62 SULLA ESPRESSIONE DELL' LXTEGRALE COIIPLETO ECC. 



y 

 ossia 



u 



— — \ ^^ d X / -w d X X / i d X — f ^, <1 X X i s dxj'r, dx 



-f- fidx-iyT, d* xyp, dx — y^, dxy'r, dx > 



ed in fine 



(58) — =|Xdx/r, dx xfzdx — /p, dx X Js d x/y, '' -K-f-J ^ d x/t, dx/^.dx 



Sia in terzo luogo I' integrale quadruplice 



1— = r p, d X fv, J * fs, <! -K r?'' * » 

 e si avra dapprima (38) 



l- = fp,dxjrY,dx/e.dxx/?dx-/Y,dxxC?dxy,dx+[?dx/^dx/Y,dx|, 



poscia coll' integrazione per parti 



JL- = r^.dx /y. d x/e. d X X/^ d X - f ? d x/p.d x/Y,d x/e,d x 



- rp,d X / Y, d X X J" ? d x/ e, d X + J ? d x/ s, d X xy ■ p, d x^Y.d x 



-f-ZlB, d X X J? d x/e,dx /y, d x -J? d x/e. d x/y, d x X /'p, d x 

 z=rp,dx/Y.dx/e,dx x/^dx-fp. dx/V. dx xj? dx/'e, dx+/?, dx X J^dx/s.dx/Y.dx 

 -r?dxjre,d,r/V,dxx/P,dx-/'e,dx X JlB, dx/Y, dx 4- J^, dx/Y,dx/e,d xj , 



cioe (38) 



(39) JL— h d x/y, d x/e, d X x/? d X — fp, d x/y, d x X f? d x/e, d x 

 -]-/ p, d X X [? d x/^ d x/y, d X - Js d x/e, dx /y, d x/p, d x . 



