<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Express \(\frac{-x^2 + 2x - 2}{(1-x)(x^2 - 3x + 1)}\) in partial fractions.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Differentiate \(\ln(x^2 - 3x + 1)\) with respect to \(x\).</span></div></li><li><div class="list-item-paragraph">Using your results in part <strong>(a)</strong> and <strong>(b)</strong>, find \(\displaystyle\int \frac{\frac{1}{2}x^2 - x + 1}{(1-x)(x^2 - 3x + 1)} \, \mathrm{d}x\).</div></li></ol>

Express \(\frac{-x^2 + 2x - 2}{(1-x)(x^2 - 3x + 1)}\) in partial fractions.

Differentiate \(\ln(x^2 - 3x + 1)\) with respect to \(x\).

Using your results in part (a) and (b), find \(\displaystyle \int \frac{\frac{1}{2}x^2 - x + 1}{(1-x)(x^2 - 3x + 1)} \, \mathrm{d}x\).

Using your results in part **(a)** and **(b)**, find \(\displaystyle\displaystyle \int \frac{\frac{1}{2}x^2 - x + 1}{(1-x)(x^2 - 3x + 1)} \, \mathrm{d}x\).

Integration Techniques

Question ef5e7118