Integration: How to Begin? 
Possible Duplicate:
Help evaluating $\int \frac{dx}{(x^2 + a^2)^2}$ 

How to I begin this integration problem?

$\begin{align}\int_{0}^{1} \frac{dx}{{\left(x^2 + 1\right)}^{2}}\end{align}$

I'm not really sure how setup the triangle to do trigonometric substitution for this problem, since I am squaring the bottom, not taking the square root of it.
Could someone please demonstrate/explain how I could do this?
Thank you for your time. 

There is a "trick" here: begin noticing that $1=x^2+1-x^2$ so 
$$\frac 1{(x^2+1)^2}=\frac{x^2+1-x^2}{(x^2+1)^2}=\frac 1{x^2+1}-\frac {x^2}{(x^2+1)^2}.$$
A primitive of the first term is well-known, for the second we integrate by parts:
$$\int\frac{x\cdot x}{(x^2+1)^2}dx=-\frac x2\frac 1{1+x^2}+\frac 12\int \frac 1{1+x^2}dx$$
so finally 
$$\int \frac{dx}{(1+x^2)^2}=\frac 12\arctan x+\frac x2\frac 1{1+x^2}.$$ 
