QFIBFSDAM INTEGRABILIBVS i g 5 



n~p 



fi ponatur x^zz^p-^^ ,iiet enim azP-^^ dz-^-hydzzzdy. Er- 

 go ax^dx-^bydxzzdy erit integrabilis fi ?i fit numerus in- 

 teger pofitivus. 



Exempla. 



Si nzzi erkyzz-^^—i " 



hb 



2 



^ b bb 3 



b 



Si «=3 eritf^:— ;f -^-x --^ 'a'1'' 



& & 



& generatim dato // numcro quocunque erit rrzferieiin- 

 finitse 



^ «-I n_2 ft_, 



^ ~^x -- ^a: -_ >1 — ?Jx -&c. 



quK tones abrumpitur quoties n eft numerus integer po- 

 fxtivus. 



Si vero ponamus 

 y=zax'u-^^x^u 2 -f-y.r^z^' _}-,^,r^^+4_e^v*tt^ -4- «Scc,. 

 transmutabitur sequatio Ar'"</;f-f-/^j'i.rzz:4;/ in 

 ax^dx-^-brjux 'udx^b(h/u ^dx-\-8cc, 

 ■= (ctr*-^2px4-4- 3 y:r^z/ 2 _|_5^c . )du-\- 

 (a.r^< '«-4-p)3:^-'«2+y^^^-'«3^_&c.) ^;f. qusc fimiliter 

 erjt integrabilis fi w fit numerus intcger pofitivus ad 

 quam formam reduci poffunt plurimi cafus particulares 

 quorum integratio fme hoc theoremate non facile fucce- 

 deret. 



"Exemph I. 

 Sit data aequatio x^ dx^2x-i)udx-Qu^-dx==[x-2u) 

 du hoc eft a—a—ezzi. /— y=z^zz:&c/— o. ^zz-i j— 2. 

 wzz^. habebitur u=zx±V2x'^ -j-^x 2^-3:^-1-3 



B b a Exemp^. 



