Question is to integrate the following integral by parts

$\displaystyle

\int {(x + 3)e^{ - x} dx}

$

Is this right?

$\displaystyle

\begin{array}{l}

u = x + 3 \\

u' = 1 \\

v' = e^{ - x} \\

v = - e^{ - x} \\

\int {(x + 3)e^{ - x} dx} \\

= (x + 3) \times - e^{ - x} - \int {1 \times - e^{ - x} dx} \\

= - (x + 3)e^{ - x} - e^{ - x} +K \\

\end{array}

$

The answer is given as

$\displaystyle

- e^{ - x} (x + 4) + K

$

but I can't see how