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f is given at an expression like (x - a)/(x - b): find f(x), then integrate it

This type of question, asked 2 times: 3 May 2023 S2, 16 Apr 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    3 May 2023 S2

    124
    If f ⁣(x−4x−2)=2x+1,  x∈R−{1,−2}f\!\left(\frac{x-4}{x-2}\right)=2x+1,\;x\in\mathbb{R}-\{1,-2\}, then ∫f(x) dx\int f(x)\,dx is equal to

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  2. Question 2

    16 Apr 2026 S2

    68
    If f(x−1x+1)=x+1f\left(\dfrac{x - 1}{x + 1}\right) = x + 1, then ∫f(x) dx=⋯\displaystyle\int f(x)\,dx = \cdots

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