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a.
Ta có:
$ \int\limits_{0}^{\frac{\pi}{6}} \frac{\cos x}{6-5\sin x + \sin^{2}x}dx$
$=\int\limits_{0}^{\frac{\pi}{6}} \frac{d(\sin x)}{6-5\sin x + \sin^{2}x}$
$= \int\limits_{0}^{\frac{1}{2}} \frac{dt}{t^2-5t+6}$
$=\int\limits_{0}^{\frac{1}{2}} \frac{dt}{(t-2)(t-3)}$
$=\int\limits_{0}^{\frac{1}{2}}(\frac{dt}{t-3}-\frac{dt}{t-2})$
$=\ln\frac{3-t}{2-t}\left|\begin{array}{l}\frac{1}{2}\\0\end{array}\right.=\ln\frac{10}{9}$
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