{\left(u \right)}\, du$$$ con $$$c=6$$$ y $$$f{\left(u \right)} = \frac{1}{u}$$$:
$${\color{red}{\int{\frac{6}{u} d u}}} = {\color{red}{\left(6 \int{\frac{1}{u} d u}\right)}}$$
La integral de $$$\frac{1}{u}$$$ es $$$\int{\frac{1}{u} d u} = \ln{\left(\left|{u}\right| \right)}$$$:
$$6 {\color{red}{\int{\frac{1}{u} d u}}} = 6 {\color{red}{\ln{\left(\left|{u}\right| \right)}}}$$
Por lo tanto,
$$\int{\frac{6}{u} d u} = 6 \ln{\left(\left|{u}\right| \right)}$$
Añade la constante de integración:
$$\int{\frac{6}{u} d u} = 6 \ln{\left(\left|{u}\right| \right)}+C$$
Respuesta
$$$\int \frac{6}{u}\, du = 6 \ln\left(\left|{u}\right|\right) + C$$$A