276 SUGLI IMEGRALI ALGEBRICI 



a^'l/A', fdx,— dj-, dx, — dx, da, — d.r„i 

 — \ 1 1-...H [ 



f'{^\) '■{x—x,)dt (x—x^)Al {x—J\)i\n 



a?-' I /A' c Ax,— Ax, d3f„ — dx, dx„ — dx„_, j 



— :_i — z\ — '. L+ — :: - + ... + — --[ . 



f(x„) {(x„ — x,)d« (x„ — xjd( (x„— x„_,)df!) 



poscia, introdolti in questa formula i valori (9) di d«,,.-dx,,, avreino 



dv' {n — \)x^-\\\ + ^xfr'X; (p — {)x''--'X„ + \xl-'X,; 

 (16) — £ = li L_L_-^_- +...+ 



xr"X. (1-1 1 



H + . .+ 



['(X,) ix, — X, X, X3 



/"(x„) Cx„ — X, 



X„ — X,^,} 



+ 



/XT' — iT^x iZ-v, a; /*r'— ^r'\ i/a', jr„ 



X, — x^ / /■'(x,) f' (x. 



V X. — X, / /■'(x,)/"(x^) V X, — x„ / /" (x.) /" (x„) 



\ X, — X3 / f' (Xj 



)r(-^3) 



— *r'\ i/^i'^, -v„ 



V »•„_, — a„ ) f'{x„_,) f 



D'altra parte, se facciamo il prodotlo dc">alori di v,, r^_, dcsuiiti dalla 

 I'ormiila (7), troviaino 



XT' X, iT^X, i'T^x„ 



*'„ »'„_, = , + -—-- -f ■ + . 



(xT' x"-''-' + xl-' x^'— ) l/^X, Z, (x'-" x^-'— + x^— x^-'-') 1/ A', .V„ 



(xT' a;?-'"' + a^r' a:?"'"') l/^ X,X, 





+ 



rK-.)f{^: 



