A shortcut for solving the ubiquitous integral ∫ xn eαx dx using only derivatives

Abstract

ABSTRACTIn this note, I present an ‘easy-to-be-remembered’ shortcut for promptly solving the ubiquitous integral for any integer n>0 using only the successive derivatives of . Some interesting applications are indicated. The shortcut is so simple that it could well be included in calculus textbooks and classes directed to first year undergraduates.