Question

若e^(-x)是f(x)的原函数,则∫x^2f(lnx)dx=?

Answer 1

简单计算一下即可，答案如图所示

Answer 2

Sf(x)dx = e^(-x) + C, C为任意常数.

f(x) = -e^(-x),
f[ln(x)] = -e^[-ln(x)] = -1/x.

Sx^2f[ln(x)]dx = Sx^2(-1/x)dx = -Sxdx = -x^2 + c,
其中,c为任意常数.

楼主威武.应该是-e^[-ln(x)].