Just Some Twos!

Calculus Level 5

Say \(f(x),g(x),h(x)\) are functions defined for all positive reals \(x\), by the following statements.

-\(f(x)=g(x)-h(x)\)

-\(f(x)=\frac{(g(x))^2-1}{g(x)}\)

-\(g(x)=x^3\)

In the first quadrant, the area enclosed between the three functions and the x-axis is given by \(\frac{2^a-2^b-2^c}{2^2}\). Find \(a+b+c\)

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