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Definite Integration

JEE Main 2007 · Annual, Paper 1 · Q3345

MathematicsHard210×since 2002Q3345

Let

F\left( x \right) = f\left( x \right) + f\left( {{1 \over x}} \right),

where

f\left( x \right) = \int\limits_l^x {{{\log t} \over {1 + t}}dt,}

Then

F(e)

equals

JEE Main 2007 · Annual, Paper 1 · Q3345

MathematicsHard210×since 2002Q3345

Let

F\left( x \right) = f\left( x \right) + f\left( {{1 \over x}} \right),

where

f\left( x \right) = \int\limits_l^x {{{\log t} \over {1 + t}}dt,}

Then

F(e)

equals