# How do int. 1/(4-11x^2)^2 ?

1. Feb 29, 2004

### Matt Jacques

How do integrate 1/(4-11x^2)^2 ?

It looks like partial fractions, but how do I do it when there is (a+bx^2)^2?

I know it is something like

1/(4-11x^2)^2 = Ax + b / (4-11x^2)^2

2. Feb 29, 2004

### HallsofIvy

Then, as is often the case with posts like this, you know incorrectly. 1 over a polynomial is NOT "Ax+ anything"!
Do you know that 4- 11x2= (2-&radic;(11)x)(2+&radic;(11)x) (sum and difference)? So that (4-11x2)2= (2+&radic;(11)x)2(2-&radic;(11)x)2?

I would suggest something like
$$\frac{1}{(4-11x^2)^2}= \frac{A}{2-\sqrt{11}x}+ \frac{B}{(2-\sqrt{11}x)^2}+ \frac{C}{2+\sqrt{11}x}+ \frac{D}{(2+\sqrt{11}x)^2}$$

Last edited by a moderator: Mar 2, 2004
3. Mar 7, 2004

### Matt Jacques

Thanks! Talk about something being really broken down! :)

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook