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$\int\limits\frac{dx}{\sqrt{(x-\frac{5}{2})^2-(\frac{1}{2})^2}}=-\int\limits\frac{dx}{\sqrt{(\frac{1}{2})^2-(x-\frac{5}{2})^2}}$
Đặt $x-\frac{5}{2}=\frac{1}{2}sint\Rightarrow t=arcsin(2x-5)$
$\Rightarrow \left\{ \begin{array}{l} dx=\frac{1}{2}cost.dt\\ \sqrt{(\frac{1}{2})^2-(x-\frac{5}{2})^2}=\frac{1}{2} cost\end{array} \right.$
$\Rightarrow -\int\limits dt=-t+C=-arcsin(2x-5)+C$
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