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Let f(x)=int (dx)/((3+4x^2)sqrt(4-3x^2))...

Let `f(x)=int (dx)/((3+4x^2)sqrt(4-3x^2)), abs(x) lt 2/sqrt3`. If `f(0)=0 and f(1)=1/(alpha beta) tan^-1(alpha/beta). alpha,beta gt 0`, then `alpha^2+beta^2` is equal to ______

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JEE MAINS PREVIOUS YEAR-JEE MAIN 2023-Question
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