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Definite integral by partial fractions

This type of question, asked 3 times: 15 May 2023 S2, 22 Apr 2025 S2, 13 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    15 May 2023 S2

    147
    ∫0π/4sec⁡2x(1+tan⁡x)(2+tan⁡x) dx=\int_0^{\pi/4}\frac{\sec^2 x}{(1+\tan x)(2+\tan x)}\,dx =

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  2. Question 2

    22 Apr 2025 S2

    146
    The value of the integral ∫12xdx(x+2)(x+3)\int_{1}^{2} \frac{xdx}{(x + 2)(x + 3)} is

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  3. Question 3

    13 May 2026 S1

    83
    The value of the integral ∫10201(x−3)(x−2) dx\int_{10}^{20}\dfrac{1}{(x - 3)(x - 2)}\,dx is...

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