# How do you find the indefinite integral of int (r^2-2r+1/r)dr?

Dec 12, 2016

This is set up nicely for us to integrate; just one small adjustment for a visual aid.

Rewrite as:

$\int \left({r}^{2} - 2 {r}^{1} + {r}^{- 1}\right) \mathrm{dr}$

So, we can visually see how we're going to use the power rule for integrating each part of the function.

Thus:

$= {r}^{2 + 1} / \left(2 + 1\right) - 2 {r}^{2} / 2 + \ln | r | + c$

Simplify:

$= {r}^{3} / 3 - {r}^{2} + \ln | r | + c$