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integral (2x^-2 + x^1/2)(-2/x + 3/2 x^2/3) dx

= integral (2x^-2 + x^1/2)(-2x^-1 + 3/2 x^2/3) dx

= integral (-4x^-3 + 3x^-4/3 - 2x^-1/2 + 3/2 x^7/6) dx

= 2x^-2 - 9x^-1/3 - 4x^1/2 + 9/13 x^13/6 + C