Question

What is the antiderivative of `e^(-3x)`?

Answer 1

The general antiderivative is `-1/3 e^(-3x)+C`. We can also write the answer as `int e^(-3x)\ dx=-1/3 e^(-3x)+C`

Explanation:

This is just a matter of reversing the fact that, by the Chain Rule, `d/dx(e^(kx))=k*e^(kx)` and also using "linearity".

Alternatively, you can use the substitution `u=-3x`, `du=-3\ dx` to write `int e^(-3x)\ dx=-1/3 int e^(u)\ du=-1/3 e^(u)+C=-1/3 e^(-3x)+C`