# Big-O Notation, integration, proof

Can anyone figure out how to prove that the $$\int_{\sqrt x}^x \frac{1}{\log^2(t)} dt = O\left(\frac{x}{\log^2(x)}\right)$$

• Your RHS cannot depend on t – phaedo Nov 2 '18 at 0:53

HINT: use $$(1/\log x)' = -1/(x\log^2 x)$$ to "solve" the integral, then have a look at LogIntegral