# 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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