aoo F X E R C I T A T f N E S 



integrabilis euadet fi multlplicetur per 



In genere autem propofita hac aequationc 



* +5( 2CX+X+ 1 )^xxdxdu-\-\oi(K~ i) ^xudx% "^ 



fi ca multiplicetur per 

 x^-^ du-^-a. x^~' ud Xy 



fiet intcgrabilis , eritque integrale : 

 \x\k-\-^x)du-\-a.x^'\k+^x)ududx-V'^cixx^~Xf^+^x)iidx-{Qdx* 

 feu x^du-\-2cf.x^-'u du dx-\-Oia x^-' ud x — ^±^- 



ergo x^ du-\-o.x" u d x -zz ■^-^-%-, \\\xiZ(\^^ 



38. In hac autem aequatione generali noftra 

 fiipQrior non contineiur : quare conditiones aequatio- 

 nis huius 



xxik+Bx^ddu^-xiC-iDx^dudx-^-lE-^-fx^udx^^Q 



accuratius inueftigemus , \t per 



x^~ ' d u -\- a x^"^ u d X 



mukiplicata fiat integrabilis. Ac primo quidem in- 

 tegrale fit 



ix^iA-\-Bx)du+ax^-'(A-^Bx)ududx-\^^x^''uudx* 



^^udx'-Qdx' 

 requiritur autem , vt fit primo 



C z= (a + ^ X) A ; D - (a 4- i X 4- 1) B 



tura 



