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