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

Calculus Level 3

011+x21x2dx \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 aπb \dfrac{a \pi}{b} , where a,ba, b are coprime positive integers, find a+ba+b.

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