16 Jun
2009
16 Jun
'09
3:10 a.m.
integrate((1/sqrt(t+3)+2)*asec(t)/(sqrt(t+1)*(t+2)),t,1,6)=2*%pi^2/15 6 1 / (----------- + 2) asec(t) 2 [ sqrt(t + 3) 2 pi I ------------------------- dt = ----- ] sqrt(t + 1) (t + 2) 15 / 1 (~ two screens into http://www.tweedledum.com/rwg/idents.htm) from a geometrical argument about orthoschemes, but, afaik, no one knows how to get it analytically. Integral_1^inf is empirically 3 pi^2/8. This suggests there may be similar such embarrassments (anyone?), and we're missing a piece of mathematics. Mma 7.0 *is* able to show Re(Integral_-1^1) = 4 pi^2/3. --rwg