2^2 
Mr. Woodhouse on the Integration 
^j(l-e*x*) r, depends on that of 7f __ 
V(i— *‘) 
and of { — -- $ .)• 
Let y ■■■-- =</0 . , i— e 2 .r=R 2 x 2 = -i— L- i — 2.2? 
I — x 1 " y 
—±Zl±i l 
‘ e 2 ' 
consequently, 
^ 1 )R 2m - I }= 
rffl { ^- 2 y Ra }R— 1 — (gffl — i) R^- 3 | ( i- Ra ) (^+ Rt l } 
=2W. (£=?) . R«- l dQ+ l z ”Z L ^- y) .R »«-3 ^ + ^+i.R-+m 
and JR* m+I dQ = . **/ ( i - ,*■) . R^- 1 — (e 2 - a) .jR* m ~ x . dd 
~^Tr^- e ')f R2m - } - d6 ’ W 
and, if (2w-{-i) be negative, either by substitution, or by taking 
the differential of ~^ ~r ■■■ ■, we have 
/ "* c ?0 __ zm — 2 2— e 2 /'rfQ 
R am + 1 W-i * i— e 7 - ' J R 2 f 
1 e 2 jry/(i-T-j: 2 ) 
*V(» — 
rf 0 2 ffl - 3 I 
5 _j r± 
i • i— e 2 : J R 2m j 
zm— i i— e 
R 2m 
Hence, it is clear that fdb . R^^ f 2W + I ) depends on fdQ . Ril 2 "*- 1 ^ 
and fdb . R 1 * 2 ( 2m_ 3) • similarly, JdQ . R* ( 2nz—l) depends on 
fdQ . R±( 2m -3) } jdQ . R±( 2 m- 5 ), consequently, fdQ . R ± ( 27W + I ) 
depends on fdQ . R and — 
Examples ; 
l. Let 2«z + i =3 2W=2, 
whenx = i, J-^rr = -{—? -f{ i). 
(*) 
