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Integral of log(1 + tan x) from 0 to pi/4 by the property x to pi/4 - x

This type of question, asked 4 times: 10 May 2023 S2, 11 May 2023 S2, 14 May 2026 S2, 19 May 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    10 May 2023 S2

    107
    ∫0π/4log⁡ ⁣(sin⁡x+cos⁡xcos⁡x)dx=\int_0^{\pi/4} \log\!\left(\frac{\sin x + \cos x}{\cos x}\right)dx =

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  2. Question 2

    11 May 2023 S2

    115
    If I=∫0π/4log⁡(1+tan⁡x) dxI = \int_0^{\pi/4}\log(1+\tan x)\,dx, then value of I is

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  3. Question 3

    14 May 2026 S2

    84
    ∫0π/4log⁡(1+tan⁡x) dx=…\displaystyle\int_0^{\pi/4}\log(1 + \tan x)\,dx = \ldots

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  4. Question 4

    19 May 2026 S2

    81
    If ∫0πlog⁡(sin⁡x) dx=k\int_0^\pi \log(\sin x)\,dx = k, then the value of ∫0π4log⁡(1+tan⁡x) dx\int_0^{\frac{\pi}{4}}\log(1 + \tan x)\,dx in terms of kk is...

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