Integrating a Fraction with a Quadratic Denominator Raised to a Power

[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

 

[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-√(11)x)(2+√(11)x) (sum and difference)? So that (4-11x²)²= (2+√(11)x)²(2-√(11)x)²?

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

 

[Matt Jacques]

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