106 RÉDUCTION. D'INTÉGRALES DÉFINIES GÉNÉRALES. 



/°° f rSin.sa: 1 w Sin.-" x. Sin. p 3: d x 

 (1 4- 2 rCos.s.T + r )i'' Cos. {bArctang.—-^ \ -— — = 

 l l^rCos.sx) q^ -\- x^ 



[d-l /Za\ '' r^a\ 



1 « = s — 2fl,2p<s<J'a, 

 + (,.._c-7)2a [{e-P'! + eP'l) + {e-P9-eP9)(l + re-'!^y']\ ^^„tie,. (35.3) 



['' f2a\ '' /2a\ 



+ (,7 _ É-7)2« f (e-p? + CP9) + (e-P9 - eP9) (1 + r e-?»)''} ] ' ^ "^actTonn^ir/; . . \ (351)' 



Ici (/ osl, Ie plus grand nombrc entier contenu dans (a — ip). 



f^- ( r Sin. S.X ]a Sin.^" x. Cos. pxdx 



l n+irCos.sx + r^)i'>Sin.{bArctaiig. > — - — , = 



J ^ ' I '^ l + rCos.sx\ q^+x^ 



o 



= (_l)n2-2«-l7r(e?_e-ï)2a(gP9^g-p,)_ |(l^ye-9sy._ 1} ,;,<,, - 2a; . (355) 

 = (_ |)''2-2''-i7i[-Z.r {(l + e-2P'ï)(l — e-2?)2''— 1} + 



_j- (el — e-1 f^o (ePi -\- e-Pl) - {(1 + re-'»)'-'— 1 — ire-?"}! 



= (_),'>2-3a-2„j^_jr+(e7_c-<?)2a(<;P9-|-e-p?)[(l+re-5'')*— l}],p = i — 2a;.(356) 



/"" ,, ( TSi7i.sx 1 xiStn.^a+i^E. Cos. »a;(i^ 



ƒ ( 1 + 2 »• '^0'. s .ï + r' )!'' Cos. Uytrrfana. -— i —; -^ = 



J ^ ^ ^ ' 1 ^1+rCos.sx] q^+a:^ 



= C— 1 )"-' 2-2''-2 n [el — e-9)2a+i [e-P7 + [ePi + e-P-?) - { (1 + re-i^)'' — 1 } ] 



=(— l)''-'2-2''-37r(«'— e-«)2a+i[(e-P9_«p'?)+(eP?4-e-P'ï)(l+re-'?»]'']'P^|"+2!-{357) 



[''-' /2a4-l\ 



e-Pïfe?— e— j)2«+i_«(2a+i-p)9^ (—l)" e-2n7_ ,jB<2a-|- J. 



o \ « / 2/)<s, 



'' /2a4-l\ 1 P entier; 



— e>-2''-i>/2'(— l)"l ' ,r2"74-(e7_e-7)2c<+i(i;P7-|-e-p?) -((l-|-rc-'?«)''— 1}1 . . . (358J 



^l—lj-z-i ■2-2-.-2jrre-p7(g,_e-ïp+i_e(2o+i-p)72(_l)n( '^"^ )ê-2„ï_ , /)<2a+J, 

 •' /2a+l\ 1 1 f)fractioiinairc; 



_C>-2«-i;./^(_l)n U2>79^.(e,_^_,-2a+l(e;,7^e-p7)_^(l^re-1»)''— 1)1 (359J 



o \ 1 ƒ ~ .■ 



