Integral of a Kind!

Calculus Level 5

\[\int _{ 1/e }^{ \tan (x) } { \frac { x }{ 1+ { x }^{ 2 } }\ dx } + \int _{ 0 }^{ 1 }{ f(x) \left( 4{ x }^{ 2 } - f(x) \right) dx } +\int _{ 1/e }^{ \cot (x) }{ \frac { dx }{ x( 1+{ x }^{ 2 } ) } } =\frac { 9 }{ 5 }\]

Let \(f(x)\) be a function satisfying the equation above. Find the value of \(f (5) \).

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