N2021 P2 Q5

N2021 P2 Q5

Junior College 2
11 marks
  1. Find \(\displaystyle\int\tan^2 5x\,\mathrm dx\).[2]
  2. Find \(\displaystyle\int_0^b\sin2x\sin3x\,\mathrm dx\).[3]
  3. Find \(\displaystyle\int_a^b\dfrac1{x\ln x}\,\mathrm dx\), where \(1<a<b\).[3]
  4. Use the substitution \(u=1+\mathrm e^{2x}\) to find \(\displaystyle\int\dfrac{\mathrm e^{2x}}{(1+\mathrm e^{2x})^3}\,\mathrm dx\).[3]

Solution:

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Finding similar questions...
Answer:(a) \(\frac15\tan5x-x+C\); (b) \(\frac12\sin b-\frac1{10}\sin5b\); (c) \(\ln(\ln b/\ln a)\); (d) \(-\frac1{4(1+\mathrm e^{2x})^2}+C\).

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