2025 IGCSE Additional Mathematics February/March 0606/12 Q12

2025 IGCSE Additional Mathematics February/March 0606/12 Q12

7 marks

It is given that \(y=x\mathrm{e}^{3x+2}\).

  1. Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\).[3]
  2. Hence find \(\displaystyle\int x\mathrm{e}^{3x+2}\,\mathrm{d}x\).[4]

Solution:

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Answer:(a) \((1+3x)\mathrm{e}^{3x+2}\) (b) \(\left(\dfrac x3-\dfrac19\right)\mathrm{e}^{3x+2}+C\)

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