Hyperbola 1

Geometry Level 4

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