2 68 
Mr. Woodhouse on the Integration 
ifV= ~ be z. \/2— 1, compute /(i) from series (6), and F(i), 
from the series (i+<?') (i-H") (i-H'") • (i + g ) • T (“7“)* 
to which it is equal, 
if <? — — be a — l, compute / (i) from series (9), and F(i) 
hyp. log. 
i m )b 
from the series ( 1 -j- v 6) (i-f"6) (1 + (i-{-jQ) . 
f h ' L w\ 
I'P, — ~^r~K to which it is equal. 
For the purposes of computation, the foregoing expression for 
B is, I believe, as simple as any that can be proposed. It is easy, 
however, by means of the preceding forms, to express it differently ; 
thus, fj ~ ] (from x=o to ,r=i) 
Consequently,^ 
— (i+g'f- (*+«*) 
cos. 0 . dQ 
W 
= 1 ' •/(*)+ 
u+g') 3 
e' (1 — e') 
•/(*)- 
(* + *')* 
e' {1—e 1 ) 
•2/(1) 
2 2f[l) 
jy 2 f COS^a . 
“ • (a+6) 3 J 
R3 6.q«+6)(a— of 
2flA 2 
or ==-r- 
Let 2 wz-f 1 == — 1; 
then, k-K = -^77— (1-** **1 ( ;K= 1 ) = Xp sF ( 1 )’ 
2^—1) • 2rfjT 
and 
« . P+e) 
E,r wi r (2 ^~° • 2af,r 
= i e i J (• L-x* ) ?/yO-~** !.(■-«' 
, „ 2 F(I) rt + 6 2 /( 1 ). 
Consequently, ^ ab • *. » 
