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Possible Duplicate:
Bounding the integral $\int_{2}^{x} \frac{\mathrm dt}{\log^{n}{t}}$

So I want to show that $\int_2^x \frac{1}{\log^n(t)}\mathrm dt=O\left(\frac{x}{\log^n(x)}\right)$, and someone suggests that I could split the integral into two parts: $\int_2^{\sqrt{x}} \frac{1}{\log^n(t)}\mathrm dt+\int_{\sqrt{x}}^x \frac{1}{\log^n(t)}\mathrm dt$, and why that immediately produces the right error term $O\left(\frac{x}{\log^n(x)}\right)$?

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    You've seen [this](http://math.stackexchange.com/questions/7793) right?2011-09-24

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