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2026 NYGH P2 Q9

2026 NYGH P2 Q9

IP 4
8 marks

Let \(\mathrm{f}(x)=\dfrac{10x-2}{(3x+1)(x-1)^2}\).

  1. Express \(\mathrm{f}(x)\) in partial fractions.[4]
  2. Hence, find the value of \(\displaystyle\int_2^4\mathrm{f}(x)\,\mathrm{d}x\), giving your answer in the form \(b+\ln a\), where \(a\) and \(b\) are rational numbers.[4]

Solution:

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Answer:(a) \(-\dfrac3{3x+1}+\dfrac1{x-1}+\dfrac2{(x-1)^2}\) (b) \(\dfrac43+\ln\dfrac{21}{13}\)

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