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