Integral von $$$\frac{1}{\ln\left(x\right)}$$$

Bestimme $$$\int \frac{1}{\ln\left(x\right)}\, dx$$$.

Dieses Integral (Logarithmisches Integral) besitzt keine geschlossene Form:

$${\color{red}{\int{\frac{1}{\ln{\left(x \right)}} d x}}} = {\color{red}{\operatorname{li}{\left(x \right)}}}$$

Daher,

$$\int{\frac{1}{\ln{\left(x \right)}} d x} = \operatorname{li}{\left(x \right)}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{\frac{1}{\ln{\left(x \right)}} d x} = \operatorname{li}{\left(x \right)}+C$$

$$$\int \frac{1}{\ln\left(x\right)}\, dx = \operatorname{li}{\left(x \right)} + C$$$A