To the power 11

Calculus Level 3

x3+x(x4+2x2+3)11dx\large \int \dfrac {x^3+x}{(x^4+2x^2+3)^{11}}\, dx

The indefinite integral above can be expressed as

(axd+bxe+c)fg+C,\frac {(ax^d+bx^e+c)^f}g + C,

where a,b,c,d,e,f,ga,b,c,d,e,f,g are all integer constants, where d>ed>e, and CC represents the arbitrary constant of integration.

Find a+bc+de+fga+b-c+d-e+f-g.

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