«^S3| ) 5 { ^'?^<' 



vnde fit integrando j/ m j^ 2» - ?-^ 2 + C , et fada refti- 

 tutione 



y = rh {a^bxf-llV{a-^^bx)^C 



Exemplum 4. 



d X 



§. 5. Si fuerit dy— :,fa(fla fubftiturionc 



{a-\-bxf 

 y (^a -h b x) — z erit dj —~\ quae formula porro ob 

 </^— =_5JL2 abit in ^j/ — ^, qua integrata fit j--^^, 

 feu faaa reftitutione , j —^-^-=-^^4- C. Vbi noteiur, 

 pro C fumi deberc ^^, 



Problema 2. 



§. 6. Si ftcerh X jun&io quaecunque rationaUs bi' 



ttarum quamitatum x ^; s, exijiente s = y(a4-bx), farmU" 

 lam dijerentialem Xd x ab irrationalitate Uberare. 



Solutio. 



Ponatur y (fl-f ^jir)=:2;, vt fit s-z^ tnt a-\-b x—;^^ 

 hincque x — ^^-~ et d x — '-^-^^; quibus valoribus 

 fubftitutis tota formula fiet rationalis. 



Exemplum i. 



§. 7. Si fuerit 



dy — — ^ ^V"' P^^^^^ 



A 3 ^{<» 



