Question

F(x)等于xF(t)在[0,X ]上的定积分,求F(x)导数

Answer 1

F(x)/x=∫(0,x)F(x)dx两边对x求导,得 [xf(x)-F(x)]/x^2=F(x),即xf(x)=(x^2+1)F(x),设F(x)=y,f(x)=y',则y'/y=(x^2+1)/x=x+1/x两边求积分,lny=1/2*x^2+lnx, 即y=x*e^[(x^2)/2]+C, y'=f(x)=(x^2+1)*e^[(x^2)/2]...