A Fundamental Criteria to Establish General Formulas of Integrals

Table 2

Remarks on principal values integrals, where

	Conditions	Theorem			Remarks
1	and	1			Which is identical to Cauchy’s theorem, obtained [4] (P.62 formula (9)).
2	and	2			Cauchy also made a mistake in this result, see [4] (P.62 formula (9)). He did not correct this mistake in the next memoir see [5, 6].
3		1			This result does not appear in [4–6, 11].
4		2			………
5		3			……….
6		4			……….