INTEGRALVM PER FACTORES. 131 

 Problema 3. 



27. Fer formulas integrales definire valorem hu> 

 his produfti intlniti ex membris fimplicibus conftantis : 



b r b -+- 1 • J+2 • b+j • £ _t_ 4 • fc .+- s • etc. 



Solutio. 



Denotante i numerum infinitum vidimus erte 



JX aX{ l-X ) ._. w -+• k .1 m-}-ku -+-n m^- kn-j-tn. 



jx m dx(i-x n ) k — l ~ z ~ m ' m -*~ n ' m + * n • e£c * 

 quae forma ad propofitam reducetnr ponendo n ___ 1 j 

 ^•4-fc — a, et mzzb, vnde fit k~a — b. Cum ergo 

 £ debeat effe numerus affirmatiuus, fi fuerit /?>>£, erit 



.yr_i— « f a—b—,j,, ( ' _. '>;*—, 



P — 



_ /** ~ Vj:(i -aQ - 5 - 1 __Jx a - b ~'dx( 1 



xf 



: jx 1 dx{i-xf- b ~ l ~~Jx a - b - l dx{i-xi 



fin autem fit £ > tf , eric inuerfe : 



,.rV.rfr -.r/-- 1 Jx l - C ~>dx(i - x)' 

 p _ _. . — < , — __ - O F T 



-~jx a - l ax^-xf- a ~'~ Jx°-^'ax(i~xf- 1 ' ^ ' ' 



Corollarium. 



28' Manifef.ttn autem eir, fi fit a)>b, valorem 



P fore infinitnm, fri autem fit b)>a, fore Vzzo. Cafii 



autem a~bnt I _=: 1 : qui cafus cum ad vtrumque 



expofitorum ?caue pertineat , euidcns elt , effe 



x a — 'dx x*dx 

 J — _— r;/— — quae integralia cafu ^zr 1 vtique 



fiunt ita ir.f.nita, Yt rationem aequalitatis obtineant, 



^—'dx .^—'dx 

 Eft autem in genere / ~—J — — — • 



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