Integral dari $$$- 8 x^{3}$$$

Temukan $$$\int \left(- 8 x^{3}\right)\, dx$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=-8$$$ dan $$$f{\left(x \right)} = x^{3}$$$:

$${\color{red}{\int{\left(- 8 x^{3}\right)d x}}} = {\color{red}{\left(- 8 \int{x^{3} d x}\right)}}$$

Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=3$$$:

$$- 8 {\color{red}{\int{x^{3} d x}}}=- 8 {\color{red}{\frac{x^{1 + 3}}{1 + 3}}}=- 8 {\color{red}{\left(\frac{x^{4}}{4}\right)}}$$

Oleh karena itu,

$$\int{\left(- 8 x^{3}\right)d x} = - 2 x^{4}$$

Tambahkan konstanta integrasi:

$$\int{\left(- 8 x^{3}\right)d x} = - 2 x^{4}+C$$

$$$\int \left(- 8 x^{3}\right)\, dx = - 2 x^{4} + C$$$A