>>19
xy=u とおくと 0≦u≦1 で dxdy=-log(u)du,
u^u = exp(u･log(u)) より
(d/du)(u^u) = (u^u){log(u)+1}.
(左辺) - (右辺) = -∫_[0,1] (u^u){log(u)+1}du = [ -u^u ](u:0〜1) = 0.
∵　u→0 のとき u･log(u)→0, u^u→1.