->I4€ ) 25 ( ^f€^ 

 — 5 ^x(i -^- xx) l'dx 



■^ " JT^X X) V~{T-^ A*) (l+^Jf)y(l+A-*)* 



qiiippe quarum rumma ipfam formulam noftram propoli* 

 tam producit; prodic enim 



_ Idx (i ^xxY -\-ldx(i -xxY 

 •^~' {i - X*} y [i -i- X*} 



d X (i -h X*) — d a V ( i -4- 3C*) 



(1 — X*) V (I H- x+J I — j:* 



Quod fi ergo duo praecedentia cxempla in fubfidium V0« 

 centur, manifefto fiet </ j' =:= ' ^P -h 5 </ Q, confequenter 

 integrale quaefitum eric ^ = ^ P 4- 5 Q , quod fequenti 

 modo exprimere licebit: 



/■ dx V(.-)-i') ~ J_ l VCi-4-a*)-t-yVi i i_ A fin. * '^ * - . 



y i — X* iv» 1 — XX ' » V * ' "^ * * 



Exemplum. 4. 



§. 41. Si propofita juerh haec formiila differetuiaUs- 



c X d X 



J V (■ -+- *■*) 



d yzn - _ Jjyl^;,.. , eius integrale imtefiigare. 



Haec formula fimili modo ac praecedens tradari 

 poteftj difcerpaiur enim in fequentes duas partes : 



l dx{i -\- X x ) _ l d X {i ~ X x) 



{1 - X x)y {x -\-x*) {i -^ X x){y i +Pj * 



•■quippe quae coniundae producunt 



dy — ldx{\ -\ - x xY -Idxji - x x Y 



(i -x*)y {1 -t- X') ~~ 



\d X. ^ X X X X d X 



(i - x^) y (i -H X') (i - X') y (i -+- X*) ' 



J&a Acad. Imp. Sc, Tom. IV. P. /. D quae 



