Integralen av $$$\pi^{x}$$$

Kalkylatorn beräknar integralen/stamfunktionen för $$$\pi^{x}$$$, med visade steg.

Bestäm $$$\int \pi^{x}\, dx$$$.

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

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

Alltså,

$$\int{\pi^{x} d x} = \frac{\pi^{x}}{\ln{\left(\pi \right)}}$$

Lägg till integrationskonstanten:

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

$$$\int \pi^{x}\, dx = \frac{\pi^{x}}{\ln\left(\pi\right)} + C$$$A

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