Just another integral

$\large \int \frac{1+x^2}{3-4\sqrt2 x + 4x^4} \, dx$

If the indefinite integral above is equal to

$\dfrac {A}{x+B} + C\tan^{-1} (x+D) + E$

for constants $A,B,C$ and $D$ with $E$ as the constant of integration, find the value of $A+B+C+D$ .