Tedious fraction decomposition integral $\int\frac{1}{(x^2-1)^2} \, dx$ I'm having this integral to resolve using fraction decomposition:
$$\int\frac{1}{(x^2-1)^2} \, dx$$
This gives me the following: 
$$\frac{A}{x+1} + \frac{B}{(x+1)^2} + \frac{C}{x-1} + \frac{D}{(x-1)^2} = \frac{1}{(x^2-1)^2}$$ 
Which results in a 4 variables system of equation...
Is there a quick way to resolve this that I'm missing out?

Alternatively start from $\frac{1}{(x^2-a)^2} = \frac{\partial}{\partial a} \frac{1}{(x^2-a)}$, then determine $\int\frac{1}{(x^2-a)} \, dx$ (this is straight forward to put the integrand into partial fractions), differentiate this wrt $a$ then set $a=1$.
