Euler E629: Expansion of the integral formula ∫dx (1/(1−x) + 1/log x) extended from x = 0 to x = 1 | English translation | OMH v1.0

English translation of Leonhard Euler's E629, "Evolutio formulae integralis ∫∂x (1/(1−x) + 1/lx) a termino x = 0 usque ad x = 1 extensae". AI use and review status: OpenAI tools assisted with the translation and LaTeX. Version 1.0 is a machine draft with limited scholarly human inspection. Version 2.0 is reserved for a fully reviewed edition. Sources: Euler Archive, https://scholarlycommons.pacific.edu/euler-works/629/; original volume facsimile, https://archive.org/details/novaactaacademia04impe.