Question

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

Answer 1

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

Rewrite as:

`int(r^2-2r^1+r^(-1))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)/(2+1)-2r^2/2+ln|r|+c`

Simplify:

`=r^3/3-r^2+ln|r|+c`