Integraal van $$$\frac{1}{u}$$$

De calculator zal de integraal/primitieve functie van $$$\frac{1}{u}$$$ bepalen, waarbij de stappen worden weergegeven.

Bepaal $$$\int \frac{1}{u}\, du$$$.

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

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

Dus,

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

Voeg de integratieconstante toe:

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

$$$\int \frac{1}{u}\, du = \ln\left(\left|{u}\right|\right) + C$$$A

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