Integraal van $$$\frac{6}{u}$$$

Bepaal $$$\int \frac{6}{u}\, du$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(u \right)}\, du = c \int f{\left(u \right)}\, du$$$ toe met $$$c=6$$$ en $$$f{\left(u \right)} = \frac{1}{u}$$$:

$${\color{red}{\int{\frac{6}{u} d u}}} = {\color{red}{\left(6 \int{\frac{1}{u} d u}\right)}}$$

De integraal van $$$\frac{1}{u}$$$ is $$$\int{\frac{1}{u} d u} = \ln{\left(\left|{u}\right| \right)}$$$:

$$6 {\color{red}{\int{\frac{1}{u} d u}}} = 6 {\color{red}{\ln{\left(\left|{u}\right| \right)}}}$$

Dus,

$$\int{\frac{6}{u} d u} = 6 \ln{\left(\left|{u}\right| \right)}$$

Voeg de integratieconstante toe:

$$\int{\frac{6}{u} d u} = 6 \ln{\left(\left|{u}\right| \right)}+C$$

$$$\int \frac{6}{u}\, du = 6 \ln\left(\left|{u}\right|\right) + C$$$A