AND ON DEFINITE INTEGRATION. 475 
where B,, B., B;, By, B;, &c. are Bernoulli’s 
- numbers. 
Therefore, since C, E, G, &c. are equal to 
nothing, the equation (6) will become 
F (x) =f (or) +(A+A)E (ax) + (B+ AN + i) 
II . 2 3 Ill 2 
f (ox) + ( Br’ +av + \t (ox) + ir + 
AW I i! *) £ (ex) + (Dh + Bw “4 ARB “| 
2.3.4 2.3.4 2.3.4.5 / 
ee (Br Sel ers ee Re Es. ee (7) 
By integrating this equation we have, 
F(x) =3 .f Jo (w+h) {=| Fon) dx +(A+h’) 
I 
2 I 2 
F(o(@))+(B+An' + ¥ je (ox) + (Ba + AW 4 
“aa (ov) + ie + Bi + AN +h *) £° (ee) te 
2.3.4 
(Dw +n” An 4 YP (00) +... &0.+C...(8) 
2.3.4 2.3.4.5 
Where the constant C must be determined by 
taking a particular value for 2 Therefore the 
