Introduction

In this document, we will discuss the question of finding

$$\int x^n {\rm e}^x {\rm d}x$$

(for $n \in \mathbb{N}$). Normally, this would involve integrating by parts $n$ times which is time-consuming, especially for higher $n$. In this document, we will find $\int_0^x t^n {\rm e}^t {\rm d}t$ in closed form so that a particular value of $n$ can be substituted in to find the required integral.