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int = Integrate[1/(x^3 - 1), x];
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I’m not quite sure what you’re going for. Your Show command basically worked. You didn’t provide a PlotRange option, and each of your individual plots has a different PlotRange option, so it’s a bit difficult to understand what you were hoping for. Maybe what you want is this:
Plot[{Sin[x], Cos[x], Tan[x]}, {x, -2 Pi, 2 Pi}]
(set the options as you wish).