# Thread: integral of (x+3)e^-x by parts

1. ## integral of (x+3)e^-x by parts

Question is to integrate the following integral by parts

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

Is this right?

$
\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

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

but I can't see how

2. Sorry, was I right in my answer?

3. all its right, but you didn't finish your answer

4. how do you mean I didn't finish my answer?

5. Originally Posted by Craka
how do you mean I didn't finish my answer?
$= - (x + 3)e^{ - x} - e^{ - x} + K = -x e^{-x} - 3e^{-x} - e^{-x} + K = -xe^{-x} - 4 e^{-x} + K$ $= -e^{-x} (x + 4) + K$.

6. whoops. Thanks.