$\int_0^{π}\frac{dx}{1+3^{\cos x}}$ is equal to:
Answer & explanation
Correct answer: option 3
$\int\limits_0^{π}\frac{1}{1+3^{\cos x}}dx=\int\limits_0^{π}\frac{dx}{1+3^{\cos(π-x)}}=\int\limits_0^{π}\frac{dx}{1+3^{-\cos x}}=\int\limits_0^{π}\frac{3^{\cos x}}{3^{\cos x}+1}dx$
$I=\frac{1}{2}\int\limits_0^{π}(\frac{1+3^{\cos x}}{1+3^{\cos x}})dx=\frac{π}{2}$