Integral 22

Calculus Level 3

\[ \displaystyle {\huge \int_{0}^{1}} \displaystyle \sqrt{\dfrac{x}{\sqrt{\dfrac{x}{\sqrt{\dfrac{x}{\sqrt{}...}}}}}} \, dx \]

If the above integral is the form of \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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