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There exist positive integers AAA, BBB, CCC such that ∫124x2+1x2−1dxx = 1Aπ+lnB−tan−1C. \int_1^{\sqrt{2}} \sqrt{\frac{4x^2+1}{x^2-1}} \frac{dx}{x} \; = \; \tfrac{1}{A}\pi + \ln B - \tan^{-1}C.∫12x2−14x2+1xdx=A1π+lnB−tan−1C. What is the value of A+B+C?A + B + C?A+B+C?
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