ET METHODES D'ÉVALÜATION DES INTÉGRALES DÉFINIES. II. III. 5. N\ 57. 



ƒ* X Sin.pxd.r, n n ^ n <^ 



'/'5 {■'>■') — :, ..^ -= - e^P"^ 1*0 -\--e—l"i 2Ï' D„(c"--'? -\- e-'""i) -(- - {e— Pi — e/"?) 2 D„e-««/ = 

 ü " ' 1 ■ </+i 



= -(e-P'i — eP'J)^Dne-"''i-\--ePi:Z'D„e-"'9 + -e-P9 2D„e'"«l, ..(195) 

 4- o 4 o 4 o 



pour p = ds -f- p', (/ <^ (,', p' <^s; 



rr 77 " 1 TT TT c 



-e-P'!Di^+-e-P1^D,i{e''^'l+e-">''/)+~Dde--P'l-{—{e~Pi—eP'!):SDne-''^l 



TT "^ TT ""1 7T f'~' TT ' J ^ . . \ •* 



= _ (e— ;>? — eP9j v- 1)^^ g-n«? -|- _ eP9 ^ D„ e-"«? -|- - e-Pi 2 D„ e'«? + - D,/ 

 -]• o 4 o J-' o 4 



/" X Sta T) v dx 1 ^ 



\ 'Pg W ' , Z' , = 7 t'/'ï :^ E„ [e"-y £i. {—q{p + ns)] — e-m Ei. {—q{p- ns)} ] — 



o 



1 '^ 



e-Pi 2 E„ [e«s? £■«. {^ (/? — n s)] — e-"'l Ei. [q {p + ns)) ] 



4 1 



1 c n 1 <= 



= ePl21i:,„e-mEi. {q{ns—p)] e-Pi:E E„ em Ei. ((/(o— ?is)),(197) 



4 _c ■' + l/n^ 4 _c 



ƒ 'PS C-^-) a J_ 2 = ~7 ^''^ ^ ^« [^""^ ^*"- (~ ? (^^ + "*)} + ^~'"' ^''- (— ? (P — "^)) ] — 



/ 9 "r "^ 4 o 



o 



1 <^ 

 e- PI 2 Tin \_em Ei. [q (p — lts) ] + e-""? £;. (5 (/? + ns)] J 



1 c 1 c 



= ePI ^Dne-m Ei.[q[ns ~p)] e-Pl :S'Dn(.'"l Ei.[q[p— ns)] , . (198) 



4 — c 4 _c 



xCos.pxdx 7J- c TT <^ n 

 g(*') — r~^ =-e-Pï.^Ert(e-««/ — e»*'/) =-e-/^'/^E„c-'"7 ,pourD>cs; . (199) 



/; 



= - e-Pi 2 E„ (e-"«? — e"«ï) + - Ec e-^P? = — — e-Pi 2 E„ e''«? — , pour /; = es ; . (2 00) 



4 o 4 4 _c -\- \/ n''- . 



■= -e-/'? ^ E„ {er-^'i — e"'i) -f- - (ePi + c-P?) ^ E,, e-m = 

 4' o -4 (i+i 



= - (ePi -\- e-Pi) 2 En e—'"^l ePi È B,, e-"'^i e— w ^ E,, e««? , .... (201) 



4 o 4 o 4. o 



pour p = ds -\- p', d<^c, p' <^s; 



n <^— 1 TT TT c ', 



= - e— P? ^ E„ (e-"s7 — e»s?) + - Ej e-2p? + - (ePi -(- (?-P?) .2" E„ e-m = 



1' o 4 4 (/_|-i f \)ouï p = ds, 



> . (202) 



TT, , . i,„ TT ''— ' 71 ''-' 71 ( ti<S: 



= _ (ePï + e- y?) ^ E„ e- m eP<i2 E„ e-m — - e-Pi2 E„ em Erf ' 



4 o 4 o 4 o 4 



011 Ü„ = D_„, E„ = E_„. 



Page 1 53. oq 



WIS- EN NATUURK. VERH. DER KONINKL. AKADEMIE. DEEL VIII. 



