Logarithmic integral from algebraic division
Logarithmic integral from algebraic division
Secondary 4
8 marks
Original parallel to supplied A Math integration references
- Express \(\dfrac{8x}{2x+3}\) in the form \(a+\dfrac{b}{2x+3}\), where \(a\) and \(b\) are integers.[2]
- Differentiate \(4x\ln(2x+3)\) with respect to \(x\).[2]
- Hence evaluate the exact value of \(\displaystyle\int_0^1\ln(2x+3)\,\mathrm{d}x\).[4]
Solution:
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Answer:\(\dfrac52\ln5-\dfrac32\ln3-1\)
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