l32 



ripheriam circuli, cajus diameter n: i. Qjuaeritur, quae- 

 nam alia integialia ab eo deduci possint ? 



S o 1 u t i o : 

 Spectemus intégrale cognitum tanquam primum termi- 

 nam hujiis sériai : 



dxJog.x x'dxlog.x x^dxlog.x a™ — ^Bxlog.x 



V(^i — x^) ' VlT^^X') ' VX^^^x^ ' ' ' Vii—x-y ' 



ac sit terminus generalis — ^ '_f ^^. ^ zn dP. Ponamus por- 

 ro , brevitatis causa, 1/(1 — x'^)z:zy , K z:^ ^ x^ y , eX. 

 S^Rlog.a:. His praemissis erit 9Rr:x"^~~'/d3:— ^ ^ ^ ^ et 



ao m — I -i ^ a'","'"' dxloe,.x i m — i -> i 



S rz: X jlog. xdx ^ ^ m^ yàx, vel 



as=zap — x^ap— ^^^'^^^^-^-î-x'-'rax, ' 



quae aequatio integrata evadit : 



-^ iri:^/^"^ V(i 'X^) ax - ;;^^ / (1 -x^) log. X + Const. 

 Hic iterum necesse est casus m^z 2p et m:zz2p -}- 1 

 seorsim tracta re. 



Evolutio casus mzz:2p. 

 5. 20. Hoc casu habemus : 



-^r^A^''"V(i-x^)ôx-^/(i-x^)log.x-^C. 



Inde eliciemus sequentia integralia : 

 1) Sumamus p = o, proinde 



