FORMl^LAS DIFFERENT. R.4T10NALFS. tof 



Exemplum. i, 



$.7. Huius formulac ditferentialis -^r ^^' intcgrale 

 inuenire. 



Qiiiii hic crt ^ ~ ■- ^_. ^, in hiic fradione pnrtcs intcgriic 

 contincntur , c]uac vcl pcr diuifioncm vcl modum nnte 

 trnditum crutae crunt x -\~ 2x -{- 2. vnde ailcitur hacc 

 intcgnilis pars j -4- .v.v -f- 2.v -f- C. Dcindc cum to- 

 tus dcnominator N cx vnico ficflorc .v— i conftet , erit 

 p— — I, ^— I et S~;j., r=:i. Lim cx ficlore.v-i 

 nihilo acquaU pofito oritur .v ~ i , quo valore in -g ~ 

 .vM-.v' fiibdituto prodit 2 , ideoque ex dcnominatore N 

 obtinctur intcgralis pars hacc 2/_;-^ — 2 /(.v— i). Qiio- 

 ni'm vcro totum intcgralc componitur ex partibus , quae 

 tam ex parte integra qu'm frada reiultant , erit intcgrale 

 foimulae propofitae ^^zt" dx haec quantitas finita —- -f- 

 A:*-i-2.v-l-C-i-2/(.v— i) cuiua vcritas j)er diffcrentiatio- 

 nem flici e comprobatur. 



Exemplum. 2. 



§.8. Huius formulae dificrentialis "^^^'^ d x inte- 

 grale inuenirc. 



(^iia variabiiis x in numcratore xx -^Ciax tot habct di- 

 nicnfioncs , quot iu dcnominatv re aa — xx pars intcgra in 

 actione -- ^_^^ - contuietur , qi-ae pcr uunfioncm eft - i , 

 vndc intcgralis pars nafcitur — .v-hC. Porro denomina- 

 Cor rt'^ — .v.v in f;idorts {a—x){a-\-x) refoluiiur : ex priori 

 a~x vx xzz.a .^ ct izz^-j;;:^- z^ '- pouto .\~^; vnde 

 intcgrali, par> cx fadorc a- x oriuntia efl -zz. -^- J ^:^ — 

 Tom. XI ^. O -'' 



