Question

How do you find the antiderivative of `e^-5x` using substitution?

Answer 1

I suspect that you want the antiderivative of `e^(-5x)`...
In fact the anti derivative of `e^-5x` is simply: `e^-5x^2/2` (you don't need substitution...`e^-5` is a constant).
However, if you want the antiderivative of `e^(-5x)` you have (if you really want to use substitution):
`inte^(-5x)dx=`
set `-5x=t`
`x=-t/5`
`dx=-dt/5`
So you get:
`inte^t*-dt/5=-1/5e^t+c`
and substituting back:
`=-1/5e^(-5x)+c`

Hope it helps