136 DE CRITERIIS INTEGRABIL; 



—dx/Md X -^ dj/N d X -h dpifV d X -/^^-^ N d x) 



+ d^(f(idx-J^'^Fdx+f^'^Ndx) 

 .. .+dt{fTdx...,'^f'^'^-^Qdx± /t^-^P^/vT/^^^W^^) 



"vbi figna fuperiora valebunt , fi nuinerus termino- 

 rum ex quibus dV componitur fuerit par znfn+^y 

 contra vero fi impar. 



5. Quum vero iam liinc prodeat : 



Vzz^flSldx-hpfNdxi-qifVdx-f^^^Ndx^-^-rifQ^dx-f^^^Ydx 



^f^''Ndx) 



...+u{fTdx....Tf^'^-'^(l^x±f^''''^?dxTP'"^^^x) 

 perpcndamus efle 



Wy^duf^^^^Ndx-pNdx+dpfl^^dx-dpfNdx-dqfdxfNdx 

 ^dqfdxfNdx-^-drfdxfdxfNdx. . . 



ideoque ob dprrqdx; dqzzrdx etc. 



N dy ^dup^^^Ndx-d pfNdx - d. qf^^^ N dx 



+ d.rf^'^Ndx...^d.uf^'^^Ndx. 

 Similiter inueniemus 



P dp± duf ^^-' ^ Fdx - d. qf ?dx-d. rf^^Vdx+d. sf ^'Wx . . . 



^duf^^^-^^Pdx 



nec noH 



Qdq^duf^^^-^lQdxzzd. rfQdx-d^s f^'^Q^dx+.... 



^d.uf^^-^^Qdx, 



His igitur valoribus in aequatione valorem ipfius V 

 exprimente iiitrodud:is , obtinebimus ; 



' dW 



