Integral 22

Calculus Level 3

01xxx...dx \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 ab \dfrac ab, where aa and bb are coprime positive integers, find a+ba+b.

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