# Indefinite integral with a rational function

1. Aug 7, 2012

### cwbullivant

EDIT: Problem found. This thread can now be ignored.

1. The problem statement, all variables and given/known data

Find the indefinite integral.

2. Relevant equations

((y^2-1)/y)^2 dy

3. The attempt at a solution

I've attempted a few things. I first attempted to split the statement inside the outer parentheses into two fractions;

(y^2/y - 1/y)^2 dy

Then to reduce it to,

(y - 1/y)^2 dy

And then foil it and take an antiderivative. This comes out to

Foiled: y^2 - 2 + 1/y^2 dy

And then the antiderivative:

y^3/3 - 2y + 1/y + C

But I appear to still be incorrect. According to Wolfram's integral calculator, the solution is

y^3/3 - 2y - 1/y

I'm close. I'm apparently missing a sign somewhere, and I can't seem to find where it is, and I don't feel comfortable plugging in the answer until I know how I got there.

Last edited: Aug 7, 2012
2. Aug 7, 2012

### gabbagabbahey

Your error is just when you are finding the anti-derivative of the last term:

$$\int \frac{1}{y^2}dy=-\frac{1}{y}+C$$