E500 -- De valore formulae integralis ∫ ((x^(a-1) dx)/lx)(1-x^b)(1-x^c)/(1-x^n) a termino x = 0 usque ad x = 1 extensae

E500 -- De valore formulae integralis \(\int \frac{x^{n-1}\,dx}{lx} \frac{(1-x^b)(1-x^c)}{1-x^n}\) a termino \(x=0\) usque ad \(x=1\) extensae

(On the value of the integral formula \(\displaystyle \int \frac{x^{n-1}\,dx}{lx} \frac{(1-x^b)(1-x^c)}{1-x^n}\) bounded at \(x=0\) and extended to \(x=1\))

Summary:

According to the records, it was presented to the St. Petersburg Academy on August 19, 1776.

Publication:

Originally published in Acta Academiae Scientarum Imperialis Petropolitinae 1777, 1780, pp. 29-47
Opera Omnia: Series 1, Volume 18, pp. 51 - 68

Documents Available:

Original Publication: E500
German translation (Artur Diener and Alexander Aycock): E500

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