Integral of $\frac{x^3-2}{x^3-x}$

As the title says, I need some help with this function: $$\int\frac{x^3-2}{x^3-x}$$ I tried it with different versions/forms of the function to get it with substitution or partiel integration:

$$\int\frac{x^3-2}{x^3-x} = \frac{x^3-2}{x(x-1)(x+1)} = \frac{x^3}{x^3-x} - \frac{2}{x^3-x}$$

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$\int\big(\frac a x + \frac b {x+1} + \frac c {x-1} +d\big)$ – Jan Dvorak Jan 17 at 13:33
Try long division – anorton Jan 17 at 13:49

try this $$\frac{x^3-2}{x^3-x} = 1 + \frac{x-2}{x^3-x}$$ Now use partial fraction.

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Why is it the same? – Giesi Jan 17 at 13:36
take LCM and see – experimentX Jan 17 at 13:37
@Giesi what is $(x^3-2)-(x^3-x)$? – Jan Dvorak Jan 17 at 13:38
Thx I get it ;) – Giesi Jan 17 at 13:43