Integral von $$$100000000 x$$$

Bestimme $$$\int 100000000 x\, dx$$$.

Wende die Konstantenfaktorregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ mit $$$c=100000000$$$ und $$$f{\left(x \right)} = x$$$ an:

$${\color{red}{\int{100000000 x d x}}} = {\color{red}{\left(100000000 \int{x d x}\right)}}$$

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

$$100000000 {\color{red}{\int{x d x}}}=100000000 {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}=100000000 {\color{red}{\left(\frac{x^{2}}{2}\right)}}$$

Daher,

$$\int{100000000 x d x} = 50000000 x^{2}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{100000000 x d x} = 50000000 x^{2}+C$$

$$$\int 100000000 x\, dx = 50000000 x^{2} + C$$$A