<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Express \(\frac{4x}{2x+1}\) in the form \(a + \frac{b}{2x+1}\), where \(a\) and \(b\) are integers.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Differentiate \(2x \ln(2x+1)\) with respect to \(x\).</span></div></li><li><div class="list-item-paragraph">Using the results in part <strong>(a)</strong> and part <strong>(b)</strong>, determine \(\displaystyle\int \ln(2x+1) \, \mathrm{d}x\).</div></li></ol>

Express \(\frac{4x}{2x+1}\) in the form \(a + \frac{b}{2x+1}\), where \(a\) and \(b\) are integers.

Differentiate \(2x \ln(2x+1)\) with respect to \(x\).

Using the results in part (a) and part (b), determine \(\displaystyle \displaystyle\int \ln(2x+1) \, \mathrm{d}x\).

Using the results in part **(a)** and part **(b)**, determine \(\displaystyle\displaystyle \displaystyle\int \ln(2x+1) \, \mathrm{d}x\).

Integration Techniques

Question 0ae41c04