Double Delight

Calculus Level 5

10x(1+x2)(1+x2y2)dxdy=πab\int_{1}^{\infty} \int_{0}^{\infty} \dfrac{x}{(1+x^2)(1+x^2y^2)} \mathrm{d}x \mathrm{d}y=\dfrac{\pi^a}{b}

Find a+ba+b.

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