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In this document, we will discuss the question of finding

$\displaystyle \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.

Alexander Frolkin 2001-06-02