2025 4E5N AM BDS P2 Q4
2025 4E5N AM BDS P2 Q4
Secondary 4
10 marks
- Factorise completely \(x^3+64\).[2]
- Hence, express \(\dfrac{3x^2}{x^3+64}\) in partial fractions.[5]
- Using the results in part (a), or otherwise, find[3]\[\int \dfrac{2x^3+3x^2+128}{x^3+64}\, dx .\]
Solution:
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Answer:\((a)(i)\ x^3+64=(x+4)(x^2-4x+16)\) \((a)(ii)\ \dfrac{3x^2}{x^3+64}=\dfrac{1}{x+4}+\dfrac{2x-4}{x^2-4x+16}\) \((b)\ 2x+\ln|x+4|+\ln(x^2-4x+16)+C\)
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