24 RÉDUCTION D'INTÉGRALES DÉFINIES GÉNÉRALES. 



ƒ" Cos." X. Sin. {{a — 1) x} d X 2-«-> « /a\ „„.,,, ,,, 

 i^^ ^— i = êï.2 e-!"»!;/. (o(2n — 1) — 



2 — " — • "■ I a\ 



— e-9 2\ «2"? £ï. (_ o (2 n — 1)} (34) 



? o \n/ 



8. Encore les formules (L) jusques a (0) donnent pour la mêmc suppo- 

 silion (/): 



/"^ xCos.'^ X.Cos. ax.Sin.pxdx " I a\ „ . 



= 2-«-27re-P9{(14-e2?)''-f-(l-)-e-2^)<-J =2-''-27re-m(l+e2o9)(l+e-'-''?)'' ,p>2a; . .(35) 



< 



=2-<'-2;r(e-P9 — e?"?)^["le-2"'? + 2-''-27ifP?^r |e-2'"?+2-n-2jie-P'ï.2'( \e'^'"i\p='i,d+p\ 

 o\nl üW o\n/ p<2,(i<a; 



=2-a-^n{e-P'i—eP^){l+e-^'i)"+2-"~^neP'i2r\e-^'''i+Z-"--ne-PQ2:r\e^''A . . . (36) 



=Z-<'-^n'e-P1—ePl]2{ \e-'^"i4-2-''-^nePl2 { ]e-^"l-\-2-<'-^7ie-Pi:S\ \e^"l j ,> = Zd 

 oWi o\n/ o\n/ ( "^<- a; ' 



"^-l/aN '' fa\ { 



=2-''-Wi^e-Pi~ePi)[l-\-e--ra^Z-''--nePi 2 l \e-'^"i-[-i-''-^ne—ri2:{ ]e^'>i\ ...(37) 



o \«/ o \"/ I 



•tandis que que l'on a pour p==2a: 



^'^aCo8.''x.Cos.ax.Sin.Zaxdx °~' /<i\ „ 

 = 2-«-2 71 e-S"? ^ \(e2"'?4- e-2"9J + 2-<'-2 7re-^<"! 



= 2-«-2 7ie-a"'? {(1 -\-c^if — e^^9-\- {l^e--'!)''—e-^'"i] -{-2-"-'^ n e-^<"l 



= 2-°-27r {(1 +e+2o';)(l +e-29)«_l} (38) 



Eiisuitc : 



["^ xCos.''x.Sin.ax.Sm.pxdx " l a\ r 



I ^+J^ ^^"'""'""f y b'"'>Ei{-q{p + Zu)]-e-^-"iEi.{->]{p-2n)]] 



— 2,-"-^ e-Pi 2 {j[e^"l Ei. {q{p~Zn)] —e-^'<l Ei. {q{p + 2n)}]. (89) ^ 



ƒ" xCo».''x.Cos.ax.Cos.pxdx " /<»\r - ^ . ,n 

 J-— — i- =-%-a-'i(fi2:\ [e'^PlEi.[-q'p^Zn)]-\-e-'i"iEi.[~q'p—2n)y\ 

 u ^ 



— 2-0-2 e-PïJ'rjp'"? iïi. (7(;>- 2 n)} + e- 2"ï£,-.(3(p+ 2 n))]. (joj 



