Question Number 91290 by mhmd last updated on 29/Apr/20
Commented by MJS last updated on 29/Apr/20
$$\mathrm{let}\:{n}=\mathrm{2}{k} \\ $$$$\underset{\mathrm{2}{k}} {\overset{\mathrm{2}\left({k}+\mathrm{1}\right)} {\int}}\frac{{dx}}{\left(\mathrm{1}+\mathrm{3}^{\mathrm{cos}\:{x}} \right)\left(\mathrm{1}+\mathrm{3}^{\mathrm{sin}\:{x}} \right)}\approx\mathrm{1}.\mathrm{57079632679}=\frac{\pi}{\mathrm{2}} \\ $$$$\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\frac{\pi{n}}{\mathrm{2}} \\ $$