Integral de $$$j_{0} x^{2} x^{s}$$$ con respecto a $$$x$$$

Halla $$$\int j_{0} x^{2} x^{s}\, dx$$$.

La entrada se reescribe: $$$\int{j_{0} x^{2} x^{s} d x}=\int{j_{0} x^{s + 2} d x}$$$.

Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=j_{0}$$$ y $$$f{\left(x \right)} = x^{s + 2}$$$:

$${\color{red}{\int{j_{0} x^{s + 2} d x}}} = {\color{red}{j_{0} \int{x^{s + 2} d x}}}$$

Aplica la regla de la potencia $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=s + 2$$$:

$$j_{0} {\color{red}{\int{x^{s + 2} d x}}}=j_{0} {\color{red}{\frac{x^{\left(s + 2\right) + 1}}{\left(s + 2\right) + 1}}}=j_{0} {\color{red}{\frac{x^{s + 3}}{s + 3}}}$$

Por lo tanto,

$$\int{j_{0} x^{s + 2} d x} = \frac{j_{0} x^{s + 3}}{s + 3}$$

Añade la constante de integración:

$$\int{j_{0} x^{s + 2} d x} = \frac{j_{0} x^{s + 3}}{s + 3}+C$$

$$$\int j_{0} x^{2} x^{s}\, dx = \frac{j_{0} x^{s + 3}}{s + 3} + C$$$A