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!


you do realize that $x^{-1}=\frac{1}{x}$, right?


  • $\begingroup$ Yeah, I wasn't thinking straight. But on a side note generally in math when we see a fraction and we see nothing obvious and there are two identical terms on the numerator and denominator should we always multiply by 1/1, x/x in this case. $\endgroup$ – mushimaster Mar 7 '18 at 17:35
  • $\begingroup$ You simply always try to simplify your expression in the most possible way, and if you notice a familiar integral, you evaluate it, if you don't then you proceed in the normal way (by parts or substitution or any other way), here i'm not multiplying by $'\frac{x}{x}'$ because it's helpful, or because there are two identical terms, i'm simplifying the expression more. $\endgroup$ – Mario SOUPER Mar 7 '18 at 17:39
  • $\begingroup$ Frankly, i'm just trying to get the 50 rep to be able to comment. $\endgroup$ – Mario SOUPER Mar 7 '18 at 18:11

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