Speculationes super formula integrali {\int} (x^ndx)/{\surd}(aa-2bx+cxx), ubi simul egregiae observationes circa fractiones continuas occurrunt
arXiv:1202.0037
Abstract
Euler evaluates the integrals in the title and recognizes a recursion between them, which he then uses to give continued fractions for the log and arctan. The paper is translated from Euler's Latin original into German.