Integral of $$$\frac{e^{t}}{100}$$$

Find $$$\int \frac{e^{t}}{100}\, dt$$$.

Apply the constant multiple rule $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ with $$$c=\frac{1}{100}$$$ and $$$f{\left(t \right)} = e^{t}$$$:

$${\color{red}{\int{\frac{e^{t}}{100} d t}}} = {\color{red}{\left(\frac{\int{e^{t} d t}}{100}\right)}}$$

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

$$\frac{{\color{red}{\int{e^{t} d t}}}}{100} = \frac{{\color{red}{e^{t}}}}{100}$$

Therefore,

$$\int{\frac{e^{t}}{100} d t} = \frac{e^{t}}{100}$$

Add the constant of integration:

$$\int{\frac{e^{t}}{100} d t} = \frac{e^{t}}{100}+C$$

$$$\int \frac{e^{t}}{100}\, dt = \frac{e^{t}}{100} + C$$$A