F. Alff. rat. fract. a den. a* + a;''. 01.,,,.^ t.,- 1 • .1 . 



Ciic. Dir. on don. rnonome. ^^^'^^^'^ ^'^- ^"^' ^ ^t 00 



J, /' ]____^A±^ ^ _jTj^ Legendre, 



7 Sin. a X (f- -\- x"" e^^'l — I ^rt. 3. N^ 



fSin.bx dx n e*v — e-**? , 



J /Sin: a X q^ -\- x- 2q e<"l — er-'"l I 



Exerc. 4. 133. — Bidotie, M^m. Turin. 1812. 231, 

 39. — Sclilomilch, Btitr. II. § 4. 



Cauchy, Lim. Imag. Add. 33. — Boncompagni, Cr. 25. 74. 

 CCos.hx xdx n e^f -\- e~^l\ 



J Sin. a X q' -\- x- 2 e"'! — , 



■ e-^1 



[Sin. kx xTanq.x \ 



4) / ^ — rfic = J 



j Sin.x p"^ -\-A>x'^ / , i = GO ; Schlomilch, Beitr. II. 4, 



Tang. X. Sin. X \ EUes soiit fautives: au liea de k raettez Z k -{- 1; leurs 



d^ = ^] valeurs sont alors oo. 



fSin. k X 



^) H — . I 



j km. X p + 



fCos.kx xCot.x Meyer. Int. De'f. 221. 



^) \~^- ■r~r A ,2 dx = Q,k = x; Elle est faiitive: mettez 2 k au lieu de A, alors la 



J ' ' va piir pn p.sr. m. 



fCos. k X X 

 7) /— dx = 



= !> 



Schlomilch, Beitr. II. 4, 



fCos.kx dx \ , k = CD 



8) / = 



'J COS.X p2 ^^2 



J Cos.x 



dx It 1 



9), 



q'^ -\- x"^ q el -\- e—fj 



/* 1 dx n \ 



10)/ = Schlomilch, Beitr. II. § 4. 



/ Cos. ax x^ -\- q"^ q e^t -\- e-'"i 



(Sin. bx X 



11)/- dx 



J Cos. ax «' -\- q"^ 



/Cos. b X 

 . 

 Cos. ax x^ 



1 e'>9 — e-^1 

 — n 



2 e'^i -X- e— o?! 

 ■^ ', Cauchy, Lim. Imag. Add. 33. — Boncompagni, 



dx n e*? -f e-*9 ' ^'■- ^^' ''*• 



.2 _L «2 



+ </' 2 gr e"? + e— «« 



(e4«V'2J_e-^a^.2)(;os.(— Vl-fe*"^ '^-e-i'^V'i)Sin.{-~\ \ 



13) f— L_ ^^^ _ ^ ^ \v/2/ __\^1U Cauchy, Sav, 



14) / —7 = TT aS«H. 



J Sin. ax 1 -f- ar* \^/ 



2/ e^V^ 2 ^. e-al/2 _ 2 Cos. (a »/ 2) 



Page 299. 38* 



