∵[∫(0,x) f(t)]' = f(x)[∫(0,x) xf(t) dt]' = [x∫(0,x) f(t) dt]'= x * [∫(0,x) f(t) dt]' + (x)' * ∫(0,x) f(t) dt= x * f(x) + 1 * ∫(0,x) f(t) dt= xf(x) + ∫(0,x) f(t) dt