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Integral of sqrt(tan x)/(sin x cos x)

The same question, asked 2 times: May 2022 S1, 26 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    May 2022 S1

    108
    If f(x)=tan⁡xf(x) = \sqrt{\tan x} and g(x)=sin⁡x⋅cos⁡xg(x) = \sin x \cdot \cos x then ∫f(x)g(x) dx\int \dfrac{f(x)}{g(x)}\,dx is equal to (where C is a constant of integration)

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  2. Question 2

    26 Apr 2025 S1

    147
    ∫tan⁡xsin⁡x⋅cos⁡x dx=\displaystyle\int\dfrac{\sqrt{\tan x}}{\sin x\cdot \cos x}\,dx=

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