(a)[4]
With the substitution $u = 2 - \sqrt{x}$, demonstrate that $I = \int_{1}^{2} \frac{2(2 - u)^2}{u}\,du$.
(b)[4]
Hence deduce that $I = 8\ln 2 - 5$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Define $I = \int_{0}^{1} \frac{\sqrt{x}}{2 - \sqrt{x}}\,dx$.