I want to integrate $$\int x e^{-2x}\cos(3x) dx$$. I've tried using integration by parts and got the results. However, I was told that it's not correct and suggested to use method as the following: $$ \begin{align}\int x e^{-2x}\cos(3x) dx &= \frac{1}{D} \left[ xe^{-2x}\cos(3x)\right] \\ &= \left[ x- \frac{1}{D}\right]\frac{1}{D}e^{-2x}\cos(3x) \end{align}$$
to calculate $\frac{1}{D}e^{-2x}\cos(3x)$, we use
$$ \begin{align}\frac{1}{D}e^{-2x}\cos(3x) &= e^{-2x}\frac{1}{D+2}\cos(3x) \\ &= e^{-2x}\frac{D-2}{D^2-4}\cos(3x) \\ &= \frac{e^{-2x}(D-2)}{-13}\cos(3x) \\ &= \frac{e^{-2x}}{-13}(-3\sin(3x)-2\cos(3x)) \end{align}$$
What is the concept behind this method? I was told that $\frac{1}{D}$ is equal to integration and I think that it's similar to integration by parts.
Thank you.