I have got this integration:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int_{-1}^{1}\frac{x^n}{(1+w^2-P^2-2wx+p^2x^2)^2}dx[/itex]

And at the same time, I can provide several results when n is small.

For example:

when [itex]n=1[/itex], the result is

[itex]\frac{2w}{(1-P^2)(1-w^2)}[/itex]

when [itex]n=2[/itex], the result is

[itex]-\frac{2(1-P^2-w^2)}{P^2(1-P^2)(1-w^2)}+\frac{\Delta}{P^3}[/itex]

when [itex]n=3[/itex], the result is

[itex]\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}[/itex]

where

[itex]\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}}}[/itex]

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?

Look forward to your kind reply!

Sincerely Yours

Jacky Wu

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# An iterative quotient integration

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**