Anwendung des sogenannten Vnrintionscnlcids rmf zioeifache und dreifache Integrale. 47 



d-dz d^dw d äw 



+ 2 Aß . rAs ^ + 2 A, . dz .dw + 2K- o's-r- + 2 A„ . dz —^ 



' '' dy- ' ' dx dy 



djzj _ djz d,ßz _ djz d-Jz _ djz d^d^dz djs d^3z 



+ B.-(-^) + ^B.ir-^+^B-^-^+2B.^-5^+2B.^- 



dy^' 



d dz dSz d^dii) dSz ddw 



' ^ dx ' dx dx ■ " dx dy 



,dSzJ d 3z d'dz d dz dddz djz dfdz dSz 



^ ' V rfy J I " dy dx-i ^ •* dy dx.dy ' ^ dy diß ^ ^ dy 



d dz d, dw d 3z d di 



I O p •" j! L 9 P ■' " 



dy dx dy dy 



d'idzj _ dldz djdjz _ dldz dldz _ dldz __ d'Jz d^Sw r\^~^^^ ^v^"' 



' W.r-i J ^ " dxi dx.dy ^ ^ dx^ dy'i ' * dx^ ' ^ dx^ dx "^ 



d,.d„dzj _ d^djz d^Sz _ d,d,3z d^djz djw __ d_^d^3z d^di 



^ ' W.r.rf2/J ' -dx.dy dy'' ^ ^ dx.dy ' ^dx-dy dx ^ dx.dy dy 



,d-dz-i d-dz d-dz ddw djdz dSw 



' ' V dy^ ) ' - dy- ' ^ (J(/-i dx ' ^ (?j/2 rfi/ 



d 3 w d 3w 



+ 0, . dio'' + 2 C3 . r;^o ^ + 2 C, . dio —^ 



dx ' dy 



.dßw ^'^ dßio d 3u 



X dy 



d dw J\ 



, a o IC . - 1 



+ J..[\-]\-dy.dx 

 auf die Form 



-> / / 



\ 



dx . dy 

 , r d dz d dz /d dz.' djz d dz 



+ ^.d^\ri,.dz^ + 2ri,.dz^+2rj,.dz^ + 2ri,.dz.äw^-rj,^+2ri,— .~ 



d 3z ,ddz-^ d dz , 



+ 2.;,^.;.. + .;, . (4-) + ^2rj,^dw + :y, . .^..- ] 



1 ,- d dz d dz /djz" djz ddz 



+ - . r/„ [«,, . .;3-^ + 2co,.o^.^+2«;3-^3-^+2c«,..\...^..+ o.,.(--)+2..e — .^ 



d (Js ,(?, dz - rf/s -, 



+ 2 w- -^- o"«ü + w. . ( ^^ 1 + 2 Wc, 4- ö"^«' + "^10 • '^^^ 



f/'"<Js rf d dz d~3z d dz ddz d 3 u- 



% • (-f^ + 3t, -^ + »l3-fv + 31.-V + 9l5^ + 31,. r)z + 31,^ 



V rfi/-' dx . dy dx- dy dx " dy 



d.d 



.dd dz d'dz d dz d dz d3w djw -^ 



V dx .dy ' ' dx- ' ■ dy * dx ' " ' *< dy dx J 



