On page 188, How did they get the following equation by lemma 10.2.3?

$I = -A_{1} \int_{3}^{x} \frac{dt}{t} + (A_{1}log(x)+A_{1}+A_{2})\int_{3}^{x} \frac{dt}{t(1+log(x)-log(t)} + O(\frac{1}{x^{1/4}})$

I have been stuck on this for a long while. Any help is appreciated. :)