1 58 DE CALCVLO INTEGRALl 



qnare ponendo mzz—q , 6i fcr.—e^h-^-^ , mutabltur 



per cafum primum algebraice integrabilis eft. In hoc 

 cafu numerus h non eft ncceflario intCv^er , pote;l enim 

 t& fradlus quicunque 



4"^. Si in formula du—x^^^^dx^a-^-hx^^f , fit 

 nrzh-\-^^ , mutabitur in fequentem diizizx^'^^ dx 

 [a-^bx^f, cuius integralis erit 



^^.^nrrw-m^g^^n^sm^ &C. -hA.v"™"''") [a-^hx^^f-^ 



lam H h fuerit cuilibet numero integro affirmativo e ac- 

 qualis , fiet ein—nwzL.—l—x , & nm—em—vizl , adeoque 

 Yzz:-{l-\-i)fa/:^x^dx(a-\-hx^f. adeoque integraleeft 

 fc=(A.t^'^"^'-+-'H-B.r^'"-^^-+-'-+-'-4-&c.-hAA:''^-') 

 (^^-^.r"^) ^-^'-{l-^-iXf^ax^dx {a-\-hxy. Verum /r^^ 

 [a-^-hx"^) ^zzf {ax^-^-hx"^^) dx {a-\-bx'^) ^-'zz . 

 /{aax^dx-^-zahx^^^dx^hhx^^^-^^^dx^a-^-hxy-^zz 

 f{a\v^dx-\''^aahx'^^-{-']ahhx-'^^dx-]-hKx^'^^)K 

 dx^a-^-hx^f-"^ atque ita porro : unde fi p fuerit integer 

 affirmatJYUS , mutabitur fx^ dx^a-^-bx^f in fd^-'x^dx-\- 

 (^_i) a ^-2 Z^.r^^V.rH-^- '-^*— ^z^-3 M,r ' ''^Vr-H&c > 



(a-\-bx'^) quod integrale vcroperprsecedentiadependeta 

 ferie q'iantitatum abfolute integrabilium -\-(^fx^dx 

 {a-^-hx"^) ubi Q eft quantitas conftans ex aduaii evolu- 

 tione formnlsE oriunda . 



Sed quid eveniet,fi p fit numerus integer, fed nega- 

 t!Anjs?H^c formula duzzx^ dx{a-\-hx'^)~^ etiam transfor- 

 mari poteft in 



duz^Ex^-{'Yx'^^-\-Gx^'^^^ecc.yx:{a^hx'^) cuius 

 inte^raiis depeadet iterum a feiie quantitatum abfclutc 



inte» 



