Let \(x\) be the eccentricity of a hyperbola and \(f\left( x \right)\) be the eccentricity of its conjugate hyperbola. Then find \[\int _{ 3 }^{ 5 }{ (f\circ f\circ f\circ f\circ f\circ f\circ f\circ f )\left( x \right) } dx\]

**Clarification:** We're composing 8 \(f\)'s

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