_MATH1013_1ABCD_2025 Subsection 5.2 (closed on 15 Nov)

Compute [math: ∫π22tan−1⁡3−3−7cot⁡x1+sin⁡x dx]\displaystyle \int _{\frac {\pi }{2}}^{2\tan ^{-1}{3}}{\frac {-3-7\cot {x}}{1+\sin {x}} dx}. (Correct the answer to 2 decimal places.)