E589 -- Investigatio valoris integralis int (x^(m-1) dx)/(1-2(x^k)cos(Q)+x^(2k)) a termino x = 0 ad x = ∞ extensi

E589 -- Investigatio valoris integralis ∫ (x^m-1 dx)/(1-2x^kcosθ+x^2k) a termino x = 0 ad x = ∞ extensi

(An investigation of the value of the integral ∫ (x^m-1 dx)/(1-2x^kcosθ+x^2k), the term to be extended from x = 0 to x = ∞)

Summary:

According to the records, it was presented to the St. Petersburg Academy on March 2, 1775.

Publication:

Originally published in Opuscula Analytica 2, 1785, pp. 55-75
Opera Omnia: Series 1, Volume 18, pp. 190 - 208
Reprinted in Institutiones calculi integralis 4, 1794, pp. 358-378 [E589a], ed. tertia, 4, 1845, pp. 358-378 [E589b]

Documents Available:

Original Publication: E589

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E589 -- Investigatio valoris integralis ∫ (xm-1 dx)/(1-2xkcosθ+x2k) a termino x = 0 ad x = ∞ extensi

E589 -- Investigatio valoris integralis ∫ (x^m-1 dx)/(1-2x^kcosθ+x^2k) a termino x = 0 ad x = ∞ extensi