The value of the definite integral$\int\limits_{ - {\pi \over 4}}^{{\pi \over 4}} {{{dx} \over {(1 + {e^{x\cos x}})({{\sin }^4}x + {{\cos }^4}x)}}} $ is equal to :

Question

The value of the definite integral

$\int\limits_{ - {\pi \over 4}}^{{\pi \over 4}} {{{dx} \over {(1 + {e^{x\cos x}})({{\sin }^4}x + {{\cos }^4}x)}}} $ is equal to :

$ - {\pi \over 2}$

${\pi \over {2\sqrt 2 }}$

$ - {\pi \over 4}$

${\pi \over {\sqrt 2 }}$

Solution

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