Does anyone know how to integrate this without using parts or u sub, just manipulating it as an indefinite integral. Like does it lok like you can use revrse product, chain, qoutient rule? Also all its x to the power of (-1) everywhere, sorry i didn't know how to put -1. I know ln is involved, but I can;t seem to figure out how to rearange things. Thanks! $$ \int \dfrac{x^{-1}}{1-x^{-1}}dx $$ EDIT: sorry I have the answer apparently I asked it a year ago!
2026-04-24 20:53:27.1777064007
Indefinite Integral without parts or u-sub
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you do realize that $x^{-1}=\frac{1}{x}$, right?
$$\int{\frac{\frac{1}{x}}{1-\frac{1}{x}}dx}=\int{\frac{1}{x-1}dx}=\ln(x-1)$$