Integral of f(x)/(f(x) + f(a + b - x)) equals (b - a)/2

This type of question, asked 8 times: 2 May 2023 S2, 15 May 2023 S2, 20 Apr 2025 S2, 21 Apr 2025 S1, 23 Apr 2025 S1, 25 Apr 2025 S1, 26 Apr 2025 S2, 15 May 2026 S2. All 8 questions below, oldest first.

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Question 1
2 May 2023 S2
114 $I = \displaystyle\int_{\sqrt{\log_e 2}}^{\sqrt{\log_e 3}} \frac{x\sin(x^2)}{\sin(x^2)+\sin(\log_e 6 - x^2)}\,dx$
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Question 2
15 May 2023 S2
134 $\int_0^{\pi/2} \frac{\cot x}{\cot x+\tan x}\,dx$
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Question 3
20 Apr 2025 S2
125 $\int_{0}^{\frac{\pi}{2}} \frac{dx}{1 + (\cot x)^{101}}=$
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Question 4
21 Apr 2025 S1
113 $\int_{2}^{4} \frac{\log x^{2}}{\log x^{2}+ \log\left( 36 - 12x+x^{2} \right)}dx$
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Question 5
23 Apr 2025 S1
122 $\int_{3}^{5} \frac{\sqrt{x}\text{ }dx}{\sqrt{8 -x}+\sqrt{x}}=$
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Question 6
25 Apr 2025 S1
108 $\int_{1}^{3} \frac{\log x^{2}}{\log\left( 16x^{2}- 8x^{3}+x^{4} \right)}dx=$
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Question 7
26 Apr 2025 S2
110 $\int_{0}^{\frac{\pi}{2}} \frac{300\sin x+ 100\cos x}{\sin x+ \cos x}\text{ }dx= \ldots$
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Question 8
15 May 2026 S2
82 $\displaystyle\int_{\pi/5}^{3\pi/10}\dfrac{1}{1 + \sqrt{\tan x}}\, dx = \cdots$
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Integral of f(x)/(f(x) + f(a + b - x)) equals (b - a)/2

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