Integral von $$$\frac{1}{126 t}$$$

Bestimme $$$\int \frac{1}{126 t}\, dt$$$.

Wende die Konstantenfaktorregel $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ mit $$$c=\frac{1}{126}$$$ und $$$f{\left(t \right)} = \frac{1}{t}$$$ an:

$${\color{red}{\int{\frac{1}{126 t} d t}}} = {\color{red}{\left(\frac{\int{\frac{1}{t} d t}}{126}\right)}}$$

Das Integral von $$$\frac{1}{t}$$$ ist $$$\int{\frac{1}{t} d t} = \ln{\left(\left|{t}\right| \right)}$$$:

$$\frac{{\color{red}{\int{\frac{1}{t} d t}}}}{126} = \frac{{\color{red}{\ln{\left(\left|{t}\right| \right)}}}}{126}$$

Daher,

$$\int{\frac{1}{126 t} d t} = \frac{\ln{\left(\left|{t}\right| \right)}}{126}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{\frac{1}{126 t} d t} = \frac{\ln{\left(\left|{t}\right| \right)}}{126}+C$$

$$$\int \frac{1}{126 t}\, dt = \frac{\ln\left(\left|{t}\right|\right)}{126} + C$$$A