Can you solve without modifying the integrand? (My twelfth integration problem)

Calculus Level 3

$\large \int_{0}^{1} \sqrt{1+\dfrac{x^{2}}{1-x^{2}}} \, dx$

If this integral can be expressed in the really nice form of $$\dfrac{a \pi}{b}$$, where $$a, b$$ are coprime positive integers, find $$a+b$$.

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