2025 EJC Promo Q11

2025 EJC Promo Q11

Junior College 1
9 marks
  1. Find \(\displaystyle \int \frac{e^{\sqrt{x-1}}}{\sqrt{x-1}}\, dx\).[2]
  2. Find \(\displaystyle \int \frac{1}{4x^2+4x+17}\, dx\).[3]
  3. Use the substitution \(u=\sqrt{2x+1}\) to find \(\displaystyle \int x\sqrt{2x+1}\, dx\).[4]

Solution:

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Answer:(a) \(2e^{\sqrt{x-1}}+C\) (b) \(\dfrac18\tan^{-1}\left(\dfrac{2x+1}{4}\right)+C\) (c) \(\dfrac{(2x+1)^{5/2}}{10}-\dfrac{(2x+1)^{3/2}}6+C\)

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