Just another integral

Calculus Level 4

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

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 $$A+B+C+D$$.

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