设f连续可微,求d∫(x-t)f'(t)dt/dx

Question

设f连续可微,求d∫(x-t)f'(t)dt/dx

Answer 1

d∫(x-t)f'(t)dt/dx 是不是有积分上限为x 积分下限为0,否则不能做!
=d∫xf'(t)dt/dx-d∫tf'(t)dt/dx
=d（x∫f'(t)dt）/dx-xf'(x)
=∫f'(t)dt+xf'(x)-xf'(x)
=∫f'(t)dt
=f(t)+c