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\int \frac{(x^{-7/6} - x^{5/6}) dx}{x^{1/3} (x^2 + x + 1)^{1/2} - x^{1/2} (x^2 + x + 1)^{1/3}}
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\int \frac{(x^{-7/6} - x^{5/6}) dx}{x^{1/3} (x^2 + x + 1)^{1/2} - x^{1/2} (x^2 + x + 1)^{1/3}}
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