高数积分题目求教 求导：积分上限是x,下限是0,t f（x^2－t^2）dt

Answer 1

令x²-t²=u²,则两边微分：-tdt=udu,u：x²-->0
∫[0-->x] tf(x²-t²)dt
=-∫[x-->0] uf(u²)du
=∫[0-->x] uf(u²)du
求导后为：xf(x²)