I know this question is very basic but I can't really make it..
$\int{e^{-2x}dx}=?$
$$\begin{align} u = -2x, &du= -2 dx\\ v = e, &dv= e dx\end{align}$$
then applying the rules $uv-\int vdu$ $$ -2xe - \int -2e dx = -2ex + 2 \int edx = -2ex + 2e $$ but the derivate of $-2ex + 2e$ is equal to $-2e$
What is wrong? thanks