you will see a collection of books. The table by Gradshteyn and Rhyzik, edited by Zwillinger is quite large, and if you look at the CD ROM, all the formulas are in digital form.
I experimented in reading the pages (via OCR) but eventually this was overtaken by hand-entry of TeX (with macros). But nearly the whole book can be (and has been, I think) converted to Mathematica syntax, and I think also into something that can be read into Lisp.
The vast majority of (interesting) formulas in these tables are not the indefinite integrals but the definite integrals.
Wolfram (for example) claims to do all the indefinite integrals in G&R. I believe this was false when first claimed. Maybe still is.
I suspect that all the material in the earlier Russian literature was copied/ improved by G&R and subsequent revisions of that.
I have also offered access to tables from CRC -- shorter but more carefully checked -- in digital form.
The places where the tables show the CAS to mess up happen when the formulas are not generic. The tables indicate when the formula needs to be changed under some assumptions, and the CAS not. Or vice versa perhaps. RJF