Question

How do I find the antiderivative of `f(x)=e^(-2x)`?

Answer 1

The exponential `e^x` derived or integrated is always equal to itself. However, you must be careful with the exponent.
In this case you have `-2` in it so you have to take into account it.
So:
`inte^(-2x)dx=e^(-2x)/(-2)+c`

You can check your result by deriving it so that you ought to get the original integrand.