What is the correct form of the partial fraction decomposition for the following integral? $$\int \frac{11 (x^{4} + 2)}{(x - 3)(x^2 - 1)^2 (x^2 + 3)^2} \, dx$$

A. $\displaystyle \int \left( \frac{A}{x - 3} + \frac{B}{(x^2-1)^2} + \frac{C}{(x^2 + 3)^2} \right)\, dx$
B. There is no partial fraction decomposition because the denominator does not factor.
C. There is no partial fraction decomposition yet because long division must be done first.
D. $\displaystyle \int \left( \frac{A}{x - 3} + \frac{B}{x+1} + \frac{C}{(x+1)^2} + \frac{D}{x-1} + \frac{E}{(x-1)^2} + \frac{Fx+G}{x^2 + 3} + \frac{Hx+I}{(x^2 + 3)^2} \right)\, dx$
E. $\displaystyle \int \left( \frac{A}{x - 3} + \frac{B}{x+1} + \frac{C}{(x+1)^2} + \frac{D}{x-1} + \frac{E}{(x-1)^2} + \frac{Fx+G}{x^2 + 3} \right)\, dx$
F. $\displaystyle \int \left( \frac{A}{x - 3} + \frac{Bx+C}{x^2-1} + \frac{Cx+D}{(x^2-1)^2} + \frac{Ex+F}{x^2 + 3} + \frac{Gx+H}{(x^2 + 3)^2} \right)\, dx$
G. $\displaystyle \int \left( \frac{A}{x - 3} + \frac{Bx+C}{(x^2-1)^2} + \frac{Dx+E}{(x^2 + 3)^2} \right)\, dx$
H. There is no partial fraction decomposition yet because there is cancellation.