We know the solutions of this integral *(Bronstein-Semendijajev mathematics manual [page474])*: 

\begin{align}
\int\limits\_{0}^{\infty}x^n \cdot e^{-ax^2}dx = \frac{1\cdot3\dots(2k-1)\,\,\sqrt{\pi}}{2^{k+1}a^{k+1/2}}\longleftarrow\substack{\text{$n$ is the exponent over $x$}\\\text{while $k=n/2$}}
\end{align}

But how do I calculate the integral if I change the upper limit from $\infty$ to $x\_1$ which is constant - for example how do I calculate this integral:

\begin{align}
\int\limits\_{0}^{x\_1}x^2 \cdot e^{-ax^2}dx
\end{align}