2024 ACS(BR) P1 Q6

2024 ACS(BR) P1 Q6

Secondary 4
8 marks
  1. Express \(\dfrac{13x-6}{x^2(2x-3)}\) in partial fractions.[5]
  2. Hence \(\displaystyle\int\dfrac{13x-6}{x^2(2x-3)}\,\mathrm{d}x\).[3]

Solution:

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Answer:(a) \(-\dfrac3x+\dfrac2{x^2}+\dfrac6{2x-3}\). (b) \(-3\ln|x|-\dfrac2x+3\ln|2x-3|+C\).

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