2 6% 
Mr . Woodhouse on the Integration 
2 m-j- 1 
.-^l.x 2n - 2 R 2W “ 1 ^- 
2» + zm+i g 2 ' ' 2M-fzm+r 
And, since a similar form is true for fx 2n ~ z . R 2m+I and 
fx 2n ~~ z . R 2m “W0, by continuing the process, we must at length arrive 
at forms such as Jx° . R 2l,+ I d9,Jx°. R 21 " -1 dQ t which have already 
p d$ 
been shown to be integrable by /Rd9,md ; or at forms such as 
x 2 ° R d9, x Za . which are integrable by JRdQ, » f° r j by 
preceding form, 
Jx 2 ' R M = kfx M ~ 2 KM + KJx 1 '-* -g- — X 2 *- ' s/TTv R. 
Similarly, 
jx 2 *- 2 R M— A '/* 2<r -+ - * 2 "~ 3 R, 
&c. 
and 
r-r-a.. (i — R 2 ) 
R 
^20-— 4 . 
■ £ — x- • R^» 
e 2 . R e 4 . R 
&C. &C. 
so that, finally, the integrals of x 2v . Rd0. , must be reduced 
to JKd6, and 
Hence, the integral of a form such as 
-s a ^dtzwz+i 
I A+B.z 2 -{-C.z 4 + &c. • dx, depends on JRdQ.znd 
X Zn dd 
If 2 /w + i be negative, or the integral of — be required, then, 
substituting in the preceding form, or, by a direct process, taking 
the differential of — ^ l~ i— (X), there will result, 
f x Zn . dQ 
J R 2 ,„ 4 -i j 
(e 1 — i) ( 2 >t— i) + 2 ffl — 2 f' x 1 ” — 2 S . (2n—2tn+d f x u ~‘ 2 d6 
(zm — i] (i — e’ 1 ) . e 2 'J R 2 '«— * (zm— i) (i— e 2 ) . e 2 'J R 2 f — 3 
X 
(2m— x) (i— e 2 j 
