Tnde 



•>3^l ) 108 ( |cf<- 



V*- V(2X' - l) / 



Has igirur partes colle<flini fumendo, habebitur integralc 

 quaefitum : 



arc. tang. i^ {2 x' - 1) - | arc. tang. vii^LzJ 



+ 1 L /'~t/(2X'-,K _ . L /X-t(3»-0x ^ 

 \.+V(2X'_,)/ \x + V(J3C-l)/ 



fiue fi fimplicitatis gratia ponatur 



y(2 jr" — l) — ^' €t ?lii^-r_ii — 1?, 



crit hoc integrale : 



arc. tang. j' - | arc. tang. ^' + 1 L {'~r) _ ■ L ('^Jj, 



§. 5. His perpenfis facilior nunc quidem patet via 

 integrationem perficiendi, quae tamen mihi primo intuitu 

 fe non obtulerat. Scilicet fi propofitae formnlae differen- 

 tialis numerator et denominator fimul multiplicentur per 

 i — X , confequimur 



d X d X _^ X d X 



(, -H x) y(2x' — 1) (i — x'} V>":' - ») {■ - *') y(2W^ — t) 



4 



Pro fecundo membro fi fubftitutio fiat V (ajc*— 1)— ^, erit 



xdx—fdy\ et i - x^ =:i{i -y*)^ 

 vnde colligitur 



~~ X d X __ a>* d 7 d y d y 



(i - x») y(2a» - j) 



Hinc 



