# Could it get any more complicated than this?

Calculus Level 5

$a \left [ \frac { \left ( \sqrt{2 + \sqrt{4+ \sqrt x }} \right )^b }{b} - \frac {c \left ( \sqrt{2 + \sqrt{4+ \sqrt x }} \right )^d }{d} + \frac {e \left ( \sqrt{2 + \sqrt{4+ \sqrt x }} \right )^f }{f} \right ]$

Ignoring the arbitrary constant, the antiderivative of function $$\sqrt{2 + \sqrt{4+ \sqrt x }}$$ can be written as the expression given above for positive integers $$a,b,c,d,e,f$$ with $$\text{gcd}(c,d) = \text{gcd}(e,f) = 1$$.

What is the value of $$a+b+c+d+e+f$$?

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