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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