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Integral de $$$5 \sin{\left(x \right)}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int 5 \sin{\left(x \right)}\, dx$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=5$$$ y $$$f{\left(x \right)} = \sin{\left(x \right)}$$$:
$${\color{red}{\int{5 \sin{\left(x \right)} d x}}} = {\color{red}{\left(5 \int{\sin{\left(x \right)} d x}\right)}}$$
La integral del seno es $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:
$$5 {\color{red}{\int{\sin{\left(x \right)} d x}}} = 5 {\color{red}{\left(- \cos{\left(x \right)}\right)}}$$
Por lo tanto,
$$\int{5 \sin{\left(x \right)} d x} = - 5 \cos{\left(x \right)}$$
Añade la constante de integración:
$$\int{5 \sin{\left(x \right)} d x} = - 5 \cos{\left(x \right)}+C$$
Respuesta
$$$\int 5 \sin{\left(x \right)}\, dx = - 5 \cos{\left(x \right)} + C$$$A