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Integral de $$$3 x^{5} \cos{\left(3 \right)}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int 3 x^{5} \cos{\left(3 \right)}\, dx$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=3 \cos{\left(3 \right)}$$$ y $$$f{\left(x \right)} = x^{5}$$$:
$${\color{red}{\int{3 x^{5} \cos{\left(3 \right)} d x}}} = {\color{red}{\left(3 \cos{\left(3 \right)} \int{x^{5} d x}\right)}}$$
Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=5$$$:
$$3 \cos{\left(3 \right)} {\color{red}{\int{x^{5} d x}}}=3 \cos{\left(3 \right)} {\color{red}{\frac{x^{1 + 5}}{1 + 5}}}=3 \cos{\left(3 \right)} {\color{red}{\left(\frac{x^{6}}{6}\right)}}$$
Por lo tanto,
$$\int{3 x^{5} \cos{\left(3 \right)} d x} = \frac{x^{6} \cos{\left(3 \right)}}{2}$$
Añade la constante de integración:
$$\int{3 x^{5} \cos{\left(3 \right)} d x} = \frac{x^{6} \cos{\left(3 \right)}}{2}+C$$
Respuesta
$$$\int 3 x^{5} \cos{\left(3 \right)}\, dx = \frac{x^{6} \cos{\left(3 \right)}}{2} + C$$$A