FORMVtAS DIFPERENT. RATIONALES. 1 1 5 



Ex his igitiir colUgitur integralis quaefiti pars ex denomi- 

 natoris N fadore {p-\-qxf oriunda fore 

 ^r ^^^ ^ M d^ I Uf^ dx_ 



sJ^qxy^qdx'^' Sjip+qxf-' '^a/^A' ^' S^ [p+qxr 



I , M ^ dx I , M ^ dx 



^(J/Z?"'- SJ [p+qxf-^'^ 2^q*dx' "^ S^(p+fvr 



I ^^M . dx 



"^ "+"i.2.3...(H-i)^Wx''-''^" 'sJp + qx 



cxiftente S rz -, r; atque in coefficientibus -vbique 



{p-\-qxf 



pofito X — "j. 



Exemplum 4. 



§. Tp. Huius fbrmulae differentialis ■ ».*t,z^^,)^ix-2]^{:,x-z) 

 integrale inuenire. 



Hic eft M=i:i — a: et N — x*{ix-iy{^x-2.y{^x-2) 

 et cum variabiJis x in numeratore M pauciores habeat 

 dimenfiones quam in denominatore N , nulla pars integra 

 in fra(flione ^ continetur , nullaque inde nafcitur integralis 

 pars. Confideremus ergo fidores denominatoris , ac pri- 

 mo quidem .v* , erit S = (2ji'-i)' (3X-2)' (4A'-3). 

 et p—Oj atque q— i \ vnde ponendum erit A"— ^ — o. 

 lam ad coefficientes requifitos inueniendos erit 



t — X 



I 



S (2*-l)'(35C-j)*( + *-3) 12 



, M ,7o-c^-;.8lX-4-^?7r-;H^ , 7 J^ 



«•S (2*— i)*(iJi.— :)»(4X— .)» «•* 9.«.* 



I j M -t7^io'^-t-'^''-'^ <^* ^*-s'<^" ^ ^^-t--'-'ifiii^'^— 2fii g;y-< -T7S8 j^' »»rj) j « 



«"•s — (2x-oS(iX-2)Mt-c-.jJ «•* — 2,6 "'*• 



P a Hinc 



