Euler E653: On repeated integration of integral formulas when an exponent is taken as variable | English translation | OMH v1.0

English translation of Leonhard Euler's E653, On repeated integration of integral formulas when an exponent is taken as variable. 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/653/; consulted original volume, Nova Acta Academiae Scientiarum Imperialis Petropolitanae, VII, with academy history for 1789, Petropoli: Typis Academiae Scientiarum, 1793, pp. 64–82, https://archive.org/details/novaactaacademia07impe; American Museum of Natural History Library / Biodiversity Heritage Library, item 38589, https://www.biodiversitylibrary.org/item/38589.