Integral von $$$\frac{49 x^{5}}{585}$$$

Bestimme $$$\int \frac{49 x^{5}}{585}\, dx$$$.

Wende die Konstantenfaktorregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ mit $$$c=\frac{49}{585}$$$ und $$$f{\left(x \right)} = x^{5}$$$ an:

$${\color{red}{\int{\frac{49 x^{5}}{585} d x}}} = {\color{red}{\left(\frac{49 \int{x^{5} d x}}{585}\right)}}$$

Wenden Sie die Potenzregel $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ mit $$$n=5$$$ an:

$$\frac{49 {\color{red}{\int{x^{5} d x}}}}{585}=\frac{49 {\color{red}{\frac{x^{1 + 5}}{1 + 5}}}}{585}=\frac{49 {\color{red}{\left(\frac{x^{6}}{6}\right)}}}{585}$$

Daher,

$$\int{\frac{49 x^{5}}{585} d x} = \frac{49 x^{6}}{3510}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{\frac{49 x^{5}}{585} d x} = \frac{49 x^{6}}{3510}+C$$

$$$\int \frac{49 x^{5}}{585}\, dx = \frac{49 x^{6}}{3510} + C$$$A