Integraal van $$$a^{u}$$$ met betrekking tot $$$u$$$

De rekenmachine zal de integraal/primitieve van $$$a^{u}$$$ met betrekking tot $$$u$$$ bepalen, waarbij de stappen worden getoond.

Bepaal $$$\int a^{u}\, du$$$.

Apply the exponential rule $$$\int{a^{u} d u} = \frac{a^{u}}{\ln{\left(a \right)}}$$$ with $$$a=a$$$:

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

Dus,

$$\int{a^{u} d u} = \frac{a^{u}}{\ln{\left(a \right)}}$$

Voeg de integratieconstante toe:

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

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

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