Integral of $$$- 7 e^{x}$$$

Find $$$\int \left(- 7 e^{x}\right)\, dx$$$.

Apply the constant multiple rule $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ with $$$c=-7$$$ and $$$f{\left(x \right)} = e^{x}$$$:

$${\color{red}{\int{\left(- 7 e^{x}\right)d x}}} = {\color{red}{\left(- 7 \int{e^{x} d x}\right)}}$$

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

$$- 7 {\color{red}{\int{e^{x} d x}}} = - 7 {\color{red}{e^{x}}}$$

Therefore,

$$\int{\left(- 7 e^{x}\right)d x} = - 7 e^{x}$$

Add the constant of integration:

$$\int{\left(- 7 e^{x}\right)d x} = - 7 e^{x}+C$$

$$$\int \left(- 7 e^{x}\right)\, dx = - 7 e^{x} + C$$$A