Integral dari $$$9 x^{20}$$$

Temukan $$$\int 9 x^{20}\, dx$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=9$$$ dan $$$f{\left(x \right)} = x^{20}$$$:

$${\color{red}{\int{9 x^{20} d x}}} = {\color{red}{\left(9 \int{x^{20} d x}\right)}}$$

Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=20$$$:

$$9 {\color{red}{\int{x^{20} d x}}}=9 {\color{red}{\frac{x^{1 + 20}}{1 + 20}}}=9 {\color{red}{\left(\frac{x^{21}}{21}\right)}}$$

Oleh karena itu,

$$\int{9 x^{20} d x} = \frac{3 x^{21}}{7}$$

Tambahkan konstanta integrasi:

$$\int{9 x^{20} d x} = \frac{3 x^{21}}{7}+C$$

$$$\int 9 x^{20}\, dx = \frac{3 x^{21}}{7} + C$$$A