Question

设函数f(x)的一个原函数为e的-x次方,则不定积分∫f(lnx)/x dx=

Answer 1

∫ f(x) = e^-x
∫ f(lnx)/x dx,令lnx = t => x = e^t => dx = e^t dt
= ∫ f(t)/e^t * e^t dt
= ∫ f(t) dt
= e^-t + C
= e^(-lnx) + C
= 1/x + C