aio DE CRITERIIS INTEGRABILIT. 



leui autem adhibitn atrcntione liquet , ftatui pofle 

 0— .v^, hu.ic iz^itur valor>-m introducendo , in ae- 

 quatione (uperiori ex crutr.o intcgrabilitatis dedu- 

 Ct-A , conLqiiemiir 



o=:A-E(X4-i) fCX(XJ-iM +X':+2C-DX(X-i)(X-a) 

 "9 i;X(X-i)-i 8l>X-6DH-tX,X-i (X-2J(X-3) 

 + i6EX,X-i;(X-2)H-72EX(X-i}+96EX+24.E-etc. 



quac aJ hanc reducitur 



e=A-B(XM)-fC(X-fiKx+2)-D(X-hi\X+2)(X+3) 



+ EiX-}-i;x+-i)(X4-3;(x++)....-4-L(x-i-i)(X-f2)....(X-^;;/). 



Si igitur cx hac aequatione finguli \alores ipfuis X 

 inucdigentur , vnajuaeque huiusmodi cxprellio x^ ^ 

 pro niultiphcatore idoneo formulac noftrae differen- 

 tialis propofitac habenda eft, integratione autcm atftu 

 inrtitiita , habebimus : 



xdv x^cldv vVv ^"'"'«/'""'jN 



B A 



'A-+-:) 



pofitis fcilicet 

 A=(X-fi)A' A'-^, 



B=(X-f-2)B'-fA' 

 C=(X-l-3:C'-i^B' C'=,-iL_--^,— + ^,^;;^, 

 ctc. etc. 



Quoniam vcro nunc intcgralc cmerj;cn5 fimilis cd: 

 formac , ac ipta aeqiiatio difici<.niialis propolita , 



