If $f(x) = {{2 - x\cos x} \over {2 + x\cos x}}$ and g(x) = logex, (x > 0) then the value of integral $\int\limits_{ - {\pi \over 4}}^{{\pi \over 4}} {g\left( {f\left( x \right)} \right)dx{\rm{ }}} $ is

Question

If $f(x) = {{2 - x\cos x} \over {2 + x\cos x}}$ and g(x) = log_ex, (x > 0) then the value of integral

$\int\limits_{ - {\pi \over 4}}^{{\pi \over 4}} {g\left( {f\left( x \right)} \right)dx{\rm{ }}} $ is

log_e3