f(x)=e^-x,则∫f'(lnx)/xdx等于?,
问题描述：
f(x)=e^-x,则∫f'(lnx)/xdx等于?,
答
f‘（lnx）= -e^-lnx=-1/x
带入不定积分，于是有∫-1/(x*x)dx=1/x +C
答
f '(x)=-e^(-x)
所以f '(lnx)=-e^(-lnx)=-1/[e^(lnx)]=-1/x
故∫f'(lnx)/xdx
=∫-1/x²dx
=1/x +C