NIntegrate[((3^(3/2) (x + 3)^(1/2 (-1 - 3))) (3^(3/2) (3.5 - x + 3)^( 1/2 (-1 - 3))))/((Sqrt[x] Beta[1/2, 3/2]) (Sqrt[3.5 - x] Beta[1/2, 3/2])), {x, 0, 3.5}]

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