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2024 CJC H1 Q2

2024 CJC H1 Q2

7 marks
  1. Find \(\displaystyle\int (4x-1)^5 - \frac{1}{3-2x} \, \mathrm{d}x\).[3]
  2. Differentiate \(e^{(3x^2-4)}\) with respect to \(x\).
    Hence, find \(\displaystyle\int xe^{(3x^2-4)} \, \mathrm{d}x\).[4]

Solution:

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Answer:(a) \(\frac{(4x-1)^6}{24}+\frac12\ln|3-2x|+C\), \(x\ne\frac32\). (b) Derivative \(6x\mathrm e^{3x^2-4}\); hence integral \(\frac16\mathrm e^{3x^2-4}+C\).

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