Integral von $$$x_{14}^{x}$$$ nach $$$x$$$

Bestimme $$$\int x_{14}^{x}\, dx$$$.

Apply the exponential rule $$$\int{a^{x} d x} = \frac{a^{x}}{\ln{\left(a \right)}}$$$ with $$$a=x_{14}$$$:

$${\color{red}{\int{x_{14}^{x} d x}}} = {\color{red}{\frac{x_{14}^{x}}{\ln{\left(x_{14} \right)}}}}$$

Daher,

$$\int{x_{14}^{x} d x} = \frac{x_{14}^{x}}{\ln{\left(x_{14} \right)}}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{x_{14}^{x} d x} = \frac{x_{14}^{x}}{\ln{\left(x_{14} \right)}}+C$$

$$$\int x_{14}^{x}\, dx = \frac{x_{14}^{x}}{\ln\left(x_{14}\right)} + C$$$A