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Write the numerator as A(denominator) + B(derivative of the denominator)

This type of question, asked 2 times: 4 May 2023 S2, 10 May 2024 S2. All 2 questions below, oldest first.

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  1. Question 1

    4 May 2023 S2

    123
    If ∫4ex−252ex−5dx=Ax+Blog⁡∣2ex−5∣+c\int\frac{4e^x-25}{2e^x-5}dx = Ax+B\log|2e^x-5|+c (where c is a constant of integration) then

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  2. Question 2

    10 May 2024 S2

    111
    ∫5tan⁡xtan⁡x−2 dx=x+alog⁡∣sin⁡x−2cos⁡x∣+c\displaystyle\int\frac{5\tan x}{\tan x - 2}\,dx = x + a\log|\sin x - 2\cos x| + c, then the value of aa is

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