E606 -- Speculationes super formula integrali \( \int\!\frac{x^n\,dx}{\sqrt{aa-2bx+cxx}} \), ubi simul egregiae observationes circa fractiones continuas occurrunt
(Speculations concerning the integral formula \(\displaystyle \int\!\frac{x^n\,dx}{\sqrt{aa-2bx+cxx}} \), where at once occur exceptional observations about continued fractions)
Summary:
According to the
records, it was presented to the St. Petersburg Academy on September 4, 1775.
Publication:
-
Originally published in Acta Academiae Scientarum Imperialis Petropolitinae 1782, 1786, pp. 62-84
-
Opera Omnia: Series 1, Volume 18, pp. 244 - 264
- A part reprinted under the title: De integratione formulae irrationalis (X);
Institutiones calculi integralis 4, 1794, pp. 31-36 [E606a], ed. tertia, 4, 1845, pp.31-36 [E606b]
Documents Available:
- Original Publication: E606
- German translation (Artur Diener and Alexander Aycock): E606
Return to the Euler Archive