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$$\int x^{-2} dx$$
$$= \int x^{-2+1}(-2+1)^{-1} dx$$
$$= \int x^{-1}(-1)^{-1} dx$$
$$= -x^{-1+1}(-1+1)^{-1} + C$$
$$= -1 \cdot x^0 + C$$
$$= -1 + C$$
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