I was trying the evaluate the integral
$$\int_{25\pi/4}^{53\pi/4}\frac{1}{(1+2^{\sin x})(1+2^{\cos x})} dx$$ from
I have since manipulated this integral into $$\int_{\pi/4}^{5\pi/4}\frac{7}{(1+2^{\sin x})(1+2^{\cos x})} dx$$
Any help on how to proceed further would be appreciated.
The value...