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Calculus Level 4

f(x)=1/etanxt1+t2dt+1/ecotx1t(1+t2)dt\large f( x ) =\int _{ 1/e }^{ \tan { x } }{ \dfrac { t }{ 1+{ t }^{ 2 } } \, dt } +\int _{1/e }^{ \cot x }{ \dfrac { 1 }{ t( 1+{ t }^{ 2 } ) } \, dt }

Find the value of f(e2)f\left(\dfrac{e}{2}\right).

Clarification: e2.71828e \approx 2.71828 denotes the Euler's number.

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