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

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

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