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For example: [tex]\int_{-1}^2 \frac{1}{x^{-3}} dx[/tex]. Intuitively, it can be simplified to [tex]\int_1^2 \frac{1}{x^{-3}} dx[/tex] and thus the infinite discontinuity at 0 is removed.

If that is not doable, can an integral converge if the end points of the domain are infinite discontinuities?

For example: Does [tex]\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} tan(x) dx = 0[/tex]?

If these kinds of functions are split in two, and limits to [tex]\infty[/tex] are taken, then algebraic manipulation of infinities are required.

Any insight would be appreciated.