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Integral of sqrt(tan x) + sqrt(cot x)

This type of question, asked 2 times: 9 May 2024 S2, 15 May 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    9 May 2024 S2

    131
    ∫(tan⁡x+cot⁡x)dx=\int\left(\sqrt{\tan x} + \sqrt{\cot x}\right)dx =

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  2. Question 2

    15 May 2026 S2

    79
    If ∫(tan⁡x+cot⁡x) dx=atan⁡−1(tan⁡x−1btan⁡x)+c\int(\sqrt{\tan x} + \sqrt{\cot x})\, dx = a\tan^{-1}\left(\dfrac{\tan x - 1}{\sqrt{b\tan x}}\right) + c, for x∈(0,π2)x \in \left(0, \dfrac{\pi}{2}\right), then a10+b5=⋯a^{10} + b^5 = \cdots

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