Product derivative for a shifted logarithm
Product derivative for a shifted logarithm
Secondary 4
8 marks
Original parallel to supplied A Math integration references
- Express \(\dfrac{3x}{3x+1}\) in the form \(a+\dfrac{b}{3x+1}\), where \(a\) and \(b\) are integers.[1]
- Differentiate \(x\ln(3x+1)\) with respect to \(x\).[2]
- Hence evaluate the exact value of \(\displaystyle\int_0^1\ln(3x+1)\,\mathrm{d}x\).[5]
Solution:
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Answer:\(\dfrac83\ln2-1\)
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