# Indefinite Integral without parts or u-sub

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?
$$\int{\frac{\frac{1}{x}}{1-\frac{1}{x}}dx}=\int{\frac{1}{x-1}dx}=\ln(x-1)$$
• 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. – Mario SOUPER Mar 7 '18 at 17:39