Indefinite integral with a rational function

[cwbullivant]

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

Homework Statement

Find the indefinite integral.

Homework Equations

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

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.

 

[gabbagabbahey]

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

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