15(5 DE CALCrW INTEGRALI, 



(a-^bx^)dO. Quare exiftente B:i= {'w — nm) aA : 

 (p-\-n — \)bm invenietiir tertia «quatio canonica 



dO. 



Ponattir tertio Orzar''"^''"-^-?, & ^0=(«w-3w) 

 C.r""^^"'-V.i"-H^P. Quare tertia sequatio canonica mu- 

 tabitur in 



(2m-;m)^B.r""*-2'"-' dx— [p-^n-z) bmCx'^'^''''^' dx-^ 

 (nm-'i,nt)aCx'''^^'^'dx-\-(p-^C}bmC?x'^'dx-^{a-V-bx'^) 

 d?. Idcircofada Czr(2m— ;7w).'zB:(p-f-«— 2)^w/,invenie- 

 tur qu^rta (yn-nm^aCx^^^^^^^^^dx^zd^p-^-x^btnVx^^dx-^- 

 (a-\-bxy?. 



Simili progreflu pervenietur tandem ad aequationem 

 aliquam canonicam (em-nni) a/^x^'^^'^~' dxz^^p-^-C^bm 

 7.x^~^dx-\-(a-\-bx'^)d'Z. In hac vero eft ^ , terminus 

 quicunque feriei numerorum naturalium l, 2, 3, &c, a 

 eft terminus feriei coefiicientum A, B, C, D cuius or- 

 dinem indicat numerus intcger e-\-i. Ac denique Z eft 

 terminus feriei indeterminatariim M , N, O, P &c. cuius 

 idem ordo eft e-\-u Sit R— ^H-^.r"*, & ultima hasc ae- 

 quatio canonica mutabitur in aequationem (em—nfn) 

 ^A.r"'"-'"*-V.r=:(/)-f-i)Z^/RH-R^Z , ducatur haec in R^ , 



fietqne(m— «/«^^^.^'^'"-'"^'^.^(^-^^^^^(/'-f-O^^^^I^ 

 -f-R^'+-'rt^, & integrandoR^-^'2=i:/(m-mw)^A.r^'"-''^' 



dx{a-^-bx^f dicatur hoczzY , eritque adeo 2— Y:R^-^'. 



Expanfis iam omnibus fiet 



Mz=A.r"'^-'^_|-B.r''"^""-f-C.r"'^5 "^-f- &c. . . A.r"'^''^-^- 

 YR-^-' qnare f^-MR^-^^jrr^A.r^-l-B.r""^-^"^ 

 -Cx^^^-^^-h&c -|-A.r'^'^^"X^-i-/'.r'")^'^'-f-Y 

 ubi funt 



