changing variables x=tan(t), d ==== %pi n \ j j 2 %pi j n ----- > (- 1) psi (-) sin(---------) d / 1 d d / ==== [ 2 2 j = 1 I t tan (t) dt = ----------------------------------- ] 2 / d 0 %pi n %pi n sec(-----) %pi n tan(-----) d d %pi n (2 log(----------) - ----------------) 3 3 2 d %pi n - -------------------------------------------- - -------. d 3 3 d It is peculiar to have an integral formula (actually infinitely many formulae) for a dense set but not the whole interval. With n=1, d=4, %pi --- 4 / 3 2 [ 2 2 %pi log(2) %pi %pi I t tan (t) dt = ---------- - ---- + ---- - %catalan ] 4 192 16 / 0 ~ .0837901790902. With d = 4 n, the sum term provides an infinite sequence of trigamma formulae for -(Catalan's constant). --rwg PS, I have Maple V. Rob Corless reports that Maple 9(!) can do atan^2, but in terms not obviously real. Hell, anything called Maple 9 ought to be able to prove the Riemann Hypothesis.