Question

How do you find the antiderivative of `e^(-2x)`?

Answer 1

Starting from the integral:
`inte^(-2x)dx=`

By substitution, you set `-2x=t`
so: `x=-t/2`
and `dx=-1/2dt`

The integral becomes:

`inte^t(-1/2)dt=-e^t/2+c`

going back to `x`:
`=-e^(-2x)/2+c`