F. Alg.rat.frai't.adt'n.afact.mononicetbinomo. TABLE 22. Lim. et oo 



1) / —. — = T Cosec. pn, 1 > /I > ; Kamus, Cr. 24. 257. — Oettingcr, Cr. 35. 13. 



'/(I ■\-x)xr r > / / ^ ' 



i dx (H-»)<^' 



2) / = ^ ^' » n Cosec. p n Oettingcr, Cr. 38. 162. 



' } {\ -\- xy-''-^^ xb+l> lc-6+2/1 p6;i ' ^ 



3) I \ +'^'^ ~ _f ^ 2' fp + o) — Z' (q) Lindmann, Stockh. llandl. 1850. II. 

 7 (1 + .r)P+'l X ^'^ ^ ^' ^^' 



4) I ' dx = n Cosec. p 7r , /> < 1 ; Dedekind, Cr. 45. 370. 



5H dx =^ Tt Sin. Uq-{-p) TTi.Cosec.qn. Cosec. pn Svanberg, Transf. § 5. 



, ixP—aP-1 x'l dx 1 > » > 



6) / = TT rtP- 1 (Cot. gn—Cot.pn), -^ ' -^ ■ Minding, Taf. II. 



J X X — a 1 > 7 ^ f^ 



(XP X~P 71 P It 



7)1 —dx = — - Tang.' — , 1>;?>0 ; SchliJmilch, Gr. 3. 278. 



r dx i + p 



S)/- — ^ = p n Cosec. p n Oettinger, Cr. 38. 162. 



f x^ dx n bn 



9)/ == —Cosec Euler, Calc. Int. 4. S. 5. 155. 



J l-|-a;« X a a 



f^l'c+b—i dx , n „ an 



'^^) I -^ -> = -1 >■ 7 Cosec. 



J 1—X'> .T" ^ ' »- 



b ' b 



dx ( — 1]9 lb — aVI'' n a n\ 



n)/ ,,,,,..„^.,, . , = ~~- .r J.._.n TZZ:r:Cosec. — 



7.ra+(Hils+i 



Oetinsrer. Cr. 3S. 



(1 +.r*)<:-^+i a-\-bc{b—a)9ll'l'>-9nb''-9+i ' bf 162. 



12)/ — rr, — r, r = (—iYi Cosec-— 



n an 



. , - Cosec. — 

 (l+,r') ' ' b b 



^ f x-P dx n pn 



13) / = Tanq.^-— Cauchv, Sav. Etr. 1827. 599. P. 2. § 5. 



J .ri—x-l X Zq Zq 



. [xP + x~P d X n pn 



14) / ' = - Sec. — V. T. 40. N'. 29. 



J .r? -|- ar— 9 x q 2 q 



, [.I'P — x-Pdx n pn -jr 



15)/ = — Tang.' — Malmsten, Cr. 38. 1, ou faut. 



J x1 — x-<l X q 2q 2 q 



^^)l \~u— ,. , V i -^t^A' = Legendre, Exerc. 4. 109. 



7K (l+.r)"i q-p + l r(p) 



Page 56. 



