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Integral de $$$\frac{a^{x}}{b}$$$ con respecto a $$$x$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \frac{a^{x}}{b}\, dx$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=\frac{1}{b}$$$ y $$$f{\left(x \right)} = a^{x}$$$:
$${\color{red}{\int{\frac{a^{x}}{b} d x}}} = {\color{red}{\frac{\int{a^{x} d x}}{b}}}$$
Apply the exponential rule $$$\int{a^{x} d x} = \frac{a^{x}}{\ln{\left(a \right)}}$$$ with $$$a=a$$$:
$$\frac{{\color{red}{\int{a^{x} d x}}}}{b} = \frac{{\color{red}{\frac{a^{x}}{\ln{\left(a \right)}}}}}{b}$$
Por lo tanto,
$$\int{\frac{a^{x}}{b} d x} = \frac{a^{x}}{b \ln{\left(a \right)}}$$
Añade la constante de integración:
$$\int{\frac{a^{x}}{b} d x} = \frac{a^{x}}{b \ln{\left(a \right)}}+C$$
Respuesta
$$$\int \frac{a^{x}}{b}\, dx = \frac{a^{x}}{b \ln\left(a\right)} + C$$$A