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Integral de $$$3^{2 x}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int 3^{2 x}\, dx$$$.
Solución
La entrada se reescribe: $$$\int{3^{2 x} d x}=\int{9^{x} d x}$$$.
Apply the exponential rule $$$\int{a^{x} d x} = \frac{a^{x}}{\ln{\left(a \right)}}$$$ with $$$a=9$$$:
$${\color{red}{\int{9^{x} d x}}} = {\color{red}{\frac{9^{x}}{\ln{\left(9 \right)}}}}$$
Por lo tanto,
$$\int{9^{x} d x} = \frac{9^{x}}{\ln{\left(9 \right)}}$$
Simplificar:
$$\int{9^{x} d x} = \frac{9^{x}}{2 \ln{\left(3 \right)}}$$
Añade la constante de integración:
$$\int{9^{x} d x} = \frac{9^{x}}{2 \ln{\left(3 \right)}}+C$$
Respuesta
$$$\int 3^{2 x}\, dx = \frac{9^{x}}{2 \ln\left(3\right)} + C$$$A