Integral de $$$\frac{e_{1}}{t}$$$ con respecto a $$$t$$$

Halla $$$\int \frac{e_{1}}{t}\, dt$$$.

Aplica la regla del factor constante $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ con $$$c=e_{1}$$$ y $$$f{\left(t \right)} = \frac{1}{t}$$$:

$${\color{red}{\int{\frac{e_{1}}{t} d t}}} = {\color{red}{e_{1} \int{\frac{1}{t} d t}}}$$

La integral de $$$\frac{1}{t}$$$ es $$$\int{\frac{1}{t} d t} = \ln{\left(\left|{t}\right| \right)}$$$:

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

Por lo tanto,

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

Añade la constante de integración:

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

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