3S HISTOIRE. 



Integrale fx n ^ n " 1 3x(A+ x^f*?*, fimile propofito, fum- 

 to tantum m -\~n pro m, X — • i pro X, eadem ratione ulte» 

 rius reducere licet, eflque 



/ x ™ -+-»-* a x ( A -+- x n ) x "-* x = jj^ x m -*- n (a -+- x*)*- 1 



m-t-n. <» v ' 



Simili modo fit 



/y»-*- 2 *- 1 3i(A + x tt ) x - 2 = * x m_t - 2n ( A -f- x tt ) x ~* 

 — (±=il2 / , x ,a - 4 - 3 n - 1 9 x ( A -4- x tt ) x "- 3 - 



m -r- yn. •» v ' 



Quae redu£tiones quomodo ulterius fint continuandae , iairi 

 fatis manifeftum eft. Exinde pro integrali propofito fponte 

 prodit feries fine fine procedens haec: 



/x m - i a.r(AH-x n ) x =r 



(q)g(AH-^r,— ^Lf^-V Xn(X-i)n /_x»Y 

 m L m-t-fAA + iv (w+«)(w+2n)\A+x7 



_ >n(X-i)n(>- g )n / x tt V + 1 

 (m-+-n)(m-+-2w)(w-t-sn) \A-»-x n / J 



cnius lex progreffus evjdens eft Integrale pro x = o eva* 

 nescit, exiftente m ^> o. 



Corollarium. 

 J. 2. 1.) Eadem methodo aliam infuper integrali* 

 exprefTionem deducere licet. Eft nimirum 



/x 7 "- 1 dx{A-h x n ) x = <x J i)n (A + i p +I x m -* 



Jporro 



(x m+u ~ l d x ( 1 -4- x , ) x - f -* = — - r - ( A -4- x tt ) x+2 x m - 2 » 



* v ' (\-f-2 Jl v ' 



