RÉDUCTION D'INTÉGRALES DÉFINIES GÉNÉRALES. 105 



/"(l + 2rCos.3.v+r^y<> Cos. IbArctang. '"^'"■^^ j ^''^•" ^- ^°^- ^ ^ rf^ = 

 ■'o ' l-\-rCos.sx] 52_j_^2 



= 2 -"-' ^ (el + e-9)« [e-P7 + (eri + e-/-?) i- {(1 + r e-7^)4 —1)1 

 = 2—2^ (êV + 6-5)" [(.-P9 _ tf9) + (,pï + Ê-P9) (1 +r.-7»)'.] , p>a, ,>2 „; . (340, 



+ i^+e-'')''ie>"> + e-Pi)^-{(l + re-9^)l'-l]] , p < „, o^^,. ^^^j^ 



oü rf est Ie plus grand iiombre entier contenu dans i (a — p). 



/j ( ^l + rCoi-.sxi g'+:c'- ~ 



= ■2~'-^l{e'> + e-^rie!"!-e-P^)^-{(l+re-l^y'-l} , p<s-a; (348) 



Hl+Zr Cos. . X + r = )1^ Cos. [b.irctang. ''■^'''•^^ _| ^ Sin.^^ ^. S in^pxd^ _ 



== (— 1)« 2-2a-l ^ (^, _ g_5^2a J^-,,, ^ (^_,,, _ gp,j 1 ((1 ^ ,, g-gsji _ 1)1 



= f— l)«2-2=-2„(<,7-e-9)2=[(«-P9+dP7) + («-P7-ePï)(l +re-9'^)'],p>2a,s>4.a;. (349) 



= (—])« 2-2«-l 7r[ê-W(e7— r-9)2«_e(2a-/.)9 ^ (—!)"[ ~ "]e-2''V- /p-2u)9 4 (_1). p \^n,, ^ 



+ (c9_e-'/)2«(e-p,_<s.,)^|(l + ^g-,,3t_j|] ,;,< 3a, 2p<.,;, entier; (350) 



= (- 1 ," 2-2.2-1 ,r[e-/'7(c9— É-9)2a_e(2a-p)9 V ( — l)'Y~"\e-2"9— e'/'-2<'}9 J (_ 1)"[ ^'^]eam/^ 

 + (c7_e-9)2«(e-py_fP7)-{(l + ^e-7.)4_ij] ,;.<2a,2/><.,pfraclionnaire; . . (351) 



= (- 1)« 2-2"-' TT [_ -ir ((l _ e-2pv)(l _ e-27)2a — 1 j + 



+ («'/_e-?)2aL-P9 + (e-P7_eP9)l[(l +r<r-7»)''— 1- i ,■ e-7'l]l , p = «_2 



r ' 2/)>s>4a; 



= r_ l)"2-2«-27rlir + (e7 — e-9j2a|(g-p;^,,,„/)^(^_,„/_^;,,^,.l^^^_^,j4jj _ _ _ ^352; 



2H 



«IS- K.N ^ATL'UIIK. VEnll. I/ER KONmKL. AKADEMIE, DEEL V. 



