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