(Beta[1 - 1/InverseBetaRegularized[1 - 1/(Sqrt[2] EllipticK(-1)), 1/4, 1/2], 1/2, 1/4] + Beta[1 - 1/InverseBetaRegularized[1 - 1/(Sqrt[2] EllipticK(-1)), 1/4, 1/2], 1/2, 3/4])/(4 Sqrt[2])

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