# Easy integral from exam

1. Sep 1, 2011

### 1MileCrash

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

From an exam in calc 2 we are reviewing simple integrals. This one was annoying because it actually contained algebra.. regardless.

$\int(\frac{1 - y^{2}}{y^{2}})^{2} dy$

2. Relevant equations

3. The attempt at a solution

First I broke it into two fractions, and turned the second into 1 as it is y squared over y squared.

$\int(\frac{1}{y^{2}} - 1)^{2} dy$

Then squared the polynomial of sorts.. to get

$\int y^{-4} - y^{-2} - y^{-2} + 1 dy$

$- \frac{y^{-3}}{3} + 2y^{-1} + y + C$

Look okay? A bit rusty in algebra..

2. Sep 1, 2011

### lineintegral1

Looks fine to me!

3. Sep 1, 2011

### Staff: Mentor

There's a mistake in your 2nd term. The coefficient of the y-1 term should be 1, not 2.

Also, a slightly different approach is to square the numerator and denominator of your fraction instead of doing the division first. This leads to the same result, though, so can't really be considered a better approach.

4. Sep 1, 2011

### 1MileCrash

How so? After integration of -y^-2 I get +y^-1, and there are two instances of -y^-2. All I did was add them together for 2y^-1.

5. Sep 1, 2011

### lineintegral1

His integral shows that he is adding y^-2 to y^-2; he just fails to simplify before he integrates. I think that's where his 2 comes from.

6. Sep 1, 2011

### Staff: Mentor

Sorry, I totally missed that there was another y-1 term. My mistake...

7. Sep 1, 2011

### 1MileCrash

No problem, thanks guys!