66 METH. INTEG. FORM. DlFFEREr^T. RATION. 



vbi cof. A ^-^~ erit vcl -{- i vcl — i , proiit w 4- i 

 fucrit vel mimcnis p.iritcr par vcl imparitcr par. 



o 



Problema 



§.52. Inucnirc iiucgralc huius fbimuLic diffcrcntiLilis 



—TTT,.:^, exilk-ntc ;// numcro intcgio niinorc qu.im 

 a « -i- I . 



Solutio. 



Huius formulac dcnominitor i -h .v^""**' vnum habct fic- 

 torcm re.ilcm i -f- .v , rcliqui fiAorcs fimpliccs omncs 

 funt im.igiiiarii ; corumquc adco loco fidorcs trinomialcs 

 accipi dcbcnt. Qiiod ad fidorcm fimpliccm i -\- x at- 

 tinet i intclligitur fi pro co ponatur i -\- rx , indc hanc 



_/_;-V"-'n-t-' ^i^ 



intcgraiis partcm cfle orituram — ^ti^j, Jt^iTx- Sit 



ergo ;' — i , atquc cx dcnominatoris fidorc i-i-.v na(cc- 



—i-i ]■""'"'+" (—1 )-"""• 

 tur intcgralis pnrs — ,7^^;— /(i H-.v) =: ^p^rrr 



/(i-i-.v) qnac adco crit -f- , „ .^ , /(i-|-.v) vbi (ignuni 



H- valct , l\ 2)1 — m fiicrit ntimcrus par , lcu (i ;/; fit 



n'.imcrus par , altcrum vcro fignum ~ valct , (1 ;/; fit 



numcrus imp.ir. 



Qiiod iam ad fiiftorcs trinomialcs attinct , fit conim ipii- 



libct i-\- px -\- qxx \ atquc cx folutionc pracccdcntis 



problcmatis poncndo zn-\-i loco zn colligirnr intcgra- 



lis pars cx hoc fa*ftf>rc oriiuitla n:: 



»n-m 



de 



Atang.*-^^'-^'»' 



