Integral dari $$$\frac{x^{9}}{3}$$$

Temukan $$$\int \frac{x^{9}}{3}\, dx$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=\frac{1}{3}$$$ dan $$$f{\left(x \right)} = x^{9}$$$:

$${\color{red}{\int{\frac{x^{9}}{3} d x}}} = {\color{red}{\left(\frac{\int{x^{9} d x}}{3}\right)}}$$

Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=9$$$:

$$\frac{{\color{red}{\int{x^{9} d x}}}}{3}=\frac{{\color{red}{\frac{x^{1 + 9}}{1 + 9}}}}{3}=\frac{{\color{red}{\left(\frac{x^{10}}{10}\right)}}}{3}$$

Oleh karena itu,

$$\int{\frac{x^{9}}{3} d x} = \frac{x^{10}}{30}$$

Tambahkan konstanta integrasi:

$$\int{\frac{x^{9}}{3} d x} = \frac{x^{10}}{30}+C$$

$$$\int \frac{x^{9}}{3}\, dx = \frac{x^{10}}{30} + C$$$A