Integral dari $$$j_{0} x^{2} x^{s}$$$ terhadap $$$x$$$

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

Masukan ditulis ulang: $$$\int{j_{0} x^{2} x^{s} d x}=\int{j_{0} x^{s + 2} d x}$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=j_{0}$$$ dan $$$f{\left(x \right)} = x^{s + 2}$$$:

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

Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=s + 2$$$:

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

Oleh karena itu,

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

Tambahkan konstanta integrasi:

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

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