<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find \(\int \frac{9x}{(2x - 1)(x + 1)^2} \, \mathrm{d}x\).</span><span class="inline-marks">[4]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Perform the following differentiations:</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Differentiate \(\frac{1}{x^2 + 1}\) with respect to \(x\).</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Differentiate \(\ln \sqrt{x^2 + 1}\) with respect to \(x\).</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence find \(\int \frac{x \ln \sqrt{x^2 + 1}}{(x^2 + 1)^2} \, \mathrm{d}x\).</span><span class="inline-marks">[4]</span></div></li></ol></li></ol>

Find \(\displaystyle \int \frac{9x}{(2x - 1)(x + 1)^2} \, \mathrm{d}x\).

Differentiate \(\frac{1}{x^2 + 1}\) with respect to \(x\).

Differentiate \(\ln \sqrt{x^2 + 1}\) with respect to \(x\).

Hence find \(\displaystyle \int \frac{x \ln \sqrt{x^2 + 1}}{(x^2 + 1)^2} \, \mathrm{d}x\).

2025 RI P1 Q4

2025 RI P1 Q4