Efficiently evaluating $\int x^{4}e^{-x}dx$ The integral I am trying to compute is this:
$$\int x^{4}e^{-x}dx$$
I got the right answer but I had to integrate by parts multiple times. Only thing is it took a long time to do the computations. I was wondering whether there are any more efficient ways of computing this integral or is integration by parts the only way to do this question?
Edit: This question is similar to the question linked but slightly different because in the other question they are asking for any method to integrate the function which included integration by parts. In this question I acknowledge that integration by parts is a method that can be used to evaluate the integral but am looking for the most efficient way. This question has also generated different responses than the question linked such as the tabular method. 

Here is a nice little trick to integrate it without using partial integration.
$$
\int x^4 e^{-x} \,\mathrm dx = \left. \frac{\mathrm d^4}{\mathrm d \alpha^4}\int  e^{-\alpha x} \,\mathrm dx   \right|_{\alpha=1} = \left.- \frac{\mathrm d^4}{\mathrm d \alpha^4} \frac{1}{\alpha} e^{-\alpha x}\right|_{\alpha=1}
$$
The idea is to introduca a variable $\alpha$ in the exponent and write the $x^4$ term as the fourth derivative with respect to $\alpha$. This is especially helpful when you want to calculate the definite integral $\int_0^\infty$ because in this case the differentiation greatly simplifies.
$$
\int\limits_0^\infty x^n e^{-x} \,\mathrm dx = (-1)^n \left. \frac{\mathrm d^n}{\mathrm d \alpha^n} \frac{1}{\alpha} \right|_{\alpha=1} = n!\stackrel{n=4}{=} 24
$$
