<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text"></span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Express \(1+4x\) in the form \(A(2x-2)+B\), where&nbsp;\(A\) and \(B\) are constants to be determined.</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Hence, find \(\int \frac{1+4x}{x^2-2x+5} \, \mathrm{d}x\)<span class="inline-marks">[4]</span></div></li></ol></li><li><div class="list-item-paragraph">Find the exact value of \(\int_{0}^{\frac{\pi}{3}} x \sin 2x \, \mathrm{d}x\)<span class="inline-marks">[3]</span></div></li></ol>

Express \(1+4x\) in the form \(A(2x-2)+B\), where \(A\) and \(B\) are constants to be determined.

Hence, find \[\displaystyle \int \frac{1+4x}{x^2-2x+5} \, \mathrm{d}x\]

Find the exact value of \[\displaystyle \int_{0}^{\frac{\pi}{3}} x \sin 2x \, \mathrm{d}x\]

Find the exact value of \(\displaystyle \int_{0}^{\frac{\pi}{3}} x \sin 2x \, \mathrm{d}x\)

2025 VJC P1 Q10

2025 VJC P1 Q10