The value of $\int_\limits{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2+3 \sin x)}{\sin x(1+\cos x)} d x$ is equal to :

Question

$\frac{10}{3}-\sqrt{3}+\log _{e} \sqrt{3}$

$\frac{7}{2}-\sqrt{3}-\log _{e} \sqrt{3}$

$\frac{10}{3}-\sqrt{3}-\log _{e} \sqrt{3}$

$-2+3\sqrt{3}+\log _{e} \sqrt{3}$

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