Integral von $$$\frac{1}{x \ln^{3}\left(x\right)}$$$ nach $$$t$$$

Bestimme $$$\int \frac{1}{x \ln^{3}\left(x\right)}\, dt$$$.

Wenden Sie die Konstantenregel $$$\int c\, dt = c t$$$ mit $$$c=\frac{1}{x \ln{\left(x \right)}^{3}}$$$ an:

$${\color{red}{\int{\frac{1}{x \ln{\left(x \right)}^{3}} d t}}} = {\color{red}{\frac{t}{x \ln{\left(x \right)}^{3}}}}$$

Daher,

$$\int{\frac{1}{x \ln{\left(x \right)}^{3}} d t} = \frac{t}{x \ln{\left(x \right)}^{3}}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{\frac{1}{x \ln{\left(x \right)}^{3}} d t} = \frac{t}{x \ln{\left(x \right)}^{3}}+C$$

$$$\int \frac{1}{x \ln^{3}\left(x\right)}\, dt = \frac{t}{x \ln^{3}\left(x\right)} + C$$$A