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**mr fantastic** The update will be unnecessary since you probably neglected to recognise it as an improper integral (the integrand is undefined at x = 0 which lies in the interval of integration). The first step is therefore to write:

$\displaystyle \lim_{\alpha \rightarrow 0} \int_{-5}^{\alpha}\frac{2}{x^3} \, dx + \lim_{\beta \rightarrow 0} \int_{\beta}^{5}\frac{2}{x^3} \, dx $.

(A pre-emptive) by the way, statements like $\displaystyle \infty - \infty$ make no sense and certainly do not equal zero ....