To the power 11

Calculus Level 3

\[\large \int \dfrac {x^3+x}{(x^4+2x^2+3)^{11}}\, dx \]

The indefinite integral above can be expressed as

\[\frac {(ax^d+bx^e+c)^f}g + C,\]

where \(a,b,c,d,e,f,g\) are all integer constants, where \(d>e\), and \(C\) represents the arbitrary constant of integration.

Find \(a+b-c+d-e+f-g\).

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