  A formalism is provided to calculate tree amplitudes in open superstring
theory for any multiplicity at any order in the inverse string tension. We
point out that the underlying world-sheet disk integrals share substantial
properties with color-ordered tree amplitudes in Yang-Mills field theories. In
particular, we closely relate world-sheet integrands of open-string tree
amplitudes to the Kawai-Lewellen-Tye representation of supergravity amplitudes.
This correspondence helps to reduce the singular parts of world-sheet disk
integrals -including their string corrections- to lower-point results. The
remaining regular parts are systematically addressed by polylogarithm
manipulations.
