Integral dari $$$32 x^{2} e^{2}$$$

Temukan $$$\int 32 x^{2} e^{2}\, dx$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=32 e^{2}$$$ dan $$$f{\left(x \right)} = x^{2}$$$:

$${\color{red}{\int{32 x^{2} e^{2} d x}}} = {\color{red}{\left(32 e^{2} \int{x^{2} d x}\right)}}$$

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

$$32 e^{2} {\color{red}{\int{x^{2} d x}}}=32 e^{2} {\color{red}{\frac{x^{1 + 2}}{1 + 2}}}=32 e^{2} {\color{red}{\left(\frac{x^{3}}{3}\right)}}$$

Oleh karena itu,

$$\int{32 x^{2} e^{2} d x} = \frac{32 x^{3} e^{2}}{3}$$

Tambahkan konstanta integrasi:

$$\int{32 x^{2} e^{2} d x} = \frac{32 x^{3} e^{2}}{3}+C$$

$$$\int 32 x^{2} e^{2}\, dx = \frac{32 x^{3} e^{2}}{3} + C$$$A