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Mathematics Question on Some Properties of Definite Integrals

The value of ∫π3π2(2+3sin⁡x)sin⁡x(1+cos⁡x)dx\int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2+3 \sin x)}{\sin x(1+\cos x)} d x is equal to

A

72−3−log⁡e3\frac{7}{2}-\sqrt{3}-\log _e \sqrt{3}

B

103−3−log⁡e3\frac{10}{3}-\sqrt{3}-\log _e \sqrt{3}

C

103−3+log⁡e3\frac{10}{3}-\sqrt{3}+\log _e \sqrt{3}

D

−2+33+log⁡e3-2+3 \sqrt{3}+\log _e \sqrt{3}

Answer

103−3−log⁡e3\frac{10}{3}-\sqrt{3}-\log _e \sqrt{3}

Explanation

Solution

The correct option is (B) : 103−3−log⁡e3\frac{10}{3}-\sqrt{3}-\log _e \sqrt{3}