Integral de $$$x^{2} \tan{\left(2 \right)} \tan{\left(4 \right)}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int x^{2} \tan{\left(2 \right)} \tan{\left(4 \right)}\, dx$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=\tan{\left(2 \right)} \tan{\left(4 \right)}$$$ y $$$f{\left(x \right)} = x^{2}$$$:
$${\color{red}{\int{x^{2} \tan{\left(2 \right)} \tan{\left(4 \right)} d x}}} = {\color{red}{\tan{\left(2 \right)} \tan{\left(4 \right)} \int{x^{2} d x}}}$$
Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=2$$$:
$$\tan{\left(2 \right)} \tan{\left(4 \right)} {\color{red}{\int{x^{2} d x}}}=\tan{\left(2 \right)} \tan{\left(4 \right)} {\color{red}{\frac{x^{1 + 2}}{1 + 2}}}=\tan{\left(2 \right)} \tan{\left(4 \right)} {\color{red}{\left(\frac{x^{3}}{3}\right)}}$$
Por lo tanto,
$$\int{x^{2} \tan{\left(2 \right)} \tan{\left(4 \right)} d x} = \frac{x^{3} \tan{\left(2 \right)} \tan{\left(4 \right)}}{3}$$
Añade la constante de integración:
$$\int{x^{2} \tan{\left(2 \right)} \tan{\left(4 \right)} d x} = \frac{x^{3} \tan{\left(2 \right)} \tan{\left(4 \right)}}{3}+C$$
Respuesta
$$$\int x^{2} \tan{\left(2 \right)} \tan{\left(4 \right)}\, dx = \frac{x^{3} \tan{\left(2 \right)} \tan{\left(4 \right)}}{3} + C$$$A