# The Sophomore's Dream

 Title: The Sophomore's Dream Author: Manuel Eberl Submission date: 2022-04-10 Abstract: This article provides a brief formalisation of the two equations known as the Sophomore's Dream, first discovered by Johann Bernoulli in 1697: $\int_0^1 x^{-x}\,\text{d}x = \sum_{n=1}^\infty n^{-n} \quad\text{and}\quad \int_0^1 x^x\,\text{d}x = -\sum_{n=1}^\infty (-n)^{-n}$ BibTeX: @article{Sophomores_Dream-AFP, author = {Manuel Eberl}, title = {The Sophomore's Dream}, journal = {Archive of Formal Proofs}, month = apr, year = 2022, note = {\url{https://isa-afp.org/entries/Sophomores_Dream.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License