AND ON DEFINITE INTEGRATION. 499 
Then, because [ne)ae=log. o(x) and jacnyar—= 
log. » (y), we shall have, putting A + 1 = > 
1 Bin 
—|\.. v)dx 
Pa ss Se oe aa | v0, (x) 
[x ]= Low) ]x Seas y 
+ Bfo(x) - a(y)} + D fo(a) - a(y) f+F 
So, (x) - a (Y) ; + &e., &e Te A eee (31) 
By taking a equal to e, equation (31) will take 
the following remarkable form : 
x 
—\ .v0,(2) dx 
£ y 7 
[%)] =[e) ] yer es , *e)__* 
; : o(y) x 
\ = im , es ae 1 a a F a 
og. .0(v) x log. .\(7) x log. .©,(@7) x we. 
~ et t32) 
asi B TW, dD at (iy, 
log. .0(y) x log. .0\(y) x log. ©, (y) x &e. 
Ex. 1.—Required the continued product of « 
factors, whose general factor is «. 
