## E589 -- Investigatio valoris integralis $$\int\! \frac{x^{m-1}\,dx}{1-2x^k\cos\theta +x^{2k}}$$ a termino $$x = 0$$ ad $$x = \infty$$ extensi

(An investigation of the value of the integral $$\displaystyle \int\! \frac{x^{m-1}\,dx}{1-2x^k\cos\theta +x^{2k}}$$, the term to be extended from $$x = 0$$ to $$x = \infty$$)

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