Integrals with exponent and polynomial: Pn(x)e^{ax}

I've found a very cute way to work with integrals like

\int_{}^{}P_n(x)e^{ax}dx

Before I always integrated it by parts, for example:

\int_{}^{}xe^xdx=xe^x-\int_{}^{}e^xdx=(x-1)e^x

In case you need to take by parts only once it's ok, but when Pn(x) is x^2 or higher degree you need more time to integrate by parts several times.
There is another better way, let's take above integral again:

\int_{}^{}xe^xdx=(Ax+C)e^x

So now you should take a derivative of the right side and solve it against left side:

xe^x=Ae^x+(Ax+C)e^x

If you divide by e^x, you see that A=1 and C=-1 so you get the same correct answer as above (but easier!)

So in common case:

\int_{}^{}P_n(x)e^{ax}dx=Q_n(x)e^{ax}

Where Pn(x) is polynomial of degree n and Qn(x) is polynomial of degree n with unknown coefficients to find using equation:

P_n(x)e^{ax}=Q'_n(x)e^{ax} + Q_n(x)ae^{ax}