# Thread: Simple Integral question w/ parts

1. Originally Posted by Chris L T521

Where are you stuck in the division process?

--Chris
Well, I guess the whole thing, like how do you get $1-\frac {1}{1+s^2}$
It's something to do with the s^2 right?

2. Originally Posted by matt3D
Well, I guess the whole thing, like how do you get $1-\frac {1}{1+s^2}$
It's something to do with the s^2 right?
You take $1+s^2~|\overline{~~~~s^2}$

We see that $s^2$ goes into $s^2$ 1 time.

Thus, we should get

$.~~~~~~~~~~~~~~~~~~{\color{blue}1}$
${\color{magenta}1+s^2}~|\overline{~~~~~~~~~s^2}$
$.~~~~~~~~~\underline{-(1+s^2)}$
$.~~~~~~~~~~~~~~~~~{\color{red}-1}$

So our quotient will be ${\color{blue}1}+\frac{{\color{red}-1}}{{\color{magenta}1+s^2}}=1-\frac{1}{1+s^2}$, where $-\frac{1}{1+s^2}$ is the remainder.

Does this make sense?

--Chris

3. This is done by polynomial long division. Check the link here to see how it is done: Polynomial Long Division

4. If you want to do it quickly without polynomial division:

$\frac{x^2}{x^2+1}$

Add one/subtract one: $\frac{(x^2 + 1) - 1}{x^2+1}$
Split: $\frac{x^2+1}{x^2+1} - \frac{1}{x^2+1}$
Cancel: $1 - \frac{1}{x^2+1}$

5. Originally Posted by Chop Suey
If you want to do it quickly without polynomial division:

$\frac{x^2}{x^2+1}$

Add one/subtract one: $\frac{(x^2 + 1) - 1}{x^2+1}$
Split: $\frac{x^2+1}{x^2+1} - \frac{1}{x^2+1}$
Cancel: $1 - \frac{1}{x^2+1}$
Aha! I remember that trick now...I remember seeing it before...

--Chris

Page 2 of 2 First 12