I'm currently stuck on the following problem: Using a change of variables but without evaulating the integral, show that:

$\displaystyle \int_{1}^{\infty}\frac{lnx}{x^2 } dx = - \int_{0}^{1}lnx dx$

I've tried all sorts of substituions (lnx, lnx/x, lnx/x^2, 1/x^2) but nothing seems to give the desired result. Could somebody please give me a hint?

Many Thanks