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Integral of (2x + 4) sqrt(x - 1) = a(x - 1)^(5/2) + b(x - 1)^(3/2): find a combination of a and b

The same question, asked 2 times: 3 May 2023 S1*, 10 May 2023 S1. Every wording below, oldest first.

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  1. Question 1

    3 May 2023 S1

    123
    If ∫(2x+4)x−1 dx=a(x−1)5/2+b(x−1)3/2+c\int(2x+4)\sqrt{x-1}\,dx=a(x-1)^{5/2}+b(x-1)^{3/2}+c where cc is a constant of integration, then the value of (2a+b)(2a+b) is

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  2. Question 2

    10 May 2023 S1

    124
    If ∫(2x+4)x−1 dx=a(x−1)5/2+b(x−1)3/2+c\int(2x+4)\sqrt{x-1}\,dx=a(x-1)^{5/2}+b(x-1)^{3/2}+c (where c is a constant of integration), then the value of a+ba+b is

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