设函数f(x) 在[1, 正无穷大]内有连续倒数∫[1,x]xf(t)dt=∫[1,x](t-x)f(t)dt,f(1)

设当x>0时,函数f(x)连续且满足f(x)=x+∫(1,x)1/xf(t)dt,求f(x) 设f(x)=∫(1,x^2) e^(-t)/t dt,求∫(0,1)xf（x）dt 若f(x) 连续,∫[0,1]xf(t)dt=f(x)+xe^x,求f(x) 证明：设f(x)在(-∞,+∞)连续,则函数F(x)=∫(0,1)f(x+t)dt可导,并求F'(x) @问几个高数题,1设函数f(x)连续,f(0)不等于0.求lim｛[∫（x-t）f(t)dt]｝／｛[x∫f(x-t)d 设函数f(x)在[0,正无穷)上连续,单调不减且f(0)>=0,试证 F(x)=1/x*∫（0到x）t^n*f(t)dt 设f(x)在区间【0,1】上有连续导数,证明x∈【0,1】,有|f(x)|≤∫(|f(t)|+|f′(t)|)dt 设f(x)连续 则d∫(0,2x)xf(t)dt/dx=? 设函数f(x)在区间[0,1]上连续,证明∫[∫f(t)dt]dx=∫(1-x)f(x)dx ①设f(x)=x+2∫(0,1)f(t)dt,求f(x). 设函数f(x)在区间[a,b]上连续,则lim(x->a)∫(a->x)f(t)dt=____,lim(x->a)1/( f(x)连续且f(x)=x+(x^2)∫ (0,1)f(t)dt,求f(x)