# Integral of a Kind!

Calculus Level 5

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

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

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