A polynomial Calculus function

Calculus Level 4

Let \(f (x) = { x }^{ 3 } - \dfrac { 3 }{ 2 } { x }^{ 2 } + x + \dfrac { 1 }{ 4 } \). Find the value of

\[\large \frac {\Large 1}{\displaystyle \int _\frac 14^\frac 34 f\left( f (x) \right) \ dx}\]

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