362 ilir Greenhill, Integrals expressed hy [Mar. 8, 



Thus, a>h, 



(4) -77~5 ^r-n ^ = - arg SD h- , - , it ^ < 6 ; 



indicating that we must put 



sin0 = ^; 



and then the integral becomes 



1 r cl(}) 



,_v [°° dx 1 (a h\ .„ 



( j —7-^5 2 — 5 — T2: = - arg sn - , - , it cc > a ; 



, . r^ dx _ 1 (x b 



,^. [^ dx 1 (& a 



As examples, 



d^ 1 /I 1 



= —7^ arcf en 



(10) 



iV(^*-l) V2 '^ V--^;' V2 

 Again, a> b> c> d, 

 dx 



\/(x — d.x — b.x — c.x — d)' 



2 /x — a. h — d 



arof sn 



\J{a — c .b — d) °- \/ X — b . a — d ' 



indicating that we must put 



— a.b — d 

 b .a — d' 



^"^^/'^V^l:^ 



