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This expression cannot be integrated using substitution, integration by parts, and other common methods. I suspect that it should be a definite integral rather than indefinite. The function can only be graphed up to x=4, because the expression under the square root becomes negative for x>4. I think the limits for the definite integration would be [0,4] the area enclosed by the curve and the axes (the lines y=8 and x=4). The number 64 has a square root of 8 and a cube root of 4, which makes the dimensions of the enclosing rectangle rational numbers: 8 units long and 4 units wide, making the area under the curve<32 square units. Using computational methods the area is about 26.9219 square units.

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