Table of Integrals, Series, and Products, 8th Edition

The Order of Presentation of the Formulas

The question of the most expedient order in which to give the formulas, in particular, in what division to include particular formulas such as the definite integrals, turned out to be quite complicated. The thought naturally occurs to set up an order analogous to that of a dictionary. However, it is almost impossible to create such a system for the formulas of integral calculus. Indeed, in an arbitrary formula of the form

${\displaystyle {\int }_a^{b}f(x)dx=A}$

one may make a large number of substitutions of the form $x=\phi (t)$ and ...