Speculationes super formula integrali {\int}   (x^ndx)/{\surd}(aa-2bx+cxx), ubi simul egregiae observationes circa   fractiones continuas occurrunt
  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. 
Leonhard Euler, Artur Diener, Alexander Aycock
math.HO