Integralen av $$$\frac{1}{\ln\left(c\right)}$$$

Bestäm $$$\int \frac{1}{\ln\left(c\right)}\, dc$$$.

Denna integral (Logaritmisk integral) har ingen sluten form:

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

Alltså,

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

Lägg till integrationskonstanten:

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

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