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

The general antiderivative is $- \frac{1}{3} {e}^{- 3 x} + C$. We can also write the answer as $\int {e}^{- 3 x} \setminus \mathrm{dx} = - \frac{1}{3} {e}^{- 3 x} + C$
This is just a matter of reversing the fact that, by the Chain Rule, $\frac{d}{\mathrm{dx}} \left({e}^{k x}\right) = k \cdot {e}^{k x}$ and also using "linearity".
Alternatively, you can use the substitution $u = - 3 x$, $\mathrm{du} = - 3 \setminus \mathrm{dx}$ to write $\int {e}^{- 3 x} \setminus \mathrm{dx} = - \frac{1}{3} \int {e}^{u} \setminus \mathrm{du} = - \frac{1}{3} {e}^{u} + C = - \frac{1}{3} {e}^{- 3 x} + C$