# 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