138 



Si in (1) per partes integraverimus, obtinebimus 



/_ 



J s 



2 



a. 



o 



x'dx 211(a) 7r 2 ^ , aT ,, x 



c^— = — — — — Cot — (4) 



Sin 2 a.r a 4a 2 7 



7S 



Jm 



ISmaxdx — ^ lSin~ — a H(a) (5). 



Ex aequatione (5) sequitur, ut sit 



J. V ^l) = f/2, . . , (3*1 



quia est*) 



j ISmxdz == § /f . 







Quum vero sit 

 invenimus esse 



Sinax V2/ v 7 ^ y 



Haec transcendens , postquam inventum est, quomodo cum H(a) con- 

 juncta sit ab eaque pendeat, posthac brevitatis caussa per L(a) denotetur. 



Transformationibns quibusdam factis prodit 



I xdx ■ jL/Cotf (i-f) + (^gYz(l-|)— iz(l) .... (ft 



<{Cosax 2a 2 4V ^^\2aJ K i} a 2 W W 

 Si in formula (6) posuenmus pro a, .r resp. _, — et in formula 



(7) pro a, .r resp. — , — , sine ullo negotio inveniemus has formulas generates 



[a/3 intra limites o et + 7r] , 



= JLlCom + C-^h*L{i - ?#) - i- Z(l) . . (9) 



/Cos^ 2/3 2 u 27 T ^ Ti 8 > 1 T y /3 2 w w 



[ct/3 intra limites o et + f] . 



*) Vide Gruncrt, Archiv d. Math. Tom. IY pag. 120. 



