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

[cscott]

Homework Statement

Find the following intergral...

Homework Equations

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

The Attempt at a Solution

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

 

[bob1182006]

sorry rushed the problem and did it wrong

 

[imranq]

hint:

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

 

[StatusX]

Try adding and subtracting x^2 in the numerator.

 

[dextercioby]

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

Daniel.