How to integrate int -1/(x^2 +1)^2 dx

1. Jan 8, 2007

cscott

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

Find the following intergral...

2. Relevant equations

$$\int{\frac{-1}{(x^2+1)^2}dx}$$

3. The attempt at a solution

I can't get anywhere with this... any hints?

Last edited: Jan 8, 2007
2. Jan 8, 2007

bob1182006

sorry rushed the problem and did it wrong

Last edited: Jan 8, 2007
3. Jan 8, 2007

imranq

hint:

$$\frac{d}{{dx}}{\arctan{x}} = \frac{1}{x^2 +1}$$

Last edited: Jan 8, 2007
4. Jan 8, 2007

StatusX

Try adding and subtracting x^2 in the numerator.

5. Jan 9, 2007

dextercioby

Make the substitution $x=\tan t$. You'll eventually get $\int \cos^2 t \ dt$ which is easy to do.

Daniel.