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