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Integral of x f(sin x) using x to pi - x

This type of question, asked 2 times: 10 May 2024 S2, 22 Apr 2025 S1. All 2 questions below, oldest first.

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  1. Question 1

    10 May 2024 S2

    106
    ∫0πxtan⁡xsec⁡x+cos⁡x dx=\displaystyle\int_0^\pi \frac{x\tan x}{\sec x+\cos x}\,dx =

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  2. Question 2

    22 Apr 2025 S1

    128
    ∫π32π3x1+sin⁡x dx=\int_{\frac{\pi}{3}}^{\frac{2\pi}{3}} \frac{x}{1 + \sin x}\text{ }dx=

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