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$$x=\int \sqrt{\frac{y}{2a-y}}dy$$

According to my textbook, it says that the substitution by $y=a(1-\cos\theta)$ will easily solve the intergral. Why does this work?

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    This doesn't answer your question, but this is #24 here: http://integral-table.com/downloads/single-page-integral-table.pdf2012-10-18

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