132 



ripheriam circuli, ciijus diameter m 1. Quaeritur, qiiae- 

 naiii alla intcgralia ab co deduci possint ? 



S o 1 u t i o : 

 Spectemns intégrale cognilum tanquam primum tcrmi- 

 num hiijus seriei : 



dxlag.x xdxlog.x x^dxlog.x x^ — ' dx log.x 



VlT—x^)' >/(, _jc2) » y(i— x"^ • • • V {x—x^) » 



ac sit terminus generalis " "^^ '_f J/.^ r= 3P. Ponaniiis por- 

 ro , brevitatis causa , / ( i — x^) m / , K zn ^x^ y y et 

 SziRlog.x. His praemissis erit 3Rr:x'" '/^x— ^^ — ^, et 

 dSz^x /log. xdx ^^ ^ — •" m •'^ /^^> vel 



as — ap — x-ap _^'^ii^* -7 -l x"-' v-ax , 



quae aequatio integrata evadit : 



/jc™ "*"' 8 jc /og. X m /"x"^ '9x log.x 

 y(i— X-) — ;i;r+i y vci— x^p 



-+- ;;rqrT/^"^ V(i -x^) ax - ;;^_^ >/ (1 -x^) log. X 4- Const. 



Hic iterum necesse est casus mzzz 2p et m=z2p-f-'i 



seorsim tractare. 



E V o î u t i o casus mm 2 p. 

 §. 20. Hoc casu habcmus : 



p x^P-^^ dx log.x __"P_ r ^'P — ' dxhg.x 



■^;ïr^/x"-V(i-x-)ax-^4^)/(i-a:')log.a: + C. 

 Inde eliciemus sequentia integralia : 

 l) Sumamus p nr o, proinde 



