Answer
See below for detailed work.
Work Step by Step
$$A=\int x^n e^{ax}dx$$
We set $u= x^n$ and $dv=e^{ax}dx$
That makes $du=nx^{n-1}dx$ and $v=\frac{1}{a}e^{ax}$
Applying integration by parts $\int udv=uv-\int vdu$, we have
$$A=x^n\times\frac{1}{a}e^{ax}-\int\frac{nx^{n-1}}{a}e^{ax}dx$$ $$A=\frac{x^ne^{ax}}{a}-\frac{n}{a}\int x^{n-1}e^{ax}dx$$
for $a\ne0$
The reduction formula has been established.
