i3i 



/ v'(i — x+) — 4 ' 8 • î:J * ■ ■ 4P / i'(i'- 



-x+) 



— 1/(1-1 ;l-7^ ^^:r(f^-ô---4F^ ^41p^^)-~ïF-;F-=4'^ 



_j I 4P-2 4p-6 4p-io„4p-i4 ,1 4p-g 4 ^-»^ ig 6 -y^zl _, C 



~^4(p-3r 4P ■•4>-4*4p-8-^ ■■^4- 4P * 4f-4 ' * * " Ï-' " 8 ^^ ^ "*" ^• 



Quo jani intégrale f yj~zr^ determinemus , statuamus 



-r, TT =^ z^ ) hinc 3 X izi ï — ; • 



"^^'-''^ - ^ /z)/(i+z^)l^(i+z^f' 



quare f~-'-^, — f ."''" ,, = z '-^ r= i /-4:% = î Arc. 



•l ^ y ( 1 — x4) J a- 1 (i — - x4) X l: ^ I H- 2^ 2 



taiie;. z :=: ^ Arc. tang. -r^-^^ — rr. Substituto hoc valore in ex- 

 pfessione praccedente, prodibit hoc intégrale : 



/ '^f^';; = i . MS ^^' . î Arc. tang. 77-^'— ^ 



J V(i — x4; 4 8 12 4P 2 O /(i x4) 



i//'i_t4U^Z!_, ^— IL"^ ^.4p-6 ' 4P^ 4P:^^4p—io 



_, L_i;tr4P_-z^ 4Pr^^4p-i4 ,1 4t::± 4p^ 10 0^2-1 _j^Cnn<:t 



^4{p-3r 4f •4P-4-4p-8^ -^S' 4P * 4p-4 - Î2 ' 8 ~^ -i '^OnSt. 



§. 18. Hacc ad ilkistrandam solutionem §. 7. sufTi- 

 eient. Que auteni praestantia methodi a nobis traditae 

 ulterius eluceat, alias séries, ab illa^ qua httcusque iisi 

 sLimus, diversas, consideremus, queni in finem sequentia 

 solvemus problemata. 



P r ohle m a. 



5. 19. Intégrale /^-^^ J^ [;^^^°] extensum ab illust, 

 L. Eulcro *) =z; — ^ log. 2 exhibitum est, dénotante tt pe- 



*) V. Acta Acacl. Imp. Petrop. T. j. P. II. De Integratione formulac 

 r^xloi,.x rabxz=o, r r? , 



J V(i-^'^) Lfldx=:z:i-' ^^'^"53. Auct. JL. tiilera. 



