F. Alg. rat. fract. 

 Circ. Dir. TABLE 431 suite. Lira. et oc. 



Circ. Inv. 



f fx\ X 1 1 ('•'• 



7) j Ardg.i-lCos.px -——; dx ^ — -^e-P? (A + i(3p7)} — -7reP?£i.(— Sp^) \ 



8)Ji..an,. [^A^ ~'—,d^ = ^^^(1 + .-^) ,P^<lA 



/■ / l\a? le?4-l f 



^)\Arclang. Tang.-x\ -— -dx = ~nl > Schlomilch, Stad. II. 18. 



/I \ \ X \ en 

 Arcianq. lCot.-£u\ -„ dx = -it I 

 I ^ jx^ -^q^ 2 el— I 



Arctanq. ~ ' - -„ \ dx = -U\ + pe-l"-) Boncompagni, Cr. 25. 74; ou il y a faut. qdx. 



F. Alg. irrat. fract. a d^n. binome. 



Circ. Dir. TABLEl 432. Lim. et oo . 



Circ. Inv. 



f „. ( I a Sin. ex \"| x 1 1 , 



■[)jSin. IqArctgA—--— U.(l + 2aCo5.ca;+a^)i?-— --d.r=-7r(l+ae-^P)?--7r 1 



J I \l-[-atos.cx j) p^-\-x^ 2 iJ I 



», / ^ ) , I a Sin. ex \) , dx n 



Z)\Cos.\qArctg.\-—- ^ .(l + 2aCos.c^+a=)k----^ = -~(l + ae-cp)9 



J ' \l-\-aCos.cx j) p^-\-x^ Up 



S^fst i A ( "•^^"•'^^ \\ {l + ZaCos.cx-\-a-^)i'i + {].-{.2aCos.cx-\-a^)-i9 



p^+, 



xdji =1 



-TT f (1 + a e—'^P)l — (1 -f a e-<^P)-7} I Boncompagni, 

 2 \Cr. 25. 74; 



ou 3,4, 5 sont 



4) I Sin. [qArctg. I -^^""" \ 1 a + 2ago^-^.^+«-;^^-(l + ga^o^-c.+a^)-l.^^^ ^/ ,,„,;^; 

 7 r \l + aCo5.c.rj) p» + ar* 



--= -TT ((l + ae-«P)?-}-(l +ae-V)-?— 2}| 



,, /"- f , / aSin.cx \ ) (l + 2aCos.c:»+a=')i?+(l + 2aCos.c^ + aM-i? , ] 



Page 555. 



== ^((l + ae-<'P}? + (l + ae-cpj-?} I 



