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Determine the exact value of the integral $\int_{\pi}^{\frac{3\pi}{2}} \frac{\sin 2x}{\sqrt{1 - \sin x}}\, dx$. Give your answer in the form $a + b\sqrt{2}$, where $a$ and $b$ are rational numbers to be found.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Take the substitution $u = 1 - \sin x$.