e^-x是f(x)的原函数,则x^2f(inx)的不定积分

Question

如题所述

Answer 1

f(x)=-e^(-x)
f(lnx)=-e^(-lnx)=-1/x
∫x^2f(lnx)dx
=∫x^2(-1/x)dx
=-∫xdx
=-x^2/2+C