Integralen av $$$2025^{x}$$$

Bestäm $$$\int 2025^{x}\, dx$$$.

Apply the exponential rule $$$\int{a^{x} d x} = \frac{a^{x}}{\ln{\left(a \right)}}$$$ with $$$a=2025$$$:

$${\color{red}{\int{2025^{x} d x}}} = {\color{red}{\frac{2025^{x}}{\ln{\left(2025 \right)}}}}$$

Alltså,

$$\int{2025^{x} d x} = \frac{2025^{x}}{\ln{\left(2025 \right)}}$$

Förenkla:

$$\int{2025^{x} d x} = \frac{2025^{x}}{2 \ln{\left(45 \right)}}$$

Lägg till integrationskonstanten:

$$\int{2025^{x} d x} = \frac{2025^{x}}{2 \ln{\left(45 \right)}}+C$$

$$$\int 2025^{x}\, dx = \frac{2025^{x}}{2 \ln\left(45\right)} + C$$$A