$\int \frac{x^2\,dx}{(a-bx^2)^2}$ How do I integrate $\int \frac{x^2\,dx}{(a-bx^2)^2}$
I've tried substitution and partial fraction decomposition, but I'm not getting anywhere.

Almost without any substitution.
Let $x=\frac{\sqrt{a} }{\sqrt{b}}y$
$$I=\int \frac{x^2}{(a-b\,x^2)^2}\,dx=\frac{1}{\sqrt{a}\,\, b^{3/2}}\int \frac{y^2}{\left(1-y^2\right)^2}\,dy$$ Now, using partial fraction decomposition
$$\frac{y^2}{\left(1-y^2\right)^2}=\frac{1}{4 (y-1)}-\frac{1}{4 (y+1)}+\frac{1}{4 (y+1)^2}+\frac{1}{4 (y-1)^2}$$ does not seem to make any problem
