The value of the definite integral \({\int }_{-\frac{\pi }{4}}^{\frac{\pi }{4}}\frac{dx}{\left(1+{e}^{x\cos x}\right)\le…

The value of the definite integral \({\int }_{-\frac{\pi }{4}}^{\frac{\pi }{4}}\frac{dx}{\left(1+{e}^{x\cos x}\right)\left({\sin }^{4}x+{\cos }^{4}x\right)}\) is equal to

[JEE Main 2021, 27 Jul (Shift 1)]