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Linear expression over the square root of a quadratic: numerator = A(derivative of the quadratic) + B

This type of question, asked 2 times: 11 May 2023 S2, 10 May 2024 S1. All 2 questions below, oldest first.

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  1. Question 1

    11 May 2023 S2

    136
    ∫2x+57−6x−x2 dx=A7−6x−x2+Bsin⁡−1(x+34)+c\int\frac{2x+5}{\sqrt{7-6x-x^2}}\,dx = A\sqrt{7-6x-x^2}+B\sin^{-1}\left(\frac{x+3}{4}\right)+c (where c is a constant of integration) then the value of A+B is

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  2. Question 2

    10 May 2024 S1

    112
    ∫x−7x2−16x+63 dx=Ax2−16x+63+log⁡∣(x−8)+x2−16x+63∣+c\int\frac{x-7}{\sqrt{x^2-16x+63}}\,dx=A\sqrt{x^2-16x+63}+\log|(x-8)+\sqrt{x^2-16x+63}|+c. Value of A is

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