nÉDÜCTION D'liNTÉGR\LES DEFIMES GÉAERALES. 69 



[^ , xSin-''-^'^ x.Cos.pxdx \ 



j f, W -^Z^ ^ ^0 ( — ')"~' 2-2<'--2-re-/'9(£?— e-«,2a + l \ 



+ - ^ A„ ( - l)«-i 2-aa-2 .T (e? _ e—yjïa+i j-g-(„s+p;, ^ g_(„,v_;,),/J \ -^ ^ ' 



....(X.) 



= (—1)"-' ■2--^<'-'^n{e^~e-i)^«+JXge-Pl -\- {eP9 + e-P9)-^ A„e-'"«l ) 



l 2 1 -•/ 



I -I- («?_,.-9)2a+i (eP7-[-e-p?)-^A„e-"S5l \entier; . (X,) 



rf / 2 (/ + ] \ 1 1 c 



2a+l 



= (— l)"-'2--'<2-2:irAo (J-Wf««— e-?)2''+l_e;2a+l-p;5^(_l)« T^ e-2«j ^ ,/;<2a+l. 



Il o \ » I lip <, S,p 



d /2a + l\ ) IC ( fractioiiiiaire; 



^e\p-2a-\)2:[—\)'' J «2»,j. _(.(g, _g_,pa+l (gM + e -P'?) - ^ A„ «-"^'1 ] . . . . (Xjj 



= Ao(— l)<'-"2-2«--',Te-P?(e?— «-V+'+-A,(— l^''-i2-2«-2jr[((l-e-2,)2a+l_ij' 



- 1 C L 



+ e-(2p+2a+l;?(e?_e-?)2''+l L|.(— lja-12-2a-2;j( gï_g-,)2a+l(e'.9-(-e-P9)__^A,,e-'«Sf lp =«—■-<<— 1. 



2 2 \2p>s>4«+2; 



1 / 

 = (-If-l 2-20-2 ;.J_A, {(l+,-2p,)(l_,-2?^2<,+l_l} ( ^^^^ 



+ (e' — e-«)2a+i \s^e~Pl -\-{ePi^e-Pi)-2: Kne-^'i\'\ ] 

 =. (—l)"-! 2-2a-27rrAJe-'''(e'' — e-'?)2a+i_e(2a+i-pn ^(_1)J '^ ]e-2"}\ 



rf /2a+l\ ) f,p=5— ~a— 1, 



— É{p-2a-ii9^(_ 1)1 ' e2'"?> )2p<s<4a+2, 



o \ " / J (pentier; . (XJ 



1 1 <: 1 



+ -A, {(14-e-2/";)(l — é-29l2<2-(-l_n_|.(g5_g-,)2a+l(e,;,^g_p,j_^A„6-'''?l 



» 2 -"y 



)=« — 2 (i — J, 



[f <* /2a + l\ \ 



A„ . e-P'(«« — e-'ï)2a+l — e(2a+l-p}'?^{— 1/1 «-2"? \ 



<l /2a+l\ „ 1 f'2»<s<4a4-2, 



- e'P-2- >k :S (- D" ( J ) e-^"'i\ /f^eti^nnaTe ; 



1 " 1 c l^') 



2 * 2 J 



