A general method for summing series
Alexander Aycock has made a draft translation into English, available online at Euler-Kreis Mainz.
This paper leads to Bernoulli numbers from an integral of an infinite series and is called a "beautiful triumph" by Euler.
Original Source Citation
Commentarii academiae scientiarum Petropolitanae, Volume 6, pp. 68-97.
Opera Omnia Citation
Series 1, Volume 14, pp.42-72.