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Tim Gan Math

2022 A-Level H2 Mathematics

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Question 8Techniques of Integration7 marks
  1. Find $\displaystyle\int{\frac{2x-1}{{{x}^{2}}+2x+1}\,}\mathrm{d}x$.

    [4]

  2. Find the exact value of $\displaystyle\int_{0}^{2}{\frac{\left| 2x-1 \right|}{{{x}^{2}}+2x+1}}\,\mathrm{d}x$.

    [3]

Solution step 1, image 1
Solution step 1, image 2
Solution step 2, image 1
Solution step 2, image 2

Final Answer:

\\(2\\ln|x+1| + \\frac{3}{x+1} + C\\); \\(4\\ln 2 - 2\\ln 3\\)