Integral von $$$228 x^{2} e^{2}$$$

Bestimme $$$\int 228 x^{2} e^{2}\, dx$$$.

Wende die Konstantenfaktorregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ mit $$$c=228 e^{2}$$$ und $$$f{\left(x \right)} = x^{2}$$$ an:

$${\color{red}{\int{228 x^{2} e^{2} d x}}} = {\color{red}{\left(228 e^{2} \int{x^{2} d x}\right)}}$$

Wenden Sie die Potenzregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ mit $$$n=2$$$ an:

$$228 e^{2} {\color{red}{\int{x^{2} d x}}}=228 e^{2} {\color{red}{\frac{x^{1 + 2}}{1 + 2}}}=228 e^{2} {\color{red}{\left(\frac{x^{3}}{3}\right)}}$$

Daher,

$$\int{228 x^{2} e^{2} d x} = 76 x^{3} e^{2}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{228 x^{2} e^{2} d x} = 76 x^{3} e^{2}+C$$

$$$\int 228 x^{2} e^{2}\, dx = 76 x^{3} e^{2} + C$$$A