Integral of $$$\sqrt{22} e^{x}$$$

Find $$$\int \sqrt{22} e^{x}\, dx$$$.

Apply the constant multiple rule $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ with $$$c=\sqrt{22}$$$ and $$$f{\left(x \right)} = e^{x}$$$:

$${\color{red}{\int{\sqrt{22} e^{x} d x}}} = {\color{red}{\sqrt{22} \int{e^{x} d x}}}$$

The integral of the exponential function is $$$\int{e^{x} d x} = e^{x}$$$:

$$\sqrt{22} {\color{red}{\int{e^{x} d x}}} = \sqrt{22} {\color{red}{e^{x}}}$$

Therefore,

$$\int{\sqrt{22} e^{x} d x} = \sqrt{22} e^{x}$$

Add the constant of integration:

$$\int{\sqrt{22} e^{x} d x} = \sqrt{22} e^{x}+C$$

$$$\int \sqrt{22} e^{x}\, dx = \sqrt{22} e^{x} + C$$$A