2025 DSS PRELIMS P1 Q4

2025 DSS PRELIMS P1 Q4

Secondary 4

8 marks

Express \(\frac{x^2+3x+2}{x^2(2x+1)}\) in partial fractions.[5]
Hence integrate \(\frac{x^2+3x+2}{x^2(2x+1)}\) with respect to \(x\).[3]

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Answer:(a) \(\displaystyle -\frac{1}{x}+\frac{2}{x^2}+\frac{3}{2x+1}\) (b) \(\displaystyle -\ln|x|-\frac{2}{x}+\frac{3}{2}\ln|2x+1|+C\)

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