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 $a+b$ .