2025 DHS Promo Q4

2025 DHS Promo Q4

Junior College 1
7 marks
  1. Find \(\int (\cos^{-1} 3x)\frac{x}{\sqrt{1-9x^2}}\, dx\).[3]
  2. Find \(\int \frac{x+1}{x^2-4x+7}\, dx\).[4]

Solution:

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Answer:(a) (-\dfrac19(\cos^{-1}3x)\sqrt{1-9x^2}-\dfrac{x}{3}+C) (b) (\dfrac12\ln(x^2-4x+7)+\sqrt3\tan^{-1}\left(\dfrac{x-2}{\sqrt3}\right)+C)

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