Ta có:
$\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{3}}\dfrac{\cos x}{1+2\sin x}dx$
$=\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{3}}\dfrac{d(\sin x)}{1+2\sin x}$
$=\dfrac{1}{2}\ln(1+2\sin x)\left|\begin{array}{l}\dfrac{\pi}{3}\\\dfrac{\pi}{6}\end{array}\right.=\dfrac{1}{2}\ln\dfrac{1+\sqrt3}{2}$