( :^T9 ) 

 3 .(—2 



t ö .(■— j: v^ 



^'^ I ., d^ is ooual to 2 x \/x—n-, wo shall find after va- 



^ Y X—71.'' 



rioiis reiluctiunö successively tbr the -t parts ut' 1 D lü- : 



B^r^ — n (3 — »-) toi-' /««- ' 5 . cü: = 



«-^ l/a; — 7i" \/x — n^ 



= — h(3— «■-) I 2 j|/;i,-_„2i„,4— 1 — ^a?i-' 2 — 



[/x—ifi 



- V3(-'-+2) 1/ l^^ton-i - J^+ VG"io-"(-ï-%-Vo«2) iöH- L-Vs <ü"-'"5 1 .(9) 

 V x-iv^ J 



Likewise : 



ƒ' o ;( — 2 n~ — n 

 -— r ~ tun- 1 — ^ «a/l- I « - . Jj; == 

 yx — n- l/a:— n^ 



r — 7t ji 



— 2 2.t]/x — n~ta7i-^—^=^ta?i-< vz~2n^\ — x lan-'^ + 



L Vx—rr' \/x—n^ 



+ 3 7*3 ia«-i 2 _ ,i (.,.. -|- 2) fa«-i w^ 1 . . . . (10) 

 The integral -Cg, viz. 



.; \/x—ni l/^'— V4 



can first be reduced to 



/>a = 2 n io-,^) [2 .*■ l/x=r,,Ti,„,-i ^ ia»-' c + 



^ l/*-Vi 



+ V3 I V - — ^ <(!«-' z.(.lx-\-\ ^jL^tcm-^ 



r 1 /'x—ri-' 



i)Ut as I |/ — tan—^ z . dx can be transformed into 



/ '« — li 



1/^ 



dx 



19* 



