RÉDUCTION D'INTÉGRALES DÉFIIVIES GÉNÉRALES. 



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i: 



Cos/'.T.Sin.ax.Sin.p.i.-dx n ^ I ^\ , ^ „ <,„ , 1 



^o_„_2le-p/((14-e2'/J"- (14-6-2'/)"} = 2-0-2 -e-P7(e2''l—l)(l +e-2./)4 



o\") 4-7 o\nj p'<2,rf<<K 



TT " /a\ T 



= 2-" — (fPi— c-P'/jJS' <ï-2"?— 2-«— eP? 

 4? Q\nj 4.7 



= 2-o-2_/gPV._c-?"'/)fl + e-2'/)'' — 2-«--'-cP'?^ c-2''v + 2-'^-2-e-P7^ «2-,, ). . . (12) 

 '/ q o\n/ 2 o\"i J 



ƒ'^CoSflX.-C0S.ax.CoS.pxdx rt Jl I "\ , n , , Q„o^ I 



q^+x^ iq O \nj ^ _ hp>^-^; 



= 2-<.-2Üc-;)9((14-c29)"-|-(l + e-2?)«) =--2-«-2"e-P'?fc>2<"?+lj(l-f-c-2ï)«] ' "^ ^ 

 S ? / 



ï-°~('cP'J + c-P''').2'rlÉ~^'"''— 2-" -"^ eP'ï.2"|''|e-2"7 + 2-<'— e-P?^ e^"i ip=2d-\-p'. 

 47^ ^ o \«/ 4'/ o \ni 4.7 o\"/ (/<2,fZ<o; 



a^ - •' 



= 2-a-2lfe,,J 1 g-;)7)(]+e-2'/)«— 2-«-2-CP'/^ U-2«7 1 O-a-S-g-,.,:^ c2"j\. . . . (U) 



7 T^ ^\ ' ' ,^ g\nl 7 o \"/ i 



("^ Cos.ox Si7i.ax.Cos.pxdx -Z-a-Q ^M, „ „. , , „ , ., „ r- r , ,0 il 



— — ~eP^^{]\e2"'lEl.{—(j{p + 2n)}—e-^"iEi.{—q[p — 2n)]\ (15) 

 9 oV'!/'- 



En prenant la sommc cl lu dilTórenco tic (15) et de (10) on oblienl; 



{ 2'+.r« q o\«j ^" 



2—0—1 n /a'. 



f 



Co««a'. .Si/i. ((a — p ./•}(/..- Z-"-! 4/"\ „ ,- r n 1 , 



q^ + A'^ 70 \"/ 



2—" — ' " i a\ 



+ ei"> ^ e-2«5 £•/. f — 7fp— 2n)} 



9 o \n/ 



II s'cnsiiit du la seconde expression, (|ne ia pri^niièic vaul encore ponr nnc 

 valcur négalivc de f. I'renons donc dans collc integrale a-\- i)=^r, p = r — a, 



17* 



