Euler E707: On the notable use of imaginary quantities in integral calculus | English translation | OMH v1.0

English translation of Leonhard Euler's E707, On the notable use of imaginary quantities in integral calculus. 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: Official Euler Archive record, https://scholarlycommons.pacific.edu/euler-works/707/; consulted original volume, Nova Acta Academiae Scientiarum Imperialis Petropolitanae, XII, with prefatory academy history through 1794, Petropoli: Typis Academiae Scientiarum, 1801, pp. 3–21, https://archive.org/details/novaactaacademia12impe; American Museum of Natural History Library / Biodiversity Heritage Library, item 38591, https://www.biodiversitylibrary.org/item/38591.