Euler E163: An easier and more expedient method for integrating rational differential formulas | English translation | OMH v1.0

English translation of “Methodus facilior atque expeditior integrandi formulas differentiales rationales” by Leonhard Euler (Eneström E163), titled “An easier and more expedient method for integrating rational differential formulas.” Prepared for Open Math Heritage with OpenAI-assisted translation, mathematical transcription and LaTeX typesetting. OMH v1.0 is a machine-assisted draft that has undergone a full, fresh AI-assisted technical audit of source coverage, translation, formulas, tables and figures where present, and rendered output. This is not a claim of human scholarly review or certification of the historical mathematics. Version 2 is reserved for a fully reviewed edition. Original publication: Commentarii academiae scientiarum Petropolitanae, vol. 14 (years 1744–1746, printed 1751), pp. 99–150; Plate I, figures 5–6, and Plate II, figure 1. Sources: https://scholarlycommons.pacific.edu/euler-works/163/; https://archive.org/details/commentariiacade14impe. The AMNH/BHL full-volume witness reports NOT_IN_COPYRIGHT. The saved BHL provider-reuse policy supports reuse of its public-domain digital files without new BHL/provider intellectual-property claims; this source-based assessment does not extend to the separate Pacific modern cover or unrelated service assets. No new translation license is assigned.