三、(本题20分)设f(x)是 [ 0,+infty ) 上非负可导函数, (0)=0, '(x)leqslant dfrac (1)(2),-|||-假设 (int )_(0)^+infty f(x)dx 收敛.求证:对任意 gt 1, (int )_(0)^+infty (f)^alpha (x)dx 也收敛,并且-|||-(int )_(0)^+infty (f)^x(x)dxleqslant (({int )_(0)^+infty f(x)dx)}^beta . =dfrac (alpha +1)(2).