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Integral of e^x (x - 1)/(x + 1)^3

The same question, asked 4 times: 3 May 2023 S1, 9 May 2023 S1, 13 May 2024 S2*, 20 Apr 2025 S2. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    3 May 2023 S1

    145
    The value of ∫(x−1)ex(x+1)3 dx\int\frac{(x-1)e^x}{(x+1)^3}\,dx is equal to

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  2. Question 2

    9 May 2023 S1

    139
    The value of I=∫(x−1)ex(x+1)3 dxI=\int\frac{(x-1)e^x}{(x+1)^3}\,dx is

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  3. Question 3

    13 May 2024 S2

    134
    ∫x−3(x−1)3ex dx=\int\frac{x-3}{(x-1)^3}e^x\,dx=

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  4. Question 4

    20 Apr 2025 S2

    132
    ∫ex(x−1)(x+1)3 dx=\int e^{x}\frac{(x- 1)}{(x+ 1)^{3}}\text{ }dx=

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