9709 P32 - Jun 2012 - Q8
2110
Let \(I = \int_{2}^{5} \frac{5}{x + \sqrt{6-x}} \, dx\).
(i) Using the substitution \(u = \sqrt{6-x}\), show that \(I = \int_{1}^{2} \frac{10u}{(3-u)(2+u)} \, du\).
(ii) Hence show that \(I = 2 \ln\left(\frac{9}{2}\right)\).
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