# An iterative quotient integration

1. Dec 7, 2012

### Wu Xiaobin

I have got this integration:
$\int_{-1}^{1}\frac{x^n}{(1+w^2-P^2-2wx+p^2x^2)^2}dx$
And at the same time, I can provide several results when n is small.
For example:
when $n=1$, the result is
$\frac{2w}{(1-P^2)(1-w^2)}$
when $n=2$, the result is
$-\frac{2(1-P^2-w^2)}{P^2(1-P^2)(1-w^2)}+\frac{\Delta}{P^3}$
when $n=3$, the result is
$\frac{2w(3w^2-2w^2P^2+P^4+2P^2-3)}{P^4(1-P^2)(1-w^2)}+\frac{3w\Delta}{P^5}$
where
$\Delta=\sinh^{-1}{\frac{P^2+w}{((1-P^2)(P^2-w^2))^{1/2}}}+\sinh^{-1}{\frac{P^2-w}{((1-P^2)(P^2-w^2))^{1/2}}}$
I have tried it in Mathematica and Maple, However the software can't figure it out.
Does any one feel familiar with this kind of integration and give me some suggestion?