135' 



S o 1 u t i o :' 

 onsideremus seriem f-^\ , J —'—- . . •/ — 7^~-^ 

 ^— ^-'^-— --*, cnJLis primas vel simplicissimus terminus est in- 

 t:egrare datum; tum posito, ut supra^, ^'_^''j°^'^ =: 3P, et 

 — log. X r=: R, prodibit x" ' d x log. a: 1= 3 P + x 9 P, vel 

 dR-^-x^^'dx^dP^rd'P, et 9R = -^x"~'5x-f-aP-4-xaP, 

 liinc integrando R=:4 3:" + P -^ fxdV -]- C , scilicet 



r'x^^dxJog.x /nlog.x — 'V-v" rx^"' dx log.x ,. f~\ 



n^/4-||- =: (nlog.x-i) x" - JJlzl^^ +- C. 

 Posito jam nzizo, nancisciinur C z=: i , quare 



/x^dxlog.x /nlog.x — - In n. fx^ ~^ dx log.x , i 



1 -i- X " ^ n^ ' J i -\- X ' M^ ' 



5- 2 3. Haec aequatio sequentes nobis praebet inte* 

 grationes : 



. .1) Si n—i, notumest esse*) /-^^r'^'z"] =-^', 

 quapropter 



— rr^ 3d eosdem termmos exlensum = — / — ,-^— r: -1 . 



2) Si n- 2, consequimur /— q:r|- = - /"r^ = - 71 

 etc. 



§. 24. Cum solutîo praecedens ad intégrale / \_^'^ 

 perducta sit ,- cujus valor ^ si quidem °^^IZ°] extendatur, 



) V. Nt)v. Comment: Tom; XIX. De vero valofe formulae integralis 



J — ~^ ^ à z , casu quo p.ost integrationem zzz 1 p.onitur- 



Auct, L.~EMlefo, pa». 39, 



