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

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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