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Unsure of my work evaluating $\int \frac{dx}{\sqrt{x + \sqrt{x + \sqrt{x + \cdots}}}}$

This Question is an Extension of this Previously Asked Question: Nested root integral $\int_0^1 \frac{dx}{\sqrt{x+\sqrt{x+\sqrt{x}}}}$ I was looking into answering the question of whether it was ...
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