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